sultan qaboos university journal for scientific research special issue 2012 vol.17. no. 2 october 2012 preface his special issue contains selected papers presented at the second international conference on numerical analysis and optimization: theory, methods, applications and technology transfer (naoii2011) held during the period january 3-6, 2011 at sultan qaboos university (squ), muscat, oman. the conference was sponsored by squ, the research council (trc) of oman, the international center for theoretical physics (ictp) of italy, microsoft (middle east and africa division); and the local sponsors the british council (oman), bank muscat, the al-anan press, and al-roya newspaper. following on from the success of the previous conference on numerical analysis and optimization (nao2008) also held at squ during the period april 6-8, 2008, the second conference brought again together prominent mathematicians, worldwide experts and active researchers from oman, usa, south america, uk, europe, asia and arab countries to meet at squ. it was a great opportunity for researchers to share knowledge and to stimulate the communication of new ideas, scientific exchange and to discuss possibilities of further cooperation, networking and mobility of senior and young researchers and research students. naoii2011 was inaugurated by he dr. hilal bin ali al-hinai, the secretary general of trc and he dr. ali bin saud bemani, the vice chancellor of squ. fourteen world leading researchers gave keynote lectures in fourteen technical sessions of the conference. in total, fourty international participants gave contributed talks. more information is available at: http://www.squ.edu.om/portals/87/conference/conference2011/index.htm. twenty of the conference papers were selected for two special issues 17(1) and 17(2) of the squ journal for science highlighting the two themes of the conference numerical optimization and numerical analysis; eleven papers were selected for issue 17(1) on numerical optimization, and nine papers were selected for issue 17(2) on numerical analysis. we wish to express our gratitude to all contributors. we are also indebted to many anonymous referees for the care taken in reviewing the papers submitted for publication. mehiddin al-baali anton purnama guest editors for the special issues 17(1) and 17(2) of squ journal for science t http://www.squ.edu.om/portals/87/conference/conference2011/index.htm cover page preface electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 279-281 © sultan qaboos university metrization of weakly developable spaces abdul m. mohamad department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman, email: mohamad@squ.edu.om. عيفةمترية الفضاءات النامية الض عبدالعظيم مؤآت محمد . نقدم في هذا البحث النظرية المترية للفضاءات النامية الضعيفة : خالصة abstract: in this note, we present metrization of weak developability. keywords: weakly developable, metrizable, weak base. 1. introduction m artin (1976) introduced the concept of weak developability in order to study the problem of the metrization of spaces with weak bases. a space x is weakly developable if and only if there is a sequence { }n n ng ∈ of covers of x such that for each x x∈ ,{ ( ) }, :nst x g n n∈ is a weak base at x . the sequence { }n n ng ∈ is said to be a weak development for the space x . if each consists of open sets, then {ng }n n ng ∈ is a development for the space x and x is a developable space (gruenhage, 1984). the idea of weak base was introduced by arhangel'skii (1966) in the study of symmetrizable spaces. it is more convenient to use the form of siwiec, (1974) and franklin, (1965). a collection w of subsets of a space x is called a weak base for x provided that to each x x∈ , there exists w such that x w⊂ 1. each member of contains xw x . 2. for any two members w and w1 2 of , there is a wxw 3 in xw , such that w w3 1 w⊂ ∩ 2 . 3. a subset of f x is closed if and only if for every point x f∉ , there exists a w in such that f w xw φ∩ = . if to each x x∈ we assign a collection xw of supersets of { }x such that { }:x x x= ∪ ∈w w is a weak base by virtue of the collections , i.e., the collectionsxw xw x satisfy conditions (1), (2) and (3) of the preceding paragraph, then we say that the collection is a local weak base at w x for each x x∈ . it is easy to show that a subset o of a space x with local weak bases { }:xw x x∈ is open if and only if for each x o∈ , there is a member w of the local weak base of xw x x∈ with . w o⊂ in this study, we prove a metrization theorem for weakly developable spaces. we assume throughout this note that all spaces are t . a topological space is a t -space if, and only if, for each pair 0 0 x and of distint points, there is a nighborhood of one point to which the other does not y 279 adbul m. mohamad belong. also, we let denote the set of all positive integers. for a collection g of subsets of a space n x , we define ( ) { }, :x g g x g g= ∪ ∈ ∈ andst ( ) ( ) ( ){ }, , :2st x g st y g st x g= ∪ ∈ , .y }ng x :ny n n k∈ y x ∈ y :y n n∈ k x n∈ : n ∈ }ng ( gy ∈ ∈ y s }:i y∪ x n i t∈ }n n ∈ :n− f x 2. main results 2.1 lemma 1 let { n n∈ be a weak development of a space x . then for every compact subset k of and any sequence of points in , there is a point in and a subsequence :ny i n of the sequences :ny n n∈ which converges to . proof. let be a compact subset of k x and let be any sequence of points in . suppose there is no subsequence of :ny n n∈ which converges to a point of { }:ny n− ∈ n . then, we note that { }:nf y n= n∈ is a closed subset of x . for if it is not true then for some point we shall have y x f∈ − ( ) 1 ,t y g∈ny s i f∩ for each i n∈ . this will imply that the subsequence :ny i will converge to , which will contradict our assumption. therefore, is closed. y f n define { }n if y i n= ≥ for each . similarly, one can show that f is closed for each . consider the open cover { n n∈ n n ∈ }:nx f n− n∈ of in k x . it is easy to see that it does not contain a finite subcover of which contradicts the fact that is compact. hence, the sequences k k :ny n n have a convergent subsequence. 2.2 lemma 2 let { n n∈ be a weak development of a space x , which satisfies the following condition: for any closed subset f of x and any point ,y x f∈ − there is an n such that st n∈ ( )g ),, n nst f .φ∩ = then every compact subset of x is closed. proof. let k be a compact subset of x . suppose is not closed. then there is a point such that k y x k∈ − ( )i k,y gst φ∩ ≠ for all i . thus for each i , let . hence, the sequence n n ( ,i t y g∈ )i k :iy i n∈ converges to . put y { } {f y= ∈i n . we claim that is a closed subset of f . for if not, then there is a point such that z x∈ − f ( ), igst z f φ∩ ≠ for all i ∈ . without loss of generality, let for all ( ), iz gy s f∩ i n∈ . this is not possible since a weakly developable space is t and hence by the hypothesis there is an 1 n n∈ such that ( ) ( ), ,yn ngst z g st φ∩ = . define { { }:n if y i= ≥ y∪ for each n n∈ . clearly, is closed for each . therefore, nf n { }x f n n∈ is an open cover of with no finite subcover of giving a contradiction. k k ∩ 2.3 theorem the following are equivalent for a space x . 1. the space x is metrizable. 2. the space x has a weak development { }n n ng ∈ such that for any closed subset of x and any point ,x f∈ − there is an i such thatn∈ ( ) ( ), ,i ig st f gst y φ∩ = 280 metrization of weakly developable spaces 3. the space x has a weak development { }n n ng ∈ such that if where is compact and v is open, then st for some . ,a v⊂ a ( ), na g v⊂ n 4. the space x has a weak development { }n n ng ∈ such that if ,x v∈ where v is open, then there exists a neighborhood u of x and ,n v∈ for which ( ), .ng v⊂st u 5. the space x has a weak development { }n n ng ∈ such that if x v∈ is open, then there exists an n n for which ∈ ( ), .2 nst x g v⊂ proof. the implication 1 is clear. the implications 3 4 , and 5 are proved in martin (1976, theorem 2.5 and theorem 2.6). to prove . let a be any compact subset of 2 5 1 3 ⇒ ⇒ 2 ⇒ 4 ⇒ ⇒ x and let v be an open subset of x containing . suppose that a ( ) (x ), .ig ust a φ∩ − ≠ let ( )i,x st a g∈ ( )x v∩ − . hence, by lemmas 2.1 and 2.2 there is a subsequence :kix k ∈ n of the sequence :ix i ∈ y g n ( ) st , which converges to a point in . now, by hypothesis there is a such that st y a .nj ∈ (( v ), i x g ), i φ∩ − = this leads to a contradiction. 3. acknowledgement the author is grateful to prof. david gauld for his kind help and suggestions on this paper. references arhangel’skii, a. 1966. mappings and spaces, russian math. surveys, 21:115--162. franklin, s. 1965. spaces in which sequences suffice. ii, fund. math. 57:107-115. gruenhage, g. 1984. generalized metric spaces, in handbook of set-theoretic topology, pp. 423-501. martin, h. 1976. weak bases and metrization, trans. amer. math. soc. 222: 338-344. siwiec, f. 1974. on defining a space by a weak base, pacific j. math. 52:233-245. received 14 may 2001 accepted 6 june 2002 281 abdul m. mohamad department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman, email: mohamad@squ.edu.om. îáçõé : äþïã ýí åðç çáèíë çáäùñí� references microsoft word bio_new.doc science and technology, 5 (2000) 1-9 © 2000 sultan qaboos university 1 ultrastructural changes in the epithelium of the stomach of aphanius dispar (cyprinodontidae), due to stress from starvation taher a. ba-omar and reginald victor department of biology, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. التجويع باستخدام المجهر اآلليالناتجة عنلغشاء الطالئي لمعدة سمك الصد ادراسة تغّيرات طاهر بن عبد الرحمن باعمر و ريجنالد فيكتور تم وصف التغّيرات التي حدثت للغشاء الطالئي لمعدة سمك الصد باستخدام المجهر اآللي نتيجة التجويع للفترات التالية : خالصـة ساعة وازدادت مع زيادة فترة التجويع حتى وصلت 24بدأت عملية التغّير في الغشاء الطالئي بعد . سـاعة 120,96,72,48,24 وتشمل هذه التغّيرات بداية اختفاء القطيرات الدهنية وتغير شكل الميتوكندريا والخاليا المخاطية وتآكل . ساعة 96 في ذروةإلى ال ن التجويع لفترات طويلة يلعب دورا كبيرا في التغييرات المرفولوجيكية لمعدة سمك وتؤكد هذه الدراسة أ . أطـراف زوائد المعدة . الصد abstract: ultrastructural changes in the epithelium of the stomach of aphanius dispar, a cyprinodont fish, due to starvation have been described. the changes in the epithelium after 24, 48, 72, 96, and 120 hours have been discussed. the degeneration of the epithelial cells commenced after 24 hours and steadily progressed till 96 hours at which the maximum change was observed. changes in response to starvation include the disappearance of lipid droplets, mitochondrial damage, goblet cells degeneration, morphological aberration of the nuclei and overall abnormalities in the structural integrity of the rugae. this study confirms that stress due to starvation causes significant pathomorphological changes in the stomach in four days. keywords: fish; aphanius dispar; stomach; epithelium histology ultrastructure; stress; starvation. istological studies describing the structure and ultrastructure of fish digestive tracts are many (osman and caceci, 1991; grau et al., 1992; gargiulo et al., 1997, 1998). most of these have also attempted to relate structures to different types of feeding, nutritional requirements, digestive functions and adaptations (kuperman and kuz’mina, 1994; murray et al., 1996). however, investigations exploring the histological changes imposed by physiological stress are very few. the food supply available to fish in its natural environment is not always optimum and periods of food shortage cause stress due to starvation. aphanius dispar (rüppell 1828), a widely distributed cyprinodont fish in the fresh and brackish waters of the middle east, is physiologically capable of coping with a variety of adverse environmental conditions. recently, we described the histology of the stomach of a. dispar using light microscopy and specifically discussed the changes in the structure and number of goblet cells in response to starvation (ba-omar et al., 1998). this study describes the ultrastructure of the epithelium of the stomach and its changes in response to stress caused by starvation. materials and methods specimens of a. dispar with a total length (tl) range of 30.4-46.3 mm, weighing from 0.430.70 gm were collected from wadi al-khod near the sultan qaboos university, sultanate of oman ba-omar and victor 2 (lat. 23ο 30' n; long. 58 ο 40'e). fish were acclimatized for two weeks in an aerated holding tank and were fed with tetramin flakes, ad libitum, twice daily. an experimental tank was prepared with dechlorinated water and held a large perspex visijar in its center containing the same water, with the same water level as that of the outside tank. after a stabilization period of seven days, 36 fish, irrespective of sex were randomly transferred from the holding tank to the outer area of the experimental tank. the feeding regimen for these fish was the same as that for those in the holding tank. the experiment was conducted after another acclimatization period of seven days. figure 1. light micrograph (lm) of a transverse section of the control fish showing rugae of the stomach (large open arrowheads) and the striated border (sb) (x100). at the start of the experiment, 30 fish were randomly transferred to the central visijar and were deprived of food. the six remaining control fish in the outer area of the experimental tank were fed ad libitum, twice daily as usual. the water in the central visijar was replaced with dechlorinated, prestabilized water at short intervals to prevent coprophagy. six starving fish were randomly sacrificed at each interval of 24, 48, 72, 96 and 120 hr for histological studies. at the end of the experiment, the six control fish, fed throughout the experimental duration were also sacrificed for histological investigations. . the fish were placed in ice bath and were immediately decapitated. the entire stomach from each fish was then removed and immediately fixed at room temperature. the methods for the preparation of specimens examined under light microscopy are given elsewhere (ba-omar et al., 1998). for transmission electron microscopy, the stomach was fixed in karnovsky fixative buffered with sodium cacodylate to a ph of 7.4 for four hours and then cut into small pieces. these were washed in cacodylate buffer and then post-fixed in 1% aqueous solution of osmium tetroxide for 1 hour and dehydrated in a series of alcohol before embedding in agar 100 resin. semi-thin and ultrathin sections were cut using reichert ultramicrotome. the semi-thin sections were stained with toluidine blue and the ultra-thin sections were stained with uranyl acetate and post-stained in lead citrate. the sections were examined using a philip109 transmission electron microscope. ultrastructural changes in the epithelium 3 figure 2. light micrograph (lm) of a transverse section of the control fish showing the different layers of the stomach; mucosa (m), submucosa (sm), muscularis (ms) with patches of skeletal muscle (arrowheads) and serosa (s) (x400). results the stomach of a. dispar is a hollow organ with four different layers: mucosa, submucosa, muscularis and serosa. the mucosa, thrown into folds of variable lengths (rugae) is composed of columnar epithelium with striated border (figure. 1). figure 3. transmission electron micrograph (tem) of the control fish showing columnar cells with their nuclei (n), mitochondria (small arrowheads), lipid droplets (l) and striated borders (sb) (x1300). ba-omar and victor 4 figure 4. transmission electron micrograph (tem) of the control fish showing goblet cells (gc) with nuclei (n), mitochondria (small arrowheads) and striated borders (sb) (x1300). the submucosa is composed of connective tissue, the muscularis is composed mainly of smooth muscle and patches of skeletal muscle and the serosa is made up of loose irregular connective tissue with mesothelial cells (figure. 2). figure 5. transmission electron micrograph (tem) of fish after 24 hours of starvation showing the the columnar cells with their nuclei (n), goblet cells (gc) and the striated borders (sb) (x980). under transmission electron microscopy, the epithelial cells of the mucosa were columnar in shape with microvilli forming a striated border with their nuclei at the basal side (figure. 3). mitochondria with ultrastructural changes in the epithelium 5 variable sizes and a number of irregular sized lipid droplets are distributed throughout the cell (figure. 3). most goblet cells were seen at the apical side of the rugae. they have irregularly shaped nuclei located at the basal side , with up to two nucleoli (figure. 4). goblet cells possess numerous densely packed electron-translucent granules which are distributed throughout the cytoplasm (figure. 4). figure 6. transmission electron micrograph (tem) of fish after 48 hours of stravation showing the damaged rugae (large open arrowhead) (x1300). after 24 hours of starvation, the epithelial cells of the mucosa are columnar in shape with most of the nuclei elongated in shape (figure. 5). most of the mitochondria were seen toward the apical side. figure 7. transmission electron micrograph (tem) of fish after 48 hours of starvation showing a darkly stained damaged cell (dc), mitochondria (small arrowheads), striated borders (sb) and debris (d) (x4800). ba-omar and victor 6 figure 8. transmission electron micrograph (tem) of fish after 72 hours of starvation showing darkly stained cells and their degeneration characteristics such as the mitochondria (small arrowheads). it shows also a round goblet cell (gc) and the striated borders (sb) (x2800). the lipid droplets were absent. the apical side possesses striated border, but some sections of the striated border were missing. the goblet cells contained numerous, densely packed electron-translucent granules and the nuclei are located at the base (figure. 5). figure 9. transmission electron micrograph (tem) of fish after 72 hours of starvation showing a basal part of a rugae with darkly stained cells showing degeneration characteristics such as empty spaces (arrowheads) and irregularly shaped nuclei (n) (x7500). after 48 hours of starvation, the apical part of the rugae showed some degree of damage. (figure. 6). the damaged cells were darkly stained with numerous empty vacuoles (figure. 7). mitochondria were ultrastructural changes in the epithelium 7 abnormal in appearance with cristae in various stages of disintegration (figure.7). the lipid droplets seen in the control were absent here. figure 10. transmission electron micrograph (tem) of fish after 96 hours of starvation showing a damaged apical part of a rugae (large open arrowhead), round goblet cells (gc) and degenerated part of the rugae (dc) (x1300). in fish subjected to 72 hours of starvation, there was an increase in the number of damaged cells (figure. 8). goblet cells were also degenerating. these cells were irregularly shaped with electron figure 11. transmission electron micrograph (tem) of fish after 120 hours of starvation showing an extensive damage of the apical part of a rugae (large open arrowheads) and a round goblet cell (gc) (x980). dense nuclei and the nuclei were also irregular in shape with deep indented margins (figure. 8). as in 48 ba-omar and victor 8 hours of starvation, mitochondria were abnormal in appearance with cristae in various stages of disintegration. the degenerating cells at the basal part of the rugae had various sized empty spaces (figure. 9). the damage caused to the mucosa was similar in fish starved for 96 and 120 hours (figures. 10, 11). the damage to the apical part of the rugae was severe characterised by extensive cell degeneration and the disappearance of microvilli (figures. 10, 11). most of the goblet cells were round and seen away from the surface and close to the basal part of the rugae (figure. 11). discussion the general histology of the stomach of a. dispar and its similarities to that of other teleosts was earlier discussed by ba-omar et al. (1998). what is referred to as stomach in this work is the morphologically distinct enlarged, sac-like portion of the gut separated from intestine by a constriction. the ultrastructure of the stomach as revealed by electron microscopy here, also confirms striking similarities between a. dispar and other freshwater teleosts (gargiulo et al. 1997, 1998). the stomachs of a. dispar with large number of well defined goblet cells in the apical region of the mucosa seem typical of omnivorous and herbivorous feeders. osman and caceci (1991) suggested that the gastric epithelial cells specialized for the secretion of neutral mucin and the increase in surface area provided by the dense striated (= brush) border were adaptations for the surface absorption of nutrients in oreochromis niloticus. although a. dispar has similar morphology of the mucosa, its role in nutrient absorption needs to be verified by histochemical techniques. the large number of lipid droplets seen in well fed a. dispar, are probably absorbed from the commercial food with at least 5% lipid content. the turnover time for lipid in the intestinal epithelium is only a few hours. therefore, it is not surprising that the epithelia of fish starved for 24 hours were devoid of lipid droplets. the ability to cope with stress is an important parameter determining the survival of fish. stress is known to induce physiological and pathomorphological changes (boddingius, 1976; 1993; pottinger and pickering, 1992, pottinger et al. 1994, szakolczai, 1997). in the european eel, stress caused the atrophy of the glandular tissue layer of the stomach (peters, 1982). stress during harvest and transport of common carp resulted in the reduction of the number of goblet cells and the detachment of columnar epithelial cells from the basement membrane (szakolczai, 1997). studies on pathological changes caused by stress due to starvation are only a few. in several teleosts including a. dispar, the responses to starvation include the reduction in mucosal mass and the decline in the number of goblet cells (boge et al., 1981; mcleese and moon, 1981; ba-omar et al., 1998). it is well known that goblet cells secrete mucuous which is used for lubrication and for protection of the mucosa against chemical and physical damage. since there is a reduction in the number of goblet cells in the stomach then this will result in the damage of the epithelial cells and other tissues (ba-omar et al 1998). this study documents, at the ultrastructural level, the process of gastric erosion caused by starvation. the significant sequence of events from 24 120 hours of starvation are, the disappearance of lipid droplets, withdrawal of goblet cells from the apical surface, damage to the striated border, a steady degeneration of mitochondria, degeneration of goblet cells and the disappearance of microvilli. acknowledgement we would like to thank mr. d.b. tobias of the biology department, college of science for his technical support and mr. r. m. cornelia of the histopathology department, college of medicine for his assistance in electron micrography. references ba-omar, t.a., victor, r. and tobias, d.b. 1998. histology of the stomach of aphanius dispar (rüppell 1828), a cyprinodont fish, with emphasis on changes caused by stress from starvation. trop. zool. 11: 11-17. boddingius, j. 1976. the influence of social rank on adenohypophyseal cell activity in salmo irideus. cell and tiss. res. 170:383-414. boge, g., rigal, a. and peres, g. 1981. a study of in vivo glycine absorption by fed and fasted rainbow trout (salmo gairdneri). j. experim. biol. 91: 285-295. gargiulo, a.m., ceccarelli, p., dall’ agelio, c. and pedini, v. 1997. ultrastructural study on the stomach of tilapia spp. (teleostei). anat. histol. and embryol. 26: 331-336. ultrastructural changes in the epithelium 9 gargiulo, a.m., ceccarelli, p., dall’ agelio, c. and pedini, v. 1998. histology and ultrastructure of the gut of the tilapia (tilapia spp.), a hybrid teleost. anat. histol. and embryol. 27: 89-94. grau, a., crespo, s., sarasquete, m.c. and gonzalez de canales, m.l. 1992. the digestive tract of the amberjack seriola dumerili, risso: a light and scanning electron microscope study. j. fish biol. 41: 287-303. kuperman, b.i. and kuz’mina, v.v. 1994. the ultrastructure of the intestinal epithlium in fishes with different types of feeding. j. fish biol. 44: 181-193. mcleese, j.m. and moon, t.w. 1989. seasonal changes in the intestinal mucosa of winter flounder, pseudopleuronectes americanus (walbaum), from passamaquoddy bay, new brunswick. j. fish biol. 35: 381-393. murray, h.m.,wright, g.m. and goff, g.p. 1996. a comparative histological and histochemical study of the post-gastric alimentary canal from three species of pleuronectid, the atlantic halibut, the yellowtail flounder and the winter flounder. j. fish biol. 48: 187-206. osman, a.h.k. and caceci, t. 1991. histology of the stomach of tilapia nilotica (linnaeus, 1758) from the river nile. j. fish biol. 38: 211-223. peters, g. 1982. the effect of stress on the stomach of the european eel. j. fish biol. 21: 497-512. pottinger, t.g and pickering, a.d. 1992. the influnce of social interaction on the acclimation of rainbow trout, onchorhynchus mykiss (waldbaum) to chronic stress. j. fish biol. 41: 435-447. pottinger, t.g., moran, t.a. and morgan, j.a.w. 1994. primary and secondary indices of stress in the progeny of rainbow trout (onchorhynchus mykiss) selected for high and low responsiveness to stress. j. fish biol. 44: 149-163. szakolczai, j. 1997. histopathological changes induced by environmental stress in common carp, japanese coloured carp, european eel and african catfish. acta veterinaria hungarica 45(1): 1-10. received 28 november 1999 accepted 25 june 2000 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 33-38 © 2001 sultan qaboos university desert nitrogen cycles: fecal nitrogen from a population of the sahelian tree locust in oman michael d. robinson department of biology, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. النيتروجين المتواجد في غائط جراد األشجار الساحلي: في الصحراءدورات النيتروجين مايكل روبنسون , أعدادها الغير منتظمةديحدد هذا البحث مقدار النيتروجين الذي تخلفه جرادة األشجار اناكريديم ميالنورودون خالل ازديا :ةخالص معدل بروتين الغائط جرام في المتر المربع وان65.22ط هو لقد وجد أن معدل تراكم الغائ. في غابة من أشجار السمر في عمان ذلك يعني إن في . جرام من الوزن الجاف الخالي من الرماد 100 جرام لكل 3.22 و 20.14الخام والنيتروجين على التوالي هما ألحادية للجراد تماثل ثلث كمية إن هذه المساهمة ا. كليوجرام من نيتروجين الغائط تحت األشجار1.1كل هكتار من الغابة يتجمع النيتروجيـن التـي تكونها الكائنات األخرى التي تعيش على األعشاب وتحولها لنيتروجين في مساحة هكتار في صحراء موهيف ) الجراد الصغير (أن هـذا يوضـح أهمية الجراد في دورات النيتروجين كما يسلط الضوء على أهمية الجندب . بشـمال أمـريكا .النيتروجين لمتنوع والمتواجد موسميا في دوراتالصحراوي ا نيتروجين الغائط, الجراد, دورات النيتروجين في الصحراء: كلمات أساسية abstract: this research quantifies the amount of nitrogen deposited by the tree locust, anacridium melanorhodon, during an irregular population outbreak in an acacia tortilis woodland in oman. the average standing crop of feces was 65.28g m-2. the mean fecal crude protein and nitrogen were respectively, 20.14 and 3.22 g/100 g ash-free dry weight. a hectare of this woodland would contain approximately 1.1 kg of fecal nitrogen beneath the trees. this single contribution by the locusts equals about one-third of the total standing crop of detrital nitrogen under perennial vegetation in a hectare of the mohave desert of north america. this, and the fact that grasshoppers are diverse and seasonally abundant in deserts, suggests they may be important organisms in nitrogen cycles. keywords: nitrogen cycles; fecal nitrogen; deserts; tree locust; grasshoppers; oman. 1. introduction p hytophagous insects are important regulators of nutrient cycles in temperate forests (mattson and addy, 1975), but our knowledge of how they interact in desert ecosystems is still elementary. during the past two decades desert nutrient cycle research has focused on nitrogen, particularly on the concentration in plant tissues, leaf litter and soil (west and skujins, 1978; skujins, 1981; west, 1981; whitford, 1986; rundel and gibson, 1996). less attention has been given to the roles of animals in desert nitrogen cycles. garner and steinberger (1989) provide an insightful model of possible nitrogen pathways, and they emphasize that zoo-transport concentrates nitrogen around perennial vegetation. field research by dean et al. (1999) documents various ways vertebrate animals interact with trees in the arid woodland of the kalahari desert. it appears that the input of fecal nitrogen by tree locusts during one of their irregular population surges has not been quantified. tree locusts (genus anacridium) are widely distributed in the arid and semi-arid regions of africa and western asia. during population outbreaks their swarms may cover several square kilometers and cause localized damage to trees (gum arabic, date and fruit trees) and other crops 33 michael robinson (popov and ratcliffe, 1968; marais and wittneben1977; showler, 1995); however, tree locusts are generally not a major pest. the sahelian tree locust, anacridium melanorhodon , is distributed in the sahelian region of africa (a. m. melanorhodon) and the coastal zone of the arabian peninsula (a. m. arabafrum). normally, they roost and feed in native trees of the xeric woodlands ( eg., acacia spp., ziziphyus spp., balanities aegyptiaca). a. m. arabafrum breeds erratically in response to winter and spring rains and may produce several generations in a year (popov and ratcliffe, 1968). the objectives of this study were to estimate the amount of fecal nitrogen deposited by the sahelian tree locust during a population outbreak, and to point out the potential importance of acridid orthopterans in desert nitrogen cycles. 2. methods the study site was located in the sultanate of oman, approximately 40 km west of muscat and 3 km southeast of sultan qaboos university (23°34.85'n, 58°11.14'e). rainfall near the study area averages 81.3 mm/year (fisher, 1994). the dominant perennial vegetation of this gravel plain includes acacia tortilis, lycium shawi, acridocarpus orientalis, jaubertia aucheri, pulicaria glutinosa, and tephrosia apollinea (nomenclature follows ghazanfar, 1992). the locusts' primary roost was in samr trees (a. tortilis). adult tree locusts appeared on the study area sometime in late march 1998, and by april 2, approximately 10 to 30 individuals were seen in the larger trees. at the time of sampling (may 69), a clearly defined circular shadow of pellets was evident beneath most trees, representing the fecal accumulation of approximately 35-40 days. by may 25 the locust population was greatly reduced, but scattered individuals were still sighted in early autumn. the standing crop of feces was quantified by collecting all fecal pellets inside four, 12.5cm square quadrats that were placed randomly beneath the canopy of 16 trees, a total of 64 sample units. anacridium feces were easily distinguished from other grasshopper species by their large size. the fecal pellets were of various ages and degrees of desiccation, which possibly affected their protein content. eleven sample units had sufficient mass for the ash and crude protein analyses. these samples represented 8 different trees (table 1). all the samples were cleaned and oven-dried (60°c) to a constant mass. crude protein was determined by the kjeldahl method. the nitrogen content was assumed to be 16% of the crude protein (cullison and lowery, 1987). samples were burned in a muffle furnace (550o c) to determine the ash content. table 1: ash, crude protein (cp) and nitrogen (n) in 11 samples of tree locust (anacridium melanorhodon) feces. values are g/100 g dry weight. crude protein and nitrogen are corrected for mineral contamination (afdw). sample ash cp (afdw) nitrogen (afdw) t1-4 9.53 20.24 22.37 3.24 3.56 t2-2 10.95 17.53 19.68 2.80 3.15 t2-3 10.28 16.59 18.49 2.65 2.96 t3-4 9.95 17.22 19.12 2.76 3.06 t4-1 11.03 17.36 19.52 2.78 3.12 t4-4 11.00 17.02 19.12 2.72 3.06 t9-3 11.76 19.01 21.54 3.04 3.45 t9-4 10.18 18.81 20.94 3.01 3.35 t15-1 10.11 18.45 20.52 2.96 3.28 t7-3 11.57 17.81 20.13 2.85 3.22 t5-2 11.61 17.80 20.14 2.85 3.22 34 locust fecal nitrogen 3. results the mean fecal dry weight biomass in a quadrat was 1.02g, or 65.28g/m². average density was 78.13 or 5000.32 pellets/m² (table 2). this represents the fecal accumulation of slightly more than one month. the mean (± one standard deviation) dry mass and length of the pellets was 12.7 mg (± 1.52) and 8.4 mm (± 1.36), respectively (n=30). the mean crude protein and nitrogen content of the feces was, respectively, 20.14 (±1.145) and 3.22 (± 0.180) g/100g ash-free dry weight (table 1). table 3 estimates the area beneath samr trees with various canopy diameters and the ash-free dry weight of feces, crude protein and nitrogen deposited by a. melanorhodon. one square meter would contain about 11.75 g of crude fecal protein and 1.88 g of fecal nitrogen. table 2: mean dry weight biomass (g) and density of tree locust (anacridium melanorhodon arabafrum, fecal pellets in 64, 12.5cm square quadrats beneath acacia tortilis trees). biomass density mean 1.02 78.13 sd 0.441 32.88 minimum 0.41 30.0 maximum 2.58 171.0 table 3 : ash-free dry weight estimates of fecal mass, crude protein and nitrogen (g) deposited by anacridium melanorhodon arabafrum in surface litter under acacia tortilis trees of various canopy diameters. diameter (m) 2 4 6 8 area (m2) 3.14 12.57 28.27 50.27 fecal mass 182.82 731.85 1645.93 2926.82 crude protein 36.82 147.42 331.54 589.55 nitrogen 5.90 23.58 53.05 934.33 4. discussion animal consumption and excretion are important pathways in nutrient cycles of desert and arid savanna (west, 1981; garner and steinberger,1989; belsky et al. 1989). grazing animals increase the amount of plant material returned to the soil and in particular the turnover rate of nitrogen. mammalian feces decompose more rapidly than non-ingested plant material, accelerating the flow of materials. vertebrate herbivores deposit dung while resting beneath trees (dean et al. 1999). the feces of a chihuahuan desert jackrabbit (lepus californicus) comprise 10% of the total litter mass beneath creosote shrubs and 13.8% in open areas (whitford et al.,1982). cowling (1977) estimates that 50-70% of the ingested nitrogen is returned as urine and a further 20% in dung. while feeding, arthropods drop frass, partially eaten leaves, herbaceous stems and feces, into the surface litter, but estimates of this contribution by desert insect herbivores are very few. in a preliminary report, boshoff (1988) estimates that immature brown locust (hoppers), at assumed swarm densities of 5000 individuals/m2, could deposit 110 kg of frass/day. the average nitrogen concentration of the frass is 0.617gn/100g dry weight. at the roost sites 1 m2 would contain about 35 michael robinson 0.093gn. i assume his data are without ash corrections; no methods are given. fecal nitrogen of adult tree locusts is 4.6 times more concentrated than the frass of the brown locust (2.85gn/ 100gdw, not corrected for ash; table 2). locusts and other folivores capture nitrogen that would otherwise be translocated from the leaf prior to abscission. nitrogen in tree locusts' feces is about 14% more concentrated than in the living leaflets of a. tortilis and 40% greater than the abscissed leaflets in the litter (m. robinson, unpublished). some of the fecal nitrogen of acridids is derived endogenously from the peritrophic membrane, which surrounds the egesta. for example, the creosote bush grasshopper, bootettix argentatus, invests 10% of the ingested protein in the peritrophic membrane. when fed a tanninrich diet, anacridium melanorhodon produces a membrane that is 0.89% of the body weight (bernays and simpson, 1990). the main forms of fecal nitrogen excreted by desert locust (schistocera gregaria) are uric acid (30-35% of total egested nitrogen) and other undetermined nitrogenous waste products (55%), such as ammonia, allantoin and allantoinic acid. the feces contain relatively little protein or free amino acids (zanotto et al. 1993). the time required to decompose tree locust feces and mineralize the nitrogen is unknown. estimates of turnover times of desert litter vary widely from 14 years (holmgren and brewster, 1972) to around two years (cormanor and prusso, 1973). binet (1981) concludes that feces decompose slowly and mineralized nitrogen could remain a long time. most of the nitrogen returned via feces and urine is lost in the gaseous form, with only 1% of the nitrogen becoming incorporated into the soil (rixon, 1970). o'brien's research (1978) in the chihuahuan desert also suggests that most of the nitrogen is volatilized during mineralization. considering their species richness and great seasonal abundance, orthopterans are probably important components in desert nutrient cycles. wisdom (1991) reports 10 genera and 13 species of grasshoppers (acrididae) occur on the sonoran desert tree prosopis glandulosa. mohave desert grasshoppers comprise as much as 8% of the total invertebrate biomass, and their bodies contribute 13 g n/ha to the nitrogen pool (rundel and gibson, 1996). grasshoppers are also abundant in the deserts of western asia and africa. popov (1980) reports 70 taxa from eastern arabia. locusts (schistocerca, locusta) are legendary for their phenomenal sporadic population surges and the economic loss they inflict on agriculture (popov et al.,1984). however, the functional role of locusts and other acridids as concentrators of plant nitrogen and as a direct link to the decomposers has not been appreciated by ecologists. the nitrogen budget of this community is unknown, but the potential input of fecal nitrogen by a. melanorhodon can be estimated. at a nearby site the density of a. tortilis averages 37 trees/ha. most of these trees have canopy diameters between 3 and 6 m (martin fisher, personal communication). assuming an average canopy diameter of 4.5 m, then approximately 30 g of fecal nitrogen would have been deposited under each tree, or 1.1 kg/ha (table 3). rundel and gibson (1996) estimate that surface litter beneath perennial vegetation of the mohave desert contains 3kg nitrogen/ha , only about two-thirds more than that contributed by tree locusts. without knowing how much fecal nitrogen is mineralized and eventually becomes available to the plants, the true impact of these irregular nitrogen inputs is impossible to assess. locusts cause great economic losses to crops, but they probably also benefit agricultural and natural ecosystems by the nitrogen they contribute through death and defecation. it remains for future research to more clearly define their role in desert nutrient cycles. 5. acknowledgements i thank professor neil forsberg and drs. richard early and eugene johnson of the department of animal and veterinary science, sultan qaboos university, and their technical staff, kanthi annamalai and andrew ritchie, for their collaboration in the analysis of samples. drs. r. chapman, s. hanrahan, s. green, c. kooyman, and g. sword provided useful advice and references. sultan qaboos university provided research facilities. 36 locust fecal nitrogen references belsky, a.j., amundson, r.g., duxbury, j.m., riha, s.j., ali, a.r. and mwonga, s.m. 1989. the effects of trees on their physical, chemical and biological environments in a semi-arid savanna in kenya. journal of applied ecology, 26: 1005-1024. bernays, e.a. and simpson, s.j. 1990. nutrition. in biology of grasshoppers. eds r.f. chapman and a. joern. john wiley & sons , new york. binet, p. 1981. short-term dynamics of minerals in arid ecosystems. in: arid-land-ecosystems: structure, functioning and management, vol 2. eds d.w.goodall and r.a. perry. cambridge university press, cambridge. boshoff, c. 1988. does the brown locust play an important role in nutrient cycling? proceedings locust symposium, macgregor museum, kimberly, south africa. south african institute of ecologists bulletin special issue, 1988: 85-96. cormanor, p.l and prusso, d.c. 1973. decomposition and mineralization in an artemisia tridentata community in northern nevada. u.s. ibp desert biome research memorandum, rm:73-79. cowling, s.w.1977. effects of herbivores on nutrient cycling and distribution. in: impact of herbivores on arid and semi-arid rangelands. australian rangeland society, perth. cullison, a.e. and lowery, r.s. 1987. feeds and feeding (4th edn.). prentice-hall inc., new jersey. dean, w.r.j., milton, s.j. and jeltsch, f. 1999. large trees, fertile islands, and birds in arid savanna. journal of arid environments, 41: 61-78. fisher, m. 1994. another look at the variability of desert climates, using examples from oman. global ecology and biogeography, 4: 79-87. garner, w. and steinberger, y. 1989. a proposed mechanism for the formation of 'fertile islands' in the desert ecosystem. journal of arid environments, 16: 257-262. ghazanfar, s. 1992. an annotated catalogue of the vascular plants of oman. scripta botanica belgica 2. national botanic garden of belgium, meise. holmgren, r.c. and brewster, s.f. jr. 1972. distribution of organic matter reserve in a desert shrub community. usda forest service research paper int-30. mattson, w.j. and addy, n.d. 1975. phytophagus insects as regulators of forest primary production. science, 190: 515-522. marais, e. and wittneben, f. 1997. the 1994 outbreak of the tree locust anacridium moestum in namibia (orthroptera: acrididae: cyrtacanthacridnae). journal of the namib scientific society, 45: 1-12. o'brien, r.t. 1978. proteolysis and ammonification in desert soils. in: nitrogen in desert ecosystems. eds n.e.west and j.skujins. dowden, hutchinson and ross, stroudsberg. popov, g. b. 1980. acridoidea of eastern arabia. journal of oman studies special report no. 2: 113-148. popov, g.b. and ratcliffe, m. 1968. the sahelian tree locust, anacridium melanorhodon. anti-locust memoirs, 9: 1-45. popov, g.b., wood, t.g. and haggis, m. j. 1984. insect pests of the sahara. in: sahara desert, ed j.l. cloudsley-thompson. pergamon press, oxford. rixon, a.j. 1970. cycling of nutrients in a grazed atriplex vesicaria community. in: the biology of atriplex. ed r.jones. csiro division of plant industry, canberra. rundel, p.w. and gibson, a.c. 1996. ecological communities and processes in a mohave desert ecosystem: rock valley, nevada. cambridge university press, cambridge. showler, a.t. 1995. locust (orthoptera:acrididae) outbreak in africa and asia, 1992-1994: an overview. american entomologist, 41: 179-185. skujins, j. 1981. nitrogen cycling in arid ecosystems. in: terrestrial nitrogen cycles: processes, ecosystem stratigies, and management impacts. eds f.e. clark and t. rosswell, ecological bulletin (stockholm), stockholm. 37 michael robinson west, n.e. 1981. nutrient cycling in desert ecosystems. in: arid-land ecosystems: structure, functioning and management. eds d.w. goodall, r.a. perry, and k.m.w. howes, vol. 2, cambridge university press, cambridge. west, n. and skujins, j. 1978. nitrogen in desert ecosystems. dowden, hutchinson & ross, stroudsberg. whitford, w.g. 1986. decomposition and nutrient cycling in deserts. in: pattern and process in desert ecosystems. ed w.g.whitford, university of new mexico press, alburquerque. whitford, w.g., repass, r., parker, l.w. and elkins, n.z. 1982. effects of initial litter accumulation and climate on litter disappearance in a desert ecosystem. american midland naturalist, 108: 105-110. wisdom, c. s. 1991. patterns of heterogeneity in desert herbivorous insect communities. in: the ecology of desert organisms, ed g.a. polis. university of arizona press, tucson. zannoto, f.p., simpson, s.j., and raubenheimer, d.1993. the regulation of growth by locusts through post-ingestive compensation for variation in the levels of dietary protein and carbohydrate. physiological entomology, 18: 425.434. received 14 november 2000 accepted 19 may 2001 38 michael d. robinson department of biology, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. state-of-the-art review of collapsing soils science and technology, 6 (2001) 13-19 ©2001 sultan qaboos university effect of ph on the removal of chromium (cr) (vi) by sugar cane bagasse nasim ahmed khan, syed iqbal ali and sohail ayub department of civil engineering, amu. aligarh university polytechnic. amu. aligarh, india. باستخدام بقاس من قصب السكر (vi)تأثير درجة الحموضة في إزالة الكروم هيل أيوب سنسيم أحمد خان ، سيد اقبال علي و بما لبيئِة ل بالنسبة ا جّدي االتي تُشكُّل تهديد و ةوسِطمت وال ِةالّصغيريها الصناعات المناطق الصناعية في الهند تُسيطُر عل :خالصة معدن الكروم على ويستخدم . هذه المخلفات عادِن الثّقيلِة في الم ومما يزيد من تفاقم المشكلة وجود بعض . تطلقه من مخلفات ملوثة ومن . الخ.. التبريد واألصباغ ودبغ الجلود أبراجوتلميع المعادن و ، ء األواني الّصناعاِت مثل طَال من عدد نحو واسع في في ة عالِيه بدرجة تّركيز أن ، كما لى صحِة البشِر والحيواناتِ ا ع وَيعتبُر خطر سام جدا )vi( معدن الكرومِ المعروف جدا أن تخفيض ال طرِق، مثل بعدة معدن الكرومِ المخلفات المحتوية على معالجة وقد تمت . ة يشكل خطراً كبيراً عليها البيئاِت المائي ريقة وقد وجد أن ط . ىعكسوالتناضح ال التّنافذ وتبخير، والكهروكيمياوي، التخفيض واليوني، االتبادل الترسيب، وال و، كيميائيال مثل ة الّزراعي الفضالت من كبيرة ات كمي وتنتجُ زراعيةُبلد الهند و. طريقة رخيصة وسهلة التنافذ هى اكثر الطرق فعالية وهى . الخ... وقشور البقوليات ومخلفات األسمدة رزِّ،األ وقش قصبوبندِق، الصدفة وهنِد، ال جوزة نبات جوت، و قصب ال سكربقاس قّدَم بشكل سهل كمكثّفاِت إلزالِة معدن تُُيمكُن َأْن العالم الثالث و بلداِن فيذه المواِد ُيمكُن َأْن تَكُوَن مفيدة على ه الناجحة ِدراسات وال هذه المكثّفاِت و. برُز إستعمال الكاربون المنشّط بشكل تجاري تُالّسابق بحاث في أغلب األ و. مياه الصرف الصناعي الكروِم من ميم دراسات ميدانية صبأخذ ذلك في االعتبار فقد تم ت و. جدوى اقتصادية كبيرة في دول العالم الثالث جدا وغير ذات غاليةُ ياعمل .المائيِةلمحاليل من ا)vi(الستخدام بقاس سكر القصب إلزالة معدن الكروم abstract: the industrial estates in india are dominated by small and medium scale industries, which are posing a serious threat to the environment by virtue of discharging effluents of a polluting nature. the problems become severe due to the presence of heavy metals in the effluents. chromium is widely used in a number of industries such as electroplating, metal finishing, cooling towers, dyes, paints, anodising and leather tanning industries. the toxicity of chromium (vi) is well known and is considered a hazard to the health of humans and animals. the presence of chromium (vi) in aquatic environments at high concentrations is also lethal to marine species. the treatment of chromium bearing effluents have been reported through several methods, such as chemical reduction, precipitation, ion exchange, electrochemical reduction, evaporation, reverse osmosis and adsorption. however among these, adsorption is found to be highly effective, inexpensive and an easy method to operate. india is an agricultural country and generates a considerable amount of agricultural wastes such as sugar cane bagassess, coconut jute, nut shell, rice straw, rice husk, waste tea leaves, ground nut husk, crop wastes, peanut hulls and fertilizer wastes. successful studies on these materials could be beneficial to developing countries and could be easily applied as adsorbents for the removal of chromium from wastewater. most of the previous work highlights the use of commercial activated carbon but these adsorbents are relatively expensive and less feasible to be used in developing countries. keeping these in view batch experiments have been designed to study the feasibility of sugar cane bagasse to remove chromium (vi) from the aqueous solutions. while evaluationg the impact of various parameters, such as adsorbent does, contact time, initial concentration and ph on chromium removal efficiency, the results indicate a prominent effect of ph on the chromium reduction by the adsorbent used in the present study. keywords: adsorption, toxicity, sugarcane, bagasse and chromium. 1. introduction most of the wastewater in industrial estates contains trace quantities of many heavy metals such as nickel, manganese, lead, chromium, cadmium, zinc, copper, iron and mercury. some of 13 nasim ahmed khan, syed iqbal ali and sohail ayub these metals are essential to the growth of biological life and absence of sufficient quantities of them could limit their growth (metacalf and eddy et al, 1994). larger concentrations, however, could cause adverse effects on humans, animals and plants. the rapid industrialization has resulted in accelerating the flux of heavy metals into surfacial environment. pollution, due to these heavy metals, has been a major source of concern to scientists and environmental engineers. the presence of any of the above mentioned heavy metals in excessive quantity will interfere with many usages of water because of their toxicity. therefore, it is desirable to measure and control the concentrations of these substances. several mishaps related to heavy metal concentrations in the aquatic environment have increased the awareness about heavy metal toxicity. among these, minamata tragedy in japan (1953-60) due to metallic mercury escaping from the laboratories and industries, mainly from chlorine manufacturing. it was acquired by aquatic life and passed along through natural food chains to humans, largely by fish. another disease “itai-itai” that occurred among the farmers who drank water-containing cadmium supplied from the jentsu river in japan (benefield ; jadleins and weand et al, 1982). chromium (vi) causes many adverse effects on humans, aquatic life and soil. some of the effects are summarized as follows; humans: nausea, vomiting (kerishnamurthy and vishwanathan) , epiesgestric pain, severe diarrhoea, haemorrhage, dermatitis by skin contact, nasal mucous membrane, ulcer (satyanarayan et al, 1995), lung cancer and tissue necrosis. aquatic life: reduction in fish production at high concentrations, chromium accumulates in fish tissues and reaches to consumers. gold fish and trout are killed at a concentration of 180 mg/l. land: soil fertility is reduced if chromium-bearing effluents are discharged on land (sohail, 1997). table 1: comparative study of different adsorbents (siddiqui, z. m. and paroor, s. 1994). adsorbent initial conc.cr (vi) mg/l equilibrium time(hr) dose (g/100ml) ph cr (vi) removal % activated ghc [8] 10 3 0.24 2 80 activated charcoal [2] 100 5 100 calcinate coke [5] 5 2 100 bagasse ash [10] 10 3 6 2 53.2 activated bagasse carbon [10] 10 1.5 1.0 0.85-2 99.97 raw bagasse [10] 10 1.5 1.0 1.0 93.5 activated coconut jute [10] 10 1.5 1.0 1.4-2 99.7 waste tea leaves carbon [7] 1.2 2 100 activated charcoal, flyash & rice husk [11] 7,,0.5 0-2 50,,100 carbon slurry [12] 1.0 0.8 2.5 91.50 rice straw [3] 10 24 1.0 1-3 100 activated charcoal [6] 10 0.5 3 max at ph 3 peat [9] 100 24 0.4-4 >2 50 fe(iii) hydroxide [1] 50.8 0.30 4-6 99 lignite [13] 3000 24 0.4 2 73.33 activated carbon [4] 5.0 2 0.2 2.5 100 2. adsorption of heavy metals on agricultural wastes the treatment of chromium bearing effluents has been reported through several methods, such as, chemical reduction and precipitation, ion exchange, electrochemical reduction, evaporation and reverse osmosis. most of these methods need high capital costs and recurring expenses such as chemicals. less attention has been paid towards the treatment of effluent containing chromium by means of the adsorption technique using agricultural wastes. (sohail et al, 1998). potential agricultural waste adsorbents are activated ground nut husk carbon (periasamy, 1991), calcinate coke (satyanarayan, 1995), bagasse ash , activated coconut jute, waste tea leaves carbon, activated 14 effect of ph on the removal of cr (vi) by sugar cane bagasse charcoal, fly ash and rice husk, and rice straw (deo, 1992). the comparative studies of different adsorbents are shown in table 1 (lal, 1992; huang, 1975; sharma, 1993; shrichand, 1994). 3. materials and methods the wastewater to be used in the investigation was prepared by dissolving a known amount of potassium dichromate in a known volume of distilled water in order to have waste of uniform characteristics and to avoid the interference with other elements. to evaluate the potential of bagasse to remove hexavalent chromium, batch experiments were carried out. wastewater containing known concentrations of cr (vi) were prepared from the stock solution and taken separately in glass stoppered conical flasks. then known quantities of the adsorbent were added to the wastewater. the system was equilibrated by shaking the contents of the flask at room temperature so that adequate contact time between adsorbent and the metal ion was maintained. the suspension was filtered through whatman no.1 filter paper and the filtrate was analyzed to evaluate the concentration of cr (vi) metal in the treated wastewater. all the analyses were performed according to standard methods (standard methods, 1989). metal analysis was carried out by using atomic absorption spectrometry (model: gbc902). 4. results and discussion while evaluating the effect of adsorbent dose, contact time and ph on chromium removal, the initial concentration of cr (vi) was kept as 50 mg/l because in chrome plating wastes, chromium concentrations vary from 3-30 mg/l [isi 7453-1977]. 5. effects of contact time at different adsorbent doses on cr (vi) removal the response of contact time on the removal of cr (vi) is presented in figure1. the observations reveal that the percentage of removal of cr (vi) increases with an increase in contact weight of adsorbent 0 20 40 60 80 100 120 0 0.5 1 1.5 2 2.5 3 3.5 4 contact time in hours % r e m o v a l o f c r( v i) 0.1 g 0.2 g 0.3 g 0.4 g 0.5 g 0.6 g 0.7 g 0.8 g 0.9 g figure 1. effects of contact time at different adsorbent (bagasse) doses on cr (vi) removal. 15 nasim ahmed khan, syed iqbal ali and sohail ayub time. the removal efficiency is further increased as the dose of bagasse increases from 0.1 to 0.9 g and the contact time varies from 0.5 to 3.5 hr. it is also observed that at 0.5 hr the removal efficiency increased from 27-80% as the adsorbent dose increased from 0.2 to 0.8 g. if the contact time is raised to 1.0 hr, the removal efficiency varies from 38 to 93% for the same variation of dose (0.2 to 0.8 g). a removal efficiency of 94% of cr (vi) is observed at a contact time of 1.5 hr with a dose of 0.70 g/50 ml. chand et al. (shrichand, 1994) observed 30% removal efficiency of cr (vi) having initial cr (vi) concentration of 10 mg/l, at ph 4.38, the contact time was 1.5 hr and dose of adsorbent was 1.2 g/100 ml. 6. effects of adsorbent dose at different contact time on chromium cr (vi) removal the effect of various bagasse dose on the removal of cr (vi) from the wastewater are shown in figure 2 .the results indicate an increase in the removal efficiency of cr (vi) with increase in the dose of raw bagasse up to a certain level, beyond which the removal efficiency remains constant. it is evident that a dose of 0.8 g/50 ml is sufficient to remove 75-100% cr (vi) in 0.5-3.5 hr. the increase in the removal efficiency with a simultaneous increase in adsorbent dose is due to the increase in surface area and hence more active sites are available for the adsorption of cr (vi). contact time 0 20 40 60 80 100 120 0 0.2 0.4 0.6 0.8 1 1.2 adsorbent dose in g/50ml % r e m o v a l o f c r( v i) 0.5 hr 1.0 hr 1.5 hr 2.5 hr 3.0 hr 3.5 hr figure 2. effects of adsorbent dose at different contact time on cr (vi) removal. 7. effect of ph on chromium (vi) removal effect of ph on cr (vi) removal shows that at lower ph, the cr (vi) removal efficiency is higher and at higher ph the removal efficiency is reduced considerably (figure 3). at ph 1.0 the removal efficiency is 100%, whereas on increasing the ph to 3.0 the removal efficiency is reduced to 15%. one of the reasons for the better adsorption capacity observed at low ph values may be attributed to the large number of h+ ions present at these ph values, which in turn neutralizes the negatively charged hydroxyl groups (-oh) on the adsorbed surface thereby reducing hindrance to the diffusion of dichromate ions. at higher ph, the reduction in adsorption may be due to an 16 effect of ph on the removal of cr (vi) by sugar cane bagasse abundance of ohions causing increased hindrance to diffusion of positively charged dichromate ions. 0 20 40 60 80 100 120 0 2 4 6 8 10 ph % r e m o v a l o f c r figure 3. effects of ph on cr (vi) removal. 8. effects of various initial cr (vi) concentrations on cr (vi) removal the results of figure 4 show that at low initial concentrations of chromium (vi) ( 5 to 10 mg/l) the removal efficiency is higher (70-100%). the removal efficiency of chromium decreases when chromium concentration is increased beyond 10 mg/l. the removal efficiency is 60% at a concentration of 20 mg/l and it decreases to 47% when chromium concentration was increased to 50 mg/l. in a similar study chand et al. (shrichand, 1994) obtained 90% removal efficiency at a cr (vi) concentration of 10 mg/l in a dose of 1.0 g/100 ml at a contact time of 1.5 hr when the ph of the solution was 2.0. fig.4 effects of initial cr (vi) concentration on cr (vi) removal 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 initial conc. of cr (vi) in mg/l % c r (v i) r e m o v a l ph=2 ph=1.5 17 nasim ahmed khan, syed iqbal ali and sohail ayub 9. rate kinetics the adsorption studies (figure 5) conducted at a fixed initial concentration and varying adsorbent doses were fitted to the linearized freundlich adsorption isotherm given below, log (x/m) = log k + 1/n log ce where, x/m is the amount of cr (vi) adsorbed per unit mass of adsorbent (mg/mg) and ce is the equilibrium concentration of aqueous solution. k is a constant, which is a measure of adsorption capacity, and 1/n is a measure of adsorption intensity. the values of the constant k and 1/n are 0.0032 and 0.235 respectively.since the values are less than 1, it indicates a favorable adsorption (shrichand, 1994). y = 0 .2358 x 2.4893 -2.55 -2.5 -2.45 -2.4 -2.35 -2.3 -2.25 -2.2 -2.15 -2.1 0 0.5 1 1.5 2 log (ce ) lo g figure 5. plot for freundlich isotherm. 10. conclusions the following conclusions can be drawn from the present study. • an adsorbent dose of 0.8 g/50 ml is sufficient to remove 80-100 % cr (vi) from a solution having an initial concentration of 50 mg/l. • the data obtained during the present study may be quite helpful in designing a full-scale adsorber for the treatment. • before applying raw bagasse for the treatment of wastewater there is a need for further investigations as the acid hydrolysis of cellulose in acidic medium produces alcohol that may increase the expand of the wastewater. • raw bagasse exhibits a high degree of cr (vi) removal and it can be utilized for the treatment of industrial wastes containing chromium (vi) concentrations between 10-100 mg/l. • the raw bagasse after adsorption can be burnt for heat recovery and the bagasse ash containing small quantities of cr (vi) can be disposed off on low-lying areas. references ayub, s; ali, s.i; khan, n.a; rao, r.a.k. 1999. extraction of chromium from the wastewater by adsorption, environmental pollution cont. journal, 2(5): 27-31. 18 effect of ph on the removal of cr (vi) by sugar cane bagasse ayub, s; ali, s.i.; khan, n.a; hasan, s.d. dec1998. treatment of wastewater by agricultural wastes, environmental pollution cont.journal.1(2): standard methods for the analysis water and wastewater. 17th ed. aph, awwa, wpcf, washington d.c, 1989, 5-8. benefield, l.d; jadleins, j.f; weand, b.l. 1982. process chemistry for water and wastewater treatment, prentice-hall, inc; engle wood cliffs, new jersey. chand, s.a; aggarwal, v.k; kumar, p, 1994. removal of hexavelent chromium from the wastewater by adsorption, indian j. environ.hlth 36(3): 151-158. deo, n. ali, m. 1992. use of a low cost material as an adsorbent in the removal of cr(vi) from the dilute aqueous solution, ijep. 12(6): 439-411. huang, c.p.wu. m.h. 1975. chromium removal by carbon adsorption. j.water pollut.cont.fed.47: 243-46. lal, j; singh, d.k., 1992. removal of chromium (vi) from the aqueous solution using waste tealleaves carbon. indian j. environ.hlth 34: 108-113. metacalf, l; eddy, h.p.1994.wastewater engineering reuse and disposal, tata mcgrow hill pub.co; new delhi, periasamy, k; srinivasan, k; murugan p.k., 1991. studies on chromium (vi) removal by activated groundnut husk carbon, indian j. environ.hlth, 31(4): 433-439. satyanarayan, s., 1995. sorption of cr (vi) and cr (iii) from water by bitruninous coal, m.tech. thesis, iit kanpur. sharma, d.c; forster, c.f, 1993.removal of hexvalent chromium using sphagnum mors peet, wat.res, 27(7): 1201-08. siddiqui, z.m; paroor, s, 1994. removal of chromium (vi) by different adsorbents–a comparative study.ijep, 14(4): 273-278. received 4 march 2000 accepted 1 june 2000 19 êãëíñ ïñìé çáíãæöé ýí åòçáé çáßñ� abstract: the industrial estates in india are dominated by small and medium scale industries, which are posing a serious threat to the environment by virtue of discharging effluents of a polluting nature. the problems become severe due to the presence of keywords: adsorption, toxicity, sugarcane, bagasse and chromium. introduction adsorption of heavy metals on agricultural wastes the treatment of chromium bearing effluents has been reported through several methods, such as, chemical reduction and precipitation, ion exchange, electrochemical reduction, evaporation and reverse osmosis. most of these methods need high capital costs effect of ph on chromium (vi) removal rate kinetics log (x/m) = log k + 1/n log ce references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 45-51 © 2001 sultan qaboos university measurements of rf radiation in the vicinity of fm and tv broadcasting stations abdulaziz s. al-ruwais department of electrical engineering, college of engineering, king saud university, p.o. box 800, riyadh 11421, saudi arabia. e-mail: asruwais@ksu.edu.sa (fm)قياسات لإلشعاع الالسلكي على مقربة من محطات البث التلفزيوني وراديو عبدالعزيز الرويس تتناول هذه الورقة العلمية موضوع القياسات الميدانية لكثافة القدرة لألشعاع الالسلكي في األماكن المجاورة لمحطة بث : خالصة ، وقد وجد أن أقصى قيمة مناسبة هي حواليvhfونية عند نطاق ومرسالت تلفزي ) fm(تحتوي على مرسالت إذاعية من نوع w/cm2 µ 2.4 على ارتفاع مترين من سطح األرض أما المتوسط فكان w/cm2µ1 وتبين أن كثافة القدرة لإلشعاع ، وفي موقع يبعد عن . مترا 15 عند ارتفاع w/cm2 µ3.5ة الالسلكي تتزايد مع االرتفاع عن سطح األرض حتى تصل إلى قيم w/cm2µ41 متر ، كانت كثافة القدرة المقاسة حوالي 185وفي موقع آخر يبعد عن المحطة بمسافة . متر 400المحطة بمسافة . متر من سطح األرض 18وذلك على ارتفاع abstract: this paper provides measurements of power density around an fm and vhf-tv broadcasting station and its variation with distance. the maximum measured value was about 2.4 µw/cm2 at a height of 2 meters above ground level while the average value was fluctuating around 1 µw/cm2. it was found that the measured power density increases with height above ground and it reaches about 3.5 µw/cm2 at a height of about 15 meters at a location of about 400 meters from the station. at a nearer distance of 185 meters from the tower another measurement was taken at a height of 18 meters, the power density increased to 41 µw/cm2. keywords: power density, antennas, broadcasting towers. 1. introduction t elevision and fm radio broadcasting is now widely used in most countries. the need for full coverage with tv and fm radio has resulted in many lower power repeater transmitters being used to bring the services to local communities. high power antennas for tv broadcasting are usually mounted on very high towers. fm radio broadcast antennas are often mounted on the same tower as the tv vhf and uhf antennas. it is almost common now to see these radio and tv broadcasting towers situated in the center of cities all over the world where residential and economic centers are located. the radio frequency (rf) radiation from broadcasting transmission has led to some regulation and control limits in some countries. radiation measurements from fm/tv towers indicate that workers inside buildings adjacent to the towers are exposed to intense electric and magnetic fields, which sometimes exceed the radiation safety standards (tell, 1978). in special cases, radiation hazards may also extend beyond the broadcasting station. tell (1976) in the united states, jokela (1998) in finland and sahalos et al. (1995) in greece are among the researchers who have dealt with radiation hazards outside the fm/tv broadcasting towers. this paper presents power density measurements around a radio fm and vhf-tv broadcast antenna tower situated in the center of riyadh, saudi arabia. these measured values have been discussed and compared with radiation safety standards. in general, the maximum exposure 45 abdulaziz al-ruwais limits of rf radiation vary with frequency. in the frequency range of vhf tv/fm broadcasting, the maximum exposure limits for general public (uncontrolled exposure) are 200 µw/cm2 for americal national standard institute (ansi)/ieee (1992), federal communications commission (fcc) (1997), cenelec (1995), finnish (1989) and japanese (1994) standards guidelines. however, it is comparatively lower (2.3 µw/cm2) for the ex-ussr standard (1984). 2. sources of tv/fm radiation and measurement procedure the fm radio in riyadh transmits 3 programs at 97.7, 100 and 102 mhz with maximum input power to the antenna of 3 kw for each. the tv station transmits two tv programs at vhf band iii (175 and 182 mhz) with 10 kw-input power for each channel. the maximum effective radiated power of the fm station is 13.64 kw for each program. the corresponding value of the tv station is 85 kw for each program. the fm and tv stations are located in downtown riyadh and their transmitting antennas are on the same tower, which is at a height of 170 m above ground level. the largest dimension of the transmitting antennas is about 11.53 m and 12.25 m for the fm and tv stations, respectively. the fm antenna consists of 2 dipole panels of dimensions [2.3 m x 2.3 m] with 4 panels on each of the four faces. the tv antenna has similar characteristics with 4 dipole panels of dimensions [3 m x 1.45 m] with 4 panels on each of the four faces. the power density is measured using narda rf radiation survey meter model 8718 with isotropic probe model 8760 that covers the frequency range from 300 khz to one ghz. the fullscale measurement is 20 µw/cm2 and the response time is selected to be 0.3 seconds. the meter accuracy is ±1% and calibrations are carried out periodically by the instrument manufacturer. during measurements, the probe is placed on a wooden tripod stand 2 m high. the meter is programmed such that it performs 4 measurements within a time interval of 6 minutes, automatically computes their "average value" as well as their "maximum" and then displays these two values on its screen when measurements are being made. both "average" and "maximum" values are recorded for every measurement. a distance of about 2 m is always maintained between the body of the operator and the probe. 3. power density calculations the far field power density around a typical broadcasting antenna can be expressed by (jokela ,1998). 2 h r4 p)(f)(fg s π φθ = ν 2 hv r4 )(f)(feirp π φθ = (1) where s is the power density (w/m2), g is the maximum gain of the antenna with reference to an isotropic radiator, fν(θ) is the vertical radiation pattern, fh(φ) is the horizontal radiation pattern, p is the input power of the antenna (w), and r ( = )2a2 hd + is the distance from antenna to observation point (m). here d is the horizontal distance from the base of the antenna tower and ha is the height of antenna above ground level, θ, φ are polar and azimuthal angle's (radians), respectively, eirp is the effective isotropically radiated power = gp, and fν(θ) and fh(φ) are normalized to unity in the direction of maximum radiation. since the horizontal radiation pattern is essentially omnidirectional, then fh(φ) can be assumed to be equal to 1. the vertical radiation pattern is not always available and therefore a relative gain factor (f) can be used instead, as recommended by the fcc report (oet bulletin 65) (fcc, 1997). furthermore, the u.s. environmental protection agency (epa) has suggested (gailey and tell, 1985) an increase factor in power density of 2.56 due to ground reflection around fm radio and tv 46 measurement of re radiation in the vicinity of fm and tv broadcast antennas. based on these two suggestions, a simpler form of the above equation can be derived where the power density is expressed in µw/cm2 (fcc, 1997). 2 2 r erpf4.33 s = (2) with erp being the effective radiated power with reference to a half-wave dipole in watts, eirp equals 1.64 erp, and f the relative field factor (relative numeric gain). the factor f (derived from relative power gain) is determined from the antenna's vertical radiation pattern if it is available. if not, f is estimated. when the point of observation is in or near the main radiated beam, it can be assumed to be 1. for an fm broadcast antenna, “the best case element studied by the epa had a maximum downward radiation field factor of less than 0.2 compared to the approximate 1.0 maximum for a dipole element” (fcc, 1997). the epa developed a computer model for estimating ground level power densities in the vicinity of some typical fm broadcast towers (fcc, 1997). the fcc's version of this fm computer model is available on the fcc world wide web site. the epa has also developed (fcc, 1997) the following formula to predict the power density at the base of tv broadcasting towers and is given by 2 2 av 2 cm/w r ]erperp4.0[f4.33 s µ + = (3) where erpv is the total peak visual erp in watts, and erpa is the total aural erp in watts. the factor of 0.4 converts peak visual erp to an rms value which is more realistic with regard to practical conditions of video transmission. an average value of f=0.2 is suggested by epa for vhf-tv antenna radiating in the downward direction. at multiple transmitter sites where several rf sources and frequencies are involved, the fcc regulations require calculating the fraction of the recommended limit incurred within each frequency interval and then taking the sum of all fractional contribution. in our case, however, the maximum exposure limit of the fm and vhf-tv is determined by most of standards at 200 µw/cm2 . therefore, using equations (2) and (3) the total power density from such multiple sources can be expressed as 2 av 2 r )]v.t(erp)v.t(erp4.0)fm(erp[f4.33 s ++ = (4) table 1: calculated values of power density around the radio fm and vhf-tv broadcasting antenna in riyadh. r (meters) f sc (µw/cm2) 100 200 300 400 500 600 700 800 900 1000 1100 0.1 0.12 0.15 0.17 0.2 0.21 0.22 0.22 0.24 0.25 0.25 0.93 0.76 0.69 0.57 0.52 0.41 0.34 0.29 0.25 0.22 0.18 where s is the power density in µw/cm2 and erp(fm) is the effective radiated power from the radio fm transmitter. applying equation (4) and using the data given in section ii, the results are tabulated in table 1. the values used for the f factor are shown in the f-column of table 1. 47 abdulaziz al-ruwais 0 0.5 1 1.5 2 2.5 100 200 300 400 500 600 700 800 900 1000 1100 t ot al p ow er d en si ty , s (m w /c m 2 ) sav-e smx-e sc east distance from tower, d(m) figure 1. variation of the maximum (smax-e) and average (sav-e) power density with distance from tower in the east direction. west 0 0.2 0.4 0.6 0.8 1 1.2 0 200 400 600 800 1000 distance from tower, d(m) t ot al p ow er d en si ty s( m w /c m 2) sav-w smx-w sc figure 2. variation of the maximum (smax-w) and average (sav-w) power density with distance from tower in the west direction. n o r t h 0 0 .2 0 .4 0 .6 0 .8 1 1 .2 1 .4 1 .6 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 d is t a n c e fro m t o w e r, d ( m ) p ow er d en si ty . s( m w /c m 2 ) s m x -n s a v -n s c figure 3. variation of the maximum (smax-n) and average (sav-n) power density with distance from tower in the north direction. the values were chosen so that they fluctuate around the average value of f=0.2, which is suggested by the epa. 48 measurement of re radiation in the vicinity of fm and tv south 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 200 400 600 800 1000 1200 distance from tower, d(m) t ot al p ow er d en si ty s( m w /c m 2 ) smx-s sav-s sc figure 4. variation of the maximum (smax-s) and average (sav-n) power density with distance from tower in the south direction. 4. results and discussion measurements of power density generated from the vhf-tv/fm antenna were taken in four directions from the antenna. the measurements started at about 70 m from the antenna tower and were repeated at several locations until about 1200m in the four directions, east, west, north and south. the results of the measurements of the "maximum" and "average" values of the power density in the four directions are shown in figures 14. the maximum (average) is defined as the maximum (average) value of the four measurements performed by the meter within 6 minutes time interval as previously explained in section 2. these results show clear variations of the measured power densities with distance as well as direction due to the effects of the surrounding environment. the calculated results of power density are also shown in these figures for comparison. the theoretical results reasonably agree with the measured values except at some locations where the theoretical model fails to predict complex reflections or due to the effects of possibly other nearby rf transmitters. the greatest measured maximum value of the power density reached was about 2.4 µw/cm2 in the east direction at a distance of about 870 m from the antenna tower. the average value of this measured power density is about 1 µw/cm2. figure 5 shows the measured variation of the power density with height at a residential building 435 m distance from the tower. the increase of power density with height is evident and reaches its maximum value of about 3.5 µw/cm2 at a height of about 15 m and a distance 435 m from the tower. on the top roof of another higher building (h = 18 m) and nearer to the tower (d = 185 m), the maximum and average values of the power density are the same and reach about 41 µw/cm2. the measured values are below the well-known standards, which is about 200 µw/cm2 excluding the russian standard, which is about 2.3 µw/cm2 at the fm/tv vhf band. the location at 185 m of the tv tower is considered in the far field region. therefore the measured plane wave power density in riyadh at this distance from the tv tower and 18m height (41 µw/cm2) is about 20 times higher than the maximum measured value in a village north of tv and fm tower in greece (sahalos et al., 1995). on the other hand, it is of the same order of magnitude of measurements carried out by jokela (1988) for an average feed power of 4 kw, and at a height of 300m and at a distance of about 180m in front of the midpoint of the tv antenna. at 2m above ground level and within distances,d, such that 90m < d < 1200m from vhf-tv/fm tower, the average power density in riyadh is close to the exposed level of 1% of the population of 15 cities in usa (tell, 1980). 49 abdulaziz al-ruwais 0 1 2 3 4 0 2 4 6 8 10 12 14 16 18 h eight above ground, h(m ) a ve ra ge p ow er d en si ty , sa v (m w /c m 2 ) w av w m x d=4 35 m from tower figure 5. variation of power density with height at a residential building 435 m from the tower. 5. conclusions measurements of power density around an fm and vhf tv broadcasting station are provided. calculated results are also included. the maximum measured value was about 41 µw/cm2 at a distance of 185 m from the antenna tower and at a height of 18m from ground level. all the results are below the maximum exposure limit (200 µw/cm2) established by the standards, for fm radio and vhf tv broad-casting. 6. acknowledgement this work was supported by king abdulaziz city for science and technology (kacst), under grant number at-1554. the author would like to thank dr. abobakr sultan, and mr. nasser mohy eldin for carrying out the measurements. the helpful discussion with dr. z.o. alhekail, prof. h.s. afifi, and dr. f.a. alhargan are appreciated. references amemiya, y. 1994. research on biological and electromagnetic environments in rf and microwave regions in japan, ieice trans. communications. e77-b: 693-698. american national standards institute (ansi),1992. safety levels with respect to human exposure to radio frequency electro-magnetic fields, 3 khz to 300 ghz, ansi/ieee c95.1-1992, ieee, new york, usa. available at http://www.fcc.gov/oet/info/software. cenelec, 1995. human exposure to electromagnetic fields. high frequency (10 ghz to 300 ghz), env 50166-2, jan. central health and epidemiological administration,1984. interim health standards and regulations on protecting the general population from the effects of the electromagnetic fields generated by radiotransmitting equipment, ussr administer of health, moscow. federal communications commission (fcc),1997. evaluating compliance with fcc guidelines for human exposure to radio frequency electromagnetic fields,” oet bulletin 65.ed./97-01, aug. federal communications commission (fcc),1997. evaluating compliance with fcc guidelines for human exposure to radio frequency electromagnetic fields, additional information for radio and television broadcast stations, supplement a (edition 97-01). gailey, p.c. and tell, r.a. 1985. an engineering assessment of the potential impact of federal radiation protection guidance on the am, fm and tv broadcasting services, 50 measurement of re radiation in the vicinity of fm and tv u.s. environmental protection agency, report no. epa 520/6-85-011, april 1985 ntis order no. pb85-245868. jokela, j., 1988. theoretical and measured power density in front of vhf/uhf broadcasting towers, health physics, 54: 533-543. jokela, k., 1989. finnish exposure standards, ssi-report 89-15, second nordic meeting on non-ionizing radiation. sahalos, j.n., vafiadis, e.e., samaras, t.s., babas, d.g. and khoukourlis, s.s., 1995. em field measurements in the vicinity of an antenna park for radiation hazard purposes, ieee trans. on broadcasting, 41: 130-134. tell, r.a., 1978. measurements of radio-frequency field intensity in buildings with close proximity to broadcast stations, washington, dc, u.s. environmental protection agency, office of radiation programs, report orp/ead-78-3. tell, r.a.a., 1976. measurements of rf intensities in the immediate vicinity of a fm broadcast station antenna, silver spring, md, u.s. environmental protection agency, office of radiation programs, tech. note orp/ead-76-2. tell, r.h. and manitply, e.d., 1980. population exposure to vhf and uhf broadcast radiation in the united states, proceedings of the ieee, 68: 6-12, jan. received 26 august 2000 accepted 30 january 2001 51 abdulaziz s. al-ruwais department of electrical engineering, college of engineering, king saud university, p.o. box 800, riyadh 11421, saudi arabia. e-mail: asruwais@ksu.edu.sa îáçõé: êêäçæá åðå çáæñþé çáúáãíé references squ journal for science, 2018, 23(2), 73-77 doi: http://dx.doi.org/10.24200/squjs.vol23iss2pp73-77 sultan qaboos university 73 effect of management system on serum copper level and haematology of jabal akhdar breed goats in two sites in al jabal al akhdar region of oman nur el huda i.e.d. osman 1 * and patrick a. bobade 2 1 directorate for research, planning and development, open university of sudan, obeid khatim street, arkaweet, sudan; 2 department of animal and veterinary sciences, college of agriculture, sultan qaboos university, p.o. box 36, pc 32, al-khoud, muscat, sultanate of oman.*email: hudaisam@gmail.com. abstract: blood samples were collected from randomly selected healthy jabal akhdar breed goats reared in two sites in the jabal akhdar region of oman. seven males and 65 female goats, age range 2 months to 4 years, raised in shnoot al-dar village were kept under a semi-intensive system (sis) and 2 males and 18 females, age range 4 months to 5 years, raised in al-ala'lana village and kept the under free range system (frs) were studied. serum cu and haematological values were measured. there were no significant (p>0.05) effects of age, sex or serum copper levels on the haematology of goats, so data was pooled and only the effects of the management system on serum cu and haematology were analysed. there were highly significant (p<0.001) differences between the two systems in all parameters studied. frs goats were higher than sis goats in mean values (± se) of serum cu (mg/l) 0.60 ± 0.07 vs 0.48 ± 0.33, red blood cells (rbc) (x10 12 /l) value 15.03 ± 0.42 vs 14.97 ± 0.25, mean cell volume (mcv) (fl) 21 ± 21 vs 19.57 ± 0.19, and haematocrit (hct) (%) value 31.84 ± 0.59 vs 29.6 ± 0.35. sis values were higher than frs in haemoglobin (hb) (g/dl) 9.34 ± 0.16 vs 9.26 ± 0.27, mean cell haemoglobin (mch) (pg) 6.21 ± 0.05 vs 6.16 ± 0.08 and mean cell haemoglobin concentration (mchc) (g/dl) 31.96 ± 0.38 vs 29.05 ± 0.64. therefore, it is evident that the management system can affect the serum copper levels and haematology of the jabal akhdar breed of goats in the jabal akhdar region of oman. keywords: haematology; serum copper; copper deficiency; oman; jabal akhdar; goats أثر نظام الرعاية على مستوى عنصر النحاس في مصل ومكونات الدم في نوع ماعز الجبل األخضر في موقعين بمنطقة الجبل األخضر بسلطنة عمان عصام الدين عثمان وباتريك أ. بوبادي ،نور الهدى ، من موقعين في منطقة الجبل األخضر بسلطنة عشوائيا جمعت عينات من الدم من نوع ماعز الجبل األخضر تبدو بصحة جيدة، تم اختيارها :صلخمال سنوات ولدت وتربت في قرية شنوت الدار بالنظام شبه المغلق 4أنثى بأعمار تراوحت ما بين شهرين و 53ذكور و 7عمان. تضمنت الدراسة عدد (sis وعدد ،)نا تربت 3أشهر و 4أنثى بأعمار تراوحت بين 81ذكور و 2 (. تم قياس كل من frsعلى نظام الرعي المفتوح ) سنوات في قرية العّلا نسبة عنصرالنحاس في مصل وقيم مكونات الدم. لم تكن هناك تأثيرات ذات دالالت إحصائية لكل من العمر، الجنس، أو مستوى عنصر النحاس في كانت هناك فروق بين النظامين ذات دالالت إحصائية المصل على قيم مكونات الدم، ولذلك ضمت البيانات وانحصرالتحليل على أثر نظام التربية فقط. 6.7± 6.0في كل من متوسط قيم النحاس )مج/ل( ) sisأعلى من نظام frs( في كل القيم التي تمت دراستها. كان نظام p<0.001) عالية جدا x 86(، عدد كرات الدم الحمراء )6.55± 6.41مقابل 82 مقابل 6.28± 28، متوسط حجم الخلية )( )(6.23± 84.47مقابل ±6.43 83.65( ) في قيم كل من الهيموجلوبين frsأعلى من نظام sis(. كان نظام 6.53± 24.0مقابل 6.34± 58.14( والهيماتوكريت )%( )±6.84 84.31 (، ومتوسط تركيز 0.08 ± 6.16مقابل 6.210.05 ±(، متوسط هيموجلوبين الخلية )بج( )6.27± 9.26مقابل 9.340.16±)ج/دس ل( ) (.استنتج من نتائج البحث أن نظام الرعاية يمكن أن يؤثر على مستويات 0.64± 29.05مقابل 0.38± 31.96هيموجلوبين الخلية )ج/دس ل( ) ح ربما يكون جزءا النحاس في مصل وقيم مكونات الدم في نوع ماعز الجبل األخضر بمنطقة الجبل األخضر بسلطنة عمان، وأن نظام الرعي المفتو من حل مشكلة نقص عنصر النحاس في أمصال الماعز العمانية. .الجبل األخضر مكونات الدم،نحاس مصل الدم،نقص عنصر النحاس،عمان،الجبل األخضر،ماعز: مفتاحيةالكلمات ال mailto:email:%20hudaisam@gmail.com nur el huda and patrick a 74 1. introduction aemtological values are useful in assessing animal health and provide vital information on the physiological, nutritional and pathological status of an animal. these values are affected by several factors such as age, breed, sex, management systems [1-3], diet [4], rumen impaction [5] and parasitism [6]. copper is an essential trace element which is associated with clinical and biochemical disorders. copper deficiency is an endemic problem in oman where low tissue, plasma or serum values have been reported in livestock by many workers [7-9]. goats comprise a very important source of meat and income to villagers in oman. jabal akdar goats, a large body size goat, comprise 20% of the total goat population of 854,060 in oman, as reported by mahgoub et al [10]. they are named after the region they inhabit, the jabal akhdar. the jabal akhdar, jebel akhdar or al jabal al akhdar, is a part of the al hajar mountain range in oman, which extends about 300 km northwest to southeast, between 50 – 100 km inland from the gulf of oman coast. the range is mostly desert, with the higher altitudes receiving around 300 mm (12 in) of precipitation annually, which is moist enough to allow the growth of shrubs and trees and to support agriculture. this gives the mountains their 'green' name [11]. goats are generally kept in medium to large herds of about 1-50 [10]. villagers either leave their goats to graze all day on a free range management system, in which they browse on acacia shrubs and other trees, or they feed them on seasonal indigenous range grass, rhodes grass hay, by-products and household leftovers [10]. this work was intended to investigate the effect of the management system on the haematology and serum copper of goats in the jabal akhdar region of oman. 2. materials and methods. blood samples were collected from the jugular vein from randomly selected, apparently healthy, jabal ahkdar breed goats, reared in two different sites in the jabal akhdar region of oman. a total of 72 goats, 7 males and 65 females, age range 2 months to 4 years, raised in shnoot al dar village (gps: n 23' 06.930 e 057' 39.507 elevation: 2289 meters above sea level (masl)) kept under the semi-intensive system (sis) and 20 goats, 2 males and 18 females, age range 4 months to 5 years, raised in al ala'lana village (gps: n 23' 06.903 e 057' 34.647 elevation: 2172 masl) kept under the free range system (frs) were included in the study. serum was collected from blood in situ, separated in vials and kept at a cool temperature, moved to the lab and then frozen. serum copper values were detected using atomic absorption spectrophotemtry. for haematology, blood was collected in edta vacuum tubes, kept at a cool temperature, moved to the lab and then analyzed immediately. haematological parameters were obtained from these fresh samples using a cell-dyn 3700 automated blood analyzer (abbott laboratory, diagnostic division, abbott park, il 60064, usa). parameters studied included the following: red blood cells (rbc), packed cell volume (pcv), haemoglobin concentration (hb), mean cell volume (mcv), mean cell haemoglobin concentration (mchc) and mean cell haemoglobin (mch). 3. statistical analysis means were compared to study the effects of the management systems, age, sex and serum copper levels on these values using type iii general linear model statistical analysis using the spss computer package. there were no effects of age, sex or serum copper levels on haematological values; so data were pooled and only the effect of the management system on serum copper (mg/l) and haematological values were studied. a serum copper concentration ≤ 0.59 mg/l was considered as low and ≥ 0.60 mg/l was considered as normal. 4. results and discussion 4.1 serum copper the effect of the management system on serum copper level is presented in table 1. frs mean serum copper (mg/l) was significantly (p<0/001) higher than mean values for sis. table 1. serum copper and haematological values (±se) of jabal akhdar goats under two management systems. parameter free range system semi-intensive system significance serum copper (mg/l) rbc (x 10 12 /l) mcv (fl) pcv (%) hb (g/dl) mch (pg) mchc (g/dl) 0.60 ± 0.07 15.03 ± 0.48 21.00 ± 0.21 31.84 ± 0.59 9.26 ± 0.27 6.16 ± 0.08 29.07 ± 0.06 0.48 ± 0.33 14.97 ± 0.25 19.57 ± 0.19 29.6 ± 0.35 9.34 ± 0.17 6.21 ± 0.05 31.96 ± 0.38 0.000 0.000 0.000 0.000 0.000 0.000 0.000 h http://en.wikipedia.org/wiki/precipitation_%28meteorology%29 effect of management system 75 the mean of serum cu in frs goats was at the bottom of the normal range, while that of the sis goats was within the low or deficient range. at the same time the numbers and proportions of goats with normal or low serum cu and mean values of each group, presented in table 2, show that there was a higher proportion of goats with normal serum cu than of those of low serum cu in frs, while there was a lower proportion of normal goats than of low serum cu goats under sis. copper deficiency can be caused by low dietary cu intake (simple cu deficiency) or dietary intake of interfering elements, particularly molybdenum and sulphur [12] or iron (secondary cu deficiency). previous reports indicate that the prevalence of cu deficiency in many omani regions could be related to low cu, high iron, sulphur and elevated molybdenum contents in different feeds [7,13]. in this study the goats in frs presented better serum cu status than the sis goats. this may indicate that the frs grazing goats, having the opportunity to select feeds [14], could have possibly selected either higher cu or lower interfering element contents than the sis goats, which mostly take feeds provided by owners, and which may be of low cu content or contain causative agents of cu deficiency. although the results still show a low cu status in some goats in the frs, it may be a management system of higher potentiality to reduce the cu deficiency problem in this area of oman. however, the high stocking rate and overgrazing in this region [15] could have led to low availability of feeds to support the grazing goats, and thus get their cu and other nutrient requirements fulfilled. 4.2 haematological values the results of the effect of the management system on haematological values are presented in table 1. there were highly significant differences (p<0.001) between the two systems on all haematological parameters studied. frs were higher than sis in mean values of rbc (x10 12 /l), mcv (fl) and pcv (%). sis values were higher than frs in hb (g/dl) mch (pg) and mchc (g/dl). similar results to these current ones were observed in west african dwarf (wad) goats by imasuen [16], west african dwarf sheep in nigeria [17] and in cattle (summarized by etim et al [1]. on the other hand, ifut et al [18] reported no significant effect of management system on the haematology of wad goats. red blood cells function as carriers of haemoglobin. the latter contains iron and is responsible for the transportation of o2 to body cells and co2 from cells to the lungs for excretion through respiration [19]. therefore, their number reflects the availability of o2 to tissues, for them to perform their normal functions of excretion of co2. in this work, the frs goats had higher rbc, mcv and, hence, pcv%. packed cell volume value indicates either an increase in number of rbcs or a reduction in plasma volume [20]. it is involved in the transport of o2 and the absorption of nutrients [19]. a higher value of pcv indicates better transportation and thus results in an increased primary and secondary polycythemia [1]. pcv and rbc can be affected by nutritional status [21] and environmental temperature [22]. therefore, it appears that frs goats were in better condition than sis goats. contrary to the present results, imasuen [16] reported higher pcv%, and rbc in sis than in frs goats while hb and mchc were similarly higher in sis than frs goats. another study which compared wad goats reared in the intensive and semi-intensive systems showed that the sis goats had higher pcv than intensive system goats [18]. packed cell volume, hb and mch values are significant indices for diagnosis of anaemia. the indices’ values and their differences between different management systems may reflect the differences in nutritional status and/or possible parasitic infestations [23]. on the other hand, compared to some other published normal haematological values, both sis and frs goats had mean hb and mchc values lower, but rbcs and pcv values higher, than in wad [24] and red sokoto [25] goats. these observations support other reports of breed differences [26]. 5. conclusion jabal akhdar goats presented different serum cu and haematology values when reared in frs rather than in sis in the jabal akhdar region of oman. the goats of the frs generally showed a better performance compared to those in table 2. numbers and (%) of goats with normal or low serum cu and mean values (mg/l ± se) in semi-intensive and free range management systems. serum cu level semi-intensive system free range system goats number (%) serum cu (mg/l) goats number (%) serum cu (mg/l) normal 20(27.8%) 0.87±0.04 11(57.9%) 0.72±0.05 low 52(72.2%) 0.33±0.02 8(42.2%) 0.45±0.06 total 72 19 significance of management system x serum cu interaction 0.005 mchc (g/d1) 29.07±0.06 31.96±0.38 0.000 nur el huda and patrick a 76 the sis, especially on the serum cu levels and rbc, mcv and pcv values. although a proportion of goats had serum cu levels within the subclinical and deficient range, it can be concluded that the frs has the potential to provide for a reduction in cu deficiency as well as higher haematological values of rbc, mcv and pcv. further studies are needed to support these findings and to find proper supplementation methods to help to totally alleviate cu deficiency and to improve the haematology and health status of jabal akhdar grazing goats in oman. acknowledgement the authors would like to convey their appreciations to mr. rashid albusaidi for blood collection and analysis and to mr. rabei almigbali for assistance in serum cu analysis. references 1. etim, nseabasi. haematological parameters and factors affecting their values. agricultural science, 2014, 2, 3747. 2. addass, p.a., midau, a. and babale, d.m. haemato-biochemical findings of indigenous goats in mubi adamawa state, nigeria. journal of agriculture and social sciences, 2010, 6, 14-16. 3. shaikat, a.h., hassan, m.m., khan, s.a., islam, m.n., hoque, m.a., bari, m.s. and hossain, m.e. haematobiochemical profiles of indigenous goats (capra hircus) at chittagong, bangladesh. veterinary world, 2013, 6, 789-793. 4. ukanwoko, a.i., ironkwe, m.o. and nmecha, c. growth performance and hematological characteristics of west african dwarf goats fed oil palm leaf meal – cassava peel based diets. journal of animal production advanced, 2013, 3, 1-5. 5. akinrinmade, j.f. and akinrinde, a.s. hematological and serum biochemical indices of west african dwarf goats with foreign body rumen impaction. niger journal of physiological science , 2012, 27, 83-87 6. sulaiman, e.g., arslan, s.h., al-obaidi, q.t., et al. clinical, haematological and biochemical studies of babesiosis in native goats in mosul. iraq journal of veterinary science, 2010, 24, 31-5. 7. ivan, m., hidiroglou, m., al-ismaily, s.i., et al. copper deficiency and posterior paralysis (shalal) in small ruminants in the sultanate of oman. tropical animal health and production, 1990, 22, 217-225. 8. osman, n.h.i., johnson, e.h. and al-busaidi, r.m. effects of breed, sex and plasma copper levels on haematological parameters in kids in oman, 13 th seminar of the 1fao-ciheam sub-network on sheep and goat nutrition. leon, spain, october 14, 2009. 9. eltahir, y.e., ali, h.m., mansour, m.h. and mahgoub, o. serum mineral contents of the omani racing arabian camels (camelus dromedaries). journal of animal veterinary advanced, 2010, 9, 764-770. 10. mahgoub, o., kadim, i.t., al-saqry, n.m. and al-busaidi, r.m. potential of omani jebel akhdar goat for meat production under feedlot conditions. small ruminant research, 2005, 56, 223-230. 11. wikipedia, 2015 jebel akhdar (oman) 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dwarf (wad) goats. journal of research in forestry, wildlife and environment, 2013, 4, 73-78. 17. olayemi, f.o., farotimi, j.o. and fagbohun, o.a. haematology of the west african dwarf sheep under two different management systems in nigeria. african journal of biomedical research, 2000, 3, 197-198. 18. ifut, o.j., inyang, u.a., ikpatt, e.a. and eyoh, g.d. eeffect of management systems on haematology, parasite status and body mass index of west african dwarf goats in university of uyo farm. nigerian journal of agriculture, food and environment, 2011, 7, 73-76. 19. isaac, l.j., abah, g., akpan, b. and ekaette, i.u. hematological properties of different breeds and sexes of rabbits. proceedings. annual conference of animal science association, niger, 2013, 24-27. 20. chineke, c.a., ologun, a.g. and ikeobi, c.o.n. haematological parameters in rabbit breeds and crosses in humid tropics. pakistan journal of biological sciences, 2006, 9 (11), 2102-2106. 21. bentrick, s. haematology, textbook of veterinary pathology. publ. williams and co baltimore, 1974, 217-224 22. baneejee, gc. a textbook of animal husbandry. 8th edn. published by raju primlani for oxford and ibj publishing co. pvt ltd, new delhi, india 2007, 1079. http://www.scopemed.org/?jid=73&iid=2013-3-1.000 http://en.wikipedia.org/wiki/ibra effect of management system 77 23. yacob, h.t., basazinew, b.k. and basu, a.k. experimental concurrent infection of afar breed goats with oestrus ovis (l1) and haemonchus contortus (l3): interaction between parasite populations, changes in parasitological and basic haematological parameters. experimental parasitology, 2008, 120, 180-184 24. daramola, j.o., adeloye, a.a., fatoba, t.a. and soladoye, a.o. haematological and biochemical parameters of west african dwarf goats. livestock research for rural development. 2005. volume 17, art. #95. retrieved may 18, 2015, from http://www.lrrd.org/lrrd17/8/dara17095.htm 25. tambuwal, f.m., agale, b.m. and bangana, a. haematological and serum biochemical values of apparently healthy sokoto goats. proceeding of 27th annual conference of nigerian society of animal production. march 17-21, 2002, 50-53. 26. pradhan, p.c. evaluation of haematological and biochemical parameters of goats of central odisha environment fed on natural grazing land of odisha, india. the pharma innovation journal, 2016, 5, 83-90. received 18 june 2017 accepted 12 october 2017 special issue on numerical analysis and optimization guest editors mehiddin al-baali and anton purnama preface his special issue contains some selected papers presented at the third international conference on numerical analysis and optimization: theory, methods, applications and technology transfer (naoiii-2014), held during january 5-9, 2014, at sultan qaboos university (squ), muscat, oman. the conference was sponsored by squ, the research council of oman, the abdus salam international center for theoretical physics (ictp, italy), ampl (usa); and the local sponsors the german university of technology (gutech) in oman, the al-anan press (oman) and al-roya newspaper (oman). the nao conference series is held once every 3 years at squ: the first conference (nao-2008) was held during april 6-8, 2008, and the second conference (naoii-2011) was held during january 3-6, 2011. the nao conference will hopefully become a forum where prominent mathematicians, worldwide experts and active researchers gather and meet to share their knowledge on new scientific methodologies and simulate the communication of new innovative ideas, promote scientific exchange and discuss possibilities of further cooperation, networking and promotion of mobility of senior and young researchers and research students. naoiii-2014 was inaugurated by he dr. abdullah bin mohammed al sarmi, the undersecretary of the ministry of higher education, he dr. ali bin saud al bemani, the vice chancellor of squ and he mrs. paola amadei, ambassador of italy to the sultanate. twenty world leading researchers gave keynote lectures in twelve technical sessions of the conference. in total, forty international participants gave contributed talks. more information is available at: http://conference.squ.edu.om/nao. thirteen of the keynote papers were selected for the edited springer proceedings in mathematics and statistics volume 134, “numerical analysis and optimization nao-iii, muscat, oman, january 2014”, where each paper was accepted after a stringent peer review process by independent reviewers. eight of the conference contributed papers were selected for this special issue 20(2) of the squ journal for science. we wish to express our gratitude to all contributors. we are also indebted to many anonymous referees for the care taken in reviewing the papers submitted for publication. mehiddin al-baali and anton purnama guest editors for the naoiii special issue 20(2) of squ journal for science t conference_eng preface new electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 23-29 © 2002 sultan qaboos university intelligent techniques for power systems vulnerability assessment mohamed a. el-sharkawi computational intelligence applications (cia) laborartory, department of electrical engineering, university of washington, seattle, wa 98195-2500, http:// cialab.ee.washington.edu. التقنيات الذكية لتقييم هشاشة نظم القوى الكهربائية محمد الشرقاوي تولي شركات إنتاج الكهرباء نظم القوى أعلى األوليات حيث تعتبر القوى الكهربائية من مسائل األمن القومي ويهتم : خالصة تعرض هذه الورقة طريقة يتم بها . ئ نظام تقييم الهشاشة بقدرة نظم القوى الكهربائية على توفير الخدمة في حاالت الطوار .تقييم هشاشة نظم القوى بشكل مباشر من دون أن تقطع الخدمة وذلك باستخدام التقنيات الذكية abstract: with power grids considered national security matters, the reliable operation of the system is of top priority to utilities. this concern is amplified by the utility’s deregulation, which increases the system’s openness while simultaneously decreasing the applied degree of control. vulnerability assessment (va) deals with the power system’s ability to continue to provide service in case of an unforeseen catastrophic contingency. such contingencies may include unauthorized tripping, breaks in communication links, sabotage or intrusion by external agents, human errors, natural calamities and faults. these contingencies could lead to a disruption of service to part or all of the system. the service disruption is known as outage or blackout. the paper outlines an approach by which feature extraction and boundary tracking can be implemented to achieve on line vulnerability assessment. keywords: intelligent techniques, vulnerability assessment, power systems 1. introduction because the trend towards deregulation is altering the manner in which electric power systems are operated, accurate vulnerability assessment is becoming vital. in the past, regulated electric utilities were able to justify improvements in system operation or infrastructure based solely on crude methods for security assessments. in a deregulated environment this is no longer the case. economic pressure tends to delay construction of new facilities forcing utilities to operate their systems closer to their security boundaries. this, in turn, demands the industry to develop better methods of quantifying real-time va. the approach to power system va involves the examination of system performance based on all postulated and credible system contingencies. such analysis allows for a means to evaluate both system performance and system reliability while meeting current and future demands. the goal is to determine if the severely disturbed system will remain in synchronization following a disturbance. if any generator loses synchronism, its protection devices will quickly remove it from the network resulting in another disturbance to the power system, which, in turn, can lead to removal of another generator. this is called a cascading outage and can lead to severe consequences such as blackouts. if the analysis indicates vulnerable or insecure operation, corrective actions must be taken to steer the system to a more viable operation, thus preventing 23 mohamed a. el-sharkawi outages should the contingency occur. a power system is said to be dynamically secure or invulnerable if it can withstand all postulated credible contingencies without violating any of the dynamic system constraints. if there is at least one contingency for which the system constraints are violated, the system is said to be vulnerable or insecure. 2. conventional methods for vulnerability assessment and their challenges accurate va requires simulating all postulated contingencies. this is very time-consuming and prohibitive process. clearly, such analysis for large-scale power systems is not only the concern of system planning and design groups, but also of operating engineers. the operating engineer will have a greater responsibility in system va analysis, and in this case, the analysis will have to be repeatedly performed. therefore, approximate but faster methods have been developed by utilities assuming a restrictive set of operating and topological conditions. utilities found it necessary to a select small subset of the most critical information. these cases are usually selected based on expert knowledge of the particular system. most of these methods are crude and can work for the operating conditions far from the border of vulnerability. near the boundary, which is likely to be the operating space for deregulated utilities, these methods are unacceptable. among these assessment methods are time domain simulations, direct stability, and hybrid methods. time domain methods require the solution of a set of non-linear algebraic and differential equations describing the power system. this method is computationally prohibitive which limits its usefulness to few off-line studies. time domain methods also fail to offer any information about the relative security of a particular case. direct stability or energy function methods seek to describe the system by an energy function (atthay, t., et al., 1979, bose, a., 1984, el-kady m, et. al., 1988, stanton, f., et. al., 1981 and 1987, chiang, h., et. al., 1994, 1995 and 1989, maria, et. al., 1990, tong, j., et. al., 1993, vaahedi, e., et. al., 1996). these methods are less computationally demanding than time domain methods, but are less accurate. direct methods are usually limited to very short-term stability studies due to the simplistic models used. hybrid methods (vaahedi, e., et. al, 1996 and mansour, y., et. al., july, 1997, 1995, and may, 1997) are a combination of time domain simulations and transient energy function methods. this hybrid method determines the system critical energy by integrating the system equations in the time domain, thus calculating the exact system trajectory. hybrids offer no speed increase over time domain methods, but do offer one key advantage: the ability to determine the relative stability of a particular operating case. the hybrid method does not suffer from the approximations and modeling limitations of the direct methods, making it appealing when high accuracy is desired. 3. role of intelligent systems pattern classifiers, such as neural networks, have great potential for achieving fast and accurate security evaluation (kumar, b., et. al., 1991, jensen, c., et. al., 1999, el-sharkawi, 1996, m., bonissone, p., et. al., 2001). the pattern classification concepts to power system engineering problems appear to be more feasible with the decline in the cost of computer memory and faster clock speeds. the primary objective of a pattern recognition technique is to monitor the power system performance and store the relevant data along with the consequent processed information in the computer memory. once the stored data constitute a sufficient representation of the different operating conditions of the power system, a classifier can be used to recognize the va status of the current operating patterns. this requires the data to be of sufficient size and highly correlated with the class. the ultimate objective is that the pattern classifier system should have the ability to classify any given new pattern or new operating condition into its appropriate class without the need to perform extensive contingency evaluations. it is worth mentioning that the pattern classifier does not require restrictive system topology or operational constraints as with conventional methods. 24 intelligent techniques for power systems 4. challenges to intelligent systems thus far, the work on intelligent systems for va, including neural networks (kumar, b., et. al., 1991, jensen, c., et. al., 1999, el-sharkawi, 1996, m., bonissone, p., et. al., 2001) are based on at least one of the following processes: 1. reducing the operating space to a subspace of a manageable size. this is implemented by ignoring large portions of system operation. 2. use extensive off-line simulations to hopefully cover the operating space of the system. the first process cannot be implemented without severely sacrificing the accuracy of the assessment technique beyond the training subspace. the second is also unrealistic process because the size and operating space of the power system is immense. for example, the va of a power system requires extensive information on such variables as: • pre-disturbance network topology. • pre-disturbance load/generation conditions. • dynamic machine data. • post-disturbance control actions. • type and duration of disturbance. • operating conditions with the above list, an unlimited number of data can exist for a given power system. moreover, some variables in the data vector may likely have a weak correlation with the va status. the curse of dimensionality states that, as a rule of thumb, the required cardinality of the training set for accurate training increases exponentially with the input dimension. attempts to identify correlations or reductions of the data vector (el-sharkawi, 1996) requires approximation to the system dynamics under restrictive conditions. if the correlation among elements in the input vector and the va status is weak, the classifier will try to force a mapping that is unlikely to result in worthwhile information. in fact, such weak correlation can stray the classifier to an undesirable region with high testing errors. therefore, the key to the success of the classifier is the effective feature extraction/selection. learning patterns based on data will succeed, given the right features to the classifier. it is a strong conviction that feature extraction/selection is the key to the success of va, and cannot be considered an “art” anymore. glorioso states, “feature extraction is the least understood and most difficult part of pattern recognition problems.” 5. proposed approach an alternate approach to matching data and machine, applicable in many important scenarios, occurs when training data can be obtained on demand at a cost. the matching of data to machine can be performed dynamically. a partially trained neural network can communicate with the data source, called an oracle, to resolve ambiguities in the operation of the machine. the oracle then, at a cost, is able to correct these areas of uncertainty by generating clarifying training data (jensen, c., et. al., 1999). the procedure in figure 1 is a candidate for application of a dynamically trained machine to the problem of power system va. the first step is the creation of a preliminary training data set. a common approach is to simulate the system in response to a few disturbances and then collect a set of pre-disturbed system variables along with their corresponding va index. for a realistic size power system, it is expected that 1. the number of variables of each data vector will be very large; 2. the collected data are sparse in the operating space; and 3. information near the va border is likely to be unavailable. 25 mohamed a. el-sharkawi in the algorithm of figure 1, three basic operations are suggested: 1. feature extraction, selection andconstruction to reduce the dimensionality of the data vector; 2. query based learning to identify areas in the operating space that are essential to the va where the initial data contains no or little information; and 3. boundary tracking to identify the nearest viable operating point on the border of the class thereby identify the va margin. training data feature extraction query boundary tracking test finish oracle figure 1: general va algorithm. 6. feature extraction feature reduction, selection and construction are techniques used to massage data into a form more conducive to training. feature selection, important when cost is associated with the acquisition of features, has, as its goal, choosing the best subset of features able to effectively perform accurate classification or regression. reducing the cardinality of the feature set by combining two or more features into a single composite feature is the goal of feature reduction. feature construction involves combining features to generate composite features. the goal is to synthesize an augmented feature space conducive to classification or regression. this occurs, for example, in support vector machines. a popular, though flexibly limited, procedure for feature reduction is through the use of autoencoder networks (reed, r.d., et. al., 1999). in the most fundamental architecture, the input features from a training data set are presented sequentially as both the input and output. if the network converges, the representation at the bottleneck hidden layer is a feature dimensional reduction of the original data. support vector machines (svms) (vapnik, 1998) map feature data into a high dimensional feature space via a nonlinear mapping, wherein linear classification/regression is performed. data is therefore molded into a form appropriate for a linear machine that occurs in the high dimensional (feature) space. doing so corresponds to nonlinear classification/regression in the low dimensional (original) input space. 7. query learning in query learning, neural network inversion can be used to identify points that, according to the network, lie near a decision surface. these points represent regions in the input space where the neural network is unsure of the proper classification. the inverted points are then presented to 26 intelligent techniques for power systems an oracle to determine their correct classification. the inverted points along with their classifications are then added to the training set and the network is retrained to a more accurate representation. this way, the initial neural network is trained by a relatively sparse data set while inversion guides the query to generate data in the areas where information is missing and needed. this results in a much leaner, and therefore less expensive, data set distributed where it is needed along the functional operating space. inversion is also an important tool for understanding the functional mapping encoded in a neural network. specifically, inversion of a neural network highlights characteristics of the input space important to a given output vector. thus, through inversion, a network codebook vector describing the important input characteristics for a particular output class can be generated. 8. vulnerability boundary due to the complexity of the power system, it is not possible to determine the dynamic security border analytically. boundary tracking is a name given to the process of inverting a trained neural network by using gradient information or any directed search to track along specific contours in order to locate new areas of interest (bounissone, p., et. al., 2001). figure 2 shows the concept. given a search point, , boundary tracking can be used to find the point that is closest to and lies on the surface 0x 0x̂ 0x cf =)(x , where c is the value of the va boundary. this point must also satisfy the operational constraint of the system. the process begins by generating random points around the search point and projecting them onto the surface, , by neural network inversion. gradient information, a genetic algorithm, or even particle swarm optimization can then be used to step down the surface until the point closest to the search point that satisfies all constraints is located. by identifying the boundary point, a va margin is computed. the va margin is a major concern in the everyday operation of the modern deregulated electric power system. information about the location of the nearest insecure operating state is valuable in that it outlines operating strategies that should be avoided. in the event of a loss of system security, it defines the nearest stable operating state. cf =)(x step 1: starting point step 2: project point on boundary. step 3: gradient descent. cxf =)( r . solution 0x̂ . search point 0x . figure 2. illustration of boundary tracking wherein training data is dynamically generated in regions only of interest in the classification process. the overall neural network mapping with the above structure contains information relating the input (feature) space to the output (security) space. the main goal is to query this mapping and extract useful information for the everyday operation of the power system. ideally, the proposed system will be able to answer questions such as: • what is the nearest unstable operating point? • what is the most stable operating configuration? • given recent trajectory, when is instability likely to occur? 27 mohamed a. el-sharkawi this information could then be used by the system operator as a tool in the everyday operation of the power system in a secure manner. an alternative method to the inversion of the neural network is to use a search technique to place as many points on the border as needed to achieve the desired interpolation accuracy among them. this process requires the use of a fast va technique and a rapid optimization search algorithm. the nn can be used as a fast va tool, and the particle swarm optimization (pso) can be used as the search technique. pso is a novel optimization technique developed by russell eberhart (eberhart, r., 1995). it is a multi-agent search technique that traces its evolution to the emergent motion of a flock of birds searching for food. it uses a number of agents (particles) that constitute a swarm. each agent (particle) traverses the search space looking for the global minimum (or maximum). the goal of the pso is to find the operating points that lies on the border under selected conditions (elsharkwai, et. al., 2000). references athay, t., podmore, r. and virmani, s. 1979. “a practical method for the direct analysis of transient stability”, ieee transactions on power apparatus and systems, pas-98(2): 573-584. bonissone, p., el-sharkawi, m.a., david fogel, and freer, s. 2001. “evolutionary computation and applications,” ieee cd-rom # ec128, 2001 bose, a. 1984. “application of direct methods to transient stability analysis of power systems”, ieee transactions on power apparatus and systems, pas-103(7): 1629-1636. chiang, h., f. wu, and varaiya, p. 1994. “a bcu method for direct analysis of power system transient stability”, ieee transactions on power systems, 9(3): 1194-1208. chiang, h., c. chu, and cauley, g. 1995. “direct stability analysis of electric power systems using energy functions: theory, applications, and perspective”, proceedings of the ieee, november 1995, pp.1497-1529. chiang, h. 1989. “a theory-based controlling uep method for direct analysis of power system transient stability”, proceedings of the international symposium on circuits and systems (ieee iscas ’89), portland, oregon, may 1989, pp. 1980-1983. el-kady, m. 1988. “dynamic security assessment utilizing the transient energy function method”, ieee transactions on power systems, pwrs-1( 3): 284-291. el-sharkawi, m.a. and dagmar niebur editors, 1996. application of artificial neural networks to power systems, ieee press, 96 tp 112-0, 1996. el-sharkawi, m.a. 1996. “neural network application to security assessment,” neural networks applications in power systems edited by t. s. dillon and d. niebur crl publishing ltd, 1996. el-sharkawi, m.a. and marks, r.j. ii, editors 1991, applications of neural networks to power systems, (ieee press, piscataway, 1991). el-sharkawi, m.a., marks, r.j. and eberhart, r. 2000. “evolutionary techniques and fuzzy logic in power systems,’ ieee tutorial, 2000 tp-142. fouad, 1987. “direct transient stability analysis using energy functions: application to large power networks”, ieee transactions on power systems, pwrs-2, (1): 37-44. jensen, c., el-sharkawi, m.a. and robert, j.marks, 1999. “power system security boundary enhancement using evolutionary-based query learning,” invited paper, international journal of engineering intelligent systems, pp.215-218, december 1999. kumar, b.r., ipakchi, a., brandwajn, v., el-sharkawi, m.a. and cauley, g. 1991. "neural networks for dynamic security assessment of large-scale power systems: 28 intelligent techniques for power systems requirements overview," first international forum on applications of neural networks to power systems, seattle, july 23 26, 1991, pp. 65 71. mansour, y., vaahedi, e., el-sharkawi, m.a. 1997. “dynamic security contingency screening and ranking using neural networks”, ieee transactions on neural networks, 8(4): mansour, y., 1995. “b.c. hydro’s on-line transient stability assessment (tsa) model development, analysis, and post-processing”, ieee transactions on power systems, 10(1): 241-253. mansour, y., ebrahim vaahedi, a.y., chang, b.r., corns, jeyant tamby and el-sharkawi, m.a. 1997. “large scale dynamic security screening and ranking using neural networks,“ ieee transaction on power systems, : 954 – 960. mansour, y., ebrahim vaahedi and el-sharkawi, m.a. 1997. “dynamic security contingency screening and ranking using neural networks,“ ieee transaction on neural networks, : 942-950. maria, g., tang, c., and kim, j. 1990. “hybrid transient stability analysis”, ieee transactions on power systems, 5(2): 384-393. particle swarm optimization, russell eberhart, proceedings ieee international conference on neural networks (perth, australia), ieee service center, piscataway, nj, iv: 1942-1948, 1995. reed, r.d. and marks, r.j. ii. 1999. neural smithing: supervised learning in feedforward artificial neural networks, (mit press, cambridge, ma, 1999). stanton, fouad. 1981. “transient stability of a multi-machine power system part i: investigation of system trajectories and part ii: critical transient energy”, ieee transactions on power apparatus and systems, pas-100(7): 3408-3424. tong, j., chiang, h., and conneen, t. 1993. “a sensitivity-based bcu method for fast derivation of stability limits in electric power systems”, ieee transactions on power systems, 8(4): 1418-1428. vaahedi, e. 1996. “enhanced “second kick” methods for on-line dynamic security assessment”, ieee winter meeting, baltimore, md, 1996. vapnik, v.n. 1998. statistical learning theory, john wiley & sons, london. received 7 june 2001 accepted 3 september 2001 29 intelligent techniques for power systems vulnerability assessment mohamed a. el-sharkawi computational intelligence applications (cia) laborartory, department of electrical engineering, university of washington, seattle, wa 98195-2500, http:// cialab.ee.washington.edu. ãíãï çáôñþçæí conventional methods for vulnerability assessment and their challenges role of intelligent systems challenges to intelligent systems proposed approach feature extraction query learning vulnerability boundary references state-of-the-art review of collapsing soils science and technology, 6 (2001) 85-92 ©2001 sultan qaboos university problems of bacteriological pollution in water wells in wadi hadramout water project *salem m. bin qadhi, #saeed y. bashir and taha o. assaggaf *department of mechanical engineering, faculty of engineering, university of aden, aden republic of yemen, #national water and sanitation authority, wadi hadramout, seiyun republic of yemen. مشكالت التلوث البايولوجي في مياه االبار في مشروع وادى حضرموت سالم بن القاضى وسعيد بشير وطه السقاف تعرض هذه الورقة مشكلة تلوث مياه الشرب في مشروع صغير هو واحد من المشاريع النموذجية في المنطقة لتوفير :خالصـة .تفاصيل المشروع كما تبين مشكلة التلوث البايولوجيوتشرح هذه الورقة . المياه لألجيال الحاضرة والقادمة abstract: this paper presents an existing problem of drinking water pollution for a small project and one of the model projects of drinking water in yemen, designed to save and preserve good quality water for the present and future generations in the area. the paper gives the details of the project and explains the problem of bacteriological pollution and the steps undertaken to solve the problem. some of the results for short-term solutions and recommendation for the long-term solutions are also given. keywords: collapsible soils, identification, laboratory tests, field tests, stabilization, foundation design. 1. introduction yemen is a developing country having a population of about 17 million depending mainly on ground water for drinking. yemen is suffering from a shortage of water and has witnessed a number of drinking water crises in some large cities . this forced the concerned authorities to give priority to drinking water projects in the country. among leading drinking water projects carried out in yemen, is the wadi hadramout drinking water project which was studied, designed and carried out by international consultants and contractors. wadi hadramout water supply project includes seiyun, shibam, al-qatin and recently tarim water supply. the project under study is seiyun drinking water project which is part of wadi hadramout water project. seiyun is the capital of wadi hadramout and is one of the historical cities in yemen. it is situated at latitude 15.580 and 48.470 longitude, 20 km from the famous historical town of shibam and 25 km from tarim. seiyun is gaining importance since it is located near the oilfields of masila and witnessing development in different fields. seiyun drinking water project was established in 1985 to replace 14 private projects established sometime in 1960. presently, seiyun drinking water supply covers seiyun, al-hawtah and 30 villages with a population of around 84,000. the estimated number of service connections by mid 1997 is 12,000. seiyun drinking water project (table 1) consists of the following: • the source of drinking water for the project is the deep acquifer ground water where the shallow aquifer water being used for agriculture, gardening and for the use in mosques. 85 salem m. bin qadhi, saeed y.bashir and taha o. assagaf • 7 boreholes with submersible pumps which abstracts an average of 15,120 m3 /day (dar alhandasah). two boreholes have been drilled but not yet equipped with pumps (kingdom of netherlands). • one main reservoir of 2,700 m3 in seiyun and 7 small reservoirs distributed in the villages having capacities of 100-200 m3 each. • a standby generator of 400 kva. • chlorine treatment plant. • main network consists of ductile iron, φ 100 − 400 mm with a total length of 85 km and branch distribution network consists of galvanized iron pipes with a currently estimated length of more than 200 km. table 1: summary of seiyun drinking water project (dar al-handasah, kingdom of netherlands and nwsa-wadi hadramout branch). item specifications 1. system configuration : number of water wells 9 of 150-200m depth and of 35-45m water depth treatment type chlorine number of storage tanks 8 storage capacity(m3) 3700 number of booster pumps 1 at al hawta length of network (km) 235 connections 12,000 2. implementation arrangements : years of design and construction 1984-1988 funding agency arab bank and ida 3. details of wells : number in use 7, 5 m, cemented number not operational (and reasons) 2 , 50 m , cemented ( not equipped) maximum water production capacity(m3/day) of wells in use 15,120 4. supply capacity and consumption : uncounted for water(%) 37 demand of existing connections met(%) 89 2. urban development problem of bactoriological pollution yemen’s population growth rate is 3.1%. due to the problem of population increase like other cities and urban areas in the world, seiyun town is facing urban development and population growth faster than that in other neighbouring towns and villages with the attraction mainly being the presence of economic administrative activities. seiyun is divided into four sectors and until recently, the expansion is mainly occurring in the south of the town where the majority of land belongs to the state. due to several factors and reasons the new housing development extended to wellfield. this urban housing development started growing closer to the wellfield in 1992 and is forming a threat to the extension plans of seiyun wellfield and increased the risk of pollution of underground water due to the use of soak pits as a draining system for more than 1500 houses of the new housing scheme (dar alhandasah, kingdom of netherlands and m.g. ondrus). recent studies and analysis revealed that there is bacteriological water pollution in some of the water wells existing in the new housing development next to the wellfield area. this problem has been considered by the water authorities management and a number of actions have been taken with the help of local and international funding agencies and consulting experts. efforts are being 86 problem of bacteriological pollution in water wells made side by side to tackle this problem in short-term and long-term measures and are being implemented. 3. problem identification we aim to study the protection of the wellfield of seiyun water source of phase i of the project consisting of 8 boreholes (1985-1995) and phase ii originally planned for 1995-2010, where the number of boreholes of the wellfield is to be increased from 9 to 12 and developing a second wellfield. the problem started when residential units were developed some 150 m downstream of the phase (1) wellfield. national water and sanitation authority (nwsa), seiyun branch, has imposed on these developments the replacement of the percolation pits by watertight septic tanks. regular water analysis is carried out by nwsa-seiyun branch. average chemical analysis of water for the year 1999 for the seven boreholes and for borehole no.4 for seven years showed that the water quality is still within the acceptable standards for domestic use for all boreholes as shown in tables 2a and 2b (dar al-handasah). table 2(a): average chemical analysis results of water for boreholes 1-7 taken at nwsa laboratory-wadi hadramout-seiyun branch-taken on 5/3/1999(nwsa-wadi hadramout branch). characteristics average result of analysis for boreholes 1-7 for year 1999 who guidelines unit temperature 26.7 °c color 0.0 15 units turbidity 0.0 5 f.t.u ph value 7.7 6.5-8.5 units conductivity 827 �s/cm t. dissolved solids 529 1000 mg/l t. alkalinity as caco3 240 mg/l t. hardness as ca co3 332 500 mg/l calcium hardness as ca co3 188 mg/l mg hardness 144 mg/l non carbonate hardness as caco3 92 mg/l bicarbonate hco3 292.8 mg/l calcium ca++ 75.2 mg/l magnesium mg 39.5 mg/l chloride cl82 250 mg/l sulphate so4 85 400 mg/l nitrate no3 3 45 mg/l nitrite no2 0.003 0.1 mg/l sodium na+ 52.7 200 mg/l fluoride f 0.0 1.5 mg/l iron fe 0.01 0.3 mg/l manganese mn+ 0.0 0.1 mg/l bacteriological examinations of water showed that the water quality is acceptable and within the acceptable standards till the year 1997 (nwsa-wadi hadramout branch). recent analysis during the period mid-1997 and thereafter showed that some of the boreholes are contaminated by non 87 salem m. bin qadhi, saeed y.bashir and taha o. assagaf fecal coliforms (dar al-handasah and m.g. ondrus). analysis for the seven boreholes in use is given in table 3. table 2(b): chemical analysis results of water borehole no.4 for different years taken at nwsa laboratory-wadi hadramout – seiyun branch (nwsa-wadi hadramout branch). result of analysis who guidelines characteristic 1986 1993 1994 1995 1996 1997 1998 who unit temperature 25 31 24 28 29 26 27 °c color 3 0.0 0.0 0.0 0.0 1 5 15 units turbidity 2 0.0 0.0 0.0 0.0 0.0 0.0 5 f.t.u ph value 7.8 7.9 7.8 7.8 7.9 7.9 7.9 6.5-8.5 units conductivity 755 732 723 780 783 768 770 µs/cm t. dissolved solids 588 768 462 480 481 491 492 1000 mg/l t. alkalinity as caco3 201 220 216 208 218 230 224 mg/l t. hardness as ca co3 295 294 290 300 288 300 306 500 mg/l calcium hardness as ca co3 160 200 198 202 206 210 212 mg/l mg hardness 135 94 92 98 82 90 94 mg/1 non-carbonate hardness as ca co3 - - - - - - 82 mg/1 bicarbonate hco3 245.2 268.4 263 254 266 230 273.2 mg/1 calcium ca++ 64 80 79 80.8 82.4 70 84.8 mg/1 magnesium mg 32.8 22.56 22 24 19.6 21.6 22.5 mg/1 chloride cl 87.3 71 74 76 75.6 78 78 250 mg/1 sulphate so4 84 30 38 36 42 48 78 400 mg/1 nitrate no3 8.3 3.5 2.6 1.4 1.8 0.88 3.96 45 mg/l nitrite no2 --0.001 0.001 0.001 0.001 0.023 0.006 0.1 mg/l sodium na+ 57 26.7 32 23 36.6 40.64 50.9 200 mg/l fluoride f 0.85 0.001 0.00 0.00 0.00 0.01 0.0 1.5 mg/l iron fe 0.04 0.00 0.00 0.00 0.01 0.0 0.1 0.3 mg/l manganese mn+ --0.2 0.1 0.7 0.2 0.0 0.0 0.1 mg/l table 3: boreholes water analysis result specifying starting date for first sign of water contamination with non-fecal coliforms (nwsa-wadi hadramout). borehole no. date of start of contamination sign of contamination after analysis 1 28/5/1997 present 2 28/5/1997 present 3 28/6/1998 6 colonies 4 25/5/1997 present 5 28/6/1998 14 colonies 6 21/9/1998 3 colonies 7 21/9/1998 5 colonies boreholes were disinfected by chlorine solution at different intervals and repeatedly. most of the boreholes gave a positive response to this method, except borehole no. 4 as shown in table 4. 88 problem of bacteriological pollution in water wells ready and to b for future ready and to be equi in use cordon sani area = 1.6 k restricted area upland area (jawl) reservoir bh7 bh6 bh5 bh4 bh3 figure it should be noted tha (a) results for typic above 200 they a above tables by th (b) table 4 results w (c) during sampling by repeating the was within the acce response to the disinf is an indication that controlled. conseque necessary actions are 4. engineering op chemical and b the quality of water borehole no.4 which behind this pollution closer to the wellfield should be protected a engineering sanitary e bh1 bh1 pped taire m2 upland area (jawl) old city housing area old city housing area new development al-heisi elarba housing scheme (1500 houses) new development yethma housing scheme (1500 houses) bh2bh1 new development housing scheme 1. actual wellfield protection zone (cordon sanitaire) for seiyun. t the results given in tables 3 and 4 are subject to the following remarks: al coliform are given in m.p.n. for colonies range from 20 to 200, and for re referred as tntc (too numerous to count), (m.g.ondrus) and noted in the e term present. ere taken after chlorination process and after closing the well for 36 hours. and analyzing there was no sign of residual chlorine present. chlorine disinfection, all the boreholes became satisfactory and water quality ptable standards. from monitoring and studies, it can be noticed that the ection process for the boreholes takes a longer time than the earlier one. this the contamination is progressing and needs to be carefully monitored and ntly, continuous monitoring for the boreholes contamination is performed and taken by the authority. tions to stop contamination threat in seiyun wellfield acteriological analyses carried out regularly by nwsa-seiyun, showed that is still within the acceptable standards except in some boreholes; mainly shows the starting of pollution with non-faecal califorms.the main reason is thought to be the new housing development. the new housing development presents a threat to the water quality on the long run. therefore, the wellfield gainst this threat. studies (dar al-handasah) have been carried out and three options are identified, presented and discussed. 89 salem m. bin qadhi, saeed y.bashir and taha o. assagaf table 4: bacteriological examination results for borehole no.4 taken at nwsa wadi hadramout branch-seiyun for the period october-november 1999 (nwsa-wadi hadramout). date collected hour collected temp.°c date of data analysis time of analysis m.p.n.t. coliform conductivity µs/cm 6-10-98 36 36 6-10-98 12:17 present 735 11-10-98 35 35 11-10-98 11:38 present 770 17-10-98 35 35 17-10-98 12:17 (5) 770 22-10-98 34 34 22-10-98 12:17 present 770 26-10-98 35 35 26-10-98 12:17 (5) 770 7-11-98 34 34 7-11-98 12:17 present 759 15-11-98 35 35 15-11-98 12:17 (2) 770 23-11-98 34 34 23-11-98 12:17 present 762 5. option 1: do minimum option (dmo) this option is the first step to reduce the contamination risk. it represents adopting watertight septic tanks to replace the existing soak pits for the localities close to the wellfield indicated in figure 1. nwsa should take responsibility for the technical, management and service aspects of this option. unfortunately, this option has numerous disadvantages related to already constructed septic tanks and some logistic matters. bh restricted area for future ready and to in use sewage treatment plant upland area (jawl) old city housin old city housing new development housing scheme reservoir bh1 bh7 bh6 bh5 bh4 bh3 bh2 figure 2. proposed skelton 90 1 upland area (jawl) g new development al-heisi elarba housing scheme (1500 houses) new development yethma housing scheme (1500 houses) bh1 sewage network for seiyun. problem of bacteriological pollution in water wells 6. option 2: cordon sanitaire the cordon sanitaire option (cso) consists of creating a sanitized area surrounding the wellfield for a distance of at least 250 m from the closest well and the replacement of the septic tanks of the new housing schemes by a sewerage collection network and a treatment plant as shown in figure 2. around 30% of the housing units of around 300 houses falling within the cso would have to be demolished, as indicated in figure 1. the protection of the water quality of the wellfield is assured by creating a sanitized zone around it as shown in figure 2. this option has several requirements such as design and construction of the localities sewerage network and controlling the septic tanks in option 1 until a sewerage network is constructed. the package treatment plant could then be dismanteled and replaced once the sewerage treatment plant of the town is operational. in this option there is a possibility for reusing the effluent of the package treatment plant for the nearby agricultural research center and for use in the cultivated land. 7. option 3: wellfield protection and septic tanks management this option is in fact a combination of options 1 and 2 above, constituting the dmo and cso in which the establishment of a protection area i.e. erecting a surrounding fence at a distance of 250 m from closest well. in addition to the protection area, the protection wellfield zone is to be widenend up to 2500 m. there must be a complete drainage system for the housing, industry, hospitals etc and pesticide and fertilizer applications should be limited. industrial, animal husbandry and storage of hazardous chemicals will not be allowed. figure 2 shows the extent of the 2500 m radius restriction area. the requirement of this option then would be: • controlling septic tanks as in option 1 above for a short term until the sewerage network is constructed. • undertake the master plan study to trace the sewerage skeleton network and identify the proper site for the treatment plant and the impact of the plant on the airport runway. then, design and construct the complete sewerage system. 8. brief discussion of options and recommendations • the long-term sustainability of the dmo is questionable as it depends on some requirements that are not possible to achieve. • the wellfield protection and septic tank management option represent an improvement on the dmo. although relatively more expensive, it remains affordable and rapidly implementable. but its feasibility depends on nwsa’s capability. nevertheless, this option is the safer as it would be hazardous to wait for the soil or water to become polluted before action is taken. • the long term option (option 3) has the advantage that the population will not be exposed to a health risk or odour nuisance since the treatment plant will not be located in the vicinity of the residential area. hence, the long-term option is recommended when the necessary funds for implementation become available. 9. cost estimate for the proposed option the housing development areas concerned by the proposed priority sewage collection network are yethma and al-hisi-el-arbaa housing schemes as shown in figures 1 and 2. their ultimate 91 salem m. bin qadhi, saeed y.bashir and taha o. assagaf population capacity is estimated as 7,020 and 12,100 respectively. their area would correspond to 40 ha and 69 ha. the construction cost of the sewage collection network and the main conveyers has been estimated using the following rates (m.g. ondrus): 1. collection network, including manholes us $ 25,000/ha 2. main conveyors, including manholes and lift station us $ 15,000/ha 3. service connections, including demolition of existing percolation pits, connection pipes and inspection chambers us $ 12,000/ha based on an estimated generated sewage flow of 2100 m3/day, and oxidation ditch type of treatment with an effluent quality of 20/30, the cost of the treatment plant is estimated as 1.5 million us dollars. the total add up initial investment and operation and maintenanace millions cost is given in table 5. table 5: investment cost (dar al-handasah),(millions us dollars). item cost network 2.726 conveyance 1.635 service connections 1.308 treatment plant 1.500 sub total 7.200 operation and maintenance cost .6145 total 7.814 10. steps and actions taken by nwsa’s • continuous monitoring of water quality at wellfield and at different points in the water distribution network. • regular samples of water are taken ,chemical and biological analysis are done. • immediate chlorine disinfection is done for water wells that show any biological pollution. • continuous consultation with consultants in case of any water contamination. • the problem of water pollution have been reported to the higher authorities of nwra and different funding agencies for funding the project of wellfields protection as given in the different options. • response for funding the wellfield protection and seiyun sanitary system is positive and being negotiated with the higher authorities. references dar al-handasah, tarim and seiyun environmental impact study, nwsawadi hadramout branch, seiyun – republic of yemen, 2. kingdom of netherlands, directorate general development cooperation. institutional strengthening , five years nwsa branches preparation phase, final report february,1999. ondrus, m.g., 1980. laboratory experiments in environmental chemistry,wuerz publishing ltd,winnipeg, canada. nwsa-wadi hadramout branch, seiyun – republic of yemen, internal interim reports. received 4 march 2000 accepted 1 june 2000 92 ãôßáçê çáêáæë çáèçíæáæìí ýí ãíçå� introduction table 1: summary of seiyun drinking water project (dar al-handasah, kingdom of netherlands and nwsa-wadi hadramout branch). item urban development problem of bactoriological pollution problem identification characteristic conductivity the long-term sustainability of the dmo is questionable as it depends on some requirements that are not possible to achieve. the wellfield protection and septic tank manageme the long term option (option 3) has the advantage that the population will not be exposed to a health risk or odour nuisance since the treatment plant will not be located in the vicinity of the residential area. hence, the long-term option is recommended when the necessary funds for implementation become available. cost estimate for the proposed option the housing development areas concerned by the proposed priority sewage collection network are yethma and al-hisi-el-arbaa housing schemes as shown in figures 1 and 2. their ultimate population capacity is estimated as 7,020 and 12,100 respectively. thei the construction cost of the sewage collection network and the main conveyers has been estimated using the following rates (m.g. ondrus): 1. collection network, including manholesus $ 25,000/ha 2. main conveyors, including manholes and lift station us $ 15,000/ha 3. service connections, including demolition of existing percolation pits, connection pipes and inspection chambersus $ 12,000/ha based on an estimated generated sewage flow of 2100 m3/day, and oxidation ditch type of treatment with an effluent quality of 20/30, the cost of the treatment plant is estimated as 1.5 million us dollars. the total add up initial investment and operation item cost network 2.726 conveyance 1.635 service connections 1.308 treatment plant 1.500 sub total 7.200 operation and maintenance cost .6145 total 7.814 steps and actions taken by nwsa’s references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 91-99 © 2002 sultan qaboos university assessment of the electrical systems interconnection in the arab world m.h. abderrazzaq hijjawi faculty for engineering technology, yarmouk university, irbid 21110, jordan, email: abder@maktoob.com. تقيم ترابط نظم القوى الكهربائية في العالم العربي مد عبدالرزاقمح إن . أحدهما إقتصادي واألخر تقني :إن اإلتجاه العالمي لربط أنظمة الكهرباء بعضها ببعض يتميز بإن له بعـد ان : خالصة أنظمة الكهرباء في العالم العربي ليست مؤهـلة فقط للربط فيما بينها بل هي في امس الحاجة لتكوين شبكة واحدة تجمعها في لقد تم، من خالل هذا العمل، استعراض مشاريع الربط الكهربائي، القائمة والمستقبلية، في العالم العربي . نظام كهربائي موحد كما تم مناقشة تطور مراحل مشروع الربط السداسي ،بما فيه الربط . من حيث قدراتها ووضعها وكذلك الظروف المتعلقة بها تم إلقاء الضوء على اهم " وأخيرا. م1998والذي تم انجازه في نهاية عام الكهربائي االردني المصري من خالل الكيبل البحري . واجهت مشروع الربط الكهربائي في مراحله األولى أو التي يتوقع أن تواجهه في مراحله المستقبلية الصعوبات الفنية التي إما abstract: the international trend of interconnecting electric power systems has two dimensions; economical and technical. electric power systems in the arab world are not only eligible, but in need for having a unified power grid. the potentials, status and conditions of the existing and future interconnections in this region are overviewed. the development of the six countries interconnection project, including the completed phase of jordan-egypt submarine link, is discussed in details. finally, the main technical problems, which either faced the first stages of the project or expected to face the interconnected systems in the subsequent stages, are highlighted. keywords: energy, interconnection, grid, submarine cable, overhead lines. 1. introduction e lectricity is the most flexible form of energy and it is considered one of the most significant indicators of economic growth. the demand for electrical energy is growing at a fast rate worldwide. however, the available resources are limited and not uniformly distributed among the countries. therefore, it is necessary to manage these resources and utilize them in optimal form. the transmission of energy among the countries is achieved either in the form of crude fuel or as electrical energy. the later form of energy transmission is found more flexible, economical and reliable for adjacent countries, planning to promote their future cooperation in the energy sector. the interconnection of electric power has been a well-established practice since the development of the three phase ac systems (ibrahim, 1996). therefore, many existing interconnections with transmission lines running across territories, having different climatic conditions and topographies, were employed a long time ago. the factors behind these interconnections, and which encouraged the countries to get involve in these projects, were mainly of economical and technical nature (sackey and zakhary, 1996). the interconnection allows for sharing the reserve margins between electrical systems. consequently countries will not need to build as many generating stations on their territories. moreover, the exchange of electrical energy in normal and emergency circumstances should improve the economies of national power systems and provide a 91 m.h. abderrazzaq high degree of security to all sides of the interconnection. generally, to benefit from all these advantages, the interconnection project requires thorough investigation followed by a solid preparation and strong commitment. the electric systems in the arab world are in need of interconnections more than other systems in the region. there are several arab countries whose national networks are not yet interconnected. unfortunately, the plans proposed to set up unified power grids in these countries many years ago progressed rather slowly. despite this difficulty, the power systems in the arab countries are more eligible for interconnection than other systems in the world due to the availability of all energy sources in the area and the ease of transmitting this energy between neighboring countries. the positive aspects of interconnection, and its impact on improving the integration capability of the economic systems and reinforcing the national grids, were clear to all decision makers in the arab countries three decades ago. however, a long time has elapsed before started thinking seriously about the vitality of the interconnection project and only a few of them are now actually working in this direction. in this work, the current interconnection projects in the arab world are overviewed and evaluated. the technical difficulties of the new interconnections are discussed based on the most recent available data. the paper will highlight the various aspects of the project linking egypt, jordan, syria, lebanon, iraq and turkey, which is currently called (eijlst) interconnection project. 2. overview of the interconnections among the arab countries some electric systems in the adjacent arab countries have been connected for years. however, these links were limited in capacity and the amount of the exchangeable energy was rather small and fluctuated from year to year (amro, 1997). this fluctuation was mainly attributed to political reasons and only in some cases to the technical difficulties. moreover, a serious look at these links shows that they have been established in response to some imminent and emergency cases, which made them not adequately planned and not designed as permanent interconnections. as a result, these weak links were incapable of carrying high quantities of electrical energy from one system to another. this in fact leads to the real need for new reliable interconnections linking all countries in the region. figures 1 and 2 show the maps of arab countries, with some links connecting neighboring systems or planned to connect them. in fact, the international trend in this direction has greatly encouraged the planners and designers of electric systems in the arab countries to go faster in the way of establishing a unified arab network. one of the largest regional projects in this direction was the six countries interconnection project, eijlst. these countries are characterized by their location and by having vital terminal points with networks in europe, asia and africa. in fact, the first and second parts of the interconnection have already been completed with the electric power networks of egypt, jordan and syria being linked. the egyptjordan link via the red sea was the real technical and economical challenge to the main eijlst interconnection project. despite the technical difficulties, which faced this project in the initial stage and which were mainly related to the 400kv oil-filled submarine cable, the link is currently serving the interconnection effectively. figure 3 illustrates the main constituents of this cable, which was of special design to withstand the extreme mechanical load, caused by the topographical and unusual depths of the red sea, (abderrazzaq and alzahawi, 1996). figure 4 shows a simplified diagram of the jordan-egypt link. on the egyptian side, it was necessary to connect taba substation with suez power station via a 400kv, 500mw, 330km transmission line, whereas in the 92 assessment of the electric systems interconnection jordanian side it was necessary to establish a new 400kv substation and to reinforce the aqaba thermal power station with extra generating units. the submarine cable connected between taba and aqaba substations is 13km long and was laid at a depth of 850m underwater. currently, the exchangeable energy between egypt and jordan reaches 130mw, but it is expected to be in the order of 350mw after the completion of the project and linking with other countries. figure 1. the map of arab countries with existing and future interconnection. 3 2 1 figure 2. the stages of the future interconnections among the gcc countries. 93 m.h. abderrazzaq oil duct copper conductor carbon paper tapes impregnated paper insulation nylon tapes galvanized steel armour polypropylene yarn and asphalt covering figure 3. main constituents of the 400kv, oil-filled submarine cable. s y r i a aqaba amman station south 400kv 400kv jordan 400kv submarine cable red sea egypt suez taba 500/400kv 500kv 500kv 750mva figure 4. simplified diagram of the egypt-jordan interconnection link. on the other side of the arab world, a number of vital projects are currently being given increased attention by decision makers. spain is already supplying morocco with electricity via a 400kv, 26km and 615m deep submarine cable, established between these two countries. morocco’s grid is also interconnected with algeria and tunisia, whereas egypt is linked to libya by a 220kv power line, which allows for 180mw to be exchanged between the two countries. this power line covers a distance of 420km along the north-western coast from alexandria to salloum on the libyan border. there are also plans for the egyptian and libyan power networks to be linked to europe across the mediterranean through italy. in addition to the eastern link with europe via turkey, egypt and libya can exchange power with europe through italy and spain. for this purpose, a 500kv network is being planned linking egypt and libya. a 400kv network is also being planned to interconnect libya, tunisia, algeria and morocco, which are currently only connected by 220kv lines. this will form the backbone of a mediterranean power pool (mpp), which will link the grids of the middle east, north africa and europe. according to gouws (1999) the anticipated completion date of the mpp is 2015. 94 assessment of the electric systems interconnection the electric systems in the gulf region have been growing rapidly in the last two decades. the presence of oil prevents any shortage in power plants and spinning reserves in these countries. despite these conveniences, the electric systems in the gulf countries are of great need to have a unified power grid for emergency purposes, for enhancing national and local networks and for saving investments, spent in building new power stations. it is worth mentioning here, that a number of promising steps have been taken by all members of the gulf cooperative council (gcc) countries in this direction. the first phase in the gulf interconnection will link saudi arabia, kuwait, bahrain and qatar in a 400kv one grid, while the second stage integrates oman and the uae into the overall grid as shown in figure 2. the sharing of the transmitted power is based on a strategic criterion and mutual benefits of each country (ibrahim, 1996). however, a number of hurdles could cause a delay in the completion of the interconnection in this region. among these problems are the relatively long distances between the countries, the presence of some unlinked national grids and the difference in power frequency between saudi arabia and other gulf countries. it is worth mentioning here, that these problems will not hider the gulf countries from going on with their recent huge plans and investments to reinforce their national grids and to make this interconnection more reliable and robust. 3. technical considerations and network studies the power systems in the arab countries have been established and developed using the experience and consultations of various foreign companies. this fact is clear from the differences in the design and ratings of the equipment used and the standards applied in the arab countries. these systems have been working separately for decades without having serious complaints. however, when these systems become a part of the interconnection, serious technical difficulties are expected to occur. one of the problems which faced the initial studies of interconnection was the lack of information, records and data, which are considered of great importance for many studies such as protection, insulation, coordination and stability studies. therefore, it is difficult to answer the question whether a specific analysis has been performed in the design stage or which measures have been made to test the equipment before putting it in operation. to avoid this situation in future, the manufacturer should carefully perform the commissioning test of the facilities, by installing the suitable recorders and analyzing the test measurements precisely (edf report, 1998). the main technical difficulties which appeared during the initial stages of interconnection or might appear in future, as shown by the simulation studies, can be summarized as follows: 3.1 power exchange problems the power exchange limits are determined for the worst case, which can face the interconnected system during its operation. therefore, the criteria applied during the study stage of the project were based on the following facts (edf report, 1998) : firstly, the systems loaded at the maximum power exchange had to satisfy the security rules following the tripping of one internal element. secondly, the tripping of the interconnection link, loaded at the maximum power exchange, should not lead to shedding more than the first step of the underfrequency load shedding scheme. finally, the tripping of the interconnection link loaded at the maximum power exchange should not lead to unacceptable overfrequency or overvoltage in power systems. the minimum value of the voltage limit, in many cases, cannot be modified to allow more imported power. table 1 provide some values for the possible exchanged power among the systems of egypt, jordan, syria and turkey. other countries will be included in future in the subsequent stages of this interconnection. 95 m.h. abderrazzaq table 1: expected values of the interchangeable energy among the ejlst countries. limits in mw egypt can import jordan can import syria can import turkey can import from egypt 50 350 350 from jordan 260 350 300 from syria 250 50 500 from turkey 220 50 620 from e+j 400 450 from s+t 250 50 from j+s+t 260 from e+j+t 700 3.2 oscillations small inter-area oscillations could appear following the conditions of a short circuit on one of the interconnection transmission lines. system configuration, involving different combinations of generators, overhead transmission lines and submarine cables may result in such type of problems. the simulations performed in the first stage of the eijlst interconnection between jordan and egypt showed that these oscillations could be well damped with the existing parameters on both sides. moreover, reinforcing the existing tie lines and enhancing internal systems are important means for improving the behavior of interconnected systems. 3.3 overvoltages one of the problems which frequently occurs during the operation of the interconnection link is the long duration temporary overvoltages. this case is usually developed when transformers are switched in at ac fault clearing or as a consequence of voltage rises due to load rejection. the harmonic currents, generated by the saturated transformer, may coincide with resonance impedance points in the system and as a consequence harmonic voltages of high amplitudes will build up. this could cause unusual overvoltages of high magnitudes. resonant overvoltages are particularly of great interest, not only when transformers have to be re-energized or during commissioning tests of the transformers, but also each time the interconnection link is put into service again after tripping. in the case of a near fault clearance in normal operation, the risk of an overvoltage occurrence also exists. in this case, the voltage significantly decreases during the fault and suddenly reappears upon fault clearance, which can be considered in some conditions almost equivalent to re-energization (edf report, 1998). the steady state overvoltages, associated with the interconnection link must be examined with no power exchange between connected systems, which is in fact the worst situation to be studied. simulations are usually performed for faults at different locations along the interconnection link. the necessary studies could be performed using specialized computer programs such as electromagnetic transient program (emtp), transient network analyzers (tna) and other simulators. according to the obtained results and to avoid the equipment damage, the suitable protection system has to be proposed. therefore, the studies performed for egypt-jordan link, came with a proposal to install overvoltage relays, set at 570kv at the suez substation on the abu zabal-suez line and at taba substation on the suez-taba line. however, on the jordan side it was necessary to install an intertripping relays at amman south substation, on the 400kv aqaba-amman south line. 3.4 frequency excursions when the rating of the ac transmission of the interconnection links is considerably higher than the small system load, severe frequency excursions could be expected. ovefrequency could 96 assessment of the electric systems interconnection arise after total or partial tripping of the interconnection. in these cases, the turbine governors are the only devices capable of controlling and restoring the system frequency, provided that no special system control action was taken, such as generator tripping or increasing the available transmitted power. on the other hand, the underfrequency conditions, which might arise due to some disturbances such as the loss of generation units can be easily controlled by shedding some loads according to the system’s load shedding scheme. the agreement on a load shedding scheme, common to all connected systems is considered one of the important issues which should be reached immediately after putting all interconnection links in operation. the tripping of some lines, included in the interconnection, will eventually cause some islanding of specific systems with loads of other grids. it is necessary in these cases to decide the criterion on which the tripping scheme has been based, to avoid complicated schemes and unnecessary shedding of some loads. table 2 provides some figures for the expected future load shedding scheme. table 2: load shedding scheme for the current constituents of the eijlst. frequency egypt jordan syria turkey 49.2 49.1 49 49 48.8 48.7 48.6 48.5 48.4 48.2 48 47.9 47.8 47.7 47.6 2% 3% 4% link tripping 10 20 20 8% 10% 15% link tripping 2% 3% 2% 7% 3% 4% 4% 8% 10% 15% link tripping 15% 8% 10% 15% link tripping 15% 3.4 generating units the generating units in interconnected systems have to be operated according to some specific conditions. these conditions concern sensitivity to frequency, voltage deviations and the means to control active and reactive power. since the power frequency is common to all units and any drop in this frequency due to a loss of generation will influence the whole system, it is vital that all interconnection parts should satisfy certain requirements with respect to frequency (e.s.ibrahim, 1996). if this factor has not been given the required attention, the most sensitive units may trip causing further frequency decay, and in worst cases, this could be developed to cascade tripping and blackout. regarding the voltage variations, the short duration dips to certain levels should not cause tripping of the unit. the control facilities should be set to keep these units running with the highest reliability. this, in fact, depends to some extent on the strength of the system. therefore, when the generator is connected to a weak system, the machine voltage is controlled by the automatic excitation system. however, the speed governor has the responsibility of controlling the machine speed and consequently the system 97 m.h. abderrazzaq frequency. on the other hand, if the generator is connected to a strong system the machine voltage and system frequency is almost constant. consequently, the role of the automatic excitation control is to fix the reactive power supplied by the generator to the network. 3.5 protection system coordination. the main aim of the protection system is to trip the faulty elements in the network and to maintain a high level of continuous service. however, the requirements for the protection can be extended to cover more strategic goals such as utilization of reactive power compensators, power exchange and load shedding schemes. since the protection philosophies employed by individual systems are different from one system to another, the integration of these systems into a common link will not be an easy task. the settings of the protective relays and their coordination procedures should be studied carefully prior to the commercial operation of the link. moreover, the backup protection system of the main transmission lines should also be reviewed by all terminals of the interconnection. finally, the difference in the design and the manufacture of the protective equipment, employed by various systems involved in the link, can cause some difficulties and false operations of the protective relays of connected countries. this needs careful assessment of the problem and the problem can be avoided by using unified standards for the equipment in the future. 4. conclusions to effectively utilize the existing energy resources in the arab countries, it would be necessary to plan the system at a national level and to support the inter-regional links to form a unified regional power grid. the integration of individual systems into a single grid is associated with new technical problems. although these difficulties are manageable, they must be seriously studied during the preparation stage of interconnection. this can be achieved by using advanced simulation techniques, computer facilities and other power related software. the deep investigation of these technical problems will protect the national grids from frequent disconnections and prevents repeated islanding from the main link. the interconnection should be employed to unify the power systems in the region in respect of standardization, high voltage equipment selection and construction. the development of the individual electric systems should come as a first and necessary step before interconnection. this comprises the updating of the network configuration, system control and protection, which are necessary for the stability and robustness of future interconnection network. references abderrazzaq, m. and alzahawi, b., 1996. the jordan-egypt red sea cable interconnection project. proceedings of the sixth iee conference ”ac and dc power transmission conference” publication no 423, 29apr-3may 1996, london, 124-127. amro, k., (editor). 1997. electrical energy bulletin of the arab countries. arab union of producers, transporters and distributers of electricity. amman, jordan. edf report, 1998. operational studies for the interconnection of the power systems of the eijlst countries. gouws, m., 1999. egyptian power surge. african energy magazine,1, no1,south africa. ibrahim, e.s., 1996. interconnection of electric power systems in the arab world. iee power engineering journal, 121-127. sackey, t. and zakhary, s.z., 1996. power wheeling through the west african interconnected system. proceedings of the sixth iee conference ”ac and dc 98 assessment of the electric systems interconnection power transmission conference” publication no 423, 29apr-3may, 1996, london, 13-18. received 22 june 2001 accepted 13 december 2001 99 assessment of the electrical systems interconnection in the arab world m.h. abderrazzaq hijjawi faculty for engineering technology, yarmouk university, irbid 21110, jordan, email: abder@maktoob.com. overview of the interconnections among the arab countries technical considerations and network studies power exchange problems the power exchange limits are determined for the worst case, which can face the interconnected system during its operation. therefore, the criteria applied during the study stage of the project were based on the following facts (edf report, 1998) : fir oscillations small inter-area oscillations could appear following the conditions of a short circuit on one of the interconnection transmission lines. system configuration, involving different combinations of generators, overhead transmission lines and submarine cable overvoltages one of the problems which frequently occurs during the operation of the interconnection link is the long duration temporary overvoltages. this case is usually developed when transformers are switched in at ac fault clearing or as a consequence of voltage when the rating of the ac transmission of the interconnection links is considerably higher than the small system load, severe frequency excursions could be expected. ovefrequency could arise after total or partial tripping of the interconnection. in thes generating units the generating units in interconnected systems have to be operated according to some specific conditions. these conditions concern sensitivity to frequency, voltage deviations and the means to control active and reactive power. since the power frequency protection system coordination. the main aim of the protection system is to trip the faulty elements in the network and to maintain a high level of continuous service. however, the requirements for the protection can be extended to cover more strategic goals such as utilization of rea conclusions references squ journal for science, 2017, 22(2), 81-88 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp81-88 sultan qaboos university 81 engineering properties of volcanic tuff from the western part of yemen adnan a. barahim*, ibrahim a. al-akhaly and is'haq r. shamsan earth and environmental science department, faculty of science, sana’a university, sana'a, yemen. *email: barahimadnan@gmail.com abstract: this paper deals with a study of the physical and mechanical characteristics of volcanic tuff and ignimbrite from six quarries located at different areas in the western part of yemen (manakha, jahran, bakhran, dar al-hanash, abaser and soraifa). in the region, volcanic tuffs and ignimbrite are locally known by their location names and have been used as solid masonry and cladding stones. all the investigated pyroclastic rocks belong to the tertiary volcanic. the standard physical and mechanical tests (void ratio, porosity, density, specific gravity, water absorption, uniaxial compressive strength and tensile strength) were carried out on the tuff and ignimbrite samples collected from different parts of the region. laboratory tests revealed that the void ratio average values range between 0.12 and 0.37, the porosity ranges between 10.57 and 27.12%, the dry density ranges between 1.66 and 2.25 gm/cm 3 , specific gravity ranges from 1.45 to 1.94, and water absorption ranges from 4.69 to 16.39%. the measured uniaxial compressive strength values range from 24 to 68 mpa, and the tensile strength values range between 4 and 10 mpa. these tuffs and ignimbrites generally are light green, gray, beige, or yellowish in color. with these colors they are favoured for building, coating and decorative stone. this paper concludes that the studied stones have acceptable to good properties as dimension stone. jahrani and manakhi tuffs are the best quality, whereas hanashi ignimbrite is of poorer quality. keywords: yemen; volcanic tuff; physical and mechanical tests; dimension stone; uniaxial compressive strength. الخواص الهندسية للتف البركاني في الجزء الغربي من اليمن إبراهيم عبد الحميد األكحلي و إسحاق ردمان شمسانعدنان عبدالعزيز بارحيم، هذه البحث يهتم بدراسة الخصائص الطبيعية والميكانيكية لعدد ستة مقالع من صخور التف البركاني و االجنبرايت، التي تقع في مديريات :صالملخ غربي اليمن )مناخة، جهران، بخران، دار الحنش، عباصر وصريفة(، وتسمى هذه الصخور بأسماء محلية نسبةً ألماكن تواجدها واستخراجها، ةمختلف ي.حيث تستخدم كأحجار بناء وواجهات. الرواسب الفتاتية البركانية قيد الدراسة تنتمي الى بركانيات اليمن والتي يعود عمرها للعصر الثالث حاد راء الفحوصات المعيارية الطبيعية و الميكانيكية )نسبة الفراغات، المسامية، الكثافة، الوزن النوعي، امتصاص الماء، قوة تحمل الضغط أ تم اج المحور ومقاومة الشد( لعينات من التف البركاني و االجنمبرايت جمعت من مواقع مختلفة. %، الكثافة الجافة 2..20و 2.00.، المسامية في المدى بين0..2و 2..2الفراغات بين ظهرت الفحوصات المختبرية ان متوسط قيم نسبةأ %، مقاومة الضغط أحاد المحور من ...1.الى .1..، امتصاص الماء من ....الى 0...،الوزن النوعي من .جرام/سم 2.20الى 11..من هذه الصخور بشكل عام ذات الوان أخضر، رماد ، بيج و اصفر، هذه االلوان ميجاباسكال. 2.الى .ميجاباسكال ومقاومة الشد من 16الى .2 إلى الطبيعية الجميلة والجذابة جعلتها مفضلة كأحجار بناء, واجهات و زينة. و خلص البحث الى ان الصخور موضوع الدراسة تمتلك صفات مقبولة ن التف الجهراني االفضل ثم المناخي ، بينما التف الحنشي هو األسوأ.جيدة كأحجار بناء، واجهات، زينة و ديكور. و من حيث الجودة كا .اليمن، التف البركاني، الفحوصات الميكانيكية و الطبيعية، احجار الواجهات، المقاومة االنضغاطية احادية المحور: مفتاحيةالكلمات ال 1. introduction imension stone refers to rock that has been cut and worked to a specific size or shape for use in building [1]. it is an important construction material, and can essentially be subdivided into structural stone and facing stone. dimension stone is used extensively for paving and tiling, interior finishes, landscaping, monuments and statuary and building restoration [2]. volcanic tuffs have been used as dimension stones in many countries since ancient times, including italy [3] and the netherlands [4]. up until the early part of the twentieth century d adnan a. barahim et al 82 structural stonework dominated, but with the development of steel-framed buildings, facing stone became more important [2]. generally, knowledge of the engineering properties of rock material has a significant role in the construction industry. no safe design of a soundly engineered construction can be accomplished without the evaluation of the engineering properties of the material [5]. volcanic tuffs are currently widely used in buildings all over the world. these new varieties display highly fascinating colors, such as green, yellow, beige and gray. thus their decorative applications are widespread worldwide. among nations, new producers of pyroclastic stone are armenia and turkey [6]. the volcanic tuff industry has received its due share of development in recent years. this development has not only been due to the physical demands of construction, but also to the aesthetic and environmental aspects of the construction industry. volcanic tuffs are used as ornamental stone and facing stones, which are relatively thin slabs, cemented or mechanically anchored to a building’s face to enhance its appearance and protect it from weathering processes. at present, there are many operational dimension stone quarries of volcanic tuff in the western part of yemen, from which raw blocks are extracted and processed as building stone and ornamental stone. the reserves are virtually unlimited. therefore, it is very important to evaluate the rock quality and to determine the engineering properties of such volcanic tuff. the information could help the present or the future engineering projects using volcanic tuffs in or around the quarry areas. tuffs dealt with in the present study belong to the yemen tertiary volcanic group of oligocene-miocene age [7]. despite their widespread occurrence in the country, there is a lack of studies of the engineering properties of these volcaniclastics and their commercial uses as building stone. for local housing and construction, easily workable rocks are required in preference to rocks with attractive aesthetic qualities. the stone is shaped and worked to finished products (slabs and building blocks). the large scale economically viable use of rocks for various building purposes requires that cheap and simple technology can be employed to reduce the cost. in yemen, the use of tertiary volcanics has a long history. the aim of this paper is to investigate the engineering and physical properties of volcanic tuffs and ignimbrites that were collected from six different sites within the yemen volcanic series. 2. study area the quarries selected for the current study are located in the western part of yemen between sana’a city in the north and taiz city in the south (figure 1). the six selected quarries are: one in jabal al-mislamah, manakha in sana’a governorate which is situated around 93 km to the southwest of sana’a city, four sites in dhamar governorate: jahran area (25 km to the northwest of dhamar city), bakhran area (13 km southwest of dhamar city), dar al-hanash area (13 km southeast of dhamar city) and abaser area (17 km southeast of dhamar city). the sixth site is in soraifa area in taiz governorate, and is located about 20 km east of taiz city (figure 1). the selected quarries occur in mountainous terrain with sparse vegetation. 3. materials and method building stones have been produced from volcanic tuff and ignimbrite rocks using hand tools, blasting and motorized machines. a geological map of the volcanic tuffs located in the western part of yemen was explored. forty two specimens of 10×10×10 cm³ dimensions were collected from quarries in six different areas where tuff and ignimbrite are processed, and they were subjected to standard physical and mechanical experiments for rock, namely void ratio, porosity, density, specific gravity, water absorption according to astm-c97 [8], and uniaxial compressive strength according to astm-c170 [9] where the shape correction is expressed by the equation σ = σc [0.778 + 0222 (l/h)], where σ is corrected compressive strength to astm, σc is measured compressive strength and (l/h) the lateral dimension to height ratio which is equal to 1 in the present studied cube case [10] . in addition specimens of 20×10×6 cm³ dimensions were used to determine tensile strength according to astm-c99 [11, 12]. each experiment was conducted on at least three specimens and the average of the obtained values was recorded. these experiments were carried out in the central laboratories, ministry of public works and roads in yemen. 4. geological features the key for identifying a potential source of stone for exploitation as dimension stone is an understanding of the geology of the region (as mentioned in [13] for aggregate), focusing on a general study of the stratigraphy, origin and structural position of the area in question. widespread volcanic activity occurred in yemen and adjacent areas during the late cretaceous and early tertiary and is believed to be associated with the vertical uplift of the afar plume and rifting of the red sea [7, 14-18]. as a result of this activity, tremendous numbers of fissure-erupted and caldera eruptive centers, dikes and volcanic flows were formed, particularly in the central highland of the country, covering almost 45,000 km 2 [19] (figure 2). al-kadasi, [20] classified tertiary volcanic outcrops in yemen in two fields; sana’a-taiz and engineering properties of volcanic tuff 83 sheharah. mattash et al, [7] divided the yemen volcanic province into the late oligocene – early miocene yemen trap series (yts) and the late miocene – recent yemen volcanic series (tvs). figure 1. location map of studied area figure 2. simplified tertary volcanic map of yemen the tertiary volcanic represents the lowest part of the cenozoic yemen volcanic province, and mainly overlies the cretaceous tawilah group sandstones and the paleogene lateritic paleosols, and in some cases the precambrian metamorphic basement rocks. these developed during the oligocene-early miocenic preand sin-rift phases. the tertiary volcanic consists of thick, bimodal volcanics, including alkaline to transitional basalts and sultanate of oman kingdom of saudi arabia adnan a. barahim et al 84 peralkaline rhyolites and their associated ignimbrites, tuffs and rhyolitic obsidian flows. the ratio of acidic to basic volcanic products is greater than 0.5. the thickness of the tertiary volcanic varies from > 2000 m in the west down to hundreds to tens of meters in the east [7]. tuffs and ignimbrites, which are the subject of this study, have rhyolitic composition and are widely found in the field. these represent a major episode of volcanic eruption widespread in the western part of yemen. table 1 shows the volume of the reserves, which exceeds 44,500,000 m² in total [21] and gives a simple description of the volcanic tuff and ignimbrite in the studied quarries, whereas figure 3 shows cubes of the studied samples. table 1. simple description of volcanic tuffs in studied quarries figure 3. samples cut into 10×10×10 cm³ from six quarries used for various tests 5. laboratory tests and results tuff and ignimbrite in the region have been used extensively for many years for a variety of purposes, for example as building, coating, outside covering and decorative stones (figures 4a, b and c). determination of their physical and mechanical properties is therefore crucial as these properties play an important role in the selection of these rocks to meet their various usages. figure 4. examples of usage of tuff as (a, b) outside covering stone; (c) decorative stone. governorate quarry location *quarry reserve (m²) local name rock name color texture sana’a manakha 16,000,000 manakhi tuff light green fine dhamar jahran 6,000,000 jahrani tuff beige fine dhamar bakhran 1,500,000 bakhrani tuff light grey fine dhamar dar alhanash 12,000,000 hanashi ignimbrite pink medium to coarse with flow texture dhamar abaser 5,600,000 abaseri ignimbrite pink medium to coarse taiz soraifa 3,400,000 soraifi tuff light grey with reddish patterns fine * from [21]. engineering properties of volcanic tuff 85 a number of laboratory tests were conducted on cube and slab specimens of volcanic tuff and ignimbrite (from manakha, jahran, bakhran, abaser, dar al-hanash and soraifa quaries) to determine their physical and mechanical properties. the tests were performed in accordance with the american society for testing and material (astm) standards. these tests, which included the determination of void ratio, porosity, density, specific gravity, water absorption, uniaxial compressive strength (ucs) and tensile strength were carried out on at least three samples from each site. the results are presented in table 2. table 2. physical and mechanical properties of the studied volcanic tuff and ignimbrite the average value of void ratio of tuff samples in the studied quarries ranges between 0.12 and 0.37 (hanishi), the porosity ranged from 10.57% to 27.12%, and the dry density ranged between 1.66 and 2.25 gm/cm 3 . their measured uniaxial compressive strength is from 24 to 68 mpa and their tensile strength (flexural test, t) ranges between 4 to 10 mpa. the brittleness ratio (t/ucs) was calculated and ranged between 13.10% and 17.58%. the correlations between ucs and water absorption, porosity, specific gravity and density are shown in figures 5a, b, c and d. figure 5e indicates the relationship between water absorption and porosity. 6. discussion previous geological studies in the area have revealed that a vast area in the western part of yemen is underlain by tuff, ignimbrite and other pyroclastic rocks representing the last volcanic eruption [7]. in the present investigation the ucs test has been carried out according to routine procedures for dimension stone. our studies show that as per isrm specification [22, 23] jahrani, manakhi and bakhrani have strong compressive strength, while abasiri and soraifi are of medium strength and hanashi is of weak to medium strength. these average values are compatible with their use as dimension stone [2]. the high density values of samples from jahran tuff indicate the basic textural characteristics of the rock. the high void ratio and porosity in samples from hanashi indicate low density values. comparisons of void ratio, porosity and water absorption of the studied samples reveal that hanashi ignimbrite has high water absorption, while jahrani tuff samples with the lowest void ratio and porosity values have the lowest water absorption rate (table 2). in this study the ucss for jahrani, bakhrani, hanashi, abasiri and soraifi have higher values compared with those in al-dery’s study [24] and similar results have been found for manakhi tuff. on the other hand, alssabri [21] found similar results for ucs for hanashi, abasiri and manakhi, and higher values for soraifi and noticably smaller values for bakhrani (table 3). the variation in test values obtained by these three studies might be due to changes in sample location within the quarries, or to subtle differences in the lithological and textural aspects of the rocks. however, all the results lie within the permitted range for use as dimension stone. furthermore, the regression analysis and correlations between the above physical and mechanical properties show that there are good correlations between ucs and water absorption, ucs and porosity, ucs and specific gravity, ucs and density, and porosity and water absorption. as can be seen from figures 5a, b, c and d, ucs decreases with increasing water absorption (figure 5a) and porosity (figure 5b), whereas increasing ucs increases specific gravity and density (figures 5 c and d), and water absorption increases with increasing porosity (figure 5e). from these comparisons, ucs was found to follow a decreasing linear relation with water absorption and porosity, and an increasing linear relation with specific gravity and density. also water absorption has an increasing linear relation with porosity. tensile strength increases with increasing density (figure 5f). figure 5g shows an inverse relationship between density and porosity, whereas figure 5h shows a direct correlation between ucs and tensile strength. local name void ratio effective porosity (%) density (gm/cm 3 ) specific gravity water absorption (%) uniaxial compressive strength, ucs (mpa) tensile strength, t (mpa) brittleness ratio t/ ucs dry sat sub normal range* 0.001 0.25 0.120 1.8 3.0 > 10 mpa 10-30% of ucs 10-30 manakhi 0.15 12.71 2.13 2.26 1.03 1.74 5.96 60 10 16.73 jahrani 0.12 10.57 2.25 2.36 1.2 1.94 4.69 68 9 12.92 bakhrani 0.24 19.62 1.81 2.01 0.93 1.68 10.82 56 8 13.45 hanishi 0.37 27.12 1.66 1.93 0.79 1.45 16.39 24 4 17.58 abasiri 0.25 20.25 1.81 2.02 0.85 1.56 11.16 35 5 13.10 soraifi 0.26 20.36 1.89 2.1 0.94 1.64 10.75 34 5 13.34 * from [2] . adnan a. barahim et al 86 (a) (b) (c) (d) (e) (f) (g) (h) figure 5. linear relationships representing comparative analysis of physical and mechanical properties of tuffs and ignimbrites. a) between ucs and water absorption. b) between ucs and porosity. c) between ucs and specific gravity. d) between ucs and density. e) water absorption-porosity relationship. f) tensile strength-density relationship. g) between density and porosity. h) between ucs and tensile strength. the medium porous structure of tuff is reflected in its density and therefore yemeni volcanic tuff is generally defined as a lightweight rock type. in addition, its water absorption due to its void ratio was also found to be high. figure 6 shows the comparison between porosity, water absorption and ucs for tuff and ignimbrite rocks in the studied area. the results show that jahrani tuff represents the best quality stone for constructional purposes, whereas hanashi ignimbrite is the worst. jahrani tuff has low porosity, low water absorption, but strong engineering properties of volcanic tuff 87 compressive strength and tensile strength. consequently, it is a good quality dimension stone, and so is manakhi tuff due to its high brittleness ratio. the studied volcanic tuffs and ignimbrites can be easily cut and processed and, in addition, their color and engineering properties play an important role in their uses as building, cladding, and decorative stones. table 3.water absorption, uniaxial compressive strength and tensile strength properties of the studied volcanic tuff and ignimbrite compared with alssabri’s study [21]. the brittleness ratio (t/ucs) ranges between 13.10% and 17.58%, which means the tensile strength is equal to 13.10 to 17.58 of ucs, and lies within the typical range (10-30 of ucs) for dimension stone applications according to [2]. figure 6. comparison between porosity, water absorption and ucs for tuff rocks in the studied quarries. 7. conclusion the volcanic tuffs and ignimbrite, in the studied quarries, have suitable physical and mechanical properties as well as a fascinating variety of colors for architectural stone in the local commercial market. these stones have high aesthetic value and lend a prestigious appearance for a long service period, and hence have commercial viability.the present study shows that jahrani tuff is of the best quality as dimension stone, whereas hanashi ignimbrite is the worst and the other tuffs and ignimbrite, having similar physical and mechanical properties, are of medium quality as dimensionstones. local name studied by water absorption (%) uniaxial compressive strength, ucs (mpa) tensile strength, t (mpa) brittleness ratio t/ ucs normal range* > 10 mpa 10-30% of ucs 10-30 manakhi resent 5.96 60 10 16.73 alssabri 0.387.34 4784 (475864 kg/cm²) jahrani resent 4.69 68 9 12.92 alssabri bakhrani resent 10.82 56 8 13.45 alssabri 19.41 17 (170 kg/cm²) 4 (40 kg/cm²) hanishi resent 16.39 24 4 17.58 alssabri 13.48 37 (375 kg/cm²) abasiri resent 11.16 35 5 13.10 alssabri 16.26 27 (270 kg/cm²) 7 (72 kg/cm²) soraifi resent 10.75 34 5 13.34 alssabri 12.10 60 (609 kg/cm²) adnan a. 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"rock characterization testing and monitoring", international society for rock mechanics, pergamon press, 1981, oxford. p. 211. 24. al-dery, z. study and classification of building stone in yemen. yemeni studies, 1991, 43, yemen, (in arabic). received 6 november 2016 accepted 9 april 2017 http://www.ejge.com/index_ejge.htm https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahukewjn46ff8e7tahwjtbqkhucmbjcqfgg3mai&url=http%3a%2f%2frstl.royalsocietypublishing.org%2f&usg=afqjcngqxtmslvsyqxoy_jttkeeowdvjlg https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahukewiy_d6v-e7tahvfnxqkhcyqdz0qfgghmaa&url=https%3a%2f%2fwww.schweizerbart.de%2fjournals%2fnjgpa&usg=afqjcneeldezubrb7tjdgqnqpvt18ioqhg https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahukewivh4bb8u7tahxhxxqkhxcxb1kqfggjmaa&url=https%3a%2f%2fwww.journals.elsevier.com%2fjournal-of-volcanology-and-geothermal-research&usg=afqjcnhteofgmmuusqqochpt2uiqat9k4q https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahukewiusb2o8-7tahudfhokhcipbveqfghamaq&url=http%3a%2f%2fwww.biodiversitylibrary.org%2fbibliography%2f50989&usg=afqjcngfxb_hlpgxmfphlwgoiyn579ltuq https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahukewiukjs69o7tahvfprokhaond0gqfggkmaa&url=http%3a%2f%2flink.springer.com%2fjournal%2f12517&usg=afqjcngurajexawg6u4o_fobf52ggxo01g https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahukewiukjs69o7tahvfprokhaond0gqfggkmaa&url=http%3a%2f%2flink.springer.com%2fjournal%2f12517&usg=afqjcngurajexawg6u4o_fobf52ggxo01g https://www.natureindex.com/institution-outputs/yemen/yemen-geological-survey-and-mineral-resources-board-gsmrb/589d80ee140ba0bc518b459e https://www.natureindex.com/institution-outputs/yemen/yemen-geological-survey-and-mineral-resources-board-gsmrb/589d80ee140ba0bc518b459e state-of-the-art review of collapsing soils science and technology, 6 (2001) 45-53 ©2001 sultan qaboos university the development of a database management in gis applications in oman osman abdallah osman akif directorate general of roads, ministry of communications, p.o. box 27, p.c. 114, muttrah, sultanate of oman. في عمان بناء قاعدة بيانات لتطبيقات نظام المعلومات الجغرافي ثمان عبداهللا عاكفع إدارِة قاعدة بياناِت ويعتبر بناء . سلطنة ُعمان جغرافيِة في المعلوماِت الضمن أنظمة قاعدة البيانات يجرى االن تطويرِ :خالصـة جموعة البرامِج على تَوحيِد م النظام قَْد ُبِنى و. جغرافيالمعلوماِت ال ضمن مشروع نظاِم الرئيسىفي ُعمان العمود الفقرِي وطنيِة .امِج إدارِة قاعدة بياناتِ ن كبر )oracle(كنظام معلومات جغرافى مع برنامج ) arc/info ( الّسـلطنةِ فـى المسـتعملِة وزارات ال َستُعالُج و . ُعمان سلطنة فينظام المعلومات الجغرافى مشروع في وزارات الُمشَاَركَة ال فى كل ِم لنظَتَسـتعمُل هذه ا و البياناتُ الَمنُْسوبةُ التي تُعّرفُ هى تلك َركة بين الوزاراِت المختلفةِ تالمعلومات الُمش وهذه . ا بينه كةرتشالممعلومات ل ا الُمشَـاَركَة ). فع امنخرائط ال (خرائط الوزاراِت الخرائط الطبوغرافية و جُد عادة على ومن الميزات الجغرافيِة التي تَ تؤخذ كمعلوماِت وصفيِة األهداف الّرئيسية فان وفقاً لذلك، و .)arc/info( برنامج طبقات مختلفة طبقاً لمبادئ ميزات الخريطِة في فَُيمكُن َأْن تَُصنّ و ـ الهـذه ل عالَج وُيديَر المعلومات ُي لتَأسيِس نظام إدارِة قاعدة بياناِت وطنِي ُيمكُن َأْن ةقترحطريقة الم ال حي تُوض ية هو ورقـِة البحث ـ تنظام إدارِة قاعدة بيانا باستعمال ةتصميم قاعدة البياناِت الُمقتََرح وسيتم . ُمشَاَركَِة في المشروعِ ال َركة بيـن الـوزارات تالُمش (oracle) ،خْلق وذلك لبيانات القاعدة بالخريطِة الجغرافيِة طبقات لَرْبطالمقترحة الورقة َستُعالُج الفكرة فان عالوة على ذلك ختام يعتبر أحد أهم الفوائد الرئيسية في تطبيق قاعدة بيانات وطنية في مجال أنظمة الوفى . جغرافيِةالمعلوماِت التطبـيقات نظاَم .المعلومات الجغرافية أن الوزارات المستخدمة لهذه القاعدة سوف تستخدم نفس المعلومات مما يفّعل تبادل المعلومات abstract: the development of applying database management applications is currently underway within geographical information systems (gis) applications in the sultanate of oman.the establishment of a national database management system in oman is considered as the backbone that is required within the geographic information system project in oman. the principal of the gis project in oman was built upon unifying the used software packages over the sultanate which is arc/info as gis package and oracle as database management software. these packages are used within the different participating ministries in the gis project in oman.the participating ministries will handle information that are shared between them. the shared information among the different ministries is the attributed data which is defined as descriptive information extracted from geographic features that usually existed on the topographic maps and the ministries maps (utility maps). the map features can be classified into different layers according to the principles of arc/info gis package. accordingly, the main objectives of this research paper is to explain the technique proposed for establishing a national database management system that can handle and manage the shared information amongst the participating ministries in the project. the proposed database design will be made using the oracle database management system. moreover, the paper will handle a proposed idea for linking the geographic map layers with the corresponding attributed database in order to create geographic information system applications. as a conclusion, it is proposed that all the government gis departments in the sultanate will share the same information within a unique national database management which can be considered one of the major benefits in applying database management in the field of geographic information systems. 1. introduction the rapid increase of using computers in mappings and related applications has created a rich variety of information on maps and their related attributes. such information is required to be 45 osman abdallah osman akif stored and handled in the proper manner. accordingly, the use of database management systems can be used to solve such data handling problems. on this basis, the production and use of maps has widely increased over the last decade in the form of geographic information system “gis”. the gis can be defined as a computerized integrated system consisting of hardware, software and third party software for capturing, processing, analyzing and presenting the map data in digital form. in addition, it has a facility to capture data from different sources and can handle such data in two different forms: vector or raster data. the core of any gis system is its database management system, in which the map (graphic) data is stored and the attributed data are also entered and manipulated. thus the data base management system is defined by different authors (burrough, 1986) as a computerized record keeping system which has the facility to maintain information and to make such information available on demand in the shortest possible time. certainly, the use of database management systems has solved numerous problems encountered in using flat files for data storage such as data redundancy, non-sharing data, integrity and security considerations (date, 1990). the data base in any gis holds spatial and non-spatial information which is extracted from the maps or any other sources of data acquisition. the spatial information reflects the geometric representation of the graphic features on the maps. the non-spatial information compiles the attributed data that is attached to the geographic features as tabular data. it also contains information about the spatial relationship among different geographic objects which is called topographical relationships (akif et al, 1992). such relationships are: sharing relation, connectivity relation and adjacency relation. such topographical information are usually stored explicitly within the geographic data base to give satisfactory information about different objects or polygons. other types of topology such as containments, near-by, belong-to can be extracted from the above mentioned types (egenhofer et al, 1989). oman has moved towards producing maps in digital form in 1987 using the autocad software package on personal computers. in 1990, the relevant authorities started to establish geographic information systems throughout the sultanate. the establishment of database management system for the geographic information system was one of the major requirements within the project. this is mainly due to the massive amount of attributed data resulting from the movement from the autocad to gis environment. accordingly, our main objective here within this investigation is to develop a technique of designing and handling the attributed database management within a selected pilot study area in the gis project in oman. 2. cad systems versus gis environment the autocad software is a developed module based upon the ideas of computer aided design (cad) and drafting systems. such systems are largely concerned with the display and manipulation of the visible material in which they do not pay much attention to the non-graphic attributes that the graphic entities may or may not have. in cad systems, the various types of geographical entities are usually limited to point and line entities while surfaces are not explicitly defined. the topographical information between lines and points are usually missing. however, it is not difficult to link the geographic features to the related attributed data base (hassan, 1992). developments have been made in the direction in which the ability to link the computer mapping system to a separate attributed database is established within a system known as automated mapping and facility management (am/fm). thus these systems have the facility to provide geographical data and related attributes. in addition, the am/fm system can corporate topological data via a separate database in which it needs to establish a linkage between the graphics and the topological databases (akif, 1991). the benefits gained from the above described systems are: the gis would record the spatial information of object locations, shape data of identifiable geographical features and the attached 46 database management in gis applications attributes. in addition, the gis is not limited to describing the real world objects as in cad systems but can cover all various basic shapes (points, lines, areas, surfaces) and relating them in the attributed database. 3. database management and its development in gis as it is obviously clear, the database management is considered as the backbone component of any geographic information system. the previous database structure types were based upon handling data through specific form of queries at the data entry level such as hierarchical and network data structures (date, 1990). actually, each of these data structures has its advantages and disadvantages. thus, the technology of the relational data structure took the advantages of these two systems and developed in an easy form, (codd, 1969). the relational idea is based upon handling and maintaining data through the existing relations. the simplicity of the relational database structure lies in its easy form which is a table. each table is a collection of numbers of rows and columns. the most beneficial aspect in the tabular database is that the tables can be linked together or related to each other via relational keys which can gather data from different related tables. this principle is similar to the real world objects of relations to each other. more developments were adopted for the relational data structure and the relational model by using the entity relationship model, erm, in which it reflects the major component of any relational database of entities, relationships and their attributed values. in the area of the gis, the relational database is the most commonly used for storing the attributed information. now-a-days, almost all those using relational database management are already object oriented. the object oriented database management system supports an abstract concept object, entity or feature having existence independent of any attributes that the object may or may not have. the most important issue in any gis is the linkage amongst geometric and nonspatial attributes (herring, 1989a). 4. database model in arc/info in this investigation, the arc/info gis commercial package from environmental systems research institute esri in california will be used. within this package, the topographical attributed tables are separated from the graphic files. this is much desirable in order to avoid any massive data to be stored in the attributed database due to the geometric (locational) information. arc/info is an object oriented system that can create the topological attributes automatically in separate tables and relate these tables with the geometric features via a unique identification number created and maintained only in arc/info. this number is used to link the geometric and topological attributes together. within the arc cartographic package, the arc macro language (aml) can be used and extended to perform searches and updating the topological attributes behind a power graphic cartographic interface. this can assemble the major aspects of gis environment (chapman, et al, 1989). the concept of the arc/info gis software is based upon classifying the geographic features into a number of primary coverages. they are: arc coverage: represents linear features such as road center lines and borders of area features. the arch features can be topologically linked to their end points (nodes) or to area on each side of them. nodes coverage: represents arc end points and intersections of line features. topologically linked to arcs. polygons coverage: represents area features. topoligically defined by arcs which compose their borders. label points: represent point features. accordingly, any geographic features can be classified into one of the above coverages. from this concept and based upon the principle of the topological relationships between different spatial 47 osman abdallah osman akif geographic features on the map, the attributed data are stored in attributed tables which are automatically created and related to the primary coverages. these tables are: pat : polygon attribute table aat : arc attribute table nat : node attribute table xat : point attribute table these tables include relational keys to relate the geometric attributes (locations of different entities) with the topological attributes. according to this concept, the handling of maps within the arc/info is based on separating the map into different layers. 5. applications of database management in gis within a pilot area in oman in the sultanate of oman a national project to establish a geographic information system over a wide area network is now underway. this project will firstly be examined within a selected pilot study area. most of the ministries, in the sultanate, are involved in this project and in particular the utility ministries and regional municipalities. thus, the proposed database design scheme within the gis project is based upon classifying the map into a number of layers and attribute files (as in arc/info criteria). such layers and their attributed files would ultimately be needed to cover all the potential requirements of gis users in oman. these layers are called geographic layers. they are: a. base mapping layer which is concerned with the topographic features on the ground including control, landmarks and contours. b. land records: include land parcels, land sub-divisions, land records and land ownerships. c. facilities: include different utilities of electricity, water lines, sewer lines, telephone lines and gas pipelines. information about the connectivity of a facility network is also included. d. environmental: includes features of natural environment such as soil, geology, hydrography and vegetation. it contains man-made features of archeological sites or environment. e. administrative areas: define the various administrative boundaries, enumeration service and statistical analysis areas. f. transportation: includes road segment, intersection or road network, traffic signals and signs. according to this classification, the base mapping layer is concerned with the geographic and topographic features, while the other five layers are concerned with the different coverages of various requirements. by using the facilities of arc/info in overlaying different coverages together, the base mapping layer will be fixed (original) for all other layers to be overlaid on the base mapping. accordingly any or all layers can be combined with the base mapping layer according to usage and requirement. having explained the geographical model of handling the geographic features on the map within gis project, the attributed database will then be established. the attributed database is divided into two main types. 6. base mapping specification the base mapping specification is established for the base mapping layers and any new production of mapping in the gis format in oman (esri, 1992). the environmental systems research institute, has developed such base mapping specifications. the specification is designed as a tabular management system in which it includes information about: a) topographical attributes of the geographic entities. 48 database management in gis applications b) non-graphic attributes attached to the geographic entities. figure 1. illustrates a sample of the polygon attribute table and its content of different attributes. layer: cultural, miscellaneous table name: cultmisp.pat table description: the cultmisp table contains polygon representing miscellaneous manmade features. polygon attribute table (pat) variable begin column defined item name item definition area 1 area 8,18f5 perimeter 9 perimeter 8,18f5 internal number 17 cultmis# 4,5b user_id 21 cultmisp_id 4,5b feature code 25 f_code 6,6c existance category 31 exs 3,31 english name 34 nam 40,40c arabic name 74 anam 40,40c product category 114 pro 3,31 item description and codes area area of polygon in square coverage units perimeter perimeter of polygon in coverage units cultmisp# internal number of polygon assinged by arc/info cultmisp_id unique user_id used to relate attribute tables. f_code feature codes : aa010 mine, aa011 quarry, ab000 disposal site, al012 archeological site, al130 monument, al260 wall figure 1. sample of base mapping specifications (after arc/info specification, 1992). 7. national database mangement system the national database management system is required to be established to cover the attributed data of the other five layers. the basic idea of such database is to handle the shared information among the participating ministries in the gis project. the benefit of such database is to avoid any redundancy or duplication of information. the term of information or shared information means, common data that is required by specific ministries. thus, it is not necessary for each ministry to store, manage and update such data. the handling of the data will be according to the principle of distributed database, in which each ministry will be responsible for creating and maintaining its own data which can be used by other ministries via the wide area network. two further aspects were required to be considered in the design of the database which are the linkage between the base mapping specifications and the national database management system as well as the compatibility between these two database types. 49 osman abdallah osman akif based upon these assumptions, a user survey is made to identify the common sharing information between the different ministries. these data are then analysed and organized in a form of application. each application is designed separately to identify the number of tables it contains and the related attributes. the relational keys for each application are identified to link the related tables within the application. the linkage between the geographic layers and the attributed database is established to support the graphic layers in front of sharing database. furthermore, from the user survey each participating ministry will be responsible for creation, storage and maintenance of one or more applications. thus, the relational database management system will be created and maintained by the participating ministries in the project according to the principle of distributed database. for example, ministry of electricity and water is responsible for creating and maintaining the attributed data related to electric lines shown in figure 2. accordingly, this ministry is responsible for creating such table, entering, maintaining and updating the data. on the other hand, a different ministry have the right to access the data without making any processing to the data. the national database management system is established to cover the large, medium and small map scales. the format of this database is similar to the base mapping specifications to simplify the interchange and access to these databases. layer: transmission lines application, electrical data table: transmission lines table description: table contains the attributes related to electric transmission lies characteristics variable begin column defined item name item defintion segment_id 1 seg_id 6,61 line name 7 line_type 15,15c no. of circuits 22 crt_no 2,21 trans. vlotage 24 volt. 3,31 overhead/ cable 27 ohl/cab 3,3c depth/height 30 d/h 4,5b minimunm clear 34 min_clear 3,4b dist./road cl 37 dist cl 4,5b length km 41 length 5,6b capacity (mav) 46 cap 5,6b cross_sec.area 51 area 4,8f2 item descriptions and codes figure 2. national database management sample table. 8. implementation and further developments implementation of the above mentioned database types is underway within the gis project in oman. the base mapping specifications is implemented in a draft copy, in which it has to be examined within a pilot study area. a pilot study area was selected to cover different areas with different topographic features. this area has large scale maps (1:5000) produced in the autocad format (dxf format). in order to apply the gis to a selected area, it is required to convert the relevant maps from autocad to 50 database management in gis applications gis format. the process of such conversion is to transfer the autocad data into the arc cartographic package. then, some manual editing are required to amend the geometric errors that are created due to the separation of the geographic layers. the manual editing can be replaced by developing number of macros to be written using the arc macro language (aml). these macros, have the facility to search automatically all existing features in specified layer and to apply certain rules which are written within the macro itself. after removing the existing errors from the geometric data, the topological attributes can be created using the facilities and arc/info. at this stage, the other non-graphic attributes such as feature codes can then be stored in the created attributed tables. these attributes can either be stored by manual or automatic technique. once, these specifications are examined after the pilot study it will be finalized to be used in the production of new maps in the gis format directly. the implementation of the national database management is started by establishing a draft copy of such database for a pilot study area. the process of the implementation is to let each responsible ministry create its tables as explained in the previous section. then, storage of the attributes will be made by manual or automatic technique. this draft copy will be examined using the products of the base mapping conversion in gis format. the graphic layers will be linked to the shared database through identifiable numbers that relate the graphics with shared database. in order to make all the governmental gis departments in the sultanate share and use the above database, a wide area network is currently being established. this wide area network will link all the participating ministries in the gis project and allow them to use the national database. once the databases have been implemented and examined between sharing ministries via the wide area network, some developments can be made to handle the national database in a form of customized applications. the customized applications are development data base management application tools that can handle the attributed data in a form of screens and driven menus. such applications can be developed using high level of computer programming languages such as c or 4gl besides the query languages of the database commercial package. for example, the facilities or utilities information can be considered as an application which consists of a number of aspects such as: a. electric facilities b. water facilities c. sewer facilities d. telecom facilities e. gas and petrol facilities f. street lighting facilities the attributed data of each of the above facilities are stored in a number of tables. for instance, in the case of electric facilities, the tables are: i) electric lines (transmission) ii) electric lines (distribution) iii) electric maintenance (lines) furthermore, inside each table there are a number of attributes that can be helpful for other users and planners. accordingly, a customized application provided the facilities which can simplify the handling of data by presenting them in a form of screens or reports instead of tables. figure (3) depicts a proposed example of such application and its driven menus for the utilities data base. 51 osman abdallah osman akif main menu electric facilities water facilities sewer facilities telecom facilities gas and pertrol facilities street lighting facilities transmission lines distribution lines mantinance of lines primary stations primary sub_stations driven menu segment_id line name: transmission_voltage length: capacity: area overhead /cable: no. of circuits depth/height: conductor type: clearance: reservation: screen for single record of the transmission line figure 3. proposed utility application. 9. conclusions with respect to the database management system, the implementation proved that the development of a database management for handling and managing the massive amount of attributed data can easily be adopted. in addition, the proper analysis of data and the design of the relational database in this project and capabilities of the attributed data can be handled and shared between the participating ministries to make the gis project simple to use and more efficient to implement with a high degree of success. sharing data between participating ministries can be considered as one of the most important applications of using the database management in the gis. furthermore, the principle of distributed database, simplified handling and managing the attributes is preferred to gathering all attributed data in a central data bank. certainly, by developing customized applications, the handling of data will be much easier and does not need highly qualified staff. the compatibility of the gis environments hardware and software in the different ministries saved considerable time and effort. the establishments of the wide area network is also considered as one of the major items that helped in the success of the gis project because it avoided data redundancy and time consumption. 52 database management in gis applications references akif, o.a. nasser, a.a. kady, m.m. and hassan, k.m., 1992. an alternative technique for updating digital map data within pilot project in egypt, paper presented at the 17th congress of isprs (2-14 august), washington d.c. akif, o.a., 1991. digital mapping, automatic structuring and classification for urban area using a graphic workstation, ph.d. dissertation, faculty of eng., ain shams univ., cairo, egypt. burrough, p.a., 1986. principle of geographic information system for land resources assessment, oxford university press, oxford. chapman, d.p. and dalton, n., 1989. a compact representation of cartographic topology using nested binary tree, auto-carto/arics, education trust, project report. date, c.j., 1990. an introduction to database systems, vol 1, fifth edition addison-wesly publication company. egenhofer, m.j. and frank, u.a., 1989. object oriented modeling in gis: inheritance and propagation, auto-carto 9 proceedings, ninth international symposium on computer assisted cartography held in baltimore, maryland u.s.a., april 2 – 7. esri, environment system for research institute., 1992. geographic information system – digital basemapping specification, sultanate of oman. hassan, k.m., 1992. towards automatic handling and updating of digital map data for land information system in egypt, m.sc. thesis, faculty of eng., ain shams univ., cairo, egypt. herring r.j., 1989a. the definition and development of a topological spatial data system, photogrammetry and lis, 2-17 march, swiss federal institute of technology (epel), eucblens, lausanne. received 4 march 2000 accepted 1 june 2000 53 èäçá þçúïé èíçäçê áêøèíþçê äùçã � introduction cad systems versus gis environment database management and its development in gis database model in arc/info base mapping specification layer: cultural, miscellaneous table name: cultmisp.pat variable defined item name layer: transmission lines application, electrical data item descriptions and codes implementation and further developments electric facilities transmission lines conclusions references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 71-80 © 2001 sultan qaboos university simple formulae for estimating the depth and dimension of some geological bodies from gravity anomalies sayyadul arafin department of physics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. عالقة بسيطة لتقريب عمق وأبعاد بعض األجسام الجيولوجية من التباينات للجاذبية األرضية سيد العارفين تقديم عالقة أو طريقة بسيطة لقياس عمق ونصف قطر بعض األجسام الجيولوجية البسيطة مثل الكرة المصمتة : خالصة إن العمق تحسب أو تقدر قيمته . نات لحساب معامالت هذا الجسم وهذه الطريقة تستخدم جميع نقاط البيا . واالسطوانة األفقية . باستخدام المتوسط لألعماق أو القيم لعدد من األعماق والتي حسبت سابقاً من القيم التقريبية والعظمى وكذلك العرض التقريبي لها باإلضافة إلى ذلك، التماثل للتباين نصف القطر لجسمين قد يحسب باستخدام المساحات تحت الخطوط الوهمية لتحديد الجاذبية ومن ذلك يحسب نصف القطر الذي ال يعتمد . للجاذبية بسبب الكرة المصمته قد استخدم لحساب الكتلة الزائدة من خط وهمي واحد إن هذه الطريقة لحساب أنصاف أقطار قد تكون أفضل من الناحية التقريبية عن طريقة حساب . على العمق المقدر أو المحسوب . المساحة و هنا نسبة الخطأ في القياسات المعنية قد شرح بالتفصيل abstract: a simple method for determining the depth and radius of some simple geological bodies such as a sphere and a horizontal cylinder is presented. the method utilizes all of the data points to calculate the body parameters. the depth is estimated from the mean of the depths determined from various fractions of the maximum anomaly and their corresponding widths. the radii of the two bodies are calculated from the areas under the respective gravity profiles. additionally , the radial symmetry of the gravity anomaly due to a sphere has been utilized to calculate the excess mass from a single profile. the radius determined from the excess mass is independent of depth estimate. this method of determining the radius is more robust than the one based on calculating the area. an error analysis showing the effects of truncation and zero-level errors on the estimated radius is also discussed. keywords: gravity anomaly, excess mass, characteristic points, sphere and cylinder. 1. introduction e arly papers on quantitative gravity interpretation found the in geophysical literature are based on the method of characteristic points. the characteristic points are the points on a gravity or magnetic profile which are easy to recognize. such points are the maximum, minimum and inflection points ( points of maximum gradient) on the curve. many authors including pentz (1940), kogbetliantz (1944), hubert (1946), skeels and watson (1949), bott and smith (1958), smith (1959 ; 1960), milcoveanu (1970) and many others have derived formulae for geological bodies and interpreted those using characteristic curves and points. this method of interpretation is quick and useful in the field to plan future field surveys. the advent of the laptop and its capability to deal with 2-d and 3-d software (martyn-antienza and garcia-abdeslem, 1999; ruotoistenmaki, 1992) in the field has somewhat made the method less efficient. besides academic interest the method can still be used in the field where a laptop is either unavailable or cannot be used for lack of electricity. 71 sayyadul arafin in the present paper a simple method of finding depth and radius of simple geological bodies such as spheres and horizontal cylinders from their gravity anomalies has been described . the method is basically similar to that described in standard geophysics text books such as dobrin (1970) and nettleton (1976). the present method proposes depth determination at a number of points on the profile and utilizes the area and volume (excess mass) under the gravity profile for the radius. the method has been applied on synthetic as well as field data. 2. method 2.1 spherical body the gravity anomaly caused by a spherical body (figure 1) is given by : r figure 1. symbols for spherical and horizontal bodies. here ∆g(x) is the gravity anomaly due to the spherical body, x is the horizontal distance along the amplitude at that point given by the maximum value of gravity , shown that the depth determined from the widths of the anomaly at the corresponding m amplitude is given by )1(])/([ 3 4 )( 2/3223 xzzrgxg +∆ = ∆ ρπ -x p -x o +x p +x r r θ z θ w gravity profile, g is the universal gravitational constant, ∆ρ is the density contrast of the body with respect to the surrounding rocks, r is the radius of the spherical / horizontal cylindrical body and z is the depth to the center of the spherical/cylindrical body. the anomaly ∆g(x) is symmetric about x=0 and has its maximum ∆gmax can be divided into n equal fractions giving n-1 points on )2( 3 )0( 2max rg z gg ρπ ∆∆∆ == 4 2 the yaxis. the distances on either side of x=0 at which these fractions occur are denoted by x j/n , where n = 2,3,4, ….. and j = 1,2,3, …..n-1. index j here is assumed to start from the bottom part of the anomaly. the distance 2xj/n is the full width of the anomaly at j/n th fraction of the maximum amplitude. the fractions of the maximum amplitude at the corresponding half-widths (x j/n ) are given by it can be )3(/]/ 3 [])/([ 3 )( // njzrgxzzrgxg jnjjjnj ρπρπ ∆=+∆=∆ fractions of the maximu 44 232/3223 )4(1) −j/(/ 3/2/= nxz njj 72 simple formulae for estimating the depth and dimension it is to be noted that for n = 2 and j =1 , the depth z1 = 1.305 x1/2 , where x1/2 is the half-width of the anomaly at half of its maximum amplitude. this particular depth formula obtained is described in the books by nettleton (1976) and dobrin (1970) . the depths so determined are the same for a noise free isolated anomaly. this is shown in figures 2 and 3 for theoretical data. however, in practice the anomaly is always contaminated with noise. the estimated depth should be either the geometric or arithmetic mean of the depths, zj , corresponding to different fractions of the maximum amplitude. for noisy data more depth estimates should be made within the noise free portion of the anomaly using equation (4). estimating the depths at different widths of the anomaly can sometimes give useful information on the shape of the body. this is explained in example 4. the dimension of the spherical body (i.e. the radius) can be estimated from the area under the anomaly curve. in doing so all the data points are taken into account. this is done by integrating equation (1) ∫ ∫ ∞ ∞− ∞ ∞− +=∆ )5(])/([)( 2/322 dxxzzcdxxg where c = 4πg∆ρr3 / 3. the left hand side of equation (5) is the area, a , under the gravity anomaly curve. now changing the variable from x to θ by the substitution of x = z tanθ , the limits of integration become -π/2 and +π/2 and the right hand side of equation (5) takes the form ∫∫ − ∞ ∞− ==+ 2/ 2/ 2/322 /2/])/([ π π θ zcdzcdxxzzc substituting the value of the gravitational constant g in the constant term c and considering the distances in kilometers and kilofeet we get respectively : ∫ ∞ ∞− = )6()kmindistances(/88.55)( 3 zrdxxg ρ∆∆ )7()kilofeetindistances(/04.17 3 zrρ∆= in reality the limits of integration are finite because our gravity profiles are finite. the left hand side of equation (6), which is the area under the observed gravity anomaly curve, can be calculated numerically by using a standard method such as the simpson's rule or simply by dividing the curve into very small segments and adding the area under each segment. following the second procedure the left hand side of equation (6) can be written in digital form so that the final expression takes the form ∑ = −= = ki ki ii zrxg )8(/88.55 3ρ∆∆∆ 3 )9(/04.17 zrρ∆= ∆xi 's have to be very small in order to get an accurate value of the area under the anomaly curve. it is convenient to deal with computations if the gravity values are sampled at equal intervals so that the ∆xi 's can be replaced with a common value ∆x. assuming that the density contrast is known from other means of measurements , the radius r now can be calculated from equation (8) or (9) depending on whether it is measured in meters or kilofeet. the calculation of r in this case involves all the measured gravity values of the profile and not just a single characteristic point such as the maximum amplitude of the anomaly. the numerical value of the area under the anomaly curve is usually much larger than the maximum amplitude of the anomaly. this allows the 73 sayyadul arafin present method to tolerate comparatively large absolute errors in the calculated value of the area. however the disadvantage of the method is that the radius depends on the estimated depth to the center of the sphere and any error in depth estimate is propagated to the estimated value of the radius. the dependence of the radius on depth is due to the fact that a sphere is a 3-dimensional body but for a horizontal cylinder the radius is independent of depth because of its two dimensionality. radius from excess mass the gravity method is the only geophysical method that can uniquely estimate the total anomalous mass or simply the excess mass causing the anomaly. this is in fact a corollary of gauss' flux theory in potential field theory (parasnis, 1997). it can be shown that the excess mass can be given as the surface integral of the gravity anomaly )10(∫∫= dsgkmassexcess ∆ where ∆g's are the gravity anomaly values measured over the surface area of the earth and ds is an element of that surface. k is a constant depending on the units used. it is 2.39x109 metric ton when area is in kilometer square and anomaly in mgals , and 26.3 imperial tons (1 imperial ton =2000lb) when area is in meter square and anomaly in mgals. (use of non-si units in exploration geophysics is sometimes unavoidable though unfortunate!). the alternative method utilizes two important facts about gravity anomaly of a spherical body. firstly the excess mass of a sphere does not depend upon its depth and secondly its gravity anomaly is radially symmetric about the centre point of the anomaly (i.e. maximum anomaly). therefore the area of the earth's surface on which this anomaly exists can be determined by integrating in radial coordinates. the excess mass is therefore given by ∫ ∫ ∞ 0 2 0 )11()( π φddrrrg∆ the gravity anomaly of a sphere being symmetric is independent of the radial angle φ and a function of the radial distance r from the center of the anomaly. any profile that crosses over the center point is the x-distance from the maximum point of the anomaly (i.e. maximum anomaly corresponds to the origin of the profile). now substituting equation (1) in equation (11) and changing the variable from x ( r is actually replaced by x now) to θ by the same manner as in equation (5) one gets )12(milligal)in gravity and kilometersin distances(for 1097.41 38 arexcessmass ρ∆×= )12(milligal)in gravity andmeter in distances(for 62.4 3 brρ∆×= the excess mass can be computed either from equation (11) in the same way used in calculating the area from equation (8) or by calculating the volume of a cone fitted to the data. the computational technique based on equation (8) has been followed in this study. 2.2 horizontal cylinder the gravity effect of a long horizontal cylinder is the same as if its mass were concentrated on a line along its axis. the gravity anomaly of such a body at any point x (figure 1) on the horizontal surface of the earth is given by ( ) )13(]/[2)( 222 xzzrgxg +∆=∆ ρπ and the maximum amplitude as before occurs at x = 0 i.e., 74 simple formulae for estimating the depth and dimension )14(/2)0( 2max zrggg ρπ ∆=∆=∆ if we consider n fractions of the maximum amplitude resulting in (n-1) number of points (figure 3) denoted by j on the y-axis, then it can be shown that the depth determined from the half-widths corresponding to these points are given by : )15()](/[/ jnjxz njj −= for n =2 , j becomes 1 and z1 = x1/2 , the standard formula found in geophysics text books (nettleton, 1976 ; dobrin 1970). the radius , r of the cylinder can be calculated in the same fashion as for the sphere calculated above. the final expressions for r of the cylinder when the distances are measured in kilometers and kilofeet are respectively: ∑ + −= = k ki ii rxg )16(66.131 2ρ∆∆∆ = 215.40 rρ∆ 0 2 4 6 8 10 12 14 16 -60 -40 -20 0 20 40 60 distance (km) a no m al y figure 2. interpretation of the gravity anomaly due to a sphere by the present method. it is to be noted that the radius of the horizontal cylinder determined from the area under the curve is independent of the depth to the centre, z. this is unlike the method which utilizes the total amplitude to determine the radius from the formulae : r2 = ∆gmaxz/ (41.91 ∆ρ) (distances in km) and r2 = ∆gmaxz/ (12.78 ∆ρ) (distances in kft) . 3. results and discussions four examples are presented here in order to show the validity of the present method. two of them deal with the theoretical data and two with the field data. example 1, synthetic data the theoretical gravity anomaly (figure 2) for a spherical body is calculated by using equation (1). the assumed parameters of the spherical body are such that radius, r =3.0 km , 75 sayyadul arafin dept and its interpretation for a horizontal cylinder are shown in figure for the horizontal cylinder are the same as for the sphere. the area unde h to the center, z = 5.0 km and density contrast, ∆ρ = 0.5 g cm-3. the depth and radius determined by using the present method of interpretation are 5.04 km and 3.00 km, respectively. the area under the curve is 149.71 mgal m. example 2, synthetic data the theoretical anomaly 3. the assumed parameters r the curve is 554.9 mgal m. the interpreted depth is 5.06 km and the radius is 2.9 km. 0 5 10 15 20 25 30 35 40 -60 -40 -20 0 20 40 60 distance (km) a no m al y figure 3. interpretation of gravity anomaly due to a horizontal cylinder by the present method. ing the radius of the cylinder accurately the gravity values should be easured over a longer distance compared to the sphere (figure 4). the tail of the anomaly for a applied to a known geological situation, which involves anomaly due to ble salt dome anomaly (nettleton, 1976).results of interpretations of this for determin m horizontal cylinder continues for a much longer distance before it reduces to zero. this effect is due to contributions to gravity effects from the ends of the horizontal cylinder. unlike the sphere , the horizontal cylinder is a two dimensional body the axial dimension of which is assumed to be infinitely long. the truncation error in the case of a horizontal cylinder is more than that of a sphere (figure 5). example 3, field data the method has been salt dome known as hum anomaly and those of example 4 obtained by nettleton (1957, 1962) are presented in table 1 for a comparison with those obtained from the present method. like all salt dome anomalies this anomaly is negative indicating mass deficiency in the subsurface. the anomaly has a total amplitude of -13.9 mgal at the centre of the profile and tapers to about -0.56 mgal on each side of the centre covering a total distance of 75 kilofeet (kft). the anomaly is quite smooth and symmetrical giving an impression of a spherical causative body. the depth determined from this anomaly by using the present method is 16.3 kft , which is the average of the depths ( z1 = 15.4, z2 76 simple formulae for estimating the depth and dimension = 16.1, z3 = 16.5, z4 = 16.6 , z5 = 16.5, z6 = 16.7 and z7 = 16.6 kft ) determined at seven fractions of the total amplitude. the area under the anomaly curve is 407.91 mgal kft from which the radius, r = 10.92 kft , is calculated by using equation (9). the depth and radius so determined are almost the same as those ( z = 16.3 and r = 11.3 kft) obtained by nettleton. any variation in the depths determined from the present method indicates deviation of the causative body from the assumed spherical model. 0 5 10 15 20 25 30 35 40 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 distance (km) a no m al y figure 4. comparison of profile lengths of a sphere and a horizontal cylinder. -5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 ratio of distance to depth (x/z) p er ce nt e rr or figure 5. truncation error on radius estimated from area under the gravity profile of a sphere and cylinder. 77 sayyadul arafin 0 2 4 6 8 10 12 0 5 10 15 20 25 30 35 40 ratio of distance to depth (x/z) p er ce nt e rr or 14 figure 6. truncation error on radius estimated from excess mass of a sphere. xample ed gulf of mexico anomaly is interpreted by nettleton (1957) by a ical body instead of a sphere. the interpretation of the same anomaly with method. e 4, field data the more complicat mushroom-shaped geolog a spherical model is not meant for a comparison but to show that estimating the depth at different fractions of the maximum amplitude can give us information on the validity of the assumed spherical model. this anomaly has a total amplitude of about -9.0 mgal and is distorted at the central part of the anomaly making the determination of the total amplitude a subjective matter. the distortion at the centre of the anomaly is believed to be due to higher density of the shallow uppermost part of the dome relative to the density of the surrounding sediments. table 1: parameters of the geological bodies obtained by nettleton (1957) and the present anomalies nettleton present method humble s xample 2 r = 11.3 .3 kft r = 1 kft alt dome, e kft ; z = 16 0.92 kft; z = 16.3 top radius : 15 kft, bottom radius 7.5 kft z = 22.4 kft gulf of mexico, example 3 mushroom-shaped body r is not determined his positive density contrast produces a positive anomaly at the centre which reduces the peak mplitude of the anomaly. nettleton has interpolated the observed amplitude to about -10.0 mgal t a in his interpretation of the anomaly in terms of a mushroom-shaped body the top of which has positive density contrast. the maximum horizontal dimension of the mushroom is about 30,000 ft at the top , minimum about 15,000 ft at the bottom and the depth to the top of the dome is about 1,300 ft. depth estimates ( z1 = 21.2, z2 = 20.1, z3 = 21.9, z4 = 23.1 , z5 = 24.4, z6 = 24.9 and z7 = 26.1 kft ) for this anomaly show a wide range of values indicating that the causative body is far from being spherical in shape. z1 is the depth determined for the half-width closest to the minimum amplitude (i.e. bottom part of the anomaly) and z7 for the half-width closest to the 78 simple formulae for estimating the depth and dimension maximum amplitude ( i.e. top part of the anomaly). depth determination from equation (4) depends upon the half-width of the anomaly. the gradual but fairly large increase in depths as one estimates depths from bottom to top of the anomaly indicates that the widths towards the top of the anomaly are increasing more than expected. this in turn means that the causative body is widening towards its top shaping up something like an inverted pyramid. -5 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 45 ratio of distance to depth (x/z) p er ce nt e rr or figure 7. combined truncation and zero-level error on radius estimated from excess mass of a sphere. are two possible sources of error that will influence the radius estimate. the truncation rror arises because of the finite length of the gravity profiles. therefore the computed areas under the ll place zero-level of the anomaly (i.e. xaxis lusion enter of geological bodies of simple geometrical shapes such as a sphere and a cylinder has been determined at a number of points along the gravity profile. the radius of the there e gravity profiles of a sphere and a cylinder and the computed excess mass of a sphere will always be less than what would have been obtained from a semi-infinite profile length. as a result the estimated value of the radius will be less than the actual value. the affects of this error are shown in figure 5 and figure 6. it can be seen from figure 5 that the truncation error is more for a cylinder than a sphere. for example for a 10% error in the radius estimate, the minimum x/z value is 1 in the case of a sphere and about 3.3 in the case of a cylinder. for the same error the profile length, in the case of radius estimate from the excess mass of a sphere, has to be about 3.5 times more than the profile length in the case of area estimate. the zero-level error is introduced when the regional gravity values are not properly removed from the data. the incorrect removal of the regional wi ) either above or below the true level thus either decreasing or increasing the true gravity values respectively. the combined affect of the truncation error and the zero-level error is shown in the case of excess mass estimate for a sphere in figure 7. the curve above is obtained by under-subtracting the regional by 10% and the curve below by over-subtracting by the same amount. 4. conc depth to the c 79 sayyadul arafin bodi references bott, m.h.p.and smith, r.a. 1958. the f the limiting depth of gravitating bodies, geophysics. 6 : 1-10. d quadratic polynomial density functions, geophysics. 64: net o., new york. troleum geologist. 46: 1815-1838. pentz, h.h., 1940. formulas and curves for the interpretation of certain 2-d magnetic and us surfaces, geophysics. 57: 623-628 63. received 14 january 2001 ccepted 27 june 2001 es is obtained from the area under the gravity profile. the radius so determined depends on the depth estimate in the case of a sphere. an alternative method based on calculating excess mass from the gravity anomaly of a sphere determines the radius which is independent of the estimated depth. a single gravity profile for a sphere has been used to calculate the excess mass by utilising the radial symmetry of such a profile. depth determination at different parts of the anomaly can give us information on the validity of the assumed spherical shape of the body. since the numerical values of the area under the gravity profile and the excess mass are much larger than the total amplitude of the anomaly the radius determined from these values is expected to be more tolerant to error than the radius estimated from a single point such as a maximum or inflection point in the profile. however this is not valid in the case of a horizontal cylinder because the truncation error is more dominant in this case resulting in less accurate estimate of the area under the observed gravity profile. the method of radius estimate from the excess mass is more robust than the method that uses the area. estimation o dobrin, m.b. 1970. introduction to geophysical prospecting (3rd edition), mcgraw hill publishing co., new york. hubert, m.k. 1946. a line integral method of computing the gravimetric effects of 2-d bodies. geophysics. 13: 215-221. kogbetliantz, e.g. 1944. quantitative interpretation of magnetic and gravity anomalies. geophysics. 9: 463-473. milcoveanu, d.1970. some formulas useful in the interpretation of gravitational and magnetic profiles. geophysics. 35: 66-73. martyn-antienza, b. and garcia-abdeslem, j. 1999. 2-d gravity modeling with analytically defined geometry an 1730-1734. tleton, l.l.1976. gravity and magnetics in oil prospecting (2nd edition), mcgraw-hill publishing c nettleton, l.l.1962. gravity and magnetics for geologists and seismologists, bulletin american association of pe nettleton, l.l.1957. gravity survey over a gulf coast continental mound, geophysics. 22 : 630-642 parasnis, d.s., 1997. principles of applied geophysics. chapman and hall , london. gravity anomalies. geophysics. 5: 295-306. ruoitstenmaki, t., 1992. the gravity anomaly of two dimensional sources with continuous density distribution and bounded by continuo skeels, d.c. and watson, r.j. 1949. derivation of magnetic and gravimetric quantities by surface integrals. geophysics. 14: 133-145. smith, r.a., 1960. some formulae for interpreting local gravity anomalies. geophysics. 8 : 607 613. smith, r.a., 1959. some depth formulae for local magnetic and gravity anomalies. geophysics. 7: 55 a 80 sayyadul arafin department of physics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. îáçõé : êþïíã úáçþé ãæ øñíþé èóí references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 303-310 © 2002 sultan qaboos university surface preparation of inas (110) using atomic hydrogen t.d. veal*, c.f. mcconville* and s.h. al-harthi** *department of physics, university of warwick, cv4 7al, united kingdom,**department of physics, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, **email: salim1@squ.edu.om. باستخدام التنظيف الهيدروجيني inas)110(تجهيز سطح مادة تيموثي فيل، كريستوفر مكنفيل و سالم بن حمود الحارثي خالية من شوائب الجو كالكربون واألكسجين inas (110)يختص هذا البحث بدراسة كيفية إنتاج سطوح نظيفة لمادة :خالصة خالية من أي يلعملية والنظرية توضح أن األسطح الناتجة من التنظيف الهيدروجين النتائج ا . بإستخدام التنظيف الهيدروجيني . تلف في خصائصها اإللكترونية والتركيبية abstract: atomic hydrogen cleaning has been used to produce structurally and electronically damage-free inas(110) surfaces. x-ray photoelectron spectroscopy (xps) was used to obtain chemical composition and chemical state information about the surface, before and after the removal of the atmospheric contamination. low energy electron diffraction (leed) and high-resolution electron-energy-loss spectroscopy (hreels) were also used, respectively, to determine the surface reconstruction and degree of surface ordering, and to probe the adsorbed contaminant vibrational modes and the collective excitations of the clean surface. clean, ordered and stoichiometric inas(110)-(1×1) surfaces were obtained by exposure to thermally generated atomic hydrogen at a substrate temperature as low as 400ºc. semi-classical dielectric theory analysis of hreel spectra of the phonon and plasmon excitations of the clean surface indicate that no electronic damage or dopant passivation were induced by the surface preparation method. keywords: inas(110), hydrogen cleaning, plasmon excitations, hreel, xps 1. introduction the preparation of clean, ordered and stoichiometric iii-v semiconductor surfaces is generally problematic without the extensive facilities available with molecular beam epitaxy (mbe). even in an mbe-chamber, the thermal desorption of oxides in the presence of an arsenic partial pressure to prepare the surface of inas is made difficult by the need for precise control of substrate temperature because the oxide and arsenic desorption temperatures are very close together (schäfer et al 2000). when mbe facilities are unavailable, the standard method of in situ cleaning of polar inas surfaces is cycles of low energy ion bombardment and annealing. however, this has been shown to cause severe structural damage, resulting in the introduction of defects, enhanced carrier concentrations and reduced mobilities within the outermost 1000 å of the material (magnée et al 1995, bell et al 1996a, bell et al 1996b). traditionally, the non-polar (110) surfaces of iii-v materials have been produced by cleaving in vacuum, as this is the fracture plane of these zincblende materials. however, from cleave to cleave large variations in the surface step densities result. these steps have been observed using scanning tunnelling microscopy where (111), (112) and (110)-type steps have all been identified on inas(110) (liang et al 1993). the consequent modification of the surface, where the reactivity is likely to be dominated by the step density profile, will result in significant non-uniformity in the surface properties with each cleave. this is 303 t.d.veal, c.f. mcconville and s.h. al-harthi evident from photoemission studies, where the expected flat-band condition, with no electron accumulation, is rarely achieved for inas(110). the surface electronic structure is extremely sensitive to the presence of cleave-induced steps, which result in downward band bending and accumulation layer formation (karlsson et al 1998). an alternative surface preparation technique, atomic hydrogen cleaning (ahc), offers an effective way of obtaining clean, undamaged inas(110) surfaces with uniform step densities. this method has previously been shown to be an efficient, relatively low temperature technique for obtaining clean, ordered and damage-free gaas(001) and inp(001) surfaces (kikawa et al 1994, petit and houzay 1992, petit and houzay 1994, goto et al 1995). ahc of the polar (100) and (111) surfaces of inas has previously been studied using auger electron spectroscopy (aes), high-resolution electron-energy-loss spectroscopy (hreels) and low energy electron diffraction (leed) (bell et al 1997, bell et al 1998). whilst the removal of contamination by ahc was confirmed by aes, no chemical state information was available to indicate the reaction mechanisms that occur during ahc. here, the use of x-ray photoelectron spectroscopy (xps) before and after ahc, with some complementary use of hreels as an adsorbate vibrational spectroscopy, permits the investigation of the processes by which ahc of inas(110) proceeds. leed was used to monitor the surface ordering before and after the cleaning process. hreels was used to study the surface vibrational modes of the contaminants on the asloaded surfaces and collective excitations of the clean surface. 2. experimental details samples from s-doped inas(110) wafers (n ~ 4 × 1018 cm-3) were individually loaded into the hreels spectrometer (base pressure < 5 × 10-10 mbar) without any ex situ treatment. molecular hydrogen was thermally cracked in an atomic hydrogen source (epi europe) as it passed over the w-filament held at ~ 2100ºc (as measured by an infrared pyrometer) with an estimated h2 → h* conversion efficiency of about 6-7% for the conditions used (sutoh et al 1995). hydrogen doses were measured in terms of molecular hydrogen exposures in kilo-langmuirs (kl) (1 kl = 10-3 torr.s). during ahc, the chamber pressure was typically 3 × 10-5 mbar. the distance between the sample and the atomic hydrogen source was approximately 5 cm. each sample was degassed for one hour to 360ºc prior to ahc, and annealed to 400ºc during ahc by a combination of the atomic hydrogen source filament and the sample filament mounted behind. hreel spectra were recorded using a range of incident electron energies between 7 and 100 ev with a resolution of 10 mev full width at half maximum (fwhm). xps spectra were collected to obtain chemical composition and chemical state information before and after ahc, using unmonochromated al kα radiation and a 150º spherical sector analyser, with an overall system resolution of ∼1.4 ev for the settings used. 3. results and discussion xps spectra from the as-loaded inas(110) surface are shown in figure 1 (dotted lines). the main contribution to the c 1s xps spectrum indicates the presence of hydrocarbons on the surface. the shoulder on the high binding energy side may be due to the presence of alcohols, carbonates formed after the adsorption of atmospheric co2, and bicarbonates (wolan et al 1997). the presence of in-oxide and as2o3 is indicated by reference to the binding energies of peaks in the in 3d, as 2p and 3d, and o 1s xps spectra (moulder et al 1992). the precise nature of the in-oxide could not be identified by xps because the different oxides are indistinguishable because of the small chemical shifts of the in 3d lines the peak positions are consistent with the presence of in2o3, the most common in-oxide, and sub-oxides such as in2o. as there is no component of the as 3d spectrum at ~ 46 ev, the presence of the other common as-oxide, as2o5, above the xps detection limit is ruled out. this oxide has previously been reported to be unstable in ultra-high vacuum, decomposing into as2o3 and oxygen within a few hours of formation (schäfer et al 2000). 304 surface preparation of inan(110) using atomic hydrogen 280 284 288 528 532 536 o 1sc 1s as2o3 inas (ch)n binding energy (ev) 40 44 1324 1328 as 2p3/2as 3d as2o3inas binding energy (ev) 444 448 452 456 460 as-loaded h-cleaned in 3d in2o3in2o3inas inas binding energy (ev) figure 1. in 3d, as 3d, as 2p3/2, c 1s and o 1s xps spectra from as-loaded inas(110) (dotted lines) and from clean inas(110) prepared by an ahc dose of 120 kl with a sample temperature of 400ºc (dashed lines). all y-axes are in arbitrary units. an approximate surface composition was determined from the relative intensities of various photoelectron peaks by applying the appropriate atomic sensitivity factor (asf) for each core level. errors in determining the surface atomic composition result from the fact that photoelectron lines for the different elements present occur at different binding energies. consequently, the photoelectrons analysed have different kinetic energies and mean free paths. this means that information contained in the xps spectra is integrated over different depths for the different elements and makes the assessment of uncertainty in the binding energies difficult. however, from straightforwardly applying the asf values and using the as 3d line for as because its associated mean free path is closer to that of the in 3d, o 1s and c 1s photoelectrons than that of the 2p3/2 line, the elemental surface composition before cleaning is 47 % o, 37 % c, 9 % in, and 7 % as. an estimate of the thickness of the oxide layer was obtained by virtue of the attenuation of the substrate signal by the oxide overlayer. the as 3d spectrum is suitable for this analysis as the chemical shift between substrate and oxide peaks is large, allowing the substrate signal alone to be 305 t.d.veal, c.f. mcconville and s.h. al-harthi examined before and after oxide layer removal. the attenuated signal from the substrate beneath the oxide layer is is given by is = is0 exp(-z/λ) (1) where is0 is the unattenuated clean surface signal obtained after ahc, z is the thickness of the oxide layer, and λ is the inelastic mean free path of the as 3d photoelectrons 27.5 å (schaefer et al 1990). allowing for the error associated with determining the peak areas, this gives an oxide layer thickness of 30 ± 5 å. this is qualitatively consistent with the information given by comparing the as-loaded spectra of the as 3d and as 2p3/2 photoelectrons and considering their different inelastic mean free paths. the lower kinetic energy (higher binding energy) as 2p3/2 electrons have a mean free path of ~ 7.5 å (schaefer et al 1990), compared with the ~ 27.5 å of the higher kinetic energy (lower binding energy) as 3d electrons. because of the exponential attenuation, over 98 % of each signal comes from within four mean free path lengths of the surface. the fact that no as 2p3/2 signal from the inas substrate is visible in the as-loaded spectrum indicates that the oxide layer is at least 30 å (4 × 7.5 å) thick. 0 100 200 300 400 (a) (b) ν(c-h) δ(c-h) ν(as-o) ν(in-o) electron energy loss (mev) figure 2. specular hreel spectra, recorded at 15 ev, with an instrumental broadening of 10 mev fwhm, from (a) an as-loaded inas(110) sample; (b) after annealing for one hour at 360ºc and a total of 120kl of atomic hydrogen cleaning at a sample temperature of 400ºc. the dotted line of spectrum (b) depicts the experimental points and the solid line is the simulated spectrum calculated using semi-classical dielectric theory. the as-loaded samples gave a very weak and broad specular elastic peak in hreels, with an angular spread of 15º full width at half maximum (fwhm); they exhibited no ordered leed pattern. figure 2 (a) shows a specular hreel spectrum from an as-loaded sample and features a peak at 106 mev almost twice the width of the elastic peak. this is attributed to a combination of in-o and as-o vibrational modes. these are known to be at ~ 87 and ~ 118 mev respectively (ibach and mills et al 1982). however, it is apparent that the broad peak at 106 mev in spectrum (a) of figure 2 cannot be solely due to the combination of two symmetric peaks centred at 87 and 118 mev. however, when the character of an intramolecular bond changes, relatively large frequency shifts can occur (ibach and mills et al 1982). it is therefore suggested that the origin of the low loss energy side of this peak is in-o vibrational modes of several different frequencies in 306 surface preparation of inan(110) using atomic hydrogen the range 87 to ~ 100 mev resulting from the various intramolecular bonds present in the different in-oxides likely to exist in the native oxide, including in2o3 and suboxides such as in2o. the peak centred at ~ 170 mev on the hreel spectrum recorded from the as-loaded inas (100) surface is due to the combined hydrocarbon deformation modes, δ(c-h) (aquino et al 1995), whilst the peak at 360 mev is attributed to the well known hydrocarbon stretching mode, ν(c-h) (ibach and mills et al 1982). the as-laoded spectrum is quite noisy and has low resolution because of the disordered nature of the atmospheric contamination present. as a result, the presence of alcohols and carbonates suggested by the c 1s xps spectrum cannot be unambiguously confirmed because their vibrational modes occur at around the same part of the spectrum as the δ(c-h) modes (jones et al 1989). the intensity of all the peaks in the as-loaded spectrum of figure 2 decreased as the incident electron energy was increased, confirming that they are due to vibrational modes and not collective excitations. a clean surface was obtained after a total of 120 kl of ahc. the xps spectra recorded from the c curs by the form as2o3 + 2inas + 12h* → in2o3 + 4ash3 ↑, here h* represents thermally excited hydrogen atoms and ↑ indicates the desorption of the in2o3 + 4h* → in2o ↑ + 2h2o ↑. the clean surface exhibited the clear, sharp (1×1) leed patterns shown in figure 3 with the recta lean surface are shown in figure 1 (dotted lines). as shown in this figure, the c 1s and o 1s signals were below the detection limit of xps. the binding energy of the in 3d lines has shifted down by 1 ev, indicative of the removal of in oxide and the presence of inas at the surface. the as2o3 peaks in the as 3d and as 2p3/2 spectral regions disappeared, with the inas peak becoming stronger in the as 3d spectrum and appearing for the first time in the as 2p3/2 region. bearing in mind the caveats mentioned earlier with regard to determination of surface atomic composition using photoemission results, these xps spectra suggest that the clean surface consists of 53 % in and 47 % as, close to the 1:1 stoichiometry expected for the non-polar (110) surface. in the case of gaas(100), it has been proposed that the removal of as2o3 oc ation and desorption of ash3, whilst the oxygen generated in this process reacts with surface gallium to form more ga2o3 (mikhailov et al 1992). a similar mechanism is proposed here with the formation of more in2o3 which is corroborated by vibrational spectroscopy results (veal and mcconville, 2000). the proposed reaction for as2o3 removal and creation of additional in2o3 is w reaction product. upon further ahc treatment, it is suggested that the in2o3 is eventually removed, by analogy with the case of ga2o3 (mikhailov et al 1992, yamada et al 1993), according to the reaction ngular spacing of diffraction spots characteristic of the (110) surface. increased surface ordering was also apparent from the more intense specular elastic peak in hreels, with a much reduced angular spread (3º fwhm). an hreel spectrum recorded from the clean surface is shown in figure 2. whilst the clean surface spectrum shown does not extend to the loss energies of all the contaminant vibrational modes, it was independently confirmed that their intensities had been reduced to below the detection limit. a series of normalised specular hreel spectra were recorded with a range of incident electron energies from a clean inas(110) surface prepared by annealing at 360ºc followed by a 120 kl dose of ahc with a sample temperature of 400ºc. the peak at ~ 90 mev in all the spectra is due to the conduction-band electron plasmon excitation. the width of this feature decreases at higher incident electron energies, whilst its intensity increases relative to the elastic peak. as the incidence energy is reduced, the plasmon peak becomes more asymmetric and less well defined on the high loss energy side; a small shift towards higher loss energy also occurs. the shoulder on the elastic peak at ~ 29 mev is assigned to fuchs-kliewer surface optical phonon excitations (mönch et al 1993): this feature does not change in loss energy, 307 t.d.veal, c.f. mcconville and s.h. al-harthi but its intensity decays rapidly with increasing incidence energy, disappearing completely above 60 ev. figure 3. (1×1) leed patterns (left) recorded using beam energies of (a) 31 ev and (b) 49 ev from inas(110) prepared by an ahc dose of 120 kl with a sample temperature of 400ºc. the inverted images (centre) and schematic diagrams (right) are also shown. the diffraction spots obscured by the electron gun are shown unshaded in the schematic pattern. the hreel spectra of the atomic hydrogen cleaned surface were analysed using the semiclassical dielectric theory of hreels (lambin et al 1990). the plasma dielectric function was based on the hydrodynamic model, with the plasma frequencies, plasmon lifetimes, and spatial dispersion coefficients as parameters (bell et al 1996b). a three-layer model was used to simulate the experimental spectra across the entire incident-electron energy range, consisting of a plasmonfree surface "dead" layer, accumulation layer, and a semi-infinite bulk. below the 35 å dead layer, the 55 å accumulation layer had a carrier concentration of 6.7 × 1018 cm-3, above a semi-infinite bulk with a carrier concentration of 3.9 × 1018 cm-3: that is, unchanged from the nominal bulk doping value given by the sample manufacturer. the band bending was estimated to be 115 mev, with a triangular potential well width of 140 å, giving a surface charge density of 6.3 ± 2.0 × 1011 cm-2. this is in agreement with the values of 1011-1012 cm-2 found on other faces of inas (olsson et al 1996, bell et al 1997) and on hydrogen terminated inas(110) (chen et al 1989). the spatial dispersion coefficient for the simulations was calculated using the thomas-fermi model (tfm), giving a value of 0.43 × 106 ms-1, which successfully reproduced the observed plasmon peak dispersion in the experimental spectra. this indicates that the hydrogen cleaning treatment does not cause subsurface damage: for ion bombarded and annealed samples spatial dispersion coefficients are significantly lower than those predicted by the tfm because of additional defect scattering (bell et al 1996b). the carrier mobility of ahc inas(110) deduced from the plasmon lifetimes used in the simulations is five times higher than for samples from the same wafer subjected to grazing incidence 500ev iba (veal and mcconville 2001), providing further evidence in favour of ahc as a surface preparation technique. an accumulation layer has also been observed on inas(110) cleavage surfaces after good mirror-like cleavages, as seen by visual inspection and leed (karlsson et al 1998). whilst an "ideal" cleavage gives a flat band condition on the inas(110) surface with no electron accumulation, the surface electronic structure is extremely sensitive to the presence of contamination and defects, resulting in downward band bending and accumulation layer formation. 308 surface preparation of inan(110) using atomic hydrogen from cleave to cleave large changes in step densities, and consequently adsorption properties and defect densities occur, resulting in significant variations in surface properties. atomic hydrogen cleaning is an effective alternative method of obtaining clean, undamaged inas(110) surfaces prior to further in situ processing. in conclusion, it has been demonstrated that clean, ordered inas(110) surfaces can be obtained by exposing the atmospherically contaminated substrates to atomic hydrogen at 400ºc with a molecular hydrogen dose of 120 kl. during atomic hydrogen cleaning, the as2o3, in-oxides and hydrocarbons are removed completely. furthermore, this process produces no detectable damage: dielectric theory simulations of the plasmon excitations in the hreel spectra indicate carrier mobilities and spatial dispersion coefficients significantly higher than those of samples prepared by iba; and below the accumulation layer the carrier concentration was found to be that of the nominal s-doping. references aquino, a. a., hill, j. j. and jones, t. s. 1995. evidence for a surface methylene species in the decomposition of trimethylgallium on gaas(100)-(4×1): a high resolution electron energy loss spectroscopy study. surf. sci. 327: 74-80. bell, g.r., mcconville, c.f. and jones, t.s. 1996a. plasma excitations and the effects of surface preparation in n-type inas(001) studied by electron energy loss spectroscopy. appl. surf. sci. 104/105: 17-23. bell, g.r., mcconville, c.f. and jones, t.s. 1996b. plasma excitations and accumulation layers in heavily doped inas(001). phys. rev. b 54: 2654-2661. bell, g.r., jones, t.s. and mcconville, c.f. 1997. accumulation layer profiles at inas polar surfaces. appl. phys. lett. 71: 3688-3690. bell, g.r., kaijaks, n.s., dixon, r.j. and mcconville, c.f. 1998. atomic hydrogen cleaning of polar iii-v semiconductor surfaces. surf. sci. 401: 125-137. chen, y., hermanson j.c. and lapeyre, g.j. 1989. coupled plasmon and phonon in the accumulation layer of inas(110) cleaved surfaces. phys. rev. b 39: 12682-12687. goto, s., yamada, m. and nomura, y. 1995. surface cleaning of si doped/undoped gaas substrates. jpn. j. appl. phys. 234: l1180-l1183. ibach, h. and mills, d.l. 1982. electron energy loss spectroscopy and surface vibrations, academic, new york. jones, t.s., ashton, m.r., richardson, n.v. and mcconville, c.f. 1989. electron energy-loss studies of insb (100). j. phys.: condens. matter 1: sb207-sb208. karlsson, h.s., viselga, r. and karlsson, u.o. 1998. electron accumulation at the inas(110) cleavage surface. title. surf. sci. 402-404: 822-826. kikawa, t., ochiai, i. and takatani, s. 1994. atomic hydrogen cleaning of gaas and inp surfaces studied by photoemission spectroscopy. surf. sci. 316: 238-46. lambin, ph., vigneron, j. and lucas, a.a. 1990. computation of the surface electronenergy-loss spectrum in specular geometry for an arbitrary plane-stratified medium. computer phys. commun. 60: 351-64. liang, y., packard, w.e., dow, j.d., ho, h. and lapeyre, g.j. 1993. monatomic steps on the inas(110) surface. phys. rev. b 48: 11942-11945. magnee, p.h.c., den hartog, s.g., van wees, b.j., klapwijk, t.m., van de graaf, w. and borghs, g. 1995. influence of low-energy ar-sputtering on the electronicproperties of inas-based quantum-well structures. appl. phys. lett. 67: 3569-3571. mikhailov, g.m., bukin, p.v., khudobin, s.a., chumakov, a.a. and shapoval, s.y. 1992. xps investigation of the interaction between ecr-excited hydrogen and the native oxide of gaas(100). vacuum 43: 199-201. monch, w. 1993. semiconductor surfaces and interfaces. springer, berlin. 309 t.d.veal, c.f. mcconville and s.h. al-harthi mouldet, j.f., stickle, w.f., sobol p.e. and bomben, k.d. 1992. handbook of x-ray photoelectron spectroscopy. ed. j. chastain. perkin-elmer corporation, eden prairie, mn. olsson, l.o., andersson, c.b.m., hakansson, m.c., kanski, j., ilver, l. and karlsson, u.o. 1996. charge accumulation at inas surfaces. phys. rev. lett. 76: 36263629. petit, e.j., houzay, f. and moison, j.m. 1992. interaction of atomic hydrogen with native oxides on inp(100). surf. sci. 269/270: 902-908. petit, e.j. and houzay, f. 1994. optimal surface cleaning of gaas(001) with atomic hydrogen. j. vac. sci. technol. b 12: 547-550. schafer, m., naumann, w., finnberg, t., hannss, m., dutschke, a., and anton, r. 2000. uv/ozone-activated growth of oxide layers on inas(001) surfaces and oxide desorption under arsenic pressure. appl. surf. sci., 158: 147-158. schaefer, j.a., persch, v., stock, s., allinger, th. and goldmann, a. 1990. etching of gaas(100) by activated hydrogen. europhys. lett. 12: 563-568. sutoh, a., okada, y., and kawabe, m. 1995. cracking efficiency of hydrogen with tungsten filament in molecular beam epitaxy. jpn. j. appl. phys. 234: l1379-l1382. veal, t.d. and mcconville, c.f. 2000. controlled oxide removal for the preparation of damage-free inas(110) surfaces. appl. phys. lett. 77: 1665-1667. veal, t.d. and mcconville, c.f. 2001. profiling of electron accumulation layers in the nearsurface region of inas(110). phys. rev. b 64: 085311. wolan, j.t., mount, c.k. and hoflund, g.b. 1997. chemical reactions induced by the room temperature interaction of hyperthermal atomic hydrogen with the native oxide layer on gaas(001) surfaces studied by ion scattering spectroscopy and x-ray photoelectron spectroscopy. j. vac. sci. technol. a 15: 2502-2506. yamada, m., ide, y., and tone, k. 1993. interaction of atomic-hydrogen with gaas(001) surface oxide – volatile ga-oxide formation. appl. surf. sci. 70/71: 531-535. received 25 december 2001 accepted 29 december 2002 310 surface preparation of inas (110) using atomic hydrogen t.d. veal*, c.f. mcconville* and s.h. al-harthi** *department of physics, university of warwick, cv4 7al, united kingdom,**department of physics, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, **email: salim1@squ.edu.om. experimental details results and discussion microsoft word elec99043.doc science and technology, 5 (2000) 35-45 © 2000 sultan qaboos university 35 voltage stability analysis of muscat power system during summer weather conditions k. ellithy*, a. gastli*, s. al-alawi*, a. al-hinai*, and z. al-abri** *department of electrical and electronics engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman, and **ministry of electricity and water, muscat sultanate of oman. تحليل استقرار الجهد الكهربائي بشبكة القوى بمسقط تحت حاالت طقس الصيف خالد الليثي ، عادل القصطلي ، صالح العلوي ، عامر الهنائي، و زاهر العبري القوى في معظم الدول من أكبر االهتمامات لتشغيل و ) نظم ( استقرار الجهد الكهربائي لشبكات ت تعتـبر مشكال :خالصـة الطرق المستخدمة في . الستقرار الجهد لشبكة القوى بمسقط تحليالً مبدئياً يصف هذا البحث . الكهربائية نظام القوى تخطـيط يستخدم تحليل الطّور لتحديد أضعف . منحنيات القدرة الفّعالة و منحنيات القدرة المفاعلّية و البحـث تعتمد على تحليل الطّور وتستخدم منحنيات القدرة الفّعالة و المفاعلّية لتحديد حافة ، إلى عدم استقرار الجهد مـناطق األحمـال فـي الشبكة التي تؤدي وقد أظهرت نتائج هذا البحث أن منطقة األحمال بجنوب الباطنة . اسـتقرار الجهد بداللة االحتياط في الميجاوات و الميجافار في ه أظهرت النتائج أن كما ،قرار الجهد بالشبكة هـي أضعف منطقة في شبكة قوى مسقط و التي يمكن أن تؤدي إلى عدم است حالة زيادة األحمال على هذه المنطقة دون زيادة مناسبة للقدرة المفاعلّية قد يؤدي إلى انهيار الجهد الكهربائي و عدم استقرار .الشبكة abstract: a systematic and general formulation of a propagation simulation program (psp) is developed for the coherent field of microwave and millimeter wave carrier signals traversing intermediate layered precipitation media taking into account the random behavior of particle size, orientation, shape and concentration distributions. based on a rigorous solution of the volumetric multiple-scattering integral equations, the formalism offers the capability of treating the potential transmission impairments on satelliteearth links and radar remote sensing generated by composite atmospheric layers of precipitation in conjunction with the finite polarization isolation of dual-polarized transmitting and receiving antennas. a multi-layered formulation is employed which encompasses an ensemble of discrete particles comprising an arbitrary mixture of ice crystals, melting snow and raindrops that may exist simultaneously along satellite-earth communication paths. keywords: muscat power system, voltage stability, modal analysis, q-v curves, p-v curves. oltage stability problems have been one of the major concerns for electric utilities as a result of heavy system loading. voltage stability is the ability of a power system to maintain acceptable steady-state voltage at all buses in the system under normal operating conditions. a power system enters a state of voltage instability (voltage collapse) when a disturbance, an increase in load demand or a change in system conditions, causes a progressive and uncontrollable fall of voltage. the problem of voltage stability has been experienced by many utilities because of loading their bulk transmission network to their maximum possible capacity to avoid the capital cost of building new lines and generation facilities. several major network collapses, caused by voltage instability problems, were reported around the world in various countries such as france, sweden, japan, belgium, and usa (taylor, 1994). most of the incidents are believed to be related to heavily stressed systems where large amounts of real and reactive power are transported over transmission lines while appropriate reactive power sources are not available to maintain a nominal voltage profile at receiving-end buses. in recent years, the problem of voltage stability and collapse has attracted considerable attention from power system researchers. many techniques have been proposed in the literature for evaluating ellithy, gastli, al-alawi, al-hinai and al-abri 36 and predicting voltage stability. among these techniques are p-v curves (pal, 1992; suzuki et al, 1992), q-v curves (d'aquila et al, 1993; vaahedi et al, 1999; schluter, 1998; taylor, 1994), modal analysis (gao et al, 1992; morrison et al, 1993; mansour et al, 1994), minimum singular value (löf et al, 1993; liu et al, 1998), sensitivity analysis (begovic and phadke, 1992; fltabo and dommel 1990), energy function (overbye and demacro, 1995; demacro and overby, 1990), reactive power optimization (tamura et al, 1982), artificial neural networks (jesasuray, 1990; el-keib and ma, 1995) and neuro-fuzzy networks (liu and su, 1998). large numbers of research papers on power systems voltage stability have been published recently by the ieee voltage stability working group (ajjarapu and lee, 1998). muscat power system supplies power to almost one million people in the capital (muscat) and its adjacent area in the sultanate of oman. there are heavy loaded areas having a voltage stability problem in the system. these load areas are summer peaking and because of heavy use of air conditioning, the loads are weather sensitive. voltage instability is most likely to occur during periods of summer or abnormal-summer weather. following the discovery of serious voltage stability problems in some heavy load areas, an intensive effort was undertaken by the ministry of electricity and water of the sultanate of oman to find solutions. in this paper, the voltage stability behavior of muscat power system is analyzed using the modal (eigenvalue) analysis, q-v curves and p-v curves methods. a computer program using matlab was developed to analyze the voltage stability of a large power system. the modal analysis method as well as p-v curves and q-v curves were part of the program. the modal analysis was used to identify the weakest load buses in the system while the p-v curves and q-v curves were used to determine the mw and mvar margins from the operating point to the voltage instability point. rusail-132 barka-132 1 2 4 3 ghubrah-132 ghubra-33 madinat qaboos-132 madinat qaboos-33 5 6 wadi adai-132 wadi adai-33 al-falaj-33 wadi kabir-33 1516 7 8 14131211 musana-33 1920 21 barka-3318 17 seeb main-33 seeb-132 29 28 10 9izki-132 izki-33 nizwa-33 nizwa-132 22 23 27 2625 bahla-33musana-132 manah-132 24 figure 1. single line diagram of muscat power system voltage stability analysis of muscat power system 37 describtion of muscat power system the single line diagram of muscat power system is shown in figure 1. muscat has a mean annual temperature of nearly 30cº and a summer daily temperature above 40cº. these high temperatures have a strong effect on the electrical load demand, especially in the summer season, since 80% of the load in the system during the summer is for air conditioning. this high demand for electric load during the summer can lead to various problems such as voltage instability. power-flow problem the power-flow problem solves the complex matrix equation: * * v s vyi == (1) where i is the nodal current injection matrix, y is the system nodal admittance matrix, v is the unknown complex node voltage vector and s is the apparent power nodal injection vector representing the specified load and generation at nodes where jqps += . the superstar refers to the complex conjugate. the power-flow (also called load-flow) problem is very closely associated with voltage stability analysis. power-flow solution is an essential tool for voltage stability evaluation. much of the research on voltage stability deals with power-flow computation method. the newton-raphson method (taylor, 1994) is the most general and reliable algorithm to solve the powerflow problem. from equation (1), we can write the equation for node k (bus k) as ∑ = = n m mkmk vyi 1 , (2) ∑ = ==+ n m mkmkkkkk vyvivjqp 1 ** )( . (3) using the following notation kmmk jkmkm j mm j kk eyyevvevv γθθ === , , . equation (3) becomes ∑∑ == −−+−−=+ n m kmmkmkkm n m kmmkmkkmkk vvyjvvyjqp 11 )sin()cos( γθθγθθ (4) the mismatch power at bus k is given by k sch kk k sch kk qqq ppp −=∆ −=∆ where pksch and qksch are the net scheduled active and reactive powers injected into the network at bus k, respectively. the pk and qk are calculated from equation (4). the newton-raphson method solves the partitioned matrix equation:       ∆ ∆ =      ∆ ∆ v j q p θ (5) where ∆p and ∆q are mismatch active and reactive power vectors, ∆v and ∆θ are unknown voltage magnitude and angle correction vectors and j is jacobian matrix of partial derivative terms calculated from equation (4). voltage stability evaluation the modal (eigenvalue) analysis (gao et al, 1992; morrison et al, 1993; mansour et al, 1994), q-v curves (d'aquila et al, 1993; vaahedi et al, 1999; schluter, 1998) and p-v curves (pal, 1992 and suzuki et al, 19924) methods are used for voltage stability evaluation and assessment of muscat power system. these ellithy, gastli, al-alawi, al-hinai and al-abri 38 methods are used to identify the probable weak load areas, which could lead the system to voltage instability. modal analysis: the modal (eigenvalue) analysis provides a powerful analytical tool for determining both proximity to, and mechanism of, voltage instability. in the modal analysis method, the system reactive power variation sensitivity to incremental change in bus voltage magnitude is found and then weak modes (weak buses) of the system are identified. the modal analysis uses the power-flow jacobian matrix. equation (5) can be rewritten as       ∆ ∆       =      ∆ ∆ vj j j j q p θ 22 12 21 11 (6) by letting ∆p = 0 in equation (6), we can write vjjp ∆+∆==∆ 12110 θ or vjj ∆−=∆ − 12 1 11θ , (7) and vjjq ∆+∆=∆ 2221 θ . (8) substitute equation (7) in (8), to get vjq r∆=∆ (9) where [ ]121112122 jjjjj r −−= . jr is a reduced jacobian matrix of the system. equation (9) can be written as qjv r ∆=∆ −1 (10) the matrix jr represents the linearized relationship between the incremental changes in bus voltage (∆v) and bus reactive power injection (∆q). the system voltage is affected by both real and reactive power variations. eliminating the real power (∆p=0) and angle part from the system equation (6), allows us to focus on the study of the reactive demand and supply problem of the system as well as minimize computational effort by reducing dimensions of the jacobian matrix j. voltage stability characteristics are analyzed by computing eigenvalues and eigenvectors of the reduced order jacobian matrix jr. the eigenvalues of matrix jr identify different modes through which the system could become voltage unstable. the magnitude of the eigenvalues provides a relative measure of proximity to instability. the eigenvectors, on the other hand, provide information about to the mechanism of loss of voltage stability. eigenvalue analysis of jr results in the following: φλγ=rj (11) where φ is the right eigenvector matrix of jr, γ is the left eigenvector matrix of jr and λ is the diagonal eigenvalue matrix of jr. equation (11) can be written as γφλ= −− 11rj , (12) where i=φγ−1 . substituting equation (12) in (10), leads to qv γ∆φλ=∆ −1 voltage stability analysis of muscat power system 39 or ∑ ∆ γφ =∆ i i ii qv λ (13) where λi is the i th eigenvalue, φi is the i th column right eigenvector and γi is the i th row left eigenvector of matrix jr. each eigenvalue λi and corresponding right and left eigenvectors φi and γi, define the i th mode of the system. the ith modal reactive power variation is defined as: iikq φ=∆ (14) m w distance to critical p oint o perating p oint p v m v a r dista nce to critical p oint o perating p oint q v (a) p -v c urve (b) q -v c urve figure 2 . mw and mvar margin to voltage instability where ki is a scale factor to normalize vector ∆qi so that 122 =φ∑ j jiik (15) with φji being the j th element of φi.the corresponding i th modal voltage variation is qv i ∆=∆ λ 1 (16) if λi =0, the i th modal voltage will collapse because any change in that modal reactive power will cause infinite modal voltage variation. if λi >0, the i th modal voltage and ith reactive power variation are along the same direction, indicating that the system is voltage stable. if λi <0, the i th modal voltage and the ith ellithy, gastli, al-alawi, al-hinai and al-abri 40 reactive power variation are in opposite directions, indicating that the system is voltage unstable. “a system is voltage-stable if the eigenvalues of jr are all positive”. it is impractical and unnecessary to evaluate all the eigenvalues of a large power system because it is known that once the minimum eigenvalue becomes zero the system jacobian becomes singular and voltage instability occurs. so the eigenvalues of importance are the critical eigenvalues of the reduced jacobian matrix jr. an algorithm for calculating the minimum eigenvalue and the corresponding left and right eigenvectors has been developed in stewart and jennings (1981). identification of the weak load buses: certain eigenvalues, which lead to voltage instability, need to be monitored more closely. the appropriate definition and determination as to which load bus (load area) significantly participates in the selected modes become very important. this requires tools for identifying load buses that are significant in producing the selected modes. verghese et al (1982) has suggested a dimensionless measure of state variables or bus participation (henceforth-called participation factor). if φi and γi represent the rightand lefthand eigenvectors, respectively, for the eigenvalue λi of the matrix jr, then the participation factor measuring the participation of the k th bus in ith mode is defined as ikkikip γφ= (17) note that for all the small eigenvalues, bus participation factors determine the area close to voltage instability. q-v curves: the q-v curves are used in this voltage stability study since they directly assess shortage of reactive power. the q-v curves (reactive power-voltage curves) technique is a more general method of assessing voltage stability. these curves are presently the workhorse method of voltage stability assessment for many utilities. q-v curves show the sensitivity and variation of bus voltages with respect to the reactive power injection. a typical q-v curve is shown in figure 2(b). the q axis shows the reactive power that needs to be added or removed from a bus to maintain a given voltage at a given load. from (8) wadi adai (15) wadi al-kabir (16) al-falaj (21) musana (29) seeb main figure 3 . system voltage profile for the base case figure 2(b), it can be seen that the curve gives reactive power margin at the test bus. the reactive power margin is the mvar distance from the operating point to the most right point of the curve. this curve can be used as an index for voltage instability (dq/dv becomes negative). near the nose of the q-v curve, voltage stability analysis of muscat power system 41 sensitivities get very large and then reverse their sign. the jacobian matrix becomes singular at the nose of the curve. this is called a saddle bifurcation node (yokoyama and sekine, 1989). musana load area barka load area λ1= 2.948 bus number figure 4. participation factors of the most critical mode eigenvalue λ=2.948 for the base case. p-v curves: the power-curves (p-v) curves are the most widely used method of estimating voltage security, providing megawatt (mw) margin type indices. the p-v curve is used to determine the mw distance from the operating point to the critical voltage. a typical p-v curve is shown in figure 2(a). the pv curves are also useful for conceptual analysis when the load characteristics as a function of voltage are analyzed. while pv-curves are helpful in understanding the phenomena of voltage stability and collapse, they are not useful for determining the reactive power support needed at various points in a power system. the results the summer peak loads of the year 1998 are taken as a base case study for the existing muscat power system. the system is designed to serve the load demand at nominal voltage and all voltages are required to be within specific limits. the mva base value is taken equal to 100 mva. the voltage profile obtained from the power flow solution of the base case condition is shown in figure 3. rusail generation bus (bus 3) was taken as the slack bus. manah and ghubrah generation buses (buses 1, 2 and 24) were considered as p-v buses. all generating units are operating on their rated power. constant power loads represent the loads. from figure 3, it can be seen that the voltage of the heavy load buses, specifically musana load bus (bus 21) is not within the specified limit ± 10%. the low voltages of these heavy load buses are due to the induction motor loads (air conditioning). the modal analysis method was applied to identify the voltage collapse areas in muscat power system for the base case. the eigenvalues of the jacobian matrix jr for the base case were computed and all the eigenvalues are positive, indicating that the system is voltage stable for the base case. it was observed that all the eigenvalues are real. this observation agrees with the fact that voltage collapse is monotonic. the critical eigenvalues for the base case are shown in table 1. while not reported in this paper, the critical eigenvalues were compared with the minimum singular values (msvs) decomposition (löf et al, 1993) of the jacobian matrix jr and the results obtained agreed with each other. the msvs were computed using matlab. ellithy, gastli, al-alawi, al-hinai and al-abri 42 table 1: most critical eigenvalues eigenvalues λ base case bus 21 stressed bus 18 stressed 6.003 6.003 4.750 4.750 4.750 3.833 3.833 3.833 2.914 2.948 0.042 0.099 the bus participation factors corresponding to the most critical mode eigenvalue (λ=2.948) for the base case are shown in figure 4. the large participation factor value (0.5) indicates a high involvement of the bus to voltage collapse. the participation factors shown in figure 4 indicate that buses 19, 20, 21, 18, and 17 (key buses in south batna area) are the buses with the highest participation factors to the critical mode. these buses are the most critical in maintaining the voltage stability of the critical mode. musana load area barka load area λ1= 0.042 bus number figure 5. participation factors of critical mode eigenvalue λ1=0.042 for load demand increase at musana area from 65mvar-base (0.65 pu) up to 142.75mvar (1.4275 pu) the load buses 21 and 18 (musana and barka load buses) in south batna area were stressed with increased reactive power load respectively. the near-nose points computed with the stressed power-flow were then analyzed using modal analysis. the critical eigenvalues for the stressed case are listed in table 1. from table 1, it can be concluded that the power stress in south batna load area can lead to voltage instability (eigenvalue λ ≈ 0). figure 5 illustrates the participation factors of the most critical mode eigenvalue for all buses. it can be seen that the key buses of south batna load area have the largest participation factors, and hence is the area vulnerable to voltage collapse. the p-v curves and q-v curves were computed for the weakest load buses (buses 18 and bus 21) at the south batna area. the curves are shown in figures 6, 7 and 8. these curves are used to determine the mw and mvar-distance to voltage instability point (voltage stability margins) of the weakest load buses of voltage stability analysis of muscat power system 43 south batna area. their margins were determined between the maximum loading point and the base case loading. their margins are given in table 2. figure 6 . p-v curves for bus 21 figure 7. p-v curves for bus 18 ellithy, gastli, al-alawi, al-hinai and al-abri 44 table 2: mvar and mw margins of the weakest load buses the calculated mw and/or mvar margins indicate how close the current operating point of the system is to the voltage instability point i.e. how much active and/or reactive load can be added to the weakest load buses before the voltage instability occurs. the calculated mvar margins could relate to the size of shunt capacitors or static var compensators in the load areas (mansour et al, 1992; vaahedi et al, 1999). figure 8 . q-v curves for bus 21 & 18 conclusions a preliminary study of voltage stability for muscat power system was presented in this paper. the analysis is based on the summer peak loads conditions of the year 1998. the weak load areas, which could lead to voltage instability, were identified using the modal analysis technique. the system bus participation factors of the critical mode were used to determine the load area, which contributes to voltage instability. it was found that south batna area is the weakest load area in the system, which could lead to voltage collapse. the mwand mvar-distance from the operating condition to the voltage instability point (voltage stability margins) for the weakest load areas have been determined from the p-v curves and q-v curves. these margins are an essential tool for voltage stability and security assessment. the extension of the results of this research work to address the security assessment of the system voltage stability and the shunt compensations for system voltage support are the subject of a future work. bus number load bus name mvar base (p.u) mw base (p.u) mvar margin (p.u) mw margin (p.u) 21 musana 0.650 1.650 0.778 1.140 18 barka 0.250 1.000 2.330 3.900 voltage stability analysis of muscat power system 45 acknowledgment the authors acknowledge the support from the ministry of electricity & water and sultan qaboos university. the authors also wish to express their appreciation for the senior engineers of the ministry in the control center for their useful comments during the course of this project. references ajjarapu, v and lee, b. 1998. bibliography on voltage stability. ieee trans. on power systems, 13: 115-125. begovic, m.m. and phadke, a.g. 1992. control of voltage stability using sensitivity analysis. ieee trans. on power systems, 7: 114-123. cigre task force 38.02.10. 1993. modeling of voltage collapse inducing dynamic phenomena. cutsem, t. 1991. a method to compute reactive power margins with respect to voltage. ieee trans. on power systems, pwrs-6: 145-156. d’aquila, r., miller, n. w. jimma, k. m., shehan, m.t. and comegys, g.l. 1993. voltage stability of the puget sound system under abnormally cold weather conditions. ieee trans. on power systems, 8: 1133-1142. demacro, c. and overbye, t. 1990. energy based security measure for assessing vulnerability to voltage collapse. ieee trans. on power systems, 5: 419-427. el-keib, 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101: 3117-3134. yokoyama, a. and sekine, y. 1989. a static voltage stability index based on multiple load flow solutions. proc. of the bulk power system voltagephenomena stability and security, missouri. received 3 april 1999 accepted 21 january 2000 squ journal for science, 2017, 22(2), 106-113 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp106-113 sultan qaboos university 106 connected components of 𝓗𝒓,𝒈 𝑨 (𝑮) haval m. mohammed salih soran university, faculty of science, mathematics department-kawa st, soran, erbil, iraq. email: haval.mahammed@soran.edu.iq abstract: the hurwitz space ℋ𝑟,𝑔 𝐴 (𝐺) is the space of genus g covers of the riemann sphere ℙ1 with 𝑟 branch points and the monodromy group 𝐺. in this paper, we enumerate the connected components of the hurwitz spaces ℋ𝑟,𝑔 𝐴 (𝐺) for a finite primitive group 𝐺 of degree 7 and genus zero except 𝑆7. we achieve this with the aid of the computer algebra system gap and the mapclass package. keywords: monodromy groups; braid orbits; connected components. 𝓗𝒓,𝒈 𝑨 (𝑮) المكونات المتصلة ل محمد صالح م. افاله ℋr,gالفضاء الهوروتيزي :صالملخ a (g) هي نوع من غالف في الفضاء الريمانيℙ1 الزمرة المونودروميةمع نقاط تفرع و g. نحن في هذا البحث ℋr,gعددنا المكونات المترابطة لمجموعات البدائية ل a (g) عداوالجنس صفرى من الدرجة .s7 و أحرز هذا الغرض من خالل النظام الحاسوبي mapclassو حزمة gapالجبري المكونات المتصلة.و مدارات بريد، المنودروميةة زمر :مفتاحيةالكلمات ال 1. introduction et ω be a finite set and |ω| = 𝑛. define a genus 𝑔 system to be a triple (𝐺, ω, (𝑥1 , … , 𝑥𝑟 )). 𝐺 is a transitive subgroup of 𝑆𝑛 such that 𝐺 =< 𝑥1, … , 𝑥𝑟 >, 𝑥1 ∙ 𝑥2 ∙ … ∙ 𝑥𝑟 = 1 and 𝑥𝑖 ∈ 𝐺\{1} 2(𝑛 + 𝑔 − 1) = ∑ 𝑖𝑛𝑑𝑥𝑖 𝑟 𝑖=1 where indxi is the minimal number of transpositions need to express 𝑥𝑖 as a product [6]. this condition is equivalent to the existence of the branched covering 𝑓: 𝑋 → ℙ1 where ℙ1 = ℂ ∪ {∞} [8]. if 𝑓 is an irreducible, then 𝐺 is primitive. let 𝐶1, … , 𝐶𝑟 be non-trivial conjugacy classes of a finite group 𝐺. the set of generating systems (𝑥1, … , 𝑥𝑟 ) of 𝐺 with 𝑥1 … 𝑥𝑟 = 1 and such that there is a permutation 𝜋 ∈ 𝑆𝑟 with 𝑥𝑖 ∈ 𝑆𝜋(𝑖) for 𝑖 = 1, … , 𝑟 is called a nielsen class and denoted by 𝒩(𝐶), where 𝐶 = (𝐶1, … , 𝐶𝑟 ). each nielsen class is the disjoint union of braid orbits, which are defined as the smallest subsets of the nielsen class closed under the braid operations [10] (𝑥1, … , 𝑥𝑟 ) 𝑄𝑖 = (𝑥1, … , 𝑥𝑖+1, 𝑥𝑖+1 −1 𝑥𝑖 𝑥𝑖+1, … , 𝑥𝑟 ) (1) for 𝑖 = 1, … , 𝑟. we denote by 𝑂𝑟 , the space of subsets of ℂ of cardinality 𝑟. the following definitions can be found in [10]. l mailto:haval.mahammed@soran.edu.iq connected components of ℋ𝑟,𝑔 𝐴 (𝐺) 107 definition 1.1 let 𝐵 ∈ 𝑂𝑟 and 𝑏0 ∈ ℙ 1 ∖ 𝐵, we call a map 𝜑: 𝜋1(ℙ 1 ∖ 𝐵, 𝑏0) → 𝐺 admissible if it is a surjective homomorphsim, and 𝜑(𝜃𝑏 ) ≠ 1 for each 𝑏 ∈ 𝐵. here 𝜃𝑏 is the conjugacy class of 𝜋1(ℙ 1 ∖ 𝐵, 𝑏0). definition 1.2. let 𝐵 ∈ 𝑂𝑟 and 𝜑: 𝜋1(ℙ 1 ∖ 𝐵, ∞) → 𝐺 be admissible. then we say that two pairs (𝐵, 𝜑) and (b̅, φ̅) are aequivalent if and only if b = b̅ and φ̅ = a ∘ φ for some a ∈ a. let [𝐵, 𝜑]𝐴 denote the 𝐴-equivalence class of (𝐵, 𝜑). the set of equivalence classes [𝐵, 𝜑]𝐴 is denoted by ℋ𝑟 𝐴(𝐺) and is called the hurwitz space of 𝐺-covers. here we enumerate the connected components of ℋ𝑟 𝐴 (𝐺) and then we show to which number of branch points 𝑟, it is connected. the mapclass package of james, magaard, shpectorov and volklein, is designed to perform braid orbit computations for a given finite group and given type. 2. preliminary as usual 𝐼𝑛𝑛(𝐺) and 𝐴𝑢𝑡(𝐺) denote the inner-automorphism and automorphism groups of a group 𝐺 respectively. a denotes a subgroup of 𝐴𝑢𝑡(𝐺). in particular if 𝐴 = 𝐼𝑛𝑛(𝐺), then the hurwitz space ℋ𝑟 𝐴 (𝐺) is denoted by ℋ𝑟 𝑖𝑛 (𝐺).the details of the following results and concepts can be found in [10] and [8]. lemma 2.1. the map ψ𝐴 : ℋ𝑟 𝐴 (𝐺) → 𝑂𝑟, ψ𝐴([𝐵, 𝜑]) = 𝐵 is covering. the fiber ψa −1(b0) = {[b0, φ]a: φ: π1(ℙ 1 ∖ b, ∞) → 𝐺 is admissible}. this φ gives a product one generating tuple (x1, … , xr) of g. define ℰr(g) = {(𝑥1, … , 𝑥𝑟 ): 𝐺 = 〈𝑥1, … , 𝑥𝑟 〉, 𝑥1 ∙ … ∙ 𝑥𝑟 = 1, 𝑥𝑖 ∈ 𝐺 #, 𝑖 = 1,2, … , 𝑟}. let a ≤ aut(g). then the subgroup a acts on ℰr(g) via sending (x1, … , xr) to (a(x1), … , a(xr)), for a ∈ a. let ℰ𝑟 𝐴 (𝐺) = ℰ𝑟 (𝐺)/𝐴 be the set of 𝐴-orbits. in particular, if 𝐴 = 𝐼𝑛𝑛(𝐺), then we have 𝐼𝑛𝑛(𝐺) = 𝐺/𝑍(𝐺). therefore ℰ𝑟 𝑖𝑛 (𝐺) is the set of 𝐺-orbits. lemma 2.2. we obtain a bijection ψ𝐴 −1(𝐵0) → ℰ𝑟 𝐴 (𝐺) by sending [𝐵0, 𝜑]𝐴 to the generators (𝑥1, … , 𝑥𝑟 ) where 𝑥𝑖 = 𝜑([𝛾𝑖 ]) for 𝑖 = 1, … , 𝑟. proposition 2.3. let c be a fixed ramifcation type in g, and the subset ℋr in(c) of ℋr in(g) consists of all [b, ∅]a with b = {b1, … , br}, ∅: π1(ℙ 1\b, ∞) → g and ∅(θbi ) ∈ ci for i = 1, … , r. then ℋr a(c) is a union of connected components in ℋr a(g). under the bijection from lemma 2.2, the fiber in ℋr a(c) over b0 corresponds the set 𝒩 a (c). this yields a one to one correspondence between components of ℋr a (c) and the braid orbits on 𝒩 a (c). in particular, ℋr in(c) is connected if and only if bracts transitively on 𝒩 in(c) = 𝒩(c) . lemma 2.4. let 𝐺 be a group and 𝑋 be a 𝐺-set. then 𝐺 acts transitively on 𝑋 if and only if there is only one orbit. proof. straightforward. corollary 2.5. let c be a fixed ramifcation type in 𝐺, and the subset ℋr in(c) of ℋr in(g) consists of all [b, ∅]a with b = {b1, … , br}, ∅: π1(ℙ 1\b, ∞) → 𝐺 and ∅(θbi ) ∈ ci for i = 1, … , r. then ℋr a(c) is a union of connected components in ℋr a(𝐺). under the bijection from lemma 2.2, the fiber in ℋr a(c) over b0 corresponds the set 𝒩 a (c). this yields a one to one correspondence between components of ℋr a (c) and the braid orbits on 𝒩 a (c). in particular, ℋr in(c) is connected if and only if there is only one braid orbit. proof. it follows from proposition 2.3 and lemma 2.4. 3. computing indices and labeling conjugacy classes the classifications of all the primitive groups of degree 7 except s7 for genus zero are given in this paper. before, we discuss computing the indices, we give an alternative formula to compute an index of an element in a group. let g be a group acting on a finite set ω and |ω| = n. if 𝑥 ∈ 𝐺, define the index of 𝑥 by 𝑖𝑛𝑑 𝑥 = 𝑛 − 𝑜𝑟𝑏 𝑥, where orb x is the number of orbits of < 𝑥 > on ω. also fix 𝑥={𝑤 ∈ 𝛺 | 𝑥𝑤 = 𝑤}, 𝑓(𝑥) = |𝐹𝑖𝑥 𝑥|. furthermore, 𝑜𝑟𝑏 𝑥 = 1 𝑑 ∑ 𝑓(𝑥 𝑖 )𝑑−1𝑖=0 where 𝑥 has order 𝑑 [6]. from the character table of a7, we see the elements of orders 2,3,4,5,6 and 7, then we compute fixed points, which are equal to 1a+2a of the elements of given orders. haval m. mohammed salih 108 the character table of 𝐴7. alternating group 𝐴7 order =2520=23. 32. 5.7 mult =6 out = 2 constructions alternating 𝑆7 ≅ 𝐺. 2 ∶ all permutations of 7 letters; 𝐴7 ≅ 𝐺 ∶ the even permutations; 2. 𝐺 and 2. 𝐺. 2 ∶ the schur double covers lattice 2𝐴7 ≅ 2. 𝐺 ∶ the symmetries of the lattice ⋀4,𝑏7 whose minimal vectors are obtained from ±(𝑖7; 0,0,0) ± (0; 𝑖7,0,0) ± (1; , 𝑥, 𝑦, 𝑧) ± (−𝑥; 1, 𝑦, −𝑧) ± (−𝑥𝑦; ,1,1,1) ± (1; 𝑥𝑦, 1,1) ± (𝑥𝑦; 0, 𝑧, 1) ±(−𝑥; 𝑦𝑧, 0,1) ± (−1; 0, 𝑥𝑦, 𝑧) ± (0; 1, −𝑥, 𝑦𝑧) by replacing each of 𝑥, 𝑦, 𝑧 by one of 𝑏7 or 𝑏7 ∗∗, and cyclically permuting the last 3 coordinates vectors 3𝐴7 ∶ symmetries of the 21 (𝑤) vectors obtained from (200 00 00), (00 11 11), (01 01 𝑤�̅�) by bodiy permuting the 3 couples, and reversing any 2 couples (see 𝐴6 (hexacode)); the lattice these generate has auomorphism group 6𝑈4(3). 2 (see 𝑈4(3)) unitary 3𝐴7 has a 3-dimensional unitary representation over 𝐹25 (see 𝑈3(5)) presentations 𝐺 ≅< 𝐴, 𝐵| 𝐴4 = 𝐵5 = (𝐴𝐵)3 = (𝐴−1𝐵𝐴2𝐵2)2 = 1 >≅< 𝑥1, … , 𝑥5|𝑥𝑖 3 = (𝑥𝑖 𝑥𝑗 ) 2 = 1 >; 𝐺 ≅< 𝐴, 𝐵| 𝐴2 = [𝐴, 𝐵2]2 = [𝐴, 𝐵3]2 = 1; 𝐵7 = (𝐴𝐵)6 > maximal subgroups specifications order index structure 𝐺. 2 character abstract alternating 360 7 𝐴6 : 𝑆6 1𝑎 + 2𝑎 𝑁(2𝐴, 3𝐴, 3𝐵, 4𝐴, 5𝐴) point 168 15 𝐿2(7) 7: 6 1𝑎 + 14𝑏 𝑁(2𝐴, 3𝐵, 4𝐴, 7𝐴𝐵) 𝑆(2,3,7) 168 15 𝐿2(7) 7: 6 1𝑎 + 14𝑏 𝑁(2𝐴, 3𝐵, 4𝐴, 7𝐴𝐵) 𝑆(2,3,7) 120 21 𝑆5 : 𝑆5 × 2 1𝑎 + 6𝑎 + 14𝑎 𝑁(2𝐴, 3𝐴, 5𝐴), 𝐶(2𝐵) dual 72 35 (𝐴4 × 3): 2 : 𝑆4 × 𝑆3 1𝑎 + 6𝑎 + 14𝑎𝑏 𝑁(3𝐴), 𝑁(2𝐴 2) triad connected components of ℋ𝑟,𝑔 𝐴 (𝐺) 109 ; @ @ @ @ @ @ @ @ @ : : @ @ @ @ @ @ @ 𝑝 𝑝′ ind 2520 power part 1a 24 a a 2a 36 a a 3a 9 a a 3b 4 a a 4a 5 a a 5a 12 aa aa 6a 7 a a 7a 7 a a 𝐵∗∗ fus ind 120 a a 2b 24 a a 2c 12 a a 4b 6 ab ab 6b 3 bc bc 6c 5 ab ab 10a 6 ab ab 12a 𝒳1 + 1 1 1 1 1 1 1 1 1 : ++ 1 1 1 1 1 1 1 𝒳2 + 6 2 3 0 0 1 -1 -1 -1 : ++ 4 0 2 1 0 -1 -1 𝒳3 o 10 -2 1 1 0 0 1 𝑏7 ** + 0 0 0 0 0 0 0 𝒳4 o 10 -2 1 1 0 0 1 ** 𝑏7 𝒳5 + 14 2 2 -1 0 -1 2 0 0 : ++ 6 2 0 0 -1 1 0 𝒳6 + 14 2 -1 2 0 -1 -1 0 0 : ++ 4 0 -2 1 0 -1 1 𝒳7 + 15 -1 3 0 -1 0 -1 1 1 : ++ 5 -3 1 -1 0 0 1 𝒳8 + 21 1 -3 0 -1 1 1 0 0 : ++ 1 -3 -1 1 0 1 -1 𝒳9 + 35 -1 -1 -1 1 0 -1 0 0 : ++ 5 1 -1 -1 1 0 -1 if 𝑥 is an element of order 2, then 𝑖𝑛𝑑 𝑥 = 𝑛 − 1 2 ∑ 𝑓(𝑥 𝑖 ) = 𝑛 − 1 2 [𝑓(𝑥 0) + 𝑓(𝑥)] = 7 − 1 2 [7 + 3] = 21𝑖=0 . if 𝑥 is an element of order 3 of type 3𝐴, then 𝑖𝑛𝑑 𝑥 = 𝑛 − 1 3 ∑ 𝑓(𝑥 𝑖) = 𝑛 − 1 3 [𝑓(𝑥 0) + 𝑓(𝑥) + 𝑓(𝑥 2)] = 7 − 1 3 [7 + 4 + 4] = 22𝑖=0 . if 𝑥 is an element of order 3 of type 3𝐵, then 𝑖𝑛𝑑 𝑥 = 𝑛 − 1 3 ∑ 𝑓(𝑥 𝑖) = 𝑛 − 1 3 [𝑓(𝑥 0) + 𝑓(𝑥) + 𝑓(𝑥 2)] = 7 − 1 3 [7 + 1 + 1] = 42𝑖=0 . if 𝑥 is an element of order 4, then 𝑖𝑛𝑑 𝑥 = 𝑛 − 1 4 ∑ 𝑓(𝑥 𝑖 ) = 𝑛 − 1 4 [𝑓(𝑥 0) + 𝑓(𝑥) + 𝑓(𝑥 2) + 𝑓(𝑥 3)] = 7 − 1 4 [7 + 1 + 3 + 1] = 43𝑖=0 . if 𝑥 is an element of order 5, then 𝑖𝑛𝑑 𝑥 = 𝑛 − 1 5 ∑ 𝑓(𝑥 𝑖 ) = 𝑛 − 1 5 [𝑓(𝑥 0) + 𝑓(𝑥) + 𝑓(𝑥 2) + 𝑓(𝑥 4)] = 7 − 1 5 [7 + 2 + 2 + 2 + 2] = 44𝑖=0 . if 𝑥 is an element of order 6, then 𝑖𝑛𝑑 𝑥 = 𝑛 − 1 6 ∑ 𝑓(𝑥 𝑖) = 𝑛 − 1 6 [𝑓(𝑥 0) + 𝑓(𝑥) + 𝑓(𝑥 2) + 𝑓(𝑥 4) + 𝑓(𝑥 5)] = 7 − 1 6 [7 + 0 + 4 + 3 + 4 + 0] = 45𝑖=0 . if 𝑥 is an element of order 7 of type 7𝐴 or 7𝐵, then 𝑖𝑛𝑑 𝑥 = 𝑛 − 1 7 ∑ 𝑓(𝑥 𝑖 ) = 𝑛 − 1 7 [𝑓(𝑥 0) + 𝑓(𝑥) + 𝑓(𝑥 2) + 𝑓(𝑥 4) + 𝑓(𝑥 5) + 𝑓(𝑥 6)] = 7 − 1 7 [7 + 0 + 0 + 0 + 0 +6𝑖=0 0 + 0] = 6. 4. algorithm and main results to obtain tables 2 and 3, we need to perform the following steps: 1we extract all primitive permutation groups 𝐺 by using the gap function [4] allprimitivegroups (degreeoperation,𝑛). 2for given degree, genus and 𝐺 we compute all possible ramification types satisfying the riemann-hurwitz formula which is given in section 3. 3we compute the character table of 𝐺 and remove those types which have zero structure constant. 4we obtain all generating types by gap codes which exist in appendix c [8]. 5for each of the remaining generating types of length greater than or equal to 4, we use the mapclass package to compute braid orbits. for tuples of length 3, we determine braid orbits via double cosets in [8]. we now give our main results as follows: lemma 4.1. the hurwitz spaces, ℋ𝑟 𝑖𝑛 (𝐶) are connected if 𝐺 = 𝐷(2 ∗ 7) or 𝐺 = 𝐴𝐺𝐿(1,7). proof. it follows from the fact that the nielsen classes 𝒩(𝐶) are the disjoint union of braid orbits but we have only one braid orbit for 𝑟 ≥ 3 and 𝑛 = 7. from corollary 2.5, we obtain the hurwitz spaces ℋ𝑟 𝑖𝑛 (𝐶) are connected. lemma 4.2. the hurwitz spaces, ℋ𝑟 𝑖𝑛 (𝐶) are connected if 𝑟 ≥ 4 and 𝐺 = 𝐿(3,2). proof. it follows from the fact that the nielsen classes 𝒩(𝐶) are the disjoint union of braid orbits but we have only one braid orbit for 𝑟 ≥ 4 and 𝑛 = 7. from corollary 2.5, we obtain the hurwitz spaces ℋ𝑟 𝑖𝑛 (𝐶) are connected. lemma 4.3. the hurwitz spaces, ℋ𝑟 𝑖𝑛 (𝐶) are disconnected if 𝐺 = 𝐴7 and 𝐺 = 𝐶7. proof. it follows from the fact that the nielsen classes 𝒩(𝐶) are the disjoint union of braid orbits but for these groups we have at least two braid orbits for some type 𝐶 as given in table 2. from corollary 2.5, we obtain the hurwitz spaces ℋ𝑟 𝑖𝑛 (𝐶) are disconnected. haval m. mohammed salih 110 finally, we enumerate the connected components of ℋ𝑟 𝑖𝑛 (𝐺) in the cases where 𝑔 = 0 and 𝐺 is a primitive group of degree 7. the total numbers of connected components of ℋ𝑟 𝑖𝑛 (𝐺) is summarized in table 1. table 1. primitive genus zero systems: number of components. degree # group iso types #rts # comp’s r=3 # comp’s r=4 # comp’s r=5 # comp’s r=6 # comp’s total 7 5 154 179 61 67 10 317 example 4.4 first of all, read the file in gap program which exists in [8] and then choose the group and the specific tuple. for instance let 𝐺 = 𝐷(2 ∗ 7) be the dihedral group and take the tuple 𝑡 = [(2,5)(3,6)(4,7), (2,5)(3,6)(4,7), (2,5)(3,6)(4,7), (2,5)(3,6)(4,7)] . the run of the program which finds the braid orbits is shown below: gap> read("qu1.g"); --------------------------------------------------------------- loading mapclass 1.2 by adam james (http://www.mat.bham.ac.uk/~jamesa) kay magaard (http://mat.bham.ac.uk/staff/magaardk.shtml) sergey shpectorov (http://web.mat.bham.ac.uk/s.shpectorov/index.html) helmut volklein (http://www.iem.uni-due.de/algebra/people/voelklein.html) for help, type: ?mapclass: --------------------------------------------------------------- gap> ll:=allprimitivegroups(degreeoperation,7); [ c(7), d(2*7), 7:3, agl(1, 7), l(3, 2), a(7), s(7) ] gap> k:=ll[2]; d(2*7) gap> checkingthegroup(k); gap> gt:=generatingtype(k,7,0); checking the ramification type 10 with 0 remaining [ [ 2, 2, 5 ], [ 2, 2, 4 ], [ 2, 2, 3 ], [ 2, 2, 2, 2 ] ] gap> t:=list(gt[4],x->cc[x]); [ (2,5)(3,6)(4,7), (2,5)(3,6)(4,7), (2,5)(3,6)(4,7), (2,5)(3,6)(4,7) ] gap> orb:=generatingmcorbits(k,0,t);; the current date is: mon 07/10/2017 enter the new date: (mm-dd-yy) total number of tuples: 336 collecting 20 generating tuples .. done cleaning done; 20 random tuples remaining orbit1: length=24 generating tuple =[ (1,4)(3,5)(6,7), (1,6)(2,3)(5,7), (1,7)(2,6)(3,4), (1,3)(2,4)(5,6) ] centralizer size=1 0 tuples remaining cleaning a list of 20 tuples random tuples remaining: 0 cleaning done; 0 random tuples remaining computation complete: 1 orbits found. http://mat.bham.ac.uk/staff/magaardk.shtml connected components of ℋ𝑟,𝑔 𝐴 (𝐺) 111 table 2. primitive groups of degree 7. group ramification type # of orbits length of largest orbit ramification type # of orbits length of largest orbit 𝐴7 (5𝐴, 5𝐴, 5𝐴) 2 1 (4𝐴, 5𝐴, 5𝐴) 8 1 (4𝐴, 4𝐴, 5𝐴) 22 1 (4𝐴, 4𝐴, 4𝐴) 24 1 (3𝐵, 5𝐴, 5𝐴) 6 1 (3𝐵, 4𝐴, 5𝐴) 10 1 (3𝐵, 4𝐴, 4𝐴) 8 1 (3𝐵, 3𝐵, 5𝐴) 2 1 (5𝐴, 5𝐴, 6𝐴) 8 1 (4𝐴, 5𝐴, 6𝐴) 8 1 (4𝐴, 4𝐴, 6𝐴) 12 1 (3𝐵, 5𝐴, 6𝐴) 6 1 (3𝐵, 4𝐴, 6𝐴) 6 1 (3𝐵, 3𝐵, 6𝐴) 2 1 (6𝐴, 6𝐴, 6𝐴) 2 1 (3𝐵, 6𝐴, 6𝐴) 2 1 (4𝐴, 6𝐴, 6𝐴) 4 1 (5𝐴, 6𝐴, 6𝐴) 2 1 (3𝐴, 5𝐴, 7𝐴) 1 1 (3𝐴, 5𝐴, 7𝐵) 1 1 (3𝐴, 4𝐴, 7𝐴) 2 1 (3𝐴, 5𝐴, 7𝐵) 2 1 (3𝐴, 3𝐵, 7𝐴) 1 1 (3𝐴, 3𝐵, 7𝐵) 1 1 (3𝐴, 6𝐴, 7𝐴) 1 1 (3𝐴, 6𝐴, 7𝐵) 1 1 (2𝐴, 5𝐴, 7𝐴) 2 1 (2𝐴, 5𝐴, 7𝐵) 2 1 (2𝐴, 4𝐴, 7𝐴) 2 1 (2𝐴, 4𝐴, 7𝐵) 2 1 (2𝐴, 6𝐴, 7𝐴) 2 1 (2𝐴, 6𝐴, 7𝐵) 2 1 (3𝐴, 3𝐴, 5𝐴, 5𝐴) 1 30 (3𝐴, 3𝐴, 4𝐴, 5𝐴) 2 40 (3𝐴, 3𝐴, 4𝐴, 4𝐴) 2 92 (3𝐴, 3𝐴, 3𝐵, 5𝐴) 1 40 (3𝐴, 3𝐴, 3𝐵, 4𝐴) 2 44 (3𝐴, 3𝐴, 3𝐵, 3𝐵) 1 26 (3𝐴, 3𝐴, 6𝐴, 5𝐴) 1 60 (3𝐴, 3𝐴, 6𝐴, 4𝐴) 1 72 (3𝐴, 3𝐴, 3𝐵, 6𝐴) 1 40 (3𝐴, 3𝐴, 6𝐴, 6𝐴) 1 22 (3𝐴, 3𝐴, 3𝐴, 7𝐴) 1 7 (3𝐴, 3𝐴, 3𝐴, 7𝐵) 1 7 (2𝐴, 3𝐴, 5𝐴, 5𝐴) 1 80 (2𝐴, 3𝐴, 4𝐴, 5𝐴) 1 170 (2𝐴, 3𝐴, 4𝐴, 4𝐴) 1 300 (2𝐴, 3𝐴, 3𝐵, 5𝐴) 1 90 (2𝐴, 3𝐴, 3𝐵, 4𝐴) 1 126 (2𝐴, 3𝐴, 3𝐵, 3𝐵) 1 62 (2𝐴, 3𝐴, 6𝐴, 5𝐴) 1 80 (2𝐴, 3𝐴, 4𝐴, 6𝐴) 1 118 (2𝐴, 3𝐴, 3𝐵, 6𝐴) 1 62 (2𝐴, 3𝐴, 6𝐴, 6𝐴) 1 44 (2𝐴, 3𝐴, 3𝐴, 7𝐴) 1 14 (2𝐴, 3𝐴, 6𝐴, 7𝐵) 1 14 (2𝐴, 2𝐴, 5𝐴, 5𝐴) 3 70 (2𝐴, 2𝐴, 4𝐴, 5𝐴) 3 120 (2𝐴, 2𝐴, 4𝐴, 4𝐴) 3 168 (2𝐴, 2𝐴, 3𝐵, 5𝐴) 1 150 (2𝐴, 2𝐴, 3𝐵, 4𝐴) 1 192 (2𝐴, 2𝐴, 3𝐵, 3𝐵) 1 44 (2𝐴, 2𝐴, 6𝐴, 5𝐴) 3 60 (2𝐴, 2𝐴, 6𝐴, 4𝐴) 3 76 (2𝐴, 2𝐴, 3𝐵, 6𝐴) 1 90 (2𝐴, 2𝐴, 6𝐴, 6𝐴) 3 36 (2𝐴, 2𝐴, 3𝐴, 7𝐴) 1 28 (2𝐴, 2𝐴, 3𝐴, 7𝐵) 1 28 (2𝐴, 2𝐴, 2𝐴, 7𝐴) 2 21 (2𝐴, 2𝐴, 2𝐴, 7𝐵) 2 21 (2𝐴, 2𝐶, 3𝐴, 3𝐴, 4𝐴) 1 168 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 6𝐴) 1 300 (2𝐴, 2𝐶, 3𝐴, 3𝐴, 2𝐵) 1 42 (2𝐴, 3𝐴, 3𝐴, 3𝐴, 4𝐴) 1 96 (2𝐴, 3𝐴, 3𝐴, 3𝐴, 6𝐴) 1 216 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 2𝐵) 1 44 (2𝐴, 2𝐶, 2𝐶, 3𝐴, 4𝐴) 1 240 (2𝐴, 2𝐶, 2𝐶, 3𝐴, 6𝐴) 1 384 (2𝐴, 2𝐶, 2𝐶, 2𝐶, 3𝐴) 1 57 (2𝐴, 2𝐶, 2𝐶, 2𝐶, 4𝐴) 1 312 (2𝐴, 2𝐶, 2𝐶, 2𝐶, 6𝐴) 1 486 (2𝐴, 2𝐶, 2𝐶, 2𝐶, 2𝐵) 1 60 (2𝐴, 2𝐴, 3𝐴, 4𝐴, 4𝐴) 1 89 (2𝐴, 2𝐴, 3𝐴, 4𝐴, 6𝐴) 1 202 (2𝐴, 2𝐴, 3𝐴, 6𝐴, 6𝐴) 1 336 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 5𝐴) 1 75 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 4𝐴) 1 80 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 3𝐵) 1 39 (2𝐴, 2𝐴, 2𝐵, 3𝐴, 4𝐴) 1 36 (2𝐴, 2𝐴, 2𝐵, 3𝐴, 6𝐴) 1 52 (2𝐴, 2𝐴, 2𝐶, 4𝐴, 4𝐴) 1 158 (2𝐴, 2𝐴, 2𝐶, 4𝐴, 6𝐴) 1 273 (2𝐴, 2𝐴, 2𝐶, 6𝐴, 6𝐴) 1 426 (2𝐴, 2𝐴, 2𝐶, 3𝐴, 5𝐴) 1 125 (2𝐴, 2𝐴, 2𝐶, 3𝐴, 4𝐴) 1 100 (2𝐴, 2𝐴, 2𝐶, 3𝐴, 3𝐵) 1 48 (2𝐴, 2𝐴, 2𝐶, 2𝐵, 4𝐴) 1 40 (2𝐴, 2𝐴, 2𝐵, 2𝐶, 6𝐴) 1 60 haval m. mohammed salih 112 (2𝐴, 2𝐴, 2𝐶, 2𝐶, 5𝐴) 1 175 (2𝐴, 2𝐴, 2𝐶, 2𝐶, 4𝐴) 1 128 (2𝐴, 2𝐴, 2𝐶, 2𝐶, 3𝐵) 1 54 (2𝐴, 2𝐴, 2𝐴, 4𝐴, 5𝐴) 1 75 (2𝐴, 2𝐴, 2𝐴, 4𝐴, 5𝐴) 1 72 (2𝐴, 2𝐴, 2𝐴, 4𝐴, 4𝐴) 1 36 (3𝐴, 3𝐴, 3𝐴, 3𝐴, 5𝐴) 1 300 (3𝐴, 3𝐴, 3𝐴, 3𝐴, 4𝐴) 2 384 (3𝐴, 3𝐴, 3𝐴, 3𝐴, 3𝐵) 1 312 (3𝐴, 3𝐴, 3𝐴, 3𝐴, 6𝐴) 1 480 (2𝐴, 3𝐴, 3𝐴, 3𝐴, 5𝐴) 1 750 (2𝐴, 3𝐴, 3𝐴, 3𝐴, 4𝐴) 1 1392 (2𝐴, 3𝐴, 3𝐴, 3𝐴, 3𝐵) 1 744 (2𝐴, 3𝐴, 3𝐴, 3𝐴, 6𝐴) 1 690 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 5𝐴) 1 1550 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 4𝐴) 1 2704 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 3𝐵) 1 1234 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 6𝐴) 1 1112 (2𝐴, 2𝐴, 2𝐴, 3𝐴, 5𝐴) 1 3000 (2𝐴, 2𝐴, 2𝐴, 3𝐴, 4𝐴) 1 4584 (2𝐴, 2𝐴, 2𝐴, 3𝐴, 3𝐵) 1 2214 (2𝐴, 2𝐴, 2𝐴, 3𝐴, 5𝐴) 1 1896 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 5𝐴) 3 1800 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 4𝐴) 3 2880 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 3𝐵) 1 3240 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 6𝐴) 3 1080 (2𝐴, 2𝐴, 3𝐴, 3𝐴, 3𝐴, 3𝐴) 1 13764 (2𝐴, 3𝐴, 3𝐴, 3𝐴, 3𝐴, 3𝐴) 1 7280 (3𝐴, 3𝐴, 3𝐴, 3𝐴, 3𝐴, 3𝐴) 1 2870 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 3𝐴, 3𝐴) 1 45692 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 2𝐴, 3𝐴) 1 79560 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 2𝐴, 2𝐴) 3 45360 (2𝐴, 2𝐴, 2𝐴, 3𝐴, 3𝐴, 3𝐴) 1 26210 table 3. primitive groups of degree 7. group ramification type # of orbits length of largest orbit ramification type # of orbits length of largest orbit 𝐴𝐺𝐿(1,7) (2𝐴, 3𝐵, 6𝐵) 1 1 (2𝐴, 3𝐴, 6𝐴) 1 1 𝐿(3,2) (3𝐴, 3𝐴, 4𝐴) 4 1 (3𝐴, 4𝐴, 4𝐴) 2 1 (4𝐴, 4𝐴, 4𝐴) 4 1 (2𝐴, 3𝐴, 7𝐵) 1 1 (2𝐴, 3𝐴, 7𝐴) 1 1 (2𝐴, 4𝐴, 7𝐵) 1 1 (2𝐴, 4𝐴, 7𝐴) 1 1 (2𝐴, 2𝐴, 3𝐴, 3𝐴) 1 30 (2𝐴, 2𝐴, 3𝐴, 4𝐴) 1 24 (2𝐴, 2𝐴, 4𝐴, 4𝐴) 1 24 (2𝐴, 2𝐴, 2𝐴, 7𝐴) 1 1 (2𝐴, 2𝐴, 2𝐴, 7𝐵) 1 7 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 3𝐴) 1 216 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 4𝐴) 1 192 (2𝐴, 2𝐴, 2𝐴, 2𝐴, 2𝐴) 1 1680 𝐷(2 ∗ 7) (2𝐴, 2𝐴, 7𝐴) 1 1 (2𝐴, 2𝐴, 7𝐵) 1 1 (2𝐴, 2𝐴, 7𝐶) 1 1 (2𝐴, 2𝐴, 2𝐴, 2𝐴) 1 24 𝐶7: 𝐶3 (3𝐵, 3𝐵, 3𝐵) 2 1 (3𝐴, 3𝐴, 3𝐴) 2 1 5. conclusion in this paper, we use the algorithm in [8] to compute braid orbits on nielsen class. an application of the algorithm is the classification of the primitive genus zero systems of degree 7. that is we find the connected components ℋ𝑟 𝑖𝑛 (𝐺) of 𝐺-curves 𝑋, such that 𝑔 = 0. in our situation, the computation shows that there are exactly 307 braid orbits of primitive genus 0 systems of degree 7. references 1. michael, d.f. and helmut, v. the inverse galois problem and rational points on moduli spaces. mathematische annalen, 1991, 290(4), 771-800. 2. daniel, f., robert, g. and kay, m. genus 0 actions of groups of lie rank 1. american mathematical society, providence, rhode island, proceedings of symposia in pure mathematics, 2002,70, 449-483. 3. daniel, f. and kay, m. composition factors of monodromy groups. annals of mathematics. second series. 2001, 154(2), 327-345. 4. the gap group. gap-groups, algorithms, and programming, version 4.6.2, 2013. http://www.gap-system.org 5. wang, g. genus zero systems for primitive groups of affine type. 2011. ph.d thesis university of birmingham, uk. 6. robert, m.g. and john, g.t. finite groups of genus zero. journal of algebra, 1990, 131(1), 303-341. 7. magaard, k., shpectorov, s. and wang, g. generating sets of affine groups of low genus. in computational algebraic and analytic geometry, american mathematical society, providence, rhode island, 2012, 572, 173-192. connected components of ℋ𝑟,𝑔 𝐴 (𝐺) 113 8. haval, m.s. finite groups of small genus. 2014. ph.d thesis university of birmingham, uk. 9. michael, g.n. on solvable monodromy groups of fixed genus. pro-quest llc, ann arbor, michigan, 1989. ph.d thesis university of southern california, usa. 10. helmut, v. groups as galois groups an introduction, volume 53, cambridge studies in advanced mathematics. cambridge university press, cambridge, 1996. received 20 february 2017 accepted 10 september 2017 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 221-229 © 2002 sultan qaboos university deregulation of electricity supply industry in oman hamed s. al-maghderi* and bruce ramsay** *ministry of housing electricity and water,oman,**university of dundee, uk. تحرير مصادر انتاج الطاقة الكهربائية في عمان حمد المغدري وبروس رمسي تدرس الفرص المتاحة والشروط الواجبة لتحرير مصادر إنتاج الطاقة الكهربائية مع اإلشارة المحددة إلى هذه الورقة : خالصة المناقشة تركز . وتبرز القضايا العامة للوائح المطلوبة لتشجيع المنافسة في مجال مصادر إنتاج الطاقة الكهربائية . سلطنة عمان .عات في إعادة تشكيل وخصخصة مصادر إنتاج الطاقة الكهربائية في عمانعلى الطرق المقررة في مجال الخصخصة والتوق abstract: this paper examines the opportunities available and the conditions needed for the deregulation of the electricity supply industry (esi), with particular reference to the sultanate of oman. the paper highlights the general issues of regulation required to encourage competition in the esi. after that, the discussion focuses on regulation methods in the privatized esi by describing the regulators control through price caps setting for regulatees, the conduct regulation process, the rate of return regulation setting, and the spot market (the pool) contract. finally, the prospects of restructuring and privatizing the esi in the sultanate of oman are examined by reviewing the current structure of the industry and government objectives in deregulation of the electricity sector as well as the regulation framework. keywords: electricity deregulation; competition. 1. introduction a round the world, electricity supply industries (esi) are proceeding with a wide rapid deregulatory reform of their structure and rules. many of the esi are currently in transition from a vertically integrated monopoly, to a more open and competitive market. of the three primary components of the esi (generation, transmission, and distribution) vertically integrated monopoly, generation is the forefront of transformation and deregulation. deregulation has the effect of decreasing government intervention in the sector, which tends to encourage a free market economy. the first consideration of an esi after privatization is to determine the type of electricity trading arrangements required for meeting consumer requirement in a competitive and efficient manner. such arrangement must consider prices, continuity, quality, and quantity of supply. regulators, prior to privatization, have three objectives in controlling the esi, namely control of the tariff, conduct and performance. these objectives will change if the esi is to be subjected to the rigours of the open market. the advent of competition and the need to protect customer rights gives rest to the government's pressing reasons to establish appropriate new esi regulations. the regulatory role is instrumental in opening up the esi markets to investment, by removing the government restrictions on the pricing and quality of the supply and encouraging new entries at different stages of the process. the regulatory effect has made a deep impact on the privatized power sector, which can be seen throughout the power industry as follows (beesley, 1998): 221 hamed s. al-maghderi and bruce ramsay 1. generationrules introduced to allow unrestricted competition have separated generation from the other sector parts and an attempt has been made to establish competitive markets. 2. transmissionexisting networks naturally remain as natural monopolies due to the vast difficulties in building new network grids. however the regulator controls access to the grid, allowing common carriage by third parties and regulates the prices for this service. 3. distributionthe network is regulated as natural monopoly and does not permit the construction of other networks in order to avoid duplication of the existing network, but the rules have opened the network to common usage with regulated charges. one of the earlier deregulations of esi was completed in chile in 1986 (yajima, 1997) and then england and wales followed the footsteps of chile. thereafter, many countries followed the reformation conducted in the chile and the uk, including the sultanate of oman. to understand the deregulation of the esi in the sultanate of oman, we have to establish the objectives and constraints that the government imposes. the government's main objective is an effective and efficient industry structure, with a deregulation framework to balance two sets of objectives. the first is the protection of the long-term public interest, whereas the second concerns the need to ensure that, so far as is practicable, the esi in the sultanate of oman is an attractive investment opportunity for international investors. the government also wishes to promote competition within the esi in order to reduce the operation costs and to increase the efficiency. to achieve this, the regulatory framework must strike a balance between providing the government with sufficient control and flexibility to implement changes in policy in order to secure the long-term protection of the interests of the cosumers, and providing an attractive investment climate for international investors to give them the confidence to invest in the esi. the esi in the sultanate of oman is currently undergoing restructuring and changing to private sector, which requires a significant change in the regulations in order to meet the requirements of private sector regulations. considering all the above circumstances, to what extent does the sultanate of oman esi require deregulation? do the present rules currently implemented need to be change? the paper will propose answers to these questions. 2. general issues of regulation the decision to privatize the esi introduces the need for changing the regulation to take the new structure and try to regulate within this externally determined structure. the regulation implemented in the public sector is not an option for any country serious about encouraging private investment in its esi. private investment requires a new model of regulation that is limited in scope and transparent. therefore, privatization puts the regulators in the position of having powerful and immediate impact on the evaluation of the electrical industries, and also has an ongoing role to preview the procedure of the industry's revaluation. 3. requirement of regulation in the esi one of the main criteria of privatization is to reduce the regulation in the esi, and encourage the competition. this is achieved in most parts of the sector, but some functions, those regarded as natural monopoly operation, require being under regulation. this is appearing in naturally monopolistic functions (transmission and distribution networks). the needs to monitor and control monopoly in the transmission, distribution, and system control are very essential because the probability of exploitation of lack of alternative power sources for the customer is very high. a natural monopolist will take into account his own cost situation together with demand conditions 222 degregulation of electricity supply industry in oman when setting output prices. he will charge a price higher than the efficient price level, which is a profit beyond compensation for the cost of capital (economic rent). this is will be directly reflected in the retail price which may cause a social and political impact. however, the coexistence of competitive supply and monopolistic activities (owner of the network) in the deregulated esi, gives the regulator a dual role in monitoring both these parts and in overseeing the vital access for competitors to the network. although his job will be more difficult if the monopolist owns the network and tries to restrict competition, in such cases regulators’ options in providing regulatory framework for this industry can be introduced by defining the objectives for the regulation. in the uk, professor stephen littlechild first regulator of the uk esi set out objectives for regulation. he suggested five objectives for regulation: • protection against monopoly, efficiency and innovation encouragement, • low cost of implementation, • promotion of competition, • maximization of proceeds from sales and enhancement of the utilities’ commercial prospects (littlechid, 2000). the economic description for the regulation objectives is that a regulator should maximize the weighted sum of customers' surplus and suppliers' profit. the relation of these two components in the regulator’s objective function affects the increment weight of customer surplus by decreasing the price. to explain this relation, suppose the weights are equal, so that allocated efficiency (relation of price to appropriate costs) is achieved by marginal cost pricing. if the revenue is insufficient to cover the total costs of the company, price should be increased above marginal cost for the demand, which is least responsive to such price increment. similarly, if the company declares high profits, the regulator's intention could be very considerable to control the profit margin in line with the regulation objectives. 4. regulation of monopoly in the esi greater efficiency of the privatized esi can be achieved by regulation promoting competition and controlling monopoly. the power of monopoly can be reduced, and breaking up cartels or reducing the size of the esi firms could increase that efficiency and competition. in recent years, however, technical progress has been increasing too rapidly to allow most monopolies to remain immune from potential competition. this is most obvious when there are alternatives to monopoly network, as in combined cycle gas turbines (ccgt) and combine heat and power (chp) are reversing some of the advantages of scale in electricity generation. in both these cases it may eventually prove cheaper for large consumers to bypass the natural monopolist’s transmission and distribution system. there is no strong economic argument for profit control in the esi with a high rate of technical innovation as long as there is free entry and the interconnection as regulated predatory behaviour can be controlled effectively. there is no restriction on price discrimination and it is sufficiently and technically feasible for the enterprise to get near enough to the economic efficiency implied by competitive output levels for any remaining inefficiencies to be of less cost than the probable costs to the customers of regulation. 5. regulation in the privatized esi regulatory policy is designed to meet the objectives of privatization and the public interest. policy creators recognize this in many aspects, though in practice the focus has been almost exclusively on efficiency. this is reflected in the design of the regulatory framework for deregulated utilities in many countries, for example the uk and the usa. the regulatory regimes 223 hamed s. al-maghderi and bruce ramsay have been effective in promoting and protecting the interests of customers and preventing the earning of excess profits through the exploitation of market power by the esi utilities. different regulatory methods are used in regulating the esi after privatization; the following explains some of them: 5.1 price cap regulation price cap regulation imposes a restraint on the rate of increase of prices with the now famous rpi x formula introduced by professor littlechild (helm, 1995). the formula allows the electricity company to increase its rates on regulated services from a base level by the change in the retail price index (rpi), reduced by the expected rate of increase of productivity x in the esi. the main target in this regulatory concept is the price, which comes closer to reflecting the underlying aim of customer protection. rpi-x is based on capping prices rather than profits, which pushes the company to achieve productivity with efficiency, and allows the company itself to control price reductions. regulatory intervention will be low because it only requires the calculation of the price indices with no need to measure the assets value or rates of return for the company. the only requirement from the company is to be sure that the average value of price increments in one year does not exceed the percentage increases in the rpi-x. for this reason price cap regulation produces incentives to improve the efficiency, because the utility carries full responsibility for its costs once the price cap has been set. customers benefit from efficiency improvements in two respects, because a price control can be set to reflect both the efficiency improvements shown during the previous price control period as being actually achievable, and the further efficiency improvements that might be reasonably expected over the duration of a new price control. in addition rpi x price control regulation was designed to be predictable, allowing electricity companies to plan several years in advance on the basis of four or five year periodic reviews. at each periodic price control review, consideration is given to the form of the price control, in particular whether rpi-x or some other form of price control such as a sliding scale or a profit control is the most appropriate for the regulation of the companies. a sliding scale control might specify that if profits move outside specified limits, prices would have to be adjusted downwards or upwards, for example to share between customers and shareholders the consequences of unexpected movements in costs. under a profit control system prices might be adjusted annually in the light of actual expenditure, including a specified profit rate of return. 6. conduct regulation conduct regulation, mainly used in the usa (tenebaum et al, 1992) concentrates on the direct administration of the operation and investment of the regulated utility. it takes on two principle forms. the first one is called green regulation that is usually described as the integrated resource planning (irp) and allows the regulator to be more involved in the companies planning and selection process. this is placed under the belief that the electric utility always produces the wrong product. irp process argues that the utility should be to produce energy services not just electricity. the method of the irp process indicates that electricity is under priced because electricity utilities and their customers do not see the full environmental costs of operating a generating plant. irp said that the utilities have little incentive to offer demand side services, which would lead to a reduction in their overall profits. the second conductive regulation is the introduction of competition in many different ways. for example, the regulator gives detailed guidelines on how to introduce competition in the new requirements for generating capacity. once the generating capacity is completed, there will be another regulatory review for the company's purchase decision made under the guidelines of the competition. 7. rate of return regulation rate of return regulation is the most commonly used form of the esi regulations in the united states, and has been in use for decades (tenebaum et al, 1992). its aim is to reduce the power of 224 degregulation of electricity supply industry in oman natural monopolies (transmission and distribution) to restrain output, raise prices, and realize supra normal profits. rate-of-return regulation is also called cost-of-service regulation in that it essentially allows electricity companies to pass through those costs which are deemed necessary by the supervising regulatory body to ensure that an adequate level of service is provided to end users of the electricity. rate-of-return regulation has both advantages and disadvantages. rate-of-return regulation allows representation of the public in matters regarding electricity company price setting, rates of return, and investment so that the company cannot restrain supply and realize monopoly profits. also rate-ofreturn regulation offers utilities few financial incentives to aggressively restrain or reduce operating costs. the disadvantages of rate-of-return regulation can be summarised by that saying detailed industry data is deemed an excessively expensive effort that will require a large bureaucratic structure. further, information the regulator obtained from the regulated industry was always incomplete, relative to the information possessed by the industry, leaving the regulator in an inferior negotiating position relative to that of the industry. 8. spot market (the pool) the spot market in the electricity industry can be defined as the immediate delivery of energy with prices depending on the supply availability and the overall volume of demand. it can be considered as a set of bilateral deals, and negotiation for selling power between the generator and buyer to the customers. the spot market is judged by settlement rules and definitions which can be summarised as follows: in ideal conditions each generator generates exactly the amount of power needed for the demand connected. however, this is impossible due to the difficulty in operating plants on this basis because customers’ demand could rise or fall faster than the generator is able to alter its output (e.g. with an on/off appliance). it is also impossible because of a generator breakdown that would need to be covered immediately in order to keep the electricity supply constant without any interruptions. due to the reasons above there will always be a difference between the contract amount and generation production, which continuously produces an imbalance of power and should be settled. for these reasons the arrangement of selling, purchasing electricity, and last minute transactions limit traders in making their own purchase and sales, as they need dispatchers and market operator (mo) to settle every deal, or solid market terms to avoid any conflicts that may arise (hunt and shuttleworth, 1999). the mo directs the electricity spot market so that all sellers receive their money and fulfil their contracts if the amount of power agreed for delivery is delivered completely, and all buyers pay for the uncontracted off-take if the consumption exceeds their contracts. among regulation methods, spot market in the electricity generates large customers with access either directly or through traders. the electricity pool supports competition in supply, where customers can choose their supplier. the electricity pool mechanism enables competition in generation, in order of which generation plant should be used, and permits all prospective suppliers to purchase in the wholesale market on the same basis. 9. deregulation of the esi in oman in oman, the esi is vertically integrated as directed by the ministry of housing, electricity and water (mhew). the process of privatisation for the esi in oman is designed to introduce competition by completely privatizing all the electricity industry with the exception of rural areas, which will remain in public hands. the new reform of the industry recognises five functions: generation, transmission and system control, distribution and supply. the esi will be unbundled to different companies with new 225 hamed s. al-maghderi and bruce ramsay regulatory framework aims to promote competition and ensure that the remaining monopolies do not exploit the advantages of privatization. 10. current structure of oman esi the esi in the sultanate of oman is currently owned and operated by the government, through the ministry of housing electricity and water (mhew). the ministry operates as a vertically integrated utility. it is responsible for: 1. determination of national electricity and desalinated water policy. 2. planning and studies required for the electricity and drinking water in the country. 3. ownership and operation of all generation, desalination, transmission, distribution and supply of electricity to customers, except manah power project and the forth coming al-kamil power project. 4. self-regulation i.e. setting specification for the materials used in the electricity industry and regulation of the tariff of energy consumption. mhew is separated into directorates general for both water and electricity to meet the above responsibilities. the unbundling process will be mainly in the directorate general of electricity, which is responsible for several organisation departments providing a very wide range of control for the esi in oman. 11. new structure for the esi in oman in order to develop a structure and create strong success of privatization where investors will be attracted to invest in the electrical power industry, the omani government demonstrates and establishes an absolute commitment to the proposed privatization process. the government policy for privatization is to limit the existing power assets within mhew to the following companies working under the law of industry. 1. three generation companies 2. three distribution companies 3. transmission company with function of operating the new dispatch centres. 4. power procurer, as a single buyer of electricity from the generators. 5. remote systems company, responsible for the esi in villages and on islands. also the establishment of regulator with well-defined rules and principles is very essential for privatizing the esi. the regulator must be capable of regulating the new structure of the esi to maintain the system in competitive mode, and there by encourage investment in the electricity sector in the country. 12. oman objectives from privatization many countries worldwide are considering privatization or the restructuring of their electrical energy industries. the main reasons are to increase efficiency and competition in order to have more choices for the economy and customers. oman is one of these countries tending to privatize their electrical industry, seeking to broaden the economy by establishing new industries. the following objectives are what the omani government will achieve from the privatization of the electrical power sector (mne, 1999): 1. security of electricity supply to the customers, which is a primary concern for the government. privatization must improve over time with less investment in installation of new generation, transmission and distribution capacity. 226 degregulation of electricity supply industry in oman 2. withdrawal of the subsidies from the power sector; this is one of the main objectives of the government in the long term. privatisation will improve that by introducing competition into the sector. 3. fuel efficiency; until now the sultanate uses open cycle power generation turbines in most of the power generation stations. with new off-takers being attracted and reserves not inexhaustible, the government needs to reconsider the value of gas and to make decisions on the efficient usage of fuel. 13. privatization recommended for oman esi when considering the optimum privatisation technique for the sultanate of oman esi, there are two important factors which need to be taken into account (mne, 1999): a. the size of the esi is very limited and has a fragmented structure, with many parts of the networks not being interconnected. the ministry of housing electricity, and water (mhew) is currently trying to improve the situation by increasing investment in the transmission system. b. the government’s objective of retaining a significant shareholding when the esi is finally floated on the muscat securities market (msm). from experience of other countries like the uk, it is clear that the most significant investor interest is likely to be in generation and consequently this should be the initial priority for the government to privatise. a successful programme of privatisation of the generation assets will create a solid foundation for the privatisation of the transmission and distribution networks. due to the lack of a fully interconnected and secure transmission system, it should be recognised that urgent and extensive investment is required in the system in order to create the necessary infrastructure of an efficient privatised power system. 14. conclusion deregulation of the electricity supply industry (esi) has gained popularity in several countries around the world. this is due to the desire to minimize political interference in the operation and management of the utilities, and the availability of a soft budget for the industry. the need for competition and greater economic efficiency has accelerated the process further. therefore, deregulation has become an important issue towards improving the esi performance, and achieving the above objectives. once a country decides to deregulate its esi it has to consider carefully some important issues so that deregulation can take place successfully. these include: 1. the establishment of a regulatory framework with strong political backing and regular public information. 2. transparency and clarity. 3. gradual restructures to prepare the esi for deregulation. 4. promotion of private sector participation. along with the esi restructuring, a powerful regulator must be established to oversee the procedures set in place for the industry's re-evaluation. in addition, where competition may be not completely achieved (i.e. transmission, distribution), the monopolistic situation has to be regulated. 227 hamed s. al-maghderi and bruce ramsay the esi restructuring will only succeed when reformers consider both the industry and the way it is regulated. the regulation scheme for the esi must provide incentives for efficiency in operation, pricing and investment. thus, the choice of a regulation schemebe it a price-cap, rate-of-return, or conduct regulation, depends on what kind of effect the regulation on the regulated industry is to achieve. a balance must be maintained between satisfying the interest of shareholders, customers and government. the participation of the private sector in infrastructure development like the esi leads to an improvement services to the customers, through an efficient and economic process, thus minimizing demands on government resources. this provides an encouragement for the deregulation program in oman, which is moving towards greater competition and private sector participation in its own esi. in view of the rapid growth of the omani esi and the forecasted increase in energy demands, deregulation of the esi is the only way to alleviate any problems. the following recommendations are hereby proposed for a successful restructuring of the omani esi: 1. establishment of an independent regulator with well-defined rules and principles prior to any unbundling or privatization process. 2. unbundling of the esi by splitting it into three generations companies, five distribution companies according to the existing regions of oman (muscat, batinah, dakhliyah, dahirah, and sharqiyah), one transmission and dispatch company to operate the connected esi independently and one power purchase company as a single buyer for the electricity in the sultanate. the remote systems in villages and islands should be unbundled and vertically integrated under one company. this is should be held for about three to five years to create incentive improvement in the esi efficiency by new management and reduce central management from the head office. 3. open competition between the distribution companies, through given rights to the customers above 1000kva of load to subscribe to any of the distribution companies that he feels will supply efficient energy to his residence, factory…etc. this will introduce competition between the distribution companies to improve their distribution electrical networks and to work in a more efficient way, which will reflect directly in reduction of losses. therefore the government subsidies will decrease. 4. privatization as a follow-up to deregulation if the government is still interested in privatization of the esi after restructuring, it should be implemented only on the generation for a start. other parts of the esi could be privatized later in stages as a joint venture with investors has technical capability to improve the efficiency and reduce the losses in the esi networks. this is due to the limited size of the esi, where it is difficult to achieve any competition, and the heavy subsidies in the system that the government will face a problem in eliminating in the short term. in addition, there were also agreements signed by the government with several ipps (united power company in manah, al-kamil power company in alsharqiyah, and barka project currently under negotiation). hence, open competition will not be possible in the near future. references beesley, m., 1998. regulating utilities: understanding the issues london business school in association with the institute of economic affairs (iea), reading. helm, d., 1995. british utility regulation oxford university press. 228 degregulation of electricity supply industry in oman hunt, s., shuttleworth, g., 1999. competition and choice in electricity, england: john wiley & sons. littlechid, s., 2000. privatisation competition and regulation. the institute of economic affairs, london. oman. mne. 1999. privatisation study. ministry of national economics, oman. tenenbaum, b., lock, r. and barker, j. 1992. electricity privatisation, structural, competition and regulatory options. energy policy, december 1992, pp.1134 -1160. yajima, m., deregulatory reforms of the electricity supply 1997. quorum books. received 12 june 2001 accepted 9 february 2002 229 deregulation of electricity supply industry in oman hamed s. al-maghderi* and bruce ramsay** *ministry of housing electricity and water,oman,**university of dundee, uk. êíñíñ ãõçïñ çäêçì çáøçþé çáßåñèç� general issues of regulation regulation in the privatized esi price cap regulation price cap regulation imposes a restraint on the rate of increase of prices with the now famous rpi x formula introduced by professor littlechild (helm, 1995). the formula allows the electricity company to increase its rates on regulated services from the main target in this regulatory concept is the price, which comes closer to reflecting the underlying aim of customer protection. rpi-x is based on capping prices rather than profits, which pushes the company to achieve productivity with efficiency, a for this reason price cap regulation produces incentives to improve the efficiency, because the utility carries full responsibility for its costs once the price cap has been set. customers benefit from efficiency improvements in two respects, because a p at each periodic price control review, consideration is given to the form of the price control, in particular whether rpi-x or some other form of price control such as a sliding scale or a profit control is the most appropriate for the regulation of the 6. conduct regulation 7. rate of return regulation 8. spot market (the pool) 9. deregulation of the esi in oman 12. oman objectives from privatization 13. privatization recommended for oman esi when considering the optimum privatisation technique for the sultanate of oman esi, there are two important factors which need to be taken into account (mne, 1999): references squ journal for science, 2018, 23(1), 19-31 doi: http://dx.doi.org/10.24200/squjs.vol23iss1pp19-31 sultan qaboos university 19 numerical simulations of a delay model for immune system-tumor interaction mohamed a. hajji* and qasem al-mdallal department of mathematical sciences, college of science, uae university, p.o. box 15551, al ain, uae. *email: mahajji@uaeu.ac.ae abstract: in this paper we consider a system of delay differential equations as a model for the dynamics of tumor immune system interaction. we carry out a stability analysis of the proposed model. in particular, we show that the system can have up to two steady states: the tumor free steady state, which always exist, and the tumor persistent steady state, which exists only when the relative rate of increase of the tumor cells exceeds the ratio between the natural proliferation rate and the relative death rate of the effector cells. we also determine an upper bound for the delay, such that stability is preserved. numerical simulations of the system under different parameter values are performed. keywords: delay differential equations, asymptotic stability, numerical simulations. باستخدام المعادالت التفاضلية التأخيريةلسرطاني ل نظام المناعة والورم االمحاكاة العددية لنموذج تفاع قاسم المدللو *حاجيعلي محمد ي. ونقوم نفترض في هذا البحث جملة من المعادالت التفاضلية التأخيرية كنموذج لديناميكيات نظام التفاعل بين األورام السرطانية والجهاز المناع :صالملخ نبين بشكل خاص امكانية احتواء النظام على حالتين ثابتتين: الحالة المستقرة الخالية من الورم، وهي موجودة دائًما، بتحليل استقرار النموذج المقترح. كما ي ومعدل الوفيات والحالة المستقرة للورم المستمر، والموجودة فقط عند تجاوز المعدل النسبي لزيادة الخاليا الورمية النسبية بين معدل االنتشار الطبيع .نعين أيضا الحد األعلى للتأخير مع المحافظة على االستقرار. وتم إجراء محاكاة عددية للنظام بتحديد قيم متنوعة للمعاملو للخاليا المستجيبه. النسبي .، محاكاة عدديةاالستقرار قاربمعادالت التفاضلية التأخيرية، ت :مفتاحيةالكلمات ال 1. introduction he immune system (is) is a very complex one. it is composed of a complex network of different cells which operate collectively by communicating information through signalling. the duty of these cells is to keep our system natural, i.e., free of foreign entities. when a foreign entity enters our system, particular immune system cells raise an alarm and send signals through the network to other immune system cells calling for an attack on the foreign entity. once the foreign substance is located and identified as non-self, the immune system plans an attack strategy. among the most deadly foreign entities are cancer cells. cancer cells are difficult to deal with because of their ability to multiply so fast that the is cannot keep up. another property of cancer cells is that they are able to camouflage the antigens (the substance that triggers the is) such that the is cannot recognise them as foreign cells. once cancer cells are identified as foreign, the is starts an attack to destroy them. the interactions between tumour cells and the immune system are very complex and require sophisticated models to describe them. mathematical models, based on ordinary differential equations, delay differential equations or partial differential equations, have proven to be useful tools in analysing and understanding the is-tumor interactions. several mathematical models have been suggested to describe the interactions between tumour and immune system [1-9]. t m.a. hajji and q. al-mdallal 20 many of these papers consider the tumor-is interaction with other factors such as treatment. in this paper, we consider a mathematical model of is-tumor interactions based on a system of delay differential equations. the delay is introduced to reflect the non-instantaneous outcome of the interaction between the immune system cells and the tumor cells. we carry out a stability analysis of the system and we simulate the system under different parameter values to explore the different asymptotic behaviors. many models that have appeared in the literature are based of the well-known kuznetsov and taylor model [1] which we describe in the next section. 2. kuznetsov and taylor model the kuznetsov and taylor mathematical model to describe the tumor-immune system interaction is based on the following: 1. the growth of tumor cells population t (in the absence of the immune system cells) follows a logistic model: (1)= (1 ), tot dt at bt dt  where a is the maximum growth rate, 1 b is the carrying capacity of the biological environment for the tumor cells, and tott is the total population of unhit t cells, ctttot = . 2. the rate of production of the immune system cells e (the effector cells), has two sources: (i) a constant normal production rate s (in the absence of the tumor cells) and (ii) a production rate caused by the presence of tumor cells. the magnitude of the second production rate is a function, ),( tcf , of the current concentrations of c and t , where c is the concentration of the complex te  . the immune system cells e die out at a rate 1 d . 3. the interaction between the effector cells e and the tumor cells t forming the complexes tec  is described by the following kinetic figure 1. interaction kinetics between e and t cells. where the c complex is formed at rate of 1 k and breaks at three different rates: 1 k giving e and t unaltered, 2 k given e (unaltered) and t d , and 3k giving ed and t (unaltered), where td and ed are altered t and e cells which are bound to die. kuznetsov and taylor’s complete model is given by the following set of differential equations 1 1 1 2 1 1 3 1 1 2 3 3 2 2 3 (2) = ( , ) ( ) , = (1 ) ( ) , = ( ) , = , = , tot e e t t de s f c t d e k et k k c dt dt at bt k et k k c dt dc k et k k k c dt dd k c d d dt dd k c d d dt                  where, again, e , t , c , e d , t d are the concentrations at the tumor site of the immune system cells (effector cells), the tumor cells, the effector-tumor cells complex, the inactived effector cells, and the inactived tumor cells, respectively. the above model was simplified based on the fact that the te  bond, which is formed at a rate of 1 k , lasts a relatively short period of time [10] and disassociates giving rise to e and t (no win situation) with a rate 1 k , numerical simulations of a delay model 21 or e d and t (tumor wins) with a rate 3k , or td amd e ( e wins) with a rate 2k , see figure 1. the inactivated effector cells e d and inactivated tumor cells t d are bound to die with rates 2 d and 3d , respectively. in [1], it was claimed that c is approximately constant, that is 0 dt dc , hence ketc  , with )/(= 3211 kkkkk   . in addition, tott was approximated by tttot  , and ),(),( teftcf  . these assumptions reduce the above system (2) to the following is-tumor interaction model, in non-dimensional form, (3) = ( , ) , = (1 ) , de s f e t met de dt dt at bt net dt      where the parameters 3= kkm , 2= kkn , and 1= dd . the function ),( tef describes the rate at which cytotoxic effector cells accumulate around the region where the t cells are localized. based on kuznetsov and taylor’s model, many researchers have derived other models by considering different forms for the function ),( tef and/or by adding additional considerations (see [3]-[8], and references therein). in [1], the authors analyzed model (3) with a holling type ii form for f . in non-dimensionl variables, their model takes the form (4) = , = (1 ) . dx xy xy x dt y dy y y xy dt              later, in [6], the authors considered kuznetsov and taylor’s model (3) with holling type i response function kettef =),( , with and without delay, where the delay was introduced to reflect the delay in the response of the immune system before proliferating effector cells. in this work, we consider (3) with a holling type i response function kettef =),( with delay introduced in both equations as described in the next section. 3. a delay model as in [6], we consider ),( tef of holling type i, but we consider the delay  according to the following biologically possible scenario. we assume that there is delay in both the proliferation of effector cells and in the disposal of tumor cells. in dimensionless form, the model we consider is (5) ( ) = ( ) ( ) , ( ) = (1 ) ( ) ( ), x t wx t y t x y t y y x t y t                   where )(tx and )(ty are the nondimensional density at the tumor site of the effector cells and of the tumor cells, respectively. all parameters in (5) are nonnegative real numbers and are approximated (see [1] and [6]) by: 3 (6) = 0.1181, = 0.04, = 0.3743, = 1.636, = 2.0 10 . w      the delay factor in model (5) models the natural delays in both the proliferation of effector cells and in the disposal of tumor cells. this is biologically meaningful as the is takes time to react and migrate effector cells to the tumor site. also, in the second equation of model (5), it models the delay in completely eradicating the tumor cells as they will not die immediately upon interacting with effector cells. our aim in studying the above model (5) is to investigate the effect, if any, of the time delay,  , in the disposal of the tumor cells. we carry out the stability analysis of the equilibrium states of the model (5) and determine necessary conditions for the local asymptotic stability. also, we determine an upper bound for the delay parameter  such that stability is preserved. numerical simulations of the model are performed to investigate the asymptotic behavior of the system. 4. steady states the steady states, ),( yx , of (5) are the solutions of the nonlinear homogeneous system m.a. hajji and q. al-mdallal 22 (7) = 0, (1 ) = 0. wxy x y y xy         from the second equation of (7) we have either 0=y or )(1= yx   . if 0=y , then from the first equation of (7) we have /=x , giving the tumor free steady state ,0)/(=0 e . if 0y , then )(1= yx   and from the first equation of (7) we have the quadratic equation for y : 0=)( 2   ywyw whose discriminant  is 0.>4)(= 22 ww   then depending on the parameter values, there may exist up to two more steady states ),( 111 yxe and ),( 222 yxe , where 1 1 (8) ( ) ( ) = , = 2 2 w w x y w w             2 2 (9) ( ) ( ) = , = 2 2 w w x y w w             the existence of 1 e and 2 e as biologically meaningful (i.e., with positive coordinates) depends on the parameters. if, as assumed, all parameters are positive, then it is clear that 0< 2 x because |)(>| w  . so 2 e does not exist as biologically meaningful. as for 1 e , since |)(>| w  , we have 0> 1 x . it remains to check when 0> 1 y . calculations reveal that 0> 1 y if and only if  </ . therefore, if  /< , we have only the tumor free steady state ,0)/(=0 e and if  </ , we have two steady states ,0)/(=0 e and ),(= 111 yxe , where 1 x and 1 y are given by (8). the value / relative to  is very important as it determines how many steady states the system can asymptotically assume. the value / measures the rate of increase of the density of the effector cells and  measures the rate of increase of the tumor cells. thus if  >)/( , this biologically means that the effector cells will take over the tumor cells, which as a result, are bound to die in the long run. on the other hand, if  <)/( , the tumor cells will always exist. now, we turn to the stability analysis of the steady states 0e and 1e . 5. stability analysis we know that a steady state is locally asymptotically stable if all the eigenvalues of the jacobian matrix of the system at the steady state have negative real parts. before we continue, we recall an important stability criterion known the mikhailov criterion [9]: mikhailov criterion: let ( )p s and ( )q s be two polynomials with deg( p )= n and deg(q ) < n . if the quasi-polynomial ( ) = ( ) ( ) s r s p s q s e   has no roots on the imaginary axis, then all roots of ( )r s have negative real parts if and only if the argument of ( )r js , = 1j  , increases by / 2n  as s . for the system (5) under consideration, the jacobian matrix at a steady state ),( yx is given by (10)= . 2 wye wxe j ye y xe                     the characteristic polynomial is (11)( ) = ( ) ( ) ,w p q e       where 2 (11)( ) = ( ) , = 2 ,p a a a y          (12)( ) = ( ) ( ).q x wya x wy     numerical simulations of a delay model 23 stability of the tumor-free steady state 0e for the steady state ,0)/(=0 e , the characteristic polynomial reduces to (13)( ) = ( )( / ).w e             we have the following proposition. proposition 1 (i) if  /> , then 0e is an unstable saddle point. (ii) if  /< , then there exists a 0>0 such that 0e is locally asymptotically stable for )[0, 0  and unstable for 0> where 1 0 2 2 2 (14) ( / )cos = . /         proof. from (14), we see that one eigenvalue is 0<=   . next, we need to analyze the roots of the quasipolynomial (15)( ) = / .r e          it is clear that if  /> , )(r in (5.7) has a positive root, since the functions  =)(f and    eg /=)( satisfy  /=(0)>=(0) gf and )(f and 0)( g , as  . this proves (i). for (ii), assume that  /< . according the mikhailov criterion, if )(r has no imaginary roots, then all its roots have negative real parts if and only if   /2.=))(( = 0=  s s jsrarg let js= ,   rs , 1= j . then (16) becomes (16)( ) = [ / cos( )] [ / sin( )].r js s j s s          let ))((= jsrarg . then as s , we have and (17)cos( ) 0 sin( ) 1.   this implies that /2=))((lim jsrarg s  . we have 0>/=(0)  r (for  /< ) and 0=(0))(rarg . thus   /2,=))(( = 0=  s s jsrarg which implies, according the mikhailov criterion, that all roots of )(r have negative real parts, provided that )(r has no imaginary roots. now let us see under what condition )(r has imaginary roots. if 0=)( jsr for some   rs , then (18)/ cos( ) = 0,s    (19)/ sin( ) = 0.s s   squaring and adding (19) and (20) gives ./=/= 2222222   ss conversely, if 222 0 /==  ss , the first value of  , say 0 , that satisfies both (19) and (20) is 1 1 0 2 2 2 0 (20) 1 ( / )cos = ( / ) = .cos /s            this implies that for 0< , )(r has no imaginary roots, and 0e is locally asymptotically stable. this completes the proof of proposition 1. □ stability of the steady state ),(= 111 yxe for ),(= 111 yxe , from equations (11)-(13), the characteristic polynomial takes the form (21)( ) = ( ) ( ) ,w p q e       m.a. hajji and q. al-mdallal 24 where 2 0 1 1 (22)( ) = ( ) , ( ) = ( ) ( ),p a a q c a x wy             where .=,2= 1101 awyxacya   before we proceed, we state and prove the following lemma about the positivity of 0c , which will be used later. lemma 2 0>== 1110  yawyxac  . proof. from the expression of   1 2= ya and )(1= 11 yx   , we can write a as 11 = xya  . substituting this into 0c , we get )].([= 1110 xywyc   now, from the expressions of 1 x and 1 y (eq. (8)), we have .= 2 )( 2 )( = 11 ww w w w xy       it follows that 0.>=)]([= 11110  yxywyc  we have the following proposition for the stability of 1 e . □ proposition 3. assume that ac 2>0 . the steady state ),(= 111 yxe is locally asymptotically stable, for )[0, 0   , where 0 is given by (24). proof. let   rsjs,= . we have (23)( ) = ( ) ( ) = ( ) ( ) js w js p js q js e x s jy s    where 2 1 1 1 1 (24)( ) = ( ) ( ) cos( ) ( ) sin( ),x s s a x wy a s s x wy s         1 1 1 1 (25)( ) = ( ) ( ) cos( ) ( ) sin( ).y s s a s x wy s x wy a s        if ))((= jswarg , it can be easily verified that (26) ( ) ( ) cos( ) = 1, sin( ) = 0. | ( ) | | ( ) |w w x s y s w j w j         this implies that =))((lim jswarg s  . for 0=s , we have 1 1 0 (27)(0) = = > 0,w x wy a a c   which implies that 0=(0))(warg . hence,   =))(( =0= s s jswarg , and 1 e would be locally asymptotically stable, provided that )(w has no roots on the imaginary axis. now, we check for pure imaginary roots of )(w . if there exists   rs such that 0=)( jsw , then 0=)(=)( sysx , or 2 11 12 (28)cos( ) sin( ) = ( ),a s sa s s a    12 11 (29)cos( ) sin( ) = ( ),sa s a s s a     where .=,= 11121111 wyxaawyxa  squaring both sides of (29) and (30) and adding, we get 4 2 1 2 (30)= 0,s a s a  where )2(=)(=,= 00 2 11 2 2 2 12 22 1 accaaaaaa   the solutions of (31) are formally written as numerical simulations of a delay model 25 2 1 1 22 (31) 4 = . 2 a a a s    it is clear that a sufficient condition for the right hand side of (32) to be positive is 0< 2 a , i.e., ac 2>0 , since 0> 0 c . in this case, the positive solution of (32) is 2 1 1 2 0 (32) 4 = 2 a a a s    therefore, if ac 2>0 , then )(w has only two pure imaginary roots 0js , where 0s is given by (33). with 0s as in (33), the first positive value of  such that 0=)(sx and 0=)(sy is 2 1 11 12 0 11 0 2 2 2 0 11 0 12 (33) ( ( ))1 = .cos a a a s a a s a s a             therefore, if ac 2>0 , then for 0< , )(w has no imaginary roots, and 1e is locally asymptotically stable. □ 6. numerical simulations in this section, we perform a number of numerical simulations to reveal the dynamics of system (5). we consider the two cases (i)  /< where only 0e exists, and (ii)  /> where both 0e and 1e exist. case 1: for the case  /< , we simulate the system with the values of 0.1= and 0.3= . the other parameters are fixed as in (6). in this case, the only equilibrium state is 0 = ( / , 0) = (0.315522, 0)e   which was proved to be asymptotically stable up to an upper bound for the delay  (see proposition 1 and eq. (21)). the calculated upper bounds according to (21) are 0 = 4.17134 and 0 = 3.22237 for = 0.1 and 0.3 , respectively. we remark that these upper bounds are valid only when the solutions ( )x t and ( )y t remain non-negative. in fact, simulations reveal that the solutions become negative for much smaller values of  , 0.05  . the outcomes of the simulations for this case are displayed in figures 2, 4, and 5. in figure 2, we display the phase portraits of system (5) for = 0.1 and = 0.3 and = 0 and = 0.05 , each with 5 differential initial conditions. they all confirm the stability of 0e , as the solutions )(tx and )(ty asymptotically tend to 0e . in figures 4 and 5, the solutions of system (5) are displayed with = 0.1 and = 0.3 , respectively, each with = 0.05 . both figures confirm the convergence of the solutions to the steady state 0 e . it is important to mention that for > 0.05 , under certain initial conditions, the solutions become negative at some time * t at which the system becomes biologically invalid. case 2: for the case  /> , we fix all parameters as in (6) and simulate the system with different delay values  . in this case, we have two steady states, 0 = ( / , 0) = (0.315522, 0)e   which is unstable and .52522)(1.61138,7=),(= 111 yxe which was proven to be locally asymptotically stable for up to 0< . from eq. (34), 0 is calculated to be 0 = 0.0880838 . to confirm these results, we simulated the system for = 0, 0.01, 0.05, 0.08, 0.09 and various initial conditions. the results are displayed in figures 6 and 7, where figure 6 displays the phase portraits for = 0, 0.01, 0.05, 0.08, 0.09 and figure 7 displays the solutions of the system for = 0.05, 0.08, 0.09 and initial condition (0) = 1, (0) = 30x y . it is to be noted that for 0 = 0, 0.01, 0.05, 0.08 <  , the solutions converge to 1 e , confirming the local asymptotic stability of 1 e . however, in the case 0 = 0.9 >  , we notice the formation of the closed orbit around 1 e . this also can be seen in the rightmost plot in figure 7, where the effector and tumor cells oscillate around 1 e . this confirms the existence of a bifurcation with respect to the parameter  as it crosses 0 = 0.0880838 . it should be also mentioned that for certain initial conditions the solutions of the system become negative in finite time. m.a. hajji and q. al-mdallal 26 figure 2. phase portraits of system (5) with different initial conditions ( (0), (0)) = (0,1), (1, 5), (2,10), (4,15)x y and (5, 20) : (a) = 0.1 and 0= , (b) = 0.1 and = 0.05. the equilibrium point is 0 = (0.315522, 0)e . figure 3. phase portraits of system (5) with different initial conditions ( (0), (0)) = (0,1), (1, 5), (2,10), (4,15)x y and (5, 20) : (a) 0.3= , 0= , (b) 0.3= and 0.05.= the equilibrium point is 0 = (0.315522, 0)e . a b a b numerical simulations of a delay model 27 figure 4. solutions of system (5) with = 0.1 and = 0.05 and different initial conditions: (a) (0) = 0, (0) 1x y  ; (b) (0) = 1, (0) 5x y  ; (c) (0) = 2, (0) 10x y  ; (d) (0) = 4, (0) 15.x y  a b c d m.a. hajji and q. al-mdallal 28 figure 5. solutions of system (5) with = 0.3 and = 0.05 and different initial conditions: (a) (0) = 0, (0) 1x y  ; (b) (0) = 1, (0) 5x y  ; (c) (0) = 2, (0) 10x y  ; (d) (0) = 4, (0) 15.x y  a b c d numerical simulations of a delay model 29 figure 6. solutions of system (5) with different initial conditions: (a) = / 0.1636    and = 0 ; (b) = / 0.1636    and = 0.05; (c) = / 0.1636    and = 0.08; (d) = / 0.1636    and = 0.09. a b c d m.a. hajji and q. al-mdallal 30 figure 7. solutions of system (5) with initial conditions: (0) = 1, (0) = 30x y : (a) = / 0.1636    and = 0.05; (b) = / 0.1636    and = 0.08; (c) = / 0.1636    and = 0.09. 7. conclusion a mathematical model for the interaction between the immune system cells and tumor cells was proposed and studied. the model was derived from kuznetsov and taylor’s model [1] by introducing a delay term which reflects the slow response of the immune system cells to the presence of tumor cells. the importance in studying this delay model is in determining the effect of the delay term on the dynamics of the system. a stability analysis of the equilibrium states was carried out. numerical simulations of the system were done for a number of different initial conditions. the simulation results confirm the theoretical stability results. numerically, it was also observed that as the delay term  crosses the upper bound 0 , the steady state 1e loses its stability, resulting in the formation of closed orbits around 1 .e this is an important result in the sense that as the is gets weaker (slower response, i.e., larger delay), the size of the tumor cells persists in an oscillating fashion (closed orbits). references 1. kuznetsov, v.a., makalkin, i.a., taylor, m. and perelson, a.s. nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. bulletin of matematical biology, 1994, 56, 295-321. a b c numerical simulations of a delay model 31 2. kuznetsov, v.a. and volkenshtein, m.v. dynamics of cellular immunological anti-tumor reactions ii. qualitative analysis of the model (in russian), mathematical methods of systems theory, frunze: kirghiz state university, 9191,1, 72-100. 3. rihan, f.a., abdel rahman, d.h., lakshmanan, s. and alkhajeh, a.s. a time delay model of tumour-immune system interactions: global dynamics, parameter estimation, sensitivity analysis. applied mathematics and computation, 2014, 232, 606-623. 4. rihan, f.a., hashish, a., al-maskari, f., hussein, m.s., ahmed, e., riaz, m.b. and yafia, r. dynamics of tumorimmune system with fractional-order. journal of tumor research, 2016, 2(1),109-115. 5. rihan, f.a. and rihan, n.f. dynamics of cancer immune system with external treatment and optimal control. journal of cancer science and therapy, 2016, 8(10), 257-261 . 6. galach, m. dynamics of the tumor-immune system competition-the effect of time delay. international journal of applied mathematics and computer science, 2003, 13(3), 395-406. 7. arciero, j.c., jackson, t.l. and kirschner, d.e. mathematical model of tumor-immune evasion and sirna treatment. discrete and continuous dynamical systems series b, 2004, 4(1),39-58. 8. kirschner, d. and panetta, j.c. modeling immunotherapy of the tumor-immune interaction. journal of mathematical biology, 1998, 37, 235-252. 9. y. kuang, 1993, delay differential equations with applications in population dynamics, london, academic press. 10. dionysiou, d.d. and stamatakos, g.s. applying a 4d multiscale in vivo tumor growth model to the exploration of radiotherapy scheduling: the effects of weekend treatment gaps and p53 gene status on the response of fast growing solid tumors. cancer inform, 2006, 2,113-121. received 15 june 2017 accepted 17 december 2017 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 157-167 © 2002 sultan qaboos university joint symbol and frame synchronization for directdetection optical communication systems eesa m. bastaki* and harry h. tan** *department of electrical engineering, faculty of engineering, united arab emirates university, p.o.box 17555, alain, u.a.e, email: eesa@uaeu.ac.ae, **department of electrical engineering, school of engineering, university of california, irvine, ca, 92717, u.s.a. تزامن الرموز واإلطارات في أنظمة االتصاالت الضوئية ذات الكشف المباشر عيسى بستاكي و هاري تان , يتعرض هذا البحث لمشكلة تزامن الرموز واإلطارات في أنظمة االتصاالت الضوئية التي تستخدم الكشف المباشر : خالصة اصة بتزامن الرموز واإلطارات لحاالت االحتماالت القصوى ويستنبط البحث العالقات الخ . بافـتراض معـرفة توقيت الشقوق .كما يناقش البحث أسباب الخطأ في اشتقاق جورج هايدس. المثلى وللحاالت دون المثلى abstract: the problem of joint symbol and frame synchronization in direct-detection optical ppm communication systems under the assumption of known slot timing is considered here. the optimum maximum-likelihood (ml) and sub-optimum rules for this joint symbol and frame synchronization problem are derived. the reason of georghiades's (1985) incorrect ml rule is discussed in this paper. keywords: frame synchronization, direct-detection, optical ppm communication, optimum maximum-likelihood. 1. introduction u nfortunately, as will be discussed in this paper, georghiades' derivation and his reported ml rule (georghiades, 1985) is not correct. this is because that derivation did not consider the end effects of each frame properly and also invoked an invalid symmetry assumption to simplify the structure of the reported decision rule. in this paper, the correct optimum ml rule is derived. simulation results presented here shows a significant improvement in correct synchronization probability performance of the correct optimum ml rule over georghiades' incorrect ml rule. in particular, for high signal-to-noise ratios, the synchronization probability performance of the correct ml rule tends to the random data-limited upper bound while the performance of georghiades' incorrect ml rule pre-saturates at a significantly lower level. we shall also consider a sub-optimum ml rule that accounts for the end effects of each frame, but also assumes the invalid symmetry assumption. this sub-optimum rule has a performance intermediate between that of the optimum ml rule and georghiades' incorrect ml rule. 2. joint symbol and frame synchronization problem we consider ppm modulation over the direct-detection optical poisson channel in which each m-ary symbol duration is divided into m time-slot divisions, and a rectangular light pulse is sent in the time slot associated with the transmitted symbol. the channel output is a poisson process with intensity rate ns λλ + when a light pulse is transmitted and nλ otherwise. here sλ is the photo157 eesa m. bastaki and harry h. tan detector count rate due to the light pulse and nλ is the count rate due to dark current and background noise. data transmission is formatted in successive frames with periodically inserted fixed synchronization patterns. each frame is assumed to consist of n data symbols composed of a fixed l-symbol sync pattern and n-l random data symbols. no assumption is made to preclude the presence of the sync pattern among the random data symbols. we shall represent each m-ary symbol as a m-dimensional vector ),...,( 10 −= mddd slot,th -i where ,...,1 ,...,1i ,..., k − 1− s ,...,l ,...,l 0 id ˆ 0 id    = otherwise.;0 theis pulselight theif;s id λ let the sync pattern be given by ),,( 10 −= lssss (1) where for , 10 −≤≤ li ).,( 10 −= miii ssss (2) in the joint symbol and frame synchronization problem, the channel output corresponding to n transmitted symbols are observed. since the pulse slot timing is known, the sufficient statistics are the photon counts in the nm time slots corresponding to the selected n transmitted symbols. let ),...,,...,,,...,( 1)1(1210 −−−−= nmmnmmm kkkkkk (3) denote this vector of nm photon counts. there are nm possible starting positions for the sync pattern s. the joint symbol and frame synchronization problem is to estimate this starting position. we consider the maximum likelihood approach here. the optimum ml rule estimates the sync pattern starting position as , where 0m̂ 1ˆ ≤≤ nmm is chosen to maximize the likelihood that are the ml photon counts corresponding to the transmitted frame sync pattern ),...,( 1ˆˆ −+lmmm kk s . 2.1 ml rule consider a candidate position m, 0 ≤≤ nmm . the starting position of s corresponds then to the count . so are the counts corresponding to random data symbols preceding mk ),...,( 10 −mkk s , are the counts corresponding to ),...,( 1−lmmk +mk s , and are the counts corresponding to random data symbols following ),...,( 1−+ nmlmm kk . in order to consider all nm-candidate starting positions, we need to consider the (n-l) random data symbols preceding and following s . hence denote )( 1−= nddd (4) to be the n-l random data symbols following s and )ˆˆ(ˆ 1−= nddd (5) to be the n-l random data symbols preceding s where ),,...,( 1−= mii dd (6) ),ˆ,...,(ˆ 1−= mii dd (7) 158 joint symbol and frame synchronization and     = ;0 .;ˆ, otherwise slotthj in the is symbolthi for the pulse theifsj i j i dd λ (8) table 1 illustrates the relation between ,,, dsk and d̂ for n=4, l=2 and m=2 for each of the nm candidate starting positions m. the ml rule chooses its estimate to be the value of m that maximizes m.given k ofon distributiy probabilit)|pr( =mk (9) similar to the approach taken in [1], )|pr( mk can be derived by averaging over the random data ,d̂ and d .d̂ and d m,given k ofon distributiy probabilit)ˆ,,|pr( =ddmk (10) for the direct-detection optical channel the components of k are all conditionally independent poisson random variables given m, d̂ and d . in examining table 1 it can be seen that there are three separate cases to consider a) case i 0 m) (mod m and )(0 =−≤≤ mlnm suppose m=qm, where 0 . then lnq −≤≤ )ˆ,,|pr( ddmk depends on (n-l-q) kd ’s and q kd̂ ’s for a total of (n-l) i.i.d. random data symbols. b) case ii ( 11) −≤≤+− nmmmln )ˆ,|pr()ˆ,,|pr( dmkddmk = depends on (n-l) i.i.d. kd̂ ’s. c) case iii 0 0)(mod and 1)( ≠=−−≤≤ kmmmlnm table 1: relationship between kdds ,ˆ,, for m=2,l=2,n=4. m m(mod m) 76543210 kkkkkkkk 0 0 1303120211011000 ddddssss 1 1 0 3 1 2 0 2 1 1 0 1 1 0 0 0 1 3 ˆ dddssssd 2 0 1 2 0 2 1 1 0 1 1 0 0 0 1 3 0 3 ˆˆ ddssssdd 3 1 0 2 1 1 0 1 1 0 0 0 1 3 0 3 1 2 ˆˆˆ dssssddd 4=(n-l)m 0 1 1 0 1 1 0 0 0 1 3 0 3 1 2 0 2 ˆˆˆˆ ssssdddd 5 1 0 1 1 0 0 0 1 3 0 3 1 2 0 2 1 1 ˆˆˆˆ sssdddds 6 0 1 0 0 0 1 3 0 3 1 2 0 2 1 1 0 1 ˆˆˆˆ ssddddss 7 1 0 0 1 3 0 3 1 2 0 2 1 1 0 1 1 0 ˆˆˆˆ sddddsss here )ˆ,,|pr( ddmk is a function of n-l-q-1 entire kd vectors and q entire kd̂ vectors as well as a function of part of another kd vector and part of another kd̂ vector. the partial vectors are at the two ends of the nm-vector k. so )ˆ,,|pr( ddmk depends on n-l-q kd 's and q+1 kd̂ 's for a total of n-l+1 i.i.d. random data symbols. this case then differs significantly from the first two cases above. 159 eesa m. bastaki and harry h. tan georghiades' incorrect derivation (georghiades, 1985) of the ml rule makes the mistake of assuming that only cases i and ii hold and does not consider case iii. in order to derive )|pr( mk , let us first consider )ˆ,,| ddmkpr( for each of the above three cases. a) case i 0 m) (mod m and )(0 =−≤≤ mlnm assume that ,qmm = (11) where . here lnq −≤≤0 )ˆ,,|pr( ddmk ')( 1 0 1 0 )!( ]')[( ts l i m j mjim k n j i n j i mjim e k ts λλ +− − = − = ++ ∏∏ +++ = ')( 1 1 0 )!( ]')[( td qn li m j mjim k n j i n j i mjim e k td λλ +− −− = − = ++ ∏ ∏ +++ ∗ ') ˆ( 1 1 0 )!( ]')ˆ[( td n qni m j mjim k n j i n j i mjim e k td λλ +− − −= − = ++ ∏ ∏ +++ ∗ (12) where t' is the pulse slot duration. we also adopt the convention here ∏ = = n mi if 1)( whenever n<m. moreover indices are interpreted modulo nm. b) case ii ( 11) −≤≤+− nmmmln here )ˆ,|pr()ˆ,,|pr( dmkddmk = ')( 1 0 1 0 )!( ]')[( ts l i m j mjim k n j i n j i mjim e k ts λλ +− − = − = ++ ∏∏ +++ = . )!( ]')ˆ[( ')ˆ( 1 1 0 td n li m j mjim k n j i n j i mjim e k td λλ +− − = − = ++ ∏∏ +++ ∗ (13) c) case iii 0 0)(mod and 1)( ≠=−−≤≤ kmmmlnm assume that ,kqmm += (14) where . .10 and 10 −≤<−−≤≤ mklnq here )ˆ,,|pr( ddmk ')( 1 0 1 0 )!( ]')[( ts l i m j mjim k n j i n j i mjim e k ts λλ +− − = − = ++ ∏∏ +++ = ')( 1)1( 1 0 )!( ]')[( td qn li m j mjim k n j i n j i mjim e k td λλ +− −−− = − = ++ ∏ ∏ +++ ∗ ')( 1 0 )1( 1 1 )1( )!( ]')[( tdkm j jkmn k n j qn n j qn jkmn e k td λλ +−−− = ++− −− −− ++− ∏ + ∗ ')ˆ( 1 )1( 1 1 )1( )!( ]')ˆ[( tdm kmj jkmn k n j qn n j qn jkmn e k td λλ +−− −= ++− −− −− ++− ∏ + ∗ ')ˆ( 1 1 0 )!( ]')ˆ[( td n qni m j mjim k n j i n j i mjim e k td λλ +− − −= − = ++ ∏ ∏ +++ ∗ (15) note that ∏∏ − = − = +− 1 0 1 0 ')( l i m j tml nse λλ (16) and that ∏∏ − = − = ++ ++1 0 1 0 ! )'(n i m j k k n mjim mjimtλ (17) 160 joint symbol and frame synchronization are independent of m. also note for the following cases that a) case i ∏ ∏∏ ∏ − −= − = +− −− = − = +−                 1 1 0 ')ˆ( 1 1 0 ')( n qni m j td qn li m j td n j in j i ee λλ '))(( tmln nse λλ +−−= , (18) b) case ii ∏∏ − = +−− − = +− = 1 '))(( 1 0 ')ˆ( , n li tmln m j td nsn j i ee λλλ (19) c) case iii ∏ ∏∏ ∏ − −= − = +− −−− = − = +−                     1 1 0 ')ˆ( 1)1( 1 0 ')( n qni m j td qn li m j td n j in j i ee λλ ,'))(1( tmln nse λλ +−−−= (20) define ∏∏ − = − = +− ++ ++ = 1 0 1 0 ! ')( 1 )'(n i m j k k ntmn mjim mjim ns t ec λλλ (21) (c1 is independent of m). then using (16) (20) in (12), (13) and (15) we obtain for the three cases the following expressions for )ˆ,,|pr( ddmk . a) case i . lnqqmm −≤≤= 0, )ˆ,,|pr( ddmk ∏∏ − = − = +++= 1 0 1 0 1 )/1( l i m j k n j i mjimsc λ ∏ ∏ −− = − = +++∗ qn li m j k n j i mjimd 1 1 0 )/1( λ ∏ ∏ − −= − = +++∗ 1 1 0 )/ˆ1( n qni m j k n j i mjimd λ (22) b) case ii ( .11) −≤≤+− nmmmln )ˆ,,|pr( ddmk ∏∏ − = − = +++= 1 0 1 0 1 )/1( l i m j k n j i mjimsc λ ∏∏ − = − = +++∗ 1 1 0 )/ˆ1( n li m j k n j i mjimd λ (23) c) case iii .10,10, −≤<−−≤≤+= mklnqkqmm )ˆ,,|pr( ddmk ∏ −− = − −−∗ km j td qne 1 0 '1 ( ∏∏ − = − = +++= 1 0 1 0 1 ' )/1( l i m j k n j i t mjims sce λλ −− ++−+ k n j qn jkmnd 1 )1()/1 λ 1 ˆ 1∏ − −= − −−∗ m kmj d ne ∏ ∏ −− = − = +++∗ qn li m j k n j i mjimd 1 1 0 )/1( λ .)/ˆ1( 1 ' )1( −− ++−+ k n j qn t jkmnq d λ ∏ ∏ − −= − = +++∗ 1 1 0 )/ˆ1( n qni m j k n j i mjimd λ (24) we next use (22) (24) to obtain (25) ∑∑ −−= d d ln ddmkmmk ˆ )(2 ).ˆ,,|pr()|pr( in order to do this, define ,)(12 lnmcc −−= (26) which is independent of m. also define for each i, 10 −≤≤ li , ,pattern sync theofsymbolth -i for theposition slot pulse )(ˆ sij = (27) and )./1( nsx λλ+= (28) 161 eesa m. bastaki and harry h. tan it then follows that ,)/1( )(ˆ 1 0 mijimmjim kk n m j j i xs ++++ =+∏ − = λ (29) ∑∏ ++ − = + i mjim d k n m j j id )/1( 1 0 λ , 1 0 ∑ − = ++= m j k mjimx (30) ∑ ∏ −− ++−−− −− = −− − + qn jkmn j qn d km j k n j qn td de 1 )1(1 1 0 1 ' )/1( λ kxe km j kt jkmns += ∑ −− = − ++− 1 0 ' )1(λ (31) and ∑ ∏ −− ++−−− −− − −= − + qn jkmnqn d k nqn m kmj td de 1 )1(1 ˆ 1 1 'ˆ )/ˆ1( λ ).( 1 ' )1( kmxe m kmj kt jkmns −+= ∑ − −= − ++−λ (32) using (29) (32) in (25) then yields a relatively simpler expression for )|pr( mk . we express the results for the three above cases below in terms of 2ln)|pr(ln)( cmkml −= (33) for the ml rule, it is equivalent to choose m to maximize l(m) since c2 is independent of m. the expressions for l(m) are identical in cases i and ii, but different in case iii. a) case i and case ii either m(mod m) = 0 or 1)( −≤≤− nmmmln ∑ − = ++= 1 0 )(ˆ)ln()( l i mijimkxml ∑ ∑ − = − = +++ 1 1 ).ln( n li m oj k mjimx (34) b) case iii 1)(0 and 0m) mod( −−≤≤≠= mlnmkm . ∑ ∑∑ − = − = − = ++           += ++ 1 1 0 1 0 )(ˆ ln)ln()( n li m j k l i mijim mjimxkxml ln(')(ln 1 ' )1( tkmxe s m kmj kt jkmns −+           −+           + ∑ − == − ++− λλ         +      +      − ∑∑ −− = − − = ++−++− kxex km j kt m j k jkmnsjkmn 1 0 ' 1 0 )1()1( lnln λ )m (35) the ml rule is to choose m, 10 −≤≤ nmm to maximize l(m), where l(m) is given by (34) for cases i and ii, and by (35) for case iii. the expression for l(m) differs in case iii from cases i and ii because of the two partial symbols at the ends of the frame. note from (34) and (35) that computation of l(m) for each m uses the counts corresponding to all n symbols in the frame. georghiades' incorrect ml rule is based on a likelihood formula which for each m uses only the counts corresponding to the l symbols of the sync pattern. since a low sync pattern overhead is desired for high data rate throughputs, the frame length n is often significantly larger than l in practice. moreover, reasonably large values of l are usually employed to reduce the probability of replication of the sync pattern in the random data portion of the frame. hence it is meaningful to consider the case when n becomes large relative to both l and m. in particular, the complexity of implementing the decision rule should be examined. table 2 gives the total number of computations in terms of the number of addition, multiplications, integer power, logarithm and exponential function evaluations to compute l(m) for all m. 162 joint symbol and frame synchronization in this table, there are a total of n+l(m-1) m's for cases i and ii and n(m-1)-l(m-1) m's for case iii. the total number of computations is evaluated in cases i and ii for all n+l(m-1) m's and also in case iii for all n(m-1)-l(m-1) m's. it can be seen from this table that, asymptotically for large n and fixed l and m, the complexity of implementing the ml rule based on computing l(m) is of order . georghiades' incorrect ml instead has an asymptotic complexity of order n. in order to obtain this reduced complexity georghiades makes the incorrect assumption that a(m) is independent of m for all , where 2n 10 −≤≤ nmm .ln)( 1 0 1 0 ∑ ∑ − = − =       = ++ n i m j k mjimxma (36) table 2: total number of computations for ml rule. total number of computations in cases i and ii computation total number addition [nm-lm+l-1][n+l(m-1)] multiplication n+l(m-1) integer power [nm-lm][n+l(m-1)] logarithm [n-l+1][n+l(m-1)] total number of computations in case iii computation total number addition [(n-l)m+l+5][n(m-1)-l(m-1)] multiplication 3[n(m-1)-l(m-1)] integer power [nm-lm][n(m-1)-l(m-1)] logarithm [n-l+3][n(m-1 (l(m-1)] exponential 2[n(m-1)-l(m-1)] suppose this assumption is true. then the ml rule can be based on choosing m to maximize l(m) a(m). the expressions for l(m)-a(m) in cases i, ii and iii are as follows. a) case i and case ii either m(mod m) = 0 or 1)( −≤≤− nmmmln . )()( maml − .ln)ln( 1 0 1 0 1 0 )(ˆ ∑ ∑∑ − = − = − = ++         −= ++ l i m j k l i mijim mjimxkx (37) b) case iii 1)(0 and 0m) m(mod −−≤≤≠= mlnmk . )()( maml − ln 'e j ts         + −λ ∑ ∑∑ − = − = − = ++         −= ++ 1 0 1 0 1 0 )(ˆ ln)ln( l i m j k l i mijim mjimxkx )ln(')( 1 )1( mtkmx s m km k jkmn −+     −+     ∑ − −= ++− λ         +         +         − ∑∑ −− = − − = ++−++− kxex km j kt m j k jkmnsjkmn 1 0 ' 1 0 )1()1( lnln λ (38) 163 eesa m. bastaki and harry h. tan the asymptotic computational complexity of computing all of the l(m)-a(m) is of order n. unfortunately, a(m) is not independent of m for all 0 1−≤≤ nmm . hence the ml rule cannot be implemented by choosing m directly to maximize l(m)-a(m). 2.2 simplified ml rule although a(m) is not independent of m for all 0 1−≤≤ nmm 0 , it is independent of m for restricted sets of integers m. specifically, define for each k, 1−≤≤ mk , }.) (mod and 10:{ kmmnmmmbk =−≤≤= (39) it can then be seen from (36) that for each k, 0 1−≤≤ mk , a(m) is independent of m for all . this property suggests the following approach towards reducing the number of computations to implement the ml rule. in order to describe this approach define kbm ∈ { })(max 1 xf ax − ∈ (40) to be the value of x achieving the following maximum: { })(max xf ax∈ (41) first note that since a(m) is independent of m for kbm ∈ , { })(max 1 mlm kbm k − ∈ = { })()(max 1 maml kbm −= − ∈ (42) but { } { }      = ∈ − −≤≤ − −≤≤ )(maxmax)(max 1 10 1 10 mlml kbmmknmm { })(max 1 10 k mk ml− −≤≤ = (43) equations (42) and (43) suggest the following two-step implementation of the ml rule. step 1 for each k, , determine 10 −≤≤ mk { })()(max m 1k maml kbm −= − ∈ . (44) step 2 the ml decision rule is the value given by m̂ { }.)(maxˆ 1 10 k mk mlm − −≤≤ = (45) the advantage of this two step approach is because the asymptotic complexity (fixed m, l asymptotic in n) of computing the [l(m)-a(m)]'s for all kbm ∈ is of order n for each k. so the asymptotic complexity of step 1 is of order n. the asymptotic complexity of computing each of the in step 2 is also of order n. so the total number of computations involved in implementing steps 1 and 2 is asymptotically of order n. table 3 gives the exact number of additions multiplications, integer powers, exponential and logarithm function evaluations. we shall call this rule the simplified ml rule. sml k )'( 164 joint symbol and frame synchronization table 3: total number of computations for simplified ml rule. total number of computations for step 1 computation total number addition (n-l)(m-1)[m(l+2)+l+4]+[n+(m-1)l](ml+l-1) multiplication [3(n-l)+l](m-1)+n integer power (n-l)(m-1)m(l+2)+[n+l(m-1)]ml logarithm (n-l)(m-1)(l+5)+[n+(m-1)l](l+1) exponential 2(n-l)(m-1) total number of computations for step 2 computation total number addition [(n-l)m+l+5](m-1)+(n-l)m+l-1 multiplication 3m-2 integer power [(n-l)m](m-1)+(n-l)m logarithm (n-l+3)(m-1)+n-l+1 exponential 2 (m-1) 2.3 sub-optimum rule the incorrect georghiades ml rule is invalid because it does not consider the case iii expression for l(m) and also because it assumes the constancy of a(m) for all m. we next consider sub-optimum rule which assumes just the constancy of a(m). this rule then chooses m to achieve the following maximum, { }.)()(max 10 maml nmm − −≤≤ (46) similar to the above discussion on the simplified ml rule, the asymptotic complexity of this sub-optimum rule is of order n. it is interesting to consider this rule because it only assumes the constancy of a(m) for all m and does not also ignore the case iii expression for l(m) as does georghiades' incorrect ml rule. hence, in comparing the performance between the ml rule, the sub-optimum rule and georghiades' incorrect ml rule, it is possible to access the performance deteriorations due to these two incorrect assumptions. the section below discusses the relevant performance results. 3. simulation results computer simulation was used to evaluate the correct synchronization probability performance. figures 1 to 6 give the simulation results on the correct synchronization probability of the ml, sub-optimal and incorrect ml rules for (n,l,m)=(4,2,2), (8,2,4), (12,2,8), (12,4,8), 165 eesa m. bastaki and harry h. tan (12,6,8) and (20,4,4) respectively. these figures give the correct synchronization probability as a function of the average signal count 'tsλ per slot for an average noise count per slot 4'=tnλ photons. it can be seen that the true ml rule performs from 3 to 5 db better than the incorrect ml rule. the performance of the sub-optimal rule is intermediate between that of the ml rule and the incorrect ml rule. in fact the performance of the sub-optimal rule is closer to that of the ml rule than to that of the incorrect ml rule. this suggests that the constancy of the a(m) is a more robust assumption than ignoring the case iii expression for l(m). 166 joint symbol and frame synchronization references bastaki, e.m., eesa, m. 1989. “frame synchronization in communication systems,” ph.d. dissertation, university of california, irvine, u.m.i., ann arbor, mi. georghiades, c.n. 1985. "joint baud and frame synchronization in direct-detection optical communication," ieee transactions on communications, vol. com-33, pp. 357-360, april 1985. received 28 june 2001 accepted 16 january 2002 167 joint symbol and frame synchronization for directdetection optical communication systems eesa m. bastaki* and harry h. tan** *department of electrical engineering, faculty of engineering, united arab emirates university, p.o.box 17555, alain, u.a.e, email: eesa@uaeu.ac.ae, **department of electrical engineering, school of engineering, university of california, irvine, ca, 92 joint symbol and frame synchronization problem 2.1 ml rule 2.2 simplified ml rule 2.3 sub-optimum rule simulation results references squ journal for science, 2017, 22(2), 120-126 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp120-126 sultan qaboos university 120 teaching statistics to engineering students – an australian experience of using educational technologies shahjahan khan 1 *, mohammad mrk khadem 2 and sujan piya 2 1 school of agricultural, computational and environmental sciences, international centre for applied climate science, university of southern queensland, toowoomba, australia; department of mathematics and statistics, college of science, sultan qaboos university, oman; 2 department of mechanical and industrial engineering, college of engineering, sultan qaboos university, oman. *email: shahjahan.khan@usq.edu.au abstract: engineers require scientific methods whereby models are developed to explain real phenomena. model building, data collection, data analysis, and data interpretation form the very core of any sound engineering practice. therefore statistical methodologies are vital components in engineering curricula and engineers should have the ability to think statistically when dealing with data. they should learn how to design and conduct wellplanned experiments to improve the efficiency of the process and the quality of products, and must learn to deal with data, and interpret results produced as a part of their data analysis skills. statistical methods are vital in engineering practices such as process monitoring by control charts, process optimization by response surface methodology, determining important factors by hypothesis testing, process modelling by regression analysis, initial pilot plant operation by design of experiments and laboratory recommendation. this paper shares some of the experiences of teaching statistics to undergraduate engineering students in an australian university, focusing on the appropriate content, teaching technique, educational technology, software package, online support and evaluation in an engineering problem solving course. results from an online survey of students are also presented. keywords: distance learning; problem-based learning; teaching statistics; screencasting; web-based teaching; on-line survey; educational technology. التعليمية التقنيات باستخدام أسترالية تجربة – الهندسة لطلبة اإلحصاء تدريس سوجان باياه كاظم و محمد ، شاهجهان خان بناء النموذج، وجمع البيانات، وتحليل البيانات، وتفسير البيانات . يتطلب المهندسون أساليب علمية لتطوير نماذج شرح الظواهر الحقيقية :صالملخ لذا فإن المنهجيات اإلحصائية هي مكونات حيوية في المناهج الهندسية، وينبغي أن يكون لدى المهندسين القدرة على .تشكل محور الممارسة الهندسية وينبغي أن يتعلموا كيفية تصميم وإجراء تجارب جيدة لتخطيط و تحسين كفاءة وجودة المنتجات، ويجب أن . التفكير إحصائيا عند التعامل مع البيانات الطرق اإلحصائية هي حيوية في الممارسات الهندسية مثل . مع البيانات، وتفسير النتائج التي تنتج كجزء من مهارة تحليل البياناتيتعلموا التعامل خالل مراقبة العمليات من خالل مخططات السيطرة، وايجاد الحلول المثلى، وتحديد العوامل الهامة من خالل اختبار الفرضية، وعملية النمذجة من تشارك هذه الورقة بعض من خبرات التدريس اإلحصاءات لطلبة الهندسة . العالقات الهندسية، و تصميم التجارب والتوصيات المختبريةتحليل ت والتقييم فيالجامعية في جامعة أسترالية تركز على المحتوى المناسب، وتقنية التدريس، والتكنولوجيا التعليمية، حزمة البرامج، والدعم عبر اإلنترن .وتقدم أيضا نتائج من استطالع الطالب الكترونيا. دورة حل المشاكل الهندسية التعلم عن بعد، التعلم القائم على المشاكل، اإلحصاءات التعليمية، التدريس، التدريس على شبكة اإلنترنت، المسح عبر اإلنترنت : مفتاحيةالكلمات ال .والتكنولوجيا التعليمية 1. introduction eaching introductory statistics to undergraduate students is quite challenging, and it is more so if the students are from non-mathematical disciplines. in general, service teaching, including teaching of statistics, is under threat due to increasing apathy from disciplines that require intense statistical knowledge in their profession. the traditional service teaching principle of teaching by experts in the discipline is not universal anymore. in engineering disciplines there has been a shift to recognise the crucial need of statistics, but the decision makers t mailto:shahjahan.khan@usq.edu.au teaching statistics to engineering students 121 are, with a few exceptions, reluctant to allow as much space in the curriculum as required to cover adequate statistical content and allow adequate teaching time. according to lindgren and zetterqvist [1] the mathematical statistics division at lund university teaches 8 core and 13 elective statistics courses within 14 different engineering programmes leading to master of science in engineering. but this seems an exception in australian universities, rather than the rule. statisticians should accept some of the responsibility for statistics not being very well received by students of other disciplines. some of the self-criticisms for statistics poor reception by others include "there continues to be a severe shortage of statisticians competent to deal with real problems" [2]; "we have historically done a very poor job of teaching statistics. … the problem is compounded because most people who teach statistics have never practiced statistics."[3]; and "for too long we in the statistics profession have tolerated poor statistics teaching, which produces courses that are often rated as the worst course or the most useless course that graduates in other fields claim they have ever taken. we too often teach what appears to the students a collection of unrelated methods illustrated by examples taken from coin-tossing, card-playing and dice-rolling."[4]. we don’t use the language of the discipline and touch the variables inherent to the learners’ degree program. generic methods do not appeal to the students learning from within. at the end we want students "to improve their ability to communicate statistical information in oral and written form, to improve interaction skills and to appreciate the fact that in real life an answer must (usually) be found, however imperfect" [5]. bisgaard [6] emphasised the essence of statistical skills for engineering professionals. the statistics curriculum in engineering should emphasise what the students are able to learn and apply in their workplace [7]. professional skills are acquired mainly by "doing" and by "seeing what others do." the learning process is basically a personal task, where the protagonist is not the teacher but the student. the teacher must be a generator of resources and facilitator of acquiring knowledge in the learning contexts, but the student is the person who is learning. active participation of students in all steps of the learning process would better prepare them for their career needs. to encourage the students' active participation, we have reduced the time spent in lecture classes and increased individual work and discussion. the role of the teacher has changed from that of "source of information" to "facilitator of learning" [8]. recently, the importance of cooperative learning in engineering has been further emphasised by [9]. the knowledge of basic methods is important, but creating a positive attitude and interest towards statistical methods in the minds of students is more crucial. we must convince students of the great value of these methods as tools for data analysis and decision-making in real problems that will arise in their future professional work. the only way to succeed in this is through the formulation and solution of real, or at least realistic, problems of direct interest to students. this must be done using the scientific method appropriate for the level of the students and sharing the teacher's experience in real projects. applying appropriate educational technologies in teaching is absolutely crucial to make sense of statistics. computer and internet provide us with endless opportunities to analyse real data more efficiently than we formerly could; therefore, it is essential to integrate suitable statistical software into the teaching of statistics. students should carry out laboratory practical tasks and hands on activities as an essential part of their learning process. they must have a feeling for what they are doing, why it is done, and what the benefit of doing so is. 2. role of statistics in engineering problems like most of the other scientific disciplines, engineering problems deal with variation, error, and uncertainty. engineering experiments produce data which are the key to solving engineering problems. real data exhibit variability and is subject to errors which obscure the criteria needed to make sound decisions. all decisions based on real data involve risk and uncertainty. statisticians could reveal the sources or causes of variability. discovering these sources and removing them are often the keys to engineering success. as a result, statistical methods are essential to address those issues. examples of some engineering variables are the coating thickness of a panel produced by a paint operation, the breaking strength of a plastic, the time/age of radial tires until the thread wears, the running time for fuses, the pressure required to separate the cap from a bottle, the power requirement for cutting metal with ceramic tools, or the annual rainfall in a city. only statistical methods can help analyse data on those or any other engineering variables. often engineering problems require a fundamental modelling approach for solving real life problems, which consists of the following steps: (1) specify the problem clearly (2) identify the factors that influence outcome variables (3) formulate a working model for the underlying relationship (4) produce data through an appropriate experiment (5) estimate/fit the working model (6) determine the important factors and test the adequacy of the model (7) revise the working model as appropriate and (8) collect additional data via a confirmatory experiment, and repeat the steps if required. as an example consider the study of the strength of a new polymer filament that is later spun into yarn. the filament’s elastic strength (s) depends on the (i) amount of catalyst (c) used, (ii) polymerization temperature (t), and (iii) pressure (p). therefore, for an engineer, the working model of the phenomenon is of the form s = f shahjahan khan et al 122 (c,t,p). a statistician would suggest a regression model to predict the strength based on the varying level of the predictors: 0 1 2 3 s c t p         this model represents a linear relationship between the response (strength) and the three factors catalyst, temperature, and pressure as the predictors. it helps the engineer to determine appropriate settings for the three factors that optimize the strength. for further details see vining and kowalski [10]. how can we determine the exact impact of the three factors on the filaments strength? which combination of the factor levels produces the optimum strength? the statistician systematically changes the amount of catalyst, the polymerization temperature, and the polymerization pressure. the engineer then conducts the experiment for each possible combination of these factors, and takes a sample of filaments and measures their strengths. this produces essential data that are key to the solution of the problem. the estimated model gives the statistician an appropriate basis for determining the important factors. the statistician will determine which of the estimated coefficients is really different from zero. if the coefficient associated with the amount of catalyst is zero, then no matter what we do with the amount of the catalyst, it has no effect on the filaments strength. the engineering method continues in this manner until the engineer finds an adequate solution that produces the optimum strength. 3. problem-based learning bringing any real problem from the engineering area and apply statistical techniques to solve it is a great way to introduce the discipline to the students. problem-based learning (pbl), pioneered in the medical school program at mcmaster university in hamilton, ontario, canada in the late 1960s by howard barrows and his colleagues has now been adopted in many other disciplines to achieve this goal. it is a student-centered pedagogy in which students learn about a topic in the context of complex, multifaceted, and realistic problems. the goals of pbl are to help the students develop flexible knowledge, effective problem solving skills, self-directed learning, effective collaboration skills and intrinsic motivation [11]. working in groups, students identify what they already know, what they need to know, and how and where to access new information that may lead to resolution of the problem. the role of the instructor (known as the tutor in pbl) is that of the facilitator of learning who provides appropriate scaffolding, guidance and support for the process, modelling of the process, and who monitors the learning [12]. the tutor must build students’ confidence to take on the problem, and encourage the students, while also stretching their understanding [13]. in collaboration with aalborg university of denmark, pbl was introduced at university tun hussein onn malaysia (uthm). since then the pbl was widely used among engineering as well as humanities lecturers at uthm [14]. recently many malaysian universities are going for pbl, purposely to improve the quality of the graduates produced. other examples are given by romero et al. [15], woods [16], schmidt et al. [17], perrenet et al. [18], viali [19], bland [20], vidic [21], and schmidt and yew [22]. the pbl method of teaching has been in practice for engineering courses at the university of southern queensland (usq), australia for several years, under the title of engineering problem solving courses. the second course of the series of 4 courses contains the application of statistics for engineering data analysis. every year an engineering topic relating to a present day problem (e.g. solar power generation or flood water management in australia) is selected by the teaching team of about 15 academics from the faculties of engineering and sciences. the problem must provide scope for students of different branches within the engineering faculty. each member of the teaching team facilitates a number of groups of students and helps guide them through to completion of the final group report and assesses them under a strict common marking rubric. the class is divided into groups of 8 students with a leader and a deputy leader from among the group members. this is done separately for external and on-campus students in the two different campuses of usq (toowoomba and springfield). in the assessment a significant weight is allocated for team work and the group report while there are also marks for individual work. the groups meet weekly to work on various engineering aspects of the problem as well as on the statistical analysis of relevant data. the group leader makes sure that the meetings are held on a regular schedule and according to agreed codes of conduct, such that everyone completes assigned tasks and contributes to the group discussions and preparation of the final report. minutes of such meetings are kept for future reference. lecture and tutorial support on selected topics is provided when needed. within each group the students also conduct peer reviews of their personal portfolios which also contribute to their final grades. recently, within the engineering problem solving and data analysis course four weeks of the second semester were exclusively devoted to the teaching of statistics, to help students analysing the data to acquire relevant statistical skills required to solve the engineering problem. two hours of lectures and two hours of tutorial time weekly were offered to all on campus students. recordings of the lectures and tutorials were provided to the external and on-campus students via the studydesk portal. the statistical package spss was used to analyse the data. support for learning spss was provided by pre-recorded online video snippets. teaching statistics to engineering students 123 4. online teaching support about three quarters of all usq students are external and they are located all over the world. traditionally usq has one of the best online support systems in the world for external students. this, coupled with the state of the art educational technology and ongoing research in teaching technology, enables usq to provide very effective support to our external students. we provide pre-lecture/tutorial notes to the students via the studydesk which are accessible from anywhere in the world. recorded live lectures, tutorials etc, including screencasting, are also made available to all students. lecture theatres are equipped with audio and screen recording facilities, but some lecturers use tablet pc to record lectures/tutorials using techsmith (camtasia) relay. khan et al. [23] use the screencasting to bridge the divide between external and on-campus students. this makes it easy for students to watch the recordings at their own pace and in their own time, either online or after downloading. further support is provided via various discussion forums, newscasts, and consultancy. there is provision for students to post messages/questions to the whole class or just to the group members, and to respond to the postings of other students. students can post any questions related to the topics of the course or a response to /explanation of others’ questions. the facilitators make sure that the discussions are on track and directed to the learning goals of the students. online quizzes are provided both for practice and assessment. the questions in the quizzes are randomised for each student from a bank of questions on all topics covered in the course. online exams are also conducted similarly. all online assessments are marked by computer and followed by automated feedback. the final group report is submitted online via the studydesk near the end of the semester. the teaching team members can access the allocated reports online and mark them for final assessment. a combination of individual assessments and group performance determine the final grade of each student. figure 1. screencasting of a slide for an introductory statistics class screencasting allows the lecturers to record the content of lecture slides on the computer screen along with the audio discussions and explanations. using the tablet technology lecturers are able to write equations or draw graphs on the computer screen which is instantly shown on the display screen. camtasia rely allows them to record the intended part or whole of any lecture and saves it in a central depository. students are able to access the recorded screencast via the link on the studydesk online. they are able to watch the recordings in their own time and at their own pace either online or by downloading them in various static or mobile formats such as mp4, ipod, etc. 5. students’ survey results the teaching team conducted an on-line survey to find the students’ opinion on various aspects of the statistics module in the course and the teaching of related topics. the survey consisted of 10 online questions of which the first 9 were multiple-choice type with answers provided in a likert scale. the last question was open ended, seeking suggestions on how the statistics content might be better presented to assist students’ learning. please see the appendix for the survey questionnaire. the summary of the survey results are provided in table 1. the survey was conducted after 4 weeks of teaching of the statistics module and after two online exams. the teaching involved two hours of lectures and two hours of tutorials in weeks 2-5. out of a class of about 450 students, 203 responded to the online survey. the responses to question 3 clearly demonstrate the important role of statistics in the course as 11.44%+54.23% ≈ 66% agree or strongly agree, whereas less than 15% disagree. the formal lecture/tutorial was supported by 27.86+39.80% ≈ 68% in question 1. in contrast, the self-learning of statistical content was favoured by less than 12% and not supported by 42.29%+33.33% ≈ 76% in question 4. these figures strongly justify formal teaching of the statistics module in the course. as such 15.42%+33.83% ≈ 49% suggested retaining this module shahjahan khan et al 124 whereas 15.42%+18.41% ≈ 34% disagreed in question 9. the module did provide adequate skills for data analysis according to 13.93%+48.76% ≈ 62% of students in question 2. all this evidence reinforces the crucial role of statistics in the course and the need for formal teaching as opposed to independent self-learning by students while doing the course. table 1. percentages of responses in the student survey brief question/ student response s agree agree undecided disagree s disagree q1 lecture/tutorial assisted learning 27.86% 39.80% 12.94% 13.43% 5.97% q2 better equipped for data analysis 13.93% 48.76% 17.41% 16.92% 2.99% q3 appreciate crucial role of statistics 11.44% 54.23% 19.40% 9.95% 4.98% q4 prefer self-learning of statistics 3.98% 7.96% 12.44% 42.29% 33.33% q6 had adequate math foundation 23.88% 55.72% 10.45% 8.96% 1.00% q8 online assessment effective 6.97% 34.83% 20.40% 16.42% 21.39% q9 retain statistics module for future 15.42% 33.83% 16.92% 15.42% 18.41% some sample responses to the open-ended question 10 are noted below:  this course has been compressed far too much; it should be spread out over 7 or 8 weeks.  i strongly agree with the inclusion of statistics in engineering.  i am actually surprised that this is the only statistical component of the engineering degree.  i think the statistics component should be a stand-alone subject.  statistics is a very important subject in engineering and therefore i think it should have more hours allocated in this course.  the statistics section needs to be placed as a totally separate course.  i would have mastered statistics if it were separate unit.  lectures were a great way to learn.  i found the tutorials good.  the lecture notes were nice and clear; they were a good help.  i learned more on this course because of statistics which i think should be run as an independent course 6. statistics teaching in engineering at other universities a survey of engineering curricula of some of the leading universities in the usa shows that every university has at least one course on statistics [24]. some universities offer it as a stand-alone separate course while others are offering it in combination with probability as “probability and statistics”. in some of the programs of those universities, for example in industrial engineering (ie) programs, statistical concepts and methods are included in a number of courses including “quality control”, “simulation”, “operations research”, “research methodology” and “engineering statistics”. a similar practice exists among the best universities in the gulf cooperation countries (gcc) region, where most of the engineering programs are accredited by abet. abet emphasises outcome based learning with continuous improvement. the learning outcome may come from a program, a course or specific part of a course. the industrial engineering program at sultan qaboos university, oman has incorporated statistical skill in many courses, such as statistical quality control, probability and statistics. the program is accredited by abet and based on the contents of these courses the outcomes include: i) an ability to apply knowledge of mathematics, science, and engineering, ii) an ability to design and conduct experiments, as well as to analyse and interpret data, and iii) an ability to identify, formulate, and solve engineering problems. such applications of statistics are widespread in all branches of engineering. the course content, delivery plan and method of assessment to check the proficiency of students in statistics is then prepared in such a way that these components ensure achieving the course outcomes. the course materials are provided to the students through an online system (on moodle platform) before they are discussed in the classroom. for each of these courses there are two lecture hours and two hours of tutorials each week, throughout the semester of 14 weeks. apart from solving textbook problems and exercises in the classroom, tutorials consist of some specific number of lab sessions where students engage themselves in hands-on experience using statistical software (e.g. excel, minitab) to solve engineering problems involving data analysis using statistical techniques. students are then assessed multiple times within the semester to check their proficiency in achieving the learning outcomes of the course. the assessment includes multiple quizzes, term tests, assignments and a group project. in their project work, students are encouraged to work on real world engineering problems where they have to perform statistical analysis very similar to the pbl approach. these courses are further linked to advanced courses such as quality control, six sigma, simulation, stochastic operations research etc. at the end of every semester a student survey is carried out to discover their point of view on the course. following is some of the typical feedback received for the courses on statistics: this course is applicable for the real world problem and is interesting. the most interesting part of the course is hypothesis testing and design of experiment. project work is very interesting as it deals with real problem. teaching statistics to engineering students 125 very useful subject in the real life and industry. 7. conclusion the survey revealed consistent opinions regarding the two main directions for the future statistics module of the course. the majority of the students think that the course allowed less than sufficient time to teach statistics. they felt that the duration of 4 weeks is not enough to learn the statistical content of the course. interestingly, most of the students suggested a stand-alone statistics course for engineering. some students were surprised that this was the only statistical component that they had seen in the whole engineering program. many of the usq students are of mature age and have long industrial experience and value statistical knowledge more than the fresh graduates who enter university directly from the colleges do. giving due weight to statistics within the engineering curriculum would benefit the profession enormously, including augmenting the employability of our new graduates. statistical methods are becoming an indispensable part of many scientific disciplines and engineering is no different. the views of the teaching team and the survey outcomes reinforce the need for increased formal teaching of statistics for engineering students. therefore, this emphasizes the necessity of offering statistics as a stand-alone course and to include it as a learning outcome for the program. the idea is to include statistical concepts and methods in as many engineering courses as possible within the program, including setting and conducting experiments and hands-on analysis of experimental data using computing software and group projects to solve real engineering problems. active participation of students and interaction among fellow colleagues [8] are essential to enhance students’ learning, and ensure hands-on statistical support in the process of teaching statistics to help solving diverse engineering problems. acknowledgement the first author acknowledges the contributions of the engineering problem solving and data analysis teaching team led by john worden for introducing the formal teaching of statistics and allowing the survey. this paper was completed when the first author was visiting sultan qaboos university, oman in the fall semester of 2016. appendix – survey questionnaire 1. do you consider the inclusion of traditional lectures and tutorials has assisted your learning of statistical concepts? likert scale: ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree 2. do you consider yourself better equipped to contribute towards the data analysis part of the set problem after formally learning basic statistical skills? likert scale: ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree 3. have you gained a better appreciation of the crucial role of statistics in engineering and spatial sciences? likert scale: ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree 4. would you have preferred to acquire this statistical knowledge through independent research and study instead of formal teaching? likert scale: ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree 5. how many hours per week (on average) have you spent in mastering the statistics content? ☐1-2; ☐2-4; ☐4-6; ☐6-8; ☐8-10; ☐>10 6. at the start of this statistics module, were your mathematical skills an adequate foundation? likert scale : ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree 7. how did you find the level of support from the statistics teaching team on the study desk, and the effective delivery of the content? ☐poor; ☐inadequate; ☐acceptable; ☐good; ☐excellent 8. do you consider that the on-line exam/test was an effective way to assess your learning? likert scale: ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree 9. based on your learning experience and support received from the teaching team, would you recommend that the statistics module be retained in eng2102? likert scale: ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree 10. how might this the statistics content be better presented to you to assist your learning? likert scale: ☐strongly agree; ☐agree; ☐undecided; ☐disagree; ☐strongly disagree references 1. alfares, h.k., al-turki, u.m. and duffuaa, s.o. developing an outcome-based industrial and systems engineering program. industrial engineering and management systems, 2010, 9(1), 60-68. shahjahan khan et al 126 2. anderson, c.w. and loynes, r.m. the teaching of practical statistics, new york: john wiley, 1987. 3. bisgaard, s. teaching statistics to engineers. the american statistician, 1991, 45(4), 274-283. barrett, t. the problem-based learning process as finding and being in flow. innovations in education and teaching international, 2010, 47(2), 165-174. doi:10.1080/14703291003718901. 4. berhannudin, m.s. adopting problem-based learning in the teaching of engineering undergraduates: a malaysian experience. proceedings of international conference on engineering education – icee 2007, september 3-7 2007, coimbra, portugal. 5. bland, j.m. teaching statistics to medical students using problem-based learning: the australian experience. bmc medical education, 4. 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http://pucrs.academia.edu/loriviali/papers/1347255/distance_learning_teaching_probability_and_statistics_to_ petroquimical_engineering_students (accessed on 17 march 2017), 2003. 22. vidic, a.d. a model for teaching basic engineering statistics in slovenia. metodološki zvezki, 2006, 3(1), 163183. 23. vining, g. and kowalski, s. statistical methods for engineers, 3rd ed (compiled by worden, j. and khan, s.), cengage learning australia, 2011. 24. woods, d.r. problem-based learning: helping your students gain the most from pbl. www.chemeng.mcmaster.ca/pbl/pbl.htm, 1995. received 18 october 2016 accepted 21 march 2017 http://en.wikipedia.org/wiki/digital_object_identifier http://dx.doi.org/10.1080%2f14703291003718901 http://www-users.york.ac.uk/~mb55/talks/ozpbl.htm http://pucrs.academia.edu/loriviali/papers/1347255/distance_learning_teaching_probability_and_statistics_to_petroquimical_engineering_students http://pucrs.academia.edu/loriviali/papers/1347255/distance_learning_teaching_probability_and_statistics_to_petroquimical_engineering_students http://www.chemeng.mcmaster.ca/pbl/pbl.htm electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 123-136 © 2002 sultan qaboos university characteristic and non-characteristic harmonics, harmonic cancellations and relevant international standards in variable speed drives syed m. islam school of electrical and computer engineering, curtin university of technology gpo box u 1987, wa 6845, australia. التوافقيات المميزة وغير المميزة ، الغاءات التوافقيات والمقياس الدولية المستخدمة في المحركات ذات السرعات المتغيرة سيد اسالم تقدم هذه الورقة مراجعة للتوافقيات في المقوم الموجي ذي الوجه الواحد وذي الثالث اوجه ، وتناقش نتائج البحوث : خالصة وتعرض الورقة المقاييس الدولية المستخدمة في دراسة التوافقيات .عرف على مصادر التوافقيات وتضخيمها الحديثة في الت iec61000-ieee519-as-2279 . أخيرا تعرض الورقة الطرق المستخدمة في التقليل من التوافقيات. abstract: this paper will present a review of characteristic harmonics in both single phase and three phase drive front end rectifiers, discuss recent research findings in identifying sources and production of non-characteristic harmonics and amplification of harmonic levels when the front end rectifiers are fed from non-ideal supply conditions. significant amount of triplens may be generated due to unbalances in utility supply voltage wave form and anticipated harmonic levels may vary widely. the paper will also discuss international harmonic standards such as the as 2279, ieee 519, and iec 61000 series applicable to rectifier loads. finally, the paper will present techniques to reduce harmonic levels by mixing of single phase and three phase non-linear loads resulting from mutual cancellations. keywords: harmonics, thd, 3rd harmonic, triplen harmonic, supply imbalance, voltage distortion, non-characteristic harmonics, harmonic standards and harmonic cancellations. 1. introduction i n variable speed drives (vsds) both voltage and frequency conversions are necessary. vsds typically converts in two stages: the front end rectifier stage and the inverter stage. the currents drawn from the supply by the vsds are no longer sinusoidal and introduce harmonics. proliferation of vsds and other non-linear loads and resulting poor power quality is of prime concern to the supply network. concerns and questions in the 90’s regarding overloaded neutral conductors, overheating and failure of motors and transformers, frequent tripping of circuit breakers and capacitor failures, were often met with unacceptable answers and limited solutions. the ieee 519-1992, as 2279, and iec 61000 series standards have been introduced to help combat the problem of poor power quality. since this problem was an increasing one, it was assumed that newly introduced equipment was the likely cause. the increased use of variable speed drives (vsds) in industry coupled with complaints about vsd shutdowns, together with the previous problems resulted in vsds becoming one of the first targets as a cause of supply harmonic problems. it is easy to see why vsds were blamed for harmonic problems, as they are normally high power devices, which inject high magnitudes of harmonic currents into the supply network. however we cannot disregard other low power devices 123 syed m. islam such as computers and discharge lighting, as the large number of them can lead to a similar impact on the supply system. any source of current harmonics can then cause an effect on other devices. due to the power quality problem, filters such as harmonic traps (mark and david, 1999; syed and creg, 1995) are designed to reduce harmonic currents from vsds and improve power quality. the design of such filters are based on the characteristic harmonic currents injected by vsds (gary and wilson, 1998; cyril, 1987; mohan, 1995; derek, 1996). these characteristic currents are usually generalised and based on an ideal supply. the effect of variation on harmonic currents could cause poor filter performance that may no longer meet standard specifications. this paper explores the relationships between harmonic currents from vsds and the associated supply. characteristic harmonic currents of vsds will be shown under perfect supply conditions, and then variations to the normal harmonic currents when the supply is non ideal will be developed with emphasis to the 3rd harmonic. simulation and experimental results of these harmonic current variations will then be discussed along with the effects that can result from this distortion. harmonic currents from the single phase rectifiers and the three phase rectifiers may be antiphasal and can cancel each other. this is an important phenomena and this paper addresses the issue. the paper is set out in the following way: in section ii of this paper, characteristic currents associated with vsds that use 6-pulse rectifiers as the front end is given. section iii introduces the concept of how the triplen harmonics are produced; the effects of voltage reduction and voltage distortion are treated separately. in section iv, simulation results are presented showing the effect of voltage reduction on current distortion. section v presents experimental results that verify the theoretical analysis. section vi discusses the harmonic cancellation issues. section vii presents some common harmonic standards applied to vsds and other non-linear loads. finally, some conclusions and recommendations resulting from this research are provided. 2. characteristic harmonic currents drawn by 6 pulse rectifiers the complete 6-pulse rectifier circuit showing the dc link inductor used for most vsds is shown in figure 1. the current drawn from the source is given by 1)( t)nsin b (i )( n ......2,1 dc1 ωω ++= ∑ ∞ = tncosati n n the dc component is zero. the fourier components an and bn are given by 1,3,5...nfor 3 4 b ,0a 2,4,6.... nfor ,0 nn === === π π n sin n i ba a nn the rms value of the ‘n’th harmonic component can be given by 3 22 )( 2 1 2/122 π π n sini n bai annn =+= it is usually the case that the neutral of the supply is not connected to the rectifier and therefore the triplens are not present. thus the first harmonic component present in the above analysis is the 5th harmonic current. in general, characteristic harmonic currents drawn by a ‘p’ pulse rectifier are related to the pulse number. the following equation shows this relationship 124 characteristic and non-characteristic harmonics h = p x n ± 1 (2) where h = the harmonic number, p = the pulse number of the rectifier and n = an integer having values of 1, 2, 3,… this means that a 6-pulse rectifier at the front end of a vsd will typically have harmonic currents of the orders 5, 7, 11, 13, 17, 19, 23, 25, …etc. the magnitudes of the harmonic currents are theoretically the reciprocals of the harmonic sequence numbers as shown above. thus 20% of 5th, 14% of 7th, 9% of 11th and so on. these theoretical harmonic current levels are based on a rectangular current wave of magnitude ± ia or id, being drawn from the supply. figure 1. complete circuit diagram of the 6-pulse rectifier. figure 2. theoretical representation of line current for an ideal 6-pulse rectifier. the ideal rectangular current waveform is shown in figure 2, the underlaying fact being that the current conducts between the cross over points of the phase voltages and is termed the conduction period. the total harmonic current distortion (thid) for this ideal current waveform is 29%. this distortion level is based on the fact that the supply voltage is ideal; that is the phase voltages are equal in magnitude and 120° out of phase with each other. the case for a practical rectifier with a dc link inductor will have a current waveform shape characterised by two raised humps, also shown in figure 2. the thid for a practical 6-pulse rectifier is 30% 50% depending on the size of the source impedance and the dc link choke. the idealised rectangular wave is a useful approximation to give a good indication of how the conduction period will change with changes in the supply voltage waveforms. 125 syed m. islam 3. production of non-characteristic (triplen) harmonic currents 3.1 effect of voltage reduction the normal current conduction period for a 6-pulse rectifier is 120°; this angle is determined by the cross over of the phase voltages ie for the a-phase current, voltage vc to va and then va to vb. the cross over points are typically 30° and 150° for the a-phase voltage. the production of triplen harmonics occurs when there is a difference in the conduction period from the nominal 120°. changes in the current conduction period can occur for two reasons; 1) due to a voltage reduction of one or two phases, 2) line voltage distortion of the supply, such as a clipped waveform. ali and geza (1991) use voltage unbalance to show a production of 3rd harmonic current. this analysis deals with phase controlled rectifiers, where the conduction angle can be controlled, to maintain a 120° conduction period for each phase current to minimise the effect of voltage imbalance and the production of a 3rd harmonic current. figure 3. effect of current conduction period with a change in voltage level. figure 3 shows that voltage va is reduced from the nominal value to a lower value. this results in a change of the conduction angle by 2 φ for the a-phase current. using this result and fourier analysis the amount of third harmonic current that will be produced from the a-phase voltage reduction can be found. the following fourier transform is used taking into account quarter-wave symmetry. ∫ π φ+ π ωω⋅ π = 2 6 )()(sin 4 tdthii dh (3) where ih = ‘h’ harmonic current magnitude, and id = drive dc current level. solving this equation gives the result for the magnitudes of the line current harmonics of the rectifier. when expanded this gives the current spectrum of a 6-pulse rectifier.             φ+ π π = 6 cos 4 h h i i dh (4) where h = 1, 3, 5, 7,..etc. in particular then the 3rd harmonic component is given by             φ+ π π = 6 3cos 3 4 3 dii (5) from equation (3), when h = 3, 9, 15…etc and φ = 0, the cosine value will be zero resulting in no triplen harmonic current. however when there is a change in the conduction angle ie φ is equal 126 characteristic and non-characteristic harmonics to some value other than zero, then the cosine value will no longer be equal to zero and triplen harmonic currents will be produced from the rectifier. the dominant component will be the 3rd as given by equation (5) but other odd order triplen harmonics, such as the 9th and 15th will be present but not as significant in magnitude as the third. these higher order triplens are divisible by 9 and 15, resulting in magnitudes that are 3 and 5 times smaller than the 3rd harmonic current. what should also be noted from equation (4), is that for other values of h and for values of φ not equal to zero changes in the magnitudes of the characteristic harmonics will also occur. for an example of the 5th harmonic, if φ = 5° then the magnitude of the 5th harmonic will increase by almost 5%. this result has been determined using an ideal case for the current waveform. however the practical rectifier will give greater distortion levels due to the double hump waveform. wilson and randae, (1998) show a variation to harmonic currents under unbalanced supply conditions. also discussed is an analysis to assess the harmonic propagation in each phase as harmonic currents change with voltage inbalance. 3.2 effects of supply voltage distortion effects of voltage distortions on the supply will have similar effects to that of voltage reduction. again the current conduction period will change from the nominal 120°. the dominant harmonic voltages present on the supply are typically 3rd, 5th and 7th and the level of these harmonic voltages can be up to 4% of the fundamental value. these values have been taken from measured results in the laboratory. the total harmonic voltage distortion being approximately 3% but limited to 5% at the pcc by supply authorities for a commercial environment. harmonic voltages can be attributed to existing harmonic producing sources such as computers, discharge lighting and vsds. figure 4 shows the effect of a 5th harmonic a-phase voltage with a lagging phase angle of 100°. the 5th harmonic voltage periodically adds and subtracts to the fundamental voltage. this will then change the current conduction period, for this case, so that the start of conduction will be less than 30° and the end of conduction will be less 150°. this situation does not allow the previous fourier transform, equation (3) to be used, as quarter wave symmetry has now been lost. figure 4. effect of 5th harmonic voltage on rectifier current conduction angle. (note: scale for 5th harmonic current is greatly magnified). this situation requires the fourier transform with half wave symmetry. this is given in equation (5). ∫ β− π α− π ωωπ = 6 5 6 )()(sin 2 tdthii h (6) solving this gives the following result. ( )             π −α−β      β−α−π π − = 3 2 2 sin 2 sin 4 hh h i i h (7) 127 syed m. islam again from equation (7) we can see that if α and β are non-zero and h = 3 then there will be a production of the third harmonic current. the values of α and β will not necessarily be the same, and both values will change with a change in phase angle of the harmonic voltage. also the other triplen harmonics will be produced but at lesser magnitudes, and variations of the characteristic harmonic currents will also occur. for different magnitudes and phase angles of harmonic voltages in the supply, it is clear that the analysis will change considerably. as the supply becomes more distorted, by voltage harmonics and/or reduction in phase voltage, a simple mathematical solution will not be obtained easily. the best method of determining the thid is with the use of a suitable software simulation program. 4. calculation of harmonics the reason for performing a harmonic analysis in a system would be to determine if the nonlinear load on the system meets the requirements of the local supply authority, which is typically based on ieee519-1992. if a system did not meet the requirements then measures would need to be taken to reduce the harmonics, for example using harmonic trap filters. typical methods used for finding the total harmonic voltage distortion (thvd) use ideal supply conditions. the effect of supply distortions, if not taken into account in the initial design, could result in poor performance. 4.1 effect of voltage imbalance pspice simulation program has been used to determine 3rd harmonic current levels from a 6pulse rectifier by reducing the a-phase voltage. the model is simulated using a circuit simulation program. the circuit used is the same as of that shown in figure 1. the results of this are shown in figure 5. phase a voltage is only reduced up to 5% of its nominal value to coincide with the typical allowed value for volt drop in a system. the results show a significant amount of 3rd harmonic current produced in the line current for a supply voltage imbalance. initial values of 3rd harmonic current are at 2% for phase a and c and 1% for phase b. the currents then reached a value of 39 and 40% for phase a and c respectively and 23% for phase b. the initial levels of 3rd harmonic for 0% voltage reduction are due to calculation errors in the software as the tolerance has been reduced to speed up the simulation. the results also show that all three line currents are affected but not by the same amounts but by the decrease of only one of the phase voltages. 3rd harmonic current vs phase a voltage reduction 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 0% 1% 2% 3% 4% 5% voltage reduction (%) h ar m on ic c ur re nt (% f) ia3 ib3 ic3 figure 5. effect on 3rd harmonic current with varying a-phase voltage. the effect of the voltage reduction will also have an effect on the other current harmonics as outlined previously.the effect can be shown by examining the change in thid of each line current for a change in phase a voltage. these results are given below in figure 6. 128 characteristic and non-characteristic harmonics thid vs phase a voltage reduction 0 10 20 30 40 50 60 70 80 0% 1% 2% 3% 4% 5% voltage reduction (%) c ur re nt d is to rt io n (% f) ia3 ib3 ic3 figure 6. effect on total harmonic current distortion with varying phase a voltage. these results show that in fact there is an increase in thid for phase a and c current and a reduction of thid for phase b current. the increase of thid is not just associated with an increase in the 3rd harmonic current. phase a and c thid have increased by 21 and 23%, respectively, which is quite significant as this could cause a reduction in performance of a trap filter designed to reduce the thid from a vsd. 4.2 effect of voltage distortion. line voltage distortion due to harmonic voltages in the supply will cause similar effects to the conduction angle as with line voltage imbalance. large variations of magnitudes and phase of harmonic voltages are possible and therefore a simple analogy is not feasible and a more realistic approach is to see the effect of “real world” voltage distortion on a vsd. to determine the distortion level of a supply it is then necessary to perform a harmonic analysis of the supply. this can be done easily with a harmonic analyser that allows for time recording. measurements can then be taken over a period of time ie. hours or even days, which will then give an indication of the level of thvd. 5. experimental results laboratory tests have been performed to verify that the above theoretical results do occur in a real world situation. an ideal case will be looked at for comparison with the non-ideal case. to obtain an ideal voltage supply, a small synchronous alternator connected to a dc motor (prime mover) was used. this source is still not perfect in the sense that there was a small amount (1%) of 3rd harmonic voltage present at no-load, however at full load the effect was negligible. this test set up is shown in figure 7. the harmonic voltage supply or distorted supply is based on the laboratory power supply, which is fed from a main transformer that also feeds other buildings in the university. the transformer is fed from the local utility. the existing amount of voltage harmonics present on the distorted supply has been measured using a harmonic analyser. the level of harmonics that are on the supply would be attributed to discharge lighting, computer loads and any distortion already present on the high voltage side of the transformer. the tests on both supplies have been performed using a 3kw vsd with a dc link reactor. the vsd has been run at the full load rating for all tests as the thid changes with variation of load and increasing with a decrease in load. the reactance of both supplies varies and this also changes the thid, which decreases with an increase in supply reactance. the measured results for the vsd harmonics for the ideal case are given in table 1. 129 syed m. islam table 1: vsd harmonic currents from ideal voltage source. h no. 1 3 5 7 9 11 thid current (%) 100.0 0.5 29.4 8.0 0.0 6.5 31.5 figure 7. experimental test set up. these results clearly show that there are no triplen harmonic currents, the small percentage of 3rd harmonic current can be neglected, as this would be attributed to the small amount of 3rd harmonic voltage present at the alternator terminals. the 5th harmonic current is approximately 10% higher whereas the 7th and 11th harmonics are slightly lower than the ideal square wave spectrum. however the overall thid is in close agreement with the ideal case. the laboratory power supply (distorted supply) was measured and the results of the harmonics present are given in table 2. these results have not been averaged and represent one time instant of the supply voltage. averaging of the harmonic voltages, magnitude and phase can in fact cause a reduction of the current harmonics, as cause-effects of the true values are not represented. the voltage supply contains the dominant harmonics and also a reduction of the phase a voltage. the recorded results for the test performed using the distorted supply are given in table 3. these results show that there is a large production of 3rd harmonic current and to a lesser extent the 9th harmonic in all 3 line currents. results also show that the other characteristic harmonics have increased as well, resulting in the thid increasing between 23% and 35% from the ideal test result. this increase can also be attributed to the decrease in supply reactance on this supply compared with the synchronous alternator used for the ideal case. the ideal thid for this supply could be in the order of 40%. this, however, cannot be measured to verify the result and has only been simulated. this then represents an increase of thid between 8% to 20%, which is quite significant. table 2: voltage supply harmonics. (a) phase a, (b) phase b, (c) phase c. h no. 1 3 5 7 thvd voltage 236.1 4.6 2 2.7 2.4% % f 100.0 1.9 0.8 1.1 angle 0 145 152 -56 (a) 130 characteristic and non-characteristic harmonics h no. 1 3 5 7 thvd voltage 239.3 2.9 4 3 2.4% % f 100.0 1.2 1.7 1.3 angle 0 151 -170 -56 (b) h no. 1 3 5 7 thvd voltage 239.1 3.5 2.2 2.8 2.1% % f 100.0 1.5 0.9 1.2 angle 0 144 166 -54 (c) table 3: measured results for current harmonics using the distorted voltage supply. (a) phase a, (b) phase b, (c) phase c. h no. 1 3 5 7 9 11 thid current (%) 100.0 11.7 44.1 36.8 4.2 12.5 60.7 (a) h no. 1 3 5 7 9 11 thid current (%) 100.0 11.2 40.9 30.8 1.2 7.7 53.5 (b) h no. 1 3 5 7 9 11 thid current (%) 100.0 18.1 48.5 37.2 3.1 12.0 65.6 (c) figure 8 shows the measured current waveform under the distorted supply. it can be seen that the peaks are no longer the same height, and the conduction period has changed slightly during this time period. figure 8. vsd line current fed from a distorted supply. 131 syed m. islam a simulation has been performed using a suitable vsd model (circuit model as in figure 1) and the distorted supply to compare the results of the software program with the practical case. microsim’s pspice circuit simulator has been used for the simulation. the output results for the harmonic currents are given in table 4. these results show that the thid is in close accord with the measured results for phases a and b, with the harmonic components within approximately 5% of the measured result. however the phase c result has a large error associated with it, and represents a reduction of 15% in thid and up to 15% error of the harmonic currents from the measured result. these errors could be due to following reasons: 1. incorrect measurements were recorded, 2. a large change in the supply distortion occurred during the testing, and 3. inaccurate modelling/simulation of the practical vsd model. the main cause for the error would most likely be due to 2 as the test system is open, and outside influences cannot be monitored easily. to further increase the accuracy of results between measured and simulated tests; a closed system would need to be used to ensure consistency of measured practical results so that the simulation model for the system can be accurately developed. table 4: simulated results for current harmonics using the distorted voltage supply. (a) phase a, (b) phase b, (c) phase c. h no. 1 3 5 7 9 11 thid current (%) 100.0 13.8 49.2 31.5 3.5 9.3 61.6 (a) h no. 1 3 5 7 9 11 thid current (%) 100.0 6.2 41.1 32.7 3.7 8.0 54.8 (b) h no. 1 3 5 7 9 11 thid current (%) 100.0 13.1 42.2 23.3 3.6 6.9 51.1 (c) 6. harmonic cancellation multi-pulse methods involve multiple converters so that the harmonics generated by one converter are cancelled by harmonics produced by other converters. if two six pulse converters are fed through two transformers of ∆-y and ∆-∆ configurations, then the secondary voltage of the first one will have 300 phase shift compared to the second one. in this case, the 5th and 7th harmonic currents will be anti phase to each other and will cancel in the line current giving rise to 11th and 13th as the first pair of harmonics which have much less amplitudes and therefore much smaller filters will be required to clean the input current waveform should this be necessary. in general, then the required minimum phase shift is 600/number of converters for harmonic cancellations. one method of harmonic cancellation is to mix single phase and three phase non-linear loads. it is seen that the 5th and the 7th harmonics produced by three phase loads and single phase loads are almost diametrically opposite in the phase plot. since, harmonics are added vectorially not arithmetically, this leads to significant cancellations. figure 9 shows the phase plot of the 5th and 7th harmonics for both single phase and three phase loads as a function of short circuit impedance. the impedance of the secondary side of the distribution transformer plays an important role in determining the magnitude and phase of the predominant harmonics discussed above. the phase angle of the 5th harmonic for typical single phase rectifier load lies in the sector of 450 to –650 and for three phase loads in the region of 1100 to –1350or +2150 (steffan, peter and blaabjerg, 2000). these two regions are almost opposite to each other resulting in cancellations. if the loads are completely balanced then exact cancellation may occur. 132 characteristic and non-characteristic harmonics figure 9. polar plots for 5th and 7th harmonics for various short circuit ratios and argument of short circuit impedance equal to 800. another method of harmonic cancellation is to employ different transformer connections to supply the three phase converters as discussed above. figure 10. two separate six pulse rectifier currents combine to a twelve pulse rectifier current. figure 10 shows two six pulse rectifiers one fed by a delta/star transformer and the other fed by a delta/delta winding transformer. in this case the secondary star winding voltage will be 300 phaseshifted from the secondary delta connected side. this will result in currents in the delta, star and input line as shown in figure 10 (derek, 1996). the resulting line current clearly will have no 5th and 7th harmonic currents as shown (i1+i2) in figure 10 and is similar to the current drawn by a twelve pulse converter. thus the first harmonic component of the current will be 11th and then 13th of amplitude 1/11th ifund and 1/13th ifund respectively. 7. harmonic standards harmonics generated by non-linear loads such as the variable speed drives are regulated by various international standards. harmonic limits are normally associated with background voltage distortions and varies from transmission to distribution systems and country to country. figure 11 shows the allowable distribution voltage %thd for various countries. in australia, the harmonic standards are in three stages. in stage 1, automatic acceptance are given to non-linear single and three phase loads of less than 0.3% of short circuit capacity at point of common coupling (pcc), between 5-75 kva for secondary distribution systems and 50-500 kva for primary distribution systems. in stage 2, loads greater than 75 kva for secondary distribution systems and 500 kva for primary distribution systems are considered. in this case, 133 syed m. islam connection is permitted according to the relation between the converter rated power and the system short circuit level, provided that the distortion level is within 75% of the permitted limits shown in table 5: figure 11. comparison of national standards. stage 3 applies to all loads that do not meet above conditions that is, loads greater than given in figure 12 and where voltage distortion is greater than 75% of table 5. stage 3 also requires detail analysis of the system and load according to a procedure described in the standard. harmonic distortion produced by the new load should be estimated before connection and should not exceed values given in table 5. if more than one customer is supplied at pcc then the supply authority can limit distortion to an equitable value between them. connection at transmission and sub-transmission level is also required to carry out detailed analysis including resonances. table 5: thd limits for equipment under stage 2, (as2279). system volts %thd odd even primary and secondary distribution systems up to 33 kv 5 4 2 transmission and sub-transmission 22, 33 and 66 kv >110 kv 3 1.5 2 1 1 0.5 figure 12. equipment size in stage 3 (as 2279). 134 characteristic and non-characteristic harmonics the basic philosophy of the ieee 519-1992 (currently under revision) is to limit: • harmonic current injected into the power system • utility responsible for maintaining voltage distortion current distortion limits are given in table 6. table 6: ieee 519 current limits. scr= i / i1 <ii ii<h<17 17<h<23 23<h<35 35<h tdd < 20 4.0 2.0 1.5 0.6 0.3 5.0 20-50 7.0 3.5 2.5 1.0 0.5 8.0 50-100 10.0 4.5 4.0 1.5 0.7 12.0 100-1000 12.0 5.5 5.0 2.0 1.0 15.0 >1000 15.0 7.0 6.0 2.5 1.4 20.0 the iec 61000 series is an internationally accepted set of standards and comprise iec 61000-3-2, 61000-3-4, 61000-3-6, 61000-3-3, and 61000-3-5. however, iec 61000-3-4 is the most relevant one for industrial installations. 8. conclusions the increased use of 6-pulse vsds will cause an increased level of harmonic currents in the supply network. these harmonic currents are characterised typically by the odd harmonics without the triplens. the analysis presented here has shown that these characteristic harmonics will vary and a production of the triplen harmonics will occur in the presence of an unbalanced or distorted voltage supply. the balance of harmonic currents will also be lost as shown from the results. a detailed study of existing voltage levels and distortion on a system to where a vsd or vsds are to be connected should be performed, as this will affect the current distortion from the vsds. the impact of the analysis presented the following; the thid will be increased leading to a possible case where harmonic current levels may not meet ieee519-1992; if harmonic trap filters are used to meet ieee519-1992 they may not reduce harmonic levels adequately to meet the specification. the paper also outlines the technique for minimisation of harmonic currents by mutual cancellation techniques. finally, relevant standards are also included. 9. acknowledgments the author gratefully acknowledges the support from alstom automation & control for the use of an alspa gd3000e vsd used for testing. references gary, w.k.chang. and wilsun, x.u. 1998. modelling of harmonic sources; power electronic converters, tutorial on harmonics modelling and simulation, ieee power engineering society, 98tp125-0, 28-34. cyril, w.lander. 1987. power electronics 2nd edition. london: mcgraw-hill, 259-274. ali, i.maswood. and geza joos. 1991, problems and solutions associated with the operation of phase-controlled rectifiers under unbalanced input voltage conditions, ieee transactions on industry applications, 27(4): 765-72. 135 syed m. islam mark, f. mcgranaghan. and david, r.mueller. 1999. designing harmonic filters for adjustable-speed drives to comply with ieee-519 harmonic limits, ieee transactions industry applications, 35(2): 312-318 mohan, undeland, robbins. 1995. power electronics: converters, applications and design, 2nd edition. new york: john wiley & sons inc., 103-113. derek, a.paice. 1996. power electronic converter harmonics: multipulse methods for clean power. new jersey: ieee press, 15-23 and 97-113. syed, m.peeran. and creg, w.p.cascadden. 1995. application, design and specification of harmonic filters for variable frequency drives, ieee transactions on industry applications, 31(4): 841-847. w.xu. and randae. 1998. analysis of unbalanced harmonic propagation in multiphase power systems, tutorial on harmonics modelling and simulation, ieee power engineering society. 98tp125-0, 61-66. steffan hansen, peter nielsen. and blaabjerg, f. 2000, harmonic cancellation by mixing non-linear single phase and three phase loads, ieee trans on industry applications, 36(1): 152-159. derek, a.paice. 1996. power electronic converter harmonics, ieee press. received 25 june 2001 accepted 20 november 2001 136 syed m. islam school of electrical and computer engineering, curtin university of technology gpo box u 1987, wa 6845, australia. characteristic harmonic currents drawn by 6 pulse rectifiers production of non-characteristic (triplen) harmonic currents 3.1 effect of voltage reduction 3.2 effects of supply voltage distortion calculation of harmonics 4.1 effect of voltage imbalance 4.2 effect of voltage distortion. experimental results harmonic cancellation conclusions acknowledgments references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 1-10 © 2003 sultan qaboos university effect of cold and hot temperature on behavioral and selected physiological measures of uromastyx aegyptius (agamidae) a.a. el-banna and a.m. aljohany department of zoology, college of science, king saud university, p.o.box 2455, riyadh 11451, saudi arabia, email: ajohany@ksu.edu.sa. أثر درجة الحرارة الباردة والعالية على السلوك وبعض القياسات الفسيولوجية للضب المصري أمين عبدالحميد البنا وعوض الجهني . تمـت دراسة االستجابات السلوكية والفسيولوجية والكيمياحيوية لدرجات الحرارة الباردة والعالية للضب المصري :خالصـة uromastyx aegyptius . ـ باإلضافة إلى مجموعة ثالثة ضابطة . م تقسيم اثني عشر ضباَ إلى مجموعتين اختباريتينوقـم ت جمعت . م ° 22 ساعة للتأقلم عند درجة حرارة 24وقد أعطيت الثالث مجموعات فترة . م ° 22حفظـت تحت درجة حرارة في ) p<0.05(ت النتائج فروقاً معنوية عينات الدم من كل حيوان عندما تصل درجة حرارة الجسم الدرجة المحددة ، وقد أظهر هذا االنخفاض في مواد التمثيل خارج ) م2º(انخفاض جلوكوز الدم ومستوى الكولسترول خالل فترة تعرض الحيوانات للبرودة أدى إلى زيادة معنوية ) م45º(أن رفع درجة حرارة الحيوان إلى . الخاليا يعكس زيادة في امتصاص الخاليا لهذه المواد )p<0.05 ( هذه التغيرات يمكن أن تعزي إلى زيادة فقد الماء بالتبخير . فـي كمـية البروتين الكلي واليوريا وحمض اليوريك خالل t3 ،t4في ) p<0.05(لم تظهر أي تغيرات معنوية . وبخاصة بسبب زيادة اللهث وما يتبعه من نقص في حجم البالزما ج هذه الدراسة إلى زيادة في حجم األيض الالهوائي في الضب خالل فترة التبريد بديل وقد أشارت نتائ . فترة التبريد أو التسخين نقص مستوى الجلوكوز من خارج الخاليا إلى داخل الخاليا مما يشير إلى استعداد الحيوان لتفادي حدوث التجمد الكامن لكي تتم . حماية الحيوان من تجمد السوائل داخل الخاليا abstract: the behavioral, physiological and biochemical response to low (2°c) and high (45°c) temperatures was studied in uromastyx aegyptius. twelve animals were divided into two experimental groups. a third control group was kept at 22 °c. all animals in the cooling, warming, and control groups were allowed a period of 24 hours for adjustments at 22 °c. blood samples were collected from each animal when body temperature reached the corresponding levels. the results showed a significant (p<0.05) decrease in blood glucose and cholesterol levels during cooling (2°c). this reduction in extracellular fluid substrates reflects an increase in cellular uptake of these substrates. warming (45°c) resulted in a significant (p< 0.05) increase in total proteins, urea, and uric acid. these later changes could be attributed to an increase in the evaporative water loss, particularly due to the increased observed panting, and the associated reduction in plasma volume. there were no significant (p>0.05) changes in t3 and t4, during cooling nor during warming. the results of this study suggest augmentation of anaerobic metabolism of the u.aegyptius during cooling as evident by reduction in blood glucose levels. furthermore, shift of glucose from the extracellular to the intracellular fluids demonstrates anticipation against potential freezing in order to protect the animal from intracellular freezing. keywords: metabolism, temperature; behaviour; blood constituents; plasma; uromastyx; lizard. 1. introduction the spiny tailed lizard uromastyx aegyptius is the largest agamid lizard and is widespread in arabia (arnold, 1986). it is a diurnal animal and becomes active during the warm part of the day. many terrestrial ectotherms, like the u. aegyptius, have a considerable capacity for behavioral and physiological thermoregulation (bartholmew, 1981). although many ectotherms are 1 a.a. el-banna and a.m. al-johany physiologically adapted to survive at low ambient temperatures, terrestrial ectotherms are particularly susceptible to freezing, and there are a variety of strategies that enable ectothemic animals to survive freezing conditions (hew et al. 1986). ectotherms exposed to high temperature can either attempt to regulate their body temperature below the air temperature or rely on biochemical adaptation for tolerance of high body temperature (cossins and bowler, 1987). additionally, high temperature causes proteins to unfold and hence enzymes protein can no longer function. however, heat shock protein (hsp) response by programming cellular activities that bind and help mutated protein to restore their shape. ulmasov, et al., (1992) and zatespina, et al., (2000) found that hsp plays a major role in the cellular response during heat stress. their findings also included a positive relationship between hsp and the magnitude of thermotolerance among lizard species. we thought that hsp dynamic relates to total plasma protein, and related measures such as albumin, and globulin. thyroid hormones are involved indirectly in thermoregulation by increasing metabolic rate and subsequently heat production. despite this, controversy exist regarding the initial calorigenic effects of thyroxin. sinha and choubey (1981) reported a positive relationship between thyroid activity and environmental temperature in u. hardwickii lizards. as thyroxin enhances cellular absorption of glucose and also influence plasma cholesterol, we included these measures in our study. thermoregulatory adjustment of the lizards are behavioral or physiological changes to deflect the body temperature from environmental heat loads (firth and belan, 1998). measurements of blood composition are commonly used to assess the way in which the environment affects the physiology of animals. therefore the objective of the present study was to investigate some aspects of physiological and biochemical responses of the u.aegyptius when exposed to low and to high temperatures. 2. materials and methods eighteen u. aegyptius (mean wt. 760 gms) were collected from the field (rumah and haradh townships around riyadh city, saudi arabia). the animals were housed in an open vivarium (2m x 1/4 m) with overhead heat and light lamps with timer control set at 12:12 for light and dark periods and kept at a constant air temperature of 22°c (room temperature). the animals were then divided into three groups (6 animals in each) of matched body weight. blood samples were collected from animals in the control group at 22°c. animals in the two experimental groups were exposed to the low and high temperatures, as described below. body temperature was maintained at 45°c for the warm group and 2°c for the cold group for 24 hrs and 48 hrs, respectively. blood samples were collected at the end of exposure time. all blood samples were collected by cardiac puncture method using vacutainers. the vials were kept at room temperature for one to two hours, then, centrifuged at 3000 rpm for 10 minutes to separate the plasma which was stored at 20°c for later analysis. 2.1. cooling procedure: exposure to low temperature all animals of the second group were placed in plexiglas chamber. a ysi model 423 thermocouple temperature probe was inserted 2 cm into the cloaca of the animal and held tight with a tape on the tail of the animal. the probe was attached to an ysi telethermometer (model 44) in conjunction with a omni scribe chart recorder to monitor the internal body temperature of the animal. each animal was placed on a multiple benched mini-cold lab model 2203 (lkb-produkter ab), and the temperature was set to 2ºc. animals were left in this environment for 48 hours before taking the blood sample. 2.2. warming procedure: exposure to the high temperature the same probe and recording instruments were tied to the animals while exposing them to the high temperature. a plexiglas chamber animal was fixed in a water-bath (gallenkemp gmbh) with temperature control thermostat set at 45ºc. each animal was introduced into the chamber and then 2 effect of cold and hot temperatures the temperature was gradually raised till the water-bath temperature and the animal body temperature reached 45 ±1ºc. after constant exposure to this temperature for 24 hr, blood samples were collected. 2.3. analysis of plasma the following components were determined quantitatively in the plasma collected from the three groups of u.aegyptius, using the biomerieax vitek (missouri, usa) kits. total protein following the principal of biuret reaction according to peters (1968); albumin according to drupt et al. (1974); triglyceride according to fossati and prencipe (1982); cholesterol according to anonymous (1989); glucose according to tender (1969); urea according to the modified berthelot reaction after patton and crouch (1977); uric acid as described by artiss and entwistle (1981). t3 and t4 were determined using enzyme immuno assay (eia). plasma globulin concentration was calculated by subtraction. fractionation of total protein was carried-out using cellulose acetate electrophoresis (helena lab. instruments ltd. u.k), and the electropherograms were then scanned using personal densitometer si (amersham pharmacia biotech), and the percentages of the different protein fractions were determined. 2.4. statistical analysis analysis of variance (anova) was utilized for testing the overall effects of cooling and warming on selected blood measures. post-hoc comparisons were conducted between pairs of means, via lsd procedure, on total protein, albumin, cholesterol, globulin, urea, uric acid, t3, and t4. 3. results 3.1 behaviour u.aegyptius are known to tolerate extreme low and high temperatures (bartholmew, 1981). the results of this study showed that when the animals were exposed to low temperature (2°c), they became lethargic and immobile. no change of color was noticed during this period. at 2°c blood circulation was very slow and the animal needed to be rubbed on the neck and back to facilitate the flow, when drawing blood. at high temperature u.aegyptius were noticed to fight for release when body temperature reached 40°c. defecation was observed after two hours of high temperature exposure. they started to pant when temperature crossed the 40°c limit. body colouration changed from a dark tan to pale yellow at 42°c. 3.2. blood components table 1 shows the concentrations of plasma proteins in u.aegyptius exposed to the low and high temperatures compared to that in u.aegyptius exposed to the room temperature (22°c). no significant difference was observed in plasma total proteins between animals exposed to the 2°c and the 22°c, but there was a significant (p<0.05) increase in plasma total proteins when animals were exposed to the 45°c. the main increase in plasma total proteins at the 45°c was due to an increase in albumin and α 1-globulin fractions. plasma albumin and the albumin/globulin ratio were significantly (p<0.05) lower in animals exposed to the 2°c (table 2). the electrophoretic separation of plasma proteins indicates that there was a significant decrease (p<0.05) in the α 2-globulin fraction when animals were exposed to either the 2°c or the 45°c. no significant change was observed in the percentages of the β and γ-globulin fractions when animals were exposed to the three different temperatures (table 2). the mean concentrations of some plasma constituents in u.aegyptius exposed to the three different temperatures are presented in table 1. there was no significant (p>0.05) difference in the concentrations of plasma triglycerides in u.aegyptius exposed to the different temperatures (table2). plasma cholesterol concentrations in animals exposed to the 22°c and the 45°c were 3 a.a. el-banna and a.m. al-johany about the same, but a significant (p<0.05) decrease in cholesterol concentration was found in animals exposed to the 2°c (table 3). the mean plasma glucose concentration in u.aegyptius at room temperature (22°c) was significantly (p< 0.05) decreased in animals exposed to the 2°c, and was significantly (p<0.05) increased in animals exposed to the 45°c (table 3). table 1: mean concentration of plasma proteins in u.aegyptiuss exposed to low, room and high temperature. temperature measure cold (2°c) room (22°c) warm (45°c) total protein (g/dl) 2.53 ± 0.27 2.90 ± 0.15 3.65 ± 0.17 albumin (g/dl) 0.98 ± 0.09 1.27 ± 0.10 1.67 ± 0.09 globulin (g/dl) 1.98 ± 0.30 1.74 ± 0.19 2.30 ± 1.10 albumin/globulin ratio 0.49 ± 0.06 0.72 ± 0.05 0.73 ± 0.05 triglyceride (mg/dl) 19.2 ± 3.5 18.3 ± 4.0 22.5 ± 1.8 cholesterol (mg/dl) 104.7 ± 15.9 234.3 ± 28.3 226.4 ± 28.4 glucose (mg/dl) 206 ± 8.8 281.9 ± 16.8 358.0 ± 12.8 urea (mg/dl) 12.3 ± 1.3 8.8 ± 0.5 12.0 ± 8.0 uric acid (mg/dl) 2.8 ± 0.3 3.1 ± 0.4 5.8 ± 0.7 t3 (ng/dl) 7.0 ± 0.5 7.6 ± 1.0 7.6 ± 0.8 t4 (µg/dl) 3.0 ± 0.2 4.1 ± 0.4 5.4 ± 0.3 table 2: summary table of anova conducted on dependent variables (measures). measure source of variation ss df ms f(value) f(probability) total protein between group within group 4.32 3.85 2 16 2.15 0.24 17.21* 3.63 albumin between group within group 1.42 0.87 2 16 0.71 0.05 12.29* 3.63 globulin between group within group 1.03 5.32 2 16 0.51 0.33 1.54 3.63 albumin / globulin ratio between group within group 0.36 1.28 2 16 0.18 0.08 2.25 3.63 glucose between group within group 74174.67 17467.53 2 16 37087.34 1091.72 33.97* 3.63 triglycerides between group within group 51.69 989.49 2 16 25.84 61.84 .41 3.63 cholesterol between group within group 64793.73 65184.06 2 16 32396.86 4074.00 7.97* 3.63 urea between group within group 45.62 82.16 2 16 22.81 5.14 4.44* 3.63 uric acid between group within group 35.68 28.36 2 16 17.84 1.77 10.06* 3.63 t3 between group within group 1.25 60.09 2 16 0.62 3.75 0.16 3.63 t4 between group within group 18.84 78.26 2 16 9.42 4.89 1.92 3.63 * p<0.05 4 effect of cold and hot temperatures there was a significant (p<0.05) increase in the mean plasma urea concentration when u.aegyptius were exposed to either the 2°c or to the 45°c (table 3). also, there was a significant (p<0.05) increase in the mean plasma uric acid concentration when u.aegyptius were exposed to the 45°c, but no change in plasma uric acid was observed in animals exposed to the 2°c and 22°c (table 3). table 3: multiple comparisons of differential mean effect using lsd method for only those variable which were significantly different. total protein albumin glucose group mean diff. sig. group mean diff. sig. group mean diff. sig. lt rt ht -0.5333* -1.2905* 0.034 0.000 lt rt ht -0.4333* -0.7988* 0.033 0.000 lt rt ht -74.700* -151.328* 0.001 0.000 rt lt ht 0.5333* -0.7571* 0.034 0.004 rt lt ht -0.4333* -0.3655 0.033 0.058 rt lt ht 74.700* -76.628* 0.001 0.001 ht lt rt 1.2905* 0.7571* 0.000 0.004 ht lt rt 0.7988* 0.3655 0.000 0.058 ht lt rt 151.328* 76.628* 0.000 0.001 cholesterol uric acid group mean diff. sig. group mean diff. sig. lt rt ht -129.746* -121.728* 0.003 0.003 lt rt ht -0.2667 -2.9657* 0.733 0.001 rt lt ht 129.746* 8.018 0.003 0.824 rt lt ht 0.2667 -2.6990* 0.733 0.002 ht lt rt 121.728* -8.018 0.003 0.824 ht lt rt 2.9657* 2.6990 0.001 0.002 *the mean difference is significant at the 0.05 level. the mean plasma t3 and t4 concentrations were not significantly different among animals exposed to the three different temperatures, although t4 concentrations were somewhat higher at the 22°c and the 45°c (table 2). 4. discussion in their natural habitat, u.aegyptius are exposed to low or high temperatures. in many instances they continue activity while air temperature is around 40°c and above (louw and gideon, 1993). they remain in their burrows when surface temperature falls below 10°c. they are not true hibernators; they may come out during winter when it is warm enough like many other lizards. they usually become active when temperature reaches 30°c, and when temperatures reache above 40°c they seek shelter in their deep underground burrows. in our study, a significant decrease in blood glucose and cholesterol levels were found in u.aegyptius exposed to 2°c for about two days. this was also associated with a significant decrease in albumin fraction of the plasma proteins, and with a significant increase in the levels of plasma urea. on the other hand, a significant increase in blood glucose, as well as a significant increase in plasma total proteins, urea and uric acid were found in u.aegyptius exposed to 45°c for 24 hours. to adjust for changes in environmental temperature many ectothermic vertebrates 5 a.a. el-banna and a.m. al-johany lower the selected body temperature during winter (hazel and prosser, 1974; case, 1976). ectotherms exposed to higher temperatures attempt to regulate their body temperature below the air temperature (huey, 1982). these alterations in the selected body temperature lead to blood biochemical changes. such modification seem to be achieved by metabolic changes which lead to changes in the composition of blood and tissues (white and somero, 1982; geiser et al., 1992). therefore, measurements of blood composition are commonly used to assess the way in which the environment affects the physiology of animals. total protein (tp) 0 0.5 1 1.5 2 2.5 3 3.5 4 2 c degrees 22 c degrees 45 c degree albumin (alb) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 2 c degrees 22 c degrees 45 c degree plasma glucose (glu) 0 100 200 300 400 500 2 c degrees 22 c degrees 45 c degree uric acid (ua) 0 1 2 3 4 5 6 7 2 c degrees 22 c degrees 45 c degree c o l e s t e r o l ( c h o l ) 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 2 c d e g r e e s 2 2 c d e g r e e s 4 5 c d e g r e e t p (m g\ dl ) a lb (g m \d l) u a (g m \d l) g lu (g m \d l) c ho l (m g\ dl ) figure 1. plot of the changes in total protein (tp), albumin (alb), glucose (glu), uric acid (ua), and cholesterol (chol) among variation in environmental temperature. when lizard species normaly encounter temperatures close to or below 0°c, they have exceptionally high survival rates (geiser and firth, 1992). these lizards survive exposure to subfreezing temperatures by supercooling, i.e., by remaining unfrozen at temperatures below the equilibrium crystallization temperature of body fluids (grenot and heulin, 1990). also, some lizards are freeze-tolerant (storey and storey, 1992; costanzo et al., 1995). ectotherms can counteract a potentially freezing ambient temperature by increasing the osmotic concentration o 6 f effect of cold and hot temperatures their body fluids so that its freezing point is depressed below the ambient temperature (withers, 1992). some ectotherms accumulate high concentration of specific solutes to depress their freezing point; these solutes are typically sugar, such as glucose or sugar alcohols. their low molecular weight maximizes the freezing point depression per mass of solute (withers, 1992; lee and costanzo, 1993). these sugars apparently have cryoprotectant effect, and they protect membranes and enzymes against cold denaturation and cold shock injury. it is important in these animals to avoid the freezing of their intracellular fluids, since intracellular ice crystals apparently destroy the integrity of intracullar membranes and organelles. in contrast, extracellular freezing does not disrupt essential cell structures and is not lethal, at least to the freeze-tolerant species (withers, 1992; lemos-espinal and ballinger, 1992). the decrease in blood could reflect a shift of glucose from the blood (extracellular fluid) to the intracellular fluids, probably through increasing cellular uptake of glucose, in anticipation of potential freezing ambient temperature. in doing that, the animals guard against intracellular freezing by depressing intracellular freezing point. the accumulation of the putative cryoprotectant glucose in tissues of lizards subjected to freeze tolerance trials had been reported (costanzo et al. 1995). the mean blood cholesterol level in u.aegyptius at room temperature (234.3 ± 28.3 mg/dl) is relatively higher than that in many mammalian species (al-tuwaijri, 1987). also, cholesterol content in u.aegyptius’s tissues is more than twice the cholesterol content of camel, lamb and cattle tissues (abu-tarboush et al. 1996). cholesterol could also have cryoprotectant effect in lizards exposed to low temperatures, and the changes in blood cholesterol level observed in the present study may indicate a role for cholesterol in thermoregulation. changes in the lipid composition of tissues and cell membranes are apparently required in order to maintain normal function at the lower body temperatures (bauwens, 1981). lizards exposed to high temperature try to reduce their body temperature below the air temperature, and this strategy of thermoregulation can only be accomplished by evaporative cooling. evaporation of water can dissipate a considerable amount of heat and lower the temperature (withers, 1992). relatively waterproof terrestrial animals are generally able to enhance evaporative cooling by markedly increasing their cutaneous or respiratory water loss. the lizard dipsosaurus totally dissipates its metabolic heat production by panting at air temperature more than 40°c, and the large agamid lizard amphibolurus can reduce its body temperature about 3.2°c below air temperature of 43°c, and the chuckwalla lizard sauromalus obseus can considerably lower its body and brain temperatures by evaporative cooling by panting (withers, 1992). in this study evoparative water loss (ewl) was not measured. however, we observed, particularly because of the increased panting, that the reduction in plasma volume could be the reason for the increased concentrations of plasma glucose, total proteins, urea and uric acid observed in u.aegyptius exposed to the 45°c. during dehydration, animals show elevated concentrations of osmolytes and proteins in their blood (dunlap, 1995). the increased plasma glucose concentration in u.aegyptius exposed to the higher temperature could also reflect a decrease in glucose uptake by tissues in order to avoid excess intracellular glucose breakdown and energy production, and excess heat load. lizards exposed to high temperature can also rely on biochemical adaptations for tolerance of high body temperature. heat stress has been shown to induce the synthesis of a family of proteins, the so-called heat shock proteins (hsps) in cells of a wide spectrum of ecologically different lizard species (ulmasov et al. 1992; feder and hofmann, 1998; zatsepina et al. 2000). the level of hsps were found to be higher in desert species than in the non-desert species (zatsepina et al. 2000), and the induction and active synthesis of hsps occurs within a temperature interval normal to the species (ulmasov et al. 1992). hsps play a key role in the cellular response to heat shock by maintaining the native state and proper folding of cellular proteins during physiological stress and by facilitating the restoration of cellular functions (morimoto, 1993; morimoto, et al., 1994). the expression of the hsp gene is tightly regulated to ensure that the response is proportional to the level of heat stress, and then repressed and terminated when normal physiological conditions recur (lindquist, 1986). we did not measure the synthesis of hsps in the present study, but these 7 a.a. el-banna and a.m. al-johany proteins can be synthesized, particularly by liver cells, within 1 to 2 hrs of exposure to the high temperature, and in desert lizards, the temperature range of induction and continuing synthesis of hsps was reported to be 36-50°c (ulmasov, et al., 1992). the changes in plasma protein and protein fractions observed in u.aegyptius exposed to the 45°c in the present study could reflect induction and synthesis of hsps. u.aegyptius exposed to different temperatures in the present study showed no changes in plasma levels of the thyroid hormones t3 and t4. it is not certain whether the thyroid hormones have a direct and immediate role in thermoregulation in lizards. sinha and choubey (1981) reported that the thyroid gland of the indian spiny tailed, u. harrdwickii, lizard appeared most active when the environmental temperature was high. when the temperature was low, the activity of thyroid gland was decreased. these authors also noted a reduction in thyroid activity in september. they did not reach a final conclusion because they found a parallel relation to the gonadal cycle. based on the results of the present study, it can be concluded that behavioral, physiological, and biochemical adjustments are altered in response to environmental temperature changes. however, the exact biological mechanisms are species specific in lizard populations. the physiological and biochemical control of thermoregulation in reptiles, and in u.aegyptius in particular, need more investigations, and as indicated by grigg and seebacher (1999) that the control of thermoregulation in reptiles is more complex than has been previously recognized. 5. acknowledgements we wish to thank dr. s. haffor for reviewing the manuscript. mr. awni el-gazawi and mr. m.y. abdulrawoof are also thanked for their technical help in the laboratory. references arnold, e.n. 1986. a key and annotated checklist to the lizards and amphisbaenians of arabia. fauna of saudi arabia 8: 335-435. artiss, j.d. and entwistle, w.m. 1981.the application of a sensitive uricase-peroxidase couple reaction to a centrifugal fast analyser for the determination of uric acid. clin chim acta.; 116(3):301-309. abu-tarboush, h. m., al-johany, a.m. and al-sadoon, m.k. 1996. proximate composition and fatty acids and cholestrol content of u.aegyptius’s meat (uromastyx aegyptius blanford 1874) at the end of winter and during spring. journal of college of agriculture of king saud university. 8 : 79-92. al-tuwaijri, a.s. 1987. standard biological data. human and experimental animals. king saud university press, riyadh, saudi arabia. anonymous 1989. the french consensus on cholesterol and dyslipoproteinemias. administration council of arcol. rev. prat.; 39(11): 972-974. review. french. bartholmew, g.a. 1981. physiological thermoregulation. in biology of the reptilia. vol. 12, physiological ecology eds c. gans and f. h. pough). academic press, new york. pp. 167-212 bauwens, d. 1981. survivorship during hibernation in the european common lizard, lacerta vivipara. copeia 1981: 741-744. case, t. j. 1976. seasonal aspect of thermoregulatory behavior in the chuckawalla, sauromalus obesus (reptilia, lacertilia, iguanidae). journal of herpetology 10: 85-95. 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49 (1-4): 464-469. peters, t. jr. 1968. proposals for standardization of total protein assays. clinical chemistry dec; 14(12):1147-59. sinha, a.k. and choubey, b.j. 1981. seasonal changes in the thyroid gland of indian spiny tailed, sand lizard, uromastix hardwickii (gray) male. z. mikrosk. anat. forsch. 95:72-80. storey, k.b. and storey, j. m. 1992. natural freeze tolerance in ectothermic vertebrates. annual review of physiology 54: 619-637. trinder, p. 1969. determination of blood glucose using 4-amino phenazone as oxygen acceptor. journal of clinical patholology.; mar; 22(2):246. 9 a.a. el-banna and a.m. al-johany ulmasov, k.a., shammakov, s., karaev, k. and evegenev, m.b. 1992. heat shock proteins and thermoresistance in lizards. proceeding of national academy of science. 89: 1666-1670. white, f.n., and somero, g. 1982. acid-base regulation and phospholipid adaptation to temperature: time course and physiological significance of modifying the milieu for protein function. physiology review 62: 40-90. withers, p. c. 1992. comparative animal physiology. saunders college publishing, new york. zatespina, o.g., ulmasov, k.a., beresten, s.f., molodtsov, v.b., rybtsov, s.a. and evegenev, m.b. 2000. thermotolerant desert lizards characteristically differ in terms of heat-shock system regulation. journal of experimental biology, 203: 1017-1025. received 18 may 2002 accepted 19 april 2003 10 effect of cold and hot temperature on behavioral and selected physiological measures of uromastyx aegyptius (agamidae) a.a. el-banna and a.m. aljohany department of zoology, college of science, king saud university, p.o.box 2455, riyadh 11451, saudi arabia, email: ajohany@ksu.edu.sa. 2. materials and methods 2.1. cooling procedure: exposure to low temperature 2.3. analysis of plasma analysis of variance (anova) was utilized for testing the overall effects of cooling and warming on selected blood measures. post-hoc comparisons were conducted between pairs of means, via lsd procedure, on total protein, albumin, cholesterol, globulin 3. results 3.1 behaviour u.aegyptius are known to tolerate extreme low and high temperatures (bartholmew, 1981). the results of this study showed that when the animals were exposed to low temperature (2(c), they became lethargic and immobile. no change of color was noticed 3.2. blood components temperature between group between group between group between group between group between group between group between group between group between group within group between group within group 4. discussion references squ journal for science, 2018, 23(2),137-146 doi: http://dx.doi.org/10.24200/squjs.vol23iss2pp137-146 sultan qaboos university 137 initial and boundary value problems for fractional differential equations involving atangana-baleanu derivative fatma s. al-musalhi 1 , nasser s. al-salti 1,2 *, and erkinjon karimov 2,3 1 department of mathematics, sultan qaboos university, p.o. box 36, pc 123, al khodh, muscat, sultanate of oman; 2 fracdiff research group, sultan qaboos university, muscat, sultanate of oman; 3 institute of mathematics, uzbekistan academy of sciences, tashkent 170, uzbekistan, *email: nalslti@squ.edu.om. abstract: in the present work, an initial value problem involving the atangana-baleanu derivative is considered. an explicit solution of the given problem in integral form is obtained by using the laplace transform. the use of the given initial value problem is illustrated by considering a boundary value problem in which the solution is expressed in the form of a series expansion using an orthogonal basis obtained by separation of variables. some examples are also given to illustrate the obtained results. keywords: atangana-baleanu derivative, initial-boundary value problem, fractional differential equation. باليانومشتقة أتنجانا معادالت تفاضلية كسرية ذات شروط ابتدائية وحدودية والتي تحتوي على فاطمة المصلحي، ناصر السلطي وإيركن كريموف في هذه الورقة تم دراسة معادلة تفاضليه تحتوي على مشتقة كسريه ألتنجانا باليانو في ظل وجود شروط ابتدائية تارة وباستخدام الملخص: باستخدام تحويل البالس. ولقد اتضحت أهمية هذه شروط حدودية تارة أخرى، وقد تم أوال إيجاد حل المعادلة في ظل وجود شروط ابتدائية المعادلة في إيجاد حل المعادلة التفاضلية في ظل وجود شروط ابتدائية وحدودية معا، والتي تم التعبير عن حلها في صورة متسلسلة رياضية. وفي األخير تم عرض بعض األمثلة لتوضيح النتائج التي توصلت لها الدراسة. مشتقة أتنجانا باليانو ، مسألة ذات شروط إبتدائية وحدودية، معادالت تفاضلية كسرية. ية:الكلمات المفتاح 1. introduction and preliminaries ecently, two newly defined fractional derivatives without a singular kernel have been suggested, namely, the caputo-fabrizio fractional derivative [1] and the atangana-baleanu fractional derivative [2]. these two new derivatives have been applied to real-life problems in various areas, for example in the fields of thermal science, material sciences, groundwater modelling and mass-spring systems [2 -7], and have been considered in a number of other recent works, see for example [8-17]. the main difference between these two definitions is that the caputofabrizio derivative is based on an exponential kernel, while the atangana-baleanu definition uses a mittagleffler function as a non-local kernel. the non-locality of the kernel gives a better description of the memory within structures with different scales. these two new derivatives are defined as follows: r fatma s. al-musalhi et al 138 σ ∈ definition 1.1. [2] let f ∈ h 1 (a, b), b > a, α ∈ [0, 1]. the caputo-fabrizio fractional derivative is defined as ( ) ( ) '( ) exp ( ) , 1 1 t cf a t a b d f t f s t s ds              (1) and the atangana-baleanu fractional derivative is given by ( ) ( ) '( ) ( ) , 1 1 t abc a t a b d f t f s e t s ds                (2) where h 1 (a, b) is the usual sobolev space, i.e., 𝐻1(𝑎, 𝑏) = {𝑓 ∈ 𝐿2(𝑎, 𝑏), 𝑓 ′ ∈ 𝐿2(𝑎, 𝑏) }, ( )b  denotes a normalization function such that b(0) = b(1) = 1, and 0 ( ) , re( ) 0, , ( 1) k k z e z z k            c is the mittag-leffler function of one parameter [18]. for properties related to these derivatives, see [2], [11], [15]. in this paper, we are concerned with solutions to initial and boundary value problems for fractional differential equations involving atanganabaleanu derivative. we first recall the mittag-leffler of two parameters , 0 ( ) , re( ) 0, re( ) 0, . ( ) k k z e z z k                c moreover, the mittag-leffler function ( )e t    is bounded (see [18]), i.e. ( ) ,e t m     (3) where m denotes a positive constant. in [2], atangana and baleanu considered the time fractional ordinary differential equation 0 ( ) ( ), abc t d f t u t   and, on using the laplace transform, they found the following solution 1 0 0 1 ( ) ( ) ( ) ( ) ( ) , ( ) ( ) ( ) t ab t f t i u t u t u s t s ds b b              where they have defined 1 0 0 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) t ab t i f t f t f s t s ds b b             to be the fractional integral associated with the fractional derivative (2). in this paper, we consider the following initial value problem (ivp) 0 0 ( ) ( ) ( ), 0, (0) , abc t d u t u t f t t u u      (4) intial and boundary value problems of fdes with a-b derivaitve 139 where 0 , .u r the solution of this ivp is obtained here by using the laplace transform, which can also be obtained by using the successive approximation method as illustrated in the arxiv version of this paper [19]. the use of such an ivp is illustrated by considering a boundary value problem in which the solution is expressed in the form of a series expansion using an orthogonal basis obtained by separation of variables. it is worth mentioning here that the fractional differential equation in (4), with or without initial condition, has also been considered by other authors, see for example [7], [20-22]. however, most of previous studies have either considered special forms of (t)f or considered only one case of  , namely, ( ) 1      b or ( ) 1      b . moreover, most of the solutions obtained previously fail to satisfy the initial condition, since the existence of a solution requires a necessary condition, namely, 0 (0)  f u , which was first addressed in the arxiv version of this paper [19]. the rest of the present paper is organized as follows. section 2 is devoted to our main result, which is an explicit solution of the ivp (4) and to solving a boundary value problem utilizing the solution of the ivp (4). we conclude this paper by presenting some examples to illustrate the obtained results. 2. main result 2.1 initial value problem here, we consider the following problem: find a solution 1 ( ) (0, )u t h  that satisfies the following equation 0 ( ) ( ) ( ), 0, abc t d u t u t f t t     (5) and the initial condition 0, (0)u u (6) where 0 , .u r the solution of this initial value problem is formulated in the following theorem: theorem 2.1.  if 0 ( ) , ( ) (0, ) , (0) , 1 b f t c f u           then the solution of the initial value problem (5) (6) is given by 0 1 ,2 0 ( ) 1 ( ) ( ) ( ) (1 ) ( ) (1 ) ( ) (1 ) ( ) ( ) ( ) ( ) . ( ( ) (1 )) ( ) (1 ) t b u u t e t f t b b b b f t e t d b b                                                            (7)  if 1 0 ( ) , ( ) [0, ) , (0) 1 b f t ac f u           , then the solution of the given ivp is given by 2 0 (1 ) (1 ) ( ) ( ) ( ), ( ) ( ) c t u t d f t f t b b           (8) where the space 1 [0, )ac  is defined as 𝐴𝐶1 ≔ {     1 0 ( ) 0 , [0, ) t f t f g z dz g l    } and 0 ( ) c t d f t  represents the caputo fractional derivative of order ( 0 1  ) and is defined as [15] 0 0 1 ( ) ( ) ( ) . (1 ) t c t d f t t y f y dy          fatma s. al-musalhi et al 140 proof. applying the laplace transform to both sides of equation (5) and using (6), we have 1 0 ( )( ) ( ) ( ), 1 1 s u s s ub u s f s s               (9) where  ( ) ( ) ( )u s u t s and   1 0 0 ( )( ) ( ) ( ) . 1 1 abc t s u s s ub d u t s s              simplifying and solving for u (s), we get 1 0 ( ) (1 ) ( ) ( ), ( ( ) (1 )) ( ( ) (1 )) b s u s u s f s s b s b                           for ( ) , 1 b      which can be rewritten as 1 0 1 0 2 ( ) (1 ) ( ) ( ) ( ( ) (1 )) ( ( ) (1 )) ( ) (1 ) ( ) (1 ) ( ) (1 ) ( ) ( ( ) (1 )) ( ( ) (1 )) ( ) (1 ) ( ) ( ( ) (1 )) ( ) ( b s u s u s f s b s b s b b b s u f s b b s b b b s b                                                                                            ( ) 1 ) f s        since the laplace transform of the mittag-leffler function is given by  1 , ( ) ( ) , s t e t s s              applying the laplace inverse will then give 0 ,1 1 ,2 ( ) (1 ) ( ) ( ) ( ) (1 ) ( ) (1 ) ( ) (1 ) ( ) * ( ) , ( ( ) (1 )) ( ) (1 ) b u u t e t f t b b b b t e t f t b b                                                         which is equivalent to the desired result as given in equation (7). note that the condition 0 (0)f u  is needed to ensure that 0 (0)u u . for ( ) , 1 b      equation (9) gives, 2 1 0 (1 ) (1 ) ( ) ( ). ( ) 1 u s s u s f s b                    intial and boundary value problems of fdes with a-b derivaitve 141 applying the laplace inverse, we obtain 2 2 0 (1 ) (1 ) (1 ) (0) 1 ( ) * ( ) ( ). (1 ) ( ) (1 ) ( ) (1 ) ( ) t t f u t t u f t f t b b b                                    using the condition 0 (0) ,f u  one can obtain the desired solution (8). remark 2.2. for the case 0  and (0) 0,u  we get 1 0 1 ( ) ( ) ( ) ( ) , ( ) ( ) ( ) t u t f t f t d b b               which coincides with the result obtained in [2]. note that the obtained results for the ivp (4) are analogous to the results obtained for the case of caputo-fabrizio fractional derivative [8]. in the next section, we consider a direct initial-boundary value problem including a partial fractional differential equation with the atangana-baleanu derivative. to obtain the solution of the direct problem, we have utilized the solution of the ivp (4). it is also worth mentioning here that the condition 0 (0)f u  makes it impossible to consider inverse source or inverse initial problems with the atangana-baleanu fractional derivative. 2.2 initial-boundary value problem now, we consider a direct problem of determining ( , )u x t in a domain  ( , ) : 0 1, 0 ,x t x t t      such that 2 1 (., ) (0,1), ( ,.) (0, )u t c u x h t  and satisfies the following initial-boundary value problem: 0 ( , ) ( , ) ( , ), ( , ) abc t xx d u x t u x t f x t x t     (10) (0, ) 0, (1, ) 0, 0 ,u t u t t t    (11) ( , 0) 0, 0 1,u x x   (12) where ( , )f x t is a given function. we begin by using the separation of variables method to solve the homogeneous equation corresponding to equation (10) along with the boundary conditions (11). thus, we obtain the following spectral problem: '' 0, (0) 0, (1) 0. x x x x      (13) which is self-adjoint and has the following eigenvalues 2 ( ) , 1, 2, 3, ... . k k k   the corresponding eigenfunctions are sin( ), 1, 2, 3, ... . k x k x k  (14) since the system of eigenfunctions (14) forms an orthogonal basis in 2 (0,1)l [23], we can then write the solution ( , )u x t and the given function ( , )f x t in the form of series expansions as follows: 1 ( , ) ( ) sin( ), k k u x t u t k x     (15) 1 ( , ) ( ) sin( ), k k f x t f t k x     (16) fatma s. al-musalhi et al 142 where ( ) k u t are the unknown coefficients to be found, and the coefficients ( ) k f t are given by 1 0 ( ) 2 ( , ) sin( ) . k f t f x t k x dx  substituting (15) and (16) into (10) and (12), we obtain the following fractional differential equation 2 2 0 ( ) ( ) ( ), abc t k k k d u t k u t f t    along with the following condition (0) 0. k u  whereupon using theorem 2.1, the solution is given by 2 2 2 2 2 2 2 1 , 2 2 0 1 ( ) ( ) ( ) ( ) (1 ) ( ( ) (1 )) ( ) ( ) ( ) , ( ) (1 ) k k t k b u t f t b k b k k f t t e t d b k                                       with (0) 0, k f  which is achieved by assuming ( , 0) 0.f x  thus, the solution ( , )u x t can now be written as 2 2 2 2 2 1 2 2 1 , 2 2 0 1 ( ) ( , ) ( ) ( ) (1 ) ( ( ) (1 )) ( ) ( ) ( ) sin( ). ( ) (1 ) k k t k b u x t f t b k b k k f t e t d k x b k                                               in order to complete the proof of the existence of solution, we need to show the uniform convergence of the series representations of 0 ( , ), ( , ), ( , ), ( , ). abc x xx t u x t u x t u x t d u x t  since the mittag-leffler function appearing in the expression of u(x, t) is bounded, the uniform convergence of the series representation of ( , )u x t is ensured by assuming ( ,.) (0, ).f x c t now, the series representation of ( , ) xx u x t is given by 2 2 2 2 2 2 2 2 2 1 2 2 1 , 2 2 0 2 2 1 1 0 (1 ) ( ) ( , ) ( ) ( ) (1 ) ( ( ) (1 )) ( ) ( ) ( ) sin( ) ( ) (1 ) ( ) ( ) sin( ) sin( ) ( ) ( ) (1 ) xx k k t k t k k k k k k b u x t f t b k b k k f t e t d k x b k b f t k x k x f e b k                                                                     2 2 ,1 2 2 ( ) . ( ) (1 ) k t d b k               assuming ( , ) t f x t is integrable, it is clear that the second term of the above series converges uniformly. for the convergence of the first term, we assume (0, ) (1, ) 0f t f t  and use integration by parts to get 1 1 1 1 1 1 1 ( ) sin( ) ( ) sin( ) ( ) , k k k k k kk k f t k x f t k x f t               intial and boundary value problems of fdes with a-b derivaitve 143 where 1 1 0 ( ) 2 ( , ) cos( ) . k x f t f x t k x dx  using the inequality 2 21 ( 2 )aa b b  and the bessel’s inequality for trigonometric series, we then have the following estimate 2 2 2 2 2 12 2 (0,1) 1 1 1 1 1 1 2 2 2 1 ( ) sin( ) ( , ) . k k x l k k k k f t k x f f x t k                      therefore, the expression of ( , ) xx u x t is uniformly convergent. the uniform convergence of 0 ( , ), abc t d u x t  can be proved in a similar way. the uniqueness of the solution can be obtained using the completeness properties of the system sin( ) .k x the main result for the direct problem can be summarized in the following theorem: theorem 2.3. assume (., ) (0,1), ( ,.) (0, )f t c f x c t  such that ( , 0) 0, (0, ) (1, ) 0,f x f t f t   1 ( , ) (0, ), t f x t l t and 2 ( , ) (0,1), x f x t l then the problem (10) (12) has a unique solution ( , )u x t given by 2 2 2 2 2 1 2 2 1 , 2 2 0 1 ( ) ( , ) ( ) ( ) (1 ) ( ( ) (1 )) ( ) ( ) ( ) sin( ). ( ) (1 ) k k t k b u x t f t b k b k k f t e t d k x b k                                               where, 1 0 ( ) 2 ( , ) sin( ) . k f t f x t k x dx  3. illustrative examples in this section, we give some examples to illustrate our results presented in theorems (2.1) and (2.3), choosing ( ) 1.b   example 1. here, we present solutions of three different initial value problems by considering different choices of ( ),f t  and 0 u .  the constant function ( ) 1u t  solves the following ivp: 0 ( ) ( ) 1, (0) 1. a bc t d u t u t u       for 1 ( ) , ( 1)f t t      , the solution of ivp (5)-(6) with 1  and 0 0u  is given by 1 , 1 ( ) ( ) ( );u t t t e t                    the solution of the following ivp: 0 ( ) ( ) ( ), (0) 1. a bc t d u t u t e t u            fatma s. al-musalhi et al 144 is given by:  (1 ) ( ) ( ) . (2 ) (2 ) 2 u t e t e t                             example 2. consider the boundary value problem (10) − (12) with ( , ) sin( ).f x t t x using theorem 2.3, the solution ( , )u x t is given by 2 1 , 22 2 2 2 1 ( , ) sin( ). 1 (1 ) (1 (1 )) 1 (1 ) u x t t t e t x                                 the obtained solution is illustrated in figures (1 − 2) for t = 1. figure 1 demonstrates the solution profile at different times for a fixed value of the order α of the fractional derivative. the effect of the nonhomogeneous term, particularly its x-dependence, is clearly seen in the solution profile. moreover, the solution increases with time and reaches its maximum when t = t = 1. the effect of the order α of the fractional derivative is shown in figure 2 at a fixed time. it shows that as α increases, the solution decreases and reaches its minimum when α = 1, which represents the classical derivative case. figure 1. graphs of u(x, t) at different times for 0.5.  figure 2. graphs of u(x, t) at t = 0.5 for different values of . intial and boundary value problems of fdes with a-b derivaitve 145 4. conclusion in this paper, we have considered an initial value problem (ivp) for a nonhomogeneous linear fractional differential equation with the atangana-baleanu derivative. an explicit solution of the ivp in integral form has been obtained using the laplace transform. the solution can be also obtained using the successive approximation method as shown in the arxiv version of this paper. a condition relating the initial data and the initial value of the nonhomogeneous term, namely, 0 (0)f u  , has been found to be necessary for the existence of a solution of the ivp. on the other hand, this condition makes it impossible to consider inverse source or inverse initial problems with the atangana-baleanu fractional derivative. we have also considered an initial-boundary value problem for a nonhomogeneous linear partial fractional differential equation with the atangana-baleanu derivative and a given time and space dependent nonhomogeneous term. a regular classical solution of this direct problem was obtained in the form of a series expansion using an orthogonal basis, which is a set of eigenfunctions of a self-adjoint spectral problem obtained by considering the corresponding homogeneous equation and using the method of separation of variables. the uniform convergence of the series solution was obtained by imposing certain conditions on the given nonhomogeneous term. the uniqueness of the solution can be obtained using the completeness properties of the orthogonal basis used. finally, a number of examples were presented to illustrate the obtained results. acknowledgment this work is funded by the research council (trc), oman under the open research grant number org/squ/cbs/13/030. references 1. caputo, m. and fabrizio, m. a new definition of fractional derivative without singular kernel. 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mophou, g.m and area, i. optimal control of diffusion equation with fractional time derivative with nonlocal and nonsingular mittag-leffler kernel, journal of optimization theory and applications (2018). https://doi.org/10.1007/s10957-018-1305-6. 23. moiseev, e.i. the basis property of systems of sines and cosines. doklady akademii nauk sssr, 1984,275, 794–798. received 23 march 2018 accepted 27 may 2018 squ journal for science, 2018, 23(1), 56-67 doi: http://dx.doi.org/10.24200/squjs.vol23iss1pp56-67 sultan qaboos university 56 heat transfer in fe3o4-h2o nanofluid contained in a triangular cavity under a sloping magnetic field mohammad m. rahman department of mathematics and statistics, college of science, sultan qaboos university, box 36, al-khod 123, sultanate of oman. email:mansur@squ.edu.om abstract: numerical simulation is performed to explore the convective heat transfer characteristics of fe3o4-h2o nanofluid contained in a right-angle triangular cavity considering three types of thermal boundary conditions at the bottom wall. no heat is allowed to escape through the insulated vertical wall, whereas the inclined wall is kept colder than the bottom one. a sloping magnetic field whose strength is unvarying acts upon the cavity. the physical model is converted to the mathematical form through coupled highly nonlinear partial differential equations. these equations are then transformed into the non-dimensional form with the help of a group of transformations of variables. a very robust pde solver comsol multiphysics that uses the finite element method (fem) of galerkin type is applied to carry out the numerical calculation. heat transfer escalation through middling nusselt number at the lowermost cavity wall is explored for diverse model parameters and thermal circumstances. the outcomes lead us to conclude that a higher degree of heat transfer is accomplished by reducing the dimension of nanoparticles and aggregating the buoyancy force through the rayleigh number. it is highest when there is a magnetic field leaning angle of 90 0 and the lowermost wall is heated homogenously. keywords: nanofluid, free convection, triangular cavity, sloping magnetic field, fem ماء تحت تأثدر مجال مغناطديي منزلق -سكيد الح ي أل حاوية مثلثة تحوي المائع النانويانتقال الحرارة في ن امحم منصور رحم ماء داخل حاوية على شكل مثلث قائم الزاوية –كييد الحديد ألخصائص انتقال الحرارة الحملي للمائع النانوي توضيحمحاكاة عددية ل تم تنفيذ :الملخص الضلع بحيث يبقى به غير ميموح الحرارة عبر الضلع الرأسيونفترض أن تهريب للضلع األسفل. ةالحراري ودأنواع من خصائص الحد ةتتضمن ثالث ادالت معبي شكل رياضإلى النموذج الفيزيائي تم تحويلومجال مغناطييي منزلق ثابت الشدة يؤثر على الحاوية. ووجود . ييفلالمائل أبرد من الضلع ال تم استخدام الحيابات العدديةإلجراء مياعدة مجموعة من المتغيرات التحويلية.ووحدات دونالمعادالت الى شكل ب ت تلكحولوخطية. غيرو تفاضلية جزئية صر اطريقة العنب عملي، حيث أن البرنامج حل المعادالت التفاضلية الجزئيةل (comsol multiphysics) ملتيفيزكس كوميول الحاسوب برنامج تم الذي جدار الحاوية األدنى من خالل (nusselt number) رقم نيلت اعتدال تصعيد انتقال الحرارة عبرويكون . نوع جاالركنمن (fem)ةالمحدود تجمع حجم الذرات النانوية و في انخفاض هصحبيت النتائج أن انتقال الحرارة بدرجة عالية فحرارية. كشالظروف ال ولمعامالت من امختلف كشافه لنموذجا لجدارل تجانسمن ييختو درجة 09عندما يميل المجال المغناطييي بزاوية ياعلوتكون الدرجة ال .(rayleigh number) هقوة الطفو عبر رقم ريلي . ييفللا طريقة العناصر المحدودة. مغناطييي منزلق، وي، حمل حراري، حاوية مثلثة، حقلمائع نان :الكلمات المفتاحدة heat transfer in fe3o4-h2o nanofluid 57 nomenclature a wave amplitude (m) ra rayleigh number a dimensional wave amplitude t temperature (k) ar aspect ratio ,u v velocity components (ms-1) b magnetic field vector ,u v nondimensional velocity components 0b magnitude of the magnetic field (nma -1 ) ,x y coordinates (m) pc specific heat at constant pressure (jkg -1 k -1 ) ,x y nondimensional coordinates c nanoparticle volume fraction greek symbols d particle diameter (nm)  thermal diffusivity (m 2 s -1 ) b d coefficient of brownian diffusion (m 2 s -1 )  coefficient of thermal expansion (k -1 ) t d coefficient of thermophoretic diffusion (m 2 s -1 )  magnetic field sloping angle ( 0 ) g gravity vector  heat capacity ratio g acceleration due to gravity (ms -1 )  nondimensional temperature h cavity height (m)  normalized nanoparticle volume fraction ha hartmann number  stream function k wave number  thermal conductivity (wm -1 k -1 ) l cavity length (m)  density (kgm -3 ) le lewis number  dynamic viscosity (kgm -1 s -1 ) nb brownian diffusion parameter  kinematic viscosity (m 2 s -1 ) nr buoyancy ratio parameter p c heat capacity (jk -1 m -3 ) nt thermophoresis parameter subscripts nu nusselt number av average p pressure (pa) c condition at cold wall p nondimensional pressure f base fluid pr prandtl number h condition at heated wall p solid nanoparticle 1. introduction atural convective heat transfer has extensive applications in numerous engineering areas such as air-cooling systems, chilling of electronic equipment, insulating buildings, harvesting solar thermal collectors, and the extraction of geothermal energy. natural convective heat transfer may also transpire in buildings’ roofs and attics. many researchers [1–4] have investigated and tested findings both experimentally and numerically for heat transfer augmentation, considering natural convection within a square, rectangular, rhomboidal, annular and triangular cavity. flack et al. [5-6] conducted experimental and numerical surveys to simulate convective heat transfer in a base fluid confined within a triangular enclosure. later on many researchers were influenced by this ground breaking work and reported results on triangular cavities. the work of akinsete and coleman [7] on a pitched roof with a horizontally suspended ceiling inside the triangular enclosure showed that the heat transfer rate through the bottom wall escalates in the direction of the intersection of the hypotenuse and base. keeping in mind the possible application of electronic components, ridouane et al. [8] simulated natural convection heat transfer flow of air in a right-angled triangular container. they found that heat transfer reduction strongly depends on the decrease of the apex angle and the rayleigh number. varol et al. [9] conducted a numerical experiment to calculate natural convective heat transfer inside a triangular container having a non-isothermal bottom wall inserted in a permeable medium. they confirmed that heat transfer is enhanced when the upright and slanted walls are heated isothermally and the bottom wall is heated nonuniformly. the work of basak et al. [10] within a triangular enclosure revealed that the heatlines are subjugated by conduction for a smaller rayleigh number, whereas convection overrides conduction for a higher rayleigh number. yesiloz and aydin [11] performed both an experimental and numerical study to scrutinize the heat relocation augmentation within a right-angled triangular enclosure which was heated from below and cooled from the side walls. they concluded that the rate of heat transfer intensifies when the rayleigh number increases markedly. a conducting fluid and an imposed magnetic field in the flow domain interact with each other and create a lorentz force that in turn overwhelms the convection fluxes, and as a consequence fluid velocity diminishes. exerting of such a magnetic field on the flow domain has extensive application in diverse circumstances. for example it could be used in metal casting, the extraction of geothermal energy, for controlling flow in fusion reactors, and growing crystals in liquids. in practical applications, the slopping of a magnetic field on the flow area is important for the proper functionality of the devices. the open literature reveals that a slopping magnetic field has a tendency to alter the fluid flow and subsequently the thermal enactment of a cavity (see ozoe and okada [12], pirmohammadi and ghassemi [13]). sathiyammmoorthy and chamkha [14] have investigated two-dimensional convective flow together with heat n m.m. rahman 58 transfer inside a square cavity considering liquid gallium and an inclined magnetic field. they showed that heat transfer within the cavity is different for perpendicularly and flatly imposed magnetic fields. they further revealed that an applied magnetic field lowers heat transmission rates. grosan et al. [15] conducted a numerical study on natural convective flow inside a rectangular cavity under the action of an inclined magnetic field. it was reported that the convective mode of heat transfer was prejudiced by the strength and alignment of the field. it was further shown that a horizontal magnetic field more effectively suppresses the flow, when compared to a field operating in an upright direction. studies of convective flow within cavities under the action of an imposed magnetic field usually considered fluids of low conductivity, which in turn limits the augmentation of heat transmission rates. however, in many practical applications, higher conductivity is required to transfer heat efficiently in sophisticated devices. a groundbreaking approach to enrich the conductivity is by mixing solid nanoparticles with the low-conductive fluid. this new type of engineered fluid is called a nanofluid (choi [16]) and has substantially higher conductivity compared to the base fluid. wide-ranging literature reviews, reporting the extensive applications of nanofluids are well documented by wong and de leon [17], das et al. [18] and mahian et al. [19], kakac and pramuanjaroenkij [20]. uddin et al. [21] carried out an excellent review work on the ultimate features of nanofluids, along with their development and applications. they also established novel correlations for brownian diffusion and thermophoresis in nanofluids. plentiful results on nanofluids are available in different configurations of flow and thermal fields. although there are lots of engineering and technological applications of the flow dynamics of nanofluids in triangular cavities, this has attracted far less attention from researchers. a mixed convective study on nanofluids inside a triangular cavity by ghasemi and aminossadati [22] showed that heat transference is enhanced by an increase of the nanoparticle loading. billah et al. [23] investigated time-dependent buoyancy influenced by heat transfer augmentation of nanofluids inside a tilted right triangular cavity. they have shown that average nusselt number as well as fluid temperature varies linearly with an increase of the nanoparticle volume fraction. recently, al kalbani et al. [24] explored buoyancy-encouraged heat transmission inside a slanted square cavity occupied with nanofluids under the action of an inclined magnetic field. they have reported that rayleigh number together with nanoparticle volume fraction intensifies heat transfer rate significantly. on the other hand, increased hartmann number reduces the global heat transfer rate within the cavity. the critical geometry leaning angle to obtain the optimum heat transmission rate significantly hangs on the loading of the nanoparticles as well as on the magnetic field direction. the above-stated models are well known one-component models, where the effects of thermophoresis and brownian diffusion of nanoparticles have not been taken into consideration. buongiorno [25] developed a twocomponent model considering these mechanisms of nanoparticles in connection with the relative velocity of the basefluid. sheremet and pop [26] followed the model of buongiorno, to study free convective heat transfer and fluid flow inside a triangular shaped cavity occupied with nanofluid implanted in a permeable medium. the outcomes of this study revealed that rayleigh and lewis numbers escalate the average nusselt number, whereas it is diminished by the increase of buoyancy-ratio, thermophoresis, and brownian diffusion parameters. taking into consideration the slip mechanisms suggested by buongiorno, rahman et al. [27] investigated hydromagnetic flow characteristics of nanofluids inside an isosceles triangular shaped cavity, considering various thermal circumstances at the bottom wall. they reported that adaptable thermal circumstances substantially control the flow and updraft fields. in keeping with the literature review, the author found that there remains a potential need to investigate the natural convective transport mechanism in fe3o4-h2o nanofluid inside a right triangular cavity, considering different updraft boundary conditions and a sloping magnetic field. fe3o4-water nanofluid has further high demand in technological applications such as in solar thermal collectors because of its upgraded thermophysical properties, convenience, and low production cost. in the present study, a finite element method of galerkin type is used to carry out a numerical simulation. the simulated results such as streamlines, isotherms, and isoconcentrations are presented graphically, whereas the average nusselt numbers are tabulated. 2. physical and mathematical modeling figure 1. diagram of the right triangular cavity with coordinate axes and boundary conditions. heat transfer in fe3o4-h2o nanofluid 59 we consider the two-dimensional time-independent viscous incompressible laminar flow of fe3o4-h2o nanofluid confined in a right triangular cavity. the flow configuration and corresponding boundary conditions for flow and temperature are displayed in fig. 1. the length of the bottom wall of the cavity is l along the x -axis and its height is h along the y -axis. the gravity [0, ]gg acts along the y -axis in the downward direction. we further consider that the temperature of the bottom wall varies uniformly ,ht t parabolically     / 1 / ,ct t t x l x l    and sinusoidally ( / ) sin( )ct t t a l kx   where h ct t t   , a is the wave amplitude and 2 /k l is the wave number. the inclined wall temperature we consider to be ct t ( c ht t ), keeping the vertical wall insulated. we assume that fe3o4 nanoparticles distribute uniformly within the base fluid water and their concentration at all boundaries is constant such that h c c . so called “slip mechanisms”, thermophoresis and brownian diffusion are taken into consideration in the lack of chemical reaction to construct the mathematical model. due to the tiny size of the nanoparticles, we may assume that fe3o4 nanoparticles and water molecules are in local thermal equilibrium. a slopping magnetic field 0 0[ cos , sin ]b b b is applied to the flow domain where  is the inclination angle with respect to the positive x -axis. the density variation of the nanofluid is tackled through incorporating the boussinesq approximation in the momentum equation. following the above-noted suppositions, the governing equations of the model are ([27]-[28]) 0 u v x y       (1)   2 2 2 2 02 2 ( ) sin cos sin f f f u u p u u u v b v u x y x x y                           (2)         2 2 2 2 02 2 ( ) sin cos cos 1 f f f c c f f c p f v v p v v u v b u v x y y x y c t t g c c g                                     (3) 222 2 2 2 ( / ) f b t c t t t t c t c t t t u v d d t x y x y x x y y x y                                                       (4) 2 2 2 2 2 2 2 2 ( / ) b t c c c c c t t u v d d t x y x y x y                           (5) where u and v are velocity components along the x and y axes respectively, p is the pressure and    /p p p f c c   is the heat capacity ratio of nanoparticles and base fluid. for descriptions of other quantities, see the nomenclature. boundary conditions for flow, temperature and particle concentration are: (i) at inclined wall ( / / 1x l y h  ): 0u v  , ct t , .hc c (6) (ii) at bottom wall ( 0y  , 0 x l  ): type 1: 0u v  , ht t , .hc c (7a) type 2: 0u v  ,     / 1 /ct t t x l x l    , .hc c (7b) type 3: 0u v  ,    a/ sinct t t l kx   , .hc c (7c) (iii) at vertical wall ( 0x  , 0 y h  ): 0u v  , 0xt  , .hc c (8) to make equations (1)-(8) dimensionless, we use the following transformation of variables: 2 2 / , / , / , / , / , ( ) / ( ), ( ) / ( ). f f f f c h c c h c x x l y y l u ul v vl p pl t t t t c c c c                     (9) m.m. rahman 60 substituting (9) into (1)-(5), we obtain the following non-dimensional governing equations 0 u v x y       (10)   2 2 2 2 2 2 pr pr ha sin cos sin u u p u u u v v u x y x x y                        (11)     2 2 2 2 2 2 pr pr pr ha sin cos cos v v p v v u v ra nr u v x y y x y                            (12) 2 22 2 2 2 u v nb nt x y x y x x y y x y                                                       (13) 2 2 2 2 2 2 2 2 (1 / ) ( / )u v le nt lenb x y x y x y                                (14) the boundary conditions (6)-(8) become (i) at inclined wall ( / 1)x y ar  : 0u v  , 0  , 1.  (15) (ii) at bottom wall ( 0y  , 0 1x  ): type 1: 0u v  , 1  , 1.  (16a) type 2: 0u v  ,  1x x   , 1.  (16b) type 3: 0u v  ,  sin 2a x  , 1.  (16c) (iii) at vertical wall ( 0x  , 0 y ar  ): 0u v  , 0 x    , 1.  (17) the dimensionless parameters appearing in equations (11)-(14) are defined as: prandtl number pr / ,f f  hartmann number 0 / ,f fha b l   rayleigh number    31 / ,f c h c f fra g c t t l     buoyancy ratio parameter      / 1 ,p f h c f f h c cnr c c t t c        thermophoresis parameter   /t h c c fnt d t t t   , brownian motion parameter   /b h c fnb d c c   , lewis number / f b le d , aspect ratio /ar h l . thermophysical properties of fe3o4 nanoparticles and h2o are listed in table 1. table 1. thermophysical properties of fe3o4 and h2o (uddin et al. [29]). thermophysical properties 3 4 fe o 2h o ρ [kgm-3] 5180 997.1 μ [kgm-1s-1] 0.001003  [wm -1 k -1 ] 80 0.613 p c [jkg -1 k -1 ] 670 4179 -5 β×10 [k -1 ] 20.6 21 pr 6.8377 heat transfer in fe3o4-h2o nanofluid 61 the nanofluid motion is exhibited in terms of stream function  that is obtained from the x and y -components of the fluid velocity as follows: u y    and .v x     (18) to measure the heat transmission rate for engineering and technological applications it is essential to calculate the average nusselt number. the nusselt number at the bottom heated wall can be defined by   0 / . f f h c y t nu lk k t t y          (19) the average nusselt number in dimensionless form at the bottom heated wall is obtained as 1 0 0 . av y nu dx y            (21) 3. numerical procedure the dimensionless model equations (10)-(14) are highly nonlinear and coupled. it is difficult to solve them analytically for the closed form solutions. thus, we solve them numerically for the approximate solutions. the finite element method of galerkin type is a very powerful tool to handle these kinds of nonlinear equations. the details of this method can be found in the textbook by zienkiewicz and taylor [30] and in the work of al kalbani et al. [31]. the numerical simulation is carried out through the very robust pdf solver comsol multiphysics. for grid independent results a widespread mesh testing is piloted for 5 10ra  . here, we examine five different non-uniform grids, named normal, fine, finer, extra fine, and extremely fine, consisting of 688, 1075, 1643, 7435 and 29157 elements in the resolution field respectively. to obtain convergent solutions, we calculate the average number at these grids to apprehend the grid refinement. table 2 shows that nuav for 7435 elements differs slightly from the value obtained for 14835 elements. to limit the computational time, it is sufficient to consider an extra fine grid consisting of 7435 elements for grid independent solutions. table 2. grid sensitivity for fe3o4-h2o nanofluid when 5 10ra  . nodes 374 588 884 3850 14835 elements 688 1075 1643 7435 29157 av nu 7.0056 7.35383 7.65316 8.65204 8.66150 figure 2. judgment of isotherms (left column) and streamlines (right column) between yesiloz and aydin [11] (top row) and the present work (bottom row) when 5 10ra  . so as to check the correctness of our numerical scheme, we have validated it against the work of yesiloz and aydin [11] for a special case. judgment of streamlines and isotherms between yesiloz and aydin [11] and the present work for 5 10ra  are depicted in figure 2. the simulated results match each other profoundly which supports the use of the present numerical scheme. m.m. rahman 62 4. numerically simulated results and discussion here we present fem generated numerical outcomes for convective flow of fe3o4-h2o nanofluid confined in a right angle triangular enclosure under the accomplishment of a sloping magnetic field of varying updraft conditions at the bottom wall. isotherms and average nusselt number are calculated for a large assortment of the regulatory factors for three dissimilar cases as mentioned in section 2. precise exertions were given to identify the role of the influential model parameters: ra , ha ,  and d on the flow and thermal fields. an enhanced heat transmission rate is predicted for homogeneously dispersed nanoparticles within the base fluid, but in reality the brownian diffusion of nanoparticles and thermophoresis can create a tiny concentration difference ( 0.01c  ) within the flow domain. following uddin et al. [21] we obtain 12 8.7591 10 b d    , 12 3.9597 10 t d    , 7 4.9591 10nb    , 7 7.5229 10nt    and 16795le  for fe3o4-h2o nanofluid considering 1% nanoparticle loading when 50 nm p d  , 300 k c t  , and 10kt  . the other model parameter values are taken as pr 6.8377 , 1ar  , 0.01nr  50ha  , / 12  , and 6 10ra  if not otherwise quantified. 4 10 5 10 6 10 7 10 ra type 1: 1  type 2:  1x x   type 3:  sin 2a x  figure 3. distributions of isotherms for diverse ra and three different updraft conditions. heat transfer in fe3o4-h2o nanofluid 63 to measure the efficiency of heat transfer in fe3o4-h2o nanofluid and determine the conductive to convective mode of heat transfer it is extremely useful to plot the isotherm contours. figure 3 displays isotherm delineations for 4 10ra  , 5 10 , 6 10 and 7 10 (top to bottom) for three different (type 1, type 2 and type 3) updraft boundary conditions. these figures reveal that isotherm delineations are further compressed adjacent to the right junction of the lowermost wall of the cavity. the close concentration of isotherm contours in a region indicates that conduction is the key mode of heat transfer. as rayleigh number increases, the compactness of the isotherm contours at the middle plane of the cavity decreases, which indicates a weaker mode of convective heat transport. a type 1 updraft boundary condition at the meeting point of hot and cold walls results in a finite discontinuity in the temperature distribution, as can be observed from figure 3. mathematically, it is a singularity, but in reality at this point the fluid temperature will converge towards the average value of the temperatures of hot and cold walls. thus, in the simulation we have considered the average value of the temperatures at the right bottom corner point of the cavity for the type 1 boundary condition (for a detailed discussion see rahman et al. [27]). in contrast the implication of non-uniform updraft boundary conditions (type 2 and type 3) eliminates the thermal singularity, as evidenced from figure 3. for all three types of thermal boundary conditions an increasing value of ra results in more distortion to the isotherms due to the resilient convection effect. overall, an increase in ra enhances the heat transmission rate. 0 20 50 100 ha type 1: 1  type 2:  1x x   type 3:  sin 2a x  figure 4. distributions of isotherms for different ha and three different updraft conditions. m.m. rahman 64 meanwhile, figure 4 depicts the impact of hartmann number on the distributions of isotherms for various updraft boundary circumstances. these figures demonstrate that advanced temperature domain and clustered isotherms appear with a type 1 thermal condition near the lowermost wall of the enclosure. this is due to the presence of a sharp temperature gradient along the vertical direction within the region. in contrast, in the upper region of the cavity, the temperature gradient is found to be quite weak for type 2 and type 3 thermal conditions. nevertheless, in all cases of thermal boundary conditions an increased ha , i.e. a stronger lorentz force, pushes the densely distributed isotherm contours away from the hot wall. it signifies the decrease of the temperature rise within the enclosure. thus, by using a magnetic field within the nanofluid flow domain we can control the heat transfer rate. in figure 5 we display the influence of the magnetic field slopping angle  on the isotherm contours for fe3o4-h2o nanofluid when ha is fixed. figure 5 demonstrates that the influence of  on the temperature field is less pronounced. the isotherm contours are distributed quite evenly between the hot bottom and cold inclined walls of the cavity. the thickness of the thermal boundary layer is higher and the isotherms become more packed for a uniformly heated bottom wall compared to a non-uniformly heated one. 0 / 4 / 3 / 2  type 1: 1  type 2:  1x x   type 3:  sin 2a x  figure 5. distributions of isotherms for different  and three different updraft conditions. heat transfer in fe3o4-h2o nanofluid 65 to determine the heat transfer rate at the hot wall of the cavity filled with fe3o4-h2o nanofluid for engineering applications we calculated the average nusselt number varying ra , ha ,  and pd in table 3. this table reveals that average nusselt number drops with the rise of ha i.e. a stronger magnetic force reduces the heat transfer rate. it also confirms that heat transmission in a nanofluid can be intensified by decreasing the nanoparticle size and increasing the buoyancy force. table 3 further confirms that the highest heat transmission is achieved when the magnetic field sloping angle is 0 90 and the bottom wall is heated uniformly. table 3. values of av nu for different model parameters and thermal boundary conditions (tbc). p d ra tbc ( 0)avnu ha  ( 100)avnu ha  0 0  0 45  0 90  1 10 5 type 1 7.94847 6.71352 6.69363 7.27715 type 2 6.98167 5.81245 5.21564 6.45643 type 3 5.99345 3.93245 4.89654 5.34562 10 6 type 1 11.11553 8.96572 7.97159 9.69044 type 2 10.23421 7.43562 6.34521 8.43563 type 3 8.43567 5.23421 5.23456 6.34521 10 7 type 1 14.99211 15.10939 12.77243 14.93098 type 2 12.67543 14.23475 10.45638 12.43521 type 3 11.45632 10.45632 9.23451 11.21532 50 10 5 type 1 6.98567 5.76543 5.45678 6.54321 type 2 5.99521 4.23421 4.12584 5.67543 type 3 4.99325 3.21456 3.02543 4.87654 10 6 type 1 10.45678 7.45632 6.78654 8.76549 type 2 9.45678 6.23457 5.67543 7.98654 type 3 7.34521 4.56743 4.12743 5.98765 10 7 type 1 14.97743 13.34563 11.34321 12.98765 type 2 11.97674 12.32156 9.76543 11.32854 type 3 10.96789 9.78654 8.98765 10.23784 5. conclusion the convective heat transfer mechanism in fe3o4-h2o nanofluid confined in a right angled triangular cavity under the action of a slopping magnetic field has been investigated considering three types of thermal boundary conditions at the bottom wall of the cavity, following the mathematical model of buongiorno. a very robust computer pde solver comsol multiphysics which uses the fem of galerkin type was used to simulate the transformed nondimensional equations governing the problem. an excellent agreement has been found among the data produced by the present code and those experimental data presented in the open literature. the simulated results were interpreted from a physical viewpoint. from the studied results we conclude that rayleigh number is a key parameter that determines the mode of heat transfer. lower ra determines conduction, whereas higher ra ( critra ) corresponds to convection. an increased value of ra induces a heat transfer rate. the applied magnetic field eases avenu considerably through the lorentz force. the magnetic field slopping angle regulates the flow configuration of fe3o4-h2o nanofluid inside the cavity. a smaller particle size increases the heat transfer rate efficiently. 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qaboos university 247 state-of-the-art methods for electric power systems voltage stability analysis t.m. al-khusaibi* , k. a. ellithy** and m.r. irving*** *ministry of electricity and water, p.o. box 105 ruwi, postal code 112, ruwi, sultanate of oman** department of electrical & electronics engineering, sultan qaboos university,p.o. box 33, postal code 123, muscat, sultanate of oman *** department of electrical engineering and electronics, brunel university, uk الطرق الحديثة لتحليل استقرار الجهد الكهربي لنظم القوى الكهربية ***، مالكلم ارفنج** ، خالد الليثي *ثاني الخصيبي الجهد ) اتزان ( تقدم هذه الورقة عرض اجمالي للطرق ذات المهارة العلمية لموضوع تحليل استقرار : خالصة مالي يصف عدداً من الطرق المنشورة و المستخدمة لحساب وهذا العرض االج . الكهربي لنظم القوى الكهربية و تستخدم هذه األدلة لتنبأ بقرب عدم استقرار أو انهيار . أدلة االستقرار للجهد الكهربي لنظم القوى الكهربية ، منحنيات القدرة الفعالة و غير الفعالة : الطرق التي وصفت في هذه الورقة كاآلتي . الجهد الكهربي لنظم القوى التحميل بطريقة الحل ) احتياطي(قيمة أحادية االنحالل، تحليل الطور ، دالة االختبار، المحددة المخفضة، حافة تعتمد هذه . معاوقة الحمل ودالة الطاقة / ، حافة التحميل المحلي، ثفنن ) لسريان األحمال (المتعدد لسريان القوى على نموذج نظم القوى المستخدم لدراسة سريان القوى و الطرق على األعمال األصلية لمؤلفيها، وتعتمد أيضا . الذي يفترض فيه على ان احمال القدرة الفعالة وغير الفعالة أهم العوامل التي تؤدي الى عدم استقرارية الجهد .)ieee 30-bus system(تم تطبيق بعض الطرق الموصوفة بالورقة على نموذج نظام القوى المعروف ب abstract: this paper presents a literature survey on the subject of voltage stability analysis of power systems. the survey describes several published methods and techniques used to determine voltage stability indices. these indices predict proximity to voltage instability and collapse problems. the q-v and p-v curves; singular value decomposition; modal analysis; test function; reduced determinant; loading margin by multiple power flow solutions; local load margins; thevenin/load impedance; and energy function are the methods which have been decribed in the paper. the methods described are based on the original work that first proposed them. they are based on the powerflow system model, where the variation of real and reactive powers are assumed to be the main parameters driving the system to voltage instability. some of the described methods were applied on the ieee 30-bus power system. al-khusaibi, ellithy and irving contents 1. introduction 248 2. methods of voltage stability analysis 249 2.1 q-v and p-v curves method (continuation method) 249 2.2 singular value decomposition method 250 2.3 modal analysis method 252 2.4 the test function method 253 2.5 the reduced determinant method 254 2.6 the loading margin method by multiple power-flow solutions 255 2.7 the local load margins method 255 2.8 the thevenin /load impedance (zii/zi) method 256 2.9 the energy function method 256 3. numerical results 257 4. conclusions 262 5. references 262 1. introduction p roblems related to voltage instability in power systems have been experienced by many utilities and are today, in many countries, one of the main concerns in power system operation and planning. forcing the transmission lines (network) to operate close to their thermal capability (maximum capacity) to avoid the cost required for new lines and power plant facilities has lead to many of these voltage instability problems, due to inadequate reactive power margin. several networks collapse caused by voltage instability problems were reported in various countries such as usa, france and japan (taylor, 1994; baribier and barret, 1980; kurita and sakurai, 1986). the phenomenon of voltage instability in power systems is characterized by a continuous decrease (drop) of system voltage, which is gradual at the initial stage and then becomes rapid. generally this is triggered by a disturbance or change in operating conditions, which creates increased demand for reactive power in excess of system capacity. the disturbance or change in operating conditions which can lead to voltage instability and collapse could be related to the unexpected increase of load level or to a sudden loss of transmission line, transformer, a generator, a slow clearing of a system fault or response of various control systems (miller, 1982). kundur (1994) has characterized the voltage collapse based on actual incidents where he described this phenomenon, indicating the initiating causes, the problem itself and the resultant phenomenon including the time frame of collapse. in the course of finding solutions to voltage stability problems, it is very helpful to classify them into two categories: large-disturbance voltage stability and small disturbance voltage stability (gao et al, 1992; kundur, 1994). to study and analyze large-disturbance voltage stability, a dynamic performance analysis is required using non-linear time simulations. this is a time consuming process in terms of cpu time and the engineering effort required for analysing the results. smalldisturbance voltage stability on the other hand can be studied with steady state or static approaches using linearization of the dynamic equations at a given operating point. most of the time, voltage stability analysis requires study of the wide range of system conditions and various contingencies. for this type of applications, the steady state or static analysis approach is more suitable and if properly used can provide insight into the voltage instability problem (gao et al, 1992). the analysis of voltage stability for a given system state involves the examination of the following two-aspects (kundur, 1994): • proximity of voltage instability: how close is the system to voltage instability? • mechanism: what are the voltage weak points and what areas are involved? how and why does instability occur? what are the contributing factors? proximity provides information regarding voltage 248 state of the art methods for electric power systems 249 security whereas the mechanism provides useful information, which may lead to prevention of voltage instability (such as system modification or operating policies and strategies), thus avoiding voltage collapse. a number of techniques and methods have been proposed in the literature for voltage stability analysis using steady state (static) method (mansour et al, 1994; kundur 1994; gao et al, 1992; venkov, 1975; ieee working group, 1990; cigre task force, 1993) . in the past, some utilities have used p-v and q-v curves at specific small number of load buses (d’aquila et al, 1993; pal 1993; suzuki et al, 1992; mansour et al, 1994; vaahedi, 1999; schluter, 1998). most of these approaches are based on power flow modes which are time consuming and do not provide insight into the causes of stability problems (kundur, 1994). other techniques have been suggested such as modal analysis (gao et al, 1992; morrison et al, 1993; kundur, 1994; mansour et al, 1994; ellithy et al 2000), singular value decomposition (löf et al, 1992; löf et al, 1993; liu et al, 1998), sensitivity analysis (bakovic and phadek, 1992; flatabo and dommel 1990), energy function (overbye and demacro, 1995; el-keib and ma, 1995), test functions (seydel, 1988), reduced jacobian determinant (ganizares et al, 1995), reactive power optimization (tamura et al, 1983), thevenin and load impedance (zii/zi) indicator (chebbo et al, 1992), artificial neural network (jeyasurya, 1990; el-keib and ma, 1995), neuro-fuzzy networks (liu et al, 1998), local margins (nagao et al, 1997), and loading margin by multiple power-flow solutions (yorino et al, 1997). these methods have wider approach and can predict voltage collapse in complex networks. 2. methods of voltage stability analysis methods to predict proximity to voltage collapse are considered an important issue by power researchers and technical staff in power systems operation, as these methods could be used on-line or offline to help dispatchers to know how close the system is to collapse. the main objective of these methods is to determine scalar magnitude that can be monitored as system parameters change. the methods should have predictable results and should be computationally inexpensive, especially for online system observation. this section describes some of the methods mentioned in the literature, with special consideration given to the modal analysis and the singular value decomposition (svd) method, due to their capability of providing information regarding voltage stability of the complete system. furthermore, they can also identify the individual voltage unstable mode and the degrees of participation of various components in the power system as well as provide better information with respect to the mechanism of voltage instability. 2.1 q-v and p-v curves method (continuation method) q-v and p-v curves are currently in use at some utilities (suzuki et al, 1992) for determining proximity to voltage collapse so that operators can make timely preventive measures to avoid system loss. the q-v curves (reactive power-voltage curves) are used in this voltage stability study since they directly assess shortage of reactive power. the q-v curve technique is a general method of assessing voltage stability. these curves are presently the workhorse method of voltage stability assessment at many utilities. q-v curves show the sensitivity and variation of bus voltages with respect to the reactive power injection. a typical q-v curve is shown in figure 1. the q axis shows the reactive power that needs to be added or removed from bus to maintain a given voltage at a given load. from figure 1-b, it can be seen that the curve gives the reactive power margin at the test bus. the reactive power margin is the mega volt-amps reactive (mvar) distance from the operating point to the furthest right hand point of the curve. this curve can be used as an index for voltage instability (dq/dv becomes negative). near the nose of q-v curve, sensitivities get very large and then reverse their sign. the jacobian matrix becomes singular at the nose of the curve. this is called a saddle bifurcation node (yokoyama and sekine, 1989). the p-v curves (active power-voltage curves) are the most widely used method of estimating voltage al-khusaibi, ellithy and irving security, providing megawatt (mw) margin type indices. the p-v curve is used to determine the mw distance from the operating point to the critical voltage. a typical p-v curve is shown in figure 1-a. the pv curves are also useful for conceptual analysis when the load characteristics as a function of voltage are analyzed. while p-v curves are helpful in understanding the phenomena of voltage stability and collapse, they are not so useful for determining the reactive power support needed at various points in a power system. figure 1. p-v and q-v curves 2.2 singular value decomposition method the singular value decomposition (svd) method is a very useful tool for analyzing matrices and related problems in many fields. it has been applied to power systems for voltage stability analysis to obtain decomposition of the jacobian matrix (löf et al, 1993). for a real square matrix a of size n, the singular value decomposition is given by (b-1) tiii n i t vuvu σ∑ = ==α 1 s where u and v are n x n orthogonal matrices, ui and vi are called the left and right singular vectors respectively, and s is a diagonal matrix with [ ])()(s adiaga iσ= i = 1, 2 , 3,…,n (b-2) 250 state of the art methods for electric power systems where σi≥0 for all i. the diagonal elements in the matrix s are usually ordered so that σ1≥σ2 ≥σ3≥……≥σn≥0. if the matrix a has rank r (r≤n), its singular values σ1, σ2, σ3,… σr are the only nonzero entries in the nxn diagonal matrix s . to use the above theory for voltage stability analysis, the linear power-flow equation based on the newton-raphson method has to be found which is established by the power-flow jacobian matrix j       ∆ ∆        =      ∆ ∆ vj j j j q p qv pv q p θ θ θ (b-3) where p∆ is the incremental change in bus real power, q∆ is the incremental change in bus reactive power, is the incremental change in bus voltage angle and v∆ is the incremental change in bus voltage magnitude. hence the full jacobian matrix can be written as, θ∆ (b-4)        = θθ θ q pv q p j j j j j the equation is re-written as, (b-5)       ∆ ∆ =      ∆ ∆ v j q p θ now, if the singular value decomposition is applied to j, one has ∑ = == n i t iii t vuvuj 1 s σ (b-6) the minimum singular value, (j) is a measure of how close the jacobian to singularity. in the case of a small distrubance, let nσ (b-7) nuq p =      ∆ ∆ where u is the last column of u, and n nv n (b-8) nn vv 1−=      ∆ ∆ σ θ where is the last column of v. from the above equations it can be concluded that for the minimum singular value and corresponding left and right singular vectors (lof et al, 1992), the following apply: the smallest singular value σ is an indicator of the proximity to the steady state stability limit. the right singular vector, corresponding tonv nσ indicates sensitive voltage. 251 al-khusaibi, ellithy and irving 252 n the left singular vector, u corresponding to nσ indicates the most sensitive direction for changes of active and reactive power injections. 2.3 modal analysis method as mentioned in conference internationale des grands reseaux electriques a haute tension ( cigre ) task force, (1993), there is a need to have an analytical method which can predict voltage collapse in complex power system networks. there is also a need to consider more detailed steady state models for main system components such as generators, static var compensators (svcs), induction motors and voltage dependent static loads. the modal analysis (eigenvalue analysis) method was proposed by gao et al, (1992), to meet the above requirements. it involves the calculation of a small number of eigenvalues and related eigenvectors of a reduced jacobian matrix. however, by using the reduced jacobian, the focus is on voltage and reactive power characteristics. from equation (b-3), and at any operating point we may keep p constant and voltage stability is evaluated by considering incremental changes between q and v. based on the above assumption let in equation (b-3), so that 0=p∆ [ ] vjvjjjjq rpvpqqv ∆=∆−=∆ −1θθ (c-1) and (c-2) qjv r ∆=∆ −1 where [ ]pvpqqvr jjjjj 1−−= θθ (c-3) rj is called the reduced jacobian matrix of the system and it directly relates the bus voltage magnitude to the bus reactive power injection. the elimination of the real power and angle part from equation (b-1) allows us to concentrate on the analysis of the reactive demand and supply problem of the system and also minimize the computational effort (gao et al, 1992). the eigenvalues and eigenvectors of the reduced jacobian matrix lead to the identification of voltage stability characteristics of the system. the eigenvalues identify the different modes, which may create the voltage instability of the system. the proximity to instability is provided relatively by the magnitude of the eigenvalues and the mechanism of instability is provided by the eigenvectors. let: ηζλ=rj (c-4) where ζ is the right eigenvector matrix of , λ is the diagonal eigenvalue matrix of , and η is the left eigenvector matrix of . r rj rj j from equations (c-2) and (c-4), we have qqv i i ii ∆=∆λ=∆ ∑− λ ηζ ηζ 1 (c-5) each eigenvalue and the corresponding right and left eigenvectors, define the ith mode of the system. the ith modal reactive power variation is: iimi kq ζ=∆ (c-6) state of the art methods for electric power systems the corresponding ith modal voltage variation is: mi i mi qv ∆=∆ λ 1 (c-7) it is seen that when the reactive power variation is along the direction of , the corresponding voltage variation is also along the same direction and the magnitude is amplified by a factor which is equal to the magnitude of the inverse of the corresponding eigenvalues. iζ the system is voltage stable if all the eigenvalues of are positive, and is voltage unstable if at least one of the eigenvalues is negative. the smaller the magnitudes of the eigenvalues, the closer the corresponding modal voltage to being voltage unstable. if the eigevalue is zero, the system is on the verge of voltage instability. rj the elements (bus, branch and generator) which participate in each mode can be obtained as follows: bus participation factors: the participation factor of bus k to mode i (kundur, 1994) is given by ikkikip ηζ= (c-8) kip kip i indicates the contribution of the ith eigenvalue at bus . the size of bus participation in a given mode indicates the effectiveness of remedial actions applied at that bus in stabilizing the mode. the bigger the value of the closer the load bus (load area) to voltage instability. k branch and generator participation factors: the participation factor of branch lj to mode (kundur, 1994) is given by branchesallforq jbranchforq p loss loss lji ∆ ∆ = max (c-9) the branches with high are those which cause mode i to be weak. ljip the participation factor of generator to mode is gk i generatorsallforq mgeneratorforq p mgk ∆ ∆ = max (c-10) generators with high are those which maintain stability of mode . gkip i lkt 2.4 the test function method this voltage stability index is based on a family of scalar test functions, (seydel, 1988) given as, llk t llk ejjet 1−= (d-1) where j corresponds to the system jacobian matrix, e is a unit vector, and l ( ) tkltlllk eejeeij +−= (d-2) 253 al-khusaibi, ellithy and irving 254 j lkj c where i represents the identity matrix. at the voltage collapse point is singular and is guaranteed not to be singular, and if l k == , then ccc t ccc ejjet 1−= (d-3) the test function family is a function of the system variables and parameters. as the system approaches collapse, the system variable change, and the critical test function shows a quadratic shape as a function of load margin ∆β. thus, cct a (d-4) 2ccat≈∆β where is a scalar constant. this allows tcc to be used to determine the system proximity to collapse. the test function index is independent of system size, which is not the case for sensitivity factors. however, determining the critical buses c is a disadvantage of using (d-3) for tcc as this might lead to significant computational costs. 2.5 the reduced determinant method this method or technique as defined by ganizares et al, (1995), is based on assuming that active and reactive power variations occur only at the system bus of interest l . the load-follow jacobian matrix can be re-ordered so that the mismatch powers for bus l are the last ones. this gives: (e-1)             ∆ ∆ ∆ ∆       =               ∆ ∆ l ll e e d b c a q p θ θ 0 0 where a, b, c and d represent the corresponding blocks of jacobian matrix j . also d is a 2 x 2 matrix. equation (e-1) can be reduced to: (e-2)       ∆ ∆ =      ∆ ∆ l i ll l l v d q p θ' where (e-3) bcaddll 1' −−= the matrix is well defined at operating points. thus, the determinant of is 'lld d ' ll a j dll det det det ' = (e-4) ' lld becomes zero only at the collapse point. state of the art methods for electric power systems 255 ' lld ' ccd cc d results for changes in the loading factor β obtained for different operating points show that det provides similar information and behavior as that of a test function. hence the loading margin can also be defined using det instead of in equation (d-3). matrix in (e-3) can be obtained by a partial factorization of the corresponding load-flow jacobian t 'll j . this suggests slightly less computation cost than determining the test function t in (d-1). lk 2.6 the loading margin method by multiple power-flow solutions this method calculates an approximation to the closest loadability by using a pair of multiple power flow solutions (yorino et al, 1997). the loading margin index is defined as the amount of additional load increase (specific pattern) for a particular operating point that may cause a voltage collapse. loading margin is widely accepted as an index of voltage collapse and can be easily generalized to be associated with the margin of some other parameter that is varied until the system reaches voltage collapse. for example: if the loads were temperature dependent, then one could define a “temperature margin” to voltage collapse. the advantages of the loading margin can be summarized as: • it is straightforward and can be easily understood. • it is not based on a specific model. • it is an accurate index. • it accounts for the pattern of load increase. the disadvantages of the loading margin can be summarized as: • it is computationally more expensive. • it requires the assumption of a direction load increase. 2.7 the local load margins method this index of proximity (nagao et al, 1997) is based on the distance from the initial load ( in mw) to the nose of the p-v curve ( in mw). at a fixed power factor and as the load at node i is increased, the load margin assumes that at other loads the loads remain constant. hence, oip ipmax lmgip i oii lmgi p pp p max max −= (g-1) this equation allows the computation of a voltage stability margin for each load point. its computation is relatively easy. however, a voltage stability margin has to be evaluated for the whole power system. therefore, one needs to calculate for the number of load nodes in the system, which may be impractical. maxp by introducing a factor the problem of computing can be considered as a problem of calculating h . thus, index defined in (g-1) can be expressed in terms of as follow: h p lmgi h max p h h hp php p oi oioi lmgi 1− = − = (g-2) al-khusaibi, ellithy and irving this index is strongly based on a power flow model and therefore, more studies are required for other types of load models. computational cost is the main disadvantage of this index, as these local margins have to be calculated for all the load buses so that proximity to collapse can be predicted with more accuracy. 2.8 the thevenin/load impedance (zii/zi) method it has been shown by chebo et al, (1992), that the voltage collapse of the system at load bus i occurs when the impedance of the load is equal to the equivalent impedance looking into the port between i and the ground i.e. zii=zii (zii/zi =1). where zii is the magnitude of thevenin impedance seen by load i and zi is the magnitude of impedance of load i. for a secure system at bus i we must have zii/zi less than one (zii/zi <1). this voltage collapse proximity indicator (zii/zi) has also been used by these authors for reactive power dispatch to minimize the possibility of voltage collapse in the system. 2.9 the energy function method the energy function method has been described by demacro and overbye, (1990), where a scalar energy function is measured depending on the system voltage magnitudes and phase angle. this scalar measure has a property of defining a local minimum of this energy. the energy function defines the height between the operable solution and a low voltage solution. it is also called potential barrier (jeyasurya, 1994). as the power system approaches operating point to voltage collapse, the height of the barrier decreases. the height of the potential barrier can provide an indicator of the proximity to voltage collapse. the energy measure is computed as: energy measure = ( )ujuiujuiij n j n i vvb θθ −∑∑ == cos 2 1 11 − ( )sjsisjsiij n j n i vvb θθ −+ ∑∑ == cos 2 1 11 ( )∫∑ −−+ = u i s i v v suti n i pdx x xq θθ )( 1 ( )( )siuisjsisjsiij n j n i vvg θθθθ −−∑∑ == cos 11 + ( ) ij n j s i n i gv ∑∑ = − = 1 1 1 ( )( )sinisjsisisi vvvv −−θθsin , where n is the number of buses in the system, gij and bij are the elements of the bus admittance matrix; vi is the bus voltage magnitude; θ the bus voltage angle, p the vector of net real power into each bus, and qi the reactive power into bus i. the superscript s stands for an operable solution and u for the type-one lowvoltage solution for the same loading condition. this method provides an indicator or a measure, where the energy measure decreases as the load increases. it is approximately zero near the point of voltage collapse. a large value of the energy measure at 256 state of the art methods for electric power systems lightly loaded conditions indicates that the system is away from voltage collapse. the sensitivities of the energy measure at different controllers can be determined. 3. numerical results the singular value decomposition method, modal analysis method, and q-v curves technique have been applied to the ieee 30bus system. figure 2 shows the singleline diagram of the ieee 30-bus system. this system is a part of the american electric power service corporation network, which is made available to electric utility industry as a standard test case for evaluating various analytical methods and computer programs for the solutions of power system problems. a matlab computer program (ellithy et al, 2000) was used to obtain the power-flow solutions and the corresponding matrices. 257 figure 2. ieee 30-bus power system al-khusaibi, ellithy and irving 258 table 1. power-flow result for base case generation load bus # voltage magnitude (p.u) voltage angle (p.u) pg (p.u) qg (p.u) pl (p.u) ql (p.u) 1 1.060 0.000 2.614 -0.130 0.000 0.000 2 1.043 -5.509 0.400 0.568 0.217 0.127 3 1.019 -7.987 0.000 0.000 0.024 0.012 4 1.010 -9.651 0.000 0.000 0.076 0.016 5 1.010 -14.414 0.000 0.394 0.942 0.190 6 1.009 -11.378 0.000 0.394 0.942 0.190 7 1.001 -13.144 0.000 0.000 0.228 0.109 8 1.010 -12.135 0.000 0.404 0.300 0.300 9 1.048 -14.522 0.000 0.000 0.000 0.000 10 1.040 -16.172 0.000 0.000 0.058 0.020 11 1.082 -14.522 0.000 0.177 0.000 0.000 12 1.054 -15.438 0.000 0.127 0.000 0.000 13 1.071 -15.438 0.000 0.127 0.000 0.000 14 1.038 -16.337 0.000 0.000 0.062 0.016 15 1.033 -16.406 0.000 0.000 0.082 0.025 16 1.041 -16.022 0.000 0.000 0.035 0.018 17 1.035 -16.336 0.000 0.000 0.090 0.058 18 1.023 -17.025 0.000 0.000 0.032 0.009 19 1.020 -17.200 0.000 0.000 0.095 0.034 20 1.024 -17.001 0.000 0.000 0.022 0.007 21 1.025 -16.616 0.000 0.000 0.175 0.112 22 1.025 -16.600 0.000 0.000 0.000 0.000 23 1.018 -16.767 0.000 0.000 0.032 0.016 24 1.006 -16.901 0.000 0.000 0.087 0.067 25 0.983 -16.279 0.000 0.000 0.000 -0.000 26 0.964 -16.729 0.000 0.000 0.035 0.023 27 0.977 -15.626 0.000 0.000 0.000 0.000 28 1.008 -11.984 0.000 0.000 0.000 0.000 29 0.956 -16.978 0.000 0.000 0.024 0.009 30 0.944 -17.951 0.000 0.000 0.106 0.019 modal analysis was applied for two cases (base case and the stressed case). the stressed case was obtained by increasing the reactive power at bus number 30. table 1 shows the power-flow results for the base case. the eigenvalues of the two cases are shown in table 2. from table 2, it can be seen that all eigenvalues are positive indicating that the system is voltage stable. the eigenvalue λ1 is the least stable mode (critical mode). for the stressed case, the system is on the verge of instability (λ1 =0.0366) but not actually unstable. table 3 gives the participation factors of the critical mode λ1 for the base and stressed cases. from the participation factors of the base case, it is clearly seen that the highest participation factor corresponds to the load bus 30. based on this information, bus 30 is the weakest bus in the system. it can be concluded that the state of the art methods for electric power systems power stress in bus 30 can lead to voltage instability. bus 30 was stressed and the results have confirmed that it is the weakest bus and the critical eigenvalue mode became much smaller. table 2. eignvalues and singular value decomposition of jacobian matrix jr modal analysis singular value decomposition eigenvalue λi base case stressed case base case stressed case 1 0.5060 0.0371 0.5060 0.0366 2 1.0238 0.8235 1.0238 0.8265 3 1.7267 1.3301 1.7267 1.3338 4 3.5808 3.3288 3.5808 3.3411 5 4.0507 3.5145 4.0507 3.5224 6 5.4527 3.9509 5.4525 3.9508 7 6.0207 5.1156 6.0207 5.1171 8 7.4360 6.3687 7.4361 6.3751 9 8.7857 8.5863 8.7857 8.5864 10 11.0447 10.7369 11.0442 10.7383 11 13.6334 12.3384 13.6333 12.3410 12 13.7279 13.3416 13.7278 13.3416 13 16.3753 14.7664 16.3757 14.7719 14 18.0785 17.5596 18.0784 17.5601 15 19.1258 18.7216 19.1264 18.7228 16 19.7817 19.4681 19.7817 19.4681 17 23.0739 22.4080 23.0736 22.4096 18 23.4238 22.9447 23.4245 22.9457 19 35.3863 34.8404 35.3868 34.8414 20 37.8188 36.9723 37.8188 36.9723 21 59.5431 58.1663 59.5429 58.1664 22 65.9541 65.3731 65.9551 65.3744 23 100.6465 97.5208 100.6465 97.5209 24 110.2056 109.1565 110.2079 109.1592 similarly, the singular value decomposition (svd) was obtained for the base and stressed cases. the svd results are given in table 2. the svd results have confirmed the same results as the modal analysis method. the q-v curves and p-v curves for the buses 30, 29, 24, and 23 were computed and are shown in figures 3 and 4. these curves are used to determine the mwand mvardistance to the voltage instability point of the weakest load buses. the p-v curves at different power factors for the weakest bus (bus 30) are also computed and are shown in figure 5. from the curves it can be observed that buses 30 and 29 have less reactive power margins (i.e. less stability margins). these agree with the bus participation factors given in table 3. from table 2, these buses have high participation in the critical mode which is on the verge of becoming unstable. the advantage of modal analysis is that it identifies groups of buses, which participate in the voltage instability. 259 al-khusaibi, ellithy and irving 260 figure 3. q-v curves for the load buses 30, 29, 24 and 23 figure 4. p-v curves for the load buses 30, 29, 24 and 23 state of the art methods for electric power systems table 3. participation factors of system buses for base case and stressed case base case λ1 =0.506 stressed case λ1 = 0.0371 bus # participation factor participation factor 3 0.0004 0.0001 4 0.0005 0.0001 6 0.0005 0.0002 7 0.0002 0.0001 9 0.0037 0.0004 10 0.0121 0.0011 12 0.0037 0.0003 14 0.0081 0.0006 15 0.0111 0.0009 16 0.0079 0.0006 17 0.0115 0.0009 18 0.0165 0.0010 19 0.0179 0.0011 20 0.0172 0.0011 21 0.0176 0.0018 22 0.0189 0.0021 23 0.0238 0.0029 24 0.0395 0.0075 25 0.1055 0.0413 26 0.1729 0.0454 27 0.1028 0.0762 28 0.0025 0.0013 29 0.1934 0.2389 30 0.2118 0.5743 figure 5. p-v curves for bus 30 at different power factors. 261 al-khusaibi, ellithy and irving 262 4. conclusions the methods for static analysis of voltage stability problems have been briefly described in this paper. based on these methods, indices are determined to predict proximity to voltage collapse. some of these methods were applied on the ieee 30-bus system for demonestration of these techniques. other methods and techniques (carpenter et al, 1984; tamura et al, 1982; el-keb and max, 1995; kwanti et al, 1986; chang and su, 1998) are mentioned in the references but due to space limitation these have not been discussed in this paper. 5. references barbier c., and barret, j.p. 1980. analysis of phenomena of voltage collapse on transmission system. review generale de iõelectricite, 89: 672-690. begovic, m.m. and phadke, a.g. 1992. control of voltage stability using sensitivity analysis. ieee trans. on power systems, 7: 114-123. bullok g.c. 1990. cascading voltage collapse in west tennessee, august 22, 1987. 44th annual protective relaying conference, georgia institute of tech. carpentier j., girard, r. and scano, e., 1984. voltage stability collapse proximity indicators compound from an optimal power flow. 8th power system computing conference, helsinki, 671-678. chebbo, a.m., irving, m.r. and sterling, m.j.h. 1992. reactive power dispatch incorporating voltage stability. iee proceedings-c, 139: 253-260. chebbo, a.m., irving, m.r. and sterling, m.j.h.1992.voltage collapse proximity indicator: 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löf, p.a., smed, t., anderson, g. and hill, d.j. 1992. fast calculation of a voltage stability index. ieee trans. on power systems, 7: 54-64. mansour, y., xu, w., alverado, f. and rinzin, c. 1994. svc placement using critical modes of voltage instability. ieee trans. on power systems, 9: 757-763. morrison, g., gao, g. and kundur, p. 1993. voltage stability analysis using static and dynamic approaches. ieee trans. on power systems, 8: 1159-1171. miller, t.j.e. 1982. reactive power control in electric systems. john wiley & sons. nagao, t., tanak, k. and tekenaka, k., 1997. development of static and simulation programs for voltage stability studies of bulk power system. ieee trans. on power systems, 12: 273-281. overbye, t. and demacro, c. 1995. improved power system stability assessment using energy method. ieee trans. on power systems, 6: 1890-1896. pal, p. 1992. voltage stability conditions considering load characteristics. ieee trans. on power systems, 7: 243249. schlueter, r. 1998. a voltage stability security assessment method. ieee trans. on power systems, 13: 14231438. seydel, r.1988. from equilibrium to chaos-pratical bifurcation and stability analysis. elsevier science, northholland. suzuki, m., wada, s., asano, t. and kudo, k. 1992. newly developed voltage security monitoring system. ieee trans. on power systems, 7: 965-972. tamura, y., mori, h. and iwamoto, s. 1982. relationship between voltage stability and multiple load flow solutions in electric systems. ieee trans. on power apparatus and systems, pas-102: 1115-1123. taylor, c. w. 1994. power system voltage stability. mcgraw-hill, new york. thomas r.j., and tiranuchit a., 1986. voltage instabilities in electric power networks. proceeding of eighteenth southeast symposium on systems theory, 359-363. vaahedi, e. mansour, y. and sun, d. 1999. large scale voltage stability constrained optimal planning and voltage stability applications using existing opf/optimal var planning tools. ieee trans. on power systems, 14: 65-74. venikov v.a., stroev v.a. and idelchick v.i. 1975. estimation of electric power system steady state stability in load flow calculation. ieee trans. on power apparatus and systems, pas-94: 1034-1041. yokoyama, a. and sekine, y. 1989. a static voltage stability index based on multiple load flow solutions. proc. of the bulk power system voltagephenomena stability and security, missouri. yorino, n., harada, s. and chen, h. 1997. a method to approximate a closet loadability limit using multiple load flow solutions. ieee trans. power system, 12: 424 – 429. received 9 september 2000 accepted 10 august 2000 263 çáøñþ çáíïíëé áêíáíá çóêþñçñ çáì� introduction methods of voltage stability analysis bus participation factors: the participation factor of bus k to mode i (kundur, 1994) is given by branch and generator participation factors: the participation factor of branch lj to mode � (kundur, 1994) is given by participation participation kwanti, h.g., pasrija a.k. and bahar l.y. 1986. static bifurcations in electric power networks: loss of steady-state stability and voltage collapse. ieee trans. on circuits and systems, cas-33: 981-991. squ journal for science, 2017, 22(2), 63-72 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp63-72 sultan qaboos university 63 luminol chemiluminescence catalyzed by silver nanoparticles for the sensitive determination of penicillamine fakhr eldin o. suliman* and kauther al-hadhrami department of chemistry, college of science, sultan qaboos university, box 36, al-khod 123, sultanate of oman. *email: fsuliman@squ.edu.om. abstract: a sequential injection method for the determination of penicillamine (pa) was developed based on quenching the chemiluminescence generated by oxidation of luminol by hydrogen peroxide in presence of silver nanoparticles (agnps). the chemiluminescence (cl) of the reaction was found to greatly enhance in presence of agnps due to the increased catalyst surface area. the method was sensitive and found suitable for analysis of penicillamine in pharmaceutical preparations. linear calibration curve is obtained in the range 0.2-1.0 g ml -1 with a relative standard deviation less than 2%. a recovery percent of 102.3 0.2 was obtained with the tablets matrix indicating reasonable selectivity of the method for pa in tablets. the mechanism of quenching of the cl reaction was investigated by uv-visible spectroscopy and transmission electron microscopy as well as by theoretical calculations using dft-b3lyp method. the covalent attachment of pa to the agnps triggers aggregation of the particles thereby diminishing the surface significantly. the method was applied for the assay of pa in pharmaceutical preparations. keywords: chemiluminescence; silver nanoparticles; sequential injection analysis; pharmaceutical preparations and penicillamine. ساعد لتحليل البنساالمينفضة كعامل م -الليمونيل الكيميائي بواسطة جسيمات النانو وميض فخر الدين سليمان و كوثر الحضرمي في تم إستحداث طريقة حقن إنسيابي لتحليل البنساالمين بواسطة تثبيط التضوءالكيميائى الناشئ عن تفاعل الليمونول مع بيروكسيد الهيدروجين :صالملخ يزداد بصورة كبيرة في وجود الجسيمات النانوية. الطريقة المستحدثة ذات حساسية عالية وجود جسيمات الفضة النانوية. التضوء الناتج عن تفاعل الليمونول نانوجرام/مل كما أن االنحراف المعياري النسبي لم 0222-222وتم تطبيقها على تحليل البنساالمين في المستحضرات الصيدالنية. وجد منحنى المعايرة بين % وهذا يدل على أن الطريقة المستحدثة  022.1 2.2 اعه من البنساالمين عند تحليله في منتجاته الصيدالنية كان%. باإلضافة لذلك ما تم استرج2يزد عن تم أيًضا في هذا البحث دراسة اآللية التي يتم بها تثبيط تضوء الليمونول بواسطة البنسالمين وذلك مناسبة لتحليل هذا الدواء في المنتجات الصيدالنية. عملية وأخرى نظرية. بإستخدام طرق بنساالمين. و التضوءالكيميائى ، جسيمات الفضة النانوية ، حقن إنسيابي، مستحضرات صيدالنية :مفتاحيةالكلمات ال 1. introduction n intense interest has been lately directed towards the design, synthesis and application of nanostructures. myriads of articles have appeared in the literature describing the wide variety of applications of these fascinating materials in analytical, biomedical, optical, electrical and magnetic fields [1–9]. the major attraction to these materials is due to the size and shape dependent optical, catalytic and electro-magnetic properties [10]. nps of narrow size distribution can be produced when all nuclei are formed at the same time; from these nuclei or seeds other nanostructures of uniform sizes can be developed. silver and gold nanoparticles have been considered as hallmark during exploitation of surface enhanced raman spectroscopy, a technique that opened new avenues in research allowing detection of agrochemicals, biochemical molecules and toxins at ultra-trace levels and making it an important diagnostic technology [11–17]. moreover, silver is known for its high toxicity to a wide range of microorganisms, this has, in turn, driven lots of attention to investigate agnps as a promising antimicrobial agent [18,19]. in many instances the surface chemistry of the nps influences their interaction with the other systems, such as microorganisms. capping agents such as citrates are used to stabilize the particles in solution; however, the physicochemical properties of the ensuing nps depends greatly on the nature of these agents [10]. a mailto:fsuliman@squ.edu.om fakhr eldin o. suliman and kauther al-hadhrami 64 the chemiluminescence of luminol was known since the first half of the previous century. luminol cl is produced by oxidizing the reagent with strong oxidizing agents such as hydrogen peroxide and usually in the presence of a catalyst. metal ions such as co(ii), cu(ii) and ag(i) have been extensively used as catalysts. agnps were found to catalyze this cl reaction producing intense emission possibly due to the high electron density imparted by the high surface area of the small particles [3,20,21]. other metal nanoparticles such as aunps, au/ag alloy nps and ptnps also enhance the cl of luminol in presence of various oxidants [20–23]. however, agnps exhibit the highest catalytic activity which has been rationalized by the lower reduction potential of ag compared to au and pt [10]. the smooth oxidation of ag produces an abundant population of hydroxyl radicals on the surface of particles and consequently intense cl is obtained. enhancement and quenching of luminol-h2o2-metal-nps cl has been used as a platform for developing a number of analytical methods for the determination of various pharmaceutical and biomedical species. for example, sensitive methods for determination of fluoroquinolones, glutathione, and the anticancer drug flutamide were developed based on their enhancement effects on the luminol-metal-nps cl [6, 20, 21, 23–24]. on the other hand, quenching of this cl reaction by n-acetyl-cysteine enabled determining low levels of this drug in pharmaceutical preparation [25]. voicescu et al. evaluated the antioxidant activity of hydroxyflavones in presence of bovine and human serum albumin using luminol-h2o2-agnps cl [26]. a method for ultrasensitive determination of dna hybridization has been developed based on luminol-agnps cl [27]. in this method the high sensitivity of the cl together with the large number of ag ions allowed specific sequence dna targets to be detected. the major advantages of cl have led to the extensive utilization of this technique for detection of analytes using flow injection analysis, sequential injection analysis, microfluidics, capillary electrophoresis and high performance liquid chromatography[28–35]. the major attraction to cl detection in these techniques stems from the high sensitivity and the simple instrumentation as only a photomultiplier tube is required, eliminating the use of expensive optics required by other techniques such as fluorescence spectroscopy. in cl the absence of an external light source does not only eliminate the need for use of monochromator but also reduces background signals and scattering generated by other species or by walls of cuvettes. penicillamine (pa), (2-amino-3-mercapto-3-methyl-butyric acid), figure 1, is a sulfhydryl molecule with a chemical structure similar to the amino acid cysteine. it is a metabolite of the antibiotic penicillin, but with no antibiotic properties. currently pa is used to treat some disorders such as wilson's disease and cystinuria [36,37]. pa treatment hinges on its binding ability of accumulated heavy elements such as copper with ensuing elimination through urination. figure 1. chemical structure of penicillamine. inspired by the above reports, the effect of pa on the cl of luminol-h2o2-agnps was investigated. we also investigated the relationship between the size and shape of agnps and the cl intensity. an analytical method was further based on the quenching effect of pa on luminol-h2o2-agnps cl and was developed using sequential injection analysis (sia) together with cl detection for the analysis of pa in pharmaceutical preparations. it is worth mentioning here that, si-technique is characterized by its low consumption of reagents compared to the pristine flow injection analysis. moreover, we investigated the mechanism of cl quenching by pa using experimental methods and theoretical calculations. 2. experimental 2.1 general all reagents were used without further purification. tri-sodium citrate (>99%), sodium borohydrate (nabh4) and hydrated hydrazine were obtained from bdh chemicals (pool, england). agno3, naoh, 30% (w/w) h2o2, penicillamine 99% and luminol (97%) were from aldrich (usa). penicillamine film coated tablets bp was from genenic (uk). ultra-pure water from a milli-q system was used for all solution preparation and experiments. transmission electron microscope (jeol jem-1230) was used for the determination of particle size and shape. absorption spectra were recorded on cary 50 conc. spectrophotometer (varian). a slm amnico bowman series-2 luminescence spectrometer was used to record emission spectra as well as to collect chemiluminescence (cl) http://en.wikipedia.org/wiki/metabolite http://en.wikipedia.org/wiki/penicillin http://en.wikipedia.org/wiki/antibiotic luminol chemiluminescence catalyzed by silver nanoparticles 65 emissions by optimizing the photomultiplier tube (pmt) voltage from 850-1000 v and by keeping the excitation slit closed. the flow-through cell for cl was fabricated from a teflon transparent tubing of 0.75 mm id. the tube is coiled in a circular pattern of 3 cm diameter and attached to a mirror to capture the maximum light intensity and placed just in front of the pmt. ab2 software was used to control all processes of the luminescence spectrometer. 2.2 synthesis of silver nanoparticles citrate-protected silver seeds were prepared as follows: 0.5 ml of 59 mmol l -1 agno3 and 1 ml of 34 mmol l -1 sodium citrate were added to 98 ml of deionized water. the solution was stirred for 15 minutes and 0.5 ml of aqueous 0.02 mol l -1 nabh4 solution, which had been stored for 2 h, was added dropwise. the resulting olive solution was stirred vigorously for 1 hour and stored for 1 day in the dark at room temperature before use. silver seeds were approximately spherical with average diameter of 12 nm from transmission electron microscopy (tem) measurements. silver nanoparticles, agnps, of various sizes and shapes were obtained starting with the seed prepared. different volumes of silver seeds (15-5 ml) were added to a solution containing 300 l hydrazine (40 mmol l -1 ) and 100 l sodium citrate (40 mmol l -1 ). to this solution 100 l of an aqueous solution of 59 mmol l -1 silver nitrate were added dropwise with vigorous stirring. the growth of the particles resulted in four different nanostructures (a1-a4). for tem analysis, 1 ml of each sample (a1–a4) was centrifuged for purification and the solid portion was washed twice with deionized water. all samples were placed in ultra-sonic machine to homogenize nanoparticles for 15 min before the preparation of the tem grids. a drop of sample was placed on wax film and the formvar/carbon film (300 mesh cu grid) was placed on the top of the drop for 30 to 60 seconds. grids were lifted from the drop with care and dried with clean filter paper and stored after that in grid box for scanning. 2.3 preparation of solutions a 10 mmol l -1 stock solution of luminol was prepared by dissolving 443 mg luminol powder in 250 ml 0.02 mol l -1 naoh solution. working solutions of 0.8 mol l -1 h2o2 were prepared daily from 30% (w/w) h2o2. a stock solution of 1000 g ml -1 of pa was prepared by dissolving 10 mg of the drug into 10 ml volumetric flask filled to the mark with deionized water. working solutions of pa were prepared by appropriate dilution. a stock solution of pa tablets was prepared by crushing six pa tablets after weighing each tablet. an amount of powder that correspond to a average tablet mass (78 mg) of pa was dissolved in 50.0 ml water. the solution was sonicated for one hour and then filtered and stored in cold for further use. working solutions of pa were prepared by appropriate dilutions of the filtered stock solution. 2.4 manifold and procedure the sequential injection analysis system used in this study is schematized in figure 2. it consists of 5.0 ml syringe pump driven by a stepper motor (24000-step full stroke), 200 cm holding coil (0.8 mm id teflon tubing, upchurch scientific, oak harber, usa), a multiposition-valve (eight ports, valco, houston, usa), 100 cm and 20 cm reaction coils (0.8 mm id teflon tubing, upchurch scientific). a second 1.0 ml syringe pump was used to drive the reagent h2o2 through the flow system. a homemade flow cell of a 3.0 cm diameter (0.8 mm id teflon tubing, upchurch scientific) attached to a mirror to maximize collection of emitted light was placed in front of the detector. all fluids were controlled by fialab for windows software. figure 2. sia manifold used for the analysis of pa with luminol-h2o2-agnps cl system. fakhr eldin o. suliman and kauther al-hadhrami 66 cl signals were obtained by aspirating the reagent luminol and standard solution of penicillamine with ag-nps into holding coil by multiposition-valve and the composite zone was then pumped by syringe pump 1 towards the detector. the second syringe pump, syringe pump 2, was synchronized to pump appropriate volumes of the oxidant h2o2 to meet the composite zone of luminol-pa-agnps at t-junction just before the reaction coil, then the mixture was passed to the flow cell and the cl emission produced was collected and measured by pmt. 2.5 molecular modeling the geometry of pa, pa-ag complex, and their dimers were optimized using the density functional theory (dft) calculations in conjunction with the b3lyp gradient-corrected hybrid [38,39]. the 6-31g(d) basis set was selected for all atoms except silver for which lanl2dz effective core potential was used [40]. the final geometry was confirmed as a true minimum by inspecting the harmonic vibrational frequencies showing no imaginary frequencies. all calculations were performed using gaussian 09 software. 3. results and discussion 3.1 synthesis and characterization of agnps agnps were prepared at room temperature using a mixture of silver nitrate, sodium citrate, and nabh4 in aqueous solution. the solution mixture turned light yellow immediately and changed to olive color upon stirring for one hour. this signals the formation of agnps. strong reducing agents favors the formation of smaller nanocrystals due to the fast rate of reaction [10,41]. further, agnps of different sizes and shapes were obtained by controlling the number of seeds in the solution. in this work we used milder reducing agents, hydrazine and citrate ions, the latter works as a capping agent as well. in presence of silver seed further reduction of silver ions results in particle growth which was inferred from a noticeable change of color of the solution. because of the catalytic effect of silver seed secondary nucleation of agnps is prohibited which leads to growth of particles [41,42]. figure 3 shows a typical tem image of ag-nanostructures. these nanostructures are of different shapes and sizes. the almost spherical particles are characterized by a size range of 4.0-20 nm in diameter. this wide range of particle size is associated with the rapid nucleation which characterizes precipitations from solutions. figure 4a shows the uv-visible absorption spectrum of agnps. the maximum absorption was at 395 nm, which is due to the presence of agnps with an average diameter of 12 nm. figure 4b shows the absorption spectra of the solution of the agnps (samples a1-a4). the prepared solutions show a visible change of color from yellow through greenish blue to red, while for a4 it was cyan. the location of peaks is closely correlated with the size of the agnps and nanoplates. the higher the size of the nps and nanoplates, the further the location of this peak extends toward the near ir region. the peak around 400 nm was due to spherical silver particles, which are caused by incomplete seeding growth in two dimensions and the percent of these spherical silver particles is few because the absorption intensity of the peak is quite weak. the origin of the peak at 338 – 360 nm was not known at present but it could be due to complexes of silver in the solution. figure 3. tem images of (a) silver nanoparticles; (b) and (c) are nanoplates for sample a2 and sample a3 respectively through step-by-step growing. luminol chemiluminescence catalyzed by silver nanoparticles 67 3.2 agnps-luminol-h2o2 cl luminol-h2o2 cl system is a popular cl system and as figure 5 shows it emits weak cl in alkaline solution in the absence of a catalyst. in this work the catalytic effect of agnps on the luminol-h2o2 cl system was investigated. when agnps were added into the system, the signal remarkably enhances. interestingly, adding ag-nanoplates enhance s the cl signal of luminolh2o2 sytem as well but to a lesser extent compared to agnps. this is due to large catalytic area provided by agnps compared to the nanoplates. we therefore, investigated the agnps-luminolh2o2 system to develop an analytical protocol for the determination of pa. figure 4. uv-vis-nir spectra of prepared agnps and nanoplate solutions: (a) agnps, and (b) samples a1-a4 respectively: (1) sample a1; (2) sample a2; (3) sample a3; (4) sample a4. 3.3 optimization the experimental factors that affect the enhancement of luminol-h2o2 cl by agnps included in this work are given in table 1. the effect of each of these factors was examined by the univariate approach where each factor was changed while keeping other factors constant. the effect of the concentration of naoh solution on the cl system was studied from 0.010 m 0.10 mol l -1 . it is well documented that oxidation of luminol by h2o2 takes place in alkaline media. the intensity of cl emission was observed to increase with naoh concentration until it reaches 0.020 mol l -1 and then it started to decrease. therefore the naoh concentration was fixed at 0.020 mol l -1 . the effect of h2o2 concentration on the cl was also studied in the range of 0.10 1.5 mol l -1 . the cl intensity increases as the concentration of h2o2 increases up to 0.80 mol l -1 , after which the signal intensity remains virtually constant with further increase in h2o2 concentration. therefore, the optimum concentration of h2o2 was selected to be 0.80 mol l -1 . table 1. factors included in the optimization study and their optimum. cl intensity was also found to increase as the concentration of the nanoparticles increases. the increase of catalytic area was the major reason for this phenomenon, because as the concentration of the nanoparticles increases, the available catalytic area increases as well and the detectable cl intensity enhances significantly. notably, the cl signal increases exponentially with an increase in the amount of agnps. the enhancement factor upon addition of the maximum amount of agnps (8 ml of as-prepared agnps) was about 300 times compared to cl emissions in the factors range optimum size of ag-nps (ag-nps) – (ag-nanoplates) agnps naoh concentration 0.010 m – 0.10 mol l -1 0.020 mol l -1 h2o2 concentration 0.10 m 1.5 mol l -1 0.80 mol l -1 ag-nps conc. 1ml in 10 ml h2o – not diluted 4 ml in 10 ml h2o fakhr eldin o. suliman and kauther al-hadhrami 68 absence of nanoparticles. however, for further experiments only 4 ml of the as-prepared agnps will be used as a compromise between sensitivity and cost. the optimum conditions for agnps-luminol-h2o2 are summarized in table 1. these conditions will be used for the determination of pa. 3.4 analysis of pa a typical sequential injection (si) results are shown in figure 5 for the quenching effect of pa on the cl of agnps-luminolh2o2 system. the luminol-h2o2 system in absence of agnps emits weak cl signal. addition of agnps increases the intensity of the signal significantly. interestingly, addition of pa results in a noticeable quenching of the cl emission especially in presence of agnps. figure 5. typical si results of (1) luminol-h2o2, (2) luminol-h2o2ag-nps, (3) luminol-h2o2ag-npspa, (4) luminol h2o2 pa. these results suggest that agnps-luminol-h2o2 can be used to develop an analytical procedure for the assay of pa in pharmaceutical forms based on quenching of this reaction. series of si runs were obtained by injecting standard solution of pa in the range 200-1000 ng ml -1 in presence of constant amount of agnps. mixing of these solutions with luminol and h2o2 generated the signals shown in figure 6. obviously, this figure shows a gradual decrease in cl with increasing concentrations of pa and as can be seen highly reproducible results are always obtai ned. this is an advantage of utilizing the si technique, where each run is affected in the same way as other runs. each standard was run in duplicate and each run was repeated three times and a relative standard deviation less 2% is obtained at all times. regression analysis of i0/i versus concentration of pa, cpa(g ml -1 ), produced the following calibration equation: i0/i = 7.80.4 cpa + 0.70.2 (r 2 =0.99). figure 6. typical si results of standard pa and pa sample produced using optimum conditions shown in table 1: (1) no pa; (2) 0.20 g ml -1 pa; (3) 0.40 g ml -1 pa; (4) 0.60 g ml -1 pa; (5) 0.80 g ml -1 pa; (6) 0.40 g ml -1 pa tablets (drug sample). luminol chemiluminescence catalyzed by silver nanoparticles 69 the proposed method was applied for the determination of pa in pharmaceutical formulations of commercial dosage forms. tablets were prepared as described before. from the si results of standards pa of different concentrations and 0.40 g ml -1 pa tablets solution, it was noticed that the prepared tablet solution of pa has the same effect as standard solution of same concentration (figure 6). the recovery for this sample was calculated to be 102.3  2.2% indicating that no interference is observed from the additives present in the tablets. 3.5 cl quenching mechanism metal cations such as co(ii) are known to catalyze the decomposition of hydrogen peroxide to produce the reactive hydroxyl radicals and the superoxide species (  o2) [43,44]. the high surface area of agnps is, therefore, responsible for the efficacy of production of large bursts of highly reactive radicals. it is also widely accepted that nps surface contribute to the creation of luminol radical intermediates. the radical-radical annihilation reaction of luminol with hydroxyl or superoxide species generates a blue cl emission. thiols such as pa possess a number of functional groups that might interact with agnps as well as with the catalytically generated species. therefore, pa is expected to compete with luminol to intermediate hydroxyl and superoxide radicals resulting in quenching of the cl intensity. moreover, the formation of ag-s covalent bond might result in covering agnps surface with pa molecules and subsequently decreases the catalytic activity of the particle surface. to investigate the mechanism of quenching of luminol-h2o2ag-nps system by pa, series of solutions containing constant amount of luminol, h2o2, agnps and varying concentrations of pa (0.0 – 5.0 g ml -1 ) were prepared. the si-cl signals for these solutions show that as the concentration of pa is increased the cl signal decreases sharply and the signal was observed to decrease more than fifty times by adding 5 g ml -1 of pa. uv-visible spectra of agnps in absence and presence of increasing amount of pa were obtained. an absorption peak was observed between 392 and 398 nm for all different concentration of pa with a change in color of the solution from dark yellow to light pink with the addition of high pa concentration. it was also observed that the absorbance decreased with an increase in pa concentration. moreover, it was observed that at high concentration of pa absorption spectra started to shift to higher wavelength and became broader. to further investigate the effect of the addition of pa to the luminol h2o2 agnps system, tem images (before and after the addition of pa) were taken as shown in figure 7. the tem images show that prior to addition of pa, the particles are highly dispersed and approximately of uniform size in aqueous solution with an average diameter of 12 nm. after the addition of pa, the agnps became highly aggregated and connected. it is worth mentioning here that these samples were prepared by centrifuging the mixture, separating the nanoparticles and washing with deionized water twice. the above observations can be explained as follows: the addition of pa to a solution containing agnps results in the covering the surface of agnps with pa through the sulfur group of pa and the surface ag atoms of the nanoparticles. this in turn leads to the aggregation of agnps due to the formation of strong hydrogen bonding between the different functional groups (carboxyl and amine groups) on the surface. this leads to the reduction of the catalytic activity of ag-nps and as a result the cl intensity of luminol decreases. figure 7. tem and photograph images of 4 nm – 25 nm ag-nps: (a) before and (b) after the addition of pa. we also performed theoretical calculations to study the possible intermolecular interaction between pa molecules attached to ag ions. the geometries of pa and its corresponding ag complex are obtained by dft calculations and the optimized geometry of pa-ag complex is shown in figure 8. the calculated ag-s bond distance is 2.398 å and the ag-s-c bond angle is 105.7. moreover, the calculated dihedral angles ncco in the complex and in the free molecule were 159.4 and 163.1 respectively. this indicates that amine and the carbonyl conserves the same planarity when complexed to silver; similar results were reported for n-acetyl-l-cysteine with silver [45]. the fakhr eldin o. suliman and kauther al-hadhrami 70 optimized structure of ag-pa-pa-ag dimer is also shown in figure 8. these dimers are formed by interaction of pa molecules with one another. inspection of this figure reveals the fact that the presence of the amino and the carboxyl groups facilitated the formation of a network of strong intermolecular hydrogen bonds. this network of hydrogen bonding is established through the interaction of the hydrogen atoms on the amine groups with the oxygen atoms on the carboxyl group. the hydrogen bond lengths between the hydrogen atoms on the amine group and the two oxygen atoms of the carboxyl group are 1.735 and 1.627 å. this in turn results in aggregation of nanoparticles and consequently the cl intensity is quenched. figure 8. dft-b3lyp optimized structures of (a) pa-ag (b) ag-pa-pa-ag. 4. conclusion in this work we successfully prepared silver nanostructures of different sizes and shapes. agnps of spherical shape with average diameter of 12 nm were found to efficiently catalyze luminol-h2o2 reaction to produce an intense cl. pa quenched 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2000 sultan qaboos university review of omani aflaj systems: an element of national water resources,technology and economic developments abulbasher m. shahalam department of civil engineering, college of engineering, sultan qaboos university, p. o. box 33, al khod 123, muscat, sultanate of oman. مصدر قومي لمصادر المياه والتقنية والتنمية االقتصادية: استعراض نظم االفالج العمانية أبو البشر محمد شاه علم يتضـمن البحث استعراضاً شامالً لالوجه المختلفه لألفالج في سلطنة عمان ومنها الزراعة والتربة ومصادر المياه :خالصـة ل ما نشر عن نظم االفالج في السلطنة، ميز الباحث وعرض العوامل التي تؤثر ومن خال . والنواحـي االقتصادية واالجتماعية كما يتعرف الباحث ايضاً في هذا النظام على مكامن الضعف . على حيوية واستمرارية هذا النظام التقليدي الفريد لمصادر المياه كما يلخص البحث في شكل جداول ورسومات بيانات .والقوة في ظل التكنولوجيا الحديثة ، باإلضافة الى اسلوب الحياة والثروة .فنية في المجاالت الديمغرافية والجغرافية والتربة والمياه والري ونمط المحاصيل وانشطة المنظمات ذات الصلة بنظم االفالج abstract: the paper includes a comprehensive review of the various aspects: agriculture, soil, water resources and socio-economic concerns associated with the aflaj facilities within the sultanate of oman. from available literature, the author identified and presented factors that affect the viability and sustainance of this traditional, existing and unique system of water resources management. the system weakness and strength at the advent of modern technology, life-style and wealth were also identified. technical data on demography, geography, soil, water, irrigation, croppattern and activities of organizations related to aflaj systems were summerized and illustrated in figures and tables. 1. introduction the sultanate of oman is located at the southeast corner of the arabian peninsula and has an area of about 309500 sq. km. it is within the geographic block lying between latitudes 16°40’n and 27°20'n and longitudes 51°50'e and 59°40'e. the coastline of the country extends about 1700 km from the strait of hormuz in the north to the border of the republic of yemen in the south. the climate of the country is hot and humid in summer (june 31-45 °c) and moderate in winter (january 20-25° c). the country experiences an average rainfall of 100 mm over the entire area with extremes of 300 mm over northern mountain regions and 55 mm over the central part of oman. the total population of the country is about 2.3 million of which nearly 74% are native omanis (mne, 1999). most of the population is concentrated in the coastal plains, which represent nearly 3% of the total land area. the country has very distinct topographical features consisting of wadis, plains and mountains. there are three main mountain ranges in the country, and all of them are along the coastline and separate the near-sea coastal plain from the interior sandy dry lands. the mountain ranges are at north (mosandom, al hazar al-gharbi, and al jabal al-akhdar), south (al-dhofar) and mid-coastline (al-huq). mountains occupy nearly 15% of the country. about 82% of the country is mainly sand and gravel desert and is part of the larger arabian desert known as the empty quarter, rub al-khali (ministry of information, mi, 1997). 1 shahalam the sultanate of oman has two main sources of water: traditional groundwater and nontraditional water produced from high-tech desalination plants and treated wastewater effluent. traditional groundwater sources may be separated into two groups: mostly confined fossil water (brackish/saline) in the central and southwest deserts and unconfined acquifers and fractured rock containment in the mountains and mountain plains (al-harthy et al., 1999; bernett, 1994; cord, 1992; gibb et al., 1975; kew, 1995; lenton, 1995; ministry of agriculture and fishery, maf, 1989; mi, 1995; ministry of water resources, mwr, 1991; 1992a; 1992b; 1994a; 1995; pdo, 1988). the latter type of ground-storage is mainly fed by rainfall in the mountain ridges in the north and south of the country. the non-traditional water is produced in desalination processes, which accounts for nearly 3 million gallons per day i.e.163000 m3/day (al-kalbani, 1993). the unconfined acquifers and fractured rock containment in many places crop-up on the surface as springs and wadi flows under artesian pressure. there are many shallow unconfined acquifers in the northern plains, that harbor water within a depth range of 7 to 15 m. this water is exploitable with even hand-dug wells. the natural water sources are the nuclei of oasis and community centers. water abstraction processes along with associated surface and/or underground channels that convey water to the community for domestic and irrigation needs are known locally as "falaj" with plural "aflaj" (mwr, 1995). in the past, the village communities, and their social structure and economy would largely depend on physical characteristics of the water source. the community size and livelihood of people depended on the quantity of natural water flow. in more recent times, particularly with the new oil wealth, some important changes in the features of national economy, education and life style have taken place. available technology and the new source of livelihood had a profound effect on the traditional way of life in the falaj community. public and private sectors in the country invested efforts and resources for extensive study programs to delineate the underground water resources and policies that may lead to planning towards optimal utilization of the resources. controlled recharge systems are developed to capture and retain scarce rainwater in the aquifer systems. diesel and electric pumps are introduced to raise relatively large volumes of water for agricultural and other purposes. consequently traditional groundwater systems are affected. in addition, modern mobility, job opportunity outside of old communities and the economy have elevated the people's aspiration for better life. the trend caused immense stress on the traditional falaj communities. the falaj systems in the country, however, retain a substantial stake in the country's water resources. more than 3000 aflaj support 35% of irrigated area and consume nearly 33% of national water demand (mwr,1995). the aflaj systems and associated communities badly need adequate attention and readjustment within the new environment for survival. during the past two decades, numerous articles and study reports directly or indirectly related to aflaj systems in oman were published. a collective reference to this information, however, is missing. this paper reviews available literature on subjects that affect various aspects of aflaj systems in oman, particularly present status of aflaj systems under the influence of modern economy, education, resource orientation and adaptation to technology. the impacts of new discovery of water and the introduction of new technologies in the augmentation of water sources and application of irrigation water are presented in the context of existing aflaj systems. 2. aflaj types the geomorphology of the sultanate of oman indicates that the region experienced surface water flow in prehistoric periods and had gradually been turned into a drier climate through time. consequently the inhabitants abandoned surface irrigation and developed innovative techniques of capturing, storing and conveying water from underground sources. most of their scanty waters originated from mountain rainfalls infiltrated into the ground and rock fractures (wilkinson, 1983). normal evapotranspiration rate in the region is above 3000 mm/yr., which is about 30 times the 2 review of omani aflaj systems average rainfall (siddeek, 1992). consequently surface water in the country is insignificant. surface runoff generated from burst of occasional rainfall persists on surface for a very short time. due to the scarcity of water, the population grew in areas where groundwater sources were reachable (mwr, 1995; wilkinson, 1977; wilkinson, 1983). afalaj supplies water to its community, not to an individual. based on collective responsibility within the community, the intricate and complex systems for sharing responsibilities and for maintaining and distributing water grew through generations. these specific aspects of falaj systems are topics of extensive studies by many organizations, particularly by agencies associated with water resources. any future policy of water resources in the country has to carefully take into consideration the intricate and delicate issues of collectiveness in ownership and responsibility of maintaining the falaj systems. nearly 3000-4000 aflaj systems are estimated to be in existence in oman (mi, 1997; mwr, 1995).they supply nearly 33% of the nation's domestic water. more than 50% of the nation's population lives in small urban and rural areas and they are dependent on groundwater sources (combined wells and aflaj systems). based on physical features of groundwater sources, the aflaj systems are divided into three discrete groups: dawudi, ghayli and ayni falaj. 2.1 dawudi falaj in this system (figure 1a), a mother well is constructed to a depth below the groundwater level in the acquifer. from the mother well, tunnels are constructed to convey water to the surface and subsequent transport to the point of claims and uses. the flows are mainly dependent on artesian pressure in the acquifer and flows by gravity. once the system is in place, the flow is natural and it does not need any direct input of external energy. figure 1. cross-section of different falaj systems 3 shahalam 2.2 ghayli falaj in ghayli type of falaj (figure 1c), groundwater crops-up on the surface in wadi beds as base flow of the wadi (valley). water is captured in depressions and channeled to the point of use. 2.3 ayni falaj hydraulic structures in ayni (spring) falaj (figure 1b) are directly fed from springs. many of such springs are hot. an example of such a system can be found at ayn-hammam-al-ali on the bawshar spring-line near muscat. most of these springs rise from limestone in the mountain ranges. 3. principle locations of falaj systems northeastern mountain terrain and wadis are the main sites for falaj. these include areas of al-batinah, adh-dhahirah, ad-dakhliyah, ash-sharqiyah and the region of madha (figure 2), (alkalbani, 1993; dutton, 1985; dutton, 1995; mwr, 1994b; mwr, 1995; mott-mcdonald, 1994c, 1989; trow, 1986; travers, 1993. figure 2. main area of aflaj, wells and springs in the sultanate of oman the hydraulic flow monitoring program initiated by the ministry of water resources (mwr) selected several areas. the number of flow monitoring stations in these programs (table 1) 4 review of omani aflaj systems indicates roughly the relative distributions of afalaj by area. the principal locations of spring based falaj systems (mwr, 1995) appeared in table 2. table 1: ministry of water resources flow monitoring stations in aflaj systems (as of january 1995) region number of monitoring stations muscat 28 al-batinah 101 al-dhahirah 69 al-dhakhilia 96 al-sharqiyah 211 dhofar 20 table 2: main locations of spring based falaj systems region location marbat scarps adjacent to southern coast in murbat salalah scarps adjacent to southern coast in salalah al-batinah coast and interior terrain of north-east oman mountains wadi khabab northern oman mountains madha north extension of north-east oman mountains 4. national growth and water balance the sultanate of oman is a fast developing country. statistical data (ministry of national economics, mne, 1999) indicated that nearly 25% of the population is in schools and universities. from population estimates of 1970 and census data of 1993, it appears that the population is growing at an approximate rate of 3.6% per year (mwr, 1995). gross national income was about us$7000 per capita in year 1996. the income level places the country as one of the affluent countries in the world. assuming an average 150 litre/day/person for domestic water use, total domestic water needs for 2,000,000 people is about 110 mm3/year. desalination processes produce about 43 mm3/year (mi, 1997). the difference of 67 mm3/year is expected to be supplied from falaj and well systems tapped in groundwater sources. according to 1993/94 statistics, about 55000 hectares (mwr, 1995) of land are under cultivation. to sustain minimum irrigation, the land may need nearly 1200 mm3/year (vegetables 413, field crop and fodders 189 and fruit trees 534 mm3/year). the amount was derived assuming a land distribution for crops as: 50% vegetables, 22% field crops/fodders and 27% fruit trees. it was further assumed that vegetables and fodders are irrigated for five months in a year while the fruit trees need irrigation throughout the year at a common rate of 3000 m3/month/hectare (mwr, 1995). if one assumes that 50% of the total domestic water supply is reclaimed for garden and fodder irrigation, the reclaimed water supply amounts to 55 mm3/year, which is insignificant compared to the total irrigation need. the bulk of the irrigation water has to come from groundwater. at an average rainfall of 100mm over the whole country, the total rainwater is about 31000 mm3/year. the country needs to capture at least 10% of this water for a sustainable water balance. this is a formidable task. the sultanate of oman undertook some highly ambitious projects towards this goal. these projects include series of recharge dams, which impound rainwater upstream dams. water infiltrates into the ground and augments groundwater storage. consequently the groundwater level rises. under the influence of such recharge efforts, many traditional afalaj wells abandoned for 5 shahalam shortage of water started reviving with a substantial production capacity. the reviving of old afalaj systems, however, needs renovation and modern management techniques integrated into the community framework for proper functioning. 5. review of some selected study reports 5.1 studies the sultanate of oman directed during the past two decades quite a number of studies towards collecting essential basic data on the nation's water resources, soils and agricultural practices. it is understood that all of these sectors are important elements in the nation's traditional falaj systems. the end objective of such information gathering is to work towards developing an optimal waterresources management policy. consequently the consideration of falaj systems remain of paramount importance in the process as the physical systems of aflaj affects water resources. aflaj communities remain integral parts of the nation's social structure, and their agricultural activities contribute directly to the nation's food production and economy. the following is a review of some of the important information gathered from recent study reports and published literature on falaj physical systems, soil characteristics of surrounding land and practices in irrigation and agriculture. 5.2 aflaj systems the references al-kalbani, (1993), dutton, (1995), mwr, (1991, 1995), and wilkinson, (1983) presented the basic aspects of aflaj systems in the sultanate of oman. in particular alkalbani (1993) described the existing management processes of aflaj and identified areas where improvements may be attainable. based on collected operational data from an associated study, the paper presented a scheme for future aflaj management in the country. dutton (1985,1995) in his articles on aflaj systems in oman delineated the physical systems of aflaj and background history of aflaj developments. he discussed in depth the origin of aflaj systems with respect to their complex relationships with water resources, community, society, economy and agriculture. the articles identified those factors that are likely to be affected by the modern technological revolution. the author presented the weaknesses and strengths of aflaj systems and their communities. he discussed the essential elements which are required to optimize the benefits of the aflaj systems and pointed out various roles that public authorities such as the ministry of water resources might play towards improving the systems contributing efficiently to the greater process of national well-being. the author elaborately outlined the elements of reactive and proactive management policies that could be adopted in the management of aflaj systems. the reactive group includes issues such as: (i) responding to daily queries about well permits, (ii) responding to daily queries about falaj extension, (iii) mediating in disputes among aflaj users, (iv) responding to queries about mother well protection, problem and crisis. the proactive activities involve well planned steps undertaken for solution and reduction of future problems related to inappropriate usages, unbalanced usages, non-equitable usages, inefficient usages and nonproductive usages. in conclusion, the author stressed that if an effective connection could be made among the traditional falaj water delivery systems, modern irrigation systems and appropriate management policies, beneficial aspects of falaj systems will be more appreciated. in this respect, the author cited the encouraging results obtained in an experimental station in the village of halban in oman. he suggested the preparation of a comprehensive database of the falaj systems that could effectively help guide future management of the systems. the ministry of water resources, sultanate of oman, published an information bulletin on the nation's water resources (mwr, 1991; mwr, 1995). the publications contained summaries of water resources in the country as of years 1991 and 1995 respectively. the latter contained the latest detailed information about the types and extent of falaj systems. the principal locations of falaj systems were identified. it included summaries of major groundwater reservoirs in the country. several case studies were carried out to test the feasibility of introducing centrally controlled aflaj irrigation systems (wahby, 1995), water management relationships with the efficiency of 6 review of omani aflaj systems water use (norman, 1997) and the effects of surrounding well on the aflaj mother-well (state consultative council, scc, 1987). wahby (1995) presented the experience of introducing a central control of irrigation water in a falaj system. during the study, it was observed that the traditional rational basis for water distribution to farmers on a time-sharing basis failed very often to meet the requirements for quantity in time. budgeting water under unsteady and unreliable flow conditions resulting from the unpredictability of artesian pressure of groundwater, is not an easy task. it is subjected to the risk of breaking the contract or assurance provided to the farmers. in contrast to supplies dependent on natural time-dependent flow, the reported study experimented with a central storage facility and associated distribution systems in falaj "keed". the study tested three irrigation systems: drip, sprinkler and bubbler. the central control system was found to be a successful means to supply water for modern irrigation methods. irrespective of varied flow conditions in the falaj, the system could deliver and maintain a constant discharge and pressure for the operation of the irrigation system. in conclusion, however, the author of the study cautiously advised about the introduction of the idea to the farmers as it may appear as a sensitive issue of changing the traditional way of water management. similar benefits of implementation of modern water management techniques were also observed in a separate study elsewhere (norman, 1997). however, in another study of a falaj "hagur" in walayat al-awabi in northern oman, investigators found that the farmers had adequate knowledge of managing irrigation water (wilkinson, 1983). even using traditional surface application of irrigation water, the farmers achieved an irrigation efficiency of 84%. the findings were in sharp contrast to the frequent assumptions that all surface irrigation systems incur unnecessarily high water losses. it was noted that the majority of farm workers in the study area were native omanis who are quite familiar with the proper water uses in the falaj systems. local laborers are expected to be more aware of the scarcity of water and thus are more careful in water uses. they are better acquainted with local irrigation factors such as time of water application and the quantity of water necessary to marginally keep the soil near to its capacity of moisture content within crop root-zone without incurring access losses. in a separate case study, the effect of personal wells on the output of the mother-well of afalaj system was studied (scc, 1987). individuals tap these wells in common acquifers, as diesel and electric pumps are nowadays easily available. modern technology and the economic conditions of the people made it easy for individuals to own their personal wells. consequently the traditional communal responsibility for afalaj system was found to be at risk. the artesian pressure in the mother-well is very often recorded to be inadequate to provide natural flows for those who still rely on the mother-well. a brgm (brgm, 1992) consulting report reviewed 12 aflaj systems in northern oman in connection with designing an engineering maintenance program for old aflaj structures. the report presented the usual maintenance works which are needed to operate the systems with efficient flow and delivery of water. 6. soil and irrigated agriculture the nation's policies on soil and irrigation management are bound to have direct impact on the country's falaj systems. a number of important studies were completed to classify soils and assess the inventory of available waters across the nation. the following is a short review of information related to these sectors. 6.1 soil various public organizations and ministries in the sultanate of oman carried out studies to classify soil at the national level (abdel-baqui, 1995; london, 1984; maf, 1990). london (1984) and maf (1990) included soil types and their extents within oman. in addition, several studies related to agriculture and water management also contained soil information for selected areas (hundertmark, 1995; kew, 1995; trow, 1986). kew (1995) reported soil characteristics in relation 7 shahalam to water resources and soil moisture relationships in the central oman areas (al-wasta). the falaj systems, however, are rare in those areas. the information contained in the articles are valuable in terms of future planning of water resources at the national level, which may have indirect effect on near-by falaj systems. abdel baqui (1995) summarized general information of soil types in oman. most soils in oman have high infiltration rate and low moisture content. in general, it is reported that common natural soil needs improvement for increasing the efficiency of irrigation water. according to those authors, about 7% of omani soils are suitable for irrigation. out of this, 4.55% is classified as marginally suitable. moreover, 77% of these marginally suitable soils face the problem of over salinity where the electric conductivity was found to be very high. table 3: water holding capacity of soils in south batinah region. note that the notations for texture categories are standard abbreviations used by the us department of agriculture and are combined with the following interpretations of associated alphabets. c = clay, f= fine, h = heavy, l= loam or light, si = silt, s= sand and v= very. coarse fragment category (% of total coarse fragment content, tcfc ) texture category 0 (> tcfc<5%) 1 2 3 4 5 (<tcfc <78%) c,cl,sic, sicl,sc 5.3* 4.8 4.2 2.9 1.6 0.5 scl,hl,hsil 4.5 4.1 3.6 2.5 1.4 0.5 si,sil 5.3 4.7 4.2 2.9 1.6 0.8 l,fsl, vfsl, hsl, hfsl 3.4 3.0 2.7 1.9 1.0 0.3 sl,csl hcsl, lvfs 2.6 2.4 2.1 1.4 0.8 0.3 ls,lfs lcs vfs fs 1.6 1.4 1.3 0.9 0.5 0.2 cs**, s 0.8 0.7 0.6 0.4 0.2 0.1 *percentage by weight; ** coarse sand most soils in oman, particularly in batinah coast (an aflaj area) are of medium coarse textured soils consisting of sands, loamy sands and sandy loams. the depth of soil varies from 30 to 100 cms in most areas. the organic matter containing nitrogen and phosphate is low in quantity. limestone in mountains in batinah region is high. calcium carbonate in soil is about 35% in batinah coast. however, in batinah, the micronutrient deficiency is less. soil ph is moderate to strong alkaline. table 3 adopted from aldel-baqui (1995) and maf (1993) shows the water holding capacities of soils in south batinah region. abdel-baqui, (1995) also presented soil horizons of oman in six categories. table 4 adopted from abdel-baqui (1995) shows important ranges of land characteristics that classify the soils as suitable, marginally suitable and non-suitable for irrigation. abdel magid (1995) presented the results of his study which indicated that the application of organic manure might improve the soil texture. omanis, however, presently widely practice the method of improving the soil texture in agricultural lands by transferring deposited silt from 8 review of omani aflaj systems upstream dams and mixing it with top soils. mixing of top 10 cm of common soils with imported silt was proven to be successful. water application could be reduced up to 40% in cases through this type of soil treatment. the author outlined schemes of soil management in irrigation systems, which was found to be effective in saving plants from the salinity that accumulates in surrounding soils from irrigation water. table 4: soil characteristics classifying irrigation suitability land characteristics suitable marginally suitable not suitable depth to restricting layer (cm) > 150 100-150 <50 rock fragments between depths of 25 and 100 cm (weighted by volume) < 15 15-35 >65 water retention difference to a depth of 150 cm or to a restricting layer (cm) >15 8-15 <6 maximum salinity within a depth of 100 cm (ec of paste extract in ds/m) <8 8-16 >16 gypsum content in 0-50 cm depth (vol. %) <10 10-25 >25 gypsum content in 50-100 cm depth (vol. %) <10 10-25 >40 slope gradient (%) <1 1-3 >5 vertical hydraulic conductivity of the least pervious layer within the depth of 100 cm (m/h) 0.5 – 15 <0.5.r>15 -depth of water-table (cm) >300 150-300 <50 expected natural drainage under irrigation good moderate v. poor erosion hazard slight moderate v. strong flooding hazard slight moderate v. strong 7. irrigated agriculture and water resources records indicate that in the last two decades, oman extensively studied its groundwater resources (al-battushi, 1997; bernett, 1994; mwr, 1994a; mott macdonald, 1991a; 1991b; petroleum development oman, pdo, 1998; mott macdonald, 1989; ws-atkins, 1990). among the various programs related to water resources the ministries of water resources and agriculture and fisheries undertook are two ambitious projects of preparing the nation’s well inventory (chandler, 1995; gibb, 1975; mwr, 1992a; 1992b; 1992c; 1993a; 1994b) and schemes of recharging acquifer systems (al-akhzarni, 1997; mwr, 1993b; mohsin, 1995; mott macdonald, 1991a; 1991b; 1994a; 1994b; 1994c; travers, 1993; ws-atkins, 1990; ws-atkins, 1992a; wsatkins, 1992b). the national well inventory program was launched in 1998. the program involves gathering information about existing wells throughout the country. the information bank includes the location of a well, well identification by number, ownership, physical characteristics, quality of water (electric conductivity ec and ph), current uses, service area, water users and water demand. the program is progressing satisfactorily and is expected to cover all wells in the country in the near future. the completion of the program will clearly identify the wells of aflaj systems along with individual wells in surroundings areas. such information is expected to directly aid the process of modern planning and management of traditional aflaj systems. 9 shahalam the purpose of the recharge dams is to store the scanty rainfall water underground. such storage is prefered for several reasons. acquifer waters are less prone to evaporation loss. recharge dams retard loss of fast flowing runoff into the sea. due to steep mountain slope and short coastal range, most of the runoff, at the coastal side of the mountains, would be lost. one of the direct benefits felt in aflaj systems is the rise of groundwater level. this was particularly observed in the northeast mountain ridges and plains. in particular, some of the aflaj-wells in al-batinah and wadi al-fulayj indicated a rise in well-water level and water production (al-battushi, 1997). this was the result of some recharge dams. as of 1996, the sultanate of oman has built 20 (16 recharge and 4 flood control) major dams (al-akhzarni, 1997). an ambitious program for constructing more dams is under consideration. in the process, about 78 potential dam sites were examined. effects of such dams on the national water resources were systematically studied and screened for feasibility and implementation. parallel to the water augmentation projects, quite a number of studies were carried out to explore the efficiency of existing irrigated agriculture and to gather data on the farmers' adaptability to modern techniques of irrigation ( al-harthy, 1995; cord, 1992; fao, 1984; fao, 1992; johnson, 1995; lenton, 1995; maf, 1989; 1993; rout, 1995; siddeek, 1992; m. macdonald, 1989). in particular, these studies in the areas of aflaj systems in the north coast of the country provided valuable information about present irrigation practices. some of these studies identified beneficial activities of public organizations that may enhance the agricultural produce of economic value. one case study indicated that about 8.5 mm3 per annum could be saved by a conversion of only 1430 hectare of surface flooding to modern irrigation system (siddeek, 1992). the study presented in siddeek (1992) also presented a typical distribution of crop pattern in a south batinah farm (table 5). the case study reported that the adaptation of modern irrigation systems and the application of differential rates of watering for different crops saved substantial amount of irrigation water. table 5: typical crop distribution in a south batinah farm crop type percentage of total land of 392 acres datepalm 22.83 greenhouse 0.34 citrus 10.78 mango 2.83 mixed ( datepalm + citrus + mango ) 3.45 other trees spp. 14.18 ornamental + lawn 0.74 winter vegetables 19.6 summer vegetables 1.63 rhodes grass 24.17 tall grass 0.45 8. management and maintenance of aflaj systems several articles (al-kalbani, 1993; bernett, 1994; de jong, 1995; dutton, 1985; 1995; hundertmark, 1995; johnson, 1995; lenton, 1995; ministry of health, mh, 1992; vermillion, 1992) covered various schemes of aflaj management in the light of the traditional ways in aflaj systems. the university of durham (uk) studied extensively various aspects of aflaj. the results were reported with suggestions to modernize the management for the revival of aflaj systems (alkalbani, 1993; 1985; 1995). 10 review of omani aflaj systems dutton (1995) identified the inherent weaknesses and strengths of the traditional aflaj management. the author itemized the elements of management activities that fall within the jurisdiction of the ministry of water resources. the items are grouped into two categories such as active and proactive management activities. the first group included issues such as responding to daily queries about well permits, falaj extension, disputes between users of aflaj mother-well protection and day-to-day problems and crises. proactive management activities involved planned steps towards a solution and reduction of future problems related to inappropriate, unbalanced, non-equitable, inefficient, and non-productive water usages. the author focused on the inherent strength of the traditional aflaj systems in their organization and management systems at community level. he pointed out that the better quality of this organizational management might be effectively used if an effective connection could be maintained between traditional aflaj delivery systems and modern irrigation practices. lenton (1995) discussed in general the privatization and irrigation management transfer from public to private organization. the approach appeared to be effective in small farms in many parts of the world. the approach appeared to have potential usage in aflaj systems in oman. following the same topic, vermillion (1992) and johnson (1995) presented results of case studies involving partial management with public agencies (such as the ministry of water resources) retaining management and control of water sources with the main distribution channels when the field management is trusted to the end-users. lenton stressed the participating approach between the public organizations and end-users. in his model of farm management, the end-users jointly participate in the operation and maintenance of irrigation systems. water users associations constituted of farmers involved in management decisions, in collecting fees to cover operation and maintenance costs and organizing maintenance activities. his approach , however, uses raw concepts. its applicability to omani national policy and farmers' well being needs to be tested. de jong and gaubh (1995) discussed water resources management at the government organization level in countries of arid regions. the authors stressed the need for strict separation of functions among environmental protection, water resources and water management functions on the one side and the concerns of water users on the other. the authors' model of water management in arid regions such as oman advocates sector separation by functions among various public organizations. rout (1995) discussed social and economic aspects of metering waters abstracted from wells in a farming area in oman. the author cautiously noted that the success of such programs would largely be dependent on the acceptance and support of the well owners for installations, monitoring and associated conservation measures. the revival of traditional aflaj systems in oman and their adaptation to modern technology and management may require major work for initial system repair with follow-up attention for day-today maintenance works. a brgm report (brgm, 1992) prepared for the ministry of agriculture and fisheries outlined in details the general items of such maintenance works in 12 aflaj systems in oman. the report provided valuable guidelines for the maintenance works involved in omani aflaj systems. 9. conclusions and recommendations the following conclusions could be drawn based upon the data collected from the available literature. 1. recharge dams appear to be a good means for better management of aflaj systems and an important element in the overall water resources management in the sultanate of oman. 2. participation approach involving end-users of aflaj communities and public organizations can be an effective tool for future decisions and future planning of projects or introducing changes in the present system. 3. aflaj systems can be linked to modern irrigation practices so that the available water is optimally utilized. 11 shahalam 4. most of the omani soils are not suitable for irrigated agriculture. the augmentation of these soils with deposited silt from upstream dams has been successful and should be continued in the future. 5. new sources of low-cost soil amendment agents should be explored. sludge from wastewater treatment plant and decomposed products of wastes from agricultural activities, oil industries and municipal solid wastes might possess good potential for the purpose. 6. clarity of the roles played by public organizations such as various ministries and local institutions will clearly help optimize the falaj management system. references abdel baqui, abdel magid, e. 1995. soil management under modern irrigation systems in oman. proceedings. proceedings of international conference "water resources management in arid countries", ministry of water resources, sultanate of oman, muscat, march 1995. oman. al-battushi, m.b. and ali, s.a. (ministry of water resources, oman). 1997. groundwater recharge of oman. proceedings of "third gulf water conference", muscat, march 1997. oman. al-akhzarni, s., o'brien, w. and cookson, i. 1997. screening of recharge dam sites in oman. proceedings of "third gulf water conference", muscat. march, 1997. oman. al-harthy, s.s., farbridge, r.a. and wyness, a.j. 1995. irrigation development in nejd, southern oman. proceedings of "international conference on water resources management in arid countries", muscat, ministry of water resources, march, 1997. muscat, oman. al-kalbani, m.k. and dutton, r.w. 1993. study for the design of an aflaj management programme, cord, university of durham, uk. bernett, j.c. and smith, o.v. 1994. the national well inventory, sultanate of oman. groundwater drought pollution and management. reeves and watts (eds), isbn 9054103515. brgm. 1992. design of maintenance works for 12 aflaj in northern oman. inception report to the ministry of agriculture and fishery, oman. chandler, m.s. and al-abri, a. 1995. quality control and technical analysis essential components of a successful well inventory. proceedings of "international conference on water resources in arid countries", ministry of water resources, muscat, march 1995, oman. cord (john farnworth). 1992. guideline discussion paper for use of water of 3000 4000 micromhos and over with modern irrigation techniques. report submitted to ministry of water resources (oman), cord, university of durham. de jong, r.l. and gaubh, g.t.z. 1995. aridity, economic development, and water sector management. proceedings of "international conference on water resources management in arid countries", muscat, ministry of water resources, march 1995. oman. pp. 228-234. dutton, r.w. 1985. modernizing falaj irrigation system a proposal for an interior action research centre. university of durham. dutton, r.w. 1995. towards a secure future for the aflaj in oman. proceedings of "international conference on water resources management in arid countries", muscat, ministry of water resources, muscat, march 1995. oman. fao. 1984. crop water requirements, irrigation and drainage paper no. 24. fao. 1992. integrated study of salalah plain, irrigation report. gibb, a. and partners, ilaco, sogreah. 1975. water resources of northern oman (final report). hundertmark, w. 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oman. trow (oman) ltd. 1986. soil profiles and infiltration rates wasit. report submitted to public authority for water resources. muscat, oman. wahby, h. and al-harthy, s.s., 1995. central controlled irrigation system for optimum use of water in falaj keed at bahla, oman interior. proceedings of "international conference on water resources management in arid countries", muscat, ministry of water resources. march 1995. oman. wilkinson, j. 1977. water and tribal settlement in south east arabia. oxford research studies in geography. clarendon press.uk. wilkinson, j.c. 1983. the origin of the aflaj of oman. j. of oman studies, 6: 177-194. ws atkins international. 1990. groundwater recharge schemes for ibri/araqi area. report submitted to the ministry of agriculture and fisheries, muscat, oman. ws atkins international. 1992a. detailed technical studies for proposed recharge facilities in wadi muaydin. report submitted to the ministry of water resources. muscat, oman. ws atkins international. 1992b. detailed technical studies for proposed recharge facilities in wadi halfayn. report submitted to the ministry of water resources. muscat, oman. vermillion, d.l. 1992. irrigation management turnover; structural adjustment or strategic evaluation. iimi review. 6(2): 3-12. received 1 january 2000 accepted 25 june 2001 14 îáçõé : íêöãä çáèíë çóêúñçöçð ôçã 2.1 dawudi falaj 2.2 ghayli falaj principle locations of falaj systems region salalah electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 55-70 © 2002 sultan qaboos university development and application of backpropagation-based artificial neural network models in solving engineering saleh mohammed al-alawi department of electrical engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. استخدام تقنية الشبكات العصبية لحل المشاكل الهندسية صالح محمد العلوي الشبكات العصبية االصطناعية هي احد برامج الكمبيوتر التي تحاكي قدرات االنسان في تمييز االشياء او اتخاذ قرارات : خالصة ء في علم الذكاء الصطناعي الذي ظهر وانتشر بسرعة ويعتبر هذا العلم جز . مبنـية على المعلومات المتوفرة او التنبؤ باالحداث فـي العقد الماضي وغطت تطبيقاته العديد من مجاالت الحياة االنسانية هذه الورقة العلمية تهدف الى نشر الوعي بخصوص هذا وجيه للمبتدئ الذي العلـم والتقنـية المسـتخدمة فيه وكيفيةتطبيقه لحل المشاكل الهندسية وكذلك تبرز هذه الورقة طرق ارشاد وت ح قائمة بالتطبيقات الهندسية ضيرغب في استخدام هذه التقنية وتشير الى المراجع التي يمكن استخدامها في هذا المجال وكذلك تو . المختلفة التي قام بها الباحث في سلطنة عمان abstract: artificial neural networks (anns) are computer software programs that mimic the human brain's ability to classify patterns or to make forecasts or decisions based on past experience. the development of this research area can be attributed to two factors, sufficient computer power to begin practical ann-based research in the late 1970s and the development of back-propagation in 1986 that enabled ann models to solve everyday business, scientific, and industrial problems. since then, significant applications have been implemented in several fields of study, and many useful intelligent applications and systems have been developed. the objective of this paper is to generate awareness and to encourage applications development using artificial intelligence-based systems. therefore, this paper provides basic ann concepts, outlines steps used for ann model development, and lists examples of engineering applications based on the use of the back-propagation paradigm conducted in oman. the paper is intended to provide guidelines and necessary references and resources for novice individuals interested in conducting research in engineering or other fields of study using back-propagation artificial neural networks. keywords: artificial neural network applications, engineering problems, back-propagation, forecasting, classification, oman. 1. introduction a rtificial neural networks (anns) is a research area that has evolved from artificial intelligence (ai) research. artificial intelligence, on the other hand, is a branch of computer science. this branch is concerned with designing computer systems that exhibit characteristics associated with intelligent human behavior. artificial intelligence research is based on many interrelated sciences and technologies such as engineering, management science, computer science, psychology, philosophy, and linguistics, and covers a wide range of applications. in addition, anns and ai provide the scientific foundation for many other growing commercial technologies such as machine learning, expert systems, natural language processing, computer vision and robotics, speech recognition systems, automatic programming, and computer-aided instructions. 55 saleh mohammed al-alawi anns are computer programs that are trained in order to recognize both linear and nonlinear relationships among the input and the output variables in a given data set. in general, ann applications in engineering have received wide acceptance. the popularity and acceptance of this technique stems from anns features that are particularly attractive for data analysis. these features include handling of fragmented and noisy data; speed inherent to parallel distributed architectures, generalization capability over new data, ability to effectively incorporate a large number of input parameters, and its capability of modeling nonlinear systems. due to these distinctive features, artificial neural networks are used to add intelligent capabilities to computer systems. ann models allow computer systems to process and recognize different voices, read in text, recognize and classify objects, sense the environment and control robotic movements, predict future trends, and even decide whether to grant a bank loan to a specific customer or not. 2. artificial neural network concepts 2.1 back-propagation paradigm one of the most common and frequently used ann paradigms is the back-propagation paradigm (simpson, 1990). this supervised learning method was developed by rumelhart based on the generalization of the least mean square error (lms) algorithm. the back-propagation algorithm uses the gradient descent search technique to minimize a cost function equal to the mean square difference between the desired and the actual net output. the network is trained by selecting small random weights and internal threshold, and then presenting all training data repeatedly by using the supervised training technique. the weights are changed until the network reaches the desired error level or the cost function is reduced to an acceptable value. 2.2 ann architecture the major building block for any ann architecture is the processing element or neuron. these neurons are located in one of three types of layers: the input layer, the hidden layer, or the output layer. the input neurons receive data from the outside environment, the hidden neurons receive signals from all of the neurons in the preceding layer, and the output neurons send information back to the external environment. these neurons are connected together by a line of communication called connection. stanley (1990) indicated that the way in which the neurons are connected to each other in a network typology has a great effect on the operation and performance of the network. ann models come in a variety of typologies or paradigms. simpson (1990) provides a coherent description of 27 different popular ann paradigms and presents comparative analyses, applications, and implementations of these paradigms. 2.3 ann operations in the back-propagation (bp) architecture, shown in figure 1, each element or neuron receives input from the real-world environment or from other processing elements, processes this input, and produces a specific output. generally, many of these processing elements perform their operations at the same time. this parallelism is a unique feature of the ann that distinguishes it from the serial processing that is usually performed by conventional computer systems. each neuron has a straightforward assignment. input coming to the neuron is associated with a weight indicating its strength. in the neuron, the values of the input are multiplied by the corresponding weights and all products are added to obtain a net value (neti). after summation, the net input of the neurons is combined with the previous state of the neurons to produce a new activation value. whether the neurons fire or not will depend on the magnitude of this value. the activation is then passed through an output or a transfer function (fi) that generates the actual neuron output. the transfer function modifies the value of the output signal. this function can be either a simple threshold function that only produces output if the combined input is greater than the threshold value, or it can be a continuous function that changes the output based on the strength of the combined input. 56 development and application of back-propagation-based typical transfer functions employed in building ann applications include a linear threshold transfer function, step function, sigmoid function, and others. neti= ∑ = n wijoj j 1 o1 input o output o2 activati function w1 ne w2 2.4 ann training the first and the definition and data relevant data and ins is vital for the develo or erroneous data are "garbage in, garbage once the ann network is then train the bp algorithm connection weights a values. the network of the problem to be training patterns are predicted results is ca general delta rule whenever the netwo continues until weig level. simpson (199 how the learning proc 2.5 ann testing a the ann mode data. it also can mem variables or trends in the network must be testing operations. t model and recording is assumed to be suc models provide corr t i on transfer function input hidden output layer layer layer figure 1. a typical back-propagation architecture. most critical step in developing an effective ann model is input and output preparation. this includes identifying variables of interest, gathering the pecting them for possible errors, missing values, and outliers. data accuracy pment of an efficient model that can provide accurate prediction. if incorrect fed to the model, this will result in incorrect prediction. as the saying goes, out". model architecture is defined, data are collected and fed to the model. the ed to recognize the relationships between the input and output parameters. uses the supervised training technique. in this technique, the interlayer nd the processing elements' thresholds are first initialized to small random is then presented with a set of training patterns, each consisting of an example solved (the input) and the desired solution to this problem (the output). these presented repeatedly to the ann model, and the error between actual and lculated. weights are then adjusted by small amounts that are dictated by the (rumelhart et al, 1988). this adjustment is performed after each iteration rk's computed output is different from the desired output. this process hts converge to the desired error level or the output reaches an acceptable 0) describes the system of equations that provides a generalized description of ess is performed by the bp algorithm. nd validation l can sometimes learn different features other than the relationships in the orize the data or part of this data without learning the relationships between the data. hence, to insure network accuracy and the generalization capability, tested on a continuous basis and should be monitored during the training and he testing operation involves passing a separate testing set to the trained ann the results. these results are compared to actual results. the trained model cessful if the model gives good results for that test set. to insure that ann ect prediction or classifications, the prediction results produced by ann 57 saleh mohammed al-alawi models can be validated against expert predictions for the same cases or it can be validated against the results of other computer programs. 3. developing an artificial neural network model step #1: ann model development starts by first conducting a feasibility study and validating the proposed application. bailey and thompson (1990) pointed out some common characteristics of a successful neural network application. they suggested that the application must be dataintensive and dependent upon multiple interacting parameters. the problem area should be rich in historical data or examples. the data set available may be incomplete, contain errors, and describe specific examples. the discriminator or function to determine solutions is unknown or expensive to discover, and the problem should require qualitative or complex quantitative reasoning. once the application is judged to be feasible and valid, resource constraints (time, equipment, money) should be evaluated. data, sources, and solution requirements should also be identified and appropriate data should be secured. step #2: the next step in the ann development process is data preparation and training. the ability of the ann to effectively learn the training set and provide accurate results is dependent upon the data preparation activity. data preparation for modeling can be broadly classified into three distinct areas: data specification, in which variables of interest are identified and collected; data inspection, in which data is examined and analyzed; and data pre-processing, in which some data may be restructured or transformed to make it more useful. data specification involves two primary activities: variable selections and determining data sources. for example, there are many social, economical, and weather variables that could possibly affect the demand forecast. a wish list of these variables for model building should be generated by the planner through scanning available literature, consulting experts in the area in question, and by conducting brainstorming sessions with colleagues. variables in this list should then be examined to assess whether historical data for such variables are available or not. for variables with readily available historical data, data sources should be identified and the data should be collected. once data for a set of candidate variables are collected, data analysis should then be used to weed out the potential input variables from the wish list generated so that only the most relevant variables are used to develop the forecasting model. to do this, several statistical methods are available for determining linear significance of variables. some of the more popular statistical techniques used are the coefficient of correlation (r), the coefficient of determination r2, and the ordinary least squares (ols) regression analysis. a detailed discussion of these statistical techniques is beyond the scope of this article, but treatments of these techniques can be found in bunn and farmer (1985), mendenhall and beaver (1994), and burden and fairies (1985). as many people discover when they try to model real-world problems and processes, clean data is a luxury that is all too rare. data collected from the different sources are generally noisy, contain many gaps and outliers, and are poorly distributed. these issues, if not properly addressed prior to the model's development, could lead to inaccurate and unreliable prediction. collected data, hence, should be inspected well and analysed carefully. the first step in data inspection is to examine individual variables for erroneous values and to remove these values from the data set after careful analysis and only if these values prove to be erroneous. each variable should also be inspected for outliers as well as missing data. once the most significant input variables are selected and carefully inspected, the forecaster should then examine the distribution of each of these variables. the shape of the distribution will indicate to the planner whether a particular variable needs data pre-processing. data pre-processing may involve any mathematical operations. common techniques include calculating sums, differences, differentials, inverses, powers, roots, averages, etc. anderson (1990) and lawrence (1991) provide a detailed description on how to perform this important task. step #3: the third step in the development process is the selection of an appropriate neural network paradigm. ann models come in a variety of typologies or paradigms. simpson (1990) provides a coherent description of 27 different popular ann paradigms and presents comparative 58 development and application of back-propagation-based analyses, applications, and implementations of these paradigms. the selection among these paradigms should be based on the application requirements and the available neural network software containing the specific paradigm. some of the factors that should be considered in the selection process include neural network size, required output type, method of training, and the time available for model development and testing. step #4: having selected the appropriate paradigm, the fourth step is to determine the network's architecture design and to select its parameters. this process involves the selection of the number of input nodes, hidden nodes, and output nodes. in addition, it also involves the selection of the network parameters such as the transfer function, learning algorithm, learning rate, momentum, and learning threshold. step #5: the next step in this process is training the model. training involves presentation of the training set to the network and periodical monitoring of the network's performance. this is a accomplished automatically by the appropriate back-propagation simulation software that was selected in step #3. based on the user choice, training cases can be presented to the network either sequentially or by following a random process. during the training process, one or several of the network parameters are changed to improve the network's performance. this process continues until weights converge to the desired error level or the output reaches an acceptable level. step #6: after training is complete, testing and validation is the final step in the development process. it is important to test the resulting ann model against both the training set and the test set. the test set should contain examples of input vectors that the network did not encounter previously. this test is a benchmark that determines how well and how accurate the trained network is performing. model validation, on the other hand, deals with comparing the results of the developed model to results obtained from common or classical models or techniques being used by the industry. the training, testing and validation process is explained in the neuroshell simulation package (1991). 4. an example of an ann application the following is an illustrative example of an ann application to forecast electrical demand for a muscat power system. detailed steps of this example can be found in islam et al. (1995). for any utility, medium-term load and energy forecasting is useful in planning fuel procurement, reserve margin, scheduling unit maintenance, diversity interchange, and system expansion planning. this type of forecast is normally prepared for the range of one to five years. 5. problem definition and its importance according to the historical monthly peak load and energy data collected from 1986 to 1992, the system's load and energy consumption appeared to be more or less cyclic, keeping in harmony with temperature, which varies from an extreme maximum of 48ºc in summer to an extreme minimum of 10ºc in winter. load demand, therefore, varies considerably from hour to hour. it is apparent that the electrical load and energy consumption pattern of this power system depends heavily on weather. on the other hand, the growth in load and energy demand depends largely on the number of consumers connected to the system. variables such as temperature, humidity, wind speed, number of connections, and other variables can be used to develop load and energy models for the muscat power system. in fact, the number of such variables is large and, depending on the type and nature of the forecast, should be carefully selected. the selection criteria could be based on human intuition, knowledge and experience and should be validated using statistical techniques to determine their contribution and correlation to the load or energy. 6. data requirements and data processing in medium-term load forecasting, generally, there are two forecasts that are prepared. these are the load forecast and the energy forecast. to develop these forecasts, the following variables 59 saleh mohammed al-alawi were identified using human intuition, brainstorming sessions, and consultation with experts in the area: absolute maximum temperature (tmax), average maximum temperature (tavmax), average maximum relative humidity (rhavmax), average relative humidity (rhav), wind speed (w), duration of bright sunshine (s), global radiation (r), precipitation (pr), vapor pressure (vp), degree days (dd), comfort index (ci), and number of connections (con). data for all of the above variables, with the exception of ci and con, were collected from the historical records of the ministry of housing electricity and water and from the records provided by an automated weather station, while ci and con are processed variables (bunn and farmer, 1985). the collected data were then examined to remove errors and outliers and to replace missing values. in addition, a correlation analysis was performed to select the appropriate variables suitable for the load and energy models. as a result of this test, the variables pr and vp were eliminated from the energy model because of their low correlation and contribution. it was also interesting to find that although some variables like w and rhmax had strong correlation to monthly electrical energy consumption, they had very little correlation to monthly peak load. 7. developing the model using the historical data for the selected variables, monthly peak load and energy consumption forecasting models were developed using an artificial neural network (ann) simulation package, neuroshell (1991). for the energy model, monthly data from 1986 to 1990 were used in model development. for the load model, the input variables selected were tpkld, rhpkld, tmax, and con. the monthly historical data used for developing the model also covered the same periods as in the energy model. similarly, in validating the ann models' results, socio-economic models (barakat and al rashad, 1993) were also generated using the same variables and historical data. these models were particularly selected for comparison since they have demonstrated giving better accuracy than the box and jenkins models, and they are more suited to high growth systems such as the muscat power system. 8. validation of results to test and validate the forecasts generated by socio-economic (se) models and ann models, monthly historical data for 1991 and 1992 were used to test these models' prediction capabilities. the resulting forecasts were then compared to the actual results, and statistical numerical measures were then calculated. for the se models, the mean absolute percentage error (mape) for the energy model was approximately 10.969 while the load model was 10.786. the testing set r2 was 0.946 and 0.719 for the two models, respectively. in comparison, the annbased energy model's mape was 1.787 and the load model was 1.870. the testing set r2 was 0.996 and 0.989, respectively. table 1 shows the comparison of these results. the monthly actual and forecasted energy consumption and peak load for 1991 and 1992 are shown in figures 2 and 3. from this figure, we can see that the se models as well as the other models did not provide highly accurate results as the ann models did. table 1: statistical results of the box and jenkins and ann model's prediction validation. technique me mad mape r2 accuracy (%) energy model (socio-economic) 18638.17 25783.50 10.969 0.946 89.03 energy model (ann) 489.67 4839.83 1.787 0.996 98.21 load model (socio-economic) 21.944 51.53 10.786 0.719 89.21 load model (ann) -1.846 1.11 1.870 0.989 98.13 60 development and application of back-propagation-based where me=mean error, mad=mean absolute deviation, mape=mean absolute percentage error. 0 100 200 300 400 500 600 700 800 j f m a m j j a s o n d month p ea k lo ad , m w actual ann forecast se forecast figure 2. actual and forecasted results for the load model. 0 50000 100000 150000 200000 250000 300000 350000 400000 j f m a m j j a s o n d month e ne rg y c on su m pt io n g w actual ann forecast se forecast figure 3. actual and forecasted results for the energy consumption model. 9. engineering applications a clear guideline on how the steps are implemented to develop ann models for different engineering applications can also be found in the following ann application papers in different engineering fields. the author and his colleagues wrote the ann application papers. 10. electrical engineering 61 saleh mohammed al-alawi 1. short-term load forecasting using artificial neural networks (al-alawi and islam, 1995). 2. forecasting monthly electrical load and energy for a fast growing utility using an artificial neural network (islam et al 1995). 3. forecasting long-term electrical peak load and energy consumption for a fast growing utility using artificial neural networks (islam and al-alawi, 1995). 4. tuning of svc damping controllers over wide range of load models using artificial neural network (ellithy and al-alawi, 2000). 5. tuning power system stabilizers over a wide range of load models using artificial neural networks (ellithy et al, 1997). 6. ann-based load identification and control of ac voltage regulator (gastli et al 2000). 7. statistical signal characterization-artificial neural network based hybrid system for electrocardiogram interpretation (al-alawi et al 1998). 8. on-line unit commitment for a generation constrained fast growing utility using artificial neural networks (islam et al 1996). 11. mechanical engineering 1. experimental investigation and failure analysis of fastened grp under bending using the finite element method and artificial neural network modeling (seibi and al-alawi, 1999). 2. an ann based approach for predicting global radiation in locations with no direct measurement instrumentation (al-alawi and al-hinai, 1998). 3. prediction of fracture toughness using artificial neural networks (seibi and al-alawi, 1997). 4. analysis and prediction of clearness index using artificial neural networks (al-alawi and al-hinai, 1996). 5. design of fiberglass/copper moulds using finite element analysis (seibi and al-alawi, 1999). 6. artificial neural networks: a novel approach for the analysis and prediction of mechanical properties of 6063 aluminum alloy (al-alawi et al 1997). 7. analysis and prediction of clearness index using artificial neural networks (al-alawi and al-hinai, 1996). 8. prediction of failure mechanisms and mechanical properties of fastened grp under bending using artificial neural networks (al-alawi et al 1996). 9. effects of joint geometry on the flexural behavior of glass reinforced plastics (seibi et al 1996). 12. petroleum and mineral resources engineering 1. matrix and cement effects on residual oil saturation in sandstone formations: a neural network approach (al-alawi et al 1998). 2. establishing pvt correlation for omani oils (boukadi et al 1998). 3. a comparison between an artificial neural network and geostatistical technique in the estimation of regionalized variables (tawo and al-alawi, 1998). 4. matrix and cement effects on residual oil saturation in sandstone formations (boukadi and al-alawi, 1998). 5. application of ann in mineral resource evaluation (al-alawi and tawo, 1998). 6. analysis and prediction of oil recovery efficiency in limestone cores using artificial neural networks (boukadi and al-alawi, 1997). 7. application of ann to predict wettability and relative permeability of sandstone rocks (alalawi et al 1996). 8. preliminary studies on using artificial neural networks to predict sedimentary facies of the petro-carboniferous glacigenic al khlata formation in oman (schuniker et al 1999). 62 development and application of back-propagation-based 9. assessment of formation damage using artificial neural networks (kalam et al 1996). 10. the application of artificial neural networks to reservoir engineering (kalam et al 1995). 13. civil engineering 1. a comparative analysis and prediction of traffic accident casualties in the sultanate of oman using ann and statistical methods (ali et al 1998). 2. a novel approach for traffic accident analysis and prediction using artificial neural networks (al-alawi, s.m. and ali, g.a. 1996). 3. intelligent monitoring and control of large engineering projects (al-alawi et al 1992). 14. other applications 1. forecasting fish exports in the sultanate of oman using artificial neural networks (luqman and al-alawi 2000). 11. water sorption isotherms of dates: modeling using gab equation and artificial neural network applications (myhara et al 1998). 15. conclusion in the past ten years, the international community has given considerable attention to developing more accurate systems and models based on artificial intelligence techniques such as artificial neural networks, expert systems and fuzzy logic. these techniques have successfully been applied in a variety of fields reporting higher accuracy compared to other classical models and methods. this paper provides basic ann concepts, outlines steps used for ann model development, and lists examples of ann-based engineering applications conducted in oman. the paper is intended to provide guidelines and necessary references and resources for individuals interested in conducting research in engineering or other fields of study using back-propagation artificial neural networks. it is recommended; therefore, to explore, learn and use such advanced techniques in order to solve some of the engineering problems and to survive current economic conditions. references al-alawi, s.m. and al-hinai, h. 1998. an ann based approach for predicting global radiation in locations with no direct measurement instrumentation. the sixth arab international solar energy conference (isec 6), march 29-april 1, 1998, sultanate of oman. al-alawi, s.m. and al-hinai, h. 1998. an ann based approach for predicting global radiation in locations with no direct measurement instrumentation”. renewable energy journal. elsevier science, u.k., 14: 199-204. al-alawi, s.m. and al-hinai, h.a. 1996. analysis and prediction of clearness index using artificial neural networks, proceedings of the world renewable energy congress, 3: 21152119, june 1996, colorado, u.s.a. al-alawi, s.m. and al-hinai, h.a. 1996. analysis and prediction of clearness index using artificial neural networks. renewable energy journal. 3: 2115-2119. al-alawi, s.m. and ali, g.a. 1996. a novel approach for traffic accident analysis and prediction using artificial neural networks, road & transport research journal, 5: 118128. al-alawi, s.m., benjamin, c.o., and omurtag, y. 1992. intelligent monitoring and control of large engineering projects, 6th oklahoma symposium on artificial intelligence, november 11-12, 1992, pp. 115-124, tulsa, oklahoma, u.s.a. 63 saleh mohammed al-alawi al-alawi, s.m., boukadi, f.h., and bemani, a.s. 1998. matrix and cement effects on residual oil saturation in sandstone formations: a neural network approach, the journal of petroleum science & technology, squ, january 24, 1998. al-alawi, s.m. and ellithy, k.a. 2000. tuning of svc damping controllers over wide range of load models using artificial neural network. electrical power & energy systems journal, 22: 405-420. al-alawi, s.m. and islam, s.m. 1995. short-term load forecasting using artificial neural networks. 2nd ieee international conference on electronics, circuits and systems (icecs'95). december 17-21, 1995. amman, jordan. pp.381-384. al-alawi, s.m., jervase, j.a., and jawad, a.m. 1998. statistical signal characterization – artificial neural network based hybrid system for electrocardiogram interpretation”. conference on computational aspects and their applications in electrical engineering, july 22-23, 1998, amman, jordan. al-alawi, s.m., kalam, m.z., and al-mukheini, m. 1996. application of ann to predict wettability and relative permeability of sandstone rocks, engineering journal of qatar university, 9: 29-43. al-alawi, s.m., seibi, a.c. and al-oraimi, s.k. 1996. prediction of failure mechanisms and mechanical properties of fastened grp under bending using artificial neural networks, proceedings of the first international conference on composite science and technology, pp. 7-12, june 18-20, 1996, durban, south africa. al-alawi, s.m., siddiqui, r.a., and albalushi, k. 1997. artificial neural networks: a novel approach for the analysis and prediction of mechanical properties of 6063 aluminum alloy, al-azhar engineering international conference in cairo, egypt, september 1997. al-alawi, s.m. and tawo, e.e. 1998. application of artificial neural networks in mineral resource evaluation”, journal of king saud university for engineering sciences, 10: 127139. ali, g.a., al-alawi, s.m., and bakheit, c.s. 1998. a comparative analysis and prediction of traffic accident casualties in the sultanate of oman using artificial neural networks and statistical methods, squ journal for science and technology, 3: 11-20. anderson, j.a. 1990. data representation in neural networks. ai expert, june, pp. 30-37. bailey, d. and thompson, d. 1990. how to develop neural networks. ai expert, june, pp. 38-47. barakat e.h. and al rashad, s.a. 1993. social environmental and economic constraints affecting power and energy requirements in fast developing areas, power eng. j., 7(4): 177184. boukadi, f. h. and al-alawi, s.m. 1998. matrix and cement effects on residual oil saturation in sandstone formations”, petroleum science and technology journal, u.s.a., 17: 99-113. boukadi, f. and al-alawi, s.m. 1997. analysis and prediction of oil recovery efficiency in limestone cores using artificial neural networks, energy & fuels journal, u.s.a., 11: 1056-1060. boukadi, f., al-alawi, s.m., al-bemani, a. and al-qassabi, s. establishing pvt correlations for omani oils”, petroleum science and technology, u.s.a., september 1998. bunn, d.w. and farmer, e.d. 1985. comparative models for electrical load forecasting, john wiley & sons. burden, r.l. and fairies, j.d. 1985. numerical analysis, prindel, webber, and schmidt. ellithy, k.a., al-alawi, s.m., and zainalabdeen, h.m. 1997. tuning power system stabilizers over a wide range of load models using artificial neural networks”, journal of engineering and applied science, cairo university, 44: 389-406. gastli, a., akherraz, m. and al-alawi, s.m. 2000. ann-based load identification and control of ac voltage regulator. proceedings of the ieee international energy conference (iec 2000), al-ain, uae, may 7-9, 2000, cd-rom. 64 development and application of back-propagation-based islam, s.m. and al-alawi, s.m. 1995. forecasting long-term electrical peak load and energy consumption for a fast growing utility using artificial neural networks, proceedings of the iee international power engineering conference (ipec’95), singapore, march 1995, pp. 690-695. islam, s.m., al-alawi, s.m., and ellithy, k.a. 1995. forecasting monthly electrical load and energy for a fast growing utility using an artificial neural network. electric power systems research journal, 34: 1-9. islam, m., al-alawi, s.m. and ledwich, g. 1996. on-line unit commitment for a generation constrained fast growing utility using artificial neural networks, the australian universities power engineering conference (aupec’96), october 2-4, 1996, melbourne, australia. kalam, m.z., al-alawi, s.m., and al-mukheini, m. 1996. assessment of formation damage using artificial neural networks, spe paper #31100, proceedings of the international symposium on formation damage control, pp. 301-309, february 14-15, 1996, lafayette, louisiana, u.s.a. kalam, m.z., al-alawi, s.m. and al-mukheini, m. 1995. the application of artificial neural networks to reservoir engineering, iatmi international symposium on production optimization, july 22-26, 1995, pp. 1-8, bandung, indonesia. lawrence, j. 1991. data preparation for a neural network. ai expert, november, pp. 34-41. luqman, a. and al-alawi, s.m. 2000. forecasting fish exports in the sultanate of oman using artificial neural networks, jordanian journal “derasat” , 22(2): . mendenhall, w. and beaver, r.j. 1994. introduction to probability and statistics, duxbury press. myhara, r.m., sablani, s.s., al-alawi, s.m. and taylor, m.s. 1998. water sorption isotherms of dates: modeling using gab equation and artificial neural network applications, lebensmittel wissenchaft und technologie (german journal), food science and technology (english name), 33: 699-706. rumelhart, d., mcclelland, j., and pdp research group. 1988. parallel distributed processing, explorations in the microstructure of cognition. 11; foundations. cambridge, ma. mit press/bradford books. schuniker, o., al-alawi, s.m., al-bemani, a.s., and kalam, m.z. 1999. preliminary studies on using artificial neural networks to predict sedimentary facies of the petro-carboniferous glacigenic al khlata formation in oman, 11th spe middle east oil show & conference (meos’99), february 20-23, 1999, bahrain. seibi, a. and al-alawi, s.m. 1999. experimental investigation and failure analysis of fastened grp under bending using the finite element method and artificial neural network modeling, the journal of science & technology, 4: 71-78. seibi, a.c. and al-alawi, s.m. 1999. design of fiberglass/copper moulds using finite element analysis. first international conference on composite science and technology, orlando, florida, june 1999. seibi, a. and al-alawi, s.m. 1997. prediction of fracture toughness using artificial neural networks. engineering fracture mechanics journal, 56: 311-319. seibi, a.c., al-oraimi, s.k., and al-alawi, s.m. 1996. effects of joint geometry on the flexural behaviour of glass reinforced plastics, proceedings of the first international conference on composite science and technology, pp. 471-476, june 18-20, 1996, durban, south africa. simpson, p.k. 1990. artificial neural systems: foundations, paradigms, applications, and implementations. (1st edition). pergamon press, inc., elmsford, ny. stanley, j. 1990. introduction to neural networks. (3rd edition). sierra madre. tawo, e.e. and al-alawi, s.m. 1999. a comparison between an artificial neural network and geostatistical technique in the estimation of regionalized variables, engineering journal of qatar university , 12:125-149. 65 saleh mohammed al-alawi ward systems group, inc. 1991. neuroshell, neural network shell program. (4th edition). frederick, md. received 17 june 2001 accepted 8 september 2001 appendix a: artificial neural networks resources books, journals and other resources on anns included in this guide are obtained from the following webpages: http://www.faqs.org/faqs/ai-faq/neural-nets/part4/ please see the above webpages for more detailed information and full review. some of the best popular introduction to anns: hinton, g.e. (1992), "how neural networks learn from experience", scientific american, 267 (september), 144-151, author's webpages: http://www.cs.utoronto.ca/dcs/people/faculty/hinton.html (official) and http://www.cs.toronto.edu/~hinton (private) journal webpages: http://www.sciam.com/ some of the best introductory books for business executives: bigus, j.p. (1996), data mining with neural networks: solving business problems--from application development to decision support, ny: mcgraw-hill, isbn 0-07-005779-6, xvii +221 pages. fausett, l. (1994), fundamentals of neural networks: architectures, algorithms, and applications, englewood cliffs, nj: prentice hall, isbn0-13-334186-0. also published as a prentice hall international edition, isbn0-13-042250-9. sample software (source code listings in c and fortran) is included in an instructor's manual. book webpages (publisher): http://www.prenhall.com/books/esm_0133341860.html smith, m. (1996). neural networks for statistical modeling, ny: van nostrand reinhold, isbn 0442-01310-8. apparently there is a new edition i haven't seen yet: smith, m. (1996). neural networks for statistical modeling, boston: international thomson computer press, isbn 1-85032842-0.book webpages (publisher): http://www.thompson.com/ publisher's address: 20 park plaza, suite 1001, boston, ma 02116, usa. reed, r.d., and marks, r.j, ii (1999), neural smithing: supervised learning in feed forward artificial neural networks, cambridge, ma: the mit press, isbn 0-262-18190-8.author's webpage: marks: http://cialab.ee.washington.edu/marks.html book webpages (publisher): http://mitpress.mit.edu/book-home.tcl?isbn=0262181908 weiss, s.m. and kulikowski, c.a. (1991), computer systems that learn, morgan kaufmann. isbn 1-55860-065-5. author's webpages: kulikowski: http://ruccs.rutgers.edu/faculty/kulikowski.html book webpages (publisher): http://www.mkp.com/books_catalog/1-55860-065-5.asp 66 http://www.faqs.org/faqs/ai-faq/neural-nets/part4/ http://www.cs.utoronto.ca/dcs/people/faculty/hinton.html http://www.cs.toronto.edu/~hinton http://www.sciam.com/ http://www.prenhall.com/books/esm_0133341860.html http://www.thompson.com/ http://cialab.ee.washington.edu/marks.html http://mitpress.mit.edu/book-home.tcl?isbn=0262181908 http://ruccs.rutgers.edu/faculty/kulikowski.html http://www.mkp.com/books_catalog/1-55860-065-5.asp development and application of back-propagation-based some of the best books on using and programming anns: masters, t. (1993), practical neural network recipes in c++, academic press, isbn 0-12479040-2, us $45 incl. disks. book webpage (publisher): http://www.apcatalog.com/cgibin/ap?isbn=0124790402&location=us&form=form2 masters, t. (1995) advanced algorithms for neural networks: a c++sourcebook, ny: john wiley and sons, isbn 0-471-10588-0 book webpage (publisher): http://www.wiley.com/ masters, t. (1994), signal and image processing with neural networks: ac++ sourcebook, ny: wiley, isbn 0-471-04963-8.book webpage (publisher): http://www.wiley.com/ additional information: one has to search. some of the best intermediate textbooks on anns: bishop, c.m. (1995). neural networks for pattern recognition, oxford: oxford university press. isbn 0-19-853849-9 (hardback) or 0-19-853864-2 (paperback), xvii +482 pages. author's webpages: http://neural-server.aston.ac.uk/people/bishopc/welcome.html hertz, j., krogh, a., and palmer, r. (1991). introduction to the theory of neural computation. redwood city, ca: addison-wesley, isbn 0-201-50395-6 (hardbound) and 0-201-51560-1 (paperbound) book webpages (publisher): http://www2.awl.com/gb/abp/sfi/computer.html ripley, b.d. (1996) pattern recognition and neural networks, cambridge: cambridge university press, isbn 0-521-46086-7 (hardback), xii +403 pages. author's webpages: http://www.stats.ox.ac.uk/~ripley/ book webpages (publisher): http://www.cup.cam.ac.uk/ devroye, l., gy "orfi, l., and lugosi, g. (1996), a probabilistic theory of pattern recognition, ny: springer, isbn 0-387-94618-7, vii +636 pages. some of the best books on neurofuzzy systems: brown, m., and harris, c. (1994), neurofuzzy adaptive modeling and control, ny: prentice hall, isbn 0-13-134453-6. author's webpages: http://www.isis.ecs.soton.ac.uk/people/m_brown.html and http://www.ecs.soton.ac.uk/~cjh/ book webpages (publisher): http://www.prenhall.com/books/esm_0131344536.html additional information: additional page at: http://www.isis.ecs.soton.ac.uk/publications/neural/mqbcjh94e.html and an abstract can be found at: http://www.isis.ecs.soton.ac.uk/publications/neural/mqb93.html some of the best comparison of anns with other classification methods: michie, d., spiegelhalter, d.j. and taylor, c.c. (1994), machine learning, neural and statistical classification, ellis horwood. author's webpage: donald michie: http://www.aiai.ed.ac.uk/~dm/dm.html additional information: this book is out of print but available online at http://www.amsta.leeds.ac.uk/~charles/statlog/ other notable books: anderson, j.a. (1995), an introduction to neural networks, cambridge, ma: the mit press, isbn 0-262-01144-1. author's webpages: http://www.cog.brown.edu/~anderson book webpages (publisher): http://mitpress.mit.edu/book-home.tcl?isbn=0262510812 orhttp://mitpress.mit.edu/book-home.tcl?isbn=0262011441 (hardback) additional information: programs and additional information can be found at: ftp://mitpress.mit.edu/pub/intro-toneuralnets/ 67 http://www.apcatalog.com/cgi-bin/ap?isbn=0124790402&location=us&form=form2 http://www.apcatalog.com/cgi-bin/ap?isbn=0124790402&location=us&form=form2 http://www.wiley.com/ http://www.wiley.com/ http://neural-server.aston.ac.uk/people/bishopc/welcome.html http://www2.awl.com/gb/abp/sfi/computer.html http://www.stats.ox.ac.uk/~ripley/ http://www.cup.cam.ac.uk/ http://www.isis.ecs.soton.ac.uk/people/m_brown.html http://www.ecs.soton.ac.uk/~cjh/ http://www.prenhall.com/books/esm_0131344536.html http://www.isis.ecs.soton.ac.uk/publications/neural/mqbcjh94e.html http://www.isis.ecs.soton.ac.uk/publications/neural/mqb93.html http://www.aiai.ed.ac.uk/~dm/dm.html http://www.amsta.leeds.ac.uk/~charles/statlog/ http://www.cog.brown.edu/~anderson http://mitpress.mit.edu/book-home.tcl?isbn=0262510812 http://mitpress.mit.edu/book-home.tcl?isbn=0262011441 ftp://mitpress.mit.edu/pub/intro-to-neuralnets/ ftp://mitpress.mit.edu/pub/intro-to-neuralnets/ saleh mohammed al-alawi feedforward networks: fine, t.l. (1999) feedforward neural network methodology, ny: springer, isbn 0-387-98745-2. husmeier, d. (1999), neural networks for conditional probability estimation: forecasting beyond point predictions, berlin: springer verlag, isbn 185233095. time-series forecasting: weigend, a.s. and gershenfeld, n.a., eds. (1994) time series prediction: forecasting the future and understanding the past, reading, ma: addison-wesley, isbn 0201626020. book webpages (publisher): http://www2.awl.com/gb/abp/sfi/complexity.html gately, e. (1996). neural networks for financial forecasting. new york: john wiley and sons, inc., isbn 0-471-11212-7. book webpages (publisher): http://www.wiley.com/ fuzzy logic and neurofuzzy systems: kosko, b. (1997), fuzzy engineering, upper saddle river, nj: prentice hall, isbn 0-13-1249916. kosko's new book is a big improvement over his older neurofuzzy book and makes an excellent sequel to brown and harris (1994). nauck, d., klawonn, f., and kruse, r. (1997), foundations of neuro-fuzzy systems, chichester: wiley, isbn 0-471-97151-0. optimization: cichocki, a. and unbehauen, r. (1993). neural networks for optimization and signal processing. ny: john wiley & sons, isbn 0-471-93010-5 (hardbound), 526 pages, $57.95. book webpages (publisher): http://www.wiley.com/ general books for the beginner: caudill, m. and butler, c. (1990). naturally intelligent systems. mit press: cambridge, massachusetts. (isbn 0-262-03156-6). book webpages (publisher): http://mitpress.mit.edu/bookhome.tcl?isbn=0262531135 chester, m. (1993). neural networks: a tutorial, englewood cliffs, nj: ptr prentice hall. book webpage (publisher): http://www.prenhall.com/ dayhoff, j. e. (1990). neural network architectures: an introduction. van nostrand reinhold: new york. freeman, james (1994). simulating neural networks with mathematica, addison-wesley, isbn: 0-201-56629-x. book webpage (publisher): http://cseng.aw.com/bookdetail.qry?isbn=0-20156629-x&ptype=0 additional information: sourcecode available under: ftp://ftp.mathsource.com/pub/publications/booksupplements/freeman-1993 mccord nelson, m. and illingworth, w.t. (1990). a practical guide to neural nets. addisonwesley publishing company, inc. (isbn 0-201-52376-0). book webpages (publisher): http://cseng.aw.com/bookdetail.qry?isbn=0-201-63378-7&ptype=1174 muller, b., reinhardt, j., strickland, m. t. (1995). neural networks.: an introduction (2nd ed.). berlin, heidelberg, new york: springer-verlag. isbn 3-540-60207-0. (dos 3.5" disk included.) book webpages (publisher): http://www.springer.de/catalog/htmlfiles/deutsch/phys/3540602070.html 68 http://www2.awl.com/gb/abp/sfi/complexity.html http://www.wiley.com/ http://www.wiley.com/ http://mitpress.mit.edu/book-home.tcl?isbn=0262531135 http://mitpress.mit.edu/book-home.tcl?isbn=0262531135 http://www.prenhall.com/ http://cseng.aw.com/bookdetail.qry?isbn=0-201-56629-x&ptype=0 http://cseng.aw.com/bookdetail.qry?isbn=0-201-56629-x&ptype=0 ftp://ftp.mathsource.com/pub/publications/booksupplements/freeman-1993 http://cseng.aw.com/bookdetail.qry?isbn=0-201-63378-7&ptype=1174 http://www.springer.de/catalog/html-files/deutsch/phys/3540602070.html http://www.springer.de/catalog/html-files/deutsch/phys/3540602070.html development and application of back-propagation-based not-quite-so-introductory literature: kung, s.y. (1993). digital neural networks, prentice hall, englewood cliffs, nj. book webpages (publisher): http://www.prenhall.com/books/ptr_0136123260.html levine, d. s. (2000). introduction to neural and cognitive modeling. 2nd ed., lawrence erlbaum: hillsdale, n.j. comments from readers of comp.ai.neural-nets: "highly recommended". maren, a., harston, c. and pap, r., (1990). handbook of neural computing applications. academic press. isbn: 0-12-471260-6. (451 pages) pao, y. h. (1989). adaptive pattern recognition and neural networks addison-wesley publishing company, inc. (isbn 0-201-12584-6) book webpages (publisher): http://www.awl.com/ refenes, a. (ed.) (1995). neural networks in the capital markets. chichester, england: john wiley and sons, inc. book webpages (publisher): http://www.wiley.com/ simpson, p. k. (1990). artificial neural systems: foundations, paradigms, applications and implementations. pergamon press: new york. wasserman, p.d. (1993). advanced methods in neural computing. van nostrand reinhold: new york (isbn: 0-442-00461-3). zeidenberg. m. (1990). neural networks in artificial intelligence. ellis horwood, ltd., chichester. comments from readers of comp.ai.neural-nets: "gives the ai point of view". zornetzer, s. f., davis, j. l. and lau, c. (1990). an introduction to neuraland electronic networks. academic press. (isbn 0-12-781881-2) subject: journals and magazines about neural networks: title: neural networks, publish: pergamon press address: pergamon journals inc., fairview park, elmsford, new york 10523, usa and pergamon journals ltd. headington hill hall, oxford ox3, 0bw, england, freq.: 10 issues/year (vol. 1 in 1988) cost/yr: free with inns or jnns or enns membership ($45?), individual $65, institution $175issn #: 0893-6080url: http://www.elsevier.nl/locate/inca/841 title: neural computation, publish: mit press address: mit press journals, 55 hayward street cambridge, ma 02142-9949, usa, phone: (617) 253-2889 freq.: quarterly (vol. 1 in 1989) cost/yr: individual $45, institution $90, students $35; add $9 outside usaissn #: 08997667url: http://mitpress.mit.edu/journals-legacy.tcl title: neural computing surveys publish: lawrence erlbaum associates address: 10 industrial avenue, mahwah, nj 07430-2262, usa. freq.: yearly cost/yr: free on-line, issn #: 1093-7609url: http://www.icsi.berkeley.edu/~jagota/ncs/ title: ieee transactions on neural networks, publish: institute of electrical and electronics engineers (ieee) address: ieee service center, 445 hoes lane, p.o. box 1331, piscataway, nj, 08855-1331 usa. tel: (201) 981-0060 cost/yr: $10 for members belonging to participating ieee societies, freq.: quarterly (vol. 1 in march 1990) url: http://www.ieee.org/nnc/pubs/transactions.html title: international journal of neural systems, publish: world scientific publishing, address: usa: world scientific publishing co., 1060 main street, river edge, nj 07666. tel: (201) 487 9655; europe: world scientific publishing co. ltd., 57 shelton street, london wc2h 9he, england. tel: (0171) 836 0888; asia: world scientific publishing co. pte. ltd., 1022 hougang avenue 1 #05-3520, singapore 1953, rep. of singapore tel: 382 5663. freq.: quarterly (vol. 1 in 1990) cost/yr: individual $122, institution $255 (plus $15-$25 for postage) issn #: 0129-0657 (ijns). 69 http://www.prenhall.com/books/ptr_0136123260.html news:comp.ai.neural-nets http://www.awl.com/ http://www.wiley.com/ news:comp.ai.neural-nets http://www.elsevier.nl/locate/inca/841 http://mitpress.mit.edu/journals-legacy.tcl http://www.icsi.berkeley.edu/~jagota/ncs/ http://www.ieee.org/nnc/pubs/transactions.html saleh mohammed al-alawi title: international journal of neurocomputing, publish: elsevier science publishers, journal dept.; po box 211; 1000 ae amsterdam, the netherlands. freq.: quarterly (vol. 1 in 1989) url: http://www.elsevier.nl/locate/inca/505628 title: neural processing letters, publish: kluwer academic publishers address: p.o. box 322, 3300 ah dordrecht, the netherlands. freq: 6 issues/year (vol. 1 in 1994) cost/yr: individuals $198, institution $400 (including postage) issn #: 1370-4621url: http://www.wkap.nl/journalhome.htm/1370-4621 title: neural network news, publish: aiweek inc. address: neural network news, 2555 cumberland parkway, suite 299, atlanta, ga 30339 usa. tel: (404) 434-2187freq.: monthly (beginning september 1989) cost/yr: usa and canada $249, elsewhere $299, remark: commercial newsletter title: network: computation in neural systems, publish: iop publishing ltd address: europe: iop publishing ltd, techno house, redcliffe way, bristol bs1 6nx, uk; in usa: american institute of physics, subscriber services 500 sunnyside blvd., woodbury, ny 11797-2999 freq.: quarterly (1st issue 1990) cost/yr: usa: $180, europe: 110 pounds url: http://www.iop.org/journals/ne title: connection science: journal of neural computing, artificial intelligence and cognitive research publish: carfax publishing address: europe: carfax publishing company, po box 25, abingdon, oxfordshire ox14 3ue, uk. usa: carfax publishing company, po box 2025, dunnellon, florida 34430-2025, usa australia: carfax publishing company, locked bag 25, deakin, act 2600, australia, freq.: quarterly (vol. 1 in 1989) cost/yr: personal rate: 48 pounds (ec) 66 pounds (outside ec) us$118 (usa and canada), institutional rate: 176 pounds (ec) 198 pounds (outside ec) us$340 (usa and canada) title: international journal of neural networks, publish: learned information freq.: quarterly (vol. 1 in 1989), cost/yr: 90 pounds, issn #: 0954-9889 subject: conferences and workshops on neural networks: the journal "neural networks" has a list of conferences, workshops and meetings in each issue. it is also available from http://www.ph.kcl.ac.uk/neuronet/bakker.html. the ieee neural network council maintains a list of conferences at http://www.ieee.org/nnc. conferences, workshops, and other events concerned with neural networks, inductive learning, genetic algorithms, data mining, agents, applications of ai, pattern recognition, vision, and related fields are listed at georg thimm's web page http://www.drc.ntu.edu.sg/users/mgeorg/enter.epl subject: freeware, shareware, and commercial software for neural networks: the webpages: http://www.faqs.org/faqs/ai-faq/neural-nets/ part 5 & 6 contains urls for the following: • several source codes for ann in c/c++ and java • a review of 44 freeware and shareware packages for ann simulation • a review of 40 commercial software packages for ann simulation please see the above webpages for detailed information or for full review: 70 http://www.elsevier.nl/locate/inca/505628 http://www.wkap.nl/journalhome.htm/1370-4621 http://www.iop.org/journals/ne http://www.ph.kcl.ac.uk/neuronet/bakker.html http://www.ieee.org/nnc http://www.drc.ntu.edu.sg/users/mgeorg/enter.epl http://www.faqs.org/faqs/ai-faq/neural-nets/part4/ saleh mohammed al-alawi 2.1 back-propagation paradigm 2.2 ann architecture 2.3 ann operations figure 1. a typical back-propagation architecture. 2.5 ann testing and validation engineering applications microsoft word math991101.final2.doc science and technology, 5 (2000) 85-104 © 2000 sultan qaboos university 85 flow past a rotating circular cylinder and a rotlet using the finite-difference method t. b. a. el bashir department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. دائرية دوارة ودوامة باستخدام طريقة الفرق المحدودة االنسياب على اسطوانة طيفور البشير باستخدام بعض التحويالت ) دوارة ( يختص هذا البحث بدراسة االنسياب المتولد من دوامة في وجود اسطوانة دائرية :خالصة هذا وقد تم التوصل إلى حل عددي يتطابق بشكل ممتاز . ودةعلـى المعادالت األساسية الحاكمة للمسألة مع طريقة الفروق المحد .مع النتائج التحليلية المتاحة ، ثم تم استخدام الطريقة نفسها للحصول على نتائج جديدة لمسألة ليس لها حل تحليلي abstract : in this paper the flow generated by a rotlet in the presence of a circular cylinder is considered. we introduce a transformation which simplifies the equations and boundary conditions. we use the finite-difference method to obtain results in excellent agreement with all the available analytical results. results are presented for reynolds numbers, based on the diameter of the cylinder, in the range 20re0 ≤≤ and the rotational parameter, α , in the range 30 ≤≤ α and strength of rotlet, β , in the range 30 ≤≤ β . the results are found to be applicable over a wide range of values of α and β . the calculated values of the drag, lift and moment coefficients and the general nature of the streamline patterns are in good agreement with analytical results . the method is then utilized to obtain new results for which no analytical solution is possible. keywords: slow flow, cylinder, rotlet. study has been made of the flow generated by rotating a circular cylinder within a uniform stream of viscous fluid in the presence of a line rotlet. with the origin of the coordinates coinciding with the centre of the cylinder, the polar coordinate system ( )ϑ,r has the boundary of the cylinder at r = a and the position of the rotlet at ( )2/3, π∗c , as shown in figure 1. there are four basic parameters that occur in this problem, namely the reynolds number, defined as a2re = vu / , the rotational parameter ua /0ωα = , the non-dimensional length acc / ∗= and the nondimensional strength of the rotlet ua/γ=β , where v is the coefficient of kinematic viscosity of the fluid, u the uperturbed main stream speed (the stream at infinity is assumed to flow parallel to the x -axis in the positive x direction), 0ω the angular velocity of the cylinder and γ the strength of the rotlet. at zero reynolds number the governing equation is the biharmonic equation. in the absence of rotlet no solution of this equation, which satisfies both the boundary conditions on the cylinder and at infinity, is possible. this arises because it is necessary to maintain in the solution a term of the form ( ) ( )ϑsinln rr in order for both the velocity components on the rotating cylinder to be satisfied. however, although a solution retaining such a term is obviously valid at points not too far away from the cylinder such a solution deteriorates as one moves further away. as such this solution fails to satisfy the boundary condition at infinity, with the exact multiple of the unwanted term at infinity remaining undetermined. this unknown constant can be established by treating the t. b. a. el bashir 86 solution of the problem as the approximation to the inner flow past the circular cylinder as the reynolds number tends to zero. then matching with the solution as obtained from the outer region where the first approximation to the navier stokes equations are the oseen equations. full details regarding these expansions and matching procedure can be found in proudman and pearson (1957). basically what this means is that the uniform flow past a circular cylinder is not a wellposed stokes problem. in fact, at zero reynolds number the problem is singular. y u r ϑ x (1,0) * ( )2/3,* πc figure 1. the geometry of the circular cylinder and the position of the rotlet however, the introduction of the rotlet , strength ∗=γ uc so that c=β , into the flow field at any given distance ∗c along the negative y -axis, allows a solution to be obtained. analytical solutions to this problem have been obtained by dorrepaal et al (1984). their work examines the flows generated in a fluid by the introduction of a line singularity, such as a stokeslet or rotlet, in the presence of a circular cylinder and shows that a phenomenon analogous to the stokes paradox exists in those flows with a uniform stream far from the cylinder. as a consequence, the uniform streaming flow past a circular cylinder, when a line stokeslet or rotlet of certain strength is present, is a wellposed problem in stokes flow. the solutions by dorrepaal et al. (1984) employed an image type approach, plus a clever and simplistic deduction, which enabled the result to be constructed devoid of most of the analysis. however, the present work has established the same solution by using a fourier series approach and has confirmed this numerically by the application of a modification to the boundary element method. the latter appears to provide an approach for the solution of the biharmonic equation, which requires only the position of the singularity, plus the physical values of the drag, lift and the moment on the circular cylinder to be known. in addition, it seems capable of being extended to accommodate the presence of several different bodies as well as allowing more complex shapes for which an analytical solution is impossible. it is intended to show that the presence of a rotlet in a uniform flow at nonzero reynolds number allows an otherwise singular problem to become well-posed as the reynolds number becomes zero. the main aim of this paper is to solve numerically the navier-stokes equations for steady, twodimensional, incompressible viscous fluid flow past a rotating circular cylinder of radius a in the presence of a rotlet of strength γ which is located at the point ( ) ( ) accr >∗= ∗ ,2/3,, πϑ . at large distances from the cylinder it is assumed that there is a uniform flow of speed u which is parallel to the negative x -axis. initially the strength of a rotlet is set to zero and the problem solved with flow past a rotating circular cylindwer and a rotlet 87 reynolds numbers 5 and 20. the results are in very good agreement with those obtained by dennis and chang (1970) and fornberg (1980). using this as an initial estimate of the solution when a line singularity is present an iterative technique is developed in order to solve the problem when a rotlet, at ( )2/3, π∗c , of small strength is introduced into the flow. as the drag, lift and moment on the circular cylinder are the most important physical quantities, as well as being easy to measure experimentally, see fornberg (1980), particular attention has been paid to these quantities in this work. having established the numerical procedure the reynolds number is decreased towards zero whilst continuing to solve over a range of non-dimensional strengths of the rotlet, namely 5.30 ≤≤ β . the question that needs to be answered is whether as re approaches zero the value of the parameter β would tend to that unique value obtained by dorrepaal et al. (1984) in their analytical solution. basic equations and boundary conditions the origin of the coordinate system is fixed at the centre of the circular cylinder of radius a and the positive x -axis taken in the same direction as that of the uniform flow at large distances from the cylinder. polar coordinates ( )ϑ,r are chosen such that 0=ϑ coincides with the positive x -axis, ( )ϑcosrx = and ( )ϑsinry = (2.1) a line rotlet of strength γ is located at the point 2/3, πϑ == ∗cr , where ac >∗ . the steady flow of an incompressible fluid in a fixed two-dimensional cartesian frame of reference can be described by the equations, ( ) ,p1. 2 uuu ∇+∇−=∇ v ρ (2.2) 0=⋅∇ u , (2.3) where p,, ρu and v are the velocity, density, pressure and the kinematics viscosity of the fluid, respectively. applying the curl operator to the two-dimensional equation (2.2) produces ( ) ,2ωωu ∇=∇⋅ v (2.4) where χ∇=ω u . in two-dimensional motion the polar resolutes of u can be expressed in terms of the streamfunction ψ by r v r vr ∂ ψ∂ −= ∂ ψ∂ = ϑϑ , 1 (2.5) where rv and ϑv are the velocity components in the r and ϑ directions, respectively. by introducing the dimensionless variables ,/,/,/ aa uuuuχχ ψ=ψ′=′=′ and ,/ uaωω =′ (2.6) then the governing equations in non-dimensional form become t. b. a. el bashir 88 ( ) ( )yx ′′∂ ′ψ′∂ −=′∇ , , re2 ω ω (2.7) ,2 ω′−=ψ′∇ (2.8) where ω′ and ψ′ are the non-dimensional scalar vorticity and streamfunction, respectively. for convenience the accent will from now on be ignored. it is required to solve equations (2.7) and (2.8) subject to the no-slip conditions imposed by the circular cylinder, namely α−= ∂ ψ∂ =ψ r ,0 on ,20,1 πϑ <≤=r (2.9) and the boundary conditions at large distances from the cylinder ( ) ( )ϑ ϑ ϑ cos 1 ,sin → ∂ ψ∂ −→ ∂ ψ∂ rr as ,20, πϑ <≤∞→r (2.10) in the presence of a line rotlet the streamfunction behaves as ≅ψ 1ln rβ− as ,01 →r (2.11) where 1r measures the distance from the rotlet and is thus given by ( )( ) ,sin2 21221 ϑrccrr ++= (2.12) where ( )2/3, πc is the position of the rotlet. in the above definition of the streamfunction the signs appearing in the expressions in (2.5) are the opposite to those given by dorrepaal et al. (1984) but follow those adopted by fornberg (1980) since it is a comparison with their results at non-zero reynolds number that is to be undertaken. for numerical convenience the perturbation streamfunction ψ is introduced as ,vy βψ −−ψ= (2.13) where ( )( ) 2122 sin2ln ϑrccrv ++= with *cc = a/ and ( )ua/γ=β being two non-dimensional parameters. expansion (2.13) has been taken so that 0→ψ as ∞→r . if the parameter 0=β the problem reduces to that solved by fornberg (1980). however, with the reynolds number equal to zero and the parameter c=β the situation is that studied by dorrepaal et al. (1984) except that the geometry in the present case corresponds to a rotation through 2/π of their flow pattern. hence, their stream is flowing along the negative y -axis with their rotlet at ( )0,*c , whereas in the present geometry the stream flows along the negative x -axis with the rotlet at ( )2/3,* πc . using expression (2.13) in equations (2.7) and (2.8) gives ( ) ( ) ( ) ( ) ( ) ( )               ++ + ∂ ∂ +               ++ + + ∂ ∂ −      ∂ ∂ ∂ ∂ − ∂ ∂ ∂ ∂ −= ∂ ∂ + ∂ ∂ + ∂ ∂ ϑ ϑ βϑ ω ϑ ϑ βϑ ϑ ωω ϑ ϕ ϑ ωϕ ϑ ωωω sin2 cos cos 2 re sin2 sin sin 2 re 2 re11 22 2222 2 2 2 rccr rc r rr rccr cr rrrrrrrr (2.14) flow past a rotating circular cylindwer and a rotlet 89 respectively. the boundary conditions (2.9) and (2.10) are then expressed in the form ( ) ( )( )2 1 sin1lnsin 2 ϑβϑψ cc ++−−= on πϑ 20,1 <<=r , (2. 16) ( ) ( ) ( )       ++ + −−−= ∂ ∂ ϑ ϑ βϑα ψ sin21 sin1 sin 2 cc c r on πϑ 20,1 <<=r , (2.17) 0 1 → ∂ ∂ = ∂ ∂ ϑ ϕϕ rr as πϑ 20, <≤∞→r . (2.18) filon (1926) showed that in the absence of any rotlet the asymptotic form for the dimensional streamfunction at large distances from the cylinder and outside the wake region is given by ψ ~ ( ) ( ) ( ) π πϑ π ϑ 22 /ln sin − ++ dl carc r , as πϑ 20, <<∞→r , (2.19) where ( )aulc l 2/ ρ= and ( )audc d 2/ ρ= , l and d being the lift and drag on the cylinder. imai (1951) found higher–order terms in this streamsfunction expansion and showed how the coefficients relate to the moment on the cylinder. in the case of zero reynolds number no solution of the equation 04 =ψ∇ which matches the free stream condition at infinity and satisfies the boundary condition on 1=r is possible. the solution, which satisfies the no slip condition on the cylinder and tends to infinity most slowly as ∞→r is ψ ~ ( ) ( ) ( )[ ]rrrra 2/12/lnsin +−ϑ (2.20) this has been obtained by discarding the term involving 3r . the non-dimensional drag is directly related to the coefficient a, via the expression aπ4 , but the solution suffers from the defect that it does not determine the value of the constant a. the neglected inertial terms are of the order ( ) ( )( ) 22 /ln rra whilst the viscous forces are of the order ( )3re/ ra and these terms are of comparable order when ( )( ) ≅arra /lnre ( )10 . hence, the stokes solution should not be expected to be valid beyond a value given by this expression. that is why the stokes solution may be an adequate representation of the fluid flow relatively close to the cylinder but cannot represent a uniform approximation to the total velocity distribution. however, it is possible to write the stokes solution in the form ( )( ) ( )( )( ) ( )[ ] ( )ϑψ sin2/12/relnreln rrrfrfra +−+−= , (2.21) where ( )ref is an arbitrary function of re . for ( ) 1re <<f and ( )rerf of order unity, the dominant term is ( )( )( ) ( )ϑsinreln rfa− . if this is to represent the external flow, namely a uniform stream ( )ϑsinur , then one must set ( )( )reln/1 fa −= . by substituting this value of a and ( )re/1 fr = into ( )( ) arra /lnre , one obtains ( )rere/ f ~ ( )10 . (2.22) , 11 2 2 22 2 ω ϑ ψψψ −= ∂ ∂ + ∂ ∂ + ∂ ∂ rrrr (2.15) t. b. a. el bashir 90 so for ( ) rere =f the stokes solution leads to a uniform stream of order unity in that region where the stokes equation ceases to be valid. this suggests that for small reynolds numbers the external uniform stream condition is reached before the stokes approximation breaks down, so that the stokes flow represents the solution in the inner region near the cylinder but the outer flow requires the introduction on an oseen variable and the procedure involves the matching of the inner and outer expansions. this matching process leads to the obvious linkage between the coefficients of the terms in oseen’s expansion in the outer region, closely related to filon’s expansion with those from the stokes solution in the inner region. hence, the appropriate value of a can be obtained, as already indicated from the solution in the outer region. any similar term in a stokes expansion, such as ( ) ( )ϑcosln rbr term in the streamfunction expansion, has its coefficient similarly related to the lift. solutions of the stokes equation represented by the form ( ) ( )ϑsinrf or ( ) ( )ϑsinrg fail to produce any moment contribution, but it can easily be seen that the solution of 04 =ψ∇ which has a non-zero moment arises from the ( )ar /ln term. using these results, it is possible from the stokes expansion far from the cylinder to establish both the force and the moment on the cylinder. the stokes solution produced by dorrepaaal et al (1984) is able to immediately produce the drag, lift and moment on the circular cylinder from its expansion at large distances from the cylinder; although the contribution from the singularity at the rotlet must first be removed from the coefficient of the ( )ar /ln term before it represents the moment on the cylinder. since the streamfunction and vorticity equations are both elliptical in nature we should supply one condition for each of the variables rather than use directly conditions (2.16), (2.17) and (2.18). it has been reported by fornberg (1980, 1985), that the choice of the boundary condition for the vorticity, ω , is not as sensitive as that for the streamfunction, ψ , and many authors have paid particular attention to the boundary condition for ψ at large distances from the cylinder. 1=ξ /, bb ff )4,()0,( ξξ ff = )0,()4,( ξξ ff = )4,()0,( ξωξω = )0,()4,( ξωξω = 0=ξ 0=n 0=f , 0=ω 4=η figure 2. the geometry of the solution domain. in this work a new numerical technique is introduced in order to avoid having to enforce the boundary condition (2.19) at large distances from the cylinder. we introduce the transformation π ϑ ηξ 2 , 1 == r (2.23) and ( ) ( ) rrrf /,, ϑψϑ = , (2.24) where ( ) ( )ηξξψηξ ,, =f . (2.25) thus, we have 0=f on 0=ξ (i.e. at ∞=r ) and this requires no approximation to be made for ψ at large distances from the cylinder. with the transformation (2.23) the solution domain ( )πϑ 20,1 <≤∞<≤ r is transformed into a finite rectangular region in the ( )ηξ, plane flow past a rotating circular cylindwer and a rotlet 91 ( )40,10 <≤<≤ ηξ , see figure 2. substituting expressions (2.23) and (2.24) into the governing equations (2.14) and (2.15) one obtains ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ,0 4 re 2 2/sin21 2/cos 2/sin21 2/sin12 2/sin 2 2/cos 2 , ,2 2 2 2 2 3 2 2 4 22 4 22 2 2 2 =              ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂       ++ + ∂ ∂       ++ + + ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂− η ω π ξ ξ ω ξ ξ ω ξ ξ ω πηξξ πηβξ η ω πηξξ πηξ π βξ πη η ω π ξ πη ξ ω ξ η ω π ξ ηξ ω π ξ cc c cc c f f (2.26) ωξ ηπ ξ ξ ξ ξ ξ −=+ ∂ ∂ + ∂ ∂ − ∂ ∂ f fff 2 2 2 2 2 2 3 4 (2.27) and the boundary conditions (2.10) and (2.11) now become ( ) ( )( ) 40,12/sin21ln2/sin 212 <≤==++−−= ηπηβπη ronfccf b (2.28) ( ) ( ) ( ) ,40,1' 2/sin21 2/sin1 2/sin 2 <≤==      ++ + ++= ∂ ∂ η πη πη βπηα ξ ronf cc cf b (2.29) 40,0,0,0 <≤=== ηξω onf (2.30) further, since the solution is periodic in η we also require that ( ) ( ) ( ) ( ) ,10,0,4,,0,4, ≤≤== ξξωξωξξ forff (2.31) which along with all the other boundary conditions are indicated in figure 2. the solution technique in order to obtain numerical solutions of the equations (2.26) and (2.27) subject to the boundary conditions (2.28), (2.29), (2.30) and (2.31) the region of integration 40,10 <≤≤≤ ηξ is covered by a rectangular mesh system of size h and k in the η and ξ directions, respectively, and a modified finite-difference approximation to the differential equations (2.26) and (2.27) is employed. if the standard central-difference approximation is employed, then it is not always possible to obtain a convergent solution especially at moderate and large values of the reynolds number. a number of schemes have been introduced with the object of improving the efficiency of the convergence of such schemes, e.g. upwind and downwind differencing as discussed by greenspan (1968). gosman et al. (1969) and runchal et al. (1969). these efficiencies arise from the fact that the difference equations are associated with matrices, which are diagonally dominant and thus amenable to iterative methods of solution. however, these schemes suffer from a deficiency in that they are only of first-order accuracy since forward or backward differences are employed to approximate first derivatives rather than the more accurate second-order centraldifference formulae. the formulation in which all derivatives are approximated by central differences is of second-order accuracy but the matrix associated with the difference equations may not be diagonally dominant. the iterative procedures may be slowly convergent or even divergent when this method is applied. there are also finite-difference schemes, which are of second-order accuracy and for which the associated matrices are always diagonally dominant. these methods rely upon rather specialized forms of local approximations and yield difference equations, which involve the t. b. a. el bashir 92 exponential function. these schemes were first introduced by allen and southwell (1955) in approximating the equation governing the vorticity during the course of finding numerical solutions for the steady two-dimensional flow past a circular cylinder. dennis and hudson (1978) showed that by a suitable adaptation of an alternative to the allen and southwell method suggested by dennis (1960), an approximation of second-order accuracy, yielding difference equations with an associated matrix which is diagonally dominant, can be obtained. these difference equations do not involve the exponential function and can be looked upon as a rather more complicated version of the central-difference formulation. the dennis and hudson method contains more terms in the finite-difference equations than the usual central-difference approximation but the presence of these extra terms is very important for the associated matrix to be diagonally dominant. numerous authors have performed several numerical experiments which confirm that the method by dennis and hudson succeeds where the standard central-difference formulation fails, see for example dennis (1960) and dennis and hudson (1978). thus, in this paper a modified version of the finitedifference approximation as described by hudson and dennis, has been used. it is found most convenient to set up a mesh system such that the mesh size in both the ξ and η directions are nhk /1== , where n is a pre-assigned positive integer. in view of the periodic conditions (2.31), and extra line of computation h+= 4η for 10 ≤≤ ξ is introduced. then we have ( ) ( )11 ++ mxn mesh points, where 14 += nm , the mesh points ( ) ( )mjniii ≤≤≤≤ 0,0,ηξ are ( )jhih, . if subscripts 0,1,2,3 and 4 denote quantities at the grid points ( ) ( ) ( ),,,,,, 000000 ηξηξηξ hh +− ( )h+00 ,ηξ and ( )00 ,ηξ h− respectively, then on using the dennis and hudson scheme, equations (2.26) and (2.27) may be written in the form 03 0 2 4 0 ** 32 0 22 0 *2* 12 0 202 0 2 2 0 2 2* 484 1 84 1 4 2 2 ω ξξ ββ ξπξ ββ ξπξξπ β h f h ff h ff h +      +++      −+=      −+ (3.1) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 40000 2* 30000 0 2 20000 2* 100002 0 202 0 2 2* ,, 4 ,, 1 ,, 4 ,, 12 2 ωηξηξ β ωηξηξ ξπ ωηξηξ β ωηξηξ ξπ ω ξπ β       −−+      +++       +++      −−=      + ebda ebda (3.2) with k h =*β , and ( ) ( )      ++= ϑ ξξ υ πξ ηξ sin 1 8 re , 00 0 02 0 00 fh a (3.3) ( ) ( )      ++= ϑ ξξπξ βηξ cos 16 re 88 re , 00 02 0 00 hh u h b (3.4) ( ) ( )       ++ + −= ϑξξ ϑξ πξ β ηξ sin21 sin1 8 re , 0 2 0 2 0 2 0 00 cc ch d (3.5) ( ) ( ) ( )       ++ −= ϑξξ ϑβ ηξ sin21 cos 16 re , 0 2 0 200 cc ch e (3.6) where ( )0,0 υu are defined as flow past a rotating circular cylindwer and a rotlet 93 ( ) ( ) . , , , 00 0 00 0 ξ ηξ υ η ηξ ∂ ∂ −= ∂ ∂ = ff u (3.7) the standard central-difference approximations may be obtained by setting the extra terms ( ) ( )0000 ,,, ηξηξ ed to be zero. we now briefly outline how the boundary conditions (2.28)-(2.30) can be implemented. the boundary condition for the vorticity on 1=ξ can be found by using taylor expansion for f and ω and inserting them in equation (2.27) to get second-order accurate finite differences. boundary conditions for ω : on ;0;0,0:40,0 0 =<≤=<≤= jmji ωηξ (3.8) on ;0;0,:40,1 njjmjni ωωηξ =<≤=<≤= (3.8) ( )         +                    +−+        −−−−−        −− = −− hh g h ghfhhhhffhh ijjnjijnijnnj nj 1 3 2 31 26 34' 6 2 2 1 6 2 6 3 2 2 1 2 π ω ω (3.9) with ( )( ) ( )            +++ ++ + −= j j j nj cccc c f η πβ η ηβ α π π 2 sin21ln 2sin21 sin1 ' 2 2 2 2 (3.10) ( )( ) ( )( )         ++ ++ −      += 2 2 2 22 2 22 sin21 21sin 42 sin 4 j j jij cc ccc g η ηβπ η ππ π π (3.11) ( ) ( ) ( )( ) ( )( )322 2 23 2 232 2 sin212 cos2sin313 j jj j cc ccccc g η ηηβπ π ππ ++ −+++ −= (3.12) on ;;,0:10,4 1iimmjnih ωωξη ==≤≤≤≤+= (3.13) on ;;0,0:10,0 10 −==≤≤≤≤= imijni ϖωξη (3.14) boundary conditions for f: on ;0;0,0:40,0 0 ==<≤<≤= jfimjηξ (3.15) on ;,0:40,1 nimj =<≤<≤= ηξ             ++      −= njccnjf nj 2 sin21ln 22 sin 2 πβπ (3.16) on ;;,0:10,4 1iim ffmjnih ==≤≤≤≤+= ξη (3.17) t. b. a. el bashir 94 on ;;0,0:10,0 10 −==≤≤≤≤= imi ffjniξη (3.18) the resulting finite-difference equations (3.1) and (3.2), subject to the boundary conditions (3.8) – (3.18), were solved iteratively. from equation (2.6) the non-dimensional speed of the uniform stream at large distances from the cylinder is unity, whereas the non-dimensional strength of the rotlet at the position ( )2/3, πc , namely β , is variable. in order to compare the results with dorrepaal et al. (1984) the value of c is fixed at the magnitude used in their calculations, namely 3=c . since the force components (drag and lift) and the moment are very sensitive to the method of solution, particular attention has been given to these quantities. if xf and yf are the dimensional drag and lift on the cylinder, then ( ) ( )( ) ϑϑσϑσπ ϑ rdf rrrrx ∫ =−= 2 0 1 sincos (3.19) ( ) ( )( )∫ =+−= π ϑ ϑϑσϑσ 2 0 1 sincos rdf rrrry (3.20) introducing the constitutive relations ,2 r p rrr ∂ ∂ +−= υ µσ (3.21) , 1       ∂ ∂ +      ∂ ∂ == ϑ υυ µσσ ϑϑϑ r rr rrr r (3.22) , 1 2       + ∂ ∂ +−= rr p r υ ϑ υ µσ ϑϑϑ (3.23) into expressions (3.19) and (3.20) results in ( ) ,sin12 2 2 22 0 ϑϑµ ϑ µ ϑ π d rr p rfx         ψ∇+         ψ+ ∂ ψ∂ ∂ ∂ − ∂ ∂ = ∫ (3.24) ( ) ,cos12 2 2 22 0 ϑϑµ ϑ µ ϑ π d rr p rfy         ψ∇+         ψ+ ∂ ψ∂ ∂ ∂ − ∂ ∂ −= ∫ (3.25) by using the ϑ̂ component of the navier stokes equations on the surface of the cylinder where the component of velocity normal to the surface is zero, namely ( )ψ∇ ∂ ∂ −=      ∂ ∂ 21 r p r µ ϑ (3.26) and substituting ω−=ψ∇2 , which is equation (2.8) but in its dimensional form, the equations (3.24) and (3.25) can be written in the form flow past a rotating circular cylindwer and a rotlet 95 ( ) ,sin22 0 2 2 ϑϑ ϑ ω ω µ π d rrr rrfx ∫                 ψ+ ∂ ψ∂ ∂ ∂ −− ∂ ∂ = (3.27) ( )∫                 ψ+ ∂ ψ∂ ∂ ∂ −− ∂ ∂ −= π ϑϑ ϑ ω ω µ 2 0 2 2 .cos 2 d rrr rrfy (3.28) the above expressions are still dimensional, but defining the lift and the drag coefficients by ( )aufc xd 2/ ρ= and ( )aufc yl 2/ ρ= (3.29) enables dc and lc to be written as ( ) ,sin2 re 2 2 22 0 ϑϑ ϑ ω ωπ d rrr rrc d                 ψ+ ∂ ψ∂ ∂ ∂ −− ∂ ∂ = ∫ (3.30) ( ) ,cos2 re 2 2 22 0 ϑϑ ϑ ω ωπ d rrr rrc l                 ψ+ ∂ ψ∂ ∂ ∂ −− ∂ ∂ −= ∫ (3.31) where ψ,r and ω are all non-dimensional. in terms of the independent variables ζ and dc,ϑ and lc become ( ) ,sin2 re 2 2 22 0 ϑϑ ϑξ ω ξ ωπ dc d                 ψ+ ∂ ψ∂ ∂ ∂ +− ∂ ∂ −= ∫ (3.32) ( ) ,cos2 re 2 2 22 0 ϑϑ ϑξ ω ξ ωπ dc l                 ψ+ ∂ ψ∂ ∂ ∂ +− ∂ ∂ −−= ∫ (3.33) when the boundary conditions on the cylinder are introduced, expressions (3.32) and (3.33) reduce to those given by fornberg (1980), except for a reversal of the sign in lc and the omission of a factor 2 in the definition of both lc and dc , which are both produced by the scaling we adopted. the moment on the cylinder ϑσ ϑ π rdrm r∫= 2 0 (3.34) becomes, in dimensional form, on substituting the appropriate constitutive equation ϑ ϑ µ π d rrrr rm         ∂ ψ∂ − ∂ ψ∂ − ∂ ψ∂ −= ∫ 2 2 22 22 0 2 11 (3.35) t. b. a. el bashir 96 introducing the moment coefficient defined by ( )22/ aumcm ρ= (3.36) results in the non-dimensional expression . 22 re 2 2 2 2 2 0 2 ϑ ϑ ω π d rrr rcm         ∂ ψ∂ + ∂ ψ∂ += ∫ (3.37) in terms of the independent variables ξ and ϑ the moment coefficient becomes ,22 re 2 2 22 0 ϑ ϑξ ω π dcm         ∂ ψ∂ + ∂ ψ∂ −= ∫ (3.38) and the boundary conditions on the cylinder reduce this expression to [ ] .2 re 2 0 2 0 ϑωω π dcm −= ∫ (3.39) formulae (3.32), (3.33) and (3.39) are evaluated using simpson’s rule. due to the need to evaluate the drag, lift and moment when 0re = we will work with the non-dimensional quantities 2/re,2/re ld cc and 2/re mc from now on, namely ( ) ( )ufuf yx µµ /,/ and ( )uam µ/ . however, when the reynolds number vanishes, that is the independence of the mainstream at infinity from the strength of the rotlet is no longer valid, it is necessary to redefine the above three quantities as ( ) ( ) ( ) ( )γγ µµ /,/ afaf yx and ( )γµ/m when discussing an iterative scheme in the following section. the results before we undertake a detailed discussion of the results it is important to stress from dorrepaal et al. (1984), and from our own investigation, that at 0re = it is impossible to obtain a solution for an arbitrary value of the parameter β , which is contrary to what occurs at non-zero reynolds numbers. in the 0re = situation there is only one unique value of β which will produce the uniform stream at infinity, and the difficulty numerically is to achieve some mechanism which will enable the numerical method to converge to this quantity. since stokes flow with a uniform flow at infinity means that body must be free of any force, one can develop an iterative numerical scheme based upon this fact to enable the unique value of β and the corresponding flow solution to be determined. exactly how this is achieved will be discussed in detail later within this section. in order to compare the results obtained by the present numerical method with those obtained previously, the values of the reynolds number 5re = and 20re = , in the absence of any rotlet ( )0=β and with the rotational parameter 1,5.0,0=α and 2, were initially investigated. solutions are obtained for the mesh sizes 20/1,15/1,10/1=h and 40/1 . it is found that the contour lines for the streamfunction and vorticity distribution are in good agreement with most of the previous investigators (dennis and chang (1970); fornberg (1980, 1985)), at both the above reynolds numbers, repeated extrapolation of results derived from 2h extrapolation of the results from 20/1,15/1,10/1=h and 40/1 produced only a 0.1% change in the coefficients of the lift and the drag when compared with the values derived directly from using 40/1=h . as a consequence it is proposed not to implement extrapolation but instead to utilize a small value of h, namely 40/1=h . values of 2re/ times the coefficients of the lift, drag and moment are presented in table 1. the lift and drag coefficients are in good agreement with those produced by fornberg (1980). flow past a rotating circular cylindwer and a rotlet 97 table 1: the variation of the coefficients of lift, drag and moment with α for 5re = and 20 . 5re = 20re = α 2/re lc 2/re dc 2/re mc 2/re lc 2/re dc 2/re mc 0.0 0.000 19.716 0.000 0.000 39.861 0.000 0.5 6.939 19.565 0.616 25.635 3.430 2.354 1.0 14.176 19.226 1.197 52.289 38.465 4.426 2.0 29122 17.514 2.246 114.275 32.515 7.026 having established that the numerical procedure is producing the correct results for 0re ≠ and 0≠α , the condition 0=β is relaxed. however, since the interest is in whether the problem is well posed as the reynolds number tends to zero, it is proposed to set α to be zero in the remainder of the calculations to be presented in this paper. such a restriction can easily be removed if required. it has already been established analytically by dorrepaal et al. (1984) that at 0re = a solution in which there is a uniform stream of unit non-dimensional strength flowing parallel to the positive y -axis is possible provided that the rotlet is placed at the non-dimensional position ( )0,c , where the non-dimensional strength of the rotlet is c=β . in the present situation the stream is flowing parallel to the positive x -axis and therefore the position of the rotlet has to be ( )2/3, πc in order to produce a solution. the question is whether the solutions at 0re ≠ for a range of values of β , namely varying non-dimensional strengths of the rotlet, can be used to predict the unique analytical value of this parameter which produces the solution at 0re = . the results of the solution by dorrepaal et al. (1984) show that there is no force or moment on the cylinder. hence, in the numerical solution it is possible that the value of β tends to its correct value for 0re = if one considers the values of the parameter β at which the quantities such as the force or moment on the cylinder are zero as the reynolds number tends to zero. to investigate this possibility values of ld cc re,re and mcre are calculated as functions of the parameter β for 5.30 ≤≤ β at 3,5re = and 1, with 20/1,10/1=h and 40/1 . figures 3, 4 and 5 show the variation of ld cc re,re and mcre as a function of the strength of the rotlet, β , for 3,5re = and 1, respectively, when using mesh sizes 10x40, 20x80 and 40x160. it is observed from figures 4 and 5 that the variations of the lift and moment as a function of β are very non-linear. however, the drag, (see figure 3) appears to behave almost linearly with respect to β , over the range 5.30 ≤≤ β for all the values of re considered. further, all the three values of re considered in this paper, predict that zero drag appears to occur close to the value of ( ) 3== cβ . it has already been established by dorrepaal et al. (1984) that only for a stream whose direction and magnitude are related to the position and strength of the rotlet will a solution be possible when 0re = . in this case only for the specific value of c=β will the problem be well-posed and produce a solution for which the values for the drag, lift and moment on the cylinder are all zero. for all other values of β one will have the force and moment dependent on this parameter. it has been shown elsewhere that when 0re = non-zero values of the drag and lift implies that there are terms of the type ( ) ( )ϑsinln rr and ( ) ( )ϑcosln rr at large values of r . similarly non-zero values of the moment require a ( )rln term. obviously the presence of such terms violates the boundary condition that 0=f as ∞→r , and it is only when all such terms are absent that one will achieve the required solution. this is why at 0re = , it is impossible to obtain a convergent solution for an arbitrary value of β , unlike the situation at 0re ≠ . however, for 0re = one can think of the lift, drag and moment as functions of β and only when these quantities acquire the value of zero will β achieve its required value, namely c=β , and produce a t. b. a. el bashir 98 figure 3. the variation of dcre as a function of β ◊◊◊ .16040**,*8020,4010 ××+++× convergent solution. hence, the technique adopted was that of a newton-raphson iteration on ( )βdc . the choice of dc rather than lc or mc being based upon the linearity of this expression with respect to β , compared with the rather complex behavior of the latter two quantities when considered as functions of this variable. the governing partial differential equation in finite-difference form, namely equation (3.1) and (3.2), were solved for two values of β , say 1β and 2β , the number of iterations being terminated after a prescribed number since due to the boundary condition posed at 0=ξ convergent solutions are impossible. the resulting two non-zero values of ( )1βdc and ( )2βdc are the values used in the newtonraphson method in order to establish a new value of β , say 3β at which ( )3βdc is estimated to be zero. flow past a rotating circular cylindwer and a rotlet 99 figure 4. the variation of lcre as a function of β ◊◊◊ .16040**,*8020,4010 ××+++× ( ) ( ) ( ) .1re,3re,5re === cba resolving for this new value of β , and using ( )3βdc together ( )1βdc or ( )2βdc , whichever is closest to zero, to produce from the newton-raphson solution a new value of β . this process is continued until the value of ( )3βdc reaches zero to within the required tolerance needed. the value of β automatically results in the correct values of lc and mc . the whole iterative procedure could equally well have been applied to setting either the values of ( )βlc or ( )βmc to zero. the resulting values of β achieved by this process were 3.0004, 3.005 and 3.0010 for the mesh seizes 40x160, 20x80 and 10x40 respectively, t. b. a. el bashir 100 figure 5. the variation of mcre as a function of β ◊◊◊ .16040**,*8020,4010 ××+++× ( ) ( ) ( ) .1re,3re,5re === cba compared with the exact analytical value of 3. the streamline and vorticity patterns produced from the numerical computation and shown in figures 6 (a) and 7 (a) are identical with those obtained from the analytical solution. figure 6 shows the streamline pattern obtained for 3=β and 3,1,0re = and 5 for fine mesh size 40x160. in these figures the effect of changing the reynolds number appears to be slight, but if we compare this figure with figure 10 the effect of the reynolds number becomes more clear. figure 7 shows the vorticity pattern for 3=β and 3,1,0re = and 5 for 40x160. the effect of changing the reynolds number is unclear, since the reynolds number is small and the strength of the rotlet is strong. figure 8 shows the streamline pattern for 5.1=β and 3,1,0re = and 5 . the region around the rotlet appears to be unaffected by the small change in the reynolds number but compared with figure 7, where the strength of the rotlet is double the present value, the decreasing strength of the rotlet causes a shrinkage of the region for the same streamline values. figure 9 shows the vorticity pattern for 5.1=β and 3,1,0re = and 5 . whilst the three figures are virtually indistinguishable, the decrease in the strength of the rotlet to half its earlier value, see figure 7, has produced a more symmetric pattern of vorticity between the rotlet and the cylinder whilst at the same time flow past a rotating circular cylindwer and a rotlet 101 figure 6 (a,b,c, d). the numerically obtained streamlines, ψ , for 3=β with a mesh size 16040 × . the streamlines labelled 1, 2 and 3 correspond to 7.00,1 and−=ψ , respectively. ( ) ( ) ( ) ( ) .5re,3re,1re,0re ==== dandcba the vortex lines of the same magnitude have been constrained in this region closer to the surface of the cylinder. this is contrary to what appears to take place above the cylinder with the vortex lines of the same magnitude showing a departure from the surface. figure 7(a, b, c, d). the numerically obtained vorticity, ω , for 3=β with a mesh size 16040 × . the streamlines labelled 1, 2 and 3 correspond to 4.00,4.0 and−=ω , respectively. ( ) ( ) ( ) ( ) .5re,3re,1re,0re ==== dandcba t. b. a. el bashir 102 figure 8 (a, b). the numerically obtained streamlines, ψ , for 5.1=β with a mesh size 16040 × . the streamlines labelled 1, 2 and 3 correspond to 7.00,1 and−=ψ , respectively. figure 10 shows the effect of the strength of the rotlet and how the results tend to those obtained by fornberg (1980). figure 10 (f) is identical with the figure obtained by fornberg (1980). further, close to the body, the flow (when β exceeds unity) appears to be dominated by the rotlet, even at a reynolds number of 20. the dominance of the rotlet is seen by the symmetrical nature of figure 8 (c). the numerically obtained streamlines, ψ , for 5.1=β with a mesh size 16040 × . the streamlines labelled 1, 2 and 3 correspond to 7.00,1 and−=ψ , respectively. ( ) ( ) ( ) .5re,3re,1re === cba flow past a rotating circular cylindwer and a rotlet 103 figure 9 (a, b, c). the numerically obtained vorticity, ω , for 5.1=β with a mesh size 16040 × . the streamlines labelled 1, 2 and 3 correspond to 4.00,4.0 and−=ω , respectively. figure 10 ( a, b, c, d, e, f). the numerically obtained streamlines, ψ , for 20re = with a mesh size 16040 × . the streamlines labelled 1, 2 and 3 correspond to 7.00,1 and−=ψ , respectively. ( ) ( ) ( ) ( ) ( ) ( ) .0,1.0,5.0,1,5.1,3 ====== ββββββ fandedcba t. b. a. el bashir 104 the flow (when β exceeds unity) appears to be dominated by the rotlet, even at a reynolds number of 20. the dominance of the rotlet is seen by the symmetrical nature of the flow about the x-axis and yaxis in the vicinity of the body. as the strength of the rotlet decreases, the symmetrical flow pattern diminishes. however, it is only when the value of β falls below 0.5 that one sees the closed streamline behind the cylinder and even when the value of β reaches 0.1 this closed region behind the cylinder is only present in the region 0<y due to the rotation from the rotlet. obviously as β tends to zero the closed streamline region will move to its symmetrical pattern about the x axis. conclusions numerical solutions of the full, steady, two-dimensional navier-stokes equations have been obtained for the fluid flow past a circular cylinder for reynolds number 5,3,1re = and 20 and rotational parameter 20 ≤≤ α when a rotlet of any given strength is placed at various positions outside the cylinder. although numerical solutions can be found for any value of reynolds number greater than zero it is well known that when the reynolds number is zero that a solution only exists provided there is a relationship between the strength of the rotlet and its location. further, when the reynolds number is zero, the analytical solutions are such that the drag, lift and moment are all identically zero. therefore in this paper we have concentrated on obtaining numerical results with the drag, lift and moment zero and developed a technique for extrapolating the results obtained at small values of the reynolds number to predict the solutions for zero reynolds number. using this technique it is found that the numerical results are in excellent agreement with all the available theoretical results. we conclude that the technique developed in this paper may be used with confidence to predict solutions for flows at zero reynolds numbers for situations where there are no analytical solutions. references allen, e., martin, a. and paris, f., 1979. boundary elements in potential and elasticity theory, comp. and stru., 10: 351-362. dennis, s.c.r. 1960. finite differences associated with second-order differential equations, quart. j. mech appl. math., 13: 487-496. dennis, s.c.r. and hudson j.d., 1978. a difference method for solving the navier-stokes equations, proc, 1st int. conf. numerical methods laminar and turbulent flow, pentech press, london, 69-78. dorrepaal, j.m., o’neill, m.e. and ranger, k.b., 1984. two-dimensional stokes flows with cylinders and line singularities, mathematika, 31: 65-75. filon, l.n.g., 1926. the forces on a cylinder in a stream of viscous fluid, proc. roy. soc., a113: 7-27. fornberg, b., 1980. a numerical study of steady viscous flow past as circular cylinder, j.fluid mech., 98: 819-855. fornberg, b., 1985. steady viscous flow past as circular cylinder, up to reynolds number 600, j. comput. phys., 161: 297320. imai, i., 1951. on the asymptotic behaviour of viscous fluid flow at a great distance from a cylinder body, proc. roy. soc., a208: 487-516. proudman, i. and pearson, j.r.a., 1957: expansions at small reynolds numbers for the flow past a sphere and a circular cylinder, j. fluid mech., 2: 237-262. received 1 november 1999 accepted 12 june 2000 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 81-90 © 2002 sultan qaboos university comparative study of load frequency controller designs for interconnected power systems m. albadi*, a. awladthani**, b. alomeiri*** and k. ellithy* *department of electrical engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. email: mbadi@squ.edu.om** oman liquefied natural gas, sur, sultanate of oman, email: ahmedawladthani@omanlng.co.om, ***ministry of electricity and water, muscat, sultanate of oman, email: so10456@hotmail.com. دراسة مقارنة لطرق تصميم نظم التحكم في تردد التيار الكهربائي نتيجة تغير األحمال في نظم القوى الكهربائية المرتبطة لليثي محمد البادي ، أحمد أوالد ثاني ، بدر العميري ، و خالد ا تـناقش هذه الورقة ثالث طرق لتصميم نظم التحكم في تردد التيار الكهربائي والطاقة المنقولة بين الشبكات في نظم :خالصـة أما التصميم الثاني فهو يعتمد على طريقة تحديد . يسمى التصميم األول بالتحكم التفاضلي الكالسيكي . القـوى الكهربائية المرتبطة تهدف جميع هذه .)optimal control( أما التصميم الثالث فيدعى نظام التحكم الكهربائي األفضل . مأقطـاب مصـفوفة الـنظ تحت تأثير تغير مفاجىء في الحمل الكهربائي أو ) التردد والطاقة المنقولة ( التصـميمات الى تحسين استجابة الشبكات المرتبطة فعالية التصميمات ) matlab( نتائج المستخرجة من برنامج المحاكاة وقد أظهرت ال . انفصال احدى وحدات التوليد عن الشبكة و نظام ) optimal control( التحكم الكهربائي األفضل كما أظهرت النتائج أيضا ان استخدام تصميم يجمع بين نظام . الـثالثة .التحكم التفاضلي الكالسيكي يعطي أفضل النتائج abstract: this paper presents a comparative study of three different load frequency (lf) controller designs for interconnected power systems. they are the conventional integral controller, a controller based on the pole-placement technique, and a controller based on optimal control law. each controller has been designed to improve the dynamic response of system frequency and tie line power flow under a sudden load change. the results obtained using a matalb computer program show the effectiveness of the lf controller designs. the results also show that the combined optimal controller with conventional integral controller can provide good damping to the system and reduce the overshoot. keywords: load frequency control, integral control, pole placement, optimal control, decentralized control. 1. introduction l arge-scale power systems are normally composed of control areas or regions representing coherent groups of generators. the various areas are interconnected through tie lines. the tie lines are utilized for energy exchange between areas and provide inter-area support in case of abnormal condition (fosha and elgerd, 1999; wood, 1996). area load-changes and abnormal conditions, such as outages of generation, leads to mismatch in scheduled power interchanges between areas. these mismatches have to be corrected via supplementary control. in recent years, usually large tie-line power fluctuations have been observed as a result of increased system capacity and very close interconnection among power systems. this observation suggests a strong need for establishing a more advanced load frequency control (lfc) scheme. 81 mailto:mbadi@squ.edu.om mailto:ahmedawladthani@omanlng.co.om albadi, awladthan, alomeiri and ellithy lfc of interconnected systems is defined as the regulation of power output of generators within a prescribed area, in response to change in system frequency, tie-line loading so as to maintain scheduled system frequency and/or established interchange with other areas within predetermined limits (fosha and elgerd, 1999; wood, 1996). in general, lfc is a very important item in power system operation and control for supplying sufficient and reliable electric power with good quality. the basic load frequency control (lfc) loop is shown in figure 1. it is known that changes in real power affect mainly the system frequency and thus the rotor angle. the input mechanical power to generators is used to control the frequency of the output electrical power. the change in tie line real power (∆ptie) and the change in frequency (∆f) are sensed and transformed into a real power command signal ∆pv which is sent to the prime mover to call for the increment in the input torque or input mechanical power to the generator. therefore, the prime mover makes change in the generator output by an amount of ∆pg, which will changes the values of ∆f and ∆ptie within a specified tolerance. a simple control strategy for any lf controller design is to keep the frequency approximately at the nominal value i.e. 50 hz, to maintain the tie-line flow at about the schedule and each area should absorb its own load changes to minimize the cost. c∆ρ g v∆ρ gg q∆∆ρ , frequency sensor load frequency control (lfc) ∆ptievalve control mechanism turbine steam many inves reported and a n order to achieve comparative of effectiveness of matalb comp 2. system mo the single l block diagram r assumed to have system as shown the state v will be used to d invariant is given figure 1. schematic diagram of lfc and avr of a generator. tigations in the area of lfc problem of interconnected power systems have been umber of control strategies have been employed in the design of lf controller in better performance (talaq and albassi, 1999; yang et al., 1998; hiyana, 1982). a three different controller designs for lfc is presented in this paper. the each controller on the system dynamic performance is investigated using uter software. delling ine diagram the two interconnected systems (two-area) is shown in figure 2. the epresenting the interconnection of two areas is shown in figure 3. each area is only one equivalent generator. the generator is equipped with governorturbine in figure 3. ariable (state-space) (fosha and elgerd, 1999; yang et al., 1998; fellach, 1987) esign the lf controller. the standard form of state-space equations of a linear time by the equations 82 comparative study of load frequency controller designs area 1 area 2 tie-line figure 2. single-line diagram of two-area. lpubxax γ∆+∆+∆=∆ • (1) udxcy ∆+∆=∆ (2) where:                                           − −− − − − −− −− − −− = 0000000 11 0 1 00000 0 11 000000 00 2 1 22 1 0000 0000000 0000000 00000 11 0 1 000000 11 0 0000 2 1 00 2 1 2 222 2222 22 22 2 2 1212 111 1111 11 111 1 bkk r hh d h tt kbk r hhh d a ggg tt ggg tt τττ ττ τττ ττ [ ]tvmcvmc pppfppppfx 2222121111 ∆∆∆∆∆∆∆∆∆=∆ t g gb             = 0 1 0000000 000000 1 00 2 1 τ τ u =[u1 u2]t is the input vector the disturbance matrix γ equals to 83 albadi, awladthan, alomeiri and ellithy t h h             − − =γ 000 2 1 00000 00000000 2 1 2 1 the disturbance to the system is [ ]21 lll ppp ∆∆=∆ 11 1 gsτ+ 11 1 tsτ+ 112 1 dsh +σ ∆_ pl1 ∆pm1∆pv1 ∆f1 σ 1 1 r generator & loadturbinegovernor ∆ u1 + + _ _ σ 21 1 gsτ+ 21 1 tsτ+ 222 1 dsh +σ ∆pl2 ∆pm2∆pv2 ∆f2 2 1 r ∆ u2 + + -σ _ + ∆p12 + _ b1 σ + + s k1− b2 σ _ s k1− + _ ace1 ace2 s t12 figure 3. block diagram of load frequency control (lfc) of two-area. 3. design of lf controller 3.1 conventional integral controller design conventional lf controller is based upon tie-line bias control, where each area tends to reduce the area control error (ace) to zero. the block diagram of two-area power system including area control error is shown in figure 3. the control error for each area consists of a linear combination of frequency and tie-line power deviation (saadat, 1999). (∑ = ∆+∆= n j iiji pace 1 ωγ ) (3) 84 comparative study of load frequency controller designs an overall satisfactory performance is achieved when γi is selected to be equal to the frequency bias factor of that area. so i i ii dr b +== 1 γ . thus, the aces for a two-area are 22212 11121 ω ω ∆+∆= ∆+∆= bpace bpace (4) to get the simulation results, use the prameters given in table 1. table 1: the prameters of two area systems. area 1 2 speed regulation –r r1=0.05 r2=0.0625 frequency sensitive load coefficient –d d1=0.6 d2=0.9 inertia constant –h h1=5 h2=4 governor time constant gτ 1gτ =0.2 s 2gτ =0.3 s turbine time constant tτ 1tτ =0.5 s 2tτ =0.6 s synchronizing coefficient –t12 t12=2 pu load disturbance lp∆ 1lp∆ =0.1875 pu 2lp∆ =0 the system response having the integral controller is shown in figures 5-7. the integral controller satisfies the desired objectives of the lfc. the only problem of this type of controller is that the system response is less damped and the overshot is large. to solve this problem, another control signals (∆u1,∆u2) are added to the system in presence of integral controller. these signals are derived from the controller designed based on pole-placement technique or based on the optimal control theory. both controllers uses the same control law xku ∆−= (5) where k =[k1 k2 …….. kn] is the controller gain vector. 3.2 design based on pole-placement technique pole placement technique (phillips and harbor, 1998) depends on shifting the poles of the open-loop system (system without controller) to desired locations on the left-half of the complex plane.the characteristic equation of the closed-loop system (system with controller) is given by si-a+bk=0 (6) suppose that the design specifications require that the poles of the equation (6) at -λ1, -λ2, ….., -λn. the desired characteristic equation for the system is sn + αn-1sn-1 +……..+ α1s + α0 = (s+λ1)(s+λ2)……(s+λn)=0 (7) the pole-placement design procedure results in a gain vector k such that equation (6) is equal to equation (7), that is si-a+bk= sn+αn-1sn-1+…...+α1s+α0 (8) 85 albadi, awladthan, alomeiri and ellithy in equation (8) there are n unknowns (k1 k2 …….. kn). equating coefficients in equation (8) yields n equations in the n unknowns. a program using matlab is developed to design the lf controller based on pole-placement technique. ackerman formula (phillips and harbor et al., 1998) is used in the program to calculate the gain vector k to satisfy equation (8). table 2 shows the poles of the system having integral controller and the desired ones, which will be achieved by the pole-placement technique. table 3 shows the damping ratio of the complex poles. from table 3, it can be observed that the damping ratio of the closed-loop system (with the pole-placement controller) is increased. the effect of the damping ratio improvement can be seen from the system dynamic response shown in figures 5-7. it can also be seen from figures 5-7 that the overshoot of the frequency deviations and tie-line power flow deviation is decreased. 3.3 optimal controller design many approaches have been proposed for lf controller design. the most promising approach is the application of linear optimal control (fosha and elgerd, 1999; yang et al., 1998; fellach, 1987). the linear optimal control has excellent characteristics in that it is able to control a system with small transients and relatively short settling time. the optimal controller is design to minimize the quadratic performance index of the following form ∫ ∞ += 0 )( dturuxqxj tt ∆∆∆∆ (9) subject to the dynamic system equation in (9), q is a positive semi-definite matrix and r is a positive definite matrix. the optimal gain vector is given by pbrk t1−= (10) where p is determined by solving the following riccati equation (nobele and daniel et al., 1988). 01 =+−+ − qpbpbrpapa tt (11) table 2: poles of the system having integral controller and the desired ones. the poles the system with integral controller only the system with integral controller and pole-placement controller λ1 -5.8468 -5.8178 λ2 -4.2717 -4.1669 λ3,4 -0.3768 ± j1.7234 -1.2480 ± j2.8824 λ5,6 -0.2231 ± j1.5992 -0.8596 ± j2.1385 λ7,8 -0.2537 ± j0.0484 -2.9886 , -0.2155 λ9 -0.3468 -1.7282 table 3: damping ratio of the complex poles. the system poles damping ratio (ζ) -0.3768 ± j1.7234 0.2136 -0.2231 ± j1.5992 0.1382 with integral controller only -0.2537 ± j0.0484 0.9823 -1.2480 ± j2.8824 0.3937 with integral controller and the pole-placement -0.8596 ± j2.1385 0.3730 86 comparative study of load frequency controller designs in an interconnected power system, each area takes charge of the lfc functions that is, it is operating its own lfc without any commitment from other systems except the case of determining the amount of power exchange. table 4 listed the gains of the centralized optimal lf controller. it is impractical to adopt a centralized lfc for interconnected systems. therefore, it is useful to apply the decentralized lfc (fosha and elgerd, 1999; yang et al., 1998) in which each system in the interconnected system makes use of locally available information to compute the control signal ∆u. table 4: gains of centralized optimal lf controller. state variable x gain vector k of area 1 (∆u1= kx) gain vector k of area 2 (∆u2= kx) ∆f1 86.8 -32.16 ∆pm1 2.53 -0.79 ∆pv1 0.72 -0.196 ∆pc1 -20 7.73 ∆p12 1.68 -0.69 ∆f2 -41.35 71.1 ∆pm2 -1.27 3.06 ∆pv2 -0.29 0.99 ∆pc2 12.12 -17.8 figure 4. system dynamic response with centralized / decentralized optimal controller. 87 albadi, awladthan, alomeiri and ellithy table 5: gains of decentralized optimal lf controller. state variable x gain vector k of area 1 (∆u1= kx) gain vector k of area 2 (∆u2= kx) ∆f1 86.8 0 ∆pm1 2.53 0 ∆pv1 0.72 0 ∆pc1 -20 0 ∆p12 1.68 -0.69 ∆f2 0 71.1 ∆pm2 0 3.06 ∆pv2 0 0.99 ∆pc2 0 -17.8 it has been found that the decentralized optimal controller gives very close results to the centralized optimal controller. this can be shown in figure 4. the effect of the optimal lf controller on the system performance can be seen from figures 5-7. the overshoot of the frequency and tie line power flow deviations is decreased and the system response is well damped. computer simulations for different sudden load change in area 1 and area 2 are reported in (al-badi et al., 2000). figure 5. area 1 dynamic response under a sudden load change in area 1. 88 comparative study of load frequency controller designs figure 6. area 2 dynamic response under a sudden load change in area 1. figure 7. tie-line dynamic response after a sudden load change in area 1. 89 albadi, awladthan, alomeiri and ellithy 4. conclusions a load frequency controller has been designed to improve the dynamic performance of interconnected power systems. the conventional integral controller, the controller based-pole placement technique and the controller based-optimal control law were considered and a comparative study between these controllers has been investigated. the results of computer simulation show that the integral controller restores the original value of the frequency and the tie-line power deviations. adding a signal derived from the optimal controller or derived from the pole-placement controller enhance the system damping and reduce the overshoot. the simulation results also show that the combined integral controller with optimal controller is more effective means for improving the dynamic performance of the system than the other controllers. the of optimal lf controller type is relatively simple and suitable for practical implementation for on-line implementation. 5. acknowledgments the authors would like to thank electrical engineering department at sultan qaboos university for their support. references al-badi, m., awladthani, a., alomeiri, b. 2000. load frequency control of interconnected power systems. undergraduate final year project, squ, muscat. feliach, a. 1987. optimal decentralized load frequency control. ieee trans. on power systems, 2: 379-386 fosha, c.e. and elgerd, o.i. 1999. the megawatt-frequency control problem: a new approach via optimal control theory. ieee trans. on power systems, 4: 563-577. hiyana, t. 1982. design of decentralized load frequency regulators for interconnected power systems. iee proceeding, pas.129: 17-23 nobele, b. and daniel, j. 1988. applied linear algebra. third edition. printice hall. ohno, h., 1996. basic study to improve performance of automatic generation control. proceeding of 12th power systems computation conference: 1157-1162 phillips and harbor , 1996. feedback control systems, third edition, prentice hall. saadat, h., 1999. power system analysis, mcgraw-hill. talaq, j. and f. albasri. 1999. adaptive fuzzy gain scheduling for load frequency control. ieee trans. on power systems,14: 145-151 wood, a. 1996. power generation, operation and control. prentice-hall. new york. yang, t., cimen, h. and o. zhu. 1998. decentralized load-frequency controller design based on structured singular values. iee proceeding on gener. transm. distrib, 145: 7-13 received 21 june 2001 accepted 11 november 2001 90 m. albadi*, a. awladthani**, b. alomeiri*** and k. ellithy* in recent years, usually large tie-line power fluctuations have been observed as a result of increased system capacity and very close interconnection among power systems. this observation suggests a strong need for establishing a more advanced load frequ the basic load frequency control (lfc) loop is shown in figure 1. it is known that changes in real power affect mainly the system frequency and thus the rotor angle. the input mechanical power to generators is used to control the frequency of the outpu table 1: the prameters of two area systems. area 1 2 speed regulation –r r˜1=0.05 r˜2=0.0625 frequency sensitive load coefficient –d d˜1=0.6 d˜2=0.9 inertia constant –h h˜1=5 h˜2=4 governor time constant =0.2 s =0.3 s turbine time constant =0.5 s =0.6 s synchronizing coefficient –t12 t12=2 pu load disturbance =0.1875 pu =0 table 2: poles of the system having integral controller and the desired ones. figure 4. system dynamic response with centralized / decentralized optimal controller. figure 5. area 1 dynamic response under a sudden load change in area 1. figure 6. area 2 dynamic response under a sudden load change in area 1. figure 7. tie-line dynamic response after a sudden load change in area 1. acknowledgments references state-of-the-art review of collapsing soils science and technology, special review (2000) 115-135 ©2000 sultan qaboos university 115 state-of-the-art review of collapsible soils amer ali al-rawas department of civil engineering, college of engineering, sultan qaboos university, p.o. box 33 al-khod 123, sultanate of oman. مراجعة و تحليل : لتربة القابلة للهبوطا عامر بن علي الرواس تالكومثل هذه التربة يحتمل أن تسبب مش . نتشر التربة القابلة للهبوط في المناطق الجافة وشبه الجافة ت :خالصـة ماسكة المتإن ظاهرة هبوط التربة تعود وبشكل رئيسي الى البنية غير . بـناء وذلك لهبوطها عند تعرضها للماء لل لهذا النوع من التربة بناء على بعض الخواص ولقد قدمت األدبيات في هذا الجانب عدة تصنيفات . التي تتمتع بها ومن . مثل المحتوى المائي والكثافة الجافة وحدود آتربرج والمحتوى الطيني وذلك كمؤشرات الحتمال هبوط التربة الضـروري اجراء قياس مباشر لمقدار الهبوط باستخدام الفحوص المعملية والحقلية عند ظهور مؤشرات الهبوط في ملحوظاً ضاً والتثبيت الكيميائي انخفا دمكهرت طرق المعالجة المختلفة مثل استبدال التربة وال ولقد أظ . المحتمل ويعتمد تصميم قواعد البناء على هذه التربة على عمق التربة ومقدار . معـدالت الهـبوط التي تسببها هذه التربة وجود هذه التربة على أعماق سطحية ، يشيع استخدام القواعد المستمرة في حالة . الهـبوط واقتصاديات التصميم . في الحاالت التي تمتد عندها التربة الى عدة أمتار تحت سطح األرض الركائز و الدعامات بيـنما ينصح بقواعد وتشمل األنواع المختلفة للتربة القابلة للهبوط ، وطرق . وتقـدم هـذه الورقة مراجعة شاملة للتربة القابلة للهبوط . ، واالختبارات المعملية والحقلية ، وطرق المعالجة ، وارشادات تصميم القواعدالتعرف والتصنيف abstract: collapsible soils are encountered in arid and semi-arid regions. such soils cause potential construction problems due to their collapse upon wetting. the collapse phenomenon is primarily related to the open structure of the soil. several soil collapse classifications based on parameters such as moisture content, dry density, atterberg limits and clay content have been proposed in the literature as indicators of the soil collapse potential. direct measurement of the magnitude of collapse, using laboratory and/or field tests, is essential once a soil showed indications of collapse potential. treatment methods such as soil replacement, compaction control and chemical stabilization showed significant reduction in the settlement of collapsible soils. the design of foundations on collapsible soils depends on the depth of the soil, magnitude of collapse and economics of the design. strip foundations are commonly used when collapsing soil extends to a shallow depth while piles and drilled piers are recommended in cases where the soil extends to several meters. this paper provides a comprehensive review of collapsible soils. these include the different types of collapsible soils, mechanisms of collapse, identification and classification methods, laboratory and field testing, treatment methods and guidelines for foundation design. keywords: collapsible soils, identification, laboratory tests, field tests, stabilization, foundation design. al-rawas 116 contents 1. introduction 116 2. types of collapsible soils 117 3. collapse mechanisms 118 4. identification and classification 119 5. laboratory tests 121 6. field tests 124 7. estimation of collapse settlement 125 8. stabilization of collapsibles soils 126 8.1 soil replacement 127 8.2 prewetting 127 8.3 controlled wetting 127 8.4 moisture control 128 8.5 compaction control 128 8.6 chemical stabilization or grouting 129 8.7 heat treatment 129 8.8 evaluation of treatment methods 129 9. foundation design 130 10. summary and conclusions 132 11. references 132 1. introduction collapsible soils are widely distributed in most parts of the world (e.g. united states of america, brazil, egypt, kuwait, south africa and china) particularly in arid and semi-arid regions. these soils pose potential threat to structures built on them when wetted. at their dry, natural state, they possess stiffness and high apparent shear strength; but upon wetting, they could exhibit a significant decrease in volume (collapsing, hydroconsolidation, hydrocompression). such soils, which exhibit this phenomenon at fairly low levels of stresses are called collapsible soils (tadepalli et al. 1992; rollins and rogers 1994). the sources of water can be either natural, such as rainfall and fluctuation in ground water table, or man-made, such as excessive irrigation and leakages from water and sewer lines. collapse may be triggered by water alone or by wetting and loads acting together. the existence of collapsible soils has long been recognized since world war ii. however, the recent infrastructure developments in arid regions, accompanied by the use of large quantities of water and the associated construction problems warrant a comprehensive investigation of these soils. the collapse of soils due to wetting may result in settlements of 2 to 6 percent of their thickness (beckwith and hansen 1989). the settlement can be large as demonstrated by irrigation canal settlements of 4.5 m in the west central part of the san joaquin valley in california (bull 1964). ismael et al. (1987) reported construction problems associated with the collapse of compacted sands in kuwait which include settlement and cracking of the ground floor slabs of many villas and buildings, failure and erosion of slopes, and settlement and cracking of highway pavements. intolerable settlements can cause extensive damage to civil engineering structures and result in significant financial losses. in the united states, the estimated cost of repair to structures at a cement plant in central utah located on collapsible soils was more than $20,000,000 (hepworth and langfelder 1988). this paper presents a state-of-the-art review of collapsible soils, with special reference to: (a) the types of collapsible soils; (b) collapse mechanisms; (c) identification and classification; (d) laboratory and field tests; (e) stabilization techniques; and (f) foundation design. state-of-the-art review of collapsible soils 117 the following symbols are used in this paper: ci = indicator; cp = collapse potential; e = void ratio at natural moisture content; eo = original void ratio; el = void ratio at liquid limit; (eo)i = initial void ratio; ∆ec = change in void ratio of the specimen upon wetting; ∆es = change in void ratio of the specimen caused by collapse of soil structure; ho = original height of the specimen; ∆h = change in height of the specimen upon wetting; ic = collapse index; ip = plasticity index; k, kd, kl = coefficients of subsidence; m = natural moisture content; pi = plasticity index; pl = plastic limit; po = overburden pressure; pc = preconsolidation pressure; ppr = proportionality limit; ∆p = pressure increment; qc = cone penetration tip resistance; r = collapse ratio; sr = degree of saturation; w = water content; εo = bearing plate settlement value corresponding to overburden pressure; εpr = bearing plate settlement value corresponding to proportionality limit. 2. types of collapsible soils the term collapsible soils encompasses a wide range of materials that exhibit the collapsing phenomenon. these materials include aeolian or wind deposits, water deposits, residual soils and colluvial deposits. the mechanisms that account for almost all naturally occurring collapsible soil deposits are debris flows and alluvial deposition, and deposition of wind-blown materials (beckwith 1995; derbyshire et al. 1995). however, bell and bruyn (1997) reported that the majority of naturally occurring collapsible soils are aeolian deposits. according to jennings and knight (1975), the soil deposits most likely to collapse are: (a) loose fills; (b) altered wind-blown sands; (c) hillwash of loose consistency; and (d) decomposed granite and other acid igneous rocks. collapsible soils are generally characterized by their loose structure of bulky shaped grains, often in the silt to fine sand size with a small amount of clay. there may be only slight cementing agents such as calcium carbonate, salts and dried clay, with combinations being common. a brief description of the common types of collapsible soils is given in the following paragraphs. aeolian deposits such as loess, dunes and other wind-blown deposits are encountered in different parts of the world. clemence and finbarr (1981) reported that loess distribution covers about 17 % of the united states, about 17 % of europe, 15 % of russia and siberia, and large areas of china. loess are also encountered in south america (i.e. argentina and uruguay) and southern africa. calcareous windblown dune sands are encountered in kuwait and some parts of the arabian peninsula (ismael et al. 1987). aeolian soils have a loose open, metastructure binded by cementing agents, which upon wetting, become weak and may dissolve causing collapse. these soils are composed primarily of quartz along with feldspar al-rawas and clay minerals. bell and bruyn (1997) reported that increasing the clay mineral content decreases the likelihood of collapse. water deposits include alluvial fans, mud flows and flash flood deposits. these deposits are laid down by water in a saturated state. they become hard and less compressible with relatively low density as they dry. the structure is usually open and porous, and soil grains are bonded together by cementing agents during the deposition. if these deposits are subsequently exposed to water accompanied with or without additional loading, they may collapse, thereby causing large settlement. alluvial deposits that exhibit collapsible phenomenon are encountered in saudi arabia and other parts of the middle east (el-nimr et al , 1992; fookes et al. 1985). residual soils cover a wide range of sizes, from clay size up to the gravel range. the collapsible structure is developed as a result of the leaching of the soluble and colloidal matter from the residual soil. this leaching of the soluble and fine materials results in a porous and unstable structure. 3. collapse mechanisms collapse mechanisms have been studied by several researchers (casagrande 1932; jennings and knight 1957; holtz and hilf 1961; burland 1965; dudley 1970; barden et al. 1973; mitchell 1993). the collapse phenomenon is primarily related to the open structure of the soil. casagrande (1932) has demonstrated that a portion of the fine-grained fraction of the soil exists as bonding material for the largergrained particles and that these bonds undergo local compression in the small gaps between adjacent grains resulting in the development of strength figure 1. at natural moisture content, these soils compress slightly as a result of increasing overburden pressures due to construction. however, the structure remains sensibly unchanged. when the loaded soil is exposed to moisture, and a certain critical moisture content is exceeded, the fine silt or clay bridges that are providing the cementation will soften, weaken and/or dissolve to some extent. eventually, the binders reach a stage where they no longer resist deformation forces and the structure collapses as shown in figure 1. figure 1. loaded structure before and after inundation (after casagrande 1932). aitchison and donald (1956) reported that for uniform spherical grains in an open cubical packing, the maximum added pressure due to the capillary effect occurs at a moisture content of about 32%. for the 118 state-of-the-art review of collapsible soils 119 densest packing of uniform spherical grains, the maximum tension occurs at 10% moisture content. investigations conducted with various collapsible soils showed that the peak effective stress values occur at moisture contents less than saturation and above 10% water content (clemence and finbarr 1981). holtz and hilf (1961) described the collapse mechanism as the result of capillary pressures approaching zero and the degree of saturation increasing to 100 %. burland (1965) described the collapse mechanism in terms of the stability at the interparticle contact points. due to wetting, the negative pore water pressure at the contact points decreases, causing grain slippage and distortion. dudley (1970) explained that as the soil dries below the shrinkage limit, the remaining water at the grains contact points is placed under tension. thus the excess water pressure becomes negative and therefore, the actual effective stress becomes larger than the total stress applied by the load. this increases the apparent strength of the soil. dudley (1970), barden et al. (1973) and mitchell (1993) explained the collapse phenomenon in terms of the cementing agents at the contact points of the soil grains. they identified four conditions required for the collapse to occur: 1. an open, partially unstable, partially saturated fabric. 2. a high enough total stress so that the structure is metastable. 3. a strong enough clay binder or other cementing agent to stabilize the structure when dry. 4. the addition of water to the soil which reduces the soil suction and thus produces the collapse. collins (1978) explained that an open fabric, which is a prerequisite for collapse, may be comprised of: (a) clothed grain-grain contacts; (b) grain bridges or buttresses comprised of either clay or silt plus possibly cementitious material such as iron oxide or carbonates; and (c) clay aggregates. the rate of collapse depends on the type of bonding and this was indicated by tadepalli et al. (1992) who reported that the collapse phenomenon is primarily related to the reduction of the matric suction during inundation. the rate of collapse depends to a large extend on the type of bonding as well as the other influencing factors. clemence and finbarr (1981) reported that collapse is more immediate in the case where soil grains are held together by capillary suction, but slow in the case of chemical cementing, and much slower in the case of clay buttresses. based on the above studies, it seems that the collapsing phenomenon is a complex one, which includes fabric, initial moisture content, initial dry density and loading conditions. it is important that these factors be looked at simultaneously in assessing the behavior of collapsing soils. 4. identification and classification the first task that a geotechnical engineer should undertake in the evaluation of collapsible soils is to visually examine the soil encountered at a particular site. this step is followed by the evaluation of the soil behavior using index tests to determine the likelihood of the soil for collapse. once the soil showed indications for collapse from visual examination and index tests, then further laboratory tests are needed for determining the magnitude of collapse. several collapse criteria based on some parameters such as dry density, atterberg limits, moisture content, void ratio, clay content and porosity have been proposed in the literature (clevenger, 1958; gibbs and bara 1962; handy 1973; feda 1966). some of these criteria are discussed in the following paragraphs. clevenger (1958) proposed a criterion based on dry density, that is, if the density is less than 1.28 mg/m3, then the soil is liable to significant settlement. on the other hand, if the dry density is greater than 1.44 mg/m3, then the amount of collapse should be small, while at intermediate densities the settlements are transitional. however, jennings and knight (1975) disputed these conclusions. it should be noted that since unstable soils have a wide range of dry densities which also apply to non-collapsible soils, the dry density alone seems to be misleading and an unreliable indicator of collapse. furthermore, other factors such as the soil moisture content, which greatly influences the soil collapse was not taken into account. al-rawas bell and bruyn (1997) reported a criterion suggested by gibbs and bara (1962) based on natural dry density and liquid limit, which distinguishes between collapsible soils and non-collapsible soils as shown in figure 2. the method is based on the premise that a soil, which has enough void space to hold its liquid limit moisture at saturation is susceptible to collapse on wetting. figure 2 shows that soils above the lines are in a loose condition, and when fully saturated will have a moisture content greater than liquid limit. handy (1973) suggested a criterion based on the ratio of liquid limit to saturation. if this ratio is less than 1, the soil is collapsible. however, if it is greater than 1, the soil is non-collapsible. dudley (1970) reported that most of the collapsing soils have liquid limits below 45 % and plasticity indices below 25%. figure 2. classification of collapsing soils (after gibbs and bara 1962). a collapse index (ic) involving natural moisture content (m), degree of saturation (sr), plastic limit (pl) and plasticity index (pi) was proposed by feda (1966). the collapse index was defined in the following formula ( )1 pi plsr/m ic − = if the collapse index was greater than 0.85, then this was indicative of collapsible soils. 120 state-of-the-art review of collapsible soils one of the key prerequisites for collapse to occur is that the soil must be partially saturated; and there appears to be a critical value for the degree of saturation (sr) below which the collapse phenomenon can occur and above which it will not occur. jennings and knight (1975) suggested a guideline, which relates the type of soil, grain size distribution and the critical degree of saturation as given in table 1. according to the soviet building code (reznik 1989), soils are identified as collapsible if their degree of saturation is less than 0.8 and the values of the indicator ci are less than the ones shown in table 2. the indicator ci is defined in the following formula )2( e1 ee ci l + − −= where el = void ratio at liquid limit, e = void ratio at natural moisture content. table 1. a guide for collapse settlement based on critical degree of saturation (after jennings and knight 1975). soil grain size distribution (mm) critical degree of saturation, (sr)crit. (%) fine gravels 1 – 6 6 – 10 fine silty sands 0.002 – 150 50 – 60 clayey silts 0.0002 – 150 90 95 das (1995) provided a summary of some soil collapse criteria based on different parameters (table 3). these criteria should be taken as indicators of the soil collapse potential, but reliance on such criteria can be misleading. therefore, direct measurement of the magnitude of collapse is essential once the soil showed indications of collapse potential. table 2. limits for the indicator ci values for different loessial soils (after reznik 1989). soil plasticity index, ip indicator ci 1% ≤ ip< 10% 0.10 10% ≤ ip< 14% 0.17 14% ≤ ip< 22% 0.24 5. laboratory tests laboratory tests are used for obtaining quantitative estimates of collapse potential, which can be used for estimating potential settlements of structures. ismael et al. (1987) carried out a study to examine the factors affecting the collapse potential of calcareous desert sands in kuwait, which included relative density, overburden pressure, and effect of soil disturbance or remolding. they reported the following conclusions: 1. the collapse potential decreases linearly with the relative density. 2. the collapse potential increases with the applied pressure at a decreasing rate. 3. disturbance of the ground soils results in a significantly higher collapse potential. 121 al-rawas direct measurement of the collapse potential using one-dimensional oedometer or consolidometer test, the most common test, have been conducted by several researchers as follows: 1. double-oedometer test (jennings and knight 1975) 2. single specimen collapse test (houston et al. 1988) and astm d5333 (astm 1993) 3. single point, multiple specimen test (noorany 1992). table 3. reported criteria for identification of collapsing soila (after das 1995). investigator year criteria denisov 1951 coefficient of subsidence: k = void ratio at liquid limit / natural void ratio k = 0.5-0.75: highly collapsible k = 1.0: noncollapsible loam k = 1.5-2.0: noncollapsible soils clevenger 1958 if dry unit weight is less than 12.6 kn/m3, settlement will be large; if dry unit weight is greater than 14.1 kn/m3, settlement will be small. priklonski 1952 kd = (natural moisture content – plastic limit) / (plasticity index) kd < 0: highly collapsible soils kd > 0.5: noncollapsible soils kd > 1.0: swelling soils gibbs 1961 collapse ratio, r = saturation moisture content / liquid limit this was presented graphically. feda 1964 kl = (wo/sr) – (pl/pi) where wo = natural water content, sr = natural degree of saturation, pl = plastic limit, and pi = plasticity index. for sr < 100%, if kl > 0.85, it is a subsident soil. benites 1968 a dispersion test in which 2 g of soil are dropped into 12 ml of distilled water and specimen is timed until dispersed; dispersion times of 20 to 30 s were obtained for collapsing arizona soils. handy 1973 iowa loess with clay (<0.002 mm) contents: 16%: high probability of collapse, 16-24%: probability of collapse, 24-32%: less than 50% probability of collapse, >32%: usually safe from collapse a modified after lutenegger and saber (1988) jennings and knight (1975) suggested a procedure using the double-oedometer for determining collapse potential by taking an undisturbed specimen at natural moisture content and placing it in a consolidometer ring. the specimen is then progressively loaded up to a pressure of 200 kpa. at this pressure, the specimen is flooded with water and left for 24 hours, and the consolidation test is then carried on to its normal maximum loading limit. figure 3 shows the stages of the collapse potential test. the collapse potential (cp) is then defined as: )3(%100 e1 ∆e h ∆h cp o c o ⋅ + == 122 state-of-the-art review of collapsible soils figure 3. typical collapse potential test result (after clemmence and finbarr 1981). where ∆h is the change in height of the specimen upon flooding, ho is the original height of the specimen, ∆ec is the change in void ratio of the specimen upon flooding and eo is the void ratio before flooding. the collapse potential is only a guide to the collapse which may be encountered. they also suggested a classification of the potential severity of collapse based on the collapse potential as shown in table 4, which classifies soils with collapse potential greater than 1% as metastable. however, in the united states, collapse values exceeding 2% are regarded as indicative of soils susceptible to collapse (lutenegger and hallberg 1988). table 4. potential severity of collapse (after jennings and knight 1975). collapse potential (%) severity of problem 0 – 1 no problem 1 – 5 moderate trouble 5 – 10 trouble 10 – 20 severe trouble > 20 very severe trouble houston and houston (1997) compared the three common laboratory tests (single specimen test, double oedometer test, and single point, multiple specimen test) based on three case studies and reported that: 123 al-rawas 1. the advantage of the single specimen test is that more useful data is obtained from the specimen. however, it is not recommended to characterize a soil with just one test specimen. 2. there is no need to test a dry sample in the double oedometer test. 3. the single point, multiple specimen test follows the actual path postulated for the field. 6. field tests field tests are frequently used to identify collapsible soils. a very simple field test is the “sausage” test (clemence and finbarr 1981). a block of soil of about 500 cm3 is taken from the test trial pit and broken into two pieces, and each is trimmed until they are approximately equal in volume. one specimen is then wetted and molded in the hands to form a damp ball. the volume of this ball is then compared with the volume of the undisturbed specimen. if the wetted ball is obviously smaller, then collapse may be suspected. this test is only a guide as to whether or not a soil can collapse. plate load tests are the most common field tests for the evaluation of allowable pressures under foundations. these tests are normally conducted near the ground surface. in this test, the water is introduced to the loaded soil and the resultant displacement due to wetting is recorded. the bearing plate settlement values for the same load intensity and soil conditions depend on their dimensions as indicated in the literature. it was reported that the former ussr building codes (reznik 1992) specify that field test loading may be performed in open pits on circular rigid plates with areas of 600, 2500, and 5000 cm2. the results of bearing plate tests are shown in the form of plate load-settlement curve (figure 4) where the proportionality limit (ppr) on this curve is accepted by the soviet engineers as the safe bearing capacity for foundations. figure 4. diagram illustrating commonly used graphical construction for selecting a proportionality limit using a load intensity-bearing plate settlement curve. po and ppr = values of overburden pressure and proportionality limit; εo and εpr = corresponding bearing plate settlements. 124 state-of-the-art review of collapsible soils the advantages of plate load test include the minimization of soil sample disturbance, larger volume of soil being tested, and the test followed the actual field situation. however, difficulties in extrapolating the plate load test to prototype foundations normally preclude the estimation of settlement from field plate load test on collapsible soil (houston and houston 1997). recent advances in field tests have eliminated the shortcomings of plate load test (houston et al. 1995). collapsible soils may also be determined in the field using the cone penetration test (cpt) results (reznik 1989). rollins et al. (1998) carried out cpt at six field locations in nephi, utah (usa) according to the astm d-3441-86. they found that the tip resistance (qc) of the soil at its natural moisture content (w = 7 % to 10 %) was typically between 3000 and 5000 kpa, but decreased to between 1,000 and 2,000 kpa for the wetter soil profile. 7. estimation of collapse settlement collapsible soils exhibit differential settlements due to differential wetting and their heterogeneity in nature, which results in structural damage and distress to structures. the procedure for estimating collapse settlement based on laboratory results is given below. laboratory tests results of soil response to wetting are necessary for estimating the collapse settlement at a particular site. jennings and knight (1975) proposed a method for calculating collapse settlement of a soil for design purposes using the results of a double oedometer test. in this test, two identical undisturbed samples prepared with minimum disturbance (normally block samples cut by hand) are used. the two samples are fitted into the oedometer rings and placed in the oedometer under a light 1 kpa seating load for 24 hours. after 24 hours, one of the samples is saturated by flooding with water, while keeping the other sample at its natural moisture content. both samples are left for a further 24 hours. if the soaked sample has swelled it is possible that either it is of an expansive type or that a rebound effect is experienced. most collapsing soils of a sandy character will show little or no change during this 24-hour soaking period. the test is then carried out in the same manner as the standard consolidation test. the e-log p graphs for both samples are plotted as shown in figure 5. the overburden pressure (po) is calculated and a vertical line corresponding to this pressure is drawn figure 5. the preconsolidation pressure (pc) is determined from the e-log p curve of the soaked sample and a vertical line corresponding to this pressure is drawn figure 5. it can be observed that the initial void ratios of the samples are not identical after the first 24 hours of loading, and that the two curves do not start from the same point. for the normally consolidated case in which (pc/po) is equal to 0.8-1.5, the compression is considered to take place on the virgin curve and the natural moisture content curve is adjusted to the (eopo) point ordinarily associated with normally consolidated soils as shown in figure 5. if the loading is increased to ∆p, then the unit settlement (mm/mm) for the soil, without changes of natural moisture content will be )4()e1/(∆e o+s if the applied loading remains constant and the soil increases in water content, then the unit additional settlement will be )5()e1/(∆e oc + if these values are used with various selected layers in the profile, the total settlement under both conditions may be calculated. it should be noted that if ∆p is small, then the accuracy of the estimates will be less. for the over-consolidated case (pc/po > 1.5), the adjustment to the curve largely follows the ordinary settlement computation practices as shown in figure 6. the only difference between the two cases lies in the determination of the point (eopo). jennings and knight (1975) examined several practical cases where 125 al-rawas collapse settlement had been recorded. they found that the agreement between the observed and predicted collapse settlements was good. figure 5. double oedometer curves and adjustments for a normally consolidated soil (after jennings and knight 1975). clemence and finbarr (1981) recommended the performance of field tests whenever possible due to the variety of mechanism supporting collapsible soils, and to check the laboratory analysis and the efficiency of the wetting technique used. however, field tests are expensive and time consuming. estimated collapse settlement based on laboratory results may not be realized in the field. for example, zhang and zhang (1995) reported that in china, the actual field collapse settlements are only 1/7 of the estimated fullwetting collapse. the most likely explanation for this is that when a soil is only partially wetted, only a portion of the full collapse potential is realized (houston 1996). 8. stabilization of collapsible soils there are several methods that can be used to minimize or eliminate the collapse of a particular soil. the choice of the appropriate method depends on the depth of the collapsing soil, type of structure to be constructed, and the cost and practicality of the method. these methods include 1. soil replacement (anayev and volyanick 1986) 2. prewetting (houston and houston 1997; hansen et al. 1989) 3. controlled wetting (bally and oltullesen 1980) 4. moisture control (mackenchinie 1980) 5. compaction control (rollins and rogers 1994; cintra et al. 1986) 6. chemical stabilization or grouting (clemence and finbarr 1981; pengelly et al. 1997) 7. heat treatment (bell and bruyn 1997) 126 state-of-the-art review of collapsible soils figure 6. double oedometer curves and adjustments for an overconsolidated soil (after jennings and knight 1975). these methods are briefly described in the following paragraphs: 8.1 soil replacement a simple solution is to excavate to the required depth and remove the collapsible soil. the removed soil can be compacted and used as the foundation soil. such technique is commonly used particularly when collapsible soil occurs at shallow depth (anayev and volyanick 1986). the replaced soil should be compacted to a density of 95-100% (aashto specifications). jennings and knight (1975) suggested that the soil should always be compacted at a moisture greater than 2% less than the optimum. 8.2 prewetting prewetting means flooding or wetting the soil which is expected to exhibit collapse upon saturation before the structure is built, so that soil collapse will be minimized after the structure is built (houston and houston 1997; gibbs and bara 1967; and hansen et al. 1989). wetting the soil can be achieved through ponding or trenches and boreholes. although prewetting is useful for canals and roadways where the induced loads are small, prewetting without preloading is not sufficient to prevent future foundation settlement. prewetting causes the soil to collapse under its existing overburden pressure. therefore, additional loads imposed by the foundation are not compensated for and will result in additional settlement (rollins and rogers 1994). 8.3 controlled wetting controlled wetting is similar to prewetting except that it is performed after the structure is in place. the quantities of water should be approximately measured and added in increments. this method is also 127 al-rawas 128 used once a structure exhibit some damage or tilt due to differential settlement. the added water should be introduced in a carefully-monitored manner to correct the tilt (bally and oltullesen 1980). 8.4 moisture control this method purports to prevent water ingress into the ground. the measures that can be used to control wetting include: (a) controlling water irrigation, (b) placing landscaping in watertight planter boxes, (c) restricting landscape vegetation adjacent to structure, (d) placing pavement or buried geomembranes around the perimeter of the structures, (e) placing effective surface and buried drainage systems, (f) informing occupants of buildings of the problems associated with collapsible soils. 8.5 compaction control one of the most practical and effective methods of minimizing soil collapse is by the use of compaction. compaction has been used for both shallow and deep collapsible soils. rollins and rogers (1994) pointed out that this method: (a) decreases the amount of collapsible soil in the zone of significant stress; (b) increases the depth to which water must percolate before it reaches collapsible materials; and (c) decreases the induced stress to which the collapsible soil is subjected. all of the above improve the soil properties and its engineering performance. in southern california (usa), collapsible soil deposits of 6 and up to 10 m deep are frequently removed and recompacted (houston and houston 1997). however, the compaction process is expected to be effective only up to about 5 m depth, with the greatest improvement in the upper 3 m (rollins and rogers 1994). if sufficiently large weights are dropped from sufficiently great heights, then the effectiveness can extend some what deeper (pengelly et al.1997).compaction can be achieved by use of rollers, displacement piles, heavy tamping (dynamic compaction), and vibration (vibroflotation or deep blasting). these methods of compaction are briefly discussed as follows. (a) rollers – rollers are used to compact soils with or without water (jones and van alphen 1980 and cintra et al. 1986). in this method, the soil is removed to the required depth, stockpiled, and then compacted in place in layers. (b) displacement piles compaction by displacement piles involves the driving of displacement piles (i.e. steel pile or precast concrete) and then withdrawing the piles and backfilling the holes with soil. densification of the surrounding soils can occur during the driving and backfilling (abelev 1975; and bally and culitza 1987). (c) heavy tamping (dynamic compaction) compaction by heavy tamping has been used to densify the collapsible soils by dropping very heavy weights, up to 30 tons, from great heights, up to 40 meters, into the soil (lutenegger 1986; rollins and kim 1994; and pengelly, et al. 1997). the weight upon hitting the ground surface imparts its energy into the soil, creating a densifying effect immediately around and to a depth below the weight. it has also been used to treat subgrade profiles consisting of collapsible alluvial materials for highway projects in new mexico (lovelace et al. 1982). bell and bruyn (1997) indicated that if loess contains a relatively high carbonate content, it may be difficult to achieve the desired results with dynamic compaction. (d) vibration (vibroflotation or deep blasting) compaction also has been achieved by vibration either by vibroflotation or deep blasting. vibroflotation involves jetting a vibrating probe into place and gravel or sand is dumped alongside the probe as it is withdrawn (lovelace et al. 1982). deep blasting is used to break down the structure of the soil, so it will densify thoroughly under its own weight (minkov et al. 1981). in both vibrating techniques, soil has been wetted beforehand. state-of-the-art review of collapsible soils 129 8.6 chemical stabilization or grouting chemical stabilization by additives such as sodium silicate and calcium chloride has been tried for many years with various degrees of success. the method develops cementation within the soil structure and thus it resists collapse when wetted. penetration of chemical solutions into the desired depth is essential for the success of the operation. the method is most applicable to fine sand deposits. the advantage of grouting is that it can be used after a structure is already in place. houston and houston (1997) pointed out that grouting provides soil improvement by one or more of the three following mechanisms: (i) if the grout viscosity is low enough and the soil permeability is high enough, the grout simply permeats into the soil and greatly strengthens and stiffens it. (ii) if the grout viscosity is high and the soil permeability is low, the grout bulb compresses and densifies the surrounding soil. this process is called compaction grouting. (iii) the third mechanism can be called soil reinforcement. if enough grout is put into the ground at enough locations and depths, then the stiff grouted zones will tend to carry the overburden and structural loads while loose zones will be unloaded to some extent. silicates stabilization is generally costly. however, it has been used successfully in the united states and other countries (pengelly et al. 1977). the injection of sodium silicate solution has been used extensively in the former soviet union and bulgaria. field and laboratory tests conducted in the former soviet union indicated that prewetting with a 2% sodium silicate solution can significantly decrease the compressibility and increase the strength of collapsible loessial soil deposits (sokolovski and semkin 1984). this method is used for both dry and wet collapsible soils that are expected to subside under the added weight of the structure to be built. this method consists of three steps: (i) injection of carbon dioxide for removal of any water present and preliminary activation of the soil. (ii) injection of sodium silicate grout. (iii) injection of carbon dioxide to neutralize the alkali. field tests on noncarbonate-type sandy soils pretreated with carbon dioxide have shown strength increase of 20-25% (clemence and finbarr 1981). the injection of ammonia alone on wet soils has been used. however, the effectiveness of ammonia is much less than that of sodium silicates. moreover, ammonia is also hazardous to use. the use of cement to reduce the collapse potential was successfully attempted. ismael et al. (1987) showed that the use of cement as an additive in small quantities of 5% resulted in a significant decrease in the collapse potential which did not exceed 0.5%. lime and bitumen emulsions have been used to stabilize loess soils, particularly in relation to road construction (bell 1993). phosphoric acid has been used in new zealand for stabilizing loess soil (evans and bell 1981). 8.7 heat treatment bell and bruyn (1997) reported on the use of heat treatment of loess in south east europe and russia by burning gas and fuel oil in pressurized boreholes. the boreholes are closely spaced and temperatures are generated up to 1000 °c , producing a stabilized soil column with a diameter of 1.5 2 m. 8.8 evaluation of treatment methods comparative studies on the effectiveness and economics of various treatment methods were reported in the literature. for example, rollins and rogers (1994) conducted a comparative study at a site located in nephi, utah (u.s.a.) to evaluate the cost and effectiveness of various treatment methods under field al-rawas 130 conditions using six full-scale tests on 1.5 m square footings. treatment methods included: (1) prewetting with water; (2) prewetting with a 2% sodium silicate solution; and (3) partial excavation and replacement with compacted granular fill; (4) dynamic compaction on dry soil; and (5) dynamic compaction on prewet soil. soil improvement was evaluated using double oedometer testing on undisturbed samples along with cone penetration tests and pressuremeter tests. the soil profile was generally composed of clayey sandy silt (cl-ml). the natural water content was generally between 7% and 10% while the liquid limit was about 22% and the plasticity index was about 5%. the grain size distribution of the soil typically consisted of 30% sand, 60% silt and 10% clay. the settlement predicted by oedometer testing and the measured settlement for various methods is summarized in table 5. it was found that the sodium silicate and dynamic compaction methods were the most effective methods in reducing the settlement of collapsible soils from more than 250 mm to less than 25 mm (table 5). but they were more expensive than the other methods. table 5: comparison of predicted and measured collapse settlement for various treatment methods (after rollins and rogers 1994). predicted collapse settlement after loading measured settlement after loading test cell treatment method before treatment (mm) after treatment (mm) collapse (mm) creep (mm) 1 no treatment 267 n/a 282 12 2 prewetting with water 270 300 243 12 3 prewetting with sodium silicate 270 32 27 9 4 partial excavation and replacement with fill 267 183 114 9 5 dynamic compaction at natural moisture 254 31a 125b 3 14 6 dynamic compaction after prewetting 396 15 11 18 a = below drop, b = between drop. rollins and rogers (1994) also presented table 6, which gives the advantages and limitations of various treatment methods. similar results on the success of using compaction were reported by souza et al. (1995) who showed that compaction can reduce collapse settlement of about 87% and increase allowable load of 110% based on their field plate load tests in brazil. it should be noted that more than one method can be used in a particular situation such as prewetting and compaction. 9. foundation design the choice of a particular foundation design depends primarily on the depth of the collapsible soil encountered, the magnitude of collapse, and the economics of the design method. in cases where the collapsible soil layer extends to a shallow depth (approximately 1.5 to 2 m), the use of continuous strip footings may provide a more economical and safer foundation than isolated footings. if the footing area becomes greater than 50% of the entire area of the building, then a mat foundation should be constructed for the entire foundation (clemence and finbarr 1981). the soil may be moistened and recompacted by heavy rollers before placing the foundations. this process is effective in eliminating settlements due to overburden pressure and additional loads. state-of-the-art review of collapsible soils 131 table 6. comparison of advantages and limitations of various treatment methods (after rollins and rogers 1994). advantages limitations (a) prewetting with water (test cell 2) low cost ease of application excessive settlement without preloading overexcavation failure to densify surface layers differential settlement likely (b) prewetting with sodium silicate (test cell 3) dramatic reduction in collapse settlement development of permanent cementation reduction in hydraulic conductivity significant in creep settlement potential for use as a remedial measure higher cost ($8-$12/cu yd) limited experience base treatment depth limited to less than 2 m (c) partial excavation and replacement with fill (test cell 4) relatively low cost ($4-$8/cu yd) ease of application extensive contractor experience with the method reduction of induced stress on collapsible soil minimum settlement for small volumes of water minimization of differential settlement treatment of surface zones only excessive settlement following wetting of deep zones. (d) dynamic compaction at natural moisture (test cell 5) dramatic reduction in collapse settlement decrease in hydraulic conductivity improvement to significant depths (>5m) higher cost ($8-$10/cu yd) potential for damage due to vibrations nonuniformity of treatment less contractor experience with method (e) dynamic compaction after prewetting (test cell 6) significant decrease in collapse settlement increased compaction efficiency prior to liquefaction reduction in level of vibrations greater uniformity of densification decrease in hydraulic conductivity improvement to significant depths (>5m) higher cost ($9-$11/cu yd) increase in creep (long-term) settlement potential for liquifaction when water content is high difficult to withdraw weight after drop drying time following treatment may be excessive less contractor experience with method difficult to measure improvement in cases where the soil layer susceptible to wetting extends to several meters (deeper than 3 to 5 m), deep foundations (piles and drilled piers) may be required to transmit foundation loads to a suitable firm strata below the collapsible soil layer. the design of piles and drilled piers must take into consideration the al-rawas 132 effect of negative skin friction resulting from the collapse of the soil structure and the associated settlement of the zone of subsequent wetting (das 1995). precollapsing techniques may be used to cause collapse before construction of foundations. such techniques include vibroflotation and ponding (flooding). however, it should be noted that even with such precollapsing techniques additional settlement may occur due to the difficulty of saturating all the collapsing soil encountered. 10. summary and conclusions the following points were drawn from this study 1. collapsing soils undergo a reduction in volume due to wetting alone or wetting and loading acting together. aeolian deposits are the most naturally occurring collapsing soil. collapsing soils are generally characterized by their loose and open structure binded by cementing agents, which upon wetting, become weak and may dissolve causing collapse. 2. collapse criteria based on index parameters such as dry density and degree of saturation were proposed in the literature for identification and classification purposes. such criteria should be used only as indicators since reliance on them can be misleading. 3. double oedometer test is widely used for estimating the collapse potential, which can be used to calculate soil collapse settlement. plate load test is the most common field test for the evaluation of allowable pressure under foundations. 4. several treatment methods were proposed for minimizing the collapse of soils such as soil replacement, prewetting, compaction control and chemical stabilization or grouting. the choice of such methods depends on the ground conditions, type of structure to be constructed, practicality and economics of the method. compaction control was the most practical and effective treatment method. 5. shallow foundations (continuous strip footings and mat foundation) are recommended when collapsing soil extends to shallow depth (1.5 to 2 m). in cases where collapsing soil extends to several meters (deeper than 3 to 5 m), deep foundations (piles and drilled piers) are recommended. 11. references abelev, m.y. 1975. compacting loess soils in the ussr. geotechnique, 25: 79-82. aitchison, g.d. and donald, i.b. 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dynamic compaction of collapsible soils. journal of geotechnical and geoenvironmental engineering, asce, 124: 699-708. rollins, k.m. and kim, j.h. 1994. u.s. experience with dynamic compaction of collapsible soils. asce special geotechnical publication no. 45, new york, 26-43. sokolovski, v.e. and semkin, v.v. 1984. chemical stabilization of loess soils. journal of soil mechanics and foundation engineering, 4: 8-11. souza, a., cintra, j.c.a. and vilar, o.m. 1995. shallow foundations on collapsible soil improved by compaction. unsaturated soils, proceedings of the first international conference on saturated soils, sept. 6-8, paris, e.e. alonso and p. delage, eds., 2, belkema press, 1017-1021. state-of-the-art review of collapsible soils tadepalli, r., rahardjo, h. and fredlund, d.g. 1992. measurement of matric suction and volume changes during inundation of collapsible soils. geotechnical testing journal, 15: 115-122. zhang, w. and zhang 1995. development of loess engineering properties research in china. unsaturated soils, proceedings of the first international conference on saturated soils, sept. 6-8, paris, e.e. alonso and p. delage, eds., belkema press. received 30 january 2000 accepted 17 june 2000 135 çáêñèé çáþçèáé ááåèæø : ãñçìúé æ � contents introduction 116 identification and classification 119 laboratory tests 121 field tests 124 estimation of collapse settlement 125 stabilization of collapsibles soils 126 soil replacement 127 prewetting 127 controlled wetting 127 moisture control 128 compaction control 128 chemical stabilization or grouting 129 heat treatment 129 evaluation of treatment methods 129 foundation design 130 summary and conclusions 132 references 132 introduction the following symbols are used in this paper: ci=indicator; identification and classification table 1. a guide for collapse settlement based on critical degree of saturation (after jennings and knight 1975). soil critical degree of saturation, (sr)crit. (%) laboratory tests table 4. potential severity of collapse (after jennings and knight 1975). collapse potential (%) severity of problem trouble 10 – 20 > 20 field tests estimation of collapse settlement stabilization of collapsible soils chemical stabilization by additives such as sodium silicate and calcium chloride has been tried for many years with various degrees of success. the method develops cementation within the soil structure and thus it resists collapse when wetted. penetratio bell and bruyn (1997) reported on the use of heat treatment of loess in south east europe and russia by burning gas and fuel oil in pressurized boreholes. the boreholes are closely spaced and temperatures are generated up to 1000 (c , producing a stab comparative studies on the effectiveness and economics of various treatment methods were reported in the literature. for example, rollins and rogers (1994) conducted a comparative study at a site located in nephi, utah (u.s.a.) to evaluate the cost a foundation design electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 53-60 © 2001 sultan qaboos university influence of aging conditions on fatigue fracture behaviour of 6063 aluminum alloy rafiq ahmed siddiqui, saeed ali alaraimi and ahmet turgutlu department of mechanical and industrial engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. 6063تأثير الظروف الزمنية على سلوك كسر إجهاد سبيكة األلومنيوم رفيق أحمد صديقي ، سعيد علي العريمي و إحمت تورغوتلو بإستخدام al-mg-si( 6063( تمت في هذه الدراسة المعالجة الحرارية لسبيكة من األلمونيوم والمغنيسيوم والسيليكون : خالصة وقد تم إختيار عدد الدورات الضرورية إلحداث . فضل درجة حرارة للمعاملة الحرارية للسبيكة درجات حرارة أقل و أعلى من أ وتم تقييم سطح الكسر للسبيكة تحت ظروف زمنية مختلفة بواسطة . كسور إجهاد تحت جهد ثابت كمعيار على مقاومة اإلجهاد ور اإللكترونية وجود سطوح شقوق مع خطوط كما وأكدت الص . الميكروسكوب البصري والميكروسكوب اإللكتروني الكاشف ووجد بأن أفضل زمن ودرجة حرارة للتقسية . ولوحظ بأن زمن ودرجة حرارة السبيكة تنتج أشكال كسور مختلفة. محددة لإلجهاد بيكة نتيجة هذا ويمكن أن تعزى الزيادة في خاصية الكسور اإلجهادية للس. كيلفن460 ساعات مع درجة حرارة 5 إلى 4يقع ما بين زيادة مدة التقسية إلى وجود ظاهرة اإلنتشار المدعم بالفراغات للحبيبات الصغيرة الناتجة عن المعاملة الحرارية، أو إلى تثبيت وعلى أية حال، فإن قلة مقاومة اإلجهاد للمدد الزائدة للسبائك يمكن أن . حركات اإلزاحة بواسطة الترسيب الناتج خالل مدة المعاملة . إلى تشكل حبيبات كبيرة من الحبيبات الصغيرةتعزى abstract: aluminum magnesium silicon (al-mg-si) 6063 alloy was heat-treated using under aged, peak aged and overage temperatures. the numbers of cycles required to cause the fatigue fracture, at constant stress, was considered as criteria for the fatigue resistance. moreover, the fractured surface of the alloy at different aging conditions was evaluated by optical microscopy and the scanning electron microscopy (sem). the sem micrographs confirmed the cleavage surfaces with well-defined fatigue striations. it has been observed that the various aging time and temperature of the 6063 al-alloy, produces different modes of fractures. the most suitable age hardening time and temperature was found to be between 4 to 5 hours and to occur at 460 k. the increase in fatigue fracture property of the alloy due to aging could be attributed to a vacancy assisted diffusion mechanism or due to pinning of dislocations movement by the precipitates produced during aging. however, the decrease in the fatigue resistance, for the over aged alloys, might be due to the coalescence of precipitates into larger grains. keywords: age hardening, fatigue, fracture, precipitation hardening. 1. introduction a luminum alloys have gained a lot of importance due to good mechanical and corrosion resistance properties. aluminum alloys, of type 6063, which consist of aluminum magnesium, and silicon, are used in several industrial applications (thornton and colangelo, 1985). the addition of magnesium and silicon improves the castability as well as corrosion resistance of these alloys (helby, 1993). alloy 6063 is produced at different tempered conditions, depending on the application required (hunsicker,1967). the tempered conditions (i.e., the solutionizing temperature, aging temperature and aging time) are responsible for the wide range of the mechanical properties exhibited by this alloy. okorafor (1991) studied the effect of 3.5% nacl solution on corrosion resistance properties of under aged, peak aged and over aged specimen by means of weight loss measurement and a potentiokinetic polarization technique. the results 53 siddiqui, al-araimi and turgutlu obtained showed that the weight loss and the rate of weight loss were functions of both heat treatment and exposure time. zajac et al (1993) investigated the hot deformation behavior of aa 6063 and aa 6005. it was found that addition of small amounts of manganese significantly helps in homogenizing and transforming the plate like beta alfesi phase to more rounded alpha alfesi phase, which increases the ductility of the material. musulin and celliers (1990) confirmed that the addition of manganese also increases quench sensitivity of the alloy even when the cooling rate is as low as 50 oc per minute. it was found that the addition of manganese accelerates the transformation of beta alfesi phase to a favorable alpha alfesi phase. fatigue crack propagation in crystalline material is normally divided into two successive stages as investigated by jiang et al (1990a ). it was concluded from their experimental work that in stage i a crack develops along the active slip plane and normal to the direction of applied stress. in stage ii, the propagation of the crack begins in under aged 6063 al-mg-si alloys. the alloy exhibits heterogeneous deformation and slip bands are formed only by one slip system. there is a strong tendency for single slip system activation, which can be attributed to the high volume fraction and small size of gp zone and low content of dispersoids. jiang et al (1990 b) studied the effect of different aging conditions on fatigue fracture behavior of al-mg-si alloy with different chemical composition and dispersoid contents. they found that the dispersoid phase could alter the mode of fatigue fracture by influencing the deformation uniformity of the alloy. the 6063 a-a system used for vertical axis wind turbine blades was investigated by van den avyle and sutherland (1988). fatigue analysis for typical materials includes two types of data (a) stress versus number of cycles (s-n curve); and (b) fatigue crack growth rate. the s-n experiment was conducted on a-a 6063 extruded material using 100 bend specimens cycled at fine alternating stress amplitudes. the cyclic crack growth rates were measured using three loading rates. figure 1. standard fatigue specimen according to bs3518 specification in mm. although considerable work has been conducted on the effect of precipitation, fatigue resistance and age-hardening parameters of 6063 al-si-mg alloy ( jiang et.al1990 a, jiang et al 1990 b, vanden avyle and sutherland 1988 ), there is still a need to investigate the combined effect of time and temperature on the fatigue properties. 2. experimental procedure extruded bars made from 6063 a-a were produced by oman national aluminum company from continuously cast billets. chemical composition is given in table 1. fatigue test specimens were prepared from extruded profiles in the college of engineering workshop at sultan qaboos university, according to the bsi 3518 standard specification, as shown 54 influence of aging conditions on fatigue fracture behaviour in figure 1. solution heat treatment of the prepared specimens was conducted by soaking them at 793 k for 2.5 hours in a furnace followed by quenching in cold water to preserve the super saturated solid solution al-mg-si alloy at room temperature. all the specimens were then kept in the deep freeze zone of the refrigerator to prevent natural aging that might occur at room temperature. the age hardening treatments were conducted in a pick stone oven at temperatures 320k, 340k, 360k, 380k, 400 k, 420 k, 440 k, 460 k, 480 k, 500k, 520k, 540k and 560k table 1: chemical composition of 6063 al-alloy. elements al si mg fe mn cu wt% balance 0.475 0.537 0.096 0.078 0.085 2 3 4 5 300 350 400 450 500 550 temperature,k n um be r o f c yc le s x 10 0 00 0 2h 3h 4h 5h 6h figure 2. effect of aging temperature at constant time on fatigue resistance properties of 6063 a-a. using different intervals i.e. 2h, 3h, 4h, 5h and 6h. the fractured surfaces of the specimens were examined using light and electron microscope. cyclic fatigue tests were conducted at room temperature, using the every denson fatigue-testing machine. constant applied stress of 339 kpa was used until fracture occurred. the number of cycles required to fracture the specimen was counted and taken as a criterion for the fatigue resistance. 2 3 4 5 1 2 3 4 5 6 7 time,hour n um be r o f c yc le s x 10 0 00 0 320k 340k 360k 380k 400k 420k 440k figure 3. effect of aging time at constant temperature (320-440 k) on fatigue resistance properties of 6063 a-a. 55 siddiqui, al-araimi and turgutlu 0 1 2 3 4 5 1 2 3 4 5 6 7 time,hours n um be r o f c yc le s x 10 0 00 0 460k 480k 500k 520k 540k 560k figure 4. effect of aging time at constant temperature (460-560 k) on fatigue resistance properties of 6063 a-a. 3. results and discussion the effect of precipitation heat treatment time and temperature on the fatigue fracture behavior of 6063 a-a is shown in figures 2-4. it is observed that, as the aging temperature increases, an increase in number of cycles to fail at constant stress is noticed (figure 2). further increase in temperature causes a sharp increase in number of cycles to fail when heat-treated between 360 k–460 k. any further increase in precipitation heat treatment temperature would cause a decrease in the number of cycles to fail at constant stress in the 6063-aluminum alloy. from figure 2 it is confirmed that the best aging temperature is 460 k when the alloy can have maximum fatigue resistance property. figures 3 and 4 represent the effect of variable time on the fatigue fracture behavior of 6063 a-a at constant temperature and constant stress. it is clear from the experimental results (figures 3-4) that the number of cycles required to fail increases with the increase in precipitation hardening time. however, if the heat treatment is carried out for more than 5 hours at higher temperature, the 6063 a-a will fail earlier. it is observed from figures 2-4 that the best time at which the 6063aluminum alloy can be made more resistant to cyclic loading at constant stress is between 4 to 5 hours. a further increase in age hardening time will cause an earlier failure in the al-alloy. it is evident from figures 2-4 that the best precipitation hardening time and temperature for 6063 aluminum alloy is between 4 to 5 hours at 460 k. figures 5 and 6 show the fatigue cracks in a partially and completely broken specimen. the crack path is irregular and gives an indication of a cleavage crack. most of the partially broken specimens show the same pattern of crack initiation, propagation and termination in peak aged and over aged alloy. the photographic view of the completely broken section of 6063 alloys after fatigue test, is shown in figure 6. the irregular crack pattern and crack surface indicates less ductility in the material and fracture appears almost like brittle fracture. an sem micrograph of 6063 aluminum alloy fractured surface is shown in figure 7 when aged for 3 h at 370 k. the photomicrograph shows a number of plateaus that are at different elevations with respect to each other. these plateaus are joined together by a wall which contains fatigue striations. at certain places some cracks are also observed along with the striations. figure 8 represents a fracture surface of 6063 a-a when heat-treated at 480k for a period of 5 hours. the micrograph shows fatigue striations which are in step like formation. the alloy was heated to peak aged temperature, which has reduced the ductility of the alloy, the surface exhibits a brittle pattern along with widely spaced striations that are nearly parallel to the grain boundary. these striations seemed to be formed by cleavage fracture. 56 influence of aging conditions on fatigue fracture behaviour the same specimen when observed at other positions in sem also shows a cleavage fracture pattern. the fracture was initiated on many parallel cleavage planes (figure 9). the cleavage surface also shows fine cleavage steps in the photomicrograph. the lower left hand side of the micrograph shows some parts of the material that have failed with inter-granular behavior. figure 10 represents a view of low cycle fatigue fractured surface. the specimen was aged for 6 h at 560k. the photomicrograph shows well defined fatigue striations that are clearly visible in sem. it also shows secondary cracks along with striations at a few places within the grains. few cleavage steps are visible which also confirms that the ductility of the 6063 alloys is reduced due to over aging. figure 5. crack initiation and propagation in 6063 al-alloy, aged for 3 h at 350 k. figure 6. fracture surface of 6063 al-alloy, aged for 5 h at 460 k. figure 7. fatigue striations in 6063 al-alloy, aged for 3 h at 370 k. 57 siddiqui, al-araimi and turgutlu from the is very much depe figure 8. figure 9. figure 10. fracture surface in alalloy, aged for 6 h at 560 k. present investigation, it is concluded that the fatigue fracture behavior ndent on the type, size distribution and amount of the precipitated particles produced during precipitation heat treatment (time and temperature). in the under aged (360 k) and peak aged (460480 k) conditions, the precipitates are heterogeneously dispersed. the heterogeneous dispersion behavior of the precipitates is very complex and it depends on many factors such as boundaries, precipitation behavior, heating time and temperature, etc. (anderson, 1959). cleavage fracture with fatigue striations, aged for 5 h at 480 k. cleavage fracture, aged for 5 h at 480 k. 58 influence of aging conditions on fatigue fracture behaviour figures 2 to 4 confirm that the fatigue resistance behavior of the alloy increases with the increase in aging temperature and time. the alloy gains its maximum resistance to fatigue failure at 460k when aged between 4 to 5 hours. further increase in aging time and temperature causes a reduction in the number of cycles to fail. the initial increase in the number of cycles to fail between 320k 460k could be explained by vacancies assisted diffusion mechanism (onurlu and tekin, 1994). in the precipitation heat treatment process, during quenching of the alloy from 793k to room temperature, a super-saturated solid solution is formed which contains a large number of vacancies. at room temperature, as well as at higher temperatures, these vacancies are highly mobile and produce gp zones, which are very rich in solute atoms. at high temperatures (460k to 480k) the density of the gp zone also increases, as a result, a distortion of the lattice planes within the zone and are extended to several atomic layers in the matrix. this distortion of lattice plane causes hindrance to the dislocations movement (jiang et.al,1990 b). therefore the fatigue resistance property of the alloy is improved in the under aged to peak aged temperature. the cond reason for the increase in resistance to fatigue fracture behavior of the alloy is due to pinning and hind angelista ,1996; jian is due to the coalescence of the precipitates into larger particles, bigger grain size steps when the alloy was over aged. references and , 26(5): a388-a390 se erance of dislocation movement by impurity atoms (blaz and ev g et.al, 1991). figure 2 to 4 also show a reduction in the number of cycles to fail in this alloy when heated for a longer period of time at higher temperatures. a decrease in the number of cycles to fail above 460 and 480k can be attributed to the coalescence of precipitates into larger particles which cause less obstacles to the movement of dislocations; hence the fatigue failure occurs in a short a period of time. 4. conclusion the fatigue resistance property of 6063 aluminum alloy is very much dependent on the precipitation hardening time and temperature. the initial increase in fatigue resistance behavior is due to an increase in density of the gp zones and distortion of lattice planes both within the zones and in the matrix. it is also due to the increase in the number of atomic impurities which cause hinderance to the dislocations movement. hence the fatigue resistance property of the alloy is improved. a decrease in the number of cycles to fail in the over aged alloy at 480k, and temperatures above and also due to annealing of defects in the lattices which cause less obstacles to the movement of dislocations. from the experimental work it is concluded that the best precipitation temperature is 460 k when 6063 aluminum alloys is aged between 4 to 5 hours. these conclusions are further supported by the sem micrographs showing mixed mode of fracture consisting of striations as well as cleavage erson, w.a. 1959. precipitation hardening aluminum base alloy, in: precipitation from solid solution, american society for metals: 150-207. blaz, l and evangelista, e. 1996. strain rate sensitivity of hot deformed al and al-mgsi alloy, materials science and engineering a, a 207: 192-201 helby, m. 1993. aluminum extrusion a flexible approach to construction, materials world, 1: 101-102. hunsicker, h.y. 1967. metallurgy of heat treatment, aluminum, american society for metals, metal park, ohio, 1: 109-161, jiang, d.m., hong, b.d. and lei, t.c. 1990 a. fatigue fracture behaviour of an under aged al-si-mg alloy. scripta metallurgica, 24: 651-654. jiang, d.m, hong, b.d. and lei, t.c. 1990 b. influence of composition and dispersoid on fatigue fracture behaviour of al-mg-si alloys, acta metallurgica sinica 59 siddiqui, al-araimi and turgutlu jiang, d.m., hong, b.d. lei, t.c., do .a. and lorimer, g.w.1991. influence of aging condition on tensile and fatigue fracture behaviour of aluminum alloy 6063, mu se in 6063 alloy and effect of quench , 951-954. alloy, corrosion prevention and control 38(6): 141-144. f material science, 29(6): 1652-1655. zaj of aluminium-mg-+++si alloys, micro rece wnham, d material science and technology; 7: 1010-1014. sulin, i. and celliers, o.c. 1990. role of mangane sensitivity in 6063. light metal proc. 119 tms annu. meet. publ. by minerals, metal and materials, metal and material soc. (tms), warrendale pa, usa okorafor, o.e. 1991. effect of heat treatment on the corrosion resistance of 6063 aluminum onurlu, s., and tekin, a. 1994. effect of heat treatment on the insoluble intermetallic phase present in an aa 6063 alloy. journal o thornton, p.a. and colangelo, v.j. 1985. fundamentals of engineering materials, prentice-hall international, pp 450-460. van den avyle, j.a. and sutherland, h.j.1988. fatigue characterization of a vawt blade material, eight asme wind energy symposium, houston, tx, usa, 22-25 january, asme, solar energy division (publication) sed , 7: 125-129 ac, s., hutchinson, b., johanson, a., gullman, l.o. and lagneborg, r. 1993.microstructure control and extrudability alloyed with manganese, journal de physique. 3(7): 251-254. ived 21 may 2000 accepted 26 november 2000 60 rafiq ahmed siddiqui, saeed ali alaraimi and ahmet turgutlu department of mechanical and industrial engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. zajac et al (1993) investigated the hot deformation behavior of aa 6063 and aa 6005. it was found that addition of small amounts of manganese significantly helps in homogenizing and transforming the plate like beta alfesi phase to more rounded alpha a references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 101-107 © 2002 sultan qaboos university 101 design of ultra fast rce photodetectors for optical communications systems joseph a. jervase and hadj bourdoucen department of information engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. email: jervase@squ.edu.om. تصميم المحسسات الضوئية لنظم االتصاالت فائقة السرعة جوزيف جرفيس وحاج بوردوسن يتمثل . التى تتحكم في نظم االتصاالت فائقة السرعة(rce) تتناول هذه الورقة الحدان األساسيان للمحسسات الضوئية : خالصة م إيجاد شكل تحليلي لكفاءة الكم تتضمن الحدود الهيكلية هـذان الحـدان في كفاءة الكم وسعة التذبذب للمحسنات المستعملة ، لقد ت .واعتمادا على النتائج التمثيلية بواسطة الحاسوب، طورت خطة للتصميم المثالي لهذه المحسسات. لتصميم المحسس الضوئي abstract: two key parameters for rce photodetectors that govern their suitability for ultrafast optical communication systems are considered. these are the quantum efficiency and the bandwidth efficiency product. a closed analytical form has been derived for quantum efficiency, which incorporates the structural parameters of the photodetector. based on the simulation results, an optimization and design procedure for these photodetectors has been developed. keywords: cavity resonators, photodetectors, photodiodes, quantum efficiency and resonantcavity-enhanced photodetectors. 1. introduction ptical photodetectors are the key components in optical communication systems. their quantum efficiency and optical bandwidth characteristics are of major importance in the design of fiber optic based data communication systems. a number of structures and design optimization techniques have been proposed in the literature to achieve high values for these two parameters (kishino, 1991), (unlu, 1992, 1995, 1998), (tan, 1995), (murtaza 1996), (tung, 1997), (jervase, 1998, 2000). one of the promising types is the resonant cavity enhanced (rce) photodetector. in the rce, the active region is placed inside a fabry-perot cavity between two mirrors made of quarter-wave stacks (qws) to allow the signal light to have more than one absorbing path inside the active region (kishino, 1991), (unlu, 1992, 1995, 1998), (tan, 1995), (murtaza, 1996), (tung, 1997), (jervase, 1998, 2000), (onat, 1998), (ozbay, 1997). the resulting structure will need only a very thin absorbing intrinsic region to achieve high quantum efficiency as well as a high speed of response. hence, rce photodiodes with quantum efficiencies close to unity can be designed. in this work, the quantum efficiency is formulated in a closed analytical form. this includes the structural parameters of the photodetector and takes into consideration the wavelength dependence of the end mirrors reflectivities and the absorption coefficient of the intrinsic region. using this formulation, an optimization and design procedure for rce photodetectors has been developed and design charts have been generated with the quantum efficiency, quality factor and frequency bandwidth as input design parameters. o mailto:jervase@squ.edu.om joseph a. jervase and hadj bourdoucen 102 2. analysis figure 1 shows the integrated device of our investigation, which is based on the system of heterojunctions in0.53ga0.47as/inp. the speed response for this type of pin structure is mainly limited by the transit time and the diffusion time of photogenerated carriers in the space charge region and the neutral regions. it is also limited by the charging and discharging time for traps at the heterojunction interfaces and by the inherent and parasitic capacitances of the structure. the last two effects can be minimized by incorporating non-absorbing lateral layers having graded heterojunctions with the active region and to have the heterojunctions and the active region depleted of any trapped charges that might be stored. in addition, the introduction of super lattice bandgap grading layers can eliminate the interface hole trapping process and consequently decrease the capacitive effect on the generated carriers. to further improve the frequency bandwidth requirements, the active region should be shortened enough to minimize the transit time of the photogenerated carriers crossing it. to reduce the device dark current, several types of junction architectures have been proposed based on the enhancement of the barrier heights at the interfaces of the ingaas active layer and the adjacent layers to decrease tunneling currents of minority carriers. pin photodetectors based on ingaas/inp have been analyzed by many researchers e.g. (bottcher, 1992) and the references therein). in fact, the typical pin photodiode configuration (dentan, 1990) has been integrated in our proposed configuration for its simplicity and ease of fabrication as well as its realistic mathematical description. si (λo/4) sio 2 (λo/4) p+ inp ningaas n+ m gaas (λo/4) alas ( λo/4) gaas (substrate) l 1 d l 2 x 0 top qws bottom qws refractive index notation n 10 n 11 n 12 n ex (n 1s ) n n ex (n 20 ) n 21 n 22 n 2s incident light sio 2 (λo /2) alas (λo/4) gaas (λo /4) n inp p+ figure 1. the rce photodetector model. the expression for quantum efficiency for the rce photodetector shown in figure 1 will be derived following a similar approach to that used in (kishino, 1991) and (jervase, 1998). this technique is based on finding the reflectivities of the top and bottom mirrors separately design of ultr fast rce photodetectors 103 and then using their values to determine the fields inside the cavity by considering the whole structure of the photodetector i.e. mirrors and cavity together. with reference to the device model shown in figure 1 for the rce photodetector, the quantum efficiency due to the power absorbed in the i-region may be expressed as follows, ( )( )( ) φ η α αα coserr1 e1er1r1 d2 21 dd 21 − −− + −+− = (1) where, [ ]{ }2121ex d)ll(2 ψψββφ ++++= (2) λ π β exex n2 = (3) λ π β n2 = (4) in the derivation of eq. 1, the pand n-regions are assumed to be transparent at the design resonant wavelength λ0=1.3µm.thus αex=0 for the material adopted in the model (inp) at this wavelength. it is apparent from eq. 1 that the external quantum efficiency depends on the design of the top and bottom qws's (r1, ψ1, r2, ψ2), the choice of the materials for the cavity (α, n, nex) and its physical dimensions (d, l1, l2) as well as the operating wavelength (λ). within the range of interest in this analysis (1.2µm < λ <1.5µm), there is no much variation in refractive indices of the different layers of the photodetector. this does not apply, however, to the iregion attenuation constant α. it has been shown in the literature that the absorption coefficient α of in0.53ga0.47as is a function of wavelength and doping (humphreys, 1985). using the experimental results in (humphreys, 1985), a nonlinear curve fitting technique has been used to obtain analytical expressions for α. with reference to eq. 1, the maximum quantum efficiency occurs when [ ] πλψλψλβλβ 2)()(d)()ll)((2 2121ex =++++ , or multiples thereof. it then follows that (kishino, 1991), (jervase, 1998), ( )( )( ) d2 21 dd 21 peak err1 e1er1r1 α αα η − −− + −+− = (5) this expression is used in a constrained optimization procedure for the design of rce photodetectors with maximum quantum efficiency. equation 5 serves as a check on the optimized values (l1, l2, d) in whether they yield the maximum quantum efficiency. the design procedure developed is summarized below: step 1: specify the resonant wavelength λ0, the quantum efficiency η, the quality factor q and the frequency bandwidth bw. step 2: select the materials for the cavity and the quarter-wave-stacks (qws’s). step 3: design the qws’s with the following guidelines: choose the number of layers n2 to achieve a reflectivity r2 at λ0 close to unity for the bottom qws. choose the number of layers n1 to achieve a reflectivity 0.6<r1<0.9 at λ0 for the top qw step 4: with the values of r1 and r2 now known, invoke a search and optimization program to determine d, l1 and l2. step 5: generate values for η for a range of wavelengths centered at λ0. step 6: for each set of d, l1 and l2, deduce fwhm and compute the quality factor and the frequency bandwidth. step 7: select the values of d, l1 and l2 that satisfy the design criteria on q, η and bw. joseph a. jervase and hadj bourdoucen 104 3. results the resonant wavelength used in this work is λ0=1.3µm. the refractive indices of the various layers of the model adopted in the analysis (figure1), are sio2(1.46), si (3.46), inp (3.20), inalgaas (3.50) and ingaas (3.73-j0.12). following the design procedure outlined earlier, 42 pairs of layers were needed to achieve a reflectivity of 0.998 at λ0. for the top qws, only one pair of layers is needed. this yields a reflectivity of 0.8. the resonance condition to achieve maximum quantum efficiency [ ] πλψλψλβλβ 2)()(d)()ll)((2 2121ex =++++ may thus be expressed for the adopted structure as )2/()( 021 λmndllnex =++ (5) where, m=1,2,3,... 1.2 1.25 1.3 1.35 1.4 1.45 1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 wavelength λ (µm) figure 2. variation of external quantum efficiency η with wavelenghth λ. figure 2 shows the variation of external quantum efficiency with wavelength using a set of generated values (d=0.1µm, l1=l2=1.465µm) in eq.1. this figure shows a dominant peak centered at λ0=1.3µm, the design wavelength. this result is physically more realistic since the proposed structure is acting as a resonant cavity filtering out all wavelengths other than λ0. the theoretical result is also in very good agreement with recently published experimental data on high-speed rce schottky photodiodes (jervase, 2000), (unlu, 1998), (onat, 1998) and high-speed si-based rce photodetectors (ozbay, 1997). with reference to figure 2, the use of the free spectral range (fsr) to the wavelength full width at half maximum (fwhm) as a measure of wavelength selectivity of detection (kishino, 1991) is no longer valid. the conventional quality factor definition used for filters design defined as the ratio of λ0 to the fwhm is more appropriate in this case as a measure of selectivity (jervase, 2000). it has been noticed that ignoring the variation of the attenuation constant α with λ results in a higher off-resonance peak for λ> λ0 and lower off-resonance peak for λ0.this is due to the fact that α monotonically decreases with λ. following a design and optimization procedure, all the sets of values obtained previously for d, l1 and l2 were used to obtain the quality factor q corresponding to every spectrum of quantum efficiency η. the objective is to obtain design charts relating the quality factor q to the maximum achievable quantum efficiency ηmax for a given structure dimensions. the joseph a. jervase and hadj bourdoucen 106 varied, quantum efficiency increases, peaks at d=0.1µm and then decreases. thus, there is an optimum value for d, which achieves maximum quantum efficiency. the bw and bwe on the other hand, decrease with increasing d. thus, for d=0.1µm, which corresponds to maximum quantum efficiency of 0.99 the bwe is 290ghz. it is worth pointing out here that the simulated values for bwe merely serve as upper limits for the bandwidth-efficiency product. in practice, other parasitic factors, such as the leakage rc, will lower the achievable values. d (µ m) figure 4. variation of efficiency η and bandwidth-efficiency product bwe with active region width d. 4. conclusion the quantum efficiency and bandwidth-efficiency product of resonant-cavity enhanced photodetectors (rce) has been formulated in closed analytical forms that incorporate device structural parameters. a search and optimization-based procedure has been developed with the quantum efficiency, quality factor and frequency bandwidth as input design parameters. design charts relating the quality factor q to the maximum achievable quantum efficiency ηmax for a given structure dimensions have also been generated. references bottcher, e.h., kuhl, d., hieronymi, f., droge, e., wolf, t. and bimberg, d. 1992. ultrafast semi-insulating inp:fe-ingaas:fe-inp:fe msm photodetectors: modeling and performance, ieee j. quantum electron., 28: 2343-2357. dentan, m. and cremoux, d.de. 1990. numerical solution of the nonlinear response of a pi-n photodiode under high illumination, j. lightwave technol., 8: 1137-1144. humphreys, d.a., king, r.j., jenkins, d., and moseley, a.j. 1985. measurement of absorption coefficients of ga0.47in0.53as over the wavelength range 1.0-1.7µm, electron. lett., 21: 1187-1189. jervase, j.a. and bourdoucen, h. 2000. design of resonant-cavity-enhanced photodetectors using genetic algorithms, ieee j. quantum electron., 36: 325-332. jervase, j.a. and zebda, y. 1998. characteristic analysis of resonant cavity enhanced (rce) photodetectors, ieee j. quantum electron., 34: 1129-1134. design of ultr fast rce photodetectors 107 kato, k. 1999. ultrawide-band/high-frequency photodetectors'', ieee trans. microwave theory tech., 47: 1265-1281. kishino, k., selim, m.u., chyi, reed, j.i., arsenault, l., and morkoc, h. 1991. resonant cavity-enhanced (rce) photodetectors'', ieee j. quantum electron., 27: 20252034. kovac, j., uherek, f., satka, a., jakabovic, j., srnanek, r., rheinlander, b., gottschalch, v., hasenohrl, s., novak, j., barna, p., barna, a. and wood, j. 1996. inalgaas-ingaas-inp rce pin photodiode for 1300nm wavelength region, iprm'96 proc., apr. 21-25, germany, pp 219-222. murtaza, s.s., nie, h., campell, j.c., bean, j.c. and peticolas, l.j. 1996. shortwavelength, high-speed si-based resonant-cavity photodetectors, ieee photon. technol. lett., 8: 927-929. murtaza, s.s., tan, i.-h., bowers, j.e., hu, e.l., anselm, k.a., islam, m.r., chelakara, r.v., dupuis, r.d., streetman, b.g., and campbell, j.c. 1996, high-finesse resonant-cavity photodetectors with an adjustable resonance frequency, ieee j. lightwave technol., 14: 1081-1089. onat, b.m., gokkavas, ozbay, m., e., ata, e.p., towe, e., and unlu, m.s. 1998. 100ghz resonant cavity enhanced schottky photodiodes'', ieee photon. technol. lett., 10: 707709. ozbay, e., saiful islam, m., onat, b., gokkavas, aytur, m.o., tuttle, g., towe, e., henderson, r.h., and unlu, m.s. 1997. fabrication of high-speed resonantcavity-enhanced schottky photodiodes, ieee photon. technol. lett., 9: 672-674. salem, a.f. and brennan, k.f. 1995. theoretical study of the response of ingaas metalsemiconductor-metal photodetectors, ieee j. quantum electron., 31: 944-953. tan, i-h., hu, e.l., bowers, j.e., and miller, b.i. 1995. modeling and performance of wafer-fused resonant-cavity enhanced photodetectors, ieee j. quantum electron., 31: 18631875. tung, h.-h. and lee, c.-p. 1997. design of a resonant-cavity-enhanced photodetector for highspeed applications, ieee j. quantum electron, 33: 753-760. unlu, m.s. and strite, s. 1995. resonant cavity enhanced photonic devices, j. appl. phys., 78: 607-639. unlu, m.s., gokkavas, m., onat, b.m., ata, e., ozbay, e., mirin, r.p., knopp, k.j., bertness, k.a., and christensen, d.h. 1998. high bandwidth-efficiency resonant cavity enhanced schottky photodiodes for 800-850 nm wavelength operation, j. appl. lett., 72: 2727-2729. unlu, m.s., kishino, k., liaw, h.j., and morkoc, h. 1992. a theoretical study of cavityenhanced photodetectors with ge and si active regions, j. appl. phys., 71: 4049-4058. received 23 june 2001 accepted 6 november 2001 joseph a. jervase and hadj bourdoucen analysis results references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 283-294 © 2002 sultan qaboos university a fluid film squeezed between two parallel plane surfaces subject to normal oscillations e. a. hamza department of mathematics, college of science, sultan qaboos university, p.o.box 36,al-khod 123, muscat, sultanate of oman, email: elsadigh@squ.edu.om. م مائع مضغوط بين سطحين متوازيين في حركة تذبذبية عمودية فل الصادق أحمد حمزة ركزت . يهتم هذا البحث بدراسة الحركة الناتجة من ضغط طبقة رقيقة مائعة بين سطحين متوازيين وفي حركة نسبية : خالصة ر بدفع مفاجئ من حالة سكون إلي تذبذب الدراسة على الحالة الخاصة الناتجة من تثبيت أحد السطحين وتحريك السطح اآلخ وباإلضافة إلى التوصل إليجاد حلول تحليلية باستعمال طريقة التشويش المنتظم والتحليل . متموج في اتجاه عمودي على مستواه تفاضلية الخطي للمعادلة التفاضلية الجزئية غير الخطية التي تحكم الحركة بصورة عامة ، فقد تم إيجاد حل عددي للمعادلة ال وباستعمال هذه الحلول تم بحث تأثير الحركة المتموجة على أشكال سرعة . الجزئية غير الخطية كاملة بطريقة الفروق المحددة .الفلم المائع وقوته الضاغطة على السطحين abstract: we study the motion which results when a fluid film is squeezed between two parallel surfaces in relative motion. particular attention is given to the special case where one surface is fixed and the other is impulsively accelerated from a state of rest to a state of sinusoidal oscillations in a direction normal to its plane. in addition to the presentation of analytic solutions which are based on the regular perturbation technique and on the linearised analysis of the resulting nonlinear partial differential equation, a numerical solution of the full nonlinear equation based on a finitedifference scheme is obtained. the effects of the sinusoidal motion on the velocity profiles and on the normal forces which the fluid exerts on the surfaces are investigated. keywords: squeezed film, impulsive acceleration, normal oscillations. 1. introduction t he earliest attempts at the problem of the behavior of a thin film of liquid squeezed between opposing surfaces can be traced to stefan (1874) and to reynolds (1886), both of whom confined their attention to the special case where inertial forces are negligible in comparison to viscous forces. their work is considered as the foundation of hydrodynamic lubrication analysis and later became known as the classical lubrication theory. interesting and useful studies of the importance of inertia effects have been motivated by the increased machine speeds and low viscosity lubricants. among authors who have studied the role played by fluid inertia are ishizawa (1966), kuzma (1967), tichy and winer (1972), jones and wilson (1975), and hamza and macdonald (1981). the mathematical analysis, when inertia terms are included, is basically based on an iteration or perturbation scheme. the last two authors presented an initial condition that describes the manner in which squeezing is initiated and discussed the length of the transition period during which the regular perturbation solution fails to approximate the exact solution accurately. the case when one of the surfaces undergoes sinusoidal oscillation in squeezing film flows has received considerable attention due to the important roles it plays in many industrial application, especially in conditions of unsteady loading in machines which is often oscillatory in nature. fuller (1956) was first to treat this problem. he obtained a solution for the pressure of the 283 e.a. hamza fluid between the surfaces by neglecting inertia terms in the navier-stokes equation. kuhn and yates (1964) extended fuller's solution by including inertia terms. their solution agrees with their experimental results. however, they did not take account of the time-dependent boundary condition and their result appears to be in error. hunt (1966) obtained a similar solution to the one given by fuller but he allowed for variation in the boundary point. he also performed some experimental work which satisfactorily agrees with his theoretical solution. terrill (1969) obtained an analytic solution that depends on two parameters, the nondimensional amplitude of the oscillation of the surface and a reynolds number that is related to the maximum velocity of the vibrating surface. different cases depending on the magnitude of the two parameters were investigated. a similar solution for the case of oscillating squeeze film with arbitrarily varying surface geometry was presented by tichy and modest (1978). they included inertia forces in the equations of motion. in the case of the thrust bearing of fixed inclination, they found that the classical lubrication solution for the load and pressure fluctuations is in error by over 100 percent for reynolds numbers as low as 5. in this study we examine the motion of an incompressible viscous flow between two parallel plane disks where one disk is fixed and the other is rapidly accelerated from a state of rest to a state of normal sinusoidal oscillations. the nondimensionalization used by terrill (1969) will be employed here. the resulting nonlinear partial differential equation that describes the flow is solved subject to boundary and initial conditions. in section (3) analytic solutions through a use of a regular perturbation technique and laplace transformation are presented and in section (4) a numerical solution to the full nonlinear equation is given. the perturbation solution is in full agreement with terrill’s results. the objective of the study is to investigate the effects of oscillations on the load-carrying capacity and on the velocity profiles. 2. equations of motion we consider the motion of a thin film of fluid squeezed between two parallel coaxial disks which are spaced a distance h(t*) apart, where h(0) = h. we choose cylindrical polar coordinates ( r* , θ* , z* ) , in terms of which the lower fixed disk is described by z* = 0 and the upper disk by z* = h( t* ) . the corresponding velocity components are ( u* , v* , w* ) . we shall assume that the fluid is at rest for t* < 0 and that at t* = 0 the upper disk moves impulsively with steady normal oscillations of frequency ω and amplitude v. the navier-stokes equations of motion are transformed to nondimensional form by referring all lengths to h , all velocities to v, time to l/ω and pressure to ρv2, where ρ denotes density. the corresponding dimensionless variables are those without the asterisks. the configuration is sketched in figure 1. z,w ε h(t) cos (t) r,u figure 1. system configuration at time t. 284 a fluid film squeezed between two plates the nondimensional equations governing the flow are: 2 21 1 ,2 2 2 u u u p u u u u u w t r z r r r rz r r ε ε  ∂ ∂ ∂ ∂ ∂ ∂ ∂   + + = − + + + −   ∂ ∂ ∂ ∂ ∂  ∂ ∂  2 21 1 ,2 2 w w w p w w w u w t r z z r rz r ε ε  ∂ ∂ ∂ ∂ ∂ ∂ ∂   + + = − + + +   ∂ ∂ ∂ ∂ ∂  ∂ ∂ r ( ) 0,wru r r z ∂ ∂ + = ∂ ∂ where r = h2 ω /v and ε = v/hω ( v denotes kinematic viscosity and ε is the nondimensional amplitude). the boundary conditions are: u = 0 at z = 0 and at z = 1 ε sin t, w = 0 at z = 0 and w = -cos t at z = 1 ε sin t. the boundary conditions on w suggest that a solution in which w is independent of r should be sought. if we choose a stream function f(z, t) which is such that u=rfz , w=-2f, the mass conservation equation will be satisfied. hence the above nondimensional momentum equations may be expressed in the form ( )2 12 ,zt z zz r zzzf f ff p fr r ε ε+ − = − + 1 2 . 2t z z f ff p f r zz ε ε− = + (1), (2) furthermore equations (1) and (2) show that p is of the form ( ) ( )2 1 2 1 , , 2 p r p t p z t= + whence differentiation of equation (1) with respect to z and then use of the change of variables z = (1ε sin t)y, t = t, leads to the equation ( ) ( ) ( ) ( )2 1cos 1 sin 2 1 sin 2 1 sinyyy yy yyt yyy yyyyt t y f f t f t f f rε ε ε ε ε− + + − − − = f . (3) equation (3) is the same equation given by terrill (1969). the transformed boundary conditions are f = 0, f = 0, y = 0; f = cos t/2, f = 0, y = 1. (4) y y the radial pressure gradient, 1 1 ( ) ,p t r r p = ∂ ∂ is given by 285 e.a. hamza 1 0 11 3 (1 sin )(1 sin ) yyy yt y p f tr t ε εε f =    = − − −  (5) the initial condition, which states that for y≠ 0,1, the vorticity is zero at time t = 0+ is 1 cos , 2 f y t= when t 0+= , (6) thus at t = 0+ the radial velocity u outside the infinitesimally thin sheets of vorticity which are formed on the surfaces is the inviscid velocity given by the continuity equation / cos /u r t 2.= if the upper disk is assumed to be of radius c and of negligible thickness, the resultant normal force, or load w is given by ( ) 002 , , , c w r p r h t p drπ  =   −∫ where p0 is the nondimensional pressure at r = c, z = h. thus the above result may be expressed in the form 3 10 c w r pπ= − ∫ dr n y (7) in general, to solve equation (3) subject to conditions (4) and (6) a numerical approach is needed and this will be discussed in section (4). however, analytic approximate results will be considered first. 3. analytic solutions the nonlinear partial differential equation (3) with conditions (4) and (6) can be solved for special practical cases when εr, r and t are small. 3.1 solution for small r. the parameter ε is the ratio of the amplitude of the oscillation of the upper disk to the distance apart of the disks and is, therefore, less than one. thus if r is small then εr will also be small. by ignoring the initial condition (6), we can obtain from equations (3) and (4) the terms of the perturbation expansion ( ) ( ) ( ) ( ) 0 1 . n n n n n f r f y r gε ∞ ∞ = = = +∑ ∑ (8) the first few terms are 2 0 3 cos , 2 f y y = −    t ( ) ( ) ( )22 21 1 2 1 1 1 cos 7 140 f y y y y y t2 , = − − − − − +  ( ) ( ) ( ) ( ) ( )2 22 2 22 1 1 1 2 1 1 cos cos , 2 1 1 sin 3880800 40 ,f y y y q t s t g y y y= − − − + = − − t ( ) ( ) (22 22 1 2 1 1 10 10 3 cos 16800 g y y y y y= − − − − ) ,t (9) where 286 a fluid film squeezed between two plates 6 5 4 3 21512 4536 1659 10878 6207 12 558,q y y y y y y= − − + − + + 4 3 214245 28490 20867 6622 3234.s y y y y= − + − − the radial pressure gradient p1 is given by ( )( ) ( ) ( ) ( ) 13 1 2 2 2 1 6 1 sin cos 28 3 cos 140 3157 1110 cos cos sin cos 1940400 10 8400 r r p p t r t r r r r t t t t ε ε ε ε −  = = − − + −   − − − +   t (10) this is the forced solution in which the initial condition (6) is neglected and so we expect it not to be valid in the region of t = 0. however, for t not small and r = o(1) and εr = o(1), the solution is a good approximation to the motion of the fluid. the particular case r = 0, which has the simple solution ( )20 3 / 2 cos ,f y y= − t has been discussed by fuller (1956), kuhn and yates (1964) and hunt (1966). terrill (1969), correctly obtained f0 , f1 , g1 and g2 through using a perturbation scheme. when cos t = 1 and sin t = 0, the solution ( the zero and first orders) reduces to the solution given by ishizawa (1966) and jones and wilson (1975). they obtained the solution correct to o((εr)2), (note that εr = hv / v is the usual squeezing reynolds number) . for this case, good agreement with experiment, even when the reynolds number was an order of magnitude greater than unity, was reported by tichy and winer (1972) and kuzma (1967). the good agreement between theory and experiment at values of εr > 1 can be explained by reference to the remarkable decrease in magnitude of the functions , > 0if i . 3.2 solution for small rε and small t . the perturbation solution described in section (3.1) cannot satisfy the initial condition which states that the vorticity is zero at t 0+= . here we look for a solution satisfying the initial condition. for t and εr small equation (3) becomes yyt yyyyrf f= (11) to solve equations (11), (4) and (6), we shall employ laplace transformation (hamza and macdonald (1981)) technique to get a solution which is rapidly convergent for t . 0→ 3.2.1 laplace transform solution the outline of the solution starts by integrating equation (11) with respect to y twice to get, ( ) ( ) ,yy tf a t y b t r f+ + = (12) where a(t), b(t) are constants of integration. multiplying equation (12) by e-st and then integrating with respect to t over [0,∞), we obtain on using the initial condition (6), ( , ) ( ) ( ) ( , ) , 2yy r y f y s a s y b s r s f y s+ + = − (13) where 0 0 ( , ) , ( ) ( ) , ( ) ( ) .st st stf e f y t dt a s e a t dt b s e b t d ∞ ∞− −= = =∫ ∫ 0 t ∞ −∫ (14) the transformed boundary conditions are 2 0, 0, 0; , 0, 1 2(1 )y s f f y f f y s = = = = = + y = (15) the general solution of equation (13) is 287 e.a. hamza 1 2 2 1 ( ) ( ) ( , ) ( ) , 2 dy dy a s b sf y s c e c e y s d d −= + + + + 2 (16) where c are arbitrary constants and 1 2, c .r=d applying conditions (15) we find that s ( ,f y s ) can be expressed as ( ) ( ) ( ) 0 , 1 / 2 , , 4 1 / 2 1 / 2 n nd n i y s d s e d d ∞ − = + =  − −  ∑f y (17) where ( ) ( ) ( )11, 1 1 d yd dy ds d y e e e e s − −− − −= − + − + − .  i y (18) for small t ( ) ( ) ( ) 111 , , 4 1 / 2 d ydy d d ddy e e de y e e f y s o s d − −− − − − − − + − −   = +  −  s (19) so that ( ) ( ) ( ) ( ) 4 1 / 2 1 / 2 1 / 2 2 1 42 4 1 / 2 1 / 2 1 / 2 1 / 2 2 4 1 / 2 2 4 1 / 2 1 / 2 1 / 2 1 / 2 1 1 2 1/ 2 erfc 2 erfc erfc 2 2 1 1 , erfc 2 erfc 2 4 2 2 1 1 erfc 2 2 erfc 2 erfc 2 2 yy y y e y y y f y t e e e ye τ ττ τ τ τ τ τ τ τ τ τ τ τ τ τ − − +− + − + − +  − + − − + −   −    = + − − −             + − + − −          ( )1 / 2 1 / 4 ,o e ττ −            + 1 2τ    (20) where /t rτ = . the radial pressure gradient, on using the conditions 0yf f= = on 0y = , is given by ( ) ( ) ( ) ( )1 3 1 0, 0, , 1 sin yyy ytp f t rf t r t ε ε ε o r = − +  − (21) i.e. ( )( ) ( ) ( ) . 1 4 1 e1 2 2 1 erfce2erfce2 rtsin1p 4/12/1 2/1 2/1 422/14 13 1                           + τ +πτ−             τ− τ +τ−− εε−= τ−− τ+−τ − (22) the form (20) of the solution to equations (11), (4) and (6) should give accurate results for 0 < t < < 2π and it can be used to estimate the importance of the initial condition. however, for other ranges of interest, nonlinear terms must be taken into account and this necessitates a numerical solution of the full nonlinear equation. 4. numerical solution to obtain satisfactory information on the nature of the flow for 0 < ε sin t < 1 and for values of r and ε which are not small a numerical solution of the governing nonlinear equations is necessary. to integrate equation (3) subject to conditions (4) and (6), we employ an implicit finite difference scheme of the crank-nicolson type. on the y-axis select uniformly spaced mesh points 288 a fluid film squeezed between two plates at , i= 1,2,3, ..., (m+1) where (m + 1)h = 1 and denote by the value of f at y = ih and t = jk, where j = 1,2,3, ..., (n -1), and sin nk = (ε) ,iy i h= j if -1. equation (3) is replaced by finite difference approximations in which central difference formulae are used for approximation of the derivatives in the y-direction and forward difference formulae are employed for the derivative in the t-direction. for example we find ( ) ( ) ( ) 4 6 22 1 1 2 4 4 6 1 1 13 5 21 1 1 1 2 2 4 6 4 2 2 j jj j j j j i i i i i i i j jj j j j j j i i i i i i i i f f f f ff f o h y h y f f f f f ff f o h y t kh y t + + − − + + + + − + −  − + − +∂ ∂  = +  ∂ ∂   − + − + −∂ ∂  = +  ∂ ∂ ∂ ∂  4 1j (23) on replacing all terms of the equations other than fyyt, by the mean of their values on the jth and (j + 1)-th line rows, we obtain from (3) ( ) ( ) ( ) ( ) ( ) ( ) 5 5 1 1 1 1 1 3 3 1 1 j j j j j i si i s si i s i s s f a f b f c+ + + + + ++ − + − = = +∑ ∑ = (24) m,,3,2,1i …= where the coefficients ( ) ( ) ( 1ji 1j si 1j si c,b,a +++ ) )− are defined in terms of h, k, r, ε, (tj + t )/2, and the values of . 1j + 1 0 2, , , j j j mf f f− +… from the boundary conditions we obtain (1 1 2 0 1, , 0, cos / 2, 0,1, , 1 .j j j j j jm m mf f f f f f t j n− + += = = = = … (25) we select 10h = 1/2l, l = 0,1,2, ...so that (10 x 2l -1) nonlinear algebraic equations must be solved. the algebraic equations were solved by use of the newton-raphson iterative technique. 4.1 computational details the program was so written that it could be used to give results for wide ranges of parameters r and ε. the calculations were performed by using double precision for the values of r and ε in the ranges and 0.10.5 500,r≤ ≤ 0.8.ε≤ ≤ for fixed r and ε, accuracy was checked by comparing the results for two consecutive l values. the range of l varies from 1 at the lower values of r and ε to 3 at the higher values. for l = 1, k was selected to be 0.000625 so that the stability parameter k/ h = 0.25. for l = 2, k was taken to be 0.000078125 and the stability parameter was 0.125. for l = 3, k was taken to be 0.9765625 x 10 2 -5 and the stability parameter was 0.0625. equation (5) which gives the radial pressure gradient in the transformed coordinates, contains a number of higher order derivatives with respect to y. for small values of t these give rise to unsatisfactory finite difference results for the radial pressure gradient. thus it is preferable, since ( )/ /p r r∂ ∂ is independent of , to integrate (5) with respect to y over [0,1] to obtain the equation y ( ) ( ) ( ) ( ) ( ) 2 1 1 23 1 1 1 0 0 sin 1 sin 1 sin 3 1 sin 2 yy y y t t t p r f t f dy ε ε ε ε ε − − = − − = + − − ∫ (26) where the integrals are evaluated by use of simpson's rule. 5. results and discussion we discuss the case of an upper surface which is rapidly accelerated from a state of rest to a state of steady oscillations normal to the lower surface which is at rest. close to the start of the 289 e.a. hamza motion the vorticity layers adjacent to both boundaries are thin and the flow is largely inviscid, the inviscid velocity distribution being specified, when sin t is not large, by ( )/ / cos /u r f z t h t= ∂ ∂ = (27) where and h(t) respectively denote the speed of the moving surface and its distance of separation from the lower surface. impulsive movement of the upper surface results in rapid acceleration of the fluid, the driving force being the radial pressure gradient, which does work to overcome fluid inertia and frictional resistance. in the early stage of motion the inertial terms dominate the flow, as vorticity diffuses the contribution due to the frictional resistance will be equal in importance to that due to fluid inertia and as the surfaces approach one another inertial resistance becomes negligible in comparison to frictional resistance since the vorticity layers adjoining the surfaces will merge and the stream function f(z,t) will tend to the classical lubrication value f cos t 0 (the manner in which f →f0 is, of course dependent on r). figures 2 and 3 present the load variation with time t for a range of reynolds number extending to r = 500 for values of ε = 0.1 and ε = 0.8, respectively. the figures indicate that for a figure 2. normal force, or load, variation with r when ε = 0.1. fixed value of ε the magnitude of the load on the disk decreases with increase of r, or equivalently with increase of the squeezing reynolds number hv/v. the result states that if v and h are held constant, a decrease in kinematic viscosity will result in a decrease in the magnitude of the load on the disk. we also notice that for fixed ε and for t = π /2 or t = 3π /2, the magnitude of the load is the same for all values of r in this range. (this can be seen, for small values of r and ε , from equation (10)). for small ε and near the vicinity of t = 0 the load is large (this large force is necessary in the early stages of motion to overcome inertial resistance). in fact as t→ 0, it can be shown from equation (22) that the load behaves like 1 / 2( ) /rtπ ε− . 290 a fluid film squeezed between two plates figure 3. normal force, or load, variation with r when ε = 0.8. figure 4. radial velocity profile development with time t when ε = 0.1 and r = 0.5, 5.0,500. 291 e.a. hamza the maximum and minimum values of the load (or equivalently the radial pressure gradient) are of particular interest in connection with surface wear and cavitation. for ε = 0.8 and r = 0.5 the maximum and minimum values of the radial pressure gradient are 335.2 and -342.4 while for ε = 0.1, r = 0.5 the corresponding values are 123.8 and -128. for fixed values of ε these maximum and minimum values of the radial pressure gradient decrease with increase of r, while for fixed values of r they increase with increase of ε. it is of interest to compare the results obtained when the radial pressure gradient in equation (7) is obtained from the numerical solution and (i) the first-order regular perturbation solution, (ii) the solution to the linearised equation (11). for r = 0.01, 0.025, 0.1, 0.5, 5, 10 and for values of t in the range 0.0005 t 0.105 this comparison is made in table 1 (the upper values correspond to ≤ ≤ table 1: comparison of (i) the numerical solution (n) and the first-order perturbation results (p) and (ii) the numerical solution (n) and the results of the linearised analysis based on equation (11) (l) for the radial pressure gradient: percent error ( )100 / /n p l n= − when ε = 0.1 and 0 < t << 1. r t 0.01 0.025 0.1 0.5 5 10 .0005 01.151 00.012 12.193 00.013 42.026 00.101 69.911 00.454 89.781 08.394 92.198 09.513 .0050 00.032 00.014 00.032 00.011 01.130 00.137 26.750 00.520 68.212 02.350 75.480 03.910 .0100 00.032 00.015 00.033 00.009 00.016 00.129 12.370 00.603 57.570 02.591 65.850 03.975 .0200 00.033 00.017 00.035 00.004 00.047 00.111 02.411 00.286 44.034 02.882 55.134 04.294 .0400 00.035 00.021 00.039 00.005 00.064 00.075 00.089 00.497 28.927 02.641 41.634 03.932 .0500 00.035 00.022 00.041 00.009 00.071 00.057 00.210 00.410 23.850 02.270 36.830 03.385 .0650 00.037 00.025 00.044 00.016 00.084 00.030 00.288 00.279 17.872 01.508 30.806 02.238 .0850 00.038 00.029 00.048 00.025 00.100 00.006 00.370 00.100 11.803 00.184 24.215 00.183 .0900 00.038 00.029 00.049 00.027 00.103 00.014 00.390 00.055 10.520 00.200 22.760 00.420 .1000 00.039 00.031 00.051 00.032 00.112 00.033 00.431 00.037 08.170 00.020 19.910 01.745 .1050 00.040 00.032 00.052 00.034 00.116 00.041 00.450 00.078 07.168 00.452 18.647 02.386 the first-order perturbation solution). the table shows that in the case of the first-order solution and for r < 0.5 the agreement for values of t in the range t ≥ 0.005 is very good. for r = 0.5 the agreement is acceptable, but for r > 0.5 the numerical and the perturbation solutions differ appreciably even at higher values of t. on the other hand the table demonstrates the remarkable agreement between the numerical solution and the solution based on equation (11). the radial velocity profiles for t in the range π /2 ≤ t ≤ 2π , for values of r = 0.5,5 and r = 500 and for ε = 0.1 and ε = 0.8 are shown respectively in figures 4 and 5. in general the magnitude 292 a fluid film squeezed between two plates f of th incre and abr ful ham hun ishi jon kuh kuz igure 5. radial velocity profile development with time t when ε = 0.8 and r = 0.5, 5, 250. e radial velocity profile increases with increase of amplitude. we also notice that as r ases the radial velocity profiles are beginning to experience oscillations with respect to time position. references amowitz, m. and stegun, i.a. 1970. handbook of mathematical functions. dover publications, inc., new york. p 224. ler, d.d.1956. theory and practice of lubrication for engineers. wiley, new york, n. y. 136-141. za, e.a. and macdonald, d.a.1981. a fluid film squeezed between two parallel plane surfaces. j. fluid mech., 109: 147-160. t, j.b.1966. pressure distribution in a plane fluid film subjected to normal sinusoidal excitation. nature, sept : 1137-1139. zawa, s.a. 1966. the unsteady laminar flow between two parallel disks with arbitrarily varying gap width. bull. of the jsme, 9: 533-550. es, a.f. and wilson, s.d. r.1975. on the failure of lubrication theory in squeezing flows. trans. asme series f, 97: 101-104. n, k.c. and y. ates, c.c. 1964. fluid inertia effect on the film pressure between axially oscillating parallel circular plates. trans. asme, 7: 299-303. ma, d.c. 1967. fluid inertia effects in squeeze films. appl. sc. res, 18: 15-20. 293 e.a. hamza reynolds, o.1874. on the theory of lubrication and its application to mr. beauchami:tower's experiments, including an experimental determination of the viscosity of olive. phil. trans. roy. soc., london, 177: 157-234. stefan, j. 1874. versuche uber die scheinbare adhesion. k.akad wissenschaften. mathnaturwissenschaftliche klasse, wien. sitzungsberichte, 69: 713. terrill, r.m. 1969. the flow between two parallel circular disks, one of which is subject to a normal oscillation. asme journal of lubrication technology, 91: 126-131. tichy, j.a. and winer, w.o. 1970. inertial considerations in parallel circular squeeze film bearings. asme ser. f, j. lubrication technology, 92: 588-592. tichy, j.a. and modest, m.f. 1978. squeeze film flow between arbitrary twodimensional surfaces subject to normal oscillations. asme journal of lubrication technology, 100: 316322. received 28 october 2001 accepted 9 december 2002 294 department of mathematics, college of science, sultan qaboos university, p.o.box 36,al-khod 123, muscat, sultanate of oman, email: elsadigh@squ.edu.om. analytic solutions 3.1 solution for small r. 3.2 solution for small �and small r references squ journal for science, 2018, 23(1), 1-7 doi: http://dx.doi.org/10.24200/squjs.vol23iss1pp1-7 sultan qaboos university 1 a one-dimensional model of thermo-electroelasticity in extended thermodynamics moustafa s. abou-dina and ahmed f. ghaleb* department of mathematics, faculty of science, cairo university, giza 12613, egypt. *email: afghaleb@sci.cu.edu.eg abstract: the subject of thermo-electroelasticity involves many complications due to the multiple ways in which the mechanical, thermal and electric fields can interact, some of these involving non-linearities. in extended thermodynamics, an additional difficulty arises due to the requirement of finiteness of the speed of propagation of the thermal disturbances. this implies, as may be observed in the extensive literature on the subject, a re-visiting of the basic postulates of thermodynamics, ultimately leading to the desired generalization. there are only a few nonlinear models dealing with this subject. in order to consider general nonlinear models, it is necessary to study linear one s first, as they represent most of the basic features of the studied phenomena. this is particularly true when the problem is tackled numerically through iteration methods, in which case the starting field equations are linear. here we study a one-dimensional system of equations of thermo-electroelasticity in extended thermodynamics and in the quasi-electrostatic regime. the nonlinear equations are given for reference only. the mixed character, parabolic-hyperbolic, of the associated linear system is established through the study of the characteristic curves. two speeds of wave propagation are given in evidence, one for the usual coupled thermoelastic wave, and the other for a second sound. parabolicity is due to the quasi-static distribution of the electric field. an example concerning the halfspace is treated numerically by the cranck-nicolson method. the curves presented clearly illustrate the propagation of two types of waves, the usual coupled thermoelastic wave, and a faster wave generated by the second sound. it is hoped that the present study will clarify the basic features of the solution, as a prelude to tackling more sample, nonlinear equations. keywords: electroelasticity; extended thermodynamics; linear theory; characteristics; cranck-nicolson method. الديناميكا الحرارية الموسعة إطار الكهروحرارية في نظرية المرونةل نموذج أحادي البعد *غالب ؤادف حمدأو أبو دينه ابرص صطفىم الميكانيكي، الحراري : بين المجاالتيتضمن موضوع المرونة الحرارية الكهربائية العديد من الصعوبات بسبب الطرق المتعددة للتفاعل :صالملخ في الديناميكا الحرارية الموسعة، تنشأ صعوبة إضافية نظرا لمحدودية سرعة انتشار االضطرابات . والكهربائي، وبعضها يتضمن ظواهر غير خطية زيارة للمفاهيم األساسية للديناميكا الحرارية، واسعة النطاق حول هذا الموضوع، إعادةال وهذا يعني، كما يمكن أيضا مالحظته في المرجعيات. الحرارية ومن أجل النظر في النماذج غير من النماذج غير الخطية التي تتناول هذا الموضوع، يوجد عدد قليل فقط . مما يؤدي في نهاية المطاف إلى التعميم المطلوب ويصدق ذلك بشكل خاص عندما تعالج . السمات األساسية للظواهر المدروسةالخطية العامة، فمن الضروري دراسة النماذج الخطية أوال ألنها تمثل معظم .المشكلة عدديا من خالل الطرق التكرارية، وفي هذه الحالة تكون معادالت خطوة البداية هى المعادالت الخطية وتعَطى .ستاتيكيارية الموسعة وفي النظام شبه الكهرووهنا ندرس نظاما أحادي البُعد لمعادالت نظرية المرونة الحرارية الكهربائية في الديناميكا الحر بواسطة من خالل النظام الخطي المرتبط "ناقصي –مكافئ " النظام المختلط الناتج من المعادالت التفاضلية يتم دراسةو .الخطية كمرجع فقط غيرالمعادالت ويرجع ذلك إلى .لما يُسمى بالصوت الثاني واآلخرى المقترنةواحدة للموجة المرنة الحرارية :انتشار الموجة المنحنيات المميزة، وتوضع سرعتان في وتوضح المنحنيات . نيكلسن -، ويتم التعامل مع مثال يتعلق بنصف فراغ رقميا بواسطة طريقة كرانك للمجال الكهربائي التوزيع شبه الكهروستاتيكي ويؤمل أن . الموجة المرنة الحرارية المعتادة المقترنة، وموجة سريعة تم إنشاؤها بواسطة الصوت الثاني :شار نوعين من الموجاتالمعروضة بوضوح انت .تمهيدا لمعالجة المعادالت غير الخطية األكثر وفرة ذه الدراسة السمات األساسية للحلتوضح ه .نيكلسن -كرانك طريقة -المنحنيات المميزة –النظرية الخطية –الديناميكا الحرارية الموسعة -المرونة الكهربائية :مفتاحيةالكلمات ال m.s. abou-dina and a.f. ghaleb 2 1. introduction he theory of thermo-electroelasticity in generalized thermodynamics may be of interest in the study of electrical disturbances which accompany the propagation of heat waves at low temperature (rybalko et al. [1], pashitskii and ryabchenko [2], and pashitskii et al. [3]). dost [4] treats the case of thermoelastic dielectrics within the nonlinear theory. ersoy [5, 6] considers electrically and thermally conducting magnetothermoelastic solids. his theory is based on the introduction of the electric current and the heat flux vectors as independent state variables. montanaro [7] develops a model of nonlinear thermoelasticity in extended thermodynamics for electrically polarizable and finitely deformable, heat conducting elastic continua. ghaleb [8] presents a fully nonlinear model for electrically polarizable, heat conducting elastic continuous media in the quasi-electrostatic approximation. kuang [9] considers wave propagation in pyroelectrics and other materials with complex structure in extended thermodynamics within the linearized theory. montanaro [10] treats the case of electrical continuous media within green and naghdi thermoelasticity theory. chandrasekharaiah [11] develops a model for piezoelectrics with the heat flux as an independent state variable. singh [12] investigates thermo-piezoelectric solids in extended thermodynamics using green-lindsay and lord-shulman theories. zhou and yang [13] investigate the propagation of plane waves in pyroelectric materials in the presence of viscous effects. solutions of concrete problems are almost inexistant in the literature. our attention was drawn lately to a recent publication concerning two-dimensional electro-magneto thermoelastic wave propagation in an electrically conducting cylinder, within the frame of extended thermodynamics with one relaxation time [14]. all of the above references illustrate a multitude of approaches, conceived to remove the paradox of infinite propagation of thermal disturbances and to incorporate the electric interactions. most of them rely on rigorous thermodynamics, meaning that the basic laws of thermodynamics are respected, as well as the celebrated clausiusduhem inequality expressing the non-negativeness of the dissipation function. however, some of these approaches still need more solid experimental verification. a common ground to all of them is the need for an enrichment of the basic thermodynamical variables describing the electro-thermomechanical system. an interesting contribution discussing the difficulties facing the different models of extended thermodynamics may be found in [15]. for dielectric materials, which are the subject of the present investigation, we use the same approach as described in [7] and [8]. the basic set of thermodynamical parameters is enriched by adjoining the heat flow vector to the classical set involving strain and the electric field. that was shown to be consistent with the basic principles of thermodynamics in earlier work by coleman et al. [16]. a new feature of the present work is the introduction of initial and boundary conditions for the heat flow vector, independently of those for temperature. in what follows, we study a one-dimensional system of linear equations of thermo-electroelasticity in extended thermodynamics and in the quasi-electrostatic regime. thus, any magnetic contributions are disregarded from the outset. the original nonlinear equations are given for reference only. it is hoped that the obtained results will be helpful in clarifying the basic features of the solution, thus laying the background for the numerical treatment the nonlinear equations using an iterative method. two speeds of wave propagation are put in evidence, one for the usual coupled thermoelastic wave, and the other for second sound. a numerical example is treated for the half-space. all the unknown functions are zeroed at a sufficiently large distance from the boundary of the half-space, as a result of which reflected waves are expected to arise. in order to avoid them, the computational grid includes so mewhat restricted time values. as noted above, future work is under progress to study nonlinear wave propagation in pyroelectric materials in two dimensions. 2. the nonlinear equations the following equations are a restriction to one spatial dimension of a more general model of electrothermoelasticity based on the introduction of the heat flow vector as an additional state variable in the free energy density of the medium and are introduced in [8]. the equations are in dimensionless form, the velocity of elastic waves being taken as unity:   ,=1 3 2 1   eeuu xx (1) ),,()(=)32(1 311 2 txfueuuuu xxxxxxxxtt   (2) ),,( 1 =) 2 1 ( 2 0 2 21 txraqqqbueu xxtxx     (3)   . 1 = 0 xt qq   (4) here, u denotes the mechanical displacement component,  is the absolute temperature as measured from a reference temperature 0 , q is the heat flow vector and e is the electric field component. these four relations represent respectively: (i) the equation of electrostatics expressing the vanishing of the divergence of the electric t a one-dimensional, model of thermo-electroelasticity 3 induction, after integration and setting the integration constant equal to zero; (ii) the equation of motion; (iii) the equation of heat conduction and (iv) the vernotte-cattaneo law which replaces the usual fourier law for heat conduction. the coefficient a in eq.(3) is the multiplicative factor of the squared heat flow vector in the expression for the free energy of the system. the other coefficients appearing in the equations denote material constants having obvious meaning. in particular, the coefficients  and  express the dependence of the elastic moduli on strain. many of these coefficients will drop out in the following sections, when considerations are restricted to the linear equations. it may be noticed that the form of the vernotte-cattaneo law used in (4) and proposed in [8] does not yield the classical fourier law for heat conduction in the limit of small relaxation times, and hence it cannot be used under such a restrictive condition. considering wave propagation in a half-space with initial uniform reference temperature 0 , the characteristic length 0 l , time 0 t and heat flow vector 0 q used to deduce the dimensionless equations are taken as follows: ,==,=,= 0 0 00 0200 cv t cl q cv k t cv k l      where  is the material density, c is the specific heat, k is the thermal conductivity and v is a characteristic velocity of propagation of the elastic waves. tentatively, for common solids the different coefficients take on the following values in the su system of units: 3 4 3 2 1 1 1 1 5 1 0 = 10 , = 10 , = 10 , = 237 , = 10 .k kgm c jkg k k w m k v ms        in what follows we consider a problem for the half-space <<0 x . the formulation necessitates a boundary condition for the new variable of state q , to be considered side by side with the boundary condition for temperature. 3. on the character of the system of linear equations following [8] and using a well-known formalism based on the introduction of the heat flow vector as an additional state variable, one gets the linear equations of electro-thermoelasticity in extended thermodynamics. in the one-dimensional case, after dimension analysis to reduce the speed of the classical coupled thermoelastic waves to unity, the governing linear equations may be written as a system of first-order partial differential equations in six unknown functions },,,,,{ rpequ  of the form: ,= 3        er x u t e (5) ),,(= 1 txf x e xx p t p             (6) ),,(= 21 txr t e t r x q t             (7) ,= q xt q        (8) ,= p x u t u      (9) ,= r x u t r       (10) the two unknown functions p and r are defined from the last two equations of the above system. the parameters  , are two positive small parameters introduced artificially for convenience. subsequently, they will be made to decrease during the computations, starting from some initial values. the function f represents the external forces of non-electric origin acting on the medium, while r denotes the volume heat supply. the other parameters appearing in the equations are dimensionless quantities involving the physical parameters of the medium. using standard analysis, it may be shown that all the characteristics of the considered linear system of equations are real, and do not depend on the two constants  , introduced earlier. four of these characteristics yield the speeds of wave propagation, for the usual coupled thermoelastic wave and for second sound: . 1 =1,= 3,41,2   vv these are the same as for the purely thermoelastic case, showing that in this linear approximation, the electric field does not influence the velocities of wave propagation. the remaining two velocities are equal to zero. m.s. abou-dina and a.f. ghaleb 4 thus the equations under consideration form a system of partial differential equations of the first order of mixed, parabolic-hyperbolic type. it is believed that the parabolic element is due to the considered quasi-electrostatic approximation. 4. numerical scheme in what follows, we use the finite difference crank-nicholson method [17] to solve the initial set of linear equations (5)-(10). for the computational work, consider finite intervals on the x and t axes. the domain in the ),( tx plane is discretized by a grid with step length hx = and time step .= kt let nm , be natural numbers, and the coordinates of the mesh points are: ,...,2,1,0,=,=,...,2,1,0,=,= mmmktnnnhx mn where .<0,,/=,)/(= ttbxamttnabh  the numerical values of the variables qpue ,,,,  and r at the grid point ),( mn tx is denoted, respectively, by m n m n m n m n m n qpue ,,,,  and . m n r we use the following differences approximations: 1. for first order time derivative ).(=)( 1 ko k uu u m n m nm nt    (11) 2. for first order space derivative .)() 22 ( 2 1 =)( 2 1 1 1 111 ho h uu h uu u m n m n m n m nm nx         (12) 3. for source term ).( 2 1 =)( 1 m n m n m n fff   (13) these expressions will be used to approximate the partial derivatives of all the unknown functions qpue ,,,,  and r in the proposed system. the above replacement changes this system into a linear algebraic system for the unknowns m n m n m n m n m n qpue ,,,,  and m n r , and then the new system can be solved easily. also, the local truncation error of this scheme is of the order ),( 2 kho  and it is well known that the crank-nicholson scheme is unconditionally stable when used to solve hyperbolic partial differential equations of the first order [17]. the system of equations is solved under the following initial-boundary conditions: 0,=,0)(=,0)(=,0)(=,0)(=,0)(=,0)( xrxqxxpxuxe  ,sin)cos(1=)(0,),cos0.5(1=)(0,,cos1=)(0, 10 tptptpttutte  ),cos(1=)(0,)),(0,(=)(0,,cos1=)(0, 0 trtrtbitqtt   0,=),(=),(=),(=),(=),(=),( txrtxqtxtxptxutxe finalfinalfinalfinalfinalfinal  and for the following values of the material and geometrical constants .=0,=0.0012,=,= 43231 qffferf   the unknowns p and r are not independent, but defined through the other unknowns. thus, the constants 10 , pp and 0r cannot be arbitrary. simple calculations show that   . 1 =, 2 1 =, 1 = 3 013 0 0          rp r p taking 0.5,=0.1,=35,==,10=350,=0,= 1  mntba 0.1.=0.98,=0.1,=0.0001,==0.5,=0.5,=0.1,= 321 bi  all variables were zeroed at finalx , on the basis that waves have not reached this point at time finalt and therefore no reflected waves will appear during this period of time. the maximal value for time is 35finalt , while the values of the a one-dimensional, model of thermo-electroelasticity 5 spatial coordinate x were allowed to run up to the value = 10 350final finalx t , in order to be able to view the fast wave travelling with velocity 3.16 1  . the solutions for the mechanical displacement, temperature, heat flow vector and electric field are represented as 3-d surfaces on figures 1-4, in which one clearly notices two separate propagating waves generated by the boundary regimes. the computations were repeated many times for different values of  and  , and it was noted that all the figures remained unchanged as these two constants were made smaller by many orders of magnitude, thus justifying their introduction for convenience. figure 1. mechanical displacement component u. figure 2. temperature  . m.s. abou-dina and a.f. ghaleb 6 figure 3. heat flow vector component q. figure 4. electric field component e. 5. conclusion a model of linear thermo-electroelasticity in extended thermodynamics and in the quasi-electrostatic approximation has been investigated using the method of characteristics, and then numerically for given initial and boundary conditions. the main ingredient in this model is a cattaneo-type evolution equation, which effectively requires the heat flow vector to be considered as an additional state function, independent of temperature. this requires the introduction of initial and boundary conditions for the heat flow vector, independently of those for temperature, a fact that represents a fundamental difference from the thermoelasticity problems solved within the frame of different theories of extended thermodynamics. for these, the additions of temporal derivatives occur in the heat equation itself. moreover, the problems are usually solved by laplace transform, with the elimination of the heat flow vector in favor of the other unknowns of the problem, hence not requiring additional limiting conditions for this variable. the presently used boundary condition for the heat flow vector is a robin thermal condition which may be controlled a one-dimensional, model of thermo-electroelasticity 7 experimentally. other types of boundary conditions for the heat flow vector may equally well be used for the computations. dimension analysis and a study of the characteristic curves has revealed the mixed “parabolic-hyperbolic” character of the system of linear equations of electro-thermoelasticity. the parabolic element is due to the used quasielectrostatic approximation. moreover, within the linear theory, the electric field does not influence the speeds of propagation of the waves. this will certainly not be true anymore in the nonlinear case. a numerical application clearly shows two types of waves: the usual, coupled thermoelastic wave and the second sound, propagating in the medium. it is hoped that the presented results, together with the future extension to include nonlinear interactions, will help investigating interesting problems in thermo-electroelasticity. references 1. rybalko, a.s., rudavskii, e., rubets, s., tikhiy, v., derkach, v. and tarapov, s. electric induction in he ii. journal of low temperature physics, 2007, 148, 527-534. 2. pashitskii, e.a., ryabchenko, s.m. on the cause of electric activity of superfluid helium upon excitation of a second sound wave and normal-component velocity oscillations in it. journal of low temperature physics, 2007, 33, 12-21. 3. pashitskii, e.a., tkachenko, o.m., grygoryshyn, k.v. and lev, b.i. on the nature of electrical activity in superfluid helium at second sound excitations. ukrainian journal of physics, 2009, 54, 89-93. 4. dost, s. on generalized thermoelastic dielectrics. journal of thermal stresses, 1981, 4(1), 51-57. 5. ersoy, y. a new nonlinear constitutive theory for conducting magnetothermoelastic solid. international journal of engineering science. 1984, 22, 683-705. 6. ersoy, y. a new nonlinear constitutive theory of electric and heat conductions for magnetoelastothermoelectrical anisotropic solids. international journal of engineering science, 1986, 24, 867-882. 7. montanaro, a. on the constitutive relations for second sound in thermo-electroelasticity. archives of mechanics, 2011, 63(3), 225-254. 8. ghaleb, a.f. coupled thermoelectroelasticity in extended thermodynamics. encyclopedia of thermal stresses (c), ed. r.b. hetnarski, springer, 2014, 767-774. 9. kuang, z.b. theory of electroelasticity, springer, 2014. 10. montanaro, a.a green-naghdi approach for thermo-electroelasticity. journal of physics: conference series, 2015, 633, 012129. doi:10.1088/1742-6596/633/1/012129. 11. chandrasekharaiah, d.s. a generalized linear thermoelasticity theory for piezoelectric media. acta mechanica, 1988, 71, 39-49. 12. singh, b. on the theory of generalized thermoelasticity for piezoelectric materials. applied mathematics and computation, 2005, 171(1), 398-405. 13. zhou, z.d. and yang, f.p. plane waves in pyroelectrics with viscous effect. acta mechanica, 2014, 225, 509-521. doi 10.1007/s00707-013-0962-7. 14. sherief, h.h. and allam, a.a. electro-magneto interaction in a two-dimensional generalized thermoelastic solid cylinder. acta mechanica, 2017, 228, 2041-2062. doi 10.1007/s00707-017-1814-7. 15. li, s. and cao, b.y. on thermodynamics problems in the single-phase-lagging heat conduction model. entropy, 2016, 18, 391-399. doi:10.3390/e18110391. 16. coleman, b.d., fabrizio, m. and owen, d.r. on the thermodynamics of second sound in dielectric crystals. archive for rational mechanics analysis, 1982, 80(2), 135-158. 17. smith, g.d. numerical solution of partial differential equations. (second ed.), oxford university press, 1978. received 4 april 2017 accepted 13 august 2017 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 81-87 © 2001 sultan qaboos university approximating the tail probability of the t-distribution: a bayesian approach mohammad fraiwan al-saleh department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. أسلوب بييز: ريب االحتمال الذيلي لتوزيع تتق محمد فريوان الصالح لقد تم استخدام أسلوب بييز في تقريب االحتمال الذيلي لتوزيع ت ، حيث تم ايجاد مجموعة من الحدود الدنيا والعليا : خالصة وقد تمت مقارنة . حدود مناسبة لالستعمال وباالعتماد على بساطة هذه الحدود ودقتها ، يمكن القول بان هذه ال . لهذا االحتمال .و قد تم بحث إمكانية استخدام هذا األسلوب لتوزيعات مهمة أخرى. بعض هذه الحدود بما هو متوفر من تقريبات abstract: a bayesian technique is used to approximate the tail probability of the t-distribution. a set of upper and lower bounds are obtained for this probability. based on their simplicity and accuracy, these bounds are very adequate to use. some members of these bounds are compared to some existing approximations. the possibility of using this new procedure for some other distributions is explored. keywords: mill’s ratio, normal distribution, t-distribution and tail probability. 1. introduction i f is a random sample from the same normal distribution with mean nxxx ,..., 21 θ and variance , both being finite but unknown, and if 2σ ))1/()(and)/( 22 −−==∑ ∑ nxxsnx iix , then the statistic sxn /)( θ− has a t-distribution. this statistic is very useful in the construction of tests and confidence intervals of θ . for a brief recent description of this distribution and its properties, see stuart and ord (1994) and johnson, et al. (1995). the importance of approximating the tail probability of this distribution is due to the fact that this probability is frequently used in constructing confidence intervals or in finding the pvalues of some statistical tests. there has been intensive work on approximating the tdistribution which produced approximations of very high accuracy, though some times very complicated. fisher (1935) gave a direct expansion of the probability density function and hence of );( νtf = ) as a series in , where v is the degree of freedom. elfving (1955) suggested the following approximation: ( ttp ≤ν 1−ν )) 2 ()5.1(()()( )4(5.122596 5 tvtvttttp v σ φσσν −++φ=≤ +−−− where 5. 2 ) 5. 5. ( tv v + − =σ , and φ φ are respectively, the cumulative distribution and the density function of the standard normal distribution. cucconi (1962) obtained the following approximation: 1)696.1185.3(96.1 5.2975,. >+−≈ − vforvvvtv , 2)212.4185.3(5758.2 5.2995,. >+−≈ − vforvvvtv 81 al-saleh where is a number with tail area (probability) (1-α,vt α ). pinkham and wilk (1954) suggested the use of the expansion: ),1(5.);()1( 1 1 )1(5.12 +<+=+∫ ∑ ∞ − = +−− vmtrwdyvy m t m i i v where ; )1(5.12111 )1()1( −−−−− +−= vvttvvw 1,...,2,1; 12 12 )1( 121 −=+− − += −+ mivi i vtww ii , and is the remainder term. mr abu-dayyeh and ahmed (1993) considered a similar problem. they provided an upper bound for mill ' s ratio )(/))(1()( xxxr φφ−= . they showed that 5.22 )),(max()( −+≤ πxxxr )( xr . al-saleh (1994) initiated a bayesian approach to approximate mill ' s ratio and hence to approximate the tail probability of the standard normal distribution. he obtained a sequence of upper bounds and a sequence of lower bounds of , each converges to . )( xr as mentioned by johnson et al. (1995), the available tables of the t-distribution are more than sufficient for almost all applications. however, a major concern raised by the above authors, is how to quickly evaluate the tail probability. it is well known that the t-distribution converges to the normal distribution as goes to infinity. thus, for v , if is the distribution function of the t-distribution then v 30≥ )(xf )()( xxf φ≈ . however this approximation is not so accurate for small . recently, li and moor (1999) suggested the approximation of by v )(xf )( xλφ , where λ is a shrinkage factor and its value is given by 2 2 24 14 x x + −+ = ν ν λ . this approximation has a much simpler form and very accurate when compared with many of the approximations listed in johnson et al. (1995). a weak point of this approximation is that it is written in terms of φ , which has no closed form and has to be obtained from tables. for other approximations of the t-distribution see johnson et al. (1995) and gleason (2000). in this paper we use the bayesian approach introduced by al-saleh (1994) to obtain new approximations of the tail probability of the t-distributions. these approximations, which turned out to be of a simple form, can give very accurate values. the possibility of applying this approach to some other distributions is discussed. 2. derivation of the bounds assume that x is a random variable, which has a tdensity with parameters θ and . then the density of v x is )1(5.21 ))(1( 1 )5(. ))1(5(. ),;( +−+γ +γ = v v xvv v vxg θπ θ , where is a positive number and v x is any real number. assume further that the median θ is positive. let )(θπ be an improper uniform prior of θ , defined by 1)( =θπ for 0>θ and zero otherwise. then the posterior density of θ for given x can be written as: )( )( )( )( )|( 0 xf xf dxf xf x θ θθ θ θπ − = − − = ∫ ∞ , 82 approximating the tail probability of the t-distribution where stands for the t density with parameter (.)f ν and zero median and stands for the corresponding cumulative distribution. the main object of this paper is to approximate the tail probability, 1 . f )(xf− now, if ν =1, the distribution function of the t-distribution is the same as that of the cauchy which has a closed form. for , the posterior expected value of is finite for v and is given by: 2≥v kθ ,,1 l=k 1− ∫∫ ∞− ∞ −=−= x kkk dttftx xf dxf xf xe )()( )( 1 )( )( 1 )|( 0 θθθθ and hence, ∫ ∞ − − − =− x k k k dttftx xf xe )()( )(1 )1( )|(θ (1) since 0>θ , we have for all values of 0)|( >−xe kθ x . thus, 0)()( >−∫ ∞ x k dttftx for even values of , k and 0)()( <−∫ ∞ x k dttftx for odd values of . k now, the last integral can be written as: )()1()()( 0 xxdttftx i ik k i k i i x k µ− = ∞      −=− ∑∫ (2) where ∫ ∞ = x i i dttftx )()(µ . integrating by parts, it can be shown that for 1;,,2 −≤= vkkli and we have 2≥v )( )1( )( 1 )( 21 1 x iv i xx iv v x i i i − − − − + − − = µ ν µµ (3) where, ).()1( 1 )(;)(1)( 2 10 xfv v xxfx v x+ − =−= µµ thus, using (3), upper and lower bounds can be obtained for the tail probability of the standard t-distribution, i.e. for the quantity )(1)(0 xfx −=µ . for even, i iµ can be written as )()()()( 01 xbxxax iii µµµ += , where, ))(()()( 2/ 2 2/ 222∑ ∏ = = −+= i k i kj jkii bxaxaxa ; ; ∏ = = 2/ 1 2 i j ji bb 83 al-saleh 11)( − − − = ii xiv v xa and iv vi i − b − = )1( . for odd, i )(xiµ can be written as )()()( 1 xxcx ii µµ = , where ))(()()( 2/)3( 1 2/)3( 3212 2/)1( 1 12 ∑ ∏∏ − = − = ++ − = + ++= i k i kj jk i j jii bxabxaxc . thus, for k with and v< 110 == cb 00 =a we have ))()()(()()()( 10 xaxxcxxbxxdttftx i ik eveni k i i ik oddi k i i ik x eveni k i k −−− ∞ ∑∑∫ ∑     −     −     =− µµ . hence, for k even we have: )4( )()()(( )()(1)( 1 0 i ik eveni k i i ik eveni k i i ik k ioddi k bx xaxxcxx xlxfx − −− ∑ ∑∑            −      =≥−= µ µ while for k odd we have )5( ))()()(( )()(1)( 1 0 i ik eveni k i i ik eveni k i i ik oddi k i k bx xaxxcxx xuxfx − −− ∑ ∑∑            −      =≤−= µ µ where is the lower bound of 1 and u is k upper bound of 1 . )( xlk thk )(xf− )(xk th )(xf− 3. numerical calculations of and u )( xlk )(xk to see how accurate and u are, the two bounds have been obtained for some values of and . for =10 and k =3, 4, the two consecutive bounds are: )( xlk )(xk v k v )( 25.65.7 8036.58929. )( 124 3 4 xxx xx xl µ      ++ + = ; )( 75.3 8571.29107. )( 13 2 3 xxx x x µ      + + =u . for =15, the two bounds are: v )(4 xl )(7203.49231.6 4944.59324. 124 3 x xx xx µ      ++ + = ; )( 4615.3 5.29359. )( 13 2 3 xxx x x µ      + + =u . and for ν =20, we have: )( 1667.46667.6 553.59498. )( 124 3 4 xxx xx xl µ      ++ + = ; ).( 333.3 3529.29510. )( 13 2 3 xxx x x µ      + + =u . 84 approximating the tail probability of the t-distribution here, 11 )1)(( 2 −+= v v v xxfµ and )1(5.21 )1( 1 )5(. ))1(5(. )( ++γ +γ = v v xvv v xf π . for a given and suitable , we take the average of the two bounds as an approximation of the tail probability 1 , i.e. for even v k )(xf− k 2 )()( )()(1 1* xuxl xxf kkk −+=≈− α (6) and for odd we have k 2 )()( )()(1 1* xuxl xxf kkk + =≈− −α (7) table 1: values of ,)(*4 xα 1α , 2α and 3α v x exacα )(*4 xα 1α 2α 3α 10 1.812 .050 .0505 .0583 .0639 .0500 2.228 .025 .0252 .0288 .0309 .0249 2.764 .010 .0100 .0093 .0123 .0098 3.169 .005 .0051 .0041 .0063 .0048 15 1.753 .050 .0506 .0595 .0609 .0500 2.131 .025 .0252 .0310 .0289 .0250 2.602 .010 .0101 .0132 .0111 .0100 2.947 .005 .0050 .0054 .0054 .0050 20 1.725 .050 .0505 .0599 .0610 .0500 2.086 .025 .0252 .0318 .0288 .0250 2.528 .010 .0101 .0136 .0111 .0100 2.845 .005 .0050 .0063 .0054 .0050 )(*4 xα is compared to the approximations provided by elfving (1955), pinkham and wilk (1954), and li and moor (1999) denoted by 1α , 2α and 3α respectively. table 1 contains the values of ,)(*4 xα 1α , 2α and 3α for selected values of and v x . the values of x are those values that are used frequently in applications, i.e. values that correspond to exact tail values of .0500, .0250, .0100, and .0050. it can be seen from this table that the value of is very accurate and closer to the exact value than the first two approximations. furthermore, the values of are almost as accurate as the values of )x(*4α )(*4 xα 3α . note that more accurate bounds can be obtained using higher values of . for example if we take =5, then k k 135 24 5 25.315.12 8571.227321.109071. µ xxx xx u ++ ++ = . table 2 contains the values of ,)(*5 xα 1α , 2α and 3α for selected values of x when =10. it can be concluded from this table that the values of are even more accurate than v )x(*5α 3α . 85 al-saleh table 2: values of ,)(*5 xα 1α , 2α and 3α v x exacα )(*5 xα 1α 2α 3α 10 1.812 .050 .0501 .0583 .0639 .0500 2.228 .025 .0250 .0288 .0309 .0249 2.764 .010 .0100 .0093 .0123 .0098 3.169 .005 .0050 .0041 .0063 .0048 4. other applications of the technique the bayesian approach, which is used in this paper to approximate the t-distribution, was used by the author to approximate the normal distribution. an inspection of the procedure reveals that it can be applied to some other distributions. if x has a density that is symmetric around zero and if we let )(xf θ−= xy , where θ is a location parameter then the density of y is )( θ−yf . if we impose a uniform prior on θ of the type 1)( =θπ for 0≥θ and zero otherwise, then the posterior density of θ given x is )( )( )( )( )|( 0 xf xf dxf xf x θ θθ θ θπ − = − − = ∫ ∞ . all moments of this density are nonnegative and hence as in section (2), it can be shown that )()1()()( 0 xxdttftx i ik k i k i i x k µ− = ∞      −=− ∑∫ where ∫ ∞ = x i i dttftx )()(µ . now, depending on the functional form of , it may be possible to obtain a recursive formula for )(xf )(xiµ like the one in equation (3). we believe that some distributions such as the lognormal, non-central t and other location types-distribution can benefit from this procedure. another useful application of the procedure is for estimating the cumulative distribution of the bivariate normal and other bivariate distributions. 5. concluding remarks there has been considerable work on the possible approximations of the tail probability of the t-distribution. simplicity as well as accuracy are important factors in assessing the value of an approximation. in this paper, we use a bayesian approach to provide a set of upper and lower bounds of this probability; the set consists of [ ]1−v members. any member of the set or a combination of members can serve as an approximation. taking the average of two consecutive lower and upper bounds can be a good choice. it turns out that this approach is a suitable one in providing simple and accurate approximations and can be used for similar problems. unlike many other approximations, the current procedure doesn’t depend on ).x(φ 86 approximating the tail probability of the t-distribution 6. acknowledgment i wish to thank the referees for their constructive comments and suggestions. references abu-dayyeh, w. and ahmed, m. 1993. some new bounds on the tail probability of standard normal distribution. journal of information and optimization sciences 14: 155159. al-saleh, m. fraiwan.1994. mill's ratio: a bayesian approach. pakistan journal of statistics 10:629-632. cucconi, o. 1962. on simple relation between the number of degrees of freedom and the critical value of studentt. memeorie academia patavina 74:179-187. elfving, g. 1955. an expansion principle for distribution functions with application to statistics. annals academiae scientiarum fennicae, series a 204:1-8. fisher, r.a. 1935. the mathematical distributions used in the common tests of significance. econometrica 3:353-365. gleason, j.r. 2000. a note on a proposed student t approximation. computational statistics and data analysis 34:63-66. johnson, n., kotz, s. and balakrishnan, n.1995. continuous univariate distribution. john wiley and sons, new york. li, b. and moor, b. 1999. a corrected normal approximation for the student t distribution. computational statistics and data analysis 29:213-216. pinkham, r. and wilk, m. 1954. tail areas of the t-distribution from a mills-ratio-like expansion. annals of mathematical statistics 34:335-337. stuart, a. and ord, j. 1994. kendall advanced theory of statistics. edward arnold, london received 5 january 2000 accepted 22 january 2001 87 mohammad fraiwan al-saleh department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. îáçõé : áþï êã çóêîïçã ãóáæè èíí introduction squ journal for science, 2017, 22(2), 89-95 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp89-95 sultan qaboos university 89 approximation properties of de la valléepoussin sums in morrey spaces ahmed kinj*, mohammad ali and suleiman mahmoud department of mathematics, faculty of science, tishreen university, lattakia, syria. *email: a.kinj@tishreen.edu.sy. abstract: in this paper, we investigate the problem of the deviation of a function 𝑓 from its de la vallée-poussin sums of fourier series in morrey spaces defined on the unite circle in terms of the best approximation to 𝑓. moreover, approximation properties of de la vallée-poussin sums of faber series in morrey-smirnov classes of analytic functions, defined on a simply connected domain bounded by a curve satisfying dini's smoothness condition are obtained. keywords: de la vallée-poussin; faber polynomials; modulus of smoothness; morrey smirnov classes. دي ال فالي بواسون في فضاءات موريتقريب الدوال بواسطة مجاميع خواص محمد علي وسليمان محمود، أحمد كنج في فضاءات موري المعرفة على دائرة 𝑓عن مجاميع دي ال فالي بواسون لمتسلسلة فورييه للدالة 𝑓بحثنا في هذه الورقة مسألة انحراف دالة :صلخمال حصلنا على خواص تقريب الدوال من صفوف موري سميرنوف المعرفة على منطقة بسيطة . وعالوة على ذلك، 𝑓الواحدة في ضوء أفضل تقريب للدالة الترابط )االتصال( ومحاطة بمنحٍن يحقق شرط ديني للملوسة بمجاميع دي ال فالي بواسون لمتسلسلة فابير. .دي فالي بواسون، كثيرات حدود فابير، معامل الملوسة، صفوف سميرنوف موري: مفتاحيةالكلمات ال 1. introduction ain approximation problems in lebesgue spaces have been studied by several authors [1, 2]. the approximation of functions of lebesgue spaces by partial sum of faber-laurent series was obtained by israfilov [3]. these results are generalized to muckenhoupt weighted lebesgue's spaces [4]. approximation properties of faber series in weighted and non-weighted orlicz spaces were dealt with by jafarov and israfilov [5-7]. the concept of morrey space, introduced by c. morrey [8] in 1938, has been studied intensively by various authors and plays an important role in many areas such as applied mathematics, the theory of differential equations, potential theory, and maximal and singular operator theory. currently there are several investigations relating to the fundamental problems in this space [9-14]. therefore, the investigation into the approximation of functions by means of fourier trigonometric series in morrey spaces is also important in these areas of research. in the present paper, we investigate the problems of estimating the deviation of functions from their de la vallée poussin sums in morrey spaces. similar results in weighted smirnov spaces and weighted smirnov orlicz spaces can be found in the papers [15-17]. 2. notation and basic definitions let 𝐺 be a finite simply connected domain in the complex plane ℂ bounded by a rectifiable jordan curve γ and 𝐺 − ∶= 𝑒𝑥𝑡 𝛤. without loss of generality, we suppose that 0 ∈ 𝐺. further, let 𝛾0 ∶= {𝑤 ∈ ℂ ∶ |𝑤| = 1}, 𝐷: = 𝑖𝑛𝑡 𝛾0, 𝐷− ∶= 𝑒𝑥𝑡 𝛾0. we denote by 𝑤 = 𝜑(𝑧) the conformal mapping of 𝐺 − onto domain 𝐷− normalized by the conditions 𝜑(∞) = ∞, 𝑙𝑖𝑚 𝑧→∞ 𝜑(𝑧) 𝑧 > 0, and let 𝜓 be the inverse mapping of 𝜑. we begin with the following definitions: m mailto:a.kinj@tishreen.edu.sy ahmed kinj et al 90 definition 2.1 [18] for 0 ≤ 𝛼 ≤ 2 and 1 ≤ 𝑝 < ∞, we denote by 𝐿𝑝,𝛼 (γ) the morrey space, as the set of locally integrable function 𝑓, with a finite norm: ‖𝑓‖𝐿𝑝,𝛼(γ) ≔ {sup 𝐵 1 |𝐵 ∩ γ| γ 1− 𝛼 2 ∫ |𝑓(𝑧)|𝑝|𝑑𝑧| 𝐵∩γ } 1 𝑝 < ∞, where 𝐵 is an arbitrary disk centered on γ and |𝐵 ∩ γ|γ is the linear lebesgue measure of the set 𝐵 ∩ γ. in the case of γ = 𝛾0 ≔ {𝑤 ∈ ℂ: |𝑤| = 1} we obtain the space 𝐿 𝑝,𝛼 (γ0). under this definition 𝐿𝑝,𝛼 (γ) is a banach space. if 𝛼 = 2 then the class 𝐿𝑝,2(γ) coincides with the class 𝐿𝑝 (γ), and for 𝛼 = 0 the class 𝐿𝑝,0(γ) coincides with the class 𝐿∞(γ). moreover, 𝐿𝑝,𝛼1 (γ) ⊂ 𝐿𝑝,𝛼2 (γ) for 0 ≤ 𝛼1 ≤ 𝛼2. thus, 𝐿𝑝,𝛼 (γ) ⊂ 𝐿1(γ), ∀𝛼 ∈ [0,2]. for given 𝑓 ∈ 𝐿1(𝛾0), let 𝑎0 2 + ∑ 𝑎𝑘 (𝑓) cos 𝑘𝑥 + 𝑏𝑘 (𝑓) sin 𝑘𝑥 ∞ 𝑘=0 (1) be the fourier series of 𝑓, where 𝑎𝑘 (𝑓) and 𝑏𝑘 (𝑓) are fourier coefficients of the function 𝑓. further, let 𝑆𝑛(𝑥, 𝑓) = 𝑎0 2 + ∑ 𝑎𝑘 (𝑓) cos 𝑘𝑥 + 𝑏𝑘 (𝑓) sin 𝑘𝑥 𝑛 𝑘=0 be the 𝑛 𝑡ℎ partial sums of series (1). we define the 𝑛 − 𝑡ℎ de la vallée-poussin sums of series (1) as 𝑉𝑛,𝑚(𝑥, 𝑓) = 1 𝑚 + 1 ∑ 𝑆𝑘 (𝑥, 𝑓) 𝑛 𝑘=𝑛−𝑚 , 0 ≤ 𝑚 ≤ 𝑛, 𝑚, 𝑛 = 1,2,3, … . definition 2.2 [19] we define the 𝑟 modulus of smoothness of a function 𝑓 ∈ 𝐿𝑝,𝛼 (𝛾0) for 𝑟 = 1,2,3, . ..by the relation 𝜔𝑝,𝛼 𝑟 (𝑓, 𝑡) ≔ sup |ℎ|≤𝑡 ‖∆ℎ 𝑟 (𝑓, . )‖𝐿𝑝,𝛼(γ0), 𝑡 > 0, where ∆ℎ 𝑟 (𝑓, 𝑥) = ∑ ( 𝑟 𝑘 ) (−1)𝑟−𝑘 𝑓(𝑥 + 𝑘ℎ)𝑟𝑘=0 . the best approximation to 𝐿𝑝,𝛼 (γ0) in the class 𝒯𝑛 of trigonometric polynomials of degree not greater than 𝑛 is defined by 𝐸𝑛(𝑓)𝐿𝑝,𝛼(γ0) ≔ inf{‖𝑓 − 𝑇𝑛‖𝐿𝑝,𝛼(γ0): 𝑇𝑛 ∈ 𝒯𝑛 }. let 𝑇∗ ∈ 𝒯𝑛 be a trigonometric polynomial such that 𝐸𝑛 (𝑓)𝐿𝑝,𝛼(γ0) ≔ ‖𝑓 − 𝑇 ∗‖𝐿𝑝,𝛼(γ0). if 𝑚, 𝑛 ∈ ℕ such that 𝑚 ≥ 𝑛, then we get 𝐸𝑚(𝑓)𝐿𝑝,𝛼(γ0) ≤ 𝐸𝑛(𝑓)𝐿𝑝,𝛼(γ0). (2) using the boundedness of operator 𝑓 → 𝑆𝑛 (. , 𝑓) in the morrey spaces 𝐿 𝑝,𝛼 (𝛾0) we get approximation properties of de la vallée-poussin sums in morrey spaces 91 ‖𝑓 − 𝑆𝑛(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ ‖𝑓 − 𝑇 ∗‖𝐿𝑝,𝛼(𝛾0) + ‖𝑇 ∗ − 𝑆𝑛(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) = 𝐸𝑛(𝑓)𝐿𝑝,𝛼(γ0) + ‖𝑆𝑛(. , 𝑓 − 𝑇 ∗)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝐸𝑛 (𝑓)𝐿𝑝,𝛼(γ0) + 𝐶‖𝑓 − 𝑇 ∗‖𝐿𝑝,𝛼(𝛾0) = (𝐶 + 1)𝐸𝑛(𝑓)𝐿𝑝,𝛼(γ0) = 𝑐𝐸𝑛 (𝑓)𝐿𝑝,𝛼(γ0), where c is a positive constant and 𝑐 = 𝐶 + 1, i.e. there exists a constant 𝑐 such the following relation holds ‖𝑓 − 𝑆𝑛(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝑐𝐸𝑛(𝑓)𝐿𝑝,𝛼(γ0). (3) definition 2.3 [9] we define the morrey-smirnov classes 𝐸𝑝,𝛼 (𝐺), 0 ≤ 𝛼 ≤ 2 and 1 ≤ 𝑝 < ∞, of analytic functions in 𝐺 as 𝐸𝑝,𝛼 (𝐺) ≔ {𝑓 ∈ 𝐸1(𝐺) ∶ 𝑓 ∈ 𝐿𝑝,𝛼 (γ)}. if we define ‖𝑓‖𝐸𝑝,𝛼(g) ≔ ‖𝑓‖𝐿𝑝,𝛼(γ), then 𝐸 𝑝,𝛼 (𝐺) becomes a banach space. definition 2.4 [20] a smooth curve γ: σ(s) is called dini-smooth if it satisfies the condition ∫ ω(𝜎′(𝑠), 𝑠) 𝑠 𝑑𝑠 𝛿 0 < ∞, 𝛿 > 0, where ω(𝜎 ′(𝑠), 𝑠) modulus of continuity of function 𝜎 ′(𝑠). by 𝒟 we denote the set of all dini-smooth curves. if γ ∈ 𝒟, then [21] 0 < 𝑐1 ≤ |𝜓 ′ (𝑤)| ≤ 𝑐2 < ∞, 0 < 𝑐3 ≤ |𝜑′(𝑧)| ≤ 𝑐4 < ∞ (4) for some constants, 𝑐1, 𝑐2, 𝑐3 and , 𝑐4. hence, if γ ∈ 𝒟 and using (4), then by [9] 𝑓 ∈ 𝐿𝑝,𝛼 (γ) ⟺ 𝑓0 ≔ 𝑓 ∘ 𝜓 ∈ 𝐿 𝑝,𝛼 (𝛾0) (5) and the function 𝑓0 +: 𝐷 → ℂ defined by 𝑓0 +(𝑤) = 1 2𝜋𝑖 ∫ 𝑓0(𝜏) 𝜏−𝑤 𝑑𝜏 𝛾0 , 𝑤 ∈ 𝐷 (6) is analytic in 𝐷 and 𝑓0 + ∈ 𝐸𝑝,𝛼 (𝐷) [9] . if γ ∈ 𝒟 and 𝑟 = 1,2,3, …, we define the 𝑟 − modulus of smoothness of 𝑓 ∈ 𝐿𝑝,𝛼 (γ) by the relation (see, [9]) ωγ,𝑝,𝛼 𝑟 (𝑓, 𝑡) ≔ ω𝑝,𝛼 𝑟 (𝑓0 +, t), 𝑡 > 0 . (7) the faber polynomials φ𝑘 (𝑡) of degree 𝑘 are defined by the relation [22] 𝜓′(𝑤) 𝜓(𝑤)−𝑡 = ∑ φ𝑘(𝑡) 𝑤𝑘+1 ∞ 𝑘=0 , 𝑡 ∈ g, 𝑤 ∈ 𝐷 −. (8) ahmed kinj et al 92 if 𝑓 ∈ 𝐸𝑝,𝛼 (𝐺), then by the definition 2.3, 𝑓 ∈ 𝐸1(𝐺) and hence 𝑓(𝑧) = 1 2𝜋𝑖 ∫ 𝑓(𝑠) 𝑠 − 𝑧 𝑑𝑠 γ = 1 2𝜋𝑖 ∫ 𝜓′(𝑤) 𝜓(𝑤) − 𝑧 𝑓0(𝑤)𝑑𝑤 𝛾0 , z ∈ g. from the last formula and the relation (8), for every 𝑧 ∈ 𝐺 we have 𝑓(𝑧)~ ∑ 𝑎𝑘 (𝑓)φ𝑘(𝑧) ∞ 𝑘=0 , 𝑧 ∈ 𝐺, (9) where 𝑎𝑘 (𝑓) ≔ 1 2𝜋𝑖 ∫ 𝑓0(𝑤) 𝑤 𝑘+1 𝑑𝑤 γ0 , 𝑘 = 0,1,2, … . the 𝑛 − 𝑡ℎ de la vallée-poussin sums of the series (9) are defined as 𝑉𝑛,𝑚(𝑥, 𝑓) = 1 𝑚 + 1 ∑ 𝑆𝑘 (𝑥, 𝑓) 𝑛 𝑘=𝑛−𝑚 , 0 ≤ 𝑚 ≤ 𝑛, 𝑚, 𝑛 = 1,2,3, … , where 𝑆𝑛(𝑧, 𝑓) = ∑ 𝑎𝑘 (𝑓)φ𝑘 (𝑧) 𝑛 𝑘=0 . we define the operator 𝑇 as follows: 𝑇: 𝐸𝑝,𝛼 (𝐷) → 𝐸𝑝,𝛼 (𝐺) 𝑇(𝑓)(𝑧) ≔ 1 2𝜋𝑖 ∫ 𝑓(𝑤)𝜓′(𝑤) 𝜓(𝑤)−𝑧 𝑑𝑤 𝛾0 , 𝑧 ∈ 𝐺. (10) in order to prove our main results, we need the following theorems. theorem 2.1 [10] if γ ∈ 𝒟, then the operator 𝑇 defined by (10) is linear, bounded, one to one and onto. moreover 𝑇(𝑓0 +) = 𝑓 for 𝑓 ∈ 𝐸𝑝,𝛼 (𝐺). theorem 2.2 [9] let 𝑔 ∈ 𝐸𝑝,𝛼 (d) with 0 < 𝛼 ≤ 2 and 1 < 𝑝 < ∞. then for a given 𝑟 = 1,2,3, … the inequality 𝐸𝑛(𝑔)𝐿𝑝,𝛼(γ0) ≤ 𝑐5 𝜔𝑝,𝛼 𝑟 (𝑔, 1 𝑛 + 1 ) , 𝑛 = 1,2,3, .. holds with a constant 𝑐5 > 0 independent of 𝑛. 3. main results in this section, we present the main results. theorem 3.1 let 𝐿𝑝,𝛼 (𝛾0) be a morrey space with 0 < 𝛼 ≤ 2 and 1 < 𝑝 < ∞, then there exists a positive constant 𝑐6 such that for any 𝑓 ∈ 𝐿𝑝,𝛼 (𝛾0), 0 ≤ 𝑚 ≤ 𝑛, 𝑚, 𝑛 = 1,2, … the inequality ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝑐6 𝑚+1 ∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛 𝑘=𝑛−𝑚 (11) is true. proof. let us chose the integer 𝑗 such that 2𝑗 ≤ 𝑚 + 1 ≤ 2𝑗+1. then 𝑓(𝑥) − 𝑉𝑛,𝑚(𝑥, 𝑓) = 1 𝑚 + 1 [𝑓(𝑥) − 𝑆𝑛−𝑚(𝑥, 𝑓)] + 1 𝑚 + 1 {∑ ∑ [𝑓(𝑥) − 𝑆𝑖 (𝑥, 𝑓)] 𝑛−𝑚+2𝑘−1 𝑖=𝑛−𝑚+2𝑘−1 𝑗 𝑘=1 } + 1 𝑚 + 1 { ∑ [𝑓(𝑥) − 𝑆𝑘 (𝑥, 𝑓)] 𝑛 𝑘=𝑛−𝑚+2𝑗 }. and from this, we get approximation properties of de la vallée-poussin sums in morrey spaces 93 ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 1 𝑚 + 1 ‖𝑓 − 𝑆𝑛−𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) + 1 𝑚 + 1 {∑ ∑ ‖𝑓 − 𝑆𝑖 (. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) 𝑛−𝑚+2𝑘−1 𝑖=𝑛−𝑚+2𝑘−1 𝑗 𝑘=1 } + 1 𝑚 + 1 { ∑ ‖𝑓 − 𝑆𝑘 (. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) 𝑛 𝑘=𝑛−𝑚+2𝑗 }. from the relation (3), we get ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ c7 𝑚+1 𝐸𝑛−𝑚(𝑓)𝐿𝑝,𝛼(𝛾0) + c8 𝑚+1 {∑ ∑ 𝐸𝑖 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛−𝑚+2𝑘−1 𝑖=𝑛−𝑚+2𝑘−1 𝑗 𝑘=1 } + c9 𝑚+1 {∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛 𝑘=𝑛−𝑚+2𝑗 }. (12) from (12) and using (2), we get ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝑐10 𝑚+1 {𝐸𝑛−𝑚(𝑓)𝑋,𝜔 + ∑ 2 𝑘−1𝐸𝑛−𝑚+2𝑘−1 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑗 𝑘=1 } + 𝑐11 1 𝑚+1 (𝑚 − 2𝑗 + 1)𝐸𝑛−𝑚+2𝑗 (𝑓)𝐿𝑝,𝛼(𝛾0). (13) on the other hand, we have ∑ 2𝑘−1𝐸𝑛−𝑚+2𝑘−1 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑗 𝑘=1 ≤ 𝐸𝑛−𝑚+1(𝑓)𝐿𝑝,𝛼(𝛾0) + 2 ∑ ∑ 𝐸𝑖 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛−𝑚+2𝑘−1−1 𝑖=𝑛−𝑚+2𝑘−2 𝑗 𝑘=2 ≤ 𝑐12 ∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛−𝑚+2𝑗−1 𝑘=𝑛−𝑚 . (14) since 2𝑗 ≤ 𝑚 + 1 < 2𝑗+1, we get 2𝑗 > 𝑚 − 2𝑗 + 1. hence (𝑚 − 2𝑗 + 1)𝐸𝑛−𝑚+2𝑗 (𝑓)𝐿𝑝,𝛼(𝛾0) ≤ ∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0). 𝑛−𝑚+2𝑗−1 𝑘=𝑛−𝑚 (15) from (13), (14) and (15) we obtain ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝑐13 𝑚 + 1 {𝐸𝑛−𝑚(𝑓)𝐿𝑝,𝛼(𝛾0) + ∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛−𝑚+2𝑗−1 𝑘=𝑛−𝑚 + ∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛−𝑚+2𝑗−1 𝑘=𝑛−𝑚 } ≤ 𝑐6 𝑚 + 1 ∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛 𝑘=𝑛−𝑚 and the inequality (11) is true. corollary 3.1 let 𝐿𝑝,𝛼 (𝛾0) be a morrey space with 0 < 𝛼 ≤ 2 and 1 < 𝑝 < ∞, then there exists a positive constant 𝑐14 such that for any 𝑓 ∈ 𝐿𝑝,𝛼 (𝛾0), 0 ≤ 𝑚 ≤ 𝑛, 𝑚, 𝑛 = 1,2, … the inequality ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝑐14 𝑚+1 ∑ 𝜔𝑝,𝛼 𝑟 (𝑓, 1 𝑘+1 )𝑛𝑘=𝑛−𝑚 (16) is true. proof. from theorem 3.1 we have ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝑐6 𝑚 + 1 ∑ 𝐸𝑘 (𝑓)𝐿𝑝,𝛼(𝛾0) 𝑛 𝑘=𝑛−𝑚 and from theorem 2.2 we get 𝐸𝑛 (𝑓)𝐿𝑝,𝛼(γ0) ≤ 𝑐5 𝜔𝑝,𝛼 𝑟 (𝑓, 1 𝑛 + 1 ) , 𝑛 = 1,2,3, … . ahmed kinj et al 94 we reach ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(𝛾0) ≤ 𝑐14 𝑚 + 1 ∑ 𝜔𝑝,𝛼 𝑟 (𝑓, 1 𝑘 + 1 ) 𝑛 𝑘=𝑛−𝑚 , 𝑛 = 1,2, … . theorem 3.2 let 𝐺 be a simply connected domain in the complex plane, bounded by a curve γ ∈ 𝒟. if 𝑓 ∈ 𝐸𝑝,𝛼 (𝐺) with 0 < 𝛼 ≤ 2 and 1 < 𝑝 < ∞, then for every 0 ≤ 𝑚 ≤ 𝑛, 𝑛, 𝑚 ∈ ℕ the estimate ‖𝑓 − 𝑉𝑛(. , 𝑓)‖𝐿𝑝,𝛼(γ) ≤ 𝑐15 ∑ ωγ,𝑝,𝛼 𝑟 (𝑓, 1 𝑘 + 1 ) 𝑛 𝑘=𝑛−𝑚 holds, where 𝑐15 is a positive constant. proof. since 𝑓 ∈ 𝐸𝑝,𝛼 (𝐺) and γ is a dini – smooth curve, then the boundary function of 𝑓 belongs to 𝐿𝑝,𝛼 (γ) and from the relation (5) we get 𝑓0 ∈ 𝐿 𝑝,𝛼 (𝛾0), and the function 𝑓0 + which defined by (6) belongs to 𝐸𝑝,𝛼 (𝐷). since 𝐸𝑝,𝛼 (𝐷) ⊂ 𝐸1(𝐷), we obtain 𝑓0 + ∈ 𝐸1(𝐷) which has the following taylor expansion 𝑓0 +(𝑤) = ∑ 𝑎𝑘 (𝑓0 +)𝑤 𝑘∞𝑘=0 , 𝑤 ∈ 𝐷. (17) let {𝑐𝑘 } be the fourier coefficients of the boundary function of 𝑓0 +, then by [23] we get 𝑐𝑘 = 𝑎𝑘 (𝑓0 +) for 𝑘 ≥ 0 and 𝑐𝑘 = 0 for 𝑘 < 0, and then by substitution in (17) we obtain 𝑓0 +(𝑤) = ∑ 𝑐𝑘 𝑤 𝑘 ∞ 𝑘=0 , 𝑤 ∈ 𝐷. note that for the function 𝑓 ∈ 𝐸𝑝,𝛼 (𝐺) the following faber series holds 𝑓(𝑧)~ ∑ 𝑎𝑘 (𝑓)φ𝑘 (𝑧) ∞ 𝑘=0 , 𝑧 ∈ 𝐺, where 𝑎𝑘 (𝑓), 𝑘 = 0,1,2, … are the taylor coefficients of the function 𝑓0 +, and by theorem 2.1 we obtain 𝑇 (∑ 𝑎𝑘 (𝑓0 +)𝑤𝑘 𝑛 𝑘=0 ) = ∑ 𝑎𝑘 (𝑓)φ𝑘 (𝑧) n 𝑘=0 and 𝑇 (𝑉𝑛,𝑚(w, 𝑓0 +)) = 𝑉𝑛,𝑚(𝑧, 𝑓), 0 ≤ 𝑚 ≤ 𝑛, 𝑛, 𝑚 = 0,1,2, … . hence, using the boundedness of operator 𝑇 defined by (10) and the relation (11), we reach ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(γ) = ‖𝑇(𝑓0 +) − 𝑇 (𝑉𝑛,𝑚(. , 𝑓0 +))‖ 𝐿𝑝,𝛼(γ) ≤ 𝑐16‖𝑓0 + − 𝑉𝑛,𝑚(. , 𝑓0 +)‖ 𝐿𝑝,𝛼(𝛾0) ≤ 𝑐17 𝑚 + 1 ∑ 𝐸𝑘 (𝑓0 +)𝐿𝑝,𝛼(𝛾0). 𝑛 𝑘=𝑛−𝑚 using the theorem 2.2 we get ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(γ) ≤ 𝑐15 𝑚 + 1 ∑ 𝜔𝑝,𝛼 𝑟 (𝑓0 +, 1 𝑘 + 1 ) . 𝑛 𝑘=𝑛−𝑚 and by the relation (7) we reach ‖𝑓 − 𝑉𝑛,𝑚(. , 𝑓)‖𝐿𝑝,𝛼(γ) ≤ 𝑐15 𝑚 + 1 ∑ ωγ,𝑝,𝛼 𝑟 (𝑓, 1 𝑘 + 1 ) . 𝑛 𝑘=𝑛−𝑚 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applications 14 (2nd edition), de gruyter, berlin/boston, 2013. 19. devore, r.a. and lorentz, g.g. constructive approximation: a series of comprehensive studies in mathematics, springer, new york, 1993. 20. pommerenke, c. boundary behavior of conformal maps: a series of comprehensive studies in mathematics, springer, berlin, 1992. 21. warschawski, s.e. uber das ranverhalten der ableitung der abildunggsfunktion bei konfermer abbildung, math. z. 1932, 35(german). 22. markushevich, a. theory of analytic functions, izdatelstvo nauka, moscow, 1968. 23. duren, p.l. theory of h p spaces: a series of monographs and textbooks, academic press, new york, 1970. received 18 october 2016 accepted 1 st august 2017 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 169-176 © 2002 sultan qaboos university analysis of electrical stresses in ac switches used for control of small power motors present in household appliances yves raingeaud, franck galtie, laurent gonthier and jean baillou university of tours, lmppower microelectronics laboratory 16 rue pierre and marie curie, bp7155, 37 071 tours cedex 2, france, tel: 02 47 42 40 00, fax: 02 47 51 01 34. email: raingeaud@univ-tours.fr, franck.galtie@st.com, laurent.gonthier@st.com, baillou@univ-tours.fr. تحليل االجهادات الكهربائية في مفاتيح التيار الكهربائي المتردد المستخدمة في المحركات الكهربائية الصغيرة الموجودة في األجهزة المنزلية تي ، لورنت جونزير و جين بيووايفس رنجيود ، فرانك جل تصف هذه الورقة دراسة التوترات الكهربائية والحرارية في المفاتيح ثنائية االتجاه المستعملة في التحكم بالمحركات :خالصة .والحملوتحليل عمل المحركات وأيضا المعرفة جيدا للتفاعالت بين المفتاح . الكهربائية الصغيرة والموجودة في األجهزة المنزلية abstract: this paper describes a study on electric and thermal stresses induced in bidirectional switches used for control of small power motors present in household appliances, in order to find out the possible weakness of the current solution generally made of a triac and to determine the requirements for new dedicated devices in the asdtm technology. first, a behavioral analysis of these motors must be performed and the interactions between the switch and the load have to be well defined. keywords: electric stress, switching components, induction motor, synchronous motor, household appliances. 1. introduction n owadays, many of the ac solid-state switches are used to drive different actuators directly supplied on the mains, such as loads which are present in the large and highly competitive household appliances industry. as the features offered to the customers have increased significantly while the price remains almost the same, suppliers have to develop new highly customized cost effective loads for high volume production (lloyd and sood, 2000). therefore, these new loads have led to new driving circuits and thereby new electric stresses in the alternative switches used in these circuits (galtié et al, 2000). in this paper, we present the behavioral analysis of different small power motors used in household appliances, i.e. in dishwashers and washing machines as drain pumps, like the singlephase induction motor and the single-phase synchronous motor. these motors are well suited to be driven directly on the mains with a very simple control circuit made of a single triac. since these motors are ‘just-proportioned’ for the running condition, a variation of this steady-state condition leads to the variation of the stress involved in the switching device. a complete study of the electrical behavior of these motors has been made regarding the application requirements, such as locked rotor condition or the european 50 hz mains shift (220vrms with a variation of ± 10%). 169 mailto:raingeaud@univ-tours.fr mailto:franck.galtie@st.com mailto:laurent.gonthier@st.com yves raingeaud, franck galtie, laurent gonthier and jean baillou from this behavioral study, it is possible to design new dedicated power switching devices in the asdtm technology developed by stmicroelectronics in tours, france, and based on the functional integration concept (pezzani and quoirin, 1995), (quoirin and pezzani, 1997). 2. the single-phase induction motors the induction motors are the most widely used in appliances. this kind of motors have poor starting performance and poor efficiency (below 30%). the power range of these motors is generally less than 100w. they are often chosen for their reliability and robustness (lloyd and sood, 2000). the different induction motors we worked on are mainly used as drain pumps and are singlephase motors. the stator is made of one or several windings. the rotor may be a short-circuited coil or a squirrel cage. the alternating current passing through the stator creates a revolving magnetic field. therefore, a current is induced in the rotor. according to the lenz relation, the rotor tries to annihilate this current involving its self-rotation. however, the rotor's speed is less than the synchronism one. indeed, the rotor must lag the stator revolving field otherwise the induced current in the rotor is cancelled and there is no motion. the speed variation between the rotor (ωr) and the stator (ωs) is called the slip. s rsg ω ω−ω = (1) since the driving torque γ is always equal to the resistant torque whenever the motor runs, a resistant torque increase leads to the rotor rate decrease and the slip tends towards one. r p ω =γ (2) figure1. torque-speed characteristics of the single-phase induction motor with: cd: direct torque, ci: inverse torque, cres: resulting torque. as it has been explained previously, the stator can only generate an alternating field that can be decomposed into two opposite rotating fields (figure 1). as it can be seen in the figure, there is no starting torque and the rotor can start in either direction. to manage this issue, a short-circuited secondary winding is added to the motor in order to shade part of the flux from the main pole. this secondary winding is called "frager's turn". since the torque characteristic is not symmetrical anymore, the motor is able to start always in the same direction with a poor torque. 170 analysis of electric stresses in ac switches 2.1 electrical modeling the three-phase model of motor (figure 2) is valid for one phase only if the motor works in steady state condition with constant speed and torque. the way to obtain all these parameters is well known. this method is well suited for motors with an "empty loaded" slip less than 1% in order to assume it as zero. since the single-phase motors tested present a slip in this condition of about 3 to 6 %, the calculation leads to an unphysical solution such as negative resistance. therefore, the model that can be used is a simple rlc type model (figure 3). the different parameters are determined thanks to the watt-full and the watt-less power measurements. as this kind of motors is "just-proportioned" for the nominal working, saturation effect or iron losses increase lead to different behaviors. thereby, the model's parameters have to be redefined in each condition: r1 l1 rfer r/glf l2 r1 l1 rfer r/glf l2 figure 2. one phase equivalent model for the induction motor with: l1: stator inductance; l2: rotor inductance brought back to the stator; lf: leakage inductance; rf: resistance corresponding to iron loss; r: rotor resistance brought back to the stator; r1: stator resistance, g: slip. "empty-loaded", "full-loaded" or locked rotor condition. moreover, a capacitor is added to the model in order to take into account the parasitic capacitance stemming from the coil turns and the coil layers. for example, for vmains = 220 vrms and in locked rotor condition, the model's parameters are the followings: r = 130 ω, l = 0.6 h, and c = 160 pf. r l c r l c figure3. simplified model for the single-phase induction motor. 2.2 behavioral analysis in a full loaded condition, the inrush current is increased by 5% and the steady state current by 10% in comparison with the empty loaded working condition. the inrush current is 3 to 5 times greater than the steady state current, but its rate of rise is limited by the inductive behavior of the stator (figure 4). the transient response duration is about 20 ms. the steady state current depends on the motor dimension and its value ranges between 1.5 and 2.5 arms. at the turn-off, the kind of induction motor we worked on cannot behave like an alternator. however, when is switch turned off, a weak oscillating emf (50 v) is generated due to the magnetic remanence (figure 5). in locked rotor condition, the overall current shape looks like that of the running condition but the steady state amplitude is always greater. indeed, the slip is equal to one and the ratio r/g is minimum. when the driving switch is turned off, a small voltage without oscillations appears on the motor terminals, due to the magnetic remanence. 171 yves raingeaud, franck galtie, laurent gonthier and jean baillou 6.16 a 1.8 a 5 0 v figure 4. inrush current and steady state current in the induction motor. c irc uit tu rn-o ff figure 5. emf on the motor terminals at the circuit turn-off. figure 6. typical presentation of a single-phase pm synchronous motor. 3. the single-phase synchronous motors construction of a single-phase permanent magnet (pm) synchronous motor is simple with the stator being a core of u-shaped laminations with two bobbin wound coils slid over the core to form the stator winding. the rotor is a simple ferrite cylindrical magnet magnetized with two poles 172 analysis of electric stresses in ac switches (figure 6). the presence of one or several permanent magnets generates a rotor field and the mains generates an ac current in the stator winding, therefore a revolving field. the pm rotor field locks in with the revolving field of the stator so that the motor runs precisely at the synchronous speed of the stator field. the torque-speed characteristic of a single-phase pm synchronous motor is shown on figure 7 where the curve is a straight line parallel to the torque axis. intersection of this line with the speed axis defines the synchronism speed ωs. with this characteristic, only an external action on the driving shaft will change the torque’s value and such action induces changing of the cr (ω) characteristics but the speed remains the same. torque speed cr1 cr2 cr3 c1 c2 c3 ω s figure 7. torque-speed characteristic of a single-phase pm synchronous motor. this kind of motor has an oscillatory starting characteristic and will start in either direction. to obtain a required direction of rotation and a minimum torque when the motor is starting, it is necessary to give an irregular shape to the air gap. these motors have found a niche market in drain pumps for washing machines and dishwashers with power ratings of around 30 w. they are replacing the single-phase induction motors because of their better efficiency close to twice that of the single-phase induction motors (about 50%) and their relatively low cost (lloyd and sood, 2000). a u-shaped, 2-pole motor is a recent variation of pm synchronous motors. 3.1 electrical modeling when the motor is running, the rotor field induces a variable flux in the stator winding. this variation generates a sinusoidal-shaped electromotive force (emf). an equivalent circuit of the motor is shown figure 8, where a capacitor is added in order to take into account the parasitic capacitance of the stator winding. for vmains = 264 vrms, the typical values obtained are r = 180 ω ; l = 1.4 h, c = 100 pf, e = 218 vrms. r e l c figure 8. equivalent circuit of synchronous motor running. 3.2 behavioral analysis in locked rotor condition, the steady-state current is typically 0.7 arms, i.e. 2.5 times greater than the running value. the most important measured (dv/dt)c (locked rotor) is 11.9 v/µs for (di/dt)c equal to 0.16 a/ms at 25°c, with switching devices specified for 1 v/µs and 0.35 a/ms at 100°c. 173 yves raingeaud, franck galtie, laurent gonthier and jean baillou circuit turn-off current in the load figure 9. presence of an oscillatory voltage at terminals of synchronous motor when the switch turns off. when the control device is switching off, the emf generated by the synchronous motor working as an alternator is not negligible since it can be up to 100 volts (figure 9). when the motor is in a deceleration phase, the voltage does not present a constant period or amplitude and modifies the applied voltage to the device during the turn-off. the emf generally decreases the amplitude of the mains applied at commutation and thus decreases the rate of increase of this voltage : (dv/dt)c. triac current voltage across the triac after turn -off re-applied voltage (250v) 450 v triac current voltage across the triac after turn -off re-applied voltage (250v) 450 v figure 10. applied voltage on the triac after the pm synchronous motor commutation. since the emf modifies the voltage across the device, the figure 10 shows that the voltage can be higher than the mains amplitude and therefore the component off-state capability must be suitable. however, in this instance, the voltage reaches only 450v that is less than the off-state voltage withstood by most of the triac (vdrm/vrrm = 600v). 4. switch-load interaction the electric behavior of the two foregoing motors induces electric and thermal stresses on the control switch and it is very important to know them either for the choice of the switch or for the design of a new component in the asdtm technology. in this section, we present the stresses 174 analysis of electric stresses in ac switches induced by the load on the switch at the turn-on, in the on-state, at the turn-off and in the offstate. 4.1 switch turn-on each kind of motors presents a parasitic capacitance due to the stator winding. so, when the device turns on while vmains = 264 vrms, the capacitive current rate of rise is about (di/dt) ≈ 15 a/µs with a weak amplitude (0.8 a). however this measured value of (di/dt) is higher than the repetitive critical rate of rise of on-state current given by conventional triacs datasheets, i.e. 10 a/µs. it would be better to fire the triac at the zero voltage crossing of the mains. figure 11. thermal simulation of a triac junction temperature during the locked rotor condition. 4.2 switch on-state the control switch on-state induces an inrush current from 2 to 5 times greater than the steady state current. the worst case occurs when each kind of motors is in locked rotor condition. in this case, the steady state current is noticeably increased and the device temperature as well. thermal simulation has been performed to determine if the switching device is able to withstand a temperature increase without causing damage or affecting the reliability. figure 11 shows the thermal simulation of a triac junction temperature (z01xx, in to92 package, stmicroelectronics) during the locked rotor condition of an induction motor. the initial temperature has been chosen equal to 60°c, i.e. the ambient temperature inside a washer. we can observe that the temperature increases over 125°c, which is the maximum temperature allowed in the device. this device is not suitable to control this kind of motor. 4.3 switch turn-off the current cancellation in the device involves the circuit turn-off. the motors being inductive loads, the device turn-off is not obtained at the zero volt of the mains. consequently, the rate of rise of the voltage (dv/dt)c is greater than the one obtained when the switching occurs at the zero voltage. this (dv/dt)c value can produce an unwanted firing especially if the current rate of decrease is high. so, the commutation capability is a function of (di/dt)c and (dv/dt)c. the most important measured (dv/dt)c is 18 v/µs for a (di/dt)c equal to 0.6 a/ms. the device used is a triac specified for itrms = 4 a, (di/dt)c = 1.8 a/ms @ (dv/dt)c = 20 v/µs at tj = 125°c. this device is well dimensioned regarding the commutation stress but it is over dimensioned regarding the current capability (4 arms instead of 1.5 arms needed in locked rotor condition). 175 yves raingeaud, franck galtie, laurent gonthier and jean baillou 4.4 switch off-state in off-state condition, the control switch must withstand a forward or reverse voltage (vdrm/vrrm) without causing an unwanted firing. indeed, the triac must not work in breakdown condition in order to avoid any instant failure or to reduce its reliability. figure 10 shows that the voltage across the triac after the turn-off reaches 450 v. consequently, a well suited device must be chosen with at least a vdrm/vrrm = 600 v. 5. conclusion the behavior analysis of different small power motors used in household appliances (diswashers and washing machines) allows a better knowledge of their empty loaded and full loaded characteristics. the single-phase induction motor and the single-phase permanent magnet synchronous motor are usually used as drain pumps. suppliers have to develop new customized loads characterized by their reliability and robustness. in these loads, current and voltage observation for different working conditions (full loaded, empty loaded, locked rotor) shows electric and thermal stresses induced on the control switch: • amplitude and duration of inrush current. • amplitude of steady state current in the locked rotor condition. • temperature increasing in the component in the steady state condition and locked rotor, • emf added to the mains when the device turns off. • (dv/dt)c and (di/dt)c when the device turns off. all these parameters must be taken into account to choose a usual component or to design a new-dedicated power switching device in the asdtm technology. references galtie, f., raingeaud, y., gonthier, l. and baillou, j. 2000. analyse de systèmes conduisant à la conception de composants dédiés dans la filière asdtm : application à divers actionneurs de petite puissance. proceedings of epf 2000, lille, france, december 2000. lloyd, j.d. and sood, p.k. 2000. motor technology for major household appliances. confortec international appliance tech. forum, paris, france, 2000. pezzani, r. and quoirin, j.b. 1995. functional integration of power devices : a new approach. proceeding of epe’95, sevilla, spain, 2.219-2.223. quoirin, j.b. and pezzani, r. 1997. intégration monolithique, état de l’art et tendance future. forum européen des semiconducteurs de puissance, club crin – see, paris, france, 9-14. received 3 june 2001 accepted 18 january 2002 176 yves raingeaud, franck galtie, laurent gonthier and jean baillou the single-phase induction motors 2.1 electrical modeling � 2.2 behavioral analysis the single-phase synchronous motors 3.1 electrical modeling 3.2 behavioral analysis references squ journal for science, 2018, 23(2), 78-84 doi: http://dx.doi.org/10.24200/squjs.vol23iss2pp78-84 sultan qaboos university 78 nutritional value of vegetable wastes as livestock feed osman mahgoub 1 *, isam t. kadim 2 , yasmin eltahir 1 , sadeq al-lawatia 1 and abdulrahim m. al-ismaili 3 1 department of animal & veterinary sciences, college of agricultural & marine sciences, sultan qaboos university p.o.box 36, pc 123, al khoud, muscat, sultanate of oman; 2 university of nizwa, sultanate of oman; 3 department of soil, water & agricultural engineering, college of agricultural & marine sciences, sultan qaboos university, po box 34, al-khod 123, sultanate of oman. *email: osmahgob@squ.edu.om. abstract: a study was carried out to evaluate the nutritional value of waste from lettuce, green cabbage, red cabbage and cauliflower to determine their potential use for feeding to livestock. vegetable wastes were dried in a solar tunnel drier. the crude protein (cp), ether extract (ee), total ash, acid detergent fiber (adf) and neutral detergent fiber (ndf) were 24.1, 2.7, 24.7, 29.3 and 29.0%; 17.7, 2.3, 13.7, 25.6, and 28.7%; 11.9, 1.9, 8.8, 23.1 and 25.6%; 10.3, 0.5, 7.0, 16.1 and 19.6 % (dm basis) in cauliflower, lettuce, green cabbage and red cabbage, respectively. the gross energy (mj/kg dm) in cauliflower and green cabbage (16.9 and 16.6) was higher than that observed in red cabbage and lettuce (14.1 and14.3). the red and green cabbage waste had higher net gas production (73 and 71 ml/g dm/12h) compared to the lettuce and cauliflower vegetable waste (51 and 48 ml/g dm/12h respectively). the green and red cabbage waste had significantly higher metabolizable energy (me) (approximately 12 mj/kg dm) than both lettuce and cauliflower waste (approximately 9 mj/kg dm). the in vitro dm and om digestibility (omd) in green and red cabbage waste was significantly higher than in lettuce and cauliflower. the green and red cabbage waste had significantly higher short chain fatty acids (scfa) (1.7 and 1.6 µmol) than lettuce and cauliflower (1.2 and 1.1 µmol). it was concluded that leafy vegetable waste (lettuce, green cabbage, red cabbage and cauliflower) is an excellent source of nutrients which can potentially be used after drying as an animal feed to reduce animal feeding costs and consequently increase farmers’ profits. this would also help in waste management and the reduction of environmental pollution. keywords: vegetable wastes; lettuce, cauliflower; cabbage. القيمة الغذائية لمخلفات الخضروات كعلف للحيوان في سلطنة عمان صادق اللواتيا وعبد الرحيم اإلسماعيلي ،ياسمين الطاهر ،عصام كاظم،عثمان محجوب إجراء دراسة لتقييم القيمة الغذائية لمخلفات الخضروات من الخس والزهرة والكرنب األخضر واألحمر لتحديد إمكانية استخدامها كعلف تم الملخص: تم تجفيف مخلفات الخضروات في مجففة شمسية وتم قياس المادة الجافة والتحليل التقريبي الكيميائي. كما تم إجراء تجربة في المختبر للحيوان في عمان. 021بعد حوالي %6.7 لقياس غاز الهضم ودرجة تحلل المادة العضوية الجافة. خفضت المجففة الشمسية وزن المادة الجافة في مخلفات الخضروات إلى ( كاآلتي: ndf( و األلياف غير المذابة )adf)المذابة في الحمض ساعة من التجفيف. كانت نسبة البروتين الخام والدهن الخام و الرماد الكلي واأللياف % من 7..0و 07.0و 6.0و ..1و 01.2% ثم 7..2و 22.0و 8.8و ..0و ..00% ثم 7..2و 02.6و 2.2و 06.6م % ث2..2و 6..2و 2.6و 0..2 روجد أعلى مستوى من الطاقة الخام في الزهرة والكرنب األخض الزهرة والخس والكرنب األخضر والكرنب األحمر على التوالي.لمادة الخام لكل من ا 62/كجم/مادة دافة(. أنتج نوعا الكرنب األخضر واألحمر غازاً أكثر )لميجا جو 2..0و 0..0( وأدناها في الكرنب األحمر والخس )07.7و ..07) مل( على التوالي. كان للكرنب األخضر واألحمر معدالت طاقة تمثيلية أعلى 8.و 0.ساعة وأكثر حتى نهاية التجربة من الخس والزهرة ) 02مل( من 60و الخس %( أعلى من.6و 80/كجم(. كان للكرنب األخضر واألحمر معدل هضم للمادة العضوية )لميجا جو ./كجم( من الخس والزهرة )لميجا جو 02) مايكرو مول( أعلى من 0.7و 0.6%(.أحتوى الكرنب األخضر واألحمر على معدالت عالية من األحماض الدهنية قصيرة السلسلة )8.و 70والزهرة ) لخس %( يليه ا..87و ..88مايكرو مول(. كان أعلى معدل هضم للمادة الجافة في المختبر في الكرنب األحمر واألخضر ) 0.0و 0.2الخص والزهرة ) %( على التوالي. ويمكن االستنتاج بأن مخلفات الخضروات الورقية مثل الخس والزهرة والكرنب األخضر واألحمر مصدر 2..6%( والزهرة )60.8) ئدات المزارع ، كما اممتاز غني بالمكونات الغذائية يمكن استخدامه بعد التجفيف كمكون لألغذية الحيوانية ، مما سيقلل من تكلفة الغذاء وبالتالي يزيد من ع يمكن أن يساعد في التعامل مع مخلفات الغذاء وتخيض معدالت التلوث البيئي. . الكرمب ،الزهرة ،الخس ، مخلفات الخضروات : مفتاحيةالكلمات ال nutritional value of vegetable wastes 79 1. introduction roduction of good, safe and cheap livestock feed is essential for profitable animal production but can exert significant pressure on natural resources and be in competition with the production of food for humans. for instance, it was reported that 53% of the cereals grown in the eu are fed to livestock [1] and that animal feed costs account for up to 70% of the cost of animal production. the fao [2] indicated that the world will need about 73% more meat and 58% more milk in 2050 for the increasing human population. however, non-conventional feed resources such as natural range plant species and agricultural by-products may help to bridge the gap between demand and supply of animal feed. vegetable and fruit wastes are envisaged to have good potential as feed resources [1]. the annual global food waste was estimated at about 1.3 to 1.6 g tonnes [1]. according to thieme and makkar [2] this is approximately one-third of global food produced and it has high environmental, economic and social impacts. the fao [3] gave a very dismal account regarding food wastage, with the estimated annual direct economic consequences of food wastage at $750 billion. the global volume of food wastage is estimated at 1.6 billion tonnes of "primary product equivalents" and a wastage for the edible part of this amounts to 1.3 billion tones. other harmful effects include methane emissions from food waste dumping and the unnecessary usage of large volumes of fresh water each year to produce food lost or wasted. it has been estimated that 1.4 billion hectares of land (28% of the world's agricultural area) is used annually to produce food that is lost or wasted. most of the economic loss is suffered by developing countries, rather than developed countries [3]. several studies have indicated that vegetable waste has good nutritive value and has potential for use as livestock feed [4,5,6]. vegetable waste may be fed freshly chopped or processed, such as when dried, composited or in feed blocks. vegetable waste could be transformed into value added products [7]. this non-conventional feed is highly sought after in arid regions, especially as maintenance feed during the dry season. cabbage and cauliflower leaves have been reported to serve as excellent sources of nutrients for ruminants and can economize the production of animals [4]. therefore, the current study primarily aims to evaluate the nutritional value of vegetable waste collected from a local vegetable market as a livestock feed, after it has been dried in a solar greenhouse-like tunnel dryer. this is to reduce the cost of animal feeding, thereby increasing farmers’ profits and reducing environmental pollution. the vegetable waste considered includes that of four leafy vegetables: lettuce (lactuca sativa), green and red cabbage (brassica oleracea var. capitata f. rubra) and cauliflower (brassica oleracea b). 2. materials and methods 2.1 vegetable waste collection and drying fresh vegetable waste from four leafy vegetables was collected from the nearby al-mawaleh fruit and vegetable market and transported to the agricultural experiments station at sultan qaboos university in muscat, sultanate of oman. the waste was weighed and spread out in a solar greenhouse-like tunnel dryer. a 15 m long and 2 m wide solar tunnel dryer (figure 1) was designed and constructed to dry up to 500 kg of fruit and vegetable wastes per batch. the first half of the tunnel base (air inlet side) was used as a flat plate air-heating solar collector and the other half as a dryer. the drying air was withdrawn from the air-heating region to the drying region of the semi-circular arched tunnel by means of fans. the fruit and vegetable wastes were uniformly distributed in the drying region. the drying temperature could be easily raised by some 5-30ºc above the ambient temperature inside the tunnel at an air velocity of approximately 0.5m/sec. figure 1. drying vegetable waste in a drying solar tunnel. p osman mahgoub et al 80 2.2 chemical analyses of feeds waste samples were dried then ground in a mill to pass through a 1 mm mesh sieve. the chemical composition of the finely ground samples of vegetable wastes were analyzed for proximate components [8] and for cell wall constituents [9, 10]. gross energy (ge) was measured using a bomb calorimeter. the samples of different wastes were evaluated by using an in vitro gas production technique [11]. short chain fatty acids were estimated according to the equation of getachew et al.[12]. the in vitro dry matter digestibility (ivdmd) was determined after 96 h of digestion, following the methods of njidda and nasiru [13]. the data were analyzed by one-way analysis of variance using the analysis of variation model in spss pc package. multiple comparison tests used tukey’s multiple-range test on spss [14]. 3. results and discussion 3.1 solar drying process the efficiency of drying the vegetable waste in the solar tunnel was tested. a total weight of 415.6 kg of a random mixture from the four vegetables was evenly spread in the drying tunnel. after drying for 120 h (6 days) the final vegetable weight was 31.6 kg indicating that the vegetable waste contained 7.6% dry matter. this demonstrated that the drying tunnel is very efficient in drying vegetable waste. the dryer was constructed with a very simple design and could be easily adopted for such operations by omani farmers [15]. similar tunnels have previously demonstrated marked efficiency in drying dates and fish (sardines) [16,17]. the high moisture content of vegetable waste increases transportation costs and also increases its susceptibility to rapid spoilage, making it important to develop practical ways to preserve it. the current study indicated that the drying process was faster in a solar tunnel dryer than under natural open-air sun drying. it was possible to reach a low moisture content in the vegetable waste within 6 days in the solar tunnel dryer compared to 8-10 days in open air natural sun drying. the improvement in the quality of vegetable waste in terms of color, brightness and absence of signs of spoilage was clearly observable. 3.2 chemical analyses of dried vegetable waste the proximate chemical analyses of the four leafy vegetable wastes revealed that lettuce and cauliflower had the lowest dry matter content (table 1), whereas the highest was observed in red and green cabbage. these values were comparable to those in published reports. for instance, wadhwa and bakshi [6] reported a dm of 10% and 13% for cabbage and cauliflower leaves, respectively. mekasha et al. [18] also reported a dm of 14.0% for cabbage waste. tobias marino et al. [5] reported a dm value of 10.2% for cabbage and 5.7% for lettuce. khan and atreja [19] reported a dm content of 7.10% for both cabbage and cauliflower. akinfemi [20] reported an extremely high dm content of 50.86% in cabbage. the high moisture contents in vegetable wastes should be taken into consideration during storage and processing. drying using solar dryers such as the one described above would be an excellent option for processing to reduce moisture under omani conditions. table 1. chemical composition of vegetable waste* vegetable waste dry matter protein fat ash adf ndf gross energy (mj/kg dm) lettuce 5.15 17.74 ± 0.08 2.65 ± 0.08 14.74 ± 1.92 25.58 ± 0.07 28.67 ± 3.54 14.08 green cabbage 11.00 11.85 ± 0.00 1.89 ± 0.00 8.75 ± 0.03 23.14 ± 0.08 25.55 ± 0.78 16.58 red cabbage 10.86 10.36 ± 0.00 00.48 ± 0.09 7.04 ± 0.02 16.13 ± 0.04 19.59 ± 0.69 14.33 cauliflower 7.07 23.05 ± 0.59 2.32 ± 0.12 13.67 ± 0.15 29.27 ± 0.49 28.97 ± 0.94 16.92 *all values except dm are expressed on % dm basis the cauliflower had the highest cp followed by that in lettuce, then green cabbage, with the lowest in red cabbage. published reports on cp vary greatly. mekasha et al. [17] reported a 14.4 % cp value for cabbage waste whereas akinfemi [19] reported a cp content of 18.4%. wadhwa and bakshi [6] reported a cp value of 20.4 and 16.1% for cabbage and cauliflower leaves, respectively, while wadhwa et al. [4] reported a cp value of 20.4% for cabbage leaves and 16.1% for cauliflower leaves, respectively. bakshi et al. [21] reported a cp content of 23.6% in fresh cauliflower leaves. tobias marino et al. [5] reported a cp value of 18.7% for cabbage and 28.2% for lettuce. khan and atreja [19] reported a cp of 22.40% in cauliflower. these studies, as well as the current study, indicate a general trend of high levels of cp in these leafy vegetables, which renders them a good source for feeding livestock. the highest fat (ee) content in the current study was in lettuce and cauliflower, while green and red cabbages contained lower levels (table 1). these levels are comparable to those reported previously for vegetable waste from these species. mekasha et al. [19] reported a 1.5% ee (on dm basis) value for cabbage waste. tobias marino et al. [5] reported an extremely low ee value of 0.5% for cabbage and 0.2% for lettuce. higher ee values were reported by thakur and bhatia [22], as 3.5 % in cauliflower leaves. akinfemi [20] also reported an ee content of 6.02% in nutritional value of vegetable wastes 81 cabbage. low fat levels are recommended for ruminant rations as high fat levels negatively influence rumen chemistry and biology. the ash content in the vegetable waste varied greatly. the highest ash content was in lettuce followed by cauliflower, while green and red cabbages had lower ash contents. wadhwa et al. [4] reported ash values of 14.0% and 17.2% (on dm basis) for cauliflower and cabbage leaves, respectively. an ash content of cauliflower leaves of 12.1% has also been reported [21]. akinfemi [19] reported an ash content of 12.1 g/100g dm) in cabbage. gupta et al.[23] reported 16.7% ash in cauliflower. similarly an ash content of 14.7% in cauliflower was reported b y khan and atreja [19]. it should be noted that high ash contents in non-conventional feeds pose a problem for their use in high proportions in mixed pelleted feeds. in the current study, cauliflower had the highest adf content followed by lettuce and green cabbage, whilst the lowest was is red cabbage. values from published reports were within this range. mekasha et al. [18] reported a 22.9% adf value for cabbage waste. wadhwa et al. [4] reported adf values of 20.0% and 23.0% for cauliflower and cabbage leaves respectively. bakshi et al. [21] reported an adf content of 23.5% in fresh cauliflower leaves. the low adf levels in vegetable waste indicates that it is easily digestible. the adf represents the fraction of indigestible material in the forage, usually cellulose fiber coated with lignin plus silica. the highest ndf content was in cauliflower followed by lettuce, and then green and red cabbage. mekasha et al. (18) reported an ndf value of 27.2% for cabbage waste. wadhwa et al. [4] reported higher ndf values of 28.0% and 34.0% for cauliflower and cabbage leaves respectively. bakshi et al. [21] reported an ndf content of 28.0% for fresh cauliflower leaves, and tobias marino et al. [5] reported a ndf value of 20.9% for cabbage and 25.6% for lettuce. the level of ndf in animal rations is important as it influences its dry matter intake and the time of rumination. the concentration of ndf in feeds is also negatively correlated with energy concentration. therefore, the adf and ndf values found by the current study, and in the literature, indicate that vegetable waste is a good potential livestock feed component, as it would make ruminant feeds more digestible. the highest gross energy (mj/kg dm) in the current study was in cauliflower and green red cabbage followed by red cabbage and lettuce. mekasha et al. [18] reported a comparable value of 17.5 mj/kg dm gross energy for cabbage waste. wadhwa et al. [4] reported an me of 13.6 and 18.4 mj/kg for cauliflower and cabbage leaves, respectively. dm indicates a similar trend of cabbage high energy value. in general, chemical analyses of waste from all four leafy vegetables indicated that they had high cp and low fat and fiber contents as well as having low adf and ndf contents. this indicates that they have a good potential to be used in ruminant diets. this is supported by previous studies. for instance, wadhwa et al. [4] reported that cauliflower leaves supplemented with minerals and common salt could sustain the body weight of bucks without adverse effects on their health. it should also be noted that published information on the composition of vegetable waste varies considerably. this may be attributed to several factors which can affect the chemical composition of feed, including the stage of growth, maturity, species or variety, soil types and growth environment [24]. 3.3 in vitro digestion of vegetable waste the gas volume produced over 96 hours is given in figure 2. the two cabbage vegetable wastes clearly produced more gas from 12 h on until the end of the experimental period. the lettuce and cauliflower vegetable waste produced significantly less gas throughout the experimental period. both cabbage wastes equally produced the highest amount of gas, whereas the lettuce and cauliflower produced lower gas volumes (table 2). this range of total gas production between 3 to 96 h was comparable to reports for waste from the same vegetable species. osman mahgoub et al 82 figure 2. in vitro gas production pattern from four leafy vegetable waste. tobias marino et al. [5] reported ranges of 10-60, 6-51 and 6-47 ml/200 mg om for cabbage, lettuce and cauliflower, respectively. high gas production indicates a good potential for rumen fermentation. the low ndf in vegetable wastes was the reason for the high in vitro gas production and digestibility [20]. the green and red cabbages in the current study had significantly higher me than both lettuce and cauliflower (table 2). tobias marino et al. [5] reported comparable me values of 10.1% for cabbage and 8.9% for lettuce. wadhwa et al. [4] reported values of 13.6 and 18.4 mj/kg dm for cauliflower and cabbage leaves, respectively. the high me levels for cabbage are in line with the higher gross energy levels reported in the current study. high energy levels in vegetable waste indicate their excellent potential as livestock feed. tobias marino et al. [5] reported me levels that followed a similar pattern of gas production to the findings of the current study. table 2. gas production parameters of lettuce, green cabbage, red cabbage and cauliflower vegetable waste. parameter lettuce green cabbage red cabbage cauliflower significance of difference mean se mean se mean se mean se total gas (ml) 50.50 b 2.082 73.33 a 1.014 71.00 a 5.575 47.83 b 0.667 p<0.0001 me (mj/kg dm) 9.07 b 0.283 12.17 a .138 11.86 a 0.758 8.71 b 0.091 p<0.0001 omd (%) 60.86 b 1.851 81.16 a 0.901 79.08 a 4.956 58.49 b 0.593 p<0.0001 scfa (µmol) 1.15 b 0.050 1.69 a 0.024 1.64 a 0.133 1.08 b 0.016 p<0.0001 me (metabolizable energy, mj/kg dm) = 2.20 + 0.136*gv + 0.057*cp + 0.0029*cf (menke & steingass, 1988) omd (organic matter digestibility) = 14.88 + 0.889*gv + 0.45*cp + 0.651*cf (menke & steingass, 1988) scfa (short chain fatty acids) = 0.0239*gv -0.0601 (getachew et al., 1999) means on the same row with similar denoting letters do not differ significantly (p>0.05) similarly, the green and red cabbages had significantly higher omd than both lettuce and cauliflower (table 2). tobias marino et al. [5] reported a comparable omd value of 79% for cabbage and 71.5% for lettuce. calculations indicated that the green and red cabbages had significantly higher short chain fatty acids (scfa) than both lettuce and cauliflower (table 2). these findings add to the value of vegetable wastes as potential livestock feeds, provided they have been provided properly processed. the red and green cabbages had the highest ivdmd values, whereas the lettuce and cauliflower had lower values (figure 3). mekasha et al. [18] reported comparable ivdmd values of 80.4% for cabbage waste. high ivdmd values indicate low cell wall constituents, which is in line with the low adf and high ndf values reported earlier. 20 30 40 50 60 70 80 90 100 110 120 0h 3h 6h 12h 24h 48h 72h 96h g a s v o lu m e ( m l) hours of fermentation lettuce red cabbage cauliflower cabbage nutritional value of vegetable wastes 83 figure 3. in vitro dry matter digestibility (ivdmd) after 96 h (%) = [(initial dm input – dm residue-blank)/ initial dm input]×100 (njidda and nasiru [13]). in general, the findings of the present study support published reports that based on chemical composition and digestibility, vegetable wastes proved to be excellent non-conventional feedstuffs equivalent to conventional green fodder. 4. conclusion waste from leafy vegetables (lettuce, green cabbage, red cabbage and cauliflower) is a rich source of nutrients which may potentially be used after drying as animal feed. the effective and efficient utilization of vegetable wastes would reduce the cost of animal feeding, increase farmers’ profits, generate an array of value-added products and help in waste management and the reduction of environmental pollution. acknowledgement the technical help of animal science students mohammed saif al-saadi and abdullah mohammed al-saadi during the experimental period is acknowledged. this study was supported by a sultan qaboos university internal grant #: ig/agr/anvs/15/01. references 1. makkar, h.p.s. opinion paper: food loss and waste to animal feed. animal, 2017, 1-3 (doi:10.1017/s17517311170000702) 2. thieme, o. and makkar, h.p.s. utilisation of loss and waste during the food-production cycle as livestock feed. animal production science,2017,(http://dx.doi.org/10.1071/an16183. 3. fao.faostat. 2017, http://www.fao.org/news/story/en/item/196402/icode/ last accessed 11.07.2017. 4. wadhwa, m., kaushal, s. and bakshi, m.p.s. nutritive evaluation of vegetable wastes as complete feed for goat bucks. small ruminant research, 2006,64, 279-284. 5. tobias marino, c., hector, b., mazza rodrigues, p.h., oliveira borgatti, l.m., marques meyer, p., alves da silva, e.j. and ørskov, e.r. characterization of vegetables and fruits potential as ruminant feed by in vitro gas production technique. livestock research for rural development,2010,22, article #168. last accessed 18.06.2017.from http://www.lrrd.org/lrrd22/9/mari22168.htm 6. wadhwa, m. and bakshi, m.p.s. utilization of fruit and vegetable wastes as livestock feed and as substrates for generation of other value-added products. technical editor: h.p.s. makkar. aphca, fao, rome, italy, 2013. 7. laufenberg, g., kunz, b. and marianne nystroem. transformation of vegetable waste into value added products: (a) the upgrading concept; (b) practical implementations. bioresource technology, 2003, 87, 167-198. 8. aoac. the official methods of analysis. association of official analytical chemists, 15 th edn. washington, dc, usa.2000. 9. roberston, j.b. and van soest, p.j. the detergent system of analysis. in: james, w.p.t., theander, o.(eds.). the analysis of dietary fiber in food. marcel dekker, newyork, usa, 1981, 123–158. 10. van soest, p.j., roberston, j.b. and lewis, b.a. methods for dietary fibre ndf and non-starch polysaccharides in 50.5 71 47 73 0 10 20 30 40 50 60 70 80 90 lettuce red cabbage cauliflower cabbage t o ta l g a s vo lu m e ( m l) type of leafy vegetable waste http://www.fao.org/news/story/en/item/196402/icode/ osman mahgoub et al 84 relation to animal nutrition. journal of dairy science,1991,74,3583–3597. 11. menke, k.h. and steingass, h. estimation of the energetic feed value from chemical analysis and in vitro gas production using rumen fluid. animal research development, 1988,28, 7-55. 12. getachew, g., makkar, h.p.s. and becker, k. stoichiometric relationship between short chain fat acids and in vitro gas production in presence and polyethyleneglycol for tannin containing browses. eaap) satellite symposium, 1999. 13. njidda, a.a. and nasiru, a. in vitro gas production and dry matter digestibility of tannin-containing forages of semi-arid region of north-eastern nigeria. pakistan journal of nutrition, 2010, 9, 60-66. 14. spss. 2007. statistical packages for social sciences. version 16, spss inc., illinois, usa. 15. basunia, m.a., handali, h.h., al-balushi, m.i., rahman, m.s., and mahgoub, o. development and performance evaluation of a solar tunnel date dryer in oman. agricultural and marine sciences, 2012,17, 2131. 16. basunia, m.a., handali, h.h., al-balushi, m.i., rahman, m.s. and mahgoub, o. drying of dates in oman using a solar tunnel dryer. xvii th world congress of the international commission of agricultural and biosystems engineering (cigr) hosted by the canadian society for bioengineering (csbe/scgab) québec city, canada june, 2010, 13-17. 17. basunia, m.a., handali, h.h., al-balushi, m.i., rahman, m.s., and mahgoub, o. drying of fish sardines in oman using solar tunnel dryers. journal of agricultural science and technology, 2011, 1, 108-114. issn2161-6264. 18. mekasha, y., tegegne, a., yami, a. and umunna, n.n. evaluation of non-conventional agro-industrial byproducts as supplementary feeds for ruminants: in vitro and metabolism study with sheep. small ruminant research, 2002, 44, 25-35. 19. khan, m.i. and atreja, p.p. chemical composition of vegetable residues from agro processing plants. proceeding of the animal nutrition conference held at ndri, karnal abstr. # 071.2001. 20. akinfemi, a. evaluation of nutritive value of vegetable wastes grownin north central nigeria using in vitro gas production technique in ruminant animals. journal of animal sciences advances, 2012, 2, 934-940. 21. bakshi, m.p.s., wadhwa, m., kaushal, s. and ameir, a.a. in-vitro evaluation of ensiled fruit and vegetable wastes. indian journal of animal nutrition, 2007,24, 12-15. 22. thakur, s.s. and bhatia, d.r. relative feeding value of three residual forage for goats. indian journal of animal health, 1985, 24, 85-87. 23. gupta, r., chanchau, t.r. and lall, d. nutritional potential of vegetable waste products for ruminants. bioresource technology, 1993, 44, 263-265. 24. chumpawadee, s., chantiratikul, a. and chantiratikul, p. chemical compositions and nutritional evaluation of energy feds for ruminants using in vitro gas production technique. pakistan journal of nutrition, 2007, 6, 607-612. received 7 november 2017 accepted 25 march 2018 microsoft word elec991201.doc science and technology, 5 (2000) 47-54 © 2000 sultan qaboos university 47 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers, part1: mathematical formulation * h.m.al-rizzo,** h.t. al-hafid, and *** j.m.tranquilla *college of information science and systems engineering, university of arkansas, 2801 south, university avenue, little rock, ar 72204; and department of electrical and electronics engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman;**electrical engineering department, united arab emirates university, al ain, united arab emirates; ***emr microwave technology corporation, 64 alison blvd., suite 105, fredericton, nb,canada, e3c 1n2. خالل طبقات المطر جة انتشار الموجات الكهرومغناطيسية لمنظومات األقمار الصناعيةنمذ النموذج الرياضي : المتراكمة حسين مظفر الريزو ، حافظ طه الحافظ ، و جم ترانكوال ى من في هذا البحث تم تطوير نموذج رياضي لبرنامج تنبؤ انتشار الموجات الكهرومغناطيسية في الطبقة السفل :خالصة هذا وقد أخذت الدراسة في االعتبار التوزيع العشوائي ألبعاد .الغالف الجوي وذلك في إطار الموجات الدقيقة والمللمترية .أشكال وكثافة الدقائق المعلقة في الجو والتي تشمل الثلج وقطرات المطر abstract: a systematic and general formulation of a propagation simulation program (psp) is developed for the coherent field of microwave and millimeter wave carrier signals traversing intermediate layered precipitation media, taking into account the random behavior of particle size, orientation, shape and concentration distributions. based on a rigorous solution of the volumetric multiple-scattering integral equations, the formalism offers the capability of treating the potential transmission impairments on satelliteearth links and radar remote sensing generated by composite atmospheric layers of precipitation in conjunction with the finite polarization isolation of dual-polarized transmitting and receiving antennas. a multi-layered formulation is employed which encompasses an ensemble of discrete particles comprising an arbitrary mixture of ice crystals, melting snow and raindrops that may exist simultaneously along satellite-earth communication paths. keywords: microwave, multiple-scattering, remote sensing. ecent demand for additional communication capacity, combined with the requirement of alleviating the congested electromagnetic (em) spectrum, has led system planners to utilize increasingly higher carrier frequencies. many attractive features for earth-space communications, radar, remote sensing and imaging applications such as improved resolution and wide absolute bandwidths essential for civilian and military high data rate transmission needs are feasible in the millimeter wave (mmw) regime. in this paper the analytical formulation of a psp, based on a rigorous solution of the volumetric multiple-scattering integral equations (ishimaru, 1977), is presented to evaluate the impairments caused by precipitation along arbitrary slant earth-space paths al-rizzo, al-hafid and tranquilla 48 utilizing the generalized multipole technique (gmt) developed by al-rizzo and tranquilla (1997). a concise matrix approach is employed for the treatment of the ensemble-averaged, coherent field of mmw signals traversing a random collection of hydrometeors including ice crystals, melting snow and rainfall. the purpose of the work reported in this paper is twofold. first, to integrate the simulation through the whole spectrum of precipitation using a multi-layered formulation which includes inhomogeneous mixture of ice at top of rain clouds and the transition from melting snow to rain below the melting layer. the second objective, and perhaps the foremost, is to extend the frequency range and improve the accuracy of previously published results, within the limitations of available meteorological data and physical parameters concerning the various forms of hydrometeors in the lower part of the atmosphere. general medium modelling an arbitrarily polarized time-harmonic incident plane em wave, propagating in the positive zdirection, is assumed. the polarization state is expressed in terms of the angle pair, (γ,δ), where γ = tan-1(e2/e1), e1 and e2 are the maximum projections of the instantaneous electric field vector along the x and y axes, respectively, and δ is the time-phase angle by which ey leads ex (kraus and carver, 1973). a cartesian coordinate system is employed, the z-axis defines the incident wave direction, pointing from the satellite antenna toward the receiving antenna at the earth-terminal location. the x and y axes coincide with the reference horizontal and vertical directions, respectively, forming a right-handed triplet where the x-axis is parallel to the local horizontal at the receiving end. complex normalized column vectors; vt of impressed and vr of received phasor voltages are defined such that pti = vti . v * ti, is the input power to the transmitting antenna and pri = vri . v * ri, i = 1, 2 is the power delivered to a matched load by the receiving antenna. the finite polarization isolation, inherently present in the transmitting and receiving antennas, is accounted for via two matrices; [ ]ta and [ ]ra which relate the incident ei and received er electric field vectors to vt and vr such that [ ] tt vae i = and [ ] rrr eav = where (bostian et al 1982)             =      2t 1t 2tj 2t 1tj 1t 2t1t y i x i v v esinesin coscos e e δδ γγ γγ             =      − − y r x r 2rj 2r2r 1rj 1r1r 2r 1r e e esincos esincos v v δ δ γγ γγ (1) the subscript t (r) refers to the transmitting (receiving) antenna, respectively and the two (nominally) orthogonal polarizations are denoted by the additional subscript 1 (2). the coherent electric field vector exiting a discrete, random anisotropic and lossy dielectric medium is related to the corresponding incident field using the eigenvalues and eigenvectors of the ensembleaveraged, complex propagation constant matrix [<k1>], the exponential form of which can be expressed as (tsoloakis and stutzman, 1982) [ ] [ ]             =      − − − − y i x i1 2j 1j l0jk y r x r e e e0 0e e e e qq λ λ (2) where l is the path length along the propagation direction and ko is the free-space wave number. the term e-jkol characterizes the pure phase-shift properties of the scatterer-free medium and [q] is the matrix of non-trivial eigenvector solutions of [<k1>] which are found from modeling the propagation of satellite communications 49 ( ) ( ) 2 k2kkkk 212 2 22112211 2,1 〉〈+〉〈−〉〈±〉〈+〉〈 =λ (3) [ ]       〉〈−〉〈− −〉〈−〉〈 = 1212 222122 kk kk λλ q (4) when the matrix of eigenvectors and its inverse are substituted into (2), then (2) can be transformed into the following concise form er(l) = e-jkol [<t>] ei(l) (5) the elements of the transmission matrix [<t>], which describes the amplitude, phase and polarization of the coherent field exiting the medium, can be written as ( ) ( ) 21 1j 122 2j 222 11 e ke k t λλ λλ λλ − −〉〈−−〉〈 =〉〈 −− 21 1j2j 122112 e e ktt λλ λλ − − 〉−〈=〉〈=〉〈 −− ( ) ( ) 21 2j 122 1j 222 22 e ke k t λλ λλ λλ − −〉〈−−〉〈 =〉〈 −− (6) the transfer-matrix equation describing the input-output relationship of the complete orthogonalpolarized, frequency re-use system can then be found by combining (1) and (5) as vr = e jkol [ar] [<t>] [at] vt (7) theoretical development for the rainfall medium a psp must include empirical or statistical averaging to account for the temporal and spatial randomness of the rain characteristics. falling raindrops are nonspherical in shape and are influenced by aerodynamic forces. as the size of a raindrop increases, a concave depression develops. pruppacher and pitter (1971),(p-p), provided 13 realistic raindrop shapes with spherical equivolume radii from 0.25 to 3.25 mm. with the exception of the limited cases presented by oguchi (1977), fang and lee (1978) and li et al. (1995), previous models considered only spherical and/or oblate spheroidal raindrops. the gmt is utilized in this paper to compute the forward scattering functions of an oblate and/or p-p raindrop, the symmetry axis of which coincides with the z-axis as shown in figure 1. a plane em wave, incident in the ki direction and inclined at an angle β with respect to the horizontal plane, is assumed. the incident electric field vector is given by .rk ie i i je−= (8) where the unit vector i describes the polarization state of the incident field. the propagation direction and the raindrop's axis of rotational symmetry define the incident plane. the incident electric field vector is decomposed into two mutually orthogonal components, parallel c ie and perpendicular ⊥ ie to the plane of incidence, respectively, as ⊥⊥+= iiiii ieiee cc (9) al-rizzo, al-hafid and tranquilla 50 in the far-field region, the forward-scattered wave has the same polarization as the incident field and the scattering process can be modeled by the following diagonal matrix equation             =      ⊥⊥⊥ −⊥ c cc c i i w0, w0, rjk s s e e ),,a(f0 0),,a(f r e e e 0 εβ εβ (10) where f║,║(a0,β,εw) and f┴,┴(a0,β,εw) are the forward scattering amplitude functions for the two principal incident polarizations and εw is the complex relative dielectric constant of water. figure 1. geometry for the scattering from an axisymmetric raindrop. at a given elevation angle, β and drop temperature, f║,║(a0,β,εw) and f┴,┴(a0,β,εw) are computed for 13 drops with spherical equivolume radii from 0.25 mm to 3.5 mm within a convergence criterion of 10-4 for a0≤ 2 mm and 10-3 for a0≥ 2 mm for the two principal polarizations. the integrals of the complex-valued scattering functions over the appropriate raindrop size distribution have been numerically evaluated using a 14-point composite simpson’s rule. the orientation geometry of an oblate and/or p-p falling raindrop is defined in the x-y plane in terms of the apparent canting angle between the projection of the symmetry axis and the reference polarization directions (oguchi, 1977). for an assemblage of identically oriented raindrops, a diagonal transmission matrix is defined, the diagonal elements describe the coherent attenuation and phase shift encountered by the principal polarizations. if the canting angle is denoted by θ, a matrix transformation is performed to bring the reference polarizations into the principal axes of the raindrop via the rotation matrix modeling the propagation of satellite communications 51       − = θθ θθ θ cossin sincos r (11) the components of the forward-scattered electric field vector are next rotated back into the reference x and y directions by applying the inverse rotation 1r −θ . the ensemble-averaged, complex propagation constant matrix, [ ]〉〈 1k which characterizes the coherent forward scattering effects due to a population of raindrops with a prescribed size, canting angle and shape distributions can then be written as [ ] [ ] ds dda )z,s,,a(n k 2 00 0 1 θθ π ∫∫∫=〉〈 fk (12) where n (a0,θ ,s, z) is the number of raindrops of a given shape, s, within a specified size, a0, and orientation, θ, intervals per unit volume of space which is a function of the spatial variable, z along the propagation direction. the forward-scattering matrix obtained from (10) after applying the rotation matrix of (11) and its inverse, when averaged over the statistical parameters of shape and canting angle distributions, can be written as { }〉〈+〉〈−+=〉〈 ⊥⊥ θθ 2,2,s0ss11 sinfcosf)p1()a(fpf cc { } 2 2sin ff)p1(ff ,,s2112 〉〈 −−=〉〈=〉〈 ⊥⊥ θ cc { }〉〈+〉〈−+=〉〈 ⊥⊥ θθ 2,2,s0ss22 cosfsinf)p1()a(fpf cc (13) where fs is the forward scattering amplitude of a spherical water drop. the common assumption of statistically independent shape and canting angle distributions has been adopted in (13). a discrete bimodal shape distribution is assumed, ps being the effective fraction of spherical and the remaining (1 ps) are oblate and/or p-p drops. for linearly polarized geo-stationary satellite transmission, the horizontal and vertical orientations at the satellite are referenced with respect to the subsatellite point as either in or perpendicular to the plane of the equator, respectively. for earth stations not located on the meridian, the electric field vector appears tilted from the local vertical or horizontal by an angle τ where (allnutt, 1989)       −= − η ξ τ sin tan tan90 10 (14) and ξ and η are the longitude and latitude of the earth station, respectively, defined with respect to the subsatellite point. if the receiving antenna is aligned to the satellite transmission, then equation (7) must be modified to [ ][ ] [ ][ ][ ] tt 1 r l0jk r e vartrav ττ 〉〈= −− (15) where the rotation matrix       − = ττ ττ τ cossin sincos r (16) al-rizzo, al-hafid and tranquilla 52 transforms the satellite's vertical and horizontal to the local vertical and horizontal at the earth station. theoretical development for the melting – layer medium the melting layer is a prominent feature of widespread rain associated with stratiform precipitation. it contains a mixture of gradually melting snowflake aggregates, which eventually form raindrops, attaining the terminal fall speed of water upon complete melting at the bottom of the layer (ekpenyong and srivastava, 1970). the establishment of a simulation model for the melting layer is imperative to accurately predict the total attenuation and phase shift for lowelevation satellites where a portion of the radio path may be contained within the layer boundary particularly in temperate maritime, northerly latitude and tropical climates. the meteorological model of the melting process developed by ekpenyong and srivastava (1970) is adopted in this paper with a spectrum of polydispersed snowflake sizes, densities and fall speeds. due to the lack of definitive information on the actual shape and orientation of partially melted snowflakes, the present model assumes a two-layered spherical scatterer shape. initially, a dry snowflake of radius rs and density ρs originating at the top of the melting layer is considered. a two-layered, concentric spherical snowflake of radius r0 with the melted water forming a uniform shell around a snow core of radius ri is assumed. if y denotes the fraction of total mass melted, then 3 w 3 i 3 0 r rr y − = (17) where rw is the radius of the resulting water drop at the bottom of the layer. the particle number density and the terminal fall speed, denoted respectively by n0 and v, depend on r0 and the height of fall (z z0) below freezing level where the 0 0c isotherm starts at z = z0, y = 0 at the top of the layer. the precipitation intensity is considered constant throughout the melting region with aggregation and breakup ignored such that a one-to-one correspondence exists between raindrops at the bottom and dry snowflakes at the top. if n(rw)drw denotes the raindrop size distribution, the corresponding distribution of the melting snow particles at any height within the melting zone can be estimated from (dissanayake and mcewan, 1978) ( ) www 000 ww 0000 dr )r(n)zz,r(v )r(v dr zz,rn − =− (18) consideration of mass conservation in a certain air volume implies ( ) 3ww3i30w3is3ss rrrrr ρρρρ =−+= (19) if the density and kinematic viscosity of air and mass of a snowflake are assumed constants during the melting process, it can be shown that the product vr remains constant that is ww00ss rvrvrv == (20) from (19) and (20), the terminal fall speed, vs of a dry snowflake can be obtained as 3/1 w s ws vv       = ρ ρ (21) at any stage of melting, the fall speed, v0, can be obtained from (17), (20) and (21) as modeling the propagation of satellite communications 53 y v v 11 v v 3 3 w s s 0               −− = (22) for a dry snowflake, ρs approaches a constant value of 0.008 g/cm3 for r0 > 0.75 cm. for smaller radii, ρs may be taken as 0.3 g/cm3. in between these two limiting values, the density can be obtained from (ekpenyong and srivastava, 1970) 2 s s r 005.0 =ρ (23) where rs is in cm, ρs is in g/cm3 and 3/1 s w ws rr       = ρ ρ (24) the dielectric constant of the snow core, εs is evaluated from the following expression (dissanayake and mcewan, 1978) 2 1 2 1 i i i s s s + − = + − ε ε ρ ρ ε ε (25) where a snowflake is treated as a two-component mixture of ice and air, εi, ρi are the complex dielectric constant and density of ice, respectively. once the mass fraction of a melted snowflake has been computed, the core and outside radii, terminal fall speed, dielectric constant of the core and particle-size distributions corresponding to a particular size of an eventually melted drop can be evaluated at any prescribed height within the melting layer. conclusions a theoretical formulation is introduced for the coherent field of a monochromatic em signal traversing a discrete medium of composite precipitation layers. the model accounts for the random behavior of particle size, orientation, shape and intensity distributions. although the degrading effects due to a single tropospheric layer of precipitation, which may hinder reliable space communications, were investigated extensively over the past three decades, the contributions at frequencies in the upper mmw band are still scarce. furthermore, little has been done to integrate the effects throughout the whole spectrum of precipitation in the lower part of the atmosphere. references allnutt, j.e. 1989. satellite-to-ground radio wave propagation, london, u.k.: peter peregrinus ltd. al-rizzo, h.m. and tranquilla, j.m. 1997. application of the generalized multipole technique (gmt) to highfrequency electromagnetic scattering from perfectly conducting and dielectric bodies of revolution, j. comput. phys., 136: 1-18. bostian, c.w, stutzman, w.l. and graines, j.m. 1982. a review of depolarization modeling for earth-space radio paths at frequencies above 10 ghz, radio sci., 17: 1231-1241. dissanayake, a.w. and mcewan, n.j. 1978. radar and attenuation properties of rain and bright band, iee conf. publ. 169-2, 125-129. ekpenyong, b.e. and srivastava, r.c. 1970. radar characteristics of the melting layera theoretical study, tech. rep. no. 16, dept. of the geophys. sci., the university of chicago and illinois inst. of techn., dept. of elect. eng., chicago, illinois. fang, d.j. and lee, f.j. 1978. tabulation of raindrop induced forward and backward scattering amplitudes, comsat. tech. rev., 8: 455-486. al-rizzo, al-hafid and tranquilla 54 ishimaru, a. 1977. theory and application of wave propagation and scattering in random media, proc. ieee, 65: 10301061. kraus, j.d. and carver, k.r. 1973. electromagnetics, new york: mcgraw-hill. li le-wei, pang-shyan kooi, mook-seng leong, tat-soon yeo, and min-zhan gao, 1995. microwave attenuation by realistically distorted raindrops: part itheory, ieee trans. antennas propagat., ap-43: 811-821. oguchi, t. 1977. scattering properties of pruppacher-and-pitter form raindrops and cross polarization due to rain : calculations at 11, 13, 19.3 and 34.8 ghz, radio sci., 12: 41-51. pruppacher, r. and pitter, r.l. 1971. a semi-empirical determination of the shape of cloud and rain drops, j. atmos. sci., 28: 86-94. tsoloakis, a. and stutzman, w.l. 1982. multiple scattering of electromagnetic waves by rain, radio sci.,12: 14951502. received 1 december 1999 accepted 19 june 2000 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 137-146 © 2002 sultan qaboos university a modified asynchronous transfer mode fuzzy policer m.r.m. rizk, h. rashwan and a. abdel aziz department of electrical engineering, faculty of engineering, alexandria university, alexandria, egypt. مراقب غيمي متطور لطور اإلرسال الغير متزامن ، هناء رشوان و أشرف عبدالعزيزمحمد رزق الفترة الزمنية (في المراقب الغيمي السابق النافذة الزمنية . تم تقديم مراقب غيمي متطور لطور اإلرسال الغير متزامن : خالصة ية غير في المراقب المتطور النوافذ الزمن . ال تتزامن مع نشاط المنبع ) الذي يتقبل فيها المراقب خاليا الطور الغير متزامن المراقب المتطور يحسن األداء من حيث االنتقائية و يخفف االختناق عبر المسار . متعاقبة و لكن تبدأ عند وصول أول خلية .هذا التحسين له أهميه كبرى في الشبكات متعددة القنوات. الخاص بالخاليا abstract: a modified fuzzy policer for asynchronous transfer mode is introduced. in a preceding fuzzy policer model the time window (time interval where atm cells are accepted in the policer) is not synchronized with the source activity. in the proposed one, the time windows are not consecutive but are triggered by the first arriving cell. the modified policer gives good improvement to the selectivity, and minimizes the congestion over the path. this improvement can be significant for multiple channels. keywords: fuzzy logic, asynchronous transfer mode, usage parameter control. 1. introduction t he basic characteristics of asynchronous transfer mode (atm) networks (de prycker, 1993) are the provision of broadband user access interfaces, packet-oriented information transfer without flow control between the user and the network, and the use of statistical multiplexing. due to these properties, a call can, in principle, exceed the negotiated traffic parameters up to the maximum capacity of the user network interface (uni) (rathgeb, 1991). one of the advantages of atm compared to other networking technologies is the support of various service qualities (de prycker, 1993). atm layer traffic control is designed to avoid network congestion by preventative traffic management. network congestion is a state when the network cannot meet the negotiated network performance objectives for established connections or for new connection requests. the goal of traffic control is to protect the network, and other users of the network, so that everyone receives the performance that they pay for and depend on (hewlettpakard, 1995). in order to achieve a guaranteed service quality qos, the user has to commit to a specific traffic contract during connection setup. the service provider should guarantee the parameters of this traffic contract. they will be one of the main factors a potential customer will be charged for. on the other hand, the service provider needs to control if the customer’s cell stream entering the network really behaves compliant to the negotiated traffic contract. if not, the network equipment has to take appropriate measures to protect the network from intentionally or accidentally misbehaving users. these so called policing functions are well defined in the atm and b-isdn specifications under the category “usage parameter control” ( upc) (catania et al., 1996). 137 m.r.m. rizk, h. rashwan and a. abdel aziz this paper presents a new fuzzy policer mechanism. a full study and evaluation of the existing fuzzy policer mechanism published in (catania et al., 1996) is performed. then a proposed modification to this fuzzy mechanism is introduced and implemented. in section one we describe the traffic source that was used in the comparison and the evaluation of the mechanisms. in section two we simulate the existing fuzzy policer mechanism, described in (catania et al., 1996) and compare the results with the published one. in section three we propose a modification to this fuzzy mechanism, which improve the performance of the policer. in section four a comparison between the leaky bucket mechanism, the existing fuzzy policer mechanism, and the modified fuzzy policer mechanism was done through a software simulation for the three mechanisms. in the last section we concluded our results and recommended some points for further study. 2. traffic source model the two-phase burst/silence model shown in figure 1 has been used for the comparison of the various mechanisms. this model has been used in earlier publications (rathgeb, 1991). it allows the relevant parameters, namely maximum cell rate, mean cell rate, and mean burst duration to be varied independently of each other. the number of cells per burst is assumed to have a geometric distribution with mean e [x]; the duration of the silence phases is assumed to be distributed according to an exponential distribution with mean e [s], and the cell interarrival time during a burst is given by tc with α−1 = ε[x] x tc (1) and β−1 = e[s] (2) the mean cell rate λ is defined as (3) α λ = β c c t t + 1 3. study of the fuzzy policer mechanism (catania et al., 1996) a software simulator using matlab (matlab, 1997) was implemented and used to validate the results for the fuzzy policer mechanism (catania et al., 1996). the figure of merit considered is the selectivity of the mechanisms. we used the source described in the above section with the same statistical parameters as in (catania et al., 1996) in order to compare the results. therefore we assumed a voice source with a peak bit-rate 32 kb/s, cell inter-arrival time tc of 12 ms, e [x] = 29 cells (mean burst duration 350 ms), and e [s] =650 ms. from equations (1), (2), and (3), taking into consideration the atm cell size is 53 bytes, the negotiated mean cell rate λn = 29 cells/s. the membership functions for the fuzzy sets are shown in figure 2, where aoi, ai, ni, and  ∆ni+1 are defined as follows: aoi the average number of cell arrivals per window since the start of the connection, ai the number of cell arrivals in the ith window, the threshold ni in the ith window indicating the current degree of tolerance the mechanism has over the source, and ∆ni+1 represents the variation to be made to the threshold ni in the i+1 window (figure 3). n is equal to the expected value of cells per window (n= t λn), max equals the maximum number of cells that can arrive in a window (t/tc), where tc is the cell inter-arrival time during a burst, ni-max =9n indicates the upper bound value for the ni variable, and n1= 3.5 n which is the value to be attributed to ni at the beginning of the connection. 138 a modified asynchronous transfer mode fuzzy policer choosing t=3 seconds in the simulation gives, n=87 cells, max=250 cells, ni-max = 783, n1=300. if pd represents the probability that the policer mechanism detects a cell excessive, the ideal behavior would be that pd is zero with the mean cell rate up to the nominal one, and pd =(σ 1)/σ for σ >1 for σ >1, where σ is the long-term actual mean cell rate of the source normalized to the negotiated mean cell rate. in order to obtain the curve pd versus σ, we assume that a variation in the cell rate is due to a change in the average number of cells per burst e (x), while the average silence time is assumed to be constant (e(s)= 650 ms). also, in order to evaluate the capabilities of the mechanisms to react to different kinds of violations, we made the mean cell rate vary by decreasing the average silence time e(s), and keeping the number of cells per burst constant (e(x)=29 cells).the chosen generated traffic source duration is about 3 minutes, which is enough for pd to go to the steady state. the following table1.gives the results of the simulation compared to the existing results. table 1: comparison between simulation results and existing results for the fuzzy policer mechanism.  σ existing fuzzy policer. [e(x)const.] pd simulated. fuzzy policer. [e(x) const.] pd existing fuzzy pol. [e(s) const] pd simulated. fuzzy pol. [e(s) const.] pd ideal behavior ( σ -1)/ σ  for σ >1 pd 0.95 0 0 0 0 0 1.0 <10-8 <10-6 <10-8 <10-6 0 1.05 0.031090 0.022 0.033753 0.02 0.04762 1.1 0.078306 0.066 0.087029 0.087 0.09091 1.2 0.135768 0.13 0.155668 0.154 0.16667 1.3 0.18623 0.185 0.211353 0.206 0.2307 1.4 0.248756 0.239 0.278909 0.26 0.2857 1.5 0.283214 0.278 0.310451 0.31 0.3333 1.6 0.327301 0.321 0.342940 0.338 0.375 1.7 0.372404 0.372 0.378184 0.375 0.4117 1.8 0.418008 0.41 0.411373 0.407 0.44444 1.9 0.457541 0.445 0.444393 0.435 0.47368 2.0 0.492144 0.4855 0.476444 0.47 0.50 139 m.r.m. rizk, h. rashwan and a. abdel aziz geometric mean ε [x] tc exponential μean ε [s] silence burst tc silence burst figure 1. two-phase burst/silence source model. membership functions for the ∆ni+1 output variable -4x -3x -2x -x 0 x 2x 3x 4x nb nm ns zero ps pm pb membership functions for the ni input variable 0.5n n 1.5n max high medium low membership functions for the a0i and ai input 0.5n n 1.5n high medium low 0 0 0.0 1.0 0.0 1.0 figure 2: membership functions for the existing fuzzy policer mechanism. 140 a modified asynchronous transfer mode fuzzy policer figure 3. system controller: 3 inputs, 1 output. aoi (3) ni (3) ai (3) ∆ni+1 (7) controller (mamdani) 18 rules membership functions for the a0i and ai input variables 0.5h h 1.5h highmedium low 0.0 1 0 0.0 highmedium low 1.0 0.5h .82h .87h 1.4h max membership functions for the ni input variable 1 0 0.0 -4x -3x -2x -x 0 x 2x 3x 4x nb nm ns zero ps pm pb membership functions for the ∆ni+1 output variable (x= h/22) figure 4. membership functions for the modified fuzzy policer mechanism. 141 m.r.m. rizk, h. rashwan and a. abdel aziz it is cl published ones 4. modified fuzzy policer model in the preceding fuzzy policer model the time window is not synchronized with the source activ table 2: the simulation results for e(s) constant. σ leaky bucket [e(s) constant] existing fuzzy [e(s) constant ] modified fuzzy [e(s)constant] ideal behavior ear from the above table that the simulation results almost coincide with the for the same traffic source model. this validates the simulated mechanism and the existing results. since our simulation is justified so we can compare these results with the results from other policer such as the one proposed in the next section. ity. in the proposed fuzzy policer mechanism the time windows are not consecutive but are triggered by the first arriving cell. c=1.42 pd policer pd policer pd ( σ -1)/ σ  for σ >1 pd 0 0 0 0.95 0 1.0 0 <10-6 <10-6 0 1.05 0 0.02 0.03 0.04762 1.1 0 0.087 0.085 0.0909 1.2 0 0.154 0.155 0.166666 1.3 0 0.206 0.212 0.2307 1.4 0.01 0.26 0.265 0.2857 1.5 0.045 0.31 0.325 0.3333 1.6 0.1 0.338 0.369 0.375 1.7 0.1552 0.375 0.408 0.4117 1.8 0.2017 0.407 0.435 0.44444 1.9 0.2472 0.435 0.469 0.47368 2.0 0.28 0.47 0.495 0.50 e used the same input and output for the fuzzy controller. the membership functions chosen for t connection is h1 = 3.5 h. w he fuzzy sets of this modified controller was obtained through trial and error until it reached a level of performance considered to be adequate as shown in figure 5.4. h represents the average number of cells arrival per trigger window for an ideal source, max is the maximum number of cells that can arrive in a window (t/tc), ni-max is equal to 9h ,and the value for the beginning of the 142 a modified asynchronous transfer mode fuzzy policer 5. performance evaluation in this section, we compare the performance of the three mechanisms [leaky bucket, existing fuzzy policer, and the modified fuzzy policer]. the figure of merit considered is the selectivity of the m rm probability, it is necessary to have either a high value for the echanisms. to assess the performance of the three mechanisms a simulator is implemented using matlab to generate the traffic source and evaluate the three mechanisms. the traffic source model used here is the same as the one used in section 3, whose statistical parameters are those typical to a real packetized source. considering a peak bit-rate of 32 kb/s and a cell interarrival time tc of 12 ms the traffic parameters are typically e [x] = 29 cells (mean burst duration 350 ms) and e [s] =650 ms. it is worth pointing out that for this kind of source, traditional policing methods proved to be inefficient. to achieve a low false ala counter limit, n, which means a poor dynamic response, or a high value for the over dimensioning factor c>2, which reduces the capability to detect a violation. for the leaky bucket n=45, c=1.42 where n is the counter limit and c is a over dimensioning factor (catania et al., 1996). figure 5. selectivity for a packetized voice source e(s) constant. 0.000001 0.00001 0.0001 0.001 0.01 0.1 0.9 1.1 1.3 1.5 1.7 1.9 σ p d leaky bucket existing fuzzy policer modified fuzzy policer ideal behavior 1 143 m.r.m. rizk, h. rashwan and a. abdel aziz for the fuzzy policer mechanism we choose a window size t=3 s (about three burst/silence) so =87 cells and n1 = 300 (catania et al., 1996). , this gives h=129 cells and h1 = 400. σ lea c=1.42 policer policer ideal behavior (  n for the modified policer mechanism a window size of t=4 s (about four burst/silence) showed a better performance compared to the existing mechanism table 3: the simulation results for e(x) constant. ky bucket existing fuzzy modified fuzzy e(x) constant pd [e(x) constant ] pd [e(x) constant ] pd σ -1)/ σ for � >1 pd 0 0 0 0 1.0 0 < < 10-6 10-6 0 1.05 0 0.022 0.015 0.04762 1.1 0 0.066 0.055 0.0909 1.2 0 0.13 0.12 0.166666 1.3 0 0.185 0.182 0.2307 1.4 0. 5 00 0.239 0.221 0.2857 1.5 0.037 0.278 0.2783 0.3333 1.6 0.095 0.321 0.333 0.375 1.7 0.155 0.372 0.392 0.4117 1.8 0.18 0.41 0.426 0.44444 1.9 0.245 0.445 0.46 0.47368 2.0 0.3 0.4855 0.4995 0.50 0.95 as discussed in section 3, in order to obtain the curve pd versus σ, we assume that a variation the cell rate is due to a change in the average number of cells per burst e (x), while the average silen nt to pd for σ greater than 1.5 as compared to the existing fuzzy mechanism. eping the num figure 6). from table 3, the modified fuzzy polic in ce e(s)=650ms time is assumed to be constant. it is shown from figure 5, which compares the selectivity performance versus cell rate variation for the three mechanism, that the modified fuzzy policer and the existing fuzzy policer give an improvement for pd compared to the leaky bucket in table 2. from the numerical values we can conclude that the modified fuzzy mechanism give an improveme in order to evaluate the capabilities of the mechanisms to react to different kinds of violations, we made the mean cell rate vary by decreasing the average silence time e(s), and ke ber of cells per burst constant (e(x)=29 cells). as expected, the modified fuzzy policer and the existing fuzzy policer give an improvement for pd compared to the leaky bucket mechanism ( er gives an improvement to pd for σ greater than 1.5  as compared to the fuzzy mechanism. 144 a modified asynchronous transfer mode fuzzy policer figure 6. selectivity performance for a packetized voice source e(x) constant. 6. conclusions de from the given results that in general the intelligent mechanisms give a good improvement to the selectivity over traditional mechanisms, and the proposed modifications to the exist chanism is reduced by a factor of 2/3 compared to the existing fuzzy policer mechanism for t traffic model. second using the modified fuzzy policer mechanism to test diffe references catania, v., ficili, g., palazzo, s o, d. 1996. a comparative analysis of fuzzy versus conventional policing mechanisms for atm networks," ieee/acm trans. networking, 4(3): 449-459. 0.0000001 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 0.9 1.1 1.3 1.5 1.7 1.9 σ p d leaky bucket existing fuzzy policer modified fuzzy policer ideal behavior we can conclu ing fuzzy policer give an improvement to the selectivity for value of σ greater than 1.5 which in turn minimize the congestion over the path. this improvement can be significant for multiple channels. also, an important conclusion is that the number of windows processed by the modified fuzzy policer me he same source and the same duration of the connection. this in turn leads to a reduction in the processor time. we recommend the following points for further study. first optimization of the membership function for a given rent traffic sources, such as video on demand, and adjust the needed variations in the membership functions. . and pann 145 m.r.m. rizk, h. rashwan and a. abdel aziz de prycker, m. 1993. asynchrounus transfer mode: solution for broadband isdn,(2nd edition) ellis-horwood. lett-pakard. 1995. tehew st & measurement application notes "traffic policing" 59637510e. rathgeb, e.p. 1991. modeling and performance comparison of policing mechanisms for atm rece matlab. 1997. the language of technical computing, the mathworks, inc., version 5.1.0.421. networks. ieee journal selected areas in communications. 9(3): 325-334. ived 26 june 2001 accepted 25 february 2002 146 a modified asynchronous transfer mode fuzzy policer m.r.m. rizk, h. rashwan and a. abdel aziz department of electrical engineering, faculty of engineering, alexandria university, alexandria, egypt. (3) study of the fuzzy policer mechanism (catania et al., 1996) if pd represents the probability that the policer mechanism detects a cell excessive, the ideal behavior would be that pd is zero with the mean cell rate up to the nominal one, and pd =(? 1)/?? for ? >1? for ? >1, where ? is the long-term actual m ideal behavior (??? -1)/????? for ? >1 pd figure 1. two-phase burst/silence source model. table 2: the simulation results for e(s) constant. ideal behavior table 3: the simulation results for e(x) constant. ??? ideal behavior electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 241-249 © 2002 sultan qaboos university derivatized pentadentate macrocyclic ligands and their transition metal complexes muhammad s. khan* , nawal k. al-rasbi *, edwin c. constable **, adrian r. dale** and jack lewis ** *department of chemistry, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman; **department of chemistry, university of cambridge, lensfield rd., cambridge cb2 1ew, uk, *email: msk@squ.edu.om. مشتقات المركبات الخماسية الحلقة ومعقداتها مع العناصر اإلنتقالية دال وجاك لويس. كونستبل، أدريان ر. الراسبي، أدوين س. خان، نوال ك. محمد س )هيدروكسي اثيل -'2,( ثنائي -1,11: تفاعالت مجموعة الهيدروكسي اثيل في المركبات خماسية الحلقة : خالصة ) ل2( أكتايين -20,18,14,12,9,6,4,2رباعي ازا سيكلوهينيكوسا -11,10,2,1ثي نايترايلو ثال -8,4;16,12;21,17 ثنائي -2,’2-) هيدروكسي اثيل هايدرازينو'2-( ثنائي 6,'6ثنائي بريدين الدهايد مع 6,2–المشتق من تفاعالت التكاثف من جموعة الهيدروكسيل اثيل في هذه الحلقات مع مركبات الثيونيل بتفاعالت االسترة كانت إيجابية وتفاعل م ) ل1(البيردين = ml3-6.x2.nh2o) m ل ذات الصيغة العامة 6-3المعقدات الفلزية من هذه المركبات . الكلورايد انتج مشتق الكلورواثيل .درست وحضرت أيضاً) فلزات الدورة األولى من العناصر اإلنتقالية abstract:the reaction of the pendant hydroxyethyl group in the planar pentadentate macrocyclic ligand,1,11-bis(2’-hydroxyethyl)-4,8;12,16;17,21-trinitrilo-1,2,10,11-tetraazacyclohenicosa2,4,6,9, 12,14,18,20-octaene (l2), derived from the condensation of 2,6-pyridinedialdehyde with 6,6’-bis(2’ hydroxyethylhydrazino)-2,2’-bipyridine (l1), has been investigated. esterification reactions are facile, and the reaction of the hydroxyethyl-substituted macrocycle with thionyl chloride yields a chloroethyl derivative. metal complexes of the new derivatized macrocyclic ligands l3-6 having general formula ml3-6x2.nh2o (m = mn, fe, co, ni, cu, zn) are readily prepared. keywords: macrocyclic ligands, coordination complexes, transition metals, esterification, functional group interconversion. 1. introduction m acrocyclic compounds of biological significance, such as the porphyrin, chlorophyll and corrin complexes have been studied for many years (smith, 1975). more recently, other macrocyclic ligands and their metal complexes have been synthesized (constable, 1999). the wide range of interest in the synthetic macrocyclic ligand complexes has arisen partly because their similarity to certain biological macrocyclic systems has enabled them to be used as models in the study of these systems. interest in the synthetic macrocyclic systems also arises due to the unusual properties they may exhibit in their own right. the tendency for a macrocyclic complex to be more stable with respect to ligand dissociation than a comparable open-chain multidentate ligand complex, over and above the chelate affect, is well documented. this phenomenon, termed the ‘macrocyclic effect’ (cabbinnes and margerum, 1969) is thought to have both kinetic and thermodynamic origins. another interesting aspect is the unusual stereochemical arrangement that may be formed on coordination of the macrocyclic ligands to the metal centers. this is particularly true of the pentadentate n5-donor macrocyclic ligands involving π-electron delocalization around the ring. a rigid stereochemical arrangment is often imposed on the metal that would not occur in 241 m.s. khan et al. the absence of the macrocyclic ligand. the geometry of unsaturated macrocycles is generally planar due to the more favorable overlap of π-symmetry orbitals. planar pentadentate n5-donor macrocyclic ligands may form five coordinate planar, six-coordinate pentagonal-based pyramidal and seven-coordinate pentagonal bipyramidal complexes with metal ions (melson, 1979; lindoy, 1989). we have been interested in the design, synthesis and coordination chemistry of a series of pentadentate n5-donor macrocycles involving poly-pyridine groups (figure 1). n n nn r1 nn r1 r2r2 n r1 = h, ch3 ; r2 = h, ch3 figure 1. polypyridyl n5-macrocycles. the rationale for choosing pyridine derivatives as components within the macrocycle framework is that they readily reduce to radical ions, thereby imparting interesting redox properties to the macrocyclic complexes. the fused rings of 2,2'-bipyridine/1,10-phenanthroline are also expected to impart additional rigidity to the macrcocyle rings. pentadentate macrocyclic ligands of this type are readily prepared by template or transient template condensations of hydrazinosubstituted 2,2'-bipyridines (ansell et al 1982a, 1982b, 1983), 1,10-phenanthroline or 2,2':6',2"terpyridines with 2,6-pyridine dicarbonyl (constable et al, 1985). we have synthesized pentadentate macrocycle l2 with pendant hydroxyethyl group that allows further structural development of the macrocycle by derivatization and the design of biometic systems (ansell et al, 1983). in this paper we wish to describe the synthesis and coordination chemistry of some such derivatized macrocyclic ligands l3-6 (figure 2). 2. materials and method all reagents were purchased from sigma aldrich and used without further purification. solvents were dried and distilled before use by standard methods. all reactions were performed under n2. infrared spectra were recorded in compressed kbr pellet on perkin elmer 983 spectrophtometer. 1h nmr spectra were recorded on bruker wm 250 or am 400 spectrometers. fast atom bombardment (fab) and electron impact (ei) mass spectra were recorded on a kratos ms 50 mass spectrometer. microanalysis was performed in the department of chemistry, university of cambridge, u.k. conductance measurements were made using a wayne kerr 242 derivatized pentadentate macrocyclic ligands universal bridge. the macrocyclic ligand salt [h2l2][pf6]2 was prepared as previously described (chung et al 1990). n n nn ch2ch2x nn xh2ch2c hh n figure 2. derivatized n5-macrocylic ligands. l2: x = oh; l3: x = o2cch3 ; l4: x = o2cch2ch3; l5: x = o2cc6h5; l6: x = cl 3. synthesis of derivatized macrocyclic ligands l3-6 3.1 synthesis of [h2l3][pf6]2 a solution of [h2l2][pf6]2·h2o (0.064 g, 0.09 mmol) in dry acetonirile (50 ml) was stirred for 12 hours with acetyl chloride (5 ml). after twelve hours the orange solution was concentrated in vacuo to 5 ml volume and treated with water (50 ml) and sufficient acetonitrile to redissolve the initial precepitate. the solution was then filtered and the filtrate treated with saturated aqueous [nh4][pf6] solution (10 ml). the orange solution was then slowly concentrated in vacuo to yield orange-red crystals of [h2l3][pf6]2·h2o (0.07 g, 96%). anal. found: c, 36.6; h, 3.4; n, 12.4. calc. for c25f12h31n7o6p2: c, 36.8; h, 3.6; n, 12.0%. infrared, 1741 cm-1. ei-ms (m/z): 487. 3.2 synthesis of [h2l4][pf6]2 the procedure was analogous to that described above for [h2l3][pf6]2. yield: 75% as orange-red crystals of [h2l4][pf6]2·h2o. anal. found: 39.5; h, 3.6; n, 11.9. calc. for c27f12h33n7o5p2: c, 39.3; h, 3.5; n, 11.9%. infrared, 1737 cm-1. ei-ms (m/z): 515. 3.3 synthesis of [h2l5][pf6]2 a solution of [h2l2][pf6]2·h2o (0.10 g, 0.14 mmol) in dry acetonirile (50 ml) was heated to reflux for 36 hours with benzoyl chloride (0.7 ml). the resulting orange solution was concentrated in vacuo to 5 ml volume when an oil formed. water (25 ml) was added and the mixture heated to 90ºc for 10 minutes to hydrolyse excess benzoyl chloride. the solution was then extracted with diethyl ether (2 x 20 ml) and the resulting aqueous suspension treated with sufficient acetonitrile to give a clear solution. this was then filtered and the filtrate treated with saturated aqueous [nh4][pf6] solution (10 ml). the orange solution was then slowly concentrated in vacuo to yield orange-red crystals of [h2l5][pf6]2·h2o (0.05 g, 40%). anal. found: c, 68.46 ; h, 5.18 ; n, 15.89. calc. for c35f12h31n7o5p2: c, 68.6; h, 5.1; n, 16.0%. infrared, 1720 cm-1. 243 m.s. khan et al. table 1: analytical data for transition metal complexes of l3-6 . compound found % calc. % c h n c h n [mnl3(h2o)2][pf6]2·h2o 34.04 3.56 11.21 33.89 3.53 11.07 [fel3(h2o)2][pf6]2·h2o 34.12 3.63 10.98 33.86 3.52 11.06 [col3][pf6]2·h2o 34.99 3.64 11.39 35.16 3.66 11.48 [nil3(h2o)2][pf6]2·mecn 35.58 3.46 12.21 35.53 3.42 12.28 [cul3(h2o)2][pf6]2·h2o 33.65 3.52 11.4 33.57 3.49 10.96 [znl3(h2o)2][pf6]2·h2o 33.28 3.42 10.89 33.50 3.49 10.94 [mnl4(h2o)2][pf6]2·h2o 35.41 3.53 10.69 35.48 3.61 10.73 [fel4(h2o)2][pf6]2·h2o 35.38 3.68 10.63 35.45 3.61 10.72 [col4][pf6]2·h2o 36.71 3.72 11.09 36.77 3.75 11.12 [nil4(h2o)2][pf6]2·mecn 36.98 3.48 11.82 37.02 3.51 11.91 [cul4(h2o)2][pf6]2·h2o 35.28 3.47 10.72 35.15 3.58 10.63 [znl4(h2o)2][pf6]2·h2o 36.27 3.65 10.89 36.18 3.71 10.94 [mnl5(h2o)2][pf6]2·h2o 29.97 2.57 11.67 30.10 2.53 11.70 [fel5(h2o)2][pf6]2·h2o 29.98 2.58 11.74 30.07 2.52 11.69 [col5][pf6]2·h2o 31.25 2.72 12.18 31.30 2.63 12.17 [nil5(h2o)2][pf6]2·mecn 32.07 2.47 13.01 31.94 2.45 12.96 [cul5(h2o)2][pf6]2·h2o 29.85 2.44 11.63 29.79 2.50 11.59 [znl5(h2o)2][pf6]2·h2o 28.09 2.28 11.01 28.14 2.36 10.94 [mnl6(h2o)2][pf6]2·h2o 50.23 3.69 11.63 50.17 3.73 11.70 [fel6(h2o)2][pf6]2·h2o 50.19 3.68 11.79 50.11 3.73 11.69 [col6][pf6]2·h2o 52.23 3.94 12.24 52.16 3.88 12.17 [nil6(h2o)2][pf6]2·mecn 48.56 3.59 13.05 48.61 3.61 12.96 [cul6(h2o)2][pf6]2·h2o 49.72 3.71 11.67 49.66 3.69 11.59 [znl6(h2o)2][pf6]2·h2o 46.94 3.52 11.01 46.89 3.49 10.94 3.4 synthesis of [h2l6][pf6]2 a solution of [h2l2][pf6]2·h2o (0.05 g, 0.07 mmol) in dry acetonirile (25 ml) was heated to reflux for 3 hours with thionyl chloride (1 ml). after this period the orange solution was evaporated to dryness in vacuo and the residue dissolved in acetonitrile (0.5 ml). diffusion of diethyl ether vapour into this solution yielded orange-red needles of [h2l6][pf6]2 (0.03 g, 67%). anal. found: 34.34; h, 2.97; n, 13.62. calc. for c21cl2f12h21n7p2: c, 34.42; h, 2.93; n, 13.68%. fab-ms (m/z): 439, 441, 443. 244 derivatized pentadentate macrocyclic ligands 4. synthesis of metal complexes of derivatized macrocyclic ligands 4.1 metal complexes of l3 a solution of [h2l3][pf6]2·2h2o in 3:1 acetonitrile/methanol was treated with a solution of 1 equivalent of an appropriate metal(ii) acetate dissolved in the minimum volume of methanol. the mixture was then heated to reflux for 15 minutes, concentrated to 1/5th volume in vacuo and treated with saturated [nh4][pf6] solution. the products were collected by filtration and dried to yield the desired complexes in a good yield (typically > 75%). analytical data are presented in table 1. 4.2 metal complexes of l4 the procedure was analogous to that used for metal complexes of l3. the desired products were isolated in > 80% yield. analytical data are presented in table 1. 4.3 metal complexes of l5 the procedure was analogous to that used for metal complexes of l3. the products were isolated in > 80% yield. analytical data are presented in table 1. 4.4 metal complexes of l6 the procedure was analogous to that used for metal complexes of l3. the products were isolated in respectable yields (typically > 65%). analytical data are presented in table 1. 5. results and discussion planar pentadentate macrocyclic ligands such as l2 may be prepared by transient template condensations of the appropriate hydrazines l1 with 2,6-pyridinedialdehyde or 2,6 diacetylpyridine. these ligands, which are of particular interest in bearing a functionalized substituent that may be further derivatized to yield encapsulating or capped macrocycles. the open-chain bishydrazines are readily prepared by the reaction of a suitable dihalo compound with α-hydroxyethylhydrazine. the free macrocyclic ligand l2 is best prepared as the hydrochloride or other salt by transient template condensations of 6,6’-bis(2’-hydroxyethylhydrazino)-2,2’bipyridine (l1) with 2,6pyridinedialdehyde in the presence of chromium(iii) chloride (scheme 1). n n nn ch2ch2oh h2nnh2 hoh2ch2c hh n o o + cr(iii)cl3.6h2o nh4pf6 [h2l2][pf6]2 l1 scheme 1. transient template synthesis of l2 . 245 m.s. khan et al. as an initial investigation into the further functionalization of these macrocyclic ligands we studied acylation reactions of l2. solutions of [h2l2][pf6]2 in acetonitrile changed in color from red to orange upon stirring overnight with excess of acetyl chloride. treatment of this orange solution with water followed by [nh4][pf6] resulted in the formation of an orange crystalline product. in the presence of an excess of acetyl chloride we anticipated the formation of the bisacetylated ligand l3, and microanalysis was in accord with the orange product being formulated [h2l3][pf6]2·2h2o. the conversion proceeds in a near-quantitative manner, and isolated yields of 96% of the salt were obtained. the ei mass spectrum of the salt exhibits a parent ion for {l3}+ at m/z 487. the infrared spectrum of the compound showed a single strong carbonyl absorption at 1741 cm-1 as expected for the bisacetylated compound. the isolated hexafluorophosphate salt was insufficiently soluble in d2o or cd3od to obtain 1h nmr spectra in these solvents, but broadened spectra could be obtained in cd3cn or cd3cocd3. unfortunately, the resonances assigned to the acetyl groups were obscured in these solvents, and it was necessary to use cd3socd3 solution, and this effect was again observed with [h2l3][pf6]2. the acetyl protons appeared as a singlet (δ 1.91) and integration confirmed that a bisacetylated derivative had been obtained. a similar smooth reaction occurred when an acetonitrile solution of [h2l2][pf6]2 was stirred with propionyl chloride, and after the usual work up, [h2l4][pf6]2 was obtained as an orange crystalline solid in 75% yield. once again, microanalysis was consistent with this formulation, and the ei mass spectrum exhibited a parent ion at m/z 515. the infrared spectrum showed a singlet strong carbonyl absorption at 1737 cm-1 as expected for the desired bisacylated product. this product is considerably more soluble in cd3od than [h2l4][pf6]2, and sharp well-resolved 1h nmr spectra could be obtained in this solvent. the most evident feature of the spectrum are the triplet (δ 1.01, 6h, j 7.5 hz) and quartet (δ 2.26, 4h, j 7.5 hz) assigned to the propionyl group. similar acylations have been demonstrated for other alkanecarboxylic acids, and the reaction appeared to be general. we also considered the formation of esters with arenecarboxylic acids, and investigated the reaction of [h2l2][pf6]2 with benzoyl chloride under a variety of experimental conditions. the macrocycle was recovered unchanged after stirring a solution of [h2l2][pf6]2 in acetonitrile with benzoyl chloride overnight. we could not obtain benzoylated products from attempted acylation under schotten-baumann conditions. eventually, the desired bisbenzoylated compound was obtained after heating an acetonitrile solution of [h2l2][pf6]2 with an excess of benzoyl chloride to reflux for 36 hours. the product of this reaction tended to be oily, but eventually orange-red crystals of [h2l5][pf6]2 were obtained by repeated crystallization from aqueous acetonitrile. the mass spectrum did not exhibit a molecular ion, but merely showed a fragmentation peak assigned to {l2}+. the infrared spectrum provides firm evidence for the formation of the desired derivatized macrocyclic product and shows strong carbonyl stretching absorption at 1720 cm-1, typical of benzoate esters. the 1h nmr spectrum of the compound in cd3socd3 solution is of interest in showing both broadened and sharp resonances in the aromatic region, figure 3a. integration of spectra obtained using very long relaxation delays between pulses indicated that the ratio of the sharp peaks to the broadened peaks was 10:11; this is in accord with the resonances assigned to protons in the macrocyclic ring being broadened as previously noted, but those of the phenyl groups being sharp. the 1h nmr spectrum of the solution of [h2l5][pf6]2 shows temperature dependent behaviour, and upon heating to 370 k is significantly sharpened, figure 3b. in addition to esterification, we have also investigated other reactions of pendant hydroxyethyl substituent in l2. numerous attempts to prepare the tosylates by reaction with 4-toluenesulphonyl chloride in a wide range of experimental conditions were unsuccessful. generally, the products were intractable tars. we have had rather more success in the reaction with thionyl chloride to yield l6. upon heating acetonirile solutions of [h2l2][pf6]2 with thionyl chloride, orange solutions were obtained, from which the salt [h2l6][pf6]2 could be isolated as orange needles. the microanalysis is in accord with this formulation, and the fab mass spectrum exhibited a parent ion at m/z 439, 441, 443 showing the expected isotopomeric distribution for a compound containing two chlorine atoms. no absorptoions due to hydroxy groups are observed in the infrared spectrum of the 246 derivatized pentadentate macrocyclic ligands compound. once again, the complex exhibits a broadened 1h nmr spectra in cd3socd3 solution. figure 3. 1h nmr spectrum of a cd3socd3 solution of [h2l5][pf6]2 at: a) 298 k and b) 370 k. we have made preliminary studies of the coordination behaviour of the derivatized ligands. the salts [h2l3-6][pf6]2 react smoothly with metal acetates in boiling methanolic solution to yield metal complexes, which may be recrystallized from aqueous acetonitrile to yield the crystalline complexes [ml3-6][pf6]2·nh2o (m = mn, fe, co, ni, cu, zn). in the absence of any structural data we propose that these complexes possess pentagonal bipyramidal geometries, in which the two axial sites are occupied by coordinated water. the infrared spectra exhibited sharp absorptions at 3604 cm-1 due to the coordinated water molecules. in the solid state, considerable shifts of the carbonyl stretching frequency occurred upon coordination of l3-5, table 2. this suggests that there is significant hydrogen-bonding interaction between the coordinated water and the carbonyl groups. conducivity in nitromethane (see table 2) indicates that all the complexes are 2:1 electrolytes (geary, 1971) corresponding to the presence of two counter ions per macrocyclic complex. taken in conjunction with the analytical data and infrared spectra, conductivity measurements provide very strong evidence for pentagonal bipyramidal coordination geometry for transition metal complexes of the derivatized macrocyclic ligands. 247 m.s. khan et al. table 2: carbonyl stretching frequency and conductivity of the complexes. νco (cm–1) λ (ohm–1cm2 mole–1) [mnl3(h2o)2][pf6]2·h2o 1716 165 [fel3(h2o)2][pf6]2·h2o 1714 160 [col3][pf6]2·h2o 1707 167 [nil3(h2o)2][pf6]2·mecn 1723 162 [cul3(h2o)2][pf6]2·h2o 1739 158 [znl3(h2o)2][pf6]2·h2o 1723 164 [mnl4(h2o)2][pf6]2·h2o 1715 164 [fel4(h2o)2][pf6]2·h2o 1716 163 [col4][pf6]2·h2o 1710 166 [nil4(h2o)2][pf6]2·mecn 1721 165 [cul4(h2o)2][pf6]2·h2o 1737 160 [znl4(h2o)2][pf6]2·h2o 1724 163 [mnl5(h2o)2][pf6]2·h2o 1718 161 [fel5(h2o)2][pf6]2·h2o 1715 163 [col5][pf6]2·h2o 1710 165 [nil5(h2o)2][pf6]2·mecn 1724 167 [cul5(h2o)2][pf6]2·h2o 1735 162 [znl5(h2o)2][pf6]2·h2o 1725 161 [mnl6(h2o)2][pf6]2·h2o 160 [fel6(h2o)2][pf6]2·h2o 162 [col6][pf6]2·h2o 164 [nil6(h2o)2][pf6]2·mecn 165 [cul6(h2o)2][pf6]2·h2o 164 [znl6(h2o)2][pf6]2·h2o 160 6. conclusion we have shown that derivatized planar pentadentate ligands may be prepared by esterification and functional group interconversions of suitable hydroxyethyl substituted macrocyclic ligand. these ligands appear to possess a coordination chemistry which parallels that of related unsubstituted ligand. 7. aknowlegments we would like to thank the department of chemistry, college of science, sultan qaboos university, oman and the engineering and physical sciences research council (epsrc), u.k. for financial support. 248 derivatized pentadentate macrocyclic ligands references smith, k.m. 1975. porphyrins and metalloporphyrins; elsevier, amsterdam. constable, e.c. 1999. coordination chemistry of macrocyclic compounds, oxford science publications. cabbinnes, d.k. and margerum, d.w. 1969. macrocyclic effect on the stability of copper (ii) tetramine complexes. j. amer. chem. soc. 91: 6540-6541. lindoy, l.f. 1989. the chemistry of macrocyclic ligand complexes, cambridge university press, cambridge. melson, g.a. 1979. coordination chemistry of macrocyclic compounds, plenum, new york. ansell, c.w.g., lewis, j., liptrot, m.c., raithby, p.r. and schroder, m. 1982. the stabilization of low oxidation state transition metal complexes. preparation and electrochemistry of cobalt(ii) unsaturated macrocyclic complexes and the stabilization of a cobalt(ii) derivative. crystal and molecular structure of [(co(ii)(l)(ch3oh)2][bf4]2 and [co(i)(l){p-(och3)3cl}[pf4]. j. chem. soc., dalton trans.: 1593-1601. ansell, c.w.g., lewis, j., raithby, p.r. and o’donoghue, t.d. 1983. synthesis of a macrocyclic metal complex incorporating peripheral hydroxyethyl tails: the x-ray structure of [mn(l1)cl][pf4]. j. chem. soc., dalton trans.: 177-179. ansell, c.w.g., lewis, j., raithby, p.r. and ramsden, j.n. 1982. synthesis and x-ray structure of a macrocyclic pentagonal bipyramidal complex of cobalt(ii). j. chem. soc., dalton trans.: 2127-2129. chung, l.y., constable, e.c., dale, a.r., khan, m.s., liptrot, m.c., lewis, j. and raithby, p.r. 1990. the transient template effect: chromium(iii)-directed synthesis of metal-free macrocyclic ligands and crystal structure of 1,11-bis(2’-hydroxyethyl)4,8,12,16,17,21-trinitilo-1,2,10,11-tetra-azacyclohenicosa-2,4,6,9,12,14,18,20-octaene hydrochloride tetrahydrate. j. chem. soc., dalton trans.: 1397-1404. chung, l.y., constable, e.c., khan, m.s., lewis, j., raithby, p.r. and vargas, m.d. 1984. structural characterization of a pentagonal bipyramidal macrocyclic chromium(iii) complex, an explanation of a chromium-mediated-template effect. j. chem. soc., chem commun.: 1425-1426. constable, e.c., khan, f.k., lewis, j., liptrot, m.c. and raithby, p.r. 1985. the preparation and coordination chemistry of 2,2’:6’,2”-terpyridine macrocycles. structural characterization of an intermediate in a transient template reaction. j. chem. soc., dalton trans.: 333-335. received 27 june 2001 accepted 20 november 2002 249 derivatized pentadentate macrocyclic ligands and their transition metal complexes muhammad s. khan* , nawal k. al-rasbi *, edwin c. constable **, adrian r. dale** and jack lewis ** *department of chemistry, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman; **department of chemistry, university of cambridge, lensfield rd., cambridge cb2 1ew, uk, *email: msk@squ.edu.om. ãíãï ó. îçä¡ äæçá ß. çáñçóèí¡ ãïæ compound found % c h n c h n references squ journal for science, 2018, 23(1) sultan qaboos university special issue based on the 4th international conference on numerical analysis and optimization guest editors mehiddin al-baali and anton purnama squ journal for science, 2018, 23(1) sultan qaboos university preface his special issue contains selected papers presented at the fourth international conference on numerical analysis and optimization: theory, methods, applications and technology transfer (naoiv-2017), held during january 2-5, 2017, at sultan qaboos university (squ), oman. more information is available at https://conference.squ.edu.om/default.aspx?tabid=2157. the naoiv-2017 conference was sponsored by squ, oman mathematics committee, comstech (pakistan), ampl (usa), german university of technology (gutech) in oman, and the british council (oman). seventeen world leading researchers gave keynote lectures. in total, thirty-seven international participants contributed talks. after the conference, selected contributions were invited to be submitted as full papers for publication in a special edited book of the springer series on proceedings in mathematics and statistics and squ journal for science. seven of the papers were selected for this special edited issue, each of which was accepted after a peer review process by independent reviewers. we wish to express our gratitude to all contributors. we are also indebted to many anonymous referees for the care taken in reviewing the papers submitted for publication. the nao conference series is held once every 3 years at squ: the first conference (nao2008) was held on april 6-8, 2008, the second conference (naoii-2011) was held on january 3-6, 2011, and the third conference (naoiii-2014) was held on january 5-9, 2014. the nao conference will hopefully remain a forum where prominent mathematicians, worldwide experts and active researchers gather and meet to share their knowledge on new scientific methodologies and simulate the communication of new innovative ideas, promote scientific exchange and discuss possibilities of further cooperation, networking and the promotion of the mobility of senior and young researchers and research students. for the naoiii-2014 conference (http://conference.squ.edu.om/default.aspx?tabid=572), a total of 13 keynote papers were published in the edited book “numerical analysis and optimization: nao-iii, muscat, oman, january 2014,” volume 134 (2015), springer series on proceedings in mathematics and statistics, and eight papers were published in the special issue on “numerical analysis and optimization,” volume 20, no. 2 (2015), squ journal for science. for naoii-2011 (http://conference.squ.edu.om/portals/16/conference2011/index.htm), nineteen papers were selected for two special issues of the squ journal for science, highlighting the two themes of the conference numerical optimization and numerical analysis. eleven papers were published in the volume 17(1) for the (2012) special issue on numerical optimization and eight papers in volume 17(2) for the (2012) special issue on numerical analysis. for the first nao-2008 conference, m.j.d. powell (who was a major figure in the world community of optimization researchers and left us during the year 2015) delivered the first plenary talk in the nao series. for more details, visit the website: http://conference.squ.edu.om/portals/16/conference2008/index.htm mehiddin al-baali and anton purnama guest editors for the special issue 23(1) of squ journal for science t https://conference.squ.edu.om/default.aspx?tabid=2157 http://conference.squ.edu.om/default.aspx?tabid=572 http://conference.squ.edu.om/portals/16/conference2011/index.htm http://conference.squ.edu.om/portals/16/conference2008/index.htm preface1_m-new 28 feb_m preface2 state-of-the-art review of collapsing soils science and technology, 6 (2001) 55-66 ©2001 sultan qaboos university use of isotope and solute chemistry to define the sources of pollution in mawqaq groundwater, hail, saudi arabia ibrahim abdulaziz al-sagaby and mohamed ali moallim earth sciences program, natural resource and environment research institute king abdulaziz city for sciences and technology (kacst), box 6086 riyadh 11442, saudi arabia. فى المياه الجوفية مصادر التّلوِث على عّرفَ التحليلية فى التإستعمال النظائر المشعِة والكيمياِء العربية السعوديةبالمملكة يل،، حا فى ماوقاق معلمالساجابي ومحمد علي زيزالعإبراهيم عبد أكثر .الجمالىزراعي و ال و صناعيستعمال المنزلى و ال اال لألغراِض المختلفِة مثل المياه الجوفية فى المنطقة ستعمُل ت :خالصة هو الهدف وقد كان . والمناطق المحيطة بها في مدينِة ماوقاق فى حقل ضحل قَْد ُجِمعتْ المياه الجوفية عينات عينة من نيمن ست نظائر ال لستعمابا مياه الجوفية ال بكتريولوجي في التلوث الو) 03 أوإن ( نترات ال مصادرالمياه الجوفية وتحديد وعية دراسة ن ). لتر/ ملغرام 500 (لمسموح به فى مياه الشرب حِد ا الملوحِة أعلِى من التركيِز متوسط وقد اتضح من نتائج الدراسة أن . ةمشعال في ) إن 03 أو إن( النّتراِت كنتروجيِن كميات عالية من صودفَ أيضا من المياه المالحة كما ثالث مجموعات وقد تم تحديد ُعمرأمكن تحديد مستقّرة المشعة النظائر وباستخدام ال. كوليفورم في بعض اآلباِرال جراثيم منطقة ، وقد تم العثور أيضا على الهذه إجراءات عالجية وبرنامِج وقد أتخذت السلطات الصحية المختصة والبلديات . وقاقالمياه الجوفية فى منطقة ما التّلوِث في ومصدر .سلطاتهذه البين لتّنسيِق طبقان بايُمَراقََبة abstract: groundwater in the area is used for different purposes like domestic, agricultural, industrial and landscaping. more than sixty groundwater samples were collected in an alluvial shallow aquifer in and around mawqaq town. the objective was to study groundwater quality and identify the sources of nitrate (no3) and bacteriological pollution in groundwater using environmental isotopes (2h, 3h and 18o). the results of the study have revealed the presence of average salinity concentration higher than the permissible limits (500 mg/l) for drinking water. three groups of water saline boundaries were identified. the presence of high nitrate as nitrogen (no3-n) was also encountered in the study area. coliform bacteria have also been identified in some wells. application of stable isotope has shown the age, origin and the sources of the pollution in the groundwater of mawqaq area. appropriate health and municipal authorities of the area have initiated remedial measures and a monitoring program is to be implemented in coordination with these authorities. keywards: salinity, bacteriological, pollution, septic tanks, nitrate, saudi and remedial. 1. introduction the shallow groundwater aquifers have been increasingly used to meet the different uses resulting from urban expansion and agricultural activities. constraints imposed by quality and growing problems of contamination has become very important issues. water supply requires an understanding of groundwater flow and the chemical processes involved in the water bearing systems in order to develop, augment and present a solution to any problem in the water supply system. shallow aquifers in the kingdom are the main water supply for rural areas and are prone to chemical change and contamination from many factors such as formational change, high pumping, salt intrusion, septic tanks and agricultural activities. concerns for water resources shortage and augmentation demands were received from the inhabitants of mawqaq town, in central saudi 55 al-sagaby and mohamed ali moallim arabia. the research presented in this paper is part of a study that covered hydrogeology, hydrogeochemical and geophysical investigations to develop water resources and to find adequate water supply in an acceptable quantity and quality for the town. the nearest similar groundwater quality studies were done in qasim and hail. few detailed studies can be found in the literature about the chemistry and quality change (alsagaby and moallim, 1996; sharaf and hussein, 1996; sowayan and allayla 1989; hussein, et. al. 1992; segar, 1988; edgell, 1989; jerias, 1986; brgm, 1985 and watban, 1976). various ideas in different topics were achieved and presented in these studies. high saline groundwater, elevated nitrate concentration and bacteriological contamination were encountered in the supply system of mowqaq town. the objective of this study is to apply solute chemistry and isotopes to clarify the sources of water quality change and biological contamination in the shallow aquifer and present a solution to the contaminated groundwater supply system. 2. description and geological setting of the study area mawqaq town lies in the middle of a wadi alluvial deposit surrounded by mountains, at an elevation of 1200 m above sea level. it lies 65 km southwest of hail the capital of the area. it is elongated in an alluvial strip towards northwest direction and depicted between longitude 410 00’ 00” and 410 20’ 00” and latitude 270 15’ 00” and 270 30’ 00”. the relevant physiographics structures (figure 1) around the town can be described as dunes in the north, mountains in the east and south and wadis in the west. three alluvial wadi trends are identified to be the main watercourses, which enter the town from the south and passes towards the north as observed from the satellite image and verified in the field. these trends were also observed from the preliminary analysis of water samples. three distinctive water types were defined from the preliminary chemical data analysis. to hail mawqaq to hail figure 1. topogaphic map of mawqaqhail area. 56 use of isotope and solute chemistry geologically, the study area is located in the middle of the northern part of the arabian shield in central saudi arabia. it is composed of a low lying plain composed of sand and gravel of various grain sizes with low strength of consolidated beds intercalated in the alluvial material deposited originally by floods from the mountains. a complex of crystalline rocks of various nature and origin surrounds this low land filled by alluvial fans. buried channels of various extensions are located. the forms and directions of the channels were controlled by structural phenomenon. small mountains of crystalline rocks are scattered in the plain. the major crystalline rocks surrounding the study area can be texturally classified into porphyry and aphanitic granite. the age of the recognized rock range from precambrian to tertiary followed by quaternary alluvial deposits in stratigraphical sequence, (figure 2). the precambrian units in the area are divided into two groups: sedimentary and volcanic (layered) rocks and plutonic rocks. the layered rocks are classified as banana formation (volcanic and hypabysal rocks) and hadn formation of silicic volcanic intercalated with fieldpathic sedimentary rocks. the rocks covering this area are characterized by the presence of medium to coarse granite, monzogranite and grandiorate with biotite and hornblende. the mawqaq complex is, in general, made of deformed, metamorphosed and foliated biotite with or without hornblende, granodiorite, tonalite, monzogranite and quartz diorite. the overall intrusive relationship of all rock types in the area is not clear, but it appears that these quartz diorites and tonalites are closely related and granodiorite and monzograinte appears to be somewhat younger. these rocks are cut by series of basalt dikes, which also appears to be related to the intrusive complex. olivine basalt of tertiary age occupies, as a field of pipeline and necks, throughout the area. quaternary alluvial and colluvim deposits of unconsolidated wadi material and pediment silt, sand and gravel occur in the study area. deposits of alluvial fan originating from the wadi drainage system were located to the south and west of jabal aja. moderate to well sort sand sized particles, but includes silt, and pebbles in the wadi channels dominate these sediments. complicated tectonic history and formation of structural diversity in consequence of tectonic events have affected the area. metamorphism of various degrees has been reported and intrusion of molten material, resulting in the creation of dikes. lineaments and faults, which control the pattern and formation of the alluvial aquifer and groundwater flow, were also found in the study area (stoesser and elliot, 1985). figure 2. simplified geologic map of mawqaq (hail area). 57 al-sagaby and mohamed ali moallim 3. methods and material more than 60 samples from water wells in the study area for water quality assessment were collected in order to achieve reasonable interpretation, evaluate the sources of groundwater salinity and delineate any possible pollution. representative chemical and bacteriological groundwater samples in the study area were used in order to assess water quality. measurements of ph, temperature, and ec were done in the field. the analyses conducted in the laboratory included major anions like ca, mg, na, k, cl, so4, hco3, no3, and hardness as caco3 and co3. sampling has been conducted with time difference of about three month. the first sampling (55 samples) was started in march 1998 and second part (11 samples) was in july 1998. figure 3. total dissolved solids in mawqaq wells, hail area. 4. results and discussion 4.1 water quality the results of the data collected from the field have shown field ph variation ranging from 7.86, slightly alkaline water, to 5.67, slightly acidic water. groundwater salinity in the aquifer changes from low to high saline along the down gradient. the maximum tds (5786 mg/l) in the aquifer is found in the north and the minimum (265 mg/l) in the south with average of about 1960 mg/l. the average salinity is higher than the permissible limit (500 mg/l) for drinking water (who, 1984). this increase of tds coincides with the decrease of well production in the area. the result also revealed an abrupt salinity change within a perimeter in some locations coupled with water well depth change in some parts of the study area, especially in the northern part. structural complexity, which controlled the depositional environment of the alluvial material of the aquifer, may have contributed to the salinity increase. figure 3 presents the pattern and distribution of salinity in the aquifer. three salinity trends and boundaries were observed from the figure. the first saline condition extends from the southern boundary to 1000 mg/l salinity (low salinity condition) and the second lies between 1000 mg/l 58 use of isotope and solute chemistry salinity boundary and 3000 mg/l-salinity boundary (moderate salinity condition). the third system of salinity is seen above 3000 mg/l salinity boundary (high salinity condition). the chemical data have also revealed that about 50% of the sampled wells high chloride concentrations above the acceptable limits for drinking water (cl>250 mg/l). about 43 % of the samples have a sulfate concentration of more than the acceptable limits for drinking water (so4 >250 mg/l). high sodium, calcium and bicarbonate concentrations were also observed (table1). geologically, the aquifer is a recent alluvial aquifer and has characteristically high saline water. 4.2 ion relationship and water composition the quality of water generally expected from an alluvial aquifer is an access of ca-hco3 water type unless influences by other materials are involved in the system. a plot of chloride versus sodium (figure 4) for the study area shows nearly a 1:1 ratio in the beginning of the graph and chloride starts increasing reaching a concentration of about 1400 mg/l (39.5 meq/l), while maintaining the same sodium concentration of up to 200 mg/l (8.7 meq/l). scattered points, were observed at the end of the graph. figure 5 displays a water type of high chloride with proportional sodium in the beginning and in the middle part, while at the end of the graph the ratio is nearly maintained constant proportion. the line nearly extrapolates to the sodium axis, indicating that high concentration of sodium is present in the system. moreover, significant concentration of sulfate scattered at three different groups with different concentrations and positive correlation between tds and sulfate were observed. figure 6 presents bicarbonate distribution as a function of total dissolved solids in the aquifer and displays three distinctive constant concentrations of bicarbonate. the possible interpretation is mixing between fresh water and saline water. this mixing could be the result of modern day recharged waters (high bicarbonate). table 1: mawqaq isotopic data serial # name delta 0-18 delta d 1. mq1 -1.72 -0.4 2. mq2 -1.95 -3 3. mq3 -0.35 -0.8 4. mq7 9.53 5. mq8 0.03 1.6 6. mq9 0.01 1.7 7. mq10 -1.38 -3 8. mq13 -0.93 -2.2 9. mq15 -0.77 10. mq17 -1.35 -1.9 11. mq19 -0.98 -4 12. mq20 -2 -7.1 13. mq22 0.46 -0.3 14. mq29 -2.21 -2.4 15. mq32 5.67 16. mq36 6.45 15.7 17. mq42 0.5 -4.6 18. mq43 -2.14 -2.3 19. mq44 -1.59 -2.9 20. mq50 -2.27 -4.5 21. mq53 -1.06 -5.2 22. mq55 -0.32 -2 hem (1970) has reported that nearly all-natural waters, in terms of chemical classification, lie between 0.55 to 0.75 (correlation coefficients for ec and tds). a mixture of water types 59 al-sagaby and mohamed ali moallim represented by nacl, caso4 and naso4 range between 0.65 to 0.75. the relationship between ec and tds is shown in figure 7. the coexistence of a good relationship is evident from the correlation coefficients (r2 = 1). the conversion factor (0.65) for the samples falls in the range designated for nacl, mg-caso4, naso4 and ca-hco3 water type by hem (1970). therefore, a mixing system of waters is prevalent in the aquifer. 4.3 groundwater pollution certain environmental conditions may have resulted in a widespread distribution of groundwater pollution in mawqaq town. in the study area, it is manifested by the way in which septic tanks are constructed. the presence of harmful contaminants indicates that environmental controls should be applied in the area. biochemical contaminant presence in the groundwater of the study area makes it necessary to initiate protection of the groundwater for the inhabitants of the town. the sources of the pollution, its impact and solutions will be considered in the following paragraphs. 4.4 nitrate pollution (no3-n) in addition to high salinity presence, very significant high nitrate concentrations, which increases towards down gradient of the aquifer, have been recorded in the study area. the nitrate concentration recorded in the water samples range from 2.8 mg/l (minimum) to 497 mg/l (maximum) with an average of 111.53 mg/l. the geographical distribution of nitrate concentration in groundwater of the alluvial aquifer is shown in figure 8. elevated concentrations are found in the northern part of the aquifer although local variations are common in some parts. artificial fertilizers for farming purposes were not used in the area (personal contact with inhabitants). the presence of nitrate as nitrogen in mawqaq groundwater is higher than the permissible limit for the drinking water (10 mg/l), which was defined by world health organization in 1981 and 1993 (edmunds and gaye, 1997). figure 4. a plot of chloride versus sodium for mawqaq wells, hail area 0 200 400 600 800 1000 1200 1400 0 500 1000 1500 2000 2500 chloride concentration (mg/l) so di um c on ce nt ra tio n high nitrate concentrations are generally assumed to be the results of human activities, but occurrences of high no3 groundwater far from man made activities have been recorded in arid and semiarid regions, especially in north africa. up to 2800 mg/l of no3-n were recorded in sudan, 60 use of isotope and solute chemistry near khartoum. this was attributed to very low recharge rates and the accumulations from vegetation over many centuries. in kalahari and libya similar problems were encountered (edmunds et. al., 1992). excess of nitrogen concentrations in groundwater, leaching from the domestic septic systems, (residential area) and wastewater disposals were also recorded in australia (gerriste, et. al. 1995) and in ontario, canada (aravena, et. al, 1993). 0 200 400 600 800 1000 1200 1400 1600 1800 0 1000 2000 3000 4000 5000 6000 7000 tds concentration ( mg / l ) su lf at e co nc en tr at io n figure 5. a plot of tds versus sulfate in the study area. 0 100 200 300 400 500 600 700 0 1000 2000 3000 4000 5000 6000 7000 tds (mg /l) b io ca rb on at e co nc en tr at io n figure 6. a plot of tds vs biocarbonate in the study area. 61 al-sagaby and mohamed ali moallim y = 0 .65 x r 2 = 1 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 ec micromhos /cm ) t d s co nc en tr at io n figure 7. electric conductivity vs total dissolved solids (tds) in the study area. 62 use of isotope and solute chemistry figure 9 presents a pattern of no3 /cl ratio. the nitrate enrichment is a wide variation of wetter and drier periods in the unsaturated soils. therefore, the mechanism of enrichment of no3– n in the system is likely to be due to the presence of leguminous plants or nitrogen fixation of indigenous plants (vegetation). it could come as a loss of nitrogen from the domestic septic tanks systems since there are no applications of fertilizers in the agricultural system or manure from the animals. the latter hypothesis (septic tanks) is more acceptable because the concentration of nitrate as nitrogen in groundwater is relatively very high in the inhabited area while nitrate concentration in the outside of the town (mq1 and mq2) is very low. 4.5 bacteriological pollution the significance of the various coliform organisms in mawqaq groundwater was considered in order to determine the nature of the pollution, detect and estimate the coliform group of bacteria. almost all the extension of aquifer was not covered for bacteriological sampling but random sampling has been conducted for this matter, especially in the northern part, where some people are utilizing water for various usage. the directorate general of health in the region has sampled about 10 wells and reported the presence of harmful bacteria in some wells. the septic tank systems are parallel with the wells in some areas, especially in the north of the town with slight difference in depth. aquifer material is mainly channeling deposits, which helps seepage, infiltration, and easy flow in the fractures and faults available in the area. 0 0.5 1 1.5 2 2.5 mq 1 mq 2b mq 3b mq 6 mq 8 mq 10 mq 13 mq 15 mq 17 mq 20 mq 23 mq 25 mq 27 mq 29 mq 31 mq 34 mq 36 mq 38 mq 41 mq 43 mq 45 mq 47 mq 49 mq 52 mq 54 mq 57 mq 59 mq 61 mq 63 mq 65 mq 67 well id # r at io o f n o 3/ c l figure 9. plot of no3/cl for mawqaq groundwater. the presence of bacteria, which lives in the intestine of human being and animals, is suspected in the groundwater system. the main point source of contaminants in shallow groundwater systems in the area and the growth of bacteria in these systems is mainly attributed to the processes, which occur in the septic systems for household wastewater disposals. the impact of septic tank systems on groundwater contamination and its consequence to the environment have been addressed and disinfection of the wells has been made with constant monitoring of the concerned authorities. 63 al-sagaby and mohamed ali moallim 4.6 isotopic application 4.6.1 tritium tritium data, which are useful for providing information for modern recharge, have been collected randomly in the study area. the tritium result has shown that the maximum content of tritium in mawqaq groundwater is about 8.7tu and the minimum is about 1tu and the average is 5.33tu. these values present a picture of a pre-and post-pump replenishment and characterization of old and young recharge in the alluvial aquifer. figure 10 shows a linear plot of tritium versus tds and emphasizes the relationship between the salinity and tritium in mawqaq groundwater. sample mq16 is spring water, which flows from the mountains, with low tds concentration and relatively moderate content of tritium. this plot shows three grouping patterns of samples in relation to the salinity of the area. first group shows low tds concentration, which represents juvenile water, and relatively high content of tritium. the second group has moderate tds concentration and relatively low tritium (transitional of two mixing system) while the third group is characterized by very high salinity and moderate tritium content. thus, this is the condition of post pump groundwater with the exceptional salinity elevation presence cases. there are rare cases in which fresh groundwater is characterized by high salinity. the attribute to the presence of high saline groundwater is due to the vicinity of the source of sabkha deposits in mawqaq area. 4.7 oxygen-18 and deuterium deep groundwater usually reflects the long-term average isotopic composition recharge waters while shallow groundwater reflects more closely short-term isotope variability in precipitation and change in the ratio of winter and summer. table 1 shows the oxygen-18 and deuterium data for the study area. figure 11 reflects the pattern of deuterium and oxygen-18 in mawqaq groundwater. the picture presents mainly three types of distribution of isotope, which has a relation with the origin of water, and replenishment of groundwater. these groups present a picture of old and young groundwater. these groupings are also mentioned earlier in figure 10. 0 1 2 3 4 5 6 7 8 9 10 0 500 1000 1500 2000 2500 3000 tds (mg /l) 3h ( sping water figure 10. tds concentration vs tritium content in the study area. 64 use of isotope and solute chemistry y = -17x + 396 r2 = 0.9897 y = -0.0755x 0.3042 r2 = 0.0134 -100 -50 0 50 100 150 200 250 300 350 400 0 5 10 15 20 25 30 delta deuteriu d el ta o xy ge n 18 gmwl mawqaq wat figure 11. istopic composition mawqaq groundwater. 5. conclusions this study has revealed progressive groundwater quality deterioration towards the central and northern part of the town (in the alluvial aquifer). groundwater salinity in the aquifer increases from low to high along the down gradient with maximum tds (5786 mg/l) is found in the north and minimum tds (265 mg/l) in the south. ion relationship sequence, water chemistry and application of stable isotopes have also shown water grouping in the study area. transitional mixing system was deducted from these results. structural constraints, improper distribution of water wells and uncontrolled pumping are the other main causes of the aquifer deterioration, especially in the central and northern part. presence of high-elevated no3-n concentration was encountered in the study area. the existence of hydraulic continuity between septic tank systems and groundwater may be the cause of the elevated nitrate concentration. some harmful bacteria have also been identified in some wells. references al-sagaby, i.a. and moallim, m.a., 1996, hydrogeochemical investigation of the water wells in and around kacst research center in qassim region, saudi arabia, internal report no.121-18-es, natural resources and environmental research institute, kacst, saudi arabia. aravena, r., evans, m.l. and cherry, j.a., 1993, stable isotopes of oxygen and nitrogen for identification of nitrate from septic systems, ground water-april-march, 31( 2): 180-186. 65 al-sagaby and mohamed ali moallim brgm, 1985, water, agriculture and soil studies of saq and overlying aquifers, study for ministry of agriculture and water, riyadh, saudi arabia. edmunds, w.m., darling, w.g., kinniburgh, s., kotoub, s. and mahgoub, s. 1992, sources of recharge at abu delaig, sudan journal . hydrol. 131: 1-24. edmunds, w.m. and gaye, c.b., 1997, naturally high nitrate concentrations in ground waters from sahel, j. of environ. quat. 26: 1231-1239. edgell, h.s., 1989. geological framework of saudi arabia groundwater resources, j. k. a.u., earth sci. v.3. special issue: 1st saudi symp. on earth sci., jeddah, pp. 267-286. gerriste, r.g., adeney, j.a. and hosking, j., 1995. nitrogen losses from a domestic septic tank system on the darling plateau in western australia, journal of water res. 29(9): 2055-2058. hem, j.d., 1970. study and interpretation of chemical characteristics of natural water, u. s. geological survey water supply paper no. 1473, pp. 363 hussein, m.t., bazuhair, a.g. and ageeb, a.e., 1992. hydrogeology of the saq formation, east of hail, northern saudi arabia, quar. j. eng. geol. 25: 57-64. jerais, a.a., 1986. hydrogeology of saq aquifer in hail region, msc. thesis, fac. earth sciences, king abdulaziz university, jeddah, saudi arabia. segar, d.a., 1988. a groundwater model of the saq and tabuk sandstone aquifers in south eastern jordan and northwestern saudi arabia, msc. thesis, school of earth sciences, university of birmingham, uk. sowayan, a.m. and allayla, r., 1989. origin of the saline groundwater in wadi ar rumah, saudi arabia, groundwater, 27(4): 481-490. sharaf, m.a. and hussien, m.t., 1996. groundwater quality in saq aquifer, saudi arabia, hydrogeological sciences journal, 41(5): 683-670. stoesser, d.b. and elliot, j.e., 1985. reconnaissance geology of al-qasr quadrangle, sheet 27/41c: open-file report usgs-of-05-2, ministry of petroleum and mineral resources, deputy ministry for mineral resources, jeddah, kingdom of saudi arabia. watban, n.f., 1976. groundwater potentiality of tabuk and saq aquifers in qassim region, msc. thesis, institute of applied geology, king abdul aziz university, jeddah, saudi arabia. world health organization (who), 1984, guidelines for drinking water quality, vol. 2, health criteria and other supporting information, geneva. received 4 march 2000 accepted 1 june 2000 66 ibrahim abdulaziz al-sagaby and mohamed ali moallim introduction methods and material jerais, a.a., 1986. hydrogeology of saq aquifer in hail region, msc. thesis, fac. earth sciences, king abdulaziz university, jeddah, saudi arabia. electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002)1-10 © 2002 sultan qaboos university design of all optical packet switching networks hussein t. mouftah department of electrical and computer engineering, queen’s university kingston, on, k7l 3n6, canada, email: mouftah@ece.queensu.ca. تعميم الشبكات ذات حزم المفاتيح البصرية التامة مفتاح . حسين ت في الشبكات dwdmالمفاتيح البصرية ومحوالت الطول الموجي تصنفان على انهما اهم مكونين لألنظمة : خالصة .البصرية التامة مستقبال دوائر حماية الشبكات , القابلة للتنظيم oxcدوائر , المفاتيح البصرية تمثل الجزء األساسي في عمل الموجهات المتغيرة .ات البصريةواإلصالح في الشبك يساعد استخدام . محوالت الطول الموجي تستخدم في التحويل من طول موجي داخل الى طول موجي آخر خارج عند الحاجة إدارة وتنظيم المفاتيح والشبكات في الطبقة البصرية , هذه المحوالت مع المفاتيح البصرية على الحصول على موجهات مستقرة .رية التامةبشكل ضروري لظهور الشبكات البص ويتضمن هذا البحث دراسة كفاءة . ولكن يجب اآلخذ بنظر االعتبار الكلفة العالية لمحوالت الطول الموجي أثناء التصميم كما يقدم البحث طريقة كفوءة الكلفة . محوالت الطول الموجي عن طريق نمذجة الشبكات البصرية بدرجات مختلفة من الحمل الموجي وفي نفس الوقت يراعى ان تكون خوارزمية الموجهات وافتراض الطول الموجي لتصميم مثالي لمحوالت الطول عند اقتران العمل بهذه الخوارزمية العامة مع مفاتيح . خوارزمية عامة تصلح لكال الشبكات ذات الحمل الكبير والحمل الصغير . ومحوالت الطول الموجي يمكن الوصول الى الشبكات البصرية التامة abstract: optical switches and wavelength converters are recognized as two of the most important dwdm system components in future all-optical networks. optical switches perform the key functions of flexible routing, reconfigurable optical cross-connect (oxc), network protection and restoration, etc. in optical networks. wavelength converters are used to shift one incoming wavelength to another outgoing wavelength when this needs to be done. always residing in optical switches, they can effectively alleviate the blocking probability and help solve contention happening at the output port of switches. the deployment of wavelength converters within optical switches provides robust routing, switching and network management in optical layer, which is critical to the emerging all-optical internet. however, the high cost of wavelength converters at current stage of manufacturing technology has to be taken into consideration when we design node architectures for an optical network. our research explores the efficiency of wavelength converters in a long-haul optical network at different degrees of traffic load by running a simulation. then, we propose a new cost-effective way to optimally design wavelength-convertible switch so as to achieve higher network performance while still keeping the total network cost down. meanwhile, the routing and wavelength assignment (rwa) algorithm used in the research is designed to be a generic one for both large-scale and small-scale traffic. removing the constraint on the traffic load makes the rwa more adaptive and robust. when this new rwa works in conjunction with a newly introduced concept of wavelength-convertible switches, we shall explore the impact of large-scale traffic on the role of wavelength converter so as to determine the method towards optimal use of wavelength convertible switches for all-optical networks. keywords: all optical networks, packet switching, wavelength division multiplexing, wavelength converters, routing and wavelength assignment. 1. introduction i t has been widely believed that dense wavelength division multiplexing (dwdm) is a promising technology for next generation internet. wdm networks have proved themselves 1 1 hussein t. mouftah to be capable of offering a transmission capability of terabit (10 bit per second) or even petabit (10 bit per second) by multiplexing traffic on to a set of wavelength channels within a single fiber as shown in figure 1. meanwhile, they do network routing, protection, restoration and management in the optical domain, which greatly improves the whole network performance. 12 15 f i b e r o p t i c s λ 1 λ 2 λ 3 λ 4 v e d i o c o n f e r e n c e b r o a d c a s t t e l e v i s i o n e e b u s i n e s s t r a n s a c t i o n m u l t i m e d i a figure 1. integrated traffic in fiber optics. in a wdm network, the traffic between each pair of source and destination (s-d) nodes can be routed based on its wavelength. a wdm network with such a feature is called wavelength-routing network (mukherjee, 1997). wavelength routing provides a flexible and efficient mechanism of setting up lightpaths for traffic demands and can do reconfiguration in case of a change in the state of a network. an important optical component that performs the routing function at each intermediate node along the lightpaths is the optical switch. it switches an entire wavelength from an input port to an output port at each intermediate node according to a certain routing scheme. by utilizing optical switches this way, the optical domain connectivity among nodes and access stations can be dynamically rearranged. this rearrangeability will allow the dynamic allocation of wavelength and capacity throughout the network to meet changing traffic, service, and performance requirement so as to provide a robust, fault-tolerant network. moreover, as the network functions of operation, administration, maintenance and provisioning move from the traditional electrical layer to the optical layer, optical switches will play a critical role. an optical switch equipped with wavelength converters is called wavelength-convertible switch. wavelength converters are used to solve the wavelength-continuity constraint existing in simple wavelength-routing networks. wavelength-continuity constraint imposes a strict condition that a lightpath must be established on a single wavelength. this leads to very inefficient utilization of wavelength resources and results in higher network blocking probability. by using wavelength converters within a switch node, one incoming traffic flow on a certain wavelength can be directed to an output port on another different available wavelength when needed. this way has the benefit of alleviating output port contention as well as increasing wavelength reuse. 2. wavelength-convertible switches despite the preferable advantage of eliminating wavelength continuity constraint so as to decrease network blocking probability, wavelength converters are costly at the current state of technology. therefore, many studies have attempted to determine the potential benefits of wavelength conversion and the efficient ways to deploy them in optical switches. 2 design of all optical packet switching networks in (lee and li, 1993), several wavelength-convertible cross-connect architectures were proposed as shown in figure 2. depending on the design, wavelength converters can be used in different architectures as dedicated, share-per-link and share-per-node. connections can choose to bypass the wavelength converter bank and stay on the same wavelengths or be directed to the converter bank to undergo shifting to another wavelength. d e d i c a t e d w a v e l e n g t h c o n v e r t i b l e s w i t c h s h a r e d p e r l i n k w a v e l e n g t h c o n v e r t i b l e s w i t c h s h a r e d p e r n o d e w a v e l e n g t h c o n v e r t i b l e s w i t c h o p t i c a l s w i t c h d e m u x d e m u x m u x w c m u xw c l o c a l a d d / d r o p o p t i c a l s w i t c h d e m u x d e m u x m u x m u x w c o s w l o c a l a d d / d r o p w c o p t i c a l s w i t c h d e m u x d e m u x m u x m u x w c w c w c w c w c w c w c l o c a l a d d / d r o p figure 2. wavelength-convertible switch architecture alternatives. the dedicated wavelength convertible switch architecture provides a full conversion capability to any wavelength. however, the high expense and inefficient use of converters make it a poor candidate for industry application. both share-per-link and share-per-node architectures use a fewer number of converters while still achieving most of the benefits of a full conversion way. in (yates and rumsewicz, 1999), the authors show that the performance offered by wavelength converters depends on a number of factors, including the number of available wavelengths, the routing and wavelength assignment algorithms, network topology and network size. in (iness and mukherjee, 1998; and torrington-smith, 2000), the authors investigated the issues of optimal use of wavelength converters in lightwave networks. the work in (iness and mukherjee, (1998) considers different versions of sparse wavelength conversion namely, sparse nodal conversion, sparse switch-output conversion and sparse range conversion to 3 hussein t. mouftah determine if the sparse use of wavelength converters can achieve the most benefits provided by full conversion. based on the observation that most of the studies show that wavelength converters are critical but not needed all the time, a half-clear wavelength-convertible switch architecture was proposed by (torrington-smith, 2000). the conclusion from (torringtonsmith, 2000) was that a half-clear wavelength-convertible switch can have similar performance characteristics as other architectures shown in figure 2, however, with much less cost. a common observation from all the above studies is that the network performance improvement due to the use of wavelength converters depends heavily on several factors such as network topology and network size, traffic load, rwa schemes, and the number of wavelengths used on each fiber link. hence, besides the design of a new optical switch architecture, one must carefully select a routing and wavelength assignment algorithm so as to match most efficiently the characteristics of the network. 3. wacosod (wavelength-convertible optical switch optimization design) considering the high cost of wavelength converters and their performance dependency on the above factors, our research objectives were to: • propose a novel optical switch architecture with x% of wavelength conversion capability such that the number x% is tunable so as to achieve the most cost-effective design for the whole network; • develop new routing and wavelength assignment schemes to deal with both large-scale and ordinary traffic (generic rwa problem) in light of the fact that all previous research efforts have been focussed on small-scale traffic, which is no more than the capacity of a single wavelength between any pair of source and destination nodes; • study the impact of large-scale traffic on the efficiency of the new wavelength-convertible switch (bifurcated traffic problem). 3.1 design of the x% wavelength-convertible switch each of the above reports holds its unique contributions to the study of wavelength converters in optical networks. however, none has yet really investigated the optimal percentage of wavelength conversion capability needed in an optical switch node, given a certain type of network topology, traffic load and network constraints. such an exploration would be very meaningful to network planners, optical switch designers and service providers, because the direct impact of such an optimization process is the cost of the whole network. o s w w c w c w c λ 1 λ 2 … λ n λ 1 λ 2 … λ n λ 1 λ 2 … λ n λ 1 λ 2 … λ n o s w figure 3. x% wavelength-convertible switch architecture. 4 design of all optical packet switching networks bearing the above goals in mind, we propose a new, flexible and cost-effective wavelength-convertible switch architecture whose prototype is shown in figure 3. in such a switch, only a certain percentage of outgoing links after the first stage optical switch can have access to the wavelength converter bank if conversion is needed. given a traffic load, a network topology and a traffic matrix, we can use a specially designed routing and wavelength assignment (rwa) algorithm to establish lightpaths for traffic flows in the optical domain with efficient use of wavelength converters. if a contention takes place at a switch output port, that wavelength will be directed to the wavelength converter bank as long as there is one wavelength converter available. with this type of architecture and given network parameters, we shall determine at what percentage of wavelength conversion capacity the network can be most cost-effective in terms of the metrics such as the number of wavelengths, network cost, network blocking probability and average traffic delay. 3.2 the routing and wavelength assignment (rwa) problem since the focus here is on core networks, the mean traffic flowing through the network is fairly steady in time domain. so we can take it as a static traffic for the simplicity and feasibility of the research. thus, the algorithm used to deal with lightpath establishment is called static rwa. solving the rwa problem for a given network topology, traffic matrix and network constraints is far from being trivial. numerical analysis has proved that rwa is an n-p hard problem (zhang and acampora, 1995; naas, 1999; mukherjee et al, 1996) since this is an example of a mixed integer linear mathematical problem (milp), for which no efficient algorithms are known to be existing for the solution of arbitrary milps. thus, the majority of the research in this area has been focussed on heuristic approaches to solve the rwa problem. for the routing problem, taking into account all possible source and destination pairs is impractical because the number of state space is exponentially increased with the network size. hence, the routing function is usually performed by well-known heuristic techniques such as the shortest path algorithm and its variations. our research has developed the shortest path algorithm to a weighted shortest path (wsp) which not only does a searching for shortest path but also adds a searching order scheme so that the largest traffic will first be selected for path search. the goal is to route the heaviest traffic in one hop for lower congestion. once the routing problem is solved, wavelength assignment is performed with the goal of maximizing the wavelength utilization and network throughput. this problem can be presented as a graph-coloring problem that is a np-complete problem. therefore, heuristic methods must be used for a practical solution (mukherjee et al, 1996; garnot et al, 1997; ramaswami and sivarajan, 1995; ravikumar et al, 1997). some of the proposed wavelength assignment algorithms are: (1) random wavelength assignment that allocates a new connection to a wavelength which is randomly chosen from the set of available wavelengths, (2) first-fit wavelength assignment which establishes a connection on the first available wavelength (mitchem, 1995; chlamtac et al, 1990). this is what we use in our approach. (3) most-used wavelength assignment which allocates to a new connection the wavelength that is used on the greatest number of fibers in the network (mokhtar and azizoglu, 1998). so far, almost all the work done before simply assumed small-scale s-d traffic which never surpasses the capacity of a single wavelength capacity. however, a more realistic situation in the backbone networks is that a pair of s-d nodes representing two major metropolitan areas may need to transmit very large-scale traffic that is well above the capacity of one wavelength from end to end. then, how to solve this traffic demand is a nontrivial problem. thus, we proposed a generic rwa (g-rwa) for both large and small-scale traffic. in response to such a challenge, we proposed a traffic splitting and waveband routing algorithm as shown in figure 4. the example in this figure shows how the large-scale traffic 5 hussein t. mouftah 32gbps is routed from its source node 1 to destination node 4. here, the traffic is split into two sub-groups consisting of three 10gbps and one 2gbps traffic flows. then, those three 10gbps traffic flows are grouped into a waveband and routed to node 4. the remaining 2gbps traffic is dealt with in wavelength routing module. the reason behind such an algorithm design is the simplicity for network control and lower network cost. obviously, this introduces computation complexity in rwa, since the pre-processing on waveband will cause the changes in available wavelength resources and network status. waveband routing 2 3 5 6 7 4 1 8gbps remaining 2gbps wavelength routing wavelength routing 6gbps 5gbps totally: 10 x 3 +2=32gbps traffic figure 4. hybrid waveband and wavelength routing. another key issue is the lightpath establishment, which requires efficient reuse of wavelengths. in (torrington-smith, 2000; and naas, 1999), lightpaths were set up in the priority order of unclear lightpath, continuous clear lightpath and non-continuous clear lightpath for the sake of saving cost, because the unclear lightpath takes advantage of the local add/drop switches to do o-e-o conversion. this method costs less than the all-optical conversion does. such an idea is very suggestive and innovative. however, besides the drawback of large o-e-o conversion delay, as the traffic load on the backbone network increases tremendously, the burden on the local conversion switches would become very heavy. in order to deal with such a situation, the local switch has to be much more powerful and hence becomes very expensive. as a result, the cost of a robust local switch surpasses the additional cost by adding more wavelengths or converters. more importantly, our research is forward-looking into the all-optical network, and we expect that no o/e conversion should get involved in the backbone networks. therefore, our research will initiate a comparison between the rwa algorithms with or without unclear lightpath (ucl) under heavy traffic load to determine which one is more cost-effective. 3.3 wacosod design with all the above innovative ideas, the simulation software is being developed as expected. the flow chart for the whole wacosod is illustrated in figure 5. given the network parameters such as network topologies, traffic matrix, traffic load request and system constraints, we first deal with traffic sorting and splitting as described in the above 32gbps traffic example. then, the large traffic is combined together into a waveband which in turn is routed to the destination node. this step is repeated until all the large scale traffic is satisfied. 6 design of all optical packet switching networks then, the network resource and status information are updated. afterwards, wavelength routing takes place to accommodate the small-scale traffic. simulation results and data are collected at the end for further analysis. t r a f f i c s o r t i n g a n d g r o u p i n g ( g i v e n t r a f f ic m a t r i x ; t r a f f i c l o a d m a t r i x ; t o p o l o g y , n u m b e r o f w a v e l e n g th s ; s y s t e m c o n s t r a i n t w a v e b a n d r o u t in g w a v e l e n g t h r o u ti n g n e t w o r k r e s o u r c e a n d s t a t u s i n f o r m a t io n r o u t i n g p a t h ( o s p f ) r o u t i n g p a t h ( o s p f ) f ir s t f i t w a v e l e n g th a s s i g n w a v e le n g th a s s ig n m e n t b a s e d o n e f f i c ie n t f i llu p a n d r e u s e w i th g i v e n n u m b e r o f w a v e le n g th c o n v e r t e r s m e t r i c s c o l l e c t o r a n a l y s i s figure 5. wacosod flow chart. 4. results and discussion wacosod was run for a nsf network with 14 nodes across north america. the simulation starts with wavelength conversion capability of 0, i.e. no wavelength converters was in optical switches. the values for the network metrics were generated at the end of a simulation. we then increased the conversion capability and repeated the simulations. in this way, network metrics corresponding to different percentages of wavelength conversion capabilities were recorded for quantitative analysis. in figure 6, it is clear that the more wavelengths that are used, the better the network throughput that is obtained, because more traffic can fit into the network. the upper group of curves represents the incremental network throughput associated with the changing percentages of wavelength converters. unclear lightpath (ucl) was allowed in rwa. the plot shows that the network with higher percentage of conversion usually achieves higher network throughput with the same number of wavelengths. this well proves the role of wavelength converters in improving network throughput. the lower two curves are for the all-optical networks (no ucl) with 50% and 25 % wavelength conversion capacities respectively. as we expected, we also see that removing ucl from network makes a poorer reuse of wavelengths so that a higher number of wavelengths is needed to retain the same level of network throughput. in this case, 18 wavelengths are needed for a 100% throughput for an all-optical network while only 16 are needed for the network with ucl. such a difference in the number of wavelengths can be ignored as the transport system can support a much higher number of wavelengths (160 per fiber so far) with much less cost on each individual wavelength. meanwhile, the o/e conversion involved in ucl will introduce a lot of processing latency as we can see in figure 7. the plot clearly tells us that on average, traffic in the alloptical networks experiences much less delay (about 20% less) because no o/e conversion gets involved. as more and more real time services, such as online teleconferences or telemedicine, are emerging, all-optical networks will take the responsibility for such qos 7 hussein t. mouftah requirements. moreover, eliminating o-e-o conversion from the backbone network will guarantee the optical layer’s transparency to data rate, protocols and traffics, which in turn simplifies the network control and management. c o m p a r is o n s f o r d if f e r e n t x % w c s 9 0 9 0 .5 9 1 9 1 .5 9 2 9 2 .5 9 3 9 3 .5 9 4 9 4 .5 9 5 9 5 .5 9 6 9 6 .5 9 7 9 7 .5 9 8 9 8 .5 9 9 9 9 .5 1 0 0 1 0 0 .5 1 0 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 # o f w a v e le n g t h s n et w or k th ro ug hp ut n o w c 1 2 .5 % w c 2 5 % w c 5 0 % w c 2 5 % w c w ith o u t u c l 5 0 % w c w ith o u t u c l figure 6. network throughput vs. number of wavelength. comparison of delays 8 8 .5 9 9 .5 10 10 .5 11 12 13 14 15 16 17 18 number of wavelengths d el ay s rwa with ucl for 50 % wc rwa with ucl for 25 % wc rwa without ucl for 25 % wc rwa without ucl for 50 % wc figure 7. delays comparison between ucl and non-ucl. an important insight into the effect of increasing wavelength conversion capability can be obtained from figure 8. for a given traffic load, the achievable benefit in network throughput by using more wavelength converters starts to be significant and then gradually levels off after a certain threshold. in this case, before getting 37.5% of wavelength 8 design of all optical packet switching networks conversion capability, the network throughput has been steadily increasing. after that, the gain drops sharply and barely changes. for this particular case, around 37% conversion capability is good enough and cost-efficient. such an observation implies that a careful selection on the number of wavelength converters in optical networks is a must. more research work should be done on finding the most cost-effective combination of the number of wavelengths, the number of converters, network gains and associated network costs. ne tw ork t h rou gh pu t vs . % o f w ave le ng th co nve rsion 99. 9 99.9 1 99.9 2 99.9 3 99.9 4 99.9 5 99.9 6 99.9 7 99.9 8 99.9 9 10 0 0 12 .5 25 37.5 5 0 62 .5 75 8 7.5 10 0 (%) w avelen gth co nversio n n et w or k th ro ug hp ut bl ock in g p ro ba b ili ty figure 8. network throughput vs. the percentages of wavelength converters. 5. summary the performance of a wavelength-convertible optical network is closely related to the architecture of the optical switch nodes, the traffic load, the network topology and the rwa algorithms. therefore, a study on an all-optical network must carefully take into consideration all these correlated factors. moreover, the interleaving influence between those factors shall be studied. the proposed x% wavelength-convertible switch architecture is an innovative idea to explore the most cost-efficient way to gain network performance enhancements. it works in conjunction with the new g-rwa algorithm to smartly do network configuration, lightpath establishment and fully use the wavelength resources. in such a way, wavelength-convertible switches can truly bring to the next generation all-optical networks more robust capabilities at as little cost as possible. in g-rwa, the waveband routing method for large-scale traffic is a cost-effective, simple-controlled and easy-implemented solution. further detailed research will use wacosod to study the role of wavelength converters in large-scale traffic by means of analyzing the network throughput enhancement due to wavelength converters, change in average traffic delay vs. traffic load, and network cost variance due to the change in wavelength converter deployment. 6. acknowledgement thanks are due to my students nabil naas, nicholas p. torrington-smith and xueli hou who have developed rwanco, wconsim and wacosod tools in their master thesis 9 hussein t. mouftah research, respectively. this work was partly supported by grants received from the natural science and engineering research council (nserc) of canada, communication and information technology ontario, and nortel networks of ottawa. references chlamtac, i., ganz, a. and kami, g. 1990. lightpath communications: an approach to high bandwidth optical wan’s. ieee trans. on communications, 40: 1171-1182. garnot, m., sotom, m. and masetti, f. 1997. routing strategies for optical paths in wdm networks. ieee international conference on communication, pp.422-426. iness, j. and mukherjee, b. 1998. sparse wavelength conversion in wavelengthrouted wdm optical networks. photonic network communication, 1: 183-205. lee, k.c. and li, v. 1993. a wavelength-convertible optical network. ieee/osa j. of lightwave technology, 11: 962-970. mitchem, j. 1995. on various algorithms for estimating the chromatic number of graph. the computer journal, 19: 182-183. mokhtar, a. and azizoglu, m. 1998. adaptive wavelength routing in all-optical networks. ieee/acm trans. on networking, 6: 197-206. mukherjee, b. 1997. optical communication networks, mcgraw-hill. mukherjee, b., banerjee, d. and ramamurthy, s. 1996. some principles for designing a wide-area wdm optical network. ieee/acm transactions on networking, 4: 684-696. naas, n.a. 1999. towards optimum design of static wavelength-routing optical widearea packet-switched networks. m.sc(eng.) thesis , queen’s university, ontario, canada. ramaswami, r., and sivarajan, k. 1995. routing and wavelength assignment in alloptical networks. ieee/acm transactions on networking, 3: 489-500. ravikumar, c.p., rain, c. and verma, v. 1997. kautz graphs as attractive logical topologies in multi-hop lightwave networks. computer communication, 20:12591270. torrington-smith, n. p. 2000. an evaluation of optical switch architectures utilizing wavelength converters. ms. of engineering, royal military college of canada, kingston, ontario, canada. yates, j.m. and rumsewicz, m.p. 1999. wavelength converters in dynamicallyreconfigurable wdm networks. ieee communications surveys, second quarter, pp.215. zhang, z. and acampora, a. 1995. a heuristic wavelength assignment algorithm for multihop wdm networks with wavelength routing and wavelength re-use. ieee/acm trans. on networking, 3: 281-288. received 2 june 2001 accepted 10 october 2001 10 design of all optical packet switching networks hussein t. mouftah department of electrical and computer engineering introduction science and technology, special review (2000) 185-207 © 2000 sultan qaboos university 185 photovoltaic cells and systems: current state and future trends hadj bourdoucen, joseph a. jervase, abdullah al-badi, adel gastli and arif malik department of electrical & electronics engineering, college of engineering, sultan qaboos university, p. o. box 33, al khod 123, muscat, sultanate of oman. الخاليا واألنظمة الشمسية ، الوضع الحالي واآلفاق المستقبلية عبد اهللا البادي و عادل القسطلي و عارف مالكحاج بوردوسن و جوزيف جرفيس و أي نظام فولطائي ضوئي . الفولطائية الضوئية هي عملية تحويل الطاقة الشمسية إلى طاقة كهربائية :خالصـة .من الخاليا الشمسية ومحول للطاقة الكهربائيةيتكون بشكل ثابت من مصفوفات األنظمـة الفولطائـية الضوئية تمتاز بأنها أنظمة موثوق بها، عملها هادئ، آمنة، وكذلك لطيفة من ناحية البيئة هذا باإلضافة إلى أنها أنظمة ذات كلفة قليلة لالستخدامات في . المحـيطة، و تعمـل علـى إدامة نفسها بنفسها .عيدة المناطق الب هـذا البحث يقدم دراسة لمكونات األنظمة الشمسية وتكاملها، صناعتها و تطبيقاتها و كذلك البحوث ذات الصلة ـ و في النهاية هناك . كما يعدد تطبيقات األنظمة الفولطائية الضوئية في عمان . الفولطائـية والضوئية ةباألنظم .لمستخدمة في صناعة الخاليا الشمسيةخالصة للمواد والتكنولوجيا الحالية والمستقبلية ا abstract: photovoltaics is the process of converting solar energy into electrical energy. any photovoltaic system invariably consists of solar cell arrays and electric power conditioners. photovoltaic systems are reliable, quiet, safe and both environmentally benign and self-sustaining. in addition, they are cost-effective for applications in remote areas. this paper presents a review of solar system components and integration, manufacturing, applications, and basic research related to photovoltaics. photovoltaic applications in oman are also presented. finally, the existing and the future trends in technologies and materials used for the fabrication of solar cells are summarized. bourdoucen, jervase, al-badi, gastli, and malik contents 1. introduction 186 2. pv energy conversion 187 3. solar cells material and technologies 193 3.1 amorphous silicon cells 194 3.2 polysilicon thin films 194 3.3 transparent conductors 195 3.4 gallium arsenide and other semiconductor compounds 195 3.5 cadmium telluride 195 3.6 copper indium diselenide (and related alloys) 195 3.7 film silicon and dye-sensitized titanium dioxide cells 196 4. pv systems 196 4.1 solar modules 197 4.2 energy storage 197 4.3 backup systems 198 4.4 power conditioning 198 5. applications 199 6. pv in oman 201 7. future trends 201 8. conclusion 203 9. references 203 1. introduction photovoltaic (pv) solar cells were originally developed for use in space, where repair is extremely expensive, if not impossible. since the pv cells use the energy from sunlight to produce electricity, the fuel is free. because of the low-maintenance, cost-effective pv systems are ideal for supplying power to communication stations on mountain tops, navigational buoys at sea, remote homes and villages, water pumping, and hybrid utility power substations. once installed, pv power systems can operate continuously with little upkeep and minimal operating costs. since they burn no fuel and have no moving parts, pv systems are clean and silent. this is especially important where the main alternatives for obtaining power and light are from diesel generators and kerosene lanterns. as we begin to realize and respect the fragility of our planet’s ecosystem, clean power choices like pv become extremely important. according to different studies, the amount of energy available to generate photovoltaic power is almost 10,000 times greater than the total world energy used today. to harness this huge potential energy source, much research work has been done in this area (moskowitz 1987, san martin 1989, moskowitz et al 1990a, moskowitz et al 1990b, nrel 1996, sayigh 1998). also, the disruption of oil supplies in the early 1970s pushed the industrialized countries to seriously consider the photovoltaic options as a potential source of energy for terrestrial uses. this application focused research attention on improving performance, lowering costs and increasing reliability. these three issues remain important today even though researchers have made extraordinary progress over the years. it is interesting to note that very soon after heinrich hertz realized the first cells using selenium, in the 1870s, this material has been rapidly used for pv cells converting light into electricity at 1% to 2% efficiency. as a result, selenium was quickly adopted in the emerging field of photography for use in lightmeasuring devices. major steps toward commercializing pv were taken in the 1940s and early 1950s, when the czochralski process was developed for producing highly pure crystalline silicon (pierret 1996). note that large single crystals of device-grade silicon used for solar cells are commonly produced using this crystal growth method. in 1954, scientists at bell laboratories depended on the czochralski process to develop the first crystalline silicon photovoltaic cell, which had an efficiency of 4% (chalin et al 1954, 186 photovoltaic cells and systems green et al 1999). the rapid evolution of silicon technology in the 1950’s saw parallel evolution in silicon cell technology such that cells of close to 15% energy conversion efficiency had been demonstrated by the 1960’s. standardization of cell design for space application seems to have inhibited innovation for about a decade, with the next burst of activity occurring in the early 1970’s. this arose from incorporating technological improvements developed in the microelectronics area. this includes photolithography, cell design improvements such as texturing of the cell surfaces, and rear contact passivation using alloyed aluminum layers. by the mid-1970’s, cells of terrestrial efficiency of close to 17% had been demonstrated. 1940 1950 1960 1970 1980 1990 2000 0 10 20 30 e ff ic ie nc y (% ) years figure 1. evolution of laboratory silicon solar cell efficiency it is apparent from figure 1 that improvements in performance have come sometimes in “steps” and sometimes in “surges.” each of these steps usually corresponds to a new technological or design feature, which is steadily exploited over a period generally lasting over a year or so. silicon by itself is used in more than 90% of the commercial solar cells in different pv systems (wiesman et al 1979, matsumura 1986, ore (us) 1989, meyers 1990, kapur and basol 1990, zweibel and mitchell 1990, brown 1991, wagner and carlson 1991, tolley and palmer, 1991, zweibel and chu 1993, luft and von roedern 1994, green et al 1999). figure 2 shows the world pv cell and modules shipments from 1988 to 1995. this review starts with a section on photovoltaic systems in which photovoltaic conversion principles, materials, manufacturing processes and current market place are discussed. description of some typical applications and uses of pv energy are presented in the subsequent section. pv specifications relevant to oman and the future trends for this technology are discussed in the following sections. conclusions drawn from this review are embodied in the last section. 2. pv energy conversion process to understand the many facets of photovoltaic power, one must understand the fundamentals of how the device works. although photovoltaic cells come in a variety of forms, the most common structure is a semiconductor material into which a large-area diode, mostly p-n junction, has been formed. figure 3 is schematic depiction of a rudimentary solar cell that shows its important features. a typical p-n 187 bourdoucen, jervase, al-badi, gastli, and malik junction solar cell consists of a shallow p-n junction formed at the front collection side, a front metallic contact stripe fingers, aback ohmic contact that covers the entire back surface, and an antireflection coating on the front surface. electrical current is taken from the device through a grid contact structure on the front that allows the sunlight to enter the solar cell. a contact on the back that completes the circuit and an antireflection coating that minimizes the amount of sunlight reflecting from the device is placed on top of it. the fabrication of the p-n junction is a key to successful operation of the photovoltaic device as well as other important iii-v and ii-iv compound semiconductor photovoltaic devices. figure 2. world pv cell and modules shipment more advanced high efficiency solar cells are shown in figures 4 and 5. figure 4 for instance, is a schematic representation of what was known as the comsat nonreflecting cell first demonstrated in 1974 (green et al 1999). the cell incorporated a textured surface formed by an isotropically etching of a silicon wafer to expose slowly etching, intersecting equivalent planes to form the square based pyramids shown. the junction was formed in the top surface by reasonably shallow phosphorus diffusion (junction depth about 0.25 µm). the rear surface often had aluminum evaporated and alloyed to form a heavily doped region along the rear surface, somewhat inappropriately known as a “back surface field.” metallization was accomplished using photolithographic techniques for the front surface and consisted of a titanium/palladium/silver tri-metal layer with the same trilayer deposited over the entire rear surface. titanium or tantalum oxides were preferred choices for the antireflection coating. these cells demonstrated efficiency under air mass zero (am0)1 radiation of 15.0–15.5%, which would correspond to efficiencies under the present global air mass 1.5 terrestrial standard of 16.7–17.2%. the air mass parameter m, is dependent on the angle of incidence α(o), the pressure p (millibars) and the path length through the atmosphere z(km). it is given by )1013/)(cos/)8.7/exp(( pzm α−= , where the different variables are shown in figure 6. 1 am0 is the power level of the solar spectrum in outer space, which is about 1.4 kw/m2. on the earth at sea level, with the sun at zenith, the power level is nearly 1kw/m2, which is the am1 spectrum. 188 photovoltaic cells and systems 1cm 2cm top metallic contacts(a) ∅ hf (b) 0.5mm 0.25µm antireflection coating layer ohmic back layer si n-layer si p-layer solar cell rl load i d rl rs (c) figure 3. schematic representation of a silicon solar cell and a simplified electric equivalent circuit for a solar cell n-type textured surface p-type p+ rear contact figure 4. cosmat non-reflecting cell (black cell) 189 bourdoucen, jervase, al-badi, gastli, and malik p+ busbar n+ n+ n+ oxide sunlight n+ busbar figure 5. rear point contact solar cell. perpendicular to concerned location atmospheric layers z: altitude, (km) α: zenithal angle of the sun, (deg.) sun α z x surface of the earth figure 6. representation of solar illumination on the earth’s surface 190 photovoltaic cells and systems when the solar cell is exposed to an optical radiation (solar in this case), the photons with energy higher than the energy gap eg of the material used in the fabrication of the p-n junction cell will be absorbed and contribute to the generation of electron-hole pairs. the remaining absorbed energy is lost in the form of heat. with reference to figure 3, if i is the current through an illuminated solar cell, vd the voltage across it and il is the current through a given connected load rl, then lds iktqvii −−= ]1)/[exp( (1) in equation (1), i stands for the photogenerated current, is is the reverse saturation current, q is the fundamental electronic charge of 1.602 x 10-19 coulombs, k is the boltzmann constant, and t is the absolute temperature. the saturation current density js is expressed in terms of the physical parameters of the material as )/exp( 11 kte d n d n nqn a i j g p p dn n a vc s s −         +         == ττ (2) where, a is the cell area, na and nd are the doping densities of acceptors and donors respectively, dn and dp, τn and τp are respectively the diffusion constants and the carriers lifetimes for electrons and holes. from equation (2), js depends exponentially on the temperature of the junction and hence, the total current through the cell is highly dependent on t. js is larger for materials with smaller bandgaps than for those with larger bandgaps eg. on the other hand, the rectifier action of a cell, i.e. its restriction of current flow to only one direction, is key to the operation of the photovoltaic device. current characteristics in the dark open-circuit voltage voltage maximum power + li gh tge ne ra te d cu rr en t short-circuit current (i) (ii) im vm characteristics under illumination (iii) (iv) figure 7. current voltage characteristics of a solar cell with and without illumination 191 bourdoucen, jervase, al-badi, gastli, and malik from the operating point of view, when light is allowed to impinge on a p-n junction device, the equilibrium conditions of the device are disturbed. minority carriers (electrons in the p material and holes in the n material) are created in sufficient quantities to lower the potential energy barrier at the junction, allowing current to flow and establish a voltage at the external terminals. the availability of current and voltage produces usable power. a current-voltage diagram, like the one in figure 7, shows the important operational parameters of the cell, among which is the short-circuit current isc, the open-circuit voltage voc, and the maximum power operating point (im and vm, respectively). the open circuit voltage voc defined at i=0 is given by       ≅ s l oc i i q kt v ln (3) the i-v curve gives the output power of the solar cell, which can be expressed as viktqvvivip ls −−== )1)/(exp( (4) the maximum power output occurs when the derivative of the power vanishes. if rs is neglected, the expressions for im and vm are given as [ )/(1ln )/(1 )/(1 ln ktqv q kt v ktqv ii q kt v moc m sl m +−≈      + + = ] (5) and       −≈    = ktqv iktqv kt qv ii m lm m sm / 1 1)/exp( (6) the maximum output power pm is thus,       −      +−≈= q kt kt qv q kt vivip moclmmm 1ln (7) the conversion efficiency of a solar cell, which is the ratio of the maximum power that a solar cell can deliver (im , vm) to the total incident power pin, can be expressed as (sze, 1981). in m ocl in mm p q kt kt qv q kt vi p vi      −      +− == 1ln η (8) this can be expressed in terms of the fill factor ff as in ocl p viff .. =η (9) 192 photovoltaic cells and systems where the fill factor ff is defined as scocmm ivivff /= (10) the fill factor ranges from approximately 0.70 to 0.85. for a typical single-crystal silicon solar cell, we find that voc ≈ 0.588 v, jsc ≈35 ma/cm 2 and ff ≈ 0.8. thus a 100cm2 cell is capable of producing about 1.6 watts (sze 1985). in the previous analysis the series resistance rs has been neglected, however, this resistance due to the front ohmic resistance is a major factor in degrading the efficiency of the solar cell. the output current i and the output power p can be rewritten as functions of rs, as follows: l s s ikt irvq ii −− − ×= }1] )( {exp[ (11) }]1ln[{ s s l ir i ii q kt ip ++ + ×= (12) it is important to note that a series resistance of only 4 to 5 ohms can reduce the available power of a given cell by more than 70%. this series resistance depends on both the architecture and the fabrication technology used. in particular, it depends on the junction depth, the impurity concentration of both acceptors and donors, and the type of front and back ohmic contacts. for a typical solar cell having an area of 2cm2, 0.25µm junction depth, substrate of 0.5mm with 1ω-cm resistivity, the series resistance is of the order of 0.7ω. 3. solar cells materials and technologies there are a number of new major developments including gainp tandem solar cells for space, the mergence of thin films of crystalline silicon, and thermophotovoltaics. a thorough presentation of the recent advances and future trends of these technologies are presented in (barnett et al 1999, wohlgemuth et al 1991, izu 1992, stanbery 1991, brown 1991). crystalline silicon solar cells are exhibiting improved and reduced cost, and continue to dominate world pv production, constituting in 1997 about 85% of the pv-market share. the crystalline market is subdivided into single or mono-crystalline and multicrystalline silicon cells and a small market share for ribbons. the major problem of relatively thick bulk crystalline silicon solar cells is availability of good quality silicon feedstock material. initiatives for starting a dedicated low-cost solar grade multicrystalline silicon production are still in pilot line phase (maurits 1998). however, thin-film solar cells of amorphous silicon-hydrogen, copper indium diselenide (cuinse), and cadmium telluride (cdte) have begun to be sold for power applications (barnett et al 1999). a very crucial step in the fabrication of crystalline silicon solar cells is ingot formation for which two competing technologies are available. these are the czochralski pulling of monocrystalline ingots and the casting process of multicrystalline silicon ingots. monocrystalline silicon has several important advantages for solar cell processing (nijs et al 1969, schmidt et al 1997, kaneko et al 1997, watanabe et al 1990). the apparent advantages of multicrystalline silicon, in general, over monocrystalline are a lower wafer cost and perfect long-term cell stability. solar cell efficiencies approaching those of monocrystalline cells are obtained in a more complicated process, comprising deposition of antireflection coating and hydrogen bulk passivation. in terms of dimensions, the standard substrate size 10.16x12.16 cm2 (4x4 in2) has been adopted for long time; however, there is recently a clear tendency toward larger sizes. most of the solar cell manufacturers base their production lines on 12.7x12.7 cm2 (5x5 in2) wafers. efficient cells processed on 15.24x15.24 cm2 (6x6 in2) and even 19.81x19.81 cm2 (7.8x7.8 in2) substrates have been reported (kaneko et al 1997). the driving force toward these larger cell sizes results from the fact that cell manufacturing and 193 bourdoucen, jervase, al-badi, gastli, and malik 194 3.1 3.2 module assembly costs show relatively small area dependence, and therefore, the cost to power ratio decreases with increasing cell size. on the other hand, the cell size is limited by its series resistance; as indicated previously, and also by limitations of module sizes due to handling, wind loads, module transportation, and system assembly (nijs et al 1969, villers and smekens 1995). due to the success of developments in multi-wire sawing, a wafer thickness of 150 µm or smaller is becoming feasible, corresponding to final cell thickness of 120 µm or lower (villers and smekens 1995). this allows an important saving of silicon material. at the same time, thinner cells correspond better to the optimum thickness if efficient light trapping and surface passivation are possible (munzer et al 1998). in spite of significant progress in slicing techniques, there is still around 200 µm of high-quality silicon per wafer lost in kerfs waste. limitations to further decrease the final wafer thickness are set by a decrease in yield due to handling problems and breakage during solar cell and module fabrication. to produce silicon directly in sheet forms, and so to avoid the costs of wafering and kerfs losses, the ribbons technology is widely used. a number of ribbon techniques have been developed and used in solar cell applications with each technique having its own advantages and disadvantages. the dendritic web technology, for instance, is one of the very few techniques that yield ribbons in single crystalline form. however, the edge-defined film-fed growth (efg) ribbon process is a technology that was initially developed in the 1970’s and had been steadily progressing into multiple silicon ribbon growth of large area sheets in the form of tubes (mackintosh et al 1978, taylor et al 1981, kalejs et al 1994, sana et al 1993). laboratory conversion efficiencies of about 14% have been reached with this technology. the string ribbon process, on the other hand, was initially developed as “edge supported ribbon” (cizek et al 1981, janoch et al 1997, wallace et al 1997), and is presently improved and commercialized. when two strings of a high-temperature material are brought up through the silicon melt, a continuous silicon film is drawn from the melt after seeding silicon. the resulting film after solidification is polycrystalline. the silicon sheets from powder technique (ssp) consists of using silicon in a powder form as the starting material. it is poured through a funnel into quartz carrier sheets (eyer et al 1989) which, first travel into a “first melting zone” where surface melting of the powder layer is achieved by a focused lampbank. laboratory scale conversion efficiencies of 13.2% were reported for 4 cm2 cells. cells fabricated with a relatively faster modified technique achieved a laboratory efficiency of 8% on 4 cm2 cells (faller 1997). finally the so-called ribbon growth on substrates (rgs) process is a horizontal ribbon growth technology where a substrate is used for the cooling over the bottom surface of the ribbon. the heat is removed by conduction, perpendicularly to the pulling direction, over the ribbon surface. the crystallization and pulling velocities are therefore decoupled, leading to high production rate (steinbach and hofs 1997, hahn et al 1997a). efficiencies of the order of 11% have been recently reported (hahn et al 1997b). amorphous silicon cells amorphous solids, like common glass, are materials in which the atoms are not arranged in any particular order. they do not form crystalline structures at all, and they contain large numbers of structural and bonding defects. it wasn't until 1974 that researchers began to realize that amorphous silicon could be used in pv devices by properly controlling the conditions under which it was deposited and by carefully modifying its composition. today, amorphous silicon is commonly used for solar-powered consumer devices that have low power requirements. significant advances have been also made in understanding amorphous silicon alloy materials and solar cells that have resulted in the achievement of high cell and module efficiency. the research results have been also translated to production, and several manufacturers have expanded their production capacity, raising the worldwide annual capacity to more than 25 mw (guha and yang 1999). polysilicon thin films polycrystalline thin-film devices require very little semiconductor material and have the added advantage of being easy to manufacture. rather than growing, slicing, and treating a crystalline ingot photovoltaic cells and systems 195 3.3 3.4 3.5 3.6 (required for single-crystal silicon), thin layers of the required materials are sequentially deposited. several different deposition techniques are available, and all of them are potentially cheaper than the ingot-growth techniques required for crystalline silicon (meyers 1990). best of all, these deposition processes can be scaled up easily so that the same technique used to make a 5.08x5.08 cm (2x2 in) laboratory cell can be used to make a 0.61x1.52 m (2x5 ft) module (russell et al 1984). transparent conductors these are alternative materials for grid contacts, which are transparent conducting oxides (tco) such as tin oxide (sno2). their advantage is that they are transparent to incoming light and yet form a good electric contact linking the semiconductor with the external circuit. gallium arsenide and other semiconductor compounds gallium arsenide (gaas) is especially suitable for use in multijunction and high-efficiency solar cells for several reasons. its energy band gap of 1.43 ev makes it ideal for single-junction solar cells. its optical absorption coefficient is high enough to require a cell of only a few microns thick to absorb most of the sunlight radiation. unlike silicon cells, gaas cells are relatively insensitive to heat within the limits of application temperatures. gaas is also characterized by its very high resistance to radiation damage. this, along with its high efficiency, makes gaas very desirable for space applications. the alloys made from gaas using aluminum, phosphorus, antimony, or indium, have characteristics complementary to those of gaas, allowing great flexibility in cell design. the greatest barrier to the widespread use of gaas cells has been the high cost of the single-crystal substrate. they are mainly used in concentrator systems, where the typical concentrator cell is about 0.25 cm2 in area. in this case, the cost is low enough to make gaas cells competitive, assuming that module efficiencies can reach between 25% and 30% and that the cost of the rest of the system can be reduced. cadmium telluride the thin-film technology next closest to commercialization is based on cadmium telluride. its cell efficiencies are high, around 16% in the laboratory, but commercial module efficiencies are likely to be in the 6% to 8% range in the first plants. considering the advantages of photovoltaics in offsetting other sources of energy, the cadmium telluride issue should be put in the same perspective as similar issues. owing to the nature of 'thin film' cdte modules, the use of cadmium in pv is always likely to remain a small fraction (under 10%) of the world's use of cadmium even if cdte modules are one day able to provide a significant fraction, over 10% of the world's electricity (moskowitz et al 1987, zweibel and mitchell 1990, moskowitz, and fthenakis 1990, moskowitz et al 1990a, moskowitz et al 1990b, alsema and van engelenburg 1992, moskowitz and zweibel 1992). cadmium telluride technology suffers from the likelihood that near-term commercialization will encounter classic start-up issues, it has a stability problem (although stability is good in some cases), and it must raise the efficiency of modules toward those attained by the best cells, which will require head-on solution of processing challenges associated with fabricating thin cadmium sulfide (cds) in manufacturing. if these problems can be solved over the next 10 years, cdte technology has a very good chance to achieve the long-term cost, performance and stability goals (stone et al 1984, moskowitz et al 1987, san martin 1989, moskowitz and fthenakis 1990, moskowitz et al 1990a, moskowitz et al 1990b, moskowitz et al 1990c, tolley and palmer 1991, alsema and van engelenburg 1992, moskowitz and zweibel 1992, zweibel and chu 1993). viewed from this standpoint, it could be regarded as the leading thin film. copper indium diselenide (and related alloys) copper indium diselenide (cuinse) cells have reached almost 18% efficiency under standard test conditions. this means that the best cuinse cell is approaching the best efficiency of a polycrystalline silicon cell. bourdoucen, jervase, al-badi, gastli, and malik 196 3.7 film silicon and dye-sensitized titanium dioxide cells several groups have tried to combine the strong performance of crystalline silicon devices with the attractive economic advantages of thin-film manufacturing technology. thicker silicon cells on ceramic or foil substrates have been relatively efficient with cells and modules efficiencies around 15% and 9% respectively. thin cells, on the other hand, have not yet reached such high efficiencies but the future of thin films looks strong (ore (us) 1989, wohlgemuth et al 1991, albright 1991, stanbery 1991, jester 1991, brown 1991, izu 1992). despite serious obstacles, amorphous silicon has established itself as a viable competitor for wafer-based crystalline silicon devices. meanwhile, the next generation of thin films, in particular cuinse and cdte, show stronger technical performance and lower potential cost (wohlgemuth et al 1991, izu 1992). 1976 1978 1980 1992 1984 1986 1988 1990 1992 1994 1996 calendar year 17 15 13 11 9 7 e ff ic ie nc y, ( % ) culnse2 cdte si-film astropower ametek photon energy boeing boeing boeing boeing kodak kodak aroo univ. of so. florida astropower bp solar boeing univ. of so. florida npel eurocis matsushita univ. of maine monceder figure 8. polysilicon thin-film solar cell efficiencies. in short, we can say that the driving force in search for and use of different materials and manufacturing processes to increase efficiency for pv cells is to reduce the overall cost to make it comparable with conventional technologies. for instance, the evolution of si-film, cdte and cuinse2 thin film solar cell efficiencies are given in figure 8 for two decades. as can be seen from the figure, the general trend of the efficiencies for the above materials is increasing over the period, thus demonstrating the decrease in cost. 4. pv systems pv systems can be grouped into the following categories: stand-alone systems with and without battery storage systems with backup power generators systems connected to a local utility systems for utility-scale power production hybrid power systems photovoltaic cells and systems table 1. confirmed terrestrial cell and sub-module efficiencies measured under the global am1.5 spectrum (1000 wm-2) at 25° c (green m. a. et al 1998). cell types efficiency η (%) area a (cm2) open circuit voltage voc (v) short circuit current density jsc (ma/cm 2) fill factor ff (%) silicon cells si (crystalline) 24.4 ± 0.5 4.00 (da) 0.696 42.0 83.6 si (multicrystalline) 19.8 ± 0.5 1.09 (ap) 0.654 38.1 79.5 si (supported film) 16.6 ± 0.5 0.98 (ap) 0.608 33.5 81.5 iii-v compounds gaas (crystalline cell) 25.1 ± 0.8 3.91 (t) 1.022 28.2 87.1 gaas (thin film cell) 23.3 4.00 (ap) 1.011 27.6 83.8 gaas (multicrystalline) 18.2 ± 0.5 4.011 (t) 0.994 23.0 79.7 inp (crystalline cell) 21.9 ± 0.7 4.02 (t) 0.878 29.3 85.4 polycrystalline thin film cdte (cell) 16.0 ± 0.2 1.0 (ap) 0.840 26.1 73.1 cdte (submodule) 10.6 ± 0.3 63.8(ap) 6.565 2.26 71.4 amorphous silicon a-si (cell) 12.7 ± 0.4 1.0 (da) 0.887 19.4 74.1 a-si (submodule) 12.0 ± 0.4 100 (ap) 12.5 1.3 73.5 (ap) = aperture area; (t) = total area; (da) = designated illumination area. table 1 provides recent summary of the status of solar cells’ efficiency, area, open circuit voltage, fill factor and current density for different materials used in current pv technologies (green m. a. et al. 1998). the main components of a typical pv system. these include solar modules, energy storage, power conditioning, and back up sub-systems. a discussion of some of the features of these components follows. 197 4.1 4.2 solar modules the pv cell is the basic unit of a pv system. a typical single cell produces a power of 1 to 2 watts, hardly enough for most applications. however, the power can be increased by connecting many cells together to form a larger unit called module. modules, in turn, can be connected to form arrays for more output electric power. energy storage in many pv systems, energy will not be used as it is produced but may be required at night or on cloudy days. if tapping into the utility grid is not an option, battery storage system will be necessary in most of the cases. storing electrical energy makes pv systems a reliable source of electric power. pv systems with battery storage are being used all over the world to power lights, sensors, recording equipment, switches, appliances, telephones, televisions, and even power tools. the drawbacks to batteries are that they decrease the efficiency of the pv system, because only about 80% of the energy channeled into them can be reclaimed. they also add to the expense of the overall bourdoucen, jervase, al-badi, gastli, and malik system and must be replaced every five to ten years. they take up considerable floor space, pose some safety concerns, and require periodic maintenance. 35% 30% 25% 20% 15% 10% 5% 0% 0 100 200 300 400 500 capital cost ($/m2) r at e or r et ur n figure 9. layout of a wind-photovoltaic system. like pv cells, batteries are direct-current devices and are directly compatible only with dc loads. however, batteries can also serve as a power conditioner for these loads by regulating power; this allows the pv array to operate closer to its optimum power output. most batteries must also be protected from overcharge and excessive discharge, which can cause electrolyte loss and can even damage or ruin the battery plates. 4.3 4.4 backup systems when power must always be available or when larger amounts of electricity than a pv system alone can supply are occasionally needed, an electric generator can work effectively with a pv system to supply the load. during the daytime, the pv modules quietly supply daytime energy needs and charge batteries. if the batteries run low, the engine generator runs at full power—its most costand fuel-efficient mode of operation—until they are charged. and, in some systems, the generator makes up the difference when electrical demand exceeds the combined output of the pv modules and the batteries. systems using several types of electrical generation combine the advantages of each. engine generators can provide an excellent backup for the pv modules. using pv and generators together can also reduce the initial cost of the system. however, having an engine generator as backup means fewer pv modules and batteries are necessary to supply power whenever it is needed. including generator makes designing pv systems more complex, but they are still easy to operate. in fact, modern electronic controllers allow such systems to operate automatically. controllers can be set to automatically switch generators, to supply ac or dc loads, or do some of each. in addition to engine generators, electricity from wind generators, small hydro plants, and any other source of electrical energy can be added to make a larger hybrid power system. power conditioning pv systems usually require power conditioners to process the generated electric power to make it suitable for meeting the specific demands of the load. it is extremely important to match these devices to the load. thus, power conditioners may have to perform a number of tasks. these include limiting current and 198 photovoltaic cells and systems 199 voltage to maximize power output, converting dc power to ac power, matching the converted ac electricity to a utility electrical network, and safeguarding the utility network system and its personnel from possible harm during repairs. the major concern in the design of dc-to-ac converters (inverters) is to minimize the losses of the converter energy conversion process. for instance, in 1996, solar plants with about 400 kw photovoltaic peak power were installed in austria, producing approximately 360 mwh (edelmoser and himmelstoss, 1999). an improvement of the total electrical efficiency of the inverters by only 1% would lead to an additional yield of 3.6mwh. the potential available in the whole world is therefore much higher. recently, new inverter concepts with increased efficiency were published (oliveira and maksimovic 1996, mantovanelli and barbi 1995, solero et al 1996, and midya et al 1996). furthermore, cost reduction in new inverter concepts requires full digital control equipment using microcontrollers or signal processors (makino et al 1995). especially in grid-connected applications, a low-distortion inverter is required due to international standardization. this requires careful selection of the inverter structure, of the switching devices, and the control concept (lai and smedley 1995). edelmoser and himmelstoss (1999) proposed a high efficiency dc-to-ac inverter for generating an ac mains (stand-alone system) or for grid connection. the new inverter leads to improved efficiency and is therefore well suited for solar and aerospace applications. due to the minimum number of components, especially the active components, reliability is improved. their proposed structure uses only off-line switches to generate the ac voltage. due to safety reasons, the input voltage (e.g., the voltage of solar cells or batteries) is limited. therefore, high currents on the primary side are necessary to obtain the required output power. the overall efficiency of the inverter depends to a high degree on the number of switching elements in the current path. thus, the structure has only one active switch in the main path. this can be obtained by applying a diode with controlled turn-off capability (like a thyristor or other derivatives). high duty cycles of the main switch at high currents lead to low duty cycles of the switchable diode. for that reason, a series connection of two active switches in the main path has to be avoided. the improvement of the efficiency is due to the new topology and not due to over dimensioning of the semiconductors. hence, an additional potential of efficiency improvement is still available. 5. applications many people are familiar with pv-powered calculators and watches, the most common small-scale applications of pv cells. however, there are numerous large-scale, cost-effective pv applications, including: water pumping for small-scale remote irrigation, stock watering, residential uses, remote villages, and marine sump pumps. lighting for residential needs, billboards, security, highway signs, streets and parking lots, pathways, recreational vehicles, remote villages and schools, and marine navigational buoys. communications by remote relay stations, emergency radios, orbiting satellites, and cellular telephones. refrigeration for medical and recreational uses. corrosion protection for pipelines and docks, petroleum and water wells, and underground tanks. utility grids that produce utility or commercial-scale electricity. household appliances such as ventilation fans, swamp coolers, televisions, blenders, stereos, and other appliances. bourdoucen, jervase, al-badi, gastli, and malik large-scale photovoltaic power plants, consisting of many pv arrays installed together, can prove useful to utilities. pv plants can be built much more quickly than conventional power plants because the arrays themselves are easy to install and connect together electrically. finally, pv power plants consume no fuel and produce no air or water pollution while they silently generate electricity. for instance, a 2-mw photovoltaic power plant has been built in california to supply 660 houses (depp (us) 1998). however, pv generation plants have several limitations that have slowed their use by utilities. under current utility accounting, pv-generated electricity still costs considerably more than electricity generated by conventional plants, and regulatory agencies require most utilities to supply electricity for the lowest cash cost. furthermore, photovoltaic systems produce power only during daylight hours and their output varies with the weather. to get a general idea on the economic feasibility of a pv system, the curve in figure 9 can be used to estimate the rate of return on a capital outlay of a pv system. in order to combine a number of electricity production and storage elements to meet the energy demand of a given facility or community, hybrid systems have been used. in addition to pv, engine generators, wind generators, small hydro plants, and any other source of electrical energy can be added as needed to meet energy demands and fit the local geographical and temporal characteristics. there are thousands of these systems in use worldwide. they range from a few tens of watts to tens of kilowatts. the smaller systems are mostly on remote residences where homeowners add a few pv modules to their existing generator set to reduce the noise and inconvenience of having a generator running all the time. convenience may be more important than cost for these homeowner-maintained systems that are installed near their homes. single-phase or three-phase pwm inverter load wind generator doubleinput single-output dc-to-dc converter photovoltaic figure 10. rate of return as a function of capital cost for pv systems. a 10 kw stand-alone wind/photovoltaic generating system prototype has been constructed (caricchi et al 1993, chalmers et al 1996, crescimbini et al 1996). figure 10 shows the layout of a system, which uses a wind turbine-driven permanent-magnet machine and a photovoltaic array as power generating units. the principal features of the system are, the double-input, single-output, d.c. to d.c. converter that combines the power generated by the wind and photovoltaic array and the d.c. to d.c. converter for charging a storage battery and supplying a.c. via a voltage source inverter. the decreasing cost of pv systems and the increasing number of manufacturers and dealers for pv equipment have contributed to widespread use of the pv technology. in pv’s early days, do-it-yourself had to search for companies that manufactured pv modules and often had to adapt or reconfigure components from other non-pv systems. today, dealers offer ready-to-use systems and state-of-the-art equipment designed specially for pv systems. many dealers have computer programs to design systems and specify appropriate components. as pv market expands, manufacturers and dealers are gaining greater experience with pv application and so making pv systems cheaper and easier to acquire. 200 photovoltaic cells and systems 201 6. pv in oman oman national electricity grid does not cover all regions because of its topography, which makes its implementation quite expensive. so, for some of the isolated regions, pv systems are undoubtedly economically viable. furthermore, pv electricity generation tends to be more cost effective in the “sun belt” region from about 40o north to 40o south, within which oman lies (al-ismaily et al, 1998). oman, with an average solar radiation of around 5.67kwh/m2/day (al-malki et al 1998), is very well suited for solar powered photovoltaic applications. this is due to the fact that sunshine availability and global insolation level have a major effect on the photovoltaic array size, as the current generated by the pv modules is directly proportional to the insolation level and sunshine duration. the more the sunshine duration, the lesser will be the pv array size. this is in fact the prevailing situation in oman where the average sunshine duration is 9.49 hours with much less seasonal variation (dorvlo and ampratwum, 1998, al-hinai and alalawi 1998). hence, this value of average sunshine availability may be taken for typical pv system sizing. however, if the sizing is critical, the regional sunshine or radiation availability data in oman may be used (dorvlo and ampratwum 1998, al-alawi and al-hinai 1998, al-hinai and al-alawi 1998). typical daily summary statistics data measured by oman department of meteorology for four weather stations at different locations (seeb, sohar and buraimi) are shown in table 2. table 2. daily summary statistics data of sunshine duration and mean solar radiation for some selected cities of oman. station mean of sunshine hours mean of solar radiation (mj/m2/day) seeb 9.59 19.48 sohar 9.10 ___ buraimi 10.24 19.30 salallah 7.88 16.22 various successful implementations of the pv technology are already in use in oman such as desalination plant in heelat ar rakah camp (al-malki et al 1998). in 1991, oman solar systems (oss) company was set up to supply the local market. the company has undertaken projects ranging from street and traffic lighting to microwave and television transmitter stations (al-ismaily et al, 1998). 7. future trends the significant advances made during recent years are due to ongoing research in industry, universities and research laboratories. the current research work is focused on developing new materials, improving the efficiency and raising the power to cost ratio. thin films for instance, are a promising path to low-cost photovoltaic systems. for thin-film products to reach their low-cost potential, additional research is needed to develop materials and processes yielding devices with higher efficiencies, more uniform performance over the entire surface area of modules, and lower production costs (schropp and rath 1999, yamamoto 1999). university researchers, and scientists are collaborating worldwide to develop prototype products largely based on amorphous silicon, cadmium telluride, copper indium diselenide, and thin-layer crystalline silicon technologies. although amorphous silicon materials have lower efficiencies than does crystalline silicon, they have the potential to be less expensive to manufacture. today, more than 15% of cells and modules produced worldwide are amorphous silicon. most products using amorphous silicon are low-power consumer items like solar watches and bourdoucen, jervase, al-badi, gastli, and malik 202 calculators. higher-power applications will demand amorphous silicon products with higher stabilized efficiencies so that more energy can be extracted from a given module area. to increase the efficiency of amorphous silicon, many researchers in the us are working under the thin film pv partnership program (doe (us), 1999). these research teams are addressing a dozen issues surrounding the design and fabrication of multijunction amorphous silicon alloy cells. in addition, researchers are developing ways to process amorphous silicon material to improve its stabilized efficiency. the most promising approach to date is hot-wire deposition. the extremely hot (2000°c) temperatures of the wire cause the feed gases to dissociate, and the active radicals are deposited at rates up to 10 times higher than those of the glowdischarge method used in industry today. future work will investigate the viability of this alternative approach to replace existing processes in industry. by 2002, working with industry on device design and material deposition techniques, the us department of energy (doe) aims to improve the stabilized efficiency of laboratory amorphous silicon devices. moreover, it expects that research results will be quickly transferred to the production line because there is a mature manufacturing base for amorphous silicon (doe (us), 1999). cadmium telluride is extensively explored because the techniques used to manufacture devices from this material including different evaporation techniques can be very low-cost. the technology also promises high efficiencies; small cells have reached nearly 16% at the laboratory but the commercial module efficiencies are still around 6%. improving module efficiencies requires a fundamental understanding of the properties of cadmium telluride which is yet limited. for example, as reported in (doe (us) 1999), some modules have shown stable performance for 6 years outdoors, while others have shown significant decreases in efficiency in few days. therefore, the mechanisms of this uncertain physical stability have to be characterized thoroughly. in addition, researchers often achieve high cell efficiencies using non-standard industry manufacturing techniques. also, the high efficiencies of small-area cells are due in part to the deposition of very thin layers of cadmium sulfide. no one has learned how to deposit such a thin layer in a module-scale device, and a thicker layer reduces efficiency by about 25%. to meet challenges like these, many efforts should be gathered to realize the potential of cadmium telluride cells for high-efficiency power modules. copper indium diselenide is also one of the potential pv materials, which gives high efficiency. it was in 1996 when researchers pushed the efficiency for devices based on this material to 17.7%, the highest efficiency reported for any thin-film cell. it is the only stable thin-film material with several years of outdoor exposure that shows no deterioration in performance. but it is not yet commercial because significant further research is needed to understand the manufacturing processes. fabricating high-quality films based on this material requires making a copper-rich layer and a copper-poor surface layer to form a junction with other alloys. researchers studying this technology still have difficulty avoiding defects that prevent the formation of uniform layers. however, to achieve quality results, it is critical to use proper temperatures and correct timings during the different steps of the process. the use of crystalline silicon is still prevalent. although its absorption of sunlight is much less effectively (10-100 times) than other thin films, thin-layer crystalline silicon cells can be more efficient than those made of other thin-film materials. the issue is to construct properly the solar cell for maximum light trapping. the main advantage of using silicon is that its characteristics are well known and its technology as well. so far, researchers have succeeded to deposit relatively thick layers of crystalline silicon on low-cost substrates. however, future work will undoubtedly focus on thinning the material to less than 50 micrometers, while developing optimal substrate, light-trapping, and interconnection schemes. on the other hand, crystalline silicon is likely to continue to dominate pv markets at least through the year 2000. with its relatively high efficiency and stability, competitive cost, and proven track record, it plays a dominant role in the whole pv market. today's crystalline silicon devices are more efficient than ever before since laboratory cells made from single-crystal silicon have measured efficiencies as high as 24%. research on manufacturing improvements has pushed the efficiencies of multicrystalline devices to nearly 18% for laboratory cells and over 15% for prototype modules. photovoltaic cells and systems 203 gallium arsenide has also been used for many years for pv conversion with a measured singlejunction efficiency greater than 25% at one sun (no concentration) and about 28% under sunlight concentration (macmillan et al 1988, maroto et al 1995). multijunction cells based on gallium arsenide and related iii-v alloys have even achieved conversion efficiencies greater than 30%. the efficiency is expected to exceed 32% after using these devices in concentrator systems (tobin et al 1990, olsen et al 1991). due to its elevated cost, this technology is mostly restricted to military and space applications. further cost reductions in manufacturing technology are necessary to expand pv markets. manufacturing costs depend on many factors of production, and a lot of research is being conducted to optimize several of them. one of these factors is the rate at which pv materials or devices are passed through the processes of material deposition, preparation, encapsulation, and connection to electrical components. the main objective is that the high-efficiency materials developed in the laboratory must ultimately be manufactured in quantity on the production line. manufacturers and systems developers conduct research to integrate pv system components for optimal performance, reliability, and lifetime. they simplify systems and select the most durable components and they work to improve balance of systems components such as inverters, batteries, and control systems. in addition to pv cells and modules, all pv systems must have other components that help to convert, deliver, and store electricity. today, balance-of-system components represent about half the cost of a pv system, but they are responsible for 99% of system repair problems. another major problem is that about 15% of the electricity generated by pv modules is lost during conversion and transmission through balanceof-system components. these include charge controllers, batteries, control systems, mounting hardware, tracking systems, wiring, and power-conditioning hardware such as inverters. failures of inverters are the primary cause of photovoltaic system problems. a number of designs for mechanical or electronic balanceof-system components have been optimized for pv systems. thus, their cost and performance should improve with improving designs. the cost of an entire pv system is also expected to decrease with rapid advances in power electronics performance. most of this fast-growing market for pv is targeted towards potential users who lack a reliable source of electricity. this potential market constitutes about 40% of the world's population whose needs often require small amounts of power for applications such as indoor lighting or pumping water. to take advantage of this huge market, efforts must be made to find ways to finance the purchase of pv systems and establish reliable installation and maintenance services. 8. conclusion the current and future trends in photovoltaic cells and systems have been reviewed in this paper.these included marketing and applications, system components and integration, manufacturing, and basic research. the cost of photovoltaic electricity is continuously falling down as the technology matures and many companies are now investing in research and pilot projects. this research has proven the value of photovoltaics in several applications. however, more work needs to be done to reduce the cost, and thus makes photovoltaic electricity competitive with other energy technologies. the cost of manufacturing equipment, in particular, must be reduced in order to keep up with the current trend of growth. as for the application of pv technology in oman, it is well suited to the environment since it receives a high degree of solar radiation throughout the year. various successful implementations for the pv technology are already in use. these include street lighting, powering of microwave repeaters and many others. 9. references al-alawi, s. m. s. and al-hinai, h. a., 1998, an ann based approach for predicting global radiation 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2018, 23(2), 95-110 doi: http://dx.doi.org/10.24200/squjs.vol23iss2pp95-110 sultan qaboos university 95 an overview survey of recent routing protocols for underwater wireless sensor networks faiza a. al-salti*, nasser m. al-zeidi, khaled day, bassel arafeh and abderezak touzene department of computer science, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *email: s81851@student.squ.edu.om abstract: with the recent advances in underwater sensor devices and technologies, underwater wireless sensor networks (uwsns) enable a variety of applications such as underwater exploration and monitoring, disaster prevention, and military surveillance and reconnaissance. however, these kinds of networks faces a number of challenges induced by the nature of the underwater environment and its influence on the physical media. therefore, new routing protocols are proposed specifically for such networks to mitigate these challenges. this paper surveys some of the recent routing protocols for uwsns. specifically, the idea of each protocol is presented as well as its advantages and disadvantages. furthermore, the presented protocols are classified into different categories. the paper is concluded with some open research issues. keywords: underwater wireless sensor networks (uwsns); acoustic channels; routing protocols; location-based routing; location-free routing. مسح شامل لبروتوكوالت التوجيه الحديثة لشبكات االستشعار الالسلكية تحت الماء داي، باسل عرفة و عبد الرازق توزين ، خالدناصر الزيدي ،السلطي هفايز ( مجموعة uwsnsمع التطورات الحديثة في أجهزة وتقنيات أجهزة االستشعار تحت الماء، تتيح شبكات االستشعار الالسلكية تحت الماء ) :صلخمال النوع من ، والمراقبة واالستطالع العسكريين. ومع ذلك، يواجه هذا متنوعة من التطبيقات مثل االستكشاف والمراقبة تحت الماء، والوقاية من الكوارث ت توجيه جديدة الشبكات عددًا من التحديات الناجمة عن طبيعة البيئة تحت الماء وتأثيرها على الوسائط المادية لالتصاالت. لذلك يتم اقتراح بروتوكوال . بشكل خاص قدمت uwsns خصيًصا لهذه الشبكات للتخفيف من هذه التحديات. تستعرض هذه الورقة بعض بروتوكوالت التوجيه الحديثة لشبكات ال شة بعض القضايا هذه الورقة فكرة كل بروتوكول ومزاياه وعيوبه. وتم تصنيف البروتوكوالت التي تم تلخيصها في فئات مختلفة. أخيراً اختتمت الورقة بمناق البحثية المفتوحة. الصوتية؛ بروتوكوالت التوجيه؛ التوجيه المعتمد على الموقع (؛ قنوات االتصال uwsnsشبكات االستشعار الالسلكية تحت الماء ) :مفتاحيةالكلمات ال الجغرافي؛ والتوجيه الغير معتمد على الموقع الجغرافي. 1. introduction ne oceans, seas, rivers and lakes cover nearly three quarters of the earth’s surface. they provide a prime source for nourishment, trade and commerce. in addition, oceans help in producing the world’s oxygen and absorbing carbon dioxide. with the increasing role of the oceans and seas in human life, there is a strong demand to explore and investigate the unexplored regions to make use of their treasures. however, due to the harsh and high-pressure underwater environment, unmanned technologies have become vital to deep-sea exploration and coastal monitoring. underwater wireless sensor networks (uwsns) are considered to be one of the promising candidates for investigating the oceans. this kind of networks consists of a collection of sensors deployed in an environment to perform a collaborative task. a sensor node is a micro-electronic device having the capability to detect, measure and transmit a variety of parameters such as temperature, salinity and pressure [1]. uwsns are envisioned to enable various applications including scientific, military and commercial applications. o faiza a. al-salti et al 96 for example, they can be used for coral reef monitoring [2], military surveillance and reconnaissance [3], oil drilling and exploration [4], and underwater pipeline monitoring [5][6]. the characteristics of terrestrial wireless sensor networks (wsns) and uwsns are different. thus, the protocols, standards and technologies used in terrestrial wsns cannot be applied directly for uwsns. the main difference is that acoustic media is the most acceptable physical layer technology in uwsns [7]. other counterparts such as electromagnetic and optical signals cannot be exploited efficiently in the underwater environment. this is because electromagnetic waves suffer from high attenuation and absorption, and hence, propagate for short range [8]. optical signals, on the other hand, suffer from scattering, absorption, and very short-range propagation [8] [7]. nevertheless the acoustic signal is the one suitable medium that works satisfactorily in the underwater environment; it is considered one of the toughest communication media in use today [9]. generally, underwater wireless sensor networks (uwsns) experience a number of challenges induced by the nature of the environment and the transmission media. particularly, acoustic speed in water is five orders of magnitude slower than the speed of radio signals in the terrestrial environment [10]. in addition, underwater channels are affected by multi-path and fading. underwater sensor nodes are equipped with batteries, which are difficult to replace or recharge. the available bandwidth is limited and inversely proportional to the transmission distance [11] [12]. in addition, the threedimensional (3d) deployment and the dynamic environment due to the passive movements of sensors with water currents cause extra challenges when designing protocols in the physical, mac, and network layers [11] [13]. due to these challenges, the routing protocols used for terrestrial wsns are not suitable for uwsns, and hence, new routing protocols have been proposed specifically for relaying data in uwsns. these routing protocols aim to address these characteristics and challenges, and mitigate their effects on the efficiency of the networks. there are a number of works found in the literature surveying and classifying these routing protocols from different perspectives. in [8], the authors provided a comprehensive description of several routing protocols. in addition, they categorized the described protocols based on their network architecture, data forwarding and protocol operation. the survey in [14] detailed a number of routing protocols; however, it did not provide any classification of the summarized protocols. the surveys in [15], [16] and [17] each concentrate on one category of routing protocols. in [15], geographic based routing schemes are reviewed and categorized based on forwarding strategy, location service and design goal. the work reported in [16] surveyed pressure based routing protocols. in [17], greedy routing protocols were summarized and classified into location-based and location-free protocols. the aim of this paper is to provide an up-to-date survey of routing protocols. basically, the idea of each protocol is clearly presented. the advantages and disadvantages of each protocol are discussed. furthermore, the paper classifies the presented protocols based on location information dependency and the number of transmitted copies of each data packet in each hop. the rest of this paper is organized as follows. section 2 describes some of the architectures that can be used for uwsns. recent routing protocols are surveyed and classified in section 3. section 4 outlines the main performance metrics commonly used in the evaluation of routing protocols for uwsns. finally, section 5 concludes the paper and proposes some open research issues. 2. architectures for uwsns a well-designed architecture and the deployment method of sensor nodes can effectively help in maximizing network capacity, minimizing energy consumption and improving network reliability. according to [18], the architectures for uwsns can be classified based on the coverage of the network and the mobility of the sensor nodes. for the network coverage, uwsns can be designed to cover a two-dimensional (2d) or three-dimensional (3d) space within the underwater environment. regarding their mobility, sensor networks can be stationary, mobile or hybrid. in a stationary uwsn, nodes are attached to surface buoys and/or anchored to the ocean floor. in a mobile uwsn, on the other hand, sensor nodes have the capability to move, for example, with water currents or as autonomous vehicles. examples of such nodes are autonomous underwater vehicles (auvs), unmanned underwater vehicles (uuvs), drifters and gliders. a hybrid network, from its name, incorporates both stationary and mobile nodes. here we review the architectures proposed for uwsns according to their coverage. in addition, the pros and cons of each type are outlined. 2.1. 2d architectures sensor nodes in this category are kept static by means of anchors or surface buoys. they are deployed on the ocean floor (as depicted in figure 1) and are responsible for monitoring 2d environments. in [19], the authors proposed a static 2d architecture for ocean bottom monitoring. in this architecture, sensor nodes are anchored at the bottom of the ocean, and they communicate directly with the underwater sinks on the surface. monitoring of underwater plates for tectonic studies is an example of an application that can use this architecture [19]. although the direct link is the simplest compared to multi-hop paths, it requires high transmission power because the distances between sensors and sinks can be long. moreover, packets from different sensors may interfere with each other and thus reduce the throughput. the longer the distance that the signal should travel, the higher the energy consumption [20] and the more interference with other signals. generally, a 2d uwsn architecture is suitable only for applications where the depth of the monitored space is less than the transmission range of sensor nodes, so that nodes an overview survey of recent routing protocols 97 can communicate directly with sink nodes. therefore, it is not applicable for environments with greater depths than nodes’ transmission ranges, such as deep oceans [13] [21]. in addition, it is not suitable for applications that require 3d monitoring or tracking. 2.2. 3d architectures the 3d uwsn architectures have attracted the attention of the research community [22]. in this kind of architecture, sensor nodes are distributed at different depths to perform a collaborative monitoring task over the 3d monitored region as illustrated in figure 2. it may consist of static, mobile or hybrid sensor nodes depending on the application requirements. while 2d architectures are used for ocean bottom or surface monitoring, 3d architectures are mainly used for ocean column monitoring. in [23], the authors proposed a 3d architecture where sensor nodes are assumed to be able to adjust their depths. the sink node has the capability to move, and exchange data and control packets with the sensors via single-hop communications. the sink node is also assumed to know the locations of the sensor nodes. in order to minimize the distance that the sink node should travel, the authors adopted a partitioning scheme in which the network is divided into clusters. then, the sink node traverses each cluster and exchanges packets with sensors belonging to each cluster. the gathered data is then transmitted to the base station at the surface. the problem with this architecture is that the sink node is assigned complex tasks, and it is a single point of failure. another concern is that the architecture is not suitable for delay-sensitive applications, as the nodes in each cluster should buffer the packets until the sink arrives to that cluster. akyildiz et al. [19] proposed a static 3d uwsn architecture for ocean column monitoring. in this architecture, sensors float at different depths. they are anchored to the bottom of the ocean by means of wires that link sensors to the anchors. the sensors are also equipped with floating buoys to pull them toward the surface. however, this architecture might not reflect real environments in which nodes may move from one point to another due to the water currents. the authors proposed a 3d mobile architecture consisting of a collection of fixed sensor nodes deployed at different depths and mobile auvs. the auvs can be used to accomplish different tasks (e.g. deploying sensors and forwarding data). another 3d architecture has been presented in [24]. it consists of bottom nodes, underwater nodes, automatic mobile nodes (e.g. auvs and uuvs) and surface sinks. the bottom nodes are anchored to the bottom of the ocean to sense the 2d area. the underwater nodes float at different depths and are equipped with floating buoys to adjust their depths. the bottom nodes, underwater nodes and automatic mobile nodes work together to achieve 3d monitoring. the automatic mobile nodes float at the surface to receive gps signals and then dive and move among underwater nodes following predefined trajectories to help in the localization process or in information gathering. the sensed information is transmitted to the surface via multi-hop paths or via automatic mobile nodes. typical applications of the 3d architecture may be surveillance applications, oceanography and monitoring of ocean phenomena (e.g. water streams and pollution) [19]. the challenges for such architectures are that sensors should regulate their depths such that the network is always connected, so that every sensor can send its data to the surface sink via multi-hop paths. in addition, ensuring the required coverage and energy efficiency is another challenge [21]. the mobility feature of sensor nodes may help in maximizing the coverage with a limited number of nodes since they can be equipped with different types of sensors and have the capability to reach points that might not be reachable by static nodes. however, mobility raises new challenges such as energy consumption, localization and connectivity maintenance [21]. it is worth mentioning that no single architecture is good for all application types. hence, network designers and engineers should select the appropriate architecture based on the requirements of their applications and the nature of the targeted environment. figure 1. a view of a 2d architecture. figure 2. a view of a 3d architecture. faiza a. al-salti et al 98 3. recent routing protocols for uwsns routing protocols for uwsns can be broadly classified into location-based and location-free. location-based routing protocols utilize location information of sensor nodes to relay data packets. since sensor nodes do not employ any addressing system (e.g. ip) [1] and because sensors are randomly deployed in the environment, location information can be used to route data packets. location-free routing protocols, on the other hand, employ other information such as hop count or link quality. the rest of this section summarizes some of these protocols. 3.1. location-based routing protocols: 3.1.1. energy efficient routing protocols energy conservation is one of the most critical tasks in uwsns; thus, careful attention is needed when designing a routing protocol. huang et al. [25] proposed a power efficient routing (per) protocol to reduce the energy consumed by sensor nodes. per consists of two modules. the first module consists of four sub-components; the fuzzifier, the fuzzy rule base, the fuzzy inference engine and the defuzzifier. each forwarder node uses a fuzzy logic technique to select two candidate nodes to relay the packet. it requires three inputs including the distance and the angle between the current forwarder and one of its neighboring nodes, and the remaining energy of the forwarder, and it works as follows. the fuzzifier takes the three inputs of the module and converts them to linguistic values. the distance value is converted to either short, medium or long, while the angle is converted to either small, medium or big. low and high are used to convert the remaining energy value. the fuzzy rule base consists of some linguistic rules and control goals used by the fuzzy inference engine along with the output of the fuzzifier to determine the appropriateness of a node to forward a data packet. the output of the fuzzy inference engine is classified into excellent, good, medium, bad and weak. the defuzzifier converts these linguistic values into non-linguistic values and based on the results, the forwarder node selects the two best candidates and sends the packet to them. the selection of two candidates by each forwarder can cause a massive growth of the forwarding tree. thus, the second module is used to prevent this unnecessary growth of the tree, and it works as follows. the forwarder node does not forward the packet to the second best selected node unless the number of duplicate packets received by the forwarder is less than a predefined threshold (δ). this will prevent unnecessary power consumption of the sensor nodes while forwarding the packets. the performance evaluation shows that per reduces the energy consumption in dense networks. however, the packet delivery ratio of per is highly dependent on the selection of the duplicate-packet’ threshold. choosing a high threshold can improve the delivery ratio but at the cost of increasing power consumption. the le-vbf [26] routing protocol was proposed to enhance the network lifetime. it is an improvement over the vector-based forwarding (vbf) [27]. in vbf, each packet carries the location of the source, sink, and forwarder (i.e. the node from which the packet is received). the idea of the vbf approach is that a virtual routing pipe from the source to the sink is constructed and the radius of the pipe is used as a threshold to determine whether a node is a candidate for forwarding a packet. when a node receives a packet, it checks whether it is located within the routing pipe and if so, it updates the packet’s header by putting its location value in the packet and then forwards the packet. otherwise, it discards the packet. in order to reduce the number of forwarders, when a dense network is used, the authors have introduced a self-adaptation algorithm to determine the density of the network within its region. upon receiving a packet, nodes within the routing pipe compute a desirableness factor to weigh their suitableness to transmit the packet. the desirableness factor is based on the position of the receiver node relative to the source node and the previous forwarder, the transmission range and the radius of the pipe. if the node is eligible to forward the packet, it holds it for a period of time before forwarding it. otherwise, it discards the packet. simulation of vbf shows that the data delivery ratio increases by increasing the density of the network and/or the radius of the routing pipe. however, nodes closer to the routing vector from the source to the destination have a high chance to be frequently selected as eligible candidates for forwarding the packet, which drains their energy and reduces the network lifetime. le-vbf suggests a solution to balance the energy consumption between nodes by including residual energy of the nodes as a factor in relay selection. in addition to the position information, each packet carries the residual energy information of the previous forwarder. when a node receives a packet, it checks whether it is located within the routing pipe and if so, it calculates its suitableness based on its position from the routing vector and its residual energy. it holds the packet for a period of time and if it does not overhear the transmission of that packet after the period elapses, it broadcasts the packet. however, the packet may be delivered with extra delay due to the waiting time at each hop. the authors in [28] proposed an energy efficient fitness based routing (eef) to achieve improved energy efficiency. eef is a depth-based routing in which the forwarder candidates are selected based on the depth information. residual energy and the distances to the sink node and to the previous forwarder are additional factors to determine the best eligible candidate. in eef, each packet carries the position and the fitness value of the sender. when a node f receives a packet from a node (say s), it discards the packet if it is located within a depth less than that of s. otherwise, it calculates its fitness value as given in (1) [28] where ef is its residual energy, depthdiff is the difference between its depth and the depth of the previous hop, dsf is its distance to the previous hop and dfd is its distance to the destination. if the fitness value is less than the fitness included in the packet, it discards the packet. otherwise, it holds the packet for a certain period of time. if the period expires without overhearing the transmission of that packet, it includes its position and fitness value in the packet and broadcasts the packet. the process continues until the packet reaches its destination. an overview survey of recent routing protocols 99 fitnessf = ef ∗ depthdiff ∗ dsf dfd (1) although the evaluation of the protocol shows that it can save energy and improve the network lifetime and endto-end delay, eef has a number of issues. first, in a dense network, a high number of nodes will receive the packet, which consumes extra energy. second, the calculation of the fitness value and the waiting time is done at every hop by each candidate node, which increases the complexity and end-to-end delay when a high traffic network is used. third, in high traffic conditions, nodes need to keep track of a large number of packets that might overflow their buffers. javid et al. [29] proposed two routing protocols called efficient and balanced energy consumption technique (ebet) and enhanced ebet to achieve efficient and balanced energy consumption. the protocols assume that the network is divided into concentric circles called ring sectors and nodes’ energy is divided into levels called energy levels. each of the protocols consists of two phases, namely a route establishment phase and a data transmission phase. during the route establishment phase of ebet, nodes share their location and energy levels. each node builds a set of routes toward the sink node based on the distance information. these routes are used in the data transmission phase to select the optimal relay based on the neighbors’ energy levels. the node with the highest energy level is selected from the set of candidates. although ebet tries to balance energy among nodes by selecting neighboring nodes with high energy levels to forward the packet, the selection might cause transmission loops, and hence waste energy without delivering data packets to their destinations. the problem is solved by the eebet such that depth information is used in building the routes. consequently, backward transmissions are avoided by always selecting those forwarders that are located in depths less than that of the node. it is worth noting that neither ebet nor eebet are suitable for highly dynamic networks due to the frequent need for updating the routes, which might incur extra overhead. the authors in [30] proposed a level-based adaptive geo-routing (lb-agr) protocol for energy efficiency and low delay. in lb-agr, sensor nodes are able to obtain their levels (i.e. the hop distances between the sensor nodes and the sink) and location information via flooding control packets initiated by sink nodes. in addition, each node maintains a neighbor table for each sink, storing some information about neighbors within two hops from the specific node (e.g. node id, its level, location, and remaining energy). data packets are routed based on the gathered information (i.e. level, location, residual energy and node density). when a node has a packet to be transmitted, it searches its neighbor table for nodes whose level is less than its own (i.e., nodes closer to the sink than itself). since more than one candidate might satisfy the condition and in order to avoid redundant transmissions of the same packet which might interfere with each other and waste energy, lb-agr calculates a desirable factor based on the remaining energy and node density (the number of one-hop neighbors whose level is closer to the sink than the node itself) to select the optimal node. the node with the highest desirable factor is selected. however, lb-agr has some issues. first, the dissemination of control packets to update neighbor information can incur extra overhead and drain nodes’ energy, especially in dense and dynamic networks. second, nodes need to store one neighbor table for each sink. this will require extra storage when multiple sinks are used or when a moderately or highly dense network is used. 3.1.2. depth-controlled routing (dcr) in uwsns, geographic routing protocols are preferred over proactive and reactive counterparts, because they do not require the establishing and maintaining of complete routes, which incur overhead and consume resources due to the dynamic nature of the underwater environment. geographic routing makes an optimal selection of the next hop with no concern about the global view of the entire path. this greediness in the relay selection creates void communication regions (i.e. holes) in the network, which occur when a node is the closest node to the sink but cannot communicate directly with it [31]. nodes located in these regions are called void nodes. in the depth-controlled routing (dcr) protocol [32], the authors suggested a solution for the void node problem by adjusting the depth of such nodes. the authors assumed that the network is static, and there is a center for monitoring that has a global vision of the network. they also assumed that the nodes have the ability to move in the vertical direction. the protocol consists of two phases: an initialization phase and a network operation phase. in the initialization phase, the nodes are localized with the help of the auvs, which transmit the location information to the sink nodes. the sink nodes send this information to the monitoring center. then, the topology control algorithm is executed by the monitoring center to determine the void nodes and their new suggested depths so that they can communicate with the sink nodes via multihop communication. consequently, the auvs dive towards their suggested depths to inform the nodes about their new depths. in the network operation phase, when a node has a packet to send, it selects the closest node to the sink from the set of its neighbors and forwards the packet to it. upon receiving the packet, this node forwards the packet in the same manner and the process continues until the packet reaches the destination node. although the protocol can reduce the number of disconnected nodes and improve the delivery of the packets to their destination, the assumption that nodes become static after the depth adjustment phase is not practical due to the dynamic nature of the environment. moreover, nodes that are close to the sink nodes are frequently selected which causes a quick depletion of their energy, hence reducing the network lifetime and creating new void nodes in the network. another issue is that it is not clear how nodes determine their neighboring nodes along with their distances. in addition, the availability of a monitoring center with a global vision of the network might not be practical. faiza a. al-salti et al 100 in [31], the authors presented a distributed topology control (dtc). in dtc, each node determines if it is located in a communication void region, and, if so, determines its new depth and starts moving to it. this operation is achieved by disseminating control packets between nodes. nodes located near the sinks are adjusted first, followed by those nodes at higher depths. as in dcr, the depth adjustment is performed before sending data packets, and, after the depth adjustment phase, the nodes are assumed to be static. 3.1.3. grid-based routing routing protocols that depend on constructing complete paths between nodes to route data packets require the exchanging of control packets in order to establish and maintain the routes. the overhead increases in the underwater environment because of the dynamic topology, which requires continuous maintenance of the routes. moreover, flooding-based routing protocols suffer from the broadcast storm problem. the increase in the number of packets propagated in the network causes a quick drain of its resources (e.g. bandwidth and energy). due to the limited resources in uwsns, there is a significant demand to reduce the amount of transmission and reception of the packets. in [33], a multi-path grid-based geographic routing (mggr) protocol is developed to reduce the number of the required control packets and prevent some nodes from forwarding data packets. mggr assumes that the network is divided into 3d logical. each cell can have up to 26 neighboring cells based on the relationship between the length of the cell side and the transmission range of the nodes. data packets are routed in a cell-by-cell manner via neighboring gateways (i.e. sensor nodes elected as cell heads). since the routes are constructed based on grid cells, there is no need to maintain the routes after construction. the protocol consists of three main components; namely, a gateway election algorithm, a mechanism for updating neighboring gateways’ information, and a packet forwarding dealing with holes. the gateway election algorithm is responsible for electing gateways based on their locations and residual energy level. a node that is closer to the center of the cell it belongs to and which has high residual energy has higher priority to be elected. the second component, as its name implies, is responsible for keeping the nodes updated with gateways in local and neighboring cells. the packet forwarding mechanism is responsible for constructing disjoint paths (i.e. paths with no common intermediate cells) from source cells to destination cells, forwarding packets to the destination and dealing with holes (i.e. cells with no gateways) in the network. the construction of the paths is performed by gateways, and only on demand when there is a need to forward data packets and there are no paths constructed yet. once the paths are constructed, the gateway stores the paths until it moves out of its cell or a new gateway is elected for that cell. when a node has a data packet to be forwarded, it looks for a gateway in the local cell. if there is a gateway, then it forwards the packet to it; otherwise, it discards the packet. when a gateway receives a packet, it selects a path from its table and forwards the packet to the gateway in the next hop. upon receiving that packet, this next gateway checks the path in the packet header and looks for a gateway in the next hop to forward the packet to it. if the gateway encounters a hole in the next-hop, it tries to re-route the packet through another path or send a negative acknowledgment to the previous hop if all routes are broken. then, the gateway in the previous hop will do the same thing as a recovery process from the hole. if the packet reaches the source gateway and all paths are broken, the packet is dropped. since nodes are continuously moving with water current, the holes might become filled with nodes and thus paths can be reused. the reachability of mggr was evaluated analytically under the effect of varying network density (i.e. number of nodes per cell), reliability level (i.e. the number of the available paths to be used), and the transmission range of the nodes. results indicate that the reachability of the protocol increases by increasing these three factors. however, the evaluation assumes a static network, which is not practical in an underwater environment. emggr [34] is an extension of mggr. the extension includes three main points: (i) updating the gateway election algorithm, by allowing nodes to serve as gateways for one or more period, depending on their remaining energy levels; (ii) modifying the construction of the routing paths; and (iii) evaluating the performance of the new protocol in a simulation package by testing its performance under the effects of varying network density, traffic load and node mobility. the performance evaluation demonstrates that emggr is an energy-efficient protocol because data packets are forwarded only by gateways and there is no need to maintain paths. the evaluation also shows a good delivery ratio of the data packets. on the other hand, emggr incurs extra delay in packet delivery due to the constructed long paths. moreover, the performance degrades in a highly dynamic topology and in sparse networks due to the nature of grid-based protocols. jiang et al. [35] proposed two grid-based routing protocols called gfgd and ggfgd. besides the assumption of the grid topology, the authors assumed that the channel link is symmetric and the nodes are stationary. in addition, they incorporated a duty-cycle mechanism (i.e. some nodes are scheduled to sleep for some time) to save energy. as in mggr and its successor, the number of neighboring cells is determined based on the relationship between the transmission range and the length of the cell side. in ggfgd, a cell can have up to 32 neighboring cells; while in gfgd, it can only have up to six neighboring cells. the proposed schemes consist of two phases; selecting the next cube to forward the packet and choosing the best candidate node from the selected cube based on the distance, residual energy and path loss. the gfgd and ggfgd protocols incorporate a duty cycle, which can balance and save energy. in addition, they use path delay, path loss and remaining energy for relay selection; however, it is not clear how nodes acquire this information. moreover, the assumption that the channel link is symmetric is not practical since acoustic channels underwater are known to be asymmetric [36]. in addition, an overview survey of recent routing protocols 101 the protocols assume a 3d stationary deployment of the nodes, which is also not practical due to the passive movement of nodes with water currents. 3.1.4. chain-based routing protocol in [37], 4-chain, 2-chain and single-chain based routing schemes for cylindrical networks (i.e. a network with a cylindrical shape) are proposed to improve network lifetime and throughput. the protocols consist of two main phases; namely, an initialization phase and a protocol operation phase. in the initialization phase, nodes broadcast their location information to be used in forming chains and optimal paths. in the protocol operation phase, the chains are formed based on the location information starting from the farthest node from the sink. a local optimal path between nodes in each chain is constructed. then, each chain is connected to the nearest node in the next chain forming a global optimal path. finally, data packets are transmitted through the global optimal path. simulation results show that the 4-chain routing scheme performs better than its counterparts do. however, the proposed protocol is not suitable for mobile underwater networks because nodes continuously change their positions. hence, location information needs to be rebroadcasted in order to reconstruct the chains and optimal path. this results in extra overhead and drains energy. 3.2. location-free routing protocols 3.2.1. channel aware routing protocols due to the limited resources such as energy and bandwidth and to the other challenges such as the high error rate of acoustic channels, there is a high demand to consider link quality when designing a routing protocol to alleviate these challenges and to avoid retransmission of the packets. basagni et al. [38] proposed a channel aware routing protocol (carp) for uwsns to take the link quality into account when selecting the next data forwarder. nodes in carp need to know their hop count to the sink (i.e. number of hops to reach the sink). this is achieved by broadcasting hello control packets initiated by the sink node in the initialization phase. when a node has one or more data packets to be forwarded, it broadcasts a ping control packet containing its hop count and the list of data packets’ ids to be forwarded, and waits for replies. upon receiving such a packet, a node drops it if its hop count to the sink is greater than the hop count included in the packet. otherwise, it replies with a pong control packet including its hop count, available buffer space, residual energy, link quality to its neighbors, and ids of the packets (from the list included in the corresponding ping packet) already received by the sink and those already received by the node itself. after receiving the pong replies, the node selects the one with the best link quality (the one that exhibited most successful transmissions recently) and lowest hop count. if there is a tie, then residual energy, buffer space and node id are used to select the optimal relay. after selecting the forwarder, the node sends only the packets that are not received by the sink and those that are not received by the selected relay. after receiving the data packets, the node sends an acknowledgement packet indicating the ids of the received packets. the protocol is simple in that nodes need to acquire only their hop counts. moreover, the protocol is studied via simulation and experiments, and the results show that it is an efficient protocol in saving energy, reducing the delay, and achieving a high delivery ratio. however, the simulation and the real experiments were conducted with a very small number of nodes (20 for the simulation and, 6 and 8 for the experiments at sea), which might not reflect the performance in a moderate or large scale-network. in addition, the ping-pong control packets exchanged in each step of relay selection could drain the energy of the nodes and reduce the network lifetime especially in high traffic networks. an enhanced version of carp called e-carp is proposed in [39] to reduce energy consumption and prolong the network’s lifetime. since some applications require that the sensed information is transmitted only if the changes between the previous and recent sensed information is higher than a certain threshold, e-carp employs this requirement. it achieves this by caching the information sensed by each node in the sink. in addition, each node also caches the information it senses to compare it with the recent sensed information and forwards the information only when the difference is higher than the predefined threshold. this can reduce the number of data packets to be forwarded especially if the threshold is large. in addition, e-carp enhances the relay selection mechanism by realizing that when the changes in the position of the nodes are relatively small, the previous candidate forwarder may be the candidate for forwarding the current packet. the performance of the protocol has been evaluated and compared with its predecessor carp. the results show an improvement in energy consumption especially when the data packet size is increased and when the bias threshold is high. however, this protocol it is not suitable if the link quality is changing frequently and if the nodes change their positions frequently. furthermore, it has high storage space (e.g. buffers) requirements. 3.2.2. routing protocols based on physical distance and residual energy bandwidth limitation and path loss are two factors that affect the design of uwsns especially when increasing the distance between the sender and the receiver. therefore, considering the physical distance towards the sink is important when selecting the next candidate to forward data packets. in [40], the authors proposed an energy-efficient routing protocol (erp 2 r) that utilizes physical distance from the sensor nodes to the sink to forward data packets towards the destination. in addition, residual energy of the nodes is taken into account to prolong the network lifetime (e.g. the time when the first node in the network loses its full energy [40]). erp 2 r faiza a. al-salti et al 102 consists of two phases. in the first phase, the sink node broadcasts a hello packet. nodes that receive this packet compute their distances to the sink using the time of arrival (toa). then, they embed their distances to the sink and their residual energy in the packet and rebroadcast it. upon receiving this packet, nodes compute their distance to the forwarders using toa and accumulate it to the distance stored in the packet as its own distance to the sink. then, they rebroadcast the packet after updating the distance and residual energy. the process continues until all nodes have computed their distances to the sink. by the end of this phase, each node knows its own physical distance and residual energy of its own and those of the neighbors. the protocol assumes that the vertical movement of the nodes in underwater is negligible, and consequently, the depth information remains the same. however, the residual energy is continually changing due to the different activities performed by sensor nodes (e.g. transmission and reception of the packets); thus, nodes periodically check their remaining energy. if the difference between the current remaining energy of a node and the previous value is larger than a threshold, it broadcasts a hello packet to inform its neighboring nodes. moreover, the cost establishment phase is performed periodically. the second phase is responsible for selecting the forwarders. during this phase, when a node has a data packet to be transmitted, it selects those nodes closer to the sink than itself and sorts them in decreasing order of their residual energy. the node checks the list and discards the packet if the id of that node is not in the list. otherwise, it holds the packet for a certain amount of time based on its position in the list to avoid redundant transmissions that might interfere with each other. if the holding time of a packet expires without overhearing the transmission of the packet, the node transmits the packet. however, if a node overhears the transmission of a packet it holds, it suppresses the transmission of that packet. this reduces the number of copies of the same packet propagated in the network and helps preserve energy. the idea of taking into account the residual energy of the nodes when forwarding data packets balances the energy among nodes and improves the network lifetime. however, the protocol has some issues. first, if a node is in the forwarding list of a packet, then, it needs to keep monitoring the transmission of that packet, and needs to store the packet until the holding time expires or it overhears the transmission of the packet by another node. in a high traffic network, the buffer might be overflowed and packets might get dropped. second, in highly dense networks, a node needs to keep track of the distance and residual energy of a large number of nodes, thus requiring a huge storage. third, when more than one sink is used, each node needs to keep track of a number of neighboring nodes for each sink and the overhead of the cost establishment phase increases. in addition, as the network density increases, the number of hello packets increases, which increases the energy consumption and reduces the network lifetime. fourth, using toa to compute distances requires the nodes to synchronize their clocks, but the paper does not mention anything regarding clock synchronization. r-erp 2 r [41] is a successor of erp 2 r. r-erp 2 r adds the link quality as a third metric in the relay selection. due to the high error-rate of the acoustic signal, which leads to high packet losses and degrades the performance of the routing protocol, the authors incorporate link quality to improve reliability and throughput. they use the expected transmission count (etx) [42] as an estimate for link quality. etx is based on the forward and reverse packet delivery ratio between two points. the link quality is computed in the cost establishment phase. in the data forwarding phase, the sender selects a node that has better link quality and high residual energy from those closer to the sink than itself, and forwards the packet to it instead of the remaining group of candidates as in the erp 2 r. upon receiving the packet, a node checks the id included in the packet. if the id is its own id, it follows the same process in forwarding the packet to the next hop; otherwise, it discards the packet. this process continues until the packet reaches the destination. although incorporating the link quality in the forwarding process helps in selecting a good candidate for packet relay, link quality in uwsns is unstable due to the nodes’ mobility. this link instability might lead to packet loss; thus, the authors incorporate an acknowledgment strategy into the protocol. upon sending a packet, a source node buffers a copy of the packet and if it overhears the packet transmission by the selected candidate, it removes the packet from its buffer. on the other hand, if it does not overhear the transmission of the packet after a period of time, it retransmits the packet. the packet is dropped after a certain number of retransmission trials. the evaluation of the r-erp 2 r shows an improvement over its predecessor, erp 2 r, in terms of network lifetime, energy consumption, end-to-end delay and delivery ratio. the acoustic link is asymmetric, in that the strength of the link in one direction might be different from the strength in the reverse direction. therefore, the etx measurement of link quality, which depends only on forward and reverse delivery ratio between two nodes, might lead to inaccurate estimation of the link quality. for example, assume we have two links sx and sy where s, x and y are three nodes. assume that the forward delivery in sx is 100 and the reverse delivery is zero, and in the second link the forward delivery in sy is 50 and the reverse delivery is 50. to forward data from the source s, the etx estimator always favors the link sy over sx although the forward delivery is much better in the link sx than in sy. the authors of [36] proposed a distance based reliable and energy efficient (dree) routing protocol, trying to improve r-erp 2 r by using another estimate for the link quality. they used the fuzzy logic based link quality estimator (f-lqe) [43] instead of etx. the f-lqe depends on a number of parameters including the stability and the asymmetry of the link, and the delivery ratio. as etx in r-erp 2 r, the f-lqe in dree is computed in the cost establishment phase and it is updated periodically. another difference between dree and r-erp 2 r is that in dree the physical distance towards the sink is not just for finding the possible candidates, but also for calculating the cost of transmission to each neighbor. in other an overview survey of recent routing protocols 103 words, a node with high link quality, high residual energy and less distance has a high priority to be the next forwarder. dree was evaluated and compared with r-erp 2 r, and the evaluation shows that dree shows a slight to small improvement over r-erp 2 r in terms of network lifetime, energy consumption end-to-end delay and delivery ratio. 3.2.3. depth-based routing protocols as mentioned earlier, providing a location-service in uwsns can be expensive due to the inability to use the gps system, and to the continuous movement of nodes with water currents. therefore, depth-based routing protocols have been proposed as an alternative to the need for location information in data transmission. in such protocols, data packets are forwarded based on depth information, which can be obtained via inexpensive depth sensors built into sensor nodes [44]. perhaps the first depth-based routing scheme for uwsns is the one proposed in [44] and called dbr. in dbr, data packets are forwarded in a greedy manner towards the sink on the surface using only depth information. basically, when a source node has a data packet to be transmitted, it includes its depth information in the packet and then broadcasts it. a node, upon receiving that packet, compares its depth with the number included in the packet. it discards the packet if it is located deeper than the source node. otherwise, it replaces the depth information in the packet with its own and then broadcasts the packet. the process continues until the packet reaches one of the deployed sinks. the main advantage of dbr is its simplicity, in that nodes need to know only their depth information. there is no need for location information and route discovery to deliver data packets to the destinations. however, the main drawbacks of dbr are void problems in sparse networks, and severe collisions between packets due to the broadcast nature of the protocol. in [45], a void aware pressure routing (vapr) protocol is proposed to handle the void problem of the dbr protocol. it consists of two main components, which are enhanced beaconing and opportunistic data forwarding. the aim of the first component is to build a directional route from each node to the closest sink node. its main idea can be summarized as follows. each sink node initiates a beacon packet containing its depth, sequence number of the packet, minimal hop count and its directional forwarding. nodes upon receiving such a beacon packet set their information accordingly and update the information in the packet by replacing the depth with their own depths, incrementing the hop count and setting the direction of the current node towards the sink. then, the packet is retransmitted. the directional forwarding is set to upward if the packet is received from a node with a depth less than that of the receiver, and downward if it is received from a deeper node. the second component uses the directional route constructed in the first component to forward data packets toward the sink nodes. although vapr succeeds in handling the void problem, executing the enhanced beaconing periodically can increase the network overhead. li et al. proposed a dbr-mac [46] to reduce the collisions in the dbr protocol. dbr-mac is a cross-layer approach that integrates a depth-based routing and a handshaking-medium access control (mac). furthermore, it aims to give those nodes with extra load (i.e. key nodes) priority to access the channel. dbr-mac uses the depth, angle and overheard one-hop neighboring nodes’ transmissions for scheduling the transmissions and giving the key nodes higher priority. the node backs-off for a certain period of time if its packet will collide with another transmission. the protocol has been evaluated via simulation. it gives a good performance in terms of throughput, energy consumption and delay at the cost of fairness between nodes. 3.2.4. diagonal and vertical routing protocol (dvrp) forwarding packets horizontally between nodes can sometimes be an extra step that increases the routing path and burdens the nodes’ energy. tariq et al. [47] proposed a diagonal and vertical routing protocol (dvrp) for uwsns to avoid such horizontal communication between nodes. dvrp is an enhanced flooding-based protocol where the flooding zone is controlled by θ = 90 ± 10 k, where 1 ≤ k ≤ 8 ensures that data packets are propagated only vertically or diagonally. when a node has a data packet to be forwarded, it first calculates its flooding zone. for example, if the selected value of k is 1, then the angle of the flooding zone ranges from 80 to 100. then, the node broadcasts a hello packet (hp) including the flooding zone. the nodes within the flooding zone reply with hello reply (hr) packets. if the waiting time expires without any reply, then the node rebroadcasts the hp packet with an increased flooding zone. if, however, one or more nodes are located within the flooding zone, they should calculate and reply with their priority based on their remaining energy and depth. if the node receives more than one hr packet, then the node with highest priority is selected as the next relay which will follow the same process until the packet reaches its destination. the protocol suffers from the problem of flooding control packets at every hop of packet propagation. the source node keeps trying to send hp packets until it receives one or more hr packets. this not only consumes high energy and reduces the network lifetime, but can also induce extra delay on packet transmission. moreover, it is not clear how the nodes calculate their priority to be the next forwarder. figure 3 classifies the above described protocols based on two criteria: location information dependency and the number of transmitted copies of each data packet in each hop. we can conclude from the figure that most of the recent routing schemes developed for uwsns are location-based routing. however, the main problem with this type of protocols is the communication void region as mentioned earlier. some of the protocols suggest recovery processes to handle this problem, such as retransmission or node adjustment as mentioned in some of the above faiza a. al-salti et al 104 summaries. chen et al. [48] have surveyed some of the available techniques for void handling in location based protocols for wsns. it is also worth mentioning that most of the above protocols avoid transmitting more than one copy of each packet to preserve the limited resources available and to avoid interference between packets. table 1 further summarizes these protocols. each of the location-based and location-free categories is further classified into sender-based and receiver-based. these are also subdivided based on the number of sinks assumed by the protocols. figure 3. classifications of routing protocols for uwsns table 1. summary of the routing protocols protocol evaluatio n method static/ dynamic topology requirements & assumptions maintained knowledge remarks s e n d e rb a se d s in g le -s in k p e r [ 2 5 ] simulation dynamic (randomwalk)  location info. is available  distance & angle between two neighboring nodes  remaining energy  counting the number of copies of each received packet  fuzzy logic inference system & decision tree are used to select next forwarders. m g g r [3 3 ] analytical analysis static  the network is viewed as 3d logical grids  own and sink location  gateways’  considered as the first grid-based routing for uwsns an overview survey of recent routing protocols 105  location info. is available  sink is static and located at the topmiddle of the grid  packets are forwarded through disjoint paths via gateways info. in local and neighboring cells  disjoint paths from local cell to sink cell  works better in dense networks e m g g r [ 3 4 ] simulation  static & dynamic (randomwalk)  same as mggr  same as mggr  an enhanced version of mggr  works better in dense networks g f g d & g g f g d [ 3 5 ] simulation  static  location info. is available  static sink  location info., residual energy, layer number for calculating the priority  history of the forwarded data packets e b e t [ 2 9 ] simulation  location information is available  distance to neighboring nodes & sinks  relay nodes  energy levels of neighbors  uses distance & energy levels of neighbors e e b e t [ 2 9 ] simulation  location and depth info. is available  distance to sinks & neighbors & their depths  relay nodes  energy levels of neighbors  solves the transmission loop problem in ebet c a r p [ 3 8 ] simulation & real experiment s static  hop distance to the sink  ids of data packets received by the node & the sink  utilizes link quality in relay selection e -c a r p [ 3 9 ] simulation  topology is relatively steady  applications does not require transmitting packets with low bias from previous sensed information  hop count  enhanced carp  suitable for specific applications & with static topologies faiza a. al-salti et al 106 m u lt ip le -s in k s d c r [ 3 2 ] simulation static  static network architecture  nodes are equipped with depthadjustment mechanism  location info. is available  global vision of the network owned by a monitoring center  non-void neighboring nodes’ location  considered as the first protocol that takes into account the nodes’ vertical movement ability l b -a g r [ 3 0 ] simulation  location info. is available  location, level & residual energy of neighbors r -e r p 2 r [ 4 1 ] simulation  nodes can compute their distances to their neighbors through toa/tdoa  distance, etx & residual energy of its own & its neighbors  enhanced erp 2 r  reliability improved by including link quality in relay selection  data packet is sent to a single node d r e e [ 3 6 ] simulation dynamic  nodes can compute their distances to their neighbors through toa  distance, flqe & residual energy of its own & its neighbors  enhanced rerp 2 r  etx is replaced by f-lqe v a p r [ 4 5 ] simulation dynamic  nodes knows their depth information  node’s depth  hop count to the closest sink  directional forwarding route toward the sink  an enhanced dbr routing  handles void problem of greedy protocols d b r -m a c [ 4 6 ] simulation dynamic  nodes knows their depth information  depth, angle & overheard one-hop neighboring nodes’ transmissions  integrates a handshaking mac with the dbr d v r p [4 7 ] simulation static sinks & mobile sensor nodes  a priority queue of the transmitted packets  an angle-based flooding protocol r e c e iv e rb a se d s in g le -s in k l e -v b f [ 2 6 ] simulation  dynamic  location info. is available  location & energy info. are included in the packet  own & sink location  residual energy  enhanced vbf  network lifetime is improved an overview survey of recent routing protocols 107 m u lt ip le -s in k s e e f [ 2 8 ] simulation  dynamic (random movement)  location info. is available  nodes are able to calculate their fitness value  multi-sink network architecture  own & sink location  an enhanced flooding-based protocol e r p 2 r [ 4 0 ] simulation  nodes can compute their distances to their neighbors through toa  distance & residual energy of its own and its neighbors  physical distance is used instead of hop count in relay selection 4. performance metrics according to the above presented routing protocols, there are four main performance metrics that are generally used to evaluate routing protocols. these are energy consumption, network lifetime, packet delivery ratio (pdr) and end-to-end delay. perhaps energy is one of the most critical resources in underwater sensor networks, for the reasons mentioned earlier. end-to-end delay is an important metric for real time applications, and pdr is important for applications that require full information about the sensed environment. they can be defined as follows: 4.1. energy consumption this is the total energy consumed by all nodes during the simulation. it includes the transmission power, the reception power and the idling power consumed by all nodes [49]: total energy = ∑(tranmission poweri + reception poweri + idling poweri n i=1 ) (2) where n is the total number of nodes used during the simulation. 4.2. packet deliver ratio (pdr) the ratio of the number of distinct data packets that are successfully delivered to the sink nodes to the total number of data packets generated at the source nodes [49]. formally, it can be written as: pdr = ∑(numberof packets received) ∑(number of packets sent) (3) 4.3. end-to-end delay the average time taken by a data packet to arrive to the destination [49]. it is computed from the time a packet is generated until it reaches the destination. only the data packets that have been successfully delivered to destinations are counted. mathematically, it can be calculated as: delay = ∑ (arrival timei − sending timei) pkts i=1 pkts (4) where pkts is the number of packets successfully delivered to the destination. 4.4. network lifetime the time span when the sensors are deployed to the time when the first node in the network loses all its energy [40]. table 2 demonstrates a performance comparison of the above surveyed protocols under the four performance metrics mentioned (energy consumption, network lifetime, pdr and end-to-end delay). table 2. performance comparison of the presented routing protocols protocol energy consumption network lifetime pdr end-toend delay per [25] fair fair fair low mggr [33] low fair fair low emggr [34] low fair fair low gfgd [35] fair fair fair fair ggfgd [35] fair fair fair high faiza a. al-salti et al 108 ebet [29] high low low fair eebet [29] high fair high fair carp [38] high fair high fair e-carp [39] fair fairs fair high dcr [32] fair low high fair lb-agr [30] high fair fair fair r-erp 2 r [41] fair fair fair fair dree [36] fair high fair fair vapr [45] fair fair high low dbr-mac [46] fair low fair high dvrp [47] high low fair high le-vbf [26] fair high low low eef [28] high low fair fair erp2r [40] high fair fair fair 5. conclusion and future research directions at present, routing protocols for underwater sensor networks (uwsns) is a hot topic that has attracted a lot of attention in the research community. this paper has surveyed recent routing protocols for uwsns. the basic idea of each protocol is presented, as well as its advantages and disadvantages. in addition, the protocols presented are classified in different ways. although the presented routing protocols have aimed to alleviate the challenges encountered in communication in the underwater environment, none of them has achieved good performance with respect to all metrics or tackled all aspects in the real environment. for example, the effect of node mobility was absent in most of the evaluation studies. thus, one of the possible future research directions is incorporating the effect of node mobility in the evaluation of the routing protocols. this will help in obtaining more realistic evaluation results. in order to achieve this, a realistic mobility model that can reflect the physical movements of sensors with water currents is needed to simulate the movements of the nodes underwater. moreover, improving routing performance of uwsns by means of a prediction mechanism on the basis of the study of node movement characteristics is another research direction. another possible future research direction is to optimize the routing protocols via cross layer design. in a noncross layer system, communication is restricted between adjacent layers. however, this restriction has been released in cross layer design. in other words, the different layers of the conventional open system interconnection (osi) model share the information and interact with each other regardless of their positions in the model. cross-layer design has been widely used in wsns to eliminate the effects of the limited resources available, such as memory and energy [50]. third, studying the effects of duty-cycle on the performance of uwsns and the methods of applying duty-cycle mechanisms to such networks is another research direction. in a duty-cycle mechanism, some nodes may be scheduled to sleep for some time [51]. this can preserve the energy of the nodes, but might have adverse effects on the delivery ratio and the end-to-end delay. finally, the study of how data aggregation techniques may affect the performance of uwsns should be addressed. data aggregation aims to reduce the amount of data to be transmitted by summarizing or compressing them before transmission [52]. such techniques are used in terrestrial wsns [52-54] for energy efficiency. it would be interesting to investigate whether they have similar benefits on the performance of uwsns. acknowledgment this work is supported by the research council (trc) of the sultanate of oman under the open research grant number rc/sci/comp/15/02. references 1. boulaiche, m. and bouallouche-medjkoune, l. eggr: energy-aware and delivery guarantee geographic routing protocol. wireless networks, 2014, 21(6), 1765–1774. 2. bondarenko, o., kininmonth, s. and kingsford, m. coral reef sensor network deployment for collecting real 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(tosn), 2015, 11(3), 1–25. received 10 september 2017 accepted 11 march 2018 squ journal for science, 2018, 23(1), 68-72 doi: http://dx.doi.org/10.24200/squjs.vol23iss1pp68-72 sultan qaboos university 68 inequalities concerning the growth of polynomials bashir a. zargar* and ahmad w. manzoor department of mathematics, university of kashmir, srinagar-190006, india. *email: bazargar@gmail.com abstract: in this paper we consider a polynomial )( zp having no zeros in the disk 1|<| z . we investigate the dependence of |)(| 1>|=| zpmax rz on |)(| 1|=| zpmax z and obtain a refinement of a famous result due to rivilin ([5], [7]). our results not only generalize some polynomial inequalities but also refine a result by aziz [1]. keywords: growth of polynomials, maximum modulus, inequalities. بتزايد الدوالعالقة المتراجحات منزورحمد أو زارجار حمدأشير ب )( دالةال الورقة هذه في نفترض :صالملخ zp 1 القرص في أصفار لها ليس التي|<| z. 1|)(| المقدار عالقة عن سنبحث>|=| zpmax rz على |)(| 1|=| zpmax z ولكنها بحسف والالد متراجحات لبعض اتعميم ليست نتائجنا إن وريفيلين. أنكيني إلى تعود معروفة نتيجةل تنظيم على والحصول [.1] عزيز نتيجةل نظيمات أيضا .الحد األقصى، المتراجحات نموذج، تزايد الدوال :مفتاحيةالكلمات ال 1. introduction et )( zp be a polynomial of degree n . then ([5] or [6], p. 347), for a fixed 1>r , we have | |= | |=1 (1)| ( ) | | ( ) | . n z r z max p z r max p z equality in (1) holds for the polynomial n zzp =)( . it was shown by rivilin ( [5] , [7] ) that if )( zp is a polynomial of degree n having no zeros on 1|<| z , then (1) can be replaced by | |= | |=1 (2) 1 | ( ) | | ( ) | . 2 n z r z r max p z max p z        inequality (2) is sharp and equality holds for ,=)( n zzp   .||=||  aziz [1] has further improved and generalized inequality (2) by proving the following result: theorem a. if )( zp is a polynomial of degree n which does not vanish in the disk kz |<| where 1k , then | |= | |=1 | |=1 (3) 1 1 | ( ) | | ( ) | | ( ) | . 2 2 n n z r z z r r max p z max p z min p z               the result is best possible and equality holds for the polynomial ,=)( nn kzzp   1.1,|=|=|| k l inequalities concerning the growth of polynomials 69 as a generalization of inequality (2), aziz [1] conjectured the following results. conjectured results. if )( zp is a polynomial of degree n which does not vanish in the disk kz |<| , then 2 | |= | |=1 (4)| ( ) | | ( ) |, < < 1, < 1 1 n n z r zn r k max p z max p z k r k k    and 2 | |= | |=1 (5)| ( ) | | ( ) |, > , > 1. 1 n n z r zn r k max p z max p z r k k k    in an attempt to answer inequality (4), dewan and hans [4] proved the following partial results. theorem b. if )( zp is a polynomial of degree n , which does not vanish in 1,<,|<| kkz then for 1<<<0 rk , ),,(),(   pm k kr rpm nn nn    provided |)(| zp and |)(| zq attain the maximum at the same point on 1|=| z , where 1 ( ) = ( ) n q z z p z and .|)(|=),(),,(|=)(| |=||=| zpmaxpmrpmzpmax zrz  the result is best possible and equality holds for nn kzzp =)( . theorem c. if )( zp is a polynomial of degree n , which does not vanish in 1,<,|<| kkz then for 1<<<0 rk (6) 1 ( , ) ( ,1) ( , ) 1 1 n n n n n r k r m p r m p m p k k k                provided |)(| zp and |)(| zq attain the maximum at the same point on 1|=| z , where 1 ( ) = ( ) n q z z p z and .|)(|=),( |=| zpminkpm kz the result is best possible and equality in (6) holds for nn kzzp =)( . in this paper we shall first present the following interesting refinement of theorem a. theorem 1. let ,......=)( 01 1 1 azazazazp n n n n    be a polynomial of degree n which does not vanish in 1,|<| kkz . then for 1,>r    | |= | |=1 | |=1 (7) 1 | ( ) | 1 | ( ) | | ( ) | 1 1 n n z r z z max p z r max p z r min p z           where 0 0 (8) | | (| | ) = | | (| | ) n n a r a m a r a m      | |=1 and = | ( ) | . z m min p z the result is sharp and equality in (7) holds for 1.|=|=||, 2 =)(   n z zp  remark 1.1. here we have replaced k by  simply not to confuse it with the region for which )( zp does not vanish. now b.a. zargar and a.w. manzoor 70 1< |||| ||)|(| = 0 0 maar amar n n    it is easy to verify the above inquality for 1< if 1.> || || 0 ma a n  to show it holds, let |)(|= 1|=| zpminm z then |)(| zpm  for 1,|=| z so that |)(|<|| zpzm n  where  is any real or complex number with 1.|<|  since )( zp does not vanish in 1|<| z the polynomial 0 .....)(=)(=)( azmamzzpzf n n n   does not vanish in 1.|<| z therefore, 1> 0 ma a n  or 1> || || 0 ma a n  , for every  with 1.|<|  choosing argument of  such that mama nn ||||=||   we get 1.|<|,||||>|| 0  maa n  letting 1||  it follows that .|||| 0 maa n  now it is easy to verify that for 1< , so 1 1 < ( 1) < 1 2 1 2 n n r r         and 11 < 2 1 2 = 2 1         nnn rrr which is true. this shows theorem 1 is an improvement of theorem a. as an application of theorem 1, we next establish the following result which, in a way, is similar to inequality (6). theorem 2. if j j n j zazp  0= =)( is a polynomial of degree n which does not vanish in 1|| z , then for 1<0 r , we have | |= | |= | |=1 (9) ( 1) 1 (1 ) | ( ) | | ( ) | | ( ) | 1 1 n n z r z r zn n r r max p z min p z max p z r r           0 0 and | | (| | ) = . | | (| | ) n n a r a m a r a m      the result is best possible and equality in (9) holds for the polynomial   n zzp =)( , where 1.|=|=||  lemmas for the proof of theorem 1, we need the following lemmas. the first lemma is due to dubinin [3, theorem 5]. lemma 1. if ,......=)( 01 1 1 azazazazp n n n n    is a polynomial of degree n which does not vanish in 1|<| z , then for every 1r 0 0 (10) | | | | | ( ) |= | ( ) |,| |= 1 | | | | n n a r a p rz q rz z r a a   where inequalities concerning the growth of polynomials 71  zpzzq n 1/=)( . equality is attained for the polynomial )( zp whose zeros lie on the unit circle 1.|=| z our next lemma is due to aziz and mohammad [2]. lemma 2. if )( zp is a polynomial of degree n , then for all 1r  and 0 < 2  |)(|1)(|)(||)(| 1|=| zpmaxrreqrep z nii   where 1 ( ) = ( ) n q z z p z . 2. proofs of theorems proof of theorem 1. let |)(|= 1|=| zpminm z . then |)(| zpm  for 1|=| z so that |)(|<|| zpzm n  for 1|=| z , where  is any real or complex number with 1|<| . since the polynomial ,......=)( 01 1 1 azazazazp n n n n    does not vanish in 1|<| z , an application of rouches theorem shows that the polynomial n mzzp )( does not vanish in 1|<| z , so that the polynomial n mzzpzf )(=)( 1 1 1 0 = ( ) .... , n n n n a m z a z a z a        does not vanish in 1|<| z for every  , 1.|<|  let mzqm z pz z fzzg nn   )(=) 1 (=) 1 (=)( and 1 ( ) = ( ). n q z z p z using lemma 1, it follows that 0 0 1.for | | | | | ( ) | | ( ) |, | | | | n n z a r a m f z g z r a a m         this implies .|)(| |||| |||| |)(| 0 0 mzq maar mara mzzp n nn         we now show that for 1|<| and 1,>r 0 0 0 0 (11) | | | | | | (| | ) < | | | | | | (| | ) n n n n a r a m a r a m r a a m r a a m           inequality (11) holds if )|)(|()|(|||)|(||||| 00 22 0 mamarmaamaarra nnnn   ),|(|||)|(||||||||| 00 22 0 mamarmaamaarra nnnn   which after a simple calculation, yields )}.|(|)|{(||||}|)|{(||| 00 2 mamaamamaar nnnn   this implies 1,r which is true. hence (11) is established. taking in particular i rez = , where 1>r and  2<0  , we get (12)| ( ) | | ( ) | i n in i p re mr e q re m         for every  with 1|<| . choosing the argument of  in (12) such that ,|||)(|=|)(| niinni mrrepemrrep    we get .|||)(||||)(| mreqmrrep ini    b.a. zargar and a.w. manzoor 72 this gives | ( ) | | | ( ) | ( ) |, 0 < 2 . i n i p re m r q re           (13) letting 1||  in (13), we get | ( ) | ( ) | ( ) |, 0 < 2 . i n i p re r m q re          adding |)(|   i rep on both sides it follows that |},)(||)({|)(|)(|1)(   iini reqrepmrrep  for all , 0 < 2   . this gives, with the help of lemma 2, that | |=1 (14)( 1) | ( ) | ( ) ( 1) | ( ) | i n n z p re r m r max p z         for all , 0 < 2   . from (14), it follows that | |=1 1 | ( ) | ( 1) | ( ) | ( ) 1 1 i n n z p re r max p z r m            for all , 0 < 2   , which is equivalent to the desired result. □ proof of theorem 2. all the zeros of )( zp lie in 1|| z ; therefore for 1,<0 r the polynomial )(rzp has all the zeros in 1> 1 || r z  . applying theorem 1 to the polynomial )(rzp , we obtain | |=1 | |=1 1 | ( ) | ( 1) | ( ) | ( 1) . 1 1 n n z z max p rz r max p rz r m          equivalently, .|)(|)( 1 1 |)(|1)( 1 |)(| |=||=|1|=| zpminrzpmaxrrzpmax rz n rz n z         taking r r 1 = , then for 1<0 r , we obtain |,)(||)(| )(1 1 1 |)(| 1)( 1 1|=||=||=| zpmaxzpmin r r zpmax r r zrzn n rzn n          which proves theorem 2. □ 3. conclusion we generalize some polynomial inequalities and refine a previous result on the dependence of |)(| 1>|=| zpmax rz on |)(| 1|=| zpmax z , where )( zp is a polynomial having no zeros in the disk 1|<| z . references 1. aziz, a. growth of polynomials whose zeros are within or outside a circle. bulletin of the australian mathematical society, 1987, 35, 247-256. 2. aziz, a. and mohammad, q.g. simple proof of a theorem of erdos and lax. proceedings of the american mathematical society, 1980, 80, 119-122. 3. dubinin, v.n. applications of schwarz lemma to inequalities for entire functions with constraints on zeros, journal of mathematical sciences, 2007, 143(3), 3069-3075. 4. dewan, k.k. and hans, s. growth of polynomials whose zeros are outside a circle, annales universitates mariae curie-sklodowska lublin-polonia, lxii, 2008, 61-65. 5. rahman, q.i. and schmeisser, g. analytic theory of polynomials, oxford university press, new york, 2002. 6. riesz, m. über einen satz des herrn serge bernstein, acta mathematica, 2007, 40(3), 30693075. 7. rivilin, t.j. on the maximum modulus of polynomials, american mathematical monthly, 1960, 67, 251-253. received 22 january 2017 accepted 26 september 2017 microsoft word chem990413.doc science and technology, 5 (2000) 11-23 © 2000 sultan qaboos university 11 homochiral acyl isocyanates as diagnostic nmr probes for the enantiomeric purity of chiral alcohols gregory h. p. roosa and anthony r. donovanb adepartment of chemistry, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman, b chemistry department, division of science, murdoch university, south street, murdoch, australia 6150. ايزوسينات األسيل كمركز كيرالي لتشخيص درجة نقاء الكحوالت المتماكبة ضوئيا بواسطة الرنين المغناطيسي جريجوري روس و أنثوني دونوفان وتمت الدراسة باستخدام . لقد تم تطوير واختبار مر كب اسيل وايزوسينات الكبريت في تفاعالته مع الكحوالت الكيرالية :خالصـة مغناطيسي النووي بتمييز اإلزاحة الكيميائية التي تسمح المركبات اإليزوسينات النشيطة بإستخدامها لتشخيص نقاوة جهـاز الرنين ال .المركبات المتماكبة ضوئيا abstract: the first reported acyl and sulfonylisocyanates were developed and tested in reactions with chiral alcohols to afford diastereomeric carbamates. nmr analysis of these investigates the chemical shift discrimination that would allow these activated isocyanates to be used as diagnostic probes of enantiomeric purity. keywords: n.m.r; enantiomeric excess; isocyanates; camphor derivatives. he past two decades have witnessed enormous strides in the art of asymmetric synthesis (gawley and aubé, 1996). the level of sophistication today allows for the construction of a vast array of complex chiral molecular structures, many of which possess useful biological properties. in such synthetic endeavors, there exists a continuing need to determine, in a facile manner, the stereochemical integrity of the stereogenic centres within the molecular architecture. historical dependence on the measurement of optical rotation requires that the absolute rotation of the product be known. failing this, confirmation may involve multi-step conversion to some alternative structure whose rotation is known. the relationship between optical purity and the rotation is not necessarily linear and the compounds must be homogeneous and free from optically active impurities. in spite of these disadvantages, optical rotations remain a popular method of determining optical purity due to the relatively low cost of the equipment involved and convenience of operation (lyle and lyle, 1983; parker and taylor, 1992). whilst chiral chromatographic approaches, such as gas chromatography (gc) and high performance liquid chromatography (hplc), have more recently gained some momentum (gawley and aubé, 1996), nuclear magnetic resonance (nmr) based methodologies have now become the mainstream choice because of convenience and general applicability (yamaguchi, 1983; parker, 1991; gawley and aubé, 1996). whilst nmr spectroscopy cannot differentiate between enantiomers in an achiral medium since their resonances are isochronous (chemical shift equivalence), diastereomers may be distinguished since certain of their resonances may be anisochronous (chemical shift non-equivalence) (figure 1). especially since the availability of high-field nmr instruments, it has been possible to reliably resolve resonances that are separated by only a few hertz (hz). thus, to determine the enantiomeric purity of a sample, nmr requires roos and donovan 12 that the enantiomers first be transformed into diastereomers through the application of some external homochiral auxiliary reagent. three types of such reagents are currently in service, chiral lanthanide shift reagents (csr), chiral solvating agents (csa) and chiral derivatising agents (cda) (parker, 1991). csrand csa-types generally form in situ diastereomeric complexes with substrate enantiomers without formal bonding occurring, whilst cda’s require the formation of discrete diastereomers with formal bonds. the successful development of cda’s in recent years has made them the method of choice, with the best known being the widely used mosher reagents (r)and (s)-mtpa (αmethoxy-α-trifluoromethylphenylacetic acids) 1 (dale et al, 1968, 1969, 1973). figure 1. representation of diastereomer formation by reaction of an external homochiral auxiliary reagent cx with a mixture of enantiomers. acylisocyanate strategy in earlier work related to the rapid determination of diastereoselection in aldol-type reactions, we had reported the general utility of trichloroacetyl isocyanate (tai) as a derivatising agent (figure 2) (roos and watson, 1991; roos et al, 1992, 1994). the special attractions of tai included: (a) since it was devoid of protons, it could be used in excess; (b) as an acylisocyanate, it was highly reactive toward even hindered alcohols and amines; (c) based on the relative shift of the diastereomeric carbamate nh chemical shifts, stereo-substructure assignments were possible. figure 2. the reaction of alcohol diastereomers r*oh with trichloroacetyl isocyanate to give carbamates. f3c ph ome nco 2(r)1 f3c ph cooh ome (s)-1 f3c ph ome cooh a b dc a bd c a b dc cx a bd c cx cx enantiomers isochronous nmr resonances diastereomers anisochronous nmr resonances r* oh + cl3c nco o r* o o n h o ccl3 homochiral acylisocyanates as diagnostic nmr 13 in order to adapt this approach to enantiomeric systems, the creation of a suitable homochiral acyl isocyanate was required. at that stage, no homochiral acylisocyanates at all had been reported in the literature. the closest recorded candidate was the isocyanate 2, which was related to the mosher system (schneider et al, 1988). the use of 2 as a cda was however limited by its low reactivity with hindered alcohols, a problem that we knew did not exist with the more reactive acylisocyanate system. after an extensive literature survey, the naturally occurring (+)-camphor molecule 3 was chosen to provide the skeleton for a suitable acylisocyanate. this choice was based on several factors: (a) the stereogenic centres present are fixed, thus reducing any likelihood of loss of chirality during preparative interconversions; (b) the 1h nmr signals of the camphor moiety would not interfere with the proposed carbamate nh shift region (δ 8-10), and other scheme 1. retrosynthetic analysis of acyl isocyanate 7 back to (+)-camphor 3. resonances (eg. 2xch3) might provide additional useful diagnostic information; (c) (+)camphor is relatively inexpensive and the product and intermediates were likely to be crystalline solids; (d) (+)-camphor has played a major role in natural product chemistry, and as such there were numerous documented interconversions (money, 1985). with these factors in mind, we were able to target the simplest acylisocyanate as compound 7. the synthetic lineage of 7 was readily envisaged to be as shown in scheme 1. scheme 2. synthetic routes to camphor-derived acyl isocyanates. 7 3 1 2 3 4 5 6 7 89 10 oo ocn oo h2n oo ho o 4o oso2cl o x x oso2x ph x 3 5 x = co2h 6 x = conh 2 7 x = conco 10 x = conh 2 11 x = conco 12 x = nh2 13 x = nco 8 x = conh 2 9 x = conco a,b c h-k d b,d e ee e f,g a. ac2o, h2so4 b. socl2 c. k2co3, kmno 4 d. aqueous nh 3 e. (cocl)2 f. phmgbr g. ptsa, toluene/heat h. nh2oh, naoh i. nano2, hcl j. kcn, hoac k. chcl3/heat roos and donovan 14 materials and methods because of the pure synthetic significance of these first reported homochiral acyl isocyanates, we have recently communicated the fundamental routes and formal characterisations of compound 7 and some related derivatives 9, 11, 13 (donovan and roos, 1996). the salient features of these preparations are summarised in scheme 2. the preparation and characterisations details of other new compounds are described under the experimental section. acyl isocyanates were then allowed to react with racemic and/or scalemic alcohols to prepare the corresponding diastereomeric carbamates as outlined in figure 3. the 1h nmr spectra were then recorded and analysed primarily for carbamate nh resonance discrimination. all spectra were recorded using either a bruker am-300 or advance dpx-300 spectrometer (1h, 300 mhz; 13c, 75.5 mhz) or a bruker amx-500 spectrometer (1h, 500.13 mhz; 13c, 125.76 mhz). spectra were run in deuterochloroform (cdcl3) with tetramethylsilane (tms, δ 0.00) as internal standard at 30°c unless otherwise stated. figure 3. the formation of diastereomeric carbamates from racemic alcohols and homochiral acyl isocyanates. results and discussions activated isocyanate application and analysis: as per our original strategy, acyl isocyanate 7 was reacted with alcohols 14-16. in the case of the diastereomeric carbamates derived from 2-butanol 14 (donovan and roos, 1996), the 1h nmr spectrum showed that the two nh signals were coincident at δ 9.77 ppm. evidence of the diastereomers was exhibited elsewhere in the spectrum with both the methyl triplet (δ 0.92 and 0.93 ppm) and the methyl doublet (δ 1.27 and 1.28 ppm) of the butyloxy adduct showing duplication. a similar unfortunate result was found with the l-phenylethanol 15 (donovan and roos, 1996). the nh signals were coincident at δ 9.86, but again there was evidence of diastereomer formation in other parts of the spectrum. ironically in this spectrum it was the gem-dimethyl of the camphor moiety (c8 δ 0.99 and 1.04 ppm and c9 δ 1.28 and 1.29 ppm) which exhibited doubling. finally, reaction of 4-benzyloxy-2-(l-hydroxyethyl)-1-methoxybenzene 16 gave a pair of carbamates in which the two nh signals were not coincident and appeared as two distinct singlets at δ 8.94 and 8.95 ppm. however, unfortunately the resolution of these signals was not sufficient for ready determination of optical purity by integration. r* o nco rr/s oh r* o n h o rr r* o n h o rs diastereomeric carbamates racemic alcohol homochiral acylisocyanate oh oh ohome obn14 15 16 homochiral acylisocyanates as diagnostic nmr 15 in any event, for the acyl isocyanate 7 to be a useful cda, it would need to be generally effective. the increased steric bulk of alcohol 16 may be the cause of the two distinct nh peaks as opposed to the earlier examples of alcohols 14 and 15 where the peaks were coincident. it was also conceivable that in this type of system that there was strong hydrogen-bonding between the carbamidic nh and the carbonyl group of the camphor skeleton. this would result in the formation of a very reasonable 6-membered ring 17 (figure 4). with the nh locked into a set conformation, the effect of the diastereomeric centres could be minimised and the chemical shifts of the nh signals very possibly equalised. figure 4. intramolecular h-bonding in camphor-derived carbamate diastereomers. in order to eliminate the above possibility of hydrogen-bonding, it was decided to redesign the acyl isocyanate in a way that effectively removed the potentially problematic carbonyl group. the first option (scheme 3) involved the ketalisation of the amide 6 to give 18. subsequent treatment with oxalyl chloride gave the acyl isocyanate 19 that exhibited the characteristic isocyanate peak at 2237 cm-1. however, numerous repeat treatments of this with racemic 2-butanol 14 failed to yield any detectable carbamate products. scheme 3. synthetic route to acyl isocyanate 19. the second strategy to obviate hydrogen-bonding involved the complete removal of the carbonyl oxygen via a chemoselective reduction/elimination protocol (scheme 4). unfortunately, whilst the reduction of amide 6 proceeded quantitatively to afford the alcohol 20, all efforts to effect the elimination of water to give alkene 21 proved fruitless. instead, the only product of note was the previously reported symmetrical tricyclic amide 22 (connolly and hill, 1991), which formed irrespective of whether baseor acid-catalysed conditions were employed. oo n h o rr/so 17 6 o oh2noc o oocnoc 18 19 a b a. 1,2-ethanediol/ptsa/heat b. (cocl)2 roos and donovan 16 one solution to the carbonyl dilemma was eventually provided by the synthesis of acyl isocyanate 9 in which the presence of an added phenyl group assisted with the final dehydration step. analysis of the carbamates formed by reaction of 9 with alcohols 14 and 15 was undertaken. the diastereomeric carbamates from alcohol 14 were recovered and fully characterised (donovan and roos, 1996). the 1h nmr spectrum of these compounds showed only a single nh peak. this peak, however, appeared at δ 6.86 ppm compared with δ 9.77 ppm for the corresponding diastereomers with acyl isocyanate 7. this observation of dramatic upfield chemical shift somewhat reinforces the proposal that hydrogen-bonding was occurring in the earlier system. the absence of this intramolecular hydrogen-bonding did not, however, result in two distinct nh peaks as hoped. once again, doubling was evident in other areas of the spectrum. scheme 4. reductive elimination approach to unsaturated acyl isocyanate 21. the reaction between isocyanate 9 and 1-phenylethanol 15 did not proceed to any measurable extent, possibly due to steric hindrance between the two phenyl groups of the alcohol and the acyl isocyanate. the lack of differentiation between the two nh protons, coupled with the absence of reaction between 9 and the benzylic alcohol, led to the termination of this pursuit. an alternative attractive solution to the carbonyl problem was presented by acyl isocyanate 11, available via a camphor-fenchone skeletal rearrangement (passerini, 1925; kocienski and kirkup, 1975). reactions of 11 with both alcohols 14 (donovan and roos, 1996) and 15 were carried out and the diastereomeric mixtures analysed. once again both cases gave carbamate nh signals which were coincident (δ 7.50 and 7.53 respectively). table 1: low temperature nmr studies of carbamate 23. mhz 300 500 shift δ1 δ2 ∆δ δ1 δ2 ∆δ 303 ok 9.770 0 9.764 9.754 0.010 273 ok 9.883 9.868 0.015 9.848 9.331 0.017 253 ok 9.959 9.938 0.021 9.931 9.909 0.022 233 ok 10.036 10.009 0.027 a similar outcome was achieved with the sulfonyl isocyanate 13, for which it was reasoned that the replacement of carbonyl by sulfonyl would not retard reactivity. as anticipated, reaction with 2-butanol 14 proceeded well, but unfortunately produced coincident nh resonances at δ 8.37. again it is worthy of note that both activated isocyanates 11 and 13 afforded derivatives which exhibited diastereomer differentiation elsewhere in their nmr spectra. 22 6 20 21 oh h2noc h2noc nabh4 h2noc homochiral acylisocyanates as diagnostic nmr 17 table 2: low temperature nmr studies of carbamate 24. mhz 300 500 shift δ1 δ2 ∆δ δ1 δ2 ∆δ 303 ok 7.459 0 7.483 0 273 ok 7.520 0 7.555 7.548 0.007 253 ok 7.568 7.561 0.007 7.609 7.602 0.007 233 ok 7.605 7.598 0.007 7.649 7.643 0.006 to this point, the 1h nmr spectra of all carbamates had been recorded at 300mhz at 30 oc and generally, with the single exception, there was no differentiation between the nh signals of the diastereomers present. it was decided to examine the nmr spectra of two of the carbamates, 23 and 24, at lower temperatures to determine if the desired resolution could be achieved under these conditions. from the results of the low temperature analyses (tables 1 and 2), it can be seen that by lowering the temperature at which the spectra of these two compounds are recorded, resolution of the low field nh signal is observed. the spectra recorded at 500 mhz exhibit this resolution at higher temperatures for both of the compounds, however, as the temperature is lowered further, the 300 mhz and 500 mhz instruments gave comparable results. compound 23, in spite of the likely presence of the hydrogen bonding between the nh proton and the carbonyl oxygen of the camphor ring system, exhibits the greater differential between the two signals. it was also necessary to verify that the resolution of the nh signals observed at low temperature was due to the different chemical shifts of the diastereomeric nh protons and not due to some conformational factor. for instance, rotation about either of the carbon nitrogen bonds present in the carbamate system may be prevented at low temperature, thus giving the appearance of two distinct singlets. a further experiment was carried out to clarify this situation. this involved the low temperature study of carbamate 25, which was derived from the acyl isocyanate 7 and the achiral 2-propanol. the data presented in table 3 showed no resolution of the nh signal when the nmr spectra are recorded at low temperature, indicating that the effect observed in tables 1 and 2 is likely to be the result of diastereomer differentiation rather than due to rotational effects. table 3: low temperature nmr studies of carbamate 25. mhz 300 shift δ1 ∆δ 300 ok 9.73 0 273 ok 9.84 0 253 ok 9.93 0 alternative strategies: it had always been possible that the distance (2 bonds) between the carbamate nh and the nearest cda-derived stereogenic centre might be a factor in determining the degree of diastereomeric resonance discrimination. reduction of this distance to the 1-bond minimum was clearly impossible to achieve with acylor sulfonyl isocyanates – since the acyl or sulfonyl function acted as a natural spacer. two alternative strategies could readily be envisaged to overcome this. o nh o oo 23 o nh o oph 24 25 ooo nh o roos and donovan 18 the first of these involved the use of an unactivated isocyanate such as 26. as mentioned earlier, the related system 2 had displayed a poor reactivity profile. however, in order to exclude the possibility that 26 might prove to be a successful cda, it was prepared and tested in reaction with methanol (scheme 5). removal of methanol in vacuo and subsequent chromatography revealed only a trace of material that was characterised by mass spectroscopy as the targeted urethane. because of the very low yield, even under the extreme conditions of boiling the isocyanate in methanol, it was apparent that the unactivated isocyanate would not be reactive enough for the purposes of reagent development. this line of approach was thus not taken any further. scheme 5. synthetic route to isocyanate 26. the second approach was prompted by the ease with which the sulfonyl isocyanate 13 had been prepared. alternative use of sulfinyl instead of sulfonyl would allow the isocyanate moiety to be part of a stereogenic centre. in addition, the sulfinyl group was envisaged to maintain the isocyanate reactivity profile with alcohols and amines. in order to test this approach, a racemic model was chosen since: (a) this was more readily synthesised; (b) diastereomer differentiation, if present, would still be evident. to this end, 4toluenesulfinylisocyanate 28 was prepared from commercial toluenesulfonyl chloride via reported methods (scheme 6) (whitmore and hamilton, 1941; kurzer, 1963; jähnchen and westphal, 1969). scheme 6. preparation and reaction of 4-toluenesulfinyl isocyanate 28. 6 bro naoh oocn meoh on h o meo 26 27 so2 soclso2cl 2zn zn 1) k2co3,koh 2) socl2 1-phenylethanol sonco on h s o o on h s o o agnco 2-butanol 29 30 28 homochiral acylisocyanates as diagnostic nmr 19 the sulfinyl isocyanate 28 was reacted with both 2-butanol 14 and 1-phenylethanol 15 added to the other (scheme 6). the two diastereomeric sulfinyl carbamate mixtures were isolated as semisolids via column chromatography. the 2-butanol derivative 29 exhibited two signals in the 1h nmr spectrum at δ 7.68 and 7.79, corresponding to the two nh protons. an analogous situation was observed for the 1-phenylethanol derivative 30, with the two nh signals occurring at δ 8.35 and 8.40 in the 1h nmr spectrum. low temperature nmr were again recorded in order to try for further resolution of the nh signal pairs (table 4). from table 4 it can be seen that the greatest difference in chemical shift for 29 occurs at 303 ok. an analysis of the spectra, however, reveals that the signals in question become much sharper at the lower temperatures and hence, more amenable to integration. for 30 the data in table 4 shows that there was marginally greater resolution at lower temperatures, with baseline resolution achieved by 283 ok. this is possibly due to the more bulky phenyl substituent present in compound 30. the sulfinyl isocyanate thus exhibited both the required reactivity as well as independent signal resolution (up to a factor of 10 greater than for acyl isocyanates) for the two nh protons. table 4: low temperature nmr studies of urethanes 29 and 30. shift δ1 δ2 ∆δ urethane 29 263 ok 8.229 8.196 0.033 273 ok 8.088 8.057 0.031 282 ok 7.981 7.952 0.029 303 ok 7.790 7.680 0.110 urethane 30 273 ok 8.845 8.794 0.051 283 ok 8.694 8.645 0.049 303 ok 8.400 8.358 0.042 conclusion the study has explored the potential of several novel homochiral activated isocyanates 7, 9, 11, 13 as in situ cda’s for diagnostic nmr probes to determine enantiomeric composition. although none of the examples studied showed themselves as generally applicable reagents at ambient temperature, the results are encouraging enough (especially at reduced temperatures) to warrant further investigation. the work has also led to the observation that sulfinyl isocyanates might prove to be overall better candidates for future development. however, in order to pursue this line further, a suitably flexible synthetic route to homochiral sulfinyl isocyanate will need to be found. experimental general: mass spectra were recorded on a perkin elmer itd ion trap detector spectrometer in the electron impact mode at an emission current of 55µa and an electron multiplier voltage of 2000 v. elemental analyses were carried out by either the australian national university analytical service unit or by the canadian microanalytical service ltd. infrared (ir) spectra were recorded as kbr discs for solids and, as indicated in the text, as thin films between kbr plates for oils, using a perkin elmer 1720-x fourier transform spectrometer. melting points were determined on an electrothermal melting point apparatus and are uncorrected. optical rotations were recorded at 20 oc using a optical activity polaar 2001 polarimeter. column chromatography refers to columns prepared as slurries of merck silica gel 60 (70-230 mesh) in the eluent. pre-adsorption was carried out on merck silica gel 60 (35-70 mesh). radial chromatography was performed using merck silica gel 60 pf254, while thin layer chromatography was carried out on aluminium plates coated with merck kieselgel 60 f254. light petroleum refers to the fraction of boiling point 65-70oc, ether to diethyl ether and bicarbonate solution to roos and donovan 20 saturated aqueous sodium hydrogen carbonate solution. all solvents were purified by distillation and, if necessary, were dried according to standard methods. the amount of residual water present in the solvents was determined using a metrohm karl fischer coulometer 684. 1′-(2-methoxy-5-benzyloxyphenyl)ethyl(1s)-[(7,7-dimethyl-2-oxobicyclo[2.2.1]hept 1-yl)carbonyl]carbamate from reaction of 7 and 16. the amide 6 (150 mg, 0.83 mmol) was dissolved in dry dichloroethane and stirred under an inert nitrogen atmosphere. oxalyl chloride (3 mol equiv) was added via syringe and the reaction mixture heated under reflux overnight. excess oxalyl chloride was removed via azeotropic distillation with dichloroethane and the reactive acyl isocyanate 7 characterised by ir (kbr plate) νnco 2244 cm-1 the acyl isocyanate was treated with 4benzyloxy-2-(1-hydroxyethyl)-1-methoxybenzene 16 (216 mg, 0.83 mmol) and heated at reflux temperature overnight to yield the carbamates (231 mg, 60%) as white prisms, mp. 105.5-106.5 oc. ir νmax 3418 (nh), 3274 (ch ar), 2929 (ch), 1783, 1715 and 1640 (c=o) and 1590 and 1501 (c=c ar) cm-1. 1h nmr δ 1.01 (3h, s, c8) one diastereomer, 1.04 (3h, s, c8) other diastereomer, 1.28 (3h, s, c9) one diastereomer, 1.29 (3h, s, c9) other diastereomer, 1.44-1.50 (2h, m, c6 endo), 1.53 (6h, d, j 6.6 hz, ch3), 1.64-1.74 (2h, m, c5 endo), 2.03 (2h, d, j 18.9 hz, c3 endo), 2.11 (2h, dd, j 4.3 and 4.3 hz, c4), 2.17-2.23 (2h, m, c6 exo), 2.45-2.61 (4h, m, c3 exo and c5 exo), 3.79 (3h, s, och3) one diastereomer, 3.80 (3h, s, och3) other diastereomer, 5.02 (2h, s, ch2ph) one diastereomer, 5.03 (2h, s, ch2ph) other diastereomer, 6.25 (2h, q, j 6.5 hz, ch), 6.80 (1h, d, j 8.9 hz, c′6) one diastereomer, 6.80 (1h, d, j 8.9 hz, c′6) other diastereomer, 6.84 (1h, dd, j 8.9 and 2.9 hz, c′4) one diastereomer, 6.85 (1h, dd, j 8.9 and 2.9 hz, c′4) other diastereomer, 7.09 (1h, d, j 2.9 hz, c′3) one diastereomer, 7.10 (1h, d, j 2.9 hz, c′3) other diastereomer, 7.31-7.46 (10h, m, ph), 9.84 (1h, s, nh) one diastereomer and 9.85 (1h, s, nh) other diastereomer. 13c nmr δ 20.3 (c8), 20.7 and 20.8 (c9) , 21.2 (chch3), 27.7 (c6), 29.2 and 29.3 (c5), 43.3 and 43.3 (c4), 43.6 (c3), 50.7 and 50.7 (c7), 56.2 (och3), 65.4 (c1), 69.0 (chch3), 70.6 (ch2ph), 111.8, 113.5 and 114.0 (c′3, 4 and 6), 127.6, 127.9 and 128.5 (c′′2-6), 130.9 and 137.2 (c′1 and c′′1), 149.7 (c10), 150.4 and 150.4 (c′2 and 5), 167.7 (c10) and 216.4 (c2). c27h31no6 (465.22) calc. c 69.7, h 6.7, n 3.0 found c 69.9, h 6.4, n 3.0% (+)-(1s)-7,7-dimethyl-2-oxobicyclo[2.2.1]heptane-1-carboxamide ethylene ketal 18. amide 6 (500 mg, 2.76 mmol), 1,2-ethanediol (0.406 ml, 8.24 mmol), and p-tsa (150 mg, 0.867 mmol) were added to benzene (30 ml). a dean-stark water trap was fitted and the mixture heated at reflux temperature for 48 h. saturated ammonium bicarbonate solution (30 ml) was added and the product extracted with ethyl acetate (3x15 ml), dried over magnesium sulfate and reduced in vacuo. column chromatography of the crude product with 25% ethyl acetate-light petroleum as the eluent yielded the starting material (170 mg, 34%) and the product 18 (327 mg, 53%) as off-white plates, mp. 122.5-124 oc. [α]d 38.5 (c 0.6, chcl3). ir νmax 3408 (nh), 2950 (ch) and 1668 (c=o) cm-1. 1h nmr δ 1.07 (3h, s, c8), 1.22-1.30 (1h, m, c6 endo), 1.28 (3h, s, c9), 1.51 (1h, d, j 13.2 hz, c3 endo), 1.78 (1h, dd, j 4.7 and 4.5 hz, c4), 1.78-1.88 (1h, m, c6 exo), 2.07-2.27 (3h, m, c3 exo, c5 exo and c5 endo), 3.79-4.03 (4h, m, och2ch2o), 5.84 (1h, s, nh) and 6.45 (1h, s, nh). 13c nmr δ 21.0 (c8), 21.1 (c9), 26.5 (c6), 26.9 (c5), 45.2 (c4), 45.8 (c3), 50.2 (c7), 61.0 (c1), 63.4 and 64.7 (och2ch2o), 116.7 (c2) and 174.3 (c10). m/z 226(m+, 16%), 181(15), 139(99), 113(55) and 99(100). c12h19no3 (225.14) calc. c 64.0, h 8.5, n 6.2 found. c 64.0, h 8.1, n 6.2 % (-)-(1s)-7,7-dimethyl-2-hydroxybicyclo[2.2.1]heptane-1-carboxamide 20. sodium borohydride (183 mg, 4.84 mmol) was suspended in 90% ethanol-water (30 ml). amide 6 (500 mg, 2.76 mmol) in ethanol (5 ml) was added dropwise and the reaction mixture stirred for 18 h at room temperature. hcl (2 ml, 1m) was added and the whole reduced in vacuo before extraction with ether. the ethereal layer was washed with water, brine, dried over magnesium sulfate and reduced in vacuo to yield the crude product 20 homochiral acylisocyanates as diagnostic nmr 21 (476 mg, 94%) which was recrystallised from ether-light petroleum as white needles, mp. 239-241 oc. [α]d -11.0 (c 0.3, chcl3). ir νmax 3397 (nh), 3184 (oh), 2959 (ch) and 1663 (c=o) cm-1. 1h nmr δ 1.05 (3h, s, c8), 1.05-1.15 (1h, m, c6 endo), 1.21-1.32 (1h, m, c5 endo), 1.25 (3h, s, c9), 1.76-1.96 (4h, m, c3 endo, c3 exo, c4 and c6 exo), 2.082.18 (1h, m, c5 exo), 3.66 (1h, s, oh), 4.05 (1h dd, j 7.6 and 3.5 hz, c2), 6.12 (1h, s, nh) and 6.67 (1h, s, nh). 13c nmr δ 20.7 (c8), 21.6 (c9), 27.2 (c6), 30.4 (c5), 45.7 (c4), 41.1 (c3), 49.6 (c7), 57.5 (c1), 77.4 (c2) and 177.2 (c10). m/z 184 (m++1, 100%), 140(89), 122(28), 95(28), 81(73) and 67(43). c10h15no2 (183.13) calc. c 65.5, h 9.3, n 7.6 found c 65.0, h 9.2, n 7.5% 7,7-dimethyltricyclo[2.2.1.02,6]heptane-1-carboxamide 22. base elimination. compound 20 (150 mg, 0.819 mmol) and triethylamine (0.199 ml, 1.44 mmol) were added to thf (10 ml) at 0 oc; followed by dimethylaminopyridine (17.5 mg, 0.144 mmol) and methanesulfonyl chloride (0.068 ml, 0.862 mmol). the reaction was stirred for 3 h under an atmosphere of nitrogen and then filtered to remove any solids, washed with cold thf and then diluted to 30 ml. potassium t-butoxide (320 mg, 2.87 mmol) was added and the reaction stirred at 0oc for 40 minutes. the mixture was then poured into aqueous citric acid (100 ml, 5%) and extracted into dichloromethane (20 ml). the organic layer was washed with water, bicarbonate solution, brine, dried over magnesium sulfate and reduced in vacuo to yield 125 mg of yellow oil. this was purified by column chromatography with 50% ethyl acetate-light petroleum as the eluent to afford the product 22 (114 mg, 84%) as off-white plates, mp. 115-116.5 oc, lit. (connolly and hill, 1991) 117-118 oc. [α]d 0 (c 0.5, chcl3). ir νmax 3471 (nh), 2966 (ch) and 1658 (c=o). 1h nmr δ 1.07 (6h, s, c8 and c9), 1.16 (2h, dd, j 10.6 and 1.1 hz, c3 endo and c5 endo), 1.49 (1h, dd, j 1.4 and 1.4 hz, c4), 1.76 (2h, dd, j 1.1 and 1.1 hz, c2 and c6), 1.75-1.81 (2h, m, c3 exo and c5 exo) and 5.70 (2h, s, nh). 13c nmr δ 22.0 (c8 and c9), 24.9 (c2 and c6), 31.17 (c3 and c5), 42.1 (c7), 43.7 (c4), 76.6 (c1) and 175.8 (c10). m/z 166(m++1, 100%), 165(21), 149(13), 124(54), 105(23), 91(14) and 79(11). acid elimination to a solution of alcohol 20 (400 mg, 0.218 mmol) in dichloroethane (10 ml) was added concentrated sulfuric acid (938 mg, 0.957 mmol). the reaction mixture was stirred for 20 minutes at room temperature, made basic with bicarbonate solution (50 ml) and extracted into dichloromethane. the organic portion was washed with water and brine, dried over magnesium sulfate and reduced in vacuo. column chromatography with 50% ethyl acetate-light petroleum as the eluent afforded the starting material 56 mg (14%) and the product 22 (91 mg, 40%). all spectral and physical data for the product obtained from this synthesis were identical to those recorded for the compound 22 recovered from the base induced elimination above. 1′-phenylethyl(1s)-[(3,3-dimethyl-2-methylenebicyclo[2.2.1]hept-1 yl)carbonyl]carbamate 24. the amide 10 (250 mg, 1.39 mmol) was dissolved in dry dichloroethane and stirred under an inert nitrogen atmosphere. oxalyl chloride (3 mol equiv) was added via syringe and the reaction mixture heated under reflux overnight. excess oxalyl chloride was removed via azeotropic distillation with dichloroethane and the reactive acyl isocyanate 11 characterised by ir (kbr plate) νnco 2239 cm-1 treatment of 11 with 1-phenylethanol (1 ml) and overnight reflux gave the starting material (84 mg, 34%) and the product 24 as an oil (262 mg, 58%) which was crystallised from light petroleum as an amorphous white solid, mp. 98-100 oc. ir νmax 3450 (nh), 3199 (ch ar), 3068 (c=ch2), 2982 (ch), 1749 and 1700 (c=o) and 1581 and 1511 (c=c ar). 1h nmr δ 1.11 (3h, s, c8)a one diastereomer, 1.11 (3h, s, c9)a one diastereomer, 1.12 (6h, s, c8 and c9) other diastereomer, 1.47-1.54 (2h, m, c6 endo), 1.55-1.61 (2h, m, c7a), 1.62 (6h, d, j 6.6 hz, chch3), 1.63-1.67 (2h, m, c5 endo), 1.76-1.83 (2h, m, c5 exo), 1.96-2.01 (2h, m, c6 exo), 2.02-2.04 (2h, m, c4), 2.15 (2h, dddd, j 12.0, 4.0, 1.9 and 1.9 hz, c7b), 4.77 (1h, s, roos and donovan 22 ch2) one diastereomer, 4.78 (1h, s, ch2) other diastereomer, 4.87 (1h, s, ch2) one diastereomer, 4.89 (1h, s, ch2) other diastereomer, 5.93 (2h, q, j 6.4 hz, chch3), 7.297.42 (10h, m, ph) and 7.53 (2h, s, nh). 13c nmr δ 21.9 and 21.9 (ch2ch3), 24.2 and 24.3 (c5), 25.9 (c9), 29.5 (c8), 30.7 and 30.8 (c6), 41.6 and 41.7 (c7), 43.1 (c3), 47.8 and 47.8 (c4), 62.0 (c1), 74.5 (ochch3), 102.2 and 102.3 (c=ch2), 126.3 and 126.3 (c′3 and 5), 128.2 (c′4), 128.6 (c′2 and 6), 140.6 (c′1), 150.1 (c=o), 163.1 and 163.2 (c2) and 170.9 (c10). c20h25no3 (327.42) calc. c 73.3, h 7.7, n 4.3 found c 72.7, h 7.6, n 4.2% (1s)-1-isocyanato-7,7-dimethyl-2-oxobicyclo[2.2.1]heptan-2-one26. hypobromite, generated in situ, by the addition of molecular bromine (380 mg, 2.4 mmol, 2 me) to an aqueous solution of sodium hydroxide (2.5 ml, 6.24 m) was added to amide 6 (217 mg, 1.2 mmol) in dichloromethane (2.5 ml). tetrapropylammonium bromide (16 mg, 0.06 mmol) was added and the reaction mixture stirred vigorously for 12 min at room temperature. after this time more water (20 ml) and dichloromethane (20 ml) were added and the organic layer separated. the aqueous layer was extracted with dichloromethane and the two organic fractions combined, dried over magnesium sulfate and reduced in vacuo. ir (kbr plate) νnco 2245. methyl (1s)-7,7-dimethyl-2-oxobicyclo[2.2.1]heptyl-1-carbamate 27. methanol (15 ml) was added to the crude isocyanate 26 (1.2 mmol) and heated at reflux temperature overnight. subsequent removal of the methanol and purification by radial chromatography with 10% ethyl acetate-light petroleum as the eluent afforded an oil (7 mg), which consisted of two components (gcms) in approximately equal amounts. one component was unidentified, the other tentatively assigned as the product 27 on the basis of the mass spectrum. m/z 211(m+, 3%), 210(39), 169(29), 135(77), 107(83), 91(42), 79(58) and 76(100). 2′-butyl-p-toluenesulfinylcarbamate 29. to the sulfinyl isocyanate 28 (5.70 mmol) was added a large excess of 2-butanol (1 ml) and the whole stirred overnight at room temperature. the reaction mixture was filtered and reduced in vacuo before chromatography on silica gel with 10-20% ethyl acetate-light petroleum as the gradient eluent yielded the product 29 as a yellow oil (303 mg, 1.18 mmol, 20.8%). ir (kbr plate) νmax 3439 (nh), 3113 (ch ar), 2872 (ch), 1726 (c=o) 1603 and 1500 (c=c ar), 1219 (so), 1095 (ars) and 853 (sn). 1h nmr δ 0.91 (6h, t, j 7.2 hz, ch2ch3), 1.25 (3h, d, j 6.3 hz, chch3) one diastereomer, 1.26 (3h, d, j 6.3 hz, chch3) other diastereomer, 1.50-1.72 (4h, m, ch2), 2.41 (6h, s, phch3), 4.83 (1h, tq, j 6.3 and 6.3 hz, och) one diastereomer, 4.84 (1h, tq, j 6.3 and 6.3 hz, och) other diastereomer, 7.31 (4h, d, j 8.1 hz, c3 and 5), 7.56 (4h, d, j 8.1 hz, c2 and 6), 7.68 (1h, s, nh) one diastereomer and 7.79 (1h, s, nh) other diastereomer. 13c nmr δ 9.5 and 9.6 (ch2ch3), 19.4 and 19.4 (chch3), 21.4 (phch3), 28.8 (ch2ch3), 75.7 (och), 124.8 (c3 and 5), 129.9 (c2 and 6), 140.5 (c4), 142.4 (c1) and 153.8 (c=o). 1′-phenylethyl-p-toluenesulfinylcarbamate 30. to the sulfinyl isocyanate 28 (5.70 mmol) was added 1-phenylethanol (0.69 g, 5.70 mmol). the reaction mixture was stirred overnight at room temperature under an atmosphere of nitrogen before filtration, reduction in vacuo and chromatography on silica gel using 10-20% ethyl acetate-light petroleum as the gradient eluent yielded the product 30 (0.685 g, 2.25 mmol, 39.5%) as a pale yellow oil. ir (kbr plate) νmax 3434 (nh), 3059 (ch ar), 2852 (ch), 1732 (c=o) 1645 and 1552 (c=c ar), 1221 (so), 1062 (ars) and 812 (sn). 1h nmr δ 1.52 (3h, d, j 6.6 hz, chch3) one diastereomer, 1.53 (3h, d, j 6.6 hz, chch3) other diastereomer, 2.33 (6h, s, phch3), 5.84 (1h, t, j 6.6 hz, och) one diastereomer, 5.85 (1h, t, j 6.6 hz, och) other diastereomer, 7.18-7.33 (14h, m, c3, c5 and c′2-5), 7.50 (2h, d, j 8.2 7 hz, c2 and 6) one diastereomer, 7.52 (2h, d, j 8.2 7 hz, c2 and 6) other diastereomer, 8.35 (1h, s, nh) one diastereomer and 8.40 (1h, s, nh) other diastereomer. 13c nmr δ 21.3 (phch3), 22.2 (chch3), 75.1 (och), 124.8 (c3 and homochiral acylisocyanates as diagnostic nmr 23 5), 126.0 (c′3 and 5), 127.0 (c′4), 128.5 and 128.5 (c′2 and 6), 129.7 (c2 and 6), 140.2 and 140.2 (c′1), 140.8 and 140.9 (c4), 142.1 and 142.1 (c1) and 153.4 and 153.5 (c=o). acknowledgments the authors would like to thank the australian research council for financial support (an apa for ard and grant 0320198155 for ghpr). references connolly, j. d. and hill, r. a. 1991. dictionary of terpenoids,vol 1. wiley, new york, 151. dale, j. a. and mosher, h. s. 1968. nuclear magnetic resonance nonequivalence of diastereomeric esters of α-substituted phenylacetic acids for the determination of stereochemical purity. j. am. chem. soc. 90: 3732-3738. dale, j. a., dull, d. l. and mosher, h. s. 1969. α-methoxy-α-trifluoromethylphenylacetic acid, a versatile reagent for the determination of enantiomeric composition of alcohols and amines. j. org. chem. 34: 2543-2549. dale, j. a. and mosher, h. s. 1973. nuclear magnetic resonance enantiomer reagents. configurational correlations via nuclear magnetic resonance shifts of diastereomeric mandelate, o-methylmandelate and α-methoxy-α-trifluoromethylphenylacetate (mtpa) esters. j. am. chem. soc. 95: 512-519. donovan, a. r. and roos, g. h. p. 1996. homochiral activated isocyanates as chiral derivatising agents. synth. commun. 26: 4603-4615. gawley, r. e. and aubé, j. 1996. tetrahedron organic chemistry series vol. 14 : principles of asymmetric synthesis. pergamon, oxford. jähchen, g. and westphal, g. 1969. zur darstelling von p-toluolsulfinylisocyanat. z. chem. 9: 305. kocienski, p. j. and kirkup, m. 1975. reaction of nitrimines with cyanide ions. j. org. chem. 40: 16811682. kurzer, f. 1963. p-toluenesulfinyl chloride. organic syntheses, collective volume. 1v. ed. n. rabjohn. wiley, new york, 937-939. lyle, g. g. and lyle, r. e. 1983. polarimetry. in asymmetric synthesis vol. 1, ed j. d. morrison. academic press, new york. money, t. 1985. camphor: a chiral starting material in natural product synthesis. nat. prod. rep. 2: 253 parker, d. and taylor, r. j. 1994. analytical methods: determination of enantiomeric purity. in asymmetric synthesis eds r. a. aitken and s. n. kilenyi. blackie, glasgow. parker, d. 1991. nmr determination of enantiomeric purity. chem. rev. 91: 1441-1457. passerini, m. 1925. reazione del cianuro di potassio con i pernitroso derivati. gazz. chim. ital. 55: 559-567. roos, g. h. p. and watson, m. c. 1991. trichloroacetyl isocyanate: rapid in situ determination of diastereomeric ratios of alcohols by 1h nmr spectroscopy. s. afr. j. chem. 44: 95-96. roos, g. h. p., manickum, t. and malissar, d. g. 1992. a facile diagnostic 1h nmr method for syn and anti hydroxy systems. j. chin. chem. soc. 39: 105-106. roos, g. h. p., manickum, t., field, j. s. and ramesar, n. 1994. x-ray crystallographic confirmation of the stereo-substructure determination by nmr spectroscopy of two diastereoselective baylis-hillman reaction products. s. afr. j. chem. 47: 33-35. schneider, h., weigand, e. f. and becker, n. 1988. linear electric field effects on 13c nmr shifts in saturated aliphatic frameworks: scope and limitations. j. org. chem. 53: 3361-3364. whitmore, f. c. and hamilton, f. h. 1941.organic syntheses, collective volume1.(2nd edition).ed.a. h. blatt.wiley,new york : 492-494. yamaguchi, s. 1983. nuclear magnetic resonance analysis using chiral derivatives. in asymmetric synthesis vol. 1, ed j. d. morrison. academic press, new york. received 13 april 1999 accepted 24 june 2000 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 15-19 © 2001 sultan qaboos university variation in seedling characteristics of five populations of acacia tortilis from the united arab emirates in response to increasing sodium chloride concentrations fatma. m. al-ansari* and rashied. s. modawi** *biology department, u.a.e. university, p.o. box 15551, al ain, u.a.e.; **biology department, al albayt university, p.o. box 130346, al-mafraq, jordan. التباين في خواص البادرات في نمط استجابة خمس عشائر من نبات أكاسيا تورتيليس من اإلمارات العربية المتحدة لتراكيز مختلفة من كلوريد الصوديوم مضوي. األنصاري والرشيد س. فاطمة م مارات العربية المتحدة وبعد إجراء تـم جمع بذور أشجار أكاسيا تورتيليس من خمسة مواقع في مدينة العين بدولة اإل : خالصـة 150 و 90 و 20كلوريد الصوديوم وهي صفر و المعاملة األولية بحامض الكبريتيك المركز نبتت تحت أربعة تراكيز من محلول و لطول ولقد كان لتركيز الملح تأثيرا معنويا على كل من نسبة إنبات البذور وسرعة اإلنبات والمحتوى المائي للبادرات . مليمول المجموع الجذري وللمجموع الخضري للبادرات ، كما أظهرت الدراسة أن التباين في نمط استجابة مجموعات البذور التي جمعت مـن مواقع مختلفة للمعاملة بالمحاليل الملحية يشير إلى وجود اختالفات وراثية في تكيف النباتات على البيئات المحلية والذي يمكن الها إلى عشائر متميزة نتيجة تأثرها بدرجات متفاوتة في انخفاض منسوب المياه الجوفية والتوسع العمراني في أن يـؤدي إلى انعز . المنطقة abstract: seeds of acacia tortilis collected from 5 sites around the city of al ain in the united arab emirates were germinated in 4 concentrations of sodium chloride (0, 20, 90 and 150 mm of nacl). percent of germination, rate of germination, seedling moisture content, root and shoot lengths and seedling lengths were all significantly affected by salt stress. seeds collected from the different sites were significantly different in their response to salinity conditions. variations in the response of seedlings from different sites to the different salt treatments suggest an underlying genetic variability within the a. tortilis populations, possibly resulting from variations in the prevailing local conditions. urbanization in the area and the changing water table may have divided a. tortilis into distinct subpopulations that are significantly different in seedling characteristics and their response to saline conditions. keywords: acacia tortilis, seed germination, variability, salt stress. 1. introduction a cacia tortilis (forssk.) hayne is a medium flat-topped tropical tree legume that belongs to the family leguminosae, subfamily mimosoidae. it is known to predominate in areas of prolonged dry season such as those prevailing in the eastern plains of the united arab emirates (western, 1989). in this semi-arid region, vegetation cover has shown considerable fluctuations. this is attributed to the scarcity of natural resources in the region, the frequent short term fluctuations in the climate and the increasing human interference. the city of al-ain of the united arab emirates (uae) (latitude 2415 , longitude 5545 and altitude 301.6 m above sea level) was established 160 km east of the gulf coast near al buraimi oasis. the area is characterized by a relatively high water table, semi-stable sand dunes with frequent outcrops of limestone. scattered stands of acacia sp. and prosopis sp. are common with high incidence of annuals after a rainy winter (western, 1989). 15 al ansari and modawi ground water constituted the major source of water for domestic and agricultural uses. ground water depletion during the last three decades may have resulted in the lowering of the water table and increased soil salinity, especially around al ain. it may have also contributed to the decline in stands of acacia and prosopis in the region (western, 1989). figure 1. relative location of the different seed collection sites around the city of al ain, uae. increasing soil salinity is a common problem that is affecting more lands in semi-arid areas. plant adaptation due to prevailing conditions demands their ability to grow at sodium chloride concentrations that are lethal to unadapted plants. plant species that are adapted to saline soils may become a valuable genetic resource. it has been suggested that a great deal of variability exists for adaptation to drought and salinity in arid and semi-arid conditions (amzallag et al., 1995). stability in the expression of such trails has been shown to correlate with coefficient of variation under uniform conditions. table 1: analysis variance summaries (mean squares) of the data for germination percentage, rate of germination and lengths of shoots, roots and seedlings of five populations of a. tortilis under saline conditions. source of variance germination percentage germination rate seedling length shoot length root length population (p) 414.79*** 5.88** 1454.8* 2552.75** 1359.96** salinity (s) 273.77*** 2.06* 10067.7*** 470.14** 1272.24** p× s interaction 20.0*** 1.65* 2091.1* 1134.28** 199.49 n s *, ** and *** = significant at .05, .01 and .001 levels respectively; ns = non-significant. stress conditions may expose unrecognized variability within and between plant populations. limited reports dealt with tree legumes of the region in relation to drought adaptations. we carried 16 variation in seedling characteristics of five populations out the study on the population biology and adaptation of one of the key species (acacia tortilis) in the changing environments of the region. the primary objective of the present study was to assess the extent of variation for salt tolerance in different populations of acacia tortilis, particularly at the initial growth stages. 2. materials and methods mature pods and seeds of a. tortilis were collected from five sites around the city of al-ain in the uae: site a, south west (zakhir); site b, west (asharej); site c, east (al-buraimi); site d, north east (al-oha); and site e, north of al-ain (al-hili). see figure 1.the urban collection sites are undisturbed areas that are at least 5 km apart, separated by major structures such as the university campus, a highway, residential areas and the city center. within each site seven to thirteen trees were sampled. seed and pod collections were made towards the end of the spring of 1996. seed moisture content was determined by weight difference before and after oven drying at 105 c for 24 h. seeds were pretreated with concentrated sulfuric acid for 30 min, thoroughly washed with distilled water, placed in 9 cm petri-dishes on “seed test thick” 9 cm filter papers (whatman’s no. 1) and kept moistened with 0, 20, 90 or 150 mm of nacl solutions. fifty seeds were placed in each petri dish with three replicates for each treatment combination. seeds were germinated at 25° c ± 1° c. the germination was assessed as the percentage of seeds with radicles emerging each day for 10 days. the mean rate of germination of each population was determined as maguire index where mi equals the sum ni /ti , where ni = the number of seeds that germinated in each time, ti from the beginning of the experiment. root and shoot lengths for each treatment were measured after 10 days of germination. data were analyzed statistically using two-way analysis of variance. table 2: the effect of nacl concentration in germination medium on seedlings root, on shoot length germination percentage and an germination rate of five populations of acacia tortilis from uae. nacl concentration (mm) 0 20 90 150 0 20 90 150 population root length (mm) germination percentage a zakhir 34.4 a* 42.9 ab 41.0 ab 29.7 ab 35.0 b 35.3 b 31.7 b 20.3 b b asharej 33.7 a 36.7 ab 48.9 a 40.6 a 42.3 ab 42.7 ab 41.7 ab 29.0 ab c al buraimi 41.8 a 49.3 a 46.3 ab 35.7 ab 41.0 ab 39.7 ab 36.7 ab 34.7 ab d al oha 41.4 a 39.8 ab 35.2 ab 21.5 b 48.7 a 48.7 a 44.0 a 42.7 a e al hili 40.9 a 34.3 b 32.2 b 28.5 ab 34.0 b 36.7 b 33.0 ab 30.3 ab shoot length (mm) germination rate (number/day) a zakhir 59.0 a 56.7 a 47.0 a 37.8 a 23.4 b 23.4 b 23.6 b 22.3 b b asharej 52.1 ab 52.4 ab 38.7 b 29.8 ab 24.3 ab 24.0 ab 23.5 b 22..0 b c al buraimi 46.8 bc 41.5 bc 38.0 bc 28.3 ab 24.7 a 24.5 a 24.6 a 26.0 a d al oha 52.8 ab 56.3 ab 40.6 ab 32.6 ab 25.1 a 24.7 a 23.9 ab 22.8 ab e al hili 47.5 b 45.9 ab 37.7 bc 25.4 b 24.3 ab 24.2 ab 24.2 ab 23.8 ab change in root length:shoot length ratio as % of control change in seedling water content as % of control a zakhir 0.0 +31 +53 +36 0.0 -0.44 -4.01 -5.68 b asharej 0.0 +8 +94 +109 0.0 -1.90 -4.25 -5.82 c al buraimi 0.0 +34 +37 +42 0.0 +0.68 -4.29 -5.76 d al oha 0.0 -9 +12 -15 0.0 -0.78 -4.36 -6.59 e al hili 0.0 -13 -1 +30 0.0 -2.94 -4.53 -4.52 * along each column means followed by the same letter are not significantly different (α = 0.05) according to duncan multiple range test. 17 al ansari and modawi table 1 shows mean square, f values and probability for the different parameters as affected by population, salinity. the five populations were significantly different in all parameters. the different populations were also significantly affected by the different salt concentrations. the data for on root lengths, shoot lengths, germination percentage and germination rate of the 5 populations of a. tortilis are presented in table 2. the five populations were significantly different in seed germination percentage (table 1). the increasing concentrations of the saline solutions decreased the germination medium was also did different nacl concentrations. the populations showed a slight but significant reduction in the rate of germination that was more pronounced at the higher salt concentrations. although the five populations of seeds were significantly different in their initial seed moisture content, their respective seedlings lost 4-4.5 % and 4.5-6.6 % of their moisture content when geminated at 90 mm and 150 mm of nacl solutions, respectively, as compared to germination in distilled water (table 2). root length of seedlings from populations d and e were markedly reduced by the higher salt concentrations. seedlings of populations a, b, c had longer roots at the 20 and 90 mm salt levels but reduced length when germinated in distilled water and 150 mm nacl. shoot length of populations a, b, d and e were not significantly reduced by the 20 mm treatment compared to the control. however, in all populations the increase in salt from 20 mm to 90 mm and then to 150 mm resulted in a significant reduction in shoot length. both root and shoot lengths as well as the overall seedling length showed significant population times salt concentration interaction. in all populations, seedling length was significantly reduced at 150-mm nacl. the effect of the higher salt concentrations was more pronounced on the shoot than on the root elongation. the is reflected in the increase in root: shoot ratio for populations a, b and c. populations d and e both showed increases and decreases in root: shoot length ratio compared to the control. 3. discussion analysis of the germination characteristics of five seed populations of a. tortilis, collected from five sites around al ain, suggests that the recently urbanized semi-arid plains of eastern u.a.e. have been under the influence of both biotic and abiotic factors. this may have started the noticeable changes in the local plant communities observed by western, (1989). the low germination percentage observed in this study at different salt levels, despite seed pretreatment with sulfuric acid suggests that the hard seed coat of the species has developed as an adaptation to permit a few seeds to germinate in the harsh conditions of the semi-arid climate. populations a and b had a very low rate of germination at the higher salt levels. seedling length was the highest at the 20 mm salt concentration for all populations except e where the control produced the longer seedlings. however, 20 and 90 mm levels of nacl seemed to have promoted root growth of population b. it has been previously suggested (saab et al 1990) that higher nacl concentrations increased root growth and decreased shoot growth. this was reflected in the increased root length : shoot length ratio with the increasing salt concentration. this was true for all the populations except d which showed a slight decline in root to shoot ratio at the 150 mm concentration. the populations were also different in their response. koehl (1996) suggested that reduced shoot : root ratio has a selective advantage in delaying the onset of critical water saturation deficit and thereby the plants ability to take up additional water from deeper soil levels. coleoptile and root growth has also been reported to be involved in seedling response to dehydration (guidera, et al, 1997). salinity is reported to cause a reduction of water uptake in many species of acacia seeds (rehman, et al, 1996). in this study this was reflected in reduced seedling water content. the variation between the population may point to possible adaptation to changing local environments. the high heritability estimates for the rate of germination in rice, chickpea and lentil reported by rao, et al (1997) and mamo, et al, (1996) may explain the high genetic variability observed variation between populations in their seedling characteristics. studies 18 variation in seedling characteristics of five populations are underway to quantify the genetic variability within this species and to correlate such adaptations with environmental attributes specific to the region. references amzallag, g.n, seligman, h and lerner, h.r. 1995. induced variability during the process of adaptation in sorghum bicolor. journal of experimental botany 46: 1017-1024. guirera, m., shroyer, j.p., kirkham, m.b. and paulsen, g.m. 1997. wheat coleoptile and root growth and seedling survival after dehydration and rehydration agronomy journal 89(5): 822-826. koehl, k. 1996. population specific traits and their implications for the evaluation of droughtadapted ecotypes in armeria maritime. botanica acta 109(3): 206-215. mamo, t., richter, c. and heiligtag, b. 1996. salinity effects on growth and ion content of some chickpea (cicer areitinum l) and lentil (lens culinaris medic.) varieties. journal of agronomy and crop science 176(4): 235-247. rao, l.v., subba, s.k. and vanisree, g. 1997. genetic variability for seedling characteristics among rice (oryza sativa l.) cultivars. seed research 24(2): 124-128. rehman, s, harris, p.j.c., bourne, w.f. and wilkin, j. 1996. the effect of sodium chloride on germination and potassium and calcium content of acacia seeds. seed sci & technology. 25: 45-57. saab, i.n., sharp, r. e., pritchard, j and voetberg, g.s. 1990. increased endogenous abscisic acid maintains primary root growth and inhibits shoot growth in maize seedlings at low water potentials. plant physiology 93: 1329-1336. western, a. 1989. the flora of the united arab emirates-an introduction. uae university, al ain, u.a.e. received 2 october 2000 accepted 21 january 2001 19 fatma. m. al-ansari* and rashied. s. modawi** ýçøãé ã. çáãäõçñí æçáñôíï ó. ãöæ� materials and methods electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 11-18 © 2003 sultan qaboos university physiological and behavioral adjustments relative to catecholamine levels during nesting in olive ridley (lepidochelys olivacea) and hawksbill (eretmochelys imbricata) sea turtles in masirah island, oman. a.y.a alkindi, i.y. mahmoud and fatma al-siyabi department of biology, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, email: aakindy@squ.edu.om. التكيفات الفيزيولوجية والسلوكية بواسطة معدالت األدرينالين والنورادرينالين للسالحف البحرية الزيتونية وصقرية النقار في جزيرة مصيرة بسلطنة عمان عبدالعزيز الكندي ، ابراهيم محمود و فاطمة السيابي درينالين والنورادرينالين في الزيتونية وصقرية المنقار من السالحف تم في هذه الدراسة ألول مرة قياس األ : خالصة لقد تم جمع عينات من الدم من . البحرية في جزيرة مصيره على بحر العرب وذلك في مجموعات السالحف بعد التعشيش النصف والساعتين ولقد تفاوتت مدة التبويض بين الساعة و . مجموعات السالحف التي أنهت التعشيش وأخرى لم تعشش بعد ولوحظت حالة من الضنى تعم هذه السالحف وهي تقوم بجهد متواصل مضني تتخلله فترات . في كال النوعين من السالحف وفي هذا اإلطار من النشاط أظهرت هذه السالحف ارتفاعاً في معدالت ثاني أكسيد الكربون والحمضية . من االسترخاء أما معدالت األدرينالين والنورادرينالين فقد كانت . صائص تستتبع التنفس الالهوائي ونقص األكسجين في الدم وهذه كلها خ وفي هذا اإلطار فإنه يبدو أن استراتيجية التكاثر . مستقره في كال النوعين، ولم تتغير معدالت الجلوكوز في النوعين أيضاً .في كال النوعين من السالحف تتشابه إلى حد بعيد abstract: plasma adrenaline (adr) and noradrenaline (na) levels were measured for the first time in natural populations of hawksbill (eretmochelys imbricata) and olive ridley (lipedochelys olivacea) in masirah island, arabian sea; one of the few protected nesting grounds remaining in the world for these two endangered species. plasma adr and na levels were assessed in individuals after they oviposited eggs and completed nesting exercises, and in individuals which were still searching for suitable nesting sites. blood samples were taken from the cervical sinuses from two groups (oviposited and non-oviposited), which spent at least 1.5 h on the nesting grounds. the duration of the nesting period varied between 1.5 and 2.0 h for both species. there was no significant difference between oviposited and non-oviposited turtles in both species. as the turtles move onto the nesting grounds, their heavy weight compresses the thoracic region making terrestrial breathing laborious and difficult. during phases of nesting, the turtles undergo brief bursts of strenuous and exhaustive exercise which usually lasts less than one minute followed by a brief recovery period which is less than the exercise phase. reptiles in general, particularly turtles, are intermittent breathers and after bursts of exercise, they appear to develop hypoxia, hypercapnia and acidemia, which are characteristic of anaerobic metabolism. the data reveals that catecholamine levels remain stable in both species during phases of nesting and may play an important role in combating stress as well as mobilizing energy reserves. the high plasma lactate and co2 levels in olive and hawksbill turtles may signify anaerobic metabolism during exercise. glucose levels remain unchanged throughout nesting in both species. there was no significant difference in the lactate and glucose values in the two species. the physiological and the behavioral adjustments in this study showed remarkable similarities in the two species and may be an important factor in the reproductive strategy for species survival. keywords: nesting, sea turtles, catecholamines, glucose, lactate, co2. 11 a.y.a. alkindi, i.y. mahmoud and fatma al-siyabi 1. introduction t he stress system in vertebrates, under the influence of the environmental factors, triggers the neuroendocrine system to secrete stress hormones such as catecholamines and glucocorticoids (stratakis and chrousos, 1995; alkindi et al., 1996; alkindi et al., 2000a; denver, 1997). in addition to hormones, there is also an increase in glucose, lactate and blood electrolytes (chrousos and gold, 1992). the nesting process is a difficult ordeal, and frequently the turtle makes several unsuccessful attempts before oviposition (alkindi et al., 2000b). as the turtles emerge from the sea, they remain on the nesting grounds for a long time (2.5– 4 h in green and 1.5-2.5 h in the olive ridley turtles) and thus undergo a tremendous stress and energy expenditure (alkindi et al., 2000b). valverde et al., (1999) speculated a lower hypothalamo-pituitary-adrenal axis (hpa) in olive ridley arribada and solitary nesters than in basking and non-nesting turtles. they concluded that the slow increase in corticosterone levels during nesting may indicate a hyporesponsiveness of hpa to turning stress which may be a physiological adaptation during the nesting process. this study is part of ongoing projects related to the behavioral and physiological studies on the natural population of sea turtles in oman. the purpose of this study is to compare the behavioral and the physiological adjustments during nesting in two species that choose the same nesting grounds. 2. methods 2.1 study area this investigation was conducted at masirah island, sultanate of oman, off the east coast of the arabian sea. 2.2 animals twelve normal healthy nesting olive ridley and hawksbill turtles without any physical defects or injuries were studied during the nesting season (n=12). the observations were conducted late in march and april. both the hawksbill and olive ridley turtles share the same nesting grounds on the island. behavioral observations were recorded during different phases of nesting. carapace length, carapace width and turtle weight were recorded. air, water, ground and cloacal temperatures were taken during the time of observations. measurements of carapace length, width and body weight were recorded after nesting. blood samples (10 ml) were taken during nesting exercise with a syringe and needle from the dorsal cervical sinuses according to the method of owens and ruiz (1980). two groups were sampled oviposited and non-oviposited which spent at least 1.5 h on the nesting grounds. several trips were made to the study area during each period for the data collection. 2.3 blood analysis catecholamine analysis: mixed standards (5ng/ml) of adrenaline, noradrenaline, 3hydroxytyramine (dopamine) and the internal standard 3,4-dihydroxybenzylamine-hbr (dhba were used for calibration of hplc instrument to quantify adrenaline, noradrenaline and dopamine in plasma samples. all reagents were from chromsystems. preparation of the sample involved the extraction of 500 µl of plasma and 100 µl of internal standard with 50 mg of acid washed alumina neutral type in a 1.5 ml polypropylene microcentrifuge tube. after mixing for 20 min. on an autovortex set at medium speed, the tube was centrifuged at 2800g for two min. the supernatant was withdrawn and the residue was treated with 0.5 ml of washing buffer, mixed using an autovortex for two minutes, centrifuged, and discarded. this washing procedure was repeated three times. the catecholamines were then 12 physilogical and behavioral adjustments recovered from the alumina by shaking with 200 µl of elution buffer for five minutes. after centrifugation (11,500g) for two minutes, the supernatant was transferred to a clean vial of polyprophyne for storage at 2-4oc (maximum storage time of two days). hplc analysis consisted of loop injection of 50 µl of the prepared sample. the mobile phase (chromsystems cat. # 5001) is specific for electrochemical detection of catecholamines. instrument conditions were constant flow of 1.2 ml/min., electrochemical detection at 600 mv, current range 10 na and damping of 1 sec. readouts in ng/ml of standards and samples were corrected for extraction efficiency to obtain direct values for plasma noradrenaline, adrenaline and dopamine concentrations. plasma glucose, lactate and co2 analyses: the beckman synchron cx systems were used to determine plasma glucose, lactate and co2 in this study. the system automatically proportions appropriate samples and reagent volumes relative to each plasma parameter. plasma glucose was measured using amperometric method utilizing glucose oxidase production of o2 and detection of ∆ potential. plasma lactate was measured using enzymatic method utilizing lactate dehydrogenase with conversion to pyruvate and the production of peroxide. peroxidase was added to produce quinoneimine and was detected at wavelength of 520nm. plasma co2 was measured using potentiometric method that utilizes ion selective electrode which measures change in potential. the standard error of the mean (sem) was calculated for the parameters. 3. results plasma adrenaline and noradrenaline levels showed no significant differences in the two species (figure 1), and also between the individuals of the same species. there was no significant difference between oviposited turtles and non-oviposited turtles. the hormonal levels remained stable throughout the nesting period. values of glucose and lactate (figure 2), and co2 (figure 3), showed no significant differences among the individuals of the same species or the two species. there was no significant difference between the cloacal temperatures, sand, air or water temperatures. 0.0 2.5 5.0 7.5 10.0 o liv e r id . a d ren a lin e h a w k sb ill a d ren a lin e o liv e r id . n o ra d ren a lin e h a w k sb ill n o ra d ren a lin e ng /m l figure 1. adrenalin and noradrenalin levels ± (n=12; sem;* = significant difference) the mean values (ng/ml) for olive ridley for noradrenaline (6.46 ± 1.00, n=11) and adrenaline (3.78 ± 0.70, n=13), and for hawksbill noradrenaline (7.00 ± 1.24, n=11) and adrenaline (6.14 ± 13 a.y.a. alkindi, i.y. mahmoud and fatma al-siyabi 1.34, n=11). the mean values (mmol/l) for olive ridley for glucose (5.38 ± 0.25, n=12) and, for hawksbill glucose (5.94 ± 0.27, n=11). the mean values (mmol/l) for olive ridley for lactate (15.43 ± 1.98, n=12), and for hawksbill lactate (19.61 ± 1.44, n=11). the mean values (mmol/l) for olive ridley for co2 (26.50 ± 1.36, n=12), and for hawksbill co2 (23.72 ± 0.78, n=11). there were no significant differences in all parameters between oviposited and non-oviposited turtles both intra-specifically and inter-specifically (figures 1-3). the mean values for temperatures (oc) for olive ridley and hawksbill turtles, respectively, are: water (25.6 ± 0.26, n=10) (26.0 ± 0.0, n=5), sand (26.4 ± 1.18, n=10) (28.2 ± 0.86, n=5), air (25.15 ± 0.72, n=10) (26.5 ± 0.31, n=5) and cloacal (27.5 ± 0.45, n=10) (27.4 ± 0.4, n=5). there was no significant difference between the cloacal temperatures, sand, air or water temperatures. 0 10 30 olive rid. glucose olive rid. lactate hawksbill glucose hawksbill lactate m m l -1 figure 2. mean glucose and lactate levels = significant difference) (n=12;± sem; * 0 10 30 olive ridley hawksbill m m l 1 figure 3. mean co2 levels = significant difference) (n=12;± sem;* the mean values (cm) for olive ridley for carapace length and width (72.75 ± 0.55, n=12; 50.91 ± 1.33, n=12) and for hawksbill (78.12 ± 1.17, n=8; 60.62 ± 2.33, n=8), for body weight 14 physilogical and behavioral adjustments (g) for olive ridley (72.33 ± 0.47, n=12) and for hawksbill (75.63 ± 0.42, n=8). there were no significant differences in values between adrenaline, noradrenaline, glucose, lactate and co2 in olive ridley and hawksbill turtles of both ovipositors and non-ovipositors, therefore, all the data were pooled (figures 1-3). 4. discussion the data on olive ridley and hawksbill reveals that there is no significant differences in catecholamine, glucose, lactate and co2 values in turtles that had already oviposited their eggs and completed all phases of nesting, and turtles which had not oviposited their eggs and had not completed their nesting phases. the stable levels of catecholamines in this study may be an important physiological adjustment to combat stress. matt et al. (1997) reported that in the male tree lizards (urosaurus ornatus), when captured within a short time, there was no apparent rise in catecholamines. however, restraint stress caused a significant increase in nordrenaline, adrenaline and dopamine plasma levels. based on the lack of intra-specific or inter-specific significant differences, it seems that both species undergo the same physiological adjustments, we suggest that the catecholamines release into the blood stream occurs in surges and the amount depends on the magnitude of the physical exercise and related physiological conditions. this assumption is based on the fact that the present data reveals a wide variation in the catecholamine values among the individuals of the same nesting group. it appears that the rise in the catecholamine values may facilitate o2 uptake, increase heart rate and mobilizes glycogen metabolism by stimulating glycogenolysis and/or gluconeogenesis. in both species, there was a large accumulation of plasma lactate and co2 which is in conformity with other reptiles. lizards that rely on anaerobic metabolism during territorial encounters produce large amounts of lactate (bennet et al., 1981; pough and andrew, 1985; wilson et al., 1990). gleeson et al. (1993) reported that in the lizard (dipsosaurus dorsalis) the skeletal muscles utilize mainly lactate under the influence of adrenaline as a gluconeogenic substrate for glycogen production. moreover, plasma adrenaline and corticosterone increased after 5 min. of exhaustive exercise; and adrenaline facilitates lactate removal by skeletal muscles while corticosterone has no effect on lactate metabolism in the lizard skeletal muscles. other studies have also confirmed that skeletal muscles in lizards are capable of resynthesizing muscle glycogen in situ shortly after strenuous exercise (gleeson, 1982, 1986, 1991; gleeson and dalessio, 1989, 1990). in the lizard, dipsosaurus dorsalis, red and white skeletal muscles in vitro, under the influence of adrenaline, are capable of synthesizing glycogen directly from lactate at many times greater than the rate of synthesizing glycogen from glucose. thus, adrenaline is not effective on glucose metabolism (gleeson et al., 1993). our data indicate that both adrenaline and noradrenaline are effective in facilitating the conversion of lactate to glycogen but not effective in conversion of glucose to glycogen, as the glucose plasma levels remain stable throughout the nesting exercise, which is in conformity with the above investigations. the olive ridley and hawksbill sea turtles undergo long and arduous exercises at different phases of nesting, lasting several hours, which includes ascent on to the beach, wandering, digging body chamber, digging egg chamber, laying eggs, filling egg chamber, filling and camouflaging body chamber, then they return to the sea. most reptiles, especially turtles including olive ridley and hawksbill, ventilate intermittently when they are subjected to severe hypoxia, acidemia and overall acid-base disturbance during exhaustive exercise periods (shelton et al., 1986; wasser and jackson, 1991; comeau and hicks, 1994). there is a general trend of adjustments in heart rate, pulmonary 15 a.y.a. alkindi, i.y. mahmoud and fatma al-siyabi vascular resistance, and pulmonary blood flow associated with hypoxia and intermittent ventilation (shelton and burggren, 1976; hicks, 1994; comeau and hicks, 1994). an increase in heart rate and pulmonary blood flow and a decrease in the pulmonary vascular resistance occurs during deep ventilation while the turtle is resting. however, during exercise, there is a decrease in heart rate and pulmonary blood flow and an increase in pulmonary vascular resistance that leads to hypoxia. in addition, there is a major shift in blood flow in the heart, affecting the pulmonary and systemic circulation (shelton and burggren, 1976). to compensate for intermittent ventilation, the heart adjusted to shunts with blood flow from right to left shunt, where the systemic venous blood bypasses the lungs and enters the systemic circulation directly, which is usually associated with shallow ventilation during the exercise phase leading to hypoxia. in the left to right shunt, the pulmonary venous blood predominately enters the pulmonary circulation relative to deep ventilation and o2 uptake during the resting phase (shelton and burggren, 1976). our observations of ridleys and hawksbills during phases of nesting showed that they go through bursts of exhaustive and forceful exercise which usually last less than one minute, but occasionally exceeded that. during this time, the turtles breathe very shallow as the throat muscles are not strongly contracting, evidenced by the lack of deep breathing movements. the extended turtle neck during exercise gives the observers the advantage of watching muscle movements. in addition, the heavy weight of the turtle compresses the thoracic region, making terrestrial breathing laborious and difficult, particularly during digging and burying activities. at rest, which is usually extended between a few seconds to over one minute, the turtle forcefully exhales a large air volume followed by ventilations. the exercise-rest cycles which occur in all phases of nesting activities are typical of intermittent breathers. stress, caused by rapid changes in environmental factors, can disrupt homeostasis and alter hormonal levels as well as other physiological and behavioral patterns through the neuroendocrine system. these changes are means of adjustment which eventually combat stress and restore homeostasis. more specifically, stress can activate the hypothalamo-pituitaryadrenal (hpa) axis that results in an increase in catecholamines, glucocorticoids, glucose and other blood components (chrousos and gold, 1992). the olive ridley and the hawksbill develop apnea, accompanied by hypercapnia, acidemia and hypoxia, which are associated with anaerobic metabolism. these conditions were also reported in the nesting green turtles, chelonia mydas (al kindi et al., 2000b). these physiological conditions are found in vertebrates, which undergo short bursts of exhaustive exercises, especially in intermittent ventilators and have been reported in fishes (jensen, 1987; bouissou et al., 1987; tang and boutilier, 1988; hughes et al., 1988; van raaij et al., 1996), in birds (le maho et al., 1992) and in turtles (wasser and jackson, 1991; west et al., 1992; comeau and hicks, 1994; johnson et al., 1998). the remarkable similarities between the two species in all of the parameters suggest that both species require the same physiological adjustments during the nesting process. the behavioral adjustments such as the short burst of strenuous exercise followed by recovery may be an important survival strategy, under the control of the neuroendocrine system. moreover, both species require the same ecological conditions during nesting, as is reflected in their behavioral and physiological requirements. 5. acknowledgments this research is supported, in part, by grant number (ig/sci/biol/01/99), deanship of postgraduate studies and research, sultan qaboos university and by the fulbright program awarded to prof. ibrahim younis mahmoud, u.s.a. and by the directorate general of wildlife and nature conservation, the ministry of regional municipalities and environment of the sultanate of oman. special thanks to richard wilbur, public affairs officer, embassy of the 16 physilogical and behavioral adjustments united states of america in muscat, oman. also special thanks to chris batchelor and helen due boje for their technical assistance. references alkindi, a.y.a., brown, j.a., waring, c.p. and collins, j.e. 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(1994). adrenergic anc cholinergic regulation of intracardiac shunting. physiol. zool. 67(6): 1325-1346. hughes, g.m., le bras-pennec, y., pennec, j.p. (1988). relationships between swimming speed, oxygen consumption, plasma catecholamines and heart performance in rainbow trout (s. gairdneri r.). exp. biol. 48: 45-49. 17 a.y.a. alkindi, i.y. mahmoud and fatma al-siyabi le maho, y., karmann, h., briot, d., handrich, y., robin, j.p., mioskowski e., chrel, y., farni, j. (1992). stress in birds due to routine handling and a technique to avoid it. am. j. physiol. 263 (regulatory integrative comp. physiol. 32): r775-r781. matt, k.s., m.c. moore, r. knapp and i.t. moore (1997). sympathetic mediation of stress and aggressive competition: plasma catecholamines in free-living male tree lizards. physiology and behavior 61: 639-647. pough, h.f. and andrews, r.m. (1985). use of anaerobic metabolism by free-ranging lizards, physiol. zool. 58: 205-213. owens, d.w. and ruiz, g.j. (1980). new methods of obtaining blood and cerebrospinal fluid from marine turtles. herpetologica 36: 17-20. shelton, g. and burggren, w.w. (1976). cardiovascular dynamics of the chelonia during apnea and lung ventilation. j. exp. biol. 64: 323-343. shelton, g., jones, d.r. and milsom, w.k. (1986). control of breathing in ectothermic vertebrates. pp. 857-901. in. n.s. sheriniack and j. g. widdicomb, eds. handbook of physiology. section 3, the respiratory system. vol. 2, control of breathing. american physiological society, bethesda, md. stratakis, c.a. and chrousos, g.p. (1995). neuroendocrinology and pathobiology of the stress system. ann. ny acad sci 771: 1-18. tang, y. and boutilier, r.g. 1988. correlation between catecholamine release and degree of acidotic stress in trout. am. j. physiol. 255: r395-r399. wasser, j.s. and jackson, d.c. (1991). effects of anoxia and graded acidosis on the levels of circulating catecholamines in turtles. respiratory physiology 84: 363-377. west, n.h., butler, p.j., bevan, r.m. (1992). pulmonary blood flow at rest and during swimming in the green turtle (chelonia mydas). phsyiological zool. 65(2): 287310. wilson, m.a., gatten, r.e. and greenberg, n. (1990). glycolysis in anolis carolinensis during agonistic encounters. physiol. behav. 48: 139-142. valverde, r.a., owens, d.s. mackenzie and amoss, m.s. (1999). basal and stress-induced corticosterone levels in olive ridley sea turtles (lepidochelys olivacea) in relation to their mass nesting behavior. j. exper. zool. 384: 652-662. van raaij, m.t.m., pit, d.s.s. balm, p.h.m. steffens, a.b. and van den thillart, g.e.e.j.m. (1996). behavior strategy and the physiological stress response in rainbow trout exposed to severe hypoxia. horomones and behavior 30: 85-92. received 28 march 2001 accepted 22 february 2003 18 physiological and behavioral adjustments relative to catecholamine levels during nesting in olive ridley (lepidochelys olivacea) and hawksbill (eretmochelys imbricata) sea turtles in masirah island, oman. a.y.a alkindi, i.y. mahmoud and fatma al-siyabi department of biology, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, email: aakindy@squ.edu.om. methods 2.1 study area 2.2 animals blood analysis results discussion references state-of-the-art review of collapsing soils science and technology, 6(2001) 21-34 ©2001 sultan qaboos university selection of liner materials and design of hazardous water facilities in saudi arabia *sahel n. abduljauwad and #ali m. dakkak *department of civil engineering, king fahd university of petroleum and minerals dhahran 31261,saudi arabia, #department of economics, king abdulaziz university, jeddah 21422, saudi arabia. اختيار وتصميم مواد تبطين مكائن التخلص من الفضالت الخطرة في المملكة العربية السعودية ساهيل عبدالجواد وعلي دكاك وقد تم انشاء عدة مصافى ومصانع . ا من الفضالت واسع االعربية السعودية قَْد انتج طيف المملكة سريع في التَطَّور ان ال :خالصـة ـ العقد بتروكـيماويات خـالل اتصميم صحيح لُمَعالََجته لحتاُج كثيرة ت ساّمة فضالت الّصناعاِت قَْد انتجتْ وهذه ، ينلماضـي ن ا ي ويقع أحد هذين . الثنين من مواقع التخلص من الفضالت الخطرة تبطينتصميم وإختيار مواد هذه الورقِةوتتناول . التخلص منهاو وصفا الورقة هذه َستُقّدُم و. الثاني في الجزِء الغربيِ يوجد دية، بينما العربية السعو الموقعيـن فـى الواليات الشرقية من المملكة .طبيعية والصناعية ونظام جمع وازالة عصارة الفضالتال تربة عن مباطن الفصال مكامال abstract: rapid development in saudi arabia has produced a broad spectrum of wastes. in the last two decades, several refineries and petrochemical industries have been established. these industries have produced sludges and other toxic wastes which need proper planning for their handling and disposal. this paper covers design and selection of liner materials for two hazardous waste disposal sites. one of them is located in the eastern province of saudi arabia, while the second one is located in the western part. the paper will present complete design details of the natural compacted and geosynthetic soil liners and the leachate collection and removal system for primary liners and leak detection/leachate collection and removal system for secondary liners. 1. introduction landfill will remain a significant component of hazardous waste management practice. landfill is often used for residues from other treatment or disposal technologies/processes. as a result of serious environment and health problems with old and abandoned dump sites and the very high costs associated with cleanup measures at contaminated sites, the concepts of a specially engineered landfill have been introduced where wastes are segregated in a site which is selected for its natural containment properties and then engineered so as to isolate the wastes as far as possible from the environment. a landfill for hazardous waste is considered a technology of last resort to be used after every effort has been made to reduce, mitigate or eliminate the hazards posed by such wastes. the disposal of hazardous wastes is a global problem. rapid development in saudi arabia has produced a broad spectrum of wastes. in the last two decades several refineries and petro-chemical industries have been established. these industries have produced sludges and other toxic wastes which need proper planning for their handling and disposal. the kingdom is fortunate in that environment concerns were recognized at an early stage of industrial development. this resulted in the establishment of agencies such as meteorology and environmental protection administration (mepa) and the royal commission for jubail and yanbu to regulate industries so that environmental damages are minimized. compacted soil liners have been used for many years as engineered hydraulic barriers for waste-containment facilities (u.s. environmental protection agency, 1985). compacted soil liners 21 sahel n. abduljauwad and ali m. dakkak are frequently used in conjunction with geomembrane to form a composite liner, which usually consists of geomembrane placed directly on the surface of a compacted soil liner. the thickness of soil liners is usually between 600 and 900 mm, but occasionally the thickness may reach 1.2-3.0 m. compacted soil liners are composed of clayey materials that are placed and compacted in layers called lifts. the materials used to construct soil liners include natural soils, bentonite, soil blends and other materials. the most common type of compacted soil liners is one that is constructed from naturally occurring soils that contain a significant quantity of clay soils that are classified as cl, ch, or sc in the unified soil classification system (uscs) outlined in astm d-2487. soil liner materials are excavated from borrow pits, which may be located either on or off-site. the soil in the borrow pit may be used directly without processing or may be processed to alter the water content, break down large pieces of materials, or remove oversized particles (abduljauwad, 1994). a survey was conducted to find suitable materials that can be used as soil liners. in the eastern province, it has been found that suitable materials are unavailable locally. however, local soils can be blended together to achieve the requirement. two types of marl were mixed together with percentages of 30% and 70%. the geotechnical properties of the mixture, compaction curves and the variation in hydraulic conductivity with moisture content indicate that the mixture satisfies all specifications for a soil liner with a hydraulic conductivity of 1 × 10−8 cm/sec and a reasonable plasticity, which will not be difficult to work with in the field (abduljauwad, 1993). for the western province facility, seven types of clay samples were collected and subjected to complete laboratory geotechnical investigation. the laboratory tests include grain size analysis, atterberg limits, compaction, hydraulic conductivity, shear strength, x-ray diffraction analysis, organic matter, and soil ph (abduljauwad, 1998). results indicate that soil no. 1 collected from nwabah is quite suitable material that can be used as a soil liner. however, since this soil contains large clods, it should be processed prior to its use in the construction of the low permeability layer by pulverizing such clods. this paper covers site selection, design and selection of liner material for disposal sites. 2. material selection and specifications soil liner materials are selected so that a low hydraulic conductivity will be produced after the soil is remolded and compacted. although the performance specification is usually hydraulic conductivity, construction quality assurance considerations dictate that restrictions should be placed on certain properties of the soil used to build a liner. for example, limitations may be placed on the liquid limit, plastic limit, plasticity index, percent fines, and percent gravel allowed in the soil liner material. also, compatibility of the waste in contact with the liner should be investigated. the process of selecting construction materials and verifying the suitability of the materials varies from one project to another. in general, the process is as follows (u.s. environmental protection agency, 1985): 1. a potential borrow source is located and explored to determine the vertical and lateral extent of the source and to obtain representative samples, which are tested for properties such as liquid limit, plastic limit, plastic fines, etc. the borrow source should also be checked for the presence of deleterious materials such as roots, organic matter, and debris. 2. once construction begins, additional observations and tests may be performed in the borrow pit to confirm the suitability of materials being removed. 3. after a lift of soil has been placed, additional construction quality assurance tests should be performed for final verification of the suitability of the soil liner materials. a variety of tests is performed at various stages of the construction process to ensure that the soil liner material conforms with specifications. however, tests alone will not necessarily ensure an adequate material; observations by qualified construction quality assurance personnel are essential to confirm that deleterious materials (such as roots, wood, organic matter, rocks, stones, bricks, 22 selection of liner materials and design of hazardous waste facilities construction or demolition debris, or other unacceptable materials that are not allowed in the specifications) are not present in the soil liner material. some soil liner materials must be processed prior to use. the principal preprocessing steps that may be required include the following: drying of soil that is too wet, wetting of soil that is too dry, removal of oversized particles, pulverization of soil clods, homogenization of a nonuniform soil, and addition of bentonite. tests are performed by construction quality assurance personnel to confirm proper preprocessing, but visual observations are needed to confirm that proper procedures have been followed and that the soil liner material has been properly preprocessed. the criteria for choosing a clay is primarily based on the recompacted hydraulic conductivity achievable under field conditions (daniel, 1990). a clay that can be compacted to obtain a low hydraulic conductivity (1 × 10−7 cm/sec or less) sample when compacted to 90-95% of the maximum proctor’s dry density at wet of optimum moisture content is chosen for a landfill liner construction. note that clay with a high liquid limit (ll) tends to develop more desiccation cracks, clay with a very low plasticity index (pi) or plastic limit (pl) is less workable, and a well-graded soil is expected to develop low hydraulic conductivity when compacted properly. therefore, the pi, ll, and some minimum requirements regarding grain size distribution should be specified. inorganic clays of medium plasticity are best suited for liner construction. usually a soil with the following specifications would prove suitable for liner construction (daniel, 1993): ll greater than or equal to 30%, pi greater than or equal to 15%, 0.074 mm and less fraction (p200) greater than or equal to 50%, and clay fraction greater than or equal to 25%. the minimum percentage compaction (usually 90-95% of the maximum modified proctor’s density) should be specified. to obtain better kneading action and lower hydraulic conductivity, all compaction must be done at wet of optimum moisture. note that the shape of the grain size distribution curves should be studied to confirm that they are close to an “inverted s” shape. the specifications regarding atterberg limits and grain size percentages are also helpful in quality control during construction. in reality, it may be difficult to obtain clay that will satisfy all the specifications described above. field experience indicates that clayey soil with the following values can also be compacted to obtain a low hydraulic conductivity liner: pi between 10 and 15%, ll between 25 and 30%, 0.074 mm or less fraction between 40 and 50%, and clay content between 18 and 25%. however, it is prudent to perform field trials for such marginal clayey soils. 3. compacted soil liners a survey was conducted in both eastern and western provinces of saudi arabia (in the vicinity of the construction sites) to find suitable natural materials that can be used as soil liners. in the eastern province of saudi arabia, it has been found that suitable materials are unavailable locally, so local soils will be blended together to achieve the required low hydraulic conductivity. a plastic marl was found that could be used for the compacted soil liner. one should be cautious about using highly plastic soils (soil with plasticity indices > 30%) because these materials form hard clods when the soil is dry and are very sticky when the soil is wet. highly plastic soils, for these reasons, are difficult to work with in the field. however, special techniques such as addition of lime or other type of soil, can alleviate some of the problems with construction utilizing highly plastic soils so that even these soils may be usable. figure 1 shows the grain size distribution for different types of marl collected from the eastern province of saudi arabia. marl # 1 has a plastic limit, liquid limit and plasticity index of 75%, 135% and 60%, respectively, while all other marls are nonplastic. a 30% of marl # 1 was mixed with 70% of marl # 2 to overcome the problem of high plasticity of marl # 1. the mixture has a plasticity index of 11%. the compaction curves and the variation in hydraulic conductivity with moisture content for marl # 1 and marl # 2 and their mixtures are shown in figures 2 and 3, respectively. marl # 1 satisfies all the requirements for soil liner, but have very high plasticity and low strength. it is very clear that the mixture satisfies all specifications for a soil liner with a reasonable plasticity, which will not be difficult to work with in the field. 23 sahel n. abduljauwad and ali m. dakkak in the western province of saudi arabia, a survey was conducted (in the vicinity of the construction site) to find a suitable natural material that can be used as a soil liner. bulk samples were collected from seven different areas. table 1 shows the locations from which the samples were collected and summarizes the visual description of samples. the collected samples were air dried and pulverized until all soil aggregations were reduced to minus 40 sieve size. samples were subjected to the following testing program: grain size analysis (sieve analysis & hydrometer tests, astm d-421 & astm d-422), atterberg limits (astm d-4318), moisture-density relationship (standard & modified proctor compaction tests, astm d-698 & astm d-1557), hydraulic conductivity tests (constant head, astm d-2434 and flexible wall permeameter, astm d-5084), unconfined compression test (astm d-2166), x-ray diffraction analysis (xrd), organic matter and soil ph. sieve number #8 0 #6 0 #2 00 #1 00 #1 40 #2 0 #4 0 1/ 2 3/ 8 3/1 4 1. 5 2 #4 #1 3 100 marl # 6 marl # 4 marl # 2 marl # 5 marl # 3 marl # 1 80 % p as si ng 60 40 20 0 1e-1 1 0.1 1e+1 1e+2 grain size, mm figure 1. grain size analyses of different types of marls for the eastern province of saudi arabia. 1.40 60 1.00 1.20 1.60 1.80 5040302010 marl # 1 marl # 2 mixed 30 % # 1 + 70 % # 2 d ry d en si ty , g /c m 3 water content, % figure 2. compaction curves of marl # 1 and marl # 2 and their mixture. 24 selection of liner materials and design of hazardous waste facilities 4 x 10-7 605040302010 mixed marl marl # 2 marl # 1 h yd ra ul ic c on du ct iv it y cm /s 3 x 10-7 2 x 10-7 1 x 10-7 0 water content, % figure 3. comparison of hydraulic conductivity curves for marl 1, 2 and the mixture. the sieve and hydrometer analyses were conducted to determine the grain size distribution as depicted in figure 4. the percentage of fines (the fraction of soil on a dry-weight basis that passes through the opening of the no. 200 sieve, opening size = 0.075 mm) for all samples exceeded 80%. many regulatory agencies require at least 50% fines. also, the maximum particle size for all samples does not exceed 2 mm and construction specifications usually restrict the maximum allowable particle size between 25 mm and 50mm for compaction consideration, but which may be much less for protection against penetration of an adjacent geomembrane. the clay content (the percentage of soil that has an equivalent particle diameter smaller than 0.002 mm) is a very important parameter that influences the hydraulic conductivity of soil. the clay contents for samples 1 to 7 are 70%, 56%, 20%, 16%, 20%, 48% and 48%, respectively. soils must have at least 10−20% clay in order to be capable of being compacted to a hydraulic conductivity of ≤ 1 × 10−7 cm/sec. sample no. 1 has the maximum percentage of clay size particles. table 1: locations and summary of visual description. sample no. location color description 1 nwabah greenish grey homogeneous, stiff bulk samples 2 rabegh-1 dark brown non-homogeneous, stiff blocks with major silt intrusion 3 rabegh-2 light brown non-homogeneous, block samples with major silt intrusion 4 al-yatma light brown to yellowish silty clay, intrusion of roots and plant leafs 5 al-mashenea light brown to yellowish silty clay, intrusion of roots and plant leafs 6 al-madinah dark brown homogeneous medium clay lumps 7 al-madinahalaqool light brown homogeneous desiccated clay 25 sahel n. abduljauwad and ali m. dakkak #2 00 #1 40 #1 00 astm sieve no.#6 0 grain size, mm #2 0 100 80 0.100 0.010 0.001 #1 0 #3 0 #4 0 p er ce nt p as si ng 60 legand hydrometer analysis sieve analysis 40 curve for sample 1 curve for sample 2 curve for sample 3 20 curve for sample 4 curve for sample 5 curve for sample 6 curve for sample 7 0 10.000 1.000 figure 4. grain size distribution curves for the samples. the plasticity characteristics of a soil are quantified by atterberg limits (liquid & plastic limits) and plasticity index. table 2 summarizes liquid limit, plastic limit and plasticity index for the investigated soil samples. the liquid limit and plasticity index of samples nos. 1, 2, 3 and 6 satisfy the required specification of soil liner materials (ll ≥ 30% & pi ≥ 15%) that can be compacted to obtain the low hydraulic conductivity of 1 × 10−7 cm/sec. table 2: summary of liquid limit, plastic limit and plasticity index for investigated soils. sample id # 1 # 2 # 3 # 4 # 5 # 6 # 7 liquid limit % 53.50 44.00 63.50 27.20 26.80 41.60 35.70 plastic limit 26.89 25.71 33.05 25.27 23.74 26.31 24.96 plasticity index 26.61 18.29 30.45 1.93 3.06 15.29 10.74 1.90 5.00 10.00 15.00 20.00 25.00 sample no. 1 sample no. 2 sample no. 3 sample no. 4 sample no. 5 sample no. 6 sample no. 7 legend d r y d e n si t y g m /c m 3 1.80 1.70 1.60 moisture content figure 5. compaction curves for investigated soils. the largest maximum dry density of 1.87 g/cm3 at an optimum moisture content of 13.85% was observed for sample no. 2, while the smallest maximum dry density of 1.71 g/cm3 at an optimum 26 selection of liner materials and design of hazardous waste facilities moisture content of 19.8% was observed for sample no. 3 (figure 5). it should be stated that sample no. 3 has the largest plasticity index of all investigated samples. sample no. 1 has the maximum dry density of 1.78 g/cm3 at an optimum moisture content of 17.75%. hydraulic conductivity of soils is measured in the laboratory with either rigid or flexible wall permeameters. in this study, both the constant head test and flexible wall permeameter, with a back pressure, were used to estimate the hydraulic conductivity of investigated soils. both methods gave almost consistent identical results. figures 6 and 7 compare the hydraulic conductivity for the investigated samples. the lowest value of 1.8 × 10−9 cm/sec was obtained for sample no. 2 and the largest value of 4.77 × 10−7 cm/sec was obtained for sample no. 5. sample no. 1 has a minimum hydraulic conductivity of 4 × 10−9 cm/sec at a water content of 21%. 2515 20 moisture content % 10 1e-6 8e-7 9.60e-7 9.20e-7 8.80e-7 8.40e-7 6e-7 7.60e-7 7.20e-7 6.80e-7 6.40e-7 4e-7 5.60e-7 5.20e-7 4.80e-7 4.40e-7 2e-7 3.60e-7 3.20e-7 2.80e-7 2.40e-7 0e+0 1.60e-7 1.20e-7 8.00e-8 4.00e-8 sample no. 4 sample no. 5 sample no. 6 sample no. 7 legend 8.00e-9 1.20e-8 2.80e-8 3.20e-8 4.80e-8 5.20e-8 6.80e-8 7.20e-8 8e-8 7.60e-8 6e-8 5.60e-8 6.40e-8 4e-8 3.60e-8 4.40e-8 2e-8 1.60e-8 2.40e-8 0e+0 4.00e-9 2515 20 moisture content % 10 sample no. 1 sample no. 2 sample no. 3 legend figure 6. comparison of hydraulic figure 7. comparison of hydraulic conductivity curves for sample no.1,2&3 conductivity curves for sample no.4,5,6&7 a critical step in design of a compacted soil liner is the determination of the range of acceptable water content and dry unit weight values of the soil. table 3 summarizes the unconfined compressive strength for the seven soil samples at their optimum moisture contents. the maximum strength of 1500 kpa was obtained for sample no. 6, while the minimum value of 680 kpa was obtained for sample no. 4. the unconfined compressive strength for sample no. 1 at the optimum moisture content is 1460 kpa. figure 8 shows the effect of molding water content on the unconfined compressive strength of sample no. 1. it can be observed that samples compacted dry of optimum have higher strengths than those compacted wet of optimum. therefore, it is very important that these results should be analyzed with compaction curve and hydraulic conductivity curves to decide on an acceptable range of water contents that should be used for the compaction of a soil liner in the field. based on the results of all geotechnical tests, it can be seen that samples no. 1 and 2 satisfy all requirements for a good soil liner material. however, as indicated earlier, the borrow area of sample no. 2 contained a large amount of blocks of silty soil and, therefore, the soil is not homogeneous. thus, sample no. 2 was excluded and sample no. 1 is the best candidate for the soil liner material. this sample satisfies grain size, plasticity, compaction, hydraulic conductivity and strength requirements. it is very important to specify the range of water contents that should be used in the construction of a soil liner in the field. it was explained earlier that it is usually preferable to compact the soil wet of optimum to minimize hydraulic conductivity. however, the soil must not 27 sahel n. abduljauwad and ali m. dakkak be placed at too high a water content. otherwise, the shear strength will be too low. there may also be a great risk of desiccation cracks forming if the soil dries, which is very much possible due to the very high temperature at the construction site, and ruts may form when construction vehicles pass over the liner. figure 8 shows the acceptable zone, which represents the zone of acceptable water content/dry unit weight combination: the maximum dry density = 1.78 g/cm3 the minimum acceptable dry density = 1.69 g/cm3 the acceptable range of water content 18% ≤ w ≤ 21% table 3: unconfined compressive strength. sample no. 1 2 3 4 5 6 7 moisture content % 17.75 13.85 19.80 18.20 16.00 18.50 17.50 unconfined compressive strength kpa 1460 960 1000 680 860 1500 1320 with these specifications, the maximum laboratory hydraulic conductivity and the minimum unconfined compressive strength will be 2.8 × 10−8 cm/sec and 800 kpa, respectively. furthermore, soil no. 1 was subjected to two more tests including organic matter and x-ray diffraction analysis to confirm its complete suitability as a liner material. the organic matter was estimated using potassium dichromate acid digestion method (handbook of agronomy). a very low value of 0.00236% was obtained. the x-ray analysis indicated that the mineralogical composition of the sample was as follows: 50% quartz (sio2), 25% chlinochlore [(mg,fe)6(si,cr)4o10(oh)8], 18% albite [(na,ca)al(si,al)3o8], 5% palygorskite (mgalsio4o10(oh).4h2o), and 2% halite (nacl). all minerals present in the sample are quite stable ones. the soil ph is 6.83. it should be emphasized that since soil no.1 consists of large bulk (clods), it should be processed at the construction site by pulverizing the soil, utilizing special clay crushing equipment. after adjusting the water content of soil, it should be compacted by heavy footed compactors with large feet that fully penetrate a loose lift of soil. 4. design of landfill the landfill in the eastern province of saudi arabia will be designed using 80 mil high density polyethylene (hdpe) geomembrane/clay composite liner. a double liner system will be used with a leachate collection layer located above the primary liner and a leak detection layer located between the two liners. a 1 m compacted soil liner (a mixture of 30% of marl # 1 and 70% of marl # 2) will be used between the natural soil and the secondary liner. the landfill will be constructed 3 m above the compacted soil liner (area method). above-ground landfills have the advantage that leachate can be drained by gravity, the facility is conspicuous and therefore is not easily forgotten and ignored, and construction of liner and drainage system components occurs on more or less level ground, which simplifies the construction. the mixture of marl # 1 and marl # 2 will be placed in a loose lift 200−300 mm thick. the water content will be adjusted to achieve the required dry density to satisfy the hydraulic conductivity requirements. heavy compactors will be used. the weight of compactors should not be so heavy that it becomes bogged down in the soil. the dry density, moisture content and hydraulic conductivity tests of the compacted soil liner were conducted for quality control purposes. a large number of density and moisture content tests were conducted during construction to ensure uniformity. furthermore, three in-situ hydraulic conductivity tests were conducted following the procedure 28 selection of liner materials and design of hazardous waste facilities discussed earlier. all tests gave an average hydraulic conductivity of 1.36 × 10−7 cm/sec which is 6.8 times greater than the laboratory hydraulic conductivity (2 × 10−8 cm/sec). this result was expected and is quite satisfactory. legend unconfined compressive strength permeability 8.00e-9 1.60e-8 2.40e-8 3.20e-8 4.80e-8 5.60e-8 6.40e-8 7.20e-8 8.00e-8 4.00e-8 0.00e+0 25201510 400 800 1200 1600 1. sample no acceptable zone 1.6 1.7 1.8 2515 20 moisture content 10 d r y d e n si t y g m /c m 3 u n c o n f in e d c o m p r e ss iv e st r e n g t h q u (k p a) p e r m e a b il it y ,k (cm /s) moisture content figure 8. acceptable zone for field compaction chlinochlore [(mg,fe)6(si,cr)4o10(oh)8], 18% albite [(na,ca)al(si,al)3o8], 5% palygorskite (mgalsio4o10(oh).4h2o), and 2% halite (nacl). all minerals present in the sample are quite stable ones. the soil ph is 6.83. to achieve a good composite action, the geomembrane was placed against the soil with good intimate contact. if stones of a size and shape that could puncture the geomembrane exist in the soil liner, the stones will be removed. to achieve an intimate contact, the surface of the compacted marl on which the geomembrane is placed should be smooth rolled with a steel-drum roller. this will be followed by the construction of the leak detection and removal system, the primary liners, and the primary leachate collection and removal system. to avoid the accumulation of leachate at the bottom of the landfill, the primary leachate collection area is graded into a series of sloped terraces. the terraces are shaped so that the leachate that accumulates on the surface of the terraces will drain to leachate collection channels. perforated pipe will be placed in each leachate collection channel to convey the collected leachate to a sump, from where it is removed for re-application to the surface of the landfill after mixing with sand (abduljauwad, 1993). the facility will be above the ground disposal site, a side slope of 3 to 1 (horizontal to vertical) will be used. a trench will be dug on the berm and the geomembrane liners will be inserted in the 29 sahel n. abduljauwad and ali m. dakkak trench for anchoring. the dimensions of the trench need to be calculated so that pullout does not occur. the possibility of potential instability that could occur in the foundation soil, the refuse, or the cover was evaluated prior to the construction of the facility. figures 9 to 11 show complete design details for the proposed landfill. leak detection pit 54m 34m9m 9m1m 1m 54 m 34 m 9m 9m 1m 1m a 3% slope 3% slope 3% slope a 3% slope bb figure 9. plan view of the landfill constructed in the eastern province. the class i landfill at yanbu of the western province of saudi arabia was designed in accordance with the resource conservation and recovery act (rcra), subpart 264 (1995). the landfill consists of a double lined waste containment cell, waste space and landfill cap. a soil fill material has been previously placed on the site at yanbu. the soil fill was placed to an elevation of 1.5 m (above sea level) and compacted. this should ensure that the site is above the flood plain and above the high groundwater table. the landfill will be constructed above the elevation of 1.5 m to ensure that hydrostatic pressure is not exerted against the geomembrane liners in the waste cell. therefore, the landfills will be constructed upward and cannot be constructed below grade. the double lined waste containment cell consists of the following from top to bottom: soil protection layer, geotextile, sand drainage layer, 60 mil hdpe liner, composite drainage net, 60 mil hdpe liner, geosynthetic clay liner (gcl), low permeability layer (compacted clay), and soil fill material (previously placed). soil no. 1 collected from nwabah will be used for the low permeability layer. following construction of the compacted soil layer, a gcl shall be utilized to help ensure waste cell containment integrity the gcl has a very low permeability (1 × 10−9 cm/sec) and will act as a supplement to the compacted soil layer. the gcl shall be prehydrated and covered immediately to minimize the loss of moisture. the gcl should also be needle punched to eliminate the danger of free swell. primary and secondary geomembrane liners will be utilized within the waste cell for dual containment. hdpe liner material was chosen to line the waste cell due to the material’s excellent chemical resistance properties. smooth liner material will be placed along the landfill bottom and textured liner material will be placed along the sideslopes and ramps. a thickness of 60 mils will be required for both containment layers. 30 selection of liner materials and design of hazardous waste facilities a composite drainage net will be used along the landfill bottom as part of the secondary leachate collection system and along the sideslopes as the primary and secondary leachate collection systems. along the bottom of the landfill, the composite drainage net will be sandwiched between two layers of hdpe liners. along the sideslopes of the waste containment cell, the secondary composite drainage net will also be between the two geomembranes. 1m ∅10 cm hdpe pipe 0.50 % slope ∅ hdpe primary liner { 200 g/m non-woven geotextile 2mm. thick sa nd l ay er s compacted marl 2mm. thick hdpe secondary liner non-woven geotextile detail bdetail a leak detection pit 1.00x1.00x1.00 m hdpe pipe 10 cm 3 1 1 3 0.50% slope detail a 2mm. thick hdpe liner concrete wall 15cm15cm 1.00m 1. 00 m 20cm detail b figure 10. section a-a through the berm, the composite liners and leachate collection system. ∅10 cm. hdpe pipe 200 g/m non-woven geotextile 25cm sand layer k<0.01cm. sec. 2mm thk. hdpe secondary liner 25 cm 25 cm 30cm 20cm 3% slope 60cm compacted 45cm 2mm thk. hdpe primary liner 200 g/m non-woven geotextile figure 11. details of the primary and secondary leachate collection system (section b-b). the primary drainage net will lay on the surface of the primary geomembrane. the primary composite drainage net will be covered immediately by a sacrificial geotextile layer to minimize uv degradation of the geotextile on the composite drainage net. the sacrificial geotextile will remain in-place until the waste is placed vertically along the sides of the waste cell. at that time, it may be removed or left in-place (figure 12). a sand drainage layer shall be placed on top of the primary geomembrane liner. sand material was chosen in lieu of a composite drainage net due to its ability to provide additional protection to underlying geosynthetic layers. the sand drainage layer shall be sloped to promote drainage toward the leachate collection and detection systems. preliminary hydraulic conductivity testing 31 sahel n. abduljauwad and ali m. dakkak shall be performed on the sand material prior to mobilization of material to the site. the sand material shall have a hydraulic conductivity greater than or equal to 1 × 10−2 cm/sec and less than 5 percent fines. plan a-section a b-section b waste lift (depth varies) top of separation berm el 4.5 prim ary g eosynthetic l iner se co nd ar y g eo sy nt he tic l in er 30cm. sand drainage layer geosynthetic clay layer single composite drainage net 60 mil. smooth hdpe liner compacted subgrade separation berm fill secondary leachate collection system primary leachate collection system 25mm. non-angular gravel material 30.5mm dia. hdpe collection pipe 30cm. soil protection layer non-woven geotextile (400g/m2) 60 mil. smooth hdpe liner 60 mil. hdpe scrub liner2% slope 2% slope non-woven geotextile (100g/m2) geotextile fabric (100g/m2) 0.6m low permeability layer1 1 1 1 1.5m bb a a leachate detection and collection sump boundary berm 3 : 1 slope 3 : 1 top of separation berm 3: 1 sl op e 3: 1 sl op e 2% 2% 2%2% cell 1 cell 2 secondary geosynthetic liners primary geosynthetic liners 3:1 3:1 separation berm fill waste lifts (depth varies) top of separation berm el= 4.5 natural site sub grade drainage net 60mil . smooth hdpe liner gcl geotextile fabric gcl . smooth hdpe liner non-woven geotextile 1.50m fill material 0.60m low permeability layer 0.30m sand drainage 0.30m soil protection figure 12. design details for hazardous waste landfill in the yanbu area. 32 selection of liner materials and design of hazardous waste facilities a soil protection layer will be required to be placed above the sand drainage layer. the soil protection layer will provide additional protection to the geosynthetic layers and prevent clogging of the sand drainage layer. the soil protection layer will be 0.3 m in depth. a thin geotextile will be placed between the soil protection layer and the sand to prevent mixing of the two materials. the initial waste layer shall be placed above the soil protection layer in a 0.6 m lift. following placement of the initial waste lift, subsequent waste lifts shall be placed at a depth of 30 cm. they shall be consolidated with compaction equipment. a minimum number of passes by the compaction equipment will be required to consolidate each waste layer. due to the unknown nature of waste entering the landfill, specific compaction requirements are not being specified. the final layer of waste will be required to be screened to less than 1.25 cm. this will be required to prevent punctures of the geosynthetic layers in the cap. waste will be placed within each of the landfill cells in a systematic manner. two cells were used for each landfill and a soil separation berm separates the cells (i.e., cells “a” and “b”). the hdpe liner runs beneath the separation berm and completely lines both cells to prevent leachate from escaping the landfill. the leachate collection systems for the landfills consist of sand, composite drainage net, gravel filled sumps, and leachate collection piping. sand bedding will lay on the top of the landfill bottom. the landfill bottom will be sloped toward leachate collection sumps at a minimum grade of 2 percent. a composite drainage net will be placed along each landfill sideslope to promote drainage to the leachate collection sumps. there are a total of six sumps within each landfill. hdpe pipe will be placed along the landfill sidewalls and enter the sumps. the hdpe pipe will then run continuously from one cell to an adjacent cell. this will allow for a contingency access point should it be needed. the hdpe pipe will be perforated on the bottom so that leachate may be pumped from each sump. a suction hose will be located within each hdpe sump pipe for pumping leachate from the sumps. figure 12 shows the complete design details for yanbu landfill. 5. conclusions due to rapid industrialization in the kingdom of saudi arabia, it has become necessary to develop waste disposal methods applicable to the local climatic conditions. also, there is a need to develop environmental awareness program in the region. suitable materials for soil liners are obtained by either blending two different types of marls or using an average plasticity homogeneous clay to achieve the required low hydraulic conductivity and good strength. 6. acknowledgements the authors acknowledge the financial support of environmental service company and almurjan environmental management & technology co. ltd. for conducting this work. the support of king fahd university of petroleum & minerals for the presentation of this paper is really appreciated. references abduljauwad, s.n. 1993. environmental impact assessment study of a proposed hazardous waste management facility in dammam, saudi arabia, report submitted to meteorology and environmental protection administration (mepa), jeddah, saudi arabia. abduljauwad, s.n. 1994. design, construction and monitoring of hazardous waste landfill, report submitted to meteorology and environmental protection administration (mepa), jeddah, saudi arabia. abduljauwad, s.n. 1998. selection of soil liner material for al-murjan landfills, report submitted to al-murjan environmental management & technology co. ltd., dammam, june. 33 sahel n. abduljauwad and ali m. dakkak daniel, d.e. 1990. summary review of construction quality control for compacted soil liners, proceedings of symposium on regulation, performance, construction, operations of waste contaminant system, san francisco, nov. 6-7, asce, new york. daniel, d.e. 1993. geotechnical practice for waste disposal, chapman & hall co., new york. u.s. code of federal regulations , 1995. 40 cfr 264, usupa, office of research and development, washington, d.c., u.s.a. u.s. environmental protection agency ,1985. draft minimum technology guidance on double liner systems for landfills and surface impoundments – design, construction and operation, epa/530-sw-014, office of solid waste and emergency response, washington, d.c., 70. received 4 march 2000 accepted 1 june 2000 34 çîêíçñ æêõãíã ãæçï êèøíä ãßçæä ç� introduction table 2: summary of liquid limit, plastic limit and plasticity index for investigated soils. table 3: unconfined compressive strength. design of landfill conclusions references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 31-43 © 2002 sultan qaboos university information security risks on a university campus amer a. al-rawas and s. millmore centre for information systems, sultan qaboos university, sultanate of oman. المخاطر المتعلقة بأمن المعلومات داخل الحرم الجامعي يف ميلمور تعامر عوض الرواس و س وذلك من خالل الخبرة في إدارة شبكة , يتعرض هذا البحث لدراسة األمن في أنظمة المعلومات داخل الحرم الجامعي :خالصة المعلومـات فـي جامعـة السلطان قابوس وعند دراسة المخاطر والتحديات التي تواجه القائمين على تقديم خدمات المعلومات أهمية المعلومات : ر عددا من الموضوعات المتداخلة ، وتشمل هذه الموضوعات اإللكترونـية ، يتعين علينا أن نأخذ في االعتبا وأنواع المخاطر التي تتعلق بتقديم خدمات المعلومات اإللكترونية , المستخدمة نوع المعلومات , لألفـراد داخـل الحرم الجامعي يقدم البحث عددا من التوصيات لتحسين أمن وبناء على مناقشة المخاطر في تقديم المعلومات اإللكترونية . للمجـتمع الجامعـي . وسـرية المعلومـات داخل الحرم الجامعي والتي يمكن أن تتبناها المؤسسات التعليمية التي تولي أمن المعلومات أهمية خاصة توصيات اجتماعية تتعلق بعادات , توصيات عامة للبيئة الجامعية بأسرها : إلـى ثالث فئات ويمكـن تقسـيم هـذه التوصـيات .وأخالقيات العمل عند أعضاء هيئة التدريس والطالب ، وتوصيات تقنية تتعلق بالخبرات والتقنيات الواجب توافرها abstract: this paper is concerned with issues relating to security in the provision of information systems (is) services within a campus environment. it is based on experiences with a specific known environment; namely sultan qaboos university. in considering the risks and challenges that face us in the provision of is services we need to consider a number of interwoven subject areas. these are: the importance of information to campus communities, the types of information utilised, and the risk factors that relate to the provision of is services. based on our discussion of the risk factors identified within this paper, we make a number of recommendations for improving security within any environment that wishes to take the matter seriously. these recommendations are classified into three main groups: general, which are applicable to the entire institution; social, aimed at the work attitudes of staff and students; and technical, addressing the skills and technologies required. keywords: security, information systems, campus environment. 1. introduction 1.1 information and the campus community c omputers, information systems, communication tools and networks all play an increasingly important part in our lives. they provide a wide variety of services to us, and there has been increasing recognition that they are key and integral to the prosperity of all developed and developing nations. this importance is recognised in some countries (white house, 2000; hansard, 1998; attorney general, 1999; hunter, 2000) that are implementing, or considering implementing, mechanisms to protect them. general security standard guidelines and policy documents have been developed. some have a very direct reference to higher education (joint information systems committee, 2001), others are more general applying to the internet community as a whole (fraser, 1997). in the government, commercial and industrial sectors there have also been efforts to formulate standards, on a national/international level (british standards bs7799, 1999; international standards organisation iso 17799). it is unclear if these latter standards have been applied to higher education, so whether they hold lessons for us is not known. 31 amer a. al-rawas and s.millmore if we consider education, and in particular higher education, specific issues related to information sharing arise. for example, a typical university environment consists of a single overall body (the institution itself) and is divided up into closely-knit communities of different sizes, large and small (faculties, departments, research teams, etc.). within and between these communities different kinds of information sharing takes place. thus within a university campus information exchange is, especially in the academic arena, a fact of life. universities are institutions that have many different roles in the wider community, however the most fundamental roles are research and education. these are built around information: its acquisition, storage, exchange and application. this means that they are highly dependent upon the utilisation of is. many universities have taken on-board the importance of information systems to the fulfillment of their academic responsibilities, and included them in their academic plans (san francisco state university, undated; university of leicester, 2000). the importance of information to universities is, in general, well recognised (harvard university, 1991). for the efficient and effective operation of the institution this information exchange should be encouraged and developed. given the signficant growth of it in the sector, along with the sharing culture, we need to consider the issues of the effective security management and control (elliot et. al., 1991; hassler, 1998; stamen, 1986). 2. types of information as with other educational bodies, a wide variety of information exists and is deployed within the campus. this information may be maintained, stored and communicated in many different ways. traditionally much is in hard copy i.e. paper format. this might include memoranda, reports, records and so forth. with the development and wide distribution of the ubiquitous pc a great deal of information has migrated from those ledgers onto the hard disks of computers. whether the minds and attitudes of the custodians of the data have made an equivalent change is another matter and is very relevant to the current issues under discussion. if we are to consider, in broad terms, the kind of data stored in university campus records, be they paper, or electronic, we can consider them to be of several particular types. these are: • administrative and infrastructure, • academic and research. within these broad classifications are a wide variety of different types of data. for example, looking at basic administrative data we might find: • university installations maintenance information, • staff, contracts and personnel details, • budgetory, financial, procurement and purchasing data, • minutes of senior, and not so senior, staff meetings. the list of broad administrative data recorded and maintained is extensive. similarly, if we were to consider the types of data retained under the academic umbrella, we might find: 32 information security risks on a university campus • student records, grades, academic plans, and reports, • examinations, past, present and future, • student project reports, • research data, interim programs and draft technical documents and papers, • library book holdings. again, there is a very wide variety of data and they may be retained in various forms of recording mechanism. frequently campus based institutions have close links with other bodies. in these cases other forms of data may be involved. for example when the university has a linked teaching hospital, as has squ, we should also consider the issue of hospital data. such data might include: • patient information, • clinical reports, including test reports, • administrative and financial information. there may also be commercial/business factors to be considered. for example, special contracts and agreements between the institution and external suppliers, sponsorship agreements or even business/academic partnership may exist. such agreements may imply quite specific needs in terms of confidentiality and integrity of information. the results of a commercially supported academic study program may, for example, be covered by commercial confidentiality agreements and have implication with respect to intellectual property or copyright laws. such agreements may even give commercial organisations rights with respect to the information security of the institution. such rights may extend to policies, procedures, audits and inspection. it is clear then that a wide variety of different types of data are retained in different records. some of this data may be highly confidential, and should only be seen by a limited number of authorised staff (for example, examination scripts), some may be public information (for example, library holdings), some may have controlled access (for example, collaborative research projects). in all cases there remains the issues of: access and control, information integrity, management, security, confidentiality, copyright, and other legal obligations. the need for proper maintenance of records, and data, in the correct and appropriate way, has not been changed by the introduction of electronic storage technologies. however, as personal computing and networks have developed the way data has been stored and is transmitted has gone through a revolution. consider table 1, technology and security relationships. studies have shown that the security issues attached to the use of information systems are real. for example in (university of california, 1998) they discuss the threats and risks to “campus computer and networks ...” along with the “integrity and confidentiality of data ...”. they have identified the needs that should be addressed when considering security (leach, undated), these needs include: • ensuring financial accountability, • use of it to reduce operating costs where possible, • prevention of unlawful use of resources, • minimising the burden of controls, • maintaining the security of academic work, • maintaining viability and goodwill. our studies are very much in-line with the comments made by these researchers. 33 amer a. al-rawas and s.millmore table 1: technology and security relationships. technology data security issues centralised host based systems closely controlled data, handled by professional staff. proprietary communications channel with limited general user access. personal computer desktop systems limited but localised access to data in departments by local staff. network based client/server controlled server based storage with data carried on a communications channel. intranet distributed computing model shared distribution of data transmitted over a local communications channel (lan). internet/extranet distributed computing model. shared distribution of data transmitted over a wide area communications channel (wan). the need, then, for security become more significant, more urgent, owing to the much wider potential for unauthorised access, misuse, and corruption. 3. security issues when we are considering the issues of information security we have specific objectives. these objectives are to ensure: • availability, is structures are there 100% of the time; • accuracy, data is faithfully, fully and correctly reproduced; • protected, data is not lost, damaged or corrupted; • privacy, information is only revealed to those who should have access. security of information, and information bearing is infrastructures, can be considered as being composed of a number of different parts. these are: • physical infrastructure components, which relate to where and how equipment is installed. • people, who access and utilise the information, • systems which are used to store and retain the accessed information, • communication technologies, used to gain access to and transport that information. in searching for a total security solution we need to address all of these issues. 3.1 infrastructure: physical access risks the first issue that must be addressed when looking at security is the physical layer. you must control strictly access to physical infrastructure and related plant and equipment. this means that protection of desktop computers from theft is not just the issue. we also need to carefully protect servers, including file, print, proxy, e-mail, web and related equipment. careful control over access to communication channels (network, telecommunications, server rooms, control rooms, data closets, cabling systems etc.) also needs to be exercised. for example, if an anti-social citizen gains access to a network control room that person may be able to reconfigure equipment to allow greater 34 information security risks on a university campus access to data resources than would otherwise be allowed. it may be possible to attach unauthorised equipment, monitor data flows, and crash systems. 3.2 people: social and geographical affinities universities, just like commerce, business and other elements of human activity, are run on people; even quite modest institutions might have a significant number of staff and large numbers of students. distance learning institutions might have extremely large student numbers, many accessing the institutions from outside. unlike organisations in trade and industry a very high percentage of the faculty, staff and the student body of a university will be expect to utilise is as a significant part of their activities. therefore higher education is predisposed to have significant numbers of is literate persons utilising the technology. people are a product of their culture, background, upbringing and the society in which they live. this means that the attitudes that they bring to important issues are formed by these lifestyles and societal influences. this is very much the case with respect to squ, since it contains a mix of faculty/staff from many different cultures, as well as students from all regions of oman. faculty, staff and students are brought together and their attitudes and affinities are such that considerable variation may be found in respect to: • work ethics, • social issues and related customs, • professional responsibilities, • privacy and security, • sharing and collaborative working. these individuals may have loyalties which are influenced by external factors. these may include: • social, tribal or national grouping; • research team, department or faculty membership. farthermore these loyalties may be stronger and more important to them then those that they have towards the institution as a whole. in recognition of the importance of these issues many professional organisations have established and published codes governing ethics in the industry (illinois institute of technology, undated). while these issues are not unique in any way to this institution they are certainly of importance when assessing our is security needs. for example, within the arab world there is very much a culture of sharing and openness between social groups, and this means that matters relating to confidentiality and security of system passwords and usernames are relevant. not to share such knowledge might be considered in some groups to be antisocial, and yet this cannot be permitted since we need to protect sensitive data and vulnerable systems. when we are considering information systems security, trust is important. there needs to be trust in the custodians of the data, as well as those who administer and utilise that data. if the loyalties of staff are more orientated towards the social groups than towards the institution then this trust will be misplaced. it is therefore important to ensure that these “trust relationships” are established properly. along with the issue of trust there is also the matter of what are the acceptable and proper ways that information can be used. especially when you have many individuals from different cultural/social backgrounds you may find that what might to some be acceptable to others may not be. similarly, activities like hacking/cracking taking in one frame of reference (for example research), may not be acceptable in others (for example administration). without clear guidelines as to proper usage we are leaving it to the user to sort out in his, or her, own mind what is the correct way to handle the information that they possess. 35 amer a. al-rawas and s.millmore other issues relating to sharing and ownership are the matters of the copying of software products and intellectual copyright. oman has developed the necessary legislation, but again the culture of sharing means that the copying of software products does still occur, and this represents a number of risks. these include: corporate exposure to legal challenges; the propagation of viruses; the wide dispersal of a variety of incompatible software products (causing maintenance problems); possible security vulnerabilities (due to the use of unsecured or otherwise dangerous products). this also leads us to consider the matter of a legal framework for the protection of information. as well as the implementation and enforcement of a proper copyright and intellectual property law there is also the matter of security and so forth for personal, corporate, and other types of data. if there is no regulatory framework to define fair use and so forth what should be the guidelines an organisation should implement with respect to its data protection responsibilities. risks arise from a wide variety of persons. they may be faculty, staff, students, visitors, contractors, guests, or persons with no reasons for being on site. the reason they have for attempting to gain access may be: • for academic, political, or economic advantage, • as an intellectual exercise (it was the challenge!), • due to a personal grudge or disagreement (with respect to the institution, or a particular individual). such persons may be able to achieve their objective by direct access to systems that are not properly secured, or via local lan or dial in services. there are documented cases of former employees, some in security sensitive positions, being suspected as being the source of sabotage to systems (texas (state of), undated). some hackers would have us believe they have a mission to improve society (garigue, undated). campus based institutions, such as those involved in tertiary education and research, face particular vulnerabilities from their student body. the student is, to a certain extent, expected to study, research and develop expertise. there is very much an expectation that they should push both the technology and their expertise. and within the campus community the students will have: • spare time to study, • available equipment and access, • motivation to perform, • knowledge available. therefore the risk may be higher than in a commercial environment, where availability of all these resources is restricted, or very closely controlled. overall then all involved in information systems need to be security aware. they need to know their rights and responsibilities. that is to say that what must be developed is a security culture within the framework of the educational establishment (cox, 2000). 3.3 systems: protecting the hardware and software personal computers provide an easy to utilise high performance method of storing information. unfortunately they also present a serious security risk from the standpoint of data protection. there are many risks to personal hardware systems that do not impact those that are centrally managed and controlled (brook, 2000, anon, 2000). some examples of risks that involve personal computers include: 36 information security risks on a university campus 3.3.1 theft, damage and loss you may assume that it requires a high degree of technical skill to perform a computer crime. this is not the case, since data in highly portable systems is easy to steal, just take the system. if information is stored on removable media then this is even easier to remove. someone with a minimal level of technical competence can remove the physical hard disk. if you are not concerned about subtlety, you can easily damage a hard disk and cause the loss of significant quantities of data. 3.3.2 copying, modification, and corruption with a somewhat greater degree of technical competence, and open access to an unsecured system, someone can simply copy the data to some other media and take it away. alternatively, data stored within the system could be modified in any number of ways. without a proper auditing and policing policy it may be impossible to detect the loss or damage. 3.3.3 software applications good security means close controls over applications. many different types of “rouge” application may be present in a pc based office system. some may be user built applications used to augment, or replace, those provided by the data centre. they may be used in preference due to familiarity or simplicity. the problem with them is that they will not be subject to the rigorous development criteria that the data centre would use during development and testing. other types of rouge applications may be shareware, freeware and other “fringe” products that should not be used within an administrative or teaching environment. they may be poorly developed, inherently insecure, have backdoors into systems, degrade system performance, waste disk space and otherwise degrade system performance. such applications may include games and utilities often packaged on magazine covers. in the case of licenced software illegally mounted, these application may leave the institution open to legal challenge should a software company subject the institute to a software audit. 3.3.4 viruses, trojans and the like computer viruses are software applications designed to perform some action that is neither expected nor required by the user of a system. a trojan is an application that allegedly performs some beneficial activity, but in fact performs some other; usually one the operator does not wish for or require. unauthorised persons may introduce these into the computer, however they are most likely the result of unsafe working practises. they may utilise a number of different vectors to infect a system. for a stand-alone system this will be via an infected diskette of cd-rom. for a network connected system it may be via the lan connection. 3.3.5 system failure computer equipment becomes technologically obsolete very quickly. however it is generally quite reliable and can continue to operate well for some years. unfortunately many office based systems now contain important data that is not fully and properly backed up and hard disk systems are particular vulnerable. if you lose your disk you can lose a considerable amount of data. there are protections, of course. mirroring, raid, s.m.a.r.t and regular backups all have their parts to play. nevertheless as a disk gets older failure becomes more likely (kari, undated). our experiences here point to between three and five years as being a good lifetime for a disk, although many do last longer. if you are performing backups remember to ensure that they are usable, by performing recovery tests on a regular basis. failure to test backups regularly may lead you to have a “false sense of security”. if you have remembered to make backups and then find they are not usable you risk serious and catastrophic data loss. 37 amer a. al-rawas and s.millmore 3.3.6 transient equipment when we discuss transient equipment we mean systems that may be utilised within the university campus but also outside. such equipment will primarily consist of portable (laptop/notebook systems). such systems may be used by students (in some universities this is almost mandatory), others may be used by staff who choose to work from home, some may be part of test and diagnostic equipment used in the field. this equipment is at specific risk for several reasons. it may be lost, stolen or damaged. confidential information may be moved to an uncontrolled and unsecured environment. lastly, these systems may be connected to a public network with the attendent risks of being infected by viruses or remotely accessed by hackers. it is interesting to observe that many companies, including pc hardware suppliers, now offer notebook security products. 3.4 networks: communication risks your lan is probably one of the most important part of your is structures. it is also an area where security is critical (quinn-andry and haller, 1998). this type of communication network possesses many advantages for the institution in terms of the cooperative sharing of information in both academic and administrative areas. unfortunately it also presents us with a number of serious exposures from the security standpoint. to ensure a well secured network your design needs to consider the issues of (quinn-andry and haller, 1998): • authentication (identifying the user), • authorisation (what the user is allowed to do), • integrity (protecting the data in transit from amendment/corruption), • encryption (to prevent data in transit being transmitted “in clear” text). the regular basic ethernet tcp/ip network utilising ipv4 provides little in the way of security controls over access, or mechanisms to prevent misuse of that access. to effectively secure such networks additional measures need to be put in place. these measures would control access, and ensure that data being passed “over the wire” was not easily accessed. there are many mechanisms that can be used to address these issues and these include one-time passwords, card access, digital certificates, secure protocols and so on. a useful discussion is contained in (read), undated) and while that document specifically applies to isues relating to internet much of the discussion is just as relevant from the standpoint of the local intranet. in implementing security controls over access to information systems through network access a balance needs to be struck. this balance needs to consider: • how much security do we require, • what are we prepared to pay for that security (that is to say what value do we place on our data), • the degree of convenience (more like inconvenience) will our faculty, staff and students tolerate. we should not make security so tight that it actively discourages the use of the resources provided. as with other institutions of this type the university has a developed an expanding lan network interconnecting into the internet, due to its internal structure protocols and this connection there are clear security exposures. these exposures can be classified as coming from: • outside the university lan via the internet, • by dial-in service, • by the attachment of unauthorised equipment, 38 information security risks on a university campus • from within the university lan, • through the use of broadcast technologies. the internet can provide a means of gaining access to a campus based system without the particular individual being physically present on the campus. this means that the border controls between the internet and your lan have to be carefully and strictly managed. if they are not fully and carefully managed then vulnerabilities may exist. commercial environments frequently configure their firewalls to block all but a few required services, the so-called “deny all” option. owing to the open nature of university operations in academic institutions the opposite view is often taken, with free access being the norm, the so-called “allow all” option. in the case of squ we tend to follow the safer commercial model. dial-in services are potential sources of security risks. with these the user may be within your campus or without. even those institutions with limited internal dial-in facilities may be at risk since internal phone lines may be set-up to reroute external calls to internal dial-in modem services. the location of remote access servers with respect to the lan, therefore, needs to be carefully considered since placement within the firewall presents definite security risks (since it will permit firewall controls to be circumvented with a simple phone call). placement outside the firewall presents a more complex access regime, so may be more secure. once the internal lan has been accessed by dial-in the security risks are the same as access via a local workstation. the lan attachment of unauthourised systems and other equipment can be a major vulnerability. network enabled windows and unix like products are now the norm. it is simple quick and easy to attach such equipment to a lan. should the newly attached equipment be misconfigured then it can predjudice the entire lan operation. for example if a pc is attached with the same ip address as your regular dhcp server then the packets may be misdirected to the wrong system. since dynamically assigned ip addresses which come from your dhcp service have a specific lease, or timeout period, the problem may not be noticed immediately but could degrade network performance over a period of several days. similarly users may, for their own convenience, create remote access servers (using a pc and modem) and attach these into the internal phone network. this would permit them to dial-in to their office number and access the lan remotely. however, since the remote access server is within the lan, and not routed through any firewall or other access control mechanism it represents a fundemental risk. should the user “publish” such a service to his/her department then the risk would grow significantly. since the vast majority of university pcs are interconnected into lans, each represents a potential risk from the standpoint of security. systems in computer laboratories are generally controlled quite loosely, since the intention is to provide quick, easy, free and open access. data may be compromised not only by gaining unauthorised access to systems across the lan, but also by monitoring of data traffic within the network. this is generally a simple process utilising a software application called a packet sniffer. such sniffers are available on the internet. more sophisticated users may be able to detect unencrypted confidential data, including usernames and passwords being passed around the lan. they may modify the content of data packets themselves or disguise themselves as other machines (using a process known as spoofing). particularly knowledgeable users may be able to send unattributable e-mail, or become a general nuisance, through routing mail through slot facilities (on the internet) or through misconfigured sendmail hosts. wireless networks are another area where security concerns have been raised. while these lans are not strictly new, until recently they have not been extensively deployed at squ owing to the absence of internationally ratified standards, low performance and high cost. they have often been proposed as possible solutions to providing connectivity both within and between buildings. many of the objections to them have now been addressed, although even ieee 802.11 based equipment operating at 11 mb/sec cannot, at present, approach the 100 to 1000 mb/sec that we deploy on our regular hard wired networks. nevertheless they are becoming more common. 39 amer a. al-rawas and s.millmore security is an issue in wireless lans due to the ability of hackers to gain access to the campus lan without any physical contact. the possibility of casual passers by being able to tap into the lan with a notebook computer and a wireless access card has been raised (ross, 2000; fisher and nobel, 2001 ; leyden, 2001). should the security encryption technology built into the wireless equipment be inadequate then access could be gained and security compromised. specific doubts have been raised as to flaws in the wired equivalent privacy (wep) algorithm (borisov et. al., undated), which is part of the ieee 802.11 standard. similarly lan connected systems are at risk from hacker/cracker attack. the objective is normally to gain system administrator status (root privilege in unix machines). often such access is facilitated by incorrectly configured systems, systems with unsecured user accounts, or unpatched systems where the os contains known vulnerabilities. there is an extensive range of hacker/cracker/ network administrator tools and resources available in the internet and via print publications (anon, 1998). frequently these tools are designed for relatively unskilled and unsophisticated users. this has given rise to the so-called “script kiddie”; someone without the extensive skills of the true hacker and, we are lead to believe, without the sense of social responsibility (garigue, undated). unauthorised access is not the only system vulnerability that we need to be aware of. probably the most well known secondary vulnerability is to the operational system availability and this is known as the denial of service attack. put bluntly, the intention is to make your system/lan unusable. again there are a wide variety of tools available on the internet for this purpose. thus we are not talking about anything that requires an extensive amount of technical competence. the final system vulnerability is the injection of unauthorised applications into your system. sometimes viruses and trojans may secure a foothold in your system through regular user activities such as e-mail and so forth. in some cases once they have secured such access they can utilise this as a stepping stone into other systems thereby propagating their activities. an example of this is the (in) famous iloveyou virus. which relies on firewalls not blocking e-mail attachments, and users being less than careful in their use of e-mail software. 4. solution strategies you need to attack a number of different areas when attempting to reduce security risks to your is structures. these may be considered as being: • general, which may be applied throughout the whole institutions, • social, which are aimed at changing the work attitudes of faculty, staff and students, • technical, which ensure you have the correct skills and technologies to address the challenges. to reduce risks we need to ensure that is systems are secure, policed, recoverable. the following lists define a number of strategies that you may choose to consider when attempting this. while they may well not be definitive they are all well worth considering. let’s address the general issues first: • committee with full academic/administrative representation (security is the responsibility of all) • security officer/team in is centre (someone has to be responsible), • security responsibilities in colleges/centres (responsible not just in the centre, also in all parts of the institution) • security reporting and feedback hotline (to ensure security issues are communicated effectively), • consider more effective authentication schemes (the basic username/password strategy is not very secure), • buy in from executive and management (support is required at the highest levels), 40 information security risks on a university campus • ensure all infrastructure installed in secure areas (keep doors to offices, control rooms locked), • limit access to secured areas to those with need (can you trust your maintenance and cleaning staff?). 4.1 social issues • develop a security minded culture (everyone should think security – not just the is centre), • code of practice/acceptable use policy (written policy, signed off by users, reminders on screens – so people know what is and is not allowed), • education with respect to proper policies and procedures (people may not read the policies, they should be reminded from time to time), • pay attention to legal and administrative framework (an institution must conform to the national laws, its is structures need to be compliant with institutional regulations also), • full, fair and effective enforcement (a policy is no good unless it is properly enforced, and seen to be so). 4.2 technical • trained technical staff with up-to-date hacker/cracker knowledge (staff should know what the vulnerabilities are before they become problems, not after a problem arises – be proactive), • monitor hacker sites to ensure that the latest exploits are known, • ensure equipment running at latest service releases with applied patches as required (all systems contain vulnerabilities, close known holes as soon as you can), • properly configured systems with good user/password security (don’t assume default configurations are secure, always change default passwords), • approved software use policy (limit range of software allowed to reduce licence violations, as well as support and other vulnerabilities from unknown products) • security probes on key and critical systems (check that your systems are secure, don’t assume they are), • effective monitoring and assessment of traffic (you’re unlikely to fix a problem you don’t know about – how do you know you’ve been hacked?), • maintain anti-virus software at latest release (to keep up with the latest development in "virusware"), • maintenance and backups of all key systems (if you lose your data you need to be able to get it back, if you’ve been hacked how can you trust your information), • storage of critical data on secured servers, not desktop systems (the knowledge of the institution is too valuable to keep on a desktop system that may not be adequately protected), • test backup systems on a regular basis to ensure that information is recoverable. 5. summary and conclusions information sharing is well recognised as being important to the academic activities of institutions like the squ. in commercial organisations this isn’t usually the case, and it would be difficult for an academic institution to adopt a typical corporate model. a wide variety of information is stored and utilised within the is structures of any academic institutions. some may be primarily administrative, but a significant amount will relate to the primary responsibilities of the organisation: education and research. information systems used within academic communities need to be developed to facilitate information exchange but also ensure the security and integrity of the data being handled. owing to the basic nature of information exchange within the academic community some risks are unavoidable. to ensure the security of is we must consider a number of factors. there are technical issues such as hardware, software, networking and physical infrastructure. similarly there are cultural and 41 amer a. al-rawas and s.millmore social issues, these are important not only with reference to the individual but also on an institutional basis (the organisational ethos). many of the risk factors may be addressed by the proper application of a number of user policies. the guidelines and procedures should be applied, on an institutional basis, to the custodians of is systems as well as the users of systems and data. users should be educated as to their responsibilities through the establishment of proper training programs. technical issues should be handled by an experienced and capable technical team. references anon, 1998, maximum security, second edition, sams publishing. anon, 2000, computer fundamentals and applications (course syllabus), chapter 8, computer security and risks, www.pentaq.co.nz/columns/computerfunctionality.html. attorney general (australia), 1999, 26th august, protecting australia’s information infrastructure, news release law.gov.au/aghome/agnews/1999newsag/601_99.htm. borisov, n., goldberg, i. and wagner, d. undated, security of the wep algorithm, university of california at berkley, www.isaac.cs.berkeley.edu/isaac/wep-faq.html. british standardas institute, 1999, information security management, specification for information security management system, bs7799-2. brook, j. 2000, computer reliability checklist – revised, www.pentaq.co.nz/columns /computerfunctionality.html. cox, a., 24th november 2000, report on creating a security culture in he and fe conference, university of glasgow, litc.sbu.ac.uk/jcalt/conference/confreport.htm. elliot, r., young, m.o., collins, v.d., frawley, d. and emares, m.l. 1991, information security in higher education, cause the association for the management of information technology in higher education, professional paper series #5. fisher, d. and nobel, c., february 9, 2001, wireless lan security holes exposed, eweek news, www.zdnet.com/eweek/stories/general/0,11011, 2684262,00.html. fraser, b. (ed), september 1997, site security handbook, rfc2196, the internet engineering task force, network working group, www.ietf.org/rfc/rfc2196.txt?number=2196. garigue, r.j., undated, hacking belief systems, an agenda for the survival of humanity in cyber-society,the activist agenda in cyber-society superior.carleton.ca/~rgarigue/hack.htm, www.infowar.com/articles/00/cyborg/cyborg3.htm. hansard (uk gov), 4 nov 1998, official debate report, house of commons hansard for 4 nov 1998 (pt 52), the stationery office ltd, department of the official report (hansard), volume: 318, part:232, isbn: 0106232983, www.parliament.the-stationery-office .co.uk/pa/cm199798/ cmhansrd/vo981104/ debtext/81104-52.htm harvard universiy, november 1991, information security handbook, version 2, www.all.net/books/document/harvard.html. hassler, a.a., 1998, guaranteed access to campus network resources: policies and issues, cause/effect, 21-no. 2:10-14, www.educause.edu/ir/library/html/cem9824.html. hunter, b., 14 april, 2000, information security: raising awareness,version 1.0, government of canada pki secretariat, chief information officer branch,treasury board of canada secretariat, www.iwar.org.uk/comsec/resources/canada-ia/infosecawareness.htm illinois institute of technology, undated, center for study of ethics in the professions, code of ethics online, computing and information systems, csep.iit.edu/codes/computer.html. international standards oreganisation, information technology – code of practice for information security management, iso/iec 17799, (the iso version of bs7799). joint information systems committee, 27th february 2001, developing an information security policy, www.jisc.ac.uk/pub01/security_policy.html. 42 http://www.pentaq.co.nz/columns /computerfunctionality.html http://www.pentaq.co.nz/columns /computerfunctionality.html http://www.zdnet.com/eweek/stories/general/0,11011 information security risks on a university campus kari, h.h., undated, latent sector faults and reliability of disk arrays, dissertation in helsinki university of technology, espoo, finland, www.cs.hut.fi/~hhk/phd/chapter3/phd_3.html. leach, j., undated, findings from the first stage of the study into the requirements for authentication, authorisation and privacy in higher education, joint information systems committee, www.jtap.ac.uk/reports/htm/jtap-015-1.html leyden, j., 29th march 2001, war driving: the latest hacker fad,the register, www.theregister.co.uk/content/archive/17976.html quinn-andry, t. and haller, k., 1998, designing campus networks, cisco press, macmillan technical publishing. read, j. (editor), et. al., undated, working paper on secure internet issues for the he community, interim report from jtap-659, university of southampton, www.jtap.ac.uk/reports/htm/jtap-032.html. ross, j.b., november 4, 2000, containing the wireless lan security risk, sans institute, www.sans.org/infosecfaq/wireless/wireless_lan.htm. san francisco state university, undated, draft self-study for wasc reaccreditation, volume i implementing the university strategic plan, chapter 14, www.sfsu.edu/~acadplan/wascss14.htm. stamen, e.m., july 1986, ownership, privacy, confidentiality, and security of data, cause/effect, 9-no. 4: 4-9. texas (the state of), donald gene burleson (appellant) vs the state of texas, state. no. 2-88301-cr court of appeals of texas, second district, fort worth, 802 s.w.2d 429 rampages.onramp.net/~dgmccown/c-txblsn.htm. university of california, may 22, 1998, improving network and computer security at the university of california, berkley, report of the itatf security working group socrates.berkeley.edu:2001/security/itatf_swg_report.html. university of leicester, 27th november 2000, management information systems, computer security policy, administrative systems, www.le.ac.uk/mis/html_docs/security.htm. white house (the), 2000, defending america’s cyberspace, national plan for information systems protection, an invitation to a dialogue, version 1. received 11 june 2001 accepted 4 february 2002 43 http://www.sans.org/infosecfaq/wireless/wireless_lan.htm information security risks on a university campus amer a. al-rawas and s. millmore centre for information systems, sultan qaboos university, sultanate of oman. abstract: this paper is concerned with issues relating to security in the provision of information systems (is) services within a campus environment. it is based on experiences with a specific known environment; namely sultan qaboos university. in cons 1.1 information and the campus community types of information security issues 3.1 infrastructure: physical access risks 3.2 people: social and geographical affinities 3.3systems: protecting the hardware and software 3.4networks: communication risks solution strategies summary and conclusions information sharing is well recognised as being i references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 199-209 © 2002 sultan qaboos university towards formulation of a complex binary number system tariq jamil*, david blest** and amer al-habsi* *department of information engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. **school of mathematics and physics, university of tasmania, launceston, tas 7250, australia. نحو نظام لألرقام المركبة الثنائية طارق جميل ، ديفيد بلست وعامر الحبسي تعامل بشي من عدم االلفة نسبة الى األرقام الحقيقة بغض النظر عن ) المعقدة(لسنوات عديدة ما زالت األرقام المركبة : خالصة في هذه األيام عمليات الحاسوب التي تشمل أرقام . الحاسوبيةانتشار استعماالتها في تطبيقات عديدة في مجاالت الهندسة الكهربائية و تنفذ في كثير من األحيان بواسطة تطبيق طريقة تقسيم أجزاء الرقم المركب إلى مكوناته وتنفيذ العمليات الحسابية ) معقدة(مركبة لعمليات الحسابية على كل جزء ثم فالجزء الحقيقي والخيالي من الرقم المركب يفصلوا عن بعض وتنفذ ا . على كل جزء على حدى هذه الطريقة في تعقيد العمليات الحسابية على األرقام المركبة تحث . تجمع النتائج لكل جزء لتركيب النتيجة النهائية للعملية المركبة يذ العمليات الحسابية على إيجاد طريقة لمعاملة األرقام المركبة تحث على إيجاد طريقة لمعاملة األرقام المركبة كوحدة واحدة وتنف ناقشنا العمليات الحسابية . j-1-)(في هذا البحث قمنا بتحليل واقتراح النظام الرقمي الثنائي المركب بأساس . عليها بطريقة مباشرة .على عددين في هذا النظام واوضحنا الدراسات القائمة حاليا في مجال الحاسوب abstract: for years complex numbers have been treated as distant relatives of real numbers despite their widespread applications in the fields of electrical and computer engineering. these days computer operations involving complex numbers are most commonly performed by applying divideand-conquer technique whereby each complex number is separated into its real and imaginary parts, operations are carried out on each group of real and imaginary components, and then the final result of the operation is obtained by accumulating the individual results of the real and imaginary components. this technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a complex number as one unit and to carry out all operations in this form. in this paper, we have analyzed and proposed a (–1–j)-base binary number system for complex numbers. we have discussed the arithmetic operations of two such binary numbers and outlined work which is currently underway in this area of computer arithmetic. keywords: complex binary number, addition, subtraction, multiplication, division. 1. introduction t he use of complex numbers in mathematics can be traced as far back as 1545 when cardano used the notation √–1 during investigation of the roots of polynomials. later, euler in 1777 introduced the abbreviation i for √–1 and originated the a + ib notation to represent complex numbers (in electrical and computer engineering, we tend to replace the symbol i with j because it is easier to distinguish between the number 1 and j than 1 and i). since then, complex numbers have played a truly unique role in the development and research of modern science and engineering. in the fields of electrical and computer engineering, the application of fast fourier transform in most digital signal processing algorithms, and the geometric analysis of pixels in graphics and image processing owe their advantage to the use of complex numbers. despite their widespread applications, complex number operations have, to a large extent, been treated as just an add-on patch to the basic operations of real arithmetic. today, even with the availability of over 199 tariq jamil, david blest and amer al-habsi 100-million transistors on a single ic-chip (geppert, 1999), virtually the entire complex arithmetic involves the application of “divide-and-conquer” technique, whereby a complex number is brokenup into its real and imaginary parts and then operations are carried out on each part as if it were a part of the real arithmetic. finally, the overall result of the complex operation is obtained by accumulation of the individual results. for instance, addition of two complex numbers (a + jb) and (c + jd) requires two separate additions (a + c) and (b + d) while multiplication of the same two complex numbers requires four multiplications (ac), (ad), (bc), (bd), one subtraction (j2bd = – bd), and one addition (ac + j(ad + bc) + (– bd)). this can be effectively reduced to just one complex addition or only one multiplication and addition respectively for the given cases if each complex number is represented as one unit instead of two individual units. the pursuance of providing equal opportunity representation to complex numbers has resulted in some efforts of defining binary numbers with bases other than 2. in 1960, donald e. knuth described a “quater-imaginary” number system with base 2j and analyzed the arithmetic operations of numbers using this imaginary base (knuth, 1960). however, he was unsuccessful in providing a division algorithm and considered it as a main obstacle towards hardware implementation of any imaginary-base number system. walter penney, in 1964, attempted to define a complex number system, first by using a negative base of – 4 (penney, 1964) and then by using a complex number (–1+j) as the base (penney, 1965). however, the main problem encountered with using these bases was again the inability to formulate an efficient divison process. stepanenko (1996) utilizes the base j√2 in which the even powers of the base yield real numbers and the odd powers of the base result in imaginary numbers. although partly successful in resolving the division problem as an “all-in-one” operation, in his algorithm “…everything…reduces to good choice of an initial approximation…” in a newton-raphson iteration which may or may not converge. in an earlier paper (jamil et al 2000), we revisited penney’s number system of base (–1+j) and extended his work by providing algorithms for converting integers, imaginary, fractional, and floating point numbers into (–1+j)-base binary number system, including description of the basic arithmetic operations based on this new number system. in this paper, we concentrate our efforts on providing algorithms and arithmetic operations for (–1–j)-base binary number system. in addition to this, we have provided algorithms for obtaining conjugate and magnitude of the given (–1–j)-base complex binary number. this will help conclude the fact that both (–1+j) and (–1–j) are excellent bases for facilitation of complex numbers’ representation as a single entity. this paper is organized as follows: in section 2 we present an analysis of (–1–j)-base binary number system. in section 3, we present algorithms for converting various types of numbers into the proposed (–1–j)-base binary number system. this is followed by an analysis of arithmetic operations in section 4. in section 5 we present algorithms for obtaining conjugate and magnitude of a given (–1–j)-base complex binary number. finally, in section 6 we present conclusion and a synopsis of the ongoing work being done by us in this area. 2. the base –1–j the value of an n-bit binary number with base (–1–j) can be written in the form of a power series as follows: an-1(-1-j)n-1 + an-2(-1-j)n-2 + an-3(-1-j)n-3 + … + a2(-1-j)2 +a1(-1-j)1 +a0 (-1-j)0 (1) where the coefficients an-1,an-2,an-3,…,a2,a1,a0 are binary (either 0 or 1). table 1 gives some real and imaginary numbers along with their complex binary representations (base –1–j). 200 towards formulation table 1: binary representations for some real and imaginary numbers (base –1–j). real no. complex binary number imaginary no. complex binary number –5 1100 1101 –j5 111 0011 –4 1 0000 –j4 111 0000 –3 1 0001 –j3 111 0111 –2 1 1100 –j2 111 0100 –1 1 1101 –j1 0011 0 0000 j0 0000 1 0001 j1 0111 2 1100 j2 0100 3 1101 j3 11 0011 4 1 1101 0000 j4 11 0000 5 1 1101 0001 j5 11 0111 3. binary representation for complex numbers 3.1 conversion algorithm for real integers1 let’s first begin with the case of positive integers n. to represent n in the proposed (–1–j)base binary number system, we express n in terms of powers of 4 using the division process. thus nbase 4 = ∑ qi 4i (2) this “normalized” representation is unique when 0≤ qi< 4. in that case the non-zero ‘digits’ …, q5, q4, q3, q2, q1,q0 are called the base 4 representation of n. if the constraint on the qi is removed, then we call it an un-normalized base 4 representation of n, which is not unique. now convert the base 4 number …, q5, q4, q3, q2, q1,q0 to base – 4 by replacing each digit in odd location q1, q3, q5, … with its negative to get (…, q5, q4, q3, q2, q1, q0)base 4 = (…, -q5, q4,q3, q2, -q1, q0) base – 4 (un-normalized) we normalize the new number (i.e. get each digit in the range 0 to 3) by repeatedly using the operation of adding four to the negative digits and adding a one to the digit on its left. this operation will get rid of the negative numbers, but might create some digits with a value of 4 after the addition of a 1. to normalize this, we replace the four by a zero and subtract a one from the digit on its left. of course this subtraction might once again introduce negative digits which will be normalized by the previous method, but this process will terminate! what is interesting is that with negative bases, all integers, positive or negative have a unique positive representation. as an example 55base10 = (3,1,3)base 4 = (3,–1,3) base – 4 = (4,3,3) base – 4 = (–1,0,3,3) base – 4 = (1,3,0,3,3) base –4 (normalized) to represent the given number in the base (–1–j), we replace each digit in base – 4 representation with a four bit sequence according to table 2, which yields: 55base10 = (1,3,0,3,3) base – 4 = 0001 1101 0000 1101 1101 base –1–j 1 see figure 1 for a program in c language to convert real integers into (–1–j)-base complex binary number system. 201 tariq jamil, david blest and amer al-habsi to convert a negative integer into (–1–j)-base representation, we simply multiply the representation of the corresponding positive integer with 11101 (equivalent to –1base–1–-j) according to the multiplication algorithm given in section 4.3. thus – 55base10 = (0001 1101 0000 1101 1101) x (11101) = 0000 0001 1100 1101 1101 0001 base –1–j figure 1: a program in c language for conversion of real and imaginary integers to (–1–j)-base complex binary number system. /* program for real and imaginary */ /* integers conversion to (–1–j)-base */ /* complex binary number system */ /* author: amer al-habsi */ #include <stdio.h> #include <conio.h> #include <math.h> #include "base1j.h" int clear(int *a, int n) { int i; for(i=0; i<n-1; i++) a[i]=0; a[n-1]=1; /*length = 1*/ return 0;} int print(int *a) { int i; for(i=max-1; i>=0; i--) printf("%i ",a[i]); return 0;} int print_bits(int *a, int n) { int i, digits; i=n-1; while(a[--i]==0) ; digits=i; for(i=digits; i>=0; i--) printf("%i",a[i]); return 0; } int sprint_bits(int *a, int n, char *s) { int i, digits; i=n-1; while(a[--i]==0 && i>=0); digits=i; if(digits==-1){ sprintf(s++,"0"); return 0; } for(i=digits; i>=0; i--) sprintf(s++,"%i",a[i]); return 0;} int int2basen(int x, int n, int a[]) { int i, remainder, dividend; i=0; do { dividend=x/n; remainder=x%n; a[i++]=remainder; if(i==max-1) return -1; x=dividend;} while(dividend!=0) ; a[max-1]=i; return 0;} int basenegative(int a[]) { int i; for(i=1; i<max-1; i+=2) a[i]=-a[i]; return 0;} int done(int a[], int n, int size) { int i; for(i=0; i<size-1; i++) if((a[i]>=n) || (a[i]<0)) return 0; return 1;} int normalize(int a[], int n) { int i; do{for(i=0; i<max1; i++) if(a[i]<0){ a[i]+=n; ++a[i+1];} for(i=0; i<max-1; i++) if(a[i]==n){ a[i]=0; -a[i+1];} while(!done(a,4,ma x)); return 0;} int normalized2bits(int bits[], int a[]) { int i, digits; i=max-1; while(a[--i]==0) ; digits=++i; for(i=0; i<digits;i++){ if(a[i]==0){ bits[i*4]=0; bits[i*4+1]=0; bits[i*4+2]=0; bits[i*4+3]=0;} else if(a[i]==1){ bits[i*4]=1; bits[i*4+1]=0; bits[i*4+2]=0; bits[i*4+3]=0;} else if(a[i]==2){ bits[i*4]=0; bits[i*4+1]=0; bits[i*4+2]=1; bits[i*4+3]=1;} else if(a[i]==3){ bits[i*4]=1; bits[i*4+1]=0; bits[i*4+2]=1; bits[i*4+3]=1;}} i=4*max-1; while(bits[-i]==0) ; digits=++i; bits[max*41]=digits; return (digits);} int normalized2string(char *s, int a[]) { int i, digits; char *lut[]= {"0000","1000","00 11","1011"}; char *temp, c; temp=s; i=max-1; while(a[--i]==0) digits=++i; for(i=0; i<digits; i++){ sprintf(s,"%s",lut[a[i]] ); s+=4;} *s='\0'; s=temp; for(i=0;i<digits*2 ;i++) { c=s[i]; s[i]=s[digits*4i-1]; s[digits*4-i1]=c; } return digits;} int int2base1j(int bits[], int r) { int temp[max*4]; int i; int minus1[]={1,0,1,1,1}; int a[max]; clear(a, max); if(r==0){ clear(bits,max*4); return 0; } if(r>0){int2basen( r, 4, a); basenegative(a); ; 202 towards formulation table 2: equivalence between base –4 and base (–1–j) representations. base –4 base (–1–j) 0 0000 1 0001 2 1100 3 1101 3.2 conversion algorithm for imaginary integers2 to obtain binary representation of a given positive or negative imaginary number, we simply multiply (according to algorithm in section 4.3) the corresponding (–1–j)-base representation of positive or negative integer with 111 (equivalent to jbase10) or 11 (equivalent to –jbase 10), as required. thus j55base10 = (0001 1101 0000 1101 1101) x (111) = 0000 0001 0001 0000 0100 0011 base –1–j – j55base10 = (0001 1101 0000 1101 1101) x (11) = 0000 0111 0111 0100 0111 base –1–j 3.3 conversion algorithm for decimal fractions3 the procedure for finding the binary equivalent for fractions in base (–1–j) is based on the usual approach to obtaining ordinary binary representations. any fraction f can be expressed uniquely in terms of powers of ½ = 2–1 such that f = r0 = f1.2–1 + f2. 2–2 + f3. 2–3 + f4. 2–4+ … up to machine limit. then the coefficients fi and remainders ri are given as follows: initially if 2r0 – 1 < 0 then f1 = 0 and set r1 = 2r0 or if 2r0 – 1 ≥ 0 then f1 = 1 and set r1 = 2r0 – 1. then if 2ri – 1 < 0 then fi+1 = 0 and ri+1 = 2ri or if 2ri – 1 ≥ 0 then fi+1 = 1 and ri+1 = 2ri –1 we continue this process until ri = 0 or the machine limit has been reached. then, for ∀fi = 1, we replace its associated 2–i according to table 3 (only the first four values of i are listed in this table; for i>4, refer to table 4). table 3: equivalence between fractional coefficients and base (–1–j) representations. i 2–i base (–1–j) 1 2–1 1.11 2 2–2 1.1101 3 2–3 0.000011 4 2–4 0.00000001 as an example, let f = r0 = 0.6875base10 initially 2r0 – 1 = 2(0.6875) – 1 = 0.375 > 0 ⇒ f1 = 1, r1 = 2r0 1 = 2(0.6875) – 1 = 0.375. then 2r1 – 1 = 2(0.375) – 1 = – 0.250 < 0 ⇒ f2 = 0, r2 = 2r1 =2(0.375) = 0.750 2 see figure 1 for a program in c language to convert imaginary integers into (–1–j)-base complex binary number system. 3 see figure 2 for a program in c language to convert real/imaginary fractions into (–1–j)-base complex binary number system. 203 tariq jamil, david blest and amer al-habsi figure 2: a program in c language for conversion of real and imaginary fractions to (–1–j)-base complex binary number system. /* program for real and imaginary */ /* fractions conversion to */ /* (–1–j)-base complex binary number */ /* system */ /* author: amer alhabsi */ #include <stdio.h> #include <stdlib.h> #include "base1j.h" #define fracpart 80 #define intpart (maxfracpart) #define arbit 0 void print_frac(int bits[], int left, int right) { int i, j; for(i=fracpart+left-1; i>=fracpart;i--) printf("%i", bits[i]); printf("."); for(i=fracpart-1, j=0; j<right; i--, j++) printf("%i", bits[i]);} void neg_frac(int bits[]) { int temp[max*4]; int i; int minus1[]={1,0,1,1,1,0, 0,0,0,0,0,0}; clear(temp,max*4); mult(minus1,bits,12,ma x,temp); for(i=0; i<max*4;i++) bits[i]=temp[i];} int frac(double f, int accumulator[]) { int i, j; double r, doublerm1; double save_f; int temp[max*4], tempsum[max*4]; int t, s, k; int f[fracpart/4]; save_f=f; if(f<0) f=-f; clear(accumulator,4*ma x); clear(temp,4*max ); clear(tempsum,4*max); for(i=0; i<fracpart/4; i++) f[i]=0; r=f; for(i=1; i<fracpart/4 && r!=0.0; i++){ doublerm1=2.0*r1.0; if(doublerm1<0.0 ){f[i]=0; r=doublerm1+1;} else{ f[i]=1; r=doublerm1;}} clear(accumulator, max); if(f[1]==1){clear(temp , max); temp[fracpart]=temp[fr acpart1]=temp[fracpart-2]=1; add(accumulator, temp, tempsum, maxarbit); for(j=0; j<max; j++) accumulator[j]=tempsum [j];} if(f[2]==1){clear(temp , max); temp[fracpart]=temp[fr acpart1]=temp[fracpart2]=temp[fracpart-4]=1; add(accumulator, temp, tempsum, 100); for(j=0; j<max; j++) accumulator[j]=tempsum [j];} if(f[3]==1){clear(temp , max); temp[fracpart5]=temp[fracpart-6]=1; add(accumulator, temp, tempsum, maxarbit); for(j=0; j<max; j++) accumulator[j]=tempsum [j];} for(i=4; i<fracpart/4; i++){ if(f[i]==1){t=i%4; s=i/4; k=8*s; clear(temp, max); switch (t) { case 0: temp[fracpart-k]=1; break; case 1:temp[fracpartk]=temp[fracpart-k1]=temp[fracpart-k2]=1; break; case 2: temp[fracpartk]=temp[fracpart-k1]=temp[fracpart-k2]=temp[fracpart-k4]=1; break; case 3:temp[fracpart-k5]=temp[fracpart-k6]=1; break;} add(accumulator, temp, tempsum, maxarbit); for(j=0; j<max; j++) accumulator[j]=tempsum [j];}} continuing according to the algorithm, we have 2r2 – 1 = 2(0.750) – 1 = 0.5 > 0 ⇒ f3 = 1, r3 = 2r2 -1 = 2(0.750) – 1 = 0.5 2r3 – 1 = 2(0.5) – 1 = 0 (stop) ⇒ f4= 1, r4 = 0 204 towards formulation thus 0.6875base 10 = 1.2–1 + 0. 2–2 + 1. 2–3 + 1. 2–4 = 1(1.11) + 0(1.1101) + 1(0.000011) + 1(0.00000001) = 1.11001101base (-1-j) (addition according to algorithm in section 4.1) it is likely that most fractions will not terminate (as our example) until the machine limit is reached. for example 0.351base 10 =1.110111001100110000011100110…base –1–j in that case, it is up to the user to terminate the process when certain degree of accuracy has been achieved. in general, to find binary representation of any 2–i, express i as 4s + t where s is an integer and 0≤t<4. then, depending upon value of t, 2–i can be expressed as given in table 4. all rules for obtaining negative integer and positive/negative imaginary number representations in base (–1–j), as discussed in previous sections, are equally applicable for obtaining negative fractional and positive/negative imaginary fractional representations in the proposed new base. table 4: equivalence between value of “t” and base (–1–j) representations. t base (–1–j) 0 0.0…(8s–1)zeroes followed by 1 1 0.0…(8s–1)zeroes followed by 111 2 0.0…(8s–1)zeroes followed by 11101 3 0.0…(8s+4)zeroes followed by 11 3.4 conversion algorithm for floating point numbers to represent a floating point positive number in the new base, we add the integer and fractional representations according to the addition rules given in section 4.1. once again, all rules for obtaining negative integer and positive/negative imaginary number representations in base (–1– j), as discussed in previous sections, are equally applicable for obtaining negative floating point and positive/negative imaginary floating point representations in the proposed new base. for example 55.6875base 10 = 0001 1101 0000 1101 1101 + 1.11001101 = 0001 1101 0000 1100 0000.1100 1101base –1–j and j55.6875base 10 = 0001 1101 0000 1100 0000.1100 1101 x 111 = 11000001000000.01110011base –1–j knowing the conversion algorithms, as described in the previous sections, the binary representation for any given complex number can be easily obtained, as shown by the following example: (55.6875 + j55.6875)base10 = 0001 1101 0000 1100 0000.1100 1101base –1–j + 11000001000000.01110011base –1–j = 0010 0011 1000 0011.1010 0010base –1–j this can be verified to be equivalent to the given complex number by calculating: (–1–j)13 + (–1–j)9 + (–1–j)8 + (–1–j)7 +(–1–j)1 +(–1–j)0 +(–1–j)–1 +(–1–j)–3 + (–1–j)–7 4. arithmetic operations for complex numbers 4.1 addition the binary addition of two complex numbers follows these rules: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 1100. these rules are very similar to the traditional binary arithmetic except for the last case where when two 1s are added, the sum is zero and (instead of just one carry) two carries are 205 tariq jamil, david blest and amer al-habsi generated which propagate towards the two adjoining positions after skipping the immediate neighbor of the sum column. that is, if two numbers with 1s in position n are added, this will result in 1s in positions n+3 and n+2 and 0s in positions n+1 and n in the sum. similar to the ordinary computer rule where 1+111 … (to limit of machine) =0, we have 11 + 111 = 0 [zero rule]. (see section 4.3 for an example of addition). 4.2 subtraction the binary subtraction of two complex numbers follows these rules: 0 0 = 0 ; 0 1 = * ; 1 0 = 1; 1 1 = 0. three of the four conditions listed in these rules are the same as for subtraction in ordinary binary system. for the case where 1 is subtracted from 0 (* case in the rules), the following algorithm applies: assuming our minuend is anan-1an-2…ak+4ak+3ak+2ak+1ak0ak-1….a3a2a1a0 and subtrahend is bnbn-1bn2…bk+4bk+3bk+2bk+11bk-1….b3b2b1b0. then, the result of subtracting 1 from 0 is obtained by changing ak →ak+1 ,ak+1 →ak+1 (unchanged) , a k+2→ a k+2 + 1 , a k+3→a k+3 + 1 , a k+4→ a k+4 +1 and bk →0. example: subtract (2–3j) from 3 solution: in base (–1–j) notation, we have 3 – (2–3j) = 1101 – (1100 – 0111 0111) ≡ 1101 – 1011 (by algorithm) = 0100 – 0010 = (0100 + 111010) – 0000 (by algorithm) = 111110 = (1+3j) 4.3 multiplication the multiplication process of two complex binary numbers is similar to multiplication of two ordinary binary numbers except that while adding the intermediate results of multiplication, the new rules for addition, as given in section 4.1, should be followed. the zero rule plays an important role in reducing the number of summands resulting from intermediate multiplications. example: multiply (2–j3)(1+j3) solution: the binary representations of the given complex numbers in base (–1–j) are: (using table 1) 2–j3 = 1100 + (1110111) = 1011base –1–j 1+j3 = 0001 + 110011 = 111110base–1–j now (2–j3)(1+j3) = 1011 x 111110 111110 1011 ========================= 111110 111110 000000 111110 ========================== 111100010 bold-faced 1s help us in recognising the pattern 111 + 11 which results in 0 (zero rule). for verificaton 111100010 = (–1–j)8 + (–1–j)7 + (–1–j)6 + (–1–j)5 + (–1–j)1 = 11 + j3 4.4 division the division algorithm is based on determining the reciprocal of the divisor (denominator) and then multiplying it with the dividend (numerator) according to the multiplication algorithm given in section 4.3. thus 206 towards formulation (a + jb) ÷ (c + jd) = (a+jb)(c+jd)–1 = (a+jb)z (3) where z = w–1 and w = c + jd we start with our initial approximation of z setting z0 = (–1–j)–k where k is obtained from the representation of w such that w ≡ (–1–j)∑ ∞= k i ia –i (4) in which ak ≡ 1 and ai ≡ 0 for i>k. the successive approximations are then obtained by zi+1 = zi (2 – wzi). if the values of z do not converge, we correct our intial approximation to z0 = –j(–1–j)–k which will definitely converge (blest and jamil, 2001). having calculated the value of z, we just multiply it with (a+jb) to obtain the result of the division. in the following examples, for the sake of clarity, we have used decimal numbers to explain the converging process of the division algorithm. let (a+jb) = 1 + j2, and w = 1+j3. our calculations for approximation of z = w–1 then begin as follows: 1 + j3 = 0001 + 110011 = 111110base–1–j = 1.(–1–j)5 + 1.(–1–j)4 + 1.(–1–j)3 + 1.(–1–j)2 + 1.(–1–j)1 + 0.(–1–j)0 ⇒ k = 5 therefore z0 = (–1–j)–5 = 0.125–j0.125 z1 = 0.15625 –j0.21875 z2 = 0.100208989 –j0.299802410 z3 = 0.1000000024 –j0.3000000010 z4 = 0.10000000 –j0.30000000 z5 = 0.1 – j0.3 z6 = 0.1 – j0.3 (converging) now 0.1 – j0.3 = 0.0111111111111111…base –1–j so (1+j2) ÷ (1+j3) = (1+j2) x (1+j3)–1 = 0101base –1+j x 0.0111111111111111…base –1–j = 1.0001001001001…base –1–j = 0.7 – j0.1 as another example, let w = –28–j15, then –28–j15 = 111100010111base –1–j = 1.(–1–j) 11 + 1.(–1–j) 10 + 1.(–1–j) 9 + 1.(–1–j)8 + 0.(–1–j)7 + 0.(–1–j)6 + 0.(–1–j)5 + 1.(–1–j)4 + 0.(–1–j)3 + 1.(–1–j)2 + 1.(–1–j)1 + 1.(–1–j)0 ⇒ k = 11 we begin by choosing z0 = (–1–j)–11 = 0.15625 + j0.15625 z1 := 0.239 + j0.0449 z2 := –0.249 + j0.128 z3 := –0.398 – j0.160 z4 := 1.014 + j5.235 z5 = –895 – j87.9 (not converging) 207 tariq jamil, david blest and amer al-habsi so we correct our initial approximation to: z0 = –j(–1–j)–11 = –0.015625 +j0.015625 z1 := –0.02393 + j0.0176 z2 := –0.0279 + j0.01556 z3 := –0.0278 + j0.01486 z4 := –0.02775 + j0.014866 (converging) the converging value of z4 can be represented in base (–1–j) and then multiplied with any given complex number to obtain the result of dividing the given complex number by –28–j15, as in previous example. 5. conjugate and magnitude of complex numbers beyond the rules for real arithmetic, complex numbers arithmetic may require the calculation of conjugates and magnitudes as well. thus, if wbase –1–j = (c + jd)base –1–j = a∑ ∞= k -i i (–1–j)i (5) then, since –j(–1–j) = –1+j, the complex conjugate of w is given by w~base –1–j = (c – jd)base –1–j = a∑ ∞= k -i i (–j)i(–1+ j)i (6) which gives c = a∑ ∞= k -i i ~(–1–j)i where ai~ = ½ (1–ji) ai and for i = 0 (mod 4), ai~ = ai ; i = 1 (mod 4), ai~ = 1110.1ai ; i = 2 (mod 4), ai~ = 0 ; and for i = 3 (mod 4), ai~ = 1.1ai the imaginary part of the conjugate d can be calculated as j (c – w). as an example, let w = 1 + j3, then its conjugate w~ will be of the form c – jd, where c and d are calculated as follows: in base (–1–j), w = 1+j3 = a5a4a3a2a1a0 = 111110base –1–j then a0~ = a0 = 0 a1~ = 1110.1a1 = 1110.1 x 1 = 1110.1 a2~ = 0 a3~ = 1.1a3 = 1.1 x 1 = 1.1 a4~ = a4 = 1 a5~ = 1110.1a5 = 1110.1 x 1 = 1110.1 thus c = a5~(–1–j)5 + a4~(–1–j)4 + a3~(–1–j)3 + a2~(–1–j)2 + a1~(–1–j)1 + a0~(–1–j)0 = 1110.1(–1–j)5 + 1(–1–j)4 + 1.1(–1–j)3 + 0(–1–j)2 + 1110.1(–1–j)1 + 0(–1–j)0 = 000000001base –1–j and d = j(c – w) = 111(000000001 – 111110) = 01101base –1–j 208 towards formulation now –jd = 11 x 1101 = 1110111 thus w~ = c – jd = 1 + 1110111 = 1010base –1–j = 1 – j3 to calculate the square of magnitude of w, we have |w|2 = ww~ = 111110 x 1010 = 111001100base –1–j to verify (1+j3)(1–j3) = 10base 10 = 111001100base –1–j 6. summary and conclusion we have described conversion algorithms and arithmetic procedures for a (–1–j)-base binary number system which allows given complex numbers to be represented as one unit. this is expected to facilitate equal opportunity representation to complex numbers and, hence, simplify their operations in today’s microprocessors. currently, work is underway to design a hardware arithmetic unit based on algorithms presented in this paper and then it will be implemented using field programmable gate arrays. references blest, d. and jamil, t. efficient division in a binary representation for complex numbers. proceedings of the ieee southeastcon 2001. clemson, south carolina. 30 march-1 april 2001. usa. geppert, l. 1999. the 100-million transistor ic. ieee spectrum. 36: 7: 23-60. jamil, t., holmes, n., and blest, d. 2000. towards implementation of a binary number system for complex numbers. proceedings of the ieee southeastcon 2000. nashville, tennessee. 7-9 april 2000. usa knuth, d.e. 1960. an imaginary number system. communications of the acm. 3: 245-247. penney, w. 1964. a numeral system with a negative base. mathematics student journal. 11(4): 1-2. penney, w. 1965. a binary system for complex numbers. journal of the acm. 12(2): 247-248. stepanenko, v.n. 1996. computer arithmetic of complex numbers. cybernetics and system analysis. 32(4): 585-591. received 8 june 2001 accepted 7 november 2001 209 tariq jamil*, david blest** and amer al-habsi* example: subtract \(2–3j\) from 3 summary and conclusion references squ journal for science, 2017, 22(2), 73-80 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp73-80 sultan qaboos university 73 synthesis and coordination chemistry of boron-functionalized poly(pyrazolylpyridyl)borate with ln(iii) metals nawal k. al-rasbi* 1 and michael d. ward 2 1 department of chemistry, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman; 2 department of chemistry, university of sheffield, sheffield, s3 7hf, uk. email: nrasbi@squ.edu.om abstract: a new family of lanthanide/boron-based complexes have been synthesized from the novel substituted poly(pyrazolylpyridyl)borate ligand containing phenyl substituents on the boron atom ph2bp py (l). the complexes have been fully characterized by analytical and spectroscopic methods. the single crystal x-ray structure and mass spectroscopy reveal the isostructural dinuclear complexes: [ln2(l)2(no3)2(oh)2] where ln = eu, gd or tb. upon excitation of the ln(iii) complexes in dcm, their luminescence spectra display narrow f–f transitions. it is found that the ligand can efficiently sensitize the tb(iii) complex because of the better triplet state energy match to the tb(iii)– 5 d0 excited states. keywords: boron; europium(iii); terbium(iii); crystal structure; emission. مركبات البورون مع بايروزول بيريدين وفلزات الالنثاناتلالتركيب والخصائص الكيميائية مايكل د. وورد و نوال الراسبي مجموعتي فينول ملتصقة يحتوي علىوالذي من ليجند البورون مع بايروزول بيريدين الالنثانات/بورون ركباتمعائلة جديدة لتم تكوين :صالملخ ph2bp بذرة البورون py (l) . المعقد ثنائي الفلز: ثبت التركيب البلوريأكما[ln2(l)2(no3)2(oh)2] حيثln = eu, gd or tb . ا لمركب التيربيوم ضوئي. وجدنا بأن الليجند يستطيع أن يتحسس f–fمركبات ف محاليلها على انتقاالت ضوئية بطبيعة الطيف الضوئي لل دلولقد بفعالية وذلك ألقتراب مستويات الطاقة بينهما. .طيف ضوئي بلوري، تركيب(، iiiتيربيوم) ،(iiiبيوم)ييور ،ورونب: مفتاحيةالكلمات ال 1. introduction oron, the only non-metal of group 13, displays a unique structural diversity in its combinations with transition metals [1]. the enormous diversity of boron chemistry ranges from polyboranes [2] to carboranes [3] to metallaboranes [4] and metal complexes of organoboron ligands [5]. in 1966, poly(pyrazolyl)borates were first reported by s. trofimenko [6]. the poly(pyrazolyl)borate ligands have been proven to be extremely popular amongst coordination chemists for a wide range of applications because of their ease of synthesis, ease of functionalisation, and the steric protection which they afford to metal centres [7]. over the years poly(pyrazolyl)borates such as bidentate bp ligands have been compared to -diketonates (chart 1) [5]. these 'first-generation' ligands are labile, rich in electron density and their coordination behavior is strongly dependent on the coordinating metal [8-11] in subsequent years, a new class of c 3 -substituted poly(pyrazolyl)borate ligands were developed in which additional coordinating groups have been attached to the pyrazolyl rings, completely changing the character of the simple first-generation ligands. constituents such as pyridine [12]. (bp py in chart 1), bipyridyl, [13] thioanisyl, [14] pyrazinyl, [15] and carboxamide [16] units have b https://mail.squ.edu.om/owa/redir.aspx?surl=orzebdj-y_8x0lhitn4bqqur0j4qch67elawngdq7emuntl360vtcg0ayqbpagwadabvadoadqawadkamwaxadkangbaahmadab1agqazqbuahqalgbzaheadqauaguazab1ac4abwbtaa..&url=mailto%3au093196%40student.squ.edu.om nawal k. al-rasbi and michael d. ward 74 been appended to the pyrazolyl c 3 positions of poly(pyrazolyl)borates, converting the ligands to polydentate chelates. the ward group prepared new ligands by the attachment of a 2-pyridyl substituent to each pyrazolyl ring at the c 3 position converting each 'arm' of the ligand to a tridentate chelate [17-18]. substitution of poly(pyrazolyl)borates is also confined largely to the boron atom [5]. the potentially reactive b–h bonds in bp py , may be replaced with either alkyl or aryl groups. suitably sized ligand substituents can help to prevent agostic interaction through steric blocking of the space above and below the poly(pyrazolyl)borate ligands [19-20]. substituents on the boron atom of bp ligands have shown great stability such as on [(ph2bp)2ni]. [21] whilst the complex [(h2bp)ag] is air-sensitive, the analogue [(ph2bp)ag] is very stable, [22] suggesting that the stability of these complexes result from a combination of steric effects and not just solely from the aromatic substituents on the pyrazolyl rings. as part of our interest in luminescent lanthanide complexes, we describe the synthesis, crystal structure and luminescence behavior of a series of lanthanide complexes with the boron-substituted bis(pyrazolylpyridyl)borate ligand: ph2bp py (l) (chart1) in which two bidentate arms are connected to a boron centre. the incorporation of two phenyl units at the boron centre has altered its sensitization properties to eu(iii) and tb(iii) ions. the x-ray crystal structure confirmed the general formulae of the complexes to be: [ln2(l)2(no3)2(oh)2] where ln = eu, gd or tb. chart 1: the structures of the poly(pyrazolyl)borates: bp, tp, bp py and ph2bp py (l). 2. experimental the boron ligand was prepared according to the method described by trofimenko [19]. l (na[ph2bp py ]): 3-(2-pyridyl)pyrazole (0.6 g, 4.14 mmol) and nabph4 (0.58 g, 1.70 mmol) were ground together finely and heated gradually to 190 °c for 4 hrs under n2. during this time, h2 gas was evolved at 150 °c and then benzene was evolved at 190 °c. any unreacted 3-(2-pyridyl)pyrazole sublimed at the top of the flask. after cooling to r.t.; the melt was washed with hot toluene (15 ml) and hexane (15 ml) and finally dissolved in ch2cl2 and concentrated in vacuum to yield 0.50 g of white powder (60%). positive-ion electrospray ms: m/z 477 [m + ]. ir(kbr) 1021 cm –1 (b–c). 11 b nmr (cdcl3): –0.819. found: c, 70.61; h, 5.09; n, 17.49. required for c28h22n6bna: c, 70.63; h, 4.62; n, 17.65%. synthesis of the complexes the complexes were prepared by combining equimolar quantities of eu(no3)3, gd(no3)3 or tb(no3)3 with the ligand in meoh and left to stand for 1 hr during which time a precipitate was formed. the precipitate was filtered off and washed with meoh to give a powder. 7 characterization data for the complexes are as follows: [eu2(l)2(oh)2(no3)2]. yield 70 %. es-ms: m/z 1310 {[eu2(ph2bp py )2(oh)2(no3)]} + . ir(kbr) 1001 cm –1 (b–c). [gd2(l)2(oh)2(no3)2]. yield 72 %. es-ms: m/z 1253 {[gd2(ph2bp py )2(oh)2]} 2+ and 1316 {[gd2(ph2bp py )2(oh)2(no3)]} + . ir(kbr) 1003 cm –1 (b–c). x-ray quality crystals were grown by slow evaporation of a dcm solution of the complex in air. [tb2(l)2(oh)2(no3)2]. yield 70 %. es-ms: m/z 1318 {[tb2(ph2bp py )2(oh)2(no3)]} + . ir(kbr) 1001 cm –1 (b–c). spectro-fluorimetric measurements uv-visible spectra were recorded on a varian cary 50 conc uv-visible spectrophotometer in range 250-800 nm. quartz cuvettes of 1 cm path length were used and solvent background corrections were applied. steady state fluorescence spectra in solid and solution states were recorded on an edinburogh fs5 fluorimeter. the solid state b n n n n n n b n n n n n n h h l = ph2bp pybppytp bp synthesis and coordination chemistry 75 phosphorescence lifetime measurements for the ln(iii) complexes were measured on perkin-elmer ls50b fluorimeter at rt and 77 k. crystallography single crystals of the complex gdl was obtained as detailed above. data was collected at 100 k, using bruker apex-ii ccd diffractometer equipped with mo-kα radiation. absorption corrections were applied in each case using sadabs. [28] the structures were solved by direct methods or heavy atom patterson methods and refined by full matrix least squares methods on f 2 using shelxl-97. [29] the hydrogen atoms were generated geometrically with isotropic thermal parameters. crystallography data (excluding the structure factors) for the reported structure have been deposited with the cambridge crystallographic data centre. 3. results and discussion the synthesis of the new bi(pyrazolylpyridyl)borate ligand: ph2bp py (l) is outlined in scheme 1. the key intermediates for formation of the ligand is 3-(2-pyridyl)pyrazole, which is prepared from 2-acetylpyridine, in the usual two-step procedure for conversion of acetyl groups to pyrazole groups. [23] then, l was prepared by reaction of 3-(2-pyridyl)pyrazole with kbph4 in a melt at 190 °c until benzene vapour is no more evolved. [24] satisfactory elemental analysis, fab mass spectra, [11] b nmr and 1 h nmr spectra confirmed the formulation of the ligand. b n n n n n n l = ph2bp py n o dma-dmf n o nme2 nh2-nh2 n n n h kbph4 190ºc reflux scheme 1. schematic route for the synthesis of ph2bp. reaction of l with nitrate salts of eu(iii), gd(iii) or tb(iii) in meoh afforded white precipitates respectively. x-ray quality crystals were grown by slow evaporation of their solutions in dichloromethane, dcm. the complexes were satisfactorily characterised by fab mass spectrometry. for example, the fragment: {[m2(l)2(oh)2(no3)]} 2+ was observed at m/z 1310, 1316 and 1318 respectively for eu(iii), gd(iii) or tb(iii) complexes. the crystal structure of [gd2(l)2(no3)2(oh)2]·ch2cl2 (gdl) in figure 1 has proved to be a dinuclear complex in which each ligand donates two bidentate sites to one metal ion, with the two metal centres bridged through two hydroxyl groups. the coordination environment about each metal centre is 8-coordinate and best described as a square antiprismatic, having an equatorial belt of four n atoms from [l] – with two bridging hydroxyl groups and one bidentate chelating (no3) – in the axial positions on either side of the mn4 plane. the four n-donor atoms from each [l] – ligand form a plane, with the gd(iii) centre lying 0.33 å out of the n4 plane. the angle between the two gd(nn) planes is 14.3°. the metal–ligand bond distances exhibit a gd–n(py) bonds are on average significantly longer than the gd–n(pz) bonds and are comparable to previously reported complexes. [12-13] selected bond distances and angles are listed in table 1. it is also worth noting that replacement of the hydrogen atoms in bp by two phenyl rings in ph 2bp py (l) changes the coordination behaviour of the ligand compared to functionalized bp which yielded mononuclear nawal k. al-rasbi and michael d. ward 76 complexes with ln(iii) ions. [12] the steric effects caused by the phenyl rings play a big role in the new structure. intra-molecular o–h··· hydrogen-bonding interactions (~2.9 å) are observed, involving one phenyl ring and the coordinating hydroxyl group, which clearly plays an important role in stabilising this complex. the steric interactions within the gd(iii) complex are shown in figure 1 (bottom). other ··· and ···ch stacking interactions between the aromatic rings and the solvent molecules, were observed in the molecular packing. figure 1 top: the crystal structure of gdl showing the two hydroxyl bridges. bottom: the -interactions within the molecule. table 1. selected bond lengths (å) and angles (˚) for gdl. gd(1)-o(1h)#1 [a] 2.253(5) gd(1)-n(11) 2.496(6) gd(1)-o(1h) 2.284(5) gd(1)-n(31) 2.554(6) gd(1)-o(1) 2.481(5) gd(1)-n(1) 2.560(6) gd(1)-n(21) 2.488(6) gd(1)-gd(1)#1 [a] 3.7240(15) gd(1)-o(2) 2.491(5) o(1h)#1-gd(1)-o(1h) [a] 69.9(2) o(1h)-gd(1)-o(2) 77.26(18) o(1h)#1-gd(1)-o(1) [a] 161.09(17) o(1)-gd(1)-o(2) 51.43(17) o(1h)-gd(1)-o(1) 128.68(17) n(21)-gd(1)-o(2) 119.06(18) o(1h)#1-gd(1)-n(21) [a] 85.19(18) o(1h)#1-gd(1)-n(11) [a] 87.62(18) o(1h)-gd(1)-n(21) 137.24(19) o(1h)-gd(1)-n(11) 135.33(18) o(1)-gd(1)-n(21) 77.82(19) o(1)-gd(1)-n(11) 79.98(18) o(1h)#1-gd(1)-o(2 [a] 147.09(17) n(21)-gd(1)-n(11) 74.63(18) [a] symmetry transformations used to generate equivalent atoms: #1 -x,-y+1,-z+1. synthesis and coordination chemistry 77 photo-physical properties the absorption spectrum of l in dcm is shown in figure 2. it shows two strong transitions at 250 and 285 nm which can be attributed to ligand-centred   * transitions from (pyrazolyl/pyridine) units [25]. figure 2. the absorption spectra of l and its ln(iii) complexes (1x10 -5 m) in dcm solutions at room temperature. metal-centred luminescence the triplet state energy ( 3 *) of l can be determined from the phosphorescence spectrum of its gd(iii) complex recorded in a mixture of ethanol/methanol solution at 77k. gd(iii) ion lacks a low lying electronic acceptor level (>30,000 cm –1 ), so its luminescence features are associated with those of the coordinated ligand. from this emission spectrum, the ligand-based triplet state energy of gdl is 28,800 cm –1 (347 nm). the luminescence from the eu(iii) and tb(iii) complexes in dcm solution are presented in figure 3. excitation of the eul at 345 nm in dcm results in intense red luminescence of eu(iii) showing characteristic peaks from the 5 d0  7 fj transitions of eu(iii) at 558, 603, 626, 662 and 711 nm. this implies that energy-transfer from the ligand triplet state to the emissive 5 d0 level of eu(iii) (ca. 17500 cm -1 ) is favourable. the presence of the 5 d0 7 f0 transition proves the presence of the eu(iii) centres in a non-centrosymmetric site in eul which agrees with the x-ray crystal structures. [26] upon excitation of the tb(iii) complex, tbl, at 345 nm in ch2cl2, its luminescence spectrum displays strong green emission from the 5 d4  7 f6-2 transitions at 632, 592, 550 and 496 nm. the energy difference between the triplet state energy of l and the 5 d4 level (20,500 cm –1 ) of tb(iii) is equal to ca. 8,300 cm – 1 . according to latva’s empirical rule, optimal sensitization for the tb(iii) luminescence requires an energy gap e( 3 *– 5 d4) more than 1,850 cm –1 . [27] therefore, l can sensitise the tb(iii) centre efficiently. by comparison to the eu(iii) complex, the situation is different. according to latva’s empirical rule, for optimal ligand to eu(iii) energy transfer, the energy gap should be no more than 2,500 cm –1 . in fact the calculated energy differencee( 3 *– 5 d0) is higher than this at around 11,300 cm –1 . therefore, the ligands can poorly transfer energy to the 5 d0 excited states and hence the luminescence from eu(iii) is weak. this result is in agreement with their observed lifetime (obs) measurements. the phosphorescence decays of the eu(iii) and tb(iii) complexes with l in dcm are mono-exponential. the luminescence lifetime of tb(iii) is longer than that from eu(iii). table 2. summary of the photophysical data for l and its ln(iii) complexes. compd max (nm) [(10 3 m -1 cm -1 ) in mecn lifetime at f-f (ms) [a] l 296(65), 248 (29) – eul 293(36), 345 (sh) 0.56 gdl 294(45), 345 (sh) – tbl 294(43), 345 (sh) 0.84 [a]  in dry dcm, the estimated standard error < 1%. 0 0.1 0.2 0.3 0.4 0.5 0.6 230 280 330 380 430 a b s o rp ti o n wavelength/nm l eul gdl tbl nawal k. al-rasbi and michael d. ward 78 figure 3. luminescence spectra of the ln(iii) complexes: (a) [eu2(l)2(no3)2(oh)2] (eul) and (b) [tb2(l)2(no3)2(oh)2] (tbl) in (1x10 -5 m) dcm solutions at room temperature. 4. conclusion the new boron-based ligand, l, which is derived from the well-known bis(pyrazolyl)borate core, has been synthesised and fully characterised. the x-ray crystal structure and ms analysis revealed the isostructural dinuclear complexes: [ln2(l)2(no3)2(oh)2], ln = eu, gd and tb. the metal centres are bridged through two hydroxyl groups. the steric effects caused by the aromatic substituents on the boron centre has played a big role in stabilizing the structures, through intra-molecular o–h··· hydrogen-bonding interactions. the photophysical investigations in dcm gave evidence that l is able to achieve ligand to metal energy transfer and intense red emission from eu(iii) and green emission from tb(iii) centres are observed in the visible region. table 3. crystallographic data for gdl. formula c29h25bcl2gdn7o4 formula weight 774.52 t (k) 100(2) k crystal system triclinic, p1̄ a (å) 11.430(4) b (å) 12.063(4) c (å) 12.255(4)  (°) 85.638(17)  (°) 80.838(18) (°) 63.208(17) v(å 3 ) 1489.1(8) z 2 dcalc 1.727  (mm-1) 2.455 crystal size (mm) 0.16 x 0.08 x 0.04 reflections collected 24005 independent reflections 6845 [r(int) = 0.0887] data / restraints / parameters 6845 / 4 / 392 goodness-of-fit on f2 0.976 final r indices a r1 = 0.0580, wr2 = 0.1419 largest diff. peak and hole (e.å -3 ) 3.722 and -1.756 acknowledgement we would like to thank the department of chemistry, college of science, sultan qaboos university for support. synthesis and coordination chemistry 79 appendix crystallographic data for the structure reported in this article have been deposited with the cambridge crystallographic data center. a copy of 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سماوي وإيمان طوالبه عندما يكون الوسط الحسابي للمتغير أداء طريقة المعاينة المرتبة الثنائية المراحل للتقدير االنحداري سوف يبحث هنا : خالصة طريقة المعاينة المرتبة حاكاة ، دلت على أن مقدر االنحدار باستخدام أن التحليالت األولية وطرق الم . المساعد غير معروف وأيضاً هو . مرتبة األخرى الأيٍّ من طرق المعاينة المرتبة وغير الثنائية المراحل هو أكثر فاعلية من مقدرات االنحدار باستخدام المرتبة وغير المرتبة، أحادية أو طرق المعاينة أفضل وأكثر فاعلية من المقدرات البسيطة باستخدام األوساط الحسابية ألي من . ثنائية المراحل abstract: the performance of a regression estimator based on the double ranked set sample (drss) scheme, introduced by al-saleh and al-kadiri (2000), is investigated when the mean of the auxiliary variable x is unknown. our primary analysis and simulation indicates that using the drss regression estimator for estimating the population mean substantially increases relative efficiency compared to using regression estimator based on simple random sampling (srs) or ranked set sampling (rss) (yu and lam, 1997) regression estimator. moreover, the regression estimator using drss is also more efficient than the naïve estimators of the population mean using srs, rss (when the correlation coefficient is at least 0.4) and drss for high correlation coefficient (at least 0.91.) the theory is illustrated using a real data set of trees. keywords: double extreme ranked set sample; double ranked set sample; extreme ranked set sample; ranked set sample; regression estimator. 1. introduction i n many applications, considerable cost savings can be achieved if the number of quantifications is only a small fraction of the number of available units, although all units contribute to the information content of the quantification. ranked set sampling (rss) is a method of sampling that can achieve this goal. rss was first introduced by mcintyre (1952). it is highly powerful and much superior to the standard simple random sampling (srs) for estimating some population parameters. rss can be applied in agricultural, environmental and human populations. for example, the level of bilirubin in the blood of infants can be ranked visually by observing: (i) color of the face. (ii) color of the chest. (iii) color of lower part of the body. (iv) color of terminal parts of the whole body. as the yellowish goes from (i) to (iv), the level of bilirubin in the blood goes higher (see samawi and al-sakeer 2001). al-saleh and al-kadiri (2000) showed that the efficiency of estimating the population mean could be improved even more by using double ranked set sampling (drss). also, they proved that ranking in the second stage is easier than in the first stage. moreover, as a variation of rss samawi et al. (1996) investigated extreme ranked set sample (erss) and also suggested double extreme 311 hani m. samawi and eman m. tawalbeh ranked set sampling (derss) samawi (2002). more details about rss can be found in kaur et al., (1995) and patil et al. (1999). in this paper, we investigate the performance of drss for estimating the population mean using the regression estimator. theoretical and numerical comparisons with other estimators will be considered. in section 2, notations, definitions and some basic results are introduced. the regression estimator using srs and, rss regression estimator (yu and lam, 1997) are introduced in section 3. our proposed regression estimator using drss and its properties are given in section 4. in section 5, we illustrate the theory using a set of data representing a real life situation. 2. sample notation and definition with some useful results 2.1 one stage sampling 2.1.1 univariate population rss involves selecting random sets each of size from the target population. in the most practical situations, the size will be 2, 3 or 4. rank each set by a suitable method of ranking, for example, by using prior information or visual inspection. in sampling notation this implies: r r r 1(1) 1( 2) 1( )11 12 12 2(1) 2( 2) 2( )21 22 2 (1) ( 2) ( )1 2 , , ,, , , , , ,, , , after ranking , , ,, , , r rr r r rr r rr x x xx x x x x xx x x x x xx x x r          →            (2.1) where ijx denotes the -th observation in the i j -th set and ( )j ix is the -th ordered statistic in the i j -th set. only the elements 1(1) 2( 2), ,..., ( )r rx x n mr= x are quantified i.e. the element with smallest rank from the first set, the second smallest from the second set, and so on until the largest unit from the -th set is measured. this represents one cycle of rss. we can repeat the whole procedure times to get a rss of size (takahasi and wakimoto, 1968). r m 2.1.2 for bivariate population samawi and muttlak (1996) modified the above procedure in the case of bivariate distributions to estimate the population ratio, /yr χµ µ= . the procedure is described as follows: first choose independent bivariate elements from a population, with bivariate distribution function . rank each set with respect to one of the variables y or 2r )y( ,f x x . suppose ranking is on variable x . apply the same procedures as in case of univariate population but for each measured unit from the x ’s, the associated unit from the y ’s is measured too. this may be repeated times to get a bivariate sample of size nm rm= . in sample notation: the sample { , =1,2,…, ; =1,2,…, } will denote the bivariate rss. ( )( ,i i kx y [ ]i i k i) r k m 2.2 double ranked samples (two stage sampling) as a variation of rss, al-saleh and al-kadiri (2000) introduced the drss procedure as follows: 1. identify r elements from the target population and divide these elements randomly 3 into sets each of size elements. r 2r 2. apply the usual rss procedure to each set to obtain r rss, each of size r . 3. employ again the rss procedure in step 2, to obtain the drss of size . r 4. we may repeat steps 1-3 m times to obtain a sample of size n rm= . in sampling notation, after ranking each sample separately in each subset, we get: 312 regression estimator using double ranked set sampling ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 2 1 1 1 1 2 1 2 2 2 1 1 1 1 2 ..... ..... ..... k k r k k k r k r k r k r r k x x x x x x x x x                ,…, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 2 1 2 1 2 2 2 1 2 ... ... ... r r r k k r k r r r k k r k r r r r k r k r r k x x x x x x x x x                , (2.2) k=1,2,…,m, where ( ) ( )l i i kx is the i-th ordered observation in the i-th sample of the l-th set in the k-th cycle. use rss scheme on each subset separately, to get ( ) ( ) ( ){ }1 1 11 1 2 2, ,...ik k k r ra x x x= k , …. ( ) ( ) ( ){ }1 1 2 2, ,...r r rik k k r ra x x x= k . then in the second stage, let w = i-th smallest observation in , then {w , ( )i i k ika ( )i i k i=1,2,…,r, k=1,2,…,m} will denote the drss. now let w , k=1, 2, …., m, be a drss, where the mean and variance of w are 1(1) ( ),...,k rw r k ( )i i k ( )iµ ∗∗ and ( ) 2 iσ ∗∗ , respectively. al-saleh and alkadiri (2000) showed that: ( ) 1 1 i r r i µ µ∗∗= ∑ = and ( ) ( )( ) 2 22 1 1 1 i i r r r i i σ σ µ∗∗ ∗∗ µ   = + −∑ ∑   = =  where µ and 2σ are the mean and the variance of the population, respectively. also, it was shown that ranking in the second stage is easier than in the first stage. 3. regression estimators using srs and rss as in ratio estimation, the linear regression estimator is used to increase the precision of estimating the population mean by using extra information in an auxiliary variable x that is correlated with the survey variable y. when the relation is approximately linear, and the line does not go through the origin, an estimate of the population mean based on the linear regression of y on x is suggested rather than using the ratio of the two variables. 3.1 regression estimator using srs let ( , )i ix y , i=1,2,…,r, be a bivariate sample from , and assume that ( , )f x y ( )ixy xi iy β εµ µ= + − + (3.1) where xµ and yµ are the means of x and y respectively, and for fixed ix , the iε ’s , i=1,2,…,r are i.i.d (independent and identically distributed) with mean zero and variance ( )2 2 1yε 2σ σ ρ−= . consider the case where xµ is unknown. the method of double sampling can be used to obtain an estimate of yµ . this involves drawing of a large random sample of size n′, which is used to estimate yµ . then a subsample of size n is selected from the original selected units to study the primary characteristic of y . setting , the first and the second-phase samples are simple random samples. then the double-sampling regression estimator 2 and n r m n rm′ = = dsy is given by ( )ds srs srsy y x xβ ′= + − , (3.2) 313 hani m. samawi and eman m. tawalbeh where 1 srs ix xrm = ∑ , 1 srs irm = ∑y , y x ′ is the sample mean of x based on observations of x in the first phase and 2r m ( )( ) ( ) 2 i isrs srs i srs x x y y x x β − −∑ = −∑ . when the underlying distribution of (x, y) is assumed to be bivariate normal, the regression estimator dsy is an unbiased estimator for yµ and its variance is given by ( ) ( ) 2 2 2 2 1 1 1 3ds y r var y n r n r m εσ ρ σ  − = + +  −  (3.3) (sukhatme and sukhatme, 1970). if the assumption of the linear relationship in (3.1) is invalid, then the srs regression estimator in (3.2) is in general a biased estimator of yµ . 3.2 regression estimator using rss consider the bivariate rss. from (3.1) the relationship between y and [ ]i k ( )i kx is [ ] ( )( ) [ ]y xi k i k i ky xµ β µ= + − +ε , i=1,2,…,r and k=1,2,…,m. (3.4) again, when xµ is unknown the method of double sampling (two-phase sampling) can be used to obtain an estimate of xµ . note that the first-phase sample is a simple random sample and the second-phase sample is a ranked set sample. then the double-sampling regression estimator rdsy based on rss as in yu and lam (1997) have given by: ( )rds rss rssy y x xβ ′= + − , (3.5) where x ′ is the sample mean of x based on the observations of the first phase. furthermore, using the basic properties of conditional moments, yu and lam (1997) showed that 2r m rdsy is an unbiased estimator of yµ under (3.4), and the variance is given by: ( ) ( ) 2 2 2 2 2 2 1 1 rssrds y zr z z var y e n s r m εσ ρ σ   −   = + +       , (3.6) where ( ) /x xz x µ σ′= − , ( ) ( ) /x xi k i kz x µ σ = −  , ( ) 1 rss i k i i z z rm = ∑∑ , ( )( ) 2 2 1 zr rssi k k i s z rm = −∑∑ z . again, if the assumption of linear relationship is invalid, the rss regression estimator in (3.5) is in general a biased estimator of yµ . next we will propose our approach for using a regression estimator for estimating yµ based on drss. 314 regression estimator using double ranked set sampling 4. regression estimator using drss 4.1 drss for regression estimator in the two-phase regression estimator using drss, for the k-th cycle, in the first stage r quantified rss samples each of size are considered. the following will denote the first stage sampling: r ` ( ) ( ) ( ){ } ( ) ( ) ( ){ } ( ) ( ) ( ){ } 1 1 1 1 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 2 , ,..., , , ,..., , , ,..., , 1, 2,..., . k k k r r k k k k r r k r r r rk k k r r k a x x x a x x x a x x x k = = = = m these sets of quantified observations, of size mr2, are used to estimate xµ , the population mean of the variable x, which is assumed to be unknown. in the second stage a bivariate drss, of size n=rm, which is { ( ) [ ]( ) }: 1 2 1 2i i k i i kw , y i , ,..., r, k , ,..., m= = is measured. note that, rankings in the second stage on the variable x are based on the exact measures, i.e. perfect ranking. also, we are not using the mr3 observation from the first stage to estimate xµ , because we quantified only mr2 of them and not all the mr3 observations and this will reduce the cost of the sampling unit in the study. 4.2 regression estimator of µy if w and are, respectively, the i -th smallest value of ( )i i k [ ]i i k y x (from the second stage of drss), and the corresponding value of y obtained from the th sample in the th set, then from (3.1), we have -i -k ( ) ( )( )y xi i k i i k y w ikµ β µ ε= + − + , 1, 2,..., , 1, 2,...,i r k m= = , (4.1) where, is the model slope, β /yβ ρ xσ σ= , and iikε are random errors as in (3.1). let rssx ∗ be the sample mean based on the r rss samples of size , i.e., 2r m ( ) 1 2 1 1 1 1 rss i i k r m r x x r m l k i ∗ = ∑ ∑ ∑ = = = . note that, (1) ( ) ( )( )121 1 1 1rss xi i k r m r e x r m l k i e x µ∗ = ∑ ∑ ∑ = = = = (4.2) (2) ( ) ( 2 2 ( )2 3 1 rss x i xvar x r m r m σ )µ µ∗ = − −∑ (4.3) (see dell and clutter (1972)). under drss, the regression estimator of the population mean yµ can be defined as ( )re ˆgd drss d rssy y x wβ ∗= + − (4.4) where, ( )( ) [ ] ( )( ) ( ) [ ]2 1 11 1ˆ , , 1 1 1 1 1 1 i i k i i k d drssi i k i i k i i k m r w w y m r m rk i w w y ym r rm rmk i k iw w k i β −∑ ∑ = == = =∑ ∑ ∑ ∑ = = = =−∑ ∑ = = and rssx ∗ as above. 315 hani m. samawi and eman m. tawalbeh 4.2.1. properties of the estimator again, using the basic properties of conditional moments and the above results, the following theorem will be proved. theorem 4.1: under (4.1) assumptions: (1) ( )re gd ye y µ= . (2) ( ) ( ) ( ) ( ) 2 *2 2 2 2 2 21 1re 1 rssy x i z rz zwvar y egd srm r m i σ β ρ σ   −  = − + + ∑    =    , where ( ) ( ) ( )( ) 2 2 1, , 11 and . i i k z ri k i k x x rss x w rss x x w µ m r z s z rm ik w µ x z z σ µ σ σ ∗ ∗ ∗ ∗ − = = −∑ ∑ == − − = = ssz proof: the prove of this theorem and two required propositions are in the appendix. 4.2.2 performance of re gdy with respect to naive estimators from the previous results, the relative precision of re gdy with respect to the naive estimators of yµ , rssy and drssy using rss and drss respectively are as follows: ( ) ( ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 1 re 2 2 2 2 2 2 3 1 2 2 2 2 2 2 2 1 1 , 1 1 , 1 1 r y i i gd rss r rss wy i iz y i r rss w y i iz x x r m rp y y z z e rm s r m z z r e s r σ σ β ρ σ σ β ρ σ σ = ∗ = ∗ = =   −   − + +       ∑ =   −   − + +       ∑ ∑ ∑ (4.5) ( ) ( ) ( ) ( ) ( ) **2 re 2 2 2 2 2 2 1 , , 1 1 y i gd drss r rss w y i iz x rp y y z z r e s r σ β ρ σ σ ∗ = ∑ =   −   − + +       ∑ (4.6) note that these relative precisions are based on the variances of the estimators. 4.2.3 performance of re gdy with respect to other regression estimators when the sample is drown from a standard bivariate normal population, the relative precision of re gdy relative to the two-phase (double sampling) regression estimator dsy based on srs (see sukhatme and sukhatme, 1970) and to the two-phase regression estimator rdsy based on rss (see yu and lam, 1997) will be respectively as follows: 316 regression estimator using double ranked set sampling ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 re 2 2 2 2 2 2 3 1 1 1 1 3 , , 1 1 y y gd ds r rss wy i iz x r rm r r m r m rp y y z z e rm s r m σ σ ρ ρ σ β ρ σ ∗ =  − − + +  − =   −   − + +       ∑ (4.7) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 re 2 2 2 2 2 2 3 1 1 1 , 1 1 rss wy y x z gd rds r rss wy x i iz x z z e rm s r m rp y y z z e rm s r m σ σ ρ ρ σ β ρ σ ∗ ∗ =   −  − + +      =   −  − + +       ∑ , (4.8) (see section 3). note that these relative precisions are based on the variances of the estimators. since t is not easy to find, the values of the above expressions simulation is used to calculate them. 4.3 simulation study 4.3.1 design of the simulation a computer simulation is conducted to study the efficiency of the regression estimator. using srs, rss, and drss bivariate normal random samples where generated when xµ =2, 4, 1, 1y xµ σ σ= = = and ρ= ]99.00.0[ −± . the performance of the regression estimators are investigated for r = 4, 5, 6, 7 and 8 and m =1, 4 and 8. using 5000 replications, estimates of the means and the mean square errors for the regression estimators were computed. the efficiency of the regression estimator is defined by ( ) ( ) ( ) /, jiji rmsermserrre = where i and j represent any type of the above sampling methods. the results for the simulation are in tables 1 and 2. table 1: the efficiency of re gdy with respect to the naive estimators based on rss and drss ρ=0.99 ρ =0.95 ρ =0.93 ρ =0.9 ρ =0.8 m r rss drss rss drss rss drss rss drss rss drss 4 4.70 2.22 2.81 1.40 2.39 1.16 2.04 0.96 1.21 0.62 5 6.92 2.40 3.55 1.32 3.06 1.09 2.53 0.92 1.29 0.58 6 9.28 2.40 4.20 1.27 3.35 1.04 2.85 0.77 1.68 0.47 7 12.95 2.60 5.68 1.17 4.71 0.91 3.18 0.70 2.05 0.39 1 8 17.30 2.78 6.97 1.07 5.95 0.81 4.01 0.63 2.32 0.39 4 11.97 2.30 7.35 1.50 6.10 1.26 4.52 1.03 3.52 0.66 5 22.78 2.55 12.04 1.38 9.84 1.16 8.73 0.92 5.06 0.55 6 38.33 2.61 19.58 1.23 15.72 1.01 11.93 0.82 6.79 0.46 7 67.94 2.68 28.73 1.18 22.37 0.97 17.13 0.72 10.23 0.40 4 8 99.25 2.68 39.02 1.12 31.18 0.80 23.86 0.64 13.42 0.36 4 26.98 2.27 18.43 1.45 15.17 1.23 12.97 1.03 8.23 0.66 5 52.75 2.50 31.41 1.31 26.66 1.11 23.61 0.89 13.89 0.54 6 120.97 2.62 60.15 1.31 44.88 1.05 34.71 0.80 18.58 0.47 7 207.09 2.67 90.35 1.17 73.47 0.93 53.73 0.70 30.22 0.41 8 8 336.46 2.73 124.39 1.05 99.13 0.83 74.28 0.60 44.91 0.35 notice that ρ takes only high positive values because the regression estimator for the population mean is used only when the correlation between the two variables is high. also, 317 hani m. samawi and eman m. tawalbeh negative values are not considered since, from (4.6) and (4.7), the relative precision depends on the absolute values of and ρ β since they are squared. 4.3.2 results of the simulation our simulation (table 1) shows that the efficiency is affected by the value of ρ. the regression estimator based on drss is more efficient than naive estimator using rss whenever the absolute value of the correlation coefficient between x and y (ρ) is more that 0.40. moreover, this efficiency is increasing as the set size or the cycle size increases. also, the regression estimator based on drss is more efficient than the naive estimator using drss whenever |ρ|>0.90. however, when |ρ|<0.98, the efficiency decreased as the set size increased and increased otherwise. moreover, in this case the efficiency is not affected by the cycle size. table 2 shows that the double sampling regression estimator using drss was always superior to the double sampling regression estimators using srs and rss. however, the efficiency was affected by the value of ρ. the efficiency increased by increasing the value of ρ. also, the efficiency decreases with increasing the set or the cycle size for small values of ρ. however, re gdy was still found to be more efficient than using other sampling methods. table 2: the efficiency of re gdy with respect to the regression estimators based on srs and rss. ρ=0.99 ρ =0.9 ρ =0.8 m r srs rss srs rss srs rss 4 2.25 2.18 1.94 1.64 1.85 1.48 5 2.47 3.43 1.72 1.90 1.87 1.33 6 2.35 2.60 1.43 1.27 1.49 1.27 7 2.80 2.74 1.56 1.44 1.37 1.23 1 8 2.93 2.89 1.51 1.40 1.32 1.21 4 2.14 2.13 1.46 1.45 1.26 1.24 5 2.40 2.39 1.45 1.44 1.24 1.23 6 2.58 2.57 1.23 1.22 1.22 1.20 7 2.73 2.73 1.41 1.38 1.20 1.18 4 8 2.89 2.87 1.38 1.36 1.19 1.17 4 2.13 2.13 1.44 1.43 1.24 1.23 5 2.39 2.39 1.43 1.43 1.45 1.21 6 2.57 2.60 1.22 1.21 1.20 1.19 7 2.73 2.73 1.39 1.39 1.19 1.18 8 8 2.87 2.87 1.36 1.36 1.17 1.16 5. applications to real data set we illustrate the double ranked set sample mean estimation procedure using a real data set which consists of the height (y) and the diameter (x) at breast height of 399 trees. see platt et al. (1988) for a detailed description of the data set. the summary statistics for the data are reported in table 3. note that the correlation coefficient ρ = 0.908. table 3: summary statistics of trees data. variable mean variance height (x) in feet 52.36 325.14 diameter (x) in cm 20.84 310.11 population size n = 399 and the correlation coefficient between x and y is ρ = 0.908. 318 regression estimator using double ranked set sampling using a set size r=3 and the cycle size m=3, we draw bivariate srs and drss, of size 9. table 4 contains all the above proposed estimators and their estimated variances using the drawn samples. table 4: results from the drawn samples sample naïve estimator of height (y) in feet estimated variance regression estimator estimated variance srs 52.49 408.88 51.19 176.04 drss 52.61 182.25 52.22 125.10 although, table 3 confirms our simulation results. it should be emphasized that the example is used as an illustration of the applicability of our proposed estimators. 6. conclusions in conclusion drss regression estimator is to be used to improve the population mean estimation whenever drss is possible to be conducted. references al-saleh, m.f. and al-kadiri, m.a. 2000. double ranked set sampling. statistics and probability letters, 48(2): 205-212. dell, t.r. and clutter, j.l. 1972. ranked set sampling theory with order statistics background. biometrics, 28: 545-555. kaur, a., patil, g.p., sinha, a.k. and taillie, c. 1995. ranked set sampling: an annotated bibliography. environmental and ecological statistics, 2: 25-54. mcintyre, g.a. 1952. a method for unbiased selective sampling using ranked set. australian journal of agricultural research, 3: 385-390. patil, g.p., sinha, a.k. and taillie, c. 1999. ranked set sampling: a bibliography. environ. ecolog. statist., 6: 91-98. platt, w. j., evans, g.w., and rathbun, s.l. 1988. the population dynamics of a longlived conifer. the amer. naturalist, 131: 391-525. samawi, h.m. 2002. on double extreme ranked set sample with application to regression estimator. metron, lx n. 1-2: 53-66. samawi, h.m. ahmed, m.s. and abu dayyeh, w. 1996. estimating the population mean using extreme ranked set sampling. biometrical journal, 38 (5): 577-586. samawi, h.m. and al-sageer, o.a. 2001. on the estimation of the distribution function using extreme and median ranked set sampling. biometrical journal, 43 (3): 357-373. samawi, h.m., and muttlak, h.a. 1996. estimation of ratio using ranked set sampling. biometrical journal, 38 (6): 753-764. sukhatme, p.v. and sukhatme, b.v. 1970. sampling theory of surveys with applications. ames: iowa state university press. takahasi, k. and wakimoto, k. 1968. on unbiased estimates of the population mean based on the stratified sampling by means of ordering. ann. inst. statist. math., 20: 1-31. yu, l.h. and lam, k. 1997. regression estimator in ranked set sampling. biometrics, 53: 10701080. appendix proposition 1. under (4.1) ( )de β β= . 319 hani m. samawi and eman m. tawalbeh proof : let ( )( ) ( )( ) 2 /ik i k i kc w w w w= − −∑∑ then [ ]( ) [ ]( ) [ ]( ) ˆ ) = . d x ik x iki i k i i k x ik i i e( e e c y x e c e y x e c e y x β   = ∑∑ ∑∑      = ∑∑     note that since and [ ]( ) ( )0 i i i i ke y wβ β= + 0ikc =∑∑ , then ( ) ( )( )( ) ( )( ) 0 0 ˆ , d w ik i i k k i w ik ik i i k e β e c β β w e β c β c w β = +∑∑ = +∑∑ ∑∑ = where 0 y xβµ µβ = − . proposition 2. ( ) ( )( ) 2 2ˆ / .d e i i kx w wβ σ= −∑∑var proof: ( ) ( )( ) [ ] ( )( ) [ ] [ ]( )2 2 ˆ . i i k i i k d i i k ik iki i k i i k w w y v ar x v ar x w w v ar c y x c v ar y x i k β  −∑∑ =    −∑∑    = =∑∑ ∑∑    using y [ ] ( )0 ii i i i kwβ β= + +ε , and since [ ]( ) ( )0i i i ie y x wβ β= + [ ]( ) 2 ei ivar y x σ= , then ( ) ( )( ) ( )( ) ( )( ) 2 2 2 2 2 ˆ . i i k e d e k i i k i i k k i w w var x i w w w w σ β σ   −  = =∑∑   − −∑∑ ∑∑    next we prove theorem 4.1 proof of theorem 4.1: (1) ( ) ( )( )re regd x y gde y e e y x= ( ) ( )( ) [ ] ( ) re ˆ 1 ˆ y gd y drss d rss y d rssi i k m r e y x e y x w x e y x w rm β β ∗ ∗ = + −  = + −∑∑    x 320 regression estimator using double ranked set sampling using (4.1), we have ( ) ( )( )( ) ( )re 1 1 1 ˆ ˆ m r y gd y y d x d rssi k k i e y x e w x w x rm µ β µ β ∗ =   = + − + −    ∑∑ ( ) ( ) y rxw xµ β µ β ∗= + − + −ss w . therefore, ( ) ( )( )re .gd x y rss xe y e x yµ β µ∗= + − = µ hence re gdy is an unbiased estimator of yµ . (2) ( ) ( ) ( )re re regd x y gd x gdvar y e var y x var e y x  = +    ( ) ( )( )re ˆ x y gd x y drss d rssvar e y x var e y x w xβ ∗   = + −     . from (1), we have ( ) ( )re gd y rsse y x β x xµ µ∗= + − , and then ( )( ) ( )( ) ( ) ( ) re 2 2 2 3 1 1 . x y gd x y rss x x rss x rss r x ii v ar e y x v ar x v ar x v ar x r m µ β µ β β β σ ∗ ∗ ∗ = = + −  = =  = ∑ also, ( ) ( )( ) ( ) ( ) ( ) ( )( ) re 2 ˆ ˆ ˆ 2 , , x y gd x y drss d rss x y drss rss d drss d rss e v ar y x e v ar y x w x e v ar y x x w v ar xy cov y x w x β β β ∗ ∗ ∗    = + −     = + − + −  but, ( )( ) [ ] [ ] ( ) ( ) [ ]( ) ( ) 2 1ˆ , 1 1 drss d rss ik rssi i k i i k k i k i rss ik i i k rss e ik cov y , β x w x cov y c y x w x rm x w c var y x rm x w c rm σ ∗ ∗ ∗ ∗   − = −∑∑ ∑∑    = − ∑∑ = − =∑∑ 0. then, ( ) ( )( ) ( ) ( )( )2re ˆ x y gd x y drss x rss y de v ar y x e v ar y x e x w v ar xβ∗  = + −  ( ) ( ) [ ]( ) 2 22 2 2 21 1 1 1 1 m r e x e x rss m r k i e i i k k i e e x w rm w w σ σ σ ∗ = = = =       = + −       −    ∑∑ ∑∑ , 321 hani m. samawi and eman m. tawalbeh clearly this implies that, ( ) ( ) ( )( ) [ ]( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 z 1 1 rss x x x e x e x xi i k rss w y x wi k k i rss w y x z x w e rm w w x z e rm rm z x z e rm rm s µ µ σ σ σ xµ µ σ ρ σ ρ σ ∗ ∗ ∗ ∗   − − −   = +      − − − ∑∑      −   = − +   −∑∑        −   = − +       ( ) ( ) 2 2 2 1 1 rss wy x z x z e rm s σ ρ ∗  −   = − +       , where ( ) ( ) ( )( ) 2 2 * , , 1 , , 11 xi i k x wi k x x rss x z w rssi k x w w z z m r x s z z x rm ik µ µ σ σ µ σ ∗ ∗ ∗ − − = = − = − =∑ ∑ == therefore, ( ) ( ) ( ) ( ) 2 2 2 re 2 2 1 1 1 1 rss wy gd x x i z x z rvar y e irm s r m σ 2ρ β σ ∗  −   = − + + ∑ =      . received 8 november 2001 accepted 31 october 2002 322 regression estimator using double ranked set sampling hani m. samawi* and eman m. tawalbeh** *department of mathematics and statistics, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman,**department of statistics, yarmouk university, irbid, jordan 211-63, *email: hsamawi@squ.edu.om. as a variation of rss, al-saleh and al-kadiri (2000) introduced the drss procedure as follows: 3. regression estimators using srs and rss applications to real data set we illustrate the double ranked set sample mean estimation procedure using a real data set which consists of the height (y) and the diameter (x) at breast height of 399 trees. see platt et al. (1988) for a detailed description of the data set. the using a set size r=3 and the cycle size m=3, we draw bivariate srs and drss, of size 9. table 4 contains all the above proposed estimators and their estimated variances using the drawn samples. sample naïve estimator of regression estimator although, table 3 confirms our simulation results. it should be emphasized that the example is used as an illustration of the applicability of our proposed estimators. conclusions in conclusion drss regression estimator is to be used to improve the population mean estimation whenever drss is possible to be conducted. references platt, w. j., evans, g.w., and rathbun, s.l. 1988. the population dynamics of a long-lived conifer. the amer. naturalist, 131: 391-525. appendix squ journal for science, 2018, 23(1), 32-42 doi: http://dx.doi.org/10.24200/squjs.vol23iss1pp32-42 sultan qaboos university 32 development of a mathematical model for simulation of macroalgae farming in the coastal areas abdolmajid lababpour department of mechanical engineering, faculty of engineering, shohadaye hoveizeh university of technology, dasht-e azadeghan 64418-78986, iran. email: lababpour@shhut.ac.ir abstract: a mathematical model consisting of a system of three coupled partial differential equations (pdes) was proposed to estimate the concentrations of nitrogen, phosphorous and macroalgae biomass in coastal open waters. however, some simplifying assumptions were used in the model to cope with the complexity of real conditions. for the macroalgae biomass, the system works as a batch mode, while input and output were accounted for nitrogen and phosphorous. the matlab pdepe feature, applying the finite element method was used in model solving and the simulation of model equations. the program was split into four functions that included the solver and post-processing of the results, a function containing the pdes, a function setting the initial conditions, and one setting the boundary conditions. for model validation, the experimental measurement of nitrogen, phosphorous and macroalgae biomass concentrations of bandar abbas coastal open waters were analyzed by standard methods at three depths of 1, 5 and 10 m. the predictive values of the developed model demonstrated its applicability for the management of coastal macroalgae cultivation systems by assessing the impact of nitrogen and phosphorous strategies on the farming system. keywords: modeling algal growth; macroalgae cultivation; algae simulation; coastal open water; numerical solution of pdes. الساحلیة المناطق في زراعة الطحالب الكبیرة لمحاكاة رياضي نموذج تنمیه عبدالمجید لباب پور الحيوية والكتلة والفوسفور النيتروجين تركيزات لتقدير ثالثة (pdes) جزئية تفاضلية معادالت يتألف من جملة رياضي نموذج حتم اقترا :صالملخ الكتلة بالنسبة إلى .حقيقيةال الشروط تعقيدات مواجهةفي النموذج تبسيطل االفتراضات بعض استخدام تمولكن . الساحلية المفتوحة المياه في الكبيرة طحالبلل depeباستخدام مميزات الماتالب ) .فوسفورالو نيتروجينال ومخرجات مدخالت تاحتسب بينما كاملة، دفعة شكل على النظام يعمل الكبيرة، طحالبلل الحيوية matlab دوال تتألف من دالة الحل أربع إلى البرنامج تقسيم وتم. معادالتة النمذج ومحاكاةفي نموذج الحل المنتهية العناصر طريقة تطبيق( تم تم اختبار النموذج، صحة من لتحقق. لالحدية لشروطوأخرى ل األولية، لشروطل دالةو الجزئية، التفاضلية المعادالت على تحتويودالة النتائج، تجهيزو معيارية طرقها بتحليلفي بندر عباس وتم المفتوحة الساحليةبالتركيز على المياه الكبيرة طحالبلل الحيوية والكتلة والفوسفور النيتروجين ات لكل منقياسال خالل من الساحلية الكبيرة الطحالب زراعة نظم لتطوير تطبيقه ت إمكانيةأظهر المقترح موذجللن التنبؤية القيمإن .رامتأ 11و 5 و 1 من ثالثة قاعمأ في .رعاالمز ظامن على والفوسفور النيتروجين استراتيجيات أثر تقييم .الجزئية التفاضلية لمعادالتل العددي الحل ،ةالساحلي المفتوحة المياه طحالب،لل المحاكاة الكبيرة، الطحالب زراعة الطحالب، نمو نمذجة :مفتاحیةالكلمات ال 1. introduction acroalgae growth typically occurs in natural and pond systems. the productivity of marine ecosystems is characterized by various biological, physical-chemical and meteorological variables such as nutrient availability, water temperature, salinity, grazers, phytoplankton, etc. [1,2]. the sustainability of macroalgae cultivation in coastal open waters is essential from environmental and economic perspectives, and for human communities [3]. independent and integrated cultivation of macroalgae in both open waters and fish ponds have been investigated [4,5]. m development of a mathematical model 33 the results of these evaluations demonstrate the crucial influence of the availability of various forms of nitrogen and phosphorous, and their effects on biomass productivity in different seasons and at various water depth levels [6]. for example, nitrate concentrations in the range of 0.1 1.0 µm were evaluated in the cultures of some species and found to have a significant effect on biomass productivity [5]. in another study nitrogen sources (sum of ammonium and nitrate) in the range of 5 to 30 mg l -1 were studied [7]. these findings suggest the requirements for managing the complex behavior of water nutrients, which are critical in macroalgae cultivation technologies [7]. modeling of macroalgae growth is difficult as the behavior of biotic and abiotic macroalgae cultivation systems are complex, and have defied precise description using mathematical models [8,9]. furthermore, it is currently impossible to reliably predict how various modifications of system parameters might affect cultivation performance, because many parameters are not included in the model equations. however, mathematical models can be effective tools for predicting macroalgae farming productivities, by analyzing and simulating nutrient removal and the macroalgae biomass growth rate [1,2,10,11]. a mars-ulves model was proposed to predict nitrate threshold values to control macroalgae blooms, due to anthropogenic nitrogen loading [7]. the ulva growth and nutrient assimilation were predicted by an ecological model with 8 biotic variables and 2 abiotic variables, of temperature and lighting. however, ecological models such as mars-ulves mostly consider hydrodynamic features which should be derived experimentally [12,13]. in addition, they are complex and require various input data [14–16]. other classes of models have been used in natural and artificial wastewater treatment technologies such as treatment pond systems (e.g. the reed model) which might be used for macroalgae cultivation [17–19]. in this regard, several removal pathways have been investigated for the reduction of nitrogen and phosphorous including nitrification-denitrification, algal uptake, and sedimentation, etc. [18]. these variations complicate the development of a robust mathematical expression to account for all these processes simultaneously. another applicable class of equations for macroalgae farming were developed for fall in modeling of photobioreactors. these models are usually focused on micro and macroalgae biomass productivity and optimum nutrient availability for maximizing productivities in artificial open and closed algae cultivation systems [20]. the typical models in these category are those which postulate time variations of variables such as lighting, gas concentrations, flow characteristics, etc. [18]. all currently applied models assume a homogeneous farming system in depth layers. this approximation is less valid in depths of greater than 3 meters. they are also less applicable when light and nutrients have strong gradients with depth [11,21]. for such cases, we need a model which considers both spatial and temporal changes during cultivation. in other words, the biomass productivity can be better predicted by developing a depth dependent model. this research provides a greatly simplified but effective model which takes time and depth variations during cultivation into account, linking the biomass growth model to nitrogen and phosphorous concentrations. in other words, we will analyze the biomass productivity and nitrogen and phosphorous assimilation using pdes and then examine the graphs generated by the model. these variables will affect both farm productivity and the safety of coastal waters. these simulations include the production of macroalgae maps at 3 depths of 1, 5 and 10 m against time. 2. model formulation one graphical and one conceptual schematic representations of the system ω (z, t) studied is shown in figure 1, (a) and (b). domain ω is defined on a rectangular (x, z) plane with 0 < x < 1 and 0 < z < h. the height of the domain is h in z direction. the macroalgae biomass is represented by green shapes, and the nitrogen and phosphorous by white circles. the light depletion with water depth is shown by a color gradient from yellow to gray. boxes indicate the components represented as state variables in the mathematical model: no, combined nitrite and nitrate, p, phosphorous, and biomass b, as an organic particles in the form of macroalgae. no3inlet = 1 gl -1 , no3 outlet = 0.4 gl -1 , po4 inlet = 0.2 gl -1 , and po4 outlet = 0.03 gl -1 . the initial macroalgae concentration in domain ω = 0.17 gl -1 (homogeneous), and initial concentrations of n and p were assumed zero in selected control volumes [3]. the system contains a mixture of seawater and suspended macroalgae b, where the biomass is grown by uptaking n and p variable compounds from water [19]. macroalgae biomass b, nitrogen n and phosphorous p concentrations were considered as state variables. the domain is exposed to air from above and no diffusible layer from bottom. for the purpose of describing the biomass growth mathematically, we consider a 1-d water column domain 0 < z < h with the z = 0 in the bottom and the bulk water interface at z = h , and set b (t, z) to be the concentration of biomass. height h is assumed constant. biomass b satisfies a no-flux condition bz| z=0 = 0 at the water bottom and a dirichlet condition bz| z=h = b 0 at the water interface. a diffusive boundary layer above the interface z = h could be included to allow for mass transfer resistance but does not qualitatively affect results. we suppose the sides of the system to be insulated. we also suppose initial conditions b (z, 0) = 0.03, 0 < z < h, i.e., application beginning at the t = 0 of macroalgae biomass of 0.03 gl -1 . a. lababpour 34 figure 1 (a). a graphical view of the entire domain ω (t, z). (b). a conceptual model scheme of nitrogen and phosphorous input, transformation and removal processes in domain ω (t, z). in the processes incorporated as pdes, b (z, t) denotes the biomass change at each time, n (z, t) denotes the nitrogen change at each point and z is the water depth, and p (x, t) denotes the phosphorous change at each point and z is the water depth. the system consists of a column of water, with variables of biomass, b, nitrogen, n and phosphorous, p concentrations (see figure 1). assimilation of nitrogen and phosphorous which is used for macroalgae feeding is not uniform in different water depths, as the profile of macroalgae concentration varies with water depths. in this study, standard convection-diffusion-reaction (cdr) systems of partial differential equations were used for macroalgae biomass production and nutrients in a one-dimensional static domain [22,23]. 2.1 biomass the aim of a biomass model equation is to describe the spatial profile of biomass b in (x, y) plane as a function of time in order to predict the effects of nitrogen and phosphorous penetration barriers. let 𝛺 ≔ (𝐿𝑥0, 𝐿𝑥 ) × (𝐿𝑦0, 𝐿𝑦 ) × (𝐿𝑧0, 𝐿𝑧 ) ⊂ 𝑅 3 be the system volume domain, in which biomass is growing, decaying or both. for modeling, the fact that the biomass growth µ and decay β rate is variable at any given depth location h inside of the domain ω, we impose that the biomass accumulate/degrade equation in 3 levels with µ 1 , µ 2 and, µ 3 , in order to take into account different biomass growth rates. that is, the biomass change in the domain is not divergent. in this case, the biomass concentration b satisfies a simplified convection-diffusion-reaction (cdr) equation of the form 𝜕𝐵 𝜕𝑡 = 𝐷𝐵 𝜕2𝐵 𝜕𝑧2 + 𝑓(𝑡, 𝐵) 𝑖𝑛 𝛺 (1) which is a function of three variables defined on a region in ω, where b is a vector of biomass (gl -1 ), f is a vector showing the kinetics of biomass growth and decay, and d b stands for the diffusion coefficient of the biomass (m 2 s −1 ). we set 𝑓(𝑡, 𝐵) = 𝜇𝐵 − 𝛽𝐵 𝑖𝑛 𝛺. (2) here b is the biomass concentration. note that here, the specific growth rate µ depends on various other nitrogen and phosphorous factors, but broadly it depends on several others such as light intensity, temperature, etc., and the extra complications are neglected for simplicity. using (2), equation (1) can be rewritten as 𝜕𝐵 𝜕𝑡 = 𝐷𝐵 𝜕2𝐵 𝜕𝑧2 + 𝜇𝐵 − 𝛽𝐵, (3) no3 po4 macroalgae assimilation assimilation f, c no3 harvest decay in-flow f, c po4 in-flow out-flow no3 po4 y z x (a) (b) development of a mathematical model 35 where the μ and β coefficients represent biomass growth and loss, respectively. in order to uniquely determine the biomass profile from eq. (3), we have to add external initial and boundary conditions. in this case, we assume that no biomass goes in or out by the bottom of ω: bz| z=h = b. moreover, for numerical convenience, we assume that b is periodic in the x and y-directions. on the other hand, assuming that on the top of the domain there is a constant biomass concentration, and since this is always defined up to an additive constant, without loss of generality, we will impose the following boundary condition: b = 0 on z = h. the solution satisfies assumed initial conditions of b (t 0 ) = b 0 = 0.03 gl -1 . 2.2 nitrogen and phosphorous for the purpose of simplicity, we assume that µ depends only on the concentration of limiting substrates, e.g., n and p. in particular, we assume that µ = µ (t,u(n,p)), which is the so called substrate uptake rate function, which indicates the reaction rate of substrate usage. we used monod kinetics for n and p uptake by macroalgae. here we define µ by the equation 𝜇 = 𝜇𝑚𝑎𝑥 𝑁 𝑘𝑁 + 𝑁 × 𝑃 𝑘𝑃 + 𝑃 (4) where µ max is the maximum biomass growth rate. the presence of macroalgae in the domain influence the n and p by assimilation. the equation which describe the diffusion and assimilation of n is 𝜕𝑁 𝜕𝑡 = 𝐷𝑁 𝜕2𝑁 𝜕𝑧2 + (𝑁)𝑖𝑛 + 𝑑1(𝑁) − 𝜇𝑌𝐵 𝑖𝑛 𝛺. (5) equation 5 has two boundary conditions: one at top water surface and the other at the bottom water. the concentration of nitrogen and phosphorous were assumed constant at the top water surface or n|z = l z = sm (the substrate concentration is at its maximum level at the top of ω) and the flux of nitrogen and phosphorous were assumed zero at the bottom surface or ∂n/∂t|z = 0 (no nitrogen goes in or out by the bottom of ω). similar equation and boundary conditions to n were also used for the phosphorous profile as follow: 𝜕𝑃 𝜕𝑡 = 𝐷𝑃 𝜕2𝑃 𝜕𝑧2 + (𝑃)𝑖𝑛 + 𝑑2(𝑃) − 𝜇𝑌𝐵 𝑖𝑛 𝛺, (6) the top boundary condition is p|z = l z = sm (the substrate concentration is at its maximum level at the top of ω) and ∂p/∂t|z = 0 (no phosphorous goes in or out by the bottom of ω). in the above equations (5) and (6), d n and d p stand for the diffusion coefficients of the nitrogen and phosphorous substrates, respectively (m 2 s −1 ). over longer durations, (5 and 6) equilibrate to c (n) = k nzz and c (p) = k pzz. note that u and µ do not explicitly depend on time or space in the model presented here. in low water layers, where b is small and c (b) = c 1 b, nitrogen concentration is depleted exponentially with length scale l = k/c 1 . thus for those nutrients like nitrogen and phosphorous, a permanent reactive penetration layer results (at least, permanent on the time scales considered here). at the top of the water column, if the concentration of biomass is saturating, then (3) simplifies to, approximately, 𝜕𝐵 𝜕𝑡 = 𝐷𝐵 𝜕2𝐵 𝜕𝑧2 + 𝐶0, (7) where the constant db is biomass diffusivity, and the constant c0 is the saturation level of c (b), so that nitrogen and phosphorous show a decreasing profile. gathering the above pde equations, we have the following model, with incorporated initial and boundary conditions. 𝜕𝐵 𝜕𝑡 = d𝐵 𝜕2𝐵 𝜕𝑧2 + 𝜇𝐵 − 𝛽𝐵, 𝜇 = 𝜇𝑚𝑎𝑥 𝑁 𝑘𝑁 + 𝑁 × 𝑃 𝑘𝑃 + 𝑃 0.0 ≤ 𝜇 ≤ 1.0, 𝐵(𝑧, 𝑡0) = 𝐵(𝑧, 0) = 0.17, 𝐵(𝐿𝑧0 , 𝑡) = 𝐵(0, 𝑡) = 0.17, 𝐵(𝐿𝑧, 𝑡) = 𝐵(𝐻, 𝑡) = 0.17, 𝒜1: 𝐵(0, 𝑧) = 𝐵(𝐿𝑥 , 𝑧) ∀𝑧 ∈ (0, 𝐿𝑧 ) 𝒜2: 𝐵(0, 𝑧) = 𝐵(𝐿𝑦 , 𝑧) ∀𝑧 ∈ (0, 𝐿𝑧 ) 𝜕𝑁 𝜕𝑡 = 𝐷𝑁 𝜕2𝑁 𝜕𝑧2 + (𝑁)𝑖𝑛 + 𝑑1(𝑁) − 𝜇𝑌𝐵, (8) a. lababpour 36 𝑁(𝑧, 𝑡0) = 𝑁(𝑧, 0) = 0.7 𝑁(𝐿𝑧0 , 𝑡) = 𝑁(0, 𝑡) = 0 𝑁(𝐿𝑧 , 𝑡) = 𝑁(𝐻, 𝑡) = 1 𝒜3: 𝑁(0, 𝑧) = 𝑁(𝐿𝑥 , 𝑧) ∀𝑧 ∈ (0, 𝐿𝑧 ) 𝒜4: 𝑁(0, 𝑧) = 𝑁(𝐿𝑦 , 𝑧) ∀𝑧 ∈ (0, 𝐿𝑧 ) 𝜕𝑃 𝜕𝑡 = 𝐷𝑃 𝜕2𝑃 𝜕𝑧2 + (𝑃)𝑖𝑛 + 𝑑2(𝑃) − 𝜇𝑌𝐵, 𝑃(𝑧, 𝑡0) = 𝑃(𝑧, 0) = 0.12, 𝑃(𝐿𝑧0 , 𝑡) = 𝑃(0, 𝑡) = 0, 𝑃(𝐿𝑧 , 𝑡) = 𝑃(𝐻, 𝑡) = 0.7, 𝒜5: 𝑃(0, 𝑧) = 𝑃(𝐿𝑥 , 𝑧) ∀𝑧 ∈ (0, 𝐿𝑧 ) 𝒜6: 𝑃(0, 𝑧) = 𝑃(𝐿𝑦 , 𝑧) ∀𝑧 ∈ (0, 𝐿𝑧 ) these model equations, namely equations (8), are nonlinear and have no simple exact solution. we note that the unknowns of the model are: b, n and p. the equations for b, n and p are the biomass balance, together with their initial and boundary conditions, and n and p substrates balance together with their initial and boundary conditions, respectively. the model has been translated to be accessible by the input solver format of the matlab pdepe feature, which is used in the solving and simulation of model equations. in the pdepe feature, the ordinary differential equations (odes) resulting from discretization in space are integrated to obtain approximate solutions at specified times to solve initialboundary value problems for parabolic-elliptic pdes in 1-d. the model parameters of maximum growth rate, coefficient of biomass decay, nitrogen and phosphorous generation results of biomass decay, diffusion coefficients, decomposition of biomass based nitrogen compounds d1, decomposition of biomass based phosphorous compounds d2, and yield were obtained from literature for gracilariopsis persica in the persian gulf or by experimental analysis as shown in table 1. to use the matlab pdepe feature for solving the model pdes, we split the program into four part functions that included the solver and post-processing of the results, a function containing the pdes, a function setting the initial conditions, and one setting the boundary conditions. the equations were translated into the matlab format. the outputs were set to obtain profiles of state variables. table 1. model parameters used for simulation of gracilariopsis persica. parameter symbol unit value ref. maximum growth rate µmax d -1 0.2 [24] death rate β d -1 0.04 [25] biomass based nitrogen compounds d1 d -1 0.023 [25] biomass based phosphorous compounds d2 d -1 0.01 [25] yield y 0.32 [25] michaelis constant for nitrogen k n µm 61.5 [26] michaelis constant for phosphorous k p µm 37 [26] nitrogen (initial) cn mg l -1 0.7 [25] phosphorous (initial) cp mg l -1 0.1 [25] 2.3 materials and methods the nitrogen, phosphorous and macroalga gracilariopsis persica concentrations in bandar abbas coastal open waters were determined in september 2016 and january 2017 according to the standard methods for 3 depths of 1, 5 and 10 m. experimental data used for model validation [5,27] were obtained from analysis of three water depths, i.e., n = 1, 5 and 10 m. 3. results and discussion we have performed numerical experiments with the corresponding initial values for n and, p and for different initial biomass concentrations. the biomass specific growth rate µ and decay β can affect the final biomass b during cultivation time. it also predicts higher biomass productivity in different depth layers. the greater the specific growth rate µ, the higher resulting biomass productivity in a shorter time. some results and analysis of macroalgae growth and nutrient assimilation are presented below. development of a mathematical model 37 3.1 time-and depth-dependent macroalgae growth the solution to the model for single state variable of biomass is shown in figure 2. the simulated results revealed a time-and depth-dependent growth pattern, decreasing from top down, corresponding to the faster growth empirically observed in cultures at depths of 1 and 5 m than at 10 m depth cultures (figure 2). the simulated results suggest utilizing a cultivation depth of ≥ 5 meters. the model estimate should be refined for differing macroalgae species and geographical locations. figure 2. estimated concentrations of macroalgae biomass influenced by water depth. 3.2 time-and depth-dependent nitrogen and phosphorous the solution to the model for n and p variations is shown in figure 3. the simulated results revealed a timeand depthdependent growth pattern with differing concentrations of nitrogen and phosphorous (figure 3). figure 3. estimated concentrations of (a) nitrogen and (b) phosphorous with water depth. figure 4 compares the measured values of biomass, nitrogen and phosphorous concentrations for three depths of 1, 5 and 10 m with the corresponding simulated values. correlation coefficients (r 2 ) with 95% confidence intervals between the model predictions and the measured biomass, nitrogen and phosphorous for different depths (figure 4) were 0.97, 0.95, and 0.96, respectively. these correlation coefficients indicate that the mathematical model successfully fitted the experimental data. a b a. lababpour 38 figure 4. measured and model simulated (a) biomass, (b) nitrogen and (b) phosphorous in three water depths. experimental (■) and fitted (-). the purpose of this research was to develop a mathematical model to assist in optimizing the cultivation performance and design of macroalgae cultivation systems in open waters. nitrogen n and phosphorous p are important elements for the growth of photosynthetic organisms in marine environments including seagrasses, macroalgae, and microalgae. their availability can improve macroalgae farms’ productivity, but at the same time may cause eutrophic phenomena which contribute to harmful conditions such as coastal red tide blooms [11,28]. therefore, control of inorganic water nitrogen and phosphorous concentrations are important in macroalgal farming activities [10,29–31]. the proposed model is different from typical existing models, since it simulates macroalgae productivity as a function of spatial and temporal variations by means of spreading biomass reaction, instead of convective biomass under the influence of substrate diffusion. indeed, the conditions describing the productivity in various water levels are a key issue in the presented model that have been extensively used in macroalgae productivity problems. the novel a c b development of a mathematical model 39 approach to biofilm modeling followed in the paper is, as far as we know, applied for the first time to the cultivation of gracilariopsis in the persian gulf area, and hence introduces local communities to a method that is likely to find application [3]. using this model, numerical simulations were performed that predict the behavior of state variables in domain in a range of different conditions. as the nutrient availability increases, there is a gradual shift towards more productivity in water depth layers. this is consistent with the fact that the greater the surface light and nutrient availability (and so the higher the growth rate is), the better suited it is for commercial macroalgae production systems [7]. the model simulation results suggest that compensation for lower than required nitrogen and phosphorous sources in coastal waters might be supplied by local wastewater, to increase macroalgal farms’ productivity [32,33]. however, the seasonal and depth variation of nitrogen and phosphorous sources in natural water are also dependent on other variables such as light and temperature, and should be considered for more accurate simulation of macroalgae cultures. integration of macroalgae cultivation with fish farming is another promising option for higher nutrient sources and economic applicability [5,34]. the model could consider two or more substrates interacting with each other and biomass productivity. this amounts to introducing new equations to the model, taking into account transport and interaction of the various substrates. the model could also consider systems with multiple water species. the most relevant characteristic of the present novel and more rigorous model approach, based on existing mathematical analysis, is that it can simulate and follow the behavior of a range of previously described models that simulate practical macroalgae cultivation behavior. detailed comparisons with experimental data including the effect of seasons and light irradiation require future research. 4. conclusion this study provides an estimate of macroalgae productivity as a function of inorganic nitrogen and phosphorous concentrations by a model of three pde equations. the important features of the model for improving understanding of the macroalgae cultivation system are its (1) parameterization of the link between nitrogen, phosphorous and biomass in terms of n and p-to-biomass ratio, and its (2) linking macroalgae growth to nitrogen-phosphorous assimilation. simulations were in reasonable agreement with the experimental data obtained from analysis of different depths of water, and illustrated the strong dependence of biomass productivity on n and p concentrations. the values predicted by the developed model are useful in providing insight on experimental data. the model may be used for further investigation of coastal macroalgae farming for the development of local communities. we are now working on refining the model by including fluid hydrodynamic and growth related parameters, in order to simulate for higher macroalgae productivity, as well as for sustainability of the coastal waters. acknowledgement the author acknowledges the support of the shohadaye hoveizeh university of technology, iran. i also sincerely acknowledge the anonymous and respected reviewers for their constructive recommendations. appendix model equations 𝜕𝑢1 𝜕𝑡 = 𝐷𝑏 𝜕2𝑢1 𝜕𝑥 2 − 𝜇𝑢1 + 𝛽𝑢1, ic : 𝑢1(𝑥, 0) = 0.1, left – bc : 𝑢1(0, 𝑡) = 0.1, right – bc : 𝑢1(𝐿, 𝑡) = 0.1. 𝜕𝑢2 𝜕𝑡 = 𝐷𝑁 𝜕2𝑢2 𝜕𝑥 2 − 𝑌1 ∗ 𝜇𝑢2, ic : 𝑢2(𝑥, 0) = 0.1, left – bc : 𝑢2(0, 𝑡) = 0.1, right – bc : 𝑢2(𝐿, 𝑡) = 0.1. 𝜕𝑢3 𝜕𝑡 = 𝐷𝑃 𝜕2𝑢3 𝜕𝑥 2 − 𝑌2 ∗ 𝜇𝑢3, ic : 𝑢3(𝑥, 0) = 0.1, left – bc : 𝑢3(0, 𝑡) = 0.1, right – bc : 𝑢3(𝐿, 𝑡) = 0.1. a. lababpour 40 program code and outputs global mu beta db dn dp y1 y2; mu = 0.4; beta = 0.1; db = 0; dn = 1e-5; dp = 1e-6; y1 = 0.3; %nitrogen yield y2 = 0.014; %phosphorous yield l = 10; %length of domain maxt = 10; %maximum simulation time m = 0; t = linspace(0,maxt,10); %tspan x = linspace(0,l,5); %xmesh sol = pdepe(m,@uu,@uuic,@uubc,x,t); u1 = sol(:,:,1); u2 = sol(:,:,2); u3 = sol(:,:,3); figure (1) surf(x,t,u1) mesh (x,t,u1) title('biomass') xlabel('depth, m','fontsize',12,'fontweight','b','fontname','arial') ylabel('time, d','fontsize',12,'fontweight','b','fontname','arial') zlabel('biomass, mg/ l','fontsize',12,'fontweight','b','fontname','arial') figure (2) surf(x,t,u2) mesh (x,t,u2) title('nitrogen') xlabel('depth, m','fontsize',12,'fontweight','b','fontname','arial') ylabel('time, d','fontsize',12,'fontweight','b','fontname','arial') zlabel('nitrogen, mg/ l','fontsize',12,'fontweight','b','fontname','arial') figure (3) surf(x,t,u3) meshc (x,t,u3) title('phosphorous') xlabel('depth, m','fontsize',12,'fontweight','b','fontname','arial') ylabel('time, d','fontsize',12,'fontweight','b','fontname','arial') zlabel('phosphorous, mg/ l','fontsize',12,'fontweight','b','fontname','arial') function [c,f,s] = uu(x,t,u,dudx) global mu beta db dn dp y1 y2; u = zeros (3,1); c = [1;1;1]; f = [db;dn;dp].*dudx; s = [-mu*u(1) + beta*u(1); -mu*y1*u(2); -mu*y2*u(3)]; end function u0 = uuic(x) u0 = [0.05; 0.7; 0.13]; end development of a mathematical model 41 function [pl,ql,pr,qr] = uubc(xl,ul,xr,ur,t) pl = [ul(1); ul(2); ul(3)]; ql = [1.1; 1.1; 1.0]; pr = [ur(1); ur(2); ur(3)]; qr = [1;1;1]; end references 1. negreanu-pîrjol, b., negreanu-pîrjol, t., paraschiv, g., bratu, m., sîrbu, r., roncea, f. and meghea, a. physical chemical characterization of some green and red macrophyte algae from the romanian black sea littoral. scientific study and research chemistry and chemical engineerin, biotechnology, food industry, 2011, 12 ,173– 184. 2. israel, 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email: alsunni@ccse.kfupm.edu.sa. غير المعامالت بواسطة طرق الحلول المثلىحساب قيمة أكبر حجم لت فؤاد محمد عيسى السني ندرس كال . ي األنظمة فنقترح طريقة تعتمد على الحلول المثلى من أجل إيجاد أكبر قدر من تغير المعامالت : خالصة طريقة المقترحة بعد تقديم ال . من األنظمة الخطية مع وجود صندوق من األخطاء في المعامالت وكذلك معين من الدوال .نستعرض استخدامها عن طريق تطبيقها على بعض األمثلة abstract: in this paper we propose a non-linear optimization based approach for the computation of the stability region for uncertain polynomials. both box of polynomials and diamond of polynomials are addressed. examples are presented as an illustration. keywords: optimization, uncertain polynomials, box polynomials, diamond polynomials. 1. introduction t he computation of the largest perturbations of a given system without violating stability is of great interest for analysis and controller design. considerable work has been reported in the literature focusing on this issue. the work in barmish (1984) makes use of the kharitonov result (kharitonov, 1978) to find the smallest destabilizing perturbations in the parameters by examining the four hurwitz testing matrices. the work assumes equal perturbations to all the parameters. in chapellat et al. (1988) a procedure for obtaining the largest stability ball is proposed. the authors in blanchini et al. (1998) proposed to find the minimum destabilizing volume for uncertain systems, and in kim et al. (1988) the case of bivariate polynomials was studied. in hollot (1988), it was proposed to use the markov parameters of a polynomial to study the stability margin, and djaferis (1989) studied polynomials with linear uncertainty. the diamond of polynomials case was studied in barmish et al. (1992). in this study we make use of the link established by mansour et al. (1992) between the celebrated kharitonov results and the positive definiteness of the associated hermite matrices (anderson, 1972), to produce a non-linear programming approach for obtaining the largest volume in the parameter space around a stable nominal polynomial. the statement of the problem is given in the following section, followed by the proposed scheme in section three. examples are presented in section four, and section five concludes the paper. 2. statement of the problem definition 1. n(s) is called an interval polynomial if it is given by 27 f.m. al-sunni n n n n slslsllsn ++++= − − 1 110 ..........)( with the parameters in the given intervals bounded below by the minimum value , and above by the maximum value (i.e. l ];[ iii ll∈ ) definition 2. p(s,d) represents diamond of polynomials if n n n n sdsdsdddsp ++++= − − 1 110 .....),( (1) with real coefficients di known to lie in the (n+1)-dimensional diamond centered at d* = (d*0….d*n). this means that d = [d0 d1 d2……dn] is a possible value for the parameters if where ndd ∈ }||.......|||:|{ **11 * 00 rdddddddd nnr ≤−+−+−= (2) and r is the radius of the diamond. definition 3. the hermite matrix h associated with a given polynomial of order n, p(s,d) is an n by n symmetric matrix with entries given by (3) 1 1 ( 1) ; , i k i ij n k n i j k k h d d j i and i j e+ − + − − + = = − ≥ +∑ ven evenjiandijh ji +<= ,; oddisji += ;0 we now present the stability results for both: the box of polynomials, and a diamond of polynomials. lemma 1: the interval polynomial n(s) is stable (kharitonov, 1978) for all li if the following four polynomials, of order n, are stable: 2 3 1 1 2 3( ) ......-0n s 1 l s l s l s−= + + + + 2 3 2 0 1 2 3( ) ......n s l l s l s l s− − −= + + + + 2 3 3 0 1 2 3( ) ......n s l l s l s l s− −= + + + + 2 3 4 0 1 2 3( ) ......n s l l s l s l s− −= + + + + lemma 2: (barmish et al., 1992) the diamond of polynomials (1) is stable for all d, if the following eight polynomials are stable: rdd ∈ p1(s,d) = p(s,d*) + r p2(s,d) = p(s,d*) r p3(s,d) = p(s,d*) +rs p4(s,d) = p(s,d*) -rs p5(s,d) = p(s,d*) + rsn-1 p6(s,d) = p(s,d*) rs-n-1 p7(s,d) = p(s,d*) + rsn p8(s,d) = p(s,d*) rsn lemma 3: (anderson, 1972) a polynomial is stable if the associated hermite matrix is positive definite. it is the objective of this paper to find the maximum range of the parameters which maintain the stability of the polynomials. both the interval and the diamond like uncertainty will be addressed. in our development, lemmas 1 and 3 will be used to formulate the problem for finding the maximum volume of uncertainty, for interval polynomials, as a 28 on the computation of the maximum uncertainty volume optimization problem. also, lemmas 2 and 3 will be used for the formulation of the case of a diamond of polynomials. 3. an optimization-based approach 3.1 interval polynomials in order to find the maximum range, we propose to find the interval ranges which maximize the volume of the box of uncertainty, vb. to fix notation, let a*i be the nominal value of parameter ai. let the parameter ai belong to the range [ . the width of this range is equal to . the volume of the box of uncertainty is given by ], ** uii l ii aa δδ −− u i l i δδ + v )( 0 u i l i n ib δδ +π= = our proposed scheme is to maximize vb1 subject to the stability constraints given by the positive definiteness of the four hermite matrices corresponding to the kharitonov polynomials. the problem of finding the maximum stabilizing volume may then be presented as )( 5 0, u i l iib vmax u i l i δδ δδ +π= = subject to the constrains given by hi > 0 i = 1, 2, 3, 4 3.2 diamond polynomials a similar approach may be suggested for the study of stability radius of a diamond of polynomials. we need to maximize the volume of the diamond, vd, subject to the positive definiteness of the eight hermite matrices associated with the eight polynomials given in lemma 2. the volume of the diamond, vd, with radius r, is a fraction multiple of the volume of the box vb, with length 2r. so the nlp problem to solve is 1)2( += nb r rvmax subject to the constraints represented by hi>0, i = 1,2……..8 with hi the hermite matrix associated with the i polynomial given in lemma 2. note that hth i are functions of one parameter, r, only. the problem of maximizing the volume vb is a non-linear optimization problem. a global maximum is not guaranteed. however, the proposed approach gives the flexibility of finding the effect of individual parameters and it also can put some constraints on the uncertainties being symmetric or not etc. the optimization can be performed using the matlab optimization routine called “constr”. this routine allows the user to provide the objective function, and the constraints of the optimization problem and produces the maximum value after the optimization is done. 4. examples 4.1 example 1 consider the following fourth order stable polynomial (barmish 1984) p(s) = s4 + 5s3 + 8s2 + 8s + 3 29 f.m. al-sunni we would like to find the values of and for the interval polynomial which maximizes liδ u iδ ))()()(( 33221100 ulululul bv δδδδδδδδ ++++= subject to hi>0, i = 1, ..4, which are the hermite matrices associated with the four kharitonov polynomials. if we restrict the changes and to be the same, then we have the situation usually studied in the literature. this is also the case studied in (barmish 1984). the result of the optimization scheme is = = 1.81, i = 0, 1, 2, 3 (this represents a one parameter optimization problem). the result is in agreement with the result reported by barmish. l iδ u iδ u iδ l iδ now we relax the constraints and assume that = , but they are different for different values of i. the resulting stability volume is given by the following parameter intervals: l iδ u iδ [[1,1], [2.318, 7.682], [6.33, 9.67], [5.93, 10.07], [1.71.4.29]] and with the removal of the above restriction, we have the following intervals: [[1,1], [5, 20.28], [8, 103365.4], [8, 30.027], [0,3]] 4.2 example 2 consider now the example studied in (blanchini el at. 1998). the example they studied is a sixth order polynomial given by p(s) = s6 + 4s5 + 4s4 + 6s3 + 3s2 + 2s + 0.5 the one parameter optimization case resulted in the values of = = 0.0512, and with different and for different i, the resulting intervals are given by: l iδ u iδ l iδ u iδ [[1,1], [3.91, 4.09], [3.91, 4.09], 5.88, 6.12], [2.99, 3.01], [1.96, 2.04], [.47, .53]] 4.3 example 3 here we consider a diamond of polynomials studied in (barmish et al., 1992) and given by: p(s) = s4 + 3s3 + 6.49s2 + 7.98s + 3.45 the objective is to find the maximum value of r, such that the polynomial (1) is stable for all parameters in dn given in (2). our proposed method resulted in the diamond dr given by dn = {d : |da-3.49| + |d1 – 7.98| + |d2 – 6.49| + |d3 – 3| + |d4 – 1|≤ 0.9593}| this is very close, but larger compared to the value of r = 0.9467 obtained in barmish et al. (1992). 5. conclusions an optimization-based approach is proposed for obtaining the largest volume of perturbations of the plant parameters, the use of which is illustrated via examples. the case of 30 on the computation of the maximum uncertainty volume polynomials with parameters which are affine in some uncertain parameters can be addressed using the proposed approach. 6. acknowledgements the author would like to express his appreciations for the support provided by kfupm. references anderson, b.d., 1972, the reduced order hermite criterion with applications to proof of lienard-chipart criterion, ieee transaction on automatic control, 17:669-672. barmish, b.o., 1984, invariance of strict hurwitz property for polynomials with perturbed coofficients, ieee transaction on automatic control, 29(10):935-936. barmish, b.r., tempo, r., hollot, c.v. and kang, h.i, 1992, an extreme point result for robust stability of a diamond of polynomials, ieee transaction on automatic control, 37( 9): 1460-1462. blanchini, f., tempo, r., and dabbcne, f., 1998, computation of the minimum destabalizing volume for interval and affine families of polynomials, ieee transaction on automatic control, 43(8):1159-1163. chapellat, h., bhattacharyya, s.p., and keel, l.h., 1988, stability margin for hurwitz polynomials, proceeding of the 27th ieee decision and control conference, 1:1392-1398. djaferis, t.e., 1989, the largest stability hypercube for families of polynomials with lincar uncertainty, american control conference, 1: 633-638. hollot, c.v., 1988, on markov’s theorem: it is like kharitonov’s but twice as nice, proceeding of the 27th ieee decision and control conference, 1: 515-518. kharitonov, v.l., 1978,syumpototic stability of an equilibrium position of a family of systems of linear differential equations differentsial’nye uravneniya, 14:2086-2088. kim, k.d., and bose, n.k., 1988 invariance of strict hurwitz property for bivariate polynomials under coofficients perturbations, ieee transaction on automatic control, 33(12):1172-1174. mansour, m., and anderson, b.d., 1992, kharitonov’s theorem and the second method of lyapunov robustness of dynamic systems with parameter uncertainties, edited by m. mansour, berlin, birkhauser. received 28 december 2001 accepted 21 may 2003 31 on the computation of the maximum uncertainty volume of stable polynomials f.m. al-sunni department of system engineering, king fahad university of petroleum and minerals, dahran 31261, saudi arabia, email: alsunni@ccse.kfupm.edu.sa. electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 109-121 © 2002 sultan qaboos university matlab and pspice dynamic model of axialfield permanent-magnet motor a.h. al-badi and a. gastli department of electrical engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email:albadi@squ.edu.om, gastli@squ.edu.om. matlabو pspice النموذج الديناميكي للمحرك الكهربائي ذي المجال المغناطيسي المحوري باستخدام عبداهللا البادي و عادل القصطلي يمكن استخدام هذا . تشرح هذه الورقة النموذج الديناميكي للمحرك الكهربائي ذي المجال المغناطيسي المحوري : خالصة تم مقارنة النموذج الديناميكي بالنتائج العملية . العابرة عند عمل هذه اآللة كمحرك أو كمولد كهربائي النموذج لدراسة االستجابة .ووجد تطابق بين النتائج مما يثبت صحة النموذج الديناميكي المستخدم abstract: in this paper a dynamic model of the axial-field, permanent-magnet machine will be discussed. the model may be used to study the transient response with the machine operating as a motor or as a generator. experimental results are compared with matlab/simulink and pspice predictions for a number of conditions, including the complete starting transient. excellent correlation is obtained which validated both modeling approaches. keywords: torus motor, dynamic model, pspice and matlab / simulink. 1. introduction o ne of the important types of axial-field permanent-magnet machines is the torus machine. a torus machine is a double-sided, axial-field, disc-type, permanent-magnet, brushless d.c. motor. it is a compact lightweight machine, which offers significant advantages in application where space is restricted, due to its extremely short axial length. it has a simple toroidal, stripwound stator core that carries a slotless toroidal winding. the rotor comprises two discs carrying six axially polarised magnets. the disc rotors act naturally as fans, so even with high electric loading good cooling of the stator winding is obtained. high magnetic loading may be achieved using sintered nd-fe-b for the magnets. the torus has very small stator leakage inductances and relatively small mutual inductances, because of the large effective air-gap compared with a conventional machine with slotted stator. the axial length of this machine can be made small, for a given power rating, because the active conductor length is the radial length of the stator winding, which falls between the rotor magnets. the axially directed end-winding lengths are relatively short, yielding low resistance compared with the end-winding resistance of a radial-field machine. because of the geometry of the machine, the self-inductances and the mutual inductances between the stator phases are constant (independent of the rotor angular position). some potential applications of torus machines include auxiliary power unit, wind-power generator, electric vehicle, high speed generator driven by a gas turbine, adjustable-speed pump drive, lawnmower motor, etc. due to the complexity of the machine-drive systems and high switching frequency in the power electronics, the mathematical analysis and the experimental development are becoming difficult to perform as well costly and time consuming. the use of simulation is therefore strongly 109 al-badi and gastli recommended so that the performance can be predicted and optimised before physically building the system. pspice and matlab are widely used by researchers and designers for the design and analysis of electric circuits and systems. they have been intensively used in the simulation of the performance of electrical machines and power electronic circuits (al-badi and green, 1998, chalmers et al 1997, gastli et al 1998, gastli and akherraz, 1998, green and al-badi, 1997). 2. mathematical model 2.1 circuit equation model the torus motor has permanent magnets on the rotor and three stator windings. the equations of the motor can be expressed as follows:           +                     +                     =           c b a c b a cbcac cbbab cabaa c b a c b a e e e i i i lmm mlm mml p i i i r r r v v v ,, ,, ,, 00 00 00 (1) where, r is the stator winding resistance (0.133 ). ω va, vb, vc are the phase voltages. ia, ib, ic are the phase winding currents. ea, eb, ec are the back emfs. la, lb, lc are the winding self inductances (200 µ h). ma,b, ma,c, mb,c are the winding mutual inductances between the three phases (73 µ h). p is the mathematical differential operator d /dt. 2.2 electromagnetic torque model the electromagnetic torque te and the equations describing the mechanical response are: mccbbaae ieieiet ω/)( ++= (2) )( mlem bttjp ωω −−= (3) mmp ωθ = mr pp ωθ = where, te is the electromagnetic torque. tl is the load torque. j is the moment of inertia of the rotating mass (0.065 kg m2). p is the pole pair number. b is the damping constant [0.00467 nm/(rad/s]. p is the differential operator. mω is the rotor speed in mechanical rad/s. mθ is the angle defining the rotor position in mechanical radians. rθ is the angle defining the rotor position in electrical radians. 3. the back emf model the back emf waveform is trapezoidal in shape, hence the transformation to d, q axis reference frame can not be easily accomplished. therefore, the a, b, c phase model will be used. 110 matlab and pspice dynamic model for the test machine with high-field magnets and air-gap winding, the effective air-gap length is constant. the measured back emf for a particular speed (104.72 rad/s) is represented in figure 1. a fourier analysis was performed on the waveform and values of the fourier coefficients up to 37th harmonic are considered (al-badi and green, 1998). 0 10 20 30 40 50 time, [ms] v ol ta ge , [ v ] 20 10 0 10 20 figure 1. the back emf. the initial model included coefficients up to 71st harmonic but this was found to have a negligible effect on the shape of the waveform. the fourier series for the back emf of phase a is given as: ( ) ( ) ([ ]37373311 1 37sin3sinsin φ−ω+φ−ω+φ−ω ω ω = teteteea ) (4) similar expressions can be obtained for the other two phases after including the appropriate phase shifts (-120o for phase b and -240o for phase c). the fourier coefficients e1, e3,…,e37 are known for the particular speed 1ω . fourier coefficients can be calculated at any speed using the following back emf-speed relationship: ω ω'' = i i e e (5) 4. pspice model for the motor drive system figures 2, 3 and 4 show the 3-phase torus motor system model, torque model, speed and position models respectively, that were developed using pspice. the description of the full model was reported in (al-badi and green, 1998). the resulting model is used to perform a comprehensive analysis of the system including the determination of the motor phase currents, line voltages, speed and electromagnetic torque. 5. matlab/simulink model a computer model of the 3-phase torus motor system was also developed using the matlab/simulink software. figure 5 shows the whole drive system with the inverter and the motor. the description of the full model is reported hereafter. the resulting model was used to perform a detailed analysis of the system including the determination of the motor phase currents and line voltages. 111 al-badi and gastli ea eb ec r r r l a l b lc m a,b dib/dt m a,c dic/dt m b,cdic/dt m b,adia/dt m c,bdib/dt m c,adia/dt v s control circuit rotor position sensor s1 s3 s5 s 4 s6 s 2 a b c ia figure 2. circuit diagram for the drive system. mcice ω/ mbibe ω/ tl r=106 maiae ω/ mbω figure 3. torque circuit, 1nm/v. jd m dtω / r=109 c=j farad l=1 h p mω r=10-9 figure 4. speed circuit ( mω ), 1 rad/s/v and position circuit (θr ), electrical. 112 matlab and pspice dynamic model +v phase a phase b phase c wm te torus machine torque va wm t speed pulses +vdc a b c -vdc mos_inverter wm pulses mosfet triggering pulse controller te wm load plot results initialize simulation clock -vdcvdc 3_phase diode bridge rectifier figure 5. torus motor drive system implemented with simulink 5.1 machine model the torus machine model described by (1) can be easily implemented with simulink blocks after separating the machine parameters matrix and the back emf model. 5.1.1 machine parameters figure 6 shows the model of the torus machine. the machine windings consist of three-phase r-l circuits with self-inductances and mutual inductances. this three-phase circuit can be implemented with the mutual inductance block build in the power system blocksets library. the mutual inductance block implements a magnetic coupling between three separate windings. the self-resistance and inductance of each winding are specified on the first three entries of the dialog box and the mutual resistance and inductance in the last entry. 5.1.2 back emf the back emf was modeled for the three phases using (4) and including the appropriate phase shift between phases. the implementation is done with simulink function block. figure 7 shows the block diagram of the implemented model. note that, for each phase, (4) was divided into four parts: part one includes all the harmonics from 1st to 9th, part two includes the sum of all harmonics from 10th to 19th, part three includes all harmonics from 20th to 29th and part 4 includes all harmonics from 30th to 37th. ωt is implemented using the integral block and integrating the electric angular velocity ω. 5.2 inverter model the inverter used was made of six power switches controlled with six synchronized pulse generators. the inverter configuration is shown in figure 8. the dc voltage supply to the inverter is generated using the three-phase ac-dc converter (rectifier) shown in figure 9. 5.2.1 switch model the power electronics switch was implemented using the mosfet model, which is a block build in the matlab power system bolckset. the mosfet is a semiconductor device controllable by the gate signal (g > 0) if its drain current id is positive (id > 0). the mosfet is connected in parallel with an internal diode that turns on when the mosfet is reverse biased (vds < 0). the model is simulated as a series combination of a variable resistor (rt) and inductor (lon) in series with a switch controlled by a logical signal (g > 0 or g = 0). the mosfet turns on when the drain-source voltage is positive and a positive signal is applied at the gate input (i.e. g = 1). the 113 al-badi and gastli mosfet block also contains a series rs-cs snubber circuit, which is connected in parallel with the mosfet. 1 te + v + i + i + i vab f(u) torque te ic ib vab ia mux ia v + v + v + wm e_c e_b e_a back emf 4 w m 3 phase c 2 phase b 1 phase a figure 6. torus machine model implemented with simulink. 3 e_a 2 e_b 1 e_c f(u) ec3 f(u) ec2 f(u) ec1 f(u) ec f(u) eb3 f(u) eb2 f(u) eb1 f(u) eb f(u) ea3 f(u) ea2 f(u) ea1 f(u) ea ec eb ea or mux s 1 p 1 wm figure 7. back emf model implemented with simulink. 114 matlab and pspice dynamic model 4 -vdc 3c 2b 1a m1 d g s m mosfet6 d g s m mosfet5 d g s m mosfet4 d g s m mosfet3 d g s m mosfet2 d g s m mosfet1 demux 2 +vdc 1 pulses figure 8. inverter model implemented with simulink 1 vdc v 3 v 2 v 1 vd(v) + v vd vdc l3 l2 l1 a k m diode6 a k m diode5 a k m diode4 a k m diode3 a k m diode2 a k m diode1 c 1 -vdc figure 9. ac-dc converter circuit. 5.2.2 gate signal model the gate pulses for the six transistors were generated by six-pulse generator blocks taken from the built in simulink library. the pulses period, duty cycle, and phases can be easily adjusted and set to desired values. figure 10 shows the block diagram of the model as it was implemented with simulink blocks. 1 pulses teta su3 sd3 teta su2 sd2 teta su1 sd1 mux s 1 p 1 wm figure 10. gate signal model implemented with simulink 115 al-badi and gastli 6. models validation the validity of both models was verified by applying them to the prediction of the performance of the torus motor drive system and comparing the simulation results with the corresponding experimental data. 6.1 at steady-state the dynamic model was first validated under steady state conditions by comparing simulated and measured phase current waveforms. figures 11 and 12 show the simulated and measured phase current and line voltage waveforms at 40.5 v, 3.78 nm. it indicated good correlation between the measured and simulated results. 6.2 at starting a 30 v rectified d.c. supply is applied across the inverter and then the switches are controlled on and off. the motor phase current and speed during starting and subsequent acceleration up to a final steady speed are shown in figures 13 and 14. figure 13 shows the experimental and simulated results of the current waveform during starting. figure 14 shows the experimental and simulated speed build up during starting. closer examination of the current waveform shows that the peak current is determined almost by the circuit resistance because the inductance is very small, also evident in the finite rise in the phase current. the figure shows also a spike superimposed on the top of each current pulse, owing to the switching which takes place every 60 degrees in other phases and to normal ripple in the rectified d.c. supply. the frequency of the first component is speed-dependent while the second is six times the a.c. supply frequency. comparison between measured and simulated results of the phase currents and speed waveforms shows good correlation between these results. 7. conclusion dynamic performance prediction of an existing torus motor drive system using pspice and matlab/simulink models has been presented and compared with the actual drive performance. the two modeling approaches have been verified and validated with the experiments. it is possible to conclude that both approaches provide satisfactory tools for the investigation of the axial-field machine drive system performance. they can be helpful in the design and analysis of any axial-field machine drive system, which includes the machine, the load, the converter and the controller. 116 matlab and pspice dynamic model 0 4 8 12 16 20 time, [ms] 10 0 -10 c ur re nt , [ a ] (a) measured 40 45 50 55 60 time, [ms] 10 0 10 c ur re nt , [ a ] (b) simulated, pspice 0 . 0 3 8 0 . 0 4 0 . 0 4 2 0 . 0 4 4 0 . 0 4 6 0 . 0 4 8 0 . 0 5 0 . 0 5 2 0 . 0 5 4 0 . 0 5 6 0 . 0 5 1 5 1 0 5 0 5 1 0 1 5 t i m e , [ s e c ] li ne c ur re nt , [ a ] (c) simulated, matlab figure 11. phase current waveforms with tl =3.78 nm, 40.5 v, speed=1000 r.p.m. 117 al-badi and gastli 0 4 8 12 16 20 time, [ms] 50 25 0 25 50 v ol ta ge , [ v ] (a) measured 40 45 50 55 60 time, [ms] -50 -25 0 25 50 v ol ta ge , [ v ] (b) simulated, pspice 0 . 0 3 8 0 . 0 4 0 . 0 4 2 0 . 0 4 4 0 . 0 4 6 0 . 0 4 8 0 . 0 5 0 . 0 5 2 0 . 0 5 4 0 . 0 5 6 0 . 0 5 8 5 0 4 0 3 0 2 0 1 0 0 1 0 2 0 3 0 4 0 5 0 t i m e , [ s e c ] l in e v ol ta ge , [ v ] (c) simulated, matlab figure 12. line voltage waveforms with tl =3.78 nm, 40.5 v, speed=1000 r.p.m. 118 matlab and pspice dynamic model 0 1 2 3 t ime, s -10 0 10 20 -20 current, a (a) measured 0 1 2 3 -2 5 -1 5 -5 5 1 5 2 5 t im e , s c u rre n t, a (b) simulated, pspice 0 0.5 1 1.5 2 2.5 3 -30 -20 -10 0 10 20 30 tim e, s c urrent, a (c) simulated, matlab figure 13. phase current transient. 119 al-badi and gastli 0 1 2 3 t i m e , s 4 0 0 2 0 0 0 6 0 0 s p e e d , r e v / m i n (a) measured 0 1 2 3 0 2 0 0 4 0 0 6 0 0 t i m e , s s p e e d , r e v / m i n (b) simulated, pspice 0 1 2 3 0 2 0 0 4 0 0 6 0 0 t i m e , s s p e e d , r e v / m i n (c) simulated, matlab figure 14. speed transient. 120 matlab and pspice dynamic model references al-badi, a.h and green, a.m. 1998. a transient model of the torus electrical machine using pspice. 33rd universities power engineering conference, september 1998, edinburgh, pp.254-257. chalmers, b.j., green, a.m., reece, a.b. and al-badi, a.h. 1997. modelling and simulation of the torus generator. iee proc. b, vol.144, 6: 446-452. gastli, a., akherraz, m. and gammal, m. 1998. matlab/ simulink/ann based modeling and simulation of a stand-alone self-excited induction generator. international conference on communication, computer and power, icccp’98, december 7-10 1998, muscat, sultanate of oman, sponsored by the ieee and iee, pp. 93-98. gastli, a., akherraz, m. 1998. matlab/simulink simulation of variable-speed busbarconnected self-excited induction generator. international conference on communication, computer and power, icccp’98, december 7-10 1998, muscat, sultanate of oman, sponsored by the ieee and iee, pp. 258-263. green, a.m. and al-badi, a.h. 1997. modelling and simulation of a torus generator using pspice. 32nd universities power engineering conference, september 1997, manchester, pp.806-809. received 24 june 2001 accepted 13 november 2001 121 matlab and pspice dynamic model of axial-field permanent-magnet motor a.h. al-badi and a. gastli department of electrical engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email:albadi@squ.edu.om, gastli@squ.edu.om. mathematical model 2.1 circuit equation model 2.2 electromagnetic torque model the back emf model pspice model for the motor drive system matlab/simulink model 5.1 machine model 5.1.1 machine parameters 5.1.2 back emf 5.2 inverter model 5.2.1 switch model 5.2.2 gate signal model models validation 6.1 at steady-state 6.2 at starting conclusion references microsoft word phys991220.doc science and technology, 5 (2000) 105113 © 2000 sultan qaboos university 105 surface plasmons for probing optical data of multilayered thin films a. rais and a. sellai department of physics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman. ت السطحية لفحص المعطيات البصرية لألفالم الرقيقة ذات الطبقات المتعددةالبالزمونا و عزوز صالي عبدالمجيد رائس على المعطيات للحصول )س.ب ( للبالزمونات السطحية البصري تحريضنبين كيف نستعمل ال ,بحث في هذا ال : خالصة ظاهرة االزدواج األقصى بين الضوء المستقطب الساقط و . فالم الرقيقة لطبقات معينة في األنظمة ذات األ والجيومترية البصرية أدنى حد وهي التبعية الحساسة توحي .التي تحسب بالنظرية المصفوفة الموحدة , تظهر كأدنى حد في معامل االنعكاس , س.ب إكمال معامل االنعكاس المقاس و ن هذه العوامل يمكن آن تحدد بدقة ب بألمعامل االنعكاس في العوامل البصرية و الجيومترية \ طبقة الهواء \المنشور : الطبقات المتعددة ىالخطة تطبق على النظام ذ simplex). "( سيمبالكس" باستعمال طريقة , المحسوب سمك , al-الثابت البصري لألكسيد : العوامل المكملة هي و بطول الموجة الثابت للضوء الساقط . al \ al \ gaas -األكسيد تظهر و .لحساب معامل االنعكاس و اإلكمال) fortran( استعملت شفرات فورطران al. سمك al ,-سمك األكسيد, طبقة الهواء زيادة على هذا ). ننو متر ( نم 633على طول الموجة , النتائج آن معامل االنعكاس النظري يناسب جيدا معامل االنعكاس المقاس على أقل تناسباً مع النظرية معامل االنعكاس وجد أن لكن ،يوافق األبحاث السابقة al -د الثابت البصري النظري لألكسي فإن وأما . تبين ظاهرة االنتثار ال توا فق األبحاث السابقة التي ثوابتهما البصرية النظرية أما , نم 458 نم و 590طول الموجتين .المعطيات الجيومترية النظرية توافق القيم المقاسة abstract: in this paper, we show how optical excitation of surface plasmons (sps) can be used to obtain optical and geometrical parameters of specific layers in multi-layered thin film systems. the optimum coupling phenomenon between incoming p-polarized light and sps appears as a minimum in the reflectance that is calculated using a standard matrix formalism. the sensitive dependence of the reflectance minimum on optical and geometrical parameters suggests that they can be determined accurately by fitting the measured attenuated total reflectance (atr) to the matrix-calculated reflectance using the simplex minimization method. the procedure is applied to the multi-layered system: prism / air gap / al-oxide / al / gaas. at fixed incident light wavelength, the fitting parameters are the al-oxide optical constant and the thickness of the air gap, al-oxide and al layers. fortran codes are implemented for the reflectance calculations and the fitting procedures. the results show that the theoretical reflectance fits well the measured atr at 633 nm wavelength. moreover, the modeled al-oxide optical constant at this wavelength agrees well with the literature. however, the reflectance fits are less good at 590 nm and 458 nm wavelengths and their modeled al-oxide optical constants show a dispersion effect in disagreement with the literature. the modeled geometrical parameters are consistent with the nominal values. keywords: surface plasmons, optical constants, thin films, attenuated total reflectance (atr) , simplex. urface plasmons ( sps) are electromagnetic ( em ) waves due to collective and coherent fluctuations performed by electron charges on a metal boundary. the sp em waves propagate along the surface and decay exponentially into the space perpendicular to the surface and have their maximum in the surface. excitation of sp modes is useful in various applications where strong em field at surfaces of interfaces is desired (raether 1988). optical excitation of surface plasmons involves coupling of the photon field to the electron density of the metallic surface. since sps are intrinsically of transverse magnetic (tm) type excitations, they may be excited by p-polarized light only. moreover, at any given energy, a photon does not have sufficient momentum parallel to the metal surface to excite the sps. the dispersion relation of sps lies, in fact, right to the light line which requires that the wavevector hω/c of incoming light should be increased to couple with that of sps. either a coupling prism or a grating a. rais and a. sellai 106 must be used to match the component of wave vector of the incident light parallel to the surface to the sp wave vector. for thin film structures of limited number of layers, the analytical calculation of the reflectance is straightforward. however, when the number of layers exceeds three, it becomes cumbersome to derive an analytical expression of the reflectance. therefore, a standard matrix formalism (azzam and bashara 1979) can be utilized instead. to fit the matrix calculated reflectance to the measured attenuated total reflectance (atr), we have chosen the simplex minimization technique which appeared to be the most suitable because the theoretical model is non-linear. the aim of this paper is to show that sps excitations can be used to extract optical and geometrical parameters of specific layers in multi-layered thin film systems. this can be achieved by fitting the measured atr to the calculated reflectance using the simplex method (nelder and mead 1965). the plan of this paper is as follows. in the first section, the experimental technique for measuring atr is described and the standard matrix formalism is briefly presented. previously obtained experimental reflectance data by one of us (tamm et al 1993), for an al/gaas sample, is used to probe the optical properties and thickness of the al-oxide layer. the second section is devoted to results and discussion, and we show how sensitive is the theoretical reflectance to certain parameters. concluding remarks are made in the last section. experiment and theory of reflectance the experimental data (reflectance versus angle of incidence) were taken using an otto configuration prism / air gap / al-oxide /al / gaas shown in figure.1 (otto 1969). the sample (al/gaas) is separated from the prism by an air gap of the wavelength order. the al-oxide and al thickness nominal values are 4 nm and 22 nm respectively. for angle of incidence in the prism, θi greater than the critical angle θc, incident light of wave-vector kl couples via the evanescent field in the air-gap to the sps (wave-vector ksp) to the metal surface with conservation of the component of the wave-vector parallel to the interfaces ksp = kl n sin θi , with n being the refractive index of the prism. the air-gap here acts as an optical tunneling barrier from which extends the evanescent optical field to the al / air interface. varying θi , allows the tuning of the incident light wave vector to that of sps until they are matched creating the resonance condition. θi sapphire prism air gap al-oxide al thin film gaas substrate figure 1. detail of arrangement for making otto configuration atr measurements onal / gaas sample. the prism-sample configuration is rotated under computer control with the reflected beam and reference beam recorded at 1000 points across any given angle scan range. the incident p-polarized surface plasmons for probing optical data of multi-layered thin films 107 beam of a given wavelength is produced by passing randomly polarized radiation from a light source through a caf2 based polarizer. the incident radiation is mechanically chopped at 1 khz and standard phase sensitive detection techniques are employed to monitor the reflected and reference beams that impinge on a suitable detector. the p-polarized reflected signal divided by the reference signal is scaled to give attenuated total reflectance (atr) as a function of internal angle of incidence. the interpretation and modeling of the measured atr requires the theoretically calculated reflectance. standard electromagnetic theory of light is routinely used to derive expressions for the complex amplitude reflection coefficients in terms of the microscopic optical properties and thickness of the different constituent layers of a given structure. the propagation of plane waves in an isotropic medium is described by the complex index of refraction n = n – j k, n is the real index of refraction and k is the extinction coefficient. the reflection and transmission are calculated using a 2 x 2 matrix formalism described in details in azzam and bashara (1979). following this formalism, if e+(z) and e(z) are the complex amplitudes of the forward and backward travelling waves perpendicular to the interface between two layers, the total field is denoted by:       = − + )( )( )( ze ze ze assuming that the equations describing the propagation of light are linear and that the tangential fields across any interface between two adjacent layers are continuous, the fields e+(z’) and e-(z”) at two different planes z’ and z” are related by a 2 x 2 matrix transformation:       ⋅      =      − + − + )"( )"( )"( )'( 2221 1211 ze ze ss ss ze ze or e(z’) = s e(z”) (1) s is a scattering matrix characteristic of the part of the structure confined between the planes z’ and z”. for a structure of m layers and m-1 interfaces confined between ambient (0) and substrate (m+1), s can be written as ∑ + = −= 1 1 )1( m i iii lis where i( i – 1) i is a 2 x 2 matrix characteristic of the interface (i-1)i and li is a 2 x 2 matrix characteristic of the ith layer. in fact, if z’ and z” are on opposite sides of the interface between layers (i-1) and i , equation (1) becomes: )0()0( )1( +=− − iiii zeize however, if z’ and z” are both inside the ith layer, equation (1) becomes: )0()0( −+=+ iiii dzelze with di the thickness of the layer. with no reflected wave in the substrate, the fields in the ambient (a) and substrate (s) are related by       =      + − + 0 s a a es e e . for a given layer i and interface i-1, the matrices i(i-1)i and li can be written as       = − − − − 1 11 )1( )1( )1( )1( ii ii ii ii r r t i ;       = β β j j i e e l 0 0 , a. rais and a. sellai 108 where t(i-1)i and r(i-1)i are the fresnel reflection coefficients of the (i-1)i interface and β is the layer phase thickness and it is given by φ λ π β cos 2 dn = with φ representing the angle between the direction of propagation in the ith layer and the normal to the interface. subsequent to calculating the different layer and interface matrices for a given stratified structure, the overall reflection can be determined from: 11 21 s s e e r a a == + − a fortran program was implemented to evaluate the different matrices, obtain s11 and s21 for p-polarized light and yield the reflectance r. these calculations were carried out at various angles of incidence θi and for different optical and geometrical parameters of the otto configuration described above. results and discussion figure 2 (a) and (b) show the calculated reflectance using the matrix formalism for different thicknesses of al-oxide layer and air gap respectively. for both graphs, increasing slightly the thickness results in increasing the reflectance minimum as well as shifting the resonance angle. note that the air gap value is kept around the incident light wavelength magnitude and the al-oxide thickness is around the nominal value. as discussed extensively by tamm et al 1991, the depth of the sp’s reflectance minimum is primarily determined by the dimension of the air coupling gap. this theoretical model assumes no wedging in the air gap which is plausible for a small diameter laser beam tracking across the prism-air gap interface as the prism-sample assembly is rotated. the effect of the al thin film thickness around the nominal value (22 nm) on the calculated reflectance is shown in figure 2(c). here, we notice almost no change of the resonance curve at high angles and a minor shift of the resonance angle. however, a significant change appears at lower angles. i n t e r n a l a n g l e o f i n c i d e n c e ( d e g r e e ) 3 4 3 6 3 8 4 0 4 2 4 4 4 6 4 8 r e f le c t a n c e 0 . 0 0 . 5 1 . 0 3 . 9 4 . 5 a l o x i d e t h i c k n e s s ( n m ) 3 . 0 (a) surface plasmons for probing optical data of multi-layered thin films 109 figure 2. the calculated reflectance as a function of incidence angle for different: (a) al-oxide thickness, al and air gap thickness are 22 nm and 650 nm respectively. (b) air gap thickness, al-oxide and al thickness are 3.4 nm and 22 nm respectively. (c) al thickness, al-oxide and air gap thickness are 3.4 and 650 nm respectively. for the three graphs, the wavelength is 633 nm and the al-oxide optical constant is 3. the effect of the al thin film thickness around the nominal value (22 nm) on the calculated reflectance is shown in figure 2(c). here, we notice almost no change of the resonance curve at high angles and a minor shift of the resonance angle. however, a significant change appears at lower angles. the calculated reflectance for different al-oxide optical constant at constant incident light wavelength (633 nm) is shown in figure 3. it is interesting to note that the curve shifts in the region around the resonance angle only. the literature values of al2o3 optical data (table1) show a minor dispersion for different wavelengths and therefore varying al-oxide optical constant around the reported value implies considering an oxide layer of different optical nature. i n t e r n a l a n g l e o f i n c i d e n c e ( d e g r e e ) 3 4 3 6 3 8 4 0 4 2 4 4 4 6 4 8 r e f le c t a n c e 0 . 0 0 . 5 1 . 0 6 5 0 4 5 0 5 5 0 a i r g a p t h i c k n e s s ( n m ) (b) i n t e r n a l a n g l e o f i n c i d e n c e ( d e g r e e ) 3 4 3 6 3 8 4 0 4 2 4 4 4 6 4 8 r e f le c ta n c e 0 . 0 0 . 5 1 . 0 2 2 2 0 2 4 a l l a y e r t h i c k n e s s ( n m ) (c) a. rais and a. sellai 110 figure 3. the calculated reflectance as a function of incidence angle for different al-oxide optical constant. the wavelength is 633 nm. the air gap, al-oxide and al thickness are 650 nm, 3.4 nm and 22 nm respectively. table 1: fitting parameters of measured atr to calculated reflectance for the multi-layered system prism/air gap/al oxide/al/gaas at different incident light wavelengths obtained to produce the theoretical curves of figure 5. the invariant parameters of the modeled reflectance were taken from the literature. εr and εi are the real and imaginary parts of the dielectric function and t is the thickness of each medium of the multi-layered system. fitting parameters invariant parameters λ(nm) air gap al-oxide al prism (ref.1) al (ref.1) gaas (ref.2) al-oxide (ref.1) t(nm) εr t(nm) t(nm) εr εr εi εr εi εr 633 772 2.98 3.50 24.4 2.298 -37.3 13.7 14.8 1.5 3.0 590 593 2.72 4.19 24.5 2.300 -33.0 11.3 15.5 1.9 3.1 458 506 3.31 3.90 23.1 2.324 -21.1 4.7 20.5 5.4 3.13 ref.1: tamm et al 1993; ref.2: palik 1985. concurrently, the same equations developed for reflectance calculations are readily utilized to obtain the evanescent field (e-field), for a particular incident angle θi and wavelength λ, in each of the structure layers. the examination of the field profile, shown in figure 4, and calculated for the geometry prism / air gap / al / gaas at resonance θi = 41.8o and λ = 633 nm reveals the surface nature of the mode excited here. the field is evanescent in the air gap, decaying away from the al / air interface into both air and al with respective decaying lengths of approximately 600 nm and 10 nm. the field is however, oscillatory in both the incident medium (prism) and the gaas substrate, indicating the radiating nature of the em fields in these media. i n t e r n a l a n g l e o f i n c i d e n c e ( d e g r e e ) 3 4 3 6 3 8 4 0 4 2 4 4 4 6 4 8 r e f le c ta n c e 0 . 0 0 . 5 1 . 0 a l o x i d e o p t i c a l c o n s t a n t 2 . 5 3 . 5 3 . 0 surface plasmons for probing optical data of multi-layered thin films 111 figure 4. the calculated e-field as a function of distance in each medium of the geometry prism / air gap / al / gaas, at resonance angle θi = 41.8 o and wavelength λ= 633 nm. the measured atr on the multi-layered system prism/air gap/al-oxide/al/gaas has been fitted to the matrix calculated reflectance by minimizing the sum of the squared residuals using the simplex method. for this purpose, a fortran code on a personal computer has been implemented. the four fitting parameters were those described above showing the reflectance sensitivity, namely: the al-oxide optical constant, the thickness of the air gap, al-oxide and al. in this process, the real and imaginary parts of the dielectric function for al, gaas and the glass prism were based on values given in the literature (tamm et 1993, palik 1985); at given wavelength, these parameters were treated as invariant in the modeling process. fits for different light wavelengths are shown in figure 5. fitting and invariant parameters are in table 1. as can be seen, the 633 nm wavelength data shows a very good fit as well as good agreement of the modeled al-oxide optical constant with the al2o3 literature value (table 1). moreover, at this wavelength, the modeled thickness of the air gap, al-oxide and al are consistent with the nominal values. on the other hand, the fits of 590 nm and 458 nm wavelengths are not as good in particular around the resonance region. as expected their corresponding al-oxide optical constants are far from the known values. the interpretation of this discrepancy may be related primarily to the wedging effect of the air gap in addition to a less pronounced dispersion effect of the al-oxide layer. we mentioned above that the theoretical model assumes no air gap wedging which is plausible as long as the light beam is small. indeed, it is the case for the 633 nm wavelength produced by a laser source but not for 590 nm and 458 nm light beams produced by an ordinary collimated source. furthermore, having different optical constants at different wavelengths for the al-oxide layer might suggest the presence of other substances, above and/or under al2o3 , with dispersion effect on the incident light. 0 2 0 0 4 0 0 e -f ie ld (a rb itr ar y un its ) 0 1 0 2 0 d is t a n c e ( n m ) 6 0 0 8 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 2 0 1 2 0 0 1 5 0 0 p r is m a ir g a p a l f ilm g a a s s u b s tr a t e a. rais and a. sellai 112 figure 5. fit of the measured atr (dots) to the calculated reflectance (line) as a function of the internal angle of incidence for different wavelengths. fitting and invariant parameters are shown in table 1. for all three wavelengths, the modeled al-oxide thickness is of the order of a few atomic layers. however it appears higher for wavelengths 590 nm and 458 nm than 633 nm. this might also suggest the presence of extra layers. the last point to be highlighted concerns the response of the structure to incoming light. the electron gas response of the al metallic layer is determined strongly by the large imaginary part of the dielectric function at all wavelengths considered here. this means that the mode excited is that of sps with the plasmon response being slightly weaker at shorter wavelength than the response at λ = 633 nm; the value of the real part of the al dielectric function εr is smaller in absolute value (see table 1). nevertheless, εr remains very much less than –1 and larger than the imaginary part εi. this fulfils the wellknown condition for existence of sps and excludes the possibility of losing a dielectric surface mode which might be present otherwise (under for example the condition εr > 0 and | εr | > εi). conclusion in this paper, we have shown how optical excitation of surface plasmons (sps) can be used to obtain optical and geometrical parameters of specific layers in the multi-layered system: prism / air gap / al-oxide / al / gaas. the modeled al-oxide optical constant at 633 nm wavelength agrees well with the literature but show a dispersion effect at 590 nm and 458 nm wavelengths in disagreement with the reported values. the geometrical parameters such as the thickness of air gap, al-oxide and al are consistent with the nominal values. considering these results, we may propose this method for probing unknown optical and geometrical data of uncertain layers in any thin film systems where good and reliable data is available for the known constituent layers.the method may also be a good technique for monitoring the thickness of thin films growing. i n t e r n a l a n g l e o f i n c i d e n c e ( d e g r e e ) 3 6 3 8 4 0 4 2 4 4 4 6 4 8 r e fl e c ta n c e 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 5 9 0 6 3 3 4 5 8 λ ( n m ) surface plasmons for probing optical data of multi-layered thin films 113 references azzam, r.m.a. and bashara, n.m. 1979. ellipsometry and polarized light. north holland. amsterdam. nelder, j.a. and mead, r. 1965. a simplex method for function minimization. comp.j., 7: 308-313. otto, a. 1968. excitation of non-radiative surface plasma waves in silver by the method of frustrated total reflection. z. physik, 26: 398-415. palik, e.d. (editor). 1985. handbook of optical constants of solids, 429. academic press. london. raether, h. 1988. surface plasmons on smooth and rough surfaces and on gratings. springer-verlag, tamm, i.r., dawson, p., connoly, m.p., raza, s.h. and gamble, h.s. 1991. fast and slow mode plasmons in ag – al. j.mod. optics, 38: 15931615. tamm, i.r., dawson, p., sellai, a., pate, m.a., grey, r. and hill, g. 1993. analysis of surface plasmon polariton enhancement in photodetection by shottki diodes, sol.st.electronics 36: 1417-1427. received 20 december 1999 accepted 18 august 2000 microsoft word math990901.doc science and technology, 5 (2000) 77-84 © 2000 sultan qaboos university 77 simple monte carlo cellular models for surface evolution h. h. albarwani and a.purnama department of mathematics and statistics, college of science, p.o.box 36, sultan qaboos university, al-khod 123, muscat, sultanate of oman. باستخدام طريقة مونت كارلو للتطور السطحينموذج خلوي مبسط حمدي البرواني وأنتون برناما تستعمل محاكاة الخلية المعروفة بمونت كارلو في بعض المجسمات البسيطة ذات السطح النشوئي حيث يحاكي النمو :خالصة إلى موقع معين في السطح على عدد السطحي بإضافة خاليا جديدة إلى السطح، هذا و يعتمد اندماج الخلية الجديدة التي تصل تم . الخاليا الموجودة حول هذا الموقع وعلى الخاليا الجديدة المحتمل التصاقها بالمواقع التي بها أقل عدد من الخاليا المطوقة مو في اتجاه تمثيل ذلك بتطبيقات معينه كمحاكاة انتشار مقدمة اللهب ، والترسيب األرضي والنمو البلوري المتباين حيث يكون الن .معين أكثر انتشارا من النمو في اتجاهات أخرى abstract : monte carlo cellular simulations are described for some simple surface evolution models. surface growth is simulated by adding new cells to the surface. the bonding of a new cell arriving to a site on the surface depends on the number of cells present around that site; new cells are more likely to stick at sites with the fewest missing surrounding cells. applications are given for simulating the propagation of a flame front and the formation of surface landforms; and the (anisotropic) growth of a crystal, where the surface may grow more rapidly in one direction than others. keywords: cellular automata, crystal growth, geomorphology. ost computational methods for solving equations of motion of a surface can be subjected to problems such as convergence and stability of the algorithm. simulations can also show unphysical features. for example, non-linear wave models simulations have shown how edges (folded surfaces) and other surface discontinuities can develop as a result of the erosion of an initially smooth surface (al-barwani, 1996). without a detailed knowledge of non-linear wave theory, computational cellular model simulations can give the same results of surface growth (smith, 1991a). cellular automata are based upon discrete dynamical systems where the state variables are chosen in a finite set and distributed on a discrete grid. the time evolution is run synchronously in all cells of the grid and each cell changes its state according to a local rule that only depends upon its neighbouring cell states. models are simple to construct but generally display very complex behaviour. cellular automata supply useful models in trying to understand and describe nature (manneville et al 1989; toffoli and margolus, 1987). simple cellular growth models have been demonstrated successfully in simulating the most realistic crystal growth performance (webb et al 1997) and erosion of landforms (smith, 1991a). in cellular models, the challenge is to choose the local relationship for representing the growth mechanism. this rule specifies how each cell is going to be influenced by some nearby cells. simple statistical rules are usually preferred but these deterministic rules may not necessarily give the shapes or growth rates observed experimentally; as from the same initial conditions, the simulations eventually lead to the same evolution. in contrast, with a probabilistic rule, the same current situations may lead to several different outcomes, each with a given probability. the effects of surface growth can be simulated by adding new cells (particles) to the surface. a new diffusing cell arriving on the surface is allowed to move around the surface until it finds a stable al-barwani and purnama 78 location to stick and become part of the surface. the probability of a new cell staying at a stable site depends on the local properties of that particular site. for example, in a surface growing from a twodimensional square cell, an edge is a likely stable site; since a site that had two adjacent edges could well have a higher probability of capturing a new cell simple monte carlo cellular models for simulating the effects of surface growth are constructed here; and simulations are performed to animate the propagation of a flame front; the formation of surface landforms; and the (anisotropic) growth of a crystal. the surface growth mechanism is specified so that the bonding of a new cell arriving to a site on the surface depends on the number of cells present around that site; that is, new cells are more likely to stick at sites with the fewest missing surrounding cells. for the case of flame propagation, an unburnt cell is more likely to become burnt if it has many surrounding burnt cells. in crystal growth, the effects of directional surface growth dependence are included in the probability for adding a new cell to the surface. simple cellular automata models a cellular automaton model consists of a two-dimensional regular uniform grid with discrete variable states assigned to at each cell. for example, to simulate the flame front propagation, each cell can be represented as a three-state variable with values of 0, 1 and 2 (figure 1). the model evolves in discrete timesteps with every new cell state being uniquely updated from the current states of its close neighbour cells states according to a definite set of rules, which are local (i.e. no action-at-a-distance is permitted) and uniform (i.e. same rules are applied to all cells). these rules are commonly deterministic, and from the same initial conditions, the simulations should invariably lead to the same final evolution. figure 1. a two-dimensional grid used for simulating the propagation of a flame front. a cell is a neighbour of another one if it has a chance to directly affect its state, i.e. via the rule, in one timestep. so typically, the neighbourhood is taken to be the cell itself and all immediately adjacent cells. for a cell (i, j), where ini ,,1 l= and jnj ,,1 l= , its neighbourhood ui, j may be defined as ( ){ }c±= ji,u ji, , (1) where c is a constant. symmetry of the neighbourhood is assumed with periodic boundary conditions so that for example, cell (1 c, 1) is defined as equal to (ni c, 1). figure 2 shows the commonly used neighbourhoods; namely, the square ( ) ( ) ( ) ( ){ }j1i1ji,j1i1ji,u ji, ,,,,, +−−+= , (2) simple monte carlo cellular models for surface evolution 79 and the hexagonal ( ) ( ) ( ) ( ) ( ) ( ){ }.,.,,,,.,,.,,,,. 1j50ij1i1j50i1-j50ij1-i1j50-iu ji, +++−+−+= (3) figure 2. cell neighbourhood in a two-dimensional grid. (a) square and (b) hexagonal. it is straightforward to construct simple cellular automata models, which will simulate the effects of surface evolution. to demonstrate the algorithm, consider as an example, a surface growing from one seed cell as illustrated in figure 3. suppose that initially only the seed cell is present; and the surface growth mechanism is postulated by adding a cell to all free edges of any existing cell on the surface. this rule is uniformly applied to all cells at each timestep, and then repeats the surface growth starting with the new (current) surface. as it can be seen from figure 3 that for this simple cellular automata model, the surface grows uniformly in four directions. by a simple change in the surface growth rule, growth can be arranged, say parallel to the coordinate axes, as shown in figure 4. that is, at even timesteps, the previous growth mechanism is prescribed on all free edges (figure 3); and at odd timesteps, the growth is limited only to cell which has two edges adjoining the current surface. the above surface growth rules are deterministic, as at each timestep the new surface is updated cyclically. the algorithms will simulate the effects of isotropic surface growth from a single seed cell, but the growth may not be observed in nature; as the simulations always eventually lead to the same new surface. in contrast, if probabilistic growth rules are employed, the current surface may grow to several different new surfaces, each with a given probability. simple monte carlo cellular models assuming a simple power law relationship, the probability for adding a new cell to the surface is calculated as, for the hexagonal neighbourhood (3), nb p       = 6 , (4) where b is the number of missing neighbouring cells (calculated using equation (3)) and n is the assumed power law dependence which determines the strength of the influence of surrounding cells. if n = 0, all surface cells have the same probability of growth. if 1=n there is a 6:1 ratio of success between a cell which is completely surrounded by other cells and one which has only a single cell as its neighbour; whereas if n = 2, the ratio is 36:1. as n increases, a smoother surface evolution will develop but simulations take longer to achieve. equation (4) also implies that the choice of an initial surface is another important factor; as the local geometry of the surface depends on n. if the surface is initially flat and isotropic (in the sense of equal probability), it will retain its flatness and hence, develop no surface structure. a monte carlo method is used to speed up the simulation, so that at each timestep, instead of updating all surface cells sequentially, a random surface cell is chosen. the growth rate of the monte carlo algorithm is about twice faster than that of the cellular automata, as demonstrated by webb et al. al-barwani and purnama 80 (1997, figure 1e). after 40 timesteps, the new surface almost completely covers the old surface for a growth rule that adds a new cell with a 50% probability if there is at least one free adjacent edge. it is also straightforward to construct simple monte carlo cellular models to simulate the effects of surface evolution. the procedure is, instead of updating all cells, to pick a cell randomly from the surface and check if its state has to be updated according to the surface growth rule prescribed. a random number generator is used to select cells from the surface. figure 3. cellular automaton animation of a single seed cell growing on all free edges of its surface, after timesteps (a) 1, (b) 2, (c) 3 and (d) 4. to update the state of a chosen surface cell, first another random number generator selects a number r between 0 and 1. if r ≤ p, then the chosen cell state is changed; but if pr > , the cell state remains unchanged. the algorithm then continues to select another surface cell at random. simple monte carlo cellular models for simulating the effects of surface evolution are constructed here; and simulations are performed to animate the propagation of a flame front; the formation of surface landforms, and the (anisotropic) growth of a crystal. the surface growth mechanism is specified so that a new cell is more likely to stick at randomly chosen surface cells with the fewest missing surrounding cells. for the case of flame propagation, an unburnt cell is more likely to become burnt if it has many surrounding burnt cells. in crystal growth, the effects of directional growth dependence are included in the probability for adding a new cell to the surface. a flame front propagation model: flame propagation is a highly complex phenomena. physically, it depends on the fuel supplied and the media on which the flame is spreading. basically, it can be illustrated as follows: a fire lit at a particular site on the surface will only spread if that site is simple monte carlo cellular models for surface evolution 81 surrounded by other sites which are already burnt. in this way, the effects of flame front propagation can be simulated using a simple monte carlo cellular model. for simplicity, the flame is assumed to propagate only from burnt to unburnt region. once a cell is burnt it remains burnt, and only interface cells (figure 1) that can be burnt. a simple algorithm used can be briefly described as follows. start initially with a square burnt region. an interface unburnt cell is chosen at random and the number of its nearest neighbours is calculated using the hexagonal neighbourhood (3). the flame propagation mechanism is postulated so that, an interface unburnt cell is more likely to become burnt if it is surrounded by many neighbouring burnt cells. this probability is calculated using equation (4) with n = 2 figure 4. cellular automaton animation of a single seed cell growing in directions parallel to the coordinate axes, after timesteps (a) 1, (b) 2, (c) 3 and (d) 4. the simulated flame front propagation is shown in figure 5. simulations showed initially, some rough flames fronts emerge from the square burnt region. after 8000 timesteps (figure 5b), the initial square shape of the burnt region still visible, but the corners start to disappear. by 20000 timesteps (figure 5c), the burnt region has begun to take a circular form and corners have completely disappeared. finally after 50000 timesteps (figure 5d), the burnt regions new shape has assumed an approximately circular formation. a land deposition model: because of the complexity of phenomena in nature, it is a difficult task, if not impossible, to decide and single out one physical process which is dominant in reshaping surface landforms. surface landscapes are generally formed through geological processes of erosion and deposition by wind and water, and volcanic eruptions. basically, particles eroded from one location are transported along the surface until they are deposited at another location. so land erosion and deposition processes can be illustrated as a result of randomly removing and adding cells to the surface; which as observed, depends mainly on the geometry of surface. in this way, the evolution of surface landforms is another example that can be simulated using a simple monte carlo cellular model. for illustration, consider land deposition on a concave surface represented initially by a cosine curve. again, the deposition of (adding) a new cell at a site on the surface is assumed to be dependentonly on the number of its neighbouring cells. the surface cells, which have more missing neighbouring cells, al-barwani and purnama 82 figure 5. monte carlo cellular model simulation of flame front propagation from an initial square burnt region, using the hexagonal neighbourhood with n = 2; after timesteps (a) 1000, (b) 8000, (c) 20000 and (d) 50000. simulations are (a) – (d) in the order left to right and top to bottom. are more likely to have deposition occurring around them. the hexagonal neighbourhood (3) is employed and the probability of adding a new cell to the surface is calculated using equation (4) with n = 2. figure 6. monte carlo cellular model simulation of land deposition on the surface represented initially by a cosine curve, using the hexagonal neighbourhood with n = 2; after time steps (a) 10, (b) 5000, (c) 28000 and (d) 50000. (a) (b) (c) (d) (b)(a) (c) (d) simple monte carlo cellular models for surface evolution 83 the simulated land deposition on a cosine curve is shown in figure 6. simulations show that the deposition of new cells is dependent on the geometry of the surface. after 28000 timesteps (figure 6c), the initial smooth surface represented by a cosine curve has completely disappeared. the more concave the surface the more material is being deposited. this in turn fills the shallow part until it reaches a stable elevation and the process reaches the steady state. after 50000 timesteps (figure 6d), the surface evolution reaches its stable position. the simple monte carlo cellular models described above simulate only the effects of isotropic surface evolution. the simplicity of the models means that it is easy to incorporate different physical effects. smith (1991a) pointed out that these effects could be incorporated simply by modifying the probability (equation (4)) of adding a new cell to the surface. next, a simple model is presented to include a directional growth dependence, where the surface is growing more rapidly in one direction. an anistropic crystal growth model: physically, a crystal is an ordered lattice of atoms in a solid. for all types of atom, the particular ordering and the extent of the ordering have important effects on the macroscopic behaviour of the crystal. a crystal growth mechanism is considered here by adding new diffusing cells to the surface. although the model of crystallization may seem to be simple, the actual surface simulated may be extremely complex. in anisotropic growth, a surface may grow more rapidly in one direction than in others. this growth mechanism can be prescribed simply by modifying the rule by weighting the added particles into specific orientation. figure 7. monte carlo cellular model simulation of anisotropic crystal growth from an initial circular seed region, using the hexagonal neighbourhood with n = 2; after timesteps (a) 1000, (b) 30000, (c) 50000 and (d) 80000. simulations are (a) – (d) in the order left to right and top to bottom. to demonstrate the anisotropic surface evolution, consider as an example a crystal growing from a spherical seed region. as before, the surface growth mechanism is prescribed so that new cells are more likely to stick at a site on the surface if the site has the fewest missing surrounding cells. a site is chosen randomly, and the number of its surrounding cells is calculated using the hexagonal neighbourhood (3). but instead of equation (4), the probability of adding a new cell to the surface is now calculated by nb p       γ= 6 , (5) where γ includes a directional growth dependence. for simplicity, take n = 2 and define al-barwani and purnama 84 yx yx + + = 22 γ , (6) so that it has a maximum 1 along the directions of coordinate axes and a minimum 2/1 where | x | = | y |. the simulated effects of crystal growth from a spherical seed region is shown in figure 7, where eventually growth occurs more rapidly along the coordinate axes. after 30000 timesteps (figure 7b) the initial spherical shape has disappeared. by 50000 timesteps (figure 7c) the crystal has grown to a new shape of a square rotated through 45° with respect to the coordinate axes. after 80000 timesteps, the final new crystal shape is shown in figure 7c. concluding remarks as it has been demonstrated that simple monte carlo model simulations give the most realistic surface evolution performance. cellular automata models, although simple to construct, by its very nature do not create the surface roughening of an edge which is caused by different rates of cell growth. monte carlo algorithms have also been found much faster than that of cellular automata (webb et al 1997). in addition to providing modeling tools, cellular models employ a scheme that avoids most of the problems associated with other surface tracking schemes, since it does not require the measurement of the derivatives and it can quickly detect topological changes. the models only used statistical approach. no particular dynamical laws are invoked to control the motion of the particles; rather the statistics and rules are presumed to contain all the necessary information. other physical effects, if required, can also be added to the models as have been demonstrated by smith (1991a,b) and toffoli and margolus (1987). references al-barwani, h.h. 1996. propagation of fronts with gradient and curvature dependent velocities. ph.d. thesis, department of mathematical sciences, loughborough university, u.k. manneville, p, boccara, n, vichniac, g.y. and bidaux, r. (editors). 1989. cellular automata and modeling of complex physical systems. springer-verlag, berlin. smith, r. 1991a. the application of cellular automata to the erosion of landforms. earth surface processes and landforms, 16: 273-281. smith, r. 1991b. modeling and simulation of particle-surface interactions, diamond and diamond-like films and coatings. plemon press, new york. toffoli, t. and margolus, n. 1987. cellular automata machines. mit press, massachusetts. webb, r.p., smith, r., al-barwani, h.h. and wilson, i.h. 1997. simple cellular models for growth. radiation effects and defects in solids, 141: 211-222. received 1 september 1999 accepted 24 february 2000 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 295-302 © 2002 sultan qaboos university periodic solutions of a system of delay differential equations for a small delay adu a.m. wasike and wandera ogana department of mathematics, university of nairobi, p.o.box 30197, nairobi kenya, email: aduwasike@yahoo.com. ت التفاضلية المؤجلة لتأجيل ثانويالحلول الدورية لمجموعة المعادال واسيكى و واندارا أوقانا. م.أدو أ . تبرهـن هذه الورقة وجود حل دوري تقاربي مستقر لمجموعة المعادالت التفاضلية المؤجلة لتأجيل ثانوي :خالصـة اضلية عادية مشوشة ، وبإستعمال نتائج التشويش للحصول على هذا البرهان تحول مجموعة المعادالت إلى مجموعة معادالت تف لها دورة τ<0تعتمد هذه الطريقة على حقيقة أن مجموعات المعادالت عند . يـتم إثـبات وجود حل دوري تقاربي مستقر وهذه المقارنة تمهد إلثبات . منتهـية ومستقرة وأيضاً يتم تقديم دراسة مقارنة لحلول المجموعات األصلية والمجموعات المشوشة .وجود حلول دورية للمعادالت األصلية عند استخدام نظرية النقطة الثابتة لشودر 0>τ abstract: we prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay τ > 0. to achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. this approach is contingent on the fact that the system of equations with τ = 0 has a stable limit cycle. we also provide a comparative study of the solutions of the original system and the perturbed system. this comparison lays the ground for proving the existence of periodic solutions of the original system by schauder's fixed point theorem. keywords: periodic solutions, delay differential equations, schauder’s fixed point theorem. 1. introduction a lthough substantial progress has been made toward the study of first order scalar delay differential equation (ddes), much less is known about the periodic solutions of systems of ddes. the need for studying a system of ddes, aside from its mathematical interest, arises from the wide variety of systems in biology and physical sciences that lead to mathematical models involving such systems. examples arise in the study of coupled oscillators with a time lag in the coupling (wasike, 1997), in the diffusion of mass across a membrane, (epstein, 1990) and in synaptic coupling (ermentrout,1990). we consider the system of equations ( ) ( ) ( ) ( )( )' ,x t d l x t x t f x tτ= − − +   (1) where here the accent ″ ′ ″ denotes differentiation with respect to time , the superscript t denotes transpose, ( ) ( ) ( ), t 1 2x t x t x t=  , , t 1 1 , , 0 1 1 l τ d   = >    295 adu a.m.wasike and wandera ogana ,τ d > 0 , )are real numbers, and ( 2f c r∈ with ( )( )1f x t and ( )( )2f x t are given by ( ),1 1 2 1f x x x x= − + ( ) ( ) ( )1 , , 12 2 2 21 2 2 1 2 1 2 1 2x x f x x x x x x− − = + − − . (2) when |x (t)| → 1, the following hypotheses are satisfied: ( ) ( ) ( ) ( ) ( ) , 0, for 0; , 0, for 0. there is >0 such that 2 1 1 2 2 1 2h1 x f x x x xf x x x h1 m f x m < ≠ > ≠ < 1.1 remarks on hypotheses (h1) is a planar negative feedback condition. it forces the solution of equation (1) to rotate about the origin in the anticlockwise sense. (h1) can be shown to hold for equation (1) by observing that ( ) ( ) ( ), and , as1 1 2 2 2 1 2 1f x x x f x x x x t→ − → →1 ). the taylor expansion of ( )(f x t about the origin yields ( ( )) (0) ( ) 2 :f x t d f x t≤ m≤ = where denotes the derivative with respect to d x . equation (1) arises from the study of a model equation of two oscillators coupled by a symmetric-diffusion-like path with a time lag. the equation is given below ( ) ( ) ( )( ) (( ) )' ,i j i ix t d l x t x t f x tτ= − − + (3) where ( ) ( ) ( ), , , , 1, 2, t k k kx t x t y t i j k i= j= ≠   and ƒ (x (t)) is given in (2). after an analysis of the linear part of equation (3), two two-dimensional invariant manifolds ( ) ( ) ( ){ }: 0,i 1 2x t x t x t t τ± = ∀ ≥− were observed with one whose dynamics on the manifold ( ) ( ) ( ){ }: 0,i 1 2x t x t x t t τ− = ∀ ≥− is described by equation (1), (see wasike, 1997). let [ ]( ) 0 , 0 , 2rc c rτ= − with ( ) [ ]{ }sup : , 0 0s s rϕ ϕ τ= ∈ − ≤ < ∞ . equation (1), subject to an initial condition , 0 rcϕ ∈ is known to have a unique solution ( ); ,dx t ϕ that satisfies it for . the solution is defined on the maximal interval of existence 0t ≥ ( ) ( )) ; ,t dτ ϕ ϕ+ +, ,t d− ≤ ∞ , and is continuously differentiable on ( )0, ,t d ϕ+   , 0, 0r c t . this solution also depends continuously on the initial condition in the following sense: for every ϕ ∈ ≥ > 0and ε , there exists > 0δ such that for all 0 rcϕ ∈ with ,ϕ ψ δ− ≤ ( ) ( ); ,x s d ; ,x s dϕ ψ ε− < , for all [ ],s tτ∈ − . see for example, hale and lunel (1993, chapter 2). more information on the basic theory on delay differential equations can be found in hale and lunel (1993), bellman and cooke (1963) or diekmann et. al. (1995) ). 296 periodic solutions of a system of delay differential equations 2. main results we show how a perturbed system of ordinary differential equations (ode) is found from equation (1) for small delays and then show that the perturbed system has an asymptotically stable periodic orbit. proposition 1. equation (1) with τ small can be written in the form ( ) ( )( ) ( )( )' ; , ,x t g x t d h x tτ= + (4) where ( )( ) ( ) ( )( ); , : , ,g x t d i d l f x tτ η τ= −   (5) with ( ), : , 1 2 d d d τ η τ τ = + (6) i is a identity matrix, and 2 2× ( )( ) ( ) ( )( ) ( ); ,h x t x t g x t d oτ τ′= − = . proof. for ( ) [ ]: 3 , , 3i t t ,τ τ= τ> the solution ( )x t , with ( ) (0 0x ϕ= ), is in ( )( )3c i τ . therefore ( ) ( ) ( ) ( ) ( )' '' ''' ..... 2 3! 2 3 x t x t x t x t x t τ τ τ τ− ≈ − + + + let, for notational convenience, equation (1) be written as ( ) ( ) ( ) ( )( ) ( )( ):x t d l x t x t f x t g x tτ τ′ = − − + = −   . (7) for τ small we have: ( ) ( )( ) ( )( ) ( ) ( ) '' ''' .... . 2 3! 2 x t x ti d l g x t f x t d l τ τ τ τ   + − = + − +    (8) simplifying equation (8) we obtain: ( )( ) (( ) ( )( ); , ) ,g x t g x t d h x tτ τ− = + where ( )( ) ( ) ( )'' ..... , 2 2d h x t i l l x t τ η   = − +    (9) and (: ,d )η η τ= . it is observed from equation (8) that ( ) ( ) ( )( ) ( ) )( )'' ' ''' ..... 2 2d x t i l df x t x t lx t τ η   = − + +    which when substituted in equation (9) gives ( )( ) ( ) ( )( ) ( )'1 2 ... 2 2 2d h x t l df x t x t τ η= − + . 297 adu a.m.wasike and wandera ogana clearly ( )( ) ( )h x t o τ= , where . , here is the usual euclidean norm. next we show that the solutions of equations (1) and (4) remain `close' for all t . indeed this also provides another way of proving existence of periodic solutions of equation (1) by schauder's fixed point theorem. 0≥ proposition 2. the solution ( )x t of equation (4) is bounded. proof. in polar coordinates, defined by ( ) ( ) ( ) ( ) ( ) ( )cos , sin ,1 2x t r t t x t r t tθ θ= = with ( ) ( ) : ox t r t= = r ,equation (1) becomes, ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ){ } ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ){ } ' ' 1 1 sin 2 cos sin , 1 cos 2 cos sin . 2r t r r dr dr t t t t t dr t t d t t t t r t θ τ θ τ θ θ τ θ τ θ θ θ τ θ θ τ = − − + + − − − + − + − = − + − + + − −θ (10) for smallτ , ( ) ( ) ( ) ( ) ( ) ( )' '. . ., . . .,t t t h o t r t r t t h o tθ τ θ τ θ τ τ τ− = − + − = − + where h.o.t. means higher order terms. using this in equation (10) we get ( ) ( ) ( )( ){ } ( )( ) ' ' ' ' ' ' 1 sin 2 cos sin 2 1 cos 2 1 cos 2 sin . 2r r r d r r r r r d r θ τ τθ θ τθ τ θ θ θ τθ τ θ = − − + − − + −     = − − − − −       ' ' , (11) by maclaurins expansion, ' ' ' ' 'cos 1 . . , sin . . . 2! 3! 2 2 3 3 h o t h o t τ θ τ θ τ θ τ θ τ θ= − + = − + (12) ignoring terms of order higher than o ( )τ and using (12) in (11) we obtain ( )( ) ( ) ( ' ' 1 , , 1 2 2 r rr )i b d r rτ θ θ    − + = +         (13) where ( ) ( ) ( ) ( 1 sin 2 cos 2 , cos 2 / 1 sin 2 d d r b d d r d τ θ τ θ τ )τ θ τ +  =   − θ ) , and the matrix ( ,r r θ is such that ( ) ( ), 2r r oθ τ= . for τ small ( ),b d τ < 1 , where . denotes a norm of a matrix, ( )( ) ( ), ,-12 2i b d i b dτ τ+ ≈ − . thus ignoring terms of ( )2o τ in (13), we obtain ( ) ( )( )' 1 1 1 sin 2 cos 22r r r d d r ,τ θ τ= − − + − θ (14) 298 periodic solutions of a system of delay differential equations ( ) ( )' 1 1 sin 2 1 cos 22d d r .θ τ θ τ= − − − − θ (15) solving equation (14), and noting that for fixed ( )txr =:,θ is given by ( ) cos 2 1 1 1 sin 2 1 2d r d τ θ τ θ   = −  − +  . (16) by binomial expansion, ( ) 1 cos 2 1 ... 2 1 1 sin 2 d r d τ θ τ θ = − + − + clearly ( )1r o τ≈ ± used in equation (14), shows that ( )x t is bounded. we now give other comparisons of the results between the solution ( ) (: ; ,x t x t d )τ= of the perturbed system equation (4) subject to initial data ( ) ( ): 0 , 0 t1x xτ  =   and the solution ( )ϕ,, dtx to equation (1) subject to the initial condition . let ( )0ϕ ϕ=  ( )0 , t 1  0 ( ) ( ) ( ): 01 11x xτ ϕ= = 0 and t the first time of return of ( )x t such that ( ) 01x t > and ( ) 02x t = . we note from the proof of proposition 2 that ( ) 0x t r≤ and ( )x t r≤ . define the set ( )( ) ( ) ( ) ( ){ }: ,r 0x c s x o sτ ϕ ϕ τ τ τ ∆ β = ∈ − ≤ − ≤ ≤ 0 with . denoting the euclidean norm. the set ( )( )x τβ is a closed bounded set. by taking initial values in this set, we wish to show that ( )x t and ( )x t remain o ( )τ `close'; that is, ( ) ( ) ( )x t x t o τ− = for all t . this is accomplished by using lemmas 1 and 2 below. 0≥ lemma 1 . for any ( )( ) ( ) ( ) ( ),x x t x t oϕ τ τ∈β − = for all t . 0≥ proof. equation (1) can be written as ( )( ) ( )( )' ; , ; ,x g x t d h x t dτ τ= + . let ( ) ( )( )' ; ,g x t dx t τ= . [ ( ) ( ) ] ( )( ) ( )( ) ( )( )d x t x t g x t g x t h x t d t − = − + where ( )( ) (( ) ( )( ) ( )( ): ; , ) , : ; ,g x t g x t d g x t g x t dϕ τ= = and ( )( ) (( ): ;h x t h x t d , )τ= . by using the inner product in 2r , we get ( ) ( ) ( ) ( ) ( ) ( ){ }''1 ,2 2d x t x t x t x t x t x t d t − ≤ − − ( ) ( ) ( ) ( ) ( ( )( ) ( ) )( )( ) ( ) ( )( ) ,x t x t d x t x t g x t g x t h x t x t x t+− − ≤ + − where denotes the derivative from the right. this simplifies to d+ 299 adu a.m.wasike and wandera ogana ( ) ( ) ( ) ( ) ( )( ) ( )( ) ( )( )( ) ( ) ( )x t x t d x t x t g x t g x t h x t x t x t+− − ≤ − + − . since ( )(on1g c x )τ∈ β , it is lipchtzian with a lipschitz constant 0 k< (say). from this we obtain ( ) ( ) ( ) ( ) (( ) ,d x t x t k x t x t h x t+ − ≤ − + since ( )( ) ( )h x t o τ= , we have ( ) ( ) ( ) ( ) ( )d x t x t k x t x t o τ+ − ≤ − + using the gronwall's inequality and bearing in mind that ( ) ( )0 0xϕ = , we get ( ) ( ) ( ) ( )( ) ( )exp ,t0x t x t o k t s ds oτ τ− ≤ − =∫ (17) hence the lemma is proved. lemma 2. let ( )n tε be an 0ε > neighborhood of t . then (i) there is [ ]* ,1 2t∈t t , with ( ) ( ) ( )0, 0, , ,1 2 1 22 2x t x t t t n tε< > ∈ such that , and ( ) )* *; , 02x t d (0, ; ,1x t dϕ ϕ= > (ii) ( )* .t t o τ− = proof (i). we show the existence of t . without loss of generality, choose * 0ε > and small enough such that ,1 2t tt t ε ε= − = + . then ( ) ( ) ( )'1 22 2 . .x t x t x tε= − h o t+ . recall that ( ) 02x t = . by the continuity of ( )( )1f x t and hypothesis ( )( ) ( ), 0 as1 2h1 f x t x t→ → 0 0 , and using as ( ),dη η τ= → 0τ → , we have ( ) ( ) ( )( ) ( )1 01 22 1x t f x t x tε η ε ε=− − → − = − ≠r similarly ( )22x t rε= . by the fact that, for any ( )( ) ( ) ( ) ( ),b x x t x t oϕ τ τ∈ − = uniformly in any bounded set in t , we have ( ) ( ) ( ),2 1 12x t x t o τ− = implying ( ) ( ) ( )2 1 12x t x t o τ= + . but ( )12x t rε=− . hence ( ) ( )2 1x t r oε τ=− + . similarly ( ) ( )2 2x t r oε τ=− + . ignoring ( )o τ and noting that ( )x t is at least c on 1 [ ],1 2t t , by the intermediate value theorem, then there is a ( ) [ ]* : , , 2d tτ= 1t∈t t such that ( )* 02x t = . proof (ii). we prove that ( )*t t o τ− = . in the neighborhood of t , we can use linear interpolation to determine t and t . for * ( ) [ ], ,1 22x t t t t∈ we have ( ) ( ) ( ) ( ) ; 2 1 2 2 12 2 1 2 2 12 2 t x t t x t t t t x t x t − + = = − 300 periodic solutions of a system of delay differential equations and for ( ) [ ], ,2 1 2x t t t t∈ ( ) ( ) ( ) ( ) ( ) ( ) ( )* 2 1 2 2 2 2 1 1 2 1 2 2 2 2 1 t x t t x t t t r t t o t x t x t r ε τ ε − + + − = = − therefore ( ) ( )* ; 2 1 2t t ot t r τ ε − − =− and by ( )*2 , /1 2t t t t o rε− =− − = τ . recall that ( )1 or τ= + . thus ( )*t t o τ− = . we now demonstrate that any solution of equation (1) with initial value in ( )(b x )τ returns to it after some t . this is shown by lemmas 3 and 4 below. * 0> first we show that at the time 0>t , ( )* 0t > of crossing the positive part of the ( )1x t (respectively, 1x ) axis, the solutions ( )x t , and ( )( )x t are still ( )o τ close. lemma 3. ( ) ( ) ( )*x t x t o τ− = proof. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) * * ' ' '* , ' 11 1 22 2 1 2 2 2 1 2 x t x t x t x t x t t t x t x t x t t t x t x t    −    − = + −     −      = − +  ( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( ) ( )( ' ' 1 , 1 . 1 1 2 2 1 2 x t f x t f x t x t f x t f x t η η η η = − − = − + − ) (18) by the continuity of ( )( )f x t and hypothesis (h1), we obtain ( ) ( ) ( ) ( )1 2 2 1 12 2' ' 2 2 21 2 1x t x t x t η η  + = − +    which tends to ( )1x t r= as 0τ → . hence, the expression in (18) above gives ( ) ( )* *x t x t t t− = − r and, by using ( )* ,t t o τ− = we have, ( ) ( ) ( )*x t x t o τ− = . lemma 4. for any t t and * ,tτ ∈ −  * ( )( ) ( ) ( ) ( )*,x t x t x t oϕ τ∈ β − = proof. by the mean value theorem, and lemma 1, ( ) ( ) ( ) ( ( ) ( )) ( ) ( )( ){ } ( ) ( ) * * * * * * * sup sup , , sup 1 2 , d d x t x t x t x t o dt dtt t t t t t i l f x t m o t t t τ τ τ τ τ η τ η τ τ                 τ   − ≤ = +   ∈ − ∈ − = − ≤ + = ∈ − proposition 3. for any ( ) ) ( ) ( )* * *, (,b x x x t b xt t tϕ τ ττ      ∈ = ∈ −  . 301 adu a.m.wasike and wandera ogana proof. the proof of this proposition shows that indeed ( )x t returns to ( )(x )τβ after some time t t . we first show that * ,tτ∈ − *  ( ) ( ) ( )o*x t x τ τ≤− . we observe that ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )* * .x x t x x t x t x t x t x tτ τ− ≤ − + − + −* * let us consider each term in turn. ( ) ( ) ( ) ( ) ( ) ( )1 0 0 0 0 x x t1x x t r o r o τ τ τ τ        − = − ≤ + − =          by lemma 3, ( ) ( ) ( )* ,x t x t o τ− = and by lemma 1, ( ) ( ) ( )* *x t x t o τ− = . thus ( ) ( ) ( )*x x t oτ τ− = . let ( ) ( ) ( ) ( ) ( ) ( )* * * *, ,t t t x t x x x t x t xτ τ τ ∈ − − ≤ − + −  ( ) τ . by the estimate above and lemma 4 we see that ( ) ( ) ( )2 ,x t x o oτ τ τ− ≤ = implying ( )( )* .tx b x τ∈ the proof of proposition 4, shows that indeed ( )x t returns to ( )( )x τβ at *tx . theorem 5. equation (1) with small τ has at least one periodic solution. proof. this follows from proposition 4 and lemmas 1-4 above. indeed we can define the poincar′e operator ( )( ) *: r ox t x ctρ ϕ ∈β → ∈ . by proposition 4, ρ is defined from a closed bounded convex set ( )( )x tβ into itself. the continuity of ρ is assured by the continuous dependence of solutions on the initial data (as shown in lemma 1) and the transversality of ( )x t with the 1x -axis (as essentially proved in lemma 2 (i)). since ρ maps b , a compact set, into itself, and is continuous, it is completely continuous. by schauder's fixed-point theorem we conclude that ρ has at least one fixed point, which corresponds to a periodic solution of equation (4). references bellman, r., and cooke,k., 1963. differential-difference equations. academic press, new york. diekmann,o.g., s.a., lunel s.m.v., walter, h.-o., 1995. delay equations springerverlag. new-york, berlin, heidelberg. hale. j.k., and lunel, s.m.v. 1993. introduction to functional differential equations. springer-verlag. new-york, berlin, heidelberg epstein, i.r. 1990. differential delay equations in chemical kinematics: some simple linear model systems. j. chem. phys. 92: 1702-1713. ermentrout, g.b., and koppell, n. 1990. oscillator death in a system of coupled nueral oscillator. siam j. appl. maths. 50: 125-146. hale, j.k. 1980. ordinary differential equations (2nd edition) krieger, malabar. wasike, a.a. m. 1997. an analytical and numerical study of a system of coupled oscillators with a time lag in the coupling. university of nairobi. ph.d. thesis university of nairobi. received 23 december 2001 accepted 17 october 2002 302 periodic solutions of a system of delay differential equations for a small delay adu a.m. wasike and wandera ogana department of mathematics, university of nairobi, p.o.box 30197, nairobi kenya, email: aduwasike@yahoo.com. electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 251-258 © 2002 sultan qaboos university effect of the fineness of artificial pozzolana (sarooj) on the properties of lime-pozzolana mixes abdel wahid hago, amer ali al-rawas and awadh al-sidairi department of civil engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email: ahago@squ.edu.om. على خواص خلطات البوزوالن مع الجير ) الصاروج(تأثير درجة نعومة البوزوالن الصناعي عبدالواحد هجو، عامر علي الرواس و عوض السديري يتأثر نمو قوة تحمل خلطات الصاروج مع الجير بدرجة نعومة الصاروج، وفى هذا البحث تمت دراسة تأثير درجة : خالصة ويعرف الصاروج علميا بالبوزوالن الصناعي، وقد تم . زيادة القوة االنضغاطية لخلطات الصاروج نعومة الصاروج على معدل ويستخدم الصاروج حاليا فى مشروع ترميم االثار . إنتاجه بحرق عينات من الطين استجلبت من مناطق مختلفة فى سلطنة عمان ا البحث تم طحن الصاروج الى درجات متفاوتة ثم خلط مع وفي هذ . التاريخية والذي تقوم به وزارة الثقافة والتراث القومي وقد أظهرت . يوما بعد الخلط ٩٠، و ٢٨، ١٤، ٧ واستخدمت الخلطة فى عمل مكعبات تم اختبارها بعد ٣:١الجير المطفأ بنسبة جيدة من الصاروج، النتائج وجود عالقة مباشرة بين درجة نعومة الصاروج وقوة تحمل الخلطات الصاروجية بالنسبة لألنواع ال كما أثبتت النتائج أن درجة نعومة الصاروج هى العامل األساسي فى . فى حين ال توجد عالقة ثابتة بالنسبة للصاروج الضعيف .زيادة نمو قوة تحمل الخلطات الصاروجية على المدى الطويل abstract: strength development of lime-pozzolana mortars is affected by the fineness of the pozzolan. this paper examines the effect of the fineness of artificial pozzolana on the strength development of lime-pozzolana mixtures. an artificial pozzolana produced by calcining clays from oman was used in this study. the artificial pozzolana is locally known as “sarooj”, and is currently being used in a big project for the restoration of historical monuments undertaken by the omani ministry of national heritage and culture. the artificial pozzolana was ground to various degrees of fineness, blended with hydrated lime with a ratio of 3:1, and the resulting mortar was used to make hardened mortar cubes. strength of mortar cubes was measured at ages of 7, 14, 28 and 90 days of casting. the experimental results show that good artificial pozzolanas show a linear correlation between the blaine fineness of the artificial pozzolana and the compressive strength, but such relationship does not exists for weak type pozzolanas. the fineness of the artificial pozzolana has its most significant effect on delayed strength gain, with more pronounced effect for good type pozzolan. key words: pozzolana, sarooj, cement, strength tests, chemical tests. 1. introduction s arooj is an artificial pozzolan produced by burning clays and is used as a cementing material by adding lime and water. in oman, sarooj has been used for thousands of years in buildings, forts and aflaj (plural of falaj which is defined as a system of distributing water to a village by gravity through built channels). worldwide, materials like sarooj are known for their good low permeability and long durability. for this reason, sarooj was extensively used in hydraulic structures. even in this century and with the ready availability of portland cements, special plants were erected to produce materials like sarooj for major dams in the world, like the aswan dam in egypt and the bhakra dam in india. 251 a.w. hago, a.a. al-rawas and a. al-sidairi when a mixture of portland cement and a pozzolana reacts, the pozzolanic reaction progresses like an acid-base reaction of lime and alkalies with the oxides (sio2, + a12o3 + fe2o3) of the pozzolana. two things happen: first, there is a gradual decrease in the amount of free calcium hydroxide with time, and second, there is an increasing formation of calcium silicates hydrates (csh) and calcium aluminosilicates that are similar to the products of hydration of portland cement. according to lea (1971), the partial replacement of portland cement by pozzolana of high sio2/r2o3 ratio has been found to increase the resistance of concrete to sulfate and sea water attack (r2o3 is approximately the summation of the a12o3 and fe2o3 contents). this is in part attributable to the removal of free calcium hydroxide formed in the hydration of portland cements by combination with the pozzolana. the end result will be that the paste will contain less calcium hydroxide and more csh and other products of low porosity. research on the hydration of blended cements made with natural pozzolanas of volcanic origin (santorin earth pozzolana) has confirmed that rather than the chemical manifestation, the physical manifestation of the pozzolanic reaction involving pore refinement of the cement paste is probably more important for the enhancement of chemical durability and mechanical strength. the shape, fineness, particle size distribution, density, and composition of pozzolana particles influence the properties of freshly mixed unhardened mortar, and the strength development of the hardened mortar. most pozzolanas tend to increase the water requirement in the normal consistency test, as a result of their micro-porous character and high surface area, when employed as an ingredient of portland-pozzolana cements or as admixtures to portland-cement (aci-91-m42). increasing the fineness of a natural pozzolan or cements can improve strength development of mortar mixes, especially if the pozzolan contains substantial proportions of mineral oxides. in early strength investigation of the reactivity of siliceous rocks, alexander (1960) found that siliceous materials such as quartz and basic or devitrified volcanic rocks, which were not regarded as likely sources of active pozzolana, were highly reactive when ground to ultra-fine powders. alexander attributed the phenomenon to the presence of a distributed layer of highly reactive material which is formed on the surface of siliceous mineral particles as a result of prolonged grinding. greenberg (1961) found that for different siliceous materials with different surface areas, the reaction rate with calcium hydroxide solution did not show a significant correlation with the surface areas of the siliceous materials. costa and massazza (1974) studied six commercial italian pozzolanas with different surface areas. they observed that the correlation between reactivity (as measured by combined lime) and surface area was valid only before 7 days, and that the activity of the pozzolanas depended on the content of r2o3. in subsequent research, rossi and forchielli (1976) did not find any correlation between surface area and reactivity with lime for the same materials examined by costa and massazza. an extensive examination of the strength of 22 pozzolanas indicated that there was no general correlation between the compressive strength at 28 days or 60 days and the surface area determined either by blaine or bet method (chatterjee 1967). day and shi (1994), by studying the effect of grinding on the strength development of natural pozzolana from central america, concluded that a good linear relationship existed, and showed that an increase of 1.5 mpa can be expected for every 100 m2/kg increase in fineness. their study included blaine fineness in the range of 250 to 550 m2/kg. most of the studies cited above used different natural pozzolanas with different surface areas. for such pozzolanas, fineness is not the only factor affecting the reactivity of the pozzolana. the chemical composition, mineral composition, glass content of the pozzolana and the cooling rate of the fused magma are also very important to reactivity. thus, it is not surprising that a lack of correlation exists when one tries to establish a universal relationship between reactivity and fineness. on the other hand, it seems that no attempts have been made to study the effect of fineness on the strength of artificial pozzolanas. for an artificial pozzolana, fineness is not the only factor that controls the strength. in additions to those controlling the strength of natural pozzolana, the strength of an artificial pozzolana is also influenced by the temperature and duration of calcination and the degree of fineness. the research described in this paper is an examination of 252 effect of the fineness of artificial pozzolana (sarooj) the correlation between the blaine surface area of an artificial pozzolan from oman (sarooj) and the strength development of artificial pozzolana-lime mixtures. 2. experimental program two types of artificial pozzolans (sarooj) were used in this study. one type of artificial pozzolan was provided by the omani ministry of national heritage and culture (designated in this paper wm) which was prepared in its factory in nakhal town using a traditional method of production. details of its method of production can be found elsewhere (hago et al 1999, 1998, 1997, 1995). the other type of pozzolana was prepared in the laboratory by burning clays obtained from al-khod town in oman (designated in this paper kh). the burning parameters (temperature and duration) were determined by using differential thermal analysis (dta). chemical tests were performed on the clays to determine their suitability for pozzolana production following standard procedures. the samples were burnt at a temperature of 780 oc and duration of 73 minutes. the pozzolana was ground in a small ball mill to six blaine fineness between 2360 and 4900 cm2/g and then blended with hydrated lime in the proportion of pozzolana:lime=3:1 by mass, and a water/pozzolana ratio of 0.5 by mass was used throughout. these proportions were determined from extensive optimization studies carried out during the first phase of the project (hago et al 95). a commercial hydrated lime from oman was used. the blaine fineness of the artificial pozzolana was measured by using air permeability apparatus following the standard procedure in the omanian standard os26 (1981). the apparatus was carefully calibrated for the type of pozzolana used. preparation of the specimens was made at a standard room temperature of 20 oc. the mixes were cast into 70 mm mortar cubes (according to os26-1981), covered with plastic covers for 3 days, then moved into a humidity controlled room at a temperature of 20 oc. after 14 days, the cubes were transferred to a curing tank and kept under water until the date of testing. the curing method was determined in the first phase of the project (hago et al 95), considering the humid conditions of the gulf, and the high water retentivity of the hydrated lime. compressive strength was determined at ages of 7, 14, 28 and 90 days. at each age of testing, three specimens were tested for compressive strength, and the reported values in figures 1-5 represent the average of three cubes at each age. 3. results and discussion designation of samples of two types of pozzolana wm and kh are given in table 1. the variation of compressive strength for the six lime-pozzolana mortars from wadi al-mawail clays (wm) are given in figures 1 and 3 while the corresponding ones for the six mixes from al-khod (kh) are shown in figures 2 and 4, for various degrees of fineness. in general, the compressive strength for all mixes in the kh group are higher than those in the wm group for all ages and for all degrees of fineness, as can be seen from figures 1 and 2. this would be expected as was indicated by the chemical analysis of the two soils given in tables 2 and 3, since the sum sumo2 for the kh clays is higher than that for wm clays. figure 1 also shows that a higher gain in strength for this type of pozzolana is not actually associated with a high degree of fineness, contrary to what one expects from a pozzolana. however, figure 2 for the kh pozzolana indicates a reasonable reaction with the increase in fineness at all ages, although with differing rates. the variation of the compressive strength of the mortars with blaine fineness is shown in figures 3 and 4 for the two types of pozzolana tested in this research, wm and kh. as can be seen from the figures, the fineness of the pozzolan does influence the development of compressive strength and the ultimate strength of the pozzolana. however, an increase in the fineness of the artificial pozzolana has the general effect of increasing the strength of the mix in a nonlinear manner for ages from 7 to 90 days. the influence is quite different for the two types of pozzolana 253 a.w. hago, a.a. al-rawas and a. al-sidairi figure1: variation of strength with age for different fineness (wm sarooj). figure 2: variation of strength with age for different fineness (kh sarooj). 254 effect of the fineness of artificial pozzolana (sarooj) figure 3: variation of strength with fineness (wm sarooj). figure 4: variation of strength with fineness (kh sarooj). 255 a.w. hago, a.a. al-rawas and a. al-sidairi figure 5: variation of rate of strength development with fineness. considered. for the wm pozzolana, no regular pattern can be identified, but an optimum fineness exists for which the strength is maximum. this comes around 375 m2/kg at all ages. for the kh pozzolana, a regular pattern can be identified. a greater influence is felt for fineness in the range of 230-275 m2/kg, followed by a gradual increase for larger degrees of fineness. the influence of fineness is better illustrated by plotting the variation of the rate of development of compressive strength (obtained by least squares fit of the data in figures 1 and 2) versus the blaine fineness, as shown in figure 5. from this figure, it can be seen that little effect is produced on the low type pozzolana wm, while for the other type of pozzolana (kh), we can distinguish two ranges of strength development. up to a fineness of 275 m2/kg, the slope of the curve is very high. within this range, there is a rapid increase in the strength, followed by a gradual slowdown. in the latter range (i.e. beyond a fineness of 275 m2/kg), the increase in the rate of strength development is not very much. at the end of the first phase, the rate of strength development increases by seven folds that at a fineness of 230 m2/kg, compared to only 2.3 folds by the end of the second phase. by considering the high cost of grinding the pozzolana to this degree and the associated high water demand that adversely affects the strength, it does not appear appropriate to carry on grinding to fineness greater than 350 m2/kg for sarooj-lime mixtures. table 1: designation of the samples tested and their degree of fineness. wm sarooj kh sarooj sample fineness (cm2/g) sample fineness (cm2/g) wm1 2360 kh1 2360 wm2 2370 kh2 2370 wm3 2430 kh3 2450 wm4 2740 kh4 2740 wm5 3630 kh5 4440 wm6 4450 kh6 4920 256 effect of the fineness of artificial pozzolana (sarooj) table 2: chemical composition of artificial pozzolana from al-khod clays. sio2 al2o3 fe2o3 cao mgo k2o na2o sumo2* 46.9 8.3 5.6 12.7 2.5 0.9 1.2 60.8 *sumo2 = sio2 + al2o3 + fe2o3 the effect of fineness on the workability and setting time of the mortars was also observed here. in general, great deterioration in workability was observed with the increase in the surface area of the pozzolana, since a fixed quantity of water was used in the preparation of the mixes. no attempts were made to correct the workability, but it was realized that, an increase in water demand results in loss of strength. for the weaker pozzolana samples wm, the effect on workability of the fineness is less than that on the workability of kh pozzolana. for both types of pozzolana, a reduction in the setting time of the mortar was obtained with the increase in fineness. table 3: chemical composition of artificial pozzolana from wadi al-mawail clays. sio2 al2o3 fe2o3 cao mgo k2o na2o sumo2* 33.5 7.12 2.46 22.74 8.43 . . 43.08 *sumo2 = sio2 + al2o3 + fe2o3 4. conclusions the main conclusions derived from this study that examined two artificial pozzolanas can be summarized as follows: 1. the properties of artificial pozzolana/lime mixes are greatly affected by the degree of fineness of the pozzolana obtained by grinding the pozzolana. 2. for low grade pozzolana, the ultimate strength of the mortar will not be affected significantly by increasing the fineness, whereas for other types of pozzolana, the strength is greatly affected. 3. the rate of strength development increases with increase in fineness for good pozzolanas at all ages. a sharp increase occurs for surface areas up to 275 m2/kg. increasing the fineness beyond this limit, produces only a mild increase in the rate of strength development, resulting in insignificant increase in strength. 4. the setting time and the workability of the mortar reduce with the increase in fineness of the pozzolana. the effect is less for low reactivity pozzolanas. however, the consistency is not significantly affected by increasing the fineness for both types of pozzolana. in general terms, whether for low reactivity pozzolan or high reactivity pozzolan, a surface area of about 350 m2/kg seems to be an optimum value in order to get the best strengths for the mixes studied here. 5. acknowledgement this research is partly supported by sultan qaboos university, for which the authors are indebted. the cooperation of the ministry of national heritage and culture is gratefully acknowledged. references aci committee 232, 1994. use of natural pozzolans in concrete: american concrete institute materials journal, july-august: 410-426. 257 a.w. hago, a.a. al-rawas and a. al-sidairi al-rawas, a.a., hago, a.w., corcoran, t.c. and al-ghafri, k.m., 1998, properties of omani artificial pozzolana (sarooj): applied clay science journal, 13(4): 275-292. alexander, k.m., 1960. reactivity of ultrafine powders produced from siliceous rocks: journal of american concrete institute, 57: 557-569. chatterjee, m.k. and lahiri, d., 1967. pozzolanic activity in relation to specific surface of some artificial pozzolans: transactions of indian ceramic society, 26:65-74. costa, u. and massazza, f., 1974. factors affecting the reaction with lime of some natural italian pozzolans: cemento, 74(4):131-139. day, r.l. and shi, c., 1994. influence of the fineness of pozzolan on the strength of lime naturalpozzolan cement pastes: cement and concrete research journal, 24(8):1485-1491. greenberg, s.a., 1961. reaction between silica and calcium hydroxide solutions, kinetics in the temperature range 30-85 oc. journal of physical chemistry, 65:12-16. hago, a.w., al-rawas, a.a., and al-harthy, a.s. 1995. the omani sarooj, sultan qaboos university, first report on the omani sarooj (classified). hago, a.w., and amer al-rawas, 1997. properties of the omani sarooj: engineering journal of the university of qatar, 10: 81-91. hago, a.w. and amer al-rawas, 1999. an investigation into the traditional method of production of omani sarooj: sultan qaboos university journal of science and technology, 4:35-43. lea, f.m., 1971. chemistry of cement and concrete, chemical publishing, inc., pp414-453. omanian standard os26, 1981. methods of testing cement-physical tests-determination of fineness: ministry of commerce and industry, directorate general for specifications and measurements. rossi, g. and forchielli, l.,1976. porous structure and reactivity with lime of some natural italian pozzolans: cemento, 76(4): 215-221. received 13 november 2001 accepted 24 september 2002 258 effect of the fineness of artificial pozzolana (sarooj) on the properties of lime-pozzolana mixes abdel wahid hago, amer ali al-rawas and awadh al-sidairi department of civil engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email: ahago@squ.edu.om. table 1: designation of the samples tested and their degree of fineness. 4. conclusions acknowledgement references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 177-185 © 2002 sultan qaboos university multi-agents architecture for scheduling and control of robotic manufacturing systems brahim bouzouia centre de development des technologies avancees. 128 mohamed gacem, el-madania, algiers (algeria). email: bbouzouia@cdta.dz. تخطيط والتحكم اآللي في أنظمة االنتاج اللينةهيكلة متعددة األوجه لل ابراهيم بوزوية تعتمد هيكلة المنهجية المقترحة على . تتضمن هذه الورقة منهجية متعددة األوجه للتحكم اآللي في أنظمة االنتاج اللينة :ةخالص : عن هذه المنهجية على الصالحيات اآلتية يحتوي النظام المتوخى . تقنية الذكاء االصطناعي الموزع واألنظمة المتعددة األعضاء الهدف من هذه الخطة هو التوزيع الحيوي . نقترح كذلك خطة تفاوض جديدة ألنظمة اإلنتاج .التخطيط،التوزيع، المتابعة والصيانة .دية العمل المبرمج تأرضغلموارد نظام اإلنتاج ل aِbstract: this paper presents an innovative multi-agent approach related to an advanced real time control of flexible manufacturing systems. the proposed architecture is based on the paradigm of distributed intelligence and multi-agent systems. the developed multi-agent prototype system integrates the following functions: scheduling, dispatching, monitoring and error handling. a new negotiation protocol for manufacturing systems is presented in this paper. the purpose of this protocol is to assign dynamic operations to the resources of the manufacturing system in order to accomplish the proposed tasks. this protocol is able to deal with exceptions. keywords: multi-agent systems, flexible manufacturing systems, distributed artificial intelligence, resource allocation, real time scheduling, and renegotiation phase. 1. introduction global competitiveness has been imposing important changes to all components of manufacturing systems, including the real time scheduling. from an emphasis on the scheduling optimality in the past, the focus has now moved to scheduling flexibility (trenteseaux, 1996). the function of a real time manufacturing cell control system can vary depending on the size of a cell, its type and the degree of decision-making capabilities. the major functions of a cell control system include the need to schedule and monitor cell resources, and the ability to react to abnormal conditions or exceptions (ouelhadj et al. 1999 ; ouelhadj et al. 1998). the major approaches of scheduling are represented by the traditional operational research techniques as combinatorial procedures, heuristic approaches and constraint analysis (balasubramania and norrie, 1997; ferber and ghallab, 1999). nevertheless, these approaches are np-complete and has shown many limitations. such systems soon became too heavy to be implemented as a centralized control program in only one computer. fortunately, distributed computing has already given some answers to the problem of how to implement efficiently communities of interactive systems. this emerging area is distributed artificial intelligence (dai) (ferber and ghallab, 1999; ramos, 1994; ferber, 1995). the framework of dai, particularly multi-agent system (mas), seams more suitable for the dynamic control of manufacturing systems. the multi-agent system paradigm represents one of the most promising approaches to 177 brahim bouzouia build complex and flexible advanced intelligent systems. the application of mas approach in dynamic scheduling and control is based on the idea that the scheduling and control agility can be extremely improved once these are based on the following key points: (i) distributed and autonomous systems instead of centralized and non-autonomous solutions; (ii) negotiation-based decision making instead of the totally pre-planned processes; (iii) uses of different problem-solvers in the same environment instead of only one fixed problem solver; and (iv) concurrent execution instead of sequential processing. several works on flexible manufacturing system control followed the paradigm of dai. here we will refer only to two of these systems: icoss and massyve. icoss (intelligent cell objects/intelligent supporting shell, lee and sen, 1994) architecture consists of two layers: the inner layer, called ico, contains cell control knowledge that perform generic cell control functions such as scheduling, dispatching, monitoring; the outer layer called iss contains cell databases that represent the specific cell environment. the two layer approach allows more efficiency in developing and implementing intelligent cell control by considering generic cell control knowledge and cell-specified databases separately. massyve (multi-agent agile manufacturing scheduling systems for virtual enterprises, rabelo, 1997) aims to investigate the use of multi-agent systems in agile scheduling, towards the operation in a virtual enterprise environment. these activities use the holos framework as base line for advanced scheduling. the information integration approach supporting a multi-agent system in massyve is based on the peer information management framework. this paper presents a new architecture and negotiation protocol (jtransactions machines) for an intelligent cell control system. we consider that requests involve due dates (deadlines) for the tasks to be carried out and some applications of this framework to distributed robotic systems. section 2 presents a new architecture for real time scheduling of manufacturing systems. section 3 and 4 illustrate how the negotiation/renegotiation protocol is established. finally, conclusions are presented in section 5. 2. a new architecture for dynamic scheduling and control of fms an automated manufacturing cell typically consists of numerical control machines, industrial robots, storage devices, automatic inspection devices, tools and fixtures and control computers. the machine tools in the cell are physically interconnected by automated material handling devices such as conveyors, agvs and robots. communication networks provide the information links within the cell. figure1 illustrates the architecture proposed in this paper. this architecture includes, essentially, two parts : one concerning resources and another concerning agents. the number of resources does not vary, except when resources are introduced or removed from the manufacturing system. the system architecture contains the following agents: initiator agent : interfaces with the user receiving orders of new tasks for the manufacturing system. this agent is responsible for launching task announcement message whenever a new task is ordered (starts the execution of scheduling process). it also maintains a global view on the activity of the resources (mirrors agents). mirror agent (ma): an autonomous agent called mirror agent represents every resource in the cell. mai represents the current situation of resource i (its status and activity). the activity is a sequence of operation to be carried out which is represented as an agenda. this agent is responsible to perform the four control functions, which are : scheduling, dispatching, monitoring and error handling. for a better output, two production targets direct the control system: • reduction of the number of late tasks : the initiator agent will start by seeking the tasks in the following order: tasks for rescheduling, urgent tasks and finally shortest tasks. 178 multi-agents architecture for scheduling and control 179 • manufacturing products at the earliest: the mirror agent contract an operation that offers the completion date nearest to the current date. intranet mirror agentn scheduling dispatching monitoring error handling mirror agent1 scheduling dispatching monitoring error handling mirror agent2 scheduling dispatching monitoring error handling user task2 taskn task1 initiator agent figure 1. the proposed architecture. 3. negotiation protocol (jtransactions machines, jt.m) let us consider the example of figure 2, which consists to produce q parts xy. the part must be polish on front and drill on sides in a specific deadline dl. drill polish figure 2. list of operations for the xy part. feed_drilling_machine(xy) and opr 1 drill(xy) xy part. feed_turning_machine(xy) and opr 2 polish(xy) xy part and opr 3 transport(xy) the jt.m protocol is based on the contract-net protocol proposed in (reid, 1992). however, this protocol improves the basic behaviour of contract-net by the distribution of control functions over all the agents of the system. the figures 3 and 4 illustrate the negotiation protocol contracting resources for execution of task. when a new request for task execution appears, the brahim bouzouia user specifies the name of the task to be carried out as well as its deadline. in order to guarantee the deadline, the negotiation between the mirror agents is performed in backward chaining. the negotiation can be summarised in the following steps : note: all messages supported by the control system contains the fields: {sen, adr} where sen is a sender of the message and adr is the addressee. step one the initiator agent extracts the last operation of the task and using knowledge about the material configuration, constructs the list of possible resources for the operation (figure 3). the mirror agents corresponding to this operation receive a message with the following format : {cd, td, q, dl, loc} where : cd is customer identifier, td is a task descriptor, q is a number of operation sequences (e.g. 5 objects xy for the example of figure 2), dl is deadline for a task delivery(date and time) and loc is the list of operations including their constraints. this message will be referred as the ‘ task announcement message ‘ (t.a.m). step two the mirror agent, that had received announcement proceeds as follows: it extracts all the operations which are concerned with the task (operations are considered from last, last but one,...). after that, the mirror agent tests the possibility to carry out at least the last operation before a deadline dl. if so, it sends ‘request messages’ (r.m) on the (n–k), where k is a number of operations extracted by mirror agent, operations corresponding to the sub-hierarchy of operations (figure 3). the propagation of requests is reiterated until there is no operation to negotiate. the request message has the following format : {cd, td, qi, dl, loc, nlo, sd, tdrr, co} opr 3 opr 2 opr 2 opr 1 opr 1 opr 3 t.a.m opr 1,2, 3 r.m opr 1,2 mainitiator agent ma ma ma ma ma r.m opr 1 figure 3. task announcement and request propagation. 180 multi-agents architecture for scheduling and control 181 where : qi is a maximum amount of operations to guarantee the deadline by sender (mai) of request, nlo is the list of remaining operations, sd is the time where the qi operations could be started, tdrr is a temporal delay required by the sen to adr on propagation request phase and oc are the constraints related to the operative duration preceding current request. step three the mirror agents which receive a request for elementary operations are the first that broach intra-level negotiation (these agents control the same resources). they proceed as follows : each mai sends to its contact the information’s about its capacity to make qi operations among the amount q (qi <= q) and the due date dli for these qi operations (dli <= dl). candidates start the same algorithm in order to select the best agents. therefore, each one obtains an identical result and knows if it participates or not at the production of xy parts(figure 4). note : the criteria for selection favours agents that offer the earliest date of manufacturing and consider the possibility of splitting the operations by several resources (∑qi = q) . an agent can negotiate with null values if it did not receive invitations to tender concerning the task in progress. the ‘negotiation message’(n.m) has the following format : {cd, qmax(i), dlmax(i)} where : qmax(i) and dlmax(i) are respectively the maximum number of operations and their deadline which mirrori of the last level can assure. ma c opr 3 t.acc.m ma m.p.m opr 3 t.f.m c opr 1 initiator agent ma n.m opr 1 ma m.p.m opr 2 ma ma c opr 2 figure 4. negotiation, contract and proposition feedback. step four after that, the selected mirror agents establish their contracts (c) and send ‘mirror proposition messages’ (m.p.m) to mirrors of the up-hierarchy (figure 4). after the reception of the proposition message, the mirror agent concerned by the last operation of all the xy parts, detects the end of the scheduling process and sends a ‘task acceptance message’ (t.acc.m) to the initiator agent (figure 4). the mirror proposition message has the following format : {cd, td, qi, dd, dli, tdrb, co} where: tdrb is a temporal delay required by the sen to adr on feedback phase proposition. on the other hand, if mirror agents are not able to guarantee the deadline (∑qi < q) the negotiation is brahim bouzouia finished without contract and a ‘task failure message’(t.f.m) is sent to the initiator agent by mirror which offers the best criteria in intra-level negotiation phase (figure 4). 3.1 dispatching, monitoring and error handling first, the module extracts a contract (operation) from its agenda and sends its preconditions to the inference engine in order to check them. the precondition operation calls the sensory equipment of the resource in order to obtain data concerning the presence of the part and its identity, and compares them with the initial status of reference. in the favourable case (no exceptions are detected after the inference), the operation is launched and a starting order is sent to the resource controller. when the operation is finished, the resource controller sends a signal specifying the operation characteristic to the inference engine. after that, the postcondition operation is launched. this operation, contrary to the first, checks the status of the operation carried out and compares them with the final status of reference. if no exceptions appear, the dispatching module executes the next operation (figure 5). selection launching the selected operation succes status local agenda clock success phase of precondition failure and diagnosis ending signal phase of postcondition ressource controller dispatcher contracts list figure 5. operation execution mechanism. inference engine facts rules results of the diagnosis status figure 6. diagnosis module. 182 multi-agents architecture for scheduling and control 3.2 the inference engine after an abnormal event, the diagnosis module (figure 6) proceeds by: • formatting facts and loading them in the facts base. • launching the inference. • it sends, the results of the inference to the concerned process(communication, rescheduling, etc). 4. exceptions and renegotiation once a task has been accepted it will be accomplished in the specified deadline if no exceptions appear. the mirror agent sends starting-orders to their appropriate resources and wait for ending signal or abnormal events. however, exceptions (e.g. machine in failure or operation has a fault) may happen and the manufacturing system control has to deal with this kind of problem. the mirror agents support monitoring functions that recognises and analyses exceptional conditions or errors of their resource, and provides a possible corrective action to these problems (renegotiation, operator call,...). when a mirror agent executes an operation, its sensory equipment informs the monitoring about the status of operation, resource or parts. this information is sent to the error handling to diagnose the errors by the use of production rules based on predicate logic formalism. for completeness reasons, we suppose that the product xy is assigned to a productive way between mirror agents ma1, ma3 and ma6. the mirror agent related with the exception (figure 7, ma3) establishes a list for all contracts affected by the failure. after that, it will send ‘contract cancellations’ messages to agents appearing in the list, as well as, an ‘operation failure’ message to the initiator agent enclosing the amount of penalty for unaccomplished operations. finally, it destroys the list. the operation failure messages has the following format: {cd, td, ano}. where : ano is the amount of penalty for unaccomplished operations. the contract cancellations messages has the following format : {cd, td, lcaf}, where : lcaf is a list of contracts affected by the failure. ma r.a.m ma6 contract concellations c opr 3 c opr 1 machine in failure ma3 r.m ma initiator agent r.m ma contract concellations ma1 c opr 2 subsequent request message r.m figure 7. renegotiation protocol. 183 brahim bouzouia local network mirror agent conveyor initiator agent figure 8. material architecture. mirror agent cnc mirror agent robot gt6 5. implementation issues 5.1 software architecture the system is implemented in object oriented programming with java2 (sun micro system) that allows multi-threading and supports agents executing on different platforms (microsoft windows 9x, unix, os2). the agents of the system use tcp/ip protocol for communication and apply a recursive algorithm for sending/receiving message object. finally, the error handling is implemented with jess5.0a6 (java expert shell system of sandia national laboratories livermore, ca). 5.2 material architecture the flexible cell on which we have applied our control system is formed by a conveyor, a cnc turn machine and a handling gt6 robot. the resources are controlled by four pentium iii 600mhz microcomputers, among them one for the operator, interconnected by a local network having a star topology (figure 8). 6. conclusion this paper addresses a cell dynamic scheduling and control architecture that applies a multiagents approach to the problem of robotic manufacturing systems. it has also presented a new negotiation protocol (jt.m) suitable for the dynamic scheduling of manufacturing tasks. this negotiation protocol is able to deal with exceptions, since a renegotiation phase of the protocol can be activated. the main advantages of this architecture are : agent autonomy, decentralised decisionmaking capability, flexibility in more changing environment, sophisticated communication system, increased fault-tolerance, real time behaviour, the agents are totally co-operative and an inherent reconfiguration. control functions (scheduling, dispatching, monitoring, error handling) are totally distributed over the entire agents in the system. there are also other functions, such as: cell initialisation, communication, user interface and tools that support visualisation of agent performance. 184 multi-agents architecture for scheduling and control references balasubramania, s. and norrie, d.h. 1997. a multi-agent intelligent design system integrating manufacturing and shop floor control, university of calagray, canada, ab, t2n in4. ferber, j. 1995. les systèmes multi-agents: vers une intelligence collective. n° ref. 5548.4 1174, iia. ferber, j. and ghallab, m.1999. problématique des univers multi-agents intelligents. journées nationales prc-greco. intelligence artificielle, toulouse, france, page 295-320. lee, k.h. and sen, s. 1994. icoss : a two-layer. object based intelligent cell control architecture computer integrated manufacturing systems, 7(2) 100_112 department of industrial engineering, northern illinois university, dekalb, il 60115-2854, usa. ouelhadj, d., hanachi, c. and bouzouia, b.1998. multi-agent system for dynamic scheduling and control in manufacturing cells. icra'98, ieee international conference on robotics and automation, louvain (belgium). ouelhadi, d., hanachi, c., bouzouia, b., moualek, a. and farhi, a.1999. a multicontract net protocol for dynamic scheduling in flexible manufacturing systems. ieee, international conference on robotics & automation detroit, michigan, usa. rabelo, r.j. 1997. a framework for the development of manufacturing agile scheduling systems – a multi-agents approach, ph.d. thesis, new university of lisbon, portugal. ramos, c. 1994. architecture and negotiation protocol for the dynamic scheduling of manufacturing systems. proceedings of ieee international conference on robotics and automation, page 8-13. reid, g.s. 1992. the contract-net protocol: high level communication and control on a distributed problem solver. ieee transactions on systems. man & cybernetics, page 20-35. trenteseaux, d. 1996. conception d’un système de pilotage distribué, supervisé et multicritère pour les systèmes automatisés de production, thèse de doctorat à l’institut national polytechnique de grenoble, france. received 4 june 2001 accepted 26 february 2002 185 multi-agents architecture for scheduling and control of robotic manufacturing systems brahim bouzouia centre de development des technologies avancees. 128 mohamed gacem, el-madania, algiers (algeria). email: bbouzouia@cdta.dz. keywords: multi-agent systems, flexible manufacturing systems, distributed artificial intelligence, resource allocation, real time scheduling, and renegotiation phase. 3.1 dispatching, monitoring and error handling 3.2 the inference engine state-of-the-art review of collapsing soils science and technology, 6 (2001) 1-11 ©2001 sultan qaboos university an assessment of solid waste and landfilis in muscat area, oman alaa el-zawahry, abulbasher m. shahalam, ramzi taha and turki al-busaidi department of civil engineering, college of engineering, p.o. box 33, sultan qaboos university, al-khod 123, musca,sultanate of oman. تقييم الفضالت الصلبة والمرادم في منطقة مسقط بسلطنةعمان عالء الظواهري و أبو البشر شاه عالم ورمزي طه وتركي البوسعيدي تمت . حول كميات الفضالت الصلبة المنتجة فى منطقة مسقط الكبرى 1998 أجريت عام دراسة تُقّدُم الورقةُ نَتاِئج :خالصة فى الّصلبة مشاكل الفضالت ميقيوات لت سن 10خاللبالبياناِت المتوفرِة تم الحصول عليها ومقارنتها التى البيانات األخيرة دراسة وقد تبين من الدراسة أن معدل انتاج الفضالت الصلبة قد زاد . البياناتمرادم عاملة كنقاط لجمع خمسة وقد استخدمت . المنطقة يوم فى ال طن 750 -800 عدل انتاج الفضالت الصلبة بقى ثابتاً عند فان م على أية حال، . خالل العقد الماضي زيادة حادة الكلى حجُم النَقَص كما . يوم/ شخص / كيلوغراِم 1.5المعدل ْبلغُ وي. ة من عقد التسعينات خالل السَّنَوات الثّالث الماضي الّصناعات والمراكز التّجارية خالل مثل ةّصالمصادر الخا المنتجة بواسطة الكمياتزادت خالل السَّنَواِت بينما للفضالت البلدية . صناعيةوالسكنية التجارية و النشاطات ال سريعة جداً بزياَْدة ت بصورة طّور قد ت ِإلى أّن سلطنة ُعمان يعود هذا و. نفس الفترة في تها بنظيرتها رنمقاعند الكميةَ عاليةُ وتعتبر هذه . ةعضويد مواعبارة عن هو ة صلبمن الفضالت ال المائة ب 80وحوالى ويجب ان . بالمائة من هذه الفضالت الصلبة يحتوى على مواد يمكن استرجاعها 40الى ان البيانات ير تُشو. البلداِن الغربيةِ فرغْ في الفضالت الصلبة التى ت كمياتُض فَستُخ مثل هذه النّشاطاِت .ت االسترجاع نمو صناعا باالمر مهتمة الهيئات تشجع ال فاءة كأّن العاملة الذى اجرى على المرادم مسح وقد اوضح ال . مرة 1.6 يزيد عمر المرادم الموجودة بحوالى مما المرادم بصورة واضحة اذا ما اخذ فى االعتبار الخطوات التى تعنى بمشاكل انتاج الغاز وحركة عصارة حّسنيل يمكن ان تت شغالت . بحلول مستقبلية ممكنةوصياتتقديم تية للمشكلة وتَتضّمُن الورقة مناقشة تفصيلو. الفضالت abstract: the paper presents the results of a 1998 study of the solid waste generation within the greater muscat city area. the recent data were compared with the available data from the last 10 years to assess the solid waste problems within the area. five operating landfills were used as the data collection points. it appeared that through the last decade, the solid waste generation rate has increased sharply. however, the rate of waste production stabilized to 750 – 800 ton/day during the last three years of the 1990s. the rate amounts to 1.5 kg/person/day. overall municipal waste volume decreased through the years while the amounts generated from private sources such as industries and commercial centers increased during the same period. this is due to the fact that the sultanate of oman is developing very fast with increasing industrial, commercial and residential activities. about 80 % of the solid wastes is organic materials. this amount is high when compared to figures found in western countries. the data indicate that about 40 percent of the solid wastes are composed of recoverable materials. the concerned authorities should encourage the growth of industries to be involved in recycling business. such activities will reduce the solid waste discharge in landfills and increase nearly 1.6 folds the expected life of existing landfills. a survey of the operating landfills indicate that the operational efficiency may be substantially improved by incorporating measures that deal with problems of gas production and leachate movements. the paper includes a detailed discussion of the problem and makes recommendations for possible future actions. keywords: solidwaste; muscat; generation; composition; disposal; management; recyling and landfills. 1. introduction muscat is the capital and most important city in the sultanate of oman. modern residential, commercial and industrial developments have spread beyond its old capital limits into surrounding satellite townships connected with highways and modern utilities. most of the 1 el-zawahry, shahalam, ramzi taha and al-busaidi developments are new and are founded on the newly found wealth of oil. as of the 1970s, the situation started to change drastically within the city, as was the case in other parts of the sultanate. the country witnessed tremendous economic development including industrialization, urban sprawl and commercial activities. this unprecedented development known as the “blessed renaissance” started as his majesty sultan qaboos assumed political power in the country. the urban area expanded from 15 to 4000 square kilometers (covers about 1.3 % of the area of the sultanate) during the last 28 years. the population of 56000 in 1970 has grown seven folds by 1988 and to about 10 folds by 1998. to manage the city, the administration is decentralized and divided into five geo-administrative areas (sub-municipalities). they are greater mutrah, bousher, al-seeb, al-amerat and quriyat. based on estimated population figures of 1989 and 1993, the growth rates of the submunicipalities are shown in table 1 (scheu, 1993). table 1: population growth rate (1989-93) in submunicipalities in muscat. population sub-municipalities 1989 1993 growth rate % per yr density greater mutrah 156180 169000 2 high bousher 102180 134000 7 medium al-seeb 103480 136000 7 low al-amerat 23230 30000 7 low quriyat 19000 23000 4 low a literature review indicated that per capita solid waste generation stabilized by 1989/90 to an amount of 1-1.5 kg/person/day (mohammed, 1995), which was very much in-line with arab world figure of 1 kg/person/day (taufiq, 1992). figure 1 depicts the solid waste production in muscat area from1970 to 1994. 25 50 60 250 410 670 970 770 0 200 400 600 800 1000 to n/ da y 19 70 19 74 19 79 19 84 19 89 19 94 19 96 19 98 year solid waste production (ton/day) figure 1. solid waste production in muscat (1970-1998). the first landfill in oman was introduced in mutrah before 1970. at that time, it served the whole region, as it was the only landfill in the area. in the course of time, as the population grew, muscat municipality started operating five landfills including mutrah. they are at al-seeb, 2 an assessment of solid waste and landfills in muscat area, oman quriyat, al-amerat, mutrah and bousher (al-barami, 1999; al-lawati, 1998). no other disposal processes are practiced. the problem of solid waste needs to be addressed both from an engineering and scientific ways. the existing landfills are grown out of need and are mostly simple open landfills without proper design. landfill problems are evident. a strategic plan for engineering management of solid waste in muscat region is required. a study was carried out to determine the existing status of the region in terms of solid waste generation, its types and distribution. the data generated provide an invaluable baseline information for future development of effective and efficient management schemes for handling solid wastes in the region. the data collected in the study are used to delineate the dimension of solid waste problems in muscat and they were used to forecast various possible outcomes and appropriate facilities capable of handling the problem. 2. study approach considering the limitation of resources and the scope of the study, it was decided to collect the solid waste data related to its composition and generation rate at the disposal site. presently, there are five well-defined operating landfills within the muscat municipality. a visit through the city undoubtedly convinces the visitors that the city is kept quite clean of unattended solid wastes. in addition, a survey of solid waste at the source requires considerable resources of personnel, time and finance. the scope of the project was limited in all these aspects. however, it was the investigators’ opinion that the possible error that may exist in data due to collecting data at the landfills is insignificant considering the large volume of wastes generated within the city. at the landfill entrances, the number of discharging trucks, and the volume and weight of wastes were recorded at random checks. for the determination of waste composition, the waste separation and sorting was accomplished also at random choice of sampling. 3. data 3.1 muscat city analyses of 10 specific samples of 800-850 kg of solid wastes from various landfills taken at random points depict the averages shown in table 2. table 2: average components in an 825-kg sample of solid wastes in muscat area. components weight in kg % food rests, vegetables and fruits 320 38.8 grass and trees rests 103 12.5 paper 30 3.6 cardboard 105 12.7 plastic 70 8.5 textiles 36 4.4 iron 29 3.5 wood 20 2.4 leather, rubber 4 0.5 glass, stones 30 3.6 rest 78 9.5 total 825 100 3.2 sub-regions the sub-regions of the greater muscat municipality with respect to solid waste generation is more or less divided into five regions contributing to five landfill sites: bousher, al-seeb, mutrah, 3 el-zawahry, shahalam, ramzi taha and al-busaidi al-amerat and quriayat. in order to delineate the regional characteristics in the trend of solid wastes generation, the discharges in landfills were separately monitored for 12 weeks during december 1998 and january and february of 1999. data of previous years were collected and compared with that of the present to establish the trends in solid wastes generation rates. figures 2a and 2b show two landfill sites at bousher and al-seeb. these are typical sights in landfills in the city. figure 2a. sludge disposal site at boushar area. figure 2b. disposal of tires at al-seeb landfill. bousher landfills an-sub landfill is located at the foot of the mountains behind the coastal plain in bousher. it is near ghala industrial area. the site has been in use since 1982. usual practice is to segregate wastes into four main types for disposal purposes. they are: 1. general domestic and commercial wastes including light industrial and clinical wastes; 2. motor vehicles and bulky industrial wastes; 4 an assessment of solid waste and landfills in muscat area, oman 3. carcasses and slaughter house wastes, and 4. sewage sludge. a trend of solid waste generation in bousher area is shown in figure 3. 0 5 0 0 0 0 1 0 0 0 0 0 1 5 0 0 0 0 2 0 0 0 0 0 2 5 0 0 0 0 s ol id w as te (t on ) 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 y e a r s o lid w a s te g e n e ra tio n in b o u s h e r a re a . figure 3. trend of solid waste generation in bousher area. 3.4 al-seeb landfills al-seeb landfill is located at the north of al-seeb wilayat, 14 km away from the center of the municipality of al-seeb. the site has been in use for quite a number of years. the site is unmarked and occupies a gently undulating landscape. nearby is moubela industrial city. it receives all types of solid wastes generated at the northern parts of muscat city. dispatched wastes are segregated into three separate categories: 1. domestic and commercial, 2. industrial and agriculture and 3. liquid and semi-liquid (sludge) for separate disposal sites. figure 4 shows the solid wastes generation trend in al-seeb landfill area for years 1992-1998. 0 10000 20000 30000 40000 50000 60000 70000 80000 s ol id w as te (t on ) 92 93 94 95 96 97 98 y ear tren d of so lid w aste g eneration in al-s eeb area figure 4. trend of solid waste generation in al-seeb area. 3.5 mutrah landfills mutrah landfill receives solid wastes from the old part of muscat city. figure 5 shows solid waste generation trend in mutrah area for the years 1992 – 1998. 5 el-zawahry, shahalam, ramzi taha and al-busaidi 3.6 al’amerat landfills the trend of municipal solid waste generation (1992-1998) in al-amerat area is shown in figure 6. 3.7 quriayat landfills the trend of solid waste generation in quriayat region is shown in figure 7 for the years 19921998. 0 20000 40000 60000 80000 100000 s ol id w as te 92 93 94 95 96 97 98 year solid waste generation in mutrah landfill area figure 5. trend of solid waste generation in mutrah landfill area. 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 6 0 0 0 0 s ol id w as te (t on ) 9 2 9 3 9 4 9 5 9 6 9 7 9 8 y e a r s o lid w a s t e g e n e r a t io n in a la m e r a t figure 6. trend of solid waste generation in al-amerat area. 3.8 municipal and other solid wastes. during the study, an attempt was made to separate the wastes in two categories of municipal and other origin (private). figures 8, 9 and 10 show the results of monitoring three landfills of alamerat, bousher and al-seeb. data of previous years are shown for comparison purposes. 6 an assessment of solid waste and landfills in muscat area, oman 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 9 2 9 3 9 4 9 5 9 6 9 7 9 8 y e a r s o l i d w a s t e g e n e r a t i o n i n q u r i a y a t a r e a i n t o n s figure 7. trend of solid waste generation in quriat area. solid waste transport ( municipal and private sources) in al-amerat area 0 50000 100000 150000 200000 250000 92 93 94 95 96 97 98 year w as te (t on ) amoun(mun) amount( private sector) figure 8. solid waste from municipal and private sources in al-amerat area. solid waste from municipal and private sources in bousher area 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000 92 93 94 95 96 97 98year w as te munc private figure 9. solid waste from municipal and private sources in bousher area 7 el-zawahry, shahalam, ramzi taha and al-busaidi solid waste from municipal and private sources in alseeb area 0 50000 100000 150000 200000 250000 92 93 94 95 96 97 98year w as te (t on ) munc. private figure 10. solid waste from municipal and private sources in al-seeb area. 4. discussion 4.1 composition of solid wastes table 3 shows a comparison of compositions of solid wastes as they changed through time. table 3: solid wastes composition 1993 and 1998 in muscat vs. that of california, usa percentage oman composition 1993 1998 california (peavy,1987)1982 food wastes 49.8 38.8 27.4 paper and cartons 17.5 16.3 28.5 glass and stones 10.5 3.6 10.3 plastics 9.0 8.5 4.6 textiles 1.0 4.4 2.3 leather and rubber negligible 0.5 1.7 iron 5 3.5 1.2 wood negligible 2.4 3.6 aluminum 0.6 8.3 rest 6.6 22.0 12.1 the data show significant changes in the content of food wastes. eating habits of the population may be changing with time. also modern packet and processed food supply greatly reduces the wastes. it is, however, expected that with time, this figure will stabilize to a lower value around 30 percent. paper and cartons content is comparatively low. glass and stones content in 1998 dropped from that of 1993 considerably. it is anticipated that this is due mainly to stones fraction. good upkeeping of the construction sites and regular road cleaning may have significant effects on this portion of the solid wastes. 4.2 solid waste generation table 4 summarizes the solid waste generation rate in the greater muscat city and the apparent solid waste generation in various regions based on the data of landfill discharges. one would 8 an assessment of solid waste and landfills in muscat area, oman expect a landfill discharge rate more or less equal to the actual generation rate provided the landfill capacities are adequate, and cross-regional transfer is not allowed. for example, in 1993, the total municipality generated nearly 2 kg/person/day. but the solid waste dumping rates in some of the landfills such as al-amerat and quraiyat were about 2 and 3 times that of waste generation rate in the city. it is apparent that part of solid wastes generated at mutrah and al-seeb was dumped in alamerat and quraiyat landfills. however, from an observation of the city solid waste generation rate and discharge rates in various landfills in 1998, it is evident that the solid wastes are not transported in significant amount from one sub-region to another sub-region. this indicates better management, economic transport and stability in overall handling of the solid wastes within the municipal area. overall the solid waste generation rate within the city dropped from 2 kg/person/day to 1.5 kg/person/day (figure 1 and table 4). the average solid-waste generation rate in the arab word is within the range of 11.5 kg/person/day. present rate hence appears to be stable and normal. table 4: per capita solid waste in muscat city and its sub-regions. population solid wastes, kg/day per capita solid wastes kg/p/d area 1993 1998 1993 1998 1993 1998 muscat (total city) 492000 526417 970000 769000 2.0 1.5 mutrah 169000 177387 247000 243000 1.5 1.4 bousher 134000 115007 293000 197000 2.2 1.7 al-seeb 136000 158064 195000 201000 1.4 1.3 al-amerat 30000 40721 115000 39000 3.8 1.00 quriyat 23000 35238 120000 89000 5.2 2.5 recent yearly solid waste generation rates in five landfills (figures 3, 4 , 5, 6, and 7), when compared with those of the previous two years (1996 and 1997), are more or less unchanged. such stable figures are extremely useful for developing an efficient solid waste management plan. however, it is a matter of concern that private sector contribution is increasing at a significant rate while municipal contribution is slightly decreasing or remaining more or less unchanged (figures 8, 9 and 10). from these figures, it might be inferred that the rates of municipal contributions have attained a stable rate. the per capita production rate is expected to remain steady. however, similar predictions cannot be made for the private sector. it appears that the portion generated by the private sector is increasing. if the trend continues, the solid waste generated from the private sector may dominate the characteristics, volume and per capita waste generation in future years. it is probably the right time to study the industrial and commercial activities along with adoption and implementation of proper management techniques to relieve the landfills from disproportionate solid waste dumps. if appropriate, strict segregation policy for separation of industrial and commercial solid wastes from those of municipal origin might be applied. 5. solid waste management the following management outline is apparently a viable, economical, and feasible approach towards a planned policy for handling solid wastes in the greater muscat municipal area. it is presented here in a form of proposal and it is expected that design details and economical aspects of these proposals will be further studied in near future. 5.1 potential of recycling of recoverable resources recycling of recoverable solid wastes is not new in the sultanate of oman. re-use of waste materials or their re-use by craftsman to produce utensils and other commodities has been practiced 9 el-zawahry, shahalam, ramzi taha and al-busaidi for a long period of time. many workshops and craftsman depended for their products on recyclable wastes (e.g. automobile parts, tires, metal sheets and aluminum scraps). the economical renaissance that started in 1970 has given considerable growth in the consumption of consumer goods, which in turn produced a legacy of recyclable wastes. a recovery scheme for the recoverable materials will at first hand reduce the quantity of solid wastes disposed off into landfills. this will in turn bring also new industries, new jobs, and recovery of resources, which directly contributes to the economic condition of the country. it is noted from the trends in industrial countries of recognizing the need for controlled management of the recycling activities. in the united states, germany and uk, the idea of using papers made of recyclable materials, and plastics made of recovered plastic scraps are commonly accepted. an estimate of the potential recyclable items in solid wastes in greater muscat area is shown in table 5. table 5: an estimate of potential recyclable solid wastes in muscat area. items possible reuse quantity ton / year paper / cardboard / textiles / wood paper making 65000 plastics plastic container 24000 iron ingots of iron 17000 aluminum cans / files 4000 leather / rubber shoes / roads 2000 recoverable materials account for about 40 percent of total yearly solid wastes of 280000 tons. recovery of these materials reduces per capita solid waste discharge in landfills from 1.5 kg/day to 0.9 kg/day. such a reduction in waste loads increases the expected operating life of landfills about 1.7 times. aluminum cans can generate an economic activity worth of ro 2,000,000 per year. the amount is derived using an ro 500/ton sale value. for utilizing the total potential of paper related recoverable materials, it is anticipated that pulp and paper making industries may be encouraged locally to grow at small scale within capacities of 30-40 tons/day. six such units may operate with available re-usable materials. approximate capital investment necessary for such an endeavor is estimated to be about 9-10 million omani rials (vogler, 1998). nearly 600-700 people will be engaged in such industries producing 250 kg paper / person/ day. 5.2 engineered design and management of the landfills the existing landfills in the greater muscat area are operating as open dumps without proper considerations to problems that may emanate from such waste disposal. the factors related to potential problems are landfill capacity, useful life, gas and leachate production and the potential of leachate contaminating the ground and groundwater. nearly 80% of the area solid wastes is organic materials (about 7% plastics, 60% rapid biodegradable materials and 12% normal biodegradable materials). of the rapidly biodegradable materials, 75% is available for bio-degradation while out of the slowly biodegradable organic materials, 50% is available for bio-degradation. about 2000 m3 of gas is expected to be generated per day at 2.5 m3/ton of solid wastes. in an engineering system, this gas may be recovered for economical use or safe discharge. depending on the nature of the organic materials, the degradation process may continue from 5 to 15 years. the gas production continues through the degradation period. the leachate production from solid wastes depends on several factors such as fill-height, rainfall, moisture content of solid wastes, field capacity (water) of solids and gas production. a sample of solid wastes from bousher landfill shows an estimate of potential average leachate production to be 747 kg/m2/yr. the estimate is based on 2.5 m3/ton/year of gas production, 15m 10 an assessment of solid waste and landfills in muscat area, oman height of the fills and rainfall of 0.102 m/year. it is equivalent to nearly 47 l/m2. the amount is relatively small. however, it might end up in groundwater flowing as seepage through unprotected bottom of the landfills. 6. conclusions and recommendations from the results of the limited study, the following conclusions and recommendations are drawn. 6.1 conclusions 1. the greater muscat area produces nearly 770 tons/day of solid wastes. this is equivalent to producing 1.5 kg/person /day. 2. the data from 1989 to 1998 substantiate the observation that the solid waste production per year in the greater muscat city appears to be steady at nearly 750-800 tons/day. 3. nearly 80% of solid wastes is organic materials. 4. out of the total 769 ton/day solid wastes, 112 tons comprise recyclable materials such as paper, cardboard, textile, wood, plastics, iron, aluminum, leather and rubber. 5. potential rate of gas production from the solid wastes generated in muscat area is about 2000 m3/day. 6. potential rate of leachate production in area landfills is about 747 l/m2/yr. 7. area landfills needs to be redesigned and operated according to efficient and safe management policy. 6.2 recommendations 1. a detailed study should be carried out to determine the basic factors necessary to design and operate the landfills safely, effectively and efficiently. 2. design factors that need to be established are: a. water flow on surface and in soil near the existing landfills. b. there are several items that need immediate attention. the items are proper landfill covers, gas collection or ventilation, leachate collection and containment systems, imperviousness of landfill bottom, leachate treatment, steps towards minimizing environmental and health risks. references al-barami, b.s. 1999. solid waste management in muscat area, final year project, department of civil engineering, sultan qaboos university, oman. al-lawati, t., al-khushari, q. and mohammed, m. 1998. muscat municipality. personal communication. mohammed, o.o. 1995. waste management in the sultanate of oman, friedrich ebert foundation, amman, jordan. peavy, h.s., rowe, d.r. and techobanoglous, g. 1987. environmental engineering, mcgraw hill, new york. scheu, m. 1993. assessment study on municipal solid waste management in muscat. wetter, germany: kaltwasser-engineering. 6-8. taufiq , m. a.v. 1992. sustainable development and the environment in the arab world. tunis: arab league educational, cultural and scientific organization (alecso), 87. vogler, j. and sarjeant, p. 1998. understanding small scale paper making, aerlington, virginia, usa: volunteers in technical assistance. received 4 march 2000 accepted 1 june 2000 11 êþííã çáýöáçê çáõáèé æçáãñçïã ýí� introduction study approach data weight in kg rest total 3.2 sub-regions figure 2a. sludge disposal site at boushar area. figure 2b. disposal of tires at al-seeb landfill. bousher landfills figure 4. trend of solid waste generation in al-seeb area. figure 5. trend of solid waste generation in mutrah landfill area. figure 6. trend of solid waste generation in al-amerat area. figure 7. trend of solid waste generation in quriat area. figure 10. solid waste from municipal and private sources in al-seeb area. electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 61-70 © 2001 sultan qaboos university ergonomic conditions in small manufacturing industries ashraf a. shikdar and saeed a. al-araimi department of mechanical and industrial engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. تأثير العوامل االنسانية في الصناعات الصغيرة أشرف شكدار ، و سعيد علي العريمي . في الصناعات الصغيرةنسانيةإل تاثير العوامل افي مديراتبحث هذة الورقة المبنية على معلومات من سبعة وعشرين : خالصة وسوء تصميم أماكن العمل ونقص والمعداتالت وجود عوامل مشتركة في هذة الصناعات تشملِ قدم اآل لىإ الدراسـة واشـارت كما توصلت الدراسة الى ان . المصنع وعدم سالمة حاالت العمل وسوء البيئة فيالتخطيط المنظم وطرق ترتيب اآلالت والعمال وى العاملة، المدراء تصلهم شكاوي االجهاد من القمن٪ 52 عشر عاما، وأن الخمسة الشركات لديها آالت يفوق عمرها من ٪ 59 78 في dba 90كما نتج عن الدراسة وجود ضوضاء فوق . األجزاء العليا للجسم في ٪ 33 في الظهر و آالم بسبب ٪ 41منهم فشلها في تطبيق نظم أبدت ادارات هذة الشركات من ٪ 44 ان و الحارة من األجواء منها ٪ 63 الشـركات بينما تعاني مـن ٪ الى ان االسباب الورقةهذا وتخلص . في المناولة اليدوية للمواد الكافي ال توفر التدريب منها ٪ 48وقوانيـن السالمة ، حيث أن يعزى الى النقص في المهارات في العوامل اال نسانية والتدريب الصغيرةالرئيسـية لـتردي العوامـل االنسـانية في الصناعات . واالتصاالت والموارد abstract: ergonomic conditions in small manufacturing industries were investigated. twenty seven managers of small manufacturing industries participated in the study. old equipment and machines, poorly designed workplaces, lack of systematic planning, layout and organization, unsafe working conditions and poor environment were found common to these industries. fifty-nine percent of companies indicated having equipment older than 15 years. fifty-two percent of company managers reported receiving complaints of fatigue from their workforce, 41% complaints of back pain, and 33% complaints of upper-body pain. seventy eight percent of companies reported a noisy environment (above 90 dba) while 63% reported a hot environment. management in 44% of the companies acknowledged failure to ensure safety rules and 48% did not provide training on manual material handling. lack of skills in ergonomics and training, communication and resources are believed to be some of the factors contributing to the poor ergonomic conditions in a sample of small manufacturing industries in malaysia. keywords: ergonomics, small manufacturing industry, worker productivity and occupational health and safety. 1. introduction e rgonomics or human factors engineering deals with the application of information about human behavior, capabilities and limitations to the design of systems, machines, tools, tasks, and environment for productive, safe and effective human use. a manufacturing industry is a complex human-machine-environment-organization system. for productive and effective functioning of this system management should ensure optimum functioning of the system components. there is a growing concern of improving productivity, safety, and quality in manufacturing industries. some of the common features of these industries are improper workplace design, illstructured jobs, mismatch between worker abilities and job demands, adverse environment, poor 61 ashraf shikdar and saeed al-araimi human-machine system design and inappropriate management programs. they lead to workplace hazards, poor workers health, mechanical equipment injuries, disabilities, and in turn reduce worker productivity and product/work quality and increase cost. it would, therefore, be extremely difficult to attain the above objectives of the manufacturing industries without giving proper consideration to ergonomics. effective application of ergonomics in work system design can achieve a balance between worker characteristics and task demands. this can enhance worker productivity, provide worker safety and physical and mental well-being and job satisfaction. many research studies have shown positive effects of applying ergonomic principles in workplaces, machine design, job design, environment and facilities design (hasselquist, 1981; rayan, 1989; schnauber, 1986; burry and helander, 1991; das, 1987; shikdar and das, 1995; das and sengupta, 1996; resnik and zenotti, 1997; das and shikdar, 1999). studies in ergonomics have also produced data and guidelines for industrial applications. the features of ergonomic design of machines, workstations, facilities are well known (grandjean, 1982; konz, 1983; sanders and mccormic, 1992; das and grady, 1983; rayan, 1987; melamed et al, 1989). however, there is still a low level of acceptance and limited application in manufacturing industries, especially in small manufacturing industries. the main concern of work system design is usually the improvement of machines and tools alone. inadequate or no consideration is given to the work system as a whole. therefore, poorly designed work systems are a common place in manufacturing industries (konz, 1983; das, 1987). neglect of ergonomic principles brings inefficiency and pain to the workforce. an ergonomically deficient workplace can cause physical and emotional stress, low productivity and poor quality of work (ayoub, 1990a, 1990b). small manufacturing industries are considered as manufacturing establishments employing 20 people or less in some places, where as in other places they are considered having less than 50 or even 100 workers. majority of the manufacturing industries are small and large facilities employing hundreds or thousand of workers are only a small fraction of the total manufacturing industries (zaidel, 1989). small manufacturing industries have specific characteristics differing from large industries in terms of facilities, resources and work systems. some of the characteristics of small manufacturing industries are: the manager is usually the owner, do not have occupational health and safety (ohs) committee, ergonomics specialists or trained personnel, usually they are located in small premises unsuitable for industrial facility, and in extremely poor conditions (zaidel, 1989). however, this study concentrated on characterizing small manufacturing shops and did not focus on ergonomic conditions of these shops. large manufacturing industries on the other hand have better awareness about ergonomics, ohs committees, personnel and resources to tackle ergonomics, productivity and safety issues. professional literature with regard to the introduction of ergonomics and safety improvements deals almost exclusively with medium and large industries. no specific study could be found in the literature on ergonomic conditions of small manufacturing industries. it is believed ergonomic deficiencies in manufacturing industries are the root causes of workplace health hazards, low level of safety and reduced worker productivity and quality. the ergonomic conditions in small manufacturing industries could be even more severe as these industries face compounding problems due to their characteristics. while ergonomics applications have gained momentum in large manufacturing industries, it is lacking severely in small manufacturing industries. therefore, the objective of this research was to conduct a study to assess the ergonomic conditions of small manufacturing industries. 2. methodology the methodology for investigating ergonomic conditions in small manufacturing industries involved: (1) development of a checklist that was mailed to the managers of industries, and (2) physically assess selected industries for ergonomic deficiencies. in this study small manufacturing industries were considered industries employing up to 50 people. a list of 100 small manufacturing 62 ergonomic conditions in small manufacturing industries industries was created from the directory of industry based on this criterion in the category of metal and metal products manufacturing. the list was representative of small manufacturing industries in the country. ergonomic problems/deficiencies may exist in any of the following system components of any manufacturing industry: 1. human operator, 2. equipment, 3. task, 4. workplace, 5. environment, 6. management. table 1 shows some major ergonomic attributes in each of these system components. the checklist was developed to collect information about these ergonomic attributes in small manufacturing industries. the checklist contained questions that required the managers to provide information as well as ticking the appropriate answers. for example, the manager of the company was required to tick the yes/no box for the question ‘do you provide a formal safety training to your workers?’. table 1: major ergonomic attributes in system components. system components ergonomic attributes human operator job training, safety training, skills, knowledge, posture, personal protective equipment, stress, fatigue, job satisfaction equipment design, emergency safety features, guards, access, controls and displays, installation, condition, maintenance task design, method, safety, jigs and fixtures, manual material handling, skills required, fatigue and rest period, repetition workplace physical space, layout of components, work height, seating arrangement, work chair design, material movement environment noise, heat, humidity, light, ventilation, dust, pollution, vibration, shopfloor condition, housekeeping management plant layout, hazard recognition, ergonomics and safety programs, ohs compliance, standard setting, feedback, attitude the checklist was mailed to the selected small manufacturing industries in perak and selangor states of malaysia and the managers of the companies were requested to return the completed questionnaire in the potage paid envelopes in confidence. they were also asked if the researcher could visit the company to physically inspect the workplace to verify the information provided in the questionnaire. twenty-seven companies returned the completed questionnaires and seven of these companies participated for a physical inspection of their companies. all the companies were in the same category (metal and metal products manufacturing) and employed between 7 and 50 people with an average of 23 people. the companies were located in the same geographical area. the physical inspection was intended to verify some of the answers in the checklist, such as confirming noise level, temperature, housekeeping, machine conditions, etc. 3. results the data obtained from the industries (n = 27) were analyzed in terms of frequency of positive or negative response to each question. table 2 presents some major responses in terms of frequency and percentage from the mangers. the analysis of the data showed serious ergonomic 63 ashraf shikdar and saeed al-araimi deficiencies in all the system components of small manufacturing industries. there was no ergonomic soundness in work systems in most of the cases. seldom the works were conducted in good ergonomic conditions. detailed analysis of the results is presented below. table 2: manager’s response to some major ergonomic attributes (n = 27), (ppe: personal safety equipment; ohs : occupational health and safety; mmh: manual material handing). system components ergonomic attributes positive response percentage (%) human operator ● worker complaints i. fatigue ii. headache iii. backache/pain iv. shoulder/neck pain v. hand/arm soreness ● worker training i. safety ii. ergonomics iii. mmh ● worker training i. use ppe 14 11 11 9 8 0 0 14 18 52 41 41 33 30 0 0 52 67 equipment ● equipment condition i. very old (>15 yrs) ii. adequate guarding iii. modifications made 16 22 11 59 81 41 task ● task design i. methods and time study ii. jig/fixture, work aid iii. specific work method 0 18 21 0 67 87 workplace ● workplace design i. use anthropometric data ii. postural flexibility iii. systematic layout iv. seating 0 11 3 16 0 41 11 59 environment ● environment condition i. noisy (>90 dba) ii. hot and humid iii. dusty 21 17 10 78 63 37 management ● management programs i. ensure safety rules ii. ergonomics program iii. motivating workers iv. housekeeping v. compliance with ohs 12 0 5 22 33 44 0 19 81 85 3.1 human operator the human operator is the most vital link in the human-machine-environment system. the system performance is largely dependent on the human operator. however, the operator is given little or no consideration in the work system design, especially in small manufacturing industries. the survey indicated ergonomics is seldom used and practically no ergonomics or safety training is provided to operators. operators complained of fatigue in 52%, back pain in 41%, shoulder or neck 64 ergonomic conditions in small manufacturing industries pain in 33% and hand or arm soreness in 30% of the companies surveyed. in an earlier study (shikdar et al, 1993) it was found that operators were unable to work in a normal standing or sitting postures due to poorly designed and installed machines, poorly designed work, inappropriate work heights and lack of suitable work chairs. poor work practices, especially in manual material handling, failing to wear personal safety equipment (ppe), lack of training for safe use of equipment, were very common. operators used inappropriate apparels. figure 1 shows some major worker complaints with respect to health and safety in small manufacturing industries. figure 1. some major worker complaints. operators were observed to work for considerably long periods of time. an understanding of human error is essential in such working conditions. the operators did not have any knowledge of ergonomics or its application for safe use of machinery and work practices. the physical inspection of the seven industries in the study showed similar results; such as operators were found not wearing ppe in the shopfloor. lack of experience and training (52%), fatigue (30%) and carelessness (26%) were sighted as the major causes of accidents and injuries. 3.2 equipment it is a fundamental principle of ergonomics that machines must be safe in operation and maintenance. however, it often becomes a source of injury in manufacturing industry. ergonomically designed equipment and proper safety training can significantly reduce accidents and injuries from equipment. little or no safety training is provided to workers in small manufacturing industries. the equipment is never assessed in terms of ergonomics. about 59% of the companies indicated they have machines that are older than 15 years and 41% companies required some sort of modifications in the machines. the modifications were mainly intended to improve machine performance and quality and seldom it was meant to improve safety of the workers. however, mechanical equipment has been blamed as the major source of injuries (59%). most of old equipment lacks in ergonomic design. in an earlier study, 370 machines were assessed and 91% were found poorly designed in terms of ergonomics (shikdar et al, 1993). among the 65 ashraf shikdar and saeed al-araimi ergonomic attributes of machine design, which were considered safety problems were traps, moving parts, controls and guards. these are, obviously, potential hazards and the sources of injuries in small factories. physical inspection showed unprotected cutting or working areas were common and there was easy access to these areas. moreover, controls were poorly designed which could cause accidents. there was a clear lack of necessary machine accessories including jigs and fixtures. safety features such as machine guards and emergency stops, etc. were either non-existent or were not in use. those machinery which had emergency stops were poorly located. companies with high mechanical injuries tended to have poorly designed machines and machines in poor condition due to poor maintenance (gardner et al, 1997). the installation of machines allowed easy access to dangerous areas too. non-ergonomically designed hand tools were very common with these industries. application of ergonomics to the design and safe use of machinery is virtually non-existent in small manufacturing industries (shikdar et al, 1993). 3.3 task small manufacturing industries depend mostly on contract jobs from the large industries. tasks are poorly designed with some specific work procedure or some instructions are provided to the workers for task performance. companies reported following a specific method (78%) although none of the companies reported using methods and time study. adequate postural control, appropriate visual requirements, need for repetitive movements, and manual material handling are not given adequate considerations. companies with better work design reportedly had fewer accidents (shikdar, et al, 1993). operators were found not using personal safety equipment (33%) in the tasks requiring the equipment. little or no consideration was given to matching the tasks to the operators in small industries. about 48% companies did not provide any training in manual material handling. manual material handling is a major source of occupational health hazards. 3.4 workplace physical inspection showed most of the small manufacturing industries were housed in unsuitable premises. workplaces were poorly designed. ergonomic guidelines have seldom been followed and no data such as anthropometric data for ergonomic design of the workplaces were available. there was inadequate working space, and workplaces were assessed as having poor workplace layout and not organized although 41% companies showed having considered postural flexibility. obstructions and crowding of equipment and materials were common in the seven companies studied in the physical inspection. although 59% companies reported that they provide figure 2. a typical small manufacturing industry. 66 ergonomic conditions in small manufacturing industries seating arrangements for the workers, the inspection indicated the chairs and other seating nt some major environmental problems in the shopfloor of small manufacturing indu arrangements were poorly designed. in the layout and design of workspaces the owners did not follow any systematic procedure. similar results were obtained in the earlier study (shikdar et al, 1993). figure 2 shows a typical small manufacturing industry with no ergonomic consideration. working posture is largely affected by workplace design. therefore, appropriate application of ergonomic data in the design of the workplace can significantly reduce musculoskeletal injuries in the workplace. 3.5 environme figure 3 shows stries. the main problems reported in terms of environment, in the surveys were excessive noise (78%), hot (63%) and dusty environments. excessive noise was considered a sound level above 90dba most of the time during the work shift. this was probably because the factories were operated in unsuitable premises. high noise level tended to be the feature of old equipment resulting in the need for protective measures. hot environment was considered to be an air temperature of 30 0c and above. it was reported that in 33% cases the operators were not using earmuffs or earplugs although there was no shortage of personal safety equipment. there was no provision to control temperature in the shopfloor, however operators wore clothing according to their needs. physical measurement in the seven audited companies confirmed these environmental conditions. figure 3. some major environmental problems in industries performance of machine tasks under adverse conditions could lead to accidents and injuries. ther r, most of the small factories were not systematically organized. constraint on spac efore, adequate consideration should be given to environment design in small factories. similar results were observed in an earlier study (shikdar, et al, 1993). 3.6 management as stated earlie e probably prohibited systematic plant layout. poor housekeeping was a common feature of the industries inspected, although, in about 81% cases the factories reported that they carry out housekeeping on a regular basis or when required. the inspection showed most companies did not have proper storage areas and materials were left laying around (figure 2). obstructions in the aisles and work areas were quite common. no ergonomics or safety programs were enforced. management of some of these industries acknowledged of failing to ensure safety rules (44%); 67 ashraf shikdar and saeed al-araimi such as wearing ppe. as reported earlier the manager is usually the owner in most small factories, so in many cases they work with other operators on the shopfloor. therefore, the communication is usually verbal and casual (zaidel, 1989; shikdar et al, 1993). 4. discussions the principles of ergonomics are directly relevant to the design of workplaces, machines, mac ’ response do not indicate a high accident and injury rate, the ergo et al, 1993 ring industries not only hinder productivity but a 5. conclusions the study indicates that the following conclusions could be drawn regarding ergonomic cond . ergonomics is seldom used in small manufacturing industries. most of the industries studied 2. e common in small manufacturing the managers as the major cause of injuries. hine guards, displays and controls and hand tools. ergonomic design of equipment applies fundamental principles and techniques of safeguarding and providing safety devices for the protection of operators. there should also be adequate warning and instructions for safe operation and maintenance of machines. despite wide spread use of guards, devices, and personal protective equipment, injuries and even deaths occur with increasing frequency. this indicates a lack of appropriate application of ergonomics in design, operation and interface. inadequate or no formal safety training, poor knowledge of hazard recognition and prevention could further aggravate the problem. a large number of unsafe and poorly designed machines and workplaces are in use in small manufacturing industries. designing out problems that can cause accidents and injuries is a better solution to preventing accidents and injuries. designing out ergonomic deficiencies can significantly reduce injuries. although the managers nomic deficiencies are clearly significant. some ergonomics are applied indirectly since the companies have to ensure occupational health and safety (ohs) regulations imposed by the government. the ohs problems identified in the study are related to ergonomic deficiencies in the system components. by designing out ergonomic deficiencies, not only accidents and injuries would reduce, but also improve worker productivity and satisfaction. small manufacturing industries have a high mechanical equipment injury rate (shikdar ; gardner et al, 1997). the ergonomic problems identified in the study were probably responsible for the high incidence rate. physical safety problems were severe. lack of ergonomics knowledge and awareness of the employers and employees could be responsible for the poor acceptance of ergonomics in the workplace. management did not check the workplaces for unsafe features and did not enforce safety rules, or provide instructions and training for safe performance. even hazard signs were not displayed in unsafe places. the poor ergonomic conditions in small manufactu lso affect health and safety of workers and quality of works and products. the study is unique as professional literature with regard to the introduction of ergonomics and safety improvements deals almost exclusively with medium and large industries. no study could be found that deals specifically with ergonomic conditions and their improvements in small manufacturing industries. since most manufacturing industries are small, attention must be given to improving ergonomic conditions of these industries. itions in small manufacturing industries in malaysia: 1 have used little or no ergonomics information and data. eighty-one percent of the companies did not carry out ergonomic assessment of their companies. non-ergonomically designed equipment and workplaces ar industries as evident from the physical audit. fifty-nine percent of the companies have old (>15 years) equipment. the old equipment is a potential hazard for accidents and injuries as they are less likely to have been ergonomically designed. mechanical equipment is blamed by 59% of 68 ergonomic conditions in small manufacturing industries 3. respectively. these health problems are serious 4. he 5. mics information or they simply ignored it considering resource constraints jority of industries are small and since it is a source of employment and support for e economy, drastic and systematic measures and changes are required in the set up and operation of s anagement must be knowledgeable and aware of benefits of ergonomics and the prevention of injuries through ergonomic design of work system. information on b. and injuries. ergonomic c. be given adequate d. in small manufacturing industries to improve worker productivity, safety, health 6. nt the contribution of mr. rajendran in the data collection process. ayoub, m.a. 1990a. ergonomic deficiencies: i. pain at work. journal of occupational medicine, 32: 52-57. 2: 131-136. boards. international journal of industrial ergonomics, 7: 207-215. 3-443. ving worker productivity. international journal worker complaints of fatigue, back pain, headache, and upper body pain were reported in 52%, 41%, 41%, and 33% of the companies, indications of ergonomic deficiencies in the work system of small manufacturing industries. poor environmental condition, especially noisy and hot, is common to most of the small industries and little consideration is given to improving it. seventy-eight percent of t companies had excessive noise (>90 dba) and 63% of the companies reported hot environment. adverse environmental condition in the shopfloor could aggravate accidents and injuries further. most of the small manufacturing industries either did not have knowledge of ergonomics, access to ergono and costs. as the ma th mall manufacturing industries. some of the strategies as evident from the study are stated below. a. employees and m ergonomics should be available to small manufacturing industries. the old and unsafe equipment should systematically be replaced or upgraded in order to have better ergonomically designed equipment to reduce accidents evaluation should be carried out on equipment before purchasing them. the work and workplace design should be carried out using ergonomic guidelines, acts and recommendations considering user population. environment must consideration. strategies should be formulated and implemented in order to introduce ergonomics systematically and environment. acknowledgeme the authors acknowledge references ayoub, m.a. 1990b. ergonomic deficiencies: ii. probable causes. journal of occupational medicine, 3 burri, g.j. and helander, m.g. 1991. a field study of productivity improvements in the manufacturing of circuit das, b. 1987. an ergonomic approach to designing a manufacturing work system. international journal of industrial ergonomics, 1: 231-240. das, b. and grady, r.m. 1983. industrial workplace layout design: an application of engineering anthropometry. ergonomics, 26: 43 das, b. and sengupta, a. 1996. industrial workstation design: a systematic ergonomic approach. applied ergonomics, 27: 157-163. das, b. and shikdar, a. 1999. participative versus assigned production standard setting in a repetitive industrial task: a strategy for impro of occupational safety and ergonomics, 5: 417-430. 69 ashraf shikdar and saeed al-araimi gardner, d., cross, j.a., fontayne, p.n., carlopio, j. and shikdar, a. 1997. gra hasselquist, r.j. 1981. increasing manufacturing productivity using human factors kon sa. s sanders, m.s. and mccormic, e.j. 1992. human factors in engineering and design. (6th sch ductivity as reflected in a new factory. trends in shik anical shik ivity improvements. applied resnik, m.l. and zanotti, a. 1997. using ergonomics to target productivity ray asfour (ed.), trends in rayan, j.p. 1989. a study of selected ergonomic factors in occupational safety. advances in zai dvances in eceived 24 january 2001 mechanical equipment injuries in small manufacturing businesses. proceedings of the 13th triennial congress of the international ergonomics association , 109-111, tempere, finland. ndjean, e. 1982. fitting the task to the man: an ergonomic approach. taylor and francis, london, uk. principles. proceedings of the human factors society – 25th annual meeting, 204-206. z, s. 1983. work design: industrial ergonomics. (2nd edition), grid columbus, ohio, u melamed, s., luz, j., najemson, t., jucha, e., and green, m. 1989. ergonomic stres levels, personal characteristics, accident occurrence and sickness absence among factory workers. ergonomics, 9: 1101-1110. edition), mcgraw hill, new york, usa. nauber, h. 1986. ergonomics and pro ergonomics/human factors iii, karwowski ed., elsevier science publishers, 459-465. dar, a., carlopio, j., cross, j., stanley, p. and gardner, d. 1993. mech equipment injuries in small businesses. in ergonomics in a changing world, proceedings of the ergonomics society of australia, 199 205, perth, australia. dar, a.a. and das, b. 1995. a field study of worker product ergonomics, 26: 21-27. improvements. computers and industrial engineering, 33: 185-188. an, j.p. 1987. a study of safety in man-machine systems. in ergonomics/human factors, iv, 505-511. industrial ergonomics and safety i, anil mital (ed), taylor and francis, 359-364. del, d. 1989. ergonomics and safety in small manufacturing shops (sms). a industrial ergonomics and safety i, anil mital (ed), taylor and francis, 391-397. r accepted 24 june 2001 70 ashraf a. shikdar and saeed a. al-araimi department of mechanical and industrial engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. methodology results human operator equipment task workplace environment management discussions conclusions acknowledgement references squ journal for science, 2018, 23(1), 8-18 doi: http://dx.doi.org/10.24200/squjs.vol23iss1pp8-18 sultan qaboos university 8 the mathematical modelling of a fixed source of dust khaled s.m. al-mashrafi department of human resources development, general directorate of education in eastern region, ministry of education, sur, p.o. box 998, p.c. 411, sultanate of oman. email: khaled2014om@gmail.com abstract: a mathematical model for the diffusion of dust particles emitted from a fixed source is investigated using the atmospheric diffusion equation. this model poses an initial boundary value problem with a second order linear partial differential equation. the steady state case of this problem when the uniform source is situated at ground level was examined by sharan et al. [1]. the solution of the unsteady case in closed form for a time dependent source is derived. two special cases, in which the source function of time is explicitly given and special values of the diffusion parameters are taken, are examined in detail. in the case when diffusion is present only in the vertical direction, it is shown that for small times, the particles spread with a front that travels with the speed of the wind. when diffusion is present only in the direction of the wind, there is no discontinuity front and the particles diffuse slowly into the direction of the wind. the solutions for the special cases considered are examined for large values of time. it is found that the solution approaches that of the corresponding steady state solution of the equation. keywords: atmospheric diffusion equation, vertical diffusion, horizontal diffusion, wind speed. الرياضي النتشار ذرات الغبار التي تنبعث من مصدر ثابت النموذج خالد سليمان المشرفي دراسة وذجنتشار جـُـزئيات الغـُــبار المنبعثة من مصدر ثابت باستخدام معادلة االنتشار الجوية. يتطلب هذا النمالي الرياض تمت دراسة النموذج :صالملخ في الحالة الخاصة التي يكون [1]سبقاً من قبل شاران ورفاقه م الحالة هذه اختبرت .حدودية ابتدائيةشروط معادلة تفاضلية جزئية خطية من الدرجة الثانية ب اختبار حالتين في هذا البحث تم .الزمنب ظاهري لجميع المصادر التي ترتبطحل ووجدالزمن. ومستقال عنعلى سطح األرض افيها مصدر الغبار متمركز تم اثبات أن امالت االنتشار. عند وجود إنتشارعمودي فقط ولزمن قصير،، مع أخذ حاالت خاصة لمععندما يكون المصدر دالة في الزمن خاصتين بالتفصيل لريح. كذلك م مالحظة أن الغبار ينتشر ببطء في اتجاه انفس إتجاه الريح، تفقط وب . أما في حالة إنتشار أفقيوبنفس سرعة الريحمقدمة الذرات الغبار تنتشر ب المعادلـة. تلكيقترب من الحل الثابت لتم اثبات أن الحل و طويال. الزمن يكون مالحاالت الخاصة التي تم افتراضها عندا ولحلتم اختبار .سرعة الريح ،نتشار أفقيإ ،انتشار رأسي ،معادلة االنتشار الجوية :مفتاحيةالكلمات ال 1. introduction he mathematical model of particles emitted from a fixed source has been investigated [1-11]. the study of transport of such particles by wind in the atmosphere is important because it causes problems to the environment [12-15]. most industrial establishments have factories with chimneys through which the fumes escape into the atmosphere outside the factory. these fumes diffuse into the surroundings causing pollution and forming a health hazard. in arid lands, as in oman, strong winds carry dust from the ground and transport it, which can cause damage to roads and also dirt in houses [16-17]. the diffusion of particles emitted from a source in the atmosphere is given by the atmospheric diffusion equation [18]. * . .( : ) . c c c c t          u d w , (1) where c is the concentration of the particles after time * t , u is the local velocity of the particles, w is the settling velocity, and d is the stress tensor given in a cartesian coordinates system by t mailto:khaled2014om@gmail.com the mathematical modelling 9 * * * * * * * * * * * * * * * * * * , x x x y x z y x y y y z z x z y z z d d d d d d d d d             d where the axis * oz is vertically upwards and the axes * ox and * oy are horizontal. the analytical study by sharan et al. [1] investigated a steady-state model for low wind speeds where the gravitational force is negligible. the air stream moved with a uniform velocity u in the x  direction. they assumed the presence of diffusion components in three coordinate directions, all of which being linearly proportional to the distance along the wind. they concluded that their result is in reasonable agreement with experimental observations. in this paper, we extend the steady state model by sharan et al. [1] to include the time variation. we assume that the wind speed is low, the diffusion varies linearly with distance along the wind direction, and gravity is ignored. in section 2, the model of the system is formulated. in section 3, the solution is calculated and examined in detail for some special cases of the diffusion parameters and the time dependence of the source. a general discussion of the solution is also presented in this section. some concluding remarks are made in section 4. 2. formulation of the model the diffusion of dust particles emitted from a fixed source situated on/or above ground level in the atmosphere is governed by the atmospheric diffusion equation (1). this equation can be written in a cartesian system of coordinates  * * *, ,o x y z in the absence of the settling velocity as , c c c c c * * * * * ** * * * * * * d d d x x y y z zt x x y y z z                                      u . (2) where , ,* * * * * *d d dx x y y z z are the components of the stress tensor in * * *, ,x y z directions, respectively. assume that the direction of the wind speed is in the * axisx  and the velocity of dust particles is given by ( , 0 , 0 ) ( , , ),u u v w u (3) where ( , , )u v w is the velocity of dust particles relative to the local wind speed and ( , 0 , 0 )u is the wind speed. if we also assume that the components , ,u v w of the dust particles’ velocity are very small in comparison with u , and the variations of concentration in all directions are similar, then the advection term in (2) reduces to c . c ~ . * u x    u (4) assume further that all three components of the diffusion are linear in * x : * * * * * * * * * , , , x x y y z z d ux d ux d ux     (5) in which , ,   are positive constants. using equations (4) (5), write equation (2) as * * * * * * * * * * * , c c c c c u ux ux ux t x x x y y z z                                    (6) which represents the linearized three-dimensional unsteady atmospheric diffusion equation in the absence of gravitational forces. this equation is solved subject to the following initial and boundary conditions * * * * * * * ( , , , ) 0 as , , ,c x y z t x y z   (7) * * * ( , , , 0) 0,c x y z  (8) * * * * * * * * (0, , , ) ( ) ( ) ( ) with (0) 0 ; 0 , q c y z t y z h f t f t u      (9) * * * * ( , , 0, ) 0, c x y t z    (10) where the dust particles emanate from a fixed source at * (0, 0, )h has a strength q for all * 0t  , * 0h  , and ( )s is dirac’s delta function. it is clear from the condition (9) that the source depends on time * t and its strength depends on the function * ( ).f t k.s.m. al-mashrafi 10 the equation (6) and the relevant conditions (7) (10) can be written in the following dimensionless form 2 2 2 2 2 2 0, c c c c c x x x a x y z x t                (11) ( , , , 0) 0 ;c x y z  (12) ( , , , ) 0 ; , , ,c x y z t x y z   (13) (0, , , ) ( ) ( ) ( ) , (0) 0, 0 ,c y z t q y z h f t f t     (14) ( , , 0, ) 0, c x y t z    (15) where * * * * * 1 , , , , ; , , 0, . , t ut x x y y z z a q h h q u                            (16) the system (11) (15) was solved by integral transform methods to obtain the solution for the concentration in the  , ,x y z plane at any time in closed form for a source of general time dependence [10-11]. the solution showed that, as well as the position of the source in the vertical direction, the diffusion parameters , ,   play an important role in the spread of the dust particles in the atmosphere. in this paper, we investigate the influence of diffusion parameters in all directions by studying the following two special cases: (1) vertical diffusion 0 , 0     and (2) longitudinal diffusion 0 , 0     . 3. analytical solutions for the model 3.1. case (1): solution in the case of vertical diffusion ( 0, 0     ) in this case, vertical diffusion is present and both longitudinal and latitudinal diffusions are absent. the solution here is given by 2 2 2 2 ( ) ( ) ( ) ( ) ( , , ) exp exp , 2 22 2 q f t x h t x h z h z c x z t x xx                       (17) where ( )h s is the heaviside function, x and q are defined in (16), and ,t z and h are redefined as * * * , , . z h t ut z h      (18) the solution (17) specifies the concentration at every point  , ,x z t of the domain. it is clear that the time dependence appears only in the amplitude of the concentration and is absent in the exponential dependence. moreover, the presence of the heaviside unit function in the amplitude of the solution represents the discontinuity in the solution across the line x t in the  ,x t plane. the solution (17) is illustrated by two examples of the source ( )f t , which are: (i) heaviside function ( )h t , and (ii) exponential function 1 , 0 t e      . the aim for choosing these specific examples is to examine the effect of the strength of the source as time varies. 1 , 0 ( ) ( ) ( ) 0 , 0 t i f t h t t      the solution (17) reduces to 2 2 2 2 ( ) ( ) exp exp , ( , , ) .2 22 2 0 , q h z h z x t c x z t x xx x t                            (19) the mathematical modelling 11 the contours of the solution (19) in the  ,x z plane are illustrated in figures 1 and 2 for different values of time t , where ( , , ) ( , , ) / .c x z t c x z t q the solution has a discontinuity at x t for small values of .t noting the transformation (18), it is obvious that the line constantx t  corresponds to * * constant,x ut  so, due to this characteristic, * * / ,dx dt u i.e. the concentration of particles travels with a speed u away from the source. this is illustrated for two sample values of  0, 5h  in figures 1 and 2, respectively. the source of particles in this case does not depend on the time. for x t , the concentration decreases away from the source and spreads further from the source as t increases. for x t , there are no particles. this situation applies for all values of the height of the source above ground level. for small values of the time t , the proximity of the front at x t to the source causes the particles to diffuse upwards, (figures 1,2(a), (b), (c)). for large values of the time ,t the discontinuity at x t has no effect on the distribution of the particles. when the source is situated on the ground, the concentration on the ground is strong but as the height increases, the particles spread over a larger area both horizontally and vertically. when t  , the distribution of particles approaches the steady state solution (figures 1(f) and 2(f)). ( ) ( ) 1 , 0 t ii f t e       the solution (17) becomes   2 2 ( ) 2 2 ( ) ( ) 1 exp exp , ( , , ) .2 22 2 0 , t xq h z h z e x t c x z t x xx x t                                (20) the contours of the solution (20) in the  ,x z plane are illustrated for different values of the time t and decay factor  in figures 3– 6, where ( , , ) ( , , ) / .c x z t c x z t q we note that the strength of the source in this case depends on the coefficient of decay  as well as on the time. figures 3 and 4 illustrate the profiles of the solution for a fixed value of 10  and different values of the time t with two different heights of the source. it is clear that there is no discontinuity in the distribution of the particles in the ( , )x z plane whatever the values of the time and height. figure 1. the isolines of the concentration ( , , ) ( , , ) /c x z t c x z t q in the ( , )x z plane when ( ) ( )f t h t and 0h  , for different values of the time: (a) 0.1t  , (b) 0.4t  , (c) 1t  , (d) 5t  , (e) 7.5t  , and (f) 10t  . note the precipitation of the particles on the ground as the time increases. note the position of the characteristic x t as t is increased. k.s.m. al-mashrafi 12 figure 2. the isolines of the concentration ( , , ) ( , , ) /c x z t c x z t q in the ( , )x z plane when ( ) ( )f t h t and 5h  , for different values of the time: (a) 0.1t  , (b) 0.4t  , (c) 1t  , (d) 5t  , (e) 7.5t  , and (f) 10.t  compare figures 1 and 2 to notice the influence of increasing the height of an industrial chimney. figure 3. the isolines of the concentration ( , , )c x z t in the ( , )x z plane when ( ) 1 t f t e    for 0, and 10h   and the time t takes the values 0.1, 0.4, 1, 5, 7.5, and 10 in (a), (b), (c), (d), (e) and (f), respectively. for large values of the time t , the distribution of the particles converges to the steady state solution (figures 3 and 4(f)). figures 5 and 6 show the profiles of the concentration in the space for a fixed value of the time 1t  and different values of the decay factor  for two different values of the height of the source. for small values of , the strength of the source is weak and its ability to push the particles far away from the origin is not strong. when   , the spread of the particles approaches the distribution of particles in case (i). comparison between the two cases of the function  f t shows that the dependence of the source on the time has an influence on the distribution of the particles in space. this applies to all values of the height (figures 1 – 6). the mathematical modelling 13 figure 4. the isolines of the concentration ( , , )c x z t in the ( , )x z plane when ( ) 1 t f t e    for 5, and 10h   and the time t takes the values 0.1, 0.4, 1, 5, 7.5, and 10 in (a), (b), (c), (d), (e) and (f), respectively. figure 5. the isolines of the concentration ( , , )c x z t in the ( , )x z plane when ( ) 1 t f t e    for 0, and 1h t  and the factor  takes the values 0.5, 1, 10, and 100 in (a), (b), (c) and (d), respectively. note the increasing of the coefficient of decay. k.s.m. al-mashrafi 14 figure 6. the isolines of the concentration ( , , )c x z t in the ( , )x z plane when ( ) 1 t f t e    for 5, and 1h t  and the factor  takes the values 1, 10, 100, and 1000 in (a), (b), (c) and (d), respectively. note when    , case 1(i) deduced from this case. 3.2. case (2): solution in the case of longitudinal diffusion ( 0, 0     ) in this case, the longitudinal diffusion * *( ) x x d is present, and both vertical and latitudinal diffusions * * * *( and ) z z y y d d , respectively, are absent. the solution in this case is given by 1 1 0 ( , ) ( ) exp , 1 t q x c x t g t s s ds s                         (21) where x and q are defined in (16), t is given in (18), (s) is the gamma function, and ( )g t is the inverse laplace transform of  f  with respect to the time t , given by     1 1 .g t l f           f  is the laplace transform of the function  f t with respect to t defined by     0 . t f f t e dt       the behavior of the concentration in this case depends on the source ( )f t as represented by ( )g t in (21). this expression gives the solution of this case in closed form. the model does not depend on height, z , or distance .y it then represents a source fixed along the z -axis at origin and having an infinite length ( 0z  ). the nature of the solution (21) is studied by using two examples of the function ( ).f t 1 , 0 ( ) ( ) ( ) . 0 , 0 t i f t h t t      in this case, the solution (21) reduces to 1 1 ( , ) , ; 1, 1 q x c x t t                             (22) the mathematical modelling 15 where  ,a x is the incomplete gamma function. for the special cases  0 , 0 , ,x t x t     , the solution (22) gives (0, ) (2 ) (2 , 0) , (2 ) q c t q         ( , 0) (2 ) (2 , ) 0, (2 ) q c x           ( , ) (2 ) (2 , ) 0 ; as , (2 ) q c x t x           ( , ) (2 ) (2 , 0) ; as . (2 ) q c x t q t          these asymptotic values confirm the initial and boundary conditions for ( , )c x t of this case. another special case occurs when 2,  when the solution (22) reduces to a simpler form. in such a case, the solution (22) becomes ( , ) ; 2.0, 2 x c x t q erfc t          (23) in which ( )erfc y is the complementary error function [19]. figure 7. the isolines of the concentration ( , )c x t of case 2(i) in the ( , )x t plane for the function ( ) ( )f t h t for some values of the diffusion parameter: ( ) 1.5a   , ( ) 2,b   ( ) 4c   , and ( ) 10d   . note the increasing of the longitudinal diffusion parameter. k.s.m. al-mashrafi 16 figure 8. the isolines of the concentration ( , )c x t in the ( , )x t plane for the function ( ) ( )f t h t for a special case of complementary error function when 2  , in the case when longitudinal diffusion only is present. compare this with figure 7 (b). the contours of the solutions (22) and (23) in the ( , )x t plane are illustrated for different values of the diffusion component  in figure 7 and for 2  in figure 8. it is clear from figure 7 that at every point of the space in the ( , )x t plane, the presence of particles decreases whenever the diffusion parameter  increases. for a fixed value of the distance ,x the concentration increases with time t . moreover, at a specific time t , the concentration of particles decreases when we move further away from the source. this last situation can happen in real life because as we move further away from the source, there will not have been enough force to carry a mass/ large numbers of particles that far. the values of  chosen for figure 8 are made for ease of comparison between the solutions (22) and (23). if we compare the two figures, we see that the computations for both cases are consistent. ( ) ( ) 1 , 0 t ii f t e       the solution for this source is given by 1 2 2 0 ( , ) 1 (1, 2 2 , ( )) , (2 ) (2 2 ) t x s q t c x t e m s t ds s                       (24) where ( , , )m a b x is a confluent hypergeometric function [19]. the contours of the solution (24) in the ( , )x t plane are presented in figures 9 and 10 for different values of the decay parameter  and the two specific values of the coefficients of the longitudinal diffusion; 2  and 10,  respectively. the quantity of particles at every point of the ( , )x t plane increases whenever the decay factor  increases for a fixed value of longitudinal diffusion . this situation must happen in real life because when the coefficient of the decay increases, the strength of the source increases. when the values of  and  are fixed, then the concentration increases as the time increases for a fixed distance .x furthermore, at a specific time ,t for fixed strength of the source and longitudinal diffusion, the concentration decreases as we move further away from the source. the mathematical modelling 17 figure 9. the profile of the concentration ( , )c x t for a fixed value of 0.25 ( 2)   and different values of the decay factor: ( ) 0.1a   , ( ) 1b   , ( ) 6c   , and ( ) 10d   . figure 10. the profile of the concentration ( , )c x t for a fixed value of 0.05 ( 10)   and different values of decay factor: ( ) 0.1a   , ( ) 1b   , ( ) 5c   , and ( ) 10d   . as shown in figures 9 and 10, for small values of  and fixed  , the diffusion of the particles in the horizontal direction is very weak and the particles need more time to diffuse in the x  direction, (figures 9 (a, b), and 10 (a, b)). as  increases, the diffusion steadily increases. for large values of the decay factor  , the concentration approaches the steady state solution. large values of  result in a strong source and whenever these values increase further the strength of the source converges to the steady state in case (i). for a fixed value of the decay factor, at every point in the plane the concentration when 2  is more than that when 10.  comparison between the two cases of ( )f t in the presence of longitudinal diffusion shows that the force of the source in case (i) is stronger than that for the source in case (ii). but the two will be identical for large values of the decay factor , for 0t  , when the strengths of the two sources become equal. the spread of particles in the horizontal direction in case (ii) is weaker than that in case (i) for 0.t  for large values of the time, the unsteady state solution approaches the steady state results obtained by sharan et al [1]. k.s.m. al-mashrafi 18 4. conclusion the diffusion of dust particles emitted from a fixed source in the atmosphere in the absence of the settling velocity has been studied mathematically. the study found the solution of the time-dependent diffusion equation in the presence of a point source whose strength is dependent on time. the solution reduces to simpler forms in special cases where the solution can be obtained in explicit expression. in case (1), diffusion in both the longitudinal and latitudinal directions was neglected. the dependence of the distribution of dust on the time variation of the source is investigated for two different functions. when the source is strong for small times, the solution shows a discontinuity. in case (2), the diffusion in the y and z directions was ignored. the profiles of the solutions showed that the concentration of dust particles in the  ,x t plane depends on the parameter of diffusion in the direction of the wind. the strong presence of this parameter led to the distribution of the dust in a larger area. the solution approaches the steady state solution of the system. references 1. sharan, m., singh, m. and yadav, a. mathematical model for atmospheric dispersion in low winds with eddy diffusivities as linear functions of downwind distance. atmospheric environment, 1996, 30, 1137-1145. 2. taylor, g. diffusion by continuous movements. proceedings of the london mathematical society a, 1921, 20, 196 212. 3. abbott, j. and francis, j. saltation and suspension trajectories of solid grains in a water stream. philosophical transactions of the royal society of london, 1977, a284, 225-253. 4. eltayeb, i. and hassan, m. on the non-linear evolution of sand dunes. geophysical journal of the royal astronomical society, 1981, 65, 31-45. 5. koch, w. a solution of the two-dimensional atmospheric diffusion equation with height-dependent diffusion coefficient and height-dependent wind speed and eddy diffusivities. atmospheric environment, 1989, 23, 17291732. 6. hill, j. similarity solutions for non-linear diffusion a new integration procedure. journal of engineering mathematics, 1989, 23,141-155. 7. eltayeb, i. and hassan, m. two-dimensional transport of dust from an infinite line source at ground level. geophysical journal international, 1992, 110, 571-576. 8. lin, j. and hildemann, l. analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities. atmospheric environment, 1996, 30, 239-254. 9. lin, j. and hildemann, l. a generalized mathematical scheme to analytically solve the atmospheric diffusion equation with dry deposition. atmospheric environment, 1997, 31, 59-71. 10. al-mashrafi, k. diffusion of dust particles emitted from a fixed source. international journal of applied mathematical research, 2015, 4(4), 454-465. 11. al-mashrafi, k. the influence of longitudinal diffusion on the transport of dust particles emitted from a fixed source. international journal of applied mathematical research, 2016, 5(1), 11-17. 12. roberts, o. 1923. the theoretical scattering of smoke in a turbulent atmosphere. proceedings of the royal society of london.,1923, a 104, 640-654. 13. smith, f. the diffusion of smoke from a continuous elevated point source into a turbulent atmosphere. journal of fluid mechanics, 1957, 2, 49-76. 14. gillette, d. threshold friction velocities for dust production for agricultural soils. journal of geophysical research, 1988, 93, 12645-12662. 15. eltayeb, i. and hassan, m. diffusion of dust particles from a point source above ground level and a line source at ground level. geophysical journal international, 2000, 142, 426-438. 16. hassan, m. and eltayeb, i. time-dependent transport of dust. journal of geophysical research, 1991, 96, 93379339. 17. gillette, d. and passi, r. modelling dust emission caused by wind erosion. journal of geophysical research, 1988, 93, 14233-14242. 18. pasquill, f. atmospheric diffusion, van nostrand, princeton. 1962 19. abramowitz, m. and stegun, i. 1965 handbook of mathematical functions, with formulas, graphs and mathematical tables, new york, dover. received 26 february 2017 accepted 27 july 2017 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 147-156 © 2002 sultan qaboos university simulation of m-sequence’s properties through matlab-simulink a. ahmad, m. j. al-mushrafi and s. al-busaidi department of information engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman. email: afaq@squ.edu.om, mufeed@omantel.net.om, albusaid@squ.edu.om. سيميولنك–م بواسطة ماتالب –نمذجة خصائص متتاليات آفاق احمد ، مفيد المشرفي و سمير البوسعيدي م -م تم تطوير وسيلة الستخدامها من قبل المهندسين لتوليد متتالية –اعـتمادا علـى دراسة تحليلية لنظرية متتاليات : خالصـة .رضينم أو لكال الغ-لتطبيقها في مجال ما ، او لفحص متتالية م من عدد الوحدات واألصفار ، طول المتتالية ، زمن دورة النبض ن -ان مجمـوع البرامج المطورة تمثل كل خواص متتاليات سيميولنك للرموز المطلوبة ان هذه المجوعة المبسطة للبرامج طورت باستخدام ماتالب. وكذلك خواص االرتباط الذاتي لمتتالية النموذج المطور كفؤ من ناحية الكلفة ، كما ان الملفات الخارجة من نماذج سيميولنك فان استخدامها ان. وكذلك القوالب المطلوبة . من قبل أي برنامج أو طريقة نمذجة abstract: based on an analytical study of the theory of m-sequences, a tool is developed to facilitate practicing engineers to either generate m-sequence for its application, or to test applied msequence, or both. the developed test–kit simulates all the properties of m-sequences including number of 1s and 0s, the run lengths, pulse periods as well as autocorrelation properties. this simplified tool is developed using matlab–simulink with required codes as well as desired blocks. the model is cost-effective and the output files of the generated simulink models can be utilized in any software program or simulation procedures. keywords: lfsr, msequence, pn codes, stream cipher, run length 1. introduction the m-sequences are of great importance in many fields of engineering and sciences. cryptography is the most prominent of these applications. one important way of generating such sequences is via linear feedback shift registers (lfsrs). in cryptography, m-sequences are used in two ways; one for designing simple forms of encrypting systems and, the other for selecting cryptographic keys (pless, 1977; konheim, 1981; meyer and matyas, 1982; barker, 1984; siegenthaler, 1985; rueppel, 1986 and 1991; davis et. al, 1994; schneier, 1996; diffie and hellman,1996; golic, 1998 and 2000; and ahmad et. al, 2001). apart from the use of m-sequences as stream ciphers, in crypto-security, they have also found a wide range of applications including error control, coding and spread spectrum communications (shannon, 1963; neumann, 1963; massey, 1969; newbridge microsystems, 1992; glaise, 1997). table1 below shows a few of such practical applications of m-sequences. the table also depicts the used lengths of the m-sequences and the sizes of the corresponding lfsrs which generate them. besides these, there are numerous other applications of m-sequences as briefly summarized below: 147 mailto:afaq@squ.edu.om mailto:mufeed@omantel.net.om a. ahmad, m. j. almushrafi, and s. al-busaidi 1. m-sequences have shown more effective probing signal than traditional gaussian white noise for studying nonlinear biological systems (chen et. al, 1996). 2. for computer and video games, the m-sequence generator is a central component (meyer, and matyas, 1982; newbridge microsystems, 1992 ; and moore, 1994). table 1: specifications of systems using m-sequences system application model length of m-sequence size of lfsr crc-12 4095 12 crc-16, ccitt 65535 16* cyclic redundancy check autodin-ii 4294967295 32 ss-7 127 7 ss-13 8191 13 radio amateurs (spread-spectrum) ss-19, a5 i 524287 19* a5 ii 4194303 22 a5 iii 8388607 23 cellular telephone (european) a5 iv 131071 17 atm networks crc-32 4294967295 32 gps satellite gpss – i, gpss ii 1023 10* * the lfsr sizes are same but each has different structures. furthermore, many fields of research (e.g. physics and even finance) are increasingly relying on large computer simulations to study phenomenon that cannot be observed directly for obvious reasons. in these circumstances, the use of m-sequences is an alternate validation methodology to avoid an unforeseen subtle statistical interaction between the m-sequence generator and the properties of simulated phenomenon (brillinger, 1981; vattulainen et al., 1994; and brothertonratcliff, 1995). as it is evident from the above-mentioned facts that the study of the art and the theory of the generating and applying of m-sequences are becoming essential for engineers and scientists in this era of information technology. moreover, the testing of m-sequences is rather becoming an updated task of system engineers and scientists rather than acquiring the knowledge of simply using the m-sequences. a lot of research papers are available in the literature which deals with the state of art of generating and testing of m-sequences by adapting different approaches (moore, 1994; brillinger, 1981; vattulainen et. al., 1994; tausworthe, 1965; geffe, 1973; blum et. al., 1986; micali and schnorr, 1991; krawczyk, 1992; l’ecuyer, 1992; entacher and leeb, 1995; golomb, 1982; knuth, 1982). this paper presents a new, simple and systematic procedural study of properties of msequences. the state of generating as well as testing of such sequences is also considered in this paper. further, based on the study of the properties of m-sequences a simplified tool is developed using matlab-simulink for generating and testing of such sequences. the model is costeffective and the output files of the generated simulink models can be utilized in any software program or simulation procedures. the developed test-kit has an attribute of either generating and testing a generated sequence and declaring it as m-sequence or failing to be m-sequence and suggests the change of the lfsr structure. it can also load / read / register the so-called msequence and then tests it for its pass / fail of being m-sequence. 2. theory of lfsr the m-sequence generator the idea of randomness reflects the impossibility of predicting the next bit of the sequence. if a generated sequence, ((s of symbols, ; .....),...s,ss) ini 21=∈ is ni ∈ from the finite field gf (2 n-1), 148 simulation pf m-sequence’s properties through matlab-simulink is not matching all the previous ones, it is called a pseudo-random or pseudo-noise (pn) sequence, the other name of the m-sequence. pseudorandom sequences are the only known sequences that satisfy these properties and are generated by lfsrs, (golomb, 1982; knuth, 1982). the lfsr most often implemented through hardware designs, is the basis of stream ciphers and other applications. in an lfsr a string of bits is stored in a chain of memory cells, where the clock pulses advance the bits towards its next succeeding memory cells. the xor of certain positions of the cells is used to produce the new bit in the string for each clock pulse with the condition that the last cell position is always used in the xor process. if each of the memory cells are initially not loaded (initial condition) with 0s, the produced sequence will cycle through a period of more than one. the produced sequence could be cycled through its maximum periodicity of 12 −= nt , where n is the number of the memory cells used in the lfsr. this maximum periodicity of the sequence can only be achieved through xor-ing only some combinations of a few particular positions of memory cells of the lfsrs. a diagram shown in figure 1, illustrates an lfsr consisting of 11 memory cells, where a combination of the memory cells 2nd and 11th is xor-ed to produce the new bits in the string of the sequence at each clock pulse. the sequence produced by this particular structure of the lfsr of figure 1 has periodicity of 2047. to make it more readable the following definitions and illustrations are given below: definition 1 the structure of an lfsr described by its xor-ed positions in polynomial form is termed as characteristic polynomial of the lfsr. for example the structure of lfsr of figure 1 is described by characteristic polynomial c11(x) = 1 + x2 + x11. 1 2 3 4 5 6 7 8 9 1 0 1 1 x o r x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 1 0 x 1 1 m sequence (binary form) scope (wave form of m-sequence) xor figure 1. an 11-bit lfsr. definition 2 the characteristic polynomial of a structure based on an n memory cells lfsr, which generates a sequence of maximum periodicity ( 12 −= nt ), is termed primitive polynomial. definition 3 if the produced sequence generated by an lfsr has maximum periodicity ( 12 −= nt ), then that sequence is known as m-sequence. 149 a. ahmad, m. j. almushrafi, and s. al-busaidi example 1 let us consider a 3-bit lfsr, described by a characteristic polynomial, c3(x) = 1 + x2 + x3. have the initial loadings as all 1s. then the generated sequence by this lfsr will be 0100111, which is of length 23 – 1; thus, the generated sequence is an m-sequence, whereas the characteristic polynomial c3(x) = 1 + x2 + x3 is primitive. 3. properties of m-sequences statistical tests on m-sequence can be performed to provide a quantitative measure of randomness. they measure the relative frequencies of certain patterns of 0s and 1s in the sequence si (golomb, 1982; knuth, 1982). we give below, the systematic study results of the properties of m-sequences. property 1 in every period of m-sequence generated by an n-bit lfsr, the total number of 1s will be equal to . 12 −n property 2 in every period of m-sequence generated by an n-bit lfsr, the total number of 0s will be one less than number of 1s i.e. number of 0s will be equal to 12 1 −−n . property 3 a period of m-sequence generated by an n-bit lfsr, has an occurrence of 1s in succession. n property 4 a period of m-sequence generated by an n-bit lfsr, does not have any occurrences of ( )1−n 1s in succession. property 5 a period of m-sequence generated by an n-bit lfsr, has an occurrence of , 0s in succession. )1( −n the term run may in general be defined as a succession of items of the same class. in a period of m-sequence the distribution of sequential occurrences of groups of 1s, and 0s (runs property for1 ), is governed by a rule presented in the form a following theorem: 2−≤≤ nx theorem 1 in a period t of m-sequence generated by an n-bit lfsr, there will be runs of (12 −x 1−− xn ) 1s, as well as 0s, for1 . 2−≤≤ nx example 2 figure 2 shows a lfsr simulated using simulink – matlab, whose degree of polynomial is n = 5, has characteristic polynomial (1 , initial condition (11111), and generates the m-sequence [s] that has period 31 (i.e. 2 )53 xx ++ 51). the output file of m-sequence in binary form is given as below (equation 1) whereas the oscilloscope waveform is shown in figure 3. 1111100011011101010000100101100 (1) 150 simulation pf m-sequence’s properties through matlab-simulink 1 2 3 4 5 6 7 8 9 1 0 1 1 x o r x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 1 0 x 1 1 m sequence (binary form) scope (wave form of m-sequence) xor figure 2. an implementation of a 5-bit lfsr with characteristic polynomial (1 + x3 + x5) using matlab – simulink. the properties 1 – 5, and theorem 1 can be tested for the above sequence of equation (1). for better explanation, the test result is presented below in the form of the table 2. table 2: run counts / total number of 1s and 0s. frequency of runs 1 0 0 1 1 1 2 2 4 4 total of 1s total of 0s succession of groups of 1s and 0s 5 1s 5 0s 4 1s 4 0s 3 1s 3 0s 2 1s 2 0s 1 1s 1 0s 16 15 property 6 the property of m-sequences – to function as pulse generator: it is also interesting to note that the m-sequence generates pulses of different frequencies. the study also, reveals that the pulse width and frequency of different pulses have definite relation with the others (see figure 3). table 3, describes this property for an m-sequence of periodicity 2n-1 with assumption that the clock pulse of lfsr has time period t. table 3: pulses generated in m-sequence. number of pulses 1 1 2x-1 ; for 21 −≤≤ nx 2x-1 ; for 21 −≤≤ nx pulse width nt (n-1)t (n-x-1)t (n-x-1)t nature of pulse active high active low active high active low 151 a. ahmad, m. j. almushrafi, and s. al-busaidi property 7 the property of auto-correlation of m-sequences: to study the statistics and behaviors of m-sequences, it is important to analyze them through their correlation functions. correlation function of two sequences can be described as the comparison of two sequences to see how much they correspond with one another. various parameters effect the correlation of two sequences including the length of sequence, phase between the sequences, and clock rate of lfsr. the act of correlating a signal through all variations of itself is known as autocorrelation. the autocorrelation function, ac (k) of an m-sequence where, n = 1 to 2.....),...,)(( 21 ini ssss =∈ n-1 can be given for its kth shift as: ki n i i ssn kac + = ∑= 1 1 )( ; 0 1−≤≤ nk (2) where, si is the value of the ith position of the m-sequence. figure 3 (a). continuous waveform of generated m-sequence of figure 2. figure 3 (b). discrete waveform of generated m-sequence of figure 2. theorem 2 the autocorrelation function of an m-sequence reaches a maximum of 2n-1 at zero shifts. for other shifts (1 ) its value will be equal to –1. 2−≤≤ nk 4. a test–kit for m-sequence generator using the simulink matlab (weizheng wang, 1997), a test – kit, shown in figure 4 is developed to test the properties 17, and theorems 1 – 2. the developed kit consists of two separate counters one which monitors the counting of total numbers of 1s and 0s. the second counter monitors the run length properties of the m-sequence. there are two scopes provided in the model of the test–kit. they are dedicated to provide the waveforms of the autocorrelation function and of m-sequence itself. a provision is also made to load the binary form of the m-sequence. all 152 simulation pf m-sequence’s properties through matlab-simulink the counters are simulated based on the algorithms to check the desired counts of runs. the developed kit reads the outputs of the second counter as in table 4. table 4: outputs of second counter output number (function) output number (function) out1 runs of 1 – 1s; out3 runs of 2 – 1s; out5 runs of 3 – 1s; out7 runs of 4 – 1s; out9 runs of 5 – 1s; out11 runs of 1 – 0s; out13 runs of 2 – 0s; out15 runs of 3 – 0s; out17 runs of 4 – 0s; out19 runs of 5 – 0s; in1 no. of 0's no. of 1's counter for counting num ber of 1s and 0s m -sequence (binary form )lfsr` s output scope (wave form of m -sequence) in1 out1 out2 out3 out4 out5 out6 out7 out8 out9 out10 out11 out12 out13 out14 out15 out16 out17 out18 out19 out20 run length m easurem ent countert 1 2 4 1 1 2 4 0 1 16 15 0 figure 4. a implementation of test-kit using simulinkmatlab 5. results and discussions we run the developed matlab-simulink model for the generated sequence of figure 2. the results for the counts of number of 1s and number of 0s as well as run lengths can be observed (according to table 4); as it is monitored through figure 4. the observed values are identical as demonstrated in table 2, which verifies the properties 1-5 and theorem 1. figure 3 is the output of 153 a. ahmad, m. j. almushrafi, and s. al-busaidi the scope, which is nothing but the wave–form of the generated m-sequence. the study of this wave–form reveals that the pulse properties are according to the rules stated in table 3. the output of another scope is shown in figure 5. it can be visualized through figure 5 that the peaks of autocorrelation values (ac (k); equation 2) are 31 at zero shifts, and for other shifts the values are –1, which verifies the theorem 2. further, it can be seen that it repeats in each cycle of the generated m-sequence. the result is satisfying the autocorrelation property of the m-sequence as given in equation 2. 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 5 0 5 1 0 1 5 2 0 2 5 3 0 3 5 a c (k )m ag ni tu de o f a ut oc or re la tio n fo r kth s hi ft of m -s eq ue nc e k t h s h i ft s o f m s e q u e n c e ( o f f i g u r e 2 ) figure 5. autocorrelation property of m-sequence of figure 2. thus, based on a systematic and procedural study of the theory of m-sequences we developed a tool to help the practicing engineers to either generate m-sequence for its application or to test applied m-sequence or both. the study presented in general in section 1 and in particular in table 1, reveals how important an m-sequence is. we tried to provide the knowledge of generating and testing of m-sequences with the least mathematical involvements to make the paper more suitable for general readers and especially for practicing engineers in the area of computer and communication. since the security is a vital issue in this age of information technology, and finally, it seems that the security responsibility has to come in any form on the shoulders of practicing engineers of all fields to avoid 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integrity, editor – g. simmons, ieee press, 1991, pp. 65-134. schneier, b., 1996. ‘applied cryptography: protocols, algorithms, and source code in c,’ john wiley & sons. siegenthaler, t. 1985. ‘decrypting a class of stream ciphers using ciphertext only’, ieee trans. on computer, vol. c-34, no.’1. 155 a. ahmad, m. j. almushrafi, and s. al-busaidi shannon, c.e., 1963. ‘the mathematical theory of communication,’ university of illinois press. (originally from: bell system technical journal, july and october 1948). tausworthe, r.c., 1965.random numbers generated by linear recurrence modulo two, mathematics of computation, 19: 201-209. vattulainen, i., ala-nissila, t., and kankaala, k., 1994. physical tests for random numbers in simulations, physical review letters, vol. 73, number 19, 7, pp. 2513-2516. weizheng wang, 1997. ‘simulink (user’s guide – version 2),’ the mathworks, inc. received 27 june 2001 accepted 22 september 2001 156 simulation of m-sequence’s properties through mat a. ahmad, m. j. al-mushrafi and s. al-busaidi department of information engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman. email: afaq@squ.edu.om, mufeed@omantel.net.om, albusaid@squ.edu.om. abstract: based on an analytical study of the the this paper presents a new, simple and systematic procedural study of properties of m-sequences. the state of generating as well as testing of such sequences is also considered in this paper. further, based on the study of the properties of m-sequences a theorem 1 weak complexes of sulfur compounds with halide ligands science and technology, special review (2000) 31-53 © 2000 sultan qaboos university 31 weak complexes of sulfur compounds with halide ligands salama b. salama* and saad wasif** *department of chemistry, college of science, sultan qaboos university, p. o. box 36, al khod 123, muscat, sultanate of oman. **university of toronto, canada دراسة للمعقدات بين مركبات الكبريت وأيونات الهالوجين سالمة بطرس سالمة و سعد واصف مع أيونات sobr2, so2cl2, socl2, so2ثالثين عاماً الماضية تمت دراسة تفاعالت مركبات الخالل في : خالصة so2cl2-x فأمكن الكشف عن وجود المعقدات -scn-, i-, br -, clالهالوجين -, sobr2-x -, socl2-x -, so2-x hfوجميعها معقدات يستحيل فصلها من المحاليل إلنخفاض طاقة تكونها -x-= cl-, br-, i-, scnحيث نجد أن o ∆ ولذا كان االعتماد على إثبات وجودها من طيف االمتصاص لكل منها في المدى kj/mol 6.03,22.51–في المدى ويعتمد ثبات المعقدات آنفة الذكر على طبيعة المذيب المستخدم للدراسة، ورقم االستقبال 380nm – 290nmالطيفي لمركب الكبريت وعلى قدرة أيونات الهالوجين على المنح االلكتروني للكبريت وكذلك على درجة حرارة التفاعل موضع -:ما نجد في التفاعلالدراسة ولقد أمكن دراسة تفاعالت إحالل أيونات الهالوجين مثل so2-i + cl = so2-cl + i وقد تمت دراسة تفاعالت إحالل لجميع ) درست بواسطة أشعة الليزر ( 1010s-1وتحدث بسرعة عالية تصل إلى المدى .خرالمعقدات آنفة الذكر ويعتمد مدى اإلحالل األيوني على المذيب المستخدم وطبيعة األيون الذي يحل محل األيون اآل so2-xوتنتمي مركبات في وسط الهرم وتعتمد زاوية s في قمة الهرم وذرة -x هندسياً إلى العائلة الهرمية حيث تقع . -xالهرم على طبيعة األيون abstract: this review summarizes the study of the formation of so2-x -, socl2-x -, sobr2-x -, so2cl2-x complexes (x= cl-, br-, i-, and scn-) in pure and mixed solvents of acetonitrile and dimethylsulfoxide over the past 30 years. spectrometry (290nm-380nm) was the principal technique used for the investigation, since the enthalpies of formation ∆hf o of the above complexes are low ( -6.03  -22.51 kj/mol ). the stability of the complexes depend on the nature of the solvent, acceptor properties of the sulfur compounds, the donor properties of the halide ions and the temperature of the reaction. also, it was found that the extent of the iodide ion replacement reactions by the other halide depends on the nature of the solvent and the halide ions. so2-i + x → so2-x + i the structures of so2-x compounds are pyramidal, with xat the top of the pyramid, the s atom at the center, and the angle depends on the nature of the halide ion. salama and wasif contents 1. introduction 32 2. detection, stoichiometry and stability of so2-x -, socl2-x -, and so2cl2-x complex species 33 2.1 detection of sulfur complex species 33 2.2 stoichiometry and complex species 34 2.3 stability constants of complex species 34 2.4 thermodynamic constants of so2-x –, socl2-x – and so2cl2-x – 34 2.5 the donor-acceptor nature of the complex species 36 2.6 correlation of the order of stability constants of different complexes with donor-acceptor properties 37 3. solvent effects on stability of so2-x –, socl2-x – and so2cl2-x – 38 3.1 pure solvents 38 3.2 mixed solvents: (mecn-dmso) 39 3.3 the so2-x – species 40 3.4 the socl2-x – and so2cl2-x – series 40 3.5 vertical correlations in table 9 41 3.5.1 the iodide complex series 41 3.5.2 the bromide and chloride complex series 41 3.6 evidence for solvent-solvent interactions 41 3.6.1 spectroscopic 41 3.6.2 vapor-pressure, viscosity, and excess functions from refractive index, dielectric constant and volume 42 3.7 a thermodynamic view of solvent effects on the stability of so2-x -, socl2-x and so2cl2-x 44 3.7.1 the significance of ∆gf o of complexes in relation to solute-solvent interactions 44 3.7.2 the dependence of ∆hf o and ∆sf o of complex species on solvent composition 45 4. ligand replacement reactions 46 4.1 correlation of stability constants with ligand replacement 48 4.1.1 the cl--ireaction 48 4.1.2 the br––i– and scn-–ireactions 49 4.2 the role of solvents in replacement reactions 49 4.3 replacement reactions in mixed solvents 50 5. structure of so2-x 50 6. conclusion 51 7. references 51 1. introduction throughout the past 30 years there has been a growing interest in the field of sulfur compounds-halide ligands chemistry. the motivation for this interest has undoubtedly arisen from various sources. witeckowa and witok (1955) investigated the reaction between so2 and iodine in the gas phase and in solutions by spectrophotometric and kinetic techniques. they suggested that the interaction between hi and so2 in aqueous solutions is due to dipole-dipole interaction. burke and smith (1959) studied the molecular complexes between hf and so2 by infrared spectroscopy. jander and tuerk (1962; 1963) studied the adduct of iodine with h2s in dichloroethane at –95 oc. the low enthalpy of formation (∆hf o = -31.8 kj /mol) was taken as indication of the charge transfer nature of the adduct formation. burow (1970) studied 32 weak complexes of sulfur compounds the solvate formation between so2 and cl -, br-, and iligands in liquid so2. gutmann (1956) isolated a number of adducts of socl2 and so2cl2 with halide ligands. sandhu et al (1960; 1962) discussed the tendency of so2cl2 to form adducts with lewis acids and lewis bases. salama and wasif et al (1971; 1973; 1994) studied the interaction of some organic sulfur compounds and so2, socl2, so2cl2, & sobr2 with cl-, br-, i-, and scnligands in acetonitrile (mecn), dimethylsulfoxide (dmso) and water (for so2 species only). the collated data are summarized in four parts: 2. detection, stoichiometry and stability of so2-x -, socl2-x -, and so2cl2-x complex species. 3. effects of solvents on the stability of complex species. 4. ligand replacement reactions in complex species and factors which affect them. 5. structure of so2-x species. 2. detection, stoichiometry and stability of so2-x-, socl2-x-, and so2cl2-xcomplex species 2.1 detection of sulfur complex species figure 1 shows the absorbance peaks of mixtures of so2 with (a) tetramethylammonium iodide, (b) tetramethylammonium bromide and (c) tetramethylammonium chloride. table 1 includes the absorbance peaks of sulfur compounds, so2, socl2 and so2cl2 with tetramethylammonium halides in which the halide was in abundance of the sulfur compound and in acetonitrile (mecn) solvent. similar peaks were obtained in dmso and water confirming earlier studies (jander et al., 1937; seel et al., 1955). figure 1. absorbance peaks of so2-x species. table 1. λmax in mecn at 298°k sulfur compound s + x– (s) cl– br– i– so2 (280)nm socl2 (280) so2cl2 (275) 292 292 293 320 322 322 380 382 375 33 salama and wasif 34 2.2 stoichiometry and complex species job’s (1928) and asmus’s (1960) methods were used to determine the complex stoichiometry. the former gave the empirical formula while the latter gave its molecular formula. the two methods showed that all complex species were of 1:1 type irrespective of the solvent used (mecn or dmso). 2.3 stability constants of complex species if the complex formation is represented by the equations so2 + x – = so2-x – (1) socl2 + x – = socl2-x – (2) so2cl2 + x – = so2cl2-x – (3) s compound + halide ligand = complex species then the equilibrium constants for reactions (1) – (3), which will be defined throughout this article as stability constants, may be represented by the equation kc = [complex]/[s compound] [x –] (4) where the parentheses represent molar concentration of each species and kc is defined by the units dm 3 mol–1 . the magnitude (or value) of kc is taken as a measure of the ability of the reacting species to associate in a complex. spectrophotometry was the principal technique used to find the concentration of all the terms in equation (4). two procedures (salama et al., 1971) were adopted to evaluate kc: (a) graphical and (b) by calculation from the molar concentrations of reactants and products. both methods (a & b) depend on the absorbances of individual species before and after they are mixed together. table 2 (salama et al., 1971) includes kc values for so2-x –, socl2-x – and so2cl2-x – in mecn at 293° or 298°k. in most cases the difference between kc values by the graphical and calculation methods does not exceed 5% which may be taken as the limit of the experimental error. the constancy of the kc data is further evidence to confirm that all the complex species were of a 1:1 type (salama et al., 1971). table 2. stability constants of so2-x –, socl2-x – and so2cl2-x – in mecn at 293° or 298° k s compound so2 socl2 so2cl2 halide ligand i– br– cl– i– br– cl– i– br– cl– kc(graphical) 37.9 192 348 152 242 367 78 40.6 10.6 kc (calculation) 38.5 190 363 150 241 362 77 41 10.2 temp.°k 298 293 293 298 298 298 298 298 298 2.4 thermodynamic constants of so2-x –, socl2-x – and so2cl2-x – table 3 includes kc data for so2-x –, socl2-x – and so2cl2-x – over a range of temperatures and their relevant thermodynamic constants. the data in table 3 point to a weak association between the sulfur compounds (electron acceptors) and the halide ligands (electron donors) of a charge transfer nature (salama weak complexes of sulfur compounds 35 et al., 1971; ketelaar et al., 1952; benesi et al., 1949; drago, 1959; rossotti et al., 1969; andrew et al., 1961). since the solvents used are polar, they possess varying tendencies to solvate the species in solution ( ions, molecules and complex species) and although we are mainly concerned with complex species in acetonitrile, yet a simple interpretation of such enthalpy data will be complicated by solvation and/or dipole interaction. comparison of the enthalpy data for the different complex species in table 4 cannot lead to linear correlations. table 3. thermodynamic constants of so2-x –, socl2-x – and so2cl2-x – in mecn complex species kc dm 3mol–1 –∆gf o kj/mol –∆hf o kj/mol –∆sf o j/k/mol so2-i – 37.9(298),34.4(303),30.8 (308) 8.99 17.5 28.5 so2-br – 260(283), 192 (293), 137 (303) 12.7 22.4 32.8 so2-cl – 519(284), 400 (293), 348 (303) 14.7 15.1 1.34 socl2-i – 190 (288), 150 (298) 12.2 16.9 15.1 socl2-br – 276 (288), 241 (298) 13.6 9.82 –12.6 socl2-cl – 447(288), 362 (298), 264 (308) 14.6 15.4 2.72 so2cl2-i – 86 (288), 77 (298), 71 (308) 10.8 6.01 -15.9 so2cl2-br – 45 (288), 39 (298), 37 (308) 9.20 10.7 4.98 so2cl2-cl – 12(288), 10.5 (298), 9.3 (308) 5.76 7.82 6.90 of the components taking part in the formation of these complexes only the acceptors (sulfur compounds) have uv absorption peaks, so2 (280nm), socl2 (280nm) and so2cl2 (275nm) (friedman, 1967). the appearance of new peaks due to the formation of the complex species arises from donor acceptor interactions. these result in spectral shifts for the acceptor which must be a function of the donor character of each halide ligand. an attempt was made to correlate such spectral shifts with the reversible potential for: e + x = x table 4. stability constants of so2-x -, socl2-x -, and so2cl2-x in mecn at 298ok cl– br– i– so2-x – 372 160 38 socl2-x – 362 241 150 so2cl2-x – 10.5 41.0 77 the linear plots of figure 2 supplement this assumption for the different species. salama and wasif figure 2. correlation of eo for the reaction e+ x ⇔ xwith acceptor spectral shifts: a, so2-x -; b, so2cl2-x -; c, socl2-x 2.5 the donor-acceptor nature of the complex species in order to understand the nature of these complexes we shall try to rationalize the stability constants data of table 4 with the nature of the halide ligands (donors) and the sulfur compounds (acceptors). table 5 summarizes some important trends (basolo et al., 1958 ; gould, 1960). table 5. physical constants of halide ions. clbri ionisation potential (kj/mol) 1251 1136 1000 electron affinity (kj/mol) 349 325 295 hydration energy of x– kj g-ion-1 356 310 255 polarisability/å 2.3 3.3 5.1 electronegativity 2.83 2.74 2.21 the iodide ion with high polarisability, low electronegativity and easy oxidation is considered to be a soft lewis base (pearson, 1963; day et al., 1969). the chloride ion with low polarisability and high electronegativity is a hard lewis base. the bromide ion is a borderline lewis base. the acceptors include so2 and socl2 in which the oxidation state of sulfur is four and so2cl2 in which it is six. so2 is a borderline lewis acid (pearson, 1963; day et al., 1969). it acts as a base toward bf3 to form the adduct so2-bf3 and as acid towards water. thionyl chloride socl2 is similar to so2 in that it has a lone pair of electrons (3s2) but one of the double bonded oxygen atoms is replaced by two cl atoms. the s-cl bond is more polarized than the s-o bond owing to the higher electronegativity of cl-, and would be expected to act as a stronger lewis acid than so2, or a better acceptor. sulphonyl chloride so2cl2, may be related to so3 (known as a hard lewis acid) (pearson, 1963; day et al., 1969) in the same manner as socl2 is related to 36 weak complexes of sulfur compounds 37 so2, and the order of acid strength is so2cl2 > socl2 > so2. the formation of the present complex species is the result of acid-base interactions between the acceptors and the donors and the order of stability given in table 4 can be discussed on this basis. 2.6 correlation of the order of stability constants of different complexes with donor-acceptor properties table 4 shows that the stability of so2-x – species falls in the order so2-cl – > so2-br – > so2-i –. sulfur (iv) forms coordination compounds owing to the electrofilic and nucleofilic nature of the sulfur atom. the former is due to the availability of the empty 3d electron orbitals and the latter to the presence of a lone pair of 3s2 electrons on the sulfur atom. thus, in such compounds as so2, sulfur acts as a σ-donor only or a π-acceptor. however, the donor-acceptor properties of the sulfur atom are exhibited almost synonymously. if the donor (or ligand) contains d-orbitals of the appropriate symmetry (i.e. not diffuse) back-donation from the sulfur atom to the donor may occur, giving rise to the d-d multiple bonding which will strengthen the ligand acceptor bond. the cl– and br– ions may accept back-donation but this seems doubtful for the i– ion because the d-orbitals become progressively diffuse and less available for backdonation as we go down the halide group. the order of complex stability can be explained on this basis. this interpretation of the stability constants order is supplemented by the classification of the halide ions as hard (cl-) borderline (br–) and soft (i–) bases and of so2 as a borderline lewis acid. the order of stability of the so2-x – complex species would follow the strength of the base and so2-cl – species would be the strongest and so2-i – the weakest, as actually found. we may now consider the socl2-x – species. table 6 includes the ratios of stability constants of so2-x – and socl2-x – species. table 6. stability constants ratios for so2-x – and socl2-x – in mecn i– br– cl– kc(so2-x –)/kc(so2-i –) 1.0 4.0 10.0 kc(socl2-x –)/kc (socl2-i –) 1.0 1.6 2.4 table 4 shows that the order of stability of socl2-x – species is similar to that of so2-x – where cl– > br– > i–. table 6 shows that the stability constants of so2-cl and socl2-i – are nearly of the same order of magnitude but kc (socl2-i -) is merely 4 times greater than kc(so2-i -) and kc(socl2-br –) and kc(socl2cl–) are only 1.6 and 2.4 times greater than kc (socl2-i –) which calls attention to new factors responsible for the observed change in ratios. the order of stability constants ratio of socl2-x – species shows that as in the case of so2-x – the chloride species is the most stable and the iodide is the least stable. this order suggests that the nature of association between the cl– and so2 is much the same as with socl2. back-donation may be considered to be the factor contributing to the stability of socl2-x – species. in socl2 the electrophilic nature is enhanced over so2 by the replacement of one oxygen atom by two chlorine atoms and the d-orbitals of sulfur are more exposed for coordination because the electron cloud is removed by the electronegative chlorine atoms, and this makes socl2 a better lewis acid than so2. although the halide ions were classified by pearson (1963) as lewis bases of varying strengths and such classification could account for the order of stabilities of so2-x – species, the situation may be different with socl2. the increased acceptor character does not appear to have changed or to have affected dramatically the nature of association with the cl– ligand. for the i– ligand this increased acid character appears to have increased the basicities of the i– and br– ligands relative to that of the cl– , so socl2 appears to be leveling up the basic character of the i– and br– ligands towards that of the cl– ligand. this leveling of relative basicities of the halide ligands appears to be another factor which determines the ratios of table 6. salama and wasif 38 a third factor relevant to table 6 is the increased ionic radii and polarisabilities of the donors. table 5 shows that the i– ligand is the most polarisable of the halide ions. other factors remaining equal, an increase in the polarisability of the donor would make the donor-acceptor interaction stronger. the dipole moments of so2 and socl2 are 1.61 and 1.60d respectively. if polarisability was the only factor one would expect the iodide complex to be the most stable. this was not so, indicating that back-donation is a still more important factor in deciding the nature of association of the halide ligands with socl2. sulphonyl chloride, so2cl2, is the strongest acceptor of this group of sulfur compounds; it has the highest dipole moment (1.86 d). the d-orbitals of sulfur here are the most exposed for coordination than in the other acceptors. the order of stability of its halide ligand complexes is: so2cl2-i – > so2cl2-br – > so2cl2-cl – which is the reverse of so2-x – and socl2-x species (table 4) suggesting that back-donation cannot be strong in the formation of so2cl2-x – complexes. the increased acidity of so2cl2 seems now to be very important. in the presence of such a relatively strong lewis acid the three lewis bases appear to lose their identity and are of merely equal strength. thus the leveling effect observed for socl2 is probably more strongly displayed. in protonic systems this leveling explains why benzoic acid and sulfuric acid are equally strong in liquid ammonia while water, alcohol, ketones…. etc are equally strong bases in pure sulfuric acid (bell, 1965; waddington, 1965). it appears that increased polarisability towards i–, the increased polarity towards so2cl2 and the increased leveling effect can account for the order of stability constants observed for socl2–x complex species. the effect of polarisability of the halide ligands on the order of stability of some metal complexes has been reported (gould, 1960). we may conclude that as the acceptor is changed from so2 to so2cl2 the nature of association also changes. with so2 dπ dπ multiple bonding from back-donation makes its association with halide ligands quite strong but with so2cl2 the dipole-dipole interaction seems to be a weaker force of association, as shown from ∆hf o values in table 3 and the kc values of table 4. 3. solvent effects on stability of so2-x–, socl2-x– and so2cl2-x– 3.1 pure solvents solvent molecules are not impartial in chemical processes and the extent to which they participate sometimes overshadows that of the other species in the reaction media. this is because the solvent represents the environment in which a chemical reaction takes place and in most cases plays the role of a donor or acceptor. the role of environment and solvent effects on chemical reactions has been discussed by a number of workers (bell, 1965; waddington, 1965; frost et al., 1961; benson, 1960; amis, 1965; gutmann, 1967, 1971; grunwald, 1949) . the kc values for so2-x –, socl2-x – and so2cl2-x – in mecn, dmso and water recorded in table 7 illustrate the solvent effects. table 7. stability constants for so2 –x –, socl2-x – and so2cl2 –x – in mecn, dmso and water at 298° k. (a = mecn, b = dmso, and c = water) cl– br– i– x– a b a b c a b c so2-x – 372 26 160 21 0.22 38 12 0.36 socl2-x – 362 18 241 21 150 35 so2cl2-x – 10 36 41 14 71 6 weak complexes of sulfur compounds comparison of kc data is limited to the values in mecn and dmso. with the exception of so2cl2-x species, the stability constants of different complexes decreased by a factor of nearly 20 in dmso as compared to mecn which is shown from the data in table 8. table 8. comparison of stability constants in mecn and dmso kc(mecn)/kc(dmso) at 298 ok. x cl br i so2-x 15 8 3 socl2-x 20 11 4 so2cl2-x 0.3 3 13 the data in tables 7 and 8 express significant changes in complex stabilities between mecn and dmso, as the kc values are lower in dmso than in mecn. there are at least two possible roles that can be played by dmso (or water) in affecting the stabilities of the complex species. it may solvate the halide ligands, which prevents them from interacting with the acceptors, i.e. sulfur compounds, or it may act as a competing acceptor, i.e. competes against so2, socl2, and so2cl2 and thus makes a complex species with the ligands and perhaps it may play the two roles depending on the environmental conditions. table 8 shows some horizontal and vertical trends. the data in column (1) show maximum decrease in kc for so2-cland also for socl2-clin dmso. this can be attributed to solvation of the clligand and possibly ion-dipole interaction in view of the high dipole moment of dmso (4.3d). in these species, stabilization results from back-donation (mines et al., 1972; chadwick, 1973) from sulfur 3d-orbitals to the donor ligand. minimum effect is shown for so2cl2-cl where kc(mecn)/kc(dmso) equals 0.3, which shows the importance of polarization and not back-donation in stabilizing so2cl2-cl species. in column (2) ratios for so2-br – and socl2-br – are nearly half those reported for the cl– species, which is regarded as reflecting the lower tendency to solvation of the br– ligand as compared to cl– by dmso. in column (3) the ratios of so2-i – and socl2-i – are nearly ¼ of the values for the cl– species. this shows the lower tendency of i– ligands to solvate and this is not unexpected due to the larger ionic size of i–. the horizontal trends in so2-x – and socl2-x – appear to agree with the conclusion that solvation of the donor ligands by dmso is important in decreasing the stability constants compared with those in mecn and that this lowering is maximal with cl– ligands and minimal with i– ligands. the kc values in water appear to support this view. for so2cl2-x – the horizontal tend is reversed compared to that shown by so2-x – and socl2-x –. this supports the view that the nature of association in so2cl2-x – is different from that in so2-x – and socl2-x – (salama et al., 1971), the former being mainly ion-dipole interaction and the latter back-donation as mentioned earlier. the lowering in stability constants of so2cl2-i and so2cl2-br is evidence that iondipole interaction is particularly strong between dmso and iodide ion (salama et al., 1991), which is understandable in view of the higher dipole moment of dmso compared with so2cl2. the data in table 8, column (3) for the iodide species show that ion-dipole interaction outweighs solvation, while those in column (1) show that solvation has the greater effect. 3.2 mixed solvents: (mecn-dmso) few workers have reported on chemical processes in mixed solvents and also specified the role of solvent. the work to be outlined reports on the stability of so2-x –, socl2-x and so2cl2 -x – in mecndmso mixed solvent, and table 9 (salama et al., 1978) includes the kc data of these complex species in mecn, dmso and mixtures of the two solvents at 298º k. the data in columns 2 and 6 were quoted from table 2. one feature appears throughout table 9. the stability constants of all complex species, at 298ºk, vary with solvent composition. in order to rationalize 39 salama and wasif 40 the kc values we shall discuss the horizontal and vertical trends in table 9. table 9. stability constants for so2-x -, socl2-x -, and so2cl2-x in mecn, dmso, and their mixtures at 298ok complex dmso mecn+dmso mecn 1:3 1:1 3:1 so2 -i – 12.1 14.1 24.7 36.7 37.9 so2 -br – 21.0 14.5 24.1 40.1 40.1 so2 -cl – 26.0 35.5 50.0 52.4 372.0 socl2 -i – 35.0 40.2 58.9 223.5 150.0 socl2 -br – 21.0 22.9 34.2 71.7 241.0 socl2 -cl – 18.0 66.7 73.8 113.0 362.0 so2cl2 -i – 6.0 30.1 50.1 142.2 76.0 so2cl2 -br – 14.0 15.5 24.6 36.2 41.0 3.3 the so2-x – species the kc values of so2-i – change gradually between the limits set for mecn and dmso as the solvent composition changes. in mecn-dmso solvent (3:1) the kc value is reduced by 2.7% compared with that in 25% dmso solvent. for so2-br – and so2-cl – the kc values are reduced in the same solvent by 75% and 85% respectively. (the kc value in mecn is taken as a reference in each case). solvation of br – and cl– ligands by dmso is clearly greater than that for the i– ligand. a similar conclusion was reached when kc for the same species were determined in mecn and dmso (salama et al., 1975). to correlate the variations in kc values with solvent composition it should be remembered that the molecules of different solvents can act as donors and/or acceptors. even if both solvent molecules have donor or acceptor character a slight difference in the donor or acceptor properties between different solvent molecules will invite donoracceptor interaction between them. the nature of such interactions in non-protic solvent mixtures such as mecn-dmso has not been studied before (waddington, 1965). over a wide range of molecular ratios of mecn and dmso one expects such interactions to exhibit different patterns which depend on the structural and geometrical characters of the molecules. we shall call this solvent-solvent interaction and may define it in terms of donor-acceptor interaction or perhaps association which vary with solvent composition. such solvent-solvent interactions may occur at the expense of other interactions in solution. for example in mecn-dmso containing so2 molecules and cl – ligands and so2-cl – complex species the following interactions are likely to occur (a) cl–-dmso, (b) cl–-mecn, (c) so2-dmso, (d) so2-mecn and (e) mecn-dmso. the stability constant of the so2-cl – species is determined by the relative magnitudes of such interactions, a strong cl–-solvent interaction (solvation) would reduce the stability of so2-cl – species, since this steric factor may prevent, to some extent, so2 and cl – from approaching each other for coordination. on the other hand a strong mecn-dmso interaction would allow more so2 to coordinate with cl– ligands and kc values become greater than the limits set for each solvent. the data for so2x – show that mecn-dmso interaction accounts partly for the change in kc with solvent changes. ligand solvation is also important in determining kc values. the kc data show that while the i–-solvent interaction is relatively weak and reduces kc by 2.7% (in 25% dmso relative to its value in mecn) those of cl–-solvent interactions and br–-solvent interactions are much stronger and reduce kc by 85% and 75% for so2-cl –and so2-br – respectively. 3.4 the socl2-x – and so2cl2-x – series the kc values for socl2-cl – and socl2-br – fall between the limits set for mecn and dmso but that for socl2-i – species exceeds the upper limit in mecn by 30% (in 25% dmso solvent). a change in solvent weak complexes of sulfur compounds 41 composition from 50 to 25% dmso is coupled with a sudden change in kc for socl2-i –. it appears that over this critical range of solvent composition the solvent-solvent interaction reaches its maximum. the nature of this interaction is not yet clear but is detectable from vapor pressure measurements (salama et al., 1985). such interactions have freed sufficient i– ligands and socl2 molecules for coordination which makes kc 30% greater than the value in mecn. with socl2-cl – and socl2br – (in 25% dmso solvent) the kc values are reduced by 69% and 71% from the value in mecn. thus, despite strong solvent-solvent interaction the br--solvent and cl--solvent interactions have outweighed solvent–solvent interactions. a similar argument applies to so2cl2-i and so2cl2-br where kc increases by 61% for the iodide species and decreases by 15% for the bromide species. 3.5 vertical correlations in table 9 3.5.1 the iodide complex series although kc values for socl2-i – and for so2cl2 -i – in 25% dmso are 30% and 64% greater than the value in mecn we find that kc for so2-i – is 2.7% less than its value in mecn. such differences in behavior are probably due to differences in the manner in which the i– ligand is coordinated to the three acceptors. the iligand is polarisable with diffuse d-orbitals suitable for ion-dipole interaction. the dipole moment of the three acceptors are in the order so2 (1.61d) socl2 (1.60d) and so2cl2 (1.86d). in 25% dmso solvent strong solvent-solvent interaction favors so2cl2-i – coordination so that the kc value exceeds that in mecn by 64%. the acceptor character of socl2 is enhanced by the replacement of one o atom in so2 by 2 cl atoms and coordination by ion-dipole interaction is relatively stronger with i – than with so2. solvent-solvent interaction helps coordination of socl2 to i and results in a kc value which exceeds that in mecn by 30%. for so2-i – the ion-dipole interaction is probably so weak that is nearly balanced by solventsolvent interaction and kc is slightly reduced by 2.7%. 3.5.2 the bromide and chloride complex series the decrease in the kc values for so2-br –, socl2-br – and so2cl2-br – (in 25% dmso solvent) by 76, 71 and 15% respectively resulted from br–solvent interaction. the difference arises from differences in the modes of coordination of the three acceptors. for so2 and socl2 back-donation is the principal mechanism by which coordination takes place to s(iv) . for so2-br – and socl2-br – solvent-solvent interaction is outweighed by br–solvent interaction and kc is reduced accordingly. for so2cl2-br coordination occurs by an ion-dipole mechanism involving s(vi). the br– ligand, being a borderline lewis base, responds favorably to this mechanism and by its solvation by dmso slightly outweighs solvent-solvent interaction and kc is reduced to a smaller extent than in the other bromides. for so2-cl – and socl2-cl – back-donation is the principal mechanism for coordination. in both species the cl–-solvent interaction outweighs solvent-solvent interaction and kc values are reduced by 85 and 69% respectively. this differing effect on kc might be due to selective solvation in the presence of different acceptors which we may describe as chemical environmental factors. 3.6 evidence for solvent-solvent interactions 3.6.1 spectroscopic using the ir (infra red) techniques, it is found that the s=o vibration band of dmso appears at 1080 cm–1 and on addition of mecn the band is shifted to 1070cm–1. the c ≡ n vibration band of mecn appears at 2250cm–1 and adding dmso at x1 = 0.5 (x1 = mol fraction) the band is shifted to 2240cm –1 (salama et al., 1985). using raman spectra it is found that the s = o vibration band appears at 1044cm–1 and on adding mecn a peak appears at 1062cm–1 while that at 1044cm–1 disappears. for mecn the c ≡ n vibration band appears at 2255cm–1 and on addition of dmso the band disappears gradually. the observed vibrational shifts salama and wasif may be taken as evidence for solvent-solvent interaction through adduct formation of the type represented by figure 3. figure 3. mecn-dmso adduct 3.6.2 vapor-pressure, viscosity, and excess functions from refractive index, dielectric constant and volume further confirmation for solvent-solvent interaction was obtained from measurements of vapor pressure and viscosity of mecn-dmso mixtures. table 10 includes vapor pressure, viscosity, ∆hvap, ∆svap, and ∆hvis, of the mixtures over the whole composition range. table 10. vapour pressures and viscosities of mecn-dmso mixtures 10(a). vapour pressure data 25% mecn t/°c p/mmhg 61.6 58.0 69.0 72.0 75.6 84.0 80.7 99.0 85.7 115.5 50% mecn t/°c p/mmhg 29.0 69.7 34.5 76.1 39.9 95.6 45.0 115.6 49.0 136.3 54.0 163.6 75% mecn t/°c p/mmhg 28.4 78.9 33.1 95.4 38.5 119.4 43.7 147.9 49.4 186.9 80% mecn t/°c p/mmhg 28.4 84.7 33.4 106.5 38.9 134.0 45.1 160.0 51.6 213.0 10(b). viscosity data t/°c 25.0 30.0 35.0 mecn 3.55 3.38 3.30 x 10–4 pas 75%mecn 5.17 4.89 4.73 50%mecn 7.44 7.04 6.68 25%mecn 11.71 10.85 10.16 dmso 19.57 17.88 16.40 42 weak complexes of sulfur compounds 10(c). thermodynamic data for vaporization and viscosity solvent mecn 80% mecn 75% mecn 50% mecn 25% mecn dmso ∆hvap kj/mol 33.2 31.8 33.3 29.1 28.2 52.9 ∆svap j/k/mol 96.0 87.1 91.4 72.9 62.7 95.8 ∆hvis kj/mol 5.48 6.57 7.74 8.24 10.6 13.3 figure 4 shows a plot of ∆hvap and ∆hvis against solvent composition. the plots are not linear and deviate over the composition range 50–70% (maximum deviation which may be taken to indicate solventsolvent interaction). the ∆svap data show a minimum value at 75% dmso suggesting maximum order for the system at this composition with probable formation of mecn-dmso adduct. 0 20 40 60 80 100 %mecn 20 30 40 50 60 e nt ha lp y of v ap or iz at io n/ kj 0 4 8 12 e nt ha lp y of v is co si ty /k j figure 4. plot of enthalpy of vaporization/kj (•) and enthalpy of viscosity /kj (♦) against %mecn the excess functions from refractive index ne, dielectric constant εe and densities ve of mecn-dmso mixtures are given in table 11 (salama et al., 1985). the data in table 11 show that the magnitude of any excess function reaches a maximum at approximately 1:1 composition. this is again taken to indicate solvent-solvent interaction. table 11. excess functions of mecn-dmso mixtures at 298ok 11(a). refractive index (ne) x1 0.1319 0.2676 0.4258 0.6899 0.7836 0.8697 ne 0.0030 0.0076 0.0087 0.0102 0.0065 0.0039 43 salama and wasif 44 11(b). dielectric constant (εe) x1 0.1319 0.2676 0.4258 0.6009 0.6899 0.7836 0.8697 εe 0.5710 0.9540 1.3180 1.4910 1.3680 1.1960 0.8630 11(c). volume (ve). (x1 = mole fraction of dmso) x1 0.1006 0.3066 0.6037 0.7061 0.8083 0.8999 0.9455 ve –0.1300 –0.2523 –0.2519 –0.1773 –0.1275 –0.0876 –0.0486 3.7 a thermodynamic view of solvent effects on the stability of so2-x-, socl2-x and so2cl2-x 3.7.1 the significance of ∆gf o of complexes in relation to solute-solvent interactions: table 12 includes the standard free energies of formation ∆gf o of so2-x and socl2-x in mecn, dmso, and their mixtures. table 12. –∆gf o (kj/mol) of complex species in different solvents at 298ok dmso: mecn dmso 3:1 1:1 1:3 mecn so2-i – 6.19 6.57 8.03 9.00 9.08 so2-br – 7.61 6.74 7.91 9.20 8.49 so2-cl – 8.12 8.95 9.75 10.9 10.6 socl2-i – 8.87 9.20 10.2 13.5 12.5 socl2-br – 7.61 7.82 8.79 10.7 13.7 socl2-cl – 7.20 10.5 10.7 11.8 14.6 the data in table 12 show that for every complex species there are several free energy minima, each corresponding to a different solvent composition. this situation is only possible if a change in the solvent composition affects continuously the coordinating ability of the halide ligand (x–) with the sulfur acceptor (so2 or socl2) and partially hinders them from complex formation and which was described as solvation. preliminary studies (wasif, unpublished work) show that halide ion solvation in mecn and dmso falls in the order cl– > br > i–,which agrees with their ionic radii and charge densities. solvation of the sulfur acceptors was studied in the present work by uv spectroscopy. figure 5 shows the absorbance of sobr2 in (a) mecn, (b) dmso and (c) 1:1 mixed solvent of mecn-dmso. it shows three distinct species which obey beer’s law. the intermediate absorbance of the 1:1 mixed solvent shows that sobr2 forms an absorbing species of intermediate character between the species in dmso and mecn. there are two possibilities in which this could happen: (1) the formation of a constant ratio of the adduct species sobr2-mecn and sobr2-dmso, (2) that sobr2 makes a species with a mixed solvent adduct e.g. (sobr2-mecn:dmso). using ccl4 as solvent the species sobr2-mecn and sobr2-dmso were detectable and their stability constants are given in table 13. the data in table 13 show that solvents mecn and dmso play a competing role against halide ligands in their coordination with the sulfur acceptors. the data also show dmso to have a greater destabilizing role weak complexes of sulfur compounds table 13. stability constants of adducts of mecn and dmso with sulfur compounds at 298°k. a so2 socl2 sobr2 so2cl2 dmso-a 2.82 6.86 3.73 17.79 mecn-a 0.34 0.07 0.11 0.68 for the complex species than does mecn, by its strong ability to solvate the halide ligands and the sulfur compounds. figure 5. dependence of absorbance of sobr2 on solvent mole fraction 3.7.2 the dependence of ∆hf o and ∆sf o of complex species on solvent composition: a second thermodynamic aspect would be to consider the significance of ∆hf o and ∆sf o for complex species in mixed solvents. table 14 includes the standard thermodynamic constants for the formation of the complex species sobr2-cl – and sobr2-br –. table 14 shows that the standard enthalpy of formation varies as the solvent composition changes from mecn to dmso. for sobr2-br – ∆hf o is nearly 10 times greater in mecn than in dmso but for sobr2cl– it is nearly 5 times greater than the value in dmso. such differences in ∆hf o values suggest that the 45 salama and wasif 46 measured enthalpy of formation is a rather complex function. it does not probably represent the heat of formation of the complex species but other heat terms are possibly embodied in this term such as heats of solvation of the halide ligands and sulfur compounds in mecn and dmso. if ∆hf o be taken as a rough measure for the complex stability, then data in table 14 would show that the complex species sobr2-x – (x = cl, br) are more stable in mecn than they are in dmso. a thorough discussion of the significance of ∆hf o data requires a knowledge of the heats of solvation of the different species in both solvents which are not at present available. this situation permits a qualitative discussion of ∆hf o data. since solute-solvent interactions are a dynamically changing process we may expect the magnitude of ∆hsolvation values to change over the solvent concentration range, which is confirmed directly from table 14. with this situation in mixed polar solvents a discussion of ∆sf o values would be difficult to interpret. table 14. thermodynamic constants of sobr2-cl – and sobr2-br – in mecn, dmso and their mixtures at 298ok. dmso: mecn dmso 3:1 1:1 1:3 mecn sobr2-br – kc dm 3 /mol –∆gf o kj/mol –∆hf o kj/mol ∆sf o j/k/mol 12 5.86 1.88 13.4 19 7.36 4.60 9.20 25 8.03 4.60 11.3 32 8.66 20.1 -38.5 203 13.3 19.2 -20.1 sobr2-cl – kc dm 3.mol–1 –∆gf o kj/mol –∆hf o kj/mol ∆sf o j/k/mol 19 7.36 1.88 18.4 36 8.95 10.0 -2.93 40 9.20 9.62 -1.26 79 10.9 16.3 -18.0 100 11.5 10.0 5.02 4. ligand replacement reactions the coordination of different ligands (cl–, br– i– or scn–) with the same sulfur acceptors giving varying stability constants suggested that they are differently coordinated and could accordingly be able to replace each other with the same acceptor. equation (5) shows a general replacement reaction between so2i– and x– (x=cl, br, scn) and figure 6 illustrates a spectrophotometric scan when scn– is added to so2iin mecn (salama et al., 1978). so2-i + x = so2-x + i (5) weak complexes of sulfur compounds figure 6. replacement of i– by scn– in mecn a) no scn–, b) [scn–] / [i–] = 0.4, c) [scn–] / [i–] = 1, d) [scn–] / [i–] = 2 in figure 6 the gradual addition of scn– solution causes a gradual disappearance of the so2-i – peak at 378 nm and appearance of a new peak at 322 nm for the so2-scn – species. table 15 includes the results of the above replacement reactions. table 15. replacement reactions in mecn, dmso and water at 298o k* (a) in mecn reaction 1) cl– + so2-i – 2) cl– + socl2-i – 3) cl– + so2cl2-i – [cl–] : [i–] 0.05(5), 0.10(8), 0.15(12), 0.20(15), 0.30(19), 0.40(23) 0.05(4), 0.10(7), 0.15(11), 0.20(15), 0.30(18), 0.40(22) 0.05(2), 0.10(3.5), 0.15(5.5), 0.20(8), 0.30(10), 0.40(12.5) 4) br– + so2-i – 5) br– + socl2-i – 6) br– + so2cl2-i – [br–] : [i–] 0.05(1.5), 0.10(3), 0.20(5), 0.30(8), 0.40(10) 0.05(2), 0.10(3.6), 0.20(5.8), 0.30(7.7), 0.40(9.3) 0.05(2.5), 0.10(4), 2.20(6), 0.30(8), 0.40(9.4) 7) [scn]– + so2-i – 8) [scn]– + so2cl2-i – [scn–] : [i–] 0.20(–), 0.50(2), 1.0(3), 2.5(4), 4.0(6) 0.20(–), 0.50(1.8), 1.0(2.9), 2.5(4), 4.0(5.9) (b) in dmso reaction 9) cl– + so2-i – 10) cl– + socl2-i – 11) cl– + so2cl2-i – [cl–] : [i–] 0.05(3), 1.0(5), 1.5(7), 2.0(10), 3.0(13), 4.0(17) 0.50(3), 1.0(4), 1.5(6), 2.0(9), 3.0(12), 4.0(15) 2.0(8), 4.0(16) 12) br– + so2-i – 13) br– + socl2-i – [br–] : [i–] 0.50(4), 1.0(6), 2.0(11), 4.0(13) 0.50(4), 1.0(5), 1.5(7), 2.0(10) (c) in water 14) cl– + so2-i – 4.0(3), 8.0(5), 12.0(7) *no replacement was observed by [scn]– in dmso. percentage replacements of the iodide species are given in parentheses. in all the above reactions the extent (or magnitude) of replacement depends on the stability constant for the reactant and product complex species. table 16 includes the kc data for reactants and products in the 47 salama and wasif replacement reactions. another factor which determines the magnitude of the replacement is the lewis basic character of the ligands and a third factor appears to be related to the donor and acceptor number of the solvent used (salama et al., 1971; pearson, 1963; day et al., 1969). table 16. stability constants for reactants and products in replacement reactions at 298ok xclbriscn so2-x 372 160 38 65 socl2-x 362 240 150 77 so2cl2-x 10 41 77 298 4.1 correlation of stability constants with ligand replacement 4.1.1 the cl--ireaction the data in table 15 show that in the presence of two halide ligands, cland iand acceptors such as so2, socl2 and so2cl2 in mecn solvent the thermodynamics would be more favorable for so2-cl and socl2-cl than for so2-i and socl2-i -. we may add that kc(so2-cl -) is nearly equal to kc(socl2-cl -) and both are much higher than kc(so2cl2-cl -)in the ratio 37: 36: 1. such a large difference in stability constants makes replacement of iby clmuch easier for so2-i and socl2-i than it is for so2cl2-i -. the data in table 15 and the plot of figure 7 illustrate this observation and we note that the percentage replacement in so2-i and socl2-i fall at a low [cl-]/[i-] on the same line and are much higher for so2cl2-i -. the replacement reaction, equation (6), seems anomalous in view of the kc(so2cl2-i -) / kc(so2cl2-cl -) ratio = 8. that this reaction, equation (6), can take place despite the reversed order of stability constants for reactant and product can only be due to the relative abundance of the cl– ligand which seems to outweigh the difference in stability constants. table 15 shows that a 20% disappearance of so2-i – requires a ligand ratio of 0.35:1 while in the case of so2cl2-i – ligand ratio [cl–] / [i–] = 1 : 1 was necessary for the same percentage replacement. by changing the ligand ratio we are merely increasing the chances of effective collisions leading to a replacement by the more abundant ligand. so2cl2-i + cl = so2cl2-cl + i (6) figure 7. comparison of replacement reactions by added cl– in mecn at 298°k (•) so2-i and socl2-i ; (o) so2cl2-i 48 weak complexes of sulfur compounds 4.1.2 the br––i– and scn-–ireactions the magnitudes of replacement for the ligands br– and scn– are not widely different (table 15). this is not unexpected since the stability constants for so2-br –, socl2-br – and so2cl2-br – are in the ratio 4:6:1 and for so2-scn – and socl2-scn – and so2cl2-scn – are in the ratio 1: 1.2 : 2.4. figure 8 shows a comparison of the replacing ability of the scn– ligand with that of cl– and br– ligands. the replacing ability of ligands fall in order cl– > br– > scn–, which parallels their lewis base character as hard, borderline and soft respectively (pearson, 1963; day et al., 1969). figure 8. comparison of amounts of replacements of i– in socl2-i – 4.2 the role of solvents in replacement reactions table 15 and figure 9 show the effect of solvents on the reaction so2-i – + x– where x= cl–. for a ligand ratio [cl–] /[i– ] = 4 the extent of replacement is 70% in mecn but only 16% in dmso and less than 2% in water. clearly a change of solvent greatly affects the degree of replacement. in dmso two factors are operative: a) dmso may solvate the cl– ligand and b) dmso may act as a potential acceptor at its s atom and compete with so2 in solution. the conclusion that dmso acts as a potential acceptor was reached using the observation of the spectrum of a solution containing cl– and i– ligands. this solution shows slow growth of two peaks at 292 nm and 365 nm and the rate of peaks growth depends on the ligand concentration and a rate constant was found to be 2 x 10–2 min–1 at 298°k. the replacement reaction so2-i – + cl– = so2-cl – + i– in dmso is ionic with a rate constant of 1010 sec-1 and therefore the addition of cl– to so2-i – in dmso is accompanied by the disappearance of the peak at 378nm (so2-i –) and the emergence of the new peak at 292 nm (so2-cl –). if this solution is left for some time the peaks at 292nm and 365nm will slowly appear for the complex species of dmso with cl– and i– ligands respectively. the sulfur atom in dmso will be the acceptor center with the following structures: ome2s-cl – and ome2s-i – respectively. recent work on photoelectron spectroscopy of sulfur compounds favors this view (guest et al., 1972; buncel et al., 1975). water appears to be a more drastic solvating agent towards the cl– ligand which results in a low degree of replacement with high ligand ratio of [cl–] / [i–] = 12. 49 salama and wasif figure 9. effect of solvents on the reaction so2-i – + cl– → so2-cl – + i– in a) mecn, b) dmso and c) water at 298°k. 4.3 replacement reactions in mixed solvents table 17 includes the replacement reaction data for the so2-i – + cl– reaction in mecn-dmso mixed solvent. for all runs the ligand ratio was [cl–]/[i–] = 4. the replacement percentage of iodide is given in parentheses. as the percentage of dmso in the solvent increases the ability of cl– to replace i– diminishes. here it is possible that the solvating power of dmso towards cl– makes it sterically difficult to replace the i– in so2-i –. table 17. replacement reaction of so2-i – + cl– in mecn-dmso mixture at 298°k dmso% 0.00(70%) 25(53%) 50(32%) 75(20%) 100(17%) 5. structure of so2-x the structures of so2-x (x= f, cl, br & i) (latajka et al., 1995) were investigated using ab initio method at the electron correlation level with effective core potential double zeta valence basis set with polarization functions. it has been found that the minimum on the potential energy surface corresponds to the cs structure of the complexes whereas the planar c2v structure is the transition state for the inversion process. the stability of so2-x complexes fall in the order so2-f -> so2-cl -> so2-br -> so2-i -. careful studies of the potential energy surfaces of the complexes clearly indicates that only one structure corresponds to the minimum. the xis in close contact with the s atom having a positive total charge. the intermolecular distance r(s …..x) increases in this series with the increase of the atomic number of x-. the shortest intermolecular distance is noted for so2-f complex. replacement of fby cl increases the distance by 2.61å and successive replacements by brand iligands cause an increase in r(s….o) value by about 0.3å. the complex formation slightly distorts the so2 subunit. the so bond is stretched while the oso bond angle slightly decreases in comparison with the values for the isolated so2 subunit. perturbation of the geometrical structure of the so2 subunit is essentially pronounced with the f ligands. 50 weak complexes of sulfur compounds 51 so2-x complexes are not planar and have cs symmetry. the nonplanarity of the complex is denoted by α which measures the angle between the c2 axis of the so2 subunit and the s….x axis. in the series of so2-x complexes the angle decreases from 71o for the so2-f complex to 61o for the so2-i complex which makes this complex less pyramidal. since in this series the intermolecular distance has increased from 1.93å for the so2-f – complex to 3.25 å for the so2-i – complex, the dipole-charge interaction becomes most important and in consequence the so2-i – is less pyramidal. in conclusion we may report that so2-f – has a rigid pyramidal structure while so2-i – is the least pyramidal in the above series of so2-x – complex species. 6. conclusion the formation of the complex species so2-x -, socl2-x -, so2cl2-x and sobr2-x where (x= cl-, br-, iand scn-) was reported during the last thirty years. the above complexes are weak of charge transfer nature and can not be isolated from solution but can be detected by spectrophotometry. their enthalpies of formation ∆hf o vary between –22.5 and -6.0 kj/mol. the stabilities of the above complexes depend on the solvent used, the acceptor properties of the scompound , the basic nature of the halide ligands and the temperature of the system. ligand replacements of the following type: so2-i + cl → so2-cl + i showed that the reaction is quite fast 1010 s-1 (detectable by laser technique) and is universal throughout all the complex species studied. the geometry of so2-x species suggest a pyramidal type with acute angle for x= cland less for x= i-. 7. references amis, e. s. 1965. effect of solvent on reaction rates, academic press, london. andrew, l. j. and keefer, r. m. 1961. molecular complexes of halogens, adv. inorg. chem. radiochem., 3: 91-131. asmus, e. 1960. determination of the composition of weak complexes, z. analyt. chem., 178: 104-116. basolo, f. and pearson, r. g. 1958. mechanisms of inorganic reactions, wiley, new york. bell, r. p. 1965. the proton in chemistry, methuen, london. benesi, h. a. and hilderbrand, j. 1949. a spectrophotometric investigation of the interaction of iodine with aromatic hydrocarbons, j. amer. chem. soc., 71: 2703-2707. benson, r. 1960. the foundations of chemical kinetics, mcgraw hill, new york. buncel, e. and leung, h. w. 1975. catalysis by tertiary amines of σcomplex formation between 1,3,5 trinitrobenzene and aniline, j. c. s. chem. comm : 19-20. burke, t. g. and smith, d. f. 1959. hf-so2 and similar vapor-phase complexes, j. mol. spectroscopy 3: 381-385. burow, d. f. 1970. internal-reflection spectroscopy of non-aqueous solvent systems: halides in liquid sulfur dioxide, develop. appl. spectrosc., 7b: 111-113. chadwick, d., frost, d. c., herring, f. g. and mclean, r. a. n. 1973. photoelectron spectra of sulfuryl and thionyl halides, canad. j. chem., 51: 1893-1905. day, m. c. and selbin, j. 1969. theoretical inorganic chemistry, reinhold and winston, new york. drago, r. s. 1959. molecular addition compounds of iodine. an absolute method for the spectrophotometric determination of equilibrium constants, j. amer. chem. soc., 81: 6138-6141. friedman, l. and wetter, w. p. 1967. purification of thionyl chloride, j. chem. soc., (a): 36-37. salama and wasif 52 frost, a. a. and pearson, r. g. 1961. kinetics and mechanisms, wiley, new york. gould, e. s. 1960. inorganic reactions and structure , holt reinhart, and winston, new york. grunwald, e. 1951. the correlation of solvolysis rates and the classification of solvolysis reactions into mechanistic categories, j. amer. chem. soc., 73: 2700-2707. guest, m. f., hillier, h. i. and saunders, v. r. 1972. ab initio calculations in extended bases and localized orbital calculations of the bonding in so2 and pf3, j. chem. soc., farad.ii: 114-120. gutmann, v. 1956. reactions in some non-aqueous ionizing solvents, quart. rev., 10: 451-462. gutmann, v. 1967. principals of coordination chemistry, in non-protonic solutions, 1st conference on non-aqueous solvents, mcmaster university, hamilton, canada. gutmann, v. 1971. phenomenological approach to cation-solvent interaction, 3rd conference on nonaqueous solvents, michigan state university, east-lansing, michigan, usa. jander, g. and ruppolt, w. 1937. the solubility of inorganic substances in liquid sulfur dioxide, z. physik. chem., a, 179: 43-51. jander, j. and tuerk, g. 1962. preparation of solid 1-diiodo-1-hydrogen sulfide, chem. ber. 95: 881888; 1963. spectrophotometric proof of charge transfer complexes of the acceptor so2 with the donors iodide ion and iodine, ingew. chem., 75 (16/17) : 792-796. job. p. 1928. formation and stability of inorganic complexes in solution, ann. chim., 9: 113-203. ketelaar, j. a. a., van de stoppe, c. goudsmit, a., and dzcubas, w. 1952. spectrophotometric study of the solvation of iodine in dioxan solution ii, rec. trav. chim., 71: 11041114. latajka, z., ratajczak, h., wasif, s. and salama, s. b. 1995. structure and energetics of so2x(x = f, cl, br, i) complexes, j. mol. str., theochem, 333: 291-296. mines, g. w., thomas, r. k., and thompson, h. t. 1972. photoelectron spectra of compounds containing thionyl and sulfuryl groups, proc. roy. soc., a329: 275-282. pearson, r. g. 1963. hard and soft acids and bases, j. amer. chem. soc., 85: 3533-3539. rossotti, f. j. c. and rossotti, h. 1961. the determination of stability constants, mcgraw hill, new york. salama, a., salama, s. b., sobeir m., and wasif, s. 1971. complex species of so2, socl2, so2cl2 with chloride, bromide, and iodide ions, j. chem. soc. (a): 1112-1117. salama, s. b. and wasif, s. 1973. complex species of so2, socl2, and so2cl2 with the thiocyanate ligand, j. chem. soc., dalton: 2148-2150. salama, s. b. and wasif, s. 1975. effect of solvent on the stability of 1:1 complexes of sulfur dioxide, sulphinyl dichloride, and sulphonyl dichloride with halogen ions, j. chem. soc., dalton: 151-153. salama, s. b., wasif, s., and khan, m. a. 1978. halide-ion replacement in 1:1 complexes of sulfur dioxide, thionyl chloride, and sulphonyl chloride with halide ions in acetonitrile and dimethylsulfoxide, j. chem. soc., dalton: 915-918. salama, s. b., wasif, s. and omer, m. m. 1978. stability constants of the weak 1:1 complexes of sulfur dioxide, thionyl chloride, and sulphonyl chloride with halide ions in the mixed solvent acetonitrile-dimethylsulfoxide at 25 oc, j. chem. soc., dalton: 918-920. salama, s. b. and wasif, s. 1985. weak complexes of sulfur and selenium oxo species. a thermodynamic view on solvent effects in mixed solvents, arab gulf j. of sc. res., 3(1): 121--131. salama, s. b. and wasif, s. 1991. weak complexes of sulfur complex species between iodide ions and dimethylsulfoxide, international jour. chem., 2(4): 149-154. salama, s. b. and wasif, s. 1994. formation of iodide ions with some arenesulfonyl chloride, asian journal of chemistry, 6(2): 381-388. sandhu, s. s. and singh, a. 1960. complexes of solvacids and ansolvo bases, j. indian chem. soc. 37: 329-333. sandhu, s. and singh, a. 1962. mechanism of the reactions of solvo-bases and solvo-acids, j. indian chem. soc . 39: 589-594. weak complexes of sulfur compounds seel, f. and riehl, l. 1955a. fluorosulfinates, z. anorg. chem., 282: 293-306. seel, f. and riehl, l. 1955b. fluorosulfinates, angew. chem., 67: 32-33. waddington, t. c. 1965. non-aqueous solvent systems, academic press, london. wasif, s. unpublished work. witeckowa, s. and witok, t. 1955. reaction between iodine and sulfur dioxide, zeszyty nauk, politech lodz.chem.spoz., 1: 73-86. received 12 december 1999 accepted 24 june 2000 53 salama b. salama* and saad wasif** ïñçóé ááãúþïçê èíä ãñßèçê çáßèñí� óáçãé èøñó óáçãé æ óúï æçõý contents 1. introduction 32 4.1 correlation of stability constants with ligand replacement 48 conclusion 51 1. introduction figure 3. mecn-dmso adduct table 13. stability constants of adducts of mecn and dmso with sulfur compounds at 298(k. 4.1 correlation of stability constants with ligand replacement conclusion electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 6 (2001) 39-44 © 2001 sultan qaboos university determination of sugar and mineral contents in some omani fruits salma m z.al-kindy, abdulrahman o abdulnour, and maryam m. al-rasbi department of chemistry, college of science, sultan qaboos university, p.o.box 36, al-khod 123, muscat, sultanate of oman والمعادن في الفواكه العمانيةكمية السكرحساب عبدالرحمن عبيد عبدالنور، مريم الراسبي, سلمى الكندي المعادن التي تمت دراستها هي الكالسيوم، . تـم تحليل مجموعة من الفواكه العمانية لمعرفة كميات السكر والمعادن بها :خالصـة لقد وجد أن كميات السكر والسكر المختزل مشابهة للكميات التي نشرت مسبقاً والتي .المغنيسيوم، الصوديوم، البوتاسيوم والفسفور لذلك فإنه يمكن تعليل . أما كميات المعادن فقد أظهرت إختالفاً واضحاً عن تلك التي نشرت مسبقاً . تمـت دراستها في أماكن أخرى .الت المستخدمةهذا اإلختالف في تركيز المعادن لتركيب التربة والطقس وأنواع السال abstract: omani fruits were analyzed for their reducing sugar, total sugar contents and some minerals. among the minerals studied were ca, mg, na, k and p. the amounts of total sugar and reducing sugar were within the range of values reported in the literature for the analysis of fruits conducted elsewhere. the amounts of the minerals differ from the reported literature values. this may be attributed to soil composition, climate and type of cultivar. keywords: omani fruits, mineral sugar. 1. introduction f ruits and vegetables are important in the omani diet. per capita fruit and vegetable consumption in oman has increased since the 1970’s as a result of the remarkable economic and social development that accelerated income growth and caused a substantial change in the diet of the population. the consumption of fruits in 1995 reached more than 90 kg per capita (omezzine, et al 1998). this change is brought about by the increase in consumer awareness towards low fat, high mineral vitamin sources of food; fruits and vegetable are usually low in calories and fat and have no cholesterol making them healthy additions to our diets. most fruits and vegetables are an excellent source of fiber, vitamins and minerals. fruits like all living things contain a wide range of different chemical compounds. an individual fruit is largely composed of living tissues, which are metabolically active and constantly changing in composition. the rate of the extent of such changes depends on the physiological role and the stage of maturity of the fruit concerned. these changes are well documented in the literature. ting and vines (1966) reported an increase in citric acid and malic acid with an increase in maturity of citrus fruits. the level of sugar and total acids in cherries was found to increase as they approach maturity. a good correlation was found between color and soluble solids development. these two indices were found to be the best indicators of maturity for good fresh market and canning quality of cherries (drake, et al 1982; marshall 1954). the level of sugar content in fruits was reported to be lower in trees with heavy crop as compared to trees with a light crop under similar growing conditions (mattus, 1966). furthermore sugar content was reported to be higher in apple fruits grown in areas of reduced moisture 39 al-kindy, abdulnour and al-rasbi availability, high temperature and high sunlight (mattus, 1966). cultivar and storage were found to significally influence the content of most sugars in apple juices (fuleki, 1989). the ash content represents the total amount of mineral matter in fruit material. the most abundant individual mineral element in fruit is potassium, the content of which is usually between 60 and 600mg/100g of fresh material. the potassium in fruit tissues occurs mainly in combination with the various organic acids in the cell sap. there is little doubt that the ph of the tissue in fruit is controlled by the potassium/organic acid balance. calcium is mainly associated with the pectic materials of the cell wall. magnesium is especially abundant in chloroplasts as a constituent of the chlorophyll molecule. studies of natural chemical constituents of fruits have important fundamental and applied uses. knowledge of composition is essential in objectively defining and evaluating the quality of fruit and fruit products, as they proceed through the channels of commerce. compositional studies provide information about the effects of climate, cultural practices, rootstocks and other biological parameters on the properties of fruits. the degree to which mineral content can vary within a plant species is illustrated by citrus fruits. for citrus fruits grown in florida, california, mexico and brazil, potassium concentrations range from 1520 to 3027mg/l and phosphorous concentration from 124 to 309mg/l were reported (mchard, et al 1980). the ultimate composition of the edible parts of plants is influenced by fertility of the soil, genetics of the plants and the environment in which the plant is grown. in this work the nutrient composition of oman fruits is determined. the contents investigated are sugar and minerals. the fruit samples studied were those usually used in the average household in oman for normal consumption. no attempt was made to obtain fruits grown from various regions of the sultanate. hence factors such as pre or post harvest, choice of cultivars, cultural practice, storage conditions and growing location were not taken into consideration, although such factors are known to play a major role in nutrients content of fruits (batten 1994, cookson 1996, fawzi et al 1996, el-fouly and shaaban 1999, shaaban and el-nour 1996). however, these aspects will be investigated in future studies since it is important to decide the localities in which improvements are required. 2. experimental 2.1 materials fruits locally grown were collected from the public authority for agriculture products in ghala. these were: quince (cydonia oblongo), sour orange (citrus aurantium), lime (citrus aurantifolia), grape fruit (citrus paradisi), sweet orange (citrus sinensis), pomelo (citrus grandisi), coconut (cocoa nucifera l), pomegranate (punica granatum), banana (musa acuminata), melon (cucumis melo), nabag (ziziphus mauritania, ziziphus namulania, ziziphus spina christi), guava (psidium guavaya) and papaya (carica papaya). all chemicals used were of analar grade and were obtained from bdh chemicals ltd, poole, england. ammonium molybdate was purchased from gaindland chemical company, sandycroft, deeside, u.k. 2.2 method 2.2.1 juice sample preparation fresh juice was squeezed from the fresh fruit. sufficient filter aid was added to form a thin paste. the paste was then filtered using a buchner funnel to obtain the clear fruit juice. 2.2.2 whole fruit sample fresh fruit samples were weighed, blended with a small amount of distilled water and filtered. the filtrate was quantitatively transferred into a 250-ml volumetric flask. 2.2.3 preparation of ash sample concentrated juice sample (50.00 ml) was placed on steam bath to remove all the water, then put in a muffle furnace at 550oc for 10 to12 hours until the ash became whitish in appearance. 6m 40 sugar and mineral contents in some omani fruits hcl (2ml) was added to dissolve the ash sample. the sample was then transferred quantitatively to a 50 ml volumetric flask. 2.2.4 determination of total and reducing sugars this was carried out according to the method of lane-eyron (ting and rouseff 1986). 2.2.5 determination of mineral elements mineral contents were determined from the ash samples solution. all the samples were duplicated and analyzed five times. analytical results with coefficient of variation (cv) more than 10 % were rejected. calcium and magnesium were determined by the atomic absorption spectrophotometry model al-pha 4 uk. absorbance of the sample was read at 422.7 nm for ca and 258.2 nm for mg. the ash sample prepared as described above was diluted ten fold with deionized water. the determination of sodium and potassium was achieved by flame photometry. (flame photometer gallenkamp, model fga-350-l uk). the ash sample solution was diluted a hundred fold for k; the original ash solution without dilution was used for na determination. the determination of phosphorous was by the colorimetric method using ammonium molybdate hcl – solution. (ting and rouseff 1986). absorbance reading of the complex was read at 650 nm using spectrophotometer pu 8620 (phillips). the ash solution was diluted fifty fold. 3. results and discussion the highest amount of total sugar content in fruit juice was found in quince and the lowest in sour oranges (see table1). 70% of total sugar found in quince was in the form of reducing sugar. the highest percentage of reducing sugar content was found in sour orange while the minimum in sweet orange (table 1). the total sugar found in omani oranges agreed well with the previously reported values (eskin, 1991) for florida orange. among the whole fruits studied, banana has the highest total sugar content and guava the minimum (table 2). pomegranate exhibited the highest percentage of reducing sugar. fleshy fruits such as melon, ziziphus mauritania, guava and papaya have reducing sugar in the range of 53-56% (table 2). the results for the total sugar content reported here for banana, ziziphus mauritania, zizphus nammulania and ziziphus spina christi are in agreement with the previously reported literature values (khan, et al 1979). table 1: amount of reducing sugar and total sugar in fruit juices g/100ml. fruits reducing sugar sucrose total sugar true total sugar % of reducing sugar % of sucrose cv % quince 8.56 3.63 12.38 12.19 70.2 29.8 0.40 sour orange 3.32 0.63 3.98 3.95 84.1 15.9 0.35 lime 3.19 1.57 4.84 4.76 67.0 33.0 0.42 grapefruit 3.55 2.54 6.22 6.09 58.3 41.7 0.55 orange 4.74 3.48 8.40 8.22 57.7 42.3 0.32 pomelo 5.81 3.13 9.10 8.94 65.0 35.0 0.61 coconut 5.12 1.10 6.28 6.22 82.3 17.7 0.52 sugar types and concentrations in fruits affect their taste. most fruits undergo changes in their sugar content during maturity. hence the monitoring of sugar contents and their respective ratio may indicate the level of maturity as well as physiological status during storage. marshall (1954) reported a 200 % increase in sugar contents of cherries during maturity. similar findings were reported for apples and pears (mattus, 1966). sugars comprise the most abundant soluble carbohydrates in citrus fruits with the exception of acidic citrus fruits such as lemon and lime. 41 al-kindy, abdulnour and al-rasbi during maturation the sugar in the juices of all citrus fruits increases both in concentration and in absolute amounts. in mature oranges, total-reducing sugar is approximately equal to sucrose (ting and rouseff 1986) while in other citrus fruits the amount of sucrose is less. mature tangerines have been reported to contain a higher sucrose content compared to fructose and glucose (ting and rouseff 1986). the ratios of sugar to sucrose of oman citrus fruits studied here were substantiate the findings of fuleki (1989) who reported that growing areas did not have a significant effect on similar to the values reported by ting and attaway, (1971) for mature citrus fruits. these results sugar composition of apples. all the values of sugar reported have an error of less than 1.0% with cv ranging from 0.4% for pomegranate to 0.6% for quince (n=10). table 2: amount of reducing sugar and total sugar for the whole fruit sample g /100g. fruits reducing sugar total sugar sucrose true total sugar % of reducing sugar % of sucrose cv % pomegranate 8.58 11.38 2.66 11.24 76.3 23.7 0.40 banana 12.95 19.53 6.25 19.20 67.4 32.6 0.45 melon 7.33 14.21 6.54 13.87 52.8 47.2 0.52 ziziphus (mauritania) 4.69 8.98 4.07 8.76 53.5 46.5 0.61 ziziphus namulania) 9.45 12.62 3.01 12.46 75.8 24.2 0.58 ziziphus (spina christi) 11.48 17.39 5.61 17.09 67.2 32.8 0.32 guava 2.87 5.26 2.27 5.14 55.8 44.2 0.38 papaya 4.93 9.24 4.09 9.02 54.7 45.3 0.53 table 3: the amount of mineral elements in fruit juice mg/100 ml. fruit k na ca mg p quince 42.6 13.3 24.3 40.5 8.0 sour orange 102.1 17.2 6.25 52.0 6.0 orange 46.3 17.8 5.92 25.0 16.0 grape fruit 7.4 8.0 29.0 25.6 22.0 pomelo 45.7 13.3 16.5 28.9 12.0 the amount of potassium in the omani fruit range from 7.4-mg/100 ml for grapefruit juice to 102.1mg/100 ml for sour orange juice (table 3). for whole fruit the concentration of potassium varies from 1.3 mg/100g for ziziphus mauritania to 20.2 mg/100 for pomegranate (table 4). the value of potassium for orange juice reported here was much lower than the values reported before for florida and brazil oranges (mchard, et al 1979). the amounts of potassium obtained from ziziphus was compared with the previously reported values, (khan, et al 1979). sour orange is a good source of potassium. individuals with concerns of hypertension are advised to reduce their sodium intake and consume foods high in potassium in order to achieve an improved sodium/potassium ratio. concentration of calcium ranges from 4.5 mg/100g for pomegranate to 20.5 mg/100g for muskmelon. no calcium was detected by our instruments for the ziziphus family and for guava (table 4). the minimum amount of calcium was found in orange and the maximum in grapefruit juice.(table 3). calcium and potassium are essential plant nutrients; and their concentrations in the juice and in the edible portion of the fruit depends upon the genetic make up, as well as the soil 42 sugar and mineral contents in some omani fruits characteristics. these elements are essential for human nutrition. their deficiencies, rather than toxicity, are of human health concerns. the amount of magnesium(mg) in fruit juice ranges from 25.0mg/ 100ml in sweet orange to 52.0mg/100ml in sour oranges. among the edible flesh fruits papaya contained the maximum concentration of the element (36.7 mg/100g) and ziziphus numulania the minimum (2.6 mg/100g). magnesium is an essential element for human, animal and plant nutrition. table 4: the amount of mineral element in whole fruit mg/g. fruits k na ca mg p pomegranate 20.2 0.75 4.5 28.7 6.0 banana 10.3 0.62 7.0 14.8 32.5 musk melon 4.3 0.03 20.5 23.9 7.5 papaya 14.1 0.84 6.4 36.7 9.5 ziziphus (mauritania) 1.3 0.03 2.64 3.2 ziziphus (numulania) 1.6 0.70 2.58 3.7 ziziphus (spina christi) 2.3 0.55 2.85 1.3 guava 2.5 0.09 2.94 0.7 sodium concentration in fruit juice is given in table 3. the values obtained in citrus fruit are higher than previously reported in the literature (mchard, et al 1979). again it reflects fruit characteristics which depend on type of soil and nutritional practices. there was no significant difference in the value obtained in the ziziphus locally grown and the literature values (khan, et al 1979). foods contribute more to the daily intake of sodium than drinking water (nrc 1977). an impressive amount of evidence has been accumulated over the last several decades, which suggests that sodium taken in excess of physiological needs induce an age–related blood pressure and hypertension. among the fresh fruit juices studied, sour orange contained the smallest amount of phosphorous (p) (6mg/100ml) and grapefruit the largest (22 mg/100g). guava contained only trace amount of p while banana had the maximum concentration (32.5mg/100g). phosphorous is essential for bone and teeth mineralization for energy use in atp, phospholipids and acid-base balance. compositional studies of the fruits is important in understanding the biosynthetic and regulatory systems of fruits, which in turn determine and control the chemical composition of the fruit. considerable data are available in the literature on the composition of fruits. yet the variability of each constituent may be so great that the data cannot be used for strict control of juice composition or for food processing. the mean values of some constituents also vary according to the geographical location. it is imperative that a data base on the composition of authentic juice be obtained from each fruit growing country using similar approved methods. data should be collected for more than a single season to study the effect of weather. furthermore, the compositional study using similar approved methods should be concurrent with the type of soil, fertilization and cultural practice. most commercial farmers use fertilizers to increase crop products. these fertilizers contain plant nutrients, which replenish the soil with the required nutrients. however, it is important to study the composition of the soil so as to evaluate the nutrient status of the soil and to investigate the bio-availability of both micro and macro elements. previous studies (el-fouly and shaaban, 1999) indicated a nutrient disturbance in the horticultural crops examined in salalah region in the sultanate of oman. this will affect the composition of fruits grown in this region. the ratio of major sugar in fruits is a characteristic feature of the fruit and serves as a fingerprint for fruit quality provided the fruits are grown using the same type of soil, cultivar and nutritional practice. 43 al-kindy, abdulnour and al-rasbi 4. conclusion the amounts of sugar in omani fruits studied here were found to be within the range reported previously for the same fruits grown elsewhere in the world. however, levels of minerals were found to be different. for example, when compared to florida oranges, omani oranges showed lower levels of k and p and higher levels of na. the effect of choice of cultivars, fertilization practice and soil of different levels of nutrient on fruit composition although important was not carried out. this is intended to form the next study in our project to quantify the properties of oman fruits. references batten, g. d. 1994 concentration of elements in wheat grain grown in australia, north america and the united kingdom. aust.j.exp.agrc-34: 51-56. cookson, p. 1996. soil research in oman : opportunities and priorities. squ j. scientific research-agriculture sciences, 1: 25-32. drake, s. r., proebstring e.l. jr and spayd, s.c. 1982, maturity index for the color grade of canned dark, sweet cherries. j.am.soc.hortic.sci.107:180. el-fouly, m.m. and shaaban, m.m.. 1999. status of some horticultural crops in salalah region, squ j. scientific res.-agricultural sciences 4(2): 47-52. eskin, n. a. 1991. quality and preservation of fruits. crc press boca raton florida. fawzi, a.f.a, shaaban, m.m. and abou el-nour. z.a.a.1996. nutritional status and nutrients removed by the fruits of three-mango cultivar grown under farm conditions. j.agric.sci., mansoura university., 12(6): 2301-2317. fuleki, t. 1989. chemical fingerprinting of fruits. detection of fraudulent activity in fresh and processed fruits in research projects summary agriculture and food research fund. pers. comm. khan, a.a., ashraf, m and nasreen, m.a. 1979. pharmacognostic studies of selected indigenous plants of pakistan. pakistan forest institute, peshawar, pp 85. mattus, g. 1966. harvest and postharvest handling of apples, american fruit grower 86(8). marshall, r.e 1954 cherries and cherry products. intersciences, new york. u.s.a. mchard, j .a., foulk, s.j. and winefordner, j.d.1979 a comparison of trace elements contents of florida and brazil orange juice. j.agric. food chem., 27:1326-1328. mchard, j.a., foulk, s.j., jorgensen, j.l., bayer, s. and winefordber, j.d.1980 analysis of trace metals in orange juice. in citrus nutrition and quality american chemical society symposium series no 143, washington, d.c, pp363-392. nrc 1977 drinking water and heath. national research council. national academy of sciences, washington, dc. omezzine, a., chomo, g.v and al-jabri, o.1998 demand analysis of selected fruits and vegetables squ j. scientific res.-agricultural sciences 3: 19-26. shaaban, m.m and abou el-nour. z.a.a.1996 the nutrient balance in egyptian clover (trifolium alexandrum) as affected by the yield. j.agric.sci., mansoura university., 21(6): 2293-2299. ting s. v and attaway j.a 1971. in the biochemistry of fruits and their products vol 1 (a.c hulme gd) academic press london and new york, 107-169. ting, s.v and rouseff, r.l 1986. citrus fruits and their products analysis and technology. marcel dekker, new york. ting, s.v and vines, h.m 1966 organic acids in the juice vesicles of florida hamlin oranges and marsh seedless grapefruit. proc.amer.soc. horti.sci.88 : 291-295. received 29 july 2000 accepted 26 november 2000 44 determination of sugar and mineral contents in some omani fruits íóçè ßãíé çáóßñ æçáãúçïä ýí çáýæ� óáãì çáßäïí , úèïçáñíãä úèíï úèï� experimental 2.1 materials fruits locally grown were collected from the public authority for agriculture products in ghala. these were: quince (cydonia oblongo), sour orange (citrus aurantium), lime (citrus aurantifolia), grape fruit (citrus paradisi), sweet orange (citru 2.2.1 juice sample preparation 2.2.4 determination of total and reducing sugars results and discussion table 3: the amount of mineral elements in fruit juice mg/100 ml. fruit conclusion references el-fouly, m.m. and shaaban, m.m.. 1999. status of some horticultural crops in salalah region, squ j. scientific res.-agricultural sciences 4(2): 47-52. eskin, n. a. 1991. quality and preservation of fruits. crc press boca raton florida. microsoft word civl990531.doc science and technology, 5 (2000) 25-34 © 2000 sultan qaboos university 25 earthquake response of a historical castle mohammed qamaruddin and ali salim al-harthy department of civil engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman هزات أرضيةبتاريخية ال نزوىقلعةتأثر علي بن سالم الحارثيومحمد قمرالدين م و 977 إذ أن هناك عدة تقارير لهزات أرضية وقعت بين سنة ، إن خطر وقوع زلزال في سلطنة عمان يعتبر حقيقة :خالصة مان وجمع بيانات أخرى من علهناك حاجة إلى عمل خارطة زلزالية . ولكن دون حدوث أضرار على اإلنشاءات م 1998سـنة قلعة نزوى مدى تأثر ففي هذه الورقة العلمية تم تقييم . أجـل وضـع مواصفات عامة لتصميم اإلنشاءات ضد القوى الزلزالية وبغياب المعلومات عن هذا). uniform building code(ستخدم المواصفات العامة للمباني بإقـوى الزلزال بالتاريخـية تشير لهذه المؤثرات و زالية ومعامل الموقع فإن دراسة رد الفعل الناتج عن الهزة تمت بإفتراض قيم مناسبة عامل المنطقة الزل . المحتملة مقاومة الزالزل من لتتمكن للقلعة إلى الحاجة إلى إجراء بعض أعمال تقوية التى توصلنا إليهاالنتائج abstract: the earthquake hazard potential in the sultanate of oman is considered real as there are several reports of felt earthquakes in the sultanate of oman during the period from years 977 to 1998, although no damage to the existing structures has been reported due to earthquakes. in oman, seismic zoning map and other basic data are required for the development of a standard code for seismic design of structures. in this paper, seismic response of a historical nizwa castle in oman is assessed employing the methodology of uniform building code (ubc, 1994). also, in the absence of data pertaining to the seismic zone factor and the site coefficient, the seismic response study is carried out by assuming appropriate values of these parameters. the results of such investigation are presented in this paper. the results show that some retrofitting measures have to be undertaken in order that the existing historical building may survive in a possible damaging earthquake. keywords: earthquake records, seismic response, uniform building code, masonry wall and equivalent static approach. he assessment of earthquake hazard involves collecting and evaluating a wide range of data pertaining to the history and occurrence of earthquakes in a region and to their origin. there are several reports of felt earthquakes in the sultanate of oman (figure 1) during the period from years 977 to 1998 (table 1). although oman does experience earthquake ground motions from time to time, no structural damage has been reported due to earthquakes. the historical records, however, suggest a possibility of such damage during the qalhat earthquake of 15th century (dickson, 1986). some major events, however, that occurred at a great distance away in southern iran, pakistan or yemen have been reported in oman. for example, several individuals reported (dickson, 1986) the effects of 27 november 1945 earthquake (m = 8.2) whose epicenter was just off the southeastern iranian makran coast about 470 km from muscat (in oman). one witness reported damage, casualties, and a tsunami surge. also, 18th april 1983 earthquake event (m = 6.5) that occurred in baluchistan was felt by some persons residing in multistory buildings in muscat (590 km from place of earthquake occurrence) and was also felt in buraimi (in oman) at an even greater distance (dickson, 1986). the yemen earthquake (m = 5.7) of 13th december 1982 was also felt by residents in salalah region (southern oman) but not in northern oman (dickson, 1986). some faults were reported in the batinah coastal plain in northen oman north to the daymaniyat islands (figure 2). khaboura fault zone (dickson, 1986) is located in south of sohar about 80 km to the vicinity of ras a’ssawadi along the coast (figure 2). no systematic investigations concerning the seismic qamaruddin and al-harthy 26 activity in oman was undertaken before 1985. earthquakes magnitudes recorded along the northeastern margin of the arabian plate have reached the most severe record magnitude of 8.2 (27 november 1945) (dickson, 1986). figure 1. felt earthquake locations in oman. the national geophysical data center in denver, colorado (u.s.a) has some seismic data from about almost all regions of the world. it turns out from such seismic data that all the earthquakes that occurred in an area between 45.0º e to 65.0º e and 10.0º n to 30.0º n (figure 3) show that a significant seismic activity is concentrated along the zagrous fault zone in iran. also, it can be seen from figure 3 that there are numerous epicenters along the batinah coastal plain and offshore of oman. prior to 1980 very few earthquakes had been recorded in oman mainly because of the lack of the local seismographic stations or sensitivity of the world seismic network or perhaps it was difficult to receive signals from events in the oman area because of placement of seismic stations (dickson, 1986). it is important to note that nearly all of the earthquakes after 1980 were reported by new stations in norway, sweden and england. the magnitude of these earthquakes ranges from 3.9 to 4.9 on modified ritcher scale. considerable efforts have already been made for assessing seismic hazard in the sultanate of oman and various other aspects of seismic monitoring in the sultanate of oman. through these efforts, it turns out that several recent earth movements have occurred in jabal salak, jabal khubayb and batinah coastal plains area (dickson, 1986). an investigation has been undertaken to assess the response to seismic forces of an existing historical masonry structure (nizwa castle) in earthquake response of a historical castle 27 the sultanate of oman. seismic analysis of the existing building has been made employing the methodology of the uniform building code (ubc), 1994. in the absence of data concerning the seismic zone factor and the site coefficient, the seismic response study is carried out selecting the appropriate basic data for the earthquake response computation. the results of such investigation are presented in this paper. methodology for earthquake response the method for earthquake response determination presented in this section is based on the requirements of the ubc, 1994. the ubc is most extensively used in the u.s.a., particularly in the western part of that country. this building code is intended to provide guidelines, and formulas, which constitute minimum legal requirements for design and construction within a particular region. these requirements are intended to achieve satisfactory performance of the structure when subjected to earthquake ground motion. the safety of the structure is not assured in the event of a major earthquake. the objective of the code is that a minor or moderate earthquake will not damage the structure and that a major earthquake will not produce collapse of the structure.whenever a building is subjected to an earthquake, its foundation will start to move randomly because of soil movement of the site under the building. then, the whole building moves due to the movement of its foundation, which causes deformations in the building. the earthquake forces can be divided into three components: vertical and two horizontals. in the present investigation, the vertical component of the ground motion is ignored. only horizontal earthquake motion is considered in two orthogonal directions, but considering one component at a time. table 1: felt earthquakes in oman (dickson, 1986) site place/city year(s) of felt earthquake(s) 1 shinas 1935,1945,1955,1965 2 liwa 1969 3 saham 1944,1945 4 buraimi 1965, 1983 5 al qabil 1934, 1968, 1971 6 nakhal 1965 (2)* 7 seeb 1983 8 muscat 1958, 1965 (4) *, 1967, 1969, 1983 (2) * 9 quriyat 1965 (3) * 10 musara 1965 11 sumayyah 1965 12 ghugrat al-tam 1965 (2) * 13 sinaw 1945 14 qalhat late 15th century 15 al kamil 1949 16 al wafi 1955 17 bilad bani bu hasan 1969 18 masirah 1965 19 salalah 1982, 1994 20 musandam 977, 1184, 1483 21 al hallaniyat 1995 * numbers in parenthesis indicate number of felt earthquakes in a particular year. building idealization details of the nizwa castle’s structural system are reported elsewhere (al-shariqi, 1998). load bearing masonry walls have been employed as a structural system in the castle. in view of this, the castle is idealized as a three-storied lumped-mass-stiffness shear building system. the earthquake response of the building is completely defined by the physical properties of its structural elements, such as its mass, stiffness, damping and load-displacement characteristics on one hand, and time qamaruddin and al-harthy 28 varying accelerations introduced at its foundation support on the other hand. thus, the evaluation of structural properties and the selection of earthquake input are the most critical factors in the earthquake response analysis. in the present investigation equivalent static approach of earthquake analysis of multistory structures is employed (ubc, 1994). equivalent static approach this method is adopted in most of the building codes for moderately high buildings due to its simplicity and due to the fact that many structures designed on the basis of code coefficients have satisfactorily withstood past earthquakes. static horizontal forces are applied based on the values of seismic coefficients to simulate the effects of the designed earthquake. the distribution of the shear forces along the height of the building is adopted to be similar to that obtained by dynamic analysis. design forces specified by most codes are smaller than those indicated by dynamic elastic analysis. however, to design any building in accordance with ubc-94, many factors should be taken into account by which the building shall be designed and constructed to resist a minimum lateral seismic force applied statically and independently in the direction of each of the two main axes of the structure. the equivalent static method used in the present study is briefly described in the following paragraphs. total base shear force: the total base shear force (v) of the structure is determined by using the relation (ubc, 1994): where, w is the seismic weight of the structure, z, the seismic zone factor, i, the occupancy importance coefficient, rw, the structural factor and c (dynamic factor) = 1.25s/t 0.66 ≤ 2.75 in which s is the site coefficient, t is the fundamental period of the building and is equal to ct (hn0.75) while hn is the total height of the building in feet. ct is the time coefficient factor which depends on the structural system of a structure to be analyzed. distribution of lateral forces: the lateral force (fx) at a height level x above the base is determined as: where ft = 0 for t < 0.7 sec or ft = 0.07tv < 0.25 for t > 0.7 sec, n is the total number of stories above the base of the building, fx, fi, fn are the lateral forces applied at level x, i and n, ft is the portion of the base force (v) at the top of the structure in addition to fn, hx, hi are the heights of level x and i above the base of the building, wx, wi are the seismic weights of ith level. storey shear force: the shear at ith storey (vx) is calculated using the formula: drift and storey lateral displacement: drift (∆x) and storey lateral displacement (δx) are computed employing ∆x = vx/ kx and δx = σ∆x ,where, kx is the flexural stiffness for ith storey. the code stipulates that the storey drift should not exceed (0.04/rw) times the storey height or 0.005 times the storey height. natural period of the building: the natural period of the building is determined using rayleigh’s method. overturning moment: the overturning moment at ith level (mx) of the building is computed by the following equation: horizontal torsional moment: diaphragms are considered flexible when the maximum wr ziwc v =       = ∑ = n 1 i iixx t x hw/hw) fv(f ∑ = += n x i xtx ffv ∑ = −+−= n 1 i xiixnt )hh(f)hh( fm earthquake response of a historical castle 29 lateral deformation of the diaphragm is more than twice the average storey drift of the associated stories. the provisions (ubc-1994) have been made for the increased shear force resulting from horizontal torsion where diaphragms are flexible. the accidental torsional moment (tx) is 0.05dvx, where d is the figure 2. epicenters and active faults along the batinah plain and offshore in oman. dimension of the building perpendicular to the direction under consideration. p-delta (p-∆) effect: the ratio (θx) of the secondary moment at ith storey (mxs) resulting from p-∆ effect to the primary moment at ith storey (mxp) is estimated by the following equation θx = mxs/ mxp = px ∆x/vxhx where m xs is the secondary moment at xth storey, m xp is the primary moment at xth storey, px is the total weight at xth storey and above, hx is the height of xth storey. qamaruddin and al-harthy 30 figure 3. seismicity in oman since 1980. according to the provision of the code, when θx at each storey level of the building is less than 0.10, there is no need to account for the p-∆ effect. diaphragm design force: the code requires that horizontal diaphragms (floors and roofs) be designed to resist the following force given by: in which wpx is the weight of the diaphragm and attached parts of the building at the ith storey. the code states that fpx need not exceed 0.75zi wpx, but it shall not be less than 0.35zi wpx.       += ∑∑ == n 1 i i n x i pxitpx w/w)ff(f earthquake response of a historical castle 31 data for seismic response in the absence of appropriate data for seismic response study, it is assumed that the nizwa castle is located in a seismic zone equivalent to seismic zone 3 (ubc-94) and hence seismic zone factor z = 0.3. seismic zone 3 has been selected in view of the historical importance of the nizwa castle. further, the foundation soil of the castle is considered such that the site coefficient s = 1.2. the structural factor (rw), the occupancy importance factor (i) and the time coefficient factor (ct) are selected as 6.0, 1.0 and 0.02, respectively, in accordance with the appropriate building material and building system of the nizwa castle. seismic weight determination seismic weight of the three storied nizwa masonry castle has been determined employing its appropriate material and mechanical properties. details of the seismic weight determination are reported elsewhere (al-shariqi, 1998). the results of the seismic weight computation of the masonry building are shown in table 2. stiffness determination of shear walls determination of the shear wall stiffness is reported in this section. a new methodology (qamaruddin, 1999) has been employed in determining the wall stiffness. in this method, the wall is divided into three elements: namely pier, top spandrel and bottom spandrel. then the three nondimensional parameters (pier aspect ratio, top and bottom spandrel aspect ratio) are evaluated for different walls. employing the appropriate tables (qamaruddin, 1999), the stiffness of the walls has been determined. in the present study, the stiffness of the walls parallel to transverse (t) and longitudinal (l) directions of the building has been computed separately. this has been done in view of the assumption that the walls located parallel to the transverse direction of the building would resist any expected ground motion occurring parallel to the transverse direction of the structure. similar is the condition for the walls located in the longitudinal direction of the building, for the expected earthquake motion in the longitudinal direction of the building. the results for the story-wise lumped stiffness of the shear walls located parallel to the transverse and longitudinal directions of the building are also tabulated in table 2. details of the stiffness determination of the shear walls are reported elsewhere (al-shariqi, 1998). seismic response of the castle earthquake response has been determined using the methodology of ubc-94 for the masonry building subjected to two orthogonal horizontal ground motions separately, taking them one at a time. the results of such response computation have been shown in tables 3 to 7. table 2: data for seismic response computation storey level storey height (m) seismic weight (kn) storey stiffness (kn/m) for t-shear walls* storey stiffness (kn/m) for l-shear walls+ 3 9 87245 3502139 6931218 2 4 884063 85230520 57793623 1 4 2178666 38868586 28148832 * t-shear walls parallel to earthquake motion in transverse direction of the castle. + l-shear walls parallel to earthquake motion in longitudinal direction of the castle. results and discussions the nizwa castle is subjected to earthquake ground motion in two orthogonal directions, i.e., longitudinal and transverse separately. the discussion of the results thus obtained (tables 3 to 7) is described in the following sub-sections. qamaruddin and al-harthy 32 lateral forces comparison: table 3: lateral force and shear force storey level lateral force, fx (kn) for t-direction* l-direction+ shear force, vx (kn) for t-direction l-direction 3 30028 25970 30028 25970 2 143186 123837 173214 149807 1 176433 152591 349647 302398 * earthquake ground motion in transverse direction of the castle. + earthquake ground motion in longitudinal direction of the castle. the results from table 3 show that the lateral forces developed in the structure subjected to ground shaking in the t-direction are about 13.5 % larger than the corresponding lateral forces values obtained for the ground motion in the l-direction in all the stories of the castle. comparison of base shear forces: it can be seen from table 3 that the values of the shear forces in the respective stories of the structure subjected to ground motion in the t-direction are also about 13.5 % higher than the corresponding values obtained for the earthquake ground motion in the l-direction. comparison of storey drifts: table 4: storey drift and lateral displacement storey level storey drift (m) for t direction ldirection lateral displacement (m) for t direction ldirection 3 0.008 0.0037 0.019 0.017 2 0.002 0.0026 0.011 0.013 1 0.009 0.01 0.009 0.01 from table 4, it is seen that the values of the storey drift show different variation trends in the building as obtained by the static method. for example, the storey drift values obtained in stories 1 and 2 are respectively about 11% and 30% higher when the structure is subjected to the l-direction of the earthquake ground shaking in comparison with the corresponding values as obtained for t-direction of the ground motion. unlike this trend, the storey drift value obtained in third floor is about 53% higher for the t-direction of the ground motion compared to the l-direction one. the above trend of storey drift variation may be attributed mainly to the variation of the storey stiffness (table 2). according to the ubc-94 code, the maximum permissible storey drift for the castle is determined as 0.020 m. from table 4, it is established that the storey drifts determined in all the stories of the castle are less than the maximum permissible value of the storey drift. in view of this, the serviceability requirement of the historical castle is met variation of lateral displacements: it can be observed from table 4 that the storywise lateral displacements of the building under the l-direction of earthquake force are about 11% and 18% higher in the first and second stories respectively in comparison with the corresponding values obtained for the t-direction of the ground motion. in contrast to this observation, the lateral displacement of the third storey in the ldirection of earthquake motion is about 10.5% lower than that obtained for the t-direction. table 5: overturning and torsional moment store y level overturning moment (kn.m) for t-direction l-direction torsional moment (kn.m) for t-direction l-direction 3 51648 70119 2 270252 233730 297928 404479 1 963108 832958 601393 816475 base 2361696 2042550 earthquake response of a historical castle 33 comparison of overturning and torsional moments: from table 5, it is observed that the overturning moment in all the stories of the structure subjected to the t-direction of the ground shaking are about 13.5% larger than those obtained for the ground motion in the l-direction. this trend is true because the lateral forces developed in the structure under the t-direction of the ground motion are more than their corresponding values for the l-direction of the earthquake shaking. but, the torsional moment values in all the stories of the masonry castle are about 26.3% higher when the structure is subjected to the ground shaking in the l-direction in comparison with the response obtained for the tdirection of the ground motion. variation of secondary moments: it is observed from table 6 that there is a different trend in the story-wise development of the secondary moment. for example, the table 6 shows greater values of the secondary moments in the first and second stories of the masonry castle subjected to the tdirection of the ground motion than the corresponding values in the l-direction of the earthquake force. but, the secondary moment in third storey of the structure for the l-direction of earthquake is greater than the corresponding secondary moment in the t-direction. table 6: primary (mxp) and secondary (mxs) moment storey level mxp (kn.m) for t-direction l-direction mxs (kn.m) for t-direction l-direction ratio of mxs/ mxp for t-direction l-direction 3 270252 233730 698 323 0.026 0.0014 2 692856 599228 1943 2526 0.0028 0.0042 1 1398588 1209592 28350 31499 0.02 0.026 it is seen from table 6 that the ratios (θx) of the secondary moment (mxs) resulting from p-∆ effect to the primary moment (mxp) in all the stories of the masonry castle are much less than 0.10. this statement is true for the castle subjected to the tas well as l-directions of earthquake ground motion. therefore, there is no need to account for p-∆ effect in the design of the castle because according to the provision of the ubc-94 code, θx at each storey level of the building should be less than 0.10. diaphragm forces variation: table 7: diaphragm forces (fpx) storey level minimum fpx (kn) computed fpx (kn) for t-direction l-direction maximum fpx (kn) 3 14398 47195 40817 30853 2 44822 76126 65839 96048 1 138522 146437 126649 296833 table 7 shows that the diaphragm forces developed in the roofing/flooring systems of the castle subject to ground shaking in the t-direction are higher than the corresponding values for the earthquake motion in the l-direction. it can also be seen from the table that the diaphragm forces developed in the third storey are more than the maximum diaphragm force permitted by the ubc-94 code. in view of this observation, it is established that the roofing system of the castle may fail in any future earthquake consistent with basic data considered in the seismic response determination of the nizwa masonry castle. conclusions firstly, the seismic activity in the sultanate of oman has been studied through available literature. then, the seismic response of the nizwa castle subjected to the expected earthquake ground shaking has been determined. based on the present study, the following conclusions can be drawn: 1. since the sultanate of oman is situated within the seismic belt, contrary to past belief, there is a possibility of occurrence of earthquakes, especially in batinah coastal plain. 2. the earthquake response analysis of the three storied nizwa castle show that there is no definite trend in the variation of different seismic responses. 3. the seismic response results may be used in the evaluation of seismic capability of the structural elements of the existing nizwa castle. if required, strengthening measures will have to be undertaken to guard against possible failure of this structure during any future earthquake. qamaruddin and al-harthy 34 4. the results of the present investigation show that some retrofitting measures with respect to the roofing system has to be undertaken in order that the existing historical building may survive in any possible future damaging earthquakes. references al-shariqi, a. 1998. seismic analysis of a historical building in oman. project report, department of civil engineering, sultan qaboos university, oman. dickson, p. 1986. preliminary assessment of the earthquake hazard in the sultanate of oman, undp consultancy mission report. international conference of building officials, 1994. uniform building code (ubc). whittier, ca. paz, m. 1997. structural dynamics theory and computation, (4th edition). chapman & hall, new york. qamaruddin, m. 1999. in-plane stiffness of shear walls with openings. j. of building and environment, 24: 109-127. received 31 may 1999 accepted 11 october 1999 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 19-25 © 2003 sultan qaboos university efficient synthesis of the plant growth regulator ancymidol heiko patzelt department of chemistry, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, email: patzelt@squ.edu.om. التصنيع الفعال لألنسيميدول المتحكم في نمو النبات هايكو باتزلت ـ : خالصة ولكن سعره المرتفع يضع . أنسيميدول يستخدم كمبطأ لنمو النبات وله تطبيقات طبية أخرى 450مانع سايتوكروم بـ تصنيع قصيرة ومنتجة لألنسيميدول بكميات كافية في هذا البحث، تم إيجاد عملية . قيوداً إقتصادية لتطبيقاته في مجاالت واسعة .وبتكلفة أقل abstract: the important cytochrome p450 inhibitor ancymidol is used as a plant growth retardant and has potential for various medicinal applications. however its high price sets economic limits to large-scale applications. here a short and high-yielding synthesis is reported, providing ancymidol in substantial amounts in a costand time-efficient way. keywords: plant growth regulator; cytochrome p450; oxygenase inhibitor. 1. introduction p lant growth retardants are applied to agronomic and horticultural crops to reduce unwanted longitudinal shoot growth without lowering plant productivity. most growth retardants act by inhibiting gibberellin biosynthesis. to date, four different types of such inhibitors are known: (a) onium compounds, such as chlormequat chloride, mepiquat chloride, chlorphonium, and amo1618, which block the cyclases copalyl-diphosphate synthase and ent-kaurene synthase involved in the early steps of gibberellin metabolism; (b) structural mimics of 2-oxoglutaric acid, which is the co-substrate of dioxygenases that catalyze late steps of gibberellin formation. acylcyclohexanediones, e.g. prohexadione-ca and trinexapac-ethyl and daminozide, block particularly 3 beta-hydroxylation, thereby inhibiting the formation of highly active gibberellins from inactive precursors; (c) 16,17-dihydro-ga(5) and related structures act most likely by mimicking the ga precursor substrate of the same dioxygenases; (d) compounds with an ncontaining heterocycle, e.g. ancymidol, flurprimidol, tetcyclacis, paclobutrazol, uniconazole-p, and inabenfide (rademacher, 2000). the crucial molecular effect of these pyrimidine and triazole derivatives seems to be the inhibition of gibberellins biosynthesis, specifically at the oxidation of ent-kaurene (1) to ent-kaurenoic acid (2, scheme 1) (coolbaugh et al., 1978). the transformation involves three oxidative steps, which all require nadph and molecular oxygen, and are catalyzed by cytochrome p450 mono-oxygenases (murphy and west, 1978). all three steps are inhibited by ancymidol with comparable efficiency (coulson et al., 1984). furthermore, ancymidol was found to inhibit certain oxidations on steroid backbones, which led to extensive pharmaceutical testing of the molecule. on the basis of this lead structure, for example, researchers from the eli lilly laboratories tried to develop inhibitors for the aromatase of human estrogen biosynthesis with the goal of providing novel breast cancer therapeutics. pyrimidine derivatives show a higher activity than their (partially) saturated analogues, and the 19 heiko patzelt hydroxyl and cyclopropyl moieties seem to be equally important for most observed effects (davenport et al., 1968; taylor et al., 1987). cyclopropyl derivatives have repeatedly been described as suicide substrates for eukaryotic cytochrome p450s (testa and jenner, 1981; ortizde-montellano, 1988; ortiz-de-montellano and reich, 1986) or were used for biosynthesis investigations (patzelt and robinson, 1993). me meme ch2 me ch2ohme me chome me coohme 1 2 scheme 1. the oxidation of ent-kaurene (1) to ent-kaurenoic acid (2) in echinocystis macrocarpa (cucurbitaceae). 2. synthesis of the p450 inhibitor ancymidol although ancymidol has recently become commercially available, the high price makes largescale applications a costly enterprise. the single published, industrial, synthetic approach, on the other hand, does not provide satisfying experimental details (taylor et al., 1987). it appeared reasonable to establish a short synthesis on the basis of the arylation of p-anisyl cyclopropyl ketone (8). the friedel-crafts acylation of anisole (3) with acryloyl chloride (4) gave the expected panisyl vinyl ketone (5) in only mediocre yields. apart from polymerisation products, up to 40% of the formal hydrochlorination product 7 were isolated. this chloride 7, however, was available directly from anisole and 3-chloropropanoyl chloride (6) in more than 90% yield. neither basecatalyzed nor thermal (santelli and bertrand, 1973) elimination of hcl from 7 would produce 5 in satisfactory yields, but when 7 was directly treated with trimethyloxosulfonium iodide (corey and chaykovsky, 1965) and two equivalents of potassium hydride, the desired p-anisyl cyclopropyl ketone (8) was obtained in up to 80% yield (scheme 2). a proposed one-pot formation of 8 by the reaction of 3 with 4-chlorobutanoyl chloride (close, 1957) did not give synthetically useful results. when the volume of solvent (dmso) in the transformation of 7 into 8 was reduced, a byproduct, which could always be detected on tlc in the reaction mixture, became the main product. it could be purified and characterized, and the unexpected bicyclic structure 9 was assigned. it presumably arises from two molecules of the ketone 7 and one methyl group from the oxosulfonium salt (scheme 3). for the formation of the cyclopropyl moiety, an in situ elimination of hcl from 7 can be envisaged. the double bond of the resulting unsaturated ketone 5 would then undergo a michaeltype attack by dimethyloxosulfonium methylide 10, derived from trimethyloxosulfonium iodide by deprotonation. ring closure can occur via an intramolecular substitution of the oxosulfonium group in 11 by the enolate carbon (trost and melvin, 1975; block, 1981). when the concentration of 5 and trimethyloxosulfonium iodide in the solution becomes too high, the enolate in 11 might be protonated before the cyclization takes place. after deprotonation at the very acidic sulfonium bearing carbon atom c(4), 12 can react with a second molecule of 5 or 7. an intramolecular aldol reaction would reversibly form the six-membered ring of 14, which, as soon as the oxide is in 1,4trans position to the sulfonium group, can cyclize to give 9 (scheme 3). this rationalization, of course, is so far purely speculative. 20 efficient synthesis of the plant growth regulator ancymidol meo cl o alcl3 cl o cl meo o meo alcl3 meo o meo o cl o o ome ome 98 763 543 me3so + i– 2 eq kh + + + 7 scheme 2. synthesis of p-anisyl cyclopropyl ketone (8). me2 s+ ch2 — o meo o cl o me mes + meo o o— meo ome mes + ome o kh o me me meo o— s+ meo o— cl -dmso ome o— o me mes + meo o o o ome ome meo o meo o 5 11 8 7 5 11 12 5 13 14 9 -cl— 10 scheme 3. proposed formation of the bicyclic side product 9 during the ancymidol synthesis. 21 heiko patzelt the concluding nucleophilic addition of 5-lithiopyrimidine (15) onto the carbonyl group of 8 proceeded cleanly as long as the temperature was kept below -100°c. it was possible to generate 15 in situ by the addition of butyl lithium to a solution of freshly sublimed 5-bromopyrimidine (16) and 8. ancymidol (17) was obtained in 73% yield after recrystallization (scheme 4). it should be mentioned that even minor warming of the reaction mixture or minute impurities in the starting material led to considerable reductions in the yield. ancymidol can thus be prepared in a very straight-forward and efficient synthesis in 55% overall yield from inexpensive anisole, and is now available in multigram quantities for biological experiments. meo oh n n n n br buli n n li 8 1716 15 -100°c scheme 4. transformation of p-anisyl cyclopropyl ketone (8) to ancymidol (17). 3. experimental 3.1 general all solvents and reagents were purchased from aldrich or fluka in their highest available quality. solvents were distilled before use and dried over an appropriate desiccant (perrin and armarego, 1988). reactions under anhydrous conditions were performed in a n2-atmosphere using standard schlenck techniques (casey et al., 1990). 3.2 3-chloro-1-(4-methoxyphenyl)-1-propanone (7) anisole (3; 54.0 g, 480 mmol) and alcl3 (64.0 g, 480 mmol) were stirred in dichoromethane (240 ml), at 0°c under an n2-atmosphere, until the solution became clear and homogenous (30 min). the flask was kept in the ice bath and 3-chloropropanoyl chloride (6; 52.0 g, 400 mmol) was added dropwise at such a speed that the solvent mildly boiled. the colour of the solution changed from bright yellow to dark red. the ice bath was removed and the reaction was stirred for further 2h at room temperature before being poured onto crushed ice. extraction with hexane and evaporation of the dried (mgso4) solvent gave 7 (74.2 g, 370 mmol, 92.5%) as light rose-coloured crystals, which could be recrystallized from hexane. m.p.: 62-63°c. 1h-nmr (300 mhz, cdcl3): 7.90 (d, 2h, [c(2',6')h], 3jortho = 8.9 hz); 6.95 (d, 2h, [c(3',5')h], 3jortho = 8.9 hz); 3.96 (s, 3h, [och3]); 3.89 (t, 2h, [c(2)h], 3j =6.9 hz); 3.45 (t, 2h, [c(3)h], 3j = 6.9 hz). 13c-nmr (50 mhz, cdcl3): 195.1 [c(1)]; 163.8 [c(4')]; 130.3 [c(2',6')]; 129.5 [c(1')]; 113.8 [c(3',5')]; 55.5 [och3]; 40.8 [c(2)]; 38.9 [c(3)]. ir (kbr): 3010w (νch aromatic), 2950m and 2920w (νch aliphatic), 2840m (νch in ch3), 1670s (νc=o), 1595s and 1510s (νcc aromatic), 1455m, 1435m, 1415m, 1350s, 1305m, 1260s (νco), 1205m, 1170s, 1110m, 1070w, 1025m, 985m, 835s and 780s (δch out-of-plane), 685m (νccl). ms (ci, nh3): 218.2 (29.9%), 216.1 (100%, [m+nh4]+), 201.2 (5.1%), 200.2 (6.4%), 199.0 (22.8%, [m+h]+). ma for c10h11clo2 (198.65): calc. c 60.46, h 5.58, cl 17.85; found c 60.39, h 5.71, cl 17.63. 3.3 trimethyloxosulfonium iodide a solution of methyl iodide (45 ml, 68 g, 480 mmol) in anhydrous dmso (16 ml, 24 g, 310 mmol (dist. from cah2)) was refluxed for 3 d under an n2-atmosphere. the solution darkened and a solid precipitated. after cooling to room temperature the solution was filtered, and the solid was 22 heiko patzelt the following preparations belong to “experimental” and should not be numbered separately. if necessary, one would have to use sub-numbering: 3.1. general 3.2. 3-chloro-1-\(4-methoxy… … …7 efficient synthesis of the plant growth regulator ancymidol washed with small portions of chcl3 and was dried in vacuo to give white crystals (16.4 g, 74.5 mmol, 24%). m.p.: 192-195°c. 1h-nmr (300 mhz, d2o): 3.24 (s). 13c-nmr (50 mhz, d2o): 64.2. ir (kbr): 2960s and 2870s (νch), 1400s (δch), 1335w, 1310m, 1225s (νcs), 1035s (νs=o), 950s, 750m. ms (ci, nh3): 93.2 (100%, [(ch3)3so]+). ma for c3h9jos (220.07): calc. c 16.38, h 4.10; found c 16.50, h 4.32. 3.4 cyclopropyl-(4-methoxyphenyl)-methanone (8) anhydrous dmso (350 ml, dist. from cah2) was slowly dropped onto a solid, intensively stirred mixture of ground trimethyloxosulfonium iodide (54.0 g, 240 mmol) and nah (10.5 g, 480 mmol (washed with anhydrous hexane and dried in vacuo)), at 0°c under an n2-atmosphere. the resulting slurry was stirred for further 30 min at room temperature. it was then cooled to 10°c inside temperature before 3-chloro-1-(4-methoxyphenyl)-1-propanone (7; 37.2 g, 240 mmol) in anhydrous dmso (120 ml) was added. the mixture was kept at that temperature for another 5 min and was then stirred at room temperature for further 2 h. the reaction was poured onto ice and was extracted with dcm (3x). the combined organic phases were washed twice with h2o and brine, and were dried over mgso4. evaporation of the solvent and column chromatography (20% etoac in hexane) gave the cyclopropylketone 8 (34.3 g, 195 mmol, 81%) as a slightly yellow oil. 1hnmr (300 mhz, cdc3): 7.80 (d, 2h, [c(2',6')h], 3jortho = 8.9 hz); 6.85 (d, 2h, [c(3',5')h], 3jortho = 8.9 hz); 3.76 (s, 3h, [och3]); 2.45 (m, 1h, [c(2)h]); 1.05 (m, 2h) and 0.8 (m, 2h) [c(3,4)h]. 13c-nmr (50 mhz, cdcl3): 199.0 [c(1)]; 163.2 [c(4')]; 131.0 [c(1')]; 130.2 [c(2',6')]; 113.6 [c(3',5')]; 55.4 [och3]; 16.6 [c(2)]; 11.1 [c(3,4)]. ir (chcl3): 3000w (νch aromatic), 2980m and 2930w (νch aliphatic), 2840m (νch in ch3), 1660s (νc=o), 1600s, 1575m, and 1510s (νcc aromatic), 1460m, 1420m, 1385s, 1305m, 1260s (νco), 1235m, 1195w, 1170s, 1120w, 1030s, 1010w, 990s, 835s. ms (ci, nh3): 177.3 (100%, [m+h]+). c11h12o2 (176.22). 3.5 2-(4-methoxyphenacyl)-1-(4-methoxyphenyl)-7-oxabicyclo[2.2.1]heptane (9) anhydrous dmso (50 ml; dist. from cah2) was slowly dropped onto a solid, intensively stirred mixture of ground trimethyloxosulfonium iodide (17.6 g, 80 mmol) and nah (3.5 g, 160 mmol; washed with anhydrous hexane and dried in vacuo), at 0°c under an n2-atmosphere. the resulting slurry was stirred for further 30 min at room temperature. it was then cooled to 10°c inside temperature before 3-chloro-1-(4-methoxyphenyl)-1-propanone (7, 12.4 g, 80 mmol) in anhydrous dmso (30 ml) was added. the mixture was kept at that temperature for another 5 min and was then stirred at room temperature for further 2 h. the reaction was poured onto ice and was extracted with dcm (3x). the combined organic phases were washed twice with h2o and brine, and were dried over mgso4. evaporation of the solvent gave a yellow oil which solidified upon cooling to 0°c. the precipitate was filtered off, washed with cooled anhydrous ether (the filtrate contained cyclopropyl-ketone 8) and recrystallized from ether/hexane (1:1) to give the bicyclic ketone 9 (5.4 g, 30.9 mmol, 38.6%) in the form of white powdery crystals. m.p.: 152-153°c. 1hnmr (300 mhz, cdcl3): 7.95 (d, 2h, [c(2'',6'')h], 3jortho = 8.9 hz); 7.30 (d, 2h, [c(2''',6''')h], 3jortho = 8.9 hz); 6.95 (d, 2h, [c(3'',5'')h], 3jortho = 8.9 hz); 6.85 (d, 2h, [c(3''',5''')h], 3jortho = 8.9 hz); 3.85 (s, 3h, [och3]); 3.80 (s, 3h, [och3]); 3.30 (m, 1h, [c(4)h]); 3.22 (d, 1h, [c(2)h], 3j = 1.0 hz); 2.31 (m, 4h, [c(3,6)h]); 1.75 (m, 2h, [c(5)h]). 13c-nmr (50 mhz, cdcl3): 200.4 [co]; 163.4 [c(4'')]; 159.0 [c(4''')]; 133.3 [c(1'')]; 130.5 [c(2'',6'')]; 129.0 [c(1''')]; 126.5 [c(2''',6''')]; 113.8 [c(3''',5''')]; 113.7 [c(3'',5'')]; 60.6 [c(4)]; 59.6 [c(1)]; 55.5 [och3]; 55.3 [och3]; 40.2 [c(2)]; 28.6, 26.9, and 23.2 [c(3,5,6)]. ir (kbr): 3060w (νch aromatic), 2995m, 2960s, 2940s, and 2910s (νch aliphatic), 2840m (νch in ch3), 1655s (νc=o), 1600s, 1570s and 1510s (νcc aromatic), 1455m, 1440m, 1420m, 1370m, 1355w, 1315s, 1285w, 1250s (νco), 1200m, 1180s, 1110m, 1030s, 990m, 960m, 895w, 845m, 825s (δch out-of-plane), 790w, 765m (δch out-of-plane), 23 heiko patzelt 690w, 630w, 610m. ms (ci, nh3): 340.2 (15.5%), 339.0 (100%, [m+h]+), 322.3 (4.7%), 321.1 (32.1%, [m+h-h2o]+). ma for c21h22o4 (338.40): calc. c 74.46, h 6.72; found c 74.03, h 6.72. 3.6 cyclopropyl-(4-methoxyphenyl)-(5-pyrimidinyl)-methanol (ancymidol) (17) n-butyllithium (1.6 m in hexane; 31.3 ml, 50.0 mmol) was slowly added (over 2 h) to a solution of 5-bromopyrimidine (16, 8.0 g, 50.0 mmol; sublimed in vacuo) and the anisylcyclopropyl-ketone 8 (8.8 g, 49.9 mmol) in anhydrous thf (100 ml), at -100°c under a n2atmosphere. stirring at that temperature was continued for a further 1 h before the solution was poured into nh4cl and extracted with etoac. the combined organic layers were washed with nh4cl, nahco3, and brine, and dried over mgso4. evaporation of the solvent gave a slightly yellow oil (12.4 g), which crystallized over night in the refrigerator. re-crystallisation from etoac gave pure ancymidol (17, 9.4 g, 36.7 mmol, 73.5%) as a white powder. m.p.: 110°c. 1h-nmr (300 mhz, cdcl3): 9.00 (s, 1h, [c(2''')h]); 8.69 (s, 2h, [c(4''',6''')h]); 7.38 (d, 2h, [c(2'',6'')h], 3jortho = 8.9 hz), 6.88 (d, 2h, [c(3'',5'')h], 3jortho = 8.9 hz); 3.81 (s, 3h, [och3]); 2.79 (s, 1h, [72]); 1.55 (m, 1h, [c(1')h]); 0.75 (m, 1h, [c(2')h]); 0.53 (m, 3h, [c(2',3')h]). 13c-nmr (50 mhz, cdcl3): 159.2 [c(4'')]; 156.9 [c(2''')]; 155.1 [c(4''',6''')]; 140.7 [c(1''')]; 137.3 [c(1'')]; 128.3 [c(2'',6'')]; 113.8 [c(3'',5'')]; 74.4 [c(1)]; 55.3 [och3]; 21.5 [c(1')]; 2.5 and 1.0 [c(2',3')]. ir (kbr): 3200br s (νoh), 3000m (νch aromatic), 2970w and 2930w (νch aliphatic), 2830w (νch in ch3), 1620s, 1580s, 1560s, and 1510s (νcc aromatic), 1460m, 1435m, 1435s, 1400m, 1305m, 1250s (νco), 1205m, 1170m, 1145m, 1110w, 1100w, 1050w, 1030m, 1010m, 990m, 980m, 960w, 910w, 880m, 850w, 825s (δch out-of-plane), 805w, 790w, 780w, 720m (δch out-of-plane), 635m. ms (ci, nh3): 257.3 (100%, [m+1]+), 228.3 (40%). ma for c15h16n2o2 (256.31): calc. c 70.29, h 6.29, n 10.93; found c 70.43, h 6.39, n 10.72. 4. acknowledgements the author is grateful to daniel rentsch, hans frohofer and norbert bild, who performed most of the spectroscopic analyses at the university of zurich, to john a. robinson for helpful discussions, and to gregory h. p. roos for valuable comments on the manuscript. references block, d.l. 1981. the chemistry of the sulphonium group. in: the chemistry of the sulphonium group (ed. by stirling, j. w.), pp. 680-702. new york: wiley. casey, m., leonard, j., lygo, b. and procter, g. 1990. advanced practical organic chemistry. new york: chapman and hall. close, w.j. 1957. an improved synthesis of cyclopropyl phenyl ketone and related substances j. am. chem. soc., 79, 1455-1458. coolbaugh, r. c., hirano, s. s. and west, c. a. 1978. studies on the specificity and site of action of ancymidol, a plant growth regulator. plant physiol., 62: 571-576. corey, e.j. and chaykovsky, d.l. 1965. dimethyloxosulfonium methylide and dimethylsulfonium methylide. formation and application to organic synthesis. j. am. chem. soc., 87, 1353-1364. coulson, c.j., king, d.j. and wiseman, a. 1984. chemotherapeutic and agrochemical applications of cytochrome p-450 ligands. trends biochem. sci., 10: 446-449. davenport, j.d., hackler, r.e. and taylor, h.m. 1968. fungicidal 5-substituted pyrimidines, european patent application (for: eli lilly & co., greenfield, in, usa). murphy, p.j. and west, c.a. 1978. an enzymic site of inhibition of gibberellin biosynthesis by amo 1618 and other plant growth retardants plant physiol., 62: 571-576. 24 efficient synthesis of the plant growth regulator ancymidol ortiz-de-montellano, p.r. 1988. suicide substrates for drug metabolizing enzymes: mechanisms and biological consequences. in: progress in drug metabolism (ed. by gibson, g.g.), pp. 99-148. london: taylor & francis. ortiz-de-montellano, p.r. and reich, n.o. 1986. inhibition of cytochrome p450 enzymes. in: cytochrome p450 (ed. by ortiz-de-montellano, p. r.), pp. 273-314. new york: plenum press. patzelt, h. and robinson, j.a. 1993. biosynthesis of the polyether antibiotic monensin a: incorporation of a polyketide chain elongation intermediate. j. chem. soc.; chem. commun., 1258-1260. perrin, d.d. and armarego, w.l. f. 1988. purification of laboratory chemicals. oxford, uk: pergamon press. rademacher, w. 2000. growth retardants: effects on gibberellin biosynthesis and other metabolic pathways. annu. rev. plant physiol. plant molec. biol, 51: 501-531. santelli, m. and bertrand, m. 1973. synthèse d'alcools ß-alléniques par réduction des ènes-2 yne-4 ols-1. première partie. bull. soc. chim. fr., 2331-2335. taylor, h.m., jones, c.d., davenport, j.d., hirsch, k.s., kress, t.j. and weaver, d. 1987. aromatase inhibition by 5-substituted pyrimidines and dihydropyrimidines. j. med. chem., 30: 1359-1365. testa, b. and jenner, p. 1981. inhibitors of cytochrome p450s and their mechanims of action. drug metabol. rev., 12: 1-117. trost, b.m. and melvin, k.l. 1975. sulfur ylides. new york: academic press. received 17 february 2002 accepted 26 may 2003 25 efficient synthesis of the plant growth regulator ancymidol heiko patzelt department of chemistry, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, email: patzelt@squ.edu.om. references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, (2002) 71-80 © 2002 sultan qaboos university experimental modeling of monolithic resistors for silicon ics with a robust optimizer-driving scheme philippe leduc (1,2), didier magnon(1), and fabrice guitton (2) (1) power microelectronic laboratory (l.m.p),tours university,16 rue pierre et marie curie, 37071 tours cedex 2, (2) application and system engineering stmicroelectronics,16 rue pierre et marie curie, 37071 tours cedex 2, france, e-mail: philippe.leduc@st.com لنظام امثل ومتين silicon rf ic’s المستخدمة في " monolithic "النموذج المعملي للمقاومات فيليب لوديك وديدي ماينون وفابريس فيتون تعتـبر اليوم مكتبة النماذج التفصيلية التي تصف السلوك الكهربائي للعناصر المتكاملة في مدى تردد الراديو اساسية : خالصـة متكاملة على سيليكون ونتج عنها دائرة أحادية النوع" tan"عملت دراسة تمهيدية على مقاومات . المعقدةلتمثيل الدوائر )type п(لعناصر مجّمعه. يقـدم هـذا البحـث طريقة الستخالص فعال لعناصر الدائرة المصممة باسلوب مثالي باستخدام الحاسب اآللي اعتمادا على قيم تشير في معظم الحاالت إلى حساب العناصر المجمعة للدائرة التي تقود إلى تمثيل دقيق لترددات الرنين نتائج البحث . ابتدائـية . الذاتي abstract: today, an exhaustive library of models describing the electrical behavior of integrated passive components in the radio-frequency range is essential for the simulation and optimization of complex circuits. in this work, a preliminary study has been done on tantalum nitride (tan) resistors integrated on silicon, and this leads to a single π-type lumped-element circuit. an efficient extraction technique will be presented to provide a computer-driven optimizer with relevant initial model parameter values (the "guess-timate"). the results show the unicity in most cases of the lumped element determination, which leads to a precise simulation of self-resonant frequencies. keywords: rf ics, tan resistors, experimental modeling, circuit optimization, guess-timate. 1. introduction t he current trend in the development of application is to combine silicon integrated circuits and high frequency circuits into a compact module. the impact of such an innovation is huge since it concerns common electronic devices: pagers, mobile phones, global positioning systems, all of which work in the radio-frequency domain. if the integration of passive components directly aims at decreasing circuit size, the electrical performance has also improved limiting interconnection parasitics. due to the micrometric dimensions of integrated circuits, electromagnetic interactions of a component with the surrounding environment become non-negligible and lead to non-trivial frequency responses. in order to anticipate design problems and quickly propose a product meeting specification requirements, it is primordial to precisely predict the behavior of a large number of passives as a function of their geometry, in a frequency range as wide as possible (until 6 ghz). the characterization of passive components requires at microwave frequencies to take into account physical phenomena such as fringing fields, skin effect, eddy currents (chen and munoz, 1997)… these phenomena, closely related to the manufacturing process and the component geometry, are 71 philippe leduc , didier magnon and fabrice guitton much too complex to be solved analytically. today, electromagnetic field-solvers are available and evaluate the field distribution using various numerical methods. to draw up an exhaustive review of all the techniques that have been proposed over the last five decades would be impractical here. instead, only the techniques that have been commonly implemented in commercial simulators will be mentioned, such as the finite difference time domain method (fdtd) (ciampolini et al., 1996), the finite element method (fem) (itoh ,1989), the method of moments (mom) (harrington, 1968) and the transmission line matrix method (tlm) (johns, 1987). a major drawback of three-dimensional (3d) structure simulations is that sophisticated skills in numerical analysis on behalf of the user are required in order to get meaningful results. furthermore, processing speed and memory capacity available on calculators considerably limit the size of the structures which can be analyzed within a reasonable amount of time (long and copeland, 1997), especially if a sufficiently fine array of sampling nodes is chosen to have any hope of an accurate computation. 2d and 2.5d simulators are rapid and allow the study of complex layouts respectively in a planar and mostly planar configuration. nevertheless, they remain inadequate because they do not completely describe the interaction with the subjacent substrate. fruitful attempts have been led to interpolate the measured response with a rational polynomial function (choi and swaminathan, 1999). a synthesis technique is then applied to generate a lumped element equivalent circuit. however, this method cannot ensure positive circuit elements to fully correlate with the physical layout. we believe a simplified circuit model based on the insights achieved from measurements greatly simplifies the numerical modeling process. advanced problems are often best solved by an evolutionary approach whereby a problem with a smaller number of variables is solved first. it also provides the circuit designer, thanks to the direct relation that can be established between a physical phenomenon and its electrical representation, with a deeper understanding of the component behavior. although electrical models derived in this experimental way cannot be scaled to reflect changes in the layout or fabrication technology, they are still imperative for more advanced models. a scalable model allows the circuit designer the flexibility to tailor the design for a given rf application. scalability implies that the electrical circuit parameters can be deduced from geometric and technological specifications, and consequently is closely linked to the underlying physics (yue and wong, 2000). they can be directly used in the time domain, performing for instance a transient analysis with spice, or in the frequency domain, using tools such as touchstone. the complete model can also be reduced to a compact form or a reflection representation (s-parameter matrix) for a fast optimization of complex rf circuits. this objective cannot be reached without a robust method to extract the model elements. zhao et al. (1997) have shown that s-parameters’ sensitivities to circuits parameters differ enormously, which means that for one objective function, local minima may very easily upset the minimization process. moreover, they propose a very interesting optimization method based on an exponential gradient learning algorithm, stemming from neural network research. once again, such a method needs good expertise in computer science to be fully exploited. this paper aims to put forward a parameter extraction process based on a deep and rigorous analysis of the model elementary cell. indeed, mathematical relations can be established for model component values to be compatible with the few qualitative measurement configurations obtained. on the one hand, the dimension of the fitting problem, the parameter variation extent and consequently, the problem complexity, are diminished. on the other hand, by providing the optimizer with good initial values, we can reduce the chance of hitting local minima. choosing the appropriate initial values not only speeds up the minimization process, but also gives rough interpretation of the measured data. thus, a commercial computer-driven optimizer oriented with explicit optimization rules becomes a powerful investigation tool. 2. test fixture design in order to obtain valuable insights into the embedded resistors, a set of resistors with increasing sizes as well as their testing structures were built onto wafer, as shown in figure 1. 72 experimental modeling of monolithic resistors dut figure 1. short, open and load coupons. experimental data were collected from the measurements of the two-port s-parameters for each resistor dummy structures. ceramic impedance-standard-substrate (iss), which provides the standard short, open, load and thru fixtures (solt), was used to calibrate until 6 ghz the general 2-port network analyzer hp-8753e up to picoprobe coplanar groundsignal-ground probes. a de-embedding procedure is necessary in order to extract the useful signal from the measurement environment. in this way, each device-under-test (dut) is accompanied by an empty pattern designed to measure the influence of the ground ring necessary to ground the probes for the network analyzer, and a filled pattern to measure the inductive effects of the pads and access lines necessary for connecting the probes to the component. a common compensation technique consists in subtracting the y parameters of the open pattern to the total y, and then subtracting the z parameters of the short pattern to the resulting z matrix. this procedure proved to be inadequate in our case, because of the testing pattern structure. the three-step method was preferred (kolding, 1999): this involves an electrical representation of the different patterns to explicitly express the parallel (zp1, zp2), serie (zs1, zs2), and transmission (zopen) related parasitics, shown in figure 2, as functions of the measured scattering parameters. zs1 zs2zopen zp1 zp2z1 z2 z3 figure 2. embedded device modeling. 3. equivalent circuit model a single π-type lumped-element circuit (as shown in figure 3) has been used to fit experimental results. this idealized representation, the simplest mentioned in the literature, is a first step to build up a model library since it permits the modeling process set up to be validated. the equivalent circuit is based on our understanding of the integrated resistor physical structure. a tan layer is deposited on a sio2 layer of thickness 1.2 µm. tan is used because of the remarkable stability of its electrical characteristics with temperature (thermal coefficient resistor of the order of ± 100 p.p.m. / °c). the silicon substrate is p+ doped and presents a bulk resistivity from 18 up to 22 mω.cm. branches z1 and z2 model the electromagnetic coupling to the substrate through the sio2 insulation layer. the thick oxide layer can be considered as a perfect dielectric and is represented with crossover capacitances cox1 and cox2. the substrate behavior depends upon 73 philippe leduc , didier magnon and fabrice guitton both its resistivity and the frequency of the propagating wave. however, the substrate tends to behave as a lossy dielectric as the operating frequency enters the giga-hertz range. csub1 and csub2 reflect the dielectric nature of the substrate whereas rsub1 and rsub2, connected in parallel, represent the effective resistances due to ohmic losses in the substrate. z1 z2 z3 figure 3. single π-model. the impedance z3 models the tan deposit. l expresses the lumped inductance of the structure, which includes the self and mutual between different lines, and can be evaluated using the greenhouse algorithm (1974). rigorously, the inductance value decreases with frequency seeing that the magnetic field penetration in the conductor diminishes with frequency. this effect remains slight and can be neglected because the inductance is principally determined by the external magnetic field distribution. the r1 and r2 resistances, controlling the z3 module respectively at low and high frequencies, approximate the frequency evolution of the current distribution in a conductor of finite thickness, this without introducing frequency dependent components. lastly, the capacitance c globally describes the proximity electric coupling existing between parallel conducting strips and the current crowding at the corners of rectangular turns. 4. model extraction optimization is encompassed in a branch of mathematics named operations research, described by bronson as being "concerned with the efficient allocation of scarce resources" (bronson,1982). it is practically assimilated to curve fitting, defined as a procedure for finding the best fitting curve to a given set of points by minimizing the offsets of the points from the curve. the figure-of-merit function, that measures the agreement between the data and the model, is conventionally arranged so that small values represent close agreement. an efficient and accurate solution to any optimization problem is not only dependent on the size of the problem in terms of the number of adjustable variables, but also on characteristics of the objective functions. optimization problems can be broadly categorized in three classes: linear problems, quadratic problems and lastly, the more difficult to solve, non-linear problems in which the objective functions and constraints are non-linear functions of the variables. a wide spectrum of numerical methods exists for finding function stationary values in a multi-dimensional topography, and can be separated in terms of the derivative information that is, or is not used. for instance, the downhill simplex search, due to nelder and mead (nelder and mead,1965), requires only function evaluations, not derivatives, whereas gradient based techniques such as the levenberg-marquardt method (more, 1977) use information about the slope of the function to dictate a direction of search where the minimum is thought to lie. 74 experimental modeling of monolithic resistors 4.1 guess-timate issue an optimization process can take many iterations to converge and can be sensitive to numerical problems such as truncation and round-off error in gradient calculations. thus, most optimization problems benefit from good starting guesses and it appears that the initial value aptness is often the cornerstone of a successful optimization. this point is all the most critical that the objective responses reveal a strong sensitivity to the different parameters. indeed, the associated error functions are then uneven and present steep slopes, which can hold even the most subtle optimization algorithms in check. the aim of the mathematical relations introduced in this paper is to reduce the system degrees of freedom and provide the trial function parameters with relevant initial values. from this estimate, it is then possible to closely match the measured data by the refinement of these parameters. this approach is simple to implement with most commercial simulators that have the capability to optimize circuit parameters, and it requires little computation time to refine the small of parameters in a decoupled lumped-element π-model. in order to gain clarity, the scope of our demonstration is limited to the elementary cell z3. the developed method rests on a thorough analysis of the function real part [ ])(3 ωzeℜ . [ ] 222 21 2 2 0 2 4 0 4 2 22 21211 3 )(1 )( )( ω ω ω ω ω ω ω crr rcrrrrr ze ++         − ⋅+⋅++ =ℜ where lc 0 1 =ω . (1) this function depends on one experimental variable: ω, and four fitting parameters: r1, r2, l and c. all the following results, summed up in table 1, can be easily extended to the substrate coupling models z1 and z2, observing that the serial capacitance cox has no effect on the impedance real part. 4.2 dc and ac resistances r1 and r2 values can theoretically be derived respectively from low and high frequency measurements, i.e.: [ ] 13 0 )(lim rze =ℜ → ω ω [ ] 23 )(lim rze =ℜ +∞→ ω ω (2) the approximations needed to establish statements (2) have been formalized to give rise to low and high frequency (lf and hf) conditions, see table 1. these relations permit to quantitatively evaluate the veracity of the implicit assumption that the highest frequency sample measured can be assimilated to infinity and the lowest frequency sample to zero. if the low frequency resistance r1 can always be evaluated with a dc measurement, the determination of r2 as a limit is trickier. the impedance imaginary part [ ])(3 ωzmℑ is being studied at present in order to avoid element determination from limit conditions. 4.3 inductance and capacitance either 20 2 12 ωω ⋅ − − =+ ll ll , 20 2 12 ωω ⋅−=− r r , with )( 2 21 1 1 rr cr l += , )( 2 21 2 2 rr cr +=l . the first-order derivative with respect to the pulsation ω is the following (3): 75 philippe leduc , didier magnon and fabrice guitton [ ]{ } 2 222 21 2 2 0 2 4 0 2222 2 0 2 2122 3 )(1 ))(( 2 )(2 )(         ++         −⋅ −−         −+⋅ =ℜ −+ ω ω ω ω ωωωω ω ω ω ω crr crrrr ze d d (3) analysis of this function leads to trinomials and fourth degree polynomials. basically, all the relations concerning l and c are results of the discriminant positivity criterion, in order to ensure real and positive solutions. three different cases were distinguished depending on the relation between r1 and r2. for each case, the existence condition of an extremum transferred to inductance l, the additive restricting relations determining the extremum nature, the capacitance intervals and the correlated l1 and l2 values compatible with an extremum at pulsation ω1, are derived (see table 1). it must be pointed out that the system has, in the worst, case two remaining degrees of freedom (r2 and c), and in most cases one degree of freedom (c). table 1: z3 elementary cell “cartography”. r relation 21 rr < 21 rr = 21 rr > limit inductances l1, l2 )( 2 21 1 1 rr cr l += )( 2 21 2 2 rr cr l += crl 21= )(2 21 1 1 rr cr l += )( 2 21 2 2 rr cr l += extremum existence intervals ] [ ] , ,0 21 +∞∪∈ lll [ ] [ ] [ , ,0 +∞∪∈ lll ] [ ] , ,0 12 +∞∪∈ lll [ ] [ ,0 1ll ∈ ] [ , 2 +∞∈ ll ] [ ,0 ll ∈ ] [ , +∞∈ ll ] [ ,0 2ll ∈ ] [ , 1 +∞∈ ll extremum nature minimum maximum minimum maximum minimum maximum limit resistance rlim ∅ ∅ 1 2 1 2 1 12 11 2 r r r r r −− −− ⋅ 1 2 1 2 1 12 11 2 r r r r r −+ −+ ⋅ inductance giving a resonance at pulsation ω1                 −⋅        −±⋅+= 2 2 2 2 2 12 2 1 2,1 11122 1 c c c cl c l ω c l 2 1 1 ω = l-c compatibility condition ∅ ∅ ] ] [ , ,0 12 +∞∪∈ ccc [ c1         −+⋅ + 11 1 21 1 2 1 221 r r i r rrω 21 1 rω 2 1 1 2 1 2 1 2 21 1 2 1 1 2         −+−⋅ + r r r r r r rω c2         −−⋅ + 11 1 21 1 2 1 221 r r i r rrω 21 1 rω 2 1 1 2 1 2 1 2 21 1 2 1 1 2         −−−⋅ + r r r r r r rω ] ] ,0 2cc ∈ [ [ , 1 +∞∈ cc bracketing intervals l1, l2 ] [ , 21 +∞∈ ll ] [ ,0 12 ll ∈ ] [ ] [ , ,0 +∞∪∈ lll ] [2121 , ),( +∞∈ lll ] [2221 ,0 ),( lll ∈ minimum maximum [ ] lim13 )( rze <ℜ ω [ ] lim13 )( rze >ℜ ω inductance choice criterion 2ll = 1ll = ∅ 2ll = 1ll = lf hypothesis validity crr )( 1 21 min + <<ω crrcrrl r ))(( 2121 1 min ++ <<ω hf hypothesis validity lc 1 max >>ω l rr 21 max + >>ω lcr r 2 1 max >>ω l rr 21 max + >>ω                 −⋅        −±⋅+= 2 2 2 2 2 12 2 1 2,1 11122 1 c c c cl c l ω 76 experimental modeling of monolithic resistors 5. examples and discussions the r1, r2, l and c parameters of the compact model have been shown to be identifiable through a combination of parameter identification and fitting with the aid of a computer-driven optimizer. in our study the eldo’s general-purpose electrical circuit optimization program opsim is used, relying on a traditional gradient descent method. to demonstrate the guesstimate accuracy, the extraction procedure outlined in the previous part is applied to the case of a 1 kω integrated resistor. • the dc resistance r is simply derived from the corresponding limit relation (2). 1 ][ )( min31 ωzer ℜ= = 975 ω. • the profile [ )(3 ]ωzeℜ is not constant in the high frequency domain. hence, the precision on the ac resistance determination is limited to a domain centered on [ ])( max3 ωzeℜ = 965 ω, for instance [930 , 1000] ω. the parameter initial value is set to the interval mean value, r2 = 965 ω. • measurements show a self-resonant frequency at approximately 0.5 ghz that is to say ω1 = 3.15×109 rad.s-1. assuming r1 > r , one can conclude that l has to belong to the interval and c to the interval in order to be consistent with the maximum observed. the value of the limit capacitance c 2 ] , 0 2c] , 1 ∞+l 15 0. ∈c [ ] ] ] 2 is straightforwardly deduced from r1 and r2 terms: c2 ≅ 0.3 pf, from which we infer the following capacitance variation domain pf. figure 4 represents the compatible inductance solutions l[ 35.0 , 1 and l2 as functions of the capacitance c. • we have [ )( 13 ωzeℜ = 1052 ω and rlim = 1022 ω. the inequality [ )( 13 ]ωzeℜ > rlim is verified, which enforces the choice of the solution l1. the inductance interval correlated to the capacitance range is consequently deduced: [ ] 700 , 300 ∈l nh. 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 150 200 250 300 350 400 450 500 550 600 650 700 capacitance (pf) r el at ed in du ct an ce (n h ) solution l1 solution l2 domain limits l1, l2 maximum domain minimum domain figure 4. compatible l and c values. 77 philippe leduc , didier magnon and fabrice guitton 10 -3 10 -2 10 -1 10 0 10 1 960 970 980 990 1000 1010 1020 1030 1040 1050 1060 frequency (ghz) r e[ z 3] (o hm ) re[z3] measured re[z3] modeled figure 5. 1 kω tan resistor, real part. 10 -3 10 -2 10 -1 10 0 10 1 -50 -40 -30 -20 -10 0 10 20 30 40 50 frequency (ghz) im [z 3] (o hm ) im[z3] measured im[z3] modeled figure 6. 1 kω tan resistor, imaginary part. 78 experimental modeling of monolithic resistors measured and modeled values of z3 are plotted as in figure 5 and figure 6 in semilogarithmic scale. the optimization stretches from 3 mhz to 6 ghz and turns on both the real and imaginary parts of the impedance as objective functions. the results are the following: r2 = 972 ω, l = 339 nh and c = 0.31 pf. a correct agreement is noticed between the real and imaginary parts of the impedance measured and the lumped element model. the coherence of the established model is controlled evaluating the low and high frequency requirements concerning ωmin = 2.07×107 rad.s-1 and ωmax = 3.77×1010 rad.s-1. the first condition imposes ωmin << 1.60×109 rad.s-1, and the second leads to ωmax >> 5.74×109 rad.s-1. the latter is not totally fulfilled and consequently, it is confirmed that the infinite limit does not appear in this case as the best way to determine the constant r2. the extracted value of the inductance, l = 339 nh, is much too large to represent a physical reality. in order to evaluate the substrate nature influence on the structural modeling of the deposit (z3), a component with the same geometry has been processed on a glassy substrate. it appears that the resonance is much less pronounced and can be neglected. indeed, as a dielectric material, glass presents a very weak conductivity, which considerably limits any magnetic coupling. we can therefore conclude that impedance z3 cannot be fully assimilated to the tan deposit on the oxide surface, but also reflects a coupling with the silicon substrate. this fact is simply explained if we keep in mind that this interaction is intrinsically distributed and cannot be rigorously reported on two parallel branches (z1, z2). moreover, applying the foregoing procedure to resistors of different layouts, it has been proved that while the size of the resistor becomes bigger and bigger, the different coupling effects will be more and more complicated, and it becomes harder and harder to fit the measurement due to the simplification inherent to a one-cell model. 6. conclusions this study has pointed out optimization issues inherent to the over-sensitivity of the measured responses to the different fitting variables. in order to solve this problem, an analytical direct method for circuit elements extraction has been developed. decoupling substrate and component modeling through a π-representation of a two-port network limits the number of fitting variables to determine simultaneously what makes parameter extraction by an optimization process more stable. if the results, qualitatively correct, are encouraging, it is clear that a single π-type lumped-element circuit is inadequate to correctly describe components of complex geometries over the total frequency domain. our research efforts are now focusing on extending the extraction procedure to a multi-cell model. references bronson, r., 1982. schaum's outline of theory and problems of operations research. new york, mcgraw-hill. chen, d.x., and munoz, j.l., 1997. theoretical eddy-current permeability spectra of slabs with bar domains. ieee transactions on magnetics, 33: 2229-2244. choi, k.l., and swaminathan, m., 1999. synthesis of equivalent circuits for two-port integral passive components. conference on high density packaging and mcms. ciampolini, p. 1996. integrated fdtd and solid-state device simulation. ieee microwave and guided wave letters, 6: 419-421. greenhouse, h., 1974. design of planar rectangular microelectronic inductor. ieee transactions php, 10: 101-109. harrington, r.f., 1968. field computation by moment methods. the macmillan co., new york. itoh, t., 1989. numerical techniques for microwave and millimeter-wave passive structure. new york, john wiley & sons. 79 philippe leduc , didier magnon and fabrice guitton johns, p.b., 1987. a symmetrical condensed node for the tlm method. ieee transactions on microwave theory techniques, 35: 370-377. kolding, t.e., 1999. on-wafer calibration techniques for giga-hertz cmos measurements. proceeding ieee 1999 international conference on microelectronic test structures, 12: 105110. long, j.r., and copeland, m.a., 1997. the modeling, characterization, and design of monolithic inductors for silicon rf ic’s. ieee journal of solid-state circuits, 32: 357-369. more, j.j., 1977. the levenberg-marquardt algorithm : implementation and theory. numerical analysis, lecture notes in mathematics 630, ed. g.a. watson, springer verlag, 105-116. nelder, j.a., and mead, r., 1965. a simplex method for function minimization. computer journal, 7: 308-313. yue, c.p., and wong, s.s., 2000. physical modeling of spiral inductors on silicon. ieee transactions on electron devices, 47: 560-568. zhao, j., frye, r.c., dai, w.w., and tai, k.l., 1997. s parameter-based experimental modeling of high q mcm inductor with exponential gradient learning algorithm. ieee transactions on components, packaging, and manufacturing technology part b, 20: 202210. received 11 june 2001 accepted 10 february 2002 80 experimental modeling of monolithic resistors for silicon ics with a robust optimizer-driving scheme philippe leduc (1,2), didier magnon(1), and fabrice guitton (2) ýíáíè áæïíß æïíïí ãçíäæä æýçèñíó� equivalent circuit model model extraction 4.1 guess-timate issue 4.2 dc and ac resistances 4.3 inductance and capacitance examples and discussions conclusions electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 11-22 © 2002 sultan qaboos university e-business development : a strategic view saad haj bakry department of electrical engineering, king saud university, riyadh, saudi arabia, email: shb@ksu.edu.sa. نظرة استراتيجية : تطوير العمل إلكترونياً سعد علي الحاج بكري ويعود ذلك إلى أن أهمية . بالنسبة للدول والمؤسسات واألشخاص " العمل إلكترونياُ " في أهمية يشهد العالم اليوم تزايداً : خالصة غاية هذا البحث هي تقديم . هذا النوع من العمل يعطيهم كفاءة أفضل ، حيث يربطهم معا في إطار متكامل على مستوى العالم ثم يعطي . يف بالعمل إلكترونياُ ، وتقديم مراجعة لتطوراته الحالية يبدأ البحث بالتعر . نظرة استراتيجية لتطوير العمل إلكترونياً وعلى أساس هذا اإلطار ، يطرح البحث . إطار عاماُ لتطوير هذا العمل ، يشمل التعريف بالعناصر المختلفة المرتبطة به لضوء على الخطط المستقبلية الالزمة التوجهات المستقبلية التي ينبغي أخذها بعين االعتبار لتطوير العمل إلكترونياً ، ويلقى ا . لذلك summary e-business is becoming increasingly important for countries, organizations and individuals, as it gives them efficiency, and as it integrates them together, and with the world at large. this paper aims at providing a strategic view of the development of e-business. it starts by identifying e-business, and by reviewing its current progress. it then presents an e-business development profile, that defines the various elements associated with it. based on the profile, the paper then provides future development guidelines, and identifies recommended plans. keywords: electronic business, electronic commerce, electronic services. 1. introduction m any publications, including magued et al (1998), have previously addressed the role of information technology (it) utilization in national development, and in the promotion of the competitiveness of organizations in various countries, operating in different fields. e-business is concerned with the collective utilization of it, and therefore it is associated with national development, and it is related to the competitiveness of organizations. the european union (eu) lisbon summit meeting of 15 european leaders, ending on march 24, 2000, has emphasized the importance of e-business for economic growth and for better jobs. this paper is concerned with introducing a strategic view for the future development of e-business, which may help interested organizations and countries. as a background to the subject, this section attempts to identify ebusiness, and to explore its current progress. 1.2 identifying e-business e-business can be defined as “publishing information, and performing different types of transactions, or chains of them, electronically over intranets, extranets, and the internet”. this may be within organizations, or between them, and with the involvement of individual customers. the outcome would widen the availability of information, and enhance work integration up to the 11 11 saad haj bakry world level; and it would also save time, movement, space and paper, and consequently lower cost (jamal-aldeen et al, 2000). in the it emerging vocabulary, there are different terms related to e-business, generated for different purposes, as explained in the following: • some terms are generated to express specific functions related to a narrower concept within the e-business scope. these include: “e-government” services, “e-commerce”, “e-bargain”, “eauction”, “e-advertisement”, “e-outsourcing”, “e-procurement”, “e-care” for customers, “elearning”, and other function oriented “e-terms” (economist june 26, 1999, business week, december 13, 1999 and information week april, 26, 1999). • other terms are concerned with providing an alternative comprehensive name to e-business. “dynamic trade”, and the “para-enterprise” have been suggested (economist june 26, 1999). • in addition, one new term emphasizes the it led change in the “business environment”, and suggests that “e” in the e-business is not only for “electronic” business, but it is also for a new “ecosystem”. this illustrates that the transformation of business to e-business does not only require the “reengineering” of the corporation, but it may also need its “reinvention” (economist, june 26, 1999, hammer m, champy j. 1993). it can be seen from the terms and definitions above, that e-business is related to different “functions”, where the term may change accordingly. it can also be seen that e-business does not only “energize” business and make it more “dynamic”, but it does also generate new “environment” and “culture” for business in future. 1.3 current progress the following are some important examples of the current development, which reflects the future potential, of e-business in different parts of the world. • considering the diffusion of innovation “s” curve (roger m.r., 1983), e-business in the us and canada is about to reach the threshold “of “hyper growth”. in other developed countries, like the european countries, it has already started, or expected to start, the initial stage of “slow growth” (economist, june 26, 1999). in addition, some developing countries like malaysia and india are considering “e-government” services (magued et al, 1998, information week april, 26, 1999). • the lisbon summit meeting, mentioned above and described as the “dot.com” summit, emphasized the promotion of e-business “growth” in europe, in order to close the gap with the us and canada. its stated goal is to build “a knowledge driven economy for economic growth and better jobs”. for this purpose it stressed that european “businesses and citizens should have access to inexpensive world class communications infrastructure, and wide range of information services” (cnn.com, 2000). • the “growth” of e-business in companies, associated with some sectors, such as computing and aerospace, has already reached the “s” curve threshold of “hyper growth”. in other companies of other sectors, it is in the “slow growth” stage , or under preparation to “start”. in 1998, the revenues of the inter-company trade on the internet were estimated at around $ 43 billion. it was also estimated that until 2003, the figure will double annually to reach $ 1.3 trillion (economist june 26, 1999). • companies are increasing their spending on it products and services to enhance their competitiveness. in 1995, american companies in different sectors were spending “2 to 10 %” of their revenues on it products and services. by 2005, this spending is expected to increase 12 e-business development: a strategic view and reach the range between “5 to 20 %” (business week february 14, 2000). it should be noted that the revenues of these companies are also expected to increase making the growth of it expenditure of a multiple nature. • international development organizations like the world bank (wb), and regional development organizations like the islamic development bank (idb) are supporting the drive toward e-business in developing countries. the world bank has an it development unit that supports e-business studies, known as “infodev” at www.worldbank.org, and the idb had explored the potential of e-business in a recent conference in africa (magued et al, 1998). this can be explored by developing countries to develop their e-business, and attempt to narrow the gap with the developed world. • it companies, such as dell, cisco, sun and ibm are using e-business to promote their revenues. from this use, some companies like ibm and sun are learning the growing ebusiness “requirements” in order to provide suitable it products to the e-business market. since the e-business technology is of wide it scope, some companies, like sap, hp, and qwest are forming “joint ventures” to provide integrated e-business solutions. in addition, many e-business development companies are being formed in response to the market demands (economist june 26, 1999, business week, 13, 1999). the above illustrates the strong drive toward the development of e-business in developed and developing countries, and in the private sector. the above also shows the interest of international and regional organizations in supporting e-business for promoting development. this drive is enhanced further by its interaction with the drive of the it companies toward developing and improving the e-business technology. countries and companies should now face the need to develop e-business, or risk possible isolation from the emerging new “work environment” and “business culture”. 1.4 this paper this paper is concerned with supporting the drive toward e-business by presenting a strategic view for its development. the view consists of two parts: the first introduces “an e-business development profile”; and the second provides “development guidelines”. ◊ the “development profile” aims at identifying the elements concerned with e-business development; while ◊ the “development guidelines” aims at exploring how to achieve such development. the two parts together would help countries and organizations to set up plans for the development of e-business, in order to enjoy its benefits, and to be integrated with the emerging global business culture. 2. development profile three main elements are usually considered in technology planning: “technology”, “organization”, and “people”: top (technology atlas team 1987, linstone ha.a, 1994). in our target profile we will add the following elements: “development”, “strategy”, and “environment”, as illustrated in figure 1. the resulting profile, with its “six elements”, can then be described as the “development stope” profile. this resulting name of the profile is expressive, from an e-business viewpoint, for two different reasons. • on the one hand, to support efficiency, e-business should at one “stope” automatically initiate a chain of transactions that perform the sequence of needed tasks. 13 saad haj bakry • on the other hand, the continuous development of it, would require continuous movement forward from one “development stope” to another, in a repeated manner, to achieve continuous competitiveness. the six elements of the proposed profile are addressed in the following, starting with the “development” issues. strategy technologytechnology peoplepeopleorganizationorganization t o p environmentenvironment developmentdevelopment figure 1: the elements of the “development stope” profile. 3. development the development of e-business would have two main “objectives”. the first is concerned with the resulting business efficiency, while the second is associated with the business integration it provides among related parties. in addition, for it companies, there is one added objective, that is promoting the it market. e-business development is of a“multidimensional nature”, for the following main reasons. ♦ it is associated with different levels: the global level, the national level, and the private level, with each may be related to different sublevels. ♦ it is concerned with different parties, as no e-business is possible without having the right development for all the parties concerned. 14 e-business development: a strategic view ♦ it is related to different elements as shown in figure 1 where the development of ebusiness requires the development of its various elements. e-business development is also concerned with “time”. in this respect two issues need to be considered. ◊ as with any innovation, the diffusion, or the development, of e-business cannot have instant multidimensional “hyper growth”, as it would follow the rules of the “s” curve (economist june 26, 1999, roger m.r. 1983), mentioned above. investment in e-business should take this into account. ◊ however, special wide scale strategic support, like the case of the lisbon summit (cnn.com, 2000), would accelerate development, and shorten the “slow growth” stage of the “s” curve moving faster toward “hyper growth” (roger m.r. 1983). 4. strategy an e-business strategy provides a “basic plan” for the development of e-business. it specifies the development objectives, and determines the development directions for achieving the objectives within a given time scale. therefore, an e-business strategy is concerned with the above e-business development multidimensional characteristics associated with different levels, different parties, and different elements on the one hand, and with its growth pattern features on the other. an e-business strategy would depend on the party issuing the strategy, and its interest. for example, as mentioned above, the european union, at the european level, issued its e-business strategy for the strategic objective of achieving higher economic growth, and better jobs. its strategic direction to achieve this was to enable european businesses and citizens to access “inexpensive it infrastructure” (cnn.com, 2000). in addition, at a company level, ibm e-business strategic direction for the strategic objective of providing suitable e-business products was to “learn by doing” (business week dec, 13, 1999). it should be noted that for any e-business strategic objective, and any strategic direction, the following “tope” elements should be take into account in setting up strategic plans. 5. technology technology is of course the enabler of e-business. it can be viewed according to the following four layers, as given in figure 2. • the bottom layer is the “communications layer”, that is the core that enables networking and the integration of information services . at this layer the public and the private communications provided by various communication networks like telephone networks, data networks, highspeed atm networks, and cellular mobile networks, would be involved. • the next layer up is the “network layer”, which enables information services, including ebusiness, to be provided at a private intra-organization level (intranet), a private interorganization level (extranet), and the world at large (internet). of course, security measures, including firewalls, provide the required protected borders between these levels. • the third layer is the layer of “e-business services”. this layer is mainly based on the “web technology”, which enables e-business services to operate on intranets, extranets, and the internet levels. in addition, the services would depend on the capabilities of the 15 saad haj bakry communications infrastructure, which determines the type of information that can be transferred including data, voice, and picture. • the top layer is the layer of the “users” who can access and use the available e-business services. depending on the given services, such users may be public, or they may be authorized private users. communications layer: telephone, data, high spped / multimedia, & cellular mobile networks figure2: the layers of e-business technology network layer: intranet, extranet, & internet e-business services layer user applications the above shows that e-business depends on the communications infrastructure, the internet, and the security needed for intranets and extranets. therefore, e-business enjoys the advantages of these networks on the one hand, and faces their problems on the other. in addition, e-business services are still in their early stages of development. they still need learning and innovations. the future development of e-business would require the development of all four levels of its technology. 6. organizations the general functional view of an organization using e-business is represented in figure 3. the view shows the levels of the e-business services, and the parties associated with each level. ◊ at the “intranet level”, e-business services involve intra-organization business transactions. the users here are the staff of the organization concerned. ◊ at the “extranet level”, e-business services involve the inter-organization business transaction, in addition to the business transactions between the organization concerned and its associated individuals. the other organizations, and the associated individuals of this levels are the partners, the suppliers, and the customers of the organization concerned. each of these would have certain information access and interaction rights, and may be involved in a chain of 16 e-business development: a strategic view business transactions. it should be noted that the extranet level is replacing an older technique known as electronic data interchange (edi), as it is more flexible, and of lower cost. ◊ the e-business services of the “internet level” involves the public business transactions between the organization concerned and its potential partners, suppliers, and customers, whether organizations or individuals. the current trend of e-business development, discussed above, indicates that most, if not all, organizations including international organizations, government departments, and private enterprises would become e-business users sooner or later, depending on their environments and businesses. those who may keep away from e-business would face isolation, and loss of competitiveness. of course organizations should develop their own e-business activities, but such development depends on various other organizations, as explained in the following: ♦ the e-business activities, at both the extranet and the internet levels, do not only involve the organization concerned, but they also involve other organizations. therefore, joint e-business development among these organizations would be needed. ♦ developing e-business requires funds for building the necessary communications and internet infrastructure. such funds may not be available, particularly in developing countries, wishing to enter the information age. here comes the role of the international and the regional development funding organizations like the wb, and the idb in supporting e-business development. ♦ it companies are the generators of the e-business technology which enables the e-business activities to take place. therefore the success of these activities would depend on the success of the e-business technology products and services provided by the it companies. 7. people people, whether individuals or associated with organizations, are both the source and the target of e-business. therefore people concerned with e-business include the following. • executives and politicians concerned with making decisions on the use of e-business in their organizations and countries, or on the support of e-business development. • it people concerned with the development and management of e-business technology and services. it should be noted here that, like the various it industries, e-business would provide good job opportunities for those people, not only in it companies, but also in organizations using e-business (beck n. 1995, business week aug, 4, 1997). • people using e-business, and enjoying its benefits. those may be individuals or associated with organizations, as discussed above. 8. environment the e-business development environment is related to the state of development of the above elements: technology, organization and people. these elements are associated in turn with the interrelated issues of “knowledge”, “economy”, and “management”, in terms of which the environment is explained in the following: ◊ knowledge can be expressed in terms of the awareness, the interest, and the qualifications of people who are the source and the target of development. 17 saad haj bakry ◊ the economy is associated with the sources of income, productivity, competitiveness, and technology infrastructure. ◊ management is related to the work culture including the regulations and the security of the organization, or the country concerned, its intra-organization and inter-organization relationships, in addition to the vision and will of its decision makers. public / global transactions internet inter-organization transactions: partners, suppliers, customers: organizations / individuals extranet intra-organization transactions: intranet security security figure 3: a multi-level functional view of e-business the “development stope” profile, described above, provides a comprehensive base for the development of e-business in various countries and organizations. it gives an understanding of the various elements involved on the one hand, and it provides a reference framework for planning, and for the evaluation of the development state, at different times, on the other. 9. development guidelines the e-business development guidelines presented here are associated with the elements of the above profile, and are considered to be of three integrated dimensions. • the first dimension is concerned with providing “what is required” in order to enable the target development to take place. 18 e-business development: a strategic view • the second dimension is associated with considering “where to look for support”, that is from the specialized organizations that may support the target development. • the last dimension is concerned with “how to plan” for the development, that is the strategic plans that need to be identified. 10. requirements the basic requirements that enable the development of e-business include the following. ♦ the availability of “knowledge” in e-business. such knowledge would include general awareness of the benefits of e-business, and the importance of using it. it would also include knowledge on how to use it, and make its benefits a reality, in addition to specialized knowledge on its management and future development. ♦ the availability of the “technology” that supports e-business. in this respect the four layers of e-business technology, discussed above, should be taken into account. ♦ the “need” for e-business development, in the organization concerned, for specific objectives such as promoting competitiveness, integration with other organizations, in addition to other possible objectives. ♦ the potential “cooperation” with other organizations so that e-business can achieve its interorganization objectives. ♦ the availability of “funds” for investment in e-business development. it should be noted that by using e-business, the investment will pay back from the resulting efficiency (jamal-aldeen and al-dheelaan 1999). ♦ the availability of the right “people” including decision makers with awareness, vision and drive, trained users, and qualified it professionals. ♦ the need to “redesign” the work flow and transactions of the organization concerned, and make efficient use of the e-business capabilities. ♦ the acceptance of the new rules of the e-business “environment” and its new “work culture”. ♦ the need to “manage” continuous change that may result from the continuous progress of it in general, and e-business tools and practices in particular. it is clear that the above basic requirements are related to the e-business “development stope” profile of the previous section. in addition, these requirements can be supported by different organizations, at different levels, as will be discussed in the following. 11. support international, regional, and national organizations, with special functions and responsibilities, would support the development of e-business in public and private organizations. such support would promote e-business development, and therefore it should be taken into account. the organizations providing the needed support are addressed in the following. 19 saad haj bakry ◊ organizations concerned with setting up “development policies” at the international, regional, and national levels. examples of such organizations include the united nations (un), the european union (eu), the organization of african unity (oau), the arab league (al), the gulf cooperation council (gcc), and the national planning departments associated with governments. such organizations should support e-business development, as it contributes to economic development, like what the eu decided to do at the lisbon summit meeting. ◊ “knowledge” organizations, such as research, education, and training institutions; publishing and information media organizations, in addition to consulting organizations. these organizations can contribute to the development of e-business knowledge and experience, and to the promotion of awareness, and the provisioning of qualifications. ◊ organizations concerned with “funding” development projects at various levels, such as the wb, the idb, in addition to various regional and national development banks. these organizations can support e-business development projects through direct funding, or through supporting useful e-business development studies in knowledge organizations. ◊ international and national technology “standards” organizations, such as the american national standards institute (ansi), the internet architecture board (iab), the international standards organization (iso), and the international telecommunications union (itu). these organizations are responsible for setting up suitable standards for the e-business technology. ◊ international and national “professional” organizations including those associated with technology professionals such as the institute of electrical and electronics engineers (ieee), the institution of electrical engineers (iee), and other technical institutions; and those associated with trade and industrial development such as the chambers of commerce and industries (cci) in different parts of the world. these organizations should cooperate with organizations in different fields to give them economic advice and technical support for their ebusiness development. ◊ “it companies” including it production and it services companies should provide fine ebusiness tools and services. they should also cooperate with the professional and standards organizations for the benefit of the e-business customers. 12. recommended plans recommended e-business development plans should make use of the support of the abovespecialized organizations, and should satisfy the requirements discussed earlier. such plans are identified in the following, and illustrated in figure 4. • “initiation plan” for setting up the e-business objectives, and its development directions. • “knowledge plans” for supporting awareness, education, training, and progress. • “technology plan” for dealing with the current e-business enabling technology and its future development. • “reengineering plan” for redesigning business processes, and regulations, according to the need of the organization concerned on the one hand, and the technology to be used on the other. “security plans” for dealing with the security requirements of the e-business at its different levels. • “staff plan” for dealing with the human resources requirements, and job specifications. • “funding plan” for the evaluation of cost, and for dealing with the funding sources. • “migration plan” for transition from the existing business to e-business without interruption. • “cooperation plans” for working with other business and support organizations. 20 e-business development: a strategic view • “change management plan” for continuous improvements in response to continuous development and change, as explained in (jamal-aldeen and al-dheelaan, 1999), (bakry, s.h. 1999). • “integration master plan” for integrating the above plans and creating harmony between them during implementation. the above-recommended plans are of general nature. they would be useful for e-business development in any country, and for any organization. knowledge & awareness technology initiationreengineering security staff funding migration cooperation change management integration figure 4: recommended e-business development plans 13. conclusions this paper has attempted to build a strategic view for the development of e-business in three main stages. the first stage provided the necessary background, which illustrated the importance of e-business and its current progress. using the background, the second stage built a profile that integrates the various elements associated with e-business development. based on the profile, the third and last stage generated guidelines for the future development of e-business by highlighting the requirements, emphasizing potential support, and identifying recommended plans. the background stage is useful for awareness, and for initiating drive toward e-business development. the profile has the advantage of providing an integrated understanding of the ebusiness architecture, which can be used as a development evaluation base. the development guidelines and the recommended plans have given answers to the questions what the requirements are, where support can be found, and how development can be planned. the three stages together would help countries and organizations plan for their own e-business development, so that they can enjoy its benefits including economic growth, competitiveness, and integration with customers and other organizations and with the world at large. 21 saad haj bakry references bakry, sh., al-dhelaan, 1999. planning information networks : the scope of the customer issues. international journal of networks management; 9(1): 28-37. bakry, sh., bakry, fh., 1999. identifying information networks profiles for planning management. international journal of networks management, 10(6): 315-322. beck, n. excelerat: growing in the new economy, 1995, harper collins. business week the global search for brain power : a shortage of programmers is hobbling technology growth., august 4, 1997. business week, e.biz : a report on electronic business, december 13, 1999. business week, why the productivity revolution will spread. february 14, 2000. cnn.com/2000/world/europe. march 24, 2000. the economist, the net imperative : a survey of business and the internet, june 26, 1999. jamal-aldeen, r., bakry, sh., nouh, a., 2000. performance based evaluations of the tangible benefits of information networks. international journal of networks management ; 10 (2): 91-101. magued diouf (ministry of industry, senegal), nun, a (multimedia super corridor, malaysia), and bakry, sh (it professor and consultant). contonou, republic of benin. islamic development bank, nov. 1998, conference on preparing the ummah for the 21st century : promotion of information technology for development. hammer, m., champy, j., 1993. reengineering the corporation. harper business (collins). infodev: world bank. internet web site: www.worldbank.org. e-mail : infodev@worldbank.com. krishnan, s. it democracy in india, april 26 1999, information week, issue: 731, www.techweb.com/se/. linstone, ha. september 1994, new era-new challenge. international journal of technology forecasting abd social change, 47(1): 1-21. roger, mr., 1983. diffusion of innovations, 3rd edition. the free press (macmillan). the technology atlas team. august 1987, a framework for technology based national planning. international journal of technological forecasting and social change, 32(1): 5-35. jamal-aldeen, r., bakry, sh., nouh, a. analysis of the cost effectiveness of information networks. international journal of neworks management: to appear. received 5 june 2001 accepted 9 september 2001 22 mailto:infodev@worldbank.com http://www.techweb.com/se/ e-business development : a strategic view saad haj bakry department of electrical engineering, king saud university, riyadh, saudi arabia, email: shb@ksu.edu.sa. introduction identifying e-business current progress 1.4 this paper development profile development strategy technology organizations people environment development guidelines requirements support recommended plans conclusions references research trends: science and technology, special review (2000) 55-71 © 2000 sultan qaboos university 55 research trends: natural products as pest, microbial disease as tumour control agents majekodunmi o. fatope, salma m. z. al-kindi and abdulrahman o. abdulnour plant chemistry research group, chemistry department, college of science, sultan qaboos university, p.o. box 36, postal code 123, al-khod, muscat, sultanate of oman, magek @ squ.edu.om. الزراعية ، واألمراض الميكروبية واألورام اآلفاتالنباتات الطبية كمواد لمحاربة ماجكودونمي فاتوبي ، سلمى الكندي و عبدالرحمن عبدالنور اإلهتمام المتزايد لقهر أمراض البشر والحيوانات واآلفات هو العامل األساسي الذي حث العلماء إليجاد :خالصة اإلختبار األحيائي هو الوسيلة المثلى لتحديد فعالية المواد المعزولة من . من مصادر حيويةالمواد الكيماوية الالزمة كما يناقش المقال الطرق . هذا المقال يركز على مجاالت كيمياء النباتات ذات الصلة بالصناعات . النباتات الطبية البحرية والنباتات والحشرات مع التركيز على الفنية المتبعة لعزل المواد النشطة حيوياً من الميكروبات والحيوانات . نشاطها العالجي واإلختبار األحيائي الالزم للتعرف عليها abstract: the zeal to conquer human, agronomic, and veterinary diseases or pests has always sustained research interests directed at finding new medications from under explored biodiversity. the adoption of bioassay methods, which correlate with prevention, inhibition and reversal of diseases or elimination of pests, in screening natural products for bioactive compounds is critical to the discovery of new medications. this article focuses on areas of natural products chemistry that connect academia with industry. it discusses the technical skills needed to find bioactive compounds from microbes, marine invertebrates, plants and insects, highlighting the mode of action of selected bioactive compounds and bioassay models for detecting them. it also reviews methods and prospects of genetic manipulation of organisms to produce unnatural natural products of therapeutic importance. fatope, al-kindi and abdulnour contents 1. introduction 56 2. screening for bioactive natural products 57 3. metabolites from microbial sources 58 3.1 antibacterial agents 59 3.2 pest control agents 59 3.3 biocontrol agents 60 4. metabolites from marine organisms 60 5. metabolites from plants 61 5.1 insecticides 61 5.2 antimicrobials 62 5.3 antitumor agents 62 5.4 cancer chemoprevention 63 6. metabolites from arthropods 63 7. genetic manipulation of organisms for bioactive metabolites 64 7.1 method for expressing foreign genes in microbes 64 7.2 methods for expressing foreign genes in plants 65 7.2.1 use of autonomously replicating virus as vectors 65 7.2.2 agrobacterium-mediated gene transfer 65 7.2.3 ‘shot gun’ or biolistic gene transfer 66 8. conclusions 66 9. acknowledgement 67 10. references 67 1. introduction the geo-ecological conditions that support life on earth vary from moderately wet and warm to extremely arid, hot or cold terrestrial environments, and from fresh waters to salty, acidic or alkaline aquatic habitats. organisms in different environments produce non-nutritional compounds called natural products or secondary metabolites. natural products are formed from a handful of diverse and universally present precursors such as acetyl-coa, amino acids or shikimates through an intricate web of enzymecatalyzed reactions (herbert 1989). the significance of natural products in the life of producing organism remains obscure. some natural products appear to protect the organisms from predators, diseases and challenges of hostile environment. others display biological activity with potential pharmaceutical and agricultural uses. several of them have no known uses. a plethora of natural products has been isolated from plants throughout the known history of humans, and within the last 50 years from marine organisms, arthropods, amphibians, fungi and bacteria. taken together, natural products have occupied a commanding position among drugs that are now used against agronomic pests, infective organisms, parasites of livestock and humans, and diseases such as cancer and malaria. they have also found useful applications in food and fragrance industry as flavoring agents. natural products compliment synthetic chemicals as a source of pharmaceuticals. structurally, natural products show little overlap with synthetic products. they could however be as toxic as synthetic chemicals. when used as crop protection agents, they are environmentally friendly. their biodegradation by soil microorganisms and re-integration into the environment are readily achieved. in establishing a research strategy that is natural products-based, the aims of the investigation must be well defined. in academia and industry, there are 3 broad reasons for scientific investigations in the area of natural products. they are 1) to find biologically active compounds. research plans are approved for bioactivity-driven isolation and identification of secondary metabolite if initial extracts (of plants, 56 research trends in natural products 57 arthropods, and broth) showed useful biological activity. in such a case a reliable bioassay is needed for success. 2) to screen transgenic organism for a single metabolite of commercial importance. an elaborate isolation scheme may be undesirable, but a selective and sensitive detection method using the best of analytical tools may be important. this is, in principle, a natural extension of the first objective with biotechnology skills playing a major role. 3) for re-classification of a confused phylogeny. secondary metabolites from each species of a genus are elaborately isolated, characterized and compared with one another. the first two objectives are the most important to pharmaceutical companies, grant awarding agencies and research establishments interested in natural products. the biological and pharmacological profiles of potentially useful bioactive metabolites are compiled to determine their safety, competitiveness and patentability. information is also gathered on how bioactive metabolites can be produced on a largescale through studies of biosynthetic pathways and the molecular biology of the producing organism. a good understanding of these parameters will enable scientists to manipulate secondary metabolism, shift secondary metabolic pathways within plant species and microbial strains and turn crops or microbes into flexible chemical factories or bioreactors. studies of secondary metabolites at the molecular level have been slow because of the complex pathways of secondary metabolism in higher organisms, and the absence of suitable genetic systems. the key to this may well be in genomic revolution, informatics and high throughput screening. this article will provide a realistic review from application perspectives, sustainable research trends in natural products within the academia industry interface, and elaborate on the opportunities and difficulties embedded in the exploitation of natural products. in this report, natural product is defined to include compounds isolated from microbes, marine organisms, arthropods, plants, and biocontrol agents, and also compounds obtained from manipulated biosynthetic pathways. 2. screening for bioactive natural products there has been growing interest within academia and pharmaceutical industries in bioactive natural products and the molecular basis of their activity. the hitherto common practice of phytochemists to isolate, characterize and publish phytocompounds without regard to bioactivities is no longer attractive to academic journals and funding agencies. three technologies are required for sourcing bioactive compounds. they are separation methods (martson and hostettmann 1991; van beek 1999), structural elucidation (massiot et al. 1999) and bioassay methods (fatope 1995, dey et al. 1991). bioassay technology for finding bioactive compounds has undergone major changes during the past decade. bioassay methods may be grouped into two: the in vivo model that involves the use of whole or target organisms, and the in vitro model that is enzyme, receptor, mode of action or mechanism-based. genomes now provide ever-increasing tool and platform for designing novel in vitro assay models, with new targets emerging for insecticides, herbicides, anti-infective and antitumor compounds. in vitro model is used as an ancillary screen to supplement primary in vivo screens. in the domain of pharmacology, a desired objective is to extrapolate data from in vitro experiments to in vivo models. many discoveries in the 1980s relied on in vivo models. there are quite a number of them used to detect anti-infective, antitumor, insecticidal and herbicidal agents (fatope, 1995; dey et al. 1991). in vivo models are now miniaturized for certain evaluations. they are less costly, easier to perform and more adaptable for natural product screenings. tests on whole organisms by nature are broad based and embrace multiple targets, unlike tests on in vitro models, which are target-specific. most pharmaceutical companies in the late 1990s have adopted mechanism-based in vitro assays that employ receptor binding or enzyme inhibition protocols on normal or transformed cell lines of animals, humans or plants. receptor-based assays involve the following general steps: • docking of test molecules to receptors that are connected to the response element of dna. • activation or inhibition of the expression of certain proteins mediating biological responses by compound receptor dna association. fatope, al-kindi and abdulnour 58 • biological response that may be beneficial or detrimental depending on dosage. receptor-based assays allow the design of cellular high throughput screening procedures. they are often expensive, sophisticated, specific, automated and may require in several cases a dedicated research technician. the adoption of receptor-based in vitro models for plant chemistry work may require a robust combination of several expensive assays. plant extracts are a complex library of chemical compounds, which are structurally and pharmacologically dissimilar. many potentially useful compounds in plant extracts are not detected in in vitro screens because the assays are too specific or because of interactions that occur among the components of extracts. a number of enzyme or receptor-based bioassays are very sensitive to phytosterols, tannins and saponins which are commonly encountered in plant extracts, and anionic polysaccharides found in marine organisms. it is thus a standard practice to subject extracts to chemical or biological dereplication protocols to eliminate compounds that could interfere with assay results. nci uses solid phase extraction cartridges for dereplication of tannins in aqueous extract, (cardellina et al. 1993; cordell 1995) or direct chromatography on sephadex g-25 or polyamide columns. anionic polysaccharides are precipitated from aqueous solution with equal volume of ethanol (cardellina et al. 1993). in vitro tests are routinely used to monitor the activity of fermentation and combinatorial synthesis products where structural differences between products are less contrasting. pure compounds or crude extracts that fail the in vivo test will face a formidable challenge, irrespective of the observed level of activity in vitro, in producing relevant applications. whatever model is adopted, screening methods must be sensitive, use a small amount of test materials, allow simple test sample preparation, give good results, have good throughput capacity, and a wide field of view. the assay output must correlate with an important function in disease etiology or microbial pathenogenicity. 3. metabolites from microbial sources bacteria and fungi cause several plant, human and animal diseases. they are also common sources of novel bioactive metabolites that have found useful applications as anti-bacterial, insecticidal, nematicidal, and herbicidal agents. the bio-diversity of microbes is immense. the metabolites they produce can be manipulated by changing the composition of the growth media, by combinatorial biosynthesis and ‘shot gun' cloning of their dna. these manipulations can be conducted with relative ease on prokaryotes, for example bacteria, because their genetic materials are contained in cytoplasmic chromosomes. it is more difficult to achieve the same level of success with organisms whose genetic materials are packaged in chromosomes located in the nucleus, the eukaryotes e.g., yeast, filamentous fungi and higher organisms. there are roughly three domains of microbial life on earth: the archeae, eubacteria and eukaryotes. microbes that love moderate environments are called mesophiles. several of them are culturable. mesophilic soil microorganisms, the actinomycetes, for example, have been and remain a major source of novel microbial metabolites (deyfuss et al. 1994). the discovery of bioactive compounds usually begins with isolation and identification of the microbes and growing them in a dish on appropriate media. the chemicals they produce are scaled-up by fermentation. the fermentation broth is extracted, fractionated, tested and purified. typically, mesophilic bacteria and yeast can be cultivated on standard mueller hinton agar or diagnostic sensitivity test agar (dst). testing is usually performed using the traditional wholeorganism based dilution, diffusion and bioautographic assay methods. these methods have been adequately reviewed by rios et al. (1988). kavanagh (1963) has also suggested the principles and limitations of antimicrobial in vivo assays. in recent years receptor-based in vitro assays have become increasingly popular for screening fermentation broth in the industry. as an illustration, merck scientists isolated the fungus pseudomassaria from a plant collected from a forest near kinshasha in the democratic republic of congo. its fermentation broth was extracted, fractionated and screened against a receptor-based assay, research trends in natural products 59 which monitors agents that interact with and activate the insulin receptors. this led to isolation of compound l-73281 with insulin-like properties (zhang et al. 1999). over the past 3 decades, scientists have collected and identified microbes that flourish in extreme environments. they include microbes from extremely hot (thermopiles, e.g., from hydrothermal vents), cold (pschrophiles, e.g., from the antarctica), acidic (acidophiles, e.g., from volcanic pools, abandoned coal mines or sour petroleum wells), salty waters (halophiles, e.g., from salty water of the dead sea in the middle east), alkaline pools (alkalophiles, e.g., from kenya soda filled lake magadi), high pressure regions (barophiles, e.g., from ocean floor) and from niches with above normal level of radiation. microbes that live in extreme environments are called extremophiles. most extremophiles are difficult to culture, yet they contain genetic materials that could code for and produce secondary metabolites that are medicinally useful. a number of them produce enzymes that have found useful applications in the biodegradation of chemical warfare agents (mulbry and rainina 1999). roughly 1/3 of drugs comes from 5% of microbes that can be cultured. advances in molecular biology are making genetic information that is potentially locked-up in these microbes accessible (see section 7.1). 3.1 antibacterial agents several research centers and pharmaceutical industries are screening broths and extracts of fermentation in a battery of assays, searching for natural products that could conquer new and re-emerging infectious diseases. the discovery of "wonder" antibiotics of the 1940s and 1950s brought great relief to the public and clinicians. however, today we have several antibiotics that are no longer effective at hitherto known therapeutic concentrations. streptococcus pneumonia is today untreatable with penicillin. multipleresistant staphylococcus aureus that is insensitive to common antibiotics is encountered in every hospital. drug resistant strains of mycobacterium tuberculosis and mycobacterium avium complex reduce the life expectancy of aids patients. most of the common antibacterials are obtained from microorganisms. the aminoglycosides, gentomycin and streptomycin, are produced by streptomycetes or micromonospora. chloramphenicol is a natural product isolated from the culture filtrate of streptomyces venezuela. oxytetracycline is produced by streptomyces rimosus. erythromycin is a metabolite of streptomyces erythreus. clindmycin is produced by streptomyces lincolinesis. the aforementioned antibiotics exert their effects on gram+ or grambacteria that they kill or suppress by inhibiting the synthesis of proteins necessary to retain their membrane. antibiotics such as penicillins, cephalosporins and vancomycin, which are also microbial products, exert their antibiotic effects by interfering with the biosynthesis of cell wall. protein synthesis is essential to the survival of bacteria, and the process may be divided into 3 segments namely: chain initiation, elongation and termination. in principle, every stage in this process is a potential target for antibiotic chemotypes and in vitro assay design. almost all medicinally useful inhibitors of protein synthesis act on the elongation stage. the chemotype docks on appropriate subunit of the bacteria ribosome, causing misreading of the bacteria genetic message. this results in the termination of the synthesis of appropriate protein by insertion of a wrong amino acid in the growing peptide chain. a search for novel antibacterial agents with broad spectrum of activity, better biological and chemical stability, and good tolerability will continue to dominate the attention of natural product chemists. 3.2 pest control agents investigations at sankyo, merck, glaxo and american cyanamid laboratories led to isolation of milbemycins and structurally related avermectins from the broths of various strains of streptomyces (panclatko 1998). their structures were determined using x-ray and other spectroscopic methods. using anthelmintic bioassay-guided fractionation, avermectins were also isolated from the filtrate culture of streptomyces avermititis (albers-schonberg et al. 1977) by scientists at merck and their structures were determined (albers-schonberg et al. 1981). the nemadectins, which are structural variants of milbemycin, were also isolated at american cyanamid from streptomyces cyanogriseus and at glaxo from fatope, al-kindi and abdulnour 60 streptomyces thermorchaensis. avermectins and milbemycins are effective against worms, ticks and flies. derivatives of avermectin are sold today for treatments of animal parasites. milbemycins are marketed as acaricides. avermectin potentiates glutamate and gaba-gated chloride channel opening (arena, 1995). the spinosyns are another group of commercially successful pest control microbial metabolites. they were obtained through screening of the culture of saccharospora spinosa, an actinomycete collected from the caribbean island (hoehn and michel 1990 and kirst et al. 1991). spinosyns are macrocyclic lactones. their initial insecticide activity was detected using the bench top mosquito larvicidal assay. researchers at eli lilly discovered them in 1989. spinosyns are effective against lepidopteran insects, a major field pest of cotton and vegetables. they also control diptera, aphids, mites, cockroaches and termites. dow elanco markets mixtures of spinosyns a and d (18:15) produced by fermentation for control of lepidopteran pests of cotton. spinosyns exert their effect through activation of nicotinic acetycholine receptors. they also modulate gaba-gated chloride channel systems. they are environmentally compatible, and have a rapid speed of action and low mammalian toxicity. 3.3 biocontrol agents some bacteria are able to protect plants from soil-borne fungal pathogens (howell and shpanovic 1980; keel et al. 1990; schippers et al. 1987; schroth and hancock 1982; weller 1988; dowling and o'gara 1994). they achieve this by producing secondary metabolites in situ on root surface that are antagonist of antibiotics, hydrolytic enzymes and siderophores (low molecular weight compounds that are produced as specific iron chelator by microorganisms) produced by infective fungus (dowling and o'gara 1994). it is not known why some rhizosphere bacteria or fungi produce antagonist chemicals that protect plant. perhaps they derive some benefit from the host plant. bacteria from the genera pseudomonas and burkholderia are particularly active as biocontrol agents (ligon et al. 1999). an antifungal agent may exert its effect by acting directly on an important function of fungus reproduction or growth. it may inhibit a function that is important to fungal pathogenicity or it may stimulate a plant defense mechanism. most antifungal biocontrol agents belong to the first group. the technologies for culturing and isolating microbial agent from soil rhizosphere have been covered in the hokkaido report (hasegawa 1986). microbes, which have demonstrated potential as biological control agents, can also act as a source of biologically active products (faull 1995). some biocontrol agents have been used clinically as antifungal agents to treat skin mycoses (tawara et al. 1989; umio et al. 1986). for instance, pyrrolnitrin produced by pseudomanas yrrocinna and myxococcus flavus is active against deutomycete, ascomycete and basidomycete fungus. it has been developed as a topical antimycotic drug for human uses (tawara et al. 1989). direct application of biocontrol agents is not wide spread in agriculture because of the difficulties of predicting the behavior of bacteria strains in the field. 4. metabolites from marine organisms the investigation of marine organisms for bioactive compounds started about 50 years ago, and the potential of marine organism has scarcely been explored (mcconnell et al. 1994). many marine organisms have been investigated for antitumor, antiviral and antiparasitic compounds (faulker 1995). it has been speculated that some metabolites of marine invertebrates have their origin in microalgae which can in principle be cultured (shimizu, 1993). in general, a large number of highly active antitumor compounds have been isolated from marine invertebrates. the best known examples include eleutherobin from eleutherobia family of corals, sarcodictyin from mediterranean stolonigeran coral, the bryostatins from bryozoan, bugula neritine, and the dolastatins from the sea hare, dolabell auriculata (may et al. 1987; schmitz et al. 1993). extracts of marine organisms being examined for antitumor compounds have been screened in a panel of about 60 human cancer cell lines in therapeutic areas of leukemia, breast, ovarian, renal, postrate, brain, colon, melanoma and lung cancers. candidates demonstrating in vitro cytotoxicity and selectivity can then be screened in more expensive in vivo assays. there are a number of simple bench research trends in natural products 61 top assays that may be adopted by smaller research groups as pre-screen or surrogate assays for antitumor activity (mclaughlin 1991; anderson et al. 1991). increased cell division, angiogenesis and metastasis are the major features of cancer cells. several anticancer agents interfere with microtubule assembly in cells, making it impossible for cells to divide. they dock to tubulin, the protein that forms microtubules, thus stabilizing or depolymerizing it. some antitumor gents interact directly with dna leading to dna cleavage and others inhibit topoisomerase i or topoisomerase ii involved in the replication of dna. suffness and pezzuto (1991) already covered bioassay methods based on different forms of carcinogenesis. unlike antibacterial agents that explore differences between the host and invading organism to establish their effect, the structure and biochemistry of cancer cells are remarkably similar to their healthy counterparts. as a result, targets for selective destruction of cancer cells are difficult to find. at best, most antitumor agents may be selective but not specific. many antitumor agents have more than one mode of action. a multiple mode of action could reduce resistance to drug. compounds that demonstrate activity in the cytotoxicity assay are also known to stop cancer cells from growing by initiating responses that resemble programmed cell death. the responses are characterized by morphological changes called apoptosis (fisher, 1994; cohen, 1993; steller 1995; wyllie 1995). in apoptosis, cell shrinkage, chromatin condensation, plasma membrane ruffling and degradation of cells into apoptotic vesicles occur. stimulus responsible for dna damage and cytotoxic agents could induce apoptosis. marine organisms have also yielded antiparasitic compounds. the red algae, digena simplex gave αkainic acid that is currently marketed as an anthelmintic. it is effective against whip worm, tape worm and some round worms. domoic acid, which is structurally related to α-kainic acid has been isolated from red algae, chondria armata and alsidium corallinum. it also has anthelmintic properties. consumption of sea foods containing domoic acid is responsible for amnesic shellfish poisoning in humans (lundholm et al. 1994). very few insecticidal compounds have been sourced from marine organisms in sharp contrast to plants. the annelid, lubriconeus heteropoda, has yielded nereistroxin from which synthetic pesticides were developed (blunden 1996). nereistoxin analogs have been developed and used as insecticides against coleopteran, and lepidopteran pests. 5. metabolites from plants plants are used extensively in rural communities as a source of medication for human, animal and agronomic diseases (mitscher et al. 1987). quite often, the uses of plants vary widely from one culture to another. comprehensive reports on plants as a source of drug discovery have regularly been found in the literature in the past 10 years (kinghorn and balandrin 1993; pettit et al. 1994). roughly, 5-15% of about 250,000 species of higher plant have been investigated systematically for bioactive compounds (balandrin et al. 1993). human diseases that are treated with plant materials include infections, parasitic diseases, cancer, diseases of the digestive and genito-urinary system, diabetics, malaria, etc. preparations taken from plants are used as well against insects, microbes, nematodes and weeds. 5.1 insecticides plant metabolites that influence behavior of insects are collectively called allelochemicals. some of them serve as repellents, food attractants, antifeedants, feeding stimulants or anti-nutritional factors. antifeedants are a group of highly successful allelochemicals used in insect control. they limit crop damage that may arise by feeding. they could also have direct physiological effect on pests but are not known to initiate responses that result in instant death. a prominent example is azadiractin from neem, azadirachta indica. azadiractin has a complex mode of action. it is a strong insect antifeedant and growth regulator. the insecticidal potential of neem has long been recognized and exploited in india. some neem insecticides are now marketed under the trade names margosan o and azatin (knauss and walter 1995). a number of plants that have yielded very promising antifeedants can be found in the meliaceae, rutaceae, fatope, al-kindi and abdulnour 62 labiatae asteraceae, annonacae, malvaceae and canellaceae families (jacobson 1989). allelochemicals could confer some degree of resistance on plants against pests. plants have an excellent record of providing novel chemicals that serve as lead compounds in the development of insecticides. bioactive compounds from the pyrethrum plant, for instance, typically illustrate this. extracts of the flower and head of pyrethrum gave pyrethrin i, which is responsible for killing and pyrethrin ii which, exerts knock-down activity on insects. however, these products are not stable to light and air (pachlatko 1998). scientists at rothamstead experimental station uk, united states department of agriculture, sumitomo in japan and several other commercial concerns successfully synthesized analogs of pyrethrin (pachlatko 1998) and developed them into multibillion dollar agrochemical businesses. the structure-activity relationships in synthetic pyrethroids are well-documented in recent reports (elliott 1996; henrick 1995). the pyrethroids interfere with sodium ion channels leading to prolonged opening of channels in the nerve membrane. this results in blockage of nerve signals and death in insects. jacobsons (1971) has reveiwed the insecticidal properties of natural products from the compositae, piperaceae and the rutaceae. they are reputed to provide insecticidal dienamides like pellitorine, pipercide, dihydropipercide and guineensine. analogs of these amides developed at sumitoto and wellcome foundation (pachlatko 1998) are very effective against weevil, rice stem borer, and housefly. the dienamides also interfere with sodium ion channels in the nerve membrane of insects. for a plant product to be useful as an insecticide in the field, it must be active in a range of climatic conditions. excellent performance in the green house or in the laboratory is not enough. it must be safe as determined by both scientific and political forces. it must have high insecticidal activity, low mammalian and non-target organism toxicity. plant extracts that exert their activity by modulating the gaba receptors, voltage dependent ion channels and antagonizing acetylcholinesterase or respiratory enzymes will make good candidates for development as insecticides. 5.2 antimicrobials plants in extreme environments like the desert are expected to have highly toxic metabolities since they have been co-existing for millennia with insects, viruses, and bacteria and fungi assaults, against which they must defend themselves (rodriquez 1983). in several instances, it has been shown that plants respond to microbial infection, stress, biotic and abiotic elicitors by producing low molecular weight compounds called phytoalexins. phytoalexins are usually not produced or accumulated by plants that are not under attack by diseases. phytoalexins usually have antimicrobial or antibiotic properties (mitscher et al. 1987). since they are induced-defense reaction products, it is implied that phytoalexins play an important role in disease resistance. a new research direction made possible by biotechnology is to identify the genes involved in phytoalexin biosynthesis and incorporate them into plants, hoping that their expression will confer resistance on the host plant. it is known that a small family of genes that produces stilbene synthase, bibenzyl synthase and pinosylvin synthase (hain et al. 1999, lanz et al. 1990) are responsible for phytoalexin biosynthesis. the transfer of the entire genes and their promoters at times present very difficult biotechnological challenges. phytoalexin genes which have been successfully transferred to plants like grapevine, rice, tobacco, tomato, potato, oil seed rape conferred disease resistance (hain, 1993). 5.3 antitumor agents plants have made significant contributions to the discovery of antitumor compounds (pettit et al. 1994). initially, nci started screening plants for anti-tumor activity using the leukemia model (l1210) lymphocytic leukemia in mice, sarcoma 180 in rats, and a range of carcinoma screens (cordell, 1995; gragg et al. 1997). since then, antitumor assays for plant-derived compounds have undergone several changes (suffness and pezzuto 1991). several discoveries from screening more than 120,000 plant extracts from over 35,000 species have been made and a number of new leads have been discovered. plant compounds such as acronycine, aristolochic acid, bruceantin, indicine-n-oxide, lapachol, maytansine, nitidine and research trends in natural products 63 tylocrebrine made it to clinical phase trials and failed. compounds such as vincristine, vinblastine, comptothecin, ellipticine and taxol (cai et al. 1997; mann 1992; wall et al. 1995; cragg et al. 1993 and foa et al. 1994) are used in treating cancer in spite of their excessive toxicity and limited clinical efficacy. vincristine and vinblastine affect tubulin depolymerisation, taxol stabilizes tubulin, campothecin inhibits topoisomerase i, adriamycin inhibits topoisomerase ii, bleomycin cleaves dna and 2-methyl-9-hydroxyellipticinium inhibits topoisomerase ii. these plant metabolites are also useful as positive controls in mechanistic studies of new antitumor agents. nci has recently increased her capacity to screen, to over 40,000 samples per year (cragg et al. 1997 and 1993), compared to glaxo wellcome’s 50,000 per day, using modern receptor-based assays that allow samples to be tested against normal and drug-resistant cell lines. 5.4 cancer chemoprevention cancer and hiv are the most insidious diseases confronting human race by the end of the past millennium. they are our tough adversaries in terms of mortality, morbidity and economic burden. the pathogenesis of cancer, unlike hiv, is sufficiently understood to permit development of drugs or micronutrients that can suppress, reverse or delay the carcinogenesis process. cancer disease begins by induction of dna mutation in a somatic cell, followed by tumorigenic expansion of cell clones, and conversion of tumor cells into benign or malignant cancer. cells from malignant cancer can invade distant tissues and give rise to cancer subpopulations. the process of cancer metastasis is well known (nicolson 1988; poste and fidler 1980). the treatment of cancer with drugs has been with us for about two decades, but the chemoprevention of cancer using herbal-based dietary agents dubbed “nutraceuticals,” is a relatively new concept. cancer chemoprevention is a biomedical science that seeks to prevent, delay or reverse the carcinogenesis process through ingestion of chemicals or dietary agents (hong and sporn 1997). novel natural products from plants, demonstrating in vitro cancer chemopreventive properties, have been discovered by a team of scientists at the university of illinois at chicago, usa using activity-guided fractionation (kinghorn et al. 1998). the chemopreventive agents include brassinin (mehta et al. 1995) and resveratol (jang et al. 1997), which are found in human herbal diets, and deguellin (udeani et al. 1997), a naturally occurring rotenoid. there are many reports in the literature on in vitro bioassay methods for finding cancer chemopreventive agents (lee et al. 1999 and 1998; pezzuto 1995). several of the bioassay methods are complex, expensive and mechanism-based. they nonetheless correlate with inhibition of physiologically significant stages in the carcinogenesis process. 6. metabolites from arthropod the mediterranean basin and a good portion of wet areas in the arabian peninsula are devoted to growing fruits and vegetables. insects, flies and diseases transmitted by viruses, damage produce. for almost 50 years, pests have been controlled by conventional methods that involved spraying with hard insecticides. in recent years, integrated pest management is being considered, for example in the olive growing industry, as a means of reducing heavy use of insecticides whose residues are now detectable in olive oil. integrated pest management encompasses the development of pest resistant plants, botanical insecticides, predators, parasitoids, microbial pesticides, cultural practices and semiochemicals as means of controlling pest and reducing the use of heavy insecticides. semiochemicals are defined as substances that transmit messages between insects, plants and animals through interaction with sensory or other forms of detection organs. they influence behavior or initiate physiological responses by acting as signals. pheromones are a type of semiochemicals emitted by insects which affect or modify the behavior of insects of the same species (jones 1994; hedin et al. 1988; hick et al. 1999). insect pheromones have been isolated, identified and synthesized from several species of insects (baker et al. 1980; blum et al. 1991; bartelt et al. 1991). they are highly volatile and tend to degrade fatope, al-kindi and abdulnour 64 rapidly in the field. pheromones have been used to control insect pests as physical traps, lure and kill devices, and mating disrupter. • physical traps: insects are lured to traps using pheromones, from where they are collected and killed. food attractant may also be used to lure insects to traps. in this process, some beneficial natural predators are also eliminated. • lure and kill: this technique is similar to mass trapping but once the insects are attracted, they are not entrapped but rather made to contact toxic or sterilizing agents which effectively eliminate them from the population. the kill insecticide may be dispensed or formulated as sticky droplets. a common insecticide used in a trap is pyrethroid deltamethrin. • mating disruption: in this technique, pheromones are used to attract and confuse male and female insects, thus making mating impossible. commercially useful products based on semiochemicals have been developed by novartis for the control of pectinophora gossypiella in cotton and cydia pomonella in apples (angst et al. 1990). 7. genetic manipulation of organisms for bioactive metabolites the metabolites produced by plants and microbes are closely linked to their ability to utilize various biosynthetic precursors. this ability is governed to a large extent by the genetic make up of the organism. the methods of manipulating the genes of microbes and plants have been with us for quite sometime. traditionally, strains of microorganisms that accumulate useful metabolites of commercial interest were achieved by mutation and selection and not by direct manipulation of genes. the process is not very predictive and requires repetitive cycles of directed mutation and analysis in order to optimize a useful trait or product. in the same way, traditional plant breeding has been used to produce plants with particular phenotypic traits. it is a repetitive process of selective elimination of undeserved traits, and the product could be unpredictable as well. in 1987, heinz g. floss made a case for creating novel "hybrid antibiotics" by direct manipulation of industrial microorganisms. this vision is now being fulfilled in the use of combinatorial biosynthesis to make novel polyketides (alvarez et al. 1996) and cephalosporin antibiotics in different streptomyces species (crawford et al. 1995), and derivatives of morphine and codeine in e. coli (french et al. 1995). the use of technology for plant transformation is also growing rapidly. today slow softening flavr-savr tomato, fiber-producing insect resistant cotton plants, maize, apple, sweet potato, and oilseed rape are cultivated in usa, and transgenic cucumber, and mosaic resistant tobacco in china (dale, 1995; schuler et al. 1998) to mention a few. the manipulation of organisms to express desired traits may be a natural research stategy in the millennium for natural products chemist and molecular biologist. thus, it is appropriate to explain, in the most elementary form, the principles involved in genetic manipulation of microbes and plants. 7.1 method for expressing foreign genes in microbes dna, the hereditary material, is found in all organisms with the exception of some viruses. organisms perform their biochemical activities in response to instructions encoded in the dna. new technologies now allow dnas from one organism to be shifted into another organism where they express themselves. to achieve this, the gene (a sequence of nucleotides in a dna molecule that specifies a particular function) is identified. using restriction enzymes, the gene is cut out from the donor organism and inserted into plasmids. a plasmid is a special kind of bacteria dna. it is found in the cytoplasm of bacteria. dna ligases may be used to cut open a plasmid, donor genes are spliced into it and then integrated into the cyclic plasmid loop. the recombined plasmid is inserted into a host organism. once inside the host organism, the plasmid replicates producing their exact copies or clones. the host organism research trends in natural products 65 or bacteria thus serves as a factory or bioreactor for producing the product expressed by the inserted gene. an application of this technology has been demonstrated in the production of microbial metabolites for improved biocontrol of plant pathogens (dowling and o'gara, 1994). it has also been adopted as a strategy for extracting genetic information from unculturable organisms (see section 3). this technology, now dubbed combinatorial biosynthesis, may be summarized in the following general steps. • genomic dnas are extracted from soil or samples collected from extreme environments (cullen and hirsh 1998). • the genetic materials are encapsulated in artificial plasmids, the bacteria artificial chromosome vector (bac) and expressed in culturable organisms e.g., escherichia coli (bac is a special liposome that can accept large insertions of dna). • the recombinant organisms are fermented, the broth extracted and screened for new bioactive compounds. the major challenges of this approach include obtaining enough pieces of clean dnas and genes that could code for metabolites that the host organism can express. it is now possible to identify the gene clusters that are critical to the biosynthesis of some antibiotics, modify and functionally re-express them in another organism to produce a new library of natural products (mcdaniel et al. 1993 and 1995). 7.2 methods for expressing foreign genes in plants the cloning of entire biosynthetic processes in prokaryotes is rather difficult and remains elusive in plants. this is because the biosynthesis of a metabolite may be controlled, not just by one or two genes as in prokaryotes, but by a complex dozen of genes, promoter, suppressors or terminators residing in a chromosome (units into which genetic materials are packaged in an organism). a number of chemical, electrical and physical methods are used for direct gene transfer (barcelo and lazzeri 1998). the principles of the 3 common methods for introducing foreign genes into plants are discussed below. 7.2.1 use of autonomously replicating virus as vectors the use of virus as vectors in the transfer of genes was not commercially available until about 6 years ago because of the problem of obtaining suitable plant virus-based vectors that can be manipulated without affecting the viability of the virus itself. the rna genomes of the tobacco mosaic virus contain ‘open reading frames’ that can be modified to express additional genes (dawson et al. 1989, donson et al. 1991). the genes of interest are inserted into the viral genome and cloned dna copies of the rna viral genomes are transcribed in vitro to give infectious rna. under certain conditions the dna copy of the rna viral genome may be used to infect plants directly. in this approach, the introduced genes are additions not substitutions for viral genes. the modified virus is used to inoculate seedlings or leaves by rubbing innoculum on them. the infected plant will thus express the foreign gene. this method is fast. however, the germline of the plant remains unmodified and as a result the expressed traits are not heritable. the shortcoming of this approach is the difficulties of inoculating plants on a large scale and the amount of genes that the virus can add on without comprising its viability is grossly limited. 7.2.2 agrobacterium-mediated gene transfer agrobacterium tumefaciens is a gramphytopathogen that causes crown gall disease in susceptible dicotyledonous plants. it is a strain of bacteria with large plasmids carrying genes that can be transferred to plant cells. two important regions for genetic information transfer are found on the plasmids of agrobacterium. the virulence region vir-gene, which is responsible for infection, is not usually transferred to the genome of plants. the t-dna region contains tumor-inducing genes, the (t1), and root-inducing fatope, al-kindi and abdulnour 66 genes, the (r1). the genes located in the t-dna region can be transferred but they are not required in the transfer process. a heavily mutated or modified t-dna region can still be transferred to the host plant genome (kung and wu 1993). the genes governing tumorigenesis are deleted from t-dna. the desired foreign genes and appropriate markers or reporter genes that are needed for selection of modified plant cells are inserted. the modified t-dna genes are replicated in e. coli and then transferred to agrobacterium tumefaciens host strain carrying plasmids from which the (t1) genes have been deleted. the re-constituted genes could be transferred to plants by smearing wounds on plant or by inoculating plant tissue cultures with modified agrobacterium tumefaciens. infected plant cells are selected with the help of embedded markers or reporter genes and re-generated. the regenerated plant can be used as a source of seed for subsequent generation of transformed plants. the process may be long and slow depending on the life cycle of the plant. if the process is uncontrolled, it can produce unwanted results such as gene silencing and co-suppression of the expression of the desired feature (flavell, 1994; finegan and mcelroy 1994). the inserted genes in this approach are inheritable. 7.2.3 ‘shot gun’ or biolistic gene transfer an alternative approach for stable gene transformation, which is equally popular and developed within the past decade, is the biolistic gene transfer. in this approach, high velocity foreign dna or gene clusters are delivered into living cells or tissue through bombardment of tissues or cells with a particle gun called a biolistic device. the process has been well detailed in several reports (klein et al. 1987 and 1989; wang et al. 1988; sanford 1990). the transformed cells are cultured and the desired traits are selected and regenerated. the gene transferred by this method is inheritable. several transgenic plants have been produced by these techniques (marchant et al 1998; schuler et al. 1998). the impact of biotechnology on pesticide delivery has been extensively covered by hammock et al. (1999). it has, for instance, allowed insecticidal proteins produced by bacillus thuringiensis, a free-living soil bacterium, to be expressed by maize and several other plants for insect control (huang et al 1999; peferoen, 1997), or plants to be modified to confer resistance to herbicides (tsaflaris 1996). in spite of the complaints and anxiety expressed by the public over transgenic plants, it certainly offers another route for generating unnatural natural products from which hitherto unknown bioactive compounds with a novel mode of action can be exploited. 8. conclusions natural products have been isolated from a variety of sources and the potential for discovering additional compounds from organisms in ecologically stressed terrestrial and aquatic environments is enormous. a recent survey (cragg et al. 1997) showed that about 35% of commonly prescribed drugs contain active ingredients derived from plant and microbial sources. roughly 60% of drugs being submitted for approval as anti-infectives have natural origin. natural products have also provided prototypes for synthesis of new insecticides. our understanding of the genetic control of biosynthesis is critical to commercial exploitation of therapeutic natural products. natural products from genetically manipulated plants and crops will continue to play significant roles in the development of pest, disease and pathogen resistant crops, and in the biosynthesis of more active and better tolerated drugs. a commercially rewarding trend in natural product research is to focus our efforts on drug discovery and development. this will allow connections to be made between academia and industry, and between ethnomedical remedies and bioactive natural products. unfortunately, our natural biodiversity is being depleted. our wealth of ethnomedical remedies that have accumulated over the years are also being lost. the twin resources have to be protected and preserved. drug discovery from natural sources is expensive. however, very viable alternatives are limited. the science and technology acquired in the process is great and desirable for a developing country. compounds from natural sources have the potential of enriching our library of candidates available for biological assessment and synthesis. techniques in molecular biology for research trends in natural products 67 designing high throughput assays, combinatorial biosynthesis, random shuffling of genes for biosynthesis of desired compounds, and novel isolation methods will continue to breath significant novelty into the scientific skills of young researchers. patent protection of novel, applicable and unobvious discoveries is necessary if the exploitation of our biota is to yield financial return, which is generally a necessary requirement to facilitate more advanced development of lead molecules. 9. acknowledgement mof is grateful to the international foundation for science, stockholm for funding his work in natural products through grants f/2018-1 and f/2018-2f. 10. references albers-schonberg g., arison b. h., chabala j. c., douglas a. w., eskola p., fischer m. h., lusi s., mrozik h., smith j. l. and tolman r. l. 1981. avermectins structure determination. j. amer. chem. soc. 103: 4216-4221. albers-schonberg g. p., burg, r. w. m. h., miller t. w. c., ormond r. e. d. and wallick g. h. s. 1977. 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االصطناعية التي تستند للمنطق الغامض لعمليات التحكم في تنقل عربات : خالصة شة استخدام الشبكات العصبوية االصطناعية والمنطق الغامض لتجهيز العربات الذكية بقابلية حركية يبدأ البحث أوال بمناق . ذكية وفي الواقع إن المنطق الغامض . الجتياز الحواجز الثابتة والمتحركة) تستخدم الغموض المنطقي(ذاتية ، ثانيا بناء شبكة عصبوية إن هذا النظام يزود العربة بعد التدريب . تطبيق الالدقة والتفكير التقريبي يحسن قابلية الشبكات العصبوية في اجتياز العوائق ب أوال التوجه نحو الهدف باستخدام شبكة عصبوية ، وثانيا تجنب الحواجز الثابتة : الموجه بالقابلية على إنجاز مهمتين هما . والمتحركة باستخدام شبكة عصبوية غامضة تختزل السلوك البشري abstract: this paper proposes a neural-network-based fuzzy logic system for navigation control of intelligent vehicles. first, the use of neural networks and fuzzy logic to provide intelligent vehicles with more autonomy and intelligence is discussed. second, the system for the obstacle avoidance behavior is developed. fuzzy logic improves neural networks (nn) obstacle avoidance approach by handling imprecision and rule-based approximate reasoning. this system must make the vehicle able, after supervised learning, to achieve two tasks: 1to make one’s way towards its target by a nn, and 2to avoid static or dynamic obstacles by a fuzzy nn capturing the behavior of a human expert. afterwards, two association phases between each task and the appropriate actions are carried out by trial and error learning and their coordination allows to decide the appropriate action. finally, the simulation results display the generalization and adaptation abilities of the system by testing it in new unexplored environments. keywords: neural-network, fuzzy logic, navigation control, intelligent vehicles. 1. introduction i t is advantageous to use neurocomputing and fuzzy logic(fl) in combination rather than exclusively to bring the behavior of intelligent vehicles (iv) near the human one in recognition, decision-making, and action. the intelligent vehicle designers search to create dynamic systems that able to navigate like humans in hostile environments. these environments can be imprecise, vast, dynamical and partially or fully not structured. to reach their targets without collisions, these vehicles must be endowed with perception, data processing, recognition, learning, reasoning, interpreting, decision-making, and action capacities. the ability to acquire these faculties to treat and transmit knowledge constitutes the key to a certain kind of intelligence. in this paper, a neural-network-based fuzzy logic is proposed for navigation control of autonomous vehicles in partially structured environments. the principal navigation problems are recognition, learning, decision-making, and action. three phases are required to recognition: inaccurate sensor data processing, construction of knowledge base, and establishment of an environment map. the approaches are based on the fuzzy logic, neural networks (nn), or 211 ahcene farah and amine chohra combination of them: neuro-fuzzy systems (chohra et al.1996,1998). indeed, this combination has been recognized as a facter in improving the learning and adaptation capacities when information is qualitative, inaccurate, uncertain, or incomplete. : 1) to make one’s way towards its target by a nn, and 2) to avoid static or dynamic obstacles by a fuzzy nn capturing the behavior of a human expert. first, the necessity of nn and fl systems to control intelligent vehicles is discussed. second, a fuzzy nn, in the form of feed forward multilayer net, combines the idea of fuzzy logic decision system and neural-network structure into an integrated neural-network-based fuzzy logic decision system. a nn is used to make one’s way towards the target, and to avoid static or dynamic obstacles a fuzzy nn captures the behavior of a human expert. afterwards, two association phases between each task and the appropriate actions are carried out by trial and error learning. 2. neuro-fuzzy navigation systems the use of the nn to process imprecise or very noisy data is more efficient than the classical techniques because of their high tolerance to noises (anderson, 1995; berns,1991). also, it was shown that the use of the fl to handle imprecise data issued from the environment and sensors was more efficient than the previous deterministic techniques (chuen,1990). this is due to the representation of the fl by fuzzy membership functions and to the state space discretization into linguistic variables. for the navigation in a dynamic environment, it is more advantageous to use an implicit representation rather than explicit one, (hung,1993). this is particularly important for the navigation since the imprecise data are processed to recognize the environment. in reality, the difficulty in the establishment of an environment map resides in the knowledge representation. thus, the approach of nn theory is appropriated as well as the one of fl to inaccurate data processing and construction of knowledge base. to solve navigation problems, nn are indispensable if the classification criteria or generalization rules are unknown since they are able to learn and generalize from examples without knowledge of rules. the use of fl theory to solve the same problems improves the efficiency if the classification criteria or generalization rules are known (given by an expert),( chuen,1990; glorennec,1991). in effect, human reasoning is not based on the classical two-valued logic because this process involves fuzzy truths, fuzzy deduction rules, etc,(zadeh,1992). thus, several nn-based approaches are oriented to design and achieve intelligent systems, which simulate the human decision-making in imprecise environments (bosacchi and masaki,1993; hung,1993). by another way, a particularity of the fuzzy rule-based approach is given by its ability to classify fuzzy iv situations, according to the degree of collision risk (chohra et al,1999) (maeda,1990). 3. the proposed navigation approach during the navigation the iv must recognize both the location of its target to make one’s way towards it, and spatial situation to avoid possible obstacles. the target localization is based on a nn recognition acquired by learning from data obtained by computing distance and orientation of the vehicle-target using a temperature field strategy. the obstacle avoidance is done by fuzzy nn from a fuzzy linguistic formulation of a human expert. 3.1 intelligent vehicle movements the movements of the vehicle are supposed possible only in three directions and consequently three actions ai (i = 1, 2, 3) are defined as action to move ahead, action to turn to the left, and action to turn to the right a = [aa, al, ar] as illustrated in figure1. 3.2 partially structured environments the interest in the mobile robotics especially in indoor environments such as: factories, passenger stations, harbors, and airports leads to effect partial structuring of these environments (chohra and farah,1996; pignon,1994). a partial spatial structuring consists of a description of 212 neural-network-based fuzzy logic navigation control obstacles in the environment other partial topological structuring in ‘rooms, corridors, doors, etc’ allows the transition from the spatial structuring to its comprehension, which brings the manner to solve the navigation problems near the human one. the possible movements of our intelligent vehicle (the robot) lead us to effect the following partial topological structure resulting in corridors, turns to the right, turns to the left, and three situations in ‘t’ (as shown in figure 1). the static obstacles are represented in two dimensions (2d) by different shapes such as rectangular, squared, circular or triangular. the vehicles are controlled by the same navigation approach where each one considers the other as a dynamic obstacle. figure 1. obstacle avoidance situations. 3.3 target localization and obstacle avoidance the situations of the target localization are defined by t = [t1, ..., t6 ] (see figure 2) while the obstacle avoidance situations are defined by o = [o1, ..., oj, ..., o6 ] (see figure 3), with j=l, ..., 6. figure 2. target localisation situations. figure 3. synoptic of the global system. 213 ahcene farah and amine chohra 3.4 global system structure three phases are necessary to develop the proposed system as shown in figure 3. during the phase 1 the system learns to recognize the situations tj while it learns to recognize the other situations oj during the phase 2. the phase 3 decides an action aj from the association and coordination stages. the used networks are multi-layer ones where information is transmitted only from one layer to the following one. 3.4.1 phase 1: neural network target localization a temperature field is defined in the vehicle environment and the task of the control system is therefore to detect the unique maximum temperature of this field. the input vector to the network has three components representing the temperature in the neighborhood of the vehicle in ahead, at the left, and at the right: xt =[ta, tl, tr ]. these components are computed according to the orientation of the target with regard to the vehicle. after learning, for each input vector the nn system must recognize in which situation it finds its target. note that the xt vector is normalized. neural network: three layers constitute the proposed nn as shown in figure 4. figure 4. target localization. layer 1: this layer represents the input layer with three (03) input nodes receiving the components of the input vector xt. this layer transmits the inputs to all nodes of the next layer. layer 2: this layer represents the hidden layer with seven (07) nodes. the output of each node is obtained as follows yk = f ( ∑ xi w2ki ), (1) where f is the output sigmoid function. layer 3: this layer represents the output layer with six (06) output nodes which are obtained by: tj = f( ∑ yk w1jk ), (2) 3.4.2 phase 2: obstacle avoidance by a fuzzy neural network a fuzzy nn is trained to capture the behavior of a human expert while controlling the obstacle avoidance operation. to mimic this control, the fuzzy linguistic formulation is used and a set of rules is then established. the input vector of the network has three components the distance to obstacles in ahead, at the left and at the right: xo =[da, dl, dr ]. after learning, for each input vector the system must recognize which situation it finds itself. the input distance variables 214 neural-network-based fuzzy logic navigation control da, dl, dr have the same three degrees of qualitative values in their problem domain: near (n), medium (m), and far (f) which are defined by the membership function illustrated in figure 5. the rules resulting from the fuzzy linguistic formulation of the human expert knowledge are: if (da is n and dl is n and dr is m) then o2, if (da is n and dl is n and dr is f) then o2, figure 5. distance membership functions to obstacles. if (da is n and dl is m and dr is n) then o3, if (da is n and dl is m and dr is m) then o4, if (da is n and dl is m and dr is f) then o2 , if (da is n and dl is f and dr is n) then o3, if (da is n and dl is f and dr is m) then o3, if (da is n and dl is f and dr is f) then o4, if (da is m and dl is n and dr is n) then o1, if (da is m and dl is n and dr is m) then o6, if (da is m and dl is n and dr is f) then o2, if (da is m and dl is m and dr is n) the o5, if (da is m and dl is m and dr is m) then o6, if (da is m and dl is m and dr is f) then o2, if (da is m and dl is f and dr is n) then o5, if (da is m and dl is f and dr is m) then o3. if (da is m and dl is f and dr is f) then o4, if (da is f and dl is n and dr is n) then o1, if (da is f and dl is n and dr is m) then o1, if (da is f and dl is n and dr is f) then o6, if (da is f and dl is m and dr is n) then o5, if (da is f and dl is m and dr is m) then o1, if (da is f and dl is m and dr is f) then o6, if (da is f and dl is f and dr is n) then o5, if (da is f and dl is f and dr is m) then o5. note that in the case (da is n and dl is n and dr is n) the vehicle must stop and when (da is f and dl is f and dr is f) the vehicle must only be controlled by the target localization network. fuzzy neural network: five layers constitute the proposed fuzzy nn as shown in figure 6. layer 1: this layer represents the input layer with three (03) input nodes receiving the components of the input vector xo =[da, dl, dr ]. this layer transmits the inputs to their corresponding membership functions in the next layer. layer 2: this layer performs the fuzzification operation and contains the input membership functions with nine (09) nodes. nodes in this layer are represented as input membership functions according to the respective linguistic input variable. each node calculates the degree of the measured data belonging to the kth membership function for the ith input variable e.g., for the input 215 ahcene farah and amine chohra variable da, we obtain { µ n(da), µ m(da), µ f(da)} with µ n(da), µ m(da), and µ f(da) the membership degrees of fuzzy sets n, m, and f respectively. this layer is not fully connected with the layer 1. the connections exist only between the input nodes in the first layer and their corresponding membership nodes in the second layer. the weights of these connections are set to 1. layer 3: this layer represents the fuzzy rule base with twenty five (25) nodes where each node represents one fuzzy rule. the activation of nodes is achieved by the min operation, then f the output sigmoid function is applied (see equation 3), as shown in figure 7. the rule association is done between membership functions of different inputs. the output of each node represents the strength of firing the rule defined by that node. this layer is not fully connected with the layer 2. each node receives only three connections, from the corresponding nodes (n, m, or f) of the first, second, and third inputs. the links in this layer are used to perform precondition matching of fuzzy rules. the weights w2pk of these connections are to be trained. rp = f(min(w2pka µ k a (da), w2pkl µ k l (dl), w2pkr µ k r (dr)) ) ) (3) layer 4: this layer with six (06) nodes performs the max operation between rules that produce the same consequences. the nodes in this layer correspond to output membership functions. the activation of nodes is achieved by the max operation, then the output sigmoid function is applied (see equation 4), as shown in figure 8. this layer is fully connected to layer 3. the weights wljp, of these connections are to be trained to indicate which rules have more or less influences over the output membership functions. oj =f( max( wlj1 r1, .., wljp rp , .., wlj25 r25 ) ) (4) figure 6. obstacle avoidance fuzzy neural network. layer 5: this output layer with one (01) node is the defuzzification process. this layer performs the defuzzification operation using the max. this layer is fully connected to layer 4 and the weights of these connections are set to 1. note that this layer is used after learning i.e., during the 216 neural-network-based fuzzy logic navigation control application. figure 7. node of layer 3. figure 8. node of layer 4. 3.4.3 learning algorithm and learning environment the learning of the two proposed networks are based on the supervised gradient backpropagation algorithm as detailed in (chohra , et al., 1999). the training is performed in a learning environment where all the situations tj and oj arc represented and only free-collision action is permitted in each situation. 3.4.4 phase 3: action both situations of tj and oj are associated by trial and error learning mechanism with the appropriate actions separately. afterwards, the coordination of the two associated phases allows the decision-making of the appropriate action. • association: learning by trial and error this learning is guided only by a feedback process, i.e., guided by a signal p provided by the environment. this signal causes a reinforcement of the association between a given situation and an action if this latter leads to a favorable consequence to the vehicle; if not, the signal p provokes dissociation. each neuron ai is connected to all neurons tj and oj through connections weighted by the coefficients uij, and vij respectively. the updating of these coefficients is achieved by: wij=-α exp(-ai situationj * t/τ ) +(α -p) (5) target localization: situationj = tj, and p = p1 if z=0, p= 0 if z=1 (6) note that for each situation tj , z is determined with regard to each action i.e., za, zl, and zr (see figure 2). for example, for the situation t3, za=1, zl=1 and zr = 0. obstacle avoidance: situationj = oj, and p = p2 if collision, p=0 if not (7) with p1 >α , p1 > p2, 0<α < p2, τ =3s , α =5 , p1=9 ,‘and p2 = 7. • target localization this association is carried out in a free-obstacle environment (0 = 0) and for each situation only one action is permitted, then the connection weights are adjusted to obtain this reinforced action represented by a full arrow in figure 2. • obstacle avoidance this association is carried out without temperature informations (t = 0) and the connection weights are adjusted to obtain this reinforced action represented by a full arrow in figure 2. 217 ahcene farah and amine chohra • coordination in each step, the robot receives information about temperatures in the neighborhood and distances to the obstacles and must make a decision concerning the direction of its next movement. the search of the maximum temperature can be interpreted as the goal of the system. the generated actions by the presence of obstacles must be interpreted as the reflex of the robot (iv) and must have precedence over those generated by the target localization. also, to ensure the coordination, the ai are computed by equation (8), where n1 is a random variable. ai = g((α -p2)oj+(α -p1)tj)+ni (8) with g(x)= x if x>0, 0 otherwise (9) 4. simulation and results to reflect vehicle behaviors acquired by learning, and to demonstrate the generalization, adaptation and decision-making capabilities of the neuro-fuzzy system, vehicles are simulated in different static and dynamic environments. 4.1 static obstacles to reflect the intelligent vehicle behaviour acquired by learning, navigation is simulated in the explored environment and in new unvisited environments. testing in an environment with static obstacles is illustrated in figure 9 (where veh=vehicle and tar=target), the vehicle succeeds in avoiding obstacles and reaches its target. 4.2 intelligent dynamic obstacles intelligent dynamic obstacles represent vehicles controlled by the same avoidance approach where each one considers others as obstacles. in the case illustrated in figure 10, three vehicles vehl, veh2, and veh3 try to reach their respective targets while avoiding themselves. in the case illustrated in figure 11 the vehicle avoids an obstacle oscillating vertically and reaches its target successfully. these kinds of non-intelligent obstacles are in reality preprogrammed, remote-guided or guided vehicles. figure 9. static obstacles. figure 10. intelligent dynamic obstacles. figure 12. a complex environment. figure 11. non-intelligent dynamic obstacles. 218 neural-network-based fuzzy logic navigation control 4.3 complex environments in a complex environment illustrated in figure 12, three vehicles intelligently avoid static and dynamic obstacles. 5. conclusion the trained nn, and fuzzy nn constitute the knowledge bases of the control system. indeed, its main feature is the use of these networks in the task of fuzzy reasoning and inference to decide static and dynamic obstacle danger degrees, and avoidance direction. tested in new unvisited environments, the intelligent vehicle avoids not only the static obstacles of different shapes but also the dynamic ones, illustrating then the generalization and adaptation capabilities of the proposed neuro-fuzzy approach. an interesting alternative for future research is the generalization of the proposed approach by increasing the number of the possible intelligent vehicle movements. references anderson, j.a. 1995, an introduction to neural networks mit press, cambridge, ma. berns, k. and dillmann, r. 1991: a neural network approach for the control of a tracking behavior. ieee 7803-0078/0600-0500. bosacchi and i. masaki, i. 1993, fuzzy logic technology & the intelligent highway system (ihs), in: proc. 2nd int. ieee conf. fuzzy systems, vol. 1, pp. 65—70. ieee inc., isbn soft bound:0-7803-0614-7, san francisco, ca. chohra, a., farah, a. and benmehrez, c. 1998, neural navigation approach for intelligent autonomous vehicles (iav) in partially structured environments, int. j,applied. intelligence, 8 (3): 219-233. chohra, a., farah, a. and benabbas, r. 1996, neuro-fuzzy navigation approach for autonomous mobile robots in partially structured environments, in: proc. int. conf. application of fuzz systems and soft computing, siegen, germany, pp.304-3 13. chohra, a., farah, a. 1996, hybrid navigation approach combining neural networks and fuzzy logic for autonomous mobile robots, in: proc. 3rd int. conf. motion and vibration control. chiba, japan. chohra, a., farah, a. and belloucif, m. 1999, neuro-fuzzy expert systm e_s_co_v for the obstacle avoidance behavior of intelligent autonomous vehicles. advanced robotics, 12(6): 667-678. chuen, c.l. 1990. fuzzy logic in control systems: fuzzy logic controller, part i & part ii.ieee trans. on sys. man and cyb., 20(2): 404-435. glorennec, p.y. 1991. les réseaux neuro-flous évolutifs: un pont entre le flou et le neuronal. insa, france,. hung, c.c. 1993. building a neuro-fuzzy learning control system. ai expert, 40-49. maeda, y. 1990: collision avoidance control among moving obstacles for a mobile robot on the fuzzy reasoning. eight cism iftomm symp. on theo. & prac. of rob. & man. pignon , hasegawa and laumond, j.p. 19994. structuration de l’espace pour les robots mobiles. revue scicntifique et technique de ia defense, 2: 17-31. zadeh, l.a. 1992. the calculus of fuzzy if/then rules. ai expert, mar.23-27. received 10 june 2001 accepted 5 february 2002 219 neural-network-based fuzzy logic navigation control for intelligent vehicles ahcene farah* and amine chohra** *ajman university of science and technology, p.o.box 5102 abu dhabi, uae, email: ahcenef@yahoo.com,**centre de developmient des technologies avancees, bp 245 el-madania, 16075, algiers, algeria. äùçã çáôèßçê çáúõèæíå çáçõøäçúí� references endocrine, physiological and histopathological responses of fish and their larvae to stress with emphasis on exposure to crude science and technology, special review (2000) 265-280 ©2000 sultan qaboos university 265 modeling flow and transport in unsaturated porous media: a review h.h. al-barwani, m. al-lawatia, e. balakrishnan, and a. purnama department of mathematics and statistics, college of science, p.o. box 36, sultan qaboos university, al-khod 123, muscat, sultanate of oman مراجعة وتحليل: ة نماذج حركة المياه و النقل في مناطق التهوية في األوساط المسامي حمدى البرواني، محمد اللواتيا، اسوارن بالكرشنان ، انتون برناما ذل كل جهد لفهم الطرق و الوسائل الممكنة لالستفادة يجب أن نب المياه الجوفية مورد طبيعي و حيوي و :خالصـة التي تحد من أعلى بالسطح اليابس و من اسفل هي تلك منطقة التهوية . فـيها بكفاءة عالية مـنها و التصـرف هي المنطقة التي من خاللها ترشح المياه مع المياه الملوثة لتصل إلى المياه الجوفية، و عليه وبالطاولـة المائـية تحديد كل من كمية و نوع المياه التي فالعملـيات المختلفة التي تحدث داخل منطقة التهوية تلعب دوراً أساسيا في ير غ بتدفق المياه و نقل المياه الملوثة في الوسط المسامي تنبؤللالطرق التقليدية . ترشـح داخـل المـياه الجوفية الطبيعة و ذلك نسبة لوجود مسامات كبيرة و عناصر على حاالت مشـبع بصورة عامة غير وافية عند تطبيقها ال مخططات النقل الملوث تحتاج إلى حل متزامن لمعادالت . عند المواقع المختلفة ص التربة منظمة و تغيرات لخوا قد ازداد كثيرا استعمال الحلول العددية و المحاكات في اآلونة األخيرة مشـبع ومعادالت النقل و الالـتدفق غـير جازه و آخر ما تم التوصل و في هذا البحث سوف نستعرض ما تم إن. الحاسـوبية المبنية علي المخططات العددية إلـيه فـي مخططـات التدفق المائي و النقل الملوث في منطقة التهوية و سوف نؤكد علي ما يجب التركيز عليه .مستقبال و خاصة ما له عالقة بسلطنة عمان abstract: underground water is a vital natural resource and every effort should be made to understand ways and means of efficiently using and managing it. the unsaturated zone, bounded at its top by the land surface and below by the water table, is the region through which water, together with pollutant carried by the water, infiltrates to reach the groundwater. therefore, various processes occurring within the unsaturated zone play a major role in determining both the quality and quantity of water recharging into the groundwater. classical methods of predicting water flow and contaminant transport processes in unsaturated porous media are generally inadequate when applied to natural soils under field conditions, due to the occurrence of macropores, structured elements and spatial variability of soil properties. contaminant transport models also require the simultaneous solution of the unsaturated flow and transport equations. for applications to field conditions, numerical solutions and computer simulations based on numerical models have been increasingly used. advances and progress in modeling water flow and contaminant transport in the unsaturated zones are reviewed, and specific research areas in need of future investigation especially relevant to oman are outlined. modeling flow and transport in unsaturated porous media contents 1. introduction 266 2. mathematical equations of water and transport in unsaturated soils 267 3. unsaturated flow models 270 4. solute transport models 272 5. concluding remarks 275 6. acknowledgment 275 7. references 275 1. introduction oman is an arid country with limited natural water resources. the rainfall is unreliable and records indicate periods of several consecutive dry years. there are few perennial streams; surface flow is usually confined to periods of a few days or even a few hours after storms. infiltration through streambeds of surface run off from the mountains is the main source of recharge to the groundwater. the main user of water in oman is agriculture. the climate will support very little rainfed agriculture and irrigation is essential. water for domestic use is traditionally obtained from aflaj, springs or shallow wells. in most traditional communities in oman, groundwater has long been extracted and directly utilised through the falaj (plural aflaj). it may consist of simple conduits conveying water from wadi channels to domestic use and irrigation systems, or consist of tunnels constructed at the water table to exploit the groundwater resource. the falaj is self-regulating; discharge declines as the upstream storage in the aquifer falls during droughts, and rises after the aquifer is recharged. in coastal regions, water is extracted from shallow wells for various purposes. desalination plants have also been established to provide domestic supplies for some coastal areas; but agriculture, which is responsible for more than 95% of freshwater consumption, is almost entirely reliant upon groundwater. since the sultanate’s water resources are fully utilised, any pollution may have immediate and serious consequences. therefore, every effort should be made to ensure that all valuable aquifers are not contaminated. increased public awareness and concern over many environmental problems is, at least partly, attributed to the fact that these problems are so visible. however, the situation is quite different for groundwater, which is hidden from sight, and renders the characterization of impacts on its quality and availability extremely difficult. consequently, problems of over-use, pollution or saltwater intrusion may develop to a critical level before being noticed. in the absence of any reliable scientific knowledge applicable to groundwater, this valuable resource cannot be effectively protected, conserved and managed. a quantitative study of water flow and contaminant transport in the unsaturated zone is a key factor in the improvement and protection of the quality of groundwater supplies. this is the region bounded above by the land surface and below by the ground water table. it is the region through which water derived from precipitation and irrigation infiltrates and transports contaminants to reach the groundwater. over-pumping of groundwater for domestic, agricultural and industrial consumption will lower the water table and can accelerate the movement of pollutant-laden surface water into the groundwater. in unsaturated soil, the water content is less than the soil porosity, and the soil water pressure head (matric potential) is negative, being less than that of free water at the same location. the unsaturated zone is inextricably involved in many aspect of hydrology: infiltration, evaporation, groundwater recharge, soil moisture storage, and soil erosion. it also contributes to the spatial and temporal distributions of plant communities under naturally occurring rainfed conditions and serves as a modifying influence on the production of cultivated crop species. thus the unsaturated zone represents the conduit through which liquid and gaseous constituents are attenuated and transformed as they are exchanged in both directions between the ground surface and the ground water table. 266 al-barwani, al-lawatia, balakrishnan, and purnama traditional deterministic modeling approaches to determine downward movement of contaminants, based upon the convection-dispersion equation for contaminant transport and the richards equation for water flow, work relatively well for homogeneous field soils and laboratory soil columns. experimental investigations, however, have shown that flow and transport processes in most fields are heterogeneous. thus, to use classical approaches for describing transport processes in natural soils under field conditions would be a misapplication of the methods. soil heterogeneity, occurring in structured, cracked or macroporous soils, and due to the inherent spatial variability of soil properties, has a distinct effect on the water flow and contaminant transport processes. since macropores act as preferential flow paths, occurrences of macropores at the field scale may increase the risk of leaching of pollutants to the groundwater. therefore, a quantitative prediction of contaminant transport in macroporous, heterogeneous soils at field or regional scales is an important matter in dealing with environmental problems. this review is an attempt to summarize some aspects of the main scientific advances and progresses in modeling water flow and contaminant transport in unsaturated porous media. although water flow and contaminant transport phenomena should be treated simultaneously, for convenience, we first discuss water flow and then deal more specifically with contaminant transport processes. we focus primarily on conceptual and mathematical, deterministic aspects of unsaturated zone flow and transport processes. the review starts with the basic physical concepts that are classically used to describe water flow and solute transport processes in unsaturated porous media. existing analytical and numerical solutions of the unsaturated water flow and contaminant equations will be discussed. for applications to field conditions, numerical solutions and computer simulations based on numerical models have been increasingly used. thus recent progress in numerical methods employed for these purposes will be examined. oman has extensive areas of active and fossil karst. the complex geological structure of oman consists of well-developed fracture systems in the rocks forming the northern mountain aquifers. the highest average annual rainfall for the sultanate is in the mountainous region with more than 300mm. perennial spring discharge from the limestones in the northern mountains can maintain surface flow over a substantial distance. the essence of fractured aquifers is the existence of an interconnected set of voids capable of conveying water and contaminants at speeds much higher than the typical darcian flow rate. as classical representations are not intended to describe flow and transport processes in natural soils under field conditions where the occurrence of macropores, fractures, karstic conduits and spatial variability of soil properties is dominant, more research is still needed for a quantitative prediction of water flow and contaminant transport in the unsaturated porous media. 2. mathematical equations of water and transport in unsaturated soils in this section, the general classical deterministic forms of the water flow and contaminant transport equations in the unsaturated zone are described. a comprehensive derivation is provided by bear (1972), pinder and gray (1977), and freeze and cherry (1979). note that there is considerable skepticism as to the validity of these equations, and gray and hassanizadeh (1991) proposed a new set of equations to describe the unsaturated flow processes obtained from averaging theory coupled with an interface thermodynamic analysis. however, this set of equations contains many more unknowns than that of classical equations. the liquid in the unsaturated zone consists of a solution of water and dissolved solid and gaseous constituents. therefore, the forces acting on the liquid cannot be restricted merely due to the earth’s gravitational field (nielsen et al., 1986). however, since direct measurement or calculation of other forces still remains undeveloped, most studies to date assumed that the net force acting on the liquid is the matrix potential and gravitational force. thus, the rate at which water moves through the unsaturated zone is according to the darcy’s velocity, z kq ∂ ψ∂ −= , (1) 267 modeling flow and transport in unsaturated porous media 268 k zh + h where is the hydraulic conductivity, ψ the (hydraulic head) total potential which can be written as in which is the (pressure) matric potential head, and z is the gravitational potential head, measured positively upward. in unsaturated flow, the void space is partly filled by air and partly by water. as air is infinitely mobile, it is generally assumed that the trapped air in the void space is at constant atmospheric pressure. =ψ combining the darcy’s velocity with the conservation of mass equation g z q t = ∂ ∂ + ∂ ∂θ , (2) leads to richards equation for water flow in the unsaturated zone. in the mixed form, the unsaturated flow equation is written as g z k z h k zt + ∂ ∂ +      ∂ ∂ ∂ ∂ = ∂ ∂θ , (3) where θ is the volumetric water content, t is time, z is the (positively upward) vertical distance, and g represents sources and sinks of water in the system. other two alternative forms of richards equation are the pressure head h-based equation g z k z h k zt h c + ∂ ∂ +      ∂ ∂ ∂ ∂ = ∂ ∂ , (4) where the specific moisture capacity c is the slope of the soil water retention curve ( )hθ ; and the moisture content θ -based equation g z k z d zt + ∂ ∂ +      ∂ ∂ ∂ ∂ = ∂ ∂ θθ , (5) where it is customary to define the coefficient of moisture diffusivity as ck=d . although these three forms are mathematically equivalent, some give better results when numerical approximation methods are applied. note that these equations show that the soil water retention curve ( )hθ and the unsaturated hydraulic conductivity k are essential components for predicting water flow in unsaturated zones. retention curves show how much is retained in the soil against gravity; its shape depends on the soil pore-size distribution and pore shapes of the porous medium. however, its derivation ignores soil matrix and fluid compressibilities and assumes that the fluid density ρ is a function of the pressure only, and is independent of concentration. equation (3) also assumes that darcy’s law is valid for unsaturated flow. the hysteretic nature of the measured soil water retention curve ( )hθ implies that the soil water content is not a unique function of h, but depends on the previous history of the soil (parlange, 1980). the effects are more pronounced by the presence of entrapped air, and by alternate rates of wetting and drying (bear, 1972). this effect introduces a nonlinearity into the richards equation (3); and hence, it is necessary to state whether a drying or wetting process is taking place along the boundary of the system (hills et al., 1989a and 1989b). hysteresis is rarely considered under field situation, due to the difficulties in measurement. numerous methods have been developed to determine the soil water retention and hydraulic conductivity functions of unsaturated soils using both in situ field and laboratory procedures (van genuchten and nielsen, 1985; bird et al., 1996, assouline et al., 1998). while in situ field measurements are the most representative of actual flow conditions, current methods are likely to remain approximate in nature (kool et al., 1987). this is due to simplifying assumptions inherent in the methods, and to problems al-barwani, al-lawatia, balakrishnan, and purnama of obtaining undisturbed samples. kool et al. (1985) developed a method to determine water retention and hydraulic conductivity functions simultaneously from transient flow data by parameter estimation. the methodology appears promising, although problems of computational efficiency, convergence, and parameter uniqueness remain unresolved (eching et al., 1994; wildenschild et al., 1997). direct field methods to determine the unsaturated hydraulic conductivity are time consuming, expensive, and usually subject to simplifying assumptions. an alternative method is the theoretical calculation from more easily measured field or laboratory soil water retention data (childs and collisgeorge, 1950; mualem, 1976; arya and paris, 1981; van genuchten and nielsen, 1985; assouline et al., 1998). this method produces analytical (non-tabular) functions that are particularly useful for inclusion in simulation models and also for a rapid comparison or scaling of the hydraulic properties of different soils. among the retention equations that have realistic shapes is the equation proposed by van genuchten (1980) ( )mnrsr hαθθθθ +−+= 1/)( , (6) where rθ and are residual and field-saturated volumetric water contents, respectively, and , n, and m are empirical constants. for the hydraulic conductivity functions, mualem’s (1976) formulation has more potential than other models as it is more applicable to a wider variety of soils (van genuchten and nielsen, 1985). αsθ the physical processes that control the solute distribution in the unsaturated zone are advection by water flow and dispersion by mixing and molecular diffusion. other processes have been noted by nielsen et al. (1986), but only summarily known, if understood at all. the classical equation that is thought to describe solute transport ( ) ( ) pcq z c d zt c t s +      − ∂ ∂ ∂ ∂ = ∂ ∂ + ∂ ∂ θ θρ , (7) where c and s are solute concentrations associated with the solution and solid phases of the soil, d is the dispersion coefficient, and p is the rate of solute removal or supply not specifically included in s. loss and gain of solute mass can occur as a result of chemical reactions or radioactive decay. the first term of the equation (7) describes the rate at which the solute interacts or exchanges with the solid matrix. both equilibrium and kinetic rate laws have been used to describe adsorption-exchange processes (nielsen et al., 1986), which are traditionally represented by the retardation coefficient, r. in practice, is used as an empirical parameter that includes all of the solute spreading mechanisms. however, in concept, the coefficient is commonly assumed to include only the effect of mechanical dispersion and molecular diffusion (bear, 1972). d the flow and transport equations previously described are found not adequate to describe field-scale spreading of contaminants transported in unsaturated soils due to the occurrence of macropores and spatial variability of soil hydraulic properties. results from field experiments (richards and steenhuis, 1988) have indicated that groundwater contamination may not be associated with the unsaturated flow. pollutant could be transported very expeditiously through certain pathways in unsaturated soils into the groundwater (ju and kung, 1997). nevertheless, the scope and impact of this preferential flow on contaminant transport under field conditions have not yet been fully characterized (flury, 1996). this is mainly because it is difficult to obtain representative patterns of preferential flow with soil coring methods (ghodrati and jury, 1990). the irregular and erratic character of hydraulic conductivity and dispersion coefficient distributions observed in natural soils has led to the development of a stochastic framework for transport modeling. in this stochastic-convective approach, contaminant is assumed to move at different velocities in isolated stream tubes without any mixing of contaminant between the tubes (dagan and bresler, 1979). 269 modeling flow and transport in unsaturated porous media 270 in light of the uncertainty in the preferential flow mechanism and hence inadequate deterministic predictions, jury and gruber (1989) developed a stochastic approach to assess the groundwater contamination. this model estimates the probability of a contaminant reaching groundwater, using the same deterministic equations that are used in the homogeneous unsaturated soils, but assuming the parameters of the equations and the variables are stochastic functions (yeh, 1992; feyen et al., 1998). another approach involves extrapolation techniques to get large scale effective parameters from the small-scale measurements (wagner and gorelick, 1986; vanderborght et al., 1996). a different approach involves the dual-porosity model proposed by gerke and van genuchten (1993), which is gaining widespread acceptance for modeling preferential water flow and solute transport. the two domains consist of the soil matrix and macropores. flow and solute transport equations for each domain are then coupled by means of exchange term accounting for the mass transfer of water and solutes between both regions (van genuchten and wierenga, 1976; gaudet et al., 1977; feyen et al., 1998). other approaches, which account for the presence of macropores that form a separate network, consider the soil as a collection of stream tubes (toride and leij, 1996). within each stream tube, the water and solute transport equations are used. it is assumed that there is no exchange of water and solute between these tubes and that within each tube, the parameters determining water flow and solute transport are deterministic, but vary between tubes. it is worth noting that in this approach neither the spatial structure of the heterogeneity of soil properties nor hydraulic conductivity and dispersion coefficient are considered (feyen et al., 1998). 3. unsaturated flow models analytical solutions, when available, provide better insight into the physics behind the transport phenomena and are computationally efficient and simple to use. however, analytical approaches are for the most part limited to situations of simple geometry domains, linear governing equations, and homogeneous systems. along with efficient numerical methods and rapidly updated computer hardware a large number of numerical models have been developed. however, the numerical technique cannot replace the analytical approaches completely, since numerical methods themselves need verification against analytical solutions because of discretization errors and convergence and stability problems that may be especially troublesome for advection-dominated and nonlinear adsorption processes. some models are intense in computational demand when modeling a heterogeneous porous medium system with uncertainties in physical properties and distributions using stochastic approaches. analytical solutions to the richards equation for unsaturated flow under various boundary and initial conditions are difficult to obtain because of the nonlinearity in soil hydraulic parameters. this difficulty is exaggerated in the case where soil is heterogeneous. generally, one has to rely on numerical approaches for predicting moisture movement in unsaturated soils, even for homogeneous soils. however, numerical approaches often suffer from convergence and mass balance problems (celia et al., 1990). numerous analytical and numerical solutions of the unsaturated flow equation have been developed (narasimhan et al., 1978; van der heijde et al., 1985; warrick et al., 1991; parlange et al., 1997; rockhold et al., 1997; miller et al., 1998). only a brief review of the modeling work is given here. exact analytical solutions typically require specialized forms of the hydraulic conductivity and diffusivity functions. the exponential hydraulic conductivity function (gardner, 1958) has been widely used, but it is known to have a limited range of application to many real soils. note that other functions, such as those developed by brooks and corey (1964) and van genuchten (1980) are more firmly established for practical applications. such special forms of the hydraulic functions make it possible to linearize the governing flow equations, and hence solve them analytically. solutions to the linearized unsaturated flow equations are generally limited to steady state flow in semi-infinite, homogeneous soils (broadbridge and white, 1988; warrick and yeh, 1990), and to transient flow in homogeneous and layered soils (srivastava and yeh, 1991). al-barwani, al-lawatia, balakrishnan, and purnama 271 exact or quasi-analytical solutions have been derived for simplified unsaturated flow equations and mostly used for verification of numerical solutions (philip, 1955 and 1957; warrick, 1974; knight, 1983). the method of characteristics has also been applied to gravity-dominated flow in the unsaturated zone (charbeneau, 1984). as it neglects the role of capillary pressure gradients, the hydraulic conductivity is set equal to the darcy (volume) flux. this approach is also useful for estimating the unsaturated hydraulic conductivity. analytical solutions are only applicable to highly simplified systems, and are not well suited for situations normally encountered in the field. initially, finite difference methods were mainly developed to predict unsaturated flow only (brandt et al., 1971; freeze, 1971); but finite element solution techniques also became available later (huyakorn et al., 1984; sudicky, 1989; paniconi et al., 1991; segol, 1993). the nonlinearity of richards equation is usually solved using an iterative procedure such as newton or picard methods (kirkland et al., 1992). perhaps the most important advantage of finite element techniques over standard finite difference methods is the ability to describe irregular system boundaries in simulations more accurately, as well as easily including nonhomogeneous medium properties. for one-dimensional simulations, finite difference methods are just as good as finite element schemes (moridis and reddel, 1991). however, several authors suggest that finite element methods lead to more stable and accurate solutions, thus permitting larger timesteps and/or coarser grid systems, and hence leading to computationally more efficient numerical schemes. one of the most successful finite difference schemes is the block centered approach, in which the spatial domain is discretized into blocks and the solutions are found at the center of these blocks. in two spatial dimensions, the scheme couples block center to only its 4 direct neighbours; therefore it is called a 5point scheme (7-point scheme in three spatial dimensions). the generated system is regularly structured (5 bands), symmetric and can be solved efficiently. this scheme was also shown to be equivalent to the lowest order mixed finite element method (ewing, 1983). to numerically solve coupled systems of equations, the solution process requires some manipulation at each timestep so that the dependence of one equation on the solution of the other is dealt with accurately. one way to overcome this is to use a fully implicit approach to solve the equations simultaneously. any nonlinearity of the generated system can be handled by newton’s method. the implicit nature of this scheme allows for larger timesteps in the simulation to find stable solutions as compared to the timesteps for explicit schemes. however, this algorithm requires solving a system of equations of order equal to twice the number of grid points for each newton iteration within each timestep. an alternative to the fully implicit scheme is to use the mixed implicit-explicit scheme. however, the explicit part of the scheme means that this algorithm is now subject to a stability constraint which severely restricts the size of the timestep and introduces numerical artifacts. another approach is to decouple the two equations, and then solve both equations by implicit schemes, where different methods and space-time grids can be used on each one. the procedure is to solve the first equation using an extrapolated approximation of the other solution, and then solve the second equation. infiltration and flow through structured soils can be substantially different from the infiltration and flow in relatively homogenous materials (beven and germann, 1982) because the structured soils contain relatively large voids, such as inter-aggregate pores, drying cracks in clay soils, decayed root channels, and other type of “macropores”. attempts to describe flow in structured soils have generally centred on tworegion approaches. one region consists of the soil matrix in which the flow is described by the conventional, darcian-based unsaturated flow equation, and the other region consists of either a single macropore or of a statistical network of macropores through which water flows primarily under the influence of gravity. the two regions are connected through some common boundary conditions, or by means of a simple source-sink term (davidson, 1985). other approaches include the use of kinematic wave theory (charbeneau, 1984; germann and beven, 1985 and 1986), where the self-sharpening wave (pulse) corresponds to an isolated wetting front drained to field capacity. modeling flow and transport in unsaturated porous media 272 in order to apply the unsaturated flow model to a field situation, the hydraulic conductivity of the site has to be specified. however, the field hydraulic conductivity distribution commonly exhibits a high degree of spatial variability (sudicky, 1986; yeh, 1992). in addition, the spatial variability also varies with the scale of the problem (dagan, 1986; gelhar, 1986). the classical deterministic approach implies that hydraulic conductivity values in a model are known and specified at all points in the solution domain. to acquire such a detailed hydraulic conductivity distribution at the scale of tens of kilometers is generally considered impractical and unfeasible. the alternative is to utilize a small number of samples to estimate the variability of hydraulic conductivity in a statistical framework. that is, the spatial variability of the hydraulic conductivity is characterized by its probability distribution estimated from samples. however, analyses of field data show that although the conductivity values vary significantly in space, the variation is not entirely random, but correlated in space (bakr et al., 1978; yeh, 1992). such a correlated nature implies that the values are not statistically independent in space and they must be treated as a stochastic process, instead of a single random variable (zhang et al., 1998). note that the stochastic approach does not provide information about the values of hydraulic conductivity at a specific location, but it provides a way to quantify its spatial variability. that is, it determines where the mean value lies and how widely the values spread around the mean value. however, in a numerical model it is required to estimate the values at certain points; in this case, the ordinary kriging is used to incorporate spatial correlation structure obtained from site measurements (de marsily, 1986). many stochastic approaches are available including the geostatistics method, the effective parameter approach, the monte carlo simulation, and the conditional simulation (yeh, 1992). although each of these methods has limitations, one should bear in mind, as already mentioned above, that the uncertainty estimates afforded by the stochastic models are themselves uncertain (de marsily, 1986). for heterogeneous soils that contain macropores, a different modeling approach is needed, as the presence of macropores in these soils may form a separate network for water flow (beven and germann, 1982). the common approach is to introduce two-region flow domain, one for macropores and the other for the soil matrix. in each flow domain, hydraulic conductivity is prescribed separately (feyen et al., 1998). another approach is to consider the heterogeneous soil as a collection of stream tubes (toride and leij, 1996). it is assumed that there is no exchange of water between these tubes, and that within each tube, the hydraulic conductivity is defined, but varies between tubes (feyen et al., 1998). 4. solute transport models transport of dissolved solutes in soils is commonly described by the advection-dispersion equation. analytical solutions have been derived for a variety of boundary and initial conditions (starr and parlange, 1976; barry and sposito, 1989; tang and aral, 1992a, 1992b; segol, 1993; leij and toride, 1995, 1998; wu et al., 1997). although these solutions are obtained for narrowly defined conditions, they have many applications such as the verification of computer codes, prediction of solute movement for large times or distances where the use of numerical models become impractical, and the determination of transport parameters from soil column studies. the majority of analytical solutions pertain to semi-infinite and infinite media. solutions are obtained by a variety of mathematical techniques including green’s functions (lindstorm and boersma, 1989), separation of variables (bruch and street, 1967), characteristics method (wilson and gelhar, 1981; charbeneau, 1984; illangasekare and doll, 1989), laplace transforms (leij et al., 1991) and fourier transforms (cleary and adrian, 1973). prediction of solute migration under field conditions requires the simultaneous solution of the unsaturated flow and solute transport equations (warrick et al., 1971; bresler, 1973). numerical solutions of the combined unsaturated flow and solute transport equations have been studied by pickens and gillham (1980); van genuchten (1982); and huyakorn et al. (1985) among others. first approximations involve or assume steady flow and constant water contents. al-barwani, al-lawatia, balakrishnan, and purnama the common approach for modeling the sorption is to assume instantaneous adsorption or exchange reactions as well as simple linearity between s and c, the solute concentrations associated with the solid and the solution phases of the soil, respectively: cks = , (8) where k is often referred to as the distribution coefficient . the source-sink term of equation (7) is often approximated by dk γµ +−= cp . assuming steady state flow, the solute transport equation (7) simplifies to the classical linear convection-dispersion equation γµ +− ∂ ∂ − ∂ ∂ = ∂ ∂ c z c v z c d t c r 2 2 , (9) where the retardation factor r is given by θρ kr += 1 , µ is first-order solute decay rate, and γ is the zero-order solute production rate. application of this equation to transport through disturbed soil columns in the laboratory and in relatively uniform field soils involving nonreactive or only weakly reactive solutes has been fairly successful. chemically controlled kinetic rate reactions of the form ( )csfts ,=∂∂ have been examined. the simplest first-order linear kinetics is commonly assumed; and ignoring the degradation terms, it leads to the coupled system ( )sck t s z c v z c d t c t s −= ∂ ∂ ∂ ∂ − ∂ ∂ = ∂ ∂ + ∂ ∂ α θ ρ ; 2 2 , (10) where α is a first-order rate coefficient. success of this model has generally been limited (van genuchten et al., 1974), thus suggesting that other than linear first-order kinetic processes dominate the sorption process during water movement. an alternative approach is to partition soil water into mobile (flowing) and stagnant (immobile or nonmoving) phases (gaudet et al., 1977). that is, convective-dispersive transport is confined to only a fraction of the liquid-filled pores, and the remainder of the pores contain stagnant water. this stagnant water has been visualized as thin films around soil particles, as dead-end pores, or as relatively isolated regions associated with unsaturated flow. van genuchten and wierenga (1986) extended the concepts of mobileimmobile water to include adsorption-desorption processes ( )imiiimmmmmmiiimmm cct c r z c v z c d t c r t c r −= ∂ ∂ ∂ ∂ − ∂ ∂ = ∂ ∂ + ∂ ∂ αθθθθθ ; 2 2 (11) where the subscripts m and i refer to mobile and immobile regions, respectively. the success of this model for a variety of solutes in laboratory scale transport processes has been clearly demonstrated (nkedi-kizza et al., 1983). adsorption-exchange inside aggregate is an important and often overlooked phenomenon in transport studies involving reactive tracers (gvirtzmann et al., 1988). sorption and exchange sites are often not located along the main fluid flow lines, but along dead-end pores, or inside clusters of particles that have larger internal surface areas. even with a small amount of stagnant water in the system, an uneven distribution of sorption sites can lead to significant preferential transport. 273 modeling flow and transport in unsaturated porous media 274 since the two-region modeling approach is conceptually pleasing and has resulted in improved prediction capabilities, it has then been extended to simulate transport in soils that contain well-defined macropores or that are made up of relatively large, uniformly sized and shaped aggregates. it is commonly assumed that the solute is transported through a single, well-defined pore or crack of known geometry, or through the voids between well-defined, uniformly sized aggregates. in addition, diffusion-type equations are used to describe the transport of solute from the larger pores into the micropores of the soil matrix (tang et al., 1981; sudicky and frind, 1982; goltz and robert, 1986; gerke and van genuchten, 1993). because of the natural complexity of unsaturated flow, methods of predicting solute transport have relied largely on finite difference or finite element approximations of the governing equations (galeati and gambolati, 1989). since advection-diffusion transport equations normally have no closed form analytical solutions, it is important to have accurate numerical approximations. when diffusion dominates the physical process, standard finite difference and element methods work well in solving these equations. however, when advection is the dominant process, these equations may present many numerical difficulties. in fact, any standard finite difference or element method will produce a solution, which exhibits non-physical oscillations (johnson, 1987). a class of eulerian methods has been developed to overcome these difficulties. the scheme uses eulerian fixed grid and improved techniques, such as upstream weighting, to generate more accurate approximations (celia et al., 1989). although it is simple to formulate and to implement the scheme, these solutions suffer from excessive time truncation errors, as the scheme requires small timesteps to generate stable solutions (eriksson and johnson, 1993; al-lawatia et al., 1999). another class of characteristic methods can also overcome the effect of advection dominated problems. the method uses a combination of eulerian fixed grids to treat the diffusive component and lagrangian coordinates by tracking particles along the characteristics to treat the advective component. it has the advantage of greatly reducing the time truncation errors, thus allowing for large timestep, but the scheme has difficulty in conserving mass and treating general boundary conditions. the eulerian-lagrangian localized adjoint method (ellam), which was first proposed by celia et al. (1990), provides a consistent framework for solving advection-dominated equations with general boundary conditions in a mass conservative manner. the ellam formulation was based on definition test functions that satisfy the homogeneous space-time adjoint equation locally, on elements that have boundaries defined by space-time characteristic curves of the equation. a second-order runge-kutta approximation of the characteristics within the framework of ellam has been developed by al-lawatia et al. (1999) for advection-diffusion equations and compared to other widely used and well known methods. ellam techniques have been extended to simulate contaminant transport in groundwater (ewing and wang, 1995). one of the distinctive features of the porous media on the field scale is the spatial heterogeneity of transport properties (vanderborght et al., 1997). these features have a distinct effect on the spatial distribution of contaminant concentration, as has been observed in field experiments (roth et al., 1991; ellsworth et al., 1991, 1996) and demonstrated by simulation of contaminant transport in unsaturated, heterogeneous soil (russo et al., 1998). description of the mixing process due to spatial variability of the unsaturated hydraulic conductivity has been advanced with the development of numerical solutions, which assume spatially variable soil properties (hills et al., 1991; ellsworth and boast, 1996); stochastic models (bresler and dagan, 1981; bresler, 1987; russo, 1993, 1995); and stochastic stream tube models, which decompose the field into a set of independent vertical soil columns (jury and roth, 1990; toride and leij, 1996). note that the predictions of these stochastic models on contaminant spreading are based on ensemble mean statistics, and hence, they may not be appropriate for particular site-specific applications. the stream tube models are distinguished by the degree of lateral mixing, which do not allow horizontal mixing; and the concentration for each tube represents a discrete value in the horizontal plane. this model is not popular due to the limited discussion of its theoretical foundation and a lack of procedures for its application (toride and leij, 1996). al-barwani, al-lawatia, balakrishnan, and purnama 275 5. concluding remarks groundwater is of crucial importance because it provides the source for most of the sultanate’s irrigation and domestic supplies. every effort should be made to understand ways and means of efficiently using and managing it. the unsaturated zone is the region through which water, together with pollutant carried by the water, must pass to reach the groundwater. therefore various processes occurring within the unsaturated zone play a major role in determining both the quality and quantity of water recharging into the groundwater. in this review we have attempted to illustrate the advances made towards the progress in the understanding of the flow and contaminant transport processes in the unsaturated zone as our soil and groundwater resources are increasingly subjected to the dangers of long-term pollution. we concentrated initially on conceptual aspects of various deterministic-mathematical approaches for modeling flow and contaminant transport in the unsaturated zone, and also on various stochastic and statistical approaches geared toward field scale variability and heterogeneity. unsaturated flow in the porous media is classically modeled using richards equation, which is often solved using numerical approximation methods, such as finite difference or finite element methods. predicting water flow and contaminant transport on a field-scale based on the current monitoring and modeling techniques is a difficult task. there are large uncertainties in predictions mainly due to our inability to depict detailed spatial distributions of soil hydraulic properties on the field-scale. due to the high costs of data acquisition, few field measurements are usually available for the characterization of flow and contaminant transport, even though the spatial distribution of a contaminant plume may be highly irregular. thus the quantitative methods used for predicting the fate of a contaminant and its potential threat to groundwater quality must provide descriptions of transport based on statistical information, which can realistically be extracted from the data. classical, deterministic representations are generally not adequate to describe flow and transport in natural soils under field conditions, due to the occurrence of macropores and structured elements. stochastic methods are simply mathematical tools used to overcome uncertainties in acquiring detailed spatial distributions of flow parameters in field scale aquifers. that is, instead of dealing with physical flow parameters, models dealt with the mean value, variance and correlation scales of the flow parameters. quantitative descriptions of water flow and contaminant transport rely mainly upon model simulations in which, due to difficulty in obtaining its input parameters, hypothetical parameters are often used. therefore, extensive validation of the models is required before the stochastic models can be widely accepted. oman has extensive areas of active and fossil karst. as aquifers are inherently heterogeneous at various observation scales, the complex geological structure of oman reflects well-developed fracture systems in the rocks forming the northern mountain aquifers. the essence of 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(nof-ʹ4) تحضير كاشف ضوئي فالفوني جديد نانو متر. أظهر الكاشف الجديد قدرة انتقائية 759نانومتر الى 754مرة مع انحراف ازرق خفيف من 022السيستين للكاشف يزداد اإلنبعاث الفسفوري سي. يستطيع ممتازه لحمض السيستين بوجود غيره من األحماض األمينية. تم التأكد من ارتباط السيستين بالكاشف الضوئي عن طريق جهاز الرنين المغناطي . (mm 200-30)من التركيز الطبيعي للسيستين في الجسم وهو أقل mm 1.63هذا المركب الكشف عن حمض السيستين عند تركيز قليل جدا يصل الى . امتصاص فوق البنفسجي نيتروأولوفين، التحضير العضوي، ضوئي، سيستين، كاشف: مفتاحيةالكلمات ال 1. introduction ysteine (cys) is an essential sulphur amino acid in living cells and plays various important roles in physiological processes [1]. in this regard, cys acts as an intramolecular linker in protein and enzyme tertiary structures via the formation of disulfide bridges, acts as an antioxidant against damage from the reactive oxygen species [2], participates in post-translational modification [3], and works as redox sensor in cell signalling pathways [4]. it is also associated with metal binding [5], detoxification [6] and metabolism [7]. numerous investigations have linked deficiency of cys to many diseases such as liver damage, hair depigmentation, slow growth in children and skin lesions [8]. high levels of cys can cause neurotoxicity, and cardiovascular and alzheimer’s diseases [9-11]. in order to verify some of these diseases and to understand the involvement of cys in biological environments, an extensive amount of research has been directed towards finding a selective analytical technique to detect and measure trace amounts of it in bio-fluid samples under physiological conditions. historically, methods like gas chromatography-mass spectrometry [12], hplc [13], uv-visible analysis [14], and electrochemical assay [15] have been utilized for this purpose. nevertheless, these analytical methods suffer from serious drawbacks such as complicated instrumentation, tedious sample preparation procedures, high analysis cost, low sensitivity and poor selectivity. recently, an analytical tool based on an organic fluorescent molecule that can selectively interact with cys and induce a fluorescence signal has become widely accepted as an efficient analytical method due to its high sensitivity, selectivity, low cost and versatility [16]. so far, a number of varieties of fluorescence-based sensors for cys and other bio-thiols have been developed [17]. c saleh n. al-busafi et al 86 the action of these probes is centered on various sensing mechanisms such as metal complex-displace coordination [18], michael addition [19], formation of thiazolidine [20], cleavage of the sulfonate ester [21] and formation of iminium ions [22]. fluorescent probes that work on 1,4-addition of cys to a michael acceptor have attracted great attention because of their high reactivity and sensitivity towards thiols [23]. the high reactivity of these probes towards cys is driven by the strong nucleophilicity of the –sh group when it reacts with an electron-poor michael acceptor fragment. their fluorescent sensitivity is attributed to the inhibition of the intramolecular charge transfer mechanism (ict) that occurs in the chromophore fragment after breaking the double bond that linked the signaling unit to the michael acceptor [24]. various -unsaturated michael acceptors have been exploited in designing effective fluorescent probes including ketone [25], nitrile [26], ester [27], nitroolefine [28] and pyrazolone [29]. the nitro group, with its powerful electron-withdrawing ability, has proven to be an effective michael acceptor moiety to enhance the conjugate addition of cysteine to a fluorescent probe [30]. in addition, different molecular frameworks have been used as fluorescence reporters, including acrylate [31], naphthalimide [32], pyrene [33], fluorescein [34], coumarin [35] and cyanine [36]. flavonoids are widespread plant products responsible for the beautiful colors of leafs and flowers [37]. most flavonoid compounds exhibit fluorescence if they are excited with visible or uv light due to the presence of rigid, flat rings with delocalized π electrons [38]. some of these compounds have been used as nutrition supplements because of their health benefits, such as antioxidant [39], uv-b protection [40], and anticancer [41] properties. in analytical chemistry, flavonol (3-hydroxyflavone) has been extensively used to detect various metal ions in aqueous samples as its fluorescence is vastly boosted by coordinating with metal ions [42]. recently, synthetic diethylamino substituted flavonol has been utilized as a turn-on fluorescent probe to analyze thiols [43]. in this paper, we present a fluorescent turn-on probe for monitoring levels of cysteine in biomedical samples. the probe contains a nitroolefin side-chain that quenches the fluorescence of the flavonoid backbone of the probe by photoinduced electron transfer (pet). however, thiol molecules react with the probe by breaking the double bond of the nitroolefin and as a result, the fluorescence intensity of the probe is significantly enhanced. 2. experimental in this work, 4ʹ-nitroolefinylflavone (4ʹ-nof) 1 was synthesized based on a flavone skeleton and equipped with a nitroolefin group as a michael acceptor to selectively detect cysteine. the synthesis of probe 1 is presented in scheme 1. cl o h o o oh + 2 (a) o o o ch(oh)2 (b) oh o o ch(oh)2 (c) o o ch(oh)2 3 4 5 (d) o o 6 h o (e) o o 1 no2 scheme 1. synthesis of probe 1, (a) pyridine, r.t., 25 min., aqueous hcl, yields 73%. (b) pyridine, koh, 50 0 c, 15 min. (c) acoh, h2so4, reflux, 1 h, yield 56.5%. (d) h2o, acoh, h2so4, reflux, 3 h, yield 74%. (e) nitromethane, ammonium acetate, acoh, reflux, 5 h, yield 46%. 2.1 reagents and apparatus all the reagents and solvents used in this study were obtained from sigma-aldrich chemical company and used without further purification. the purity of the synthesized compounds was checked by tlc and analyses were carried out on 0.25 mm thick pre-coated silica plates (dc-fertigplatten adamant uv254). plates were visualized by a uvgl-58 handheld 254/365 nm uv lamp. column chromatography was performed using silica gel 60 å (63–200 µm). melting points were determined using gallenkamp-mpd350.bm2.5 melting point apparatus (uk). a rotary synthesis of a flavone based fluorescent probe bearing nitroolefin moiety 87 evaporator was used to evaporate solvents. ir spectra were recorded on agilent technologies carry 630 ftir (malaysia). 1 h nmr spectra were recorded using a 700 mhz bruker avance spectrometer. chemical shifts () for proton resonances were expressed in parts per million (ppm) relative to tms as internal standard and coupling constants (j) in hz. the following abbreviations were used: s, singlet; d, doublet; m, multiple and dd: doublet of doublet. 13 cnmr spectra were recorded using a 700 mhz bruker avance spectrometer. chemical shifts () for carbon resonances were expressed in parts per million (ppm). mass spectra were obtained using maldi-tof analysis which was performed using two matrices, namely hcca and a graphite in ultraflex tof/tof instrument. a shimadzu (model multispec-1501) uv–vis spectrophotometer (shimadzu, japan) and a perkin-elmer (model ls 55) fluorescence spectrometer (perkin-elmer, u.k) were used to collect absorption and fluorescence spectra, respectively. 2.2 preparation of probe 1 2.2.1 synthesis of 2-acetylphenyl(4-dihydroxymethyl)benzoate 3 a mixture of 2'-hydroxyacetophenone (2.72 g, 20.0 mmol) and 4-formylbenzoyl chloride 2 (3.36, 20.0 mmol) in pyridine (5.0 ml) was stirred at room temperature for 25 min. after cooling, the reaction mixture was poured into a mixture of 60 ml aqueous hcl (3%) and 30 g crushed ice. the product was extracted with dichloromethane (3×20 ml) and the organic layers were combined and dried over sodium sulfate, filtered and concentrated under a vacuum to give a reddish brown crude liquid which was purified by column chromatography on silica gel using petroleum ether/ethyl acetate (8:2) for elution to give compound 3 as a white powder (4.13 g, 73%). mp: 81.1-82.0 °c. ir (neat) υmax in cm -1 : 3032 (c-h), 1601 and 1415 (c=c), 1723 (c=o, ester), 1684 (c=o, ketone), 1281 and 1242 (c-o); 1 h nmr (700 mhz, cdcl3) δ in ppm: 2.17 (s, 2h), 2.55 (s, 3h), 6.77 (s, 1h), 7.24 (m, 1h), 7.40 (m, 1h), 7.6 (m, 1h), 7.74 (d, 2h, j=8.1 hz), 7.89 (m, 1h), 8.26 (d, 2h, j=8.1 hz); 13 c nmr (176.0 mhz, cdcl3) δ in ppm: 29.62 (ch3), 70.84 (ch), 124.04 (ch), 126.50 (ch), 126.69 (chx2), 130.78 (ch), 130.83 (-c), 130.98 (chx2), 131.03 (c), 133.70 (ch), 145.37 (c), 149.26 (c), 164.47 (-c=o), 197.58 (c=o). maldi-tof m/z: calcd for c16h14o5 286.28; found 286.29. 2.2.2 synthesis of 4ʹ-dihydroxymethylflavone 5 a mixture of 2-acetylphenyl(4-dihydroxymethyl)benzoate 3 (4.0 g, 14.0 mmol) and pyridine (8 ml) in a 50 ml rbf was warmed in a hot water bath at 50 °c until compound 3 dissolved completely. finely powdered potassium hydroxide (0.6 g, 10.7 mmol) was added and the reaction mixture was stirred for 15 minutes at 50 °c. after cooling, the mixture was poured into a 100 ml beaker containing aqueous acetic acid solution (10%, 10 ml). the yellow solid intermediate 4 was collected using buchner filtration, and then dissolved in a mixture of acetic acid (8 ml) and concentrated sulfuric acid (0.25 ml). the reaction mixture was heated under reflux for 1 hour. the cooled mixture was poured into ice and stirred with a glass rod. the solid product was collected by suction filtration, washed with water and re-crystallized from ethanol to give compound 5 as yellow crystals (2.26 g, 56.5%). mp: 130.7-131.54 °c. ir (neat) υmax in cm -1 : 3039 (c-h), 1642 (c=o), 1462 (c=c), 1280 and 1242 (c-o); 1 h nmr (700 mhz, cdcl3) δ in ppm: 6.76 ( s, 1h), 6.81 ( s, 1h), 7.41 ( m, 1h), 7.55 ( m, 1h), 7.69 ( m, 1h), 7.72 (d, 2h, j= 8.4 hz ), 7.94 (d, 2h, j=8.4 ), 8.21 (dd, 1h, j=1.3 , j= 8.0 hz ); 13 c nmr (176.0 mhz, cdcl3) δ in ppm: 70.69 (ch), 108.29 (ch), 118.18 (ch), 123.99 (c), 125.52 (c), 126.81 (ch), 126.82 (chx2), 126.98 (ch), 133.28 (c-h), 134.08 (chx2), 143.31 (c), 156.26 (c), 162.16 (c), 178.33 (c). maldi-tof m/z: calcd for c16h12o4 268.26; found 268.19. 2.2.3 synthesis of 4ʹ-formylflavone 6 4ʹ-dihydroxymethylflavone 5 (2.04 g, 7.60 mmol) was dissolved in a mixture of acetic acid (86 ml), water (30.4 ml) and sulfuric acid (6.08 ml). the mixture was refluxed for 3 h and the reaction was monitored using tlc. the cooled mixture was poured into ice/water, filtered and dried under a vacuum. the crude product was recrystallized from ethanol to give compound 6 as an orange powder (1.62 g, 74%). mp: 172.4-172.5 °c. ir (neat) υmax in cm -1 : 3072 (c-h), 1698 (c=o: aldehyde), 1630 (c=o: ketone), 1460 (c=c), 1282 (c-o); 1 h nmr (700 mhz, cdcl3) δ in ppm: 6.71 (s, 1h), 7.43 ( m, 1h), 7.58 (dd, 1h, j=8 hz, j=0.5 hz), 7.72 ( m, 1h ), 8.01 ( d, 2h, j=7.0 hz), 8.08 (2h, d, j=7.0 hz), 8.21(dd, 1h, j=8.0 hz, j=1.6 hz), 10.09 (s, 1h); 13 c nmr (176.0 mhz, cdcl3) δ in ppm: 109.19 (ch), 118.24 (ch), 124.42 (c), 125.69 (ch), 125.88 (ch), 126.96 (chx2), 130.23 (chx2), 134.29 (ch), 137.15 (c), 138.17 (c), 156.30 (c), 161.76 (c), 178.32 (c), 191.40 (c). maldi-tof m/z: calcd for c16h10o3 250.25; found 250.21. 2.2.4 synthesis of 4ʹ-nitroolefinylflavone (4ʹ-nof) 1 a mixture of 4ʹ-formylflavone 6 (0.5 g, 2.00 mmol), nitromethane (0.24 g, 4 mmol), ammonium acetate (0.37 g, 4.8 mmol) and acetic acid (8 ml) was heated under reflux at 100 °c for 5 hours. after cooling, the reaction mixture was poured into 100 ml of water and the product was extracted by ethyl acetate (3×30 ml), dried over na2so4, filtered, and evaporated under reduced pressure. the resulting solid was recrystallized from ethanol to give compound 1 as an orange powder (0.23 g, 46%). mp: 231.5-234.8 °c. ir (neat) υmax in cm -1 : 3106.41 (c-h), 1570.08 (c=c), 1628.26 (c=o), 1499.3, 1331.6 (n-o); 1 h nmr (700 mhz, dmso) δ in ppm: 8.3 (d, 1h, j=13 hz), 8.19 (d, 2h, j=7 hz), 8.16 (s, 1h), 8.02 (d, 2h, j=8 hz), 7.84 (m, 1h), 7.80 (d, 1h, j = 8 hz), 7.50 (m, 1h), 7.16 (s, 1h). 13 c nmr saleh n. al-busafi et al 88 (176.0 mhz, cdcl3) δ in ppm: 191.5 (c=o), 177.18 (c), 161.5 (c), 155.7 (c), 139.44(ch), 137.91 (c), 136.29(ch), 134.49 (ch), 130.34 (ch), 129.92 (2ch), 127 (2ch), 125.70 (c), 124.8 (ch), 123.4 (ch), 118.64 (ch). maldi tof m/z: calcd for c17h11no4 293.27; found 293.16. 2.2.5 uv-visible and fluorescence spectra measurements stock solutions (8 mmol/l) of amino acids including cysteine (cys), alanine (ala), phenylalanine (phe), serine (ser), tyrosine (tyr), aspartic acid (asp), arginine (arg), histidine (his) and lysine (lys), glutathione (gsh) and nacetylcysteine in 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (hepes) buffer (10 mmol/l, ph 7.5) were prepared. a stock solution of probe 1 (5 mmol/l) was also prepared in acetonitrile (acn). for uv-vis spectra measurements, 10 μl of probe stock solution was mixed with 30 μl of each amino acid, diluting the mixture to 5 ml with hepes/ acn (3:2, v/v). for fluorescence spectrum measurement, (1 mmol/l) of working stock solution of probe was prepared by placing 1 ml of the probe stock solution into a 5 ml volumetric flask. all fluorescence measurements were done using a 330 nm excitation wavelength with the excitation and emission slit widths of 10 nm. fluorescence spectra were measured 15 min after the addition of the analyte. the fluorescence titration experiments were performed using a probe 1 concentration of 0.5 mm in ch3cn-hepes (10 mmol/l, ph=7.5, 2:3, v/v) with cys concentration range of 0−1.2 mmol/l at room temperature. 2.2.6 detection limit the detection limit was calculated based on the fluorescence titration. in the titration experiment, (0.5 mmol/l) probe gave a good linear relationship between the fluorescence intensity and the cys concentration from 0 to1 mmol/l (r 2 = 0.9985). the detection limit was then calculated with the equation: detection limit = 3σ/m, where σ is the standard deviation of blank measurements and m is the slope between intensity versus cysteine concentration. the emission intensity of 5 without cys was measured ten times and the standard deviation of blank measurements was determined. 3. results and discussion 3.1 selectivity and competition studies 3.1.1 uv-visible absorption spectra first, the uv-visible absorptions of probe 1 in the absence and presence of l-cysteine (cys) and non-thiol amino acids (l-alanine (ala), l-phenylalanine (phe), l-serine (ser), l-tyrosine (tyr), l-aspartic acid (asp), l-arginine (arg), l-histidine (his) and l-lysine (lys) in 10 mmol/l hepes buffer/ch3cn (4:1, v:v) were measured. as shown in figure 1, probe 1 displays a maximum absorption at 340 nm, while in the presence of cys the absorption maximum was blue-shifted to 300 nm with obvious enhancement in the absorption intensity. on the other hand, non-thiol amino acids showed almost no effect in the absorption of the probe at 340 nm. in addition, amino acids with highly polar sidechains (tyr, asp, arg, his and lys) enhanced the absorption intensity of probe 1 at 266 nm. such effects can be attributed to the hydrogen bonds and dipole-dipole forces between the probe and these acidic and basic amino acids. figure 1. uv/vis absorption spectra of 1 (0.01 mmol/l) (dashed line) in ch3cn-hepes (10 mmol/l, ph 7.5) in the presence of 0.05 mmol/l analytes including: ala, phe, ser, cys, tyr, asp, arg, his and lys. the spectra were acquired 60 min after cys addition. synthesis of a flavone based fluorescent probe bearing nitroolefin moiety 89 under the same conditions, the uv-visible absorptions of 1 when added to other thiol compounds such as nacetyl-l-cysteine and glutathione (gsh) were examined (figure 2). n-acetyl-l-cysteine showed absorption maxima at 311 nm with lower intensity compared to p1-cys, while gsh caused a maximum absorption at 259 nm with a shoulder at 320 nm. figure 2. uv/vis absorption spectra of 1 (0.01 mmol/l) in ch3cn-hepes (10 mm, ph 7.5) in the presence of 0.05 mmol/l analytes including gsh, cys and n-acetyl-l-cysteine. 3.1.2 the fluorescence spectra next, we explored the sensing response of probe 1 (0.01 mmol/l) towards cys and other non-thiol amino acids by fluorescence spectroscopy. as displayed in fig. 3, probe 1 alone in 10 mmol/l hepes buffer/ch3cn (4:1, v/v) at ph 7.5 exhibits weak fluorescence at 457 nm. the feeble fluorescence of 1 is related to the presence of a nitroolefin moiety that acts as an electron acceptor for the photoinduced electron transfer process. the presence of non-thiol amino acids (ala, phe, ser, tyr, asp, arg, his and lys) induced a negligible fluorescence enhancement. however, in the presence of cys there was a significant boost in the fluorescence intensity of 200 fold observed at 459 nm with a slight blue shift of 2 nm. these results indicate that the presence of non-thiol amino acids has no effect on the ability of probe 1 to detect cys. we can say that probe 1 is an excellent fluorescent sensor to detect cys in biomedical samples without interference from other amino acids. figure 3. fluorescence spectra of 1 (0.01 mmol/l) with various analytes (0.05 mmol/l) including: ala, phe, ser, cys, tyr, asp, arg, his and lys in ch3cn-hepes (10 mmol/l, ph 7.5) (λex = 470 nm, slit: 10 nm/10 nm). inset photo is of 1 in the absence (a) and presence (b) of cys. saleh n. al-busafi et al 90 furthermore, under the same conditions, we investigated the fluorescence behavior of probe 1 in response to other thiol compounds such as gsh and n-acetyl-l-cysteine. as shown in figure 4, both gsh and n-acetyl-lcysteine caused almost no fluorescence enhancement when mixed with probe 1, which means there is no interference from thiol compounds with cys detection. figure 4. fluorescence spectra of 1 (0.1 mmol/l) and (0.5 mmol/l) of each thiol in ch3cn-hepes (10 mmol/l, ph 7.5, 2:3 v:v), λex = 470 nm. 3.2 the ph effect the fluorescence of probe 1 towards cys was also explored in the ph range from 3.0 to 8.0 (figure 5). when cys (0.08 mmol/l) was added to probe 1 (0.01 mmol/l), the fluorescence was almost constant in the ph range from 3.0 to 7.0, but increased rapidly when the ph reached 7.5 and then decreased back at ph 8.0. interestingly, there was a slight blue shift in the maximum wavelengths at lower ph values, which may be attributed to the protonation of the oxygen atom of the carbonyl group leading to ring cleaving. these results support the application of this fluorescent probe in physiological conditions. figure 5. effect of ph on the fluorescence intensity of 1 (0.01 mmol/l) in the presence of cys (0.08 mmol/l) in ch3cn-hepes (10 mmol/l, 4:1v/v) upon exciting at 330 nm. ex slit was set as 5 nm. em slit was set at 10 nm. inset: the linear correlation of the reaction against different ph values (3-8). synthesis of a flavone based fluorescent probe bearing nitroolefin moiety 91 3.3 sensitivity studies a series of concentration-dependent fluorescence experiments was performed in order to assess the detection sensitivity of probe 1 at ph 7.5 in 10 mmol/l hepes buffer/ ch3cn (3:2, v/v) towards cys. as displayed in figure 6, when the concentration of cys was allowed to increase from 0 to 1.2 mmol/l, the fluorescence intensity of the solution of probe 1 (0.5 mmol/l) gradually increased. in the titration experiment, probe 1 gave a linear relationship between the fluorescence intensity and cys concentration (figure 7), from which the detection limit for cys was calculated to be 1.63 μmol/l, which is lower than the normal human intracellular cysteine concentration (30-200 μmol/l. this result further proved that probe 1 is highly sensitive to cys. figure 6. fluorescence spectra of 1 (0.5 mmol/l) in ch3cn-hepes (10 mmol/l, ph=7.5, 2:3, v/v) with cys (0−1.2 mmol/l). excitation at 330 nm. ex slit and em slit were both set at 10 nm. figure 7. a plot of fluorescence intensity changes of 5 at 480 nm against concentration of cys from 0 to 1.2 mm. 3.4 reaction mechanism and 1 hnmr study the reaction of cys with probe 1 is a typical michael addition reaction in which the –sh group in cys acts as a michael donor and the nitroolefin group in probe 1 acts as a michael acceptor. the nucleophilic –sh group connects to the β-carbon atom of the α,β-unsaturated nitro moiety in probe 1 since it is the most electrophilic site due to the electron withdrawing effect of the nitro group (scheme 2). saleh n. al-busafi et al 92 o o no2 h h o o no2 s nh2 ho o 1 probe 1-cys adduct ho nh2 o sh scheme 2. proposed sensing mechanism of probe 1 towards cys. this mode of addition can be confirmed by 1 h-nmr. figure 8 displays 1 h-nmr spectra of probe 1 (spectrum a) and of probe 1-cys adduct (spectrum b). the most deshielded proton in probe 1 is h- , which appears as a doublet at 8.33 ppm and couples with h-which is located at 8.17 ppm (fig. 8, spectrum a). with the addition of 10 equiv cys to a solution of probe 1 in dmso-d6/d2o (2:1, v/v), the signals of h- and h-protons have disappeared (figure 8, spectrum b). in addition, signals of other protons in rings a, b, and c have changed their positions. figure 8. 1 h-nmr spectra of probe 1 (a) and probe 1-cys adduct (b). 4. conclusion a blue-emitting fluorescent probe based on flavone structure was successfully synthesized for selective detection of cys in the presence of thiol and non-thiol amino acids. the sensing mechanism of the probe was designed via michael addition of cys to a α, β-unsaturated nitro moiety. an increase in the fluorescence intensity accompanied with a bathochromic shift was observed when cys was added to a 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fluorescence enhancement in micellar media and its applications to niobium and tantalum ultratrace determinations. analytical chemistry, 1985, 57, 1681-1687. 43. lan, m., wu, j., liu, w., zhang, h., zhang, w., zhang, x. and wang, p. highly sensitive fluorescent probe for thiols based on combination of pet and esipt mechanisms. sensors and actuators b: chemical, 2011, 156, 332-337. received 3 july 2017 accepted 21 february 2018 squ journal for science, 2017, 22(2), 96-105 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp96-105 sultan qaboos university 96 an evaluation of the mathematics foundation course in sultan qaboos university: does high school performance matter? m. mazharul islam*, asma al-ghassani & ahmed y. s. al-hadhrami department of mathematics and statistics, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman, *email: mislam@squ.edu.om. abstract: although the mathematics foundation program was introduced in sultan qaboos university (squ) half a decade ago, there has been no evaluation or assessment of the program. the aim of this study was to evaluate the students’ performance in the mathematics foundation course in squ and to examine the predictive value of a student’s high school performance for success in the math foundation course. the study considered a sample of 551 students who took the math course (math2107) during 2014 spring semester. more than 95% of the students were admitted to squ with a high school score of 80 and above. the analysis revealed that, in general, female students were admitted to squ with a significantly higher average high school score than the male students. the findings indicate a very unsatisfactory performance of the students in the mathematics foundation course as the mean gpa was 1.66 and more than half (59%) of the students obtained a gpa less than 2 (i.e. below grade c), of which 14% failed and 35% obtained grade d. female students outperformed male students in the mathematics course. high school mathematics performance, gender and cohort of students were identified as significant predictors of success in the mathematics foundation course. to increase the success rate of the mathematics course, the high school curriculum needs to be aligned with the university standards and the admission authority should continue to give more attention to high school mathematics scores along with overall high school performance while making admission decisions for the college of science in squ. keywords: predict; foundation; high school score; sultan qaboos university, oman. مادة الرياضيات التأسيسية بجامعة السلطان قابوس : هل األداء بالمرحلة الثانوية مهم ؟ تقييم أحمد الحضرميو مزهرال اسالم ، أسماء الغسانيمحمد التاسيسي للرياضيات قد تم إدخاله في جامعة السلطان قابوس منذ نصف عقد من الزمان، لم يكن هناك تقييم أو على الرغم من أن برنامج :صالملخ في جامعة السلطان قابوس ودراسة القيمة ( fpm0105للبرنامج. هدفت هذه الدراسة إلى تقييم أداء الطالب في مادة الرياضيات التاسيسيه ) ديرتق مادة الرياضيات أكملواطالبا 555. ونظرت الدراسة في عينة من ( fpm0105) المرحلة الثانوية للنجاح في هذه المادهالتنبؤية ألداء الطالب في (math2107 خالل فصل الربيع )درجة فما فوق. 01٪ من الطالب في جامعة السلطان قابوس بدرجة الثانوية العامه 55. تم قبول أكثر من 2152 مقارنة بالطلبة من ذواتي المعدل العالي بالثانويه العامه تم قبولهن في جامعة السلطان قابوساللواتي ت و بصورة عامه التحليل أن الطالبار وأظه ٪(55) وأكثر من نصف الطلبة 5.11المعدل العام الذكور. وتشير النتائج إلى أن أداء الطلبة في مادة الرياضيات غير مرضي للغاية حيث بلغ متوسط . الطالبات تفوقن على الطالب d٪ حصلوا على درجة 55٪ رسبت و 52(، منها c) أي أقل من درجة 2المعدل التراكمي أقل من حصلوا على الطالب كمؤشرات هامة للنجاح في مادة الذكور في مادة الرياضيات. وقد تم تحديد أداء الرياضيات في المرحلة الثانوية العامه، ونوع الجنس ودفعة لزيادة معدل النجاح في مادة الرياضيات التاسيسيه، يجب أن تكون المناهج الدراسية في المرحلة الثانوية متوافقة مع معايير التاسيسيه.الرياضيات لمرحلة ام لالجامعة، ويجب على سلطة القبول مواصلة إعطاء المزيد من االهتمام لدرجات الرياضيات في المرحلة الثانوية جنبا إلى جنب مع األداء الع الثانوية عند القبول في كلية العلوم في جامعة السلطان قابوس. ، سلطنة عمان. الثانوية العامة، جامعة السلطان قابوس عالمة ،التنبأ، التأسيسي :مفتاحيةالكلمات ال 1. introduction he massive expansion of higher education across the world is one of the important development features of our time. the increase in the number of students as well as in that of public and private higher educational institutions, has been associated with an enormous increase in the international mobility of the students over the t an evaluation of mathematics foundation course 97 last few decades [1, 2]. a profound change in the educational system and concern about the quality of higher education and its standardization has also emerged as an issue [3]. at the same time, many new systems have been introduced for academic standardization and quality control in higher education. the introduction of academic foundation programs (also called preparatory programs) by a growing number of higher education institutions across the globe is one such new program. these programs are typically for those high school graduates who lack necessary skills in english, mathematics and information technology (it) at the time of entering higher education institutions, and they have become especially prevalent in today’s world of internationalization and cross-border academic mobility. in some countries, such as in britain, international foundation programs (ifps) exist alongside a range of other university preparatory programs that are offered primarily to domestic students. the ifp is offered not only for improving the linguistic ability of a student, but also to bridge the gap between the british 13year pre-university school system and the 12-year system common to a majority of education systems around the world. additionally, ifps are designed to help students meet minimum academic requirements for entry into an undergraduate degree program as well as to prepare them culturally for life and study in a new study environment. in this era of globalization, the dominance of the english language as a medium of higher education, research and trade is undeniable. it is now a common phenomenon in almost all universities in non-english speaking countries, where courses are mostly taught in english in place of their native languages. in the middle eastern countries including the sultanate of oman, universities and higher educational institutions teach courses mostly in english in place of their native language arabic, which is the language of instruction from primary to secondary school level. as a result, students admitted into universities and higher educational institutions are facing language difficulties. it has also been observed that, globally, students entering higher educational deal with their first year institutions do not have sufficient mathematical skills or mathematical background to mathematics courses, and because of this, universities and colleges have seen huge failure and dropout rates [4, 5]. the problem is particularly severe in oman [6]. students are also facing it problems in the higher educational institutions. thus, to bridge the language, mathematics and it gaps, most middle eastern universities have introduced a preparatory program of english language, mathematics and it which is known as a foundation program (fp). the main objective of these programs is to create an atmosphere conducive to a smooth transition from the secondary school to the university. in 2009, the ministry of higher education in oman released a decision about introducing a foundation program (fp) in all private and public universities and colleges. the program became a mandatory introduction to study in all universities and higher educational institutions. following that directive, sultan qaboos university (squ), the only public university and the premier institution for higher education in oman, introduced a fp in the 2010/2011 academic year. the main objective of the programme is to achieve the required educational goals set by the omani authority for academic accreditation [7]. within oman’s tertiary education system, the fp is now playing a key role in preparing secondary school graduates for further study by upgrading their english, mathematics, computing and general study skills [8, 9]. in the mathematics component of the fp at squ, particularly in science based colleges, courses are offered at two levels: basic and advanced. to decide the level of mathematics to be offered to a student, a placement test and an exit test are conducted prior to the beginning of the semester. the basic mathematics course (i.e.fpmt0101) is offered to those students who do not pass the placement test, while the mathematics for sciences course (i.e. fpmt0105) is offered to those who do not pass the exit test. this study is concerned with performance on the fpmt0105 course. the main objective of the course is to prepare the students for calculus and higher mathematics. its primary topics cover basic mathematics, elementary functions (polynomial, rational, exponential, logarithmic, and trigonometric) and their various applications in solving real world problems. although the fp in squ has been running for the last six years, to our knowledge, there has been no statistical evaluation or assessment of the program performance and how far it is predicting a student’s academic success in their degree program. since mathematics is a key course in the fp, the main objectives of this study are to evaluate students’ performance in the fpmt0105 course and to determine how far a student’s high school performance can predict success in the foundation mathematics course. the study findings are expected to provide valuable information and guidelines for the concerned authority and squ administration, for further improvement of quality of education at both secondary and undergraduate level. the study is expected to bridge the research gap regarding the performance of students of the fp in oman, and thus may serve as a pilot study for future research to be conducted in this area. 2. literature review over the last century or more, many attempts have been made to identify the predictors of college grades and performance. most of this research has primarily focused on the predictive power of cognitive factors of students such as high school performance (i.e., high school grades) and scores on standardized tests, such as the american college testing program’s assessment (act) and the college board’s scholastic aptitude test (sat) [10,11]. generally, these studies have found that high school performance and standardized test scores were the most important predictors of success in college and suggested that these cognitive factors could be used to make accurate and appropriate admission and placement decisions for students [12-19]. traditionally, cognitive factors m. mazharul islam et al 98 such as high school achievement score, sat or act are widely considered as admission criteria by most higher education institutions in the majority of countries. some institutions, such as squ, use only the high school achievement scores, while others use both high school scores and standardized scores (sat or act) to select students [20-23]. a significant body of literature suggests that high school performance is the best predictor of success in undergraduate studies and has more predictive power than the standardized tests or any other factor [24-29]. some studies have emphasized that the academic performance of the undergraduate students in any college or university depends not only on cognitive factors but also on non-cognitive factors (e.g., teaching and institutional quality, students’ motivation and so on) and demographics (e.g., gender, ethnicity, location) [30,31]. studies have also found that students’ non-cognitive characteristics, such as educational aspirations, study habits, and motivation, as well as their involvement in extra curriculum activities, are significantly related to their success in college [30, 32]. studies have shown that students who took more mathematics courses at high school level performed better in college education and obtained higher scores in standardized tests of mathematics as well as college admission tests [33, 34]. the stronger the background in mathematics which students achieved in high school, the more likely they were to earn college degrees [16, 35, 36]. adelman [16] observed that students who took a mathematics course beyond algebra in high school were two times more likely to complete their bachelor’s degree without significant delays in the united states of america. mathematical knowledge is important to the modern world. it facilitates understanding of the wide range of problems of the 21st century. for centuries, mathematics has helped us in solving the secrets of nature since modern scientific thinking was formed with mathematical concepts, and scientific concepts are interconnected by the rules of mathematics. thus, mathematics is considered to be the language of science [37]. with this in mind, educational institutions teach basic mathematics to their students [38]. 3. data and methodology the data for the study was obtained from the student database maintained by the deanship of admission and registration (a & r) office of squ. the sample comprised 551 students who took the mathematics foundation course fpmt0105 during spring 2014. the course was taught by instructors from the foundation program unit under the supervision of the department of mathematics and statistics, college of science, squ. the final grade in fpmt0105 of the 551 students along with their gender, cohorts, high school mathematics scores, high school scores and college of study were obtained from the archive of the a & r office. students’ grades in fpmt0105 were recorded on a 4 point scale using letter grades a=4, a-= 3.7, b+=3.3, b=3.0, b-=2.7, c+=2.3, c=2.0, c=1.7, d+=1.3, d-=1.0 and f=0.0. the raw scores (out of 100) of fpmt0105 were also available. data was obtained from students’ records as an excel spreadsheet and then imported into spss for statistical analysis. the study considered the performance of the fpmt0105 course as an outcome or dependent variable, while gender, cohort of study, college of study, high school mathematics score and overall high school scores were considered as predictors or independent variables. the overall high school scores included mathematics scores. both descriptive and inferential statistics were used for data analysis. descriptive statistics were computed for all key variables. inferential statistics techniques involved correlation analysis, cross tabulation and chi-square test, analysis of variance (anova) and multiple regression analysis. for correlation analysis, we employed both product-moment and ‘biserial’ correlation coefficients, because some of our variables (e,g. gender, college) are categorical variables. in 1909, karl pearson (39) developed the biserial correlation coefficient as a special case of pearson’s product-moment correlation. the product-moment correlation is applied when two variables are quantitative (e.g. gpa and high school scores) and measured either in ratio or interval scale, whereas in the case of biserial correlation one of the variables is measured on a dichotomous scale (e.g. gender: male/female) using a numeric code. the word biserial refers to the separate sets of values of the quantitative variable which are associated with the two values, say 0 and 1, of the dichotomous variable. biserial correlation is a widely used statistical technique in social research and biostatistics. in correlation analysis, we have also considered the r-squared statistic (also called co-efficient of determination). in the case of simple linear correlation, the r-squared statistic is simply the square of the simple correlation coefficient r, indicating the proportion of variation in the performance of fpmt0105 explained by the predictors. the goal of multiple regression analysis was to model the relationship between a predictor and a response variable after controlling the effects of other variables. to obtain the adjusted effect of a predictor on the success of the fpmt0105 course, we employed multiple logistic regression analysis, considering fpmt0105 success as the outcome variable ( i y ) and the characteristics of the students as predictors. a gpa of 2 or more in fpmt0105 was considered as success. thus a multiple logistic regression model was fitted considering fpmt0105 success ( i y ) as a dichotomous response variable, with coding ‘1’ if the ith student obtained gpa 2 or more and ‘0’ otherwise, and characteristics of the student as predictor variables ( i x ). then )1pr(  ii yp can be defined as the probability of the response equal to 1 and i p can be modeled using logit link function where iy has a bernoulli distribution. then, we can write the logistic regression model as an evaluation of mathematics foundation course 99 1 1 2 2 log ....... 1 i i i k ki i i p x x x p                 , (1) where, k refers to number of predictors, α and β are the intercept and slope of predictor variables and  is the error term. β is the log of the odds ratio and exp(β) is the odds ratio (or). by definition, the odds ratio of the reference category is 1.00. an odds ratio greater than 1.00 for a category of the predictor variable indicates a higher likelihood of the outcome in that category as compared with that of the reference category after adjusting the effects of other predictors. 4. results a. background characteristics of students table 1 shows the distribution of students by selected background characteristics. of the total 551 students who took the fpmt0105 course, more than sixty percent (62%) were male and 38% were female. the higher number of male students in our sample may be due to the fact that the sample comprised students from four different cohorts starting from 2010 to 2013, and most of the students from older cohorts are male students. this is evident from the distribution of students by cohorts and gender (table 1). the distribution of the students by cohort of study indicate that nearly half (48%) of the students were from the 2012 cohort followed by the 2013 cohort (35%). these two cohorts accounts for 83% of the total students and the rest (17% ) of the students came from the 2011 cohort (14%) and 2010 cohort (3%). most of the female students were from the younger cohorts, while most of the male students were from the older cohorts. for example, almost two-thirds (65%) of the female students were from the youngest cohort of 2013, while 61% of the male students were from the older cohort of 2012. table 1. percentage distribution of students by background characteristics most of the students in our sample came from the colleges of engineering (47%) and of science (41%), accounting for 88% of the total students from these two colleges. about 9% of the students were from the college of characteristics gender total (n=551) female (n=209) male (n=342) gender male 62.1 female 37.9 cohort 2010 2.4 4.1 3.4 2011 6.2 18.1 13.6 2012 26.3 60.8 47.7 2013 65.1 17.0 35.2 college agriculture & marine science 14.8 5.6 9.1 education 4.8 1.8 2.9 engineering 31.6 56.1 46.8 science 48.8 36.5 41.2 high school math score (in %) < 70 13.7 8.5 70-79 2.4 28.7 18.7 80-89 34.4 38.6 37.0 90-100 63.2 19.0 35.8 mean score (±sd) 91.1 ± 5.0 80.6 ±9.5 84.6 ± 9.6 [min, max] score [77, 100] [50, 98] [50, 100] high school score (in % ) < 70 1.2 0.7 70-79 0.5 3.8 2.5 80-89 3.3 73.4 46.8 90-100 96.2 21.6 49.9 mean score (±sd) 93.1  2.1 86.6  4.9 89.1  5.0 [min, max] score [80, 97] [56, 95] [56, 97] total 100 100 100 m. mazharul islam et al 100 agriculture and marine science and a small proportion (3%) were from the college of education. more than half (56%) of the male students were from the college of engineering. on the other hand, the proportion of female students was higher from all the colleges except the college of engineering. table 1 also shows the distribution of students according to their high school mathematics scores and overall high school scores out of 100. the sample data indicate that the average high school scores and the high school mathematics scores of the admitted students in squ were 89(±5.0) and 85(±9.6) respectively. the high school score ranges from 56 to 97, while high school mathematics scores ranges from 50 to 100. about 97% of the students had high school scores 80 and above, and 3% students had overall high school score below 80 markswhilst more than one-third (36%) of the students had high school mathematics scores of 90 and above, 37% had scores of 80 to 89 and 8.5% scored below 70. table 2. means and standard deviations of high school math score and high school score by gender. high school performance gender test of significance† male female high school math score 80.6 (±9.5) 91.1 (±5.0) t = 14.67, p < 0.001 overall high school score 86.6 (±4.9) 93.1 (±2.1) t = 18.88, p < 0.001 † test of significance is based on t-test, comparing two sample means of male and female students under the assumptions that the samples are independent and that they are drawn from two populations with equal variance. the distribution of high school scores and high school mathematics scores by gender of the students indicate a huge difference between male and female scores. female students obtained admission to squ with both higher average high school and high school mathematics scores. for example, 96% of the female students had a high school score of 90 and above, while the corresponding figure for male students was 22%. female students had an average high school score of 93.0(±2.1) as opposed to 87 (±4.9) for the male students, the difference being statistically significant (t = 18.88, p<0.001) (table 2). high school mathematics scores also follow a similar pattern across the gender of the students. the size of the effects of gender on high school mathematics and overall high school score, measured by etasquared (η 2 =between ss/total ss), indicates that gender explained 39.4% of the variation in high school mathematics scores and 28.2% in overall high school scores respectively. table 3. percentage distribution of grades in fpmt0105 by gender of students. letter grade gender total number female male a 3.83 1.17 2.18 12 a7.66 0.88 3.45 19 b+ 14.83 2.05 3.09 17 b 16.27 2.63 6.90 38 b7.18 0.58 7.80 43 c+ 11.48 9.65 6.90 38 c 10.05 10.53 10.34 57 c12.44 3.51 10.34 57 d+ 8.13 29.53 13.25 73 d 6.70 17.25 21.42 118 f 1.44 22.22 14.34 79 total 100.0 100.0 100.00 551 b. performance in fpmt0105 and its covariates students’ performances in the fpmt0105 course were measured by the aggregate scores obtained in quizzes, homeworks, tests and the final examination. the aggregate scores, evaluated out of 100, were converted into letter grades and the grade point average (gpa) in a 4-point scale. the results are presented in table 3 by gender. overall, 5.6% of the students obtained grade a, 17.8% grade b, 27.6% grade c, 34.7% grade d and 14% of students failed (obtained grade f) in the course (figure 1). the data indicate that half (49%) of the students obtained below grade c which in terms of grade point average is below 2, indicating a very poor performance of the students in the mathematics foundation course. the overall grade point average in fpmt0105 was 1.66. table 4 presents the results of differential analysis and analysis of variance (anova) showing differential effects of some selected factors on mean gpa in fpmt0105. gender of the students shows a significant differential effect on mean gpa in fpmt0105. female students performed better than male students. the mean gpa of female students was two times higher than of male students (2.41 vs. 1.20). cohort of the students shows significant positive association with the mean gpa in fpmt0105. recent cohorts performed better than their older counterparts. for example, the mean gpa was 2.55 for the 2013 cohort compared to 0.52 for the 2010 cohort. fpmt0105 performance varies significantly with the college of study of the students. students from the college of agriculture and marine an evaluation of mathematics foundation course 101 science showed the lowest performance (mean gpa 1.27), while the students from the college of education exhibited the highest performance (mean gpa 2.32). high school mathematics scores and overall high school scores showed significant positive association with the performance in fpmt0105. for example, the mean gpa was 0.92 for the students with high school scores less than 70, and the corresponding figure for the students with high school scores 90100 was 2.24. figure 1. distribution of grade in fpmt0105 by gender of students table 4. mean gpa with 95% confidence interval (95% ci) for the mathematics foundation course (fpmt0105) by characteristics of students. characteristics mean gpa 95% ci f ratio and p-value total 1.66 1.57 1.75 gender 250.12, p<0.001 male 1.20 1.11 1.29 female 2.41 2.29 2.53 cohort 166.79, p<00.1 2010 0.52 0.24 0.79 2011 0.57 0.40 0.73 2012 1.39 1.30 1.48 2013 2.55 2.45 2.67 college 9.32, p<0.001 agriculture & marine science 1.27 1.06 1.48 education 2.32 1.74 2.89 engineering 1.84 1.71 1.97 science 1.49 1.35 1.63 high school mathematics score (in %) 78.94, p<0.001 < 70 0.61 0.43 0.79 70-79 1.04 0.90 1.17 80-89 1.56 1.44 1.68 90-100 2.33 2.19 2.48 overall high school score (in % ) 79.83, p<0.001 < 70 0.92 -0.78 2.63 70-79 1.13 0.79 1.47 80-89 1.08 0.99 1.17 90-100 2.24 2.12 2.35 2 11.5 5.6 5.3 38.3 17.8 23.7 34 27.6 46.8 14.8 34.7 22.2 1.4 14.3 0 5 10 15 20 25 30 35 40 45 50 p e rc e n t a b c d f m. mazharul islam et al 102 4.3 predictor of fpmt0105 success to examine whether there is a significant relationship between fpmt0105 performance and high school performance and other characteristics of students, we first employed correlation analysis. the results are presented in table 5. the results indicate that all the correlation coefficients between fpmt0105 scores and the given set of predictors, except college of study, were found positive and significant at 0.01 level. overall high school score, high school mathematics score and gender of student have moderate positive correlation with fpmt0105 score and are close to each other. cohort of study shows the highest correlation coefficient with fpmt0105 score. the r-squared statistic indicates that cohort of study explained 45% of the variation in performance on the fpmt0105 course. high school mathematics score explained 33% of the variation in performance on the fpmt0105 course, while overall high school score explained 29.5% of the variation for this course. this indicates that high school mathematics scores have slightly higher predictive value in explaining variation in fpmt0105 performance than overall high school scores. table 5. correlation coefficients and r-squared statistics for fpmt score and gender, high school mathematics score, overall high school score, and cohort of students. correlation coefficient (r) r-squared statistic high school math score 0.575 ** 0.331 high school total score 0.543 ** 0.295 gender 0.548 ** 0.300 college of study -0.037 0.001 cohort of study 0.674 ** 0.454 ** correlation is significant at the 0.01 level (2-tailed). table 6. multiple logistic regression analysis of success in mathematics foundation course showing the adjusted odds ratio of factors effecting the success. factors b odds ratio 95% ci for odds ratio p-value lower upper cohort .000 2010/2011 reference 2012 1.71 5.53 1.78 17.78 .003 2013 3.39 29.67 8.98 99.05 .000 gender female 1.40 4.05 1.62 10.18 .003 male reference college .372 agriculture & marine science -.640 .52 .18 1.46 .221 engineering .072 1.08 .03 1.14 .301 education .340 1.40 .63 2.10 .401 science reference high school mathematics score .098 1.10 1.03 1.16 .001 overall high school score .034 1.03 0.89 1.07 .705 constant -13.388 .000 .001 the correlation analysis, however, shows the relationship between two variables without controlling the effects of other variables. to obtain the adjusted effect of a predictor on the success of fpmt0105 we employed multiple logistic regression analysis. table 6 presents the results of multiple logistic regression analysis. multiple logistic regression analysis identified high school mathematics score, cohort and gender of students as significant predictors of mathematics foundation course (i.e. fpmt0105) success. the result indicates that one unit increase in high school mathematics score increases the odds of success in fpmt0105 by 1.10 times (or=1.10; 95%ci=1.03-1.16). cohort appeared as the most significant predictor of success in the foundation mathematics course. the older the cohort, the worse the performance in the mathematics foundation course. for example, students from the recent cohort of 2013 were 30 times more likely to be successful in their mathematics foundation course than those from the older cohort of 2010/2011 (or=29.67; 95%ci=8.98-99.05). female students were 4 times more likely to perform better than male students in their mathematics foundation course (or=4.05; 95%ci=1.62-10.18). 5. discussion the analysis of background characteristics of the sampled students revealed that among the admitted students in squ, female students had significantly higher average scores in both high school mathematics and overall high school an evaluation of mathematics foundation course 103 scores than male students. for example, the high school scores of male students ranges from 56 to 96 with an average of 86.6, while for female students it ranges from 80 to 97 with an average of 93. this indicates that many boys with relatively less qualification than girls were admitted in the university. this might be one of the reasons why boys are consistently underperforming in squ than girls. one recent study has documented that female students in squ are outperforming boys [40]. the higher performance of girls than boys in almost all levels of education is, however, a global phenomenon in recent times [41-43]. oman is not an exception. since high school performance is the only requirement for entry into squ and females are doing better than male students at high school level, then there should be more female students than males in squ in recent time. however, if we look at the overall gender ratio of the admitted students over the years, there is a more or less 50:50 ratio of male-female students in squ. this raises a question: does the admission process favor boys with lesser high school scores than girls for admission to squ for the sake of maintaining a 50:50 ratio of boys and girls among the admitted students? however, we do not have any supporting documentation to answer this questions. it is worth mentioning here that enrolling under-qualified students in a university leads to a misuse of resources, particularly in a public university like squ where education is free. besides, failing to select the most able and motivated candidates might have serious negative impacts on a discipline as well as on the university in general in the long run. our analysis reveals a very poor performance by the students in the mathematics foundation course (i.e. fpmt0105) as their mean gpa was 1.66 and more than half (59%) of the students obtained a gpa of less than 2 (i.e. below grade c); of these 14% failed and 35% obtained grade d, although 97% of these students entered squ with an overall high school score of 80 and above, and 91% with a high school mathematics score of 70 and above. this is a very dismal scenario regarding the best students of the nation, as squ is the only public university and the premier institution for higher education in oman, which attracts the best students from all over the country. the results indicate that the omani high school curricula, particularly in mathematics, are falling short in preparing students for success in their postsecondary education. analyzing data from the high school and beyond, adelman [16] found that the high school curriculum exerted a more powerful influence on bachelor’s degree attainment than did test scores, high school class rank, and high school grade point average. it has been argued that rigorous high school courses including mathematics help prepare students for the college learning environment and enhance their ability to succeed in higher education [16, 44]. our findings indicate significant differential effects of gender on performance in the mathematics foundation course. female students had significantly higher mean gpa (2.41) than male students (1.20). nearly two-thirds (73%) of the male students obtained less than c grade, while the figure was 29% for the female students. the proportion of students with f grade was also significantly higher for male students than female students (22% vs. 1%). these students with less than c grade are at higher risk of dropping out from the university or repeating the course, lengthening their academic life and thus becoming a burden on the family, society and the university administration. the differential analysis indicates unadjusted significant effects of cohort, college of study, high school math score and overall high school score on mathematics foundation course performance. correlation analysis also shows significant correlation between mathematics foundation course performance and gender, cohort, high school mathematics score and overall high school scores. correlation analysis also shows that high school mathematics scores have higher predictive value than overall high school scores. high school mathematics score explained 33% of the variation in performance on the mathematics foundation course, while high school total score explained 29.5% of the variation in mathematics foundation course score. multivariate analysis identified gender, cohort, and high school math scores as the significant predictors of mathematics foundation course performance. overall high school score becomes an insignificant predictor in multivariate analysis. this is mainly because the effect of high school mathematics scores mediate overall high school scores. the findings of this study correspond with those of many others which have found that high school mathematics performance is a significant predictor of college mathematics success [17, 18, 23, 45]. ma [46] showed that students exposed to advanced mathematics courses at the middle and junior high school level had high mathematics achievement in subsequent academic life. 6. conclusion the study findings reveal a very gloomy scenario of performance in the mathematics foundation course in squ, particularly among the male students. the results indicate that many students are entering post-secondary education with little preparation and are thus unable to cope with the college curricula, although they have a very good grade in high school. this may be due either to high schools giving inflated scores to their students, or to the contents of the high school mathematics curriculum falling far short of college standard. in order to improve the situation, high school curricula needs to be aligned with college standards. policy makers should give due attention to this matter. the findings of this study suggest the need for more careful admission decisions to improve the success in the foundation program. both gender and high school performance should be taken into consideration in an equitable manner to have fairer admission decisions. the findings further suggest that the admission authority should give more attention not only to overall high school scores but also to high school mathematics scores, particularly for admission into science based colleges in squ, because 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http://www2.ed.gov/rschstat/research/pubs/toolboxrevisit/ electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 187-198 © 2002 sultan qaboos university robust longitudinal aircraftcontrol based on an adaptive fuzzy-logic algorithm abdellatif elshafei department of electrical engineering, cairo university, giza, egypt (currently on leave at the united arab emirates). )fuzzylogic(معتمد على الخوارزم المنطقي المشوش التحكم الطولي المكين بالطائرة ال عبداللطيف الشافعي لدراسة رد الطائرة إلى مناورة سريعة ، يمكن اعتبار النموذج الطولي للطائرة لفترة زمنية قصيرة ، هذا النموذج غير : خالصة نموذج قوي معتمد على الخوارزم المنطقي تقترح هذه الورقة استخدام . خطي بدرجة كبيرة ويتضمن شكوك في قيم المعامالت عن نجاح النموذج " f16"المشوش ، تم تنفيذ نظامان معتمدين على هذا الخوارزم وقد كشفت نتائج المحاكاة على نموذج طائرة .المستخدم ِِِabstract: to study the aircraft response to a fast pull-up manoeuvre, a short period approximation of the longitudinal model is considered. the model is highly nonlinear and includes parametric uncertainties. to cope with a wide range of command signals, a robust adaptive fuzzy logic controller is proposed. the proposed controller adopts a dynamic inversion approach. since feedback linearization is practically imperfect, robustifying and adaptive components are included in the control law to compensate for modeling errors and achieve acceptable tracking errors. two fuzzy systems are implemented. the first system models the nominal values of the system’s nonlinearity. the second system is an adaptive one that compensates for modeling errors. the derivation of the control law based on a dynamic game approach is given in detail. stability of the closed-loop control system is also verified. simulation results based on an f16-model illustrate a successful tracking performance of the proposed controller. keywords: adaptive control, fuzzy logic control, robust control, flight control. 1. introduction h istorically, the trend in the flight control industry has been to use classical techniques for control design (nelson 1998). acceptable performance, simple control structure, and moderate computational burden are the reasons for adopting classical control techniques. the approach is to design several point controllers throughout the operating region and connect them using gain scheduling (adams, et al 1994). interpolation or blending point controllers we often use trial and error with little theoretical guidance. any performance and robustness guarantees in the individual operating regions are lost in the transition region between point controllers (spillman 2000). dynamic inversion methods avoid the scheduling problem via feedback linearization (adams, et al 1994). like gain scheduling, dynamic inversion does not guarantee performance and robustness since cancellation is practically imperfect. to enhance the robustness of the inverse flight controller, a design based on µ synthesis is proposed by reiner et al (1995). the design utilizes a linearized model of the aircraft. therefore, it is useful for small uncertainty in the system parameters. a fixed controller is proposed by chaing et al (1990) for a fighter aircraft with multiple control efforts. one condition along the manoeuvre trajectory is chosen as nominal and several other conditions along the manoeuvre h∞ 187 elshafei trajectory represent the uncertainty for which the robust controller is designed. sliding mode control is another approach that is suggested by hedrick and gopalswamy (1990) to achieve a high g − command and satisfy flying quality specifications. however, control saturation significantly alters the performance for a high g − command. µ g − −= to take into account the relation between real-time parameter variations and performance requirements, linear parameter varying (lpv) control is examined by spillman (2000) to determine whether it is practical for large envelop flight control designs. the approach is combined with synthesis to ease conservatism. the method is based on linear matrix inequalities and can be solved using the interior point method (boyd et al 1994). the proposed controller does not allow parameters’ rates to be modeled nor does it allow the locations of the controller poles to be constrained. a robust adaptive controller is proposed by singh and steinberg (1996) as an alternative approach that ensures stability in the presence of parametric uncertainty. to derive the control law, a hypersurface is designed such that for any trajectory evolving on this surface, the system tracking error tends to zero. the objective of the control law is to drive the system error to the required hyper-surface. however, the derivation assumes that the unknown nonlinear terms depend linearly on the parameters to be estimated. recently, an adaptive fuzzy logic algorithm was proposed for flight control systems (wilson, 2000). an inner loop controller is designed based on a linearized aircraft model. then, an outer-loop controller is employed based on fuzzy logic. we propose here a robust adaptive fuzzy-logic algorithm for flight control during a fast pullup manoeavre. the control law is based on feedback linearization. since feedback linearization can hardly be exact, the control law is augmented to include adaptive and robustifying components so that the system can cope with modeling uncertainties and achieve acceptable tracking. in section 2, an f-16 short-period approximation of the longitudinal model is introduced. the need for a robust adaptive fuzzy-logic controller is discussed. in section 3, adaptive fuzzy-logic control is reviewed. although it does not guarantee robustness, it is used to develop a fuzzy model for the nominal nonlinearity of the system. the estimate of the nominal nonlinearity is used in the control law of section 4 for feedback linearization. a complete derivation of the proposed control law is presented in section 4. in section 5, the implementation details and simulation results are depicted. section 6 concludes the paper. 2. modeling equations and design objectives the aircraft motions can be classified as lateral and longitudinal motion (nelson 1998). the rolling and yawing of the aircraft characterize the lateral motion. in the longitudinal mode, one assumes that the motion is confined in the vertical plane. our interest here is directed to the command, a fast pull-up manoeavre that takes place in the vertical plane. hence, we focus on the longitudinal dynamics. the phugoid and the short period modes characterize the longitudinal dynamics of an aircraft. the phugoid period is an order or two longer than the short period mode. to study the aircraft response to the g − command, it is sufficient to consider a short period approximation of the longitudinal dynamics. the required model is derived by assuming that the aircraft horizontal velocity u remains constant and by dropping the pitch angle from the states. the short-period approximation of the longitudinal model, referred to the aircraft body frame, is summarized in lee and hedrick (1994) as ( ) αα αα α 22 coscos sincos q mu dl + + & (1) yyi m q =& (2) ukeke ee +−= δδ& (3) 188 robust longitudinal aircraftcontrol α is the angle of attack, is the pitch rate, q eδ is the elevator angle, and u is the control signal. the angle of attack is defined as u w =αtan , where w is the velocity along the axis of the aircraft body frame, u is the velocity along the −z −x axis of the aircraft body frame and is the pitch moment of inertia. the aerodynamic forces and moments are defined as yyi lmd and ,, ( )eccsqd edd δα δα += (4)       ++= ecq v cc csql el t lq l δα δα (5)       ++= ecq v cc cscqm em t mq m δα δα 2 (6) tv is the aircraft speed, q is the dynamic pressure, and the coefficients are responsible for the lift, drag, and pitch moment of the aircraft. the definitions and typical numerical values of the variables and parameters used in (1)-(6) are given in appendix 1. iic the output y is the normal acceleration felt at the pilot’s position. ( )t ( ) q g l aty xn &+= (7) mg dl an αα sincos + = (8) an is the acceleration at the center of gravity of the aircraft. equations (1), (2), (3), and (7) can be written as ( ) ubxfx +=& (9) ( ) ( )xhty = (10) where [ ] 3reqx t ∈= δα , u , r∈ ry ∈ , and [ ]tekb 00= differentiating (10) once yields ( ) ( ) ( )uxxty β+∆=& (11) define ( )x∆ and ( )xβ to be ( ) ( ) ( )xf x xh x ∂ ∂ =∆ (12) ( ) ( )b x xh x ∂ ∂ =β (13) it is straightforward to show that ( )xβ is given by ( ) [ ] em yy x eedele ci scq g l kcc mg sq kx δδδ ααβ ++= sincos (14) as shown in lee and hedrick (1994), ( )xβ is non-zero. hence, the nonlinear system (9)-(10) has a relative degree equal to one and admits feedback linearization. choose the control law as ( ) ( )[ ]vx x u +∆−= β 1 (15) we select v such that the output would track a reference trajectory . this is achieved by ( )ty dy keyv d −= & (16) 189 elshafei in the ideal case, the positive constant k determines the location of the closed loop pole of the error model. the error signal is defined as dyye −= (17) the reference signal is assumed to be smooth such that its derivative exists. dy dy& to adapt to various flying conditions, the nonlinear functions ( )x∆ and ( )xβ can be estimated on-line. fuzzy logic provides an attractive technique to represent such non-linearity. the power of fuzzy models stems from the universal approximation theorem (kosko 1997). from the implementation point of view, adaptive fuzzy systems are attractive since they depend linearly on the parameters to be estimated. in section 3, an adaptive fuzzy-logic controller is derived. the control law becomes ( ) ( )[ ]vx x u +∆−= ˆ ˆ 1 β (18) ( ) ( )xx t ζθ ∆=∆ ˆˆ (19) ( ) ( )xx t ζθβ βˆˆ = (20) where ζ is the vector of fuzzy basis functions to be defined later, ∆θ̂ is the vector of estimated parameters used to model ( )x∆ , and βθ̂ is the vector of estimated parameters used to model ( )xβ . according to the universal approximation theorem (wang 1994), there exist fuzzy systems that approximate the functions ( )x∆ and ( )xβ with arbitrary accuracy. however, to avoid the rule explosion phenomenon, the size of ζ is kept small. this helps in reducing the rule base and lightening the computational burden but introduces modeling errors and raises the robustness issues. in section 4, we redesign the control law such that the effect of modeling error is accommodated and compensated for. 3. adaptive fuzzy-logic control of the longitudinal motion in this section, we design an indirect adaptive algorithm to control the aircraft acceleration so that it tracks a given g − command. the control law is given in (18). as pointed out earlier, the estimates will have modeling errors when they are compared with their true values β̂ and ∆̂ β and ∆ . in wang (1994), a supervisory controller is added to the control law to ensure robustness. the supervisory controller utilizes a sign function and may lead to chattering so it is not used here. in this paper, we will use the estimates ∆ as nominal values of β̂ and ˆ oo β and ∆ . in the coming section, a robust adaptive controller is redesigned based on oo β and ∆ . consider the t-s fuzzy system with center average defuzzification. the fuzzy systems are used to model the nonlinear functions β and ∆ . assume for example that ∆ is modeled using m rules that are denoted as . the imrrr ,,, 21 l th rule takes the form ir if is and is and is then is 1x if1 2x if2 3x if3 ∆ iθ . the linguistic variables , , and correspond to the state variables 1x 2x 3x α , , and q eδ , respectively. each linguistic variable is assigned a fuzzy set that is defined using a guassian membership function jx i jf i jf µ ; let belong to the universe of discourse u . the membership function .3,2,j 1= jx r⊂j i jf µ maps to the set ju 0 1, . the consequent of the i th rule is assigned the singleton value iθ . the function ∆ is modeled as 190 robust longitudinal aircraftcontrol ( ) ∑ ∑ = ==∆ m i i m i ii x 1 1 µ µθ (21) where iµ is the strength of the i th rule when it is fired and is calculated as ∏ = = 3 1j fi ij µµ (22) it is assumed that the fuzzy system is constructed such that 0 1≤≤ iµ and for all . equation (21) can be written as 0 1 ≠∑ = m i iµ 3,2,1, =∈ jux jj ( ) ( )xx t ζθ ∆=∆ (23) where [ ] ( ) [ ] mi x m i i i i mi t mi t ,,1, 1 1 1 l ll ll == = = ∑ = ∆ µ µ ζ ζζζζ θθθθ the functions ,,,1, mii l=ζ are called the fuzzy basis functions. in an adaptive system, the values ,, ml,1, ii =θ , are tuned on-line to ensure the fuzzy model is close enough to match the actual system. an expression similar to (23) can model the nonlinear function β . it follows from (11) and (17) that ( ) ( ) dd yuxxyye &&&& −+∆=−= β (24) using (16) and (18), it is possible to write as dy& ( ) ( ) keuxxyd ++∆= β̂ˆ& (25) substituting (25) into (24), the error model can be expressed as ( ) ( ) keuxxe −+∆= β~~& (26) the error functions ∆ ~ and β ~ are defined as βββ θθθ θθθ ˆ~ ˆ~ −= −= ∆∆∆ based on the universal approximation theorem, there are fuzzy systems and that can approximate ∆ and ∗∆ ∗β β with arbitrary degree of accuracy. hence, it is possible to write ( ) ( ) ( )xxx t ζθ ∆∗ =∆≈∆ (27) ( ) ( ) ( )xxx t ζθββ β=≈ ∗ (28) using (19), (20), (27), and (28), the error model (26) becomes ( ) ( ) kexxe tt −+= ∆ ζθζθ β ~~ & (29) the estimation errors, ∆θ ~ and βθ ~ , are defined as βββ θθθ θθθ ˆ~ ˆ~ −= −= ∆∆∆ to derive the adaptation laws of ∆θ ~ and βθ ~ , consider the candidate lyapunov function 191 elshafei βββ θθθθ ~~ 2 1~~ 2 1 2 1 2 γ+γ+= ∆∆∆pev (30) the weighting factor, p, and the weighting matrices, ∆γ and βγ , are positive definite. the time derivative of (30) along the trajectory (29) is ( ) ( ) ββββ θθθθζθζθ &&& ~~~~~~2 γ+γ+++−= ∆∆∆∆ tttt peuxpexpkev (31) the adaptation laws are chosen as ( )pexζθ 1~ −∆∆ γ−= & (32) ( )peuxζθ ββ 1 ~ −γ−=& (33) equations (32) and (33) force the right hand side of (31) to be negative definite. hence, equation (30) becomes a true lyapunov function and the error model (29) is asymptotically stable. although it is possible to argue that adaptive fuzzy logic control ensures that ( )te will converge to zero, we have to remember that the above discussion overlooks the modeling errors ( )∗∆−∆ and ( )∗− ββ . these modeling errors are inherent in fuzzy models because of the limitations on the sizes of the rule bases. in wang (1994), a supervisory control signal is added to the adaptive fuzzy controller to ensure stability. however, the supervisory control signal is implemented using a function and may lead to the well-known chattering phenomenon. this observation motivates the use of the robust adaptive fuzzy controller that is derived in section 4. ().sgn 4. robust adaptive fuzzy-logic control consider the input-output differential equation (11). assume that the nominal values ( )xo∆ and ( )xoβ are available. for example, they could be provided by an expert or estimated based on an adaptive algorithm. the control law is selected as ( ) ( )[ ]oo o x x u ν β +∆−= 1 (34) the control signal oν is defined below. its objectives are to ensure tracking of the desired output trajectory and robustness in the presence of modeling errors. substituting (34) into (11) leads to ( ) ( ) ( ) ( ) ( ) ( )x x x x x xy o o oo o ∆−+      −+∆= β β νν β β 1& (35) define oν and γ as follows odo ukey +−= &ν (36) ( ) ( ) ( ) ( ) ( ) ( )x x x x x x o o o o ∆−      −+∆= β β ν β β γ 1 (37) the control signal u , defined below, consists of two components; an adaptive fuzzy component and a robustifying component. substituting (36) and (37) into (35), it is possible to write the system error model as o oukee ++−= γ& (38) let be a fuzzy system that would approximate ∗γ γ with an acceptable accuracyε , i.e. εεγγε γγ <−= ∗ , (39) the fuzzy system is defined as ∗γ 192 robust longitudinal aircraftcontrol ( )dd t yyx &,,ζθγ γ ∗∗ = (40) where ∗γθ is the optimal parameter vector that satisfies (39) and ().γζ is the vector of fuzzy basis functions. the dependency of γ ζ on ,, dyx and follows from (36), (37), and (49). in the special case where dy& ββ =o , the basis functions γζ depend on x only; see (37). it is possible to rewrite (38) as ∗+++−= γεγ oukee& (41) the control component u is designed such that it cancels the effect of the modeling error and ensures robustness in the presence of o ∗γ γε . let be ou ( ) edd t o uyyxu +−= &,,ˆ γγ ζθ (42) where γθ̂ is the estimate of ∗ γθ and u is the robustifying component to be defined below. equation (41) can be rewritten as e γγγ εζθ +++−= e t ukee ~ & (43) where γγγ θθθ ˆ ~ −= ∗ noting that γε acts as a disturbance applied to the error model (43), the calculations of γθ̂ and will be based on a dynamic game approach (chen et al 1998). the objective is to find the optimal control law u that minimizes a performance index, eu e j , in the presence of the worst-case disturbance [ ]ft,0l2∈γε . consider the following minimax problem [ ] [ ] ( )∫ γ ∈ε∈ ρε−+ γ f ffe t e tltlu dtruqe 0 222 ,0,0 maxmin 22 define the performance index as j (∫ −+= ft e dtruqej 0 2222 γερ ) (44) where ,q ,r and ρ are positive weighting factors to be chosen by the designer and they have a standard interpretation in the optimal control literature. equation (44) can be rewritten as ( ) ( ) ( ) ( ) ( ) ( )ff tt f tttpepej γγγγ θθσ θθ σ ~~1 0 ~ 0 ~1 0 22 −+−= ( ) ( ) ( ) ( ) ( ) ( )∫      ++−++ ft t e dttttpedt d ttrutqe 0 22222 ~~1 γγγ θθσ ερ (45) carrying out the derivative inside the integral sign and substituting for from (43), we can rewrite (45) as ( )te& ( ) ( ) ( ) ( ) ( ) ( )ff tt f tttpepej γγγγ θθσ θθ σ ~~1 0 ~ 0 ~1 0 22 −+−= ( ) ( ) ( ) ( ) ( ) ( )∫ +−+−+ ft ee tetputtrutepkq 0 2222 22 γερ ( ) ( ) ( ) ( ) ( ) ( ) ( )dttttettptetp tt γγγγγ θθσ ζθε & ~~2~ 22 +++ (46) by completing the squares, it is possible to rearrange (46) as 193 elshafei ( ) ( ) ( ) ( ) ( ) ( )ff tt f tttpepej γγγγ θθσ θθ σ ~~1 0 ~ 0 ~1 0 22 −+−= ( ) ( ) ( )( )∫ ++             −+−+ ft e tpetrur te r ppkq 0 22 2 2 1112 ρ ( ) ( ) ( ) ( ) ( ) dtttetptpet t       ++      −+ γγγγ θσ ζθ ρ ρε & ~1~ 2 1 2 (47) the minimax problem is achieved by selecting 0 11 2 2 2 =      −+− ρr ppkq (48) ( )te r p ue −= (49) ( ) ( )tetp γγ ζσθ −=& ~ (50) the optimal control law (49) guarantees the worst-case error to be ( ) ( )t p te γε ρ 2 = (51) it follows from (39) and (51) that e is finite since ( )t ( )tγε is bounded by ε . the error, , can be made smaller by decreasing ( )te ρ . on the other hand, r must be chosen such that 2 1 ρ 1 ≥ r to ensure that (48) has a positive definite solution, p hence, if ρ is decreased, r must also be decreased which may lead to excessive control actions. in order to further investigate the stability of the closed-loop control system, consider the following candidate lyapunov function γγ θθσ ~~ 2 1 2 1 2 t p ev += (52) the time derivative of (52) along the trajectory (43) is γγ θθσ & && ~~1 t p ee +=v γγγγγ θθ σ εζθ & ~~1~2 t e t p eeueke ++++−= (53) using (49)-(51), it is possible to rewrite (53) as       −+−= 2 2 4 11 ρ ε ρ γ rp k p v& (54) it is clear that the right hand side of (54) is negative definite provided that and ,0>k ,0>p 2 11 ρ ≥ r . all the previous conditions can be satisfied since ρ and ,,, rpk are the designer’s choice. so, we conclude that the proposed control algorithm stabilizes the aircraft error model (43). the implementation details and some simulation results of the proposed controller are given in section 5. 194 robust longitudinal aircraftcontrol 5. implementation of the proposed controller in this section, we illustrate via simulation the performance of the proposed controller. the implementation steps can be summarized as follows: 1obtain the nominal values o and βo∆ . this can be done based on an expert’s knowledge or on an identification algorithm. in the present aircraft model, we assume that oβ is given by (14) and is estimated based on the adaptive technique described in section 3. o∆ 2select positive values for the controller’s parameters σρ and ,,,, qrk . then, solve (48) for p . note that we must select 2 11 ρ ≥ r to ensure that the solution of (48) yields a positive definite answer. 3assume ∗γθ to be locally constant and use the adaptation law (50) to calculate the estimate γθ̂ . practically, the projection algorithm is implemented, instead of (51), to guarantee a bounded estimate γθ̂ (wang 1994). 4calculate the control signal u . it follows from (34), (36), (42), and (49), that u is given by ( ) ( )     −−−+∆−= e r p keyx x u t do o γγ ζθ β ˆ1 & (55) 0 1 2 3 4 5 -4 -2 0 2 4 6 secs. % t ra ck in g er ro r r = 3.33 0 1 2 3 4 5 -4 -2 0 2 4 6 secs. % t ra ck in g er ro r r = 1 0 1 2 3 4 5 -4 -2 0 2 4 6 secs. % t ra ck in g er ro r r = 0.5 0 1 2 3 4 5 -0.04 -0.03 -0.02 -0.01 0 0.01 secs. % t ra ck in g er ro r r = 0.1 figure 1. tracking error performance of the proposed controller for different attenuation factors .2 r=ρ two fuzzy systems are included to implement (55). the first fuzzy system calculates the nominal value ∆ . the second fuzzy system is an adaptive one and is meant to compensate the function ; see (41) and (42). the input to the first fuzzy system is the state vector o ∗γ x . each state is assigned three guassian membership functions corresponding to the linguistic values positive, zero, and negative. all membership functions are normalized and have standard deviations 0.33. the centers of the membership functions are placed at 1, 0, and –1, respectively. the normalization 195 elshafei factors of α , q , and δe are selected to be 0.667, 0.1, and 2, respectively. the second fuzzy system has two additional inputs; namely and . the membership functions are similar to those used for dy dy& x with the normalization factors adjusted according to the command signal. it is assumed that the nominal value (xo )β is 20% off the true value ( )xβ . the controller parameters are selected as ,500=p , =2= ρr ,2σ and . the initial values of 1=k γθ̂ are initialized with random numbers in the range . the reference trajectory, , is generated via a first order system with a one-second time constant. figure 1 depicts the performance of the proposed controller for a [ , ]05.005.0− dy 5g command signal for different values of r . as expected, as r decreases, the tracking error decreases. however, figure 2 shows that the cost of a very small tracking error is an unacceptably active control signal. 0 1 3 -0.4 -0.2 0 0.2 0.4 secs. 3.33 u 2 -0.4 -0.2 0 0.2 0.4 u 1 3 secs. 0.5 u -0.4 -0.2 0 0.2 0.4 u 2 4 5 r = 0 1 3 4 5 secs. r = 1 0 2 4 5 -0.4 -0.2 0 0.2 0.4 r = 0 1 2 3 4 5 secs. r = 0.1 figure 2. control activities of the proposed controller for different attenuation factors ρ2 = r. 6. conclusions the short-period approximation of the aircraft longitudinal model is highly nonlinear. fuzzy logic has been used to compute the nominal values of such non-linearity. based on the nominal values of the non-linearity, conventional feedback linearization has been modified to ensure robustness and acceptable performance. adaptive and robustifying components have been added to the feedback linearization control law. the derivation of the proposed controller has been given in detail. it has been also shown that the tracking error has remained finite and made small using a certain tuning parameter. the stability of the proposed control system has been verified using the second method of lyapunov. simulation results have confirmed our theoretical analysis and demonstrated the capability of the system in tracking a high g-command with acceptable error and control activity. 7. acknowledgement the research council of the united arab emirates university supported this research (project # 01/11-7-12). 196 robust longitudinal aircraftcontrol appendix 1: variables definitions and values at mach 0.9 and 6096 m altitude. variable definition value aρ air density 0.65381 kg/m 3 q dynamic pressure 25.0 tavq ρ= n/m 2 s surface area 27.87899 m2 c mean aerodynamic cord 3.450336 m xi distance from cg to pilot 4.244645 m m mass 9530.302 kg g g-acceleration 9.8 m/sec.2 u horizontal velocity 284.4 m/sec. yyi moment of inertia 73046.53 kg m 2 ke elevator gain 20.0 αlc aerodynamic force due to α 4.0 /degree lqc aerodynamic force due to q 3.162 (unitless) elc δ aerodynamic force due to eδ 0.55 (unitless) αmc aerodynamic moment due to α 0.1146 (unitless) mqc aerodynamic moment due to q -2.382 (unitless) emc δ aerodynamic moment due to eδ -0.6933 (unitless) αdc aerodynamic force due to α 0.151261 (unitless) edc δ aerodynamic force due to eδ 0.009912 (unitless) references adams, r.j., buffington, j.m., sparks, a.g., and banda, s.s., 1994. robust multivariable flight control, springer-verlag, new york. boyd, s., el ghaoui, l., feron, e., and balakrishnan, a. 1994. linear matrix inequalities in system and control theory. siam, philadelphia. chaing, r.y., safanof, m., g., k., madden, k.p., and tekawy, j.a. 1990. a fixed controller for a super-maeuverable fighter aircraft performing the herbst manoeuvre. the 29th ieee cdc, honolulu. chen, b.s., uang, h.j., and tseng, c.s.1998. robust tracking enhancement of robot systems including motor dynamics: a fuzzy-based dynamic game approach. ieee trans. on fuzzy systems, 6: 538-552. hedrick, j.k. and gopalswamy, s. 1990. nonlinear flight control design via sliding methods. j. guidance, 13: 850-858. kosko, b. 1997. fuzzy engineering. prentice hall, new jersey. lee, a.w. and hedrick, j.k. 1994. application of approximate i/o linearization to aircraft flight control. journal of dynamic systems, measurement, and control, 166: 429-436. nelson, r.c.1998. flight stability and automatic control. wcb/mcgraw-hill, singapore. reiner, j., balas, g.j., and garrad, w.l. 1995. robust dynamic inversion for control of highly maneuverable aircraft. journal of guidance, control and dynamics, 18: 18-24. singh, s. and steinberg, m. 1996. adaptive control of feedback linearizable nonlinear systems with application to flight control. journal of guidance, control, and dynamics, 19: 871-877. 197 elshafei spillman, m.s. 2000. robust longitudinal flight control design using linear parametervarying feedback. journal of guidance, control, and dynamics, 23: 101-108. wang, l.x. 1994. adaptive fuzzy systems and control. prentice hall, new jersey. wilson, h.w. 2000. the use of fuzzy logic in adaptive flight control systems. aeronautical journal, 104: 31-37. received 6 june 2001 accepted 13 february 2002 198 robust longitudinal aircraftcontrol based on an adaptive fuzzy-logic algorithm abdellatif elshafei department of electrical engineering, cairo university, giza, egypt (currently on leave at the united arab emirates). 2. modeling equations and design objectives 3. adaptive fuzzy-logic control of the longitudinal motion state-of-the-art review of collapsing soils science and technology, 6(2001) 35-43 ©2001 sultan qaboos university tailings from mining activities, impact on groundwater, and remediation khalid al-rawahy department of petroleum and mineral resources engineering, college of engineering, college of engineering, sultan qaboos university, p.o. box 33, al-khod 123, sultanate of oman. الفضالت الناتجة عن نشاطات التعدين وتأثيرها على المياه الجوفية، وطرق التخلص منها خالد الرواحي مجموع المواد الصلبة ، :التّاليةالملوثات شَملتْ في الغالب المعالجة عملياتو من عملياِت التّعديِن تدفق الفضالت :خالصة معادن ُمذَوَّبة لحديد فى تعدين الفوالذ، والمعادن فى عمليات تعدين الالفلزات ، ية ، المواد الصلبة المترسبة، ا حمضالأو القاعدية ، ويعتبر بالوسائِل التّقليدية التجزئة اومتقالتي ة من الملوثات ذّرات صلب يتكون من المواد الصلبة معلّق ،في التّعديِن الالحديديِ زرنيخة التى توجد فى خام التعدين ومعالجات الفضالت تتضمن ال الّرئيسي يةالمعدنوالملوثات . اًسام المعادِن الُمذَوَّبة من عدد ة معالجلوالتخلص تستخدم للتخلص من الفضالت الصلبة برك . خارصينالنيكل و وال زئبق والرصاص وال نحاس وال الكادميومو لى بعض الكيماويات المستخدمة فى عوفي بعض األوقات المواد الصلبة معلّق على من هذه البرك ه الفضالت ويحتوى الناتج ايم وقد يحدث . ويعتبر تسرب المواد من أحواض المعالجة فى عمليات التعدين احد مصادر تلوث المياه الجوفية . استخالص الخام وتناقش هذه الورقة التلوث المحتمل للمياه . تسرب مياه الفضالت من احواض المعالجة فيما اذا كانت االحواض رديئة التصميم .جوفية الناتج من مخلفات انشطة التعدين والخيارات المحتملة لمعالجة ذلكال abstract: effluent wastes from mining operations and beneficiation processes are comprized mostly of the following pollutants: total suspended solids (tts), alkalinity or acidity (ph), settleable solids, iron in ferrous mining, and dissolved metals in nonferrous mining. suspended solids consist of small particles of solid pollutants that resist separation by conventional means. a number of dissolved metals are considered toxic pollutants. the major metal pollutants present in ore mining and beneficiation waste waters include arsenic, cadmium, copper, lead, mercury, nickel, and zinc. tailings ponds are used for both the disposal of solid waste and the treatment of waste-water streams. the supernatant decanted from these ponds contains suspended solids and, at times, process reagents introduced to the water during ore beneficiation. leakage of material from tailings pond into groundwater is one possible source of water pollution in the mining industry. percolation of wastewater from impoundment may occur if tailings ponds are not properly designed. this paper addresses potential groundwater pollution due to effluent from mining activities, and the possible remediation options. 1. introduction metals occur naturally in the ground in a wide range of economic concentrations: from approximately 0.05% for uranium, through 0.5-1.5% for copper, to approximately 60-70% for iron, and invariably occur with a wide range of minor and trace metals. the resulting waste piles, tailings ponds, and slag dumps are unsightly and may impose environmental hazard. non-ferrous metal mining activities across the world have produced a variety of environmental problems. three types of contamination created by large-scale metal extraction have been identified (moore and luoma, 1990). waste rock, tailings, and slag are primary contaminants. metals are also associated with a wide range of minor and trace elements. metals or metalloids that may be found at contaminated mine sites include: as, cd, cr, cu, pb, hg, ni, se, ag, zn (mclean and bledsoe, 1992). secondary 35 al-rawahy contamination may occur in groundwater, sediments, and soils. there are two primary reasons for concern of trace elements in waters, soils, or mine spoils (pierzynski, 1994): 1. elevated human and animal exposure to the metals can occur through food chain transfer, ingestion of wind-blown dust, or direct ingestion of soil. 2. the phytotoxic potential of the metals can limit biomass production (pierzynski, 1994). many non-ferrous metals occur as sulfides such as pyrite, sphalerite, galena and chalcopyrite. sulfides may not be completely removed during milling process, and may lead to acidic waste as the mineral is comminuted during processing. effluent from milling and flotation process is normally slurried into tailings ponds. over time, and due to a number of factors, including weathering (oxidation, and hydrolysis), and biological activity (bacterial action), extreme acidity conditions may result in the tailings. the main consequence of having acid conditions in the tailings environment is the dissolution of heavy metal ions from residual minerals containing them (e.g., cu, zn, ni, pb, hg). as a result, tailings, and consequently seepage (if any) to underground water sources, may contain high residual quantities of dissolved heavy metals, thereby impacting the quality and usability of the water, as well as the surrounding environment. this paper discusses the nature of effluent, which results from mining and milling stages of non-ferrous metal ores, impact on groundwater, and remediation options. 2. mining and generation of effluent waste mineral ores are extracted from both surface and underground mining operations. effluent waste from mining activities is generated from three general sources: waste rock dumps, milling, and tailings. waste rock dumps represent the extracted material that has to be transported from a mine to a processing plant in order to concentrate and obtain the mineral. since natural concentrations of non-ferrous metals in rocks is generally low, large tonnage of material is extracted. most of this ore remains as waste. the production of a ton of copper can generate five hundred tons of waste, depending on the grade of the ore, and the amount of overburden removed (tilton, 1994; ayres, 1992). the extracted material and the associated ore and waste rock greatly increase the surface area of material exposed to the surface and hence affected mainly by water and oxygen. the ore and waste rock undergo oxidation by coming in contact with rainwater, surface water, and oxygen in the air. where sulfidic deposits (for example, pyrite fes2) are being worked, acidic run-off results causing a serious problem. acid is generated by the following oxidation reactions: 2fes2 + 2h2o + 7o2 → 2feso4 + 2h2so4 2feso4 + 2 h2so4 + o2 → 2fe2(so4)3 + 2h2o fe2(so4)3 + 6h2o → 2fe(oh)3 + 3h2so4 the effect of acid generation can lead to higher concentration of heavy metals and other toxic elements into run-off solutions. when these solutions come in contact with stream or other surface waters contamination may result. this may pose threat to human health and the environment at large. since natural concentrations of non-ferrous metals in rocks is generally low, large amount of waste in the form of overburden and tailings results from mining and milling processes. the production of concentrates is schematically shown in figure 1. milling is the operation that separates concentrate from gangue. the flotation process is an integral part of milling. the end product of the milling process is the concentrate of the desired metal(s). the slurry, which contains the discarded process water, unwanted gangue, reagents, frothers, collectors and other chemicals 36 tailings from activities, impact groundwater, and remediation added during the flotation stage, passes to the tailings area. before decanted into the tailings, the slurry may be chemically treated to remove (by oxidation) organic reagents having high oxygen demand, and any cyanides which may be present (barbour, 1994). extraction waste rock mining crushing disposal grinding milling concentration tailings concentrate for sale figure 1. major stages in the production of non-ferrous concentrates (barbour, 1994). 3. tailings: characteristics, disposal and impoundment most mineral processing plants produce, in slurry form, fine grained waste material, which result from milling operations. this waste forms the tailings, which must be disposed of in a proper way. the tailings, which contain residual quantities of chemicals and potential contaminants from the processing and milling of ores, are generally confined to a specific area for safety and environmental reasons. tailings differ in different mining operations. chemical composition, physical characteristics-including abrasiveness, particle size, specific gravity, ph, all influence the flow, settlement, and toxicity of the tailings. these factors also have major influence on treatment methods in order to minimize environmental damage on receiving streams or other bodies of water. tailing management is, therefore, of major environmental importance. the long-term effect of contaminant transport via wind, surface drainage and seepage are major concerns for the mining industry. many tailings problems arise from the low strength of tailings deposit, their ongoing consolidation, erosion by wind and water, spillage and tailings water seepage (bell, 1997). since tailings differ in different mining operations, (the details and mechanics of tailings disposal system are highly site-specific to suit the particular operation in a specific location. tailings usually are transported as slurries through pipes (by pumping or by action of gravity). settlement characteristics are important to avoid blockages and breakdown in operations. the disposal of tailings from milling operations is a major task for mining and mineral processing companies. in most cases, a major fraction of the ore mined eventually ends up as tailings. the material must be disposed of in an environmentally safe way so as to minimize adverse environmental impacts. the classic method to dispose of tailings was to discharge them into a lake, stream, or across nearby land. the two most common practices of tailings disposal have been: 1. to size the tailings, and use the coarse fraction (sand) for construction of a tailings dam, while placing the fine fractions (slimes) in the resulting tailings pond, and 2. to size the tailings, and use the coarse fraction for backfill underground (possibly mixed with cement), while sending the fine fraction to a surface tailings pond. 37 al-rawahy factors such as increased in tonnage mined, environmental awareness and increased government regulation, have resulted in changes in techniques of tailings disposal. impoundment of tailings behind dams is standard industrial practice. the dam structure must be designed and constructed such that it will not fail during use or in later years, (post-mining). this is important, because failure of the dam would necessarily result in the release of vast quantities of slimes from the tailings pond. pollution of waterways, (lakes, rivers) must also be prevented or minimized. in contrast to waste rock, slurry transportation of mine tailings provide a wide range of options for disposal (barbour, 1994): • narrow deep valleys versus disposal in shallow valleys or plain land. • location to minimize adverse environmental impact on adjacent streams, surface waters, and ground water. treatment cost required for tailings water disposal into a particular stream need to be compared to those of discharging the untreated tailings into a more distant but environmentally and commercially unimportant stream. disposal to sea is also a viable option (due to its enormous absorptive capacity). • tailings impoundment should be located away from people and human activity as much as possible. failure of tailings dam can have serious consequences to humans and other activities located nearby. impoundment of tailings behind dams is generally applied in most mining operations. the main objective is to isolate the tailings using the best technology available for containment so that the release of potential contaminants can be prevented or minimized. the conventional technique (sudbury, 1992) utilizes spigotting whereby a tailing slurry pipeline encircles an impoundment area to permit discharge at many points through small pipes or hoses – spigots – inserted through the wall of the main pipe. surplus slurry discharges from the end of the pipe inside the impoundment area. coarse sands settles around the periphery providing granular material with which to build up the dam. in addition, the granular tailing material also provides good support for a peripheral access along the top of the dam to service the pipeline, while the high permeability of the coarse sands avoids dam failure due to hydrostatic pressure. fine slimes flow to the inside of the impoundment area with a clarification pond forming in the center. this system, however, has serious drawbacks for sulfide-bearing tailings. acid generation and the resulting metal dissolution may lead to a serious problem especially in areas where the underlying soil is highly permeable; seepage of contaminated effluent into groundwater may adversely impact the quality of the receiving waters. in mountainous terrain local failure of a berm can result in an extensive and uncontrolled spread of waste. in addition, dry elevated tailings may accelerate wind blown heavymetal contaminated dust. 4. mining effluent and potential environmental impacts effluent wastes from mining operations and beneficiation processes are comprized mostly of the following pollutants: total suspended solids (tss), alkalinity or acidity (ph), settleable solids, iron in ferrous mining, and dissolved metals in nonferrous mining. suspended solids consist of small particles of solid pollutants that resist separation by conventional means. solids in suspension that will settle in one hour under quiescent conditions are settleable solids. acid conditions prevalent in the minerals industry usually result from the oxidation of sulfides in mine waters or discharge from acid leach beneficiation processes. alkaline leach beneficiation processes also contribute to effluent waste loading. iron is often present in natural waters and is derived from common iron minerals in the substrata increasing iron levels present in process water and mine drainage. a number of dissolved metals are considered toxic pollutants. the major metal pollutants present in non-ferrous ore mining and beneficiation waste waters include arsenic, asbestos, cadmium, copper, lead, mercury, nickel, and zinc. surface water pollutants primarily originate from three major sources: precipitation run-off, mine dewatering, and process waters. the characteristic of the effluent stream is generally 38 tailings from activities, impact groundwater, and remediation determined by the mineralogy of the ore and the beneficiation process. beneficiation processes include gravity separation, froth flotation utilizing reagents, chemical extraction, and hydrometallurgy. surface mining can generate large volumes of sediment through precipitation runoff. if the sediments cannot be contained but are allowed to reach adjacent waterways they may become pollutants. for many mines, mine dewatering may contribute to a significant source of waste water. it is usually low in suspended solids, but may contain dissolved minerals or metals. water, which accumulates in surface mine, pits or underground mine workings is likely to be heavily loaded with sediment or dissolved salts or both. as a result, mine de-watering can easily result in heavy pollution loads in the receiving waters. pumping to maintain dry conditions may also lower the water table reducing the yield of nearby wells, springs, and seeps. mine waters originate from groundwater flows, as well as from rainfall and run-off. thus mine de-watering can significantly affect receiving waters. water should be diverted from mine pits or workings if possible, as water pumped out of the mine will most likely require treatment before it can be discharged from the mine area. process waters are those used in transportation, classification, washing, concentrating, and separation of ores. as an effluent, it usually contains heavy loading of suspended solids, and in nonferrous metal mining, contains dissolved metals as well. it also contains process reagents. since mining operations occupy large surface areas, precipitation run-off may contribute a major volume of waste-water and pollutant loading this water typically contains suspended solids, such as minerals, silt, clay, sand, and possibly dissolved toxic metals. other possible sources of water pollution include acid mine drainage and tailings pond leakage. the leaching of water through any mine waste or structure containing sufficient pyrites or other sulfides can produce acid drainage. tailings ponds are used for both the disposal of solid wastes and the treatment of waste-water streams. the supernatant decanted from these ponds contains suspended solids and, at times, process reagents introduced to the water during ore beneficiation. percolation of waste-water from impoundment may occur if tailings ponds are not properly designed. the aqueous component of tailings slurry from the mill usually contains some concentration of surface-active frothers and collectors. in addition, where acid conditions are present in flotation circuits, relatively high amounts of cations such as iron, manganese, cadmium, mercury, lead, and zinc may be present in specific circumstances (barbour, 1994). problems in tailings area are exacerbated where sulfidic (example, pyritic) deposits are being worked, due to the presence of acidity by oxidation in presence of water. when the impoundment is in active use, it is usually saturated with water; air access is limited; but when the pond level falls, condition for rapid development of acidity, due to bacterial oxidation with thiobacillus ferrooxidans develops. this can pose serious threat due to acid mine drainage after operations have formally ceased. if cyanide has been used in the extraction circuit, as in most gold concentrating processes, it may be necessary first to convert it to relatively harmless cyanate by oxidation immediately upon leaving the floatation circuit. flow characteristics of the effluent as well as uses of the receiving bodies of water is important. where it is necessary to preserve the existing uses of the receiving body, conventional treatment (precipitate heavy metals by addition of neutralizers, and ph adjustment) is used. whatever disposal option is selected, adequate monitoring should be practiced to ensure that any significant changes in the quality of the receiving body are quickly detected, assessed, and remedied. 5. tailing impoundment and disposal: planning and avoidance of disaster special precautions are required to prevent groundwater contamination. all mining and processing operations require detailed emergency plans designed to mitigate the effects of major accidents on both the operating personnel and near-neighbors. mine safety is of utmost importance 39 al-rawahy and this should be part of regulatory and professional requirements. close attention must be given to stability of waste piles and tailing areas, particularly dams and retaining walls for tailings disposal areas. in the location of tailing areas every effort must be made to choose a location with the minimum possible risk to downstream population. proper management of the tailings in post mining period should be incorporated. as indicated earlier, the main objective of tailing impoundment is to isolate the tailings so as to minimize adverse environmental impacts, especially on groundwater. the following considerations are significant to achieve the desired objective (sudbury; 1992, sengupta, 1993): • selection of impoundment site is of critical importance. a detailed geological and geotechnical study of the proposed site is crucial to assess suitability of area for impoundment e.g., permeability, structure in the area-faults, folds, fractures and joints in order to minimize seepage and dam failure. hydrology of the area as well as type of tailings involved should also be considered. • installation of liner in the impoundment area. this is important in order to prevent or to minimize release of contaminants (if any) from the pond area into the underlying groundwater sources or streams and waterways. • presence of alkaline mineralogy (such as limestone) in the impoundment locality and high carbonate content in the groundwater are desirable features (see, remediation) • where possible, every effort should be made to divert surface waters, local run-off from disposal area. this can be achieved by using stream diversions, peripheral ditches, and underdrain pipes. • thickened discharge (60-70% solids) method of tailings disposal avoids steep tailing slopes; discharge on top of tailings in cone shaped hill with maximum slope angles of 3-5°. this results in high deposit stability, low rate of seepage to surrounding area and periodic wetting by the tailings slurry. a low peripheral dam is built with an impermeable clay or synthetic liner to channel effluent water to a single location for treatment. with suitable cover, the cone is to be kept fully saturated with water to prevent acid-generating conditions. low permeability and low slope of the cone will result in slow rate of migration of contamination that natural processes will be able to assimilate. thickening should be at disposal site to reduce high energy cost of pumping thickening tailings. 6. acidity in the tailings ponds and remediation options waste rock dumps and tailings ponds are the most visible end result of the mining process. in mining and processing of sulfide ores, acid generation due to weathering is a more challenging problem facing mining industry. the effect of acid generation can lead to higher concentration of heavy metals and other toxic elements into solutions. unless the weathering is prevented or the water is treated, acid mine drainage can pose threat to human health and the environment. the main consequence of having acidity (h+) and fe3+ in the tailings environment is the oxidative dissolution of heavy metal ions from residual minerals containing them. thus: zns + 2fe3+ → 2fe2+ + zn2++ s0 cuo + h2so4 → cu2+ + so4 2+ h2o pbs + 2fe3+ → 2fe2+ + pb2+ + s0 during the operating life of a mine, the tailings are normally covered by the supernatant mill effluent, leaving only the beaches exposed; this minimizes wind erosion. when mining ends, some sort of tailings and waste rock management is required to minimize serious environmental impact. the drying out period for the tailings area depends on a number of factors, including proportion of 40 tailings from activities, impact groundwater, and remediation slimes, amount of rainfall, and weather conditions. when tailings area have adequately dried, it is common practice to establish vegetation. control of ph by heavy liming is usually the first step, followed by application of the plant nutrients nitrogen and phosphorus. where tailings or waste rock is highly pyritic, revegetation is much more difficult due to the generation of acid as indicated earlier. a number of options for impoundment and remediation techniques have been proposed, and investigated (sudbury, 1992; pierzynski et.al., 1993; sengupta, 1993). some of these options are listed below: • ‘conditioning’ of tailings (i.e., concentrate, remove, or isolate the sulfide minerals from tailings) so that sulfide-oxidation-producing acid will be minimal. • promote vigorous healthy biological activity-plant, animal, aquatic life on the surface of the impoundment following closure (revegetation) • isolate the uppermost flow of groundwater system by means of a cut-off structure • exclusion of water with impermeable barriers such as synthetic membrane covers • exclusion of oxygen through placement of cover with extremely low oxygen diffusion characteristics: soil, water, and synthetic materials. • ph control to inhibit acid generation. if the potential for acid drainage exists through excess acid-producing material (like oxidation of pyrite), addition of neutralizing material, such as carbonate and hydroxide compounds will produce a neutral to alkaline ph in the associated water. the common additives are limestone (caco3), lime (cao or ca(oh)2), and sodium hydroxide (naoh). lime and sodium hydroxide provide greater neutralization than limestone per unit weight, but the greater unit cost and the environmentally unacceptable high ph (approaching 10 and above), retracts their use. • control bacterial action: when the ph of waste pile drops below 4, the rate of acid generation increases fivefold or more due to the presence of thiobacillus ferrooxidans. the use of bacterial control compounds such as anionic surfactants (sodium lauryl sulfate), organic acids, and food preservatives can control bacterial action. the purpose of bactericides is to create a toxic environment for bacteria so that the inorganic rate of acid generation cannot be enhanced. • covers and seals offer the ability to restrict the access of oxygen and water to reactive wastes. for this to be effective, the cover must have a low permeability to either air or water, it must have no imperfections where entry of outside agents can occur. a variety of materials may be used in this context depending on local availability and site conditions. these include: different types of soils, synthetic membranes, water and a combination of soil and water (which result in saturated soil), and materials such as concrete and asphalt. example of cover materials and their permeability to water are shown in table 1. • marine disposal: possible option for mines that are situated in close proximity to marine water body. seawater has a greater absorptive capacity for ‘contaminants’ as well as higher alkalinity than freshwater. the underlying significant factor is to delineate areas where fisheries value is minimal and where waste disposal may be environmentally acceptable. otherwise, long pipelines or barges may transport the waste far offshore, but the associated costs would be high (sengupta, 1993). 7. case study in oman in 1982, oman mining company (omco) started copper mining and smelting operations at lasail area west of sohar, northern oman. mining and processing activities continued until 1994 (after the mines were depleted). the annual production was about 1.1x106 t. the production of copper ore (mainly from pyrite-chalcopyrite) totaled some 15 million tonnes in the 11-year operation. before water well development in 1989, seawater was used for milling. during this period, some 11 million tonnes of sulfide-rich tailings and five million cubic meters of seawater have been disposed of behind the unlined lasail tailings dam, located at the upper stream of the wadi suq (ministry of water resources, mwr, 1996). 41 al-rawahy mine pollution in the area mainly includes groundwater pollution by salty water seepage from the tailings dam, a slope failure, land subsidence at the mined out area, water pollution of mine water at the mined out area (acid drainage), and air pollution due to soot and dust with high sox concentrate from the smelter and refinery plant. seepage from the tailings dam has effectively impacted the quality of ground water. there have been complaints that groundwater pollution in wadi suq has advanced to the extent that 85% of nearby village wells are salinised and undrinkable, while 50% of former agricultural wells in the area are unsuitable for irrigation (mwr, 1996). there is also a potential for toxic metal mobility if the ph of the tailings solution is not effectively monitored and controlled. table 1: alternative cover materials (source: sengupta, 1993). cover material permeability to water (m/sec) advantages/disadvantages compacted clay 10-9 –10-11 availability of large quantities problematic in many areas; subject to erosion, cracking, and root penetration; good sealing if protected and maintained compacted till 10-7 –10-9 as above, but generally more permeable compacted topsoil 10-5 –10-8 as above, but less robust, more permeable; questionable longevity peatland bog 10-5 –10-6 need to maintain in saturated condition; normally impractical for elevated waste dumps and sideslopes concrete 10-10 –10-12 subject to cracking, frost, and mechanical damage asphalt 10-20 as above hdpe synthetic impermeable requires proper bedding and protective cover; highly impermeable; life span unlikely to exceed 100 years; subject to root and mechanical penetration 8. conclusions this paper presented a summary of potential environmental damage on groundwater due to tailings impoundments, and the possible remediation options. it is important to note that tailingsrelated groundwater pollution can be minimized or prevented if a proper tailings management program is in place. in cases where pollution has affected the quality of receiving waters, remediation is neither rapid nor easy. references ayres, r.u. 1992. toxic heavy metals: materials cycle optimization. in proceedings of the national academy of sciences usa, 89: 815-20. barbour, a.k. 1994. mining non-ferrous metals: in mining and environmental impacts, issues in environmental science and technology, editors: r.e. hester and r.m.harrison, royal society of chemistry. bell, l.c. 1997. addressing the environmental impact of mining in australia-the role of research and development. in apec-gemeed, environmental cooperation workshop for 42 tailings from activities, impact groundwater, and remediation sustainable development on mining activities, proceedings. october 27-31, 1997., ministry of international trade and industry (miti), metal mining agency of japan, tokyo, japan. mclean, j.e. and bledsoe, b.e. 1992., behavior of metals in soils, epa ground water issue, epa/540/s-92/018, us env. prot. agen., washington, dc. ministry of water resources, 1996. grounwater pollution and remediation in wadi suq. pierzynski, g.m., schnoor, j.l, bauk, m.k.; tray, j.c., licht, l.a., ericksou, l. e., 1994. vegctative remediation at superfound site in mining and environmental impacts, issues in environmental science and technology, editors: r.e. hester and r.m.harrison, royal society of chemistry. sengupta, m. 1993. environmental impacts of mining monitoring, restoration, and control. lewis publishers. tilton, j.e. 1994. mining waste and the polluter-pays principle in the united states. in mining and the environment. edited by roderick g. eggert. resources for the future, washington, d.c. received 4 march 2000 accepted 1 june 2000 43 çáýöáçê çáäçêìé úä äôçøçê çáêúïí� introduction mining and generation of effluent waste mineral ores are extracted from both surface and underground mining operations. effluent waste from mining activities is generated from three general sources: waste rock dumps, milling, and tailings. figure 1. major stages in the production of non-ferrous concentrates (barbour, 1994). tailings: characteristics, disposal and impoundment mining effluent and potential environmental impacts acidity in the tailings ponds and remediation options zns + 2fe3+ ? 2fe2+ + zn2++ s0 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 45-53 © 2002 sultan qaboos university biological effects of em radiations from mobile phones adel a. ali and ahmed m. al-naamany department of electrical and electronic engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. الصحية لإلشعاعات الناجمة عن الهواتف المتنقلةاآلثار عادل أحمد علي و أحمد محمد النعماني بدأ االهتمام يتزايد حول اآلثار الصحية الناجمة عن استخدام الهاتف السيار، كما ان المعلومات المؤكدة عن تلك اآلثار : خالصة في انتظار نتائج األبحاث العلمية حتى يمكن التأكد بصورة قاطعة الصحية بدأت في االنتشار أيضا، ويبقى العديد من التساؤالت وتتجه الكثير من المناقشات حول اآلثار الصحية لإلشعاع . وحاسمة من مدى خطورة أو عدم خطورة تلك اآلثار على الصحة العامة لذا ينبغي على العلماء . لدى المواطنين الناجم عن الهاتف السيار إلى النواحي العاطفية والغير علمية، مما يزيد من حدة القلق . والمتخصصين القيام بدورهم بالمساهمة بتوعية المواطنين بصورة علمية مبسطة حتى يمكن تفهم تلك اآلثار بصورة غير مشوهة ث لم يثبت وبصورة عامة يمكن القول بعدم وجود ما يدعو إلى القلق من اآلثار الناجمة عن اإلشعاع وذلك على المدى القصير ، حي . أي آثار سلبية على الصحة الجسمية أو النفسية abstract: direct health effects could result following exposure to rf by thermal (heating effects). recent studies have shown that there are public fears on effects that can be caused mainly by holding mobile phones close to the body, or as a result of possible non-thermal effects from both phones and base stations. this paper offers an overview on the biological effects of electromagnetic radiation caused by mobile phones. exposures of individuals to rf radiation from these sources will depend upon their proximity and may be above those from mobile phone base stations, although still well below guidelines. from a review of the scientific literature, it is concluded that there were no established health effects from exposure to the rf fields from mobile phones. however, there are gaps in knowledge requiring further research, but current knowledge suggests that rf exposure to levels below the guidelines were not a risk to health. keywords: electromagnetic radiation, mobile phones, exposure, biological effects. 1. introduction m obile phones and base stations both emit radio frequency (rf) radiation. in both cases levels of exposure generally reduce with increasing distance from the source. for mobile phones, exposures will be principally to the side of the head for hand-held use, or to the parts of the body closest to the phone during hands-free use. lin (2000) and moulder (2000) point out that, base station emissions, exposures of the general population will be to the whole body but normally at levels of intensity many times less than those from handsets. a biological effect occurs when a change can be measured in a biological system after the introduction of some type of stimuli. however, the observation of a biological effect, in and of itself, does not necessarily suggest the existence of a biological hazard. icnirp (1998) stipulate that biological effect only becomes a safety hazard when it "causes detectable impairment of the health of the individual or of his or her offspring". there are many published reports in the scientific literature concerning possible biological effects resulting from animal or human exposure to rf energy. biological effects that result from heating of tissue by rf energy are often referred to as "thermal" effects. it has been known for many years that exposure to high levels of rf radiation can be harmful due to the ability of rf 45 adel a. ali and ahmed m. al-naamany energy to heat biological tissue rapidly. this is the principle by which microwave ovens cook food, via exposure to very high rf power densities, i.e., on the order of 100 mw/cm2 or more can clearly result in heating of biological tissue and an increase in body temperature. tissue damage in humans could occur during exposure to high rf levels because of the body’s inability to cope with or dissipate the excessive heat that could be generated. under certain conditions, exposure to rf energy at power density levels of 1-10 mw/cm2 and above can result in measurable heating of biological tissue (but not necessarily tissue damage). the extent of this heating would depend on several factors including radiation frequency; size, shape, and orientation of the exposed object; duration of exposure; environmental conditions; and efficiency of heat dissipation. the following discussion only provides highlights of current knowledge, and it is not meant to be a complete review of the scientific literature in this complex field. a number of references are listed at the end of this document that provide further information and details concerning this topic and some recent research reports that have been published 2. the radio frequency spectrum x-rays, ultraviolet light, visible light, infrared light, microwaves, radio-frequency radiation (rf or rfr), and electromagnetic fields from electric power systems are all parts of the electromagnetic spectrum. the parts of the electromagnetic spectrum are characterized by their frequency (or wavelength), and different electromagnetic frequencies produce fundamentally different types of biological effects. cellular and personal communication systems (pcs) reside in the ultra high frequency (uhf) region from 300 to 3000 mhz. here classical mathematical analysis with maxwell’s equations is usually appropriate, and there are few, if any, biological effects that cannot be attributed directly or indirectly to the heating of tissue (bernhardt et al, 1997; verschave et al, 1998; lai and singh, 1995; and brusick et al., 1998). like any wave-related phenomenon, electromagnetic energy can be characterized by a wavelength and a frequency. the wavelength (λ) is the distance covered by one complete electromagnetic wave cycle. the frequency is the number of electromagnetic waves passing a given point in one second. the wavelength λ of an electromagnetic wave is related to the frequency (f) and velocity (v) by the expression v = f λ (1) in free space the velocity of an electromagnetic wave is equal to the speed of light, i.e., approximately 3x 108 m/s. we usually talk about electromagnetic sources as though they produced waves of energy. however, electromagnetic energy can also act like particles, particularly at high frequencies; and the energy of these particles (photons) increases as the frequency increases. the energy carried by an em photon ξ in joules is ξ = h f (2) where h (6.625x10-34 js-1) is the planck constant and f is the frequency of the wave in hz (cycles/s). ieee standard (1992) for safety levels with respect to human exposure to radio frequency electromagnetic fields emphasize the importance of the particle nature of electromagnetic energy because the energy per particle (photon energy) is a major determinant of what biological effects a particular frequency of electromagnetic energy will have. 3. terminology and units for measuring radio-frequency radiation for radio-frequency radiation, the energy flux, in watts per square meter (w/m2 or mw/cm2), across a surface is called the "power density". power density measures the strength of the incident 46 biological effects of em radiation from mobile phones radio-frequency radiation and is the favored metric of external exposure to radio-frequency radiation; in part because it is relatively easy to measure. table 1: cnirp reference levels for public exposure at mobile telecommunications frequencies freq (mhz) electric field strength (v/m) magnetic field strength (a/m) power density (w/m2) 400–2000 2000 –3000 1.375 f ½ 61 0.0037 f ½ 0.16 f /200 10 f is the frequency in mhz. however, power density is an imperfect indicator of the relevant conditions inside an irradiated organism. instead, scientists specify a metric of internal exposure, the specific absorption rate, sar (in w/kg). the sar is generally used as the dose metric in laboratory experiments, and sar serves as the scientific basis of modern radio-frequency radiation safety standards. for typical biological tissue, the sar is given by ρ σ 2 esar = (3) e is the electric field strength in the tissue, σ  is the conductivity of the tissue, ρ is the mass density of the tissue. the si unit of sar is w/kg. the international commission on non-ionizing radiation protection (icnirp, 1998) has recently recommended power-density guidelines for limiting exposure of the general public to rf radiation. these limits keep humans from being overheated by restricting exposures to levels that are relatively weak, compared, for example, to summer sunshine, which peaks at roughly 1000 w/m2. table1 presents the icnirp reference levels for public exposure at mobile telecommunications frequencies (icnirp, 1998). the maximum allowed level is 10 w/m2 (1mw/cm2). table 2: standards for base station antennas power density mw/cm2 types of installation 0.0002 typical near a modern phone tower 0.01 maximum near a cell phone tower 0.4 -1.2 fcc/icnirp/ieee/nrpb public exposure standards 4 unconfirmed reports of effects 40 reproducible effects 100 clear hazards table 2 shows moulder’s (2000) comparison of the icnirp 1mw/cm2 standard with expected radiation levels near base stations. also depicted are the power density levels associated with possible effects. 47 adel a. ali and ahmed m. al-naamany 4. effects of radiation in terms of potential biological effects, the electromagnetic spectrum can be divided into four portions with three of these portions being of non–ionizing part of spectrum as follows: 1. the non-ionizing portion of the spectrum, which can be subdivided into: a. the optical radiation portion, where electron excitation can occur (e.g., visible light, infrared light). b. the portion where the wavelength is smaller than the body, and heating can occur (e.g., microwave ovens, mobile phones, broadcast tv, fm radio). see figure 1 and 2. c. the portion where the wavelength is much larger than the body, and heating seldom occurs (e.g., am radio, power frequency fields, static fields). 2. the ionizing radiation portion, where direct chemical damage can occur (e.g., x-rays). 106 104 102 1 10-2 10-4 10-6 10-8 10-10 10-12 102 104 106 108 1010 1012 1014 1016 1018 1020 tv fm radio heating lamp tanning booth medical x-rays wavelength in meters frequency in hz mobile phones am radio power lines figure 1. mobile phone position in electromagnetic spectrum. 106 104 102 1 10-2 10-4 10-6 10-8 10-10 10-12 elf radiorf microwave mw ultraviolet x-rays 102 104 106 108 1010 1012 1014 1016 1018 1020 infrared non-ionizing ionizing non thermal low induced currents thermal high induced currents heating optical electronic excitation photochemical effects broken bonds dna damage wavelength in meters frequency in hz figure 2. electromagnetic spectrum. 48 biological effects of em radiation from mobile phones to effect a change in biological material through which it is passing, an em wave must deposit enough energy to alter some structure significantly. but every material particle within the body already possesses an average thermal kinetic energy (in joules, j) of the order of kt; where k (1.38x10-23 j/k) is the boltzmann constant and t is the absolute temperature (in kelvin, k), and these particles continually collide with other particles of similar energy. for a change to occur in biological material the em wave seemingly should transfer energy considerably above kt to selected particles, and at 310 k (37oc, body temperature), kt is 4.3 x10-21 j. another standard of comparison is the chemical bond, because to be effective in promoting change the field should be able to deposit packets of energy larger than the bond energy, and bonds are typically within an order of magnitude of an electron volt (1.6x10-19j). table 3 shows comparisons between the bond energy of the human cells and the heat energy as well as the photon energy. in the uhf realm (300 to 3000 mhz) the energy ξ of one photon can be estimated using (2). it can be shown that ξ<2x10-24 j is less than 0.1% of either kt (4x10-21 j) or the bond energy (1.6x10-19j). table 3: energy comparisons. heat energy: k t ~ 4.3 x10-21 joules bond energy: e v ~ 1.6x10-19 joules photon energy: h f at uhf ~ (0.2-2.0) x10-24 joules 5. near field and far field standards intensity is expressed either as an electric (magnetic) field strength in v/m (tesla), or as a power density, in units of watts/cm2, according to whether we deal with a near or far field conditions, the former being relevant to handset use, and the latter to public exposure in the vicinity of a base-station. cited values are usually average ones, which in the case of the gsm duty cycle are 1/8 of the peak values. it should be noted that the current preoccupation with attempting to assess the relative merits of different makes of handset in terms solely of the maximum recorded (rms) sar values is open to the objection that a low value does not necessarily mean a correspondingly low overall electromagnetic absorption. there are two reasons for this: i) the cited maximum value for a given model refers to a single location (relative to the head), which does not necessarily correspond either to the location of the phone when in use, or to the conditions that obtain during a call, ii) there is a vast variation in the spatial radiation patterns of different antennae. accordingly, the energy deposited in the head by a low sar model with an antenna that radiates diffusely can exceed that from a high sar model with more localised emission characteristics. 6. antenna location criteria sites should be designed so that people cannot access areas that exceed public exposure standards. in general, public exposure standards will not be exceeded at distances more than 2 meters above or below an antenna, and more than 6 meters away from the antenna in the direction of the main lobe, and behind a high-gain antenna (moulder, 2000). if there are areas accessible to workers that exceed the public exposure standard, workers must know where these areas are. workers must know what precautions to take. if there are areas accessible to workers that exceed the occupational exposure standard, workers must know where these areas are. workers must power-down and lock out the antennas before entering these areas. people who live or work at the top of buildings that have roof top antennas have concern regarding radiation hazards. base station antennas on towers are highly unlikely to cause any health hazards, however, antennas on roof tops my cause health hazards. 49 adel a. ali and ahmed m. al-naamany 7. human exposure the meaning of the 1.6 w/kg local sar limit in the ieee/ansi standard as per lai and singh (1995) and the similar 2–4 w/kg local sar restrictions in the icnirp guidelines as stipulated by brusick et al (1998) can be judged by noting that this closely matches the human whole-body resting metabolic rate, and is of the order of one-eighth of the brain’s resting metabolic rate. a typical cellular telephone has a time-averaged power output of 600 mw or less and yields numerically modeled brain sars which may sometimes have exceed the 1.6w/kg limit, but which generally lie within the ansi/ieee ‘‘controlled environment’’ limit of 8 w/kg averaged over 6 min (icnirp, 1998; foster and moulder, 2000). this 600 mw is less than 1% of the body’s normal resting metabolic output and under 4% of the brain’s normal resting metabolic output. in ‘‘uncontrolled environments’’ ansi/ieee as mentioned in ieee standard for safety levels with respect to human exposure to radio frequency electromagnetic fields (1992) limits the spatial-average sar to 0.08 w/kg whole-body, and to 1.6 w/kg as averaged over any 1g of tissue; under ansi/ieee it is permissible to average both power density and sar over 30-min intervals. the icnirp (1998) ‘‘basic restrictions’’ on sar are similar to the ansi/ieee limits see table 4 sar or specific absorption rate is the rate at which rf energy is imparted to a unit of mass of a biological body. table 4: permissible sars by different international organizations. sar w kg-1 nrpb all people icnirp workers public ansi/ieee controlled uncontrolled whole body 0.4 0.4 0.08 0.4 0.08 head 10 (10 g) 10 (10 g) 2 (10 g) 8 (1 g) 1.6 (1 g) averaging time 6 min 6 min 6 min 6 min 6 min 8. ongoing research and the precautionary measures having reviewed all relevant epidemiological studies, national radiological protection board (nrpb) concluded that the results were inconclusive and did not provide an adequate starting point from which to derive exposure guidelines (moulder et al, 1999; kustler et al, 1997; usepa, 1996, repacholi, et al, 1997; foster et al., 1997). instead, therefore, the guidelines were based on the potential of rf radiation to cause illness or injury through heating of body tissues. while some research had suggested that adverse health effects might occur from exposures lower than those needed to produce significant heating, the evidence for this was not considered sufficiently robust to form a basis for the derivation of exposure guidelines. there is an extensive amount of research on the biological effects of rf energy. thermal hazards were well understood. well-accepted standards existed to prevent thermal injuries, however, little of the research dealt with cancer, little dealt with the kind of pulse modulated rfr produced by modern phones and little dealt with smallvolume near-field rfr exposure. there are many un-replicated reports of “effects” at “low exposure” levels. the independent expert group on mobile phones (2000) terms of reference is: “to consider present concerns about the possible health effects from the use of mobile phones, base stations and transmitters, to conduct a rigorous assessment of existing research and to give advice based on the present state of knowledge. to make recommendations on further work that should be carried out to improve the basis for sound advice.” 50 biological effects of em radiation from mobile phones the expert group report on mobile phones and health was published in may 2000. the 160page report is a based on a comprehensive summary of scientific literature and gathering of stakeholder opinions. the report concludes that the balance of existing scientific evidence does not suggest adverse health effects, there is scientific evidence suggesting there might be biological effects, the extent of uncertainty about the true position justifies a precautionary approach. in line with a precautionary approach, the report recommends a range of measures designed to be prudent and other recommendations designed to empower members of the public in their choices relating to mobile phone technology. for hands free kits, the report recommends that the government sets up an independent, testing system for hands free kits and shielding devices so that consumers have access to clear and impartial advice. the expert group believes that, on the basis of the evidence currently available, there is no need for the general population to be worried about the use of mobile phones. in line with the precautionary approach highlighted in the report, the expert group notes that individuals may choose to • use phones for as short a time as possible • use phones with low specific energy absorption rate (sar) values • use hands-free kits and other devices provided they have been proved to reduce sar. exposure to members of the public from macro-cell base stations is very much less than current guidelines. in giving special attention to schools, the expert group was responding very largely to public concern rather than any proven health hazard. in defining the “beam of greatest intensity”, the aim of the recommendation by the expert group was to ensure that the accessible location where the greatest exposure to the radio frequency radiation signal occurs is not within school grounds. it would be up to the operator to demonstrate this by measurement or other means. since there are no scientific grounds for setting guidelines below the levels set by the international commission for non-ionizing radiation protection (icnirp) for the public, the expert group avoided setting exposure limits for school buildings and grounds below these limits. for the same reason it did not wish to recommend that there should be a particular minimum distance between the base station and the school. 9. conclusions understanding of cellular phone health effect is evolving. many questions must be answered before consistent, dependable and scientific conclusions can be drawn. however, there is no immediate cause for concern from short-term exposure. no physiologic or pathologic consequence. exposure criteria must be evaluated periodically. some people’s well being may be adversely affected by the environmental impact of mobile phone base stations sited near their homes, schools or other buildings, as well as by their fear of perceived direct effects. this may only happen if the required exposures guidelines/limits are neglected by the telecommunication organizations and the mobile vendors/manufacturer. measurements that have been made indicate that exposures of the general population from base stations are typically many hundreds, or thousands of times lower than existing exposure guidelines. there are concerns, nevertheless, about whether the emissions from all base stations are uniformly low, about whether the emissions could cause unknown health effects, and whether, with the increased use of mobile telecommunications, their output will have to rise. discussions about biological impacts of electromagnetic fields are highly emotional. the concern on health effects is expected to increase as newer generations of mobile communications are set to appear in the market with even more applications. the third generation mobile is expected to incorporate both voice and data with much wider coverage. as a result, anxiety and feelings are expected to dominate the discussions. it is necessary to establish confidence in science and research. such confidence can only be created in the general public if detailed information is 51 adel a. ali and ahmed m. al-naamany supplied. scientists and engineers are called upon to provide sound contributions in order to help making discussions more objective. it seems advisable to draw general conclusions from the present discussions for the introduction of future-oriented technologies. careful consideration must be given in time to the consequences of (new) technologies for people and the environment including psychological effects on the general public in respect of introduction. it may be assumed that the subject of implications of electromagnetic fields for the environment will continue to be in the focus of discussions for quite some time in the future until new findings are available. references bernhardt, j.h., matthes, r. and repacholi, m.h. 1997. non-thermal effects of rf electromagnetic fields. international commission on non-ionizing radiation, oberschleissheim. brusick, d., albertini, r., mcree, d., peterson, d., williams, g., hanawalt, p. and preston, j. 1998. genotoxicity of radio frequency radiation. environ. mol. mutagen. 32:1–16. foster, k.r. and moulder, j.e., “ are mobile phones safe?” ieee spectrum, pp23-28 august 2000. foster, k.r., erdreich, l.s. and moulder, j.e., 1997. weak electromagnetic fields and cancer in the context of risk assessment. proc. ieee, 85: 731–746. ieee standard for safety levels with respect to human exposure to radio-frequency electromagnetic fields, 3 khz to 300 ghz (ieee c95.1–1991). the institute of electrical and electronics engineers, inc., new york, 1992. independent expert group on mobile phones, expert group report on mobile phones and health, may 2000. international commission on non-ionizing radiation protection (icnirp), 1998. "guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 ghz)," health physics, 74: 494-520. kustler, n., balzano, q. and lin, j.c., 1997. mobile communications safety. chapman and hall, london. lai, h. and singh, n.p., 1995. acute low-intensity microwave exposure increases dna singlestrand breaks in rat brain cells. bioelectromagnetics, 16: 207–210. lin, j. evidence for biological effects of radio frequency radiation interpretation and implications, mobile phones, is there a health risk? 7-8 december 2000, london, uk. moulder, j.e., characterizing the concerns over base station sitting mobile phones, is there a health risk? 7-8 december 2000, london, uk. moulder, j.e. “cell phones and cancer: what is the evidence for a connection?” radiation research, vol. 151, 5: 513–531, may 1999. repacholi, m.h., basten, a., gebski, v., noonan, d., finnie, j. and harris, a.w., 1997. lymphomas in em-pim1 transgenic mice exposed to pulsed 900 mhz electromagnetic fields. radiat. res. 147: 631–640. united states environmental protection agency (usepa), 1996. proposed guidelines for carcinogen risk assessment. fed. regist. 61: 17960–18011. verschaeve, l. and maes, a., genetic. 1998. carcinogenic and teratogenic effects of radio frequency fields. mutat. res. 410: 141–165. received 13 june 2001 accepted 7 october 2001 52 biological effects of em radiation from mobile phones appendix a: internet web sites for further information note: all internet addresses below should be preceded by "http://". also, some url’s may be case sensitive 1. american radio relay league: www.arrl.org 2. american national standards institute: www.ansi.org 3. bioelectromagnetics society: www.bioelectromagnetics.org 4. cost 244 (europe): www.radio.fer.hr/cost244 5. dod: www.brooks.af.mil/afrl ( select radiofrequency radiation) 6. european bioelectromagnetics association: www.ebea.org 7. electromagnetic energy association: www.elecenergy.com 8. federal communications commission: www.fcc.gov/oet/rfsafety 9. icnirp (europe): www.icnirp.de 10. ieee: www.ieee.org 11. ieee committee on man & radiation: www.seas.upenn.edu/~kfoster/comar.htm 12. international microwave power institute: www.impi.org 13. microwave news: www.microwavenews.com 14. j moulder, med. coll. of wisconsin.: www.mcw.edu/gcrc/cop/cell-phone-healthfaq/toc.html 15. national council on radiation protection & measurements: www.ncrp.com 16. nj dept radiation protection: www.state.nj.us/dep/rpp (select non-ionizing radiation) 17. richard tell associates: www.radhaz.com 18. us osha: www.osha-slc.gov/sltc (select subject: radio frequency radiation) 19. wireless industry (ctia): www.wow-com.com 20. wireless industry (pcia): www.pcia.comworld health organization emf project: www.who.ch/peh-emf appendix b: glossary agnir advisory group on non-ionizing radiation ansi american national standards institute base station facility providing transmission and reception for radio systems. for macro cells, the infrastructure comprises either roofor mast-mounted antennas and an equipment cabinet or container. for smaller micro cells and pico cells, the antennas and other equipment may be housed in a single unit. dna deoxyribonucleic acid. the compound that controls the structure and function of cells and is the material of inheritance gsm global system for mobile communications or groupe spéciale mobile. the international, pan-european operating standard for the new generation of digital cellular mobile communications. enables mobile phones to be used across national boundaries. pcn operators work to the same standard but at different frequency allocations. icnirp international commission on non-ionizing radiation protection nrpb national radiological protection board sar specific energy absorption rate. third generation the next evolution of mobile phone technology based on umts and expected to result in widespread use of videophones and access to multimedia information. 53 http://www.arrl.org/ http://www.ansi.org/ http://www.bioelectromagnetics.org/ http://www.radio.fer.hr/cost244 http://www.brooks.af.mil/afrl http://www.ebea.org/ http://www.elecenergy.com/ http://www.fcc.gov/oet/rfsafety http://www.icnirp.de/ http://www.ieee.org/ http://www.seas.upenn.edu/~kfoster/comar.htm http://www.impi.org/ http://www.microwavenews.com/ http://www.mcw.edu/gcrc/cop/cell-phone-health-faq/toc.html http://www.mcw.edu/gcrc/cop/cell-phone-health-faq/toc.html http://www.ncrp.com/ http://www.state.nj.us/dep/rpp http://www.radhaz.com/ http://www.osha-slc.gov/sltc http://www.wow-com.com/ http://www.who.ch/peh-emf adel a. ali and ahmed m. al-naamany abstract: direct health effects could result following exposure to rf by thermal (heating effects). recent studies have shown that there are public fears on effects that can be caused mainly by holding mobile phones close to the body, or as a result of the radio frequency spectrum terminology and units for measuring radio-frequency radiation effects of radiation near field and far field standards antenna location criteria sar nrpb icnirp ansi/ieee head averaging time having reviewed all relevant epidemiological studies, national radiological protection board (nrpb) concluded that the results were inconclusive and did not provide an adequate starting point from which to derive exposure guidelines (moulder et al, 19 conclusions appendix a: internet web sites for further information state-of-the-art review of collapsing soils science and technology, 6(2001) 67-83 ©2001 sultan qaboos university a finite volume runge-kutta ellam method for the solution of advection diffusion equations mohammed al-lawatia*, robert c. sharpley** and hong wang** *department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36 al-khod 123, sultanate of oman,**industrial mathematics institute, department of mathematics, university of south carolina, columbia, south carolina 29208, usa. بالحجوم المحدودة لحل معادالت اإلنتقال واإلنتشار) إيالم ( طريقة رونج وكوتا محمد اللواتي ، روبرت شاربلى ، وهونج وانج يختص هذا البحث بتصميم طريقة عددية بالحجوم المحدودة تعتمد على المنحنيات المميزة لحل معادالت اإلنتقال :خالصة تستخدم هذه الطريقة تقريب رونج وكوتا من الرتبة الثانية للمنحنيات . ات في األوساط المسامية واإلنتشار التي تمثل إنتقال الملوث تتميز الطريقة (eulerian lagrangian localized adjoint method , ellam). "إيالم"المميزة في إطار طرق ة متماثلة كما تؤدي إلى حلول عددية دقيقة حتى المقترحة في مخططها بالحفاظ على الكتلة وتحويل المعادالت الحاكمة إلى صور معروفة لحل مثال نمطي لتوضيح نقوم بعرض بعض التجارب العددية لمقارنة عدة طرق. في ظل إستخدام خطوات زمنية كبيرة . كفاءة الطريقة المقترحة abstract: we develop a finite volume characteristic method for the solution of the advectiondiffusion equations which model the contaminant transport through porous medium. this method uses a second order runge-kutta approximation for the characteristics within the framework of the eulerian lagrangian localized adjoint methods (ellam). the derived scheme conserves mass, symmetrizes the governing equations and generates accurate numerical solutions even if large time steps are used. numerical experiments comparing several competitive methods using a standard test example are presented to illustrate the performance of the method. keywords: characteristics methods, comparison of numerical methods, eulerian-lagrangian methods, numerical solutions of advection-diffusion equations, runge-kutta methods. 1. introduction many problems arise in the numerical simulation of subsurface contaminant transport and remediation within porous media. the model equations, which describe such processes, are advection-diffusion equations which are known to present many numerical difficulties especially when advection dominates the physical process. standard centered difference methods and galerkin finite element methods (fem) then generate solutions which exhibit non-physical spurious oscillations. standard upwinding methods on the other hand usually eliminate these types of oscillations in their solutions. however they suffer from excessive numerical diffusion which smears out sharp fronts of the solutions where important chemistry and physics take place. many specialized methods have been developed which aim at resolving the difficulties mentioned when applied to both linear and nonlinear problems. a large class of these methods, usually referred to as eulerian methods, use some form of upstream weighting and improved techniques in their formulations over fixed spatial grids. this class includes the petrov-galerkin fem methods (bouloutas and celia, 1991; westerink and shea, 1989), the streamline diffusion methods (hughes and mallet, 1986; johnson, 1987), the flux corrected transport methods (boris and book, 1997; tóth and odstrčil, 1996), and the high resolution methods from fluid dynamics 67 al-lawatia, robert c. sharpley and hong wang which include the essentially non-oscillatory method (eno) and the weighted eno method (shu 1999), and the godunov methods (dawson, 1991; van leer, 1984), as well as many other methods. these methods which are characterized by ease of formulation and implementation, succeed in suppressing the artificial oscillations which are present in standard methods. however, their solutions tend to be dominated by time truncation errors. moreover they impose restrictions on the size of the time step taken for reasons of stability and accuracy. a second class of methods, usually referred to as characteristic methods makes use of the dual nature of the governing equation which includes hyperbolic as well as parabolic components (douglas and russell, 1982; pironneau, 1982). these methods incorporate eulerian grids with lagrangian tracking along the characteristics to treat the advective part of the equation. this treatment allows for larger time steps to be used in the simulation. moreover, it significantly reduces the time truncation errors when compared to eulerian methods. however, these methods have difficulty in conserving mass and in treating general boundary conditions. the eulerian lagrangian localized adjoint method was developed by celia, russell, herrera, and ewing (1990) as an improved extension of characteristic methods which maintains their advantages and enhances their performance by conserving mass and treating general boundary conditions naturally in its formulation. this first ellam formulation (celia et al, 1990) was a finite element formulation for one-dimensional constant-coefficient advection diffusion equations. the strong potential that this formulation has shown, led to the development of formulations for variable coefficient equations (russell and trujillo, 1990; wang et al, 1992), for non-linear equations (dahle et al, 1995), as well as finite volume formulations (healy and russell, 1993). most of the ellam formulations developed use a backward euler approximation in time along the characteristics due to its simplicity and stability. these formulations are therefore only first order accurate in time. the authors have recently developed second order in-time ellam methods for advection-diffusion equations (al-lawatia et al, 1999). the derived schemes were shown to have a higher order in-time convergence rate compared to the backward euler ellam methods. in general, ellam methods generate regularly structured systems which are symmetric and positive definite and thus can be easily solved numerically. a principal drawback, however, to the increased use of ellam methods has been the increased effort required to implement the method within existing simulators, since it is somewhat more involved than several of the other methods. in this paper we develop a finite volume ellam method for the solution of variable coefficient advection-diffusion equations in one spatial dimension which uses a second order runge-kutta approximation for the characteristics. this method uses finite volume test functions in the spacetime domain defined by the characteristics which permits implementation with little code change in many existing simulators, whether they be legacy codes or more modern modularized versions. numerical experiments are presented to illustrate the performance of the method developed and to compare it with many widely used and well-perceived methods, such as the streamline diffusion method, monotone schemes, essentially non-oscillatory methods, and flux corrected schemes. 2. development of the runge-kutta ellam method the model problem we consider is the following one-dimensional advection-diffusion equation and initial condition (1) [a,b]x(x),u)u(x, .t],[t(a,b),xf(x,t),)d(x,t)u(v(x,t)uulu xxt ∈= ∈∈=−+≡ 00 0 where v is the velocity field and is the positive diffusion coefficient. to close the system, we assume ( b )-periodic boundary conditions. suus ∂∂= / , ),( tx ),( txd a− 68 a finite volume runge-kutta ellam method 2.1 partition and characteristic curves let i and n be two positive integers. following healy and russell (1993), we define a partition of the space-time domain [ ],0[], tba × of equation (1) as follows: (2) ....: ,...0: 2/12/32/1 10 bxxxa tttt ix n t =<<<= =<<<= +δ δ the partition xδ divides the spatial domain into grid blocks (finite volumes) of size . we denote the center of block , by which represents a grid point in our discretization. multiplying equation (1) by a test function that vanishes outside and integrating by parts we obtain a weak form of equation (1) ],[b 2/12/1 +−= iii xx ix∆ (] × t ib ix w ]1+,,[ nn tba ∫ ∫ ∫ ∫ ∫∫ ∫ ∫ ∫ + ++ + += +−−+ + + ++ b a t t b a nn t t b a xt t t b ax b a t t b a xx nn n n n n n n n n dxdtwfdxtxwtxu dxdtwvwudtwuduv dxdtwuddxtxwtxu 1 11 1 ,),(),( )()( ),(),( 11 (3) where which takes into account the fact that is discontinuous in time at time t . we note from the periodicity of formulation that the third integral on the lefthand side of equation (3) vanishes. ),(lim),( txwtxw ntt n →+ = n ),( txw in the ellam framework (celia et al, 1990), the test functions in equation (3) are selected to satisfy (exactly or approximately within the tolerance of the accuracy desired) the homogeneous equation of the hyperbolic part of the adjoint equation of equation (1) ),( txw 0=+ xt wvw (4) which reflects the lagrangian nature of equation (1). this implies that the test functions should be chosen to be constant along the characteristics. these characteristics are given by solutions of initial value problems of the ordinary differential equation ).,( tyv dt dy = (5) solving this equation analytically for a generic velocity field, however, is not possible, and so we must consider approximate solutions. in the formulation of our scheme, we approximate the characteristics by a second order runge-kutta method and define the characteristic curve emanating from a point ), tx( , with ],[ 1+∈ nn ttt using heun's method: ( ))),,()((),( 2 )( ),,( θθ θ θ txvtxvtxv t xtx −++ − +=χ , (6) where θ determines the time position along the characteristic. 69 al-lawatia, robert c. sharpley and hong wang 2.2 the finite volume runge-kutta ellam scheme in the finite volume runge-kutta ellam scheme, we define the test function associated with the grid point by ),( txwi ),...,1( iixi =    ∈∈χ = ++ otherwise,,0 ],,[,b),;( if,1 ),( 11 nn i n i ttttxt txw (7) and extend to be constant back along the approximate characteristics (6) into the space-time strip [ . iw [× nt ],], 1+ntba the runge-kutta ellam scheme can be formulated by evaluating the space-time integrals in equation (3) along the approximate characteristics. we evaluate the second (source) term on the right hand side of equation (3) by a trapezoidal quadrature ( ) ∫ ∫ ∫ ∫ ∫ ∫ ∫ + − + − + − + − + + + ∆ + ∆ = +χ+ ∆ = χχ= + ++ ++ 2/1 2/1 * 2/1 * 2/1 2/1 2/1 2/1 2/1 1 1 ),( 2 ),( 2 ),;(),(),( 2 ),;()),,;(( ),(),( 1 1*1 11 i i i i i i i i n n n n x x f i x x nn x x f i nn x nn x x t t n x n t t b a i edxtxf t dxtxf t edxtxttxftxf t dsdxtxsstxsf dydssywsyf (8) where is the foot of the approximate characteristic emanating from ( and is the truncation error due to the application of the trapezoidal rule. ),;( 1* +χ= nn txtx ), 1+ntx f ie we evaluate the second (i.e., diffusion) term on the left hand side of equation (3) in a similar manner as was done with the source term but noting that w is a dirac-delta function at the two end points and , ),( 1+nix tx 2/1−ix 2/1+ix ( ) d i x xx n x x xx n x d i nnn ix nnn x x x nn x n ix n x x x t t n ix n x n x t t b a iyy etxdu t txdu t edxttxtwttxtdu txttxwtxdu t dsdxstxswstxsudtxs dydssywsyud i i i i i i i i n n n n + ∆ + ∆ = +χχ ×χ+ ∆ = χχχ= − + − + + − + − + + == + ++ +++ +++ ∫ ∫ ∫ ∫ ∫ * 2/1 * 2/1 2/1 2/1 2/1 2/1 2/1 2/1 1 1 ),)(( 2 ),)(( 2 )),,;(()),,;()(( ),;(),(),)(( 2 )),,;(()),,;()()(,;( ),(),)(( 1 11 111 111 (9) where we used the identity in the third equality. ),;()),,;(()),,;(( 111 +++ χχ=χ nx n ix n ix txsstxswstxsw 70 a finite volume runge-kutta ellam method the finite volume runge-kutta ellam can then be formulated from the weak form (3) using the periodic boundary conditions to drop the third term on the left hand side, dropping the fourth term on that same side by our choice of test functions (main idea of ellam), and by substituting equations (8) and (9), dropping both error terms and . finally, we choose as trial functions which are piecewise linear in space on adjacent grid points at time t and obtain the following runge kutta ellam scheme f ie d ie u 1+n [ ] [ ] ∫∫ ∫ ∫ + − + − + − + − ∆ + ∆ + − ∆ −= − ∆ + + +− + + + − + * 2/1 * 2/1 2/1 2/1 * 2/1 * 2/1 2/1 2/1 .),( 2 ),( 2 ),)((),)(( 2 ),( ),)((),)(( 2 ),( 1 * 2/1 * 2/1 1 2/1 1 2/1 1 i i i i i i i i x x n x x n n ix n ix x x n n ix n ix x x n dxtxf t dxtxf t txdutxdu t dxtxu txdutxdu t dxtxu (10) the first integral on the left hand side of equation (10) is a standard integral which can be computed as follows 1 1 1 1 1 1 1 11 1 1 1 4 2 44 ),( 2/1 2/1 + + + + + + − −+ − − + ∆+∆ ∆∆ +   ∆+∆ ∆ +    ∆+∆ ∆ + ∆ + ∆+∆ ∆∆ =∫ + − n i ii iin i ii i ii iin i ii ii x x n u xx xx u xx x xx xx u xx xx dxtxu i i (11) for a non-uniform partition xδ and as , 84 3 8 ),( 11 11 1 1 2/1 2/1 + + ++ − + ∆+ ∆ + ∆ =∫ + − n i n i n i x x n u x u x u x dxtxu i i (12) for a uniform one. the second integral on the right hand side of equation (10), which represents a source/sink integral, can be evaluated in a similar manner. the remaining integrals in equation (10) which are defined at time t require more careful evaluation. the tracking approach we use to evaluate these terms is forward tracking, which avoids the grid deformation problems associated with backward tracking schemes and is more feasible for multiple dimensions. in this approach numerical integration rules are applied at time t where the solution (and the associated weight) at each quadrature point is forward tracked while the value of the test function is determined at the location to which the quadrature point is tracked at time . however, using the test functions given by equation (7) presents mass conservation difficulty when the courant number is close to an integer, since forward tracked quadrature points could come very close to end points of the cell blocks which could result in mass not being accurately distributed among the nodes. healy and russell (1993) suggest using alternative test functions which approximate the functions given in equation (7) and try to distribute mass more accurately while maintaining local mass conservation. we use their approach and approximate the first integral on the leftside of equation (10) according to n n 1+nt ∫ ∫ + − ≈ * 2/1 * 2/1 ),(),(),( i i x x b a n i nn dxtxwtxudxtxu (13) 71 al-lawatia, robert c. sharpley and hong wang where the test function introduced is defined by                +∈      ∆ − − ∆+∆ ∆ −∈ ∆+∆ −+∆ −+∈ +∈ ∆+∆ −+∆ −∈      ∆ − − ∆+∆ ∆ = + + − − ∆ ++ + + + + ∆ + + ∆ ∆ + ∆ + ∆ − ∆ −− − ∆ ∆ − − ∆ − − − − + otherwise.,0 ],,[,161 ],,[, )(16 ],,[,1 ],,[, )(16 ],,[,161 ),( 162/12/1 1 2/1 1 2/1162/1 1 2/1 162/1162/1 162/12/1 1 2/1 2/1162/1 1 2/1 1 1 1 1 1 1 i ii i ii ii i i x ii i i ii i i x i ii x x ii x i x i x ii ii x x ii i x i i i ii i n i xxx x xx xx x xxx xx xxx xxx xxx xx xxx xxx x xx xx x txw (14) 3. numerical experiments in this section we present numerical results to illustrate the performance of the finite volume runge-kutta ellam (rk-ellam) method developed in this paper and compare it to other well known methods. 3.1 convergence rates of the runge-kutta ellam scheme we observe numerically the order of convergence of the finite volume rk-ellam method developed for equation (1). in order to make comparisons with earlier results in (al-lawatia et al, 1999), we choose as a test problem the standard transport of a gaussian hill with initial configuration given by       −− = 2 2 2 )( exp),( σ c o xx txu (15) where the center is and the spread 3.0=cx .0316.0=σ the spatial domain is [ and we simulate over a time interval of [0,1]. the velocity field considered is v and the diffusion coefficient is set to . the right hand side in equation (1) is generated from this data and the analytical solution (see section 5.1 of al-lawatia et al, (1999) for details). ]2,0[], =ba x1.01+=tx ),( 410−=d in order to obtain the order of convergence in space (respectively, time) in this experiment, we perform runs varying the mesh size (respectively, x∆ t∆ ) with the remaining mesh size being fixed with small value, so that the contribution to the residual error due to that variable is negligible. we then use a linear regression to fit the data and obtain the order of convergence in the chosen variable whose size was varied. the process is then repeated for the remaining variable. table 1. contains the norms of the errors generated for our runs as well as the estimated order of convergence and corroborates that the scheme is second order in time. 1l 3.2 comparison of the runge-kutta ellam method with other schemes we perform numerical experiments which present a comparison of the finite volume rungekutta method developed in this paper with some well known and widely used methods, including the galerkin (gal), quadratic (qpg), and cubic (cpg) petrov-galerkin finite element methods, the streamline diffusion finite element method (sdm), the monotone upstream-centered scheme 72 a finite volume runge-kutta ellam method for conservation laws (muscl), the minmod scheme, the essentially non-oscillatory method (eno) and weighted eno (weno), and flux-corrected transport (fct) methods. see al-lawatia et al, (1999) and the references cited there for a discussion of most of these methods, their implementation, and the advantages and disadvantages of their use for numerically solving advection-diffusion problems. the qpg and cpg methods (bouloutas and celia,1991; westerink and shea, 1989) incorporate some upwinding in the test space as compared to the standard finite element method (gal). using the same principle, the sdm incorporates some upwinding by adding multiple of the linearized hyperbolic operator to the test functions in the space-time finite element formulation of equation (1) (hughes and mallet 1986; johnson 1987). table 1: spatial and temporal convergence rates of the rk-ellam method. x∆ t∆ 1l error x∆ t∆ 1l error 1/500 1/6 2.591498 × 310− 1/60 1/500 2.094592 210−× 1/500 1/8 1.436987 × 310− 1/65 1/500 1.866031 210−× 1/500 1/10 9.097415 × 410− 1/70 1/500 1.649212 210−× 1/500 1/12 6.239286 × 410− 1/75 1/500 1.436851 210−× 1/500 1/14 4.496829 × 410− 1/80 1/500 1.231351 210−× temporal rate = 2.06 spatial rate = 1.83 figure 1. analytic and rk-ellam solution 60/1=∆x , . 10/1=∆t 73 al-lawatia, robert c. sharpley and hong wang table 2: the performance of the rk-ellam method. x∆ t∆ 1l error cpu figure 1/60 1/5 2.478001 × 310− 0.1 1/60 1/10 7.232906 × 410− 0.3 1 this results in numerical diffusion being added only in the direction of the streamlines. the amount of diffusion added depends on the value taken for a constant which appears in the formulation. there is no clear optimal choice for this constant and is heavily problem dependent. following our reasoning and explanations in (al-lawatia et al,1999), we consider three different values for c , namely 1.0, 0.1 and 0.0001. the muscl and minmod schemes are godunov methods which are known to work well for hyperbolic conservation laws, and are extended for the advection-diffusion equations by operator splitting of the equation. in our experiment we consider the formulation given by (dawson, 1991; van leer, 1984). in a similar manner, the eno and weno which are high-order methods can be extend to solve the advection-diffusion equations (shu, 1999). the eno formulation of order k uses a polynomial interpolation over the locally smoothest stencil from k-1 candidates. this treatment provides a non-oscillatory interpolation which accurately resolves sharp fronts of the solution. the weno formulation uses a convex combination of all candidate stencils. this allows for higher order (2k-1) approximation of smooth data while maintaining the advantages of eno. in our experiments we consider eno and weno of order k=3 while the roe flux is used to guarantee upwinding. the last method we consider is the flux corrected transport scheme (fct) which adds a high-order (anti-diffusive) term to a low order solution and a limiter which controls the amount of anti-diffusion added thus avoiding the formation of new minima or maxima. in these experiments we consider two fct formulations, the etb-fct which is due to boris and book (1997) and the yd-fct which is due to odstrčil (tóth and odstrčil, 1996). c table 3: the performance of the galerkin and petrov-galerkin fem method. x∆ t∆ gal 1l error qpg cpg cpu fig 1/60 1/71 3.932535 210−× 2.735581 210−× 7.066083 × 310− 7.2 2a 1/60 1/120 1.696879 × 210− 1.227225 × 210− 3.699256 310−× 11.6 1/60 1/180 9.112832 × 310− 1.109330 × 210− 3.501284 310−× 48.4 1/60 1/500 3.501284 × 310− 1.296422 × 210− 2.792321 310−× 50.8 1/120 1/180 6.872490 × 310− 5.672787 × 310− 1.131020 310−× 34.5 1/120 1/500 1.034087 × 310− 1.876571 × 310− 2.635279 410−× 95.5 1/180 1/500 9.516502 × 410− 5.742545 × 410− 1.572651 410−× 143.4 2b tables 2-7 display errors for the various methods described in the previous paragraph and with groupings determined according to their common features. in the example runs, we use a base spatial grid size of =1/60 which is needed to resolve the analytical solution. in the rk-ellam simulation we use a time step of =1/10 which gives a courant number of 7.08. the rk ellam solution is presented in figure1, which matches the analytical solution with no noticeable artifacts. the norm of the error is given in table 2. all other methods have a restriction on the x∆ t∆ 1l 74 a finite volume runge-kutta ellam method size of the courant number, for reasons of either accuracy or stability. therefore we chose a =1/60 for the sdm (since it performs better when t∆ t∆ = x∆ ) and a time increment of t∆ = 1/71 for the other methods to insure that the courant number is less than one. we then vary t∆ and x∆ separately until we find a solution comparable to that of rk-ellam. for compactness of presentation, we only display representative results in tables 2-7 for all methods 10 10 10 10 10 10 10 10 10 table 4: the performance of the streamline diffusion method with c=1.0,0.1, 0.0001. x∆ t∆ sdm c=1.0 1l error sdm c=0.1 sdm c=0.0001 cpu fig 1/60 1/60 6.355122 210−× 2.826175 × 2− 1.778362 210−× 31.3 3a 1/60 1/120 4.840039 210−× 1.640467 × 2− 8.693459 310−× 61.9 1/60 1/180 4.301432 210−× 1.286264 × 2− 6.161846 310−× 91.8 1/120 1/60 1.352609 110−× 1.924898 × 2− 1.162379 210−× 65.7 1/120 1/120 2.705920 210−× 7.321247 × 3− 3.517420 310−× 125.2 1/120 1/180 1.973977 210−× 4.391139 × 3− 1.805112 310−× 186.0 1/180 1/60 4.366757 210−× 1.642966 × 2− 1.011792 210−× 100.8 1/180 1/120 2.008301 210−× 5.029804 × 3− 2.493366 310−× 189.3 1/180 1/180 1.249368 210−× 2.550667 × 3− 1.145603 310−× 276.2 3b table 5: the performance of the muscl and minmod methods. x∆ t∆ muscl minmod fig 1l error cpu 1l error cpu 1/60 1/71 3.346351 × 310− 0.3 7.759972 × 310− 0.3 4a 1/60 1/180 1.694678 × 210− 0.9 4.127991 210−× 0.9 1/120 1/137 4.059827 × 310− 1.3 2.969584 310−× 1.3 1/120 1/180 3.272317 × 310− 1.7 5.032843 310−× 1.7 1/120 1/300 3.164429 × 310− 2.7 1.374573 210−× 2.8 1/120 1/500 4.423000 × 310− 4.5 1.802668 210−× 4.7 1/180 1/206 4.643784 × 310− 2.9 4.077129 310−× 3.0 1/180 1/300 4.339222 × 310− 4.2 1.300853 310−× 4.4 4b 1/180 1/500 4.166763 × 310− 6.8 5.043802 310−× 7.1 1/300 1/343 4.996610 × 310− 7.9 4.809775 310−× 8.2 1/300 1/500 5.013427 × 310− 11.7 3.558838 310−× 12.4 1/400 1/456 5.102536 × 310− 14.0 5.007080 310−× 14.7 1/400 1/700 5.155649 × 310− 21.8 4.349918 310−× 23.6 75 al-lawatia, robert c. sharpley and hong wang (a) x∆ =1/60, t∆ =1/71 76 (b) ∆ =1/180, x t∆ =1/500 figure 2. gal, qpg, and cpg solutions. a finite volume runge-kutta ellam method (a) x∆ =1/60, t∆ =1/60 77 (b) x∆ =1/180, t∆ =1/180 figure 3. sdm solutions with c = 1.0, 0.1, 0.0001. al-lawatia, robert c. sharpley and hong wang table 6: the performance of the essentially and weighted essentially non-oscillatory schemes. x∆ t∆ eno weno fig 1l error cpu 1l error cpu 1/60 1/71 6.65187 × 210− 0.4 1.90804 × 210− 0.5 5a 1/60 1/120 2.53934 210−× 0.7 1.18621 × 210− 0.8 1/60 1/142 2.49706 210−× 0.8 1.13589 × 210− 0.9 1/60 1/180 2.50508 210−× 1.0 1.09337 × 210− 1.2 1/60 1/500 2.45552 210−× 2.8 1.03442 × 210− 3.1 1/120 1/180 5.86976 310−× 1.9 1.69107 × 310− 2.3 1/120 1/300 5.35956 310−× 3.3 1.02646 × 310− 3.6 1/120 1/500 5.16344 310−× 5.7 8.22716 × 410− 6.0 1/180 1/500 1.60086 310−× 8.3 3.46900 × 410− 9.3 5b 1/180 1/700 1.52986 310−× 11.5 2.82685 × 410− 12.8 considered. these tables include the errors in the norm, and the cpu time (measured on a sun workstation) used in the simulations. in addition we present in figures 2-6 two representative plots for each of the groups of methods described above. one plot uses 1l x∆ and that are as close to those used in the rk-ellam solution in figure 1 as possible, while the other plot uses and fine enough so that a solution comparable to that of the rk-ellam is generated. t∆ x∆ t∆ table 7: the performance of the flux-corrected transport methods etb-fct and yd-fct. x∆ t∆ etb-fct yd-fct fig 1l error cpu 1l error cpu 1/60 1/71 5.62674 × 310− 0.4 9.31359 × 310− 0.5 6a 1/60 1/120 1.11100 210−× 0.7 1.96143 × 210− 0.8 1/60 1/142 1.17590 210−× 0.8 2.04608 × 210− 1.0 1/60 1/180 1.56634 210−× 1.0 2.16396 × 210− 1.3 1/60 1/500 2.17876 210−× 2.8 2.50837 × 210− 3.6 1/120 1/180 1.74395 310−× 2.0 3.20607 × 310− 2.4 1/120 1/300 2.47444 310−× 3.2 3.92427 × 310− 4.1 1/120 1/500 3.74297 310−× 5.6 4.30095 × 310− 7.1 1/180 1/500 8.77504 410−× 8.3 1.32257 × 310− 10.9 6b 1/180 1/700 1.09927 310−× 11.5 1.34855 × 310− 15.4 78 a finite volume runge-kutta ellam method (a) x∆ =1/60, t∆ =1/71 (b) x∆ =1/180, t∆ =1/300 figure 4. muscl and minmod solutions 79 al-lawatia, robert c. sharpley and hong wang . (a) x∆ =1/60, t∆ =1/71 (b) ∆ =1/180, x t∆ =1/500 figure 5. eno and weno solutions. 80 a finite volume runge-kutta ellam method (a) x∆ =1/60, t∆ =1/71 (b) x∆ =1/180, t∆ =1/300 figure 6. etb-fct and yd-fct solutions. 81 al-lawatia, robert c. sharpley and hong wang 4. summary in this paper we develop a finite volume characteristic method for the solution of variable coefficient advection diffusion equations in one-space dimension. this method uses a second order runge-kutta approximation for the characteristics within the framework of the eulerian lagrangian localized adjoint method. the derived scheme conserves mass, fully utilizes the transient behavior of the governing equation, and generates accurate numerical approximations even for large values of the courant number, and thus it permits large time steps in thesimulation. numerical experiments are presented which show that, in the context of linear advection-diffusion equations, the finite volume runge-kutta ellam method outperforms many well perceived and widely used methods, in a standard test example, including the galerkin and petrov-galerkin fem, the streamline diffusion method, the flux-corrected transport methods, and the high resolutions methods muscl, minmod, essentially non-oscillatory method (eno) and weighted eno. the reader is referred to (al-lawatia et al, 1999) for other experiments which compare two finite element formulations of ellam to a wide range of well perceived and widely used methods. 5. acknowledgment this research was supported in part by grants onr/aro-depscor-daag55-98-1-1002 and onr-n00014-91-j-1076. references al-lawatia, m. sharpley, r.c. and wang, h. 1999. second-order characteristics methods for advection-diffusion equations and comparison to other schemes, advances in water resources, 22(7):741-768. boris, j.p. and book, d.l., 1997. flux-corrected transport. i. shasta, a fluid transport algorithm that works, journal of computational physics,135(2):172-186. bouloutas e.t. and celia, m.a. 1991. an improved cubicpetrov-galerkin method for simulation of transient advection-diffusion processes in rectangularly decomposable domains, comp. meth. appl. mech. engrg. 91: 289-308. celia, m.a. russell, t.f. herrera, i. and ewing, r.e. 1990. an eulerian-lagrangian localized adjoint method for the advection-diffusion equation, advances in water resources 13:187206. dahle, h.k. ewing, r.e. and russell, t.f. 1995. eulerian-lagrangian localized adjoint methods for a nonlinear advection-diffusion equation, comp. meth. appl. mech. engrg. 122:223-250. dawson, c.n. 1991. godunov-mixed methods for advective flow problems in one space dimension, siam j. numer. anal. 28:1282-1309. douglas, j. jr. and russell, t.f. numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, siam j. numer. anal. 19:871-885, 1982. healy r.w. and russel, t.f. 1993. a finite-volume eulerian-lagrangian localized adjoint method for solution of the advection-dispersion equation, water resour. res. 29:2399-2413. hughes t.j.r. and mallet, m. 1986. a new finite element formulation for computational fluid dynamics iii, the general streamline operator for multidimensional advective-diffusive systems, comp. meth. appl. mech. engrg. 58:305-328. johnson, c. 1987. numerical solution of partial differential equations by the finite element method, cambridge university press, cambridge. pironneau, o. 1982. on the transport-diffusion algorithmand its application to the navier-stokes equations, numer. math. 38:309-332. russell t.f. and trujillo, r.v. 1990. eulerian-lagrangian localized adjoint methods with variable coefficients in multiple dimensions, in: gambolati, et al., eds., computational methods in surface hydrology 357-363, springer-verlag, berlin. 82 a finite volume runge-kutta ellam method shu, c-w. essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in: a. quarteroni, ed., advanced numerical approximation of nonlinear hyperbolic equations, lecture notes in mathematics, cime subseries, springerverlag, to appear. tóth, g. and odstrčil, d. 1996. comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems, journal of computational physics, 128(1): 82-100. van leer, b. 1984. on the relation between the upwind-differencing schemes of godunov, engquist-osher and roe, siam j. sci. statist. comput. 5:1-20. wang, h. ewing, r.e. and russell, t.f., 1992. ellam for variable-coefficient convectiondiffusion problems arising in groundwater applications, in: russell et al. (eds.), computational methods in water resources ix, vol. i, computational mechanics publications and elsevier applied science, london and new york, 25-31. westerink, j.j. and shea, d. 1989. consistent higher degree petrov-galerkin methods for the solution of the transient convection-diffusion equation, int. j. numer. meth. engrg. 28:10771101. received 4 march 2000 accepted 1 june 2000 83 øñíþé ñæäì æßæêç \( åíáçã \) èçáí introduction temporal rate = 2.06 cpu fig cpu fig minmod fig cpu cpu weno fig cpu cpu yd-fct fig cpu cpu summary acknowledgment references boris, j.p. and book, d.l., 1997. flux-corrected transport. i. shasta, a fluid transport algorithm that works, journal of computational physics,135(2):172-186. bouloutas e.t. and celia, m.a. 1991. an improved cubicpetrov-galerkin method for simulation of transient advection-diffusion processes in rectangularly decomposable domains, comp. meth. appl. mech. engrg. 91: 289-308. electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 7 (2002) 323-332 © 2002 sultan qaboos university deletion designs michael kamau gachii, john wycliff odhiambo and anne wachira department of mathematics, university of nairobi , p.o.box 30197, nairobi, kenya, email: gachii@uonbi.ac.ke. التصاميم اإلنشاطية مايكل كامايو جاشي ، جون ويكلف أوديامبو و آن واشيرا يقدم هذا البحث طريقة إلنشاء نوع من التصاميم العاملية ذات التكرارات المحددة المرنة في شكل مجموعات ويعطي :خالصة . تعابير جبرية إليجاد نقص المعلومات في التفاعالت ذات الرتب المنخفضة abstract: in this paper a method of constructing a class of flexible single replicate factorial designs in blocks is given. simple expressions for calculating loss of information on low order interactions is presented. keywords: asymmetrical factorial designs, generalised cyclic designs, loss of information. 1. introduction c onsider a single replicate factorial experiment involving n factors factors f occurring at levels. let a ,f f iis ...1 2 na ,..., ;1 2 nf a a= denote a treatment combination, where a ( 0 ) is the level of factor f . the number of treatment combinations is then given by i s 1i ia s≤ ≤ − i v 1 n i i = = ∏ (1.1) these treatment combinations will always be lexicographically ordered. that is a treatment combination appears before another treatment combination a if and only if for the first u such that a we have for 1 v a ...1 2 na a a= * * *...1 2 na a a= au ≠ * u * uu aa < ≤ ≤u n. suppose we wish to construct a v 1 n i i = = s∏ single replicate factorial experiment in blocks. we first construct a single replicate single replicate preliminary block design, say d , using one of the known methods, such that for ...1 2 r× × × ir ≥ n i n r r p s 1, 2,...,i = . we can then select l r ,si i i= − i levels of the i-th factor of d and delete from dp p all treatment combinations where factor f occurs at any of the selected levels. the resulting s sil ...1 2 ns× × × single replicate design is referred to as a j-th order deletion design if levels are deleted from j factors. bose (1947) laid the foundation of factorial designs. he used finite euclidean geometry to construct symmetrical factorial designs in blocks. kishen and srivastava (1959) extended the method of finite geometries to the construction of balanced confounded asymmetrical factorial designs thereby introducing the idea of deletion. john and dean (1975) proposed a simple method of confounding based on the properties of generalised cyclic designs from a set of generating 323 m.k. gachii, j.w. odhiambo and a. wachira treatments or generators and showed that the confounding patterns could easily be determined from these generators. more recently voss (1986) has constructed nearly orthogonal single replicate factorial designs in blocks. he uses the deletion technique where he deletes from the first factor, without loss of generality, to obtain first order deletion designs. the most recent contribution in this direction is that of chauhan (1989) who generalized the work by voss (1986), by constructing efficient single replicate designs using the generalized deletion technique. starting from an single replicate generalized cyclic design, levels are deleted from the first factors, without loss of generality , to obtain an ( ) deletion design. ns 1m 1 1 m n ms l s −− the overall objective of the present study is to give results for the general order deletion designs of the form s s which are proper, for 1( ) 11 mn m l− − 1l s≤ ≤ − and less than or equal to the number of generators of the preliminary single replicate generalized cyclic design. the efficient proper single replicate designs of the form 1m ( ) 1ns l s −− given by chauhan (1989) thus become special cases of the results obtained in this study. the method proposed by john and dean (1975) is used to construct the preliminary single replicate factorial design, which is always symmetric. that is, factor occurs at sif i s= levels for all 1, 2,...,i n= . conditions are given which guarantee the existence of either proper or improper deletion designs. simple formulas for calculating the loss of information, due to confounding with blocks, on main effects and two factor interactions are given. a simple method of choosing a fraction for estimating main effects and low order interactions is also given. 2. notations we shall first assume the fixed effects linear model ah a h ahy µ τ β ε= + + + (2.1) where denotes the observed yield from treatment combination a in the h-th block; ahy aτ denotes the effect of the treatment combination a ; hβ denotes the effect of the h-th block and ahε are uncorrelated random errors with mean zero and variance 2σ . let ( )ahy y= and ( )aτ τ= denote v 1× vectors of observations and treatment effects respectively, each lexicographically ordered by a. that is the i-th row corresponds to the i-th treatment in the above arrangement of the v treatment combinations. we shall denote the incidence matrix, the intrablock matrix, the diagonal matrix of block sizes and the number of blocks, respectively, by n, a, k and b . the i-th row of the incidence matrix n corresponds to the i-th lexicographically ordered treatment combination . the qa 1× vectors of ones and of zeros will be denoted by 1 and , respectively. a generalized interaction will be denoted by a where q 0q x ...1 2 nx x x x= such that 1x j = if jf is present in the interaction and otherwise. a v contrast vector will be denoted by c where 0jx = 1× x c c (2.2) ........1 2x xx 1 2c c= ⊗ ⊗ ⊗ n x n with being an vector of ones if ixic lis × 0,jx = otherwise it is an s li × contrast vector. the minimum variance unbiased estimator of the generalized interaction a is represented by cx x τ′ , where iτ , the i-th element of τ , is the estimate of the fixed effect of the i-th treatment combination. we shall denote the set of n factors { by , ,..., }1 2 nf f f { }1, 2,..., n . then for a non-empty subset will denote the vector (factorial) space of contrast vectors { , ,..., } {1, 2,.., }, ( , ,..., )1 2 r 1 2 ri i i n v i i i⊂ 324 deletion designs xc corresponding to the estimator of the generalized interaction xα , where { } { , ,..., }1 2 rj i i i⊂ and jx 0= otherwise. all the notations corresponding to the preliminary design will carry the subscript p while those corresponding to the deletion design will carry no subscript. m n 1 = sumg 2 3 ,..., mg g g ( -1 m 1m d p a j s≤ / 2 / 2jl a s= = 1j 1 / 2j s s s a − 1, ..., s a = − + ( ) -ssi j ( ) si f 3. some properties of deletion designs we start by giving results useful in constructing deletion designs which can be used to estimate the main effects and also the results are useful in calculating loss of information due to confounding in blocks. theorem 1: if is a generalized cyclic design generated by generators such that of the first rows of an identity matrix of order and are the last rows of an identity matrix of order , then there exists a proper deletion design of order , provided . ns ( -n m + 1 ≤ )1 ) j , n m m let be the jd ir s× matrix obtained from an js s j× identity matrix by deleting the t-th row if the t-th level is deleted from factor in the preliminary design d to obtain the deletion design . in our study, . we now state the following result. jf p , s s j= = 1, 2,..., j n lemma 1: suppose levels are deleted in descending order from factor f and let j be an s s× permutation matrix with 1 in the -th column of the 0-th row. then for aja j we have ( ) ( ) ' ' , if 0 if 0 and 1, 2,..., 1 2 , if 1, 2,..., and , if 1, 2,..., 1 0, if , 1,...and 0 or if j j a j j js l s l j j j j j j j s l s l a l d p d l s l l a a s l a l a a a l s a s a ≠− −  =  − = = −  = − =  − − = + + −  = − − + ≠ and for a s we have / 2 j > ( ) ( ) ' ' , if 0 2 if 1, 2,..., , if ..., 0, if , 1, 1 j ja j js 1 s 1 j j j j s l s l l a l d p d l a l l s a l a a s − − =   =  − = − −  = + − next let c be the contrast vector represented by one of the columns of the matrix j ( ) s which span the space of dimensional contrast vectors, where s is an s dimensional identity matrix and that is an s'( ) ( ) 1 1 ,s s sj = ( ) s× matrix of 1 . also, let the rows and the columns of the matrix ' s ( ) ( ) s ssl j− be numbered as 0,1, 2,..., 1s − . note if levels were deleted from factor l jj in the preliminary factorial design, then the contrast vector c is one of the columns of the matrix ( ) ( ) s l ( )ls s lj− −− 1,i − where l s 2,..., 1.= − 325 m.k. gachii, j.w. odhiambo and a. wachira lemma 2: ( ) ( ) ( ) ' ' 1 , if 0 , if 0 and 0 1 if 0 and 1, 2,..., 1 j j a j j j j j j s s a c d p d c s l a s l s l a l s  − =  = − = ≠  − − − = = − next for a and we have the following results. 0j ≠ 1, 2,..., 1l = s − a lemma 3: if a s and ( provided a s/ 2j ≤ 1, 2,..., jl = / 2j ≠ when / 2l s= ) or if and then / 2ja s> 1, 2,...,l = js a− , for or and 2 , for , otherwise j 1 j 2 j 1 a j j j j j j 1 2 l c c c c d p d c s l c s 2ω ω ω ω ω − ∈ ∈ ∉ ′ ′ = − ∈ ∩  − ω∩ l= ) where of the matrix {the columns 1, 2,..,1 ja iω = − ( ) (( ) s l ss l i j l− −− − } = {the columns , 1 2ω , 0, 1, 2, ......, 1ja i i l+ = − ,1,0s l− − ,...,2 −= li of the matrix ( ) ( ) ( )s l j s ls l i − −− − }. lemma 4: if a sj ≤ / 2 and l a a s aj j j= + + − −1 2, ,..., 1 then 1, for or and , for , otherw ise j j j 2 j 1 a j j j j j j j 1 2 j a c c c c d p d c s l a c l s a ω ω ω ω ω  − 2∈ ∈ ∉  ′ ′ = − − ∈ ∩  − − ∩ ω where of the matrix {the columns 0,1,2,...,1 jaω = ( ) ( ) ( )s l ss l i j l− −− − }, {the columns s-l-2 jaω = of the matrix ( ),i i+ = 0,1, 2,.., 1ja − ( ) ( )s ls l i j s l− −−− }. lemma 5: if a s and l s or if / 2j < , 1,..., 1j ja s a s= − − + − / 2 and / 2ja s l s= = then 0.= a j cj j j jc d p d′ ′ lemma 6: if a s and then / 2j > 1, 2,..., 1j jl s a s a a= − + − + −j , for and , for 2 , otherw ise j j 1 j 2 j 1 a j j j j j j j 1 2 j a s c or c c c d p d c a l c a l s 2ω ω ω ω ω  − ∈ ∈ ∉  ′ ′ = − ∈ ∩  − − ω∩ where of the matrix {the columns , 1, 2,...,1 ja i i lω = − = ( ) ( ) ( )s l ss l i j l− −− − }, {the columns s, 0,1, 2,.., 12 ja l i i s aω = − − = j− − of the matrix ( ) ( ) ( )s l ss l i j l− −− − }. lemma 7: if a s and then c d/ 2j > , 1,..., 1j jl a a s= + − 0. a j j j j jp d c′ ′ = 4. loss of information on main effects dean (1978) showed that for a given vector c , the loss of information x , 0 1x xϕ ϕ≤ ≤ , due to confounding in blocks is given by 326 deletion designs 1x x c x x x c nk n c c ϕ ′ − ′ ′ = (4.1) where is the incidence matrix and is a diagonal matrix of block sizes. n k we shall use the notation ( ) a j a s l j j sj d 1 d p d 1 l− −′ ′= where ( a j a s l j j sj d 1 d p d 1−′ ′= )l− d is as given in lemma 1 and d d .......a a a a a a1 2 k 1 2 kd= × × × we shall also write d c* a j a j j jj d p d c j′ ′= (4.2) where c d is as given in lemmas 2, 3, 4, 5, 6, and 7. a j j j j jp d c′ ′ 1− ms we consider deletion designs of the form blocks of size derived from an s generalized cyclic design d with 1 1( ) with n m m n ms s l b sλ− −− = p 1(1/ ) ( ) n m mk s s lλ −= n (1/ ) and m np pk s bλ λ −= = where n is the number of factors, is the order of the deletion design constructed, is the number of generators and with 1m ib m 1 1/ m i λ = = ∏ ( ), ; 1, 2,..., ,i icf s g i m= =b h as given by john and dean (1975). we give here two results on loss of information on main effects. theorem 2: loss of information due to confounding in blocks on any factor whose levels were not deleted from d to obtain d , is given by 1 ( 1, 2,..., )jf j n m= − p 1 2 1 * . 1 22 1 ... .. ... ..... ...... ( 1)( ) 1 2 n aa a jj 1 j 1 na a a 1 2 j j 1 n x n m mm w da a a a a a a a s s l s λ ϕ − + − + + − ∑ ∑ ∑ = − − d where 1, ... is in the initial block of ... 0, otherwise 1 2 n p 1 2 n if a a a d w a a a = =   a proof: the contrast vector c is as given in (2.2) c is an s unit vector for is an x xt t 1× , 1, 2,..., ; xt1 tt j t n m c≠ = − ( ) 1s l− × unit vector for t n 1, 2, ...,m n1 1n m= − + − + and j x jc is any of the columns of the matrix ( ) ( )s sjsi − . without loss of generality, let c be the i-th column of the matrix x j j ( ) ( )s ssi − j . then we have { ( 1) ( 1) } ( )n m j mx x j 1 2 j 1 j 1 1 1c c is s s s i s s s l− −′ − − − = + − + − − −  = (4.3) ( 1)( ) m n m1s s l s −− − 1 327 m.k. gachii, j.w. odhiambo and a. wachira but (( ) 1 n mm m m s1 1 k s s l λ ) i λ− −−= − (4.4) from john and dean (1975), and chauhan (1989) we have, ' 1 1 1 1 1 11 2 1 2 . ... ...... x ax a xx x n n1 n n n nna a an c n n c w c d p d c c d p d ca a a ′′′ xn′ ′= ⊗ ⊗∑ ∑ ∑ = (4.5) 1 2 * 1 2 1 2 1 1 . ... ... ... ... n a jn j j na a a w da a a a a a a a− +∑ ∑ ∑ d therefore using (4.2), (4.3), (4.4) and (4.5) in (4.1) we obtain theorem 2. theorem 3: loss of information due to confounding in blocks on any factor whose levels were deleted from d to obtain d , is given by 1 1 ( 1, 2,..., )jf j n m n m n= − + − + p 1 * 1 2 1 1 2 1 1 2 22 1 ... ... ... ... .... ( 1)( ) a jj 1 j n j 1 j na a an x n m mm w da a a a a a a a a a s l s l s λ ϕ − + − + + − ∑ ∑ ∑ = − − − d where 1 2 1 2 1, if ... is in the initial block of w =... 0, otherwise n p n a a a a d a a a =   proof: the contrast vector c is as given in (2.2), c is an sx txt 1× unit vector for t n ; is an ( unit vector for 11, 2,...,= − m xt tc ) 1s l− × 1 1, and 1, 2,..., j x jt n m n m n c≠ = − + − +t j is any of the columns of the matrix ( ) (( ) )s l j− si− − l−s l . without loss of generality, let jx jc be the i-th column. then we have 1 1 1 1 1 12 1 { ( ) ( 1) ( ) ( 1) ( ) }( ) n m j n m 1 x x j n mn m n m j n m n j is s l c c s l s s l s l i s s l s l − − + − ′ − + −− − − + −  − + =   − − − + − − − − −  1 − = ( (4.6) )( )s l s l sm n m− − − −1 1 1 but we know that * 1 1 ' 1 2 1 2 1 2 . ... ... ... ... a jn j j+ n x x a a an c nn c w d da a a a a a a a ′ = ∑ ∑ ∑ cf.(4.4). therefore using (4.4), (4.5) and (4.6) in (4.1) theorem 3 follows. 5. confounding in deletion designs the following results in confounding in generalized cyclic designs are due to john and dean (1975). the number of degrees of freedom confounded with blocks for any given interaction, α x is given by y k (5.1) 1 2 11 2 1/ ... ( )... j jn n n xx a a a a j w za a a = = ∑ ∑ ∑ ∏ 328 deletion designs where 1, if 0 and 1 1, if 0 and 1 1, if 0 j j j x j jj j s a x z aa x  x − = =  = − ≠ =  = and 1 2 1 2 1, ... is in the initial block of ... 0, otherwise n p n if a a a a d wa a a = =   if the number of degrees of freedom in (5.1) is zero the interaction is unconfounded with blocks and if it is the interaction is totally confounded with blocks. consider any interactions between the n factors, say the interactions of the factors let ( 1) n x j j 1 s = −∏ ., ,...,i i i1 2 rf f f (5.2) '(( ))ija a= where a is from the i-th generator ij 1` 2 1 2... , 1, 2,..., and , ,..., .i i i ing a a a i m j i i ir= = = consider all the f f× sub matrices contained in the 1j -th, 2j -th, .... fj -th rows of a and let ...1 2 fj j j h be the absolute values of their determinants ( , ).f r f m≤ ≤ define fh as follows . (5.3) 1 2 1 21 2 1, if =0 ( \ { , ,..., } { , ,..., }) if 0< <... 0, if f f j j j f r f h hcf h j j j i i i f f m = ⊂ >      m = in our case the treatment combinations in the initial block are of the form 1 1 2 2 ... ( 0,1,..., 1; 1, 2,..., )m m i iu g u g u g u k i m+ + + = − = the number of treatments in the initial block with -th, -th, ..., -th factors all zero is given by where 1i 2i ri 1 2... m r i i ir s w− 1 -1 1 1 2 1 22 1 2 ( , / ) if and 0 s ( \ { , ,..., } { , ,..., }) if . .. ...r r f f r f = r g i i i g rj j g hcf s h h r m h w hcf w j j j i i i g r mj ≤ ≠∏ = ⊂ < ≤ 1 2 1 2 1 2 (w \ { , ,.., } { , ,.., }, if (5.4) .. r g m rj j m s hcf j j j i i i r mj −       ⊂ >  where g is such that and 1 20 and ... 0.g g gh h h+ +≠ = = 1g = if 1 0h = . let y be denoted by x ..1 2 hj j j y where x has the 1j -th, 2j -th, ..., hj -th digits unity and the remainder zero. then it can be shown that for the interactions of the factors the number of degrees of freedom confounded with blocks is given by 1 2 ,i if f ,..., r if (5.5) 1 ... ... ... 1 2 1 21 2 1 1 21 ( \ { , ,.., } { , ,.., }) 1 r r g r i i i i i j j j g r g y w y j j j i i i − = = − ⊂∑ − 329 m.k. gachii, j.w. odhiambo and a. wachira we now give the following results. theorem 4: for the generalized cyclic designs of theorem 1, all the main effects are estimable with full efficiency. proof: for the main effect of factor , 1, 2,...,jf j n= we have, using (5.3), and w1 1h = 1j = by (5.4). thus, using (5.5), y 0j = . theorem 5: all the r-factor interactions among any number of the first ( )1n m− + factors, and all the r-factor interactions among at least two of the first ( )1n m− + factors, and any number of the last factors, are partially confounded with blocks provided ( 1m − ) r m≤ . proof: for the r-factor interaction, r we have from equation (5.4) 2, 3,.., 1,n m= − + )r 1 ...1 2 r r j j jw s= and thus equation (5.5) yields ...1 2 0 ( r r j j jy s≠ < − thus all the interactions between at least two of the first ( )1n m− + factors are partially confounded with blocks. for the submatrices of the matrix corresponding to the r-th factor interactions between at least two of the first 3, 4,..., ,r n= r r× a ( )1n m− + factors and any number of the last ( )1m − factors are singular. therefore using equation (5.4) we obtain 1 2 ...2 r r j j jw s −= and using equation (5.5) we get ...1 2 0 ( r r j j jy s )r≠ < − we can therefore conclude that all these factor interactions are partially confounded with blocks. hence the theorem. r confounding in deletion designs has been studied by chauhan (1989). theorem 6 below is due to her. let α x be a given interaction. then the factors or simply {1 2, ,..., nf f f }1, 2,..., n can be partitioned into three mutually exclusive and exshaustive sets and1 2 3ω , ω ω as follows: 1ω contains the factors whose levels were not deleted from d to obtain d , that is {p }1, 2,..., n m− 1 ; contains the factors whose levels were deleted from d to obtain d and these factors are not in the factorial space v , that is the factors 2ω p x { }1,n m 2,...,1 1n m 1n m a− + − + − + ; 3ω contains the factors whose levels were deleted from d to obtain d and these factors are in the factorial space , that is factors{ p xv }1 11,n m a n m− + + − ( ),..., rj 1 j 2,..., ;n a+ ... jx= = = 0= 1 r = ,1, 2,..., ma+ 1 2 j jx x . we shall write the factorial space as v j j if and all other xv 1 2, x ‘s are zero, where 1 2 , } {{ , ... r 1, 2,..., }j j j n 1 2, ,..., {ri i i⊆ . let { , then we have the following theorem. 1}m} 1, 2,..., n⊂ − theorem 6: (chauhan (1989)). let the contrast vector 1 2 1( , ,..., , 1, x rc v i i i n m a∈ − + + 1n m− + a + 2,..., )n and let 330 deletion designs c (5.6) 'x xp d c= then where 1 2 1 1( , ,..., , , 1, 2,..., ) x p p rc v i i i g n m a n m a∈ ⊕ − + + − + + n )2(g ω∈ ρ 1 2 ...d ; that is g belongs to the power set of denotes the direct sum, where and 2ω ⊕ nd d d= ⊗ ⊗ ⊗ again where is as defined in lemma 1. jd we now state the following results: theorem 7: for the deletion designs of order m derived from generalized cyclic designs of theorem 1, all the main effects of the first factors are partially confounded with blocks, while all the main effects of the last m factors are fully estimable. ( n m− ) ) this makes it possible to proof the following theorem. theorem 8: if then for the deletion designs of the form 1,m = 1 (ns s l− − the main effects of the first factors are partially confounded with blocks and the loss of information on factor f is given by ( 1n − 1, 2,...,j = ) j ( )1n − ϕ x l s s = − −( )(1 l) provided . / 2l s< proof: from theorem 7 we know that the main effects of the first ( )1n − factors are partially confounded with blocks. ( ) ( ) 1 2 1 2 1 1 1 2 * ... ... ...... 1 n jj+ n n a a a a a a a a a a a a x 2 n m 2 w d d s s l s ϕ + − = − − ∑ ∑ ∑ j 2 (5.7) using theorem 2. but by lemma 1, if 0 ≠ l / then (5.8) , 0 2 , , n n a n n n n n s l if a d s l if l a or a l s s l a if a l or if a l s − =  = − ≤ + ≤  − − < + > therefore due to the nature of the treatment combinations in the initial block, lemma 2 and equations (5.7), (5.8) yield: 2 2 2 1 2 1 ( 1)( ) 2 ( ) ( 2( 1) 1) ( 1)( ) n l 1 n n n n a x n s s s s l s s s l a s s s l s s l s ϕ − − − − = − − − − − − − − − −∑ = − − l s l = − as required. 6. concluding remarks these designs give us a simpler method of constructing asymmetrical factorial designs in incomplete blocks. we note that confounding patterns are easily determined from the information gathered from the preliminary factorial designs. expressions for loss of information in terms of the number of levels, s, of the factors in the preliminary design and the number of levels, l, deleted from ‘j’ factors have been derived. 331 m.k. gachii, j.w. odhiambo and a. wachira references bose, r.c. 1947. mathematical theory of the asymmetrical factorial design, sankya, 8: 107-166. chauhan, c.k. 1989. construction of efficient single replicate designs, preprint. gachii, k.m. 1993. on the construction of deletion designs, ph.d thesis, university of nairobi. gachii, k.m. and odhiambo, j.w. 1998. asymmetric single replicate designs, south african statistical journal, 32:1-18. john, j.a. and dean, a.m. 1975. single replicate factorial experiments in generalized cyclic designs: i symmetrical arrangements, journal of the royal statistical society, b, 37: 63-71. voss, d.t. 1986. first order deletion designs and the construction of efficient nearly orthogonal factorial designs in small blocks, journal of the american statistical association, 81: 813-818. received 9 november 2001 accepted 28 october 2002 332 deletion designs michael kamau gachii, john wycliff odhiambo and anne wachira department of mathematics, university of nairobi , p.o.box 30197, nairobi, kenya, email: gachii@uonbi.ac.ke. ãçíßá ßçãçíæ ìçôí ¡ ìæä æíßáý ãæï 2. notations (2.2) photovoltaic cells and systems: science and technology, special review (2000) 137-155 © 2000 sultan qaboos university 137 geological and engineering classification systems of mudrocks amer al-rawas*, tariq cheema** and mohammed al-aghbari* *department of civil engineering, college of engineering, sultan qaboos university, p. o. box 33, al khod 123, muscat, sultanate of oman, and **department of earth sciences, college of science,sultan qaboos university, p. o. box 36, al khod 123, muscat, sultanate of oman. أنظمة التصنيف الجيولوجي والهندسي للصخور الطينية الرواس ، وطارق شيما ، ومحمد األغبري عليعامر واجه عادة في تي تُ تعرف الصخور الطينية بانها مجموعة متعددة من الصخور الرسوبية الطينية ناعمة الحبيبات وال :خالصة ازاحة الغطاء الترابي والتغيرات في المحتوى الرطوبي للتربة الى ونتيجة للحفر، فقد يؤدي . معظم انواع المشاريع الهندسية ونظراً الن معظم هذه . تغيير بنية انواع محددة من الصخور الطينية التي تبدو متصلبة وتحويلها الى مادة شبيهة بالتربة . معقدة ت مشكالالصخور ليست لديها القدرة على التحمل ، فقد اكتسبت السمعة بانها صخور رخوة منطوية على حيث ان . وتواجه الجيولوجيين والمهندسين مشكلة اختيار عوامل كافية لتقييم السلوك الهندسي للصخور الطينية بصورة دقيقة ال يعتبر كافيا على االطالق ، ولذا يفضل عادة استخدام مجموعة من ) على سبيل المثال حجم الحبيبات (استخدام عامل واحد وتعتبر قوة الضغط ، ودليل التحمل ، وخصائص اللدونة ، وقدرة االنتفاخ ، واالمتصاص ، . ه الصخور العوامل لتصنيف هذ وللتغلب على هذه المشكلة فقد كرس مؤخرا اهتمام . والكثافة بعض العوامل التي استخدمها العديد من الباحثين في الماضي لمحتوى الطيني ، التركيب الطيني ، البنية ، معدالت تكرار ، ا حجم الحبيبات (بحثي واسع الستخدام الخواص الجيولوجية وتصف هذه الورقة أصل وحدوث الصخور . مع الخواص الهندسية الغراض التصنيف ) الكسر ، درجة الترقق ، وغيرها .الطينية ومختلف انواع فحوص وأنظمة التصنيف abstract: mudrocks are a diverse group of very fine-grained argillaceous sedimentary rocks that are frequently encountered in most types of engineering projects. upon excavation, the release of overburden stress and changes in the moisture content may cause certain apparently well indurated mudrocks to slake, producing a soil-like material. because many mudrocks are nondurable, they have gained a reputation as problematic soft rocks. geologists and engineers are confronted with the problem of selecting adequate parameters for accurately evaluating engineering behavior of mudrocks. the use of a single parameter (e.g. grain-size) is never considered to be enough and a combination of several parameters are normally preferred for the classification of mudrocks. compressive strength, slake durability index, plasticity characteristics, swelling potential, absorption and density are some of the parameters that had been used by several investigators in the past. in order to overcome this problem, considerable research attention has recently been devoted to the use of geological properties (grain size, clay content and clay composition, texture, fracture frequency, degree of lamination, etc.) in conjunction with the engineering characteristics for classification purposes. this paper describes the origin and occurrence of mudrocks, and their different types of classification tests and systems. al-rawas, cheema, and al-aghbari contents 1. introduction 138 2. origin and occurrence of mudrocks 138 3. geological terminology 139 4. mudrock classifications 139 4.1 grain size classifications 141 4.2 mineralogical classifications 141 4.3 strength classifications 142 4.4 testing procedures 143 4.5 durability classifications 144 4.6 swelling potential classifications 148 4.7 soil-like mudrocks classifications 152 5. conclusions and summary 152 6. references 152 1. introduction mudrocks which include shales, mudstones, siltstones and claystones are defined as fine to very fine-grained silici-clastic sediments or sedimentary rocks (grainger, 1984). they account for approximately two-thirds of the strategraphic column (blatt, 1982) and one-third of the total land area (franklin, 1983). many of the mudrocks that are commonly encountered in engineering projects exhibit deterioration, swelling and shrinking phenomena due to low durability to weathering and exposure to changes in their moisture content, which results in slope stability problems, ground heave and embankment failures, and subsequently damage and distress to structures. expansive mudrocks swell when given access to water and shrink when they dry out. the problems associated with expansive mudrocks are worldwide, occurring in several countries mainly in arid and semi-arid regions in australia, asia, middle east, africa, europe, united states of america and south america. the cost of damage and repair to structures affected by expansive mudrocks and soils are alarming. in the united states alone, the annual losses are between $6 billion and $11 billion in damages to houses, buildings, roads, etc. (nuhfer, 1994). the cost of repair to buildings and light structures in the united kingdom has been estimated at $100 million per annum (williams et al., 1985). the classification of mudrocks presents an important problem due to their wide range of engineering geological characteristics (gamble, 1971). although several mudrock classification schemes have been proposed (underwood, 1967; morgenstern and eigenbrod, 1974; olivier, 1976, potter et al., 1980; taylor and spears, 1981; grainger, 1984; taylor, 1988), none have gained general acceptance. this lack of acceptance may be attributed to the fact that classifications do not take into account the geological and engineering properties in their entirety and are based on very few classification parameters. also the laboratory/field tests used for the classification purposes inheret some degree of uncertainty which is not accounted for while classifying mudrocks. the classifications are also considered to be of limited use because they are developed using a small number of samples representing a limited variety of mudrocks. the aim of this paper is not to suggest a new classification system but to provide a condensed critical review of existing geological and engineering classifications of mudrocks. it includes origin, mineralogical composition, geological and engineering classifications, and some applications of mudrocks. 2. origin and occurrence of mudrocks mudrocks are formed under depositional environmental conditions in which fine sediment is abundant and water energy is sufficiently low to allow suspension settling of fine silt and clay. they are particularly characteristic of marine environments adjacent to major continents at places where the sea floor lies below 138 classification systems of mudrocks 139 storm wave base levels (potter et al., 1980). in addition, mudrocks can form in lakes and in quiet-water parts of rivers and in lagoonal, tidal-flat, and deltaic environments (boggs, 1987). mudrocks are by far the most abundant type of sedimentary rocks. this is because of the fine-grained silici-clastic products of weathering which greatly exceed coarser particles. mudrocks commonly occur interbedded with sandstones and limestones in units ranging in thickness from a few millimeters to tens of metres. some varieties of mudrocks (e.g. shales) are found to be hundreds of metres thick with widespread areal extent (boggs, 1987). 3. geological terminology the term “mudrock” generally refers to fine-grained sedimentary rocks and includes shales, mudstones, claystones and siltstones. however, there is a lack of agreement among researchers on the classification of fine-grained sedimentary rocks due to their wide range of geological and engineering characteristics. the main sources of ambiguities are: (a) the term “shale” can be used in a restricted sense as a fissile or laminated rock, (tourtelot, 1960). it has also been used as a group name for all fine-grained sedimentary rocks by many authors, (grainger, 1984). (b) the use of the term “mudrock” in engineering geology to encompass argillaceous engineering “rocks” as opposed to clay “soils”, (de freitas, 1981; taylor and spears, 1981). (c) there is a lack of agreement on both the grain size definition and grain size distribution for siltstones, mudstones and claystones. to avoid this confusion, it is suggested that the term “mudrock” be used as a general group name and the term “shale” be restricted to the fissile or laminated rocks, (ingram, 1953; blatt et al., 1972; spears, 1980; taylor and spears, 1981). therefore, the terms “mudstone”, “siltstone” and “claystone” should be restricted to non-fissile rocks (clark, 1954). grainger (1984) proposed a broad definition which includes all fine-grained soils and considers grain size, mineral composition, texture and compressive strength. mudrock is defined as fine to very finegrained silici-clastic sediment or sedimentary rock. further, the descriptive terms of this definition have been quantitatively defined as shown in figure 1. since natural materials encountered in practice are borderline and difficult to classify as either “hard soil” or “soft rock”, it is suggested that a broad definition of mudrocks is used and includes engineering clay soils. this preference is supported by the fact that a competent mudstone at surface may well behave like a clay in a deep mining situation. the inclusion of clay soils in the definition of mudrocks has been previously suggested by taylor and spears (1981) and grainger (1984). 4. mudrock classifications mudrocks may be classified into different types based on their geological and engineering properties. the identification of the most useful and relevant index rock properties is of prime importance, as description of lithology alone can lead to gross errors, (olivier, 1979). some of the other prerequisites for rock classification are mentioned by franklin (1970) and bieniawski (1974a). they suggested that classification should be: 1. based on measurable parameters which can be determined by relevant tests quickly and cheaply in the field. 2. involve only rapid testing techniques which are able to cope with a large number of routine samples. 3. testing techniques should be simple enough to be carried out by semi-skilled field laboratory staff. 4. the range of test results values should allow for a sufficient power of discrimination when applied to various test samples. al-rawas, cheema, and al-aghbari non-mudrock (sandstone, etc) > 35 < 35 < 65> 65 non-mudrock (limestone, etc) < 50> 50 non-mudrock (tuff, etc) < 50> 50 non-mudrock (chert, etc) > 100< 100 non-mudrock (slate, argillite, etc) mudrock sample % of total wt. = clastic grains 3. texture sem thin section % of grains < 60 µm (by wt.) 1. grain size distribution sieving thin section % of total wt. = quartz + clay % of total wt. = silicates 2. composition chemical analysis xrd thin section σc (mn/m 2) 4. compressive strength perpendicular to fabric unconfined compression point load cone indenter figure 1. the definition of mudrock (grainger, 1984). 140 classification systems of mudrocks keeping in mind the above mentioned recommendations, classification based on geological properties such as grain size and mineralogy are reviewed here. similarly, engineering index properties worth considering are strength, durability, swelling and plasticity characteristics. since geological properties control the engineering behaviour of rocks, (vutukuri et al., 1974; tsidzi, 1990), they are discussed first. 4.1 grain size classifications grain size is an important parameter in the classification of mudrocks. purnell and netterberg (1975) presented table 1 summarizing some of the commonly used geologic classifications. table 1 was extended to cover the classification proposed by pettijohn (1975). the classifications differ mainly in the use of the group term. the classifications of ingram (1953), pettijohn (1957), and blatt et al. (1972) use mudrock as the group term, whereas those of twenhofel (1939) and pettijohn (1975) use mudstone and argillaceous sediment, respectively. grain size classification requires the determination of clay size fraction which is normally done by carrying out a grain size distribution analysis. the procedure is described in british standard 1377 (1990) and in d-422 (astm, 1990) and involves wet sieving and hydrometer analysis. for indurated mudrocks, samples have to disaggregated first by cycles of wetting and drying as crushing will break the original clay minerals (spears, 1980). poorly indurated mudrocks may disaggregate after one or two cycles, whereas well indurated mudrocks may require up to eight cycles (dick et al., 1994). table 1. some geological classifications of mudrocks(1) (purnell and netterberg 1975). notes: (1) mudrock : sedimentary rock composed of at least 50% silt plus clay, with no restriction as to their relative amounts or as to the breaking characteristics (ingram 1953). (2) an indurated material is strictly only one which does not slake (disintegrate) in air or water. (3) an argillite is a rock indurated by slight metamorphism to a material between a mudrock proper and a slate. the term is generally used for rock which is none-fissile (clark 1954), but if fissile, does not yet possess the slaty cleavage of a slate. (4) the particle size of > 0.01 mm is used for the definition of siltstone. 4.2 mineralogical classifications the mineralogical composition of mudrocks plays an important role in their behavior, particularly the “soil-like” mudrocks. without a thorough understanding of the mineralogical composition, engineering 141 al-rawas, cheema, and al-aghbari 142 behavior of mudrock can neither be fully appreciated nor accurately predicted, (taylor and spears, 1981). in the case of siltstones and coarse mudstones, non-clay minerals such quartz, calcite, dolomite, etc. form a major proportion of the total minerals present in the material. in claystones, fine mudstones, shales and stiff clays, clay minerals such as montmorillonite, kaolinite, illite and chlorite are normally abundant. pettijohn (1957) indicated that generally, the average mudrock contains one-third quartz, one-third clay and mica like minerals and one-third other minerals such as carbonates and iron oxides. based on the geological history, climate and weathering processes, the mineralogical composition of mudrocks may vary from one locality to another. however, the engineering behavior of mudrocks not only depend on the amount of clay minerals but also on the types of minerals present (jeremic, 1981). most of the construction problems associated with expansive mudrocks reported in the literature (alrawas et al., 1998) were attributed to the presence of montmorillonite, which is well known as the most “active” clay mineral. in general, older sediments contain less montmorillonite and more illite and chlorite than the younger and are therefore likely to be less problematic. clay minerals are formed by the alteration of the primary rock minerals due to complex processes. in silica rich rocks and minerals in which calcium and magnesium cations are present, under climatic conditions in which evaporation exceeds precipitation, ph is high and leaching conditions are favorable for the formation of montmorillonite (smectite group). on the other hand, in rocks and minerals in which alumina is abundant, magnesium and calcium cations are absent, and in areas where rainfall is relatively high and drainage is good, conditions favor the formation of kaolinite, (tourtelot, 1973). the classification of sediments and sedimentary rocks are based on a triangular diagrams whose apices are sand, silt and clay. in case of mudrocks, depending upon the effectiveness of dispersing techniques, concentration can be biased toward clay or silt categories (picard, 1971). also, spears (1980) notes that the actual grain size analysis can be time consuming for indurated mudrocks where difficulty in disaggregation of the rock may not reveal the real percentage of clay size fraction. spears (1980) proposed a classification based on quartz content (table 2) in which mudrocks are categorized into two groups based on whether a rock is fissile or non-fissile. fissile mudrocks group encompasses flaggy siltstone and shale types, whereas non-fissile mudrocks group encompasses massive siltstone and mudstones types. siltstones are recognized as containing > 40 % quartz. table 2. proposed classification based on quartz percantage (spears, 1980). mudrocks quartz percentage fissile non-fissile > 40% quartz flaggy siltstone massive siltstone 30-40% quartz very coarse shale very coarse mudstone 20-30% quartz coarse shale coarse mudstone 10-20% quartz fine shale fine mudstone < 10% quartz very fine shale very fine mudstone spears (1980) recommends the determination of quartz content directly rather than indirectly through the grain size. in the laboratory, chemical dissoultion or x-ray diffraction methods can be adopted. mudrocks in the field can be compared with standard rocks of known quartz content (by using hand lens and naked eye), sense of touch, and other physical properties such as hardness. 4.3 strength classifications strength is one of the important index parameters used for the engineering classification of mudrocks. several researchers, (deere and miller, 1966; underwood, 1967; morgenstern and eigenbrod, 1974; anon, 1977; grainger, 1984), developed classification systems based on strength. classification systems of mudrocks 143 deere and miller (1966) proposed a scheme based on a plot of the uniaxial compression strength (ucs) and tangent modulus of deformation. the scheme divides the strength of mudrocks into four zones: very low (ucs < 25 mn/m2), low (ucs 25-50 mn/m2), medium (ucs 50-100 mn/m2) and high (ucs > 100 mn/m2). similarly, the ucs values of as low as 0.17 mn/m2 for weak mudrocks and as high as 103 mn/m2 for well cemented mudrocks are reported by underwood (1967). morgenstern and eigenbrod (1974) conducted strength softening tests on 14 different mudrocks. they classified mudrocks into mudstones, hard clays, stiff clays, and medium clays. another classification system based on uniaxial compression strength (ucs) was proposed by the united kingdom geological society working party report (anon, 1977). the system classifies mudrocks into four classes: a very soft rock (ucs < 40 kn/m2), a very weak rock or hard soil (ucs 0.6-1.25 mn/m2), a weak rock (ucs 1.25-100 mn/m2) and a very strong rock (ucs > 100 mn/m2). grainger (1984) proposed yet another mudrock classification based on the uniaxial compressive strength values. the ucs values of 0.6 mn/m2, 3.6 mn/m2, and 100 mn/m2 were proposed as boundaries between fine-grained soil like mudrocks, non-indurated mudrocks, and indurated mudrocks, respectively. 4.4 testing procedures depending upon the type of mudrock, different strength test procedures have been recommended. for very weak mudrocks (or clayey soils), grainger (1984) recommends the straightforward undrained triaxial method of compression testing as specified by morgenstern and eigenbrod (1974). however for stronger indurated mudrocks, the uniaxial compression strength (ucs) is suggested. the choice of uniaxial compressive strength (ucs) for mudrock classification is based on the fact the ucs is the most widely used design parameter in rock engineering. it has been used in most rock mass classification systems for engineering purposes, (bieniawski, 1973; barton et al., 1974; laubscher, 1977), and is an important parameter in rock mass strength criterion, (hoek and brown, 1980). the uniaxial compressive strength is also used in estimating workability of rock, (franklin et al., 1971; wood, 1972), evaluating the use of rock as a construction material, and predicting the utilization possibilities of a tunnel boring machine (jenni and balissat, 1979). according to a survey reported by bieniawski (1974b), mining engineers request the uniaxial compressive strength more often than any other rock material property. the procedure for the uniaxial compressive strength test has been standardized by both the international society for rock mechanics (isrm) and the american society for testing and materials (astm) designation d-2938-71a. the mudrock core sample of length twice the diameter ratio is tested in an uniaxial testing machine. although, the procedure to determine ucs by using ucs testing machine is simple, it requires sophisticated laboratory equipment and meticulously prepared rock cores of specific dimensions. these rock cores are not always available. also, loosely cemented, poorly indurated, and highly laminated mudrocks disintegrate during drilling process, making it almost impossible to obtain core samples even with special drilling techniques. as a result, determination of compressive strength by standard procedures tends to be expensive, time consuming, tedious, and sometimes impossible. the problem is further compounded by the fact that mudrocks disintegrate during the drilling process making it almost impossible to obtain core samples even with special drilling techniques. this limitation lured the researchers (olivier, 1976; grainger, 1984) to recommend point load testing for the indirect determination of uniaxial compressive strength. the point load test measures the point load index (is) which is multiplied by a conversion factor "k" in order to obtain the uniaxial compressive strength of a rock. this k value not only depends on the rock type but also on the sample size and shape. the widely accepted k value for most rocks is 24 for 54 mm diameter core (broch and franklin, 1972). however, for mudrocks, k values of as low as 8 to as high as 35 are reported (carter and sneddon, 1977, norbury 1986). cheema (1993) performed point load tests on cube-shaped pieces of different mudrock samples. the procedure involved cutting first 15 to 20 pieces of each mudrock sample by a thin-bladed rocksaw, and then, testing by using a point load tester. they followed the procedure as described by broch and franklin al-rawas, cheema, and al-aghbari (1972). however, because of the penetration of cones in the soft mudrocks, the distance in between the platens (d) was measured after the penetration and was used while calculating the point load index. cheema (1993) calculated the point load index (is) by the following formula: is = p/d² where p is the applied load and d is the distance between the platens after penetration. the mudrock classifications based on the compressive strength by deere and miller (1966) and the united kingdom geological society working party report (anon, 1977) systems are of limited value because their use of the compressive strength as the sole classification parameter and therefore, they are unable to differentiate between rocks of variable durability. 4.5 durability classifications durability is a property that indicates the ability of mudrocks to withstand disintegration due to weathering. durability can be evaluated by the slake durability index test (franklin and chandra, 1972), the rate of slaking test (morgenstern and eigenbrod, 1974), the modified soundness test (wood and deo, 1975) and the simple slake test (stollar, 1976). however, the slake durability index test is the most widely used test (dick et al., 1994). 144 example: durability (2 cycle) = 70 plasticity index = 5 plotted position • classified as medium durability low plasticity • 25 10 2 cycle slaking durability, id2,% retained very high high medium lowvery low 1.0 100 98 85 95 med. high 6030 0 pl as tic ity in de x, p i h ig h m ed iu m l ow figure 2. durability-plasticity chart of gamble (1971). classification systems of mudrocks several classification systems were developed to assess the durability behavior of mudrocks. gamble (1971) developed a durability-plasticity chart (figure 2) for mudrocks based on two-cycle slake durability tests. the chart divides durability into six classes: very low, low, medium, medium high, high and very high. taylor and spears (1981) suggested the adoption of gamble’s (1971) classification for less indurated types of mudrocks. morgenstern and eigenbrod (1974) developed a durability classification system based on liquid limit and rate of slaking values. olivier (1979) developed a classification system based on a plot of the swelling coefficient (free swelling from an oven-dry to a saturated condition) against uniaxial compressive strength (figure 3). the system recognizes six rock durability classes: excellent (class a), good (class b), fair (class c), moderately poor (class d), poor (class e) and very poor (class f). the system is particularly relevant to compacted and weakly cemented rocks. the major limitations of the system are the heterogeneous sedimentary rock masses and the variation of strength and free swelling properties of the rock material. taylor and spears (1981) indicated that olivier’s (1979) classification seems to be a promising approach for moderately strong to very strong mudrock types. 145 very high highmed.lowvery low 1000 10010 01 001 10 .0 . 0. 0001 . sw el lin g c oe ff ic ie nt 0 uniaxial compressive strength (mn / m2 ) 3 . durability classification of olivier figure ( 1979 ) strohm (1980) developed a durability classification system for highway embankment design based on lithologic characteristics, durability tests and field performance of mudrocks used in the construction of highways in the united states. franklin (1983) proposed a quantitative rating system based on second-cycle slake durability index (id2), plasticity index (pi), and point load strength index (is50). grainger (1984) developed a classification scheme based on strength and durability, (figure 4), which recognized three classes of mudrocks: soil-like mudrocks, non durable mudrocks and durable mudrocks. a compressive strength of 0.6 mn/m2 is taken to be the upper limit of soil-like mudrocks. a non-durable rock has a compressive strength of 0.6-3.6 mn/m2 or 3.6-100 mn/m2 and a slake durability less than 90%. al-rawas, cheema, and al-aghbari soil non-durable rock durable rock > 90 < 90 3.6-100 < 0.6 0.6-3.6 mudrock slake durability % 6. durability 2 cycle slake durability test σc (mn/m 2) 5. compressive strength perpendicular to fabric quick undrained triaxial compression figure 4. the classification of mudrock by strength and durability (grainger, 1984). a compressive strength of 3.6-100 mn/m2 and a slake durability greater than 90% is recommended for a durable rock. grainger’s (1984) classification has the advantage of using both strength and durability, however, it lacks the description of the quality of mudrocks. further, the compressive strength of 0.6 mn/m2 proposed by grainger’s (1984) system as the upper limit of soil-like mudrocks is markedly lower than its equivalent proposed by the working party report (anon, 1977). further classifications by grainger (1984) using the quartz content, (determined by xrd analysis), and the flakiness ratio for the classification of non-durable and durable mudrocks are shown in figures 5 and 6 respectively. dick et al. (1994) proposed a new durability classification based on lithologic characteristics, (table 3), in which durability is classified into three classes: low, medium and high. the second-cycle slake durability index (id2) was used as a measure of the durability, whereas clay content, clay-mineral composition, texture, microfracture frequency, absorption, adsorption, dry density, void ratio, and atterberg limits were used to characterize mudrock lithology. the classification requires an initial geologic classification of mudrocks into claystones, mudstones, shales, etc. using the potter et al. (1980) before the use of the system. according to this classification, all claystones and mudstones with slickensided features have low durability, (id2 < 50%), whereas mudstones characterized by the presence of rough-surfaced microfractures, shales and siltstones have low, (id2 < 50%), to high, (id2 > 85%), durability. table 3. mudrock-durability classification system based on lithologic characteristics (dick et al. 1994). mudstone shale combined siltstonesiltshale durability claystone slickensided imf (microfractures/cm) absorption (%) absorption(%) argillite high: id2 > 85% na na < 0.4 < 5.5 < 5 all medium: 50 < id2 < 85% na na 0.8-0.4 10-5.5 9.5-5 na low: id2 < 50% all all > 0.8 > 10 >9.5 na 146 classification systems of mudrocks figure 5: the classification of non-durable mudrock (grainger, 1984). 20-40< 20 > 40 10. composition xrd analysis % of total wt. = quartz 11. anisotropy fragment dimensions flakiness ratio c/b non-durable mudrock non-durable siltstone silty clayshale nondurable claystone > 2/3 < 2/3< 2/3 non-durable mudstone < 2/3 clayshale shale durable mudstone < 2 > 2 > 2 < 2 durable claystone silty shale durable siltstone > 40 < 20 20-40 durable mudrock max. strength /min. strength 13. anisotropy point load cone indenter % of total wt. = quartz 12. composition xrd analysis figure 6. the classification of durable mudrock (grainger, 1984). 147 al-rawas, cheema, and al-aghbari 4.6 swelling potential classifications the first step in dealing with expansive sediments or sedimentary rocks is to identify their capacity for volume change. once rocks have been identified as expansive, a quantitative characterization of their swelling potential is necessary for design predictions. unfortunately, there is no standard definition of the term swelling potential, available in the literature, (holtz, 1959; seed et al., 1962; snethen, 1979). further, there is no standard swelling potential test, and therefore, it is difficult to make reliable comparisons between results from different sources. the swelling potential of a soil or a rock can be simply defined as a measure of its ability to swell or the pressure required to prevent swelling. table 4. shrinkage limit and linear shrinkage guide to potential expansion (after altmeyer, 1955). shrinkage limit as a percentage linear shrinkage as a percentage degree of expansion <10 >8 critical 10-12 5-8 marginal >12 0-5 noncritical table 5. data for making estimates of probable volume change for expansive soils (after holtz and gibbs, 1956). data from index tests* colloid content (% minus 0.001 mm) plasticity index (%) shrinkage limit (%) probable expansion (% total volume change) degree of expansion >28 >35 <11 >30 very high 20-31 25-41 7-12 20-30 high 13-23 15-28 10-16 10-20 medium <15 <18 >15 <10 low * based on vertical loading of 1.0 psi table 6. degree of expansion based on percent passing no. 200 sieve, liquid limit and standard penetration resistance (after chen, 1965). laboratory and field data* percent passing no. 200 sieve liquid limit (%) standard penetration resistance (blows/ft) probable expansion (% total volume change) degree of expansion >95 >60 >30 >10 very high 60-95 40-60 20-30 3-10 high 30-60 30-40 10-20 1-5 medium <30 <30 <10 <1 low * based on loading of 1000 psf. 148 classification systems of mudrocks table 7. swelling potential classification based on plasticity index (after chen, 1988). swelling potential plasticity index (%) low 0-15 medium 10-35 high 20-55 very high 35 and above atterberg limits, clay content and activity are widely used for indirect quantification of mudrocks swell potential. many classifications systems provide qualitative assessment of the degree of expansion such as low, medium, high and very high, or noncritical, marginal and critical. altmeyer (1955) developed a criteria based on shrinkage limit and linear shrinkage as given in table 4. however, recent research failed to show conclusive evidence of the correlation between swelling potential and shrinkage limit (chen, 1988). holtz and gibbs (1956) proposed a classification system based on atterberg limits and clay content as shown in table 5. chen (1965) developed a classification based on percent passing the no. 200 sieve size, liquid limit and standard penetration resistance (table 6). he also developed a criteria for the estimation of swelling potential based on plasticity index alone as given in table 7, (chen, 1988). seed et al. (1962) established a relationship between the percentage of clay sizes, activity and swelling potential (figure 7) based on tests done on clays compacted to maximum density at optimum water content according to the american association of state highway officials (aashto). raman (1967) proposed a classification for the degree of expansion based on plasticity index and shrinkage index (table 8). dakshanamurthy and raman (1973) proposed a classification scheme based on liquid limit alone (table 9). van der merwe (1975) developed a chart for determining expansiveness of soils, (figure 8), based on plasticity index and clay content. figure 7. swelling potential classification 0 1 0 10 20 30 4 clay fraction (seed et al ., 1962). 2 3 4 5 6 7 8 0 50 60 70 80 90 100 (% < 0.002 mm) a ct iv ity low med high very high 149 al-rawas, cheema, and al-aghbari table 8. degree of expansion classification based on plasticity index and shrinkage index (after raman, 1967). plasticity index (%) shrinkage index (%) degree of expansion <12 <15 low 12-23 15-30 medium 23-32 30-40 high >32 >40 very high table 9. swelling potential classification based on liquid limit (after dakshnaamurthy and raman, 1973). swelling potential liquid limit (%) none 0-20 low 20-35 medium 35-50 high 50-70 very high 70-90 extra high >90 figure 8. swelling potential classification (after van der merwe, 1975). 0 10 20 30 40 50 70 80 0 10 20 30 40 50 60 70 80 90 100 clay fraction (%<0.002 mm) pl as tic ity in de x a=2.0 a=1.0 a=0.7 very high a=0.6 60 (% ) a=0.5 high a=activity medium low researchers have attempted to evaluate the various classifications available in the literature. snethen et al. (1977) evaluated seventeen classification methods for predicting swelling potential. they found liquid limit and plasticity index are the best indicators of swelling potential along with natural conditions and environment. therefore, they developed a classification scheme for swelling potential based on liquid limit 150 classification systems of mudrocks and plasticity index and in situ soil suction as an indicator of natural conditions and environment, (table 10). table 10. degree of expansion based on liquid limit, plasticity index, and in situ suction (after snethen et al., 1977). liquid limit (%) plasticity index (%) soil suction * potential swell potential swell classification >60 >35 >4 >1.5 high 50-60 25-35 1.5-4 0.5-1.5 marginal <50 <25 <1.5 <0.5 low * soil suction at natural moisture content. flakiness ratio c/b 9. anisotropy fragment dimensions clay > 2/3 < 2/3 shaly clay shaly silty clay < 2/3 > 2/3 silty clay > 65 < 65 silt below a-lineabove a-line soil-like mudrock % of <60 µm grains < 2 µm 8. grain size distribution sedimentation plot on plasticity chart 7. plasticity liquid limit plastic limit figure 9. the classification of soil-like mudrock (grainger, 1984). it should be noted that the above classification systems were developed based on test results of various types of soils and rocks from different parts of the world which were tested under different testing conditions. therefore, each system might be applicable to only certain types of materials under specific conditions and might not be applicable to others. the index properties can be used as indicators of soils and 151 al-rawas, cheema, and al-aghbari 152 rocks swell potential, but the reliance on such empirical systems can be misleading. nelson and miller (1992) indicated that the use of such systems has led to overly conservative construction in some places and inadequate construction in others. prediction testing and analysis are needed to provide reliable information on which to base design decisions. various methods have been reported in the literature for the measurement of soils and rocks swelling potential. the most common methods include the swell-consolidation method, loaded-swell method and constant volume method, which utilize the one-dimensional consolidation oedometer (jennings and knight, 1957; komornik, and david, 1969; al-rawas 1999). other methods for estimating swelling potential use soil suction (mckeen and hamberg, 1981). these methods include tensiometers, axis translation, filter paper, thermocouple psychrometers and thermal matric potential sensors. nelson and miller (1992) provided good summary of common methods in use for estimating soils and rocks swelling potential. 4.7 soil-like mudrocks classifications grainger (1984) developed a classification system for soil-like mudrocks based on plasticity, grain size and anisotropy (figure 9). the system is a modification to the plasticity chart (casagrande, 1948) incorporating the percentage of clay fraction (< 2 µm) and the flakiness ratio (shortest dimension divided by the intermediate dimension). the advantage of the system is that it classifies clays into different types. 5. conclusions and summary the term “mudrocks” refers to a group of fine to very fine argillaceous sedimentary rocks. these rocks commonly occur interbedded with sandstones and limestones in units ranging in thickness from a few millimeters to several meters. clay minerals such as montmorillonite greatly influence the behaviour of certain mudrocks (i.e. mudstones and shales) causing swelling and shrinking problems. therefore, qualitative and/or quantitative characterization of clay minerals is important in the study of mudrocks. several mudrocks classifications were reported in the literature based on different parameters including grain size distribution, mineralogical composition, strength, durability and swelling potential. some of these classifications involve simple and inexpensive tests such as grain size distribution and plasticity tests while others are expensive, sophisticated and time consuming such mineralogical tests. the choice of a particular test depends primarily on the quality of samples. the use of a single parameter in the classification may not give a reliable characterization of the material and therefore it is recommended whenever possible to use a combination of classification parameters. for the evaluation of mudrocks, it is recommended to initially perform basic geotechnical engineering tests such as atterberg limits, clay content, activity, etc. based on the results of these tests and the quality of samples, further tests can be performed. strength, durability and swelling tests should be performed for full characterization of mudrocks. classifications of mudrocks based on these tests should be veiwed simultaneously for assessing the actual behaviour of mudrocks. 6. references al-rawas, a.a. 1999. the factors controlling the expansive nature of the soils and rocks of northern oman. engineering geology, 53: 327-350. al-rawas, a. a., guba, i. and mcgown, a. 1998. geological and engineering characteristics of expansive soils and rocks in northern oman. engineering geology, 50: 267-281. altmeyer, w.t. 1955. discussion of engineering properties of expansive clays. proc. am. soc. civil eng. 81: separate no. 658, 17-19. astm. 1990. standard method for particle-size analysis of soils (d-422). in annual book for astm standards, philadelphia, 91-97. anon, a. 1977. working party report on the description of rock masses for engineering purposes. quarterly journal of engineering geology, london, 10: 355-88. classification systems of mudrocks 153 barton, n., lien, r., and lunde. j. 1974. engineering classification of rock masses for the design of tunnel support. rock mechanics, 6: 189-236. bienawski, z.t. 1973. engineering classification of jointed rock masses. trans. south african inst. min. met., 15: 335-343. bieniawski, z.t. 1974a. geomechanics classification of rock masses and its application in tunnelling. proc. 3rd congr. int. soc. rock mech., denver, ila, 27-32. bienawski, z.t. 1974b. estimating the strength of rock materials. jour. south african inst. min. met., 74: 312-320. blatt, h. 1982. sedimentary petrology. w.h. freeman and company, san francisco. blatt, h., middleton, g. and murray, r. 1972. origin of sedimentary rocks. prentice-hall, englewood cliffs, usa, 634 pp. british standard 1990. methods of test for soils for civil engineering purposes. british standards institution, london, 28 pp. boggs, jr. s. 1987. principles of sedimentology and stratigrphy, merrill publishing company, columbus (oh), 784 pp. broch, e., and franklin, j.a. 1972. the point load strength test. int. jour. rock mech. min. sci., 9: 669697. carter, p.g., and sneddon, m. 1977. comparison of schmidt hammer, point load, and unconfined compression test in carboniferous strata. in attewell, p.b. 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york, 610 pp. underwood, l.b. 1967. classification and identification of shales. journal of the soil mechanics and foundation classification systems of mudrocks division, american society of civil engineers, 93: sm6, 97-116. van der merwe, d.h. 1975. contribution to specialty session b, current theory and practice for building on expansive clays. proceedings of the 6th regional conference for africa on soil mechanics and foundation engineering, durban, 2: 166-167. vutukuri, v.s., lama, r.d., and saluja, s.s. 1974. handbook on mechanical properties of rocks. trans technical publications, bay village, oh, usa, pp. williams, a.a.b., pidgeon, j.t. and day, p.w. 1985. expansive soils. the civil engineer in south africa, july 1985, 367373. wood, a.m.m. 1972. tunnels for roads and motorways. quaterly journal of engineering geology, london, 5: 111126. wood, l.e. and deo, p. 1975. a suggested system for classifying shale materials for embankments. bulletin of the association of engineering geologists, 12: 39-54. received 31 january 2000 accepted 29 june 2000 155 amer al-rawas*, tariq cheema** and mohammed al-aghbari* ãäùãé çáêõäíý çáìíæáæìí æçáåäïó� úçãñ úáí çáñæçó ¡ æøçñþ ôíãç ¡ æã� introduction 138 origin and occurrence of mudrocks 138 geological terminology 139 mudrock classifications 139 4.4 testing procedures 143 introduction origin and occurrence of mudrocks geological terminology mudrock classifications 4.4 testing procedures depending upon the type of mudrock, different strength test procedures have been recommended. for very weak mudrocks (or clayey soils), grainger (1984) recommends the straightforward undrained triaxial method of compression testing as specified by mo is = p/d² table 4. shrinkage limit and linear shrinkage guide to potential expansion (after altmeyer, 1955). table 5. data for making estimates of probable volume change for expansive soils (after holtz and gibbs, 1956). plasticity index (%) table 6. degree of expansion based on percent passing no. 200 sieve, liquid limit and standard penetration resistance (after chen, 1965). liquid limit (%) table 7. swelling potential classification based on plasticity index (after chen, 1988). table 10. degree of expansion based on liquid limit, plasticity index, and in situ suction (after snethen et al., 1977). references microsoft word biol-2.doc science and technology, 6 (2001) 21-31 © 2001 sultan qaboos university 21 plasma analysis in normal green sea turtles, chelonia mydas, during two different periods of nesting at ras alhadd, sultanate of oman abdulaziz.y.a. alkindi, ibrahim.y. mahmoud* and humaid khan department of biology, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman,*fulbright senior scholar,usa. االستجابات الفيزيولوجية من خالل التحاليل البالزمية للسالحف البحرية الخضراء االعتيادية خالل فترتين مختلفتين من التعشيش في منطقة رأس الحد بسلطنة عمان عبدالعزيز الكندي، ابراهيم محمود و حميد خان ملت مجموع البروتين والكولسترول وحمض الالآتيك تمت دراسة المكونات البالزمية للسالحف الخضراء التي ش : خالصة والجلوآوز وحمض اليوریك واليوریا وثاني أآسيد الكربون وأیونات البالزما من الكالسيوم والبوتاسيوم والصودیوم والماغنيسيوم ون السالحف عالية الكثافة وفي وقد تم جمع عينات الدم في الفترة بين یونيو و أآتوبر حيث تك. والفوسفات الكلورید و ملحية البالزما . وتمت المقارنة بين الفترتين فيما یخص مكونات البالزما المذآورة آنفًا. الفترة القليلة الكثافة بين نوفمبر و مایو من مواسم التعشيش مجموع البروتين ولكن معدالت . و لم تظهر أیونات البالزما ما عدا الفوسفات والكلورید أیة فروق إحصائية مهمة بين الفترتين وحمض اليوریك أظهرت إحصائيًا فروقًا مهمة ولم یكن آذلك بالنسبة لليوریا وآذلك بالنسبة لملحية البالزما فلم یكن هناك أیة فروق ویمكن القول أن السالحف البحریة أثناء التعشيش تتعرض لجهد . إحصائية مهمة بين الفترة عالية الكثافة والفترة قليلة الكثافة اصل ومضني وتكون آمثيالتها من الزواحف المائية التي تتنفس باستخدام الرئة في حالة وجودها على األرض حيث توظف متو وبالنسبة الرتفاع مجموع البروتين في الفصل عالي الكثافة یمكن , التنفس الالهوائي آوسيلة سریعة للحصول على الطاقة الالزمة آما یمكن تأویل ارتفاع . ث وفرة ونوعية الغذاء في المياه القریبة من أماآن التعشيشإرجاعه إلى ظروف تغذیة السالحف من حي معدل حمض الالآتيك وزیادة أیونات البالزما بتأثرها بحالة الضغط والجهد المضني لسلوك التعشيش ولالزدحام والتنافس الشدیدین فًا موضوعيُا مهمًا بقياس هذه المكونات في بالزما السالحف إن هذه الدراسة حققت هد. بين السالحف في الموسم العالي الكثافة الخضراء أال وهو تقييم التغيرات الفسيولوجة التي تطرأ على هذه السالحف أثناء التعشيش في ظل ظرفين مختلفين من االزدحام .والكثافة على مدار دورة سنویة آاملة abstract: plasma composition which includes total protein, cholesterol, lactate, glucose, uric acid, urea, co2, and electrolytes (ca ++, k+, na+, mg++, po4 -3, cl-), and plasma osmolarity were analyzed in normal adult nesting green turtles chelonia mydas. blood samples were collected in june-october at the peak of the nesting season and in november-may during the non-peak period. plasma electrolytes values, except for po4 -3 and clwere significant between the two periods. values for total proteins and uric acid were significantly different during the two periods but urea values were insignificant. osmolarity was unchanged during the two periods. during nesting the sea turtles undergo strenuous and exhaustive exercise and like other lung breathing reptiles, they ventilate intermittently, thus, they rely on anaerobic metabolism during the nesting exercise. plasma concentrations of lactate and co2 were significant but glucose values remained stable and unchanged during the two nesting periods. higher concentrations of total protein during june compared to october may be related to the type and the availability of diet in the waters near the nesting sites. high concentrations of electrolytes and lactate are perhaps related to more stressful conditions during june because of higher crowding and intense competition for nesting sites. the aim of this study was to analyze the role of these parameters during nesting activity to evaluate changes under two different crowding conditions and gather information for future population health assessments. keywords: plasma composition, osmolarity, nesting and sea turtles. alkindi, mahmoud and khan 22 1. introduction smoregulation and acid-base balance are the major physiological problems that face marine turtles because the sea, which is their natural environment, is almost three times more concentrated in electrolytes than their body fluid (see lutz, 1997). salt influx in marine turtles is basically derived from two sources, food material such as marine algae and grasses, and swallowing large amounts of seawater during food intake (lutz, 1997). this large salt load is counter to normal physiological functions and must be excreted as soon as it enters the body to maintain normal osmolarity and body function. the major organs, which are responsible for salt excretion, are two modified lachrymal glands with their main ducts open into the posterior canthus of each eye (abel and ellis, 1966; marshall and saddlier, 1989). these glands are responsible for about 90% of salt excretion. the rest of the body plays a minor role in reducing the salt load with approximately 5% through the cloacal chamber, and the rest excreted through the kidney and the scutes of the plastron (lutz, 1997). glycogen is the main metabolic energy source of muscles which enables the turtle to synthesize glucose by gluconeogenesis, which takes place primarily in the liver. it has been suggested that carbohydrate metabolism increases because of the activation of anaerobic glycolysis (dunn and hochachka, 1986), which results in elevated levels of blood glucose and lactate. in fish, elevation in glucose levels could be triggered by stress (see alkindi, et al, 2000a). in addition, blood lactate levels may also be affected by physiological stress (pickering, et al, 1982). in a study of rainbow trout, glucose oxidation was depressed by high lactate levels, even when glucose production was stimulated by exhaustive activity. moreover, a rise in lactate in vitro was attributed to rising lactate and pco2 , and partially to stimulatory effects of elevated catecholamine levels (wood, et al, 1990). in reptiles, during post-exercise period, the skeletal muscle of the lizard dipsosaurus dorsalis utilizes mainly lactate as a gluconeogenic substrate for glycogen production (gleeson, et al, 1993). other studies have also confirmed that skeletal muscles in lizards are capable of resynthesizing muscle glycogen in situ shortly after strenuous exercise (gleeson, 1982, 1986, 1991; gleeson and dalessio, 1989, 1990). assessment of blood chemistry in marine turtles has not been studied extensively, especially on adult marine turtles. hasbun, et al, (1998) studied blood chemistry in adult and sub-adult green turtles caught in trawls. other studies focused on juvenile green turtles (aguirre, et al, 1995; bolton and bjorndal, 1992) and captive green turtles (norton, et al, 1990). lutz (1997) has recently done an extensive review on the regulation of salt, water and ph balance in sea turtles. the purpose of this study is to examine the effect of nesting during peak and non-peak periods, on values of plasma electrolytes, total protein, urea, uric acid, co2, cholesterol, glucose and lactate in normal nesting turtles. during the nesting process, the turtles undergo a sudden and stressful change which is different from the normal marine condition (alkindi, et al, 2000b). the turtles spend several hours looking for the ideal nesting sites and during this period they have to make some physiological adjustment in the chemistry of their body fluids as well as their metabolism. up to date, changes in the plasma parameter in nesting turtles have not been evaluated and this investigation will thoroughly monitor such changes. 2. methods of investigation 2.1 study area this investigation was conducted at ras al-hadd turtle reserve at the sultanate of oman, specifically at ras al junaz, along the coastal line of the arabian sea. 2.2 animals normal healthy nesting green turtles without any physical defects or injuries were studied during two periods of the nesting season: june-october during peak nesting period (average 100200 turtles/night) and during non-peak nesting period november-may (average 5-10 turtles/night). o plasma analysis in normal green sea turtle, chelonia mydas 23 blood samples (10 ml) were taken during nesting exercise with a syringe and needle from the dorsal cervical sinuses according to the method of owen and ruiz (1980). several trips were made to the study area during each period for the data collection. 2.3 blood analysis the beckman synchron cx systems were used to determine plasma parameters in this study. the system automatically proportions appropriate samples and reagent volumes relative to each plasma parameter. table 1: methodology of analysis for blood plasma parameters using beckman synchron cx systems. detection reaction mechanism parameter methodology abs (560) endpoint biuret protein colorimetric abs(520) phosphomolybdate blue complex phosphate colorimetric abs(520) mg-calmagite complex magnesiumcolorimetric abs(650) ca-arsenazo iii complex calcium colorimetric potential ion selective electrode sodium potentiometric potential ion selective electrode potassium potentiometric potential ion selective electrode chloride potentiometric potential ion selective electrode co2 potentiometric ∆potentialglucose oxidase production of o2 glucose amperometric abs(520) lactate dehydrogenase with conversion to pyruvate and the production of peroxide. peroxidase addition to produce quinoneimine. lactate enzymatic abs(520) cholesterol esterase/cholesterol oxidase with production of peroxide. peroxidase addition to produce quinoneimine. cholesterolenzymatic ∆mho urease addition to form ammonium ion. urea enzymatic abs(520) uiricase to produce allontoin and hydrogen peroxide. hydrogen peroxide reacts with 4-aminoantipyrine ( 4-aap) and 3.5-dichloro-2-hydroxybenzene sulfate (dchbs) in presence of peroxidase to form a quinonimine. uric acid enzymatic osmolarity is analyzed by measuring the freezing point of plasma using an osmometer that utilizes the depression of the freezing point of plasma and is compared to that of pure water. 3. results total protein concentrations were significantly higher during the peak period (figure1). values for electrolytes (na+, k+, ca++ and mg++) were significantly higher during the peak period while po4-3 and clvalues were not significant (figures 2,3). values for co2 were found significantly higher during non-peak periods (figure 4). lactate values were significantly higher during the peak period, while glucose values remained stable throughout the nesting season (figure 5). cholesterol was significantly higher during the peak period (figure 6). urea values were not significant, while uric acid values were significantly higher during the peak period (figure 7). osmolarity concentrations remained stable throughout the nesting season (figure 8). alkindi, mahmoud and khan 24 figure 1. mean total protein levels (±sem); *=significant difference. figure 2. mean sodium and chloride levels (±sem); *= significant difference. figure 3. mean potassium, calcium, magnesium and phosphate levels (±sem), *=significant difference. 0 10 20 30 40 50 protein peak protein non-peak* g/ l 0 50 100 150 chloride peak chloride non-peak sodium peak sodium non-peak * m m ol /l -1 0 1 2 3 4 5 potassium peak potassium non-peak calcium peak calcium non-peak magnesium peak magnesium non-peak phosphate peak phosphate non-peak * * * m m ol /l -1 plasma analysis in normal green sea turtle, chelonia mydas 25 figure 4. mean carbon dioxide levels (±sem); *=significant difference. figure 5. mean glucose and lactate levels (±sem); *=significant difference. figure 6. mean cholesterol levels (±sem) *=significant difference. 0 10 20 30 carbon dioxide peak carbon dioxide n-pk * m m ol /l 0 10 20 glucose peak glucose non-peak lactate peak lactate non-peak * m m ol /l -1 0.0 2.5 5.0 7.5 10.0 cholest. peak cholest. non-peak* m m ol /l alkindi, mahmoud and khan 26 figure 7. mean uric acid and ammonium levels (±sem); *=significant difference. figure 8. mean blood osmolarity (±sem). 4. discussion the status of the blood chemistry during nesting activities has not been explored thoroughly in the past and most previous investigations dealt with turtles in their marine environment or subjected to experimental conditions (holmes and mcbean, 1964; kooistra and evans 1976; bolten and bjorndal 1992; lutz, 1997). marine turtles are subjected to a brief terrestrial condition encountered during their nesting exercise. this study was directed at an examination of blood chemistry during this episodic transition period of marine to terrestrial environment. the present investigation reveals that the normal natural populations of the green turtles in ras al-hadd maintain constant plasma osmolarity while they are on the nesting grounds throughout the nesting season, even though some electrolyte values differ in peak and non-peak nesting periods. we suggest that these changes are temporary and they are not detrimental to the overall health of the turtles. they appear to be capable of adjusting rapidly to normal osmotic and ionic regulatory conditions. our field observations indicate the lachrymal glands are always active in secreting salt at the time of nesting. furthermore, the green turtle can tolerate prolonged time from seawater to freshwater without osmotic problems (holmes and mcbean, 1964). in another investigation (kooistra and evans, 1976) marine turtles transferred from seawater to freshwater and after 25 h, the turtle’s orbital salt glands stopped secreting salt and after 17 days in freshwater, the efflux of 0.00 0.25 0.50 0.75 uric acid peak uric acid non-peak urea peak urea non-peak * m m ol /l -1 0 100 200 300 400 osmolarity peak osmolarity non-peak m os m /l plasma analysis in normal green sea turtle, chelonia mydas 27 na has declined 97% and the cloaca became the major organ of secretion. these experiments provide us with some evidence that marine turtles can adjust to different sets of environmental conditions without any difficulty. hasbun, et al, (1998) investigated the blood chemistry of normal male and female adult and sub-adult green turtles in ras al-khaimah of the united arab emirates during the month of may, prior to the nesting season. blood samples were collected within an hour of capture. although some of their blood was collected from sub-adults and some males, there were indications of close similarities with our data from the peak period. the two studies present an interesting comparison since the turtles were collected from close regions and also the blood samples from ras alkhaimah were collected shortly after capture, so the electrolyte values remained unchanged from the marine environment. even though the turtles from ras al hadd spent a long time on the nesting grounds under stress and exhaustive exercise, their electrolyte levels remained stable despite the change of environment. in comparing the present electrolyte data, we find that na+, k+, ca++ and mg++ levels were significantly higher during peak periods over non-peak periods, while cland po4-3 were not significantly different. the differences in values may be related to stress which has been known to change the electrolyte levels in fish (see alkindi, et al, 2000a), or the differences could be related to individual variations at the time of sampling. during the peak period, nesting turtles are under tremendous pressure because of crowding stress, which may contribute to the rise in electrolyte levels. plasma electrolyte levels reported previously (lutz and dunbar-cooper, 1987; lutz, et al, 1986) were similar to the present data for na+, cland k+ but their values for ca++ and mg++ were lower than those reported here. the high plasma ca++ levels in the present data were taken from normal nesting turtles which usually have higher ca++ levels than previous data taken from nonnesting turtles, males, or sub-adults. nicholson and lutz (1989) reported that the salt glands in the green turtles maintain the same salt concentration whether loading the turtles with hypertonic nacl solution or hypertonic sucrose solution. they postulated that the glands regulate salt levels by maintaining relatively constant electrolyte levels. this was attributed to their adjustment to the marine conditions. moreover, holmes and mcbean (1964) found that na+/k+ ratio remains the same during the secretory activity of the glands. however, nicholson and lutz, (1989) reported that in the green sea turtle, there was a change in the flow rate and concentration of salt during secretion; it reached a peak and gradually declined to lower levels before dropping off to zero. from the previous investigations, the secretory contents of inactive salt glands in the green turtle are similar to our results on plasma osmolarity. however, when these glands are active, the ionic components of the glands rise rapidly to an average of 1900 mosm/l, which is almost six-fold higher than the plasma level and twice that of seawater (lutz, 1997). in the green turtle, salt efflux is accomplished by the esophagus and the lachrymal salt glands (lutz, 1997). the food they ingest, which consists of marine grasses and algae and the seawater they swallow during feeding are the two sources of salt load. swallowed seawater (incidental drinking) adds a significant amount of salt load to the body. the response of the animal is immediate ejection by a powerful esophageal reverse peristalsis to force the water through the nostrils while the food material is held by closely packed conical papillae in the esophagus (bjorndal, 1985). about 90% of salt secretion from food material takes place in the salt lachrymal glands. these two methods, which maintain normal osmolarity, are vital for the survival of marine turtles in a hostile environment. our data indicate that chloride and sodium are the major plasma electrolytes while the remainder of the electrolytes had lower values. furthermore, the ratio of ionic components of salt glands and the plasma are of similar concentrations, and the plasma electrolytes in our study also maintained the same ratio of ionic concentration as that of the salt glands. in this investigation, plasma urea levels were low during peak (0.62 ± 0.08 m mol/l) and nonpeak (0.44 ± 0.09 m mol/l) periods and there was no significant difference between the two alkindi, mahmoud and khan 28 periods. urea levels from urine reported from other studies were higher than the plasma urea from this investigation. this is not surprising since plasma urea is much lower than that of the kidney. the following investigators measured urea levels in urine: bjorndal (1979) 12.9 m mol/l; nicholson and lutz (1989) 8.9 m mol/l; prange and greenwald (1980) 2 m mol/l. the discrepancy in these values may be related to age of turtle, type of food intake and the length of time urine remains in the bladder to be subjected to reabsorption for water and ionic transport (stetson, 1989). total protein plasma levels in our study and that of bolten and bjorndal (1992) were similar despite age or size differences. frair and shah (1982), on the other hand, reported that in green turtles there was a significant correlation between total protein and carapace length. furthermore, it must be stated that the nesting turtles during peak period at ras al hadd remain in the waters near the nesting grounds for at least 1.5-2 months to oviposit 3-5 clutches. during this time, the large number of turtles may consume most of the food in the area, which may have resulted in a decrease in food reserve, leading to the observed significant lower values of total protein during non-peak period. adjustment to the proper ph in the sea turtles is of an extreme importance, since they spend a great deal of time underwater depending primarily on anaerobic respiration (wood, et al, 1984). on land, the green turtles, during nesting exercise, ventilate intermittently, depending primarily on anaerobic respiration (alkindi, et al, 2000b). dissociated products of lactic acid (lactic ions and h+) can cause severe acid-base disturbances and can hinder the oxygen uptake but catecholamine immediate release can facilitate oxygen uptake in most vertebrates (alkindi, et al, 2000a). in fishes, blood osmolarity and electrolyte concentrations may be affected by stress (aldrin, et al, 1979; alkindi, et al, 2000a), hypoxia, certain environmental pollutants (alkindi, et al, 1996) and osmoregularity dysfunction, which is characterized by blood electrolyte imbalance (carmichael, et al, 1984b; alkindi, et al, 1996; alkindi, et al, 2000a). drastic changes in plasma lactate levels have also been observed in nesting green turtles at ras al hadd (alkindi, et al, 2000b). when the turtles emerge from the sea they generally go through exhaustive physical exercises during nesting phases. before a turtle chooses its final site to lay its eggs, it frequently makes several digging attempts at several sites, with each attempt followed by abandonment. these abandonments are related to unfavorable conditions such as a lack of soil moisture and soil obstacles. nesting is a long ordeal and usually takes between 2.5-4.5hr, sometimes longer. under these conditions, the green turtles are subjected to a high degree of stress, evidenced by high plasma catecholamine levels during nesting exercises compared to lower levels when the green turtles first emerge from the sea (alkindi, et al, 2000). they undergo bursts of strenuous and exhaustive forceful exercise which usually last for less than one minute followed by a recovery period lasting 10-30 seconds for deep breathing (alkindi, unpublished data). under these exercise-recovery phases as shown in the present data, the turtles develop apnea accompanied by hypercapnia and acidemia associated with high-rise in co2, which is primarily related to anaerobic metabolism. this condition persists throughout the nesting exercises as catecholamines play a major role in glycogen metabolism by stimulating glycogenolysis and/or gluconeogenesis (alkindi, et al, 2000). lactate values in this study were significantly higher during the peak periods over the nonpeak periods. this may be attributed to the fact that the turtles work much harder during the peak period with higher crowding pressure and more severe competition for nesting space than during the non-peak period. glucose levels, however, remain stable throughout the nesting season with no significant differences observed between the two periods. the stable glucose levels may be influenced by catecholamines which stimulate glycogenolysis during nesting. catecholamines also facilitate removal of lactate from muscles into the blood stream (alkindi, et al, 2000b). there is a drastic increase in plasma lactate and co2 levels in submerged sea turtles, which is indicative of anaerobic metabolism (lutz, 1997). based on our data, this condition can also occur in the green turtle during the nesting process. comparing the lactate values from both conditions plasma analysis in normal green sea turtle, chelonia mydas 29 revealed surprisingly similar results. these results indicate that sea turtles can physiologically adjust to different sets of conditions and are also frequently faced with acid-base disturbances. this condition appears to be corrected by switching to aerobic respiration to avoid acidemia and hypercapnia. sea turtles are known to stay submerged for a long time searching for food. for example the loggerhead sea turtles spend about 97% of their time submerged (lutz and bentley, 1985) which consequently leads to rapid accumulation of co2, depletion of o2 and an acid-base disturbance. while under water, the depletion of o2 triggers anaerobic respiration resulting in accumulation of lactic acid and co2. wood, et al. (1984) reported that when green sea turtles swim vigorously underwater for 15 minutes blood ph falls from 7.66 to 7.21 and lactate levels increases from 0.6 to 14.4 m mol/l. plasma lactate could reach 35 m mol/l when green turtles were forced to submerge for two hours (hslatala, et al, 1975) while in the loggerhead, plasma lactate reached 16.2 m mol/l after they were caught in fishing nets for 30 minutes. these values are comparable to the present data as the nesting turtles also go through vigorous exercises in short bursts while they rely mainly on anaerobic respiration. the higher cholesterol plasma levels in the turtles from ras al hadd during the summer months (peak period) may be related to the requirement for a large amount of cholesterol for the growth and maturation of the ovarian follicles. during the fall, the cholesterol level dropped off significantly because the follicles had already attained the mature size. plasma profiles from natural populations of sea turtles are urgently needed so they can be used with other physiological parameters to assess the health and physiological conditions of a population (rosskopt and woerpel, 1982; jacobson, et al, 1991; bolten and bjorndal, 1992). there is a steady decline in populations of sea turtles all over the world due to the rapid spread of pollution in marine habitats and the destruction of many feeding and nesting grounds. as a result, there is a rapid spread of diseases such as fibropapilloma reported among many geographical populations (jacobson, et al, 1989; balazs and pooley, 1991). the data from this study will be used as a reference guide for future assessment of nesting populations relative to health conditions, reproductive potential and growth. 5. acknowledgments this research was supported, in part, by grant number (ig/sci/biol/01/99), deanship of postgraduate studies and research, sultan qaboos university and by the fulbright program awarded to prof. ibrahim younis mahmoud, u.s.a. and by the directorate general of wildlife and nature conservation, the ministry of regional municipalities and environment of the sultanate of oman. special thanks to richard wilbur, public affairs officer, embassy of the united states of america in muscat, oman and to chris batchelor and helen due boje for their technical assistance. references abel, j.h. and ellis, r.a. 1966. histochemical and electron microscope observations on the salt secreting lachrymal glands of marine turtles. am. j. anat. 118: 337-358. aguirre, a.a., balazs, g.h, spraker, t.r. and gross t.s. 1995. adrenal and hematological responses to stress in juvenile green turtles (chelonia mydas) with and without fibropapillomas. physiol. zool. 68: 831-854. aldrin, j.f., messager, j.l. and mevel, m. 1979. essai sur le stress de transport chez le saumon coho juvenile salmon (oncorhynchus kisutch). aquaculture 17: 279-289. alkindi, a.y.a., brown, j.a., waring, c.p. and collins, j.e. 1996. endocrine, osmoregulatory, respiratory and haematological parameters in flounder exposed to the water soluble fraction of crude oil. j. fish biol. 49: 1291-1305. alkindi, mahmoud and khan 30 alkindi, a.y.a, brown, j.a. and waring, c.p. 2000a. endocrine, physiological and histopathological responses of fish and their larvae to stress with emphasis on exposure to crude oil and various petroleum hydrocarbons. journal for scientific research. science and technology special review 2000 : 1-30. alkindi, a.y.a., mahmoud, i.y. and woller, m.j. 2000b. catecholamine response in sea turtles during nesting. abstracts, vol 26(1) 30th annual meeting of the society of neuroscience. abstract 143.7. balazs, g.h. and pooley, s.g. 1991. research plan for marine turtle fibropapilloma. national oceanographic and atmospheric administration technical memorandum (nmfs noaa-tm-nmfs-swfsc-156), honolulu, hawaii, pp113. bjorndal, k.a. 1979. urine concentration of ammonia, urea and uric acid in the green turtle (chelomia mydas). comp. biochem. physiol. 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lizard (dipsosaurus dorsalis). j. comp. physiol. 156: 277-283. gleeson, t.t. 1991. patterns of metabolic recovery from exercise in amphibians and reptiles. j. exp. biol. 160: 187-207. gleeson, t.t. and dalessio, p.m. 1989. lactate and glycogen metabolism in the lizard (dipsosaurus dorsalis) following exhaustive exercise. j. exp. biol. 144: 377-393. gleeson, t.t. and dalessio, p.m. 1990. lactate: a substrate for reptilian muscle gluconeogenesis following exhaustive exercise. j. comp. physiol. 160: 331-338. gleesson, t.t., dalessio, p.m., carr, j.a., wickler, s.j. and mazzeo, r.s. 1993. plasma catecholamine and corticosterone and their in vitro effects on lizard skeletal muscle lactate metabolism. amer. physiol. soc. 34: r632-r639. hasbun, c.r., lawerence, a.j., naldo, j., samour, j.h. and al-ghais, s.m. 1998. normal blood chemistry of free-living green sea turtles (chelonia mydas) from the united arab emirates. comparative. hematology international 8: 174-177. holmes, w.n. and mcbean, r.l. 1964. some aspects of electrolyte excretion in the green turtle (chelonia mydas). j. exp. biol. 41: 81-90. hslatala, m.p., standaert, t.a., pierson, d.j., hochachka, p.w., owen, t.g., allen, j.f. and whittow g.c. 1975. multiple end-products of anaerobiosis in diving vertebrates. comp. biochem. physiol. 50b: 17. jacobson, e.r., gaskin, j.m., brown, m.b. harris, r.k., gardiner, c.h., lapointe, j.l., adams, h.p. and reggiardo, c. 1991. chronic upper respiratory tract disease of free-ranging desert tortoises (xerobates agassizii). j. wildl. dis. 27: 296316. jacobson, e.r., mansell, j.k., sundberg, j.p., hajjar, m.e., eichmann, l., ehrhart, l. m., walsh, m. and murru, f. 1989. cutaneous fibropapillomas of green turtle (chelonia mydas). j. comparative pathol. 101: 39-52. plasma analysis in normal green sea turtle, chelonia mydas 31 kennish, m.j. 1994. practical handbook of marine science, 2nd ed. crc marine science series, crc press, boca raton, fl. kooistra, t.a. and evans, d.h. 1976. sodium balance in the green turtle (chenonia mydas) in seawater and freshwater. j. comp. physiol. 107: 229-240. lutcavage, m.e., lutz, p.l. and baier, h. 1987. gas exchange in the logger head sea turtle (caretta caretta). j. exp. biol. 131: 365-372. lutz, p.l. 1997. salt, water and ph balance in the sea turtle. in the biology of sea turtles. edited by p.l. peter and j.a. musick. crc press. n.w. boca raton, florida, u.s.a., pp. 343-361. lutz, p.l. and t.b. bentley, 1985. respiratory physiology of diving in the sea turtle copeia. 1980(3): 671-679. lutz, p.l. and dunbar-cooper, a. 1987. variations in the blood chemistry of the loggerhead sea turtle caretta caretta. fish bull. 1985: 37-43. lutz, p.l., lutcavage, m. and hudson, d. 1986. physiological effects of oil on sea turtles, in study on the effects of oil on marine turtles. minaral management service, contract number 14-12-0001-30063, pp 91-127. marshal. a.t. and saddlier, s.r. 1989. the duct system of the lachrymal gland of the green sea turtle (chelonia mydas). cell tissue res. 257: 399-404. nicholson, s.e. and lutz p.l. 1989. salt gland function in the atlantic green sea turtle. j. exp. biol. 144: 171-184. norton, t.m., jacobson, e.r. and sundberg, j.p. 1990. cutaneous fibropapillomas and renal myxofibroma in green turtle, chelonia mydas. j. wild. dis. 26: 265-270. owens, d.w. and ruiz, g.j. 1980. new methods of obtaining blood and cerebrospinal fluid from marine turtles. herpetologica 36: 17-20. pickering, a.d., pottinger, t.g. and christie, p. 1982. recovery of the brown trout (salmo trutta l.) from acute handling stress: a time-course study. j. fish. biol. 20: 229244. prange, h.d. and greenwald, l. 1980. effects of dehydration on the urine concentration and salt gland secretion of the green sea turtle. comp. biochem. physiol. 66a: 133-136. rosskopf, w.j. jr. and woerpel, r.w. 1982. the use of hematologic testing in diagnostic medicine: an introduction. chelonian documentation center newsletter 1: 30-34. stetson, d.l. 1989. turtle urinary bladder: regulation of ion transport by dynamic changes in plasma membrane area. am. j. physiol. 257: r973-r981. wood, s.c., gatz, r. n. and glass, m. l., 1984. oxygen transport in the green turtle, j. comp. physiol., 154: 275-280. received 30 january 2001 accepted 17 may 2001 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 55-60 © 2003 sultan qaboos university steady state analysis of a upfc as voltage regulator for optimal position in the transmission line s. ali al-mawsawi and mohammed r. qader department of electrical engineering, university of bahrain, p.o.box 32038, email: salmosawi@eng.uob.bh (upfc) حيد سريان الطاقة الكهربائية في تو تحليل مرحلة االستقرار للمتحكم كمنظم للجهد من أجل موقع مثالي على خط نقل القوى محمد رضا قادرولي الموسوي عالسيد ب دوراً يلع) upfc(في خالل السنة الحالية من الواضح أن تنصيب المتحكم في توحيد سريان الطاقة الكهربائية : خالصة معتمداً على )pwm(ولهذا السبب فإن عرض معدل النبض . استقرار النظام ةمهماً في قاعدة التأثير غير الخطي لسلوكي ) upfc ( الكهربائية من ىكمنظم للجهد الكهربائي يمكن نمذجته وتحليله من أجل استنتاج الموقع المثالي على خط نقل القو . الذي يلعب دوراً ذا مغزى في التأثير غير الخطي ) upfc ( لورقة، فقد تم توضيح موقع خالل الدراسة التي تمت في هذه ا و الطاقة الكهربائية ) active power(المستقاة من الحاسوب بأن توزيع الطاقة الكهربائية المؤثرة كما أنه تم استعراض النتائج .معامل التعديل للجهازالساريتان يمكن التحكم بهما بتغير ) reactive power(الحيثية abstract: it has recently been illustrated that the unified power flow controller (upfc) installation location plays an important role in effecting nonlinearly in the upfc steady state performance of the system. a pulse width modulation (pwm) based on upfc as a voltage regulator is modeled and analyzed to investigate the optimal position in the transmission line. from the study made in this paper, it is shown that the location of upfc plays a significant part in effecting nonlinearly. it is also found from the simulation results that the distribution of the active and reactive power flows can be controlled by varying the modulation index of the device. keywords: facts, upfc, voltage regulator , active and reactive power. 1. introduction the concept of a unified power flow controller (upfc) has been proposed recently(gyugyi, 1992; gyugyi and hingorani 1990; gyugyi et al., 1995). the upfc has the potential to become one of the most important flexible ac transmission systems (facts) since it can provide various types of compensation, i.e., voltage regulator, phase shifting regulator, impedance compensation and reactive compensation. practically, the upfc is implemented by using two similar solid-state phase voltage source inverters (shunt compensation block and series compensation block) which are connected through a common dc link capacitor as shown in figure 1 (gyugyi et al., 1995) and each inverter is coupled with a transformer. in the last few years, a number of landmark publications have appeared in the literature, which described the basic operation of the upfc (gyugyi, 1992; gyugyi and hingorani, 1990; and gyugyi et al., 1995). gyugyi (1994) has proposed the concept of the upfc to control independently both the real power and the reactive power flows at the sending and receiving ends of the transmission line. he also compared the performance and equipment of the upfc to the more conventional, but related, 55 s. ali al-mawsawi and mohammed r. qader power flow controllers such as the thyristor controller series capacitor and the thyristor controller phase angle regulator. he claimed that, due to the capability and performance of the upfc in controlling the power flow in transmission lines, this device becomes the most important facts device. furthermore, it has been presented in reference (fuerte-esquivel and acha 1997) that the upfc can control active and reactive power and voltage magnitude simultaneously. this showed that caution has to be exercised with the upfc model since it has been assumed that the shunt converter is operating at unity power factor. this paper deals with the mathematical modeling and analysis of a pulse-width-modulation (pwm) based upfc operating as voltage regulator implemented on a single machine connected to infinite bus through parallel transmission lines. the steady-state performance simulation results of the system are presented for different value of the modulation index. in addition, the optimum position of the upfc device is investigated. x2 vr∠0 inv2 inv1 vs∠δ α mpqmsh +vpq − x4 x3 pin ~ θ figure 1. upfc controller. 2. mathematical model the study system on which the upfc device is implemented is shown as a single line diagram in figure 2. a synchronous machine feeds an active power p1 and reactive power q1 to an infinite bus-bar via a parallel transmission lines. vs is the sending end voltage with δ load angle, vr is the receiving end voltage, and x2, x3, x4 are the transmission lines impedance. vpq is the series injected voltage of inverter (2). ipq is the transmission line current passing through the series compensation block of the upfc. vsh is the shunt input voltage of inverter (1) and xsh is the leakage reactance of the shunt transformer, which is assumed to be purely inductive for simplicity. p3, q3 ~ psh + ppq = 0 vsh ish ipq is vp • v q • xsh +vpq -~ x4x3 x2 vr∠0 vs∠δ p2, q2 pin ~ figure 2. single line diagram of the study system. in order to operate the upfc systems as a voltage regulator, the voltage vpq should be injected to the transmission line in phase with the transmission line voltage vp. this can be seen in the vector diagram shown in figure 3. 56 steady state analysis of a upfc as voltage regulator β∠= pqp vv (1) ish vp jishxsh vr δ β jis x1 is vpq vq jipq x2 vsh vs ipq figure 3. vector diagram of figure 2. if the upfc is an operating base on the pwm method, the magnitude of vpq can be calculated as (mohan, et al. 1998), 0.35pq pqv m= v dc (2) where mpq is the modulation index of the inverter (2) and it is varying from 10% to 100%. on the other hand, the voltage magnitude of the input voltage vsh of the inverter (1) is: 0.35sh shv m v= dc (3) where msh is the modulation index of the inverter (2) and its value is assumed to be constant (msh = 100%). therefore, from equation (2) and (3), we can confirm that; pq pq shv m v= (4) in general, sh shv v α= ∠− (5) where α is the angle with respect to the transmission line voltage vp as shown in figure 3. this angle will determine the amount of the power demand to the inverter (2) from inverter (1). from the vector diagram of figure 3 it can be seen that; ( ) (p sh sh s pqv v jx i iβ α= ∠ − + − ) (6) equating the real and imaginary parts of equation (6) leads to; 3 4 3 4 4 cos( )[1 ] cos( ) cos( ) cos( ) sh ssh sh p sh sh pq sh r x vx x v v x x x x v x v x x β β α δ β + + = − + + + (7) 3 4 3 4 sin( )[1 ] sin( ) sin( ) sin( )sh pqsh ssh shp sh x vx vx x v v x x x x β β α δ β+ + = − + − (8) hence, the active and reactive power at the shunt compensation block is calculated as 57 s. ali al-mawsawi and mohammed r. qader sin( )sh psh sh v v p x α= , 2 cos( )sh p shsh sh s v v v x x α= h −q (9),(10) the active and reactive power of the series compensation block is determined as 4 cos( 90)pq rpq v v p x β= − + (11) 2 4 4 4 sin( 90)pq p pq pq rpq v v v v v q x x x β= − − + (12) for the sake of simplicity, it is assumed that the active power consumed by this facts device is zero. therefore, from (9) and (11) 0pq shp p+ = (13) hence, the input power (p1) can be determined as 1 2 3 sin( ) sin( )s ps r v vv v p x x δ δ β= + (14) therefore; if shrs vvvp and ,,,1 are given (known), then equations (4), (7), (8), (13) and (14) can be solved. accordingly, the upfc can be operated as a voltage regulator with different operation points by varying the modulation index mpq from 10% to 100%. in addition, if x3 is varied with respect to x4, then an investigation for locating the optimum position of the facts device along the transmission line is also possible. 3. simulation results the system in figure 1 has been modeled and simulated by using the matlab package program. an active power (p1) supplied to the grid by the synchronous machine selected to be 40 mw, the terminal sending end voltage vs = 66.9 kv and the receiving end voltage vr = 65.4 kv. the two parallel transmission lines are assumed to be identical and each having a series reactance of (x=20 ω). hence the power injected by the generator will be equally divided on the two transmission lines before installing the facts device (i.e. p2 = p3 = 20 mw). on the other hand, vsh is selected to be 20% of the terminal line voltage vp before the installation of the facts device. the steady-state performance results have been tested by varying the series modulation index mpq from 10% to 100%. in addition, the effect of the installation location of the facts device has been investigated. figure 4 shows that at each position the terminal line voltage (vp) can be controlled by varying the modulation index mpq. however it can be seen that, the vp is more sensitive to the variation of the modulation index mpq as the installation of the facts device is more close to the receiving terminal bus. in addition, minimum value of vp can be obtained when the device is installed at position around mid point of the transmission line. figures 5 and 6 show that, at each position, the distribution of the active power flow in both lines can be controlled by varying the modulation index mpq. however, it can be seen that, in some positions the power flows in both lines are more sensitive to the variation of the modulation index mpq. figure 7 shows that the reactive power flow (q3) through the transmission line on which the facts device is installed, is highly sensitive to the change of the modulation index mpq , whereas 58 steady state analysis of a upfc as voltage regulator the reactive power flow of the other line (q2) is slightly sensitive to the change of the modulation index mpq as shown in figure 8. furthermore, figure 7 shows that the reactive power (q3) is decreasing as the position is increasing and this is because both angles β and δ are also decreasing as the percentage position is increasing as shown in figures 9 and 10. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0.5 1 1.5 2 x 10 7 positionm index p3 0 0.2 0.4 0.6 0.8 1 0 0.5 1 2 3 4 5 6 x 10 4 position m index vp figure 4. terminal voltage vp for various figure 5. active power flow p2 for various modulations index. modulation index. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 2 4 6 8 10 x 10 8 positionm index q3 figure 6. active power flow p2 for various. figure 7. reactive power flow q3 for various modulations index. modulation index. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 2 2.5 3 3.5 x 10 7 positionm index p2 figure 8. reactive power flow q2 for various figure 9. variation of angle (β) for 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0 0.05 0.1 0.15 0.2 positionm index beta 0 0.2 0.4 0.6 0.8 1 0 0.5 1 6 6.5 7 7.5 x 10 6 positionm ind e x q 2 various modulation index. modulation index. 59 s. ali al-mawsawi and mohammed r. qader figure 10. load angle (δ) for various modulation index. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 0.1 0.12 0.14 positionm index delat 6. conclusions s been modeled as a voltage regulator. the system with parallel transmission lines has been simulated using a matlab program package. in this case a pwm scheme has been used gyugyi, l. 1992. unified power flow co pt for flexible e ac transmission systems, iee proceeding-c, 139(4): 323-331. r systems 9(2): 904-911. r ns, cigre .23-203. smission fue wer studies, iee proceeding-c moh eceived 4 august 2001 ccepted 25 april 2003 the upfc ha to control the operation of the series compensation block of the upfc. it has been shown that by varying the modulation index (mpq), the active power flow distribution in the parallel transmission lines can be controlled. in addition, the effect of the installation location of such facts device has been discussed. furthermore, the simulation results have shown that the reactive power flow is highly sensitive to the variation of the modulation index (mpq) on the line connected to the device, while it is much less sensitive to the variation of mpq on the other line. references ntroller conce gyugyi, l. 1994. dynamic compensators of ac transmission lines by solid state synchronous voltage source. ieee trans. on powe gyugyi, l. and hingorani, n.g., nannery, p.r. and tai, n. 1990. advanced static va compensators using gate-turn-off thyristors for utility applicatio gyugyi, l., schauder, c.d., williams, s.l., rietman, t.r., torgerson, d.r. and edris, a. 1995. the unified power flow controller: a new approach to power tran control, ieee transactions on power delivery, april 1995. rte-esquivel, c.r. and acha, e. 1997. unified power flow controller: a critical comparison of newton-raphson upfc algorithms in po generation transmission distribution, 144(5):457-464. an, n. undelard, t.m. and robbins, w.p. 1998. power electronics converters applications and design, john wiley and sons. r a 60 steady state analysis of a upfc as voltage regulator for optimal position in the transmission line s. ali al-mawsawi and mohammed r. qader department of electrical engineering, university of bahrain, p.o.box 32038, email: salmosawi@eng.uob.bh figure 1. upfc controller. 2. mathematical model 3. simulation results figure 6. active power flow p2 for various. figure 7. reactive power flow q3 for various modulations index. modulation index. 6. conclusions references electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 61-65 © 2003 sultan qaboos university characterizations of ksemimetric spaces abdul m. mohamad department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman, email: mohamad@squ.edu.om. kة من الصنف لفضاءات شبه المترياتمييز عبدالعظيم مؤات محمد . بطرق مختلفة ومتكافئةkنقوم في هذا البحث بكتابة الفضاءات شبه المترية من الصنف : خالصة abstract: in this paper, we prove, for a space x, the following are equivalent: 1. x is a ω ∆1 space with a regular-gδ-diagonal, 2. x is a ω ∆2 space with a regular-gδ-diagonal, 3. x is a semi-developable space with gδ (3) -diagonal, 4. x is a ω ∆1-space with a gδ(3)-diagonal, 5. x is a ω ∆2 -space with a gδ(3)-diagonal, 6. x is a q, β -space with a g*δ (2)-diagonal, 7. x is a semi-developable space with g*δ (2)-diagonal, 8. x is a semimetrizable, c-stratifiable space, 9. x is a c-nagata β -space, 10. x is a k-semimetrizable. keywords: ω ∆ space,ssemidevelopable space, -semimetrizable space, k β -space, g *δ (2)-diagonal, gδ (3)diagonal, regular-gδ -diagonal, semi-stratifiable, c -semi-stratifiable. 1. introduction a space x is semimetrizable if there exists a real valued function d on x x× such that 1. d x ( ) ( ), = , 0.y d y x ≥ 0 2. d x if and only if ( ), y = .x y= . 3. for ,m x x m⊂ ∈ if and only if ( ) ( ){ }, inf , : m d x y y m= ∈ 0.= 0 d x if in addition, d satisfies. 4. d h whenever and k are disjoint compact subsets of ( ), k > h x , then x is said to be semimetrizable (arhangel'skii, 1966) . let { k − } nn ng ∈ be a sequence of covers of a space x . 1. suppose { } nn ng ∈ satisfies the following property: if, ( ), ,nx st x g∈ n then the sequence nx has a cluster point. 61 adbul m. mohamad (a) if, for each , g is an open cover of nn ∈ n x , then x is called a ω ∆ -space (borges, 1968). (b) if, for each , is an open subset of nn ∈ (st , )nx g x , then x is called a 1ω ∆ -space (gittings, 1975). (c) if, for each , nn ∈ x ∈ int , then x is called a ( , nx g )st ω ∆2–space (gittings, 1975). . 2. if for each x x∈ , ( ){ } nn∈ , nx gst is a local base at x , then x is called a semi-developable space. if in addition, for each , nn ∈ ( )n,gst is an open subset of x x , then x is called a semi developable space. 3. if, for each , gnn ∈ n is an open cover of x and for each x x∈ , ( ) { }3 , ,n nst x g x=∩ then x has a g diagonal. ( )3 −δ 4. if, for each , nn ∈ ng is an open cover of x and for each x x∈ , ( ) { }2 ,n nst x g x=∩ , then x has a g diagonal. * (2δ )5. if, for each , st is an open subset of nn ∈ ( , ) nx g x and for each x x∈ , ( ) { },n nst x g x=∩ , then x has a s diagonal. 2 − 6. if, for each , nn ∈ x ∈ int st and for each ( , nx g ) x x∈ , { }( , ) ,n nst x g x=∩ then x has a 2α -diagonal. 7. if, for each , gnn ∈ n is an open cover of x and for any pair of distinct points , , x y x∈ there exist neighborhoods u and of v x and , respectively, and , such that y nn ∈ (st , )nu g v = , φ∩ equivalently, ( , nst v g ) = , u φ∩ then x has a regulargδ -diagonal. a coc-map (= countable open covering map) for a topological space x is a function from n x× into the topology of x such that for every x x∈ , and n n∈ , x∈g(n, x) and g(n + 1, x) g(n,x). a space ⊆ x is called β -space if x has a coc-map g such that if ( ), nx g n x∈ for every , then the sequence n∈n nx has a cluster point. a space x is called q space if − x has a coc-map g such that if ( ,n )x g n x∈ for every then the sequence n,n ∈ nx has a cluster point. a space x is called c-semi-stratifiable (martin, 1973) (c-stratifiable) if there is a sequence ( ),g n x of open neighborhoods of x such that for each compact set ( ){ }, if ( , )= , : ,g n k g n x x k⊂ ∈∪k x then ( ){ } ( ){ }( ), : 1 , : 1g n k n k g n k n k≥ = ≥ =∩ ∩ . the coc-map : ng x τ× → is called a c-semi-stratification (c-stratification) of x . a space x is called c-nagata if it is first countable, cstratifiable space. throughout this paper, all spaces are assumed to be t 2 − spaces unless otherwise stated explicitly. the letter always denotes the set of all positive integers. n 2. main results lemma 1 : every space with a g diagonal has a g diagonal. (3) -δ * (2) -δ proof. let { } nn ng ∈ be a g diagonal sequence for (3) -δ x . we want to prove that ( ) { }2nn st x∈∩ , ng x= for every x x∈ . suppose we have ( )2 ,n t x g∈ nq s . for every open set such that q and for each ∩ u u∈ nn ∈ 2 ( , ) .nst x g u φ≠∩ 62 characterizations of k-semimetric spaces in particular, if g ng∈ is such that q g∈ then 2 ( , ) .nst x g g φ≠∩ so, q s as this holds for all , it follows that 3 ( , ). nt x g∈ n x q= . lemma 2: any space with a gδ* (2)-diagonal is a c-stratifiable space. proof. let ng be a sequence of open covers of a space x such that ( )2n , {n nst x g x∈ =∩ }. define a coc-map by g ( ) ( ), , ng n x st x g= . we must prove that ( ),g n k k=∩ for any compact subset of x . let p k∉ . then, for each , there exists an integer k k∈ ( )n k such that ( )( )2 , .n kp st k g∉ therefore there is an open set u(k) containing p such that ( ) ( )( ), .2 n kst k gu k φ= k k ∩ ,k k since is compact, we can find a finite number of points of such that 1 2 ,..., rk ( )( ){ },i n kk g : 1, 2,...,st i r= covers . let k ( ){ }maxn n= : 1,k i 2,..., ,i r= and ( )1 .i iu u k== ∩ then ( ), .nu st k g φ∩ = that is,u g ( ),n k φ=∩ . this implies ( ), .p g n k∉ theorem 1: every 1ω ∆ -space with s2-diagonal is an o-semidevelopable space. proof. let { } nn ng ∈ be a countable family of covers of a space x illustrating that x is a ω ∆ 1space. since x has an -diagonal, there exists a sequence 2s :n nν n ∈ of covers of x such that, for each x x∈ and (n, , nn st x )ν∈ is an open subset of x and ( ) {n x }n ,n st x ν∈ =∩ . for each , let nn ∈ ( ) ( ){ }1 1: , , , 1, 2,..., .n nn i i i i i i i iu u u g v g g v i nν= == = ∩ ∈ ∈ =∩ ∩ it is easy to see that u refines u for all 1n + n nn ∈ and that, for each x x∈ , ( ) { }n ,n nst x u x∈ =∩ . furthermore, for each x x∈ and nn ∈ ( ) ( )( ) ( )( )1 1, ,n nn i i i ist x u st x g st x ,ν= == ∩ ∩ ∩ and thus st is an open subset of ( , nx u ) x . also it is easy to check that : nnu n ∈ is a ω ∆ 1 sequence for x . it remains to show that : nnu n ∈ is a semi-development for x . suppose instead that : nnu n ∈ is not a semi-development for x . then there is a point x , an open neighborhood w of x , and a sequence nx such that for all , n ( ),n nx st x u∈ and nx w∉ . since :nu n ∈ n is a 1ω ∆ -sequence for x , the sequence nx has a cluster point p . clearly p w∉ so p x≠ . by choice of :n nν ∈ n , there are in and a neighborhood v of k n p such that ( ), kx .v st ν φ=∩ now for n , k≥ ( ) ( ) ( ), k, ,n nt x u st x k sx us t x ν∈ ⊂ ⊂ so .nx v∉ this contradicts the fact that p is a cluster point of nx . thus : ∈ nnu n is a semi-development for x . theorem 2: the following are equivalent for a regular 2ω ∆ -space x : (1) x is semimetrizable; (2) x is semi-stratifiable; (3) x is θ -refinable and has a gδ-diagonal; (4) x has a g*δ-diagonal; 63 adbul m. mohamad (5) x has 2α -diagonal. (6) x is semidevelopable. proof. the only implications requiring comment are (5) ⇒ (6) and (6) (1). to prove (5) ⇒ (6), let { ⇒ }ng be a countable family of covers of x illustrating that x is a 2ω ∆ -space. let : n nnν ∈ be an 2α -sequence for x . let the sequence :nu n n∈ be defined as in the proof of theorem 2.3. since for each x x∈ and nn ∈ , ( ) )( ) ( )x∩1 1n n= = , ,i∩ ∩x u i ( ν x x u∈ : ∈ n x ω ∆ x ω ∆ x x ω ∆ x ω ∆ x x x x β x 2∆ β ⇒ ω ∆ n x 0n 0n n> ) u⊂ ( 2 , ngy v { }0 1 2,nxn n , n x ( ,y g )st (3 , . ⇔ sphere ered at x ( ,x ), y < / .n { }i= 1/ spher center . ( ng,t x ( < ( ( ), ,n i i iintst nst x g inst= ), .n we have inst it follows, exactly as before, that nu n is a semi-development for x . the implication (6) (1) follows from (alexander, 1971), theorem 1.3. ⇒ theorem 3: for a space x, the following are equivalent: 1. is a 1-space with a regular -gδ-diagonal, 2. is a 2-space with a regular-gδ-diagonal, 3. is a semi-developable space with gδ (3)-diagonal, 4. is a 1-space with a g δ (3)-diagonal, 5. is a 2-space with a g δ (3)-diagonal, 6. is a q, β -space with a g *δ (2)-diagonal, 7. is a semi-developable space with g *δ (2)-diagonal, 8. is a semimetrizable, c-stratifiable space, 9. is a c-nagata -space, 10. is a k-semimetrizable. proof. it is clear that 1 ⇒ 2, 3⇒ 4, 4⇒ 5, 8⇒ 9. the implication 5⇒ 6 follows by lemma 2.5 and since every ω -space is a q, β -space. the implication 6⇒ 7 follows by facts every β -space with a g *δ -diagonal is a semi-stratifiable space, every q-space with a g *δ -diagonal is first countable and every first countable, semi-stratifiable space is a semimetrizable. the implication 7 8 follows by lemma 2.2 and since every t⇒ 0 semi-developable space is a semimetrizable. the implication 9⇒ 8 follows by facts every c-stratifiable, -space is semi-stratifiable and every first countable, semi-stratifiable space is a semimetrizable. 1 8 follows by lemma 2.2, theorem 2.3. for 2⇒ 3. suppose that x is a 2 -space with a regular-gδ-diagonal. every space with a regular-gδ-diagonal has a g *δ -diagonal. by theorem 2.4, x is a semi-developable space. let { }ng be a semi-development and regulargδ-diagonal-sequence. to see that g satisfies the gδ(3)diagonal-sequence, let x y≠ points in x , u and v open sets containing and respectively, and an integer such that if , then no member of g meets both u and v . let and be integers such that st and y n 1n 2n ( 1 , nx g ) ⊂st . ma= n . then no member of g meets both st and . thus ( ), ng n )ngy s∉ t y for 10 3. let { }1/ cent .n =g n it is clear that x ng is a sequence of covers of and if and only if )ngy st∈ ( 1d x therefore ng is a semidevelopment for x . now let nterior of e ed atng n it is clear that ng is a sequence of open covers of x and if then )y s∈ ), y 1/ n.d x if there exist distinct points x and x 64 characterizations of k-semimetric spaces y such that ( )3 , ny st x g∈ for all n n∈ , then there are sequences nx and ny such that ( ) ( )n n, , ,n nx st x g∈ y st y g∈ and ( ),nt x gny s∈ n . let { } { }1 :nk x x n ω= ∈∪ and { }2k y= { }:ny n ω∈∪ 1 2k k φ=∩ ( )1 2, 0k ,= n x d x ( ) ( ){ }, 1y / inf j= ∈ : , ist y g∉ ( , n )x st y g∈ ( , h ( ), .y 1/ n< h ) 0.= nx ny k h ( ),n nd x y < 1/ n x nx ny in x x y ( ) 1/ i< ( ), kx g, . we may assume with both sets compact. but d k a contradiction. conversely, let g be a semi-development and gδ(3)-diagonal-sequence for . define a semimetric on by n xd x . from the definition if and only if d x assume there exist disjoint compacta k and such that d k we can find two sequences and in and respectively, such that . note that is sequential and t so that 2 and have convergent subsequences. let and in y be subsequences of nx and ny converging to and , respectively. without loss of generality, we may assume ( ), in x < k 1/ id x and for each since d x it follows that there is no such that . this contradiction completes the proof. , in y 3t d y y sn.i ∈ ( , 1/ i in n y i) < ∉ references alexander, c.1971. semi-developable space and quotient images of metric spaces, pacific j. math 37: 277-293. arhangel'skii, a. 1966. mappings and spaces, russian math. surveys, 21:115-162. borges, c. 1968. on metrizability of topological spaces, canad. j. math. 20:795-804. gittings, r. 1975. on o-semimetrizable space, studies in topology, academic press, new york, 179-188. gruenhage, g. 1984.generalized metric spaces, handbook of set-theoretic topology 423 501. martin, h.w.1973. metrizability of m-spaces, canad. j. math., 25:840-841. received 15 may 2001 accepted 20 february 2003 65 abdul m. mohamad department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman, email: mohamad@squ.edu.om. îáçõé : äþæã ýí åðç çáèíë èßêçèé � references microsoft word elec-2.doc science and technology, special review (2000) 209-225 © 2000 sultan qaboos university 209 converged networking: a review of concepts and technologies adel ahmed ali and ahmed m. al-naamany department of electrical, electronics and computer engineering, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. استعراض األفكار و التقنيات: شبكات االتصال المتكاملة عادل أحمد علي وأحمد محمد النعماني وتستخدم الشبكات المتكاملة في . برزت فكرة الشبكات المتكاملة في اآلونة األخيرة والقت الكثير من االهتمام : خالصة ویأخذ التكامل عدة أنماط نذآر منها تكامل . بكة موحدةنقل االتصاالت الهاتفية ، و إشارات التلفزة و المعلومات عبر ش .المعلومات ، تكامل البروتوآوالت ، تكامل التطبيقات ، تكامل التقنيات ، و تكامل أجهزة االتصاالت ددة ات المتع ل المعلوم يلة لنق ول آوس ى القب تحوذت عل ة اس بكة عالمي بحت ش ت و أص بكة اإلنترن ورت ش د تط ولق وأصبح من المتوقع أن تكتمل شبكة اإلنترنت في المستقبل القریب . ة والمرئية و الهاتفية وغيرها آاإلشارات المسموع وقد طرحت العدید من األفكار حول تكامل الشبكات، نذآر منها على سبيل . لتصبح الشبكة العالمية لنقل المعلومات ، مما یتيح االستفادة القصوى من الشبكات المثال تكامل شبكات االتصاالت و شبكات الحاسبات لتصبح شبكة واحدة وتستعرض هذه الدراسة تقنيات الشبكات وتقدم بشكل مبسط المعلومات الضروریة التالية . الهاتفية و شبكة اإلنترنت أساسيات الشبكات ، تقنية الشبكات ، أنواع اإلشارات المنقولة و تكامل شبكات االتصاالت و : لفهم هذه التقنية الهامة .ات الحاسباتشبك abstract: converged networking is an emerging technology thrust that integrates voice, video, and data traffic on a single network. converged networking encompasses several aspects, all of which are related to the aggregation of networking activity. such aspects include, payload convergence, protocol convergence, physical convergence, device convergence, application convergence, technology convergence, etc. in recent years the internet has developed into a global data network that is highly accepted as a multimedia information platform, which has the potential to develop into an alternative carrier network in the future. several convergence scenarios have been recently proposed, ranging from integrating communication services and computer application into two separate networks, to building a seamless multimedia network, which converges the central office based network and the internet in a single network, thereby enabling telecommunications operators and service provider's tremendous investment in existing network infrastructure to be fully utilized. this paper offers introduction and review of the networking technologies. the paper presents the existing multiple networks into two infrastructures: an atm/frame relay (ethernet)based corporate network with integrated voice, video, and data traffic and an internet-based network for secure intranet, extranet and remote access. this work is aimed at summarizing the internetworking basics and technologies which are essential for the emerging converged networking systems. the specific areas addressed here are networking basics, networking technologies, types of traffic, and convergence of computer and communication networks. adel.ahmed.ali and ahmed m.al-naamany 210 contents introduction 211 internetworking basics 212 2.1 open systems interconnection (ost) references model 214 2.2 transmission control protocol/internet protocol (tcp/ip) 216 2.3 information formats 216 2.4 connection-oriented and connectionless network services 217 3. networking technologies 217 3.1 asynchronous transfer mode (atm) 217 3.2 ethernet 218 3.3 frame relay 218 3.4 synchronous optical network (sonet) and board-band integrated service digital network (bisdn) 219 3.5 fiber distributed data interface (fddi) 219 3.6 digital subscriber line 219 3.7 asymmetric digital subscriber line (adsl) 220 4. multimedia 220 4.1 multimedia technologies and standards 220 4.2 compression standards 220 5. converged networking 220 5.1 convergence between public switching and the internet 220 5.2 convergence between atm and ethernet 221 6. concluding remarks 224 7. references 225 nomenclature atm asynchronous transfer mode bgp border gateway protocol bisdn broadband integrated services digital network catv cable television cmip common management information protocol csma/cd carrier-sense multiple access with collision detection ftam file transfer access and management ftp file transfer protocol gif graphics interchange format ieee the institute of electrical and electronic engineers ip internet protocol iso international organization for standardization isp internet service provider lan local area network llc logical link control mac media access control mmf multimode fiber mpeg motion picture experts group nic network interface card nbp name binding protocol nsp network service provider osi open systems interconnection ospf open shortest path first converged networking 211 qos quality of service pace priority access control ppp point to point protocol pots plain old telephony system rip routing information protocol scp session control protocol sdms switched multi-megabit data service smf single-mode fiber smtp simple mail transfer protocol sna system network architecture sdh synchronous digital hierarchy sonet synchronous optical network tcp transmission control protocol tcp/ip transmission control protocol/internet protocol tiff tagged image file format vtp virtual terminal protocol wan wide-area network zip zone information protocol 1. introduction ecently the world has seen the introduction of converged information technology applications. we are now seeing computers mimicking the telephone and televisions as well as elementary teleconferencing. the advent of television, which will incorporate some of computer functions and telephone, is now also a reality. however apart from all of the above the major advancement is on the industrial networks and work place, which converged networking, applications are on the rise. this review paper aims to cover the internetworking basics and technologies as well as the types of traffics (cisco 1997). converged networking is an emerging technology thrust that integrates voice, video, and data traffic on a single network. the market drivers for converged networks are cost reduction; support for sophisticated, highly integrated applications; and the provision of greater network flexibility and functionality (collins et.al. 1997) and (rafter 1997). payload convergence is that aspect of converged networking wherein different data types are carried in the same communications format. protocol convergence is the movement away from multi-protocol to single protocol (typically ip) networks (cisco 1997). physical convergence occurs when payloads travel over the same physical network equipment regardless of their service requirements. device convergence describes the trend in network device architecture to support different networking paradigms in a single system. application convergence represents the appearance of applications that integrate formerly separate functions. technology convergence signifies the move toward common networking technologies that satisfy both lan and wan requirements. new technologies spur new application development, and new applications, in turn, fuel the need for further technology advancements. in a relatively short time span, network connections have evolved from shared or switched ethernet to shared or switched fast ethernet to accommodate rising bandwidth demand. within the enterprise networks, business applications are now advancing to embrace highresolution graphics, video, and other rich media types that exceed the capacity of even fast ethernet performance. this latest generation of bandwidth-intensive applications can be organized into four categories as depicted in figure 1, i.e. scientific modeling, medical imaging applications, multimedia and graphical publication and finally video and videoconference applications that are getting bigger in size from megabytes to gigabytes to terabytes. r adel.ahmed.ali and ahmed m.al-naamany 212 internet and intranet applications create unpredictable any-to-any traffic patterns. increasingly, with servers distributed across the enterprise and users accessing web sites inside and outside the corporate network, there is no way to predict where traffic will go. data warehousing and backup applications handle gigabytes or terabytes of data distributed among hundreds of servers and storage systems. bandwidth-intensive group-ware applications such as desktop videoconferencing, interactive whiteboarding, and real-time video that support mission-critical business applications not only require more raw bandwidth, they also demand low latency and limited jitter to be effective to accommodate bandwidthintensive applications, two networking technologies are available, with products and technical support, viz., atm, frame relay and gigabit ethernet. for the last few years, there has been considerable debate over whether atm or gigabit ethernet will win in the marketplace (chang et.al 1999 and braden et.al. 1994). on the other hand, the internet has developed to become a global data network, which attracts numerous users, especially with the variety of information and multimedia applications offered online. although still in its infancy with regard to reliability and guaranteed grade of service, the internet is highly accepted as an information platform by users and information content providers alike. the high investments being made in the internet by the computer industry, network carriers, and service providers may prove that the internet will meet the expectations for exponential growth predicted by analysts and boosted performance claimed by the internet industry (white et.al. 1997). bandwidth intensive applications video / videoconferencing medical imaging applications multimedia and graphical publications scientific modeling figure 1. categories of bandwidth intensive applications this paper is organized as follows: in section 2 internetworking basics are summarized. networking technologies are presented in section 3, followed by a summary of the main features of the multimedia traffic in section 4. a converged networking based on (atmframe relay-ethernet)/ (internet) is presented in section 5, and some concluding remarks are summarized in section 6. 2. internetworking basics different media (audio, video, animation, data) are included in multimedia-networked applications, thus leading to the integrated services information infrastructure concept. the infrastructure is composed of terminals and servers interconnected by means of data links (pipes) via intermediate network nodes. converged networking 213 network nodes are routing and switching devices to implement the required exchange of information among network hosts. networks are usually equipped with data links (either physical links or links realized by sub networks), by switches and routers, and by auxiliary network servers. network servers typically provide real-time address translation and routing functions; or they serve for network and service management tasks, including service billing. table 1. summary of wan technologies an inter-network is a collection of individual networks, connected by intermediate networking devices that functions as a single large network. internetworking refers to the industry, products, and procedures that meet the challenge of creating and administering inter-networks. lans evolved around the pc revolution. lans enabled multiple users in a relatively small geographical area to exchange files and messages, as well as access shared resources such as file servers. wans interconnect lans across normal telephone lines (and other media), thereby interconnecting geographically dispersed users. table 1 presents a summary of wan technologies. today, high-speed lans and switched inter-networks are becoming widely used, largely because they operate at very high speeds and support such high-bandwidth applications as voice and videoconferencing. internetworking evolved as a solution to three key problems: isolated lans, duplication of resources, and a lack of network management. isolated lans made electronic communication between different offices or departments impossible. duplication of resources meant that the same hardware and software had to be supplied to each office or department, as did a separate support staff. this lack of network management meant that no centralized method of managing and troubleshooting networks existed. wan technology typical uses asymmetric digital subscriber line (adsl) a new modem technology. coverts existing twisted pair telephone lines into access path for multimedia ad high-speed data communications. adsl transmits more than 6 mbps to a subscriber and as much as 640 kbps more in both directions. analog modem used by telecommuters and mobile users who access the network less than two hours per day or for backup for another type of link. leased line leased lines can be used for point to point protocol (ppp) networks and hub and spoke topologies, or for backup for another type of link. integrated services digital networks (isdn) isdn can be used for cost effective remote access to corporate networks. it can be used in both private and carrier provided networks. frame relay frame relay provides a cost effective, high speed, low latency mesh topology between remote sites. it can be used in both private and carrier provided networks. switched multi megabit data service (smds) smds provides high speed, high performance connections across public data networks. it can also be deployed in metropolitan area networks (mans). x.25 x.25 can provide a reliable wan circuit or backbone. it also provides support for legacy applications. wan, atm wan and atm can be used to accelerate bandwidth requirements. it also provides support for multiple qos classes for differing application requirements for delay and loss. adel.ahmed.ali and ahmed m.al-naamany 214 2.1 open systems interconnection (osi) reference model the osi reference model describes how information from a software application in one computer moves through a network medium to a software application in another computer. osi is a conceptual model composed of seven layers, each specifying particular network functions as shown in figure 2 (comer 1999). ftp, telnet, smtp, snmp nfs xdr rpc tcp ip arp, rarp not specified application presentation session transport network data link physical figure 2. osi model layers the osi model provides a conceptual framework for communication between computers, but the model itself is not a method of communication. actual communication is made possible by using communication protocols. in the context of data networking, a protocol is a formal set of rules and conventions that governs how computers exchange information over a network medium. a protocol implements the functions of one or more of the osi layers. a wide variety of communication protocols exist, but all of them tend to fall into one of the following groups: lan protocols, wan protocols, network protocols, and routing protocols. lan protocols operate at the physical and data link layers of the osi model and define communication over the various lan media. wan protocols operate at the lowest three layers of the osi model and define communication over the various wide-area media. routing protocols are network-layer protocols that are responsible for path determination and traffic switching. finally, network protocols are the various upper-layer protocols that exist in a given protocol suite. table 2 summarizes the main tasks performed by each of the seven layers of the open system interconnection (osi) reference model: two key types of application-layer implementations are tcp/ip applications and osi applications. tcp/ip applications are protocols, such as telnet, ftp, and that exist in the internet protocol suite. osi applications are protocols, such as ftam, vtp, and cmip that exist in the osi suite. converged networking 215 table 2. seven layers of the open system interconnection (osi) reference model no main functions 7 functions typically include identifying communication partners, determining resource availability, and synchronizing communication. two key types of application-layer implementations are tcp/ip applications and osi applications. tcp/ip applications are protocols, such as telnet, ftp, and smtp that exist in the internet protocol suite. osi applications are protocols, such as ftam, vtp, and cmip that exist in the osi suite. 6 provides a variety of coding and conversion functions that are applied to application layer data. these functions ensure that information sent from the application layer of one system will be readable by the application layer of another system. common data representation formats are ebcdic and ascii. some well-known standards for video include quicktime mpeg. among the well-known graphic image formats are gif, jpeg, and tiff. gif is a standard for compressing and coding graphic images. jpeg is another compression and coding standard for graphic images, and tiff is a standard coding format for graphic images. 5 establishes, manages, and terminates communication sessions between presentation layer entities. communication sessions consist of service requests and service responses that occur between applications located in different network devices. some examples of session-layer implementations include zip, the appletalk protocol that coordinates the name binding process; and scp, the decnet phase iv session-layer protocol. 4 implements reliable inter-network data transport services that are transparent to upper layers. functions typically include flow control, multiplexing, virtual circuit management, and error checking and recovery. some transport-layer implementations include tcp, nbp, and osi transport protocols. 3 provides routing and related functions that enable multiple data links to be combined into an inter-network. some common routing protocols include bgp, an internet inter-domain routing protocol; ospf, a link-state, interior gateway protocol developed for use in tcp/ip networks; and rip, an internet routing protocol that uses hop count as its metric. 2 provides reliable transit of data across a physical network link. different data link layer specifications define different network and protocol characteristics, including physical addressing, network topology, error notification, sequencing of frames, and flow control. 1 responsible for actually placing information on the medium. it defines the electrical, mechanical, procedural, and functional specifications for activating, maintaining, and deactivating the physical link between communicating network systems. its specifications define voltage levels, timing of voltage changes, physical data rates, maximum transmission distances, and physical connectors. a pp lic at io n p re se nt at io n se ss io n t ra ns po rt n et w or k d at a lin k p hy si ca l adel.ahmed.ali and ahmed m.al-naamany 216 2.2 transmission control protocol/internet protocol (tcp/ip) tcp/ip is a set of communications protocols, that grew out of a research project that was funded by the u.s. department of defense. the tcp/ip networking scheme implements peer-to-peer client-server architecture. any computing system in the network can run tcp/ip server software and can provide services to any other computing system that runs complementary tcp/ip client software. in tcp/ip, a connection internet layer protocol that provides the best-efforts datagram delivery service. note that the functional layer tcp/ip corresponds to the osi model network layer. the internet layer provides routing and relaying functions that are used when data must be passed from a host to some other network in the internet. it operates in the source and destination hosts and in all the routers along the path between the hosts (comer 1999). table 3. comparisons of communication switching techniques 2.3 information formats common information formats include frame, packet, datagram, segment, message, cell, and data unit. a frame is an information unit whose source and destination are data link layer entities. a frame is circuit switching message switching datagram packet switching virtual circuit packet switching dedicated transmission path no dedicated path no dedicated path no dedicated path continuous transmission of data transmission of messages transmissions of packets transmissions of packets fast enough for interactive too slow for interactive fast enough for interactive fast enough for interactive messages are not stored messages are filed for later retrieval packets may be stored until delivered packets are stored until delivered the paths is established for entire conversation route established per message route established per packet route may be established for entire conversation call setup plus negligible transmission delay message transmission delay per hop packet transmission delay per hop call setup plus packet transmission delay busy signal if called party is busy no busy signal sender may be notified if packet not delivered sender notified of connection denial overload may block call setup: no delay for established call overload increases message delay overload increases packet delay overload may block call setup: increases packet delay user responsible for message loss protection network responsible for messages network may be responsible for individual packets network may be responsible for packet delay usually no speed or code conversion speed and code conversion speed and code conversion speed and code conversion fixed bandwidth for call duration dynamic use of bandwidth dynamic use of bandwidth dynamic use of bandwidth no overhead bits after call setup overhead bits in each message overhead bits in each packet overhead bits in each packet converged networking 217 composed of the data-link layer header (and possibly a trailer) and upper-layer data. a packet is an information unit whose source and destination are network-layer entities. a packet is composed of the network-layer header (and possibly a trailer) and upper-layer data. data from upper-layer entities is encapsulated in the network-layer header and trailer. the term datagram usually refers to an information unit whose source and destination are networklayer entities that use connectionless network service. a message is an information unit whose source and destination entities exist above the network layer (often the application layer). a cell is an information unit of a fixed size whose source and destination are data-link layer entities. cells are used in switched environments, such as atm and smds networks. a cell is composed of the header and payload. the header is typically 5 bytes long. the payload contains upper-layer data that is encapsulated in the cell header and is typically 48 bytes long (comer 1999). 2.4 connection-oriented and connectionless network services in general, networking protocols and the data traffic that they support can be characterized as being either connection-oriented or connectionless. in brief, connection-oriented data handling involves using a specific path that is established for the duration of a connection. connectionless data handling involves passing data through a permanently established connection. connection-oriented network service carries two significant disadvantages over connectionless, static-path selection and the static reservation of network resources. connection-oriented services, however, are useful for transmitting data from applications that don't tolerate delays and packet resequencing. voice and video applications are typically based on connection-oriented services. as another disadvantage, connectionless network service does not predetermine the path from the source to the destination system, nor are packet sequencing, data throughput, and other network resources guaranteed. connectionless service, however, offers two important advantages over connection-oriented service: dynamic-path selection and dynamic-bandwidth allocation. connectionless services are useful for transmitting data from applications that can tolerate some delay and resequencing. databased applications typically are based on connectionless service. table 3 presents a comparison of communication switching techniques. networking technologies the networking technologies are the means by which the multimedia is transported. thus, in this section, the major characteristics of such technologies will be described. 3.1 asynchronous transfer mode (atm) asynchronous transfer mode (atm) is a networking technology that contains a flexible multiplexing and switching technique, which provides variable bandwidth for local-area and wide-area networks. unlike ordinary synchronous configurations, atm permits flexible allocation of available bandwidth for data, voice, images and video (onvural 1995). atm uses a scalable architecture, making it easily upgradable; it allows a virtually unlimited number of users to have dedicated, high-speed connections with high-performance network servers (zhou et.al. 1995). a connection-oriented technology, atm delivers true qos on a per-connection basis, allowing for the convergence of voice, video, and data traffic. because it guarantees the necessary bandwidth and latency characteristics while protecting each call from the effects of every other call on the backbone, qos is vital for real-time applications such as videoconferencing or video-on-demand. bursty data traffic on one connection, for example, will not impact the smooth flow of real-time voice and video on another. interconnection of these types of networks is shown in figure 3 above. atm uses a connection-oriented operation. it establishes a sequence of switches, so that a connection is made from the source to the destination. such a connection is called a virtual circuit connection (vcc) adel.ahmed.ali and ahmed m.al-naamany 218 prycher (1995). the switches can be established to perform simplex, duplex, multicast, and broadcast communications. a virtual connection (vc) is a connection between a switching node and the next node; hence, a vcc consists of a series of vc’s. there are two kinds of vcs: 1) a permanent vc (pvc) for a leased line and 2) a switched vc (svc) for a dynamically established connection. to simplify the management of vc’s, a number of vc’s with the same starting and ending node is grouped together as a virtual path (vp). to identify a vp or a vc, a number is used as the identifier and is labeled vpi/vci (vp identifier/vc identifier) (liew 2000). qos signaling qos signaling ...... policy management, accounting host client connected networkconnected network figure 3. basic qos implementation 3.2 ethernet a form of lan data link that uses ieee 802.3/iso 8802-3 carrier-sense multiple access with collision detection (csma/cd) standards. the ethernet was originally designed to connect stations by a coaxial cable (10base5, thick cable and 10base2, thin cable), and later, it evolved to use twisted pairs to connect stations to a hub (10base-t). the transport rate is 10 mb/s. to improve the rate, the fast ethernet (100base-t) was developed to accommodate 100 mb/s and must use a hub to connect stations. the 100base-t can use two pairs of category 5 utp (unshielded twisted pair) or four pairs of category 3 utp cables. ethernet has survived as an essential media technology because of its tremendous flexibility and its relative simplicity to implement and understand. fast ethernet is 100 mbps version of the csma/cd (ethernet) standard. gigabit ethernet is ethernet that provides speeds of 1000 mbps (1000 base-x). it uses the same ethernet frame format and media access control technology as all other 802.3 ethernet technologies. it also uses the same 802.3 full-duplex ethernet technologies and 802.3 flow control. like its ethernet and fast ethernet precursors, gigabit ethernet is a physical (phy) and mac layer technology, specifying the layer 2 data link layer of the osi protocol model. 3.3 frame relay frame relay is a high-performance wan protocol that operates at the physical and data link layers of the osi reference model. frame relay originally was designed for use across integrated services digital network (isdn) interfaces. today, it is used over a variety of other network interfaces as well. frame relay is an example of a packet-switched technology. packet-switched networks enable end stations to converged networking 219 dynamically share the network medium and the available bandwidth. variable-length packets are used for more efficient and flexible transfers. these packets then are switched between the various network segments until the destination is reached. statistical multiplexing techniques control network access in a packet-switched network. the advantage of this technique is that it accommodates more flexibility and more efficient use of bandwidth. most of today's popular lans, such as ethernet and token ring, are packet-switched networks. 3.4 synchronous optical network (sonet) and broad-band integrated service digital network (bisdn) the sonet was developed by bellcore for wide area networking and it is an american national standard institute (ansi) standard that is used in the u.s. and canada. the european counterpart, synchronous digital hierarchy (sdh) is an itu-t standard. the sonet and sdh are physically compatible at synchronous transport signal sts-3c (155.52 mb/s) and synchronous transport module stm-1. the sonet uses a frame to carry lower-speed information (tributaries: video, audio, and data). the bandwidth for each tributary is guaranteed. the sonet uses synchronous multiplexing (smux) and add/drop multiplexers (adm) to insert a signal from a source and to extract a signal at the destination. the bisdn uses atm over the sonet to multiplex signals. the cells are packed in the sonet frame’s payload. bisdn provides lan and metropolitan area network (man) connections, including 802.x, fddi, frame relay, and switched multimegabit data service (smds). 3.5 fiber distributed data interface (fddi) fiber distributed data interface is a networking technology that uses a dual ring topology, often with dual networking equipment (concentrators, etc.). fddi facilitates redundancy and protection of the network. if a device fails, the primary and secondary rings enter a "wrap" state to form a logical connection and thus maintain the logical ring in the event of a link failure. fddi is capable of data rates of 100 mbps over fiber optic cable (smf and mmf) 3.6 digital subscriber line digital subscriber line (dsl) technology is a modem technology that uses existing twisted-pair telephone lines to transport high-bandwidth data, such as multimedia and video, to service subscribers. the term xdsl covers a number of similar yet competing forms of dsl technologies, including adsl, sdsl, hdsl, radsl, and vdsl. xdsl is drawing significant attention from implementers and service providers because it promises to deliver high-bandwidth data rates to dispersed locations with relatively small changes to the existing telecommunication infrastructure. voice network dsl network core network data voice dsl modem work stations telephone internet lan switch coppe r wire figure 4. a typical dsl utilization adel.ahmed.ali and ahmed m.al-naamany 220 this technology offers capability to utilize twisted pair copper wires for high-speed data and voice communications. see figure 4 for its typical configuration. xdsl services are dedicated, point-to-point, public network access on the local loop between a network service provider's (nsp's) central office and the customer site, or on local loops created either intra-building or intra-campus. currently the primary focus in xdsl is the development and deployment of adsl technologies and architectures. 3.7 asymmetric digital subscriber line (adsl) adsl technology is asymmetric. it allows more bandwidth downstream from an nsp's central office to the customer site than upstream from the subscriber to the central office. this asymmetry, combined with always-on access (which eliminates call setup), makes adsl ideal for internet/intranet surfing, videoon-demand, and remote lan access. users of these applications typically download much more information than they send. adsl down stream rate ranges from 1.544 mbps for distances of less than 5.5 km to 8.448 mbps for distances of less than 2.7 km. the upstream speeds ranges from 16 kbps to 640 kbps (see table 7 depicting the copper access transmission speeds). such rates expand existing access capacity by a factor of 50 or more without new cabling. adsl can literally transform the existing public information network from one limited to voice, text, and low-resolution graphics to a powerful, ubiquitous system capable of bringing multimedia, including full motion video, to every home at the beginning of the 21st century. 4. multimedia 4.1 multimedia technologies and standards table 4 summarizes some of the popular and widely used multimedia technologies or products. quicktime, video for windows, and indeo (intel video, and the new international standard organization (iso) standard entitled multimedia and hypermedia information coding expert group (mheg) (ganter 1997 and kathleen 1996). 4. 2 compression standards table 5 presents a summary of some of the most prominent compression standards (hwa wu et.al. 1998). developed by the iso, viz., jpeg for still pictures and mpeg for motion pictures. the proprietary graphics interchange format (gif) is the most widely used format in the internet and bulletin board service. converged networking several convergence strategies have been recently presented in the literature. two convergence scenarios are briefly outlined in this section. a comprehensive discussion is planned for part 2 of this paper. 5.1 convergence between public switching and the internet the internet has evolved from a classical, closed-community data network into the infrastructure for the global information society. however, performance degradation in the trunk networks due to long holding times of subscribers logged into the internet, has resulted in serious degradation of pstn/isdn user services and substantial loss of pstn/isdn operator revenue due to (ulrich et.al., 1998): lost calls to subscribers who are busy due to internet usage. migration of pstn/isdn services into the internet, for example fax replaced by e-mail and voice telephony potentially replaced by low-quality voice over ip. converged networking 221 to counteract such effects, either external xdsl devices can be used to divert the internet traffic into a data network before it hits the pstn/isdn, or controlling internet traffic in the central office as part of pstn/isdn traffic in an optimized manner (jeon et.al. 1998 and barzilai et.al. 1998). table 4. multimedia technologies and standards multimedia technologies developer compression & playback application quicktime used for pc and macintosh apple computer software supports motion picture expert group (mpeg), an iso compression standard, indeo (intel video), kodak’s photo cd format, and musical instrument digital interface (midi) video for windows designed specifically for pc microsoft software designed to playback videos in a small window using software; the size of small windows is 320x 240 pixels (quarter vga screen) in an intel 486 computer or 640x 480 pixels (vga screen) in an intel pentium computer equipped with a graphics accelerator indeo (intel video) david sarnoff research center hardware card: digital video interface (dvi) can achieve 160: 1 compression ratios and store 70 min of video on a cd-rom. a major application of indeo is videoconferencing. mpeg iso distribution of interactive multimedia applications in a multi vendor client /server environment 5.2 convergence between atm and ethernet the most widely used lan, the ethernet, has low throughput and scalability problems and is not suitable for multimedia communication. it is important to overcome these problems without a significant amount of new investment. there are several new developments on the horizon (delgrosi et.al. 1995 and garrahen et.al. 1993). priority access control enabled workgroup switch (pace) gives multimedia communication a high priority and improves the ethernet efficiency to 98%. cell in frames (cif) allows conversion between the atm cells and the ethernet frame format, so the atm cells can reach an ethernet station without the need to replace the nic in a computer (zhou et.al. 1999). adel.ahmed.ali and ahmed m.al-naamany 222 table 5. compression standards table 6 compares typical bit rate requirements of some video services, with and without the use of compression. compression standards developer application compression ratio joint photographic expert group (jpeg) iso/iec jtc1/sc29 wg10 continuous-tone (color or grayscale) still images for audio graphical conferencing, color fax, image archiving, desktop publishing, multimedia, and medical imaging. 7-27:1 for motion pictures 24:1 for video conferencing mpeg-1 compressing video on digital storage media (cd-rom) at 1 to 1.5 mb/s or through communication networks at various rates 130:1 mpeg-2 interlaced digital video, cable, and satellite tv high definition tv (hdtv) high-quality digital storage media video service over communication networks 30–100:1 mpeg-4 universal access capabilities for robustness in error-prone environments and content-based scalability contentbased interactivity for content-based multimedia data access content-based manipulation and bit stream editing hybrid natural and synthetic data coding, as well as improved temporal random access. is o /i e c j t c 1/ sc 29 w g 11 m pe g is fo r m ot io n pi ct ur es . converged networking 223 table 6. bit rate requirements of video services service example raw compressed real time (1/4 screen, low resolution) (126 x 120 pixels) (9bits/pixel; 15 frames/sec.) 2,074 64 real time (1/4 screen, high resolution) (128 x 240 pixels) (9bits/pixel; 15 frames/sec.) 4,147 384 real time (full screen, high resolution) (128 x 240 pixels; 9 bits/pixel; 30 frames/sec.) 8,294 2,000 non-real time, low resolution server (352 x 240 pixels; 9 bits/pixel; 10 frames/sec.) 7,603 384 vcr-quality server (352 x 240 pixels; 24 bits/pixel; 30-frames/ sec.) 60,825 1,100 studio quality server (640 x 480 pixels; 24 bits/pixel; 30 frames/sec.) 221,184 4,000 high-definition tv (hdtv) (1,125 lines; 24 bits/pixel; 30 frames/sec.) 800,000 60,000 – 127,000 table 7. copper access transmission technologies applications mode date rate meaning name data communications duplex 1200 bps to 28,800 bps voice band modems v.22 v.32 v.34 isdn service voice and data communications duplex 160 kbps digital subscriber line dsl t1/e1 service feeder plant, wan, lan access, server access duplex duplex 1.544 mbps 2.048 mbps5 high data rate digital subscriber hdsl same as hdsl plus premises access for symmetric services duplex duplex 1.544 mbps 2.048 mbps single line digital subscriber line sdsl internet access, video on demand, simplex video, remote lan access, interactive multimedia down up 1.5 to 9 mbps 16 to 640 kbps asymmetric digital subscriber line adsl same as adsl plus hdtv down up 13 to 52 mbps 1.5 to 2.3 mbps very high data rate digital subscriber line vdsl v id eo adel.ahmed.ali and ahmed m.al-naamany 224 6. concluding remarks we can conclude from the above review that, ethernet (802.3) is the most widely used lan standard and its upgrade fast ethernet can provide connections of a 100 mb/s rate. previously widely used token ring (802.5) provides both 4 and 16 mb/s rates. 100vg-anylan (802.12) provides 100 mb/s for multimedia communication. switched lan’s provide better efficiency, whereas the shared media lan’s can experience problems in scaling up. developments in fiber optics technologies are expected to further improve lan and wan transmissions to 10 gb/s over a single fiber. high capacity electronic ip routers are in development and are expected to reach several terabits per second. these advancements and attempts to extend these highdata-rate capabilities to the high end users will revolutionize the networks capabilities (kuznetsou. 2000). gigabit ethernet has the capability to provide gigabit connections among hubs and servers, so there is more bandwidth for multimedia communication. h.320 is a videoconferencing standard over isdn, h.323 is used for shared computer networks (such as lan’s and the internet), and h.324 is used for pots(plain old telephony system). atm will be the standard for delivering mpeg-2 high-quality video over network (worsley et.al. 1997). dsl/catv will deliver broadband information to users directly. multimedia applications with high-quality video will significantly enhance the information exchange, which, in turn, will stimulate many industrial applications that have in the past been considered impossible. atm provides qos that is critical for multimedia communication. sonet is the standard for a high-speed wan. the seamless integration of frame switching with cell switching would have a potential of merging frame relay with atm (liew 2000 and awdeh et.al. 1995). it is evident that xdsl will play a crucial role over the next decade or more as telephone companies enter new markets for delivering information in video and multimedia formats. new broadband cabling will take decades to reach all prospective subscribers. success of these new services will depend on reaching as many subscribers as possible during the first few years. by bringing movies, television, video catalogs, remote cd-roms, corporate lans, and the internet into homes and small businesses, xdsl will make these markets viable and profitable for telephone companies and application suppliers alike. the central office (co) of today will evolve into an optimized internet access point that fully supports the telecom operators’ strategy to reuse their investment in the pstn/isdn infrastructure and to provide new subscriber services based on internet technology. such approach enables evolutionary extensions for broadband subscriber access starting from the installed narrow band infrastructure in the pstn/isdn balancing user demand for internet services with telecommunication investments. this approach contributes to a convergence of pstn/isdn and the internet toward a seamless multimedia network of the future. convergence of the telecommunications and computer industries to a common vision of networking models for an integrated services information infrastructure is essential to meet the stringent requirements of multimedia applications. on the other hand, atm and gigabit ethernet may each dominate certain markets, and they may compete in others. however, researchers are already trying to incorporate the capabilities of each technology into the other. they have developed rsvp to give ethernet networks capabilities along the lines of atm’s quality of service, as well as lan emulations to let an atm network connect to ethernet desktops. in addition, vendors are working on bridges, routers, and switches that will connect the two technologies. the growing use of multimedia communication applications with specific bandwidth and real time delivery requirements has created the need for an integrated services internet in which traditional best effort datagram delivery can coexist with additional enhanced quality 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(available ftp: ds.internic.net/rfc/rfc1190.txt.) de prycher, m. 1995. asynchronous transfer mode: solution for broadband isdn, 3rd ed. chichester, u.k.: ellis horwood. garrahan, j. j, russo, p. a, kitami, k. and kung, r. 1993. intelligent network overview, ieee commun. mag., 31: 30–36. gartner group, 1997. interactive media: integrative view and commentary, march 28, 1997. jeon, w.s, jeong dong geun, and choi chong-ho. 1998. an integrated services mac protocol for local wireless communications, 1998. ieee transactions on vehicular technology, 47: 352-364. liew, s.y., lee, t.t. 2000. bandwidth assignment with qos guarantee in a class of scalable atm switches, ieee transactions on communications, 48(3): 377 –380. mark kuznetsov, m.; froberg, n. m.; henion, s.r.; rao, h.g.; korn, j.; rauschenbach, k.a.; modiano, e.h.; chan, v.w.s. a next-generation optical regional access network. ieee communication magazine, 38(1): 66-72. murphy, k. 1996. multimedia applications on rise within corporate webs: shockwave, other tools being more widely deployed, webweek, december 6, 1996. onvural, r. 1995. asynchronous transfer mode networks: performance issues, 2nd ed. norwood, ma: artech house. peifang, z. and oliver, y. 1999. integrated cell and frame switching in atm networks, ieee communications letters, 3(6): 183-184. rafter, m. v. 1997. exodus invests in data centers as high-end outsourcing market booms. webweek, december 15, 1997. schoen, u., hamann, j., jugel, a., kurza, h., and schmidt, c., 1998. convergence between public switching and the internet, ieee communications magazine, january 1998, pp 50-64 white, p and crowcroft, j. 1997. the integrated services in the internet: state of the art, proceedings of the ieee, vol. 85, no. 12, december 1997, pp 1934-1946. worsley, d.j, and ogunfunmi, t.1997. isochronous ethernet-an atm bridge for multimedia networking, ieee multimedia, january-march 1997, pp 58-67. zhou, p. and yang, o. 1997. a new design of central-queueing atm switches, in proc. ieee globecom’97: 541–545. received 31 january 2000 accepted 30 june 2000 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 107-114 © 2003 sultan qaboos university solvent extraction of thorium(iv) by didodecylphoric acid fawwaz i. khalili, khaled m. mousa and ehsan i. soudani department of chemistry, university of jordan,ammanjordan, email: f_khalili99@yahoo.com. من محلول بوساطة حامض ثنائي دوديكيل الفسفوريك ) 4(+استخالص الثوريوم فواز الخليلي، خالد موسى و إحسان السوداني المذاب في الكلوروفورم، حامض ثنائي دوديكيل الفسفوريك من محلول بيرآلورات باستعمال ) 4(+تم استخالص الثوريوم :خالصة ى عمليات االستخالص ، ترآيز حامض الهيدروآلوريك،زمن االستخالص ، ترآيز المتصلة و قد درست تأثيرات العوامل التالية عل واستخدمت قيم معامل التوزيع عند درجات . ، درجة الحموضة ، القوة األيونية ، نوع االلكتروليت و اختالف درجات الحرارة عشوائية المصاحبة لعملية االستخالص ، وحددت حرارة مختلفة لحساب التغير في المحتوى الحراري و الطاقة الحرة و درجة ال ) .n 2 أو=1 حيثالمتكونص عند االستخال آذلك صيغة المعقد ) ( )th cio r hrn4 5-n4 n− abstract: solvent extraction of thorium (vi) ion from perchlorate solution using didodecylphosphoric acid, ddpa, in chloroform diluent was studied. the effects of stripping hydrochloric acid concentration, stripping time, extraction time, ddpa concentration, ph, ionic strength, supporting electrolyte and temperature on the extraction processes have been studied. from the distribution coefficient values at different temperatures, the enthalpy, the free energy and the entropy changes associated with the extraction processes were determined. the composition of the complex formed was established to be th(clo4)4-nrn(hr)5-n where, n=1 or 2 and (hr)2 represents the dimer of ddpa. keywords: thorium(iv); solvent extraction; ddpa; thermodynamics. 1. introduction solvent extraction enjoys a favored position among separation techniques, due to its simplicity, speed and wide scope (dean, 1969). the distribution coefficient (kd) of a solute (a) between an organic phase and an aqueous phase is given by [ ] [ ]d org aqk = a / a (1) generally, dialkylphosphoric acids extract uranium ( )vi ion in non polar diluents by a cation exchange mechanism (baes et al. 1958; bunus et al. 1978; marcus and kolarik, 1976; mason et al. 1970; sato, 1965) according to the following reaction ( ) ( ) aq org 2+ + 2 2 2 aq2 2 uo +2hr uo hr +2h (2) the extraction equilibrium constant is expressed as follows ( ) ( )             2+ 2 2 2 org aq ex 22+ 2 2 orgaq uo hr h k = uo hr 107 mailto:f_khalili99@yahoo.com fawwaz i.khalili, et al. or ( )      2 2+ ex d 2 orgaq k h / hrk = where ( ) [ ]   2+ d 2 2 2 aqorg k = uo hr / uo 2 it is well known that di(2-ethylhexyl)phosphoric acid, d2ehpa, in many diluents is an effective extractant for actinides from mineral acid solutions (sato ,1967; baes,1962; kiwan and amin, 1973). peppard et al. (1957a, b; 1959) have described the application of d2ehpa to the fractionation of the trivalent lanthanides plus yttrium, to the isolation of certain carrier-free radioactive m(ili) nuclides, to the mutual separation of certain m(iii) actinides and to the separation of ce(iv) from m(iii) actinides and lanthanides. mason et al. (1981) studied the extraction of u(vi) and th(iv) from an aqueous nitrate phase by bis(2,6-dimethyl-4heptyl)phosphoric acid, hd(dibm)p, in n-heptane and benzene diluents. the extraction stiochiometries and the corresponding expression for the extraction equilibrium constants were determined. the equilibrium study of extraction of lanthanide ions with didodecylphosphoric acid, ddpa, was carried out by kondo et al. (1989). the extracted species into toluene diluent was found to be lnr3.3hr and the extraction equilibrium constants for the three lanthanide ions, that is, samarium(iii), europium (iii) and gadolinium (iii) were obtained. khaled et al. (1999) studied the extraction of u(vi) from an aqueous perchlorate phase by didodecyl phosphoric acid, (ddpa) in toluene the extracted species was found to be uo2(clo4)(hr2)(hr)2 where, (hr)2 represents the dimer of ddpa. the optimum conditions for the extraction were studied and the thermodynamic parameters were calculated. this work describes an investigation of the extraction of thorium(iv) by ddpa from perchlorate solution. 2. experimental reagents: the extractant, didodecylphosphoric acid, ddpa, was prepared and purified as described in the literature (kondo et al. 1989). 0.0 0.2 0.4 0.6 0.8 1.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 extraction time (hr) k d figure 1. variation of kd with extraction time at 25 oc. 108 solvent extraction of thorium(iv) the organic solution was prepared by dissolving ddpa into chloroform. the aqueous solution was prepared by dissolving thorium perchlorate into perchloric acid sodium perchlorate solution. the ph of the aqueous solution was adjusted using a 1.0-m perchloric acid and the ionic strength was adjusted using a 1.0-m sodium perchlorate solution. all other chemicals were of ar grade. doubly distilled water was employed to make up aqueous solutions, and distilled water was employed for washing all glassware. measurement of extraction eqilibrium: equal volumes (10.0 ml) of the organic and aqueous solutions of known concentrations were shaken in a 30 ml vial at a required temperature, and allowed to attain equilibrium. the thorium(iv) ion concentration in the aqueous solution was 8.0 ppm. after about 4 hours, the two solutions were separated and aliquotes (1.0 ml) were taken for analysis. concentration of thorium(iv) was determined spectrophotometrically with a du-7 spectrophotometer using 1,8dihydroxynaphthelene-3,6-disulphonic acid-2,7-bis[(azo-2)-phenyl arsonic acid], arsenazo(iii), as spectrophotometric reagent(savvin, 1961). scanning was performed for a standard solution of thorium-arsenazo(iii) complex against a reagent blank in the range λ= 400-800 nm. a wavelength of λ= 660 nm was chosen to be the optimum wavelength of measurement. figure 2. variation of [th(iv)]rec/th(iv)]aq with hcl concentration, [th(iv)]rec is the amount recovered from the organic phase. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 [ hcl ] [t h( iv )] re c/ th (iv )] a q best extraction time was chosen by extraction of several samples of the same concentration for different periods (figure 1). best stripping hydrochloric acid concentration of 3.0 m was determined by shaking 2.0 ml of the equilibrated organic solution (5.0 x 10-4 m ddpa) and 10.0 ml hydrochloric acid at different concentrations for 24 hours (figure 2). best stripping time was chosen by shaking 10.0 ml of 3.0 m hydrochloric acid solution and 2.0 ml of the equilibrated organic solution of the same concentration (5.0 x 10-4 m ddpa) for different periods (figure 3). the best ddpa concentration was chosen by extraction of several solutions of thorium(iv) ion by extractant solutions at different concentrations (figure 4). the optimum ph was chosen by extraction samples at ph values of 0.0, 0.20, 0.31, 0.40, 0.60, 0.80 and 1.00 (figure 5). the effect of the ionic strength was studied by extraction of several samples at ionic strength of 0.10, 0.50, 1.00, 1.50 and 2.00 m (figure 6). the effect of the supporting electrolyte was studied by extraction of several samples of different supporting electrolytes of naclo4, nacl and nano3 (figure 7). the thermodynamic parameters were obtained by studying the extraction of several samples of thorium(iv) ion at the temperatures of 20.0, 25.0, 27.7, 32.0 and 39.0±0.2 oc (figure 8). all 109 fawwaz i.khalili, et al. experimental data were obtained with only one variable in each experiment; the other variables were kept constant. figure 3. variation of [th(iv)]rec/th(iv)]aq with stripping time. 3. results and discussion effect of extraction time: from figure 1 establishes that equilibrium was attained in three hours, a time of four hours was selected. stripping of thorium(iv) from the organic phase: hydrochloric acid solution was used for stripping of th(iv) from the organic phase. figures 2 and 3 demonstrate that a 3.0 m hydrochloric acid is sufficient for stripping of th(iv) with stripping time of at least 1/2 hour, and can be confirmed by the material balance with a percentage error of about 2% or less. effect of extractant concentration: from figure 4 it is seen that the kd value for th(iv) increases with the increase of the ddpa concentration. a straight line of a slope ≈ 2.5 was obtained. this means that 2.5 dimer molecules of ddpa are involved in the formation of the thorium-ddpa complex since ddpa has been shown to be dimeric in chloroform (kondo et al. 1989). figure 4. variations of kd with log [ddpa] at 25 oc. 0.7 0.72 0.74 0.76 0.78 0.8 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 stripping time (hr) slope = 2.54 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 -3.8-3.7-3.6-3.5-3.4-3.3-3.2-3.1 log [ddpa] lo g k d [t h( iv )] re c/ t h( iv )] aq effect of ph: from figure 5 it is clear that the kd value for th(iv) is directly proportional to the ph. this proportionality is shown for two different concentrations of ddpa (3.0 x 10-4 and 4.0 x 10-4 m) against an aqueous perchloric acid sodium perchlorate solution of constant ionic strength of 1.0 m. 110 solvent extraction of thorium(iv) figure 5. variation of log kd with ph at 25 oc. slope=1.55 slope=1.56 -1.5 -1 -0.5 0 0.5 1 0.00 0.20 0.40 0.60 0.80 1.00 1.20 ph lo g k d 3.00e-4 m ddpa 4.00e-4 m ddpa from the extractant dependency and the ph dependency, the extracted species can be written in the form th(clo4)4-nrn(hr)5-n which means that a mixed ion exchange solvation mechanism was involved in the extraction of th(iv)from perchlorate solution into ddpa solution according to the following equilibrium reactions. where n is equal to 1 or 2. ( ) ( ) ( ) ( ) + aq org org n+ 4 4 n4-n 2 4-n 5 th c1o + 2.5 hr th c1o r hr + 1.55 h figure 6. variation of kd with ionic strength, [ddpa] 5x10-4 m at 25 oc. slope=0.63 2 2.3 2.6 2.9 3.2 3.5 3.8 0.00 0.50 1.00 1.50 2.00 ionic strength k d correspondingly, the extraction equilibrium constant is ( ) 1.55 2.5+ ex d 2 orgaq k =k h / hr      (7 where, is the concentration of the hydrogen ion in the aqueous phase, is the distribution coefficient and [(hr)2]org is the concentration of ddpa dimer in the organic phase at equilibrium. substitution of the previous values in equation (3) gives kex = 1.27x10 h+  dk 7. a similar mechanism was found by many authors (kiwan et al, 1971; marcus et al. 1973) for the extraction of th(iv) by dialkylphosphoric acid extractant. effect of ionic strength: figure 6 shows that the d increases as the ionic strength (i) increases. this is explained by the increase of the thermodynamic activity of the metal salt extracted and the decrease of the activity of water as the ionic strength increases (kolarik, 1982). k 111 fawwaz i.khalili, et al. effect of supporting electrolyte: from the data shown in figure 7 it is clear that the extraction of thorium(iv) ion from both perchlorate and nitrate solution is approximately the same and easier than the extraction of thorium(iv) ion from chloride solution. moreover, the same slope of about 2.5 in three cases, means that the mechanism of the extraction is independent of the supporting electrolyte present in the aqueous phase. slope=2.46 slope=2.51 -1.800 -1.500 -1.200 -0.900 -0.600 -0.300 0.000 0.300 -3.800-3.700-3.600-3.500-3.400-3.300-3.200-3.100 log [ddpa] lo gk d naclo4 nano3 nacl figure 7. variation of log with log [ddpa] for different supporting electrolyte, [ddpa] 5x10dk 4 m at 25 oc. figure 8. variation of log kd with 1/t, [ddpa] = 5x10-4 m. slope=1768 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 3.2e-03 3.3e-03 3.3e-03 3.4e-03 3.4e-03 3.5e-03 1/t lo gk d effect of temperature: it is seen from the data in figure 8 that the kd values decrease with increasing temperature, which is in agreement with the behavior reported for the extraction of th(iv) ion (mason et al,1981). the van’t hoff’s equation in the form given by equation (8) can be used to calculate the enthalpy change (∆h) associated with extraction of th(iv). ( ) 1og 1/ 2.303 k h t r ∆ = ∆ ∆ o (8) the plot of log kd vs. 1/t is shown in figure 8. the plot is linear in agreement with equation (8). the value of ∆h obtained from this plot using least squares method is -33.9 ± 0.8 kj mol-1. it is seen that extraction of th(iv) is exothermic. the values of free energy and entropy changes were 112 solvent extraction of thorium(iv) calculated using equations (9) and (10) g rt in∆ = −o k (9) sg h t∆ = ∆ − ∆o o o (10) and these values were found to be ago= -40.5 ± 2.1 kj mol-1 and ∆so = 22.1 ± 5.3 jk-1mol-1. a positive entropy change accompanies the dehydration of th(iv) ion which is known to be highly hydrated. the extraction system was found to be spontaneous. this is in agreement with our previous work for u(vi) (khaled et al 1999). 4. conclusion the equilibrium study of the extraction of thorium(iv) ion with didodecylphosphoric acid was carried out. the extracted species into chloroform diluent was found to be th(clo4)4-nrn(hr)5-n where, n=1 or 2 and (hr)2 represents the dimer of ddpa. the extraction equilibrium constant was obtained and the extraction system was found to be spontaneous due to the positive entropy change as well as the negative enthalpy change which favors the extraction of th(iv) ion. references baes, c.f. jr. 1962. the extraction of metallic species by dialkylphosphoric acids. j. inorg. nucl. chem. 24: 707-720. baes, c.f. jr., zingaro, r.a and coleman, c.f. 1958. . the extraction of uranium(vi) from acid perchlorate solutions by bis(2-ethylhexyl)phosphoric acid in hexane. j. phys. chem. 62: 129-136. bunus, f.t., domocos, v.c and dumitrescu, p. 1978. synergic extraction of uranium from phosphate solutions with di-(2-ethylhexyl)phosphoric acid and tri-noctylphosphine oxide. j. inorg. nucl. chem. 40: 117-121. dean, j.a. 1969.chemical separation methods, pp. 18-44. van nostrand reinhold, new york. khaled, m.m and khalili, f.i. 1999. solvent extraction of uranium(vi) by didodecylphosphoric acid. science and technology. 4:15-21. kiwan, a.m and amin, r.s. 1973. extraction of uranium(vi) by di-(2ethylhexyl)phosphoric acid from perchloric acid solutions. j. inorg nucl. chem. 35: 3315-3321. kolarik, z. 1982. gmelin handbook of inorganic chemistry. vol. d2, 8th. edition, p. 34. springer-verlag, berlin. kondo k, momota, k. and nakashio, t. 1989. equilibrium of solvent extraction of lanthanides with didodecylphosphoric acid. solvent ext. ion exch. 7: 1027-1041. luginin, v.a and tserkoviintskaya, i.a. 1976. mechanism of the extraction of uranium(vi) by di-(2-ethylhexyl)phosphoric acid from mineral acid solutions. porb. soverm. anal. khim. 1: 148-155. marcus, y., and kolarik, z. 1976. thermodynamics of liquid-liquid distribution reactions-iii. j inorg nucl chem. 38: 1069-1073. mason, g.w., griffin, h.e and lewey, s.m. 1981. j. inorg. nucl. chem. 43: 391-395. mason, g.w., schofer, n.l and peppard, d.f. 1970. the extraction of u(vi) and selected m(iii) cations by bis neo-octylphosphoric acid in two different hydrocarbon diluents. j. inorg nucl chem. 32: 3911-3922. peppard, d.f., mason, g.w. driscoll, w.j and mccarty, s. 1959. extraction of thorium(iv) by di esters of orthophosphoric acid. j. inorg. nucl. chem. 13: 138-150. peppard, d.f., mason, g.w. maieer, j.l and driscoll, w.j. 1957. fractional extraction of the lanthanides as their di-alkylorthophosphates. j. inorg. nucl. chem. 4: 334-343. rozen, a.m., martynov, b.v. anikin, v.i and mamaev, l.a. 1973. extraction 113 fawwaz i.khalili, et al. capability of sulfoxides. soviet radiochem. 15: 121-123. sato, t. 1965. the extraction of uranium(vi) from hydrochloric acid solutions by di-(2ethylhexyl)phosphoric acid. j. inorg. nucl. chem. 27: 1853-1860. sato, t. 1967. the extraction of thorium from nitric acid solutions by di-(2 ethylhexyl)phosphoric acid. j. inorg nucl. chem. 29: 555-563. savvin, s.b. 1961. analytical use of arsenazo(iii). talanta. 8: 673-685. received 15 december 2002 accepted 24 october 2003 114 solvent extraction of thorium(iv) by didodecylphoric acid fawwaz i. khalili, khaled m. mousa and ehsan i. soudani department of chemistry, university of jordan,ammanjordan, email: f_khalili99@yahoo.com. 2. experimental correspondingly, the extraction equilibrium constant is references microsoft word stat991020.doc science and technology, 5 (2000) 115-123 © 2000 sultan qaboos university 115 a generalization of the hypergeometric distribution e.k. elsheikh* and a. benmerzouga** *salalah teachers college of education, salalah, sultanate of oman **department of mathematics and statistics, sultan qaboos university, p. o. box 36 al-khod, p. c. 123 muscat, sultanate of oman تعميم للتوزيع فوق الهندسي على بن مرزوقة , الفضل خليفة الشيخ نقدم في هذا البحث تعديال للتوزيع فوق الهندسي يأخذ بعين االعتبار الحالة التي تكون فيها وسيلة المعاينة منحازة إلى :خالصـة ندرس .تكون تحته كل العينات متساوية االحتمال أحد النوعين الذين يجري منهما االختيار وذلك في مقابلة التوزيع الهندسي الذي خصـائص هـذا التوزيع الذي أسميناه التوزيع فوق الهندسي المعمم بما يشمل استخالص وتقييم نوعاً من التقريب الطبيعي لهذا .التوزيع abstract : in this paper we introduce a modification of the hypergeometric distribution that caters for the case when the sampling scheme favours the inclusion of units of one of the two types involved, as opposed to the hypergeometric distribution under which all samples are equally likely. the properties of the resulting distribution, termed the generalized hypergeometric, are studied, including the derivation and numerical assessment of a normal approximation of the distribution. keywords: hypergeometric distribution; recurrence relations; normal approximation. he celebrated capture recapture scheme ( see , for example, tuckwell 1995 ), as applied to the estimation of the number of fish in a lake, runs as follows. catch a number of fish s, say, from the lake, mark them and then release them in the lake. now, re-catch another sample of fish, of size n, say, from the lake. if x is the number of marked fish in this latter sample, then assuming x has a hypergeometric distribution, the total number of fish in the lake can be estimated. however, after the trauma of being caught and marked, the marked fish might, perhaps, be more likely to be caught again compared to the fish that escaped that experience. if that were the case, the hypergeometric model would not be applicable. the correct model should make samples with few marked fish less likely and samples with many marked fish more likely as compared to the hypergeometric model. one such model is the generalization of the hypergeometric distribution that we consider here. the distribution first arose when considering a stochastic model for two species competing on a fixed number of sites. this model will be described in section 2. the assumptions of the model and the resulting equilibrium distribution resemble their counterparts in the stochastic approach to the kinetics of chemical reactions (see, for example, mcquarrie 1967, formosinho and miguel 1979, and hall 1983). we make full use of the techniques used in studying those distributions to investigate the properties of the generalized hypergeometric distribution. a stochastic model for two competing species consider two species a and b with total fixed sizes s and m, respectively, competing on n fixed sites. initially some of the sites, r0 say, are occupied by species a and the rest by species b. we assume that all of the sites will continuously be occupied, but the number of sites occupied by either species may increase or decrease, respectively, by pushing out, or being pushed out by, members of the other e.k.elsheikh and a benmerzouga 116 species. more specifically, denoting by x(t) the number of sites occupied by species a at time t, we assume that: (i) the probability that x(t) increases by one in (t, t+h) is )())())(((1 ho+htx-ntx-sk ; (ii) the probability that x(t) decreases by one in (t, t+h) is k x t m n + x t h + o h2 ( )( ( )) ( ) ; and (c) the probability of more than one event in (t, t+h) is o(h), where k1 and k2 are positive constants, and o(h) is such that .0 )( lim 0 = → h ho h it might help the argument to think, tentatively, of the two species as political parties and the n sites as seats of a parliament that is being continuously updated according to the rules specified in (i), (ii), and (iii). the parameters k1 and k2 are then measures of competitiveness of the two parties. differential difference equation and equilibrium solution let pr(t) = p( x(t) = r x(0) = r0). it easily follows from the assumptions that pr satisfies the differential difference equation ).())())((( )()1)(1()()1)(1( 21 1211 tprnmrkrnrsk tp+r+n-m+r+ktp+r-n+r-s k= dt (t)pd r +r-r r +−+−−− (2.1) the equilibrium solution is obtained by putting the derivative equal to zero and solving for pr = pr(∞). it is easy to see that it satisfies pr-nr-sk=p+r+n-m+r r+r ))(()1)(1( 1 , (2.2) where k=k1/k2. (2.3) putting r = 0,1,..., and making successive substitutions leads to the equilibrium solution r r 0p = k s!n!(m n)! r!(s r)!(n r)!(m n + r)! p . (2.4) the constant p0 can be obtained by noting that the summation of pr over all values of r is equal to 1. this distribution is a generalization of the hypergeometric distribution and can justifiably be called a generalized hypergeometric (gh) distribution. however, the term generalized distribution may mean a different thing in the literature. see for example, johnson and kotz (1969), pp. 158-60. the hypergeometric distribution corresponds to the special case k = 1. in fact, stressing the dependence on k, pr can be written as             −       = n m kp rn m r s kkp rr )()( 0 (2.5) putting k = 1 and summing over all r gives       +       = n ms n m p )1(0 . (2.6) a generalization of the hypergeometric distribution 117 that is , the distribution reduces to the hypergeometric distribution. thus, if k =1, the number of sites occupied by species a is effectively determined by taking a simple random sample of size n from the s+m units in the two species and counting the units that belong to species a. in this case all samples of size n are equally likely. the case k > 1 is more favorable to inclusion of units of type a than the case k = 1. one should expect that situations in which a few sites are occupied by a are less likely, and those in which many sites are occupied by a are more likely, compared to the hypergeometric case. the reverse should be expected when k<1. it is reasonable to interpret the number of sites r occupied by species a as few or many according as r is less than or greater than the average number of sites, µ, occupied by species a. one obvious result to expect is that µ(k) should be an increasing function of k. we now see how these expectations are met by the gh distribution. let g x k( , ) and h x( ) denote, respectively, the probability generating functions (pgf) of the gh distribution and the hypergeometric distribution. thus h x g x( ) ( , )= 1 . now, from (2.5), we have (1)p(kp(1)pk=(k)p 00r r r ) . (2.7) summing over all r gives )(kp(1)p=h(k) 00 (2.8) likewise, multiplying both sides of (2.7) by r, summing over all r and using the above result gives h(k)(khk=(k) )′µ . (2.9) note also that h(k)(1)pk=(k)p r r r . (2.10) multiplying both sides by xr and summing over all r expresses the pgf g in terms of h as )h(k(kx)h=k)g(x, . (2.11) using (2.11), or multiplying both sides of (2.2) by xr and summing over all r, leads to the following differential equation of g(x, k) ksng (k(s + n 1)x + m n + 1) dg dx + (kx 1)x d g dx = 0 2 2 . (2.12) let )()1()( kppk rrr =ψ for r a non-negative integer in the support of rp . it follows from (2.10) that r r kkhk /)()( =ψ (2.13) we can now prove the following theorem. theorem 1: keeping the other parameters fixed: (a) )(krψ is an increasing or decreasing function of k according as r < µ(k) or r > µ(k); (b) µ(k) is an increasing functions of k. proof: the first assertion follows by differentiating (2.13) with respect to k, noting where the derivative is positive or negative, and expressing the condition in terms of )(kµ , using (2.9). the assertion concerning µ(k) follows if we can establish that the derivative with respect to k is positive. it follows from (2.9) that ( )[ ]22 }][][{ kh(k)hk-(k)hk(k)hh(k)= dk (k)d ′′′+′ µ (2.14) differentiating both sides of (2.11) twice with respect to x and putting x = 1 gives µµσ -+=1))-e(x(x=h(k(k)hk 22)2 ′′ . (2.15) e.k.elsheikh and a benmerzouga 118 substituting for µ(k) its expression in (2.9) leads to d (k) dk = (k) k > 0 2µ σ . (2.16) the essence of the comparison between the gh and the hypergeometric distributions is captured in the following corollary that easily follows from theorem 1 . corollary: (a) pr(1) > pr(k) if and only if r < µ(k); (b) µ(k) > µ(1) if and only if k >1. moments of the gh distribution it is difficult to express the moments of the gh distribution, including the mean and variance, in simple algebraic functions of the parameters. in this section we develop relations that provide convenient means of evaluating the mean and variance without the need to compute the probabilities in (2.4). note that putting x = 1 in (2.12) leads to the relationship µ µ σ µ µ σ(m n + )+ = k(s )(n )+ k2 2 . (3.1) we need to eliminate σ 2 in order to get a relation involving µ alone. this can be achieved by investigating the variation of the mean with each of the four parameters of the distribution keeping the others fixed. in the case of k this leads to a first order differential equation, while for m, s, and n it leads to recurrence relations. as for other moments, it can be shown, by differentiating (2.12) r times and putting x = 1, that the factorial moments satisfy the relations 0=1)m-+(k1)m+r+n-m+1)-2r-n+-(k(sr)m-r)(n-k(s rrr 21 ++ , (3.2) r = 0, 1, 2,... variation of the mean with k substituting (2.16) in (3.1) and noting that when k = 1 the mean reduces to that of the corresponding hypergeometric distribution, we get the following theorem. theorem 2: the mean of the gh distribution varies with k according to the differential equation )-)(n-k(s-)+n-(m= dk d 1)-k(k µµµµ µ , (3.3) with initial value )( m+sns=(1)µ . (3.4) it is difficult to solve this differential equation analytically but a numerical solution should be possible. once the mean is computed, σ 2( )k can be evaluated from (3.1). note also, from (2.16), that σ 2( )k can be obtained from the slope of the curve of µ( )k at k. recurrence relations for the mean first note that, considering the dependence of pr on s, for fixed k, m, and n, we have from (2.4) )11 (sp)-(sp(s)pr)-(s=)-(sps 00rr , (3.5) a generalization of the hypergeometric distribution 119 true for all r . summing over all r gives )1][ (sp)-(sp(s)-s=s 00µ . (3.6) multiplying (3.5) by r and summing over all r leads to )1][1 2 (sp)-(sp(s)-(s)-(s)s=)-(ss 00 2 σµµµ . (3.7) substituting (3.6) in (3.7) we get ]1].[[2 )-(s-(s)(s)-s=(s) µµµσ . (3.8) following similar steps, it can be shown that ]11].[[2 )-n,-(m-n)(m,n)(m,-n=n)(m, µµµσ . (3.9) finally, by interchanging m and s, and µ and µb, where µb is the average number of sites occupied by species b, it follows from (3.8) that ]1].[[2 )-(m-(m)(m)-m=(m) bbb µµµσ . (3.10) but b (m) = n (m)µ µ . thus ]1].[[2 (m)-)-(m(m)+n-m=(m) µµµσ . (3.11) substituting (3.8), (3.9), and (3.11) in (3.1) and introducing suitable starting values for computational purposes leads to the following theorem. theorem 3: the mean varies with each of the parameter(s) shown as argument, with the other parameters fixed, according to the following recurrence relations (i) ]11[]11[ )-(sk)-(+kn+s+n-m)-(sks-)-(ss+ksn=(s) µµµµ , with µ(0) = 0. (3.12) (ii) ( )]11[]11[ -mk)-(+m)+k(s)-(mk)-n)(-(m-ksn=(m) µµµ , with µ(0) = n. (3.13) (iii) ]111[]111[ )-n,-(mk)-(+ks+m)-n,-(mk)-n(+ksn=n)(m, µµµ , (3.14) with µ(0, m) = 0 and µ(n, 0) = n. it is desirable to have a relation that describes the variation of the mean with n alone. this easily follows by suitably substituting (3.14) in either of (3.12) or (3.13). the resulting relation is given in the following corollary. corollary: the mean varies with n according to the following relation ][][ 1)-(nk)-(1+1+n-m+ks1)-(n-skn=(n) µµµ , with initial value µ(0) = 0. (3.15) elsheikh (1997) has derived similar recurrence relations for the equilibrium means of some distributions arising in chemical reactions. these relations are best illustrated by an example. e.k.elsheikh and a benmerzouga 120 example consider a gh distribution with parameters m = 6, s = 5, n = 4, and k = 2. the distribution can be worked out using (2.2). it turned out that it has mean and variance given by µ = 632/275, and 2σ = 51576/2752. using relation (3.14), the most feasible in this case, with the given starting value, one can directly verify that µ(1) = 5/8, µ(2) = 28/23, µ(3) = 87/49, and finally, µ(4) = 632/275, in agreement with the correct value. the variance now can be obtained from (3.1). the other relations given by theorem 3 give exactly the same values. note that for the latter relations the variance can also be obtained from (3.8), or (3.9), or (3.11) according to the relation that was used to obtain the mean. approximating the mean and variance note that when the minimum of n, s, m is fairly large then µ(s) should not differ much from µ(s-1). using this in (3.12), the mean can be expected to be well approximated by the positive root of the equation µ µ µ µ(m n + ) = k(s )(n ) . (3.16) differentiating (3.16) with respect to k and using (2.16) gives )-)(n-k(s=+)-k(n+)-k(s++n-(m 2 µµσµµµµ ][ . (3.17) using (3.1) again we get µµµµσ +n-m + -s + -n += 2 11111 . (3.18) numerical computation using the recurrence equations derived in section 3 indicates that the error in these approximations does not exceed 1, irrespective of the values of the parameters. noting that the random variable is integer-valued, the approximations are thus very good. maximum likelihood estimation first assume that all parameters of the distribution are known except k. this situation may arise when we suspect that the sampling scheme is favorable to one of the two types concerned and we want to quantify the extent of that. the likelihood function is conveniently expressed in (2.10). differentiating with respect to k and equating the derivative to zero gives the maximum likelihood estimate (mle) of k as the solution of the equation h(k)k=rh(k) ′ . (4.1) using (2.9), we have the mle of k as the solution of µ(k) = r (4.2) using (4.2) with (3.16), we get an approximate expression of the mle of k as ( )r-nr)-(sr)+n-r(m=k̂ . (4.3) the second situation to consider is when all parameters are known except m. we think of m here as the number of unmarked fish, and we assume that k is known from previous experiences. it is straightforward from (2.4) that (m))p-(mr)p+n-(m=)-(m(m)pn)p-m(m rr 11 00 . (4.4) summing over all r gives a generalization of the hypergeometric distribution 121 )-(m)p+n-(m=(m)n)p-m(m 100 µ . (4.5) using (4.5) in (4.4) we can express the likelihood ratio (lr) as r+n-m +n-m = )-(mp (m)p=lr(m) r r µ 1 . (4.6) the mle of m is given as }lr(m):{m=m 1maxˆ ≥ . (4.7) this simplifies, in light of (4.6), to $ maxm = {m: (m) r}µ ≥ . (4.8) since µ obviously increases with m (see (3.10)), it follows that $m is given by the integer part of the solution for m of the equation µ(m) = r (4.9) using (4.9) with (3.16) gives an approximate expression of $m as     r r)+r)-r)(k(s-(n =m̂ . (4.10) where [ x ] is the integer part of x. it is interesting to note that when k = 1 the approximate mle of m reduces to that given by the hypergeometric distribution. it is to be noticed from the preceding derivation that the same likelihood equation resulted in the estimation of k and m. if both of them are unknown, it is necessary to take more than one observation from the distribution. binomial and normal approximations of the distribution assume k and n are finite, s → ∞, m → ∞, such that s/m = λ . it follows from (2.2) that pr)-(nk=p)+(r r1+r λ1 . (5.1) this corresponds to a binomial distribution with parameters n and p = kλ /(1+kλ). if n is large the normal approximation of the binomial distribution should be in effect. a normal approximation of the distribution, not necessarily through the binomial, is also possible. the derivation that follows is essentially due to dunstan and reynolds (1981). we have , from (2.2), r)+n-r(m )+r-)(n+r-k(s = p p 1-r r 11 . (5.2) if the minimum of n, s, and m is large, the mode m defined by }{ 1>pp:r=m rr 1max − , (5.3) approximately satisfies the equation )+m-)(n+m-k(s=m)+n-m(m 11 . (5.4) it follows from (5.2) that, for j > 0 p p p p tm j m m i m ii j i i j + + + −= = = =∏ ∏ 11 1 (5.5) where i -1 -1 t (1 i s m + 1 )(1 i n m + 1 )(1+ i m ) (1+ i m n + m )≅ . (5.6) thus, e.k.elsheikh and a benmerzouga 122 ]exp[ ) m+n-m 1 + m-s 1 + m-n 1 + m 1 -i(t i ≅ . (5.7) it follows that m+ j m 2p p (j )≅ exp 2 2σ , (5.8) where 1 = 1 m + 1 n m + 1 s m + 1 m n + m2σ . (5.9) hence the distribution can be approximated by a normal distribution with mean µ and variance σ2 as given by (5.4) and (5.9). as the mean of the distribution is well approximated by the solution of (3.16), the approximate mean can be used in place of the mode. as noticed by hall (1983), the derivation above is rather vague about the relative sizes of the parameters for which the approximation holds, apart from the requirement that the values of m, s, and n should be large, which is almost always met as far as chemical reactions are concerned. hall has provided conditions on the parameters under which the distribution converges to normality. the approach we adopt here is to resort to numerical computations. numerical assessment of the normal approximation the analysis is restricted to n s m≤ , . we considered values of n from as small as 10. the cumulative distribution function corresponding to (2.4) was computed at each possible integral value and compared to the value given by the normal distribution function with mean and variance given by (3.16) and (3.18), respectively. a continuity correction was used. for each set of parameters the maximum difference was recorded. the approximation was taken as satisfactory so long as the maximum absolute difference does not exceed 0.001. initially, extensive exploratory computations were carried out by varying the parameters n, m, s, and k. it was noticed that the quality of the approximation was closely related to the values of n and µ/n, where µ is the approximate mean given by the positive solution of (3.16). a program was then written to facilitate the investigation of the range of values of µ/n, for each n, under which the approximation is satisfactory. the calculations were run separately for k k< >1 1and . it was found that the approximation can be good for values of n as small as 30. the results can be summarized for the two cases of k as follows. case of k > 1: (i) for n ≥ 30 the approximation is found to be satisfactory for µ/n ∈ [0.23, 0.59] and it gets better as k approaches 1. (ii) for n ≥ 50 also the approximation is found to be satisfactory provided µ/n ∈ [0.15, 0.69] and it gets better as k approaches 1. (iii) for n ≥ 100 also the approximation is found to be satisfactory provided µ/n ∈ [0.086, 1.0] and for all values of k. case of k < 1: (i) for n ≥ 30 the approximation is found to be satisfactory for µ/n ∈ [0.399, 1.0) and it gets better as k approaches 1. (ii) for n ≥ 50 also the approximation is found to be satisfactory provided µ/n ∈ [0.282, 1.0) and it gets better as k approaches 1. (iii) for n ≥ 100 also the approximation is found to be satisfactory provided µ/n ∈ [0.092, 1.0) and for all values of k. acknowledgements thanks are due to anonymous referees for their helpful comments and suggestions. a generalization of the hypergeometric distribution 123 references dunstan, f. d. j. and reynolds, j. f. 1981. normal approximations for distributions arising in the stochastic approach to chemical reactions kinetics. j. appl. prob. 18: 263-267. elsheikh, e. k. 1997. recurrence relations for the equilibrium means of distributions arising in chemical reactions. sultan qaboos university journal for scientific research – science and technology. 2: 77-85. formosinho, s. j. and miguel, m. da g. m. 1979. markov chains for plotting the course of chemical reactions. j. chem. education 56: 582-585. hall, a. 1983. on the roles of the bessel and poisson distributions in chemical reactions kinetics. j. appl. prob. 20: 585595. johnson, n. l. and kotz, s. 1969. discrete distributions. john wiley & sons. new york. mcquarrie, d. a. 1967. stochastic approach to chemical kinetics. j. appl. prob. 4: 413-478. tuckwell, h. c. 1995. elementary applications of probability theory. chapman & hall. new york. received 20 january 1999 accepted 25 june 2000 squ journal for science, 2019, 24(1),18-22 doi: 10.24200/squjs.vol24iss1pp18-22 sultan qaboos university 18 effect of alarm chemicals and predator kairomones on the behaviour of two species of mosquito larvae derek roberts*, nargis r. al-alawi and mai k. al-gharibi department of biology, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *email: derekmr@squ.edu.om. abstract: mosquito larvae have developed a variety of responses to reduce the risk of predation, but this requires them to be able to identify the different species of predators and respond accordingly. we investigated the behavioural response of two mosquito species to three chemical signals: kairomones from two predators, and also to alarm semiochemicals from killed mosquito larvae. culex perexiguus mosquito larvae are primarily surface filter-feeders. in response to all three chemical signals, they significantly reduced feeding by the high-risk active bottom scraping of biofilms in favour of the less active (and so lower predator-detection risk) surface filter feeding. active escape swimming (instead of feeding) also increased for all three signals, but was much less for dragonfly nymph kairomones. dragonflies are almost entirely bottom feeders and so are a much lower danger to surface feeding mosquitoes compared with damselfly nymphs, which feed at all depths. culiseta longiareolata mosquito larvae normally have a high level of bottom-feeding. this was significantly reduced to all three chemical signals, but escape swimming only occurred for dragonfly kairomones (which are natural predators for the bottom-feeding larvae). keywords: culex perexiguus; culiseta longiareolata; mosquito larvae; predator kairomones; anti-predator defense. وكيرومونز الكائنات المفترسة على سلوك نوعين من يرقات البعوضأثر المواد الكيمائية التنبيهية العلوي ومي الغاربي ، نرجس سترديريك روب يرقات البعوض مجموعة متنوعة من اإلستجابات للتقليل من خطورة اإلفتراس وذلك بقدرتهم على التعرف على مختلف األنواع لقد طورت :صلخمال وإشارات كيميائية وهما المفترسة واإلستجابة وفقاُ لكل نوع. في هذه الدراسة تحققنا من اإلستجابة السلوكية لنوعين من البعوض لثالثة مواد كيميائية تنبيهية ن نوعان من الكيرومونز من نوعين مفترسين ومن مواد شبه كيميائية من يرقات بعوض ميت. إن يرقات بعوض الكيولكسي بيركسيقص في األساس هي م ة عن عتادالكائنات التي تتغذى عن طريقة الترشيح السطحي. كرد فعل للثالث إشارات الكيميائية قللت يرقات البعوض إلى درجة عكسية من تغذيتها الم شكل هذه النوعية من التغذية تطريقة الترشيح السطحي التي هي أقل خطورة عليها من اإلفتراس إلى التغذية على البيوفيلم المتواجد في القاع األسفل حيث الثالثة الكيميائية ولكن تم ذلك هروباً من اإلشارات التغذية زادت اليرقات في حركة سباحتها عليها من اإلفتراس. وبدالً من أن تقضي وقتاً أكبر فيخطر الكيرومونز. تتغذى ذبابة التنين )اليعسوب( كلياُ على القاع لذا هي أقل خطورة من اإلقتراس دةلمارية ذبابة التنين )اليعسوب( لدرجة أقل في حالة حو بعوض كليسيتا لونقيأريوالتا لمادة ما تتغذى على القاع بكثافة بالمقارنة بمقترنات األجنحة التي ال تتغذى على القاع وانما على الترشيح السطحي. إن يرقات حدثت لذبابة التنين )اليعسوب( لمادة الكيرومونز وهي في إن حالة الهروب سباحة اإلشارات الكيميائية، في حين إنخفضت تلك بشكل كبير عندما واجتوقد األصل مادة افتراسية لليرقات التي تتغذى على القاع. الحماية من اإلفتراس. ، فتراس الكيولكس بيركسيقص ، كيلوسيتا لنقيأرلوالتا ، يرقات البعوض ، كيرومونز اإل :مفتاحيةال كلماتال 1. introduction many mosquito larvae live in very small pools of water where, due to their low activity, they are vulnerable to aquatic predators. however, not all predators are of equal danger. fish in particular may eliminate all mosquito larvae from an aquatic habitat [1]. the larvae should thus have a phenotypic plasticity, responding differently to different predators depending on the risk that the particular predator poses to them. thus culiseta longiareolata macquart strongly responds to fish, dragonfly and damselfly nymphs, but not to nepids [2], which do not feed on mosquito larvae. similarly as prey, damselfly nymphs [3] and dragonfly nymphs [4, 5] alter their response to specific predators depending on the risk. closely related mosquito species may show different responses to a specific predator, with no response to predators to which they are not normally exposed [6, 7]. effect of alarm chemicals and predator kairomones 19 this phenotypic plasticity requires being able to identify specific predators. in many aquatic habitats, visibility is poor and the vision of mosquito larvae is very limited, so chemical kairomones given off by predators have many advantages to the mosquito. as the kairomone disperses through the water, it allows the larva to detect a predator that is not visible [8]. mosquito larvae have been shown to respond differently to different predator kairomones and so are able to identify the predator and tailor their response accordingly [9]. they also respond to alarm semiochemicals from damaged conspecific larvae [10], which indirectly show the presence of predators. most mosquito larvae spend much of their time in relative inactivity by filter feeding at the surface, and part of their time in active moving over the bottom where they scrape biofilms. however, bottom-feeding is risky, as the constant movement attracts predators and also makes the larvae accessible to benthic predators such as dragonfly nymphs [11]. in this study, we investigate two different mosquito species having different behavioural responses to predators: a) reducing active bottom-scraping in favour of increasing the less active surface filter-feeding; b) actively swimming to escape away from the predator. 2. materials and methods eggs rafts of the two mosquito species, culex perexiguus theobald and cs. longiareolata, were collected from temporary rock pools in wadi qurai near sumail about 60km from the university in northern oman. after hatching, the larvae were fed daily with yeast powder. the two predators, dragonfly crocothemis erythraea brullé and damselfly ischnura evansi morton nymphs, were collected from small fish-free pools in wadi al-khod about 5 km from the university and then kept separately in small jars. each was fed daily on larvae of the mosquito species being tested. mosquitoes and predators were kept in a lab temperature of 23 o c. during the experiment, the predators were individually kept in 4 l water containers. fourth (final) instar mosquito larvae (initially cx. perexiguus, later cs. longiareolata) were individually kept in 16 polystyrene jars. each 8 cm diameter jar contained 400 ml of distilled water. these jars each had water pumped into them using 16 peristaltic pumps (wpx1 from welco ltd, tokyo, japan) at a calibrated flow of 17 ml/h from the four 4 l containers (so each container connected to four mosquito jars) (figure 1). figure 1. experimental set up showing: peristaltic pumps at the top; mosquito jars in middle row; predator containers alternating with waste jars on bottom row. there was thus no visual contact between predator and mosquito, but the mosquitoes were receiving water containing either dragonfly or damselfly kairomones. the mosquito jars then overflowed into waste jars. exp. 1: control. the experiments started on day 1 with all 16 mosquito jars having distilled water pumped into them as a control. after leaving for 30 min to allow the larvae to settle, ten records were made at 10 minute intervals on the behaviour of each larva. over a 5 sec period, it was recorded whether the larva was feeding or actively swimming, and whether the feeding was surface inactive filter feeding or active feeding on the bottom by scraping of biofilms. exp. 2: mosquito alarm chemicals. after completing the 1 st experiment, each of the water containers had added to it four finely chopped up mosquito larvae releasing alarm semiochemicals: the water containing these chemicals was then pumped into the 16 jars of mosquito larvae. after a 5 minute interval to allow mixing of the water, 10 recordings at 10 minute intervals were made as previously. at the end of the experiment, the mosquito jars were flushed with distilled water overnight and the mosquito larvae were fed. exp. 3: predator kairomones. dragonfly nymphs were kept unfed in each of the four 4 l containers overnight to allow a build-up of predator kairomones. the following morning, this water was pumped into the jars containing the same mosquito larvae as previously. the larvae were allowed to settle for 30 min, then activity and feeding type recordings were made as previously. these experiments were repeated for a total of three replicates using fresh mosquito larvae and fresh predators in each replicate, so that the responses of a total of 48 larvae were recorded. the experiments were then repeated using derek roberts et al 20 damselfly nymphs to replace the dragonfly nymphs. they were then further repeated using cs. longiareolata mosquito larvae, to see the effect of both dragonfly and damselfly kairomones, as well as the effect of alarm semiochemicals. the data were arcsine transformed and then analyzed using a univariate analysis of variance (anova) with spss (ver 21, spss, chicago, ill, usa). significant differences were separated by tukey’s hsd (honestly significant difference) test. the graphs used back transformations of the data to calculate mean number ± se of bottom feeding and of active swimming larvae. 3. results figure 2 (a,b). mean number (± se) of feeding (non-swimming) cx. perexiguus larvae for controls; exposed to alarm chemicals; damselfly kairomones and dragonfly kairomones. figure 2 (c,d). mean number (± se) of bottom-feeding cx. perexiguus larvae for controls; exposed to alarm chemicals; damselfly kairomones and dragonfly kairomones. letters show tukey differences in the anova. cx. perexiguus larvae (figure 2) significantly (anova, f = 28.4; df = 2; p < 0.0001) increased their swimming escape activity in response to alarm semiochemicals from chopped up mosquito larvae and to kairomones from predatory damselfly nymphs (with tukey showing no difference between the two responses). they also showed a smaller increase in escape swimming in response to dragonfly nymphs (f = 4.9; df = 2; p = 0.5). surface filter-feeding (at the expense of reduced bottom feeding) significantly increased in response to both alarm semiochemicals (f = 83.1; df = 2; p < 0.0001) and damselfly kairomones (with a tukey test showing that the response was much greater to damselfly kairomones), as well as to dragonfly kairomones (f = 147.9; df = 2; p < 0.0001). cs. longiareolata larvae (figure 3) showed no response in swimming activity to either chopped mosquito alarm semiochemicals or to damselfly kairomones (f = 0.05; df = 2; p = 0.95), figure 3 (a,b). mean number (± se) of feeding (non-swimming) cs. longiareolata larvae for controls; exposed to alarm chemicals; damselfly kairomones and dragonfly kairomones. figure 3 (c,d). mean number (± se) of bottomfeeding cs. longiareolata larvae for controls; exposed to alarm chemicals; damselfly kairomones and dragonfly kairomones. letters show tukey differences in the anova, but did increase swimming escape responses to dragonfly nymph kairomones (f = 48.3; df = 2; p < 0.0001). bottom-feeding was significantly reduced by the presence of both alarm semiochemicals (f = 70.6; df = 2; p < 0.0001) and damselfly kairomones (the frequency of responses to these two stimuli were not significantly different from each other) as well as to dragonfly kairomones (f = 52.7; df = 2; p < 0.0001). effect of alarm chemicals and predator kairomones 21 4. discussion mosquitoes have developed a number of strategies to reduce their predation risk, since the larvae may be trapped in small pools of water with no possibility of escape. at the time of oviposition, the adult females carefully test the available water bodies for chemical kairomones indicating the presence of predators and then avoid those where the kairomones are present [12, 13, 14]. however, their response may depend on the risk posed by a particular predator, and so they may still oviposit where less dangerous predators are present [15]. this does not solve the problem of predators arriving after oviposition. the larvae thus have various possible strategies to reduce their risk. a common response in all aquatic prey is to reduce activity, since most predators are better at seeing movement rather than detail [16, 17]. however, inactivity will affect the efficiency of feeding resulting in a trait compensation, in which the rate of larval development is slowed down. thus culex sinaiticus has been found to prolong its larval development by reducing feeding in the presence of dragonfly nymphs, but not to respond to damselfly nymphs [11]. similar results were found in anopheles quadrimaculatus [18] and culex pipiens [19]. this strategy, however, extends the period in which the larva is exposed to the predator. a few species such as cx. perexiguus shorten the larval development in the presence of predators, but this results in smaller and so most probably less competitive adults [20]. less drastic behavioural changes available to the larva include escape swimming, in which the larva spends several minutes swimming to a new location away from the predator, and in reducing bottom-feeding. many mosquito species feed both at the surface by filter-feeding on floating microorganisms and on the bottom by scraping biofilms covering surfaces. their choice depends on food availability, but also the preferred feeding method varies between species. however, bottom-feeding is more risky, because the high level of activity attracts the attention of predators, especially dragonfly nymphs sitting on the bottom. the reduction of bottom-feeding in the presence of predators has been shown to occur in a number of studies [21, 22, 23], and has been recorded for cs. longiareolata [11]. this behavior was found for both species in the present study. similarly, both species reduced bottom-feeding in response to alarm semiochemicals from chopped up larvae, but in cx. perexiguus, this was at a significantly lower level compared with the response to predator kairomones. alarm chemicals from damaged conspecific larvae are known from other studies to enhance antipredator defenses [21, 24]. stopping feeding and actively swimming away from a predator source was shown by cx. perexiguus to all three alarm signals, but to a much smaller extent to dragonfly kairomones, possibly because dragonflies sit on the bottom and so can be avoided by surface feeding. in contrast, cs. longiareolata (a major bottom-feeder) only swam in response to dragonfly kairomones, and so is more selective in its response. 5. conclusion both cs. longiareolata and cx. perexiguus mosquito larvae reduced the more risky bottom-feeding in preference for an increase in surface filter-feeding (which is less visible to a predator) in response to kairomones from both dragonfly and damselfly nymphs, as well as to alarm pheromones from damaged conspecific larvae. however, in cx. perexiguus, this response was significantly greater when to either of the predator kairomones than to the alarm pheromones, but in cs. longiareolata, there was no significant difference between them. actively swimming to escape from predator kairomones or alarm pheromones was shown by cx. perexiguus, but cs. longiareolata only swam in response to dragonfly kairomones, and not to the other two factors. acknowledgement we thank sultan qaboos university for providing facilities. references 1. griffin, l.f. and knight, j.m. a review of the role of fish as biological control agents of disease vector mosquitoes in mangrove forests; reducing human health risks while reducing environmental risk. wetlands ecological management, 2012, 20, 243-252. 2. roberts, d.m. mosquito larvae change their feeding behavior in response to kairomones from some predators. journal of medical entomology, 2014, 51, 368-374. 3. chivers, d.p., wiseden, b.d. and smith, r.j.f. damselfly larvae learn to recognise predators from chemical cues in the predator’s diet. animal behaviour, 1996, 52, 315-320. 4. hopper, k.r. flexible antipredator behavior in a dragonfly species that coexists with different predator types. oikos, 2001, 93, 470-476. 5. stoks, r.m., mcpeek, m.a. and mitchell, j. l. evolution of prey behavior in response to changes in predation regime: damselflies in fish and dragonfly lakes. evolution, 2003, 57, 574-585. 6. sih, a. antipredator responses and the perception of danger by mosquito larvae. ecology, 1986, 67, 434-441. 7. kesavaraju, b., and juliano, s.a. differential behavioral responses to water-borne cues to predation in twocontainer-dwelling mosquitoes. annals of the entomological society of america, 2004, 97, 194-201. derek roberts et al 22 8. takahara, t., kohmatsu, y., maruyama, a., doi, h., yamanaka, h. and yamaoka, r. inducible defense behavior of an anuran tadpole: cue-detection range and cue types used 10 against predators. behavioural ecology, 2012, 23, 863868. 9. ferrari, m.c.o., wisenden, b.d. and chivers, d.p. chemical ecology of predator-prey interactions in aquatic ecosystems: a review and prospectus. canadian journal of zoology, 2010, 88, 698-724. 10. ferrari, m.c.o., messier, f. and chivers, d.p. threat-sensitive learning of predators by larval mosquitoes culex restuans. behavioural ecology and sociobiology, 2007, 62, 1079-1083. 11. roberts, d.m. responses of three species of mosquito larvae to the presence of predatory dragonfly and damselfly larvae. entomologia experimentalis et applicata, 2012, 145, 23-29. 12. angelon, k.a. and petranka, j.w. chemicals of predatory mosquito fish gambusia affinis in fluence selection of oviposition site by culex mosquitoes. journal of chemical ecology, 2002, 28, 797-806. 13. walton, w.e., van dam, r.a. and popko, d.a. ovipositional responses of two culex (diptera: culicidae) species to larvivorous fish. journal of medical entomology, 2009, 46, 1338-1343. 14. silberbush, a. and blaustein, l. mosquito females quantify risk of predation to their progeny when selecting an oviposition site. functional ecology, 2011, 25, 1091-1095. 15. why, a.m., lara, j.r. and walton, w.e. oviposition of culex tarsalis (diptera: culicidae to waters from conspecific larvae subject to crowding, confinement, starvation, or infection. journal of medical entomology, 2016, 53, 1093-1099. 16. werner, e.e. and anholt, b.r. ecological consequences of the trade-off between growth and mortality rates mediated by foraging activity. american naturalist, 1993, 142, 242-11272. 17. ferrari, m.c.o., messier, f. and chivers, d.p. variable predation risk and the dynamic nature of mosquito antipredator responses to chemical alarm cues. chemoecology, 2008, 17, 223-229. 18. knight, t.m., chase, j.m., goss, c.w. and knight, j.j. effects of interspecific competition, predation, and their interaction on survival and development time of immature anopheles quadrimaculatus. journal of vector ecology, 2004, 29, 277-284. 19. beketov, m.a. and leiss, m. predation risk perception and food scarcity induce alterations of life cycle traits of the mosquito culex pipiens. ecological entomology, 2007, 32, 405-410. 20. roberts, d.m. predator feeding vibrations encourage mosquito larvae to shorten their development and so become smaller adults. ecological entomology, 2018, 43, 534-537. doi: 10.1111/een.12519. 21. juliano, s.a. and gravel, m.e. predation and the evolution of prey behavior: an experiment with tree hole mosquitoes. behavioural ecology, 2002, 13, 301-311. 22. awasthi, a.k., molinero, j.c., wu, c.h., tsai, k.h., king, c.c. and hwang, j.s. behavioral changes in mosquito larvae induced by copepod predation. hydrobiologia, 2015, 749, 113-123. 23. gimonneau, g, pombi, m., dabiré, r.k., diabaté, a., morand, s. and simard, f. behavioural responses of anopheles gambiae sensu stricto m and s molecular form larvae to an aquatic predator in burkino faso. parasites & vectors, 2012, 5, 1-11. 24. dalesman, s., rundle, s.d., coleman, r.a. and cotton, p.a. cue association and antipredator behaviour in a pulmonate snail, lymnaea stagnalis. animal behaviour, 2006, 71,789-797. received 9 september 2018 accepted 10 october 2018 microsoft word biol030604.doc 1-5 squ journal for science, 9 (2004) © 2004 sultan qaboos university 1 thermal effects on the body mass, transpiration rate, feeding and food conversion of the pillbug armadillo officinalis (isopoda, oniscidea) fed on the dry leaf of punica granatum abdelgader k. youssef and g. achuthan nair department of zoology, faculty of science, university of garyounis, p. o. box 9480, benghazi, libya, email: gachuthannair@yahoo.com. كتلة الجسم و معدل النتح والتغذية و التحول الغذائي للبقة المدرعة الحرارية على التأثيرات )armadillo officinalis ( المتغذية على أوراق الرمان الجافة)(punica granatum عبدالقادر يوسف وأكوتان ناير الكفايـة اإلنتاجيـة , اية التمثيل الغذائي كف, مالحظات الدراسة اشتملت على كتلة الجسم معدل النتح :خالصة المدرعة التحول الغذائي و االيضى للبقة , التمثيل الغذائي, التغذية: من كل معدالت و الصافية اإلجمالية )pillbug armadillo officinalis ( والتى أقلمت على درجتي حرارةc °14 و c °21 يوم 15 و لمدة أي قيمة معتبـرة عنـد لم يعطيالتأقلم الحراري . الجافة punica granatum )(ق الرمانو غذيت علي أورا علي أي حال درجتي الحرارة المنوه عنهمـا ) p>0.05, t=1.09( اختالف الزيادة الوزنية للبقة المدرعة (p<0.01, t=9.01) و الرطوبـة p<0.01, t=9.53)( وضحتا اختالفات معتبرة في معـدل النـتح و معـدل التحـول الغـذائي (p<0.05, t=3.76) معدل التغذيـة (p<0.05, t=5.16)كفاية التمثيل الغذائي (p<0.05, t=2.58) الحيوانات لوحظ عليها أنها تتغذي تغذية جيدة علي أوراق الرمان في . بين البق المدرع الغذائي التمثيل نسبة . c° 14فضل عند درجة حرارة لكن كفاية التمثيل الغذائي هي أ c°21درجة حرارة )assimilated food( عند درجة حـرارة 3.21% أنسجة جديدة كانإلى و المتحول c° 14 6.30% و 2.05% كان c°21 و c° 14 االستهالك الغذائي للبقة المدرعة عند درجتي الحرارة , فقط c°21عند درجة ألوراقائيـة ي الكيم للتركيبة مختصرة بنبذة زودت الدراسة .التوالييوميا علي من وزن الجسم 3.79% و .في البرية a.officinalis الحراري علي نشاط الأيضا التأثيرالرمان و ناقشت abstract: observations were made on the body mass; transpiration rate; assimilation efficiency; gross and net production efficiencies; feeding, assimilation, conversion and metabolic rates of the pillbug armadillo officinalis dumeril acclimatized at 14º and 21 °c for 15 days and fed on the dry leaf of punica granatum (pomegranate). abdelgader k. youssef and g. achuthan nair 2 a brief description is given on the chemical composition of p. granatum leaf. the difference in body mass increments of a. officinalis between the acclimatized temperatures was not significant (t = 1.09; p>0.05). however, significant differences were discernible on the transpiration rate (t = 9.53; p<0.01), moisture (t = 9.01; p<0.01), assimilation efficiency (t = 5.16; p<0.01), feeding (t = 3.76; p<0.05) and conversion (t = 2.58; p<0.05) rates between the woodlice acclimatized at 14º and 21 °c. better feeding of p. granatum leaf by these animals was observed at 21° c, but better assimilation efficiency at 14 °c. only 3.21% assimilated food at 14° c and 6.30% at 21 °c were converted into the production of new tissues. the food consumption of a. officinalis at 14º and 21° c was 2.05% and 3.79% body mass/day respectively. the effect of temperature on the activity of a. officinalis in the field is discussed. keywords: armadillo officinalis; punica granatum; transpiration; body mass; feeding and assimilation. 1. introduction he coastal region of benghazi (20º 10’ n, 20º 06’ e), libya, like other mediterranean coasts (kheirallah, 1980; warburg et al. 1984) is colonized by the pillbug, armadillo officinalis dumeril. casual collections showed that these woodlice occurred in large numbers in shady places where the soil moisture was moderate. detailed studies were conducted by us before in benghazi on the transpiration, behavior, growth and feeding habits (nair et al. 1989), conversion of leaf litter (nair and fadiel, 1991), relation of body dimensions and the soil factors influencing the abundance (nair and al-jetlawi, 1993), breeding and population biology (al-jetlawi and nair, 1994), thermobiology (nair et al. 2001) and food preference and litter breakdown (nair et al. 2002) of this woodlouse. the present study investigates the impact of temperature acclimatization (14º c and 21º c) on the transpiration rate, increment in body mass, moisture, feeding and food conversion of a. officinalis fed on the dry leaves of punica granatum (pomegranate) for 15 days. pomegranate trees are common in benghazi and a. officinalis forms the major component of the decomposer fauna of the fallen litter from these trees. 2. materials and methods a. officinalis having body mass ranging from 65 to 72 mg were selected for the study. 10 pillbugs (5 males and 5 non-gravid females) each, after starving them for eight hours to evacuate their gut contents, were maintained at 14º c and 21º c in a gallenkamp incubator. each animal, after taking its initial body mass near to 0.01 mg in a sartorius balance, was kept in a glass petridish (5 cm diameter, 2.5 cm height) containing a layer of wet filter paper (62 ± 2 % r.h.) at the bottom. 300 mg of the dry leaf of punica granatum macerated with water for 12 hours to make it soft, was provided as food. the experiment lasted for 15 days, after which the body mass of the animal was determined. the remaining leaf and the fecal matter ejected by the pillbug were collected, dried and weighed. after measuring the transpiration rates, they were kept at 60º c for four days, dried and weighed to determine the moisture content. the experiment was repeated again and there was not much variations in the values between the replications, so the data were combined and the mean values of 20 pillbugs at each temperature were taken. to study the transpiration rates, the pillbugs were weighed individually to 0.01 mg and exposed separately for one hour over calcium chloride at the same temperature (14º or 21º c) in which they were maintained previously for 15 days, before re-weighing. the results are expressed as water-loss in mg/cm2 /h. the surface area of the animal was calculated from the formula 2 3s = kw , where s = surface area, w = initial weight of the animal, k = constant. a value of k = 12 was adopted as it has been t thermal effects on a. officinalis 3 used by cloudsley-thompson (1969) and nair et al. (1989) for african woodlice, and nair and nair (1985) for indian species. this value is also the mean calculated by edney (1951) for british species. consumption of food (c ) of a. officinalis exposed to 14º and 21º c was estimated in terms of mg dry food consumed by it for 15 days, assimilation (a) was calculated by subtracting the amount of dry fecal matter (fe) ejected from the total food consumed (c ). the production rate (p) (due entirely to the increase in live body mass ) was determined as the difference between the body mass of the animal at the beginning and at the end of the experimental period. metabolism (r ) represents the difference between a and p. assimilation efficiency (ae) was calculated by expressing a as a percentage of c. gross (ge) and net (ne) production efficiencies were estimated expressing p as a percentage of c and a separately. rates of feeding (fr), assimilation (ar), conversion (cr) and metabolism (mr) were determined by dividing c, a, p and r by half the sum of initial and final weights of the animal and then by the duration of the exposure period and expressed in terms of mg/g live wt/day. t-tests (grimm, 1993) were done to find out the significance or otherwise of the data. 3. results and discussion duke (1992) reported that the leaf of p. granatum contains betulic acid, ursolic acid, corelagin, strictinin, tannin, granatins, casuariin, d-mannitol, 2-0-galloylpunicalin, 2-(2-propenyl)-delta-piperideine, 1,2,3,4,6-penta-0-galloyl-beta-d-glucose and 1.2.4.6-tetra-0-galloyl-beta-d-glucose. our observations in the field revealed that the leaf of p, granatum is a preferred food for a. officinalis in the field, which was later confirmed through the laboratory studies on the food preference shown by them. also, higher breakdown of the dry leaf of p. granatum by these animals was observed in the field when compared with the breakdown of the dry leaf of citrus limonia (lemon) (nair et al. 2002). table 1. temperature acclimatization (14oc and 21oc) for 15 days on the increment in body mass, transpiration rate, moisture, feeding and food conversion (mean ± se) of a officinalis fed on punica granatum dry leaf as food, t-values and their levels of significance. total number of woodlice kept at each temperature: 20 animals exposed to the temperatures of si.no factors 14 o c 21 o c t p 1 increment in body mass (mg) 0.97± 0.33 1.39± 0.21 1.09 1. >0.05 2 transpiration rate (mg/cm2/h) 0.71± 0.01 1.01 ± 0.03 9.53 2. <0.01 3 moisture (%) 52.20± 0.18 49.71 ±0.14 9.01 3. <0.01 4 assimilation efficiency (%) 81.16 ± 3.21 62.51 ± 1.67 5.16 4. <0.05 5 gross production efficiency (%) 3.06 ±1.13 3.87 ± 0.54 0.65 5. >0.05 6 net production efficiency (%) 3.94 ±1.34 6.11 ± 0.82 1.38 6. >0.05 7 feeding rate (mg/g live wt/day) 23.57 ± 2.02 38.22± 3.33 3.76 7. <0.05 8 assimilation rate (mg/g live wt/day) 19.29 ±1.97 23.66 ± 1.83 1.63 8. >0.05 9 conversion rate (mg/g live wt/day) 0.62 ±0.20 1.49 ± 0.27 2.58 9. <0.05 10 metabolic rate (mg/g live wt/day) 18.67±2.06 22.17 ± 1.65 1.33 10. >0.05 abdelgader k. youssef and g. achuthan nair 4 table 1 shows the increment in body mass; transpiration rate; moisture; assimilation efficiency; gross and net production efficiencies; feeding, assimilation, conversion and metabolic rates of a. officinalis at 14º and 21º c for 15 days fed on the dry leaf of p. granatum, the t-values and their levels of significance. there was an average increase of 0.97 mg in body mass of a. officinalis at 14º c which increased further to 1.39 mg in those at 21º c, even though the difference in increment in body mass between acclimatized temperatures was insignificant (t = 1.09; p>0.05). the transpiration rate of 14º c acclimatized a. officinalis was 0.71 mg/cm2/h, which increased significantly (t = 9.53; p<0.01) to 1.01 mg/cm2/h in those at 21º c. the cuticle of land isopod is more permeable than that of insect (wallwork, 1970) and it was previously believed that an oriented layer of lipid molecule, which functions as a water-proofing mechanism is lacking from isopods (beament, 1961). later, however, warburg (1965) and edney (1968) suggested that some type of water-proofing mechanism may be present in some species. measurement of transpiration rates of several species of woodlice at various temperatures demonstrated a sharp increase at higher temperatures suggesting that the ability of waterproofing barrier is reduced at high temperatures (cloudsley-thompson, 1977; nair and nair, 1985). this phenomenon might not have taken place in the present study since the higher temperature of 21º c was well within their tolerance limits and temperature acclimatization might be the sole criterion for their differences in transpiration rates. our previous studies (nair et al., 1989, 2001) on a. officinalis revealed that the exponential regression models fitted on transpiration in relation to temperatures were good and acclimatization of these pillbugs to different temperatures for a week had marked effects on their transpiration and behavior, when later exposed to rising temperatures. a significant difference (t = 9.01; p<0.01) in moisture content was discernible in a. officinalis acclimatized between 14º c (52.20%) and 21º c (49.71%). significantly higher assimilation efficiency (t = 5.16; p<0.01) was recorded in those acclimatized at 14º c (81.16%) than those at 21º c (62.51%). the values of gross and net production efficiencies, and also of feeding, assimilation, conversion and metabolic rates were higher in a. officinalis exposed at 21º c when compared with the values recorded at 14º c. however, significant differences existed only between their feeding (t = 3.76; p < 0.05) and conversion (t = 2.58; p< 0.05) rates. warburg (1987) opined that isopods in general seem to be efficient digesters but somewhat inefficient assimilators and that food consumption varies with species. in the present study an inverse relationship was observed in a. officinalis on its feeding rate and efficiency of assimilation of the leaves of p. granatum. better feeding was discernible in those kept at 21º c, but better assimilation efficiency was observed in those at 14º c. only a small percentage of the assimilated food (3.21% at 14º c and 6.30% at 21º c) was converted into the production of new tissues. the food consumption of a. officinalis fed on p. granatum was 2.05% body mass/day at 14º c and 3.79% body mass/day at 21º c. these values were lower than those reported for porcellio scaber (2.59% body mass/day at 14º c; 4.19% body mass/day at 21º c), another woodlouse which co-exists with a. officinalis in the field and were given p. granatum as food for 15 days (unpublished data). in conclusion, temperature acclimatization has a significant impact on the transpiration rate, moisture, assimilation efficiency, feeding and conversion rates of a. officinalis fed on p. granatum, but not so on their increment in body mass, gross and net production efficiencies, assimilation and metabolic rates. the effects of temperature on the activity of these pillbugs were confirmed in the field where they were found in large numbers crawling over the soil surface and actively feeding on the leaf litter when the surface temperature ranged between 18 and 29º c, even though activities were restricted to shady places. it was evident that a restricted grade of temperature gradient was essential for normal activity and feeding. except for short summer months of august/september, the temperature range of the habitats of these animals was well within their tolerance limits. thermal effects on a. officinalis 5 4. references al-jetlawi, a.a. and nair, g.a. 1994. breeding and population biology of armadillo officinalis (sopoda: oniscidea) in benghazi,libya. j. arid envts., 27: 241-255. beament, j.w.l. 1961. the water relations of the insect cuticle. biol. rev., 36: 281-320. cloudsley-thompson, j.l. 1969. acclimation, water and temperature relations of the woodlouse metoponorthus 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mnaouer, k. day, m. al-towaiq and f.a. masoud department of computer science, college of science, sultan qaboos university, p.o.box 36,al khod 123, muscat, sultanate of oman, email: fawaz@squ.edu.om تقويم األداء لنظم قواعد البيانات باستخدام شبكات بتري الملونة عادل بن منور، خالد داي، محمد الطويق، و فّواز أحمد مسعود . في هذه الورقة قام الباحثون بتصميم نماذج لنظم قواعد البيانات المكررة والمرآزية وذلك باستخدام شبكات بتري الملونة:خالصة إّن النماذج التي تم تصميمها قد حققت الغرض المطلوب من الدراسة . اسة مستفيضة للمقارنة بين أداء هذه النماذجوقد تم إجراء در و قد تم تدقيق صحة التصاميم المقترحة بإجراء . من حيث تغطية المتغيرات الديناميكية لنظم قواعد البيانات التي خضعت للدراسة والنسبة بين عمليتي بخضاعها لضوابط متغيرة منها سرعة المعالج وسرعة شبكة ألحواسيعدة تجارب محاآاة عملية والتي تّم إ وقد أعطت نتائج المحاآاة مدلوال يشير إلى أّن نظم قواعد البيانات المكررة تتمتع بكفاءة أداء أعلى منها في . القراءة والكتابة لألنظمة الرد على االستعالمات المرسلة وأيضا في حالة التشبع التي ال يستطيع فيها حال نظم قواعد البيانات المرآزية وذلك نسبة إلي زمن ولكن تم رصد تحسن نسبي في أداء نظم قواعد البيانات المرآزية عندما تكون سرعة . النظام االستجابة ألية زيادة في المدخالت .المعالج والشبكات آبيرة جدا بالمقارنة مع نظم قواعد البيانات المكررة abstract: we propose colored petri net (cpn) models for replicated and centralized database systems and conduct a comparative study of their performance. the designed cpn models capture the dynamics of the studied database systems and estimate their expected performance with an appropriate level of abstraction. a number of simulation experiments were performed under various load conditions of varying parameters such as server speed, network speed, and read/write ratio. the simulation results show that under similar operation conditions, replicated systems exhibit higher performance than centralized systems in terms of query response time and system saturation levels. however, centralized systems become more competitive when their network and server speeds are much higher than those of the replicated systems. keywords: client-server, centralized databases, colored petri net, performance evaluation, replicated databases. 1. introduction t he traditional setting of database systems is based on the centralized client-server architecture. in such systems, a central server handles requests coming from a number of remote clients. a more recent development consists of deploying multiple service points keeping a copy of the data at each service point (replica). database queries are submitted to replicas independently. the service replicas cooperate in servicing the queries and maintaining data consistency. database queries are either read queries processed locally or write queries propagated to all replicas. the replicated setting can be a viable alternative for many reasons. firstly, it can offer a distributed base for data that can be scaled up and down to meet varying needs and demands. secondly, it increases data availability, system robustness and fault tolerance. finally, it allows deployment of clusters of workstation that offer aggregate computing power and storage capacity. on the negative side, replicated database systems may impose substantial communication overhead especially with a high ratio of write queries resulting in poor query response time. the aim of this study is to investigate the conditions under which replication is a more attractive solution than centralization in terms of performance. 33 a.b. mnaouer et al the type of consistency control method used affects the performance of the replicated system. two broad models of consistency control are known in the literature. the first one is the asynchronous model (also known as the lazy update model) where changes introduced by a transaction are propagated only after the transaction has been committed (wiesmann et al., 2000). the second one is the synchronous model (also known as the eager model) where a transaction should not commit until full synchronization with all replicas is completed (wiesmann et al., 2000). it is argued that synchronous models are hardly feasible in practice due to problems related to synchronization delays, deadlock avoidance, and scalability (gray et al., 1996). however, it is asserted in wiesmann et al., (2000) that group communication primitives may be a solution for building good performance synchronous replication models (kemme and alonso, 2000; kemme and alonso, 1998; pedone et al., 1997; pedone et al., 1998). a number of consistency control methods have also been studied in the literature (beeri et al., 1989; guerraoui and schiper, 1997; wiesmann et al., 1999; day et al., 2001). in this study we assume asynchronous replication with minimum communication overhead with only one update message broadcasted to all replicas for each write query. this assumes a fault-free system in order for the updates to be delivered to all replicas. modeling fault-tolerant consistency control protocols is beyond the scope of this paper. the targeted performance evaluation is conducted using colored petri nets (cpn). cpns represent powerful means for modeling and prototyping complex, distributed, and parallel systems (jensen 1992, 1994). cpns were used successfully for modeling various systems such as vlsi chip design (shapiro 1991), communication protocols (mnaouer et al., 1999; mnaouer et al., 2002; morera and gonzalez, 1999), and algorithm analysis (jorgensen and kristensen, 1999). we propose two cpn models for centralized and replicated database systems. the cpn models are used for simulating the two systems and comparing their query response times and system saturation levels as functions of the load under various conditions of network latency, query service time, and query read/write ratio. the paper is organized as follows. in the next section, a description of the evaluated centralized and replicated system models is given. section 3 gives an informal overview of colored petri nets followed by a detailed description of the designed cpn models used in the simulation. the simulation results are presented and discussed in section 4. concluding remarks on the work are provided in section 5. 2. overview of the centralized and replicated database system models in a typical centralized database system, a database server is connected to a number of clients via a switched network. database queries sent from clients to the server are subject to two communication delay components: a client-switch (τcs) delay and a switch-server delay (τss). in real situations, the switch-server link can be 1, 10, or even 100 times faster than the client-switch link. in a fully replicated client-server database system, each site runs a replica of the database server, hence acting as a server as well as a client. that is the case when all the sites are included in the replication scheme. read database queries are processed locally while write queries are processed both locally and remotely at all replicas. propagation of write queries is performed via a switched network. figure 1 shows the components of the centralized and replicated database systems. in figure 1.a the arrival of transactions to the server, in the centralized system, is assumed to form a poisson process of average arrival rate nλ transactions per second (where n represents the number of clients involved in the system). the service time for a transaction at the server is assumed to be a random variable corresponding to an exponential distribution of the service time with average service rate of µc transactions per second. let τcs be the average communication delay between a client and the switch and τss the average communication delay between the switch and the server. the message switching time at the switch is assumed negligible. 34 performance evaluation of database systems figure 1.b shows the components of the replicated database system. we do not consider any particular replication control method; however we assume asynchronous replication with minimum inter-replica communication with only one update message broadcasted to all the replicas for every write transaction request. the assumption is realistic in the sense that many commercial database replication systems opt for the asynchronous replication model, and therefore, allow transient inconsistent states of the database system to exist (kemme and alonso, 2000). we wanted also to analyze the performance of replicated versus centralized database systems subject to the variation of server speed, network speed, and read/write ratio parameters while isolating the performance issues related to the application of more complex consistency control mechanisms. figure 1a. the centralized model figure 1b. the replicated model figure 1a. the centralized model figure 1b. the replicated model in this system each of the n processors (replica) is holding a copy of the database and serves both as a client and as a server. an average of λ transactions per second are assumed to be generated at each replica. a portion wλ of this rate corresponds to write transactions that have to be broadcasted to all processors. the remaining (1-w)λ rate corresponds to read transactions that can be processed locally. since each write transaction is propagated to all processors, the total arrival rate of write transactions to each processor is nwλ. the overall arrival of transactions to each replica (read or write), is assumed to follow a poisson process. the service time for a transaction at each processor is assumed exponentially distributed with average service rate of µr transactions per second. the average replica-to-switch communication delay is assumed the same as τcs of the centralized model. 3. colored petri nets we start by presenting an informal overview of cpns before describing the details of the proposed cpn models for the centralized and replicated database systems. 3.1 overview of colored petri nets a petri net is a network of interconnected locations and activities, with rules that determine when an activity can occur, and specify how its occurrence changes the states of the associated locations. petri nets can be used to model systems of any type. they are particularly useful in facilitating the design and analysis of complex distributed systems that handle discrete flows of objects and information (jensen 1992, 1994). 35 a.b. mnaouer et al cpns represent an extension of petri nets. they are graphical models that use the concept of colored tokens to represent data structures and state conditions. the presence of data or state conditions is marked by colored tokens in locations. each token has an associated token color that specifies the type of data it is representing (usually representing arbitrary complex data values). the locations are represented graphically by ellipses and called places. each place is associated with a color set that specifies the type of tokens (i.e., data) that may reside in the location. activities are represented by rectangles called transitions, which govern the occurrence of events in the system. places can be either input or output places for a transition. places and transitions are linked through directed arcs modeling the flow of data. each arc has an associated arc expression that controls the transition’s occurrence. this expression specifies the number of tokens consumed by the transition, or the number of tokens that is produced after its occurrence. when the number of tokens in each input place of a transition satisfies the corresponding arc expression, then the transition is said to be enabled. an enabled transition can fire (i.e., occur) at any time. when it fires, it consumes as many tokens from its input places, as specified by their corresponding arc expressions, and produces as many tokens in its output places as specified by their corresponding arc expressions. additional conditions for the enabling of the transition can be specified through the guard of the transition. all the boolean conditions specified in the guard must evaluate to true for the transition to be enabled. cpn modeling and simulation is supported by various simulation packages such as the design/cpn tool (jensen et al., 1996) used in this study. in this tool, the different parts of a cpn model are constructed in different cpn pages. this helps making use of the cpn hierarchy constructs that enable the designer to breakdown the complexity of the modeled system into different layers with different abstraction levels. in the design/cpn there is a provision for using a declaration node that can be used to record the color sets, constants, variables, and function definitions. figure 2 depicts a small cpn diagram used for processing shipping orders. the transition process orders has one input place, order in, and one output place order out. the token color order is associated with the place order in, and the equivalent token color productshipped is associated with the place order out. the color set order is declared to hold big and small as data values (see declaration node). a variable ordent is declared in the declaration node. order (color set) productshipped out p (* declaration node *) color order = with big | small timed; color productshipped = order; var ordent : order; (* variable declaration*) order out process orders order in 2`ordent [ordent = big] (a guard) 1`big++ 2`small (initial marking expression) an arc expression @+5 a time region 1`ordent figure 2. components of a cpn1 the guard of the transition specifies that ordent should be bound only to tokens having the value big. the binding means that the variable ordent of the arc expression from the place order in is substituted by any token that is part of the current marking of the place subject to the constraint of the transition guard. an arc expression is evaluated against the current marking of (i.e., current distribution of tokens on) the input places of the transition. in the displayed (initial marking) state the transition may be enabled if the cpn is simulated, since at the start of the 1 the figure is taken and edited from a tutorial of design/cpn by meta software corporation 36 performance evaluation of database systems simulation the initial marking of places becomes a current marking for the cpn. when the transition occurs it will consume the token big (of which only one instance exists in order in) and produces two instances of big into the output place. place fusion is one hierarchy construct that enables a place to be present physically on different cpn pages while representing a single conceptual place. all the physical places, in this case, are known to belong to the same fusion set. there can be two types of places that may belong to the same fusion set that helps construct hierarchies. socket places and port places. socket places are found one hierarchy level and they are mapped to port places belonging to a cpn described in a lower level of the hierarchy. thus, this mapping of socket places and port places ensures the connection between cpns constructed at different hierarchical levels. the place order out is declared as a socket place that will be used to connect to another cpn page in which a more complete shipping process with additional operation is described. substitution transition (st) is the second hierarchy construct that enables to hide lower level design details into the lower abstraction level. the st construct allows the designer to relate a transition (and its surrounding arcs) in an upper level to a more complex activity (modeled by a detailed cpn) hidden in a lower level of the hierarchy. the transition process order can be designed to represent a st that hides more elaborate details of product shipping that is hidden in the current level of the model. finally, the concept of time stamps that may be associated with timed tokens is used for the purpose of performance evaluation. each timed token will bear an associated time stamp at each creation in accordance to a global clock maintained by the simulator. in figure 2, the transition process order has an associated time region (denoted by @+5) that specifies that the occurrence of the transition takes 5 time units. the associated timestamps of the produced big tokens will be augmented with 5 units. see jensen (1992, 1994, 1996) for more details. 3.2 cpn models for the database systems a top down approach was adopted in the modeling. a top page that models the overall cpn layout is constructed. in this top page, a single st transition represents the server, and a set of st transitions represent the different clients connected to the server. figure 3a and figure 3b depict the top page for the centralized model and the replicated model respectively. figure 3a. centralized model cpn top page. figure 3b. replicated model cpn top page. notice that in figure 3a, the communication goes from the clients to the server through the switch node. clients usually get replies to their queries back from the server. however, to simplify the model, computation of the delay is done at the server considering a round trip delay. in figure 3b, the communication goes from switch to clients. this abstracts the fact that clients broadcast their write queries to all the other clients to maintain consistency. 37 a.b. mnaouer et al figure 4 shows the declaration node used for both models where color sets, variables, function declarations and definitions are given. figure 5 shows the cpn page modeling a generic client operation in the centralized model. transition gen_req represents query request generation. the place gen is used as a time trigger that initiates query generation. its token color is tr, representing a timed token color. a token t is generated after each firing of gen_req producing a time stamp calculated using the texp(1.0/iar) function that generates a random variable exponentially distributed with mean iar (i.e., the interarrival time). the generated token is specified by the expression of the arc connecting the transition gen_req to the place generated. figure 4: the declaration node used for both models figure 5. a cpn page modeling a generic client operation in the centralized model. 38 performance evaluation of database systems notice that the size of the query (field sz) is also exponentially distributed with mean m (m is set to 100 kb considering big size transactions). the transition send_req is used to send the queries to the switch place. it is at this transition that the transmission delays are applied (considering both directions) in the time stamp denoted by the mark @. the transmission depends on the query size. the place switch is a fusion place that links to the cpn page modeling the server depicted in figure 6. figure 6. a cpn page modeling the server operation in the centralized model. in figure 6, the place idle and the transition process represent the availability of the server. the transition recv-req is used to model reception of queries from clients that are treated according to a fifo policy, enforced as follows: any incoming query is assigned a request id (i.e., field rid) extracted from the token on the place gid2. the fifo enforcement is done at the transition process using its guard (i.e., [#rid q = i]). the place gid4 is acting as a semaphore with its single token consumed through the variable i by the transition process when the processing of a new query is started. a new token pointing to the next query in sequence is produced by the transition comp-del when the processing and delay computation of the previous query is finished. then, the next query is processed. the transition comp-del and the two places tot-delay and received-fin are used for computing the accumulated two-way response delay. a snap-shot of the simulation is shown in the figure displaying token values. figure 7 describes the cpn model of the switch in the replicated model. read queries are processed locally by clients. write requests are propagated through the switch to all other nodes. in order to simplify the model, the write queries are issued by the switch and sent to all nodes. the place idle and the transition req-gen represent the state where the switch is available. the transition req-gen generates requests according to a poisson process regulated using the place gen with a timed token t. after each firing of req-gen a new request is generated into the place wr-req that includes a request identifier (i.e., field rid), a generation time (i.e., field gt loaded with current time) and a query size. the transition produces also a token t with a time stamp computed using the function texp(10.0/iaw). the inter-arrival time of write requests is denoted iaw, and 10.0/iaw represents the arrival rate from 10 different clients. the transition broadcast sends the write query requests to all clients through the places tocl1 through tocl10 (connecting to other cpn pages modeling clients). this allows clients to update their replicas. the delay component applied to the transition broadcast represents twice the time the client switch communication delay (i.e., tcs * #sz q). 39 a.b. mnaouer et al figure 7. a cpn page modeling the switch operation in the replicated model. figures 8 and 9 represent the cpn page modeling the clients in the replicated model (part i and part ii). in figure 8, write requests are received through the port place tocl1. the transitions merge 1 and merge 2, are modeling the queuing of local read requests and external write requests into the same queue. the transition gen_rer represents the generation of local read requests. the place gid1 serves as a semaphore, used for sequencing requests into the queue place. the transition process is used to process requests according to the order of their arrival. the second part of the client model is depicted in figure 9. firing the transition process produces a query token in the place tocl1_2, and captures the synchronization token on the place cnt. in addition, the transition process has an associated timestamp calculated based on the query size. when the timestamp associated with the current token (i.e., query) expires, the token is consumed by the transition recv_wrr, modeling the end of processing. the transition recv_wrr, is used to compute the delay incurred by the query (adding up the difference between generation time and arrival time) that is added to the token residing in the place acc-delay. firing the transition recv_wrr releases the synchronization token into the place cnt with a value equal to the number of the next query. the places acc delay and recved req belong to two global fusion sets present in all client models and representing one logical place each. figure 8. a cpn page modeling the client of the replicated model (part i) 40 performance evaluation of database systems figure 9. a cpn page modeling the client of the replicated model (part ii) 4. simulation results a set of simulation experiments were conducted. measures of query response time as a function of query arrival rate are obtained. in the first set we have varied the processing speed of the central server (µc). in the second set, different network connection speeds (τss) between the server and the switch are studied. in the third set, we have investigated the effect of the read-write ratio on the performance of the replicated system. along with the plots standard deviations of the means and 95% confidence intervals were computed for three selected points for each plot. 4.1 simulation set i in this first experiment we plot the query response time in the centralized system (tc) and in the replicated system (tr) as functions of the query arrival rate (λ) for different server speeds µc. we use the following assumptions for this experiment: τcs = 0.1 sec, τss = 0.01 sec, µr = 10 queries/sec, w = 0.2, n = 10 (# of clients). 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 1 5 10 15 20 25 30 0.21 0.23 0.25 0.27 0.29 0.31 0.33 0.35 1 4 5 7 9 tc λ ref.value 5 mean 0.152 std.deviation 0.003 95 % conf. interval of mean 0.1493 0.1541 λ tr figure 10.1. tr vs load (re 15 25 0.1594 0.1763 0.003 0.0037 0.1572 0.1617 0.1734 0.1793 ref.value mean 0. std.deviation 0. 95 % conf. interval of mean 0. 0 plicated). figure 10.2. tc vs. load (cent 41 4 7 9 2348 0.2489 0.3239 0028 0.00092 0.0058 2325 .2371 0.2482 0.2495 0.3198 0.3279 ralized : µc = µr). a.b. mnaouer et al the query response time tr of the replicated model (figure 10.1), is lower than the query response time tc of the centralized model for the three considered server speeds (µc = µr, µc = 5 µr, µc = 10 µr). τcs = 0.1 sec, τss = 0.01 sec, µr = 10 queries/sec, w = 0.2, n = 10 (# of clients). 0.216 0.218 0.22 0.222 0.224 0.226 0.228 0.23 0.232 0.234 10 20 30 40 45 tc tc2 0.210 0.220 0.230 0.240 0.250 0.260 20 40 60 80 100 tc tc3 λ ref. value 20 30 40 mean 0.2214 0.2243 0.229 std. deviation 0.0019 0.0007 0.0008 95 % conf. interval of mean 0.2200 0.2228 0.2238 0.2248 0.2282 0.2295 λ ref. value 40 60 80 mean 0.22 0.221 0.223 std. deviation 0.0004 0.0006 0.0019 95 % conf. interval of mean 0.2199 0.2206 0.2204 0.2213 0.2211 0.2245 figure 10.3. tc vs. load (cent.: µc = 5µr). figure 10.4. tc vs. load (cent: µc = 10µr). the load saturation level (λ at which t becomes very large due to system congestion) of the replicated model is substantially higher than that of the centralized model in the first case (µc = µr) and are comparable when µc is set to five times µr. only when µc was set to ten times µr (figure 10.4) the load saturation level of the centralized model has become substantially higher than that of the replicated model. we conclude from this experiment that the replicated model performs better than the centralized model unless a very powerful server is used in the centralized model (such as ten times, or more, faster than a replica). 4.2 simulation set ii in this second experiment, we plot tc and tr as functions of λ for different server-switch transmission delays τss. we use the following assumptions for this experiment: τcs = 0.1 sec, µc = 100 queries/sec, µr = 100 queries/sec, w = 0.2, n = 10 we plot tc and tr as functions of λ for different server-switch transmission delays τss. the client-switch transmission delay is computed based on a 10mbps client-switch connection. the server-switch connection bandwidth will be tested with the values 10mbps, 100mbps, and 1gbps. since we focus here on studying the impact of the communication speeds, we fix the centralized server and all replicas’ processing speeds at 100 queries per second. the response time tr of the replicated model (figure 11.1) is lower than the response time tc of the centralized model for various server-switch transmission delays τss. in all cases the load saturation level of the replicated model is almost three times higher than that of the centralized model. it can be seen in figures 11.2, 11.3, and 11.4 that the communication delay has little effect on the centralized system since each query (or query reply) is transmitted only once. the effect of the communication delay is however greater on the replicated system since write queries are broadcasted to all replicas, especially for high ratios of write queries (w). the effect of w is studied in the next simulation set. 42 performance evaluation of database systems 0.17 0.18 0.19 0.2 0.21 tc r 4 0.13 0.14 0.15 0.16 1 5 10 15 20 25 30 ref. value 5 mean 0.152 std. deviation 0.003 95 % conf. interval of mean 0.1493 0.1541 λ t λ figure 11.1. tr vs lo .3 simulation set iii in this last experi (w) of write queries. t µc = 100 queries/sec, µ 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.1 2 4 tc t 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.1 2 4 6 8 9 tc 15 25 0.1594 0.1763 0.003 0.0037 0.1572 0.1617 0.1734 0.1793 ref. value 40 60 80 mean 0.414 0.419 0.445 std. deviation 0.0034 0.0025 0.004 95 % conf. interval of mean 0.4112 0.4162 0.4174 0.4208 0.4420 0.4473 ad (replicated). figure 11.2. tc vs. load (centralized : τss = τcs). ment tc and tr are plotted as functions of λ for different values of the ratio he following is assumed for this experiment: τcs = 0.01 sec, τss = 0.001 sec, r = 10 queries/sec, n = 10. 6 8 9 λ c 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.1 2 4 6 8 9 λ tc tc 43 a.b. mnaouer et al ref. value 4 6 8 mean 0.236 0.244 0.26 std. deviation 0.0006 0.0029 0.0011 95 % conf. interval of mean 0.2357 0.2365 0.2417 0.2456 0.2593 0.2610 ref. value 4 6 8 mean 0.217 0.226 0.243 std. deviation 0.0009 0.0005 0.0016 95 % conf. interval of mean 0.2161 0.2174 0.2260 0.2267 0.2414 0.2436 figure 11.3. tc vs. load (cent: τss =0.1 τcs). figure 11.4. tc vs. load (cent.: τss = 0.01τcs). even though we use here for the centralized model a ten times faster server (as compared to the replica speed) and a ten times faster server-switch connection (as compared to the replicaswitch connection), the replicated model was able to perform better in terms of delay and load saturation level, especially for small ratios of write queries (w) (figures 12.1, 12.2, 12.3, and 12.4). (note that figure 12.1 and 12.2 are the same as figures 11.3 and 10.1, reproduced here for the sake of the comparison). 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.1 2 4 6 8 9 tc 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 1 5 10 15 20 25 30 tc figure 12.1. tc vs. load (centralized). figure 12.2. tr the gain in response time and saturation load of the centraliz model is not as substantial as the invested resources (ten times more faster switch-server communication link). 0.17 0.19 0.21 0.23 0.25 0.27 0.29 0.31 0.1 5 10 15 20 λ tr tr 0.199 0.209 0.219 0.229 0.239 0.249 0.1 2 tr ref. value 5 10 15 mean 0.184 0.19 0.203 std. dev. 0.0013 0.0024 0.0025 95 % conf. int. of mean 0.1835 0.1854 0.1884 0.1919 0.2011 0.2047 λ tr λ 44 vs. load (replicated: w=0.2). ed model over the replicated powerful server and ten times 4 6 8 10 λ tr performance evaluation of database systems figure 12.3. tr vs. load (replicated: w=0.4). figure 12.4. tr vs. load (replicated: w=0.8). 5. conclusion we have proposed a colored petri net–based performance evaluation of the relative merits of the centralized approach and the replicated approach for network-based database systems. a number of simulation experiments have been carried out. in addition to the well-known benefits of higher reliability and data availability of replicated solutions (as compared to centralized ones), our simulation results have revealed that the replicated solutions may offer smaller query response time and higher load saturation levels. it can also be concluded that in order to compete with replicated systems, the centralized solution requires using much more powerful database servers. it is to be noted that we have assumed replicated systems with minimum synchronization overhead involving a single broadcast message per write transaction. for more complex synchronization protocols, further investigation of the effect of the consistency control method on the performance of the replicated system is needed. references beeri, c., bernstein, p.a., and goodman, n. 1989. a model for concurrency in nested transaction systems, journal of the acm, 36:230–269. day, k., ben mnaouer, a., masoud, f.a., and towaiq, m. 2001. a fault tolerant asynchronous data replication protocol, proceedings of the iasted: international conference on applied informatics (ai2001), february 19 to february 22, 2001, in innsbruck, austria, 2001. gray, j.n., helland, p., and d.o’neil, s.p. 1996. the dangers of replication and a solution, proceedings of the 1996 acm sigmod intl. conf. on management of databases, pp. 173-182, montreal, canada, june 1996. sigmod. guerraoui, r., and schiper, a. 1997. software-based replications for fault tolerance, ieee computer, 30: 68-74. jensen, k. 1992, 1994: coloured petri nets: basic concepts, analysis methods and practical use. vol.1 and vol.2, monographs in theoretical computer science, springer-verlag, 1992, 1994. ref. value 4 6 8 mean 0.207 0.212 0.218 std. deviation 0.0034 0.0012 0.0007 95 % conf. int. of mean 0.2048 0.2098 0.2114 0.2131 0.2171 0.2185 jensen, k., christensen, s., huber, p., and holla, m. 1996. design/cpn: a reference manual, computer science dept, university of aarhus, denmark, 1996. jorgensen, j. b., kristensen, l. m. 1999. computer aided verification of lamport's fast mutual exclusion algorithm using coloured petri nets and occurrence graphs with symmetries. ieee transactions on parallel and distributed systems. 10: 714-732. kemme, b., and alonso, g. 1998. a suite of database replication protocols based on group communication primitives, proceedings of the 18th international conf. on distributed computing systems (icdcs’98), amsterdam, the netherland, may 1998. kemme, b., and alonso, g. 2000. a new approach to developing and implementing eager database replication protocols”, acm transactions on database systems 25: 333-379. mnaouer, a.b., sekiguchi, t., fujii, y., ito, t., and tanaka, h. 1999. colored petri nets based performance evaluation of the static and dynamic allocation policies of the 45 a.b. mnaouer et al asynchronous bandwidth in the fieldbus protocol, advances in petri nets (lncs 1605: 93130), special issue on the application of petri nets to communication networks, springerverlag 1999. mnaouer, a. b., day, k., shihab, k. 2002. impact of leaky bucket regulation on the performance of combined i/o buffering in atm switches, the 2002 ieee intl. conf. on systems, man, and cybernetics, hammamet, tunis, 6-9 october 2002, mp1a2, 1-6. morera, p.h., gonzalez, t.m. p. 1999. a cpn model of the mac layer. in k.jensen (ed.): proceedings of the 2nd workshop on practical use of coloured petri nets and design/cpn, aarhus 1999, department of computer science, university of aarhus, 153-172. pedone, f., gherraoui, r., and schiper, a. 1997. transaction reordering in replicated databases, proceedings of the 16th symposium on reliable distributed systems (srds-16), durham, north carolina, usa, october 1997. pedone, f., gherraoui, r., and schiper, a. 1998. exploiting atomic broadcast in replicated databases, proceedings of europar’98, sept. 1998. shapiro, r.m. 1991. validation of a vlsi chip using hierarchical coloured petri nets. journal of microelectronics and reliability, special issue on petri nets, pergamon press, vol. 31, no. 4, pp. 607-625, 1991. jensen, k and rozenberg, g. 1991. high-level petri nets. theory and application. springerverlag, pp. 667-687. wiesmann, m., pedone, f., and schiper, a. 1999. a systematic classification of replicated database protocols based on atomic broadcast, proceedings of the 3rd european research seminar on advances in distributed systems (ersads'99), madeira island, portugal, april 1999. wiesmann, m., pedone, f., schiper, a. kemme, b., and alonso, g. 2000. database replication techniques: a three parameter classification, proceedings of 19th ieee symposium on reliable distributed systems (srds2000), nürenberg, germany, october 2000. ieee computer society. received 24 march 2002 accepted 19 april 2003 46 performance evaluation of database systems using colored petri nets a.b. mnaouer, k. day, m. al-towaiq and f.a. masoud department of computer science, college of science, sultan qaboos university, p.o.box 36,al khod 123, muscat, sultanate of oman, email: fawaz@squ.edu.om ???? ?? ????? ???? ???? ???? ??????? ? ????? ???? ????? figure 4 shows the declaration node used for both models where color sets, variables, function declarations and definitions are given. 4. simulation results 5. conclusion microsoft word math031007.doc squ journal for science, 9 (2004) 25-31 © 2004 sultan qaboos university 25 solution of a nonlinear functional equation valery c. covachev* and h. ali yurtsever** *department of mathematics and statistics, college of science, sultan qaboos university, p. o. box 36, al khod 123, muscat, sultanate of oman, email: valery@squ.edu.om, **department of mathematics, faculty of science and literature, fatih university, istanbul, turkey حل معادلة دالية غير خطية فاليري كريستوف كوفاتشف و حسن علي يورتسيفر يعتمد. معادلة دالية غير خطيةبحل الخاصة و) 2004( لنظرية ريستيسكي تعميم هذا البحث نقدم في :خالصة مثل هذا النوع من لحل طريقة المصفوفات مع λ االختيارية المجموعة في λ علي تعريف البارامتر البرهان .المعادالت abstract: in the present paper a generalization of a theorem of i.b. risteski (2004) concerning the solution of a nonlinear functional equation is given. the proof is based on a parametric approach by introducing a parameter λ in an arbitrary set λ , and on a matrix method for solving linear functional equations. keywords: nonlinear functional equation; symmetric group. 1. introduction unctional equations find applications in biology, social sciences, engineering, as well as in many other branches of mathematics and a great number of such applications can be found in the monograph by aczel (1966). this has led to considerable interest in the study of functional equations and has given rise to numerous articles and monographs on this subject. the present paper is devoted to the study of a nonlinear functional equation which generalizes the quadratic complex vector functional equation solved by i.b. risteski (2004). to the best of our knowledge, up to now this type of nonlinear functional equation has not been considered in the literature. we carried out our research to shed some light on this field of nonlinear functional equations. the results presented here and in (risteski, 2004) supplement and extend some of the results in (risteski et al 1999, 2000a, 2000b). in order to prepare the background for our study, we present the result of i.b. risteski (2004). let v be a complex finite-dimensional vector space and let there exist mappings , : nf g v v→ . ( ) 1 2i i n≤ ≤z f valery c. covachev and h. ali yurtsever 26 will denote vectors in the vector space v . multiplication of two arbitrary vectors ( )1 2, , , t nu u u=u … and ( )1 2, , , t nv v v=v … in v is defined as ( )1 1 2 2, , , t n nu v u v u v=uv … . i.b. risteski (2004) gave the following result. theorem 1. the general solution of the nonlinear complex vector functional equation ( ) ( )1 1 1 2 2, , , , , ,n n n n nf f− + +z z z z z z… … ( ) ( )1 1 1 2 2, , , , , ,n n n n nf f− + += z z z z z z… … ( ) ( )1 1 2 1 3 2, , , , , , ,n n n n n nf f− + + ++ z z z z z z z… … ( ) ( )1 1 2 1 2 1, , , , ,n n n n nf f− + −+ + z z , z z z z… … ( )2n ≥ (1) is given by ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 2 1 2 1 2 2 2 1 2 1 2 , , , n n n n n n n f f f f f f f f f f = u u u u u u u u u u u u … , (2) where ( ) 1if i n≤ ≤ are arbitrary functions in v . in the next section we shall consider a slightly generalized version of (1). in the proof of the theorem we shall use techniques developed in risteski (2002) and risteski and covachev (2000, 2001). on the other hand, the method used in risteski (2004) cannot be used in the proof of this theorem without imposing a very restrictive assumption on the equation considered. 2. statement of the problem in this part of our paper, we shall consider the generalized nonlinear complex vector functional equation ( ) ( )1 1 1 2 2, , , , , ,n n n n nf g− + +z z z z z z… … ( ) ( )1 1 1 2 2, , , , , ,n n n n nf g− + += z z z z z z… … ( ) ( )1 1 2 1 3 2, , , , , , ,n n n n n nf g− + + ++ z z z z z z z… … ( ) ( )1 1 2 1 2 1, , , , ,n n n n nf g− + −+ + z z , z z z z… … ( )2n ≥ . (3) if f g≡ , equation (3) is reduced to (1). it is easy to see that if a component of f is identically 0 , then the corresponding component of g may be arbitrary. similarly, if a component of g is identically 0 , then the corresponding component of f may be arbitrary. so we need to consider only solutions ( ),f g of equation (3) for which no component of f or g is identically 0 . thus we may suppose that (3) is a scalar functional equation. moreover, the arguments ( ) 1 2i i n≤ ≤z may belong to an arbitrary set v (with at least 1n + distinct elements). furthermore, it is easily seen that the function f depends on the arguments ( ) 11 1, , nn v −− ∈z z… as on a parameter. so solution of a nonlinear functional equation 27 we can slightly generalize equation (3) by introducing a parameter λ in an arbitrary set λ instead of ( ) 11 1, , nn v −− ∈z z… . for convenience we write iz instead of ( ) 0n i i n+ ≤ ≤z . thus we consider the equation ( ) ( ) ( ) ( )0 1 2 1 0 2, , , , , , , ,n nf g f gλ λ=z z z z z z z z… … ( ) ( ) ( ) ( )2 1 0 3 1 1 0, , , , , , , , ,n n nf g f gλ λ −+ + +z z z z z z z z z… … ( )2 ,n ≥ (4) where : f vλ× → c and : ng v → c . 3. main result theorem 2. each solution ( ),f g of the nonlinear functional equation (4), such that none of the functions f and g is identically 0 , is given by ( ) ( ) ( ) 1 , , n i i i f f gλ λ = = ∑u u (5) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 2 1 2 1 2 2 2 1 2 1 2 , , , n n n n n n n g g g g g g g g g g = u u u u u u u u u u u u … , (6) where ( ): : 1i if and g v i nλ → → ≤ ≤c c are arbitrary functions in v . proof : let us introduce the function ( ) ( ) ( )0 1 0 1, , , , , , , .n nf f gλ λ=z z z z z z… … (7) it satisfies the linear functional equation ( ) ( )0 1 2 1 0 2, , , , , , , , , ,n nf fλ λ=z z z z z z z z… … (8) ( ) ( )2 1 0 3 1 1 0, , , , , , , , , , , .n n nf fλ λ −+ + +z z z z z z z z z… … we will not solve equation (8). instead, we will just find the form of the solutions of (8) which can be represented as (7). to this end, we use a method similar to that in risteski (2002) and in risteski and covachev (2001). below we will denote by ns the symmetric group of degree n (or symmetric group on n letters, see feyzioğlu (1990)). this is the group of all one-to-one mappings of the set { }1, 2, , n… onto itself, and its elements are called permutations (of 1, 2, , n… ). here, for our convenience, we denote by 1ns + the group of all one-to-one mappings of the set { }0,1, 2, , n… onto itself. let 1nsα +∈ . this means that ( ) ( ) ( )( )0 , 1 , , nα α α… is a permutation of the indices ( )0,1, , n… . then equation (8) is equivalent to the linear homogeneous system ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )( )0 1 2 1 0 2, , , , , , , , , ,n nf fα α α α α α α αλ λ−z z z z z z z z… … (9) valery c. covachev and h. ali yurtsever 28 ( ) ( ) ( ) ( ) ( )( )2 1 0 3, , , , , , nf α α α α αλ− −z z z z z… ( ) ( ) ( ) ( )( ) 11 1 0, , , , , 0, .nn nf sα α α αλ α +−− = ∈z z z z… this system of ( )1 !n + equations has a nontrivial solution if and only if its determinant is 0 . we will not show that this determinant is 0 , but we will use the form of the nontrivial solution and eventually obtain a solution of (8) admitting the factorization (7). according to risteski (2002) and risteski and covachev (2001), a possible nontrivial solution of (8) has the form ( ) ( ) ( ) ( )( ) 1 0 1 0 1, , , , , , , , , n n n s f c hα α α α α λ λ +∈ = ∑z z z z z z… … (10) where 1: nh v +λ× → c is an arbitrary function, and cα are complex constants (which may also depend on λ ). however, it is easy to see that if ( )0 1, , , , nf λ z z z… has the form (7), then ( )0 1, , , , nh λ z z z… must admit the factorization ( ) ( ) ( ) ( ) ( )0 1 0 0 1 1, , , , ,n n nh c g g gλ λ=z z z z z z… (11) where : c λ → c and ( ): 0ig v i n→ ≤ ≤c are arbitrary functions. thus the representation (10) takes the form ( ) ( ) ( )( ) ( )( ) ( )( ) 1 0 1 0 10 1, , , , , n n n n s f c g g gα α α α α λ λ +∈ = ∑z z z z z z… (12) where we have denoted ( ) ( )c c cα αλ λ= . by virtue of (7) we must have ( ) ( ) ( ) ( )( ) ( )( ) ( )( ) 1 0 1 0 10 1, , , . n n n n s f g c g g gα α α α α λ λ +∈ = ∑z z z z z z… (13) since g is not identically 0 , there exists an n -tuple ( )1 2, , , nn v∈a a a… such that ( )1 2, , , 0ng ≠a a a… . we set ( )1, ,i i i n= =z a … in (13) and find ( ) ( ) ( ) ( ) ( ) ( ) ( )1 1 1 0 1 00 1 , , , , n n n ii s i f g c g gα α α α λ λ − − +∈ = = ∑ ∏z a a z a… (14) i.e., ( )0,f λ z can be represented as ( ) ( ) ( )0 0 0 , . n i i i f d gλ λ = = ∑z z (15) now equation (13) can be written in the form ( ) ( ) ( ) ( ) ( ) ( ) ( )1 1 0 1 0 0 0 1 , , . n nn n i i n i jj i i s j d g g g c gα α α λ λ − += = ∈ =   =     ∑ ∑ ∑ ∏z z z z z… (16) from (16) it follows that solution of a nonlinear functional equation 29 ( ) ( ) ( ) ( ) ( )1 1 1 2 1 , , , , 0,1, , . n n n jj s ji c g g i n d α α α λ λ − +∈ = = =∑ ∏z z z z… … (17) now the quotients ( ) ( )/ ic dα λ λ must all be independent of λ . moreover, if we compare two of these representations of ( )1 2, , , ng z z z… , for 0i = and for some 0i ≠ , and we give suitable values to all but one of the variables 1 2, , , nz z z… , we find that ( )0g z is expressed as a linear combination of ( ) ( )1 , , ng gz z… . we can then write ( ) ( ) ( )0 0 1 , , n i i i f f gλ λ = = ∑z z (18) ( ) ( )( )1 2 1 , , , . n n n j j s j g c gα α α∈ = = ∑ ∏z z z z… (19) equation (18) shows that, in fact, equation (5) is valid. it remains to prove that (up to a constant factor) equation (6) also holds. to this end we will determine the constants cα (up to a common factor) so that the pair ( ),f g given by (18) and (19) satisfies equation (4): ( ) ( ) ( )( )0 1 1n nn i i j j i s j f g c gα α α λ = ∈ = ∑ ∑ ∏z z ( ) ( ) ( ) ( ) ( )( ) ( ) 1 1 1 01 1 1n n i i j j i s j f g c g gα αα α α λ − −= ∈ ≠ = ∑ ∑ ∏z z z ( ) ( ) ( ) ( ) ( )( ) ( ) 1 1 2 02 1 2n n i i j j i s j f g c g gα αα α α λ − −= ∈ ≠ + +∑ ∑ ∏z z z ( ) ( ) ( ) ( ) ( )( ) ( ) 1 1 0 1 . n n i i n j jn i s j n f g c g gα αα α α λ − −= ∈ ≠ +∑ ∑ ∏z z z thus for each 1, 2, ,i n= … we must have ( ) ( )( )0 1n n i j j s j g c gα α α∈ = ∑ ∏z z ( ) ( ) ( ) ( )( ) ( ) 1 1 1 01 1n i j j s j g c g gα αα α α − −∈ ≠ = ∑ ∏z z z ( ) ( ) ( ) ( )( ) ( ) 1 1 2 02 2n i j j s j g c g gα αα α α − −∈ ≠ + +∑ ∏z z z ( ) ( ) ( ) ( )( ) ( ) 1 1 0 . n i n j jn s j n g c g gα αα α α − −∈ ≠ + ∑ ∏z z z (20) it is easily seen that each term on the left cancels with some term on the right-hand side of (20). indeed, let us take the term ( ) ( )( ) ( )( )0i i ji j j i g c g gα α α ≠ ∏z z z valery c. covachev and h. ali yurtsever 30 for some fixed nsα ∈ . suppose that ( )i kα = . then this term is identical with the term on the right ( ) ( ) ( ) ( )( ) ( ) 1 1 0 .i k j jk j k g c g gα αα α − −≠ ∏z z z now we have to determine (up to a common factor) the coefficients cα so that the remaining terms on the right-hand side of (20) cancel pairwise. the terms on the right ( ) ( ) ( ) ( )( ) ( ) 1 1 0i k j jk j k g c g gα αα α − −≠ ∏z z z and ( ) ( ) ( ) ( )( ) ( ) 1 1 0i j j j g c g gβ ββ β − −≠ ∏z z z for k ≠ cancel each other if and only if ( ) ( ) ( ) ( )1 1 , , ,k i k iα β β α− −= = = ( ) ( ) ( )1 , 0.j j j k c cα βα β α −= ∀ ≠ + = this means that ( ) ( ) ( ) { } { }1 1 1, , 1, 2, , \ , .k k m m m n kβα βα βα− − −= = = ∀ ∈ … thus the permutation 1βα − is a transposition (exchanges the indices k and and keeps all other indices fixed), i.e., β and α are permutations of different signature (one even and one odd). consequently, we must have if is even, if is odd, c c cα α α  =  − for some constant 0c ≠ . thus ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 2 1 2 1 2 2 2 1 2 1 2 , , , . n n n n n n n g g g g g g g c g g g = z z z z z z z z z z z z … finally, we can replace the functions ( )if λ by ( )icf λ for 1, 2, ,i n= … . thus we have shown that any solution ( ),f g of equation (4), such that none of the functions f and g is identically 0 , must have the form (5) and (6). it remains to show that every pair of functions ( ),f g of the form (5) and (6) is a solution of equation (4). indeed, by virtue of the equations (5) and (6) we obtain ( ) ( ) ( ) ( )0 1 2 1 0 2, , , , , , , ,n nf g f gλ λ−z z z z z z z z… … ( ) ( ) ( ) ( )2 1 0 3 1 1 0, , , , , , , , ,n n nf g f gλ λ −− − −z z z z z z z z z… … solution of a nonlinear functional equation 31 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 1 1 0 1 1 1 1 0 1 0 1 0. i i i n n n i i i i i n n n n n g g g g g g f g g g g g g λ = = =∑ z z z z z z z z z z z z this completes the proof of theorem 2. remark 3. it is clear that the solutions of equations (1) and (4) as given, respectively, by (2), (5) and (6), coincide if we assume that 1nv −λ = and f g≡ . 4. references aczel, j. 1966. lectures on functional equations and their applications. academic press, new york, london. feyzioğlu, a.k. 1990. a course on algebra. boğaziçi university publication, istanbul. risteski, i.b. 2002. matrix method for solving linear complex vector functional equations. international journal of mathematics and mathematical sciences, 29: 217-238. risteski, i.b. 2004. solution of some nonlinear complex vector functional equations. african diaspora journal of mathematics, 1: 49-57. risteski, i.b. and covachev, v.c. 2000. on some general classes of partial linear complex vector functional equations. sci. univ. tokyo j. math., 36: 105-146. risteski, i.b. and covachev, v.c. 2001. complex vector functional equations. world scientific, new jersey-london-singapore-hong kong. risteski, i.b., trenčevski, k.g. and covachev, v.c. 1999. a simple functional operator. new york j. math., 5: 139-142. risteski, i.b., trenčevski, k.g. and covachev, v.c. 2000a. cyclic complex vector functional equations. appl. sci., 2: 13-18. risteski, i.b., trenčevski, k.g. and covachev, v.c. 2000b. on a linear vector functional equation. in some problems of applied mathematics. eds a. ashyralyev and h.a. yurtsever. fatih university publications, istanbul. received 7 october 2003 accepted 25 april 2004 squ journal for science, 2017, 22(2), 114-119 doi: http://dx.doi.org/10.24200/squjs.vol22iss2pp114-119 sultan qaboos university 114 finite element approximation of variational inequalities: an algorithmic approach messaoud boulbrachene department of mathematics and statistics, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman. email: boulbrac@squ.edu.om. abstract: in this paper, we introduce a new method to analyze the convergence of the standard finite element method for elliptic variational inequalities with noncoercive operators (vi). the method consists of combining the so-called bensoussan-lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart, and then between the true solution and the approximate solution. keywords: variational inequalities, algorithm, finite element, l  error estimate. تقريب العناصر المنتهية للتباينات المتفاوتة: المنهج الخوارزمي مسعود بولبراشن باستخدام المؤثرات إلى التحدث عن طريقة جديدة لتحليل نقطة إلتقاء العناصر المنتهية للتباينات البيضاوية المتفاوتة نتطرق في هذا البحث الملخص: التقلص. غير اإللزامية. حيث تتكون هذه الطريقة من دمج خوارزمية بنسوزان ليونز مع تمييز الحلول في السياق المستمر والمنفصل كنقطة ثابتة من ديرات األخطاء المثلى أوال من الخوارزمية المستمرة والعنصر النظير المنتهي، وانتهاًء بالحل الصحيح، والتقريبي. كما تشتق تق .التباينات المتفاوتة، الخوارزمية، العنصر المنتهي، تقدير األخطاء: مفتاحيةالكلمات ال 1. introduction he theory of variational inequalities finds its roots in the work of signorini [1] and fichera [2] concerning unilateral problems. the mathematical foundation of the theory was widened by the invaluable contributions of stampacchia [3] and then developed by the french and italian schools (stampacchia [4], brezis [5], mosco [6], bensoussan-lions [7]). it has emerged as an interesting and fascinating branch of applicable mathematics with a wide range of applications in industry, finance, economics, and in social and pure and applied sciences. this field is dynamic and is experiencing an explosive growth in both theory and applications; as a consequence, research techniques and problems are drawn from various fields. the ideas and techniques of variational inequalities are being applied in a variety of diverse areas of science and prove to be productive and innovative. in this paper, we are concerned with the standard finite element approximation of the noncoercive problem associated with elliptic variational inequalities (vi): find u  k such that ( , ) (f, v u)a u v u   v  k (1) here,  is a bounded domain of nr , with boundary  , f in ( )l  , and   2, ( )w   such that  / n 0 on  , (.,.) is the inner product in 2 l (  ), k is the closed convex set 1 { ( ) such that }k v h v     (2) and (.,.)a is the bilinear form defined by ,u v  1 ( )h  , t mailto:mohammad@squ.edu.om finite element approximation of variational inequalities 115 , 0 , 1 1 ( , ) ( ) u n n j k k j k kj k k u v u a u v a b v a x v dx x x x                  , (3) where the coefficients ,j k a , k b 0 a ( , 1,..., nj k  ) are sufficiently smooth, and satisfy 2 , , 1 | | n j k j k j k a       n  r , 0  , x  (4) 0 a (x) > 0 , x  . (5) denoting by v h the finite element space consisting of continuous piecewise linear functions, h r the usual interpolation operator, and where { v such that } h h h k v v r    , (6) we define the discrete counterpart of (.) by find h h u k such that ( , ) ( , ) h h h h a u v u f v u v k   . (7) in stochastic control problems, the coefficients k 0 b (x), a (x) can be such that the bilinear form (3) does not satisfy the usual coercivity assumption, making the problem under consideration noncoercive. hence, in order to handle the noncoercive situation, we consider the equivalent vis: ( , ) ( , ) b u v u f u v u v k    (8) and ( , ) ( , ) h h h h h b u v u f u v u v k    (9) for the continuous and discrete problems, respectively, where  > 0 is large enough so that the new bilinear form      , , ,b u v a u v u v  (10) is strongly coercive on 1 ( ),h  that is, 1 2 ( ) ( , ) h b v v v   , 0  . (11) the standard finite element approximation for vis with noncoercive operators was first studied in [9], where an optimal error estimate was established by means of a subsolution method. in a recent work [10], we developed a new method to carry out the approximation of the same problem, combining the bensoussan-lions (bl) algorithm and the concept of subsolutions. in the present paper, we instead combine, in both the continuous and discrete contexts, the blalgorithm with the characterization of the solution as a fixed point of a contraction. the novelty that results from this combination resides in the fact that the generated algorithm is both monotone and geometrically convergent with a rate of convergence depending explicitly on the coercivity parameter  . combining the geometrical convergence results with standard finite element maximum norm error estimates for elliptic vis, we first establish an error estimate between the continuous algorithm and its finite element version, and then between the exact solution and the finite element approximate. an outline of the paper is as follows: in section 2, we recall some qualitative properties and standard finite element error estimate results for elliptic coercive vis. in section 3, we establish, in both the continuous and discrete cases, the geometrical convergence of the algorithm. finally, in section 4, we give the finite element error analysis. 2. preliminaries let g in l  (  ) and = (g)  be the solution of the following coercive vi: find k such that ( , ) ( , ) b v g v v k     (12) lemma 1. [7] let g and g in l  (  ), and ω and  be the corresponding solutions to vi (12). then g g implies   . proposition 1. under conditions of lemma 1, we have 1 g g          messaoud boulbrachene 116 proof. for ,g g in l  (  ) we consider ( )g   and ( )g   the corresponding solution to vi (.). let also = 1 g g      . then, since g g g g     , 0 0 0 (( ( ) ) / ( ) ( ( ) ) ( ( ) 0) g a x g a x because a x                making use of lemma 1, we get 0 ( , ) ( ( ( ) ) , )g g a x        on the other hand, one has 0 ( , ) ( ( ( ) ) ; )g g a x                indeed, 0 ( , ( )) ( , ) (( ( ) ) , )b v f b v a x v               0( , ) (( ( ) ), )g v a x v    so 0 ( , ( )) ( ( ( ) ) , ( )) ; b v g a x v v v                      therefore, 0 0 ( ( ( ) ) ; ) ( ( ( ) ) ; )g a x g a x             that is    the roles of and g g being symmetric, we similarly get    and the result follows. now, let ( ) h h h g k    denote the solution of the discrete counterpart of vi (12), that is, ( , ) ( , ) h h h h b v g v v k     remark 1. lemma 1 and proposition 1 stay true in the discrete case, provided the stiffness matrix is an m-matrix (this will be thoroughly explained in section 3). theorem 1. [11] there exists a constant c independent of h such that 2 2 | log | h ch h     (13) 3. algorithms 3.1 the continuous algorithm consider the following mapping : ( )t l k    such that w tw   ,where is the unique solution of the following coercive vi ( , ) ( , ) b v f w v v k      now, starting from 0 u  , we define the sequence n 1 ( ) n u  by 1n n u tu   , n 1  (14) such that each iterate n u solves the coercive vi 1 ( , ) ( , ) n n n n b u v u f u v u v k      (15) note that, thanks to lemma 1, the above sequence is monotonic decreasing. theorem 2. under conditions of proposition1, the mapping t is a contraction. therefore, its unique fixed point coincides with the solution of vi (1), and we have the error bound 0 1 1 n n u uu u        finite element approximation of variational inequalities 117 proof. let w and w in ( )l   , ( ), ( )f w f w         be the corresponding solutions to vi (.). then, making use of proposition 1, we have tw tw        1 f w f w         w w        which yields the contraction of .t the error bound follows straightforward from the fact that t is a contraction. 3.2 the discrete algorithm for the sake of simplicity, we suppose that  is polyhedral. we then consider a regular and quasi-uniform triangulation h  of  , consisting of n simplices  . denote by h , the mesh size of h , with h being the diameter of . for each h   , denote by 1 ( )p  , the set of polynomials on  with degree no more than 1. the 1 p conforming finite element space is given by 1 1 { ( ) c( ) : v/ ( )} h v v h p       . (16) let , 1 ( ) i m i m h  denote the vertices of the triangulation h  , and let i , 1 ( )i m h   denote the functions of h v which satisfy i ( ) , 1 , ( ) j ij m i j m h    so that the functions i  form a basis of v h . for every 1 ( ) c( )v h    , the function ( ) i 1 ( ) ( ) ( ) m h h i i r v x v m x    (17) represents the interpolate of v over h  . the convergence analysis of the discrete algorithm will require the monotonicity of the stiffness matrix. definition 1. a real d d matrix (c ) ij c  with c 0 ij  , i j  , 1 ,i j d  , is called an m-matrix if c is nonsingular and 1 0c   (i.e., all entries of its inverse are nonnegative). denote by b the matrix with generic coefficient i i ( , ) ,1 , ( ) ij j j b a dx i j m h         . (18) since the bilinear form (.,.)b is coercive, then the matrix b is positive definite and 0iib  , 1 ( )i m h  . furthermore, if the matrix ( ) jk a involved in the bilinear form (3) is symmetric, then mesh conditions for which the off-diagonal entries of b satisfy 0,ijb i j   . lemma 2 [13],[14] the matrix b is an mmatrix. theorem 3. [9] under conditions of lemma 2, the discrete vi (7) has a unique solution. let us now consider the mapping : ( ) h h t l k    such that h h w t w   , where h  is the unique solution of the following discrete coercive vi: ( , ) ( , ) v h h h h b v f w v k       . starting from 0 h h u r  , we define the discrete algorithm by 1 h n n h h u ut   , n 1  (19) such that each iterate n h u solves the coercive vi 1 ( , ) ( , ) n n n n h h h h h b u v u f u v u v k      . (20) as, in the continuous case, thanks to remark 1, the above sequence is monotonic decreasing. theorem 4. under conditions of lemma 2, the mapping h t is a contraction. therefore, its unique fixed point coincides with the solution of vi (7) and we have messaoud boulbrachene 118 0 1 1 h hh n h n uu u u        . (21) proof. similar to that of theorem 3. 4. ( )l   error analysis this section is devoted to proving the main results of this paper. next, we shall estimate the error in the maximum norm between the nth iterates n u of the algorithm and its finite element counterpart n h u . for that, let us first introduce the following sequence of coercive vis. indeed, let us define the sequence   1 n h n u  such that n hu solves the discrete vi 1 ( , ) ( , ) n n n n h hh h b u v u f u v u v k      (22) where n u is the nth iterate of the continuous algorithm. from now on, c will denote a constant independent of both n and h . lemma3. we have 2 2 | log | n n hu u ch h    (23) theorem 5. we have 2 2 | log | n n h u u ch h    (24) proof. we proceed by induction. indeed, let 2 2 ( ) = | log |h ch h . then, using standard error estimate in the maximum norm, we have 0 0 2 2 | log | h h u u r ch h       which, combined with theorem 4 and estimate (23), yields 1 1 1 1 1 1 0 0 0 0 2 ( ) ( ) 1 (1 ) ( ) = ( ) 1 hh hh h h h h u u u u u u t th u u h u u h h                             now assume that 1 1 1 ( ) 1 n n n h u u h           then, combining again theorem 4 and estimate (23), we get 1 1 1 1 ( ) ( ) 1 ( ) ( ) 1 1 1 ( ) 1 n n n n n n h hh h n n h h h n n h n n u u u u u u t th u u h u u h h h                                           finite element approximation of variational inequalities 119 theorem 6. we have 2 2 | log | h u u ch h    . (24) proof. indeed, combining theorems 2, 4, and 5 we have 0 1 2 2 0 1 | log | 1 1 n n n n h h h h n n h h u u u u u u u u u u ch h u u                         so passing to the limit, as n  , we get 2 2 | log | h u u ch h    . 5. conclusion based on the constructive bensoussan-lions algorithm and the banach fixed point principle, we have derived error estimate in the maximum norm of the standard finite element approximation of elliptic variational inequalities with non coercive operators. this new approach turns out to be successful and may be extended, in a future work, to system of variational inequalities related to hjb equations. references 1. signorini, a. on some static issues of continuous systems. annals of the scuola normale superiore di pisa, 1933, 2, 231-251. 2. fichera, g. elastostatic problems with unilateral constraints; the signorini problem with ambiguous contingency conditions. national academy of the lincei, 1964,7, 91-140 3. stampacchia, g. bilinear coercive forms on convex sets. comptes rendus de l' academie des sciences, paris, 1964, 258, 4413-4416 . 4. lions, j.l. and stampacchia, g. variational inequalities. communication in pure and applied mathematics., 1967, 20, 493-519. 5. brezis, h. equations and nonlinear in dual vector spaces. annals of fourier institute, grenoble, 1968, 18, 115175. 6. mosco, u. implicit variational problems and quasi-variational inequalities. lecture notes in mathematics, springer, berlin 1975, 543, 83-156. 7. bensoussan, a. and lions, j.l., application of variational inequalities to stochastic control problems. gauthiersvillars, 1982, paris. 8. rodrigues, j.f. obstacle problems in mathematical physics. 1987, north-holland, new york. 9. cortey-dumont, p. on variational inequalities with non coercive operators, rairo, 1985, 2, 195-212. 10. boulbrachene, m. on the finite element approximation of variational inequalities with noncoercive operators. numerical functional analysis and optimization, 2015, 36, 1107-1121. 11. cortey dumont, p. on the finite element approximation in the l  norm of variational inequalities with nonlinear operators. numerische mathematik, 1985,47, 45-57. 12. atkinson, w. and han, k. theoretical numerical analysis, 3rd edition, 2010, springer. 13. lu, c., huang. and qiu, j. maximum principle in linear finite element approximations of anisotropic diffusion-convection--reaction problems. numerische mathematik, 2014, 3, 515-537. 14. vejchodsky, t. the discrete maximum principle for galerkin solutions of elliptic problems. european journal of mathematics, 2012, 10, 5-43. received 30 march 2017 accepted 25 september 2017 squ journal for science, 2018, 23(1), 43-55 doi: http://dx.doi.org/10.24200/squjs.vol23iss1pp43-55 sultan qaboos university 43 a new second order approximation for fractional derivatives with applications haniffa m. nasir* and kamel nafa department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al-khod 123, sultanate of oman. *email: nasirh@squ.edu.om abstract: we propose a generalized theory to construct higher order grünwald type approximations for fractional derivatives. we use this generalization to simplify the proofs of orders for existing approximation forms for the fractional derivative. we also construct a set of higher order grünwald type approximations for fractional derivatives in terms of a general real sequence and its generating function. from this, a second order approximation with shift is shown to be useful in approximating steady state problems and time dependent fractional diffusion problems. stability and convergence for a crank-nicolson type scheme for this second order approximation are analyzed and are supported by numerical results. keywords: grünwald approximation, generating function, fractional diffusion equation, steady state fractional equation, crank-nicolson scheme, stability and convergence. تطبيقاتها معمن الدرجة الثانية للمشتقات الكسرية تقريب جديد كمال نافعو *حنيفة محمد ناصر درجاتاللمشتقات الكسرية. نستخدم هذا التعميم لتبسيط براهين ل يةلتقريبالد اجرنومن نوع درجة عالية بناء ةنظريلنقترح في هذا البحث تعميما :صالملخ متتالية استخدامكسرية بالمشتقات لل يةلتقريبالد اجرنونوع بدرجة عالية لمشتقات الكسرية. كما نقوم ببناء مجموعةلالمعروفة ات تقريبال المتعلقة بأنواع من االنتشار الكسريومسائل ثابتة مسائل الحالة اللتقريب من الدرجة الثانية مع االنسحاب مفيد في تقريب حقيقية عامة والدالة المولدة لها. وبهذا تم برهان أن ا . نكلسن لتقريبات من الدرجة الثانية ودعمهما بنتائج عددية-كرانك وتم تحليل االستقرار والتقارب لطريقة من نوع المرتبطة بالزمن. نكلسن، االستقرار والتقارب.-، معادلة االنتشار الكسري، الحالة الثابتة للمعادلة الكسرية، طريقة كرانكالدالة المولدة ،لداجرنوتقريبات :مفتاحيةالكلمات ال 1. introduction ractional calculus has a history that goes back to l’hospital, leibniz and euler [1,2]. a historical account of early works on fractional calculus can be found, for example, in [3]. fractional integral and fractional derivative are extensions of the integer order integrals and derivatives to a real or complex order. various definitions of fractional derivatives have been proposed in the past, among which the riemann-liouville, grünwald-letnikov and caputo derivative are common and established. each definition characterizes certain properties of the integer order derivatives. recently, fractional calculus found its way into the application domain in science and engineering. the field of application includes, but is not limited to, oscillation phenomena [4], visco-elasticity [5], control theory [6] and transport problems [7]. fractional derivatives are also found to be suitable to describe anomalous transport in an external field derived from the continuous time random walk [8], resulting in a fractional diffusion equation. the fractional diffusion equation involves fractional derivative either in time, in space or in both variables. fractional derivative is approximated by the grünwald approximation obtained from the equivalent grünwaldletnikov formula of the riemann-liouville fractional derivative. numerical experience and theoretical justifications have shown that application of this approximation as it is in the space fractional diffusion equation results in unstable solutions when explicit, implicit and even when the crank-nicolson (cn) type schemes are used [9]. f h.m. nasir and k. nafa 44 the latter two schemes are popular for their unconditional stability for classical diffusion equations. this peculiar phenomenon for the implicit and cn type schemes is corrected and the stability is restored when a shifted form of the grünwald approximation is used [9,10]. the grünwald approximation is known to be of first order with the space discretization size h in the shifted and non-shifted form and is, therefore, useful only in first order schemes such as explicit euler (forward) and implicit euler (backward) for the fractional diffusion equation. since the cn approximation scheme is of second order in time step  , tadjeran et al. [11] used extrapolation improvement for the space discretization to obtain a second order accuracy. subsequently, second order approximations for the space fractional derivatives were obtained through some manipulations on the grünwald approximation. nasir et al. [12] obtained a second order accuracy through a non-integer shift in the grünwald approximation, displaying super convergence. convex combinations of various shifts of the shifted grünwald approximation were used to obtain higher order approximations in chinese schools [13, 14, 15, 16, 17], some of which are unconditionally stable for the space fractional diffusion equation with cn type schemes. zhao and deng [18] extended the concept of super convergence to derive a series of higher order approximations. earlier, lubich [19] obtained some higher order approximations for the fractional derivative without shift for orders up to 6. numerical experiments show that these approximations are also unstable for the fractional diffusion equation when the methods mentioned above are used. shifted forms of these higher order approximations diminish the order to one, making them unusable as chen and deng [20,21] noted. in this paper, we construct a new second order grünwald type approximation which can be used with shifts without reducing its order. we apply this second order approximation in steady state problems and time dependent fractional diffusion problems. a cn type scheme is devised for this approximation and a justification for stability and convergence is given. the rest of the paper is organized as follows. in section 2, definitions and notations are introduced. in section 3, the main results of generalization are presented. in section 4, approximations of order one and two with shifts are constructed. in section 5 the constructed second order approximation is applied to devise numerical schemes for steady state and time dependant space fractional diffusion equations. stability and convergence for the scheme of fractional diffusion equations are analysed in section 6. supporting numerical results are presented in section 7 and conclusions are drawn in section 8. 2. definitions and notations denote by r),( 1 l , the space of lebesgue integrable functions:    <|)(||=)(1 dxxffl . let )()( 1 rlxf  and assume that it is sufficiently differentiable so that the following definitions hold. the left and right riemann-liouville fractional derivatives of order r are defined respectively as , )( )( )( 1 =)( 1       d x f dx d n xfd n x n n x rl     (1) and , )( )( )( 1)( =)( 1       d x f dx d n xfd nxn nn rl x       (2) where =n is an integer with nn <1  and )( denotes the gamma function. the corresponding left and right grünwald-letnikov (gl) fractional derivatives are given respectively by ),(1)( 1 lim=)( 0= 0 khxf kh xfd k kh x gl              (3) ),(1)( 1 lim=)( 0= 0 khxf kh xfd k kh gl x              (4) where !)1( 1)( = kkk           . it is known that the riemann-liouville and grünwald-letnikov definitions are equivalent [22]. hence, from now onwards, we denote the left and right fractional derivatives as )(xfdx   and )(xfdx   respectively. a new second order approximation 45 the fourier transform (ft) and inverse ft of an integrable function )()( 1 lxf are given by dxexffxf xi     )(=)( ˆ=:)))(((f and )(=)(ˆ=)))((ˆ( 1 xfdefxf xi       f respectively. the ft is linear: ).(ˆ)(ˆ=)))(()((  gfxgxf f for a function f at a point r,  x , the ft is given by ).(ˆ=)))(((   fexf xi f if )(),( xfdxf x   and )()( 1  lxfdx  , the fts of the left and right fractional derivatives are given by )(ˆ)(=)))(((   fixfd x f and )(ˆ)(=)))(((   fixfd x   f respectively [22]. for a fixed h , the grünwald approximations for the fractional derivatives in (1) and (2) are obtained by simply dropping the limit in the gl definitions (3) and (4) as ( ) ( ) , , =0 =0 and 1 1 ( ) = ( ) ( ) = ( ) h k h k k k f x g f x kh f x g f x kh h h                respectively, where ( ) = ( 1) k k k g         . when )(xf is defined in the intervals ],[ ba , it is zero-extended outside the interval to adopt the definitions of fractional derivatives and their approximations. the sums are restricted to a finite up to n which grows to infinity as 0h . often, n is chosen to be = x a n h      and = b x n h      for the left and right fractional derivatives respectively, to cover the sum up to the boundary of these domain intervals, where ][ y is the integer part of y . the left and right fractional derivatives, in this case, are denoted by )(xfdxa  and )(xfdbx  respectively. the grünwald approximations are of first order accuracy and display unstable solutions in the approximation of fractional diffusion equation by implicit and cn type schemes [9]. as a remedy, a shifted form of grünwald formula with shift r is used: ,>),)(( 1 =)( )( 0= , axhrkxfg h xf k rn k rh        (5) ,<),)(( 1 =)( )( 0= , bxhrkxfg h xf k rn k rh        (6) where the upper limits of the summations have been adjusted to cover the shift r . meerchaert et al. [9] showed that for a shift 1=r , the shifted approximations )(1, xfh    are also first order approximations with unconditional stability restored in implicit euler and cn type schemes for space fractional diffusion equations. as for higher order approximations, nasir et al.[12] derived a second order approximation with a non-integer shift, /2= r , displaying super convergence. ).()(=)( 2 /2, hoxfdxf xah     (7) tian et al. [13] used convex combinations of different shifted grünwald forms to obtain two second order approximations: )()(=)()( 2 ,2,1 hoxfdxfxf xaqhph     (8) with )2( 2 = 1 qp q    and )2( 2 = 2 qp p    for 1)(1,(1,0),=),( qp . hao et al. [14] obtained an quasi-compact order 4 approximation. all the above approximations are based on the shifted grünwald approximations rh , . the weights )( k g are the coefficients of the taylor series expansion of the power function  )(1 z . h.m. nasir and k. nafa 46 higher order approximations were also obtained earlier by lubich [19], establishing a connection with the characteristic polynomials of multistep methods for ordinary differential equations. specifically, if )(),( zz  are the characteristic polynomial [23] of a multistep method of order p , then          )(1/ )(1/ z z gives the weights for the grünwald type approximation of the same order for the fractional derivative of order  . from the backward multistep methods, lubich [19] derived higher order approximations of up to order six in the form   ))(1 1 (=)( 1= j j z j zw  . the generating functions )(zw given in table 1 are of order  for 61  . table 1. lubich approximation generating functions.    zzw 1=)( 1         2 2 2 1 2 2 3 =)( zzzw         32 3 3 1 2 3 3 6 11 =)( zzzzw         432 4 4 1 3 4 34 12 25 =)( zzzzzw         5432 5 5 1 4 5 3 10 55 60 137 =)( zzzzzzw         65432 6 6 1 5 6 4 15 3 20 2 15 6 20 49 =)( zzzzzzzw 3. generalization of grünwald approximation in this section, we generalize the concept of shifted grunwald approximation to an arbitrary sequence of weights and analyse its properties. this generalization is then used to construct higher order approximations for fractional derivatives. for a sufficiently smooth function )(xf , denote the left grünwald type operator with shift r and weights rkw , as ).)(( 1 =)( , 0= , hrkxfw h xf rk k rh       (9) definition 1 a sequence  rkw , of real numbers is said to approximate the fractional derivative )(xfdx   at x with shift r in the sense of grünwald if ).(lim=)( , 0 xfxfd rh h x      definition 2 a sequence  rkw , of real numbers is said to approximate the fractional derivative )(xfdx   at x with shift r and order 1p if ).()(=)( , p rhx hoxfxfd    (10) we consider the generating function k rkk zwzw ,0= =)(   of the weights rkw , which will play a central role in constructing approximations. remark 1 1. analogous definitions hold for the right fractional derivative with the same weights rkw , . we denote the right grünwald approximation as )(, xfrh    . a new second order approximation 47 2. the property (10) is the consistency condition for the grünwald type approximation operator  rh   , to the fractional differential operator. this consistency condition tells that the order of approximation is at least one. 3. for convenience, we do not distinguish the sequence of weights rkw , and its generating function )( zw in the above definitions, and in the discussions and results that follow. the following theorem establishes an equivalent characterization of the generator )( zw for an approximation of fractional differential operator with order 1p and shift r . theorem 1 let mnn ,<1   be a non-negative integer, )()( 1 r   nm cxf and )()( 1 rlxfd k x   for 10  nmk . then, the generating function )( zw of a real sequence }{ ,rkw approximates the left fractional differential operator for )(xf with order p and shift r , mp 1 , if and only if ).(1=)( 1 :=)( przz r zoeew z zg    (11) moreover, if l lplr zrazg )(1=)( =   , we have for the left fractional derivative ).()()()(=)(, mp xp p xrh hoxfdrahxfdxf     (12) proof. taking the ft of )(, xfrh    in (9), with the help of linearity, we obtain )))()((( 1 =)))((( , 0= ,    hrkxfw h xf rk k rh     ff )(ˆ 1 = )( , 0=    few h ihrk rk k    )(ˆ)( )( = , 0=      fiew ih e kih rk k rih    )(ˆ)()(= , 0=    fiew z e kz rk k rz          )(ˆ))((=)(ˆ))((=    fizgfiew z e r z rz  ),(ˆ)()(=)(ˆ)()(= 0=0=   fihrafizra ll l l l l l    where we have used hiz = . taking the inverse ft, we have ).()()(=)( 1 0= , mll xal m l rh hohxfdraxf       (13) now, (11) holds if and only if 0=)(1,=)( 0 rara l , for 1,1,2,= pl  . equation (12) holds immediately. □ remark 2 the equivalent condition (11) for order p approximation in theorem 1 holds for the right fractional derivative as well. in fact, the condition on the generating function )( zw for the right fractional derivative is ))((1=)( )( 1 :=)( przz r zoeew z zg      which is equivalent to (11). one of the consequences of theorem 1 is the following consistency condition. corollary 1 if the generating function )( zw gives a consistent approximation of the left and right fractional differential operators, then , =0 and hence(1) = 0, , = 0. k r k w w   proof. by remark 1 and 2, the order p is at least one. when 0z , the condition (11) becomes ))((1=)( przz zozeew    . take the limit as 0z . h.m. nasir and k. nafa 48 using theorem 1, one can check algebraically the following propositions for the generating function of approximation operators known previously in [12, 13, 19, 20]. proposition 1 the approximation given by (7) is of second order. proof. the coefficients )( k g have the generating function )(1 z . since the shift of the approximation is = / 2 ,r  it is enough to check the function   )(1 1 =)( /2 zz ee z zg   . taylor series expansion gives that )( 24 1=)( 42 2 zozzg   which confirms the second order. □ proposition 2 the approximation given by (8) is of second order accuracy. proof. since ph , and qh , have the same generating function  )(1 z with shifts p and q respectively, check the taylor series of      )(1)(1=)( 21 zqzzpz ee z ee z zg   which gives )( 224448 1=)( 32 2 zoz pqqp zg           . □ proposition 3 the lubich generating functions ,6,1,2,=),( pzwp in table 1 are of order p accurate without shift. moreover, if a non-zero shift r is introduced to the approximation, the orders reduce to one. proof. when there is no shift ( 0=r ), taylor expansion gives )(1=)/( pz p zozew    . when 0r , the order is determined by ),(1=))())(1((1=)/( zozozozewe pz p rz    for 61  p reducing the orders to 1. □ 4. construction of higher order approximation we construct higher order approximation generating functions for fractional derivatives with shifts by the use of theorem 1. the importance of theorem 1 is that the construction process is entirely confined to algebraic manipulation with the aid of taylor series expansion. in this paper, we choose the form   )(=)( 2 210 p p zzzzw   (14) for the generators. consider the taylor series expansion .)(=)( 1 =)( 0= l l l rzz r zraeew z zg     (15) for an order p approximation, we set the first p coefficients )(ra l to satisfy (11) in theorem 1. that is, we impose conditions 0=)(1,=)( 0 rara k for = 1, 2, , 1k p  . first and second order shifted grünwald approximations have been constructed by the above algebraic method and we have the following. theorem 2 the first and second order shifted grünwald approximations with shift r are given respectively by  )(1=)( 1, zzw r  and   . 2 12 2 2 3 ==)( 22 2102,                                z p r z r p r zzzw r (16) the generating function )(1, zw r corresponds to the shifted grunwald formula )(, xfrh  in (5) and (6) for the left and right fractional derivatives respectively, and is independent of the shift r . )( 2, zw r gives the second order grünwald type approximations given by (9) with coefficients rkw , obtained from the taylor series expansion of )(2, zw r . note that when there is no shift )(2,0 zw gives the lubich approximation )(2 zw in table 1. we denote the grünwald approximation of order p by , 1, 2,( ), =p ru x p for left and right fractional derivatives respectively. a new second order approximation 49 the grünwald weights rkw , can be computed by a recurrence formula [24,25]. lemma 1 let j jj zzw   0= =)( , where rj , 0> and m mm zwzw   0= =))((  . then, the coefficients m w satisfy the recurrence form 1.,)1)(( 1 =,= 1=0 00   mwmj m ww jjm m j m     (17) for the generating function )(2, zw r , being the power of a polynomial of degree 2 , the upper limit of the summation in (17) goes up to only 2=,2)(min m for 2m . 5. applications to fractional differential equations in this section, we apply the fourth order grünwald type approximation derived in the previous section to fractional differential equations. 5.1 steady state problems consider the steady state problem ,),(=)( bxaxfxudxa   (18) .=)(,=)( 21  buau consider a uniform partition bxxxxa n =<<<<= 210  of the problem domain ],[ ba with subinterval size 1,0,1,2,=,= 1   nixxh ii  . problem (18) at i x is approximated by ,,0,1,2,=),(= 2 2, nihofu iir    where )(= ii xuu and nixff ii ,0,1,2,=),(=  . in order to keep the discrete values i u within the computational domain, we choose the shift 1=r . neglecting the )( 2 ho remainder term, we get the approximation scheme ,0,1,2,=,=ˆ12, nifu ii     (19) where i û are the solutions of (19) and hence the approximation of the exact solution i u for 1,1,2,= ni  . let t nn uuuuuu ],ˆ,,ˆ,ˆ,[= 1210   , t n fffff ],,,,[= 210  with the boundary conditions incorporated in u as )(= 10 au  and )(= 2 bu n  . then, the matrix formulation of (19) is given by ,=2,1 fua where 2,1a is an 1)(1)(  nn toeplitz matrix given by     ,0, 1, =),( 1,1 2,1 elsewhere jiw jia ji where 1,1 jiw are the coefficients of the taylor series expansion of the generating function )(2,1 zw . after imposing boundary conditions, we obtain the ready-to-solve second order scheme as ,ˆ=ˆˆ 002,1 nn uauafua  where 2,1 â is the reduced matrix of size 1)(1)(  nn obtained from 2,1a by deleting the first and last rows and columns, fu ˆ,ˆ are obtained from fu , respectively by deleting their first and last boundary entries. n aa , 0 are the first and last column vectors of the matrix 2,1a reduced at both ends as above. 5.2 approximation of fractional diffusion equation we consider the numerical approximation of the space fractional diffusion equation defined in the domain ][0,],[ tba  : ),,(),(),(= ),( 21 txftxudktxudk t txu bxxa     (20) with the initial and boundary conditions h.m. nasir and k. nafa 50 ],[),(=,0)( 0 baxxsxu  ],[0,),(=),(),(=),( 21 ttttbuttau  where ).( txu is the unknown function to be determined; 21 , kk are non-negative constant diffusion coefficients with 0 21  kk , i.e, not both are simultaneously zero, and ),( txf is a known source term. the boundary conditions are set as follows: if 0 1 k , then 0)( 1 t and if 0 2 k , then 0)( 2 t . we assume that the diffusion problem has a unique solution. the space domain ],[ ba is partitioned into a uniform mesh of size n with subintervals of length nabh )/(=  , and the time domain ][0, t into a uniform partition of size m with subintervals of length mt/= . these two partitions form a uniform partition of the 2-d domain ][0,],[ tba  with grid points ),( mi tx , where ihax i = and mmnimt m  0,0,=  . we use the following notations for conciseness: ),(= mi m i txuu , )( 2 1 = 11/2 mmm ttt   and ),(= 1/2 1/2   mi m i txff . we present the cn type scheme with the order 2 approximation in space using 2,1 . using the approximations  12,212,12,1 ='   kk of order 2, the crank-nicolson type scheme at 1,0),0,(  mmnitx mi is ).()( 2 1 '= 221/21 2,1 1 hofuu uu m i m i m i m i m i       (21) let m u be the solution of (21) after neglecting the )( 22 ho  terms with tm n m n mmmm uuuuuu ]ˆ,ˆ,,ˆ,ˆ,ˆ[= 1210   , where m i û becomes the approximation of the exact values m i u with mm uu 00 =ˆ and m n m n uu =ˆ . then, (21) becomes 1.0,0,)ˆˆ(' 2 =)ˆˆ( 1/21 2,1 1   mmnifuuuu m i m i m i m i m i   thus, the crank-nicolson type scheme in matrix form reads 1,,0)(=)( 1/211   mmfuubuu mmmmm   (22) where tm n mmm ffff ],,,[= 1/2 1 1/2 1 1/2 0 1/2     . the matrix b corresponding to the operator '2,1 is given by ).( 2 = 2,122,11 t akakb    re-arranging for 1m u and m u , we have 1.,0,1,2,=,)(=)( 1/21   mmfubiubi mmm   (23) let b̂ be the reduced matrix from b and 1/2ˆ mf be the reduced vector from 1/2m f as was in section 5.1. after imposing the boundary conditions, equation (23) reduces to the ready-to-solve form 1,,0,1,2,=,ˆˆˆ)ˆ(=ˆ)ˆ( 1/21   mmbfubiubi mmmm  where )()(=ˆ 1 0 1 00 m n m nn mmm uubuubb   and n bb , 0 are the first( th 0 ) and last( th n ) column vectors of the matrix b reduced again as before, and i is the unit matrix of appropriate size. 6. stability and convergence we establish the stability of the crank-nicolson type scheme (23). we closely follow the analysis in [14] and present some required results. let 0}==,),,,,(=|{= 010 ninh vvvvvvvvv r be the space of grid functions in the computational domain in the space interval ],[ ba . for any h vvu , , define the discrete inner product and its corresponding norm respectively as a new second order approximation 51 .),(=||a=),( 1 1= uuundvuhvu ii n i ||  then, we have the following: lemma 2 let   0= }{ kk t be a double sided real sequence such that (i) 0 kk tt for 0,k (ii) 0 =   j n nj t for 0n . then, the toeplitz matrix ][= jin tt  of size 1n is negative definite for 0n . proof. for 0=n , 0 0 t . this matrix of size 1 is negative definite. for any positive integer n and for any nonzero 1)( n -dimensional vector t n vvvvv ],,,,[= 210  , consider the quadratic form jiij n j n in t vvtvtv  0=0== . summing the terms diagonally, we have jkj kn j kk n k j n j jkj kn j k n nk n t vvttvtvvtvtv        1 0=1= 2 0= 0 1 0== )(== )|||(1/2)(|)(|| 22 1 0=1= 2 0 jkj kn j kk n k vvttvt     || 0||=||)(|| 2 = 2 1= 2 0     |||||| vtvttvt k n nk kk n k which completes the proof. □ lemma 3 the matrices 2,1 â and t a 2,1 ˆ and hence their corresponding operators  12 ,  and  12 ,  respectively are negative definite for 2.1  proof. the matrix 2,1 â of size 1)(1)(  nn has the form . 1 =ˆ 1,12,13,12,11,1 0,11,14,13,12,1 0,11,12,13,1 0,11,12,1 0,11,1 2,1                       wwwww wwwww wwww www ww h a nnn nnn    by virtue of lemma 2, it is enough to prove that the coefficients ,1kw of the generator k kk zwzw ,10=2,1 =)(   satisfy the following properties for 21  . 1 0,1 0,1 2,1 ,1 ,1 =0 0, 0, = 0 for 3 and 0 for all 2. n m m m k k w w w t t w m w n           let     )(= 1 2 12 2 1 2 3 =)( 2 210 2 2,1 zzzzzw                          . then, 0 1 2 3 = 0    , 0 2 2= 1    and 0 1 2 1 = 2    for 21  . now, 0= 00,1   w and 0= 1 1 01,1     w . also,   20 2 1 2 002,10,1 21)( 2 1 =     ww  )(21)( 2 1 = 020 2 1 2 0     h.m. nasir and k. nafa 52 0, 2 2)1)(( 21)( 2 1 = 0 2 1 2 0                  0.62)(1 6 1 = 20 2 11 3 03,1     w we show that 0,1 mw for all 4m inductively.    0,122)12(3)2)((1 4! 1 = 2 2 2 02 2 10 4 1 4 04,1     w   0.60)204)3)((( 5! 2)1)(( = 2 2 2 02 2 10 4 1 1 5 0 5,1       w assuming that k w is non negative for 13  mk , we have for 6m , 0))2(2)1(( 1 = 22,111,1 0 ,1     mmm wmwm m w for 21  , since 2,11,1,  mm ww , 1 ),2(2),1(  mm  and 2  are all non-positive for 6m . from corollary 1, we have the consistency condition 0= 0= kk w  in general which is true for )(2,1 zw as well. since 0,1=   knk w for 3n , the last inequality follows from the consistency condition. □ lemma 4 the approximation operator '2,1 is negative definite. proof. for any h vv  , since the diffusion coefficients 21 , kk are non-negative, we have 0),(),(=),'( 12,212,12,1   vvkvvkvv  . □ theorem 3 if ),,,(= 121 m n mmm vvvv   be the solution of the problem 101,1,=' 1/2 2,1 1/2   mmnisvv m i m i m it  (24) 0=0,=0 m m m vv .0),(= 0 0 nixvv ii  then, .|||||| 1 0= 0          |||||| l m l m svv  proof. taking the inner product of (24) with 1/2m v , we have ).,(=),(),( 1/21/21/2 2 1/21/2   m i m i m i m i m i m it vsvvvv since 0),'( 1/21/2 2,1   m i m i vv from lemma 4, we get ).,(),( 1/21/21/2   m i m i m i m i vsvv   since )( 1 = 11/2 m i mm vvv     and )( 2 1 = 11/2 mmm vvv   , we have         )( 2 1 ),( 1 =),( 111/21/2 mmmmmm vvvvvv    ),(),( 2 1 = 11 mmmm vvvv    ||||),()||||( 2 1 = 1/21/2221 ||||||||   mmmmmm vsvsvv   .|||||| 2 1 1 |||||| mmm vvs   the inequality in the last two lines reduces to a new second order approximation 53 1.0,|||||| 1   mmsvv mmm ||||||  summing this for the first m inequalities, we have .0,|||||| 1 0= 0 mmsvv l m l m    ||||||  from the above estimates, we have the following stability result. □ theorem 4. the cn type difference scheme (23) of order 2 is unconditionally stable for 21  . for the convergence of the approximate solution from the cn type scheme, we have the following. theorem 5. the approximate solutions of the cn type scheme (23) with the given initial and boundary conditions are convergent for 21  . proof. let mmm uue ˆ=  be the error vector of the exact and approximate solutions mm uu ˆ, of the diffusion problem (20) respectively. then the error of the internal grid values m ê satisfy the system 1,01,1,=' 1/2 2,1 1/2   mmniree m i m i m it  0,=0,= 0 m m m ee 1,10,= 0  nie i where m i r are the remainder terms in (21) with )(|| 22 hcr m i  || for some constatnt 0>c . theorem 3 gives the estimate ).(|||| 22 1 0= hncre l m l m     |||| the convergence is then established as 0, h . □ 7. numerical results we test the approximation scheme devised in subsection 5.1 using the steady state test problem 1,0, )1( 1)(10 =)( 0     xx n n xud n x   10=(1)0,=(0) uu with the exact solution n xxu 10=)( . we set 8=n and test for values of the parameter  with 1.1,1.5= and 1.9 . the number of grid subintervals n corresponding to the discretization size = (1 0) /h n was considered for values = 16, 32, ,1024n . the maximum error   pp uu and the computed convergence orders are listed in table 2. table 2. second order approximation with shift 1=r using )(2,1 zw . = 1.1 = 1.5 = 1.9 n   |||| uu order   |||| uu order   |||| uu order 16 4.8893e-01 — 2.5141e-01 — 1.3365e-01 — 32 1.1592e-01 2.08 6.4851e-02 1.95 3.3951e-02 1.98 64 2.7227e-02 2.09 1.6450e-02 1.98 8.5491e-03 1.99 128 6.3685e-03 2.10 4.1396e-03 1.99 2.1446e-03 2.00 256 1.4873e-03 2.10 1.0383e-03 2.00 5.3703e-04 2.00 512 3.5020e-04 2.09 2.5997e-04 2.00 1.3437e-04 2.00 1024 8.7574e-05 2.00 6.5044e-05 2.00 3.3606e-05 2.00 this test confirms the theoretical justification of second order for the approximation )(2,1 zw . we consider the following test example for the fractional diffusion problem (20). h.m. nasir and k. nafa 54 let ))(1( )1( 1)( =),,(        mm xx m m mxg and 55 0 )(1=)( xxxs  . 1 2 diffusion coefficients: = 1, = 1.k k 0 source function: ( , ) = ( ( ) ( , 5, ) 5 ( , 6, ) t f x t e s x g x g x      )).,10,(),9,(5),8,(10),7,(10  xgxgxgxg  0 initial condition: ( , 0) = ( ).u x s x boundary conditions: (0, ) = 0, (1, ) = 0.u t u t 0 exact solution: ( , ) = ( ) . t u x t s x e  the test problem was applied to the cn type numerical scheme developed in subsection 5.2. all computations were performed using python language with scipy libraries [26] on an i7 notebook computer with 2.7ghz speed and 12gb memory and windows operating system. the second order approximation )(2,1 zw was tested for = 1.1,1.5 and 1.9 . table 3 lists the maximum error and the order of convergence for grid sizes = = 16, 32, ,1024n m . the partition subinterval sizes are then = 1/ m and = 1/h n for time and space, respectively. table 3. second order of convergence for cn type scheme with )(2,1 zw . 1.1= 1.5= 1.9= hn 1/=   |||| uu order   |||| uu order   |||| uu order 16 1.0544e-05 — 9.0719e-06 — 5.6905e-06 — 32 2.8172e-06 1.90 2.3208e-06 1.97 1.4309e-06 1.99 64 7.3008e-07 1.95 5.8863e-07 1.98 3.5731e-07 2.00 128 1.8606e-07 1.97 1.4836e-07 1.99 8.9332e-08 2.00 256 4.6984e-08 1.99 3.7252e-08 1.99 2.2338e-08 2.00 512 1.1806e-08 1.99 9.3341e-09 2.00 5.5852e-09 2.00 1024 2.9592e-09 2.00 2.3362e-09 2.00 1.3964e-09 2.00 the test results show that the second order approximation with )(2,1 zw is justified for its order of convergence and unconditional stability with the cn type scheme. 8. conclusion a new second order grünwald type approximation for fractional derivative with shift is constructed algebraically from a generalization of the grünwald approximation for the left and right fractional derivatives in terms of generating functions. numerical schemes for this approximation to solve steady state problems and time dependent fractional diffusion problems were devised with proof of stability and convergence. the approach of generating functions could be a useful tool for constructing difference approximation formulas for fractional derivatives. acknowledgement the authors are grateful to the reviewers for their useful comments and suggestions. this research is supported by sultan qaboos university internal grant no. ig/sci/domas/16/10. references 1. leibniz, g.w. 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2003 sultan qaboos university realization of a simplified controllability computation procedure: a matlabsimulink based tool ali al-lawati and afaq ahmed department of information engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email: lawati@squ.edu.om. تيسير حساب قابلية التحكم بواسطة أداة مطورة بماتالب سيمولنك على اللواتي و آفاق أحمد الميزة . الرقمية مةاألنظ مبسطة لحساب قابلية التحكم بفروع شبكات أداة سميولنك تم تطوير –باستخدام ماتالب : خالصة الخواص . األمثل لألداة المطورة تكمن في قابلية تحليل األنظمة ذات التصاميم المتغيرة للحصول على التصميم األساسية سهولة إدخال المعطيات المختلفة لعناصر النظام الرقمي في محاكاة للشبكة باإلضافة إلى اإلضافية لهذه األداة تشمل سهولة إجراء . لمتغيرةالبيئات ا abstract: with the use of matlab-simulink a simple tool has been developed to compute the controllabilities of nodes as well as branches of digital system networks. the primary advantage of this tool may be for such conditions where the study of controllability analysis of a system with different possible designs is required to give an optimal design solution. the ease of network simulation procedures together with the simple methodologies for inputting the different assigned parameters to the respective elements of the system in dynamic environments, are additional attributes of this tool. keywords: testability, digital electronic system, controllability, controllability transfer function, matlab-simulink. 1. introduction t he increasing functional complexity of digital electronic components and systems makes testing a challenging task, particularly under the constraints of maintaining a high quality of products at low and competitive market prices. reports reveal that, on average, a proportion of up to 70% of the total production cost is required as against the testing cost (bennetts, 1984; williams, 1986; könemann, 1998; zorian, 1999). thus, an optimal test strategy can give a substantial competitive advantage in a market comprising billions of electronic components and systems. it is, therefore, not surprising that the major technology organizations like "national technology roadmap for semiconductors" of the united states treat testing as a key technology component with significant importance (könemann, 1998). although testing incurs a lot of effort, it is an important means of reducing the overall cost significantly. while the actual material cost is only a negligible proportion of the product value, the cost of repair increases by a factor of more than10 (see figure 1) with each production stage (bennetts, 1984; bardell et al. 1987). it is much cheaper to reject several dies than to locate and exchange a defective chip in a complete system. as a consequence, no customer is willing to bear the risk of using defective components and most likely can only accept suppliers that guarantee low defect rate and/or often perform an incoming test for supplied parts. 131 ali al-lawati and afaq ahmed 0 0.5 1 1.5 2 2.5 3 3.5 chip board system field lo g( re la tiv e re pa ir c os t) figure 1. testability cost. low defect rate of a product can be guaranteed by extensive outgoing product tests only. vlsi chips have reached an enormous complexity, and yet their density doubles every 2 years (williams, 1986; sun and serra, 1992; könemann, 1998). this makes it impossible to rule out faults during design and production, even with the best design tools and fabrication processes available. however, short time-to-market is critical to profitability. if testing facilitates rapid diagnosis and thus provides a means to avoid fatal production delays resulting from excessive debug time or shipping defective products, it is worth the additional cost. availability of a system (or of redundant system’s components) can be significantly increased if testing is employed to allow rapid diagnosis after a failure. these facts clearly show the economic potential of an efficient test strategy in the rapidly growing area of dependable systems. although the two fields of design and test application appear quite disjoint it is technically and economically attractive to merge them. it will be shown that the concepts of design-for-testability (dft) and built-in self-test (bist) provide an ideal starting point for a unified test approach for the complete life cycle of a digital electronic system. it is the fact that testability relates to cost, which needs to satisfy some technical requirements within a budgeted testing allowance. however, this fact necessitates the measurements of testability levels at each node of digital electronic circuits. therefore, numerical assessment of the controllability features of a circuit design, leading to a measurement of circuit’s testability, can be of great importance particularly during the design stage of the circuit. the method of analyzing digital electronic systems for its controllability is a problem that is not being adequately addressed during the design phase. continuous controllability monitoring and analysis is essential to refine the system design for the better goals like enhancements of transparency, reliability, availability, and maintainability. there is no specific tool available which can give the complete system’s controllability analysis for different behavioral responses of nodes. researchers in the field of digital circuit testing have been constantly working in the process of developing a tool to study the controllability / observability as well as testability of digital systems (bennets, 1981, 1984; berg and hess, 1982; cerny and mauras, 1990; fritzemeier, et al. 1989; goldstein and thigpen, 1980; grason, 1979; kapur et al. 1991; koren, 1979; ratiu et al. 1982; stephenson and grason, 1976). these tools cannot be easily implemented for analyzing systems. their program data files are not user friendly; therefore it is difficult to describe a system and its related input and output files. hence the need to overcome these problems is the motivation for this research work. here we present the development, design and use of a user-friendly tool to compute and scan the complete controllabilities information of digital system circuits. 132 realization of a simplified controllability computation procedure 2. controllability controllability reports the cost of placing a node in a circuit at a predetermined logic value. placing this value on a primary input is “free”. however, it is possible to assign a minimal cost, say 1, to any primary input. the cost increases as the node depth in the circuit increases. this cost will also depend on the type of gate, the logic value to be imposed on the line, and whether the circuit is combinational or sequential. for example, controlling the output of a multi-input and gate to logic 1 requires the control of all of its inputs to logic 1, while for an or it is sufficient to control only one of the inputs to logic 1. controlling a node at a second level requires controlling the input at level 1 as well as those at level 0 (the primary inputs). thus, there is a cost for stepping from one level to another. controllability indicates how easily the system state can be controlled by the primary inputs (pins) of a circuit. quantitative controllability ratings can be determined for each node in the circuit; most often an average over all nodes is given. in the example in figure 2 the controllability of node d is a measure of how easy it is to set the output of block a to a logical 1 or 0 by assigning values to the primary inputs of the circuit. it is a function of the controllability of nodes a, b and c. a b api d c b po figure 2. test point insertion. testability can be substantially improved if more nodes are made available directly at primary inputs and outputs. as a consequence, test points are inserted in areas of low testability to allow direct observation or control of an otherwise internal node. although heuristic approaches exist, optimal placement of test points is still an open issue (eichelberger et al. 1991; seiss, et al. 1991). controllability of a node is an important property which indicates how easy it is to control the node on its excitations / responses, operations, and behaviors. node designers (developers) look at the "controllability" of a node in three aspects (aas and mercer, 87; butler et al. 1992; jerry and youjin, 1999; savir, 1983; savkin, 1998): a) behavior control, b) feature customization, and c) installation and deployment. the first deals with the controllability of its behaviors and responses corresponding to its operations and excitations. the next refers to the built-in capability of supporting customization and configuration of its internal functional features. the last refers to the control capability on node 133 ali al-lawati and afaq ahmed installation and deployment. however, once the system is designed and installed, the continuous study of controllability of its behaviors is an essential aspect to maintain the system. 3. controllability computational background since the controllability of a node is a measure of probability to set the response with desired signal using the excitation signals, controllability of a system depends on how correct a node is transferring its set (designed) controllability property to its output lines. definition 1: controllability transfer function (ctf) is a measure of the level of controllability transfer of a node to its succeeding node(s) or branch(es). in a digital system, controllability transfer function (ctf) of any node can be computed by simulating the test inputs and their behavioral output characteristics with respect to the node. using these characteristics, a mathematical relationship can be established as given below (bennets et al. 1981; bennets, 1984). absolute[ (0) (1)] 1 [ (0) (1)] n n ctf n n = − + (1) where is the total number of ways that a logic 0 can be produced on the node output and similarly, is the total number of ways of producing a 1. thus, the ctf is 1 in the case where and are equal (as, for example, in the case of using exclusive or gate as a node). in the unlikely event of n or being 0, the ctf would be 0, indicating that there is no control of the output state. generally, 0 < ctf <1. table 1 contains examples of ctf calculated values for basic building blocks of digital systems having different number of input lines. ( )0n n ) n ( )1 (1(0n ) ( )0 ( )1n table 1: calculated values of ctf for basic logic gates. number of inputs gate logic 2 3 4 5 and 0.5000 0.2500 0.1250 0.0625 nand 0.5000 0.2500 0.1250 0.0625 or 0.5000 0.2500 0.1250 0.0625 nor 0.5000 0.2500 0.1250 0.0625 exor 1.0000 1.0000 1.0000 1.0000 exnor 1.0000 1.0000 1.0000 1.0000 not 1 definition 2: controllability input to a node is a single valued controllability measurement of different inputs to that node. in practice, multiple input lines with different controllability values are connected to a single node. thus, the overall controllability of the input (cyinput) to a node will be the average of the controllabilities of the individual input lines (cyinput-1, cyinput-2, ….,cyinput-i,…,cyinput-n) feeding the node (bennets et al. 1981), i.e. cyinput = ∑ = n 1i i-inputcyn 1 (2) definition 3: controllability output of a node is the value of the controllability available at the output of that node. 134 realization of a simplified controllability computation procedure the controllability of the output (cyoutput) of a node will depend on ctf and cyinput (bennets et al. 1981), which can be related as shown in equation 3: (coutput) = ctf x cyinput (3) definition 4 : the branches bifurcating from a stem branch are known as fan-outs branches. the problem occurs at points of reconvergence of fan-out branches where the lack of independence of signal values on reconvergent paths can cause many remade decisions during a test cycle. this is effectively a lack of controllability at these points of reconvergence and is modeled by artificially reducing the controllability value at the destination of such fan-out branches (bardell et al. 1987). let f denote the number of branches (destinations) for a particular fan-out stem. stephenson and grason (1976), found that good results are produced when the controllability assigned to each destination is obtained by dividing the controllability of the fan-out stem by: 1 + log10 (f). definition 5: primary inputs are those essential signals, which are the basis of the design of the system as a resource. definition 6: primary outputs are those essential signals, which are the basis of the design of the system’s goal. 4. developed tool using matlab-simulink, a simplified tool is developed to study the exhaustive controllability analysis of digital system circuits where the user is supposed to define only the connectivity of the circuit. to illustrate the design, a digital system circuit of full adder is considered (see figure 3). figure 4 shows its realized model through the use of matlabsimulink. x y s c z figure 3. a circuit model of a full adder (version 1). 135 ali al-lawati and afaq ahmed figure 4. simulation model of figure 3. in the simulated design (see figure 4) each node box (node_1, node_2,…) has the same structure so that it can be copied to create as many nodes as is required in the system. this simplifies the procedure of defining the system’s nodes. the node block requires information about the ctf of the node and the number ( f ) of fan-out branches to propagate the controllability accordingly to its f output lines. the user can provide the information about ctf and f, by invoking the respective windows (see in figures 5 and 6). figure 5. control transfer function (ctf) window. figure 6. fan-out window. 136 realization of a simplified controllability computation procedure in the simulation, (p_input) is used to depict the value of controllability of primary inputs. all the primary input lines generally have the same controllability level of 1. however, through this design provision of any desired value of primary input controllability (ranging 0 to 1) can be assigned via invoking the window in figure 7. p_input blocks can be simply copied and pasted as many times as per the requirements of the nodes. the desired different primary input controllability values can be assigned to each block. to scan the controllability values at any branch an output device (controllability _scanner) is provided in the simulation model. the computed values of node controllabilities are made available at ncsps (node controllability scan points) of each of the simulated nodes of circuits. figure 7. primary input window. c x y s z figure 8. a circuit model of a full adder (version 2). 5. simulation demonstration and results to demonstrate and test the developed design, two different circuits realizing the same functions of full adders (see figures 3 and 8) have been considered. the respective simulations of those circuits are shown in figures 4 and 9. the scanned controllabilities for each of the nodes of the simulation models of figure 3 and 8 are given in table 2. 137 ali al-lawati and afaq ahmed table 2: node controllabilities of simulated models. nodes simulated models 1 2 3 4 5 6 7 8 9 figure 3 1.0000 0.5000 0.8843 0.4422 0.2355 x x x x figure 8 0.5000 0.5000 1.0000 0.3843 0.7686 0.1922 0.2882 0.4884 0.1681 it can be seen from table 2 that the nodal controllabilities at the output nodes are different despite the fact that both circuits perform the same function. node 3 (figure 4) and node 8 (figure 9) represent the sum bits for the respective circuits of figures 3 and 8 and have different values of 0.8843 and 0.4884, respectively. similarly it can also be observed that node 5 (figure 4) and node 9 (figure 9) represent the carry bits for the respective circuits of figures 3 and 8 and have different values of 0.2355 and 0.1681 respectively. it is also observed that the controllabilities of connecting links to these nodes are quite different as shown in table 3. table 3: controllabilities of connecting links of some nodes of simulated models. connecting links simulated models a3 b3 a5 b5 a8 b8 a9 b9 figure 3 0.7686 01.000 0.4422 0.5000 x x x x figure 8 x x x x 0.1922 0.7686 0.3843 0.2882 6. practical complex systems and validation of simulation results to demonstrate the validation of results we further consider the practical approach of the system simulation. we simulated the complex digital systems by portioning the system into pieces of building blocks. to experiment our developed tool we hereby consider three cases of system buildings. as shown in figures 10–12, these cases are hybrid; series (cascaded) and parallel, c x y s z figure 9. simulation model of figure 8. 138 realization of a simplified controllability computation procedure respectively. let us consider the building block of the system shown in figure 13. the scanned nodal controllability of this basic building block is found as: 1, 1, 1, 1, 0.75, 0.375, 0.2969, 0.2617, and 1123, respectively, for the nodes from 1 – 9. the average level of controllability of the block is 64.4%. the scanned nodal controllability’s graphs of each case are shown, respectively, in figures 14 – 16. this demonstrates that the use of the developed tool is feasible in total practicality. figure 10. hybrid model (case 1). figure 11. series model (case 2). figure 12. parallel model (case 3). 139 ali al-lawati and afaq ahmed figure 13. model of basic building block. 0 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4 5 6 7 8 9 node c on tr ol la bi lit y block 1 block 2 block 3 figure 14. scanned nodal controllability graph for case 1. 7. discussions and conclusions it can be seen from the results in table 2, which were obtained from the developed matlab-simulink-based tool, that the full adder realized in figure 3 is much better, in terms of controllability than the one in figure 8. the circuit of figure 3 is much more controllable than the circuit given in figure 8. this demonstrates that the developed tool is helpful in the design of better controllable systems. controllability monitoring (scanning) for each of the connecting branches as well as nodes of the circuits is an essential process to realize the targeted goal of the system. as an example, it can be visualized through the results of table 3 that the circuit of figure 8 needs test-point insertions to enhance the testability of the designed circuit, which demonstrates the applicability of the developed tool. since, the program creates an exhaustive table where all the possible input instructions are demonstrating their propagated effects that are very helpful in the analysis and design of transparent systems and helps in isolating the critical nodes. 140 realization of a simplified controllability computation procedure 0 0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 5 6 7 8 9 node c on tr ol la bi lit y block 1 block 2 block 3 figure 15. scanned nodal controllability graph for case 2. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1 2 3 4 5 6 7 8 9 node c on tr ol la bi lit y block 1 block 2 block 3 figure 16. scanned nodal controllability graph for case 3. further, figures 13-16 demonstrate how simply the developed simulation model measures the levels of the controllability for complex digital systems. this in-house developed program has the ability to measure controllability at any node of systems consisting of any number of blocks with any type of connectivity. this paper has demonstrated the simplified procedure to study the exhaustive controllability analysis of digital system circuits. using the matlab-simulink, the developed design has been made user-friendly where the simplified mechanism (although it invokes windows) can be adapted to furnish the dynamics of the network. also, the incorporated program for this development can easily be modified to cope with the requirement of the user. further, graphical, 141 ali al-lawati and afaq ahmed numerical and tabular forms of the results can be obtained using this incorporated program as per the suitability and the data can be easily transported as well. unlike vhdl or pspice, matlab is the only language which provides all these attributes in totality. since matlab is a common teaching tool for many of the courses of engineering curricula, the developed simulation model is not only useful for commercial purposes but it is also helpful for teaching purposes. thus, this developed tool is of much importance particularly in such cases where it is desired to analyze the controllability of a network of a large size with different and changing parameters. references aas, e.j. and mercer, m.r. 1987. algebraic and structural computation of signal probability and fault detectability in combinational circuits, proceedings of the 17th international symposium on fault-tolerant computing, pp. 72-77. bardell, p.h., mcanney, w.h., and savir, j. 1987. built-in test for vlsi (pseudorandom techniques), john wiley & sons, pp. 43-60. bennets, r.g., maunder, c.m., and robinson, g.d. 1981. camelot: a computeraided measure for logic testability, j ieee proceedings, e-128: 177-189. bennetts, r.g., 1984. design of testable logic circuits, addison wesley. berg, w.c., and hess, r.d. 1982. comet: a testability analysis and design modification package, proceedings international test conference, pp. 364-378. butler, k.m., kapur, r., ross, d.e., and mercer, m.r. 1992. the roles of controllability and observability in design for test, proceedings ieee vlsi test symposium. cerny, e., and mauras, c. 1990. tautology checking using cross-controllability and crossobservability relations, proceedings ieee international conference on computer-aided design, pp. 34-37. eichelberger, e.b., lindbloom, e., waicukauski, j.a., and williams, t.w. 1991. structured logic testing, prentice hall, englewood cliffs, n.j. fritzemeier, r.r., nagle, h.t., and hawkins, c.f. 1989. fundamentals of testability – a tutorial, j ieee transactions on industrial electronics, 36(2): 117-128. goldstein, l.h., and thigpen, e.l. 1980. scoap sandia controllability / observabilty analysis program, proceedings 17th acm / iee design automation conference, pp. 190-196. grason, j. 1979. tmeas, a testability measurement program, proceedings 16th acm / iee design automation conference, pp. 156-161. jerry, g., and youjin, z. 1999. tracking software components, technical report, san jose state university, usa, ( http://www.engr.sjsu.edu/gaojerry/report/main.htm). kapur, r., butler, k.m., ross, d.e., and mercer, m.r. 1991. on bridging fault controllability and observability and their correlations to detectability, proceedings of the european test conference , pp. 333-339. könemann, b. 1998. creature from the deep submicron lagoon, keywords to the 10 th itg workshop on test methodenund zuverlässigkeit von schaltungen, herrenberg, germany, march. koren, i. 1979. analysis of the signal reliability measure and an evaluation procedure,” j ieee transactions (computers), c-28 (3): 244-249. ratiu, i., sangiovanni-vincentelli, a., and pederson, d.o. 1982. victor: a fast vlsi testability analysis program, proceedings international test conference, pp. 397-401. savir, j. 1983. good controllability and observability do not guarantee good testability, j ieee transactions (computers), c-32 (12): 1198-1200. savkin, a.v. 1998. controllability of complex switched server queueing networks modelled as hybrid dynamical systems, proceedings of 37th ieee conference on decision and control, pp 289-293. 142 http://www.engr.sjsu.edu/gaojerry/report/main.htm realization of a simplified controllability computation procedure seiss, b., trouborst, p., and schult, m. 1991. test point insertion for scan-based bist", proc. international test conference, ieee cs press, pp. 253-262. stephenson, j.e., and grason, j. 1976. a testability measure for register transfer level digital circuits, proceedings of 6th annual fault-tolerant computing symposium, pp. 101107. sun, x., and serra, m. 1992. merging concurrent checking and off-line bist, proc. international test conference, sept. 20-24 1992, baltimore, md, ieee cs press, pp. 958967. williams, r.w. 1986. ibm perspectives on the electrical design automation industry, keywords to ieee design automation conference. zorian, y. 1999, testing the monster chip, ieee spectrum, 36(7): 54-60. received 7 june 2001 accepted 3 december 2003 143 realization of a simplified controllability computation procedure: a matlabsimulink based tool ali al-lawati and afaq ahmed department of information engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email: lawati@squ.edu.om. 2. controllability 3. controllability computational background where � is the total number of ways that a logic 0 can be produced on the node output and similarly, � is the total number of ways of producing a 1. thus, the ctf is 1 in the case where � and � are equal (as, for example, in the case of using exclusive number of inputs definition 2: controllability input to a node is a single valued controllability measurement of different inputs to that node. definition 3: controllability output of a node is the value of the controllability available at the output of that node. definition 4 : the branches bifurcating from a stem branch are known as fan-outs branches. definition 5: primary inputs are those essential signals, which are the basis of the design of the system as a resource. definition 6: primary outputs are those essential 4. developed tool figure 3. a circuit model of a full adder (version 1). figure 8. a circuit model of a full adder (version 2). 5. simulation demonstration and results table 2: node controllabilities of simulated models. simulated models nodes 1 2 3 4 5 6 7 8 9 figure 3 1.0000 0.5000 0.8843 0.4422 0.2355 x x x x figure 8 0.5000 0.5000 1.0000 0.3843 0.7686 0.1922 0.2882 0.4884 0.1681 it can be seen from table 2 that the nodal controllabilities at the output nodes are different despite the fact that both circuits perform the same function. node 3 (figure 4) and node 8 (figure 9) represent the sum bits for the respective circuits o table 3: controllabilities of connecting links of some nodes of simulated models. simulated models connecting links a3 b3 a5 b5 a8 b8 a9 b9 figure 3 0.7686 01.000 0.4422 0.5000 x x x x figure 8 x x x x 0.1922 0.7686 0.3843 0.2882 6. practical complex systems and validation of simulation results 7. discussions and conclusions electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 67-75 © 2003 sultan qaboos university m synchronization and oscillator death in diffusively coupled lattice oscillators adu a.m. wasike department of mathematics, university of nairobi, p.o.box 30187, nairobi kenya, email: aduwasike@yahoo.com. تزامن وموت المتذبذب في المتذبذبات الشبكية المقرنة انتشارياُ واسيكيأدو يهتم هذا البحث بدراسة التزامن وتوقف التذبذب لمتذبذبات مستوية ذات عدد زوجي موجب مقرنة إلى أقرب متذبذبات : خالصة لكل متذبذب حل دوري . شاري خطي ومتماثل ، ثنائية وثالثية من خالل مسار انت في شبكية صحيحة على مستويات آحادية اثبتت الدراسة أن في بعض حاالت التفارق يوجد تزامن متماثل وتزامن غير متماثل يناظر كل حل دوري متماثل وغير . جاذب من غير متماثل يكون عند التفارق الضعيف ، التزامن المتماثل يوجد في حالة التفارق القوى بينهما التزا . متماثل على الترتيب . وهذا يختفي إلى األصل بعد تفارق قوي معين abstract: we consider the synchronization and cessation of oscillation of a positive even number of planar oscillators that are coupled to their nearest neighbours on one, two, and three dimensional integer lattices via a linear and symmetric diffusion-like path. each oscillator has a unique periodic solution that is attracting. we show that for certain coupling strength there are both symmetric and antisymmetric synchronization that corresponds to symmetric and antisymmetric non-constant periodic solutions respectively. symmetric synchronization persists for all coupling strengths while the antisymmetric case exists for only weak coupling strength and disappears to the origin after a certain coupling strength. keywords: lattice differential equations, bravais lattice, dynchronization and oscillator death. 1. introduction this paper is concerned with the synchronization and mutual extinction of oscillations of a system of ordinary differential equations (odes) indexed by points in an -dimensional integer lattice { }, 1, 2,mz m ∈ 3 . this system is what we shall refer to as lattice differential equations (ldes).by a lattice oscillator, we mean a system of ldes with every lattice points having an attracting periodic orbit. they have been great interest in the synchronization of coupled oscillators on a onedimentional integer lattice. aside from the mathematical interest in the problem (see for instance aronson et. al. 1987, and references therein, coupled oscillators occur in other fields. in biology the papers of ermentrout and koppel (1990,1992) provide us with examples where synchronization and oscillator death occur. in chemistry bar-eli (1985) and crowley and epstein (1989) consider the synchronization and oscillator death for some chemical oscillators. ldes are also found in cellular neural networks (cnn), (see for example chua and roska 1993. metallurgy is another area where lattice systems can be found (cahn 1960). (private communication) has considered synchronization of coupled oscillators of subsystems that are described by a second order damped forced duffing ordinary differential equation. the oscillators are linearly and diffusively coupled both in position and velocity to their nearest neighbours. he found that synchronization that occurred for large values of the coupling 67 mailto:aduwasike@yahoo.com adu a.m. wasike strength for both identical nonidentical oscillators is mainly influenced by the damping in the individual oscillators and dissipation of the coupling component of the system. much of the work on synchronization and cessation of oscillations is done on a one-dimensional lattice and coupling involves only one variable of each subsystem. this is known in the literature as scalar coupling (bar-eli 1985). there is less repertoire on this subject in two and three-dimensional cases and when all variables in the subsystems at each lattice site are involved in the coupling. the problem we consider in this paper is the synchronization and cessation of oscillation of planar oscillators that are linearly and symmetrically coupled via a diffusion-like coupling to their nearest neighbours on one, two and three dimensional lattices. as a special case of the general results, we consider a canonical model where each oscillator is a truncated normal form to cubic order for a general planar oscillator near a hopf bifurcation point. these types of planar oscillator that were considered by poincar’e in 1891 (perko 1998, p. 351) in his works on limit cycles, lend themselves to an easy analytical treatment. the dynamics of each oscillator is governed by the solution of the equation. ( ) 2: , 1, 2, 3,.....,j jz z t r j∈ = ( )2 :j j j j jz a z z z g z= − = , (1.1) where 1 1 , 1 1 a −  =     . denotes the euclidean norm, and the “dot” denotes differentiation with respect to time t . the solution of equation (1.1) for any initial condition in {2 \ 0r is a unique limit cycle that attracts the whole of { }2 \ 0 ,r see for instant (perko 1998, page 356). we couple the differential equations in (1.1) to yield various lattice structures. we shall first consider the dynamics of the system when coupling yields a one-dimensional lattice and then proceed to consider the two and three dimensional lattices cases. 2. one dimensional lattice now, let us couple the identical subsystems in equation (1.1) to yield n 2≥ ( ) ( ),z b k z f z= + (2.1) where denotes the coordinates of a point on the lattice, ( 1 2, ,....., t nz z z z= ) ( )b k a real symmetric matrix depending on the coupling strength , is given by k 0≥ ( ) 1b k k= ∆ l⊗ with ( ) ( )1 1 1 1 1 0 0 ... 0 0 0 1 2 1 0 ... 0 0 0 1 1 0 1 2 1 ... 0 0 0 , ; 1 1 : : : : ... : : : 0 0 0 0 ... 1 2 1 0 0 0 0 ... 0 1 1 n nr l− × −    −   −    ∆ = − ∈ =         −   −  (2.2) where denotes the kronecker product, and ⊗ ( ) ( ) ( ) ( )( )1 2, ,..., . t nf z g z g z g z= this type of coupling corresponds to a symmetric nearest neighbour coupling on a linear lattice with neumann boundary conditions. we observe that if we had taken each subsystem in dr say, then the matrix above could be replaced by a dl d× matrix whose entries are all 1’s. this coupling differs from the one considered in hale (private communication) where is a d identify matrix. l d× 68 synchronization and oscillator death we say that equation (2.1) is synchronized or has symmetric solutions if its solution is in the set z { }21 1 2: : ... 0 ,n nz r z z zθ = ∈ = = = ≠ for all t . we refer to this set as the ‘diagonal ‘ in 0≥ 2nr (fujisaka and yamada 1983). oscillator death occur when there is a mutual cessation of oscillation in all oscillators for certain coupling strengths. that is, when is a constant for all t for some positive values of k the z 0≥ . invariant subspace { }21 : : 0,1n jz r z j n∏ = ∈ ≠ ≤ ≤ −1 , defines antisymmetric solutions to equation (2.1) or antisymmetric synchronization. these two subspace are the most readily observed and are of great interest in practical problems. the analysis of the evolution of the periodic solutions of equation (2.1) with as a parameter is facilitated by analyzing the flow restricted to the invariant manifolds ∏ and k 11 θ . proposition 1.1. we let be an even integer. then there exists a constant for which equation (2.1) defines antisymmetric solutions for all 0 n 0 0k > 0k k< < . moreover, there is oscillator death for k . 0k> proof. the proof involves the determinates of the eigenvalues of ( )b k and an appropriate change of coordinates. it is well known (householder 1964) that the eigenvalues of ∆ are 1 0 0, 2 2 cos ,1 1,s s s n n π λ λ= = − − ≤ ≤ − and they are simple. if is an even number, then clearly n / 2 2nλ = − is an eigenvalue and the corresponding eigenvector is v v where for a given v is a (/ 2 1 2, ,....., ; t n v v= )n 2i1 2 ,i= ± 2 2× identify matrix with v v the eigenvalues of are ( )1 1 , 1, 2,...., j j j j+ = − = 1.−n k l 0 10, 2 .kµ µ= = 2 the set ∏ is a subspace of the generalized eigenspace corresponding to the eigenvalues 1 ,α 0,1.µ α− = we show that for any solution of equation (2.1) with an initial point in , there is oscillator death for all and antisymmetric synchronization for consider the coordinate transformation given by 1∏ ( )00, .k k∈ 0k k> 1 . 1 1 , 1 1, n j j j j w z z j n y z n+ = = − ≤ ≤ − = j∑ (2.3) if we let w w then w and satisfy the odes ( )1 2 1: , ,...., , t nw w −= y ( ) ( ) 2 2 2 1 , , 1 , n n jj w k lw f w y r y g z r n − = = ∆ ⊗ + ∈ = ∈∑ (2.4) where ( ) ( )1 1 2 1 0 0 ... 0 0 0 1 2 1 0 ... 0 0 0 0 1 2 1 ... 0 0 0 , : : : : ... : : : 0 0 0 0 ... 1 2 1 0 0 0 0 ... 0 1 2 n nr − × −    −   −   ∆ = − ∈      −   −  (2.5) 69 adu a.m. wasike and the function ( ) ( ) ( )( )1 1, , ,......., , , t nf w y f w y f w y−= with ( ) ( ) ( )( )1, , 1j j jf w y g z g z j n+= − 1.≤ ≤ − taking an initial condition in the manifold 0y 1,∏ we find that the solution of the second equation in (2.4) is for all t and the governing equations reduce to the decoupled system of the form 0y = 0≥ 20y r= ∈ , (2.6) ( )2 1 2 1 2 1 2 2 ,nj n j jw kl lw g w− − −= − ⊗ + ∈ r )n (2.7) where the solution (1, 2, 3,......., / 2 .j = ( )2 1j −w of equation (2.7) corresponds to antisymmetric solutions of the system (2.1). to show the existence of we need consider the case for let only as the system equation (2.7) is decoupled and the result for n will follow easily. let t 0,k 2n = 2> ( ) ( )2 2 , tan 2 1 2 . 1 2 1 k k k k α α φ= = = − − + we introduce a change of coordinates in equation (2.7) with n 2= given by 1 1 0 sin cos . cos sin0 1 u w v α φ φ φα  +    =      −     φ (2.8) the equation (2.7) becomes { ( ) ( ) ( ) ( ) ( ) ( ) ( ) } ' ' 2 2 2 2 22 1 1 2 2 sin 2 1 2 cos 2 1 1 1 2 cos 2 1 2 2 sin 2 1 . 1 k k k u v k k u v u v u i v k α φ φ α α φ φ α α α  +  − − − −   =    −    − + − + +   + − −   −   −    (2.9) in which the prime denotes differentiation with respect to time. in polar coordinates defines by ( ) ( ) ( ) ( )cos , sin ,u p t t v p t tσ σ= = equation (2.9) becomes ( ) ( ) 2 ' 2 ' 2 1 cos 2 1 2 1 1 1 2 sin 2 . p ,p k p k α σ α σ α α σ   = − − − − = − − + −  (2.10) solving for 0p′ = p in the first equation in (2.10), one finds that ( )( )* 1 2 1p k 2α= − − (2.11) provided 1 and 2k> 1,α < is the radius of a unique invariant circle. ' 0σ < when 70 synchronization and oscillator death 0 1k≤ < / 2 and * ' * 0, when ; 0, when . p p p p p < >  > < therefore is the underlying point set if a limit cycle of (2.10) and attracts all of *p ( )2 \ 0, 0r as that exists when if we let t → ∞ 0 1/k≤ < 2. ( ) ( ) ( )( )1 cos , ,t t r tθ=w r then it can be shown that equation (2.7) with 0 1/ 2,k< < admits a unique and asymptotically stable periodic orbit with period t ( )α and radius ( )r α given by ( ) ( ) ( ) ( )( ) ( )( ) 2 2 1 2 12 , . 1 cos 21 2 t r t α απ α α α θ φα − − = − +− clearly at i.e. there is no oscillation. simple analysis shows that for the origin for system (2.7) is stable. 0 1/ 2, 0;k k r= = = 0 ,k k> 3. two-dimensional lattice we consider an simple (or bravais) square lattice. let z in n× ,1 , ,ij j n≤ ≤ be coordinate of the site oscillator and the matrix z z( ), thi j , 1 .: n i jij =  =   let ( )n1, ,......z z z z= with z r 2 1,nr ×∈ as its column. let ve1 r≤ ≤ ,n rth c z denote the vector valued function of ,z and ⊗ be the kronecker sum (see graham 1981, for details on matrix tensor algebra). the system of differential equations describing the dynamics on the n n× lattice is given by ( ) ( ),h k g= +z z z (3.1) where ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) .1 1 1 2, 1, and : , ,....,nij ni jh k k l g g z f z f z f z= = ∆ ⊗∆ ⊗ = =    z equation (3.1) is symmetrically synchronization when 0ijz z= ≠ for all ij . this occurs when ( ) 0, 0h k zµ= = ≠z z with 0µ = as an eigenvalue of ( ).h k indeed, the eigenvalues of are ( )h k ( )( ) ( ){ }: : , 0 , 1s ph k s p nασ µ µ λ λ µ= = + ,≤ ≤ − with , , , 0,1,p s αλ λ µ α = as defined in section 2. clearly 0µ = is an eigenvalue of and by equation (3.1), there is symmetric synchronization. in this case, the plane will be ramified with traveling-wave like pattern solutions to equation (3.1). ( )h k to facilities the understanding of other dynamics, we define some subspaces invariant to the flow defined by equation (3.1). here, we shall follow a trend similar to that in mallet-paret and chow (1995a, 1995b) where pattern formations are considered for lde’s with a first order scalar ode at each lattice site. let { } ( ){ } ( ){ } { } 1 1 1 1 1 1 : , ,1 1 , : 1 ,1 1 , : 1 , ,1 : . j j j j j j j j j j t z z z z j n z z z j n z z z z j n z z θθ πθ ππ πθ πθ + + + θ = = ∈θ ≤ ≤ − ∏ = = − ∈θ ≤ ≤ − ∏ = = − ∈∏ ≤ ≤ − ∏ = ∈∏ 1 , we further make a coordinate transformation defined thus 71 adu a.m. wasike 1 1 1 ,1 1, and . n j j j j w z z jn y z n+ = = − ≤ − = j∑ (3.2) using this in equation (3.1) we get : ( ) ( ) ( ) ( ) ( ) ( ) 2 1 1 1 1 2 1 , 1 , n n n n n n jj w k i l w l w i g w y r y b k y f z r n − − − = = ⊗ ∆ + ∆ ⊗ + ∈   = + ∈∑ (3.3) where ( )1 1,..., ,nw w w −= ( ) ( ) ( )( )1 1, , ,....., , ,ng w y g w y g w y−= with ( ) ( ) ( )1, ,1j jg w y f z f z j n+= − 1.≤ ≤ − on the subspace θθθ ( ) ( ) { } 2 1 2 0 , , 1, 2,......, . n n n w r y z f z r nβ β β −= ∈ = = ∈ ∈ (3.4) the system in this case is symmetrically synchronized and the dynamics are described by equation (3.4). proposition 2.1. let be an even integer. then there exists a constant for which the simple lattice equation (3.1) is ramified with horizontal and vertical bands of antisymmetric solutions for all moreover, oscillator death occurs for n 1 0k > ( 10, .k k∈ ) 1.k k> proof. on θπ∏ and πθ∏ , we have horizontal and vertical bands of stripes respectively and their flows are governed by the decoupled odes, ( )( ) (2 1 2 1 2 1 2 0, 2 ,j n n j j y w i b k ki l w f w− − =   = ⊗ − ⊗ +    )− n (3.5) where w w since all z( )2 1 2 11 , with 1, 2, 3,...., / 2. j j j j+ −= − = 1,j ∈θ equation (3.5) reduces to decoupled odes. thus / 2n ( ) ( )2 1 2 1 2 12j n jw ki l w f w+ −= − ⊗ + ,j − (3.6) which upon the use of equation (2.7), proposition 2.1 is proved with 1 1/ 2k = . proposition 2.2. let be an even integer. then there is a constant for which the lattice equation (3.1) is ramified with checkerboard like solutions for all n 2 0k > ( )20, .kk ∈ moreover, oscillator death occurs for . 2kk > poof. the subspace ππ∏ represents vertical (horizontal) bands of symmetric and antisymmetric oscillators. this subspace constituted a checkerboard. a unit square on a checkerboard is constituted by four subsystems on a square lattice. within each square, the subsystems are of alternate signs with their nearest neighbours. if 2 2× ( )z t represents an oscillator, then 72 synchronization and oscillator death ( ) ( ) ( ) ( ) z t z t z t z t −    −  is the unit square. the entire checkerboard is defined by these squares that alternate is sign. the subspace ππ∏ is invariant under the flow defined by equation (3.1) and its flow governed by the solution of the equations / 2n ( ) ( )2 1 2 1 2 14j jw ki l w f w− −= − ⊗ + ,j − (3.7) we notice that equation (3.7) is similar to equation (2.7). the proof of the proposition 2.2 follows easily if we replace k in equation (2.7) with . we find that 2k 2 1/ 4k = . 4. three dimensional lattice we consider an simple cubic lattice. let n n n× × ,1 , , ,pqrz p q r n≤ ≤ be the coordinate of the ( , , th)p q r site oscillator with its dynamics described by equation (1.1). we shall assume that the coupling is to the nearest neighbour and the coupling forces are equal and acting along the axes of the cube. thus the oscillator can only interact with the oscillators z z six in all. let where pqrz 1 2, ,=z z z 1 1, ,p q r p q r p q rz± ± 1,± ( ): ....., tnz , , 1: . n qr p q rr p z =   =z the system of differential equations describing the dynamics of the entire lattice system is given by ( ) ( ),k= +z h z g z (4.1) where ( ) ( ) ( )( ) ( ) ( ) ( )( )1 1 1 1, ,...., , t n nk k i l g g = ∆ ⊗∆ ⊗ ⊗∆ ⊗ = h g z z z with g g( ) ( ) , , 1 . n r pqr p q r z =  =  z to determine the invariant subspaces available to equation (4.1), we find the eigenvalues of and the corresponding eigenvectors. we have ( )kh ( )( ) ( )( ){ }: : , 0 , , 1p q rk pασ µ µ λ λ λ µ= = + + ,q r n≤ ≤ −h where , , , ,p q r αλ λ λ µ are as defined in section 2 with each rλ occurring with multiplicity .n { } { } { } ( ){ } ( ){ } ( ){ } { } 1 1 1 1 1 1 000 : , ,1 1 , : , ,1 1 , : , ,1 1 , : 1 , ,1 1 : 1 , ,1 : 1 , ,1 : 0 . j j j j j j j j j j j j j j j j j j j j j j n j n j n j n j n j n θθθ θθ ππθ ππ θπθ θπ θθπ θθ θππ θπ πππ ππ + + + + + + θ = = ∈θ ≤ ≤ − ∏ = = ∈∏ ≤ ≤ − ∏ = = ∈∏ ≤ ≤ − θ = = − ∈θ ≤ ≤ − ∏ = = − ∈∏ ≤ ≤ − , 1 , 1 ,∏ = = − ∈∏ ≤ ≤ ∏ = = z z z z z z z z z z z z z z z z z z z z z z z z z z − the system of equations defining the dynamics on these manifolds follows readily with the coordinate transformation 1 1 : , 1 1 : . j j j n jj j n n + = − 1,≤ ≤ − = ∑ w z z y z (4.2) using equation (4.2 in equation (4.1), we get 73 adu a.m. wasike ( ) ( )( ) ( ) ( ) ( ) 1 1 1 : , 1 , n n jj k i l h k g n =  ∆ ⊗ ⊗ ∆ ⊗∆ ⊗ +  = + ∑ w w y y z ,g w y (4.3) where ( ) ( ) ( ) ( )( )1 1 1 1,...., , , , ,......, , , tt n ng g− −= =w w w g w y w y w y with ( ) ( ) ( )1, , 1j jg g j n+= − 1,≤ ≤ −y z zg w on , ,θθθθ =w 0 and the flow is governed by ( ), 1,...., .gβ β β= =z z n (4.4) we thus see that the system is synchronized proposition 3.1. let be an even integer. then for all n ( )30,k k∈ the simple three-dimensional lattice equation (4.1) has layers of checkerboards. besides, oscillator death occurs for . 3k k> proof. on the subspace ,ππθ∏ the flow is defined by the solution of the decoupled equation ( ) ( )4 , , 1,...., ,j j jnk i l f j nβ β β β= − ⊗ + =zz z ( 4.5) where jβ z is the column of thj βz k . thus we shall have layers of checkerboards that persist for . notice the similarity of equation (4.5) with equation (2.7). thus replacing in equation (2.7) with we find that 0 k< < 1/ 4 ) k 2k 3 1/ 4.= proposition 3.2. let be an even integer. then there exists a constant k such that for all the simple three-dimensional lattice equation (4.1), has sheets with vertical bands of stripes of checkerboards. moreover, oscillator death occurs for . n 4 0> ( 40,k k∈ 4k k> proof. on the subspace ,πθθ∏ the flow is defined by the solution of the decoupled equation ( ) ( )2 , , 1,..., ,j j jnk i l f j nβ β β β= − ⊗ + =.z z z (4.6) where jβ z is the column of thj βz . thus the entire system in the three-dimensional space is composed of sheets with vertical bands of stripes. clearly, we see from equation (2.7) that this regime persists for . proposition 3.2 follows with 0 1k< < / n 4 1/ 2.k = on ,θπθ∏ the flow is defined by the solution of the decoupled equations in (4.6). the solutions represent layers of sheets with horizontal band strips that persists for 0 1 3n /k 2.< < proposition 3.3. let be an even integer. then there exists a constant k for which the simple three-dimensional lattice equation (4.1) has layers of horizontal sheets with horizontal bands that persist for all moreover, oscillator death occurs for n 5 0> 5.k k>( 50, .k k∈ ) proof. on the subspace πθθθ the flow is defined by the solution of the decoupled equations ( ) ( )2 1 2 1 2 12 1, 2,...., / 2.j n j jk i l g j n− − −= − ⊗ + =w w w (4.7) thus we shall have horizontal bands of synchronized sheets, like a “stack of sandwiches” that persists for 0 . proposition 1.1 follows with k1k< < / 2 5 1/ 2= . on ,θππ∏ the flow is governed by equation (4.7) and we have sheets with horizontal bands. proposition 3.4. let be an even integer, then there exists a constant for which the simple three-dimensional lattice equation (4.1), has layers of horizontal sheets of checkerboards that persist for all n ( 0k σ > )0,k k σ∈ . moreover, oscillator deaths occur for k k σ> . proof. on the subspace πππ∏ , the flow is defined by the solution of the decoupled equations ( ) ( )2 1 2 1 2 -14 , 1, 2,...., / 2.j n j jk i l g j n− −= − ⊗ + =w w w (4.8) 74 synchronization and oscillator death thus the entire system in three-dimensional space is composed of layers of horizontal sheets of checkerboard. this dynamical regime persists for 0 1/k 4.< < proposition 3.4 follows with . 6 1/ 4k = 5. discussion in lde’s on the bravais lattices given in equations (2.1),(3.1) and (4.1) the coupling matrices ( ) ( ) { }( ), ,b k h k h k have 0 0λ = as an eigenvalue. thus any solution to these equations that pass through a point in the generalized eigenspace corresponding respectively, shall be symmetrically synchronized. that is, they shall be in the set 0 , 1, 2, 3 v i vµ λ = 1, , , ,θθ θθθθ θ θ n respectively. for an even number of oscillators in the bravais lattice, the coupling matrices have / 2 2λ = − as an eigenvalue. from equations (2.7),(3.7),(4.5), we see that any solution to equation (2.1),(3.1),(4.1) through a point in the generalized eigenspace belonging to / 2 2nλ = − will always be antisymmetric for some coupling strength : 0k < k k≤ and there shall be oscillator death for . thus simple bravais osillators with each osillator as given in equation (1.1) can either lead to synchronization or oscillator death depending on the initial conditions and the strength of coupling. k k≥ references aronson, d.g., doedel, e.j., and othmer, h.g. 1987. an analytical amd numerical study of the bifurcations in a system of linearly coupled oscillators. physica d 25: 20-104. bar-ell, k. 1985. on the stability of coupled chemical oscillators. physica d. 14: 242-252. chn, j.w. 1960. theory of growth and interface motion in crystalline material, acta metallurgica 8: 554-562. chua, l.o, and roska, t. 1993. the cnn paradigm. ieee trans. circuits syst., 40: 147-156. m.f. crowley, m.f., epstein, i. 1989. experimental and theoretical studies of a coupled chemical oscillator : phase death, multistability, and in-phase and out of phase and entrainment. j. phys. chem. 93: 2496-2502. ermentout, g.b. koppel, n. 1994 inhibition-produced patterning in chains of coupled nonlinear oscillators. siam j. appl. maths. 54: 478-507. h. fujisaka, h. and yamada, h. 1983. stability theory of synchronized motion in coupledoscillator systems prog. theor. phys. 69: 32-47. graham, a. 1981. kronecker products and matrix calculus with applications, ellis horwood limited. householder. a.s. 1964. the theory of matrices in numerical analysis. blaisdell. mallet-paret, j. and chow, s.-n. 1995. pattern formation and spatial chaos in lattice dynamical systems ii. ieee trans. circuits syst. 42: 752-756. perko, l. 1998. differential equation and dynamical system 2nd. ed. springer-verlag, newyork, berlin heidelberg. 19. poincacare, h. 1891 memoire sur les courbes dfnites par une equation differentielle,. j. mathematiques, 7: 375-421. received 11 june 2002 accepted 28 april 2003 75 synchronization and oscillator death in diffusively coupled lattice oscillators adu a.m. wasike department of mathematics, university of nairobi, p.o.box 30187, nairobi kenya, email: aduwasike@yahoo.com. microsoft word phys070107.doc 67-74 squ journal for science, 12 (1) (2007) © 2007 sultan qaboos university 67 limits of the efficiency of imaging with obstructing apertures a.t. mohammed department of astronomy, college of science, university of baghdad, jadiria, iraq, email: arobie33@yahoo.com. حدود الكفاءة عند التصوير باستخدام فتحات معرقلة للضوء علي طالب محمد استخدام حلول عددية ذات بعدين لتقييم كفاءة الفتحات المعرقلة للضوء من خالل دراسة تأثيرها على حدود قدرة :خالصة تضمن البحث حساب معدل شدة وعرض دالة االنتشار النقطية ، معدل مركبة الترددات لدالة التضمين االنتقالية . التحليل النتائج أوضحت ان الفصل بين الخطين يصبح مميزاً عند .من الخطوطوكذلك معدل الحلقات الجانبية لصورة زوج . مرة من نصف قطر الفتحة االصلية0.6استخدام نصف قطر اإلعاقة المركزية أكبر او يساوي تقريباً abstract: two-dimensional numerical solutions are carried out to asses the quality of obstructing apertures in terms of the diffraction limited resolution. this include the quality of the point spread function (psf), the modulation transfer function (mtf), and an image of double lines. these are average intensity of the psf (ai), maximum intensity of the psf,(mi), full width at half maximum of the psf (fw) average frequency components of mtf (afc), and average side loops of an image of a double lines. the results indicate that the separation of the two lines becomes recognizable using central obstruction of radius equal to or greater than approximately 0.6 times the radius of the primary aperture. keywords: obstructing apertures, optical systems, resolution, fourier transform, image quality. 1. introduction ll telescopes have an inherent limitation to their angular resolution due to the diffraction of light at the telescope aperture. the diffraction causes an optical system to behave as a low-pass filter in the formation of an image. the cut-off frequency is directly determined by the shape and size of the limiting pupil in the optical system. the incoming light is approximately a plane wave since the source of the light is so far away. there are several criteria for analyzing the performance of an optical imaging systems. the rayleigh criterion is generally regarded as a fundamental limit in predicting the performance of optical imaging systems. according to the rayleigh criterion, the theoretical resolving power of 5 m optical telescope ( λ=400 nm) are 0.02′′≅ . this value shows the relationship between the resolving power and the telescope apertures. in addition to that criterion, measurements of mtf, strehl ratio, and diffraction limited resolution are also very well a a.t. mohammed 68 considered in quantifying optical systems (william and bucklund 1989, harvey and ftaclas 1995, brummelaar and bagnuolo 1995, brammelaar et al. 1994, baldwin et al. 2001, granieri et al. 1998, jean-marc et al. 2004, mohammed et al. 1990, milanfar and shakouri, 2002). many studies have been presented in the literatures concerning imaging with obstructing aperture (fienup 2000, mohammed 2006, chakraborty and thompson 2005). the aim of this paper is to present the quantitative assessment of the limitations imposed by obstructing apertures on the psf and mtf in order to determine the constraints on the efficiency of imaging with such apertures. 2. theory the fundamental equation to be used for the formation of an image by an ideal optical system is given by: ydxdyyxxfpsyxoyxi ′′′−′−′′=∫∫ ∞ ∞− ),(),(),( (1) ),(),(),( yxpsfyxoyxi ⊗= (2) equations (1) and (2) are equivalent and representing a convolution equation. where i(x,y) is the observed image intensity, o(x,y) is the object intensity, psf (x,y) represents the image blurring function caused by the imaging system and ⊗ denotes convolution operator. the fourier transform of (2) is given by: v)t(u, v).o(u, v)i(u, = (3) where i(u,v) and o(u,v) are, respectively, the complex fourier transforms of the image intensity i(x,y), and the object intensity o(x,y); t(u,v) which represents the fourier transform of the psf, is an important function known as the optical transfer function (otf). the modulation or amplitude of the complex function t(u,v) is called mtf. in general, the resolution of an imaging system is limited only by the luck of large optical elements that are free from inherent distortions. now consider an extremely distant quasimonochromatic point source located on the optical axis of a simple imaging system. in the absence of atmospheric turbulence, this source would generate a plane wave normally incident on the lens. in the presence of the atmosphere, the plane wave incident on the inhomogeneous medium propagates into the medium, and ultimately a perturbed wave falls on the lens. the field distribution incident on the lens can be expressed as, ),(),( γηφγη ieu = (4) where ),( γηφ is the random phase of the incident wavefront and the variables ),( γη represent distances in the pupil function. the instantaneous psf of the entire telescope atmosphere system is given by: 2)],(),([),( γηγη uhftyxpsf = (5) limits of the efficiency of imaging with obstructing apertures 69 figure 1. telescope apertures:(a) uniform ( 0ε = ), (b) 0.6ε = where h ),( γη represents the pupil function and ft denotes fourier transform operator. the corresponding otf is the fourier transform of the psf, thus y)]ft[psf(x,v)t(u, = (6) equation (6) can also be written in terms of the pupil function and the field distribution incident on the lens as, γηγγηηγη γγηηγη ′′′−′− ′−′−=∫∫ ∞ ∞− dduu hhvut ),(*),( ).,(*),(),( (7) where * denotes complex conjugate. the variables η and γ are related to the fourier space variables u and v by υλγλη f,fu == , where λ is the wavelength and f is the focal length. 3. simulations the size of the pupil function h(u,y) is taken to be a two dimensional circular function of radius r and of unity magnitude; this array )nm( × is of size 512512 × pixels. this size is taken as large as possible in order to keep the theoretical diffraction limiting resolution vanishing to zero inside this array. this aperture is said to be a uniform aperture. the central obstructing aperture is simulated by calculating the parameter ε. this parameter represents the ratio of the radius of obstructing circle (r) to the radius of the uniform aperture, r, i.e., rr=ε . telescope apertures of ε = 0 and ε = 0.6 are demonstrated in figure 1. we consider the object to be imaged is an extremely distant quasimonochromatic point source located on the axis of an optical telescope. in the absence of atmospheric turbulence, this source would generates a plane wave ( ), 0 and ( , ) 1uφ η γ η γ= =⎡ ⎤⎣ ⎦ . the psfs are computed via equation (5). the perspective plots of the central regions of these psfs (14 pixels by 14 pixels ) are shown in figure 2. (a) (b) a.t. mohammed 70 figure 2. perspective plots of the central regions of psf’s, (a) uniform aperture,(b) ε = 0.2,(c) ε = 0.4, (d) ε = 0.6 and (e) ε = 0.8 (f) ε = 0.9. it should be pointed out here that the central spikes of the psfs are very sharp. this is because r is taken to be very large, r=120 pixels. the line plots through the centre of these regions are shown in figure 3. figure 3. plots through the central regions of the psfs. (a) uniform aperture,(b) ε = 0.2,(c) ε = 0.4,(d) ε = 0.6,(e) ε = 0.8 and (f) ε = 0.9. the mtfs are also computed according to equation (6) or (7) respectively and absolute values are taken for t(u,v). the results are shown in figure 4. (a) (b) (c) (d) (e) (f) (a) (c) (d) (e) (f) (b) n or m al iz e in te ns ity n or m al iz e in te ns ity no. of pixels no. of pixels 2 limits of the efficiency of imaging with obstructing apertures 71 a m tf n no. of pixels b c d e f bε =0.2 aε =0 cε =0.4 dε =0.6 eε =0.8 fε =0.9 figure 4. mtf’s (a) uniform aperture,(b) ε = 0.2,(c) ε = 0.4,(d) ε = 0.6 (e) ε = 0.8 and (f) ε = 0.9 the above images are then normalized to their maximum values according to the following equation: )0,0( ),( ),( mtf yxmtf yxmtfn = (8) figure 5. central plots through figure 4. where mtf(0,0) represents the value of the central spike. the central lines of the normalized mtfs (i.e. mtfn ) are plotted in figure 5. (a) (b) (c) (d) (e) (f) a.t. mohammed 72 (a) (b) (c) (d) (e) (f) (g) the psfs at different values of ε are convolved with the double line object presented in figure 6(a). the lines are one pixel wide separated by a distance of 2 pixels. this value is chosen because the full width of the psf of the uniform aperture is 3 pixels. the results are shown in figure 6. figure 6. line convolutions:(a) uniform aperture, (b) ε = 0.2, (c) ε = 0.4, (d) ε = 0.6, (e) ε = 0.8 and (f) ε = 0.9. the images in figure 6 are then normalized to one at their maximum values and the central lines through these images are plotted. the results are presented in figure 7. figure 7. normalized intensities through the center of the images in figure 6. (a) uniform aperture,(b)ε = 0.2,(c) ε = 0.4,(d) ε = 0.6,(e) ε = 0.8 and (f) ε = 0.9. n or m al iz e in te ns ity no. of pixels a b d e f c limits of the efficiency of imaging with obstructing apertures 73 for ε = 0, the line plot shows a little peak at the center. as ε increases, the separation of the double lines becomes recognizable and the side loops become severe. the normalized maximum intensity values (mi) of the psfs are calculated and presented in the table 1 given below as follows. first, the maximum value of the psf of the uniform aperture (ε = 0) is calculated. secondly, the maximum intensity values at different ε are divided by the maximum value at ε = 0. this measure is taken in order to examine the dropness in the value of the central spike of the psf as a function of ε . table 1. the variation of mi, ai, fw, afc and sl at different values of ε. sl afc fw ai mi ε 1 1 3 1 1 0 1.0808 0.9604 3 1.0412 0.9224 0.2 1.2373 0.8406 3 1.19 0.707 0.4 1.5328 0.6410 1 1.56 0.411 0.6 2.3403 0.3607 1 2.77 0.13 0.8 3.0122 0.1902 1 5.26 0.0362 0.9 the average intensity values (ai) of the psf at different ε is computed by: ∑∑ ∑∑ = = = = = m 1y n 1x 1 1 y)(x,),(a m y n x upsfyxpsfi (9) where psfu (x,y) is the psf at ε =0. the average frequency components (afc) of mtf (u,v) at different ε are computed by: ∑∑ ∑∑ = = = = = m 1 n 1 1 1 ),(),mtf(afc u v m u n v u vumtfvu (10) where mtfu (u,v) is the mtf at ε =0. the full width of the psf (fw) at different ε are also calculated and presented in this table. these values indicate the width of the central spike of the psfs. the summation of all values that located outside the double lines of the psfs at different ε (see figure.6) are computed and the values are then divided by the corresponding value of the uniform aperture. the results are describing the actual weight of the side loops (sl). 4. conclusions the following conclusions could be drawn : 1. the mi value decreases by a factor of 30≅ as ε goes from ε = 0 to ε = 0.9. this great reduction in the height of central spike will enhance the probability of detecting faint companion (figure 7 describes normalized intensity not actual intensity). 2. as ε increases, ai increases and at ε = 0.9, ai increases by a factor of 5≅ . this is of course will create artifacts in the observed images (see figure. 2). 3. fw reduced dramatically as ε increases. for ε = 0.6, fw reduces by a factor of 3. this will enhance the resolution by a factor of 3. a.t. mohammed 74 4. afc reduces by nearly a factor of 5≅ at ε = 0.9. this is because the build up of the side loops in the psfs. afc is inversely proportional to ε. 5. the sl increases by a factor of 3 at ε = 0.9. sl is linearly proportional to ε. 6. references baldwin, j.e., tubbs, r.n., cox, g.c., mackay, c.d., wilson, r.w. and anderson, m.i. 2001. diffraction limited 800 nm imaging with 2.56 m nordic optical telescope. astronomy and astrophysics 368: l1-l4. brummelaar, t.a. and bagnuolo, w.g. 1995. strehl ratio and visibility in long baseline stellar interferometry. optics letters 20: 521-23. brummelaar, t.a., bagnuolo, w.g. and ridgway, s.t. 1994. strehl ratio and coherence loss in long baseline interferometry. technical report, center for high angular resolution astronomy georgia state university, no. 6. chakraborty, a. and thompson, l.a. 2005. 10 7− contrast ratio at 4.5 λ /d:new results obtained in laboratory experiments using nonfabricated coronograph and multi-gaussian shaped pupil masks. optics express 13: 2394. debes, j. 2003. high contrast imaging with gaussian aperture pupil mask. astro-ph 0301051, v 1. fienup, j.r. 2000. mtf and integration time versus fill factor for sparse-aperture imaging system. proc. spie. 4091 a-06 san diego, ca. granieri, s., enrique, e. and furlan, w.d. 1998. performance analysis of optical imaging systems based on fractional fourier transform. journal of modern optics 45: 1797-07. harvey, j.e and ftaclas, c. 1995. diffraction effects of telescope secondary mirror spiders on various image quality criteria. applied optics 34: 6337-49. jean-marc, d., leger, d., rogues, s. and valorge, c. 2004. modulation transfer function estimation from non specific images. optical engineering 43: 1355-65 donal, f.o’shea; ed. milanfar, p. and shakouri, a. 2002. statistical analysis of diffraction limited images. ieee icip. mohammed, a.t., rashid, n.m. and sadik, a.r. 1990. computer simulations of astronomical objects as seen by ground based optical telescope. optics and lasers in engineering 12: 223-43. mohammed, a.t. 2006. quantitative analysis of imaging with apodized square apertures. iraqi journal of science 47: 255-61. song, jong.sup., lee yun woo, song jae bong, lee in won, yang ho-soon, choi youngwan, and dual jae heungo jo. 2002. dual testing of a large aperture optical system. proc. spie, interferometry xi:applications, 4778: 227-36. william, c. and becklund, o. 1989. introduction to the optical transfer function. wiley series in pure and applied optics. received 7 january 2007 accepted 23 october 2007 photovoltaic cells and systems: 27-32 squ journal for science, 13 (2008) © 2008 sultan qaboos university ornithopod and sauropod dinosaur remains from the maastrichtian al-khod conglomerate, sultanate of oman ann s. schulp*, patrick m.o'connor**, david b. weishampel***, abdul razak al sayigh, abdulrahman al-harthy****, john w.m. jagt and axel f. hartman*****. natuurhistorisch museum maastricht, de bosquetplein 6/7, nl6211kj maastricht, the netherlands,*email: anne.schulp@maastricht.nl; **ohio university, department of biomedical sciences, 228 irvine hall, athens, oh 45701, usa;*** johns hopkins university, school of medicine, center for functional anatomy & evolution, 1830 e monument street, baltimore, md 21205, usa;**** department of sciences, college of science, sultan qaboos university, p.o.box 36, al-khod 123, muscat, sultanate of oman; *****brunei shell petroleum, epe/21 bsp brunei, p.o. box 245, nl 2501ce den haag, the netherlands. )الحصى المتالحمة(كونجلومتيرات الديناصورات من المستريختين الخوض أورنيثوبود وثوروبود بقايا جون عبد الرحمن الحارثي، ويشمبل، عبدالرزاق الصايغ، . ب. أوكونور، ديفيد . م.اسكولب، باتريك . س.آن هارتمان. ف.ماجت واكسل .و. 65اف عظام ديناصور منقرض في رواسب مفتتات صخرية يزيد عمرها على أدت الدراسات الميدانية إلى اكتش :خالصة . في منطقة الخوض وفنجا بسلطنة عمان وفي طبقات تعرف بتكوين كونجلومرات الخوض ) العصر الكريتاسي (مليون سنة لديناصـور قـري وعظمة العمـود الف لديناصور ساربود الدراسات األولية تشير إلى أن العظام تمثل القدم الخلفي األيسر نوبسبب عدم وجود أجزاء متكاملة من العظام فإنه من الصعب جداً معرفة الساللة التي ينتمـي إليـه هـذا . اورنيثوبود . إلى حد كبير ديناصور رابدودون وزالموكسسان يشبهما إال أنهانالديناصور abstract: fieldwork in the upper cretaceous (maastrichtian) al-khod conglomerates in the sultanate of oman led to the discovery of a large bone fragment tentatively identified as a partial distal left humerus of a sauropod and an ornithopod dorsal vertebra. the very fragmentary state of preservation of the dorsal vertebra makes specific attribution difficult, but it shows remarkable similarities to the rhabdodontid dinosaurs rhabdodon and zalmoxes. keywords: sultanate of oman; late cretaceous; maastrichtian; dinosauria; ornithopoda; sauropoda. 27 mailto:anne.schulp@maastricht.nl anne s. schulp et al. 1. introduction d inosaur fossils in the sultanate of oman were recognized for the first time by nolan et al. (1990) while logging the type section of the al-khod conglomerate formation. a short reconnaisance in 1997 by two of us (ass and afh) confirmed the potential of the al-khod conglomerate outcrops for further vertebrate palaeontological fieldwork. during this reconnaisance, one of us (afh) discovered a theropod caudal vertebra (schulp et al., 2000). subsequent fieldwork in 1998 (e.g. buscalioni et al., 2004) yielded additional material, of which an ornithopod dorsal vertebra and a fragmentary sauropod humerus are described in the present contribution. 2. material institutional abbreviations – all fossil material recovered from al-khod is permanently deposited in the collections of the sultan qaboos university, sultanate of oman. the specimens described here are numbered squ-2-65 and squ-2-76, respectively, where ‘2’ refers to the al-khod-locality. locality – both elements described here were recovered from the type locality of the al-khod conglomerate formation (nolan et al. 1990; schulp et al., 2000; buscalioni et al., 2004), located approximately 30 km west of muscat, sultanate of oman. age – the al-khod conglomerate formation has previously been assigned a maastrichtian age (see nolan et al., 1990; schulp et al., 2000). the stratigraphy and sedimentology of these deltaic deposits are described in detail in these contributions, and is not repeated here. recent analysis (by aa-s) of microfossils from the base of the jafnayn formation (which conformably overlies the al-khod conglomerate) confirms the maastrichtian age of the al-khod conglomerate. systematic palaeontology dinosauria owen, 1842 saurischia seeley, 1888 sauropoda marsh, 1878 (figure 1a-c) figure 1. squ-2-65 – sauropod left distal humerus from the maastrichtian al-khod conglomerate formation, sultanate of oman, in cranial (a), medial (b) and caudal (c) views. scale bar equals 10 mm. 28 ornithopod and sauropod dinosaur specimen – squ-2-65 is a partial distal left humerus, collected by afh as three isolated fragments in float from the lowermost part of the section. description – although the specimen was collected as three separate fragments, morphology of the fracture surfaces allows a confident assembly of the individual pieces into a single element (figure 1). we tentatively interpret the specimen to represent the distal half of a left humeral diaphysis of an indeterminate sauropod, spanning from just below mid-shaft to the expanded region just proximal to the ulnar and radial condyles. the medial edge of the element is better preserved than the lateral, the former extending approximately 6 cm further distally than the latter (figure 1a). the element exhibits a maximum length (proximodistal) of 34 cm, with a 31.5 cm diaphyseal circumference at the proximal end. the proximal surface is elliptical in cross-section, with the long axis oriented transversally (11.5 cm mediolaterally by 8.5 cm craniocaudally). the distal end of the diaphysis is deflected cranially (figure 1b). although incomplete distally, it is apparent that the mediolateral flaring characteristic of sauropod humeri is asymmetric, being more pronounced along the medial edge. a slight ridge is present on the craniomedial edge of the element (figure 1a) and forms the medial border of a shallow fossa on the cranial surface. the caudal aspect is poorly preserved (figure 1c), with original bone surface only remaining on the proximal two-third of the element. although the proximal portion of the olecranon fossa is preserved (figure 1c), incomplete preservation of the caudodistal end renders the determination of either (1) the size and position of supracondylar ridges (and thus the relative development the olecranon fossa) or (2) the shape, position, and relative sizes of the radial and ulnar condyles impossible. ornithischia seeley, 1888 ornithopoda marsh, 1881 (figure 2a-d) figure 2. squ-2-76 – ornithopod dorsal vertebra from the maastrichtian al-khod conglomerate formation, sultanate of oman, in posterior (a), left lateral (b), anterior (c) and right lateral (d) views. scale bar equals 10 mm. 29 anne s. schulp et al. specimen – squ-2-76 is a vertebral centrum with partially preserved neural arch. description – this mid-dorsal vertebra of an as yet undetermined rhabdodontid dinosaur is undeformed and nearly complete, lacking only the left transverse process, the adjoining quarter of the caudal aspect of the centrum, and the preand postzygapophyses. the centrum is broadly spindle shaped, slightly longer than high – the axial length is 60 mm while the centrum is 58 mm wide and 53 mm tall. the cranial and caudal surfaces are parallel to each other in lateral view and both are relatively circular (with a small dorsal indentation for the neural canal) and slightly amphiplatyan. in lateral view, the centrum has a prominent ventral concavity between the cranial and caudal margins. here it forms a gently rounded surface that is continued as the compressed lateral walls of the centrum. only a faint expression of the neurocentral suture is visible on the right side of the specimen, probably indicating that the individual was close to reaching skeletal maturity. the thick pedicle arches laterally to form the base of the transverse process. the neural canal, surrounded by the pedicle and stout lamina that forms the base of the neural spine, is ovate and of moderate size (transverse diameter of the neural canal is 40% transverse diameter of the centrum). the neural arch and spine extend nearly the entire length of the centrum. the neural spine is moderately thick, tall, and rectangular. its dorsal edge is only slightly expanded. the parapophysis, for the capitulum of the associated rib, is positioned beneath the intersection of the pedicle and transverse process. 3. discussion asymmetric flaring of the sauropod distal humerus in squ-2-65 is reminiscent of the condition observed in several lithostrotians such as rapetosaurus (curry rogers and forster 2001, figure 3e), paralititan (smith et al., 2001, figure 2a), and to a lesser degree malawisaurus (gomani, 2005, figure 20). moreover, it is unlike the symmetrical flaring observed in saltasaurids (i.e., derived lithostrotians; see upchurch, 1998, figure 12), not to mention many other (non-lithostrotian) sauropod taxa (e.g., diplodocoids). although the absence of other diagnostic features in squ-2-65 does not allow for a more specific assignment, the potential lithostrotian affinities outlined for it are generally consistent with the known distribution of specific sauropod subclades in maastrichtian-age strata. the latest cretaceous sauropod record of afro-arabia is extremely limited (weishampel et al., 2004) and includes only three maastrichtian occurrences, an associated basal titanosauriform hind limb from morocco (pereda-suberbiola et al., 2004), a possible ‘brachiosaurid’ femur from egypt (rauhut and werner, 1997), and a dorsal vertebra referred to titanosauria from jordan (wilson et al., 2006). from the arabian peninsula, the only sauropod occurrences thus far reported (e.g., fragmentary vertebrae; tracks) are from jurassic strata exposed in northern yemen (jacobs et al., 1999; schulp et al., 2008). although squ-2-76 lacks apomorphies known for rhabdodontidae or the three members of this group (see weishampel et al., 2003), the vertebra from oman is closely similar to the dorsals of those ornithopods of about the size and phylogenetic position as species of rhabdodon and zalmoxes. however, they differ from those of tenontosaurus, the latter being dorsoventrally ovate in cranial/caudal views (ostrom, 1970) and of thescelosaurus and dryosaurus, which have highly elevated transverse processes (gilmore, 1915; galton 1974, 1981). the latest cretaceous ornithopod record of afro-arabia is even more limited than the sauropod record (weishampel et al., 2004; lamanna et al., 2004; see also martill et al., 1996), which underscores the palaeobiogeographical significance of the al-khod conglomerate. 4. conclusion the maastrichtian al-khod dinosaurian fauna comprises at least three taxa: a medium-sized theropod (schulp et al., 2000), a small ornithopod, and a medium-sized sauropod. based on the presence of the three dinosaurian taxa, along with two previously reported crocodyliforms (buscalioni et al., 2004) and other as yet undescribed forms (e.g., turtles), the al-khod conglomerate formation has yielded the taxonomically most diverse terrestrial vertebrate fauna from the latest cretaceous of the middle east. moreover, it represents one of 30 ornithopod and sauropod dinosaur the very few temporally constrained late cretaceous vertebrate-bearing locales in all of afro-arabia. the generally poor state of preservation however, is most unfortunate, as it in most cases precludes specific taxonomic assignment. 5. acknowledgements the research was conducted by the sultan qaboos university, al-khod, sultanate of oman, the natuurhistorisch museum maastricht and the vrije universiteit amsterdam, the netherlands, supported in various ways by the petroleum development of oman, shell international exploration and production, and the molengraaff foundation. three anonymous reviewers provided helpful feedback. 6. references buscalioni, a.d., schulp, a.s., jagt, j.w.m., hanna, s.s. and hartman, a.f. 2004. late cretaceous neosuchian crocodiles from the sultanate of oman. cretaceous research, 25: 267-275. curry rogers, k. and forster, c.a. 2001. the last of the dinosaur titans: a new sauropod from madagascar. nature 412: 530-534. galton, p.m. 1974. notes on thescelosaurus, a conservative ornithopod dinosaur from the upper cretaceous of north america, with comments on ornithopod classification. journal of paleontology 48: 1048-1067. galton, p.m. 1981. dryosaurus, a hypsilophodontid dinosaur from the upper jurassic of north america and africa: postcranial skeleton. paläontologische zeitschrift, 55: 271-312. gilmore, c.w. 1915. osteology of thescelosaurus, an ornithopodous dinosaur from the lance formation of wyoming. proceedings of the united states national museum, 49: 591-622. gomani, e.m. 2005. sauropod dinosaurs from the early cretaceous of malawi, africa. palaeontologia electronica, 8:27a: 37 pp. jacobs, l.l., murry, p.a., downs, w.r. and el-nakhal, h.a. 1999. a dinosaur from the republic of yemen. in fossil vertebrates of arabia. eds p.j. whybrow and a. hill. yale university press, new haven, ct. pp. 454-459. lamanna, m.c., smith, j.b., attia, y.s. and dodson, p. 2004. from dinosaurs to dyrosaurids (crocodyliformes): removal of the post-cenomanian (late cretaceous) record of ornithischia from africa. journal of vertebrate paleontology, 24: 764-768. marsh, o.c. 1878. principal characters of american jurassic dinosaurs. part i. american journal of science (3) 16: 411-416. marsh, o.c. 1881. principal characters of american jurassic dinosaurs, part v. american journal of science, (3) 21: 417-423. martill, d.m., frey, e. and sadaqah, r.m. 1996. the first dinosaur from the hashemite kingdom of jordan. neues jahrbuch für geologie und paläontologie, monatshefte, 1996: 147-154. nolan, s.c., skelton, p.w., clissold, b.p. and smewing, j.d. 1990. maastrichtian to early tertiary stratigraphy and palaeogeography of the central and northern oman mountains. in the geology and tectonics of the oman region. eds a.h.f. robertson, m.p. searle and a.c. ries. geological society london, special publication, 49: 495-519. ostrom, j.h. 1970. stratigraphy and paleontology of the cloverly formation (lower cretaceous) of the bighorn basin area, wyoming and montana. peabody museum of natural history bulletin, 35: 1-234. owen, r. 1842. report on british fossil reptiles, part ii. report of the british association for the advancement of science, 11: 60-204. pereda-suberbiola, x., bardet, n., iarochène, m., bouya, b. and amaghzaz, m. 2004. the first record of a sauropod dinosaur from the late cretaceous phosphates of morocco. journal of african earth sciences, 40: 81-88. 31 anne s. schulp et al. rauhut, o.w.m. and werner, c. 1997. first record of a maastrichtian sauropod dinosaur from egypt. palaeontologica africana, 34: 63-67. schulp, a.s., hanna, s.s., hartman, a.f. and jagt, j.w.m. 2000. a late cretaceous theropod caudal vertebra from the sultanate of oman. cretaceous research, 21: 851-856. schulp, a.s., al-wosabi, m. and stevens, n.j. 2008. first dinosaur tracks from the arabian peninsula. plos one 3(5): e2243. doi:10.1371/journal.pone.0002243 seeley, h.g. 1888. the classification of the dinosauria. report of the british association for the advancement of science 1887: 698-699. smith, j.b., lamanna, m.c., lacovara, k.j., dodson, p., smith, j.r., poole, j.c., giegengack, r. and attia, y. 2001. a giant sauropod dinosaur from an upper cretaceous mangrove deposit in egypt. science, 292: 1704-1706. upchurch, p. 1998. the phylogenetic relationships of sauropod dinosaurs. zoological journal of the linnean society, 124: 43-103. weishampel, d.b., barrett, p.m., coria, r.a., leloeuff, j., xing, x., xijin, z., sahni, a., gomani, e.m.p. and noto, c.r. 2004. dinosaur distribution. in the dinosauria. eds d.b. weishampel, p. dodson and h. osmólska. university of california press, berkeley/los angeles. pp. 517606. weishampel, d.b., jianu, c.m., csiki, z. and norman, d.b. 2003. osteology and phylogeny of zalmoxes (n.g.), an unusual euornithopod dinosaur from the latest cretaceous of romania. journal of systematic palaeontology, 1: 65-123. wilson, j., mustafa, h. and zalmout, i. 2006. latest cretaceous reptiles from the hashemite kingdom of jordan. journal of vertebrate paleontology, supplement to 26(3): 140a. received 29 december 2007 accepted 31 january 2009 32 microsoft word math080424-f edited_checked.doc 53-59 squ journal for science, 14 (2009) © 2009 sultan qaboos university 53 transform domain characterization of dual group codes of cyclic group codes over elementary abelian groups adnan abdulla zain department of electronics and communications engineering, faculty of engineering, university of aden, yemen. email: adnan_zain2003@yahoo.com. )آبل(الوصف في المجال المتحول للشفرات المزدوجة للشفرات الدورية على الزمر من نوع عدنان عبداهللا زين في تعريف االزدواجية بين المجموعات الجزئية للمجموعة ، ) آبل( من نوع استخدمت مجموعة رموز الزمر :خالصة في هذا البحث تم تطوير الوصف في المجال المتحول . رمزوالتي تم تعميمها لتعريف االزدواجية بين الشفرات على ال =−1 (للشفرات الدورية ذات طول mpn (على هذه الزمر واستنتاج الوصف لشفراتها المزدوجة . abstract: the group of characters of an elementary abelian group mpz has been used to define duality between its subgroups, which in turn is extended to duality between group codes. the transform domain description of the dual codes of cyclic group codes of length 1−= mpn over mpz has been developed in this paper. several example codes and their duals have been presented also. keywords: group codes, cyclic codes, dual codes, abelian groups. 1. introduction he transform domain description of cyclic linear codes over )( mpgf using discrete fourier transform (dft) defined over an extension field rmpgf )( is well known (blahut, 1997). the transform domain description of cyclic group codes over an elementary abelian group ....mp p p pz z z z= ⊕ ⊕ ⊕ (m-times), using discrete fourier transform (dft) defined over an extension group ( )m r m m mp p p pz z z z= ⊕ ⊕ ⊕… (r-times) has been developed by zain and rajan (1997) ; this class of codes are subgroups of the cartesian product group ( ) ....m n m m mp p p pz z z z= ⊕ ⊕ ⊕ (ntimes), which amounts to relaxing the condition of linearity, t adnan abdulla zain 54 hence yielding a larger class of codes that contains the class of linear codes. the important class of reedsolomon codes over )( mpgf where the length of the code n is equal to 1−mp has been generalized to reed-solomon group codes over the elementary abelian group mpz , which is the additive group of )( mpgf (zain and rajan, 1995). the dual codes of systematic group codes over finite abelian groups have been characterized (zain and rajan, 1997) in terms of the endomorphism of the abelian group that defines the group code. in this paper, using the structural properties of the dual codes of cyclic group codes of length 1−= mpn over mpz , their characterization in the transform domain is presented. several example codes and their duals are presented also. the paper is organized as follows. section 2 presents the mathematical preliminaries that are relevant to the development of the main results. in section 3 the main theorem that characterizes the codes and their duals in the transform domain is proved. illustration of the applicability of the main theorem with examples codes and their duals is presented in section 4. conclusions and suggestions for further work are given in section 5. 2. mathematical preliminaries the minimum mathematical background that is necessary for the development of the main result of the paper is presented in the following two subsections. 2.1 group characters, inner product and dual subgroups a character of a group g is a homomorphism of g into the group of units of the field of complex numbers *c or group of units of any appropriate field in which there exist an thm − root of unity, where m is the exponent of g. let ^ g be the set of characters of g. result (1)( hungerford, 1989): gg ≅ ^ (1) under the above isomorphism, the elements of ^ g can be indexed with the elements of g as follows: gxgx gg x ∈∀∈→ → , : ^ ^ η η (2) let h be a subgroup of g . definition (1) ( hungerford, 1989): the subgroup dh of g is said to be the dual of the subgroup h if eh dh =)(η (3) where e is the identity element in the group of units. definition (2) ( hungerford, 1989): a subgroup h of g is said to be self dual if hh d = . (4) transform domain characterization of dual grup codes 55 an inner product on g is defined next. the indexing of the characters of g with the elements of g can be done such that the mapping: *cgg →× given by , ( ), ,xx y y x y gη< >= ∈ (5) is symmetric in both arguments. this mapping will be called an inner product on g ( delsarte 1972). result (2)( hungerford, 1989): ghh d = . (6) where | . | stands for the cardinality of the set. 2.2 elementary abelian discrete fourier transform (eadft) let mpz denote the elementary abelian group, )( m pzaut the group of automophrisms of m pz , and n denote the length of the code where n and p are relatively prime. definition (3) (zain and rajan, 1995): the transform vector of ,1,,1,0 , ),,,,( 110 −=∈= − → nizaaaaa mpin …… denoted by ,1,,1,0 , ),,,,( 110 −=∈= − → njzaaaaa mpjn …… is defined by )( 1 0 i ij n i j aa α − = ⊕= (7) where )( iaα denotes the image of ia under the action of the automorphism )( m pzaut∈α whose order is n . the eadft transform defined above is invertible (zain and rajan, 1995), and its inverse is given below: 1,,1,0,)( 1 0 1 −=⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⊕λ= − − = − niaa j ij n j ni …α (8) where 1−λn is the inverse of an automorphism of m pz defined by: m pn zxxxx ∈∀⊕⊕=λ n times)()( (9) the following definition is important to the characterization of the class of codes that are cyclic. definition (4) (zain and rajan, 1997): (invariant subgroups): let g be a group and h be a subgroup of )(gaut . a subgroup of g which is invariant under the action of h on g is called a h -invariant subgroup of g . definition (5)(zain and rajan, 1997):(conjugacy classes): the mp -conjugacy class containing 10 , −≤≤ mpjj is the set })(,,)(,,{)( 12, −≡ jemmmnp pjpjjpjjc … where )( ulomod )( mem pjpj j = , and je is the exponent. adnan abdulla zain 56 2.3 transform domain characterization of cyclic group codes the transform domain characterization of the class of codes that are group codes ( not necessarily linear codes), cyclic and of length 1−= mpn over the elementary abelian group mpz presented in (zain and rajan 1995), identifies two cases as shown below: • case 1, in this class of cyclic group codes, all the transform components are free. • case 2, in this class of cyclic group codes, the transform components that are in the same conjugacy class are related. in this paper, we consider case 1 which is the class of codes of length n that is equal to 1−mp , in which the transform components that lie in the same conjugacy class are all either free or zeros. 3. main theorem the following theorem gives the transform domain characterization of the dual codes of the cyclic codes, whose transform components that lie in one conjugacy class are all either free or assigned zeros, (those codes covered by case 1). theorem (1): if c is a cyclic group code of length 1−= mpn over mpz whose transform vectors are all free and take values from the following js -invariant subgroups of m pz , jnjj sss ,,, 21 … for the components njjj ,,, 21 … , respectively, then the transform vectors of the dual code dc take values from the following js -invariant subgroups, djn d j d j sss ,,, 21 … respectively for the components )(,),(),( 21 njnjnjn −−− … . proof: let ),,,( 110 − → = naaaa … be the transform vector of the code vector caaaa n ∈= − → ),,,( 110 … . by definition of the eadft and its inverse, we have 1,,1,0,)( 1 0 1 −=⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⊕λ= − − = − niaa j ij n j ni …α given that the transform vectors take values from jnjj sss ,,, 21 … invariant subgroups for the components njjj ,,, 21 … respectively, we have 1,,1,0 ,21 −=⊕⊕⊕= nisssa jnjji …… . (10) now, let dn cbbbb ∈= − → ),,,( 110 … and ),,,( 110 − → = nbbbb … be its transform vector, so we have 1,,1,0,)( 1 0 1 −=⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⊕λ= − − = − nibb j ij n j ni …α (11) since the components of the transform vector )(,),(),( 21 njnjnjn −−− … take values from the d jn d j d j sss ,,, 21 … invariant subgroups, we have 1,,1,0 ,21 −=⊕⊕⊕= nisssb d jn d j d ji …… . (12) next we compute the inner product >< →→ ba, : transform domain characterization of dual grup codes 57 eesssbba n i d jns d js d js n iia n i jnjji =π=∗∗∗π=π>=< − = − = − = →→ 1 021 1 0 1 0 )}()()({)(, 21 ηηηη … where ∗ stands for the operation in the group of units. now, we want to show that nd gcc = . since jnjj sssc …21= , and djn d j d j d sssc …21= , we have nd jnjn d jj d gggsssscc === ……11 this completes the proof. 4. illustrations of the theorem the usefulness of the main theorem is best demonstrated with the following two numerical examples, where a length 3 cyclic group code over the elementary abelian group with four elements is characterized in the transform domain, then by using the theorem, its dual is also characterized and obtained. example (1): let }11,01,10,00{22 ><><><><=⊕≅ zzg . then we define },,,{ 11011000 ^ ><><><><= ηηηηg according to the following inner product mapping *cgg →× given by gyxyyx x ∈>=< , ),(, η where }1,0{2 * =≅ zc since 2 is the exponent of g . the detailed mapping is given in table 1: table 1. characters mappings <00> <10> <01> <11> ><00η 0 0 0 0 ><10η 0 1 0 1 ><01η 0 0 1 1 ><11η 0 1 1 0 table 2 gives all possible dual subgroups of 22 zzg ⊕≅ . table 2. subgroups and their duals. subgroup ( h ) dual subgroup ( dh ) {<00>} {<00>, <10>, <01>, <11>} {<00>, <10>} {<00>, <01>} {<00>, <01>} {<00>, <10>} {<00>, <11>} {<00>, <11>} {<00>, <10>, <01>, <11>} {<00>} adnan abdulla zain 58 note that the subgroup {<00>, <11>} is self-dual. example (2): length 3 code over 22 zzg ⊕≅ and its dual. the transform vectors for the code are listed in the first column where the characterization for the conjugacy classes is as follows: }11,01,10,00{ },00{ },10,00{ 210 ><><><><=><=><><= aaa . according to the theorem the dual code should have the following characterization for the conjugacy classes: }01,00{0 ><><=b , which is the dual subgroup of }10,00{ ><>< }11,10,10,00{1 ><><><><=b , which is the dual subgroup of }00{ >< }00{2 ><=b , which is the dual subgroup of }11,10,10,00{ ><><><>< the detailed listing of the code vectors and the transform vectors of the code and its dual is presented in table 3. table 3. code vectors and their transforms. transform vector code vector transform vector dual code vector 210 aaa 210 aaa 210 bbb 210 bbb <00> <00> <00> <00> <00> <00> <00> <00> <00> <00> <00> <00> <00> <00> <10> <00> <11> <01> <00> <10> <00> <00> <11> <10> <00> <00> <01> <01> <00> <11> <00> <01> <00> <01> <01> <01> <00> <00> <11> <01> <11> <10> <00> <11> <00> <01> <10> <11> <10> <00> <00> <10> <01> <11> <01> <00> <00> <10> <00> <11> <10> <00> <10> <10> <10> <10> <01> <10> <00> <10> <11> <01> <10> <00> <01> <11> <01> <00> <01> <01> <00> <11> <01> <10> <10> <00> <11> <11> <10> <01> <01> <11> <00> <11> <10> <00> 5. conclusions the structural properties of the dual codes of cyclic group codes of length 1−= mpn over the elementary abelian group mpz have been used to present and prove a theorem that gives the characterization, in the transform domain, of the dual codes in terms of the dual subgroups of the group mpz . as an example a length 3 cyclic group codes over 22z is characterized in the transform domain, then its dual code is obtained. further work can be done to generalize the main result to other classes of cyclic group codes whose transform characterization contains components that are related (zain and rajan, 1997), and to quasi-cyclic codes (dey and rajan, 2003). 5. references blahut, r.e. 1997. theory and practice of error control codes, addison-wesely. delsarte, p. 1972. bounds for unrestricted codes by linear programming. philips research dev. j., 27: 272289. dey, b.k. rajan b. s. 2003. dft domain characterization of quasi-cyclic codes", applicable algebra in engineering, communication and computing, springer-verlag, 13(1): 453-474. transform domain characterization of dual grup codes 59 hungerford, t.w. 1989. algebra, springer-verlag. zain, a.a. and rajan, b.s. 1997. m-psk bcm using cyclic codes over elementary abelian groups. proceedings of isit, ulm, germany, june 29-july 4 1997, p.410. zain, a.a. and rajan, b.s. 1995. reed-solomon group codes. proceedings of isit, british columbia, canada, 17-22 september 1995, p.495. zain, a.a. and rajan, b.s. 1997. dual codes of systematic group codes over abelian groups. applicable algebra in engineering, communication and computing, springer-verlag, 8(1): 71-83. received 24 april 2008 accepted 24 may 2009 squ journal for science, 2019, 24(2), 88-94 doi:10.24200/squjs.vol24iss2pp88-94 sultan qaboos university 88 synthesis of pullulan-mediated silver nanoparticles (agnps) and their antimicrobial activities yusra al-owasi 1 , abdulkhadir elshafie 2 , nallusamy sivakumar 2 * and saif n. al-bahry 2 1 department of biochemistry, sultan qaboos university hospital, sultan qaboos university, p.o box 36, pc 123, alkhoud, muscat; 2 department of biology, college of science, sultan qaboos university, p.o box 36, pc 123, alkhoud, muscat. *email: apnsiva@squ.edu.om. abstract: the synthesis of silver nanoparticles (agnps), using plant extracts, bacteria, fungi and yeasts, and their antimicrobial activities have been widely investigated and well documented. however, pullulan agnps and their antimicrobial activities have not received much attention. the objective of this study was to synthesize pullulan agnps, characterize them, and test their antibacterial and antifungal activities. pullulan was extracted from aureobasidium mangrovei isolated from oman and, using uv-vis spectroscopy and fourier transform infrared (ftir), found to be identical to the commercial pullulan obtained from sigma, usa. transmission electron microscopy (tem) showed that most of the synthesized particles were poly-dispersed, irregular in shape, and most were spherical with an average size of 9.76 nm. pullulan-mediated agnps were found to have antibacterial activities, and the anova test showed that there were no significant differences between agno3, pullulan and pullulan-mediated agnps for all the bacteria tested. pullulan-mediated nanoparticles were found to have antifungal activity against curvularia lunata, fusarium incarnatum, aspergillus niger, aspergillus flavus, aspergillus ochraceus and penicillium sp. the anova test also revealed that there was a significant difference in antifungal activity between pullulan and pullulan-mediated agnps, pullulan-mediated nanoparticles having shown a higher inhibitory activity than pullulan. pullulan and pullulan-mediated nanoparticles could be used in the food industry and are safer than silver nitrates. keywords: pullulan; pullulan-mediated silver nanoparticles; antibacterial and antifungal activities; aureobasidium mangrovei. نشطتها المضاده للمكيروباتأمن البوليوالن و نتاج الجسيمات النانويه الفضيه إ ، عبدالقادر الشفيع، سيفا كومار و سيف البحري يسرى العويسي ( باستخدام المستخلصات النباتية والبكتيريا والفطريات والخميرة وأنشطتها المضادة للميكروبات تم agnpsانتاج الجسيمات النانوية الفضية ) :صلخمال وأنشطتها المضادة للميكروبات اهتماما كبيرا. الهدف بولوالن من ةيوتوثيقها بشكل جيد. ومع ذلك ، ال تلقى الجسيمات النانوية الفض بحثها على نطاق واسع ن من ، وتمييزها ، واختبار أنشطتها المضادة للبكتيريا والفطريات. تم استخراج البوليوال بولوالنة النانوية يمن هذه الدراسة هو تجميع جزيئات الفض aureobasidium mangrovei ، المعزولة من عمان وتبين أنها مطابقة للبليوالن التجاري الذي تم الحصول عليه من سيغما ، الواليات المتحدة األمريكية معظم الجسيمات ( أنtem. أظهر الفحص المجهري اإللكتروني )fourier infrared (ft-ir)و uvباستخدام التحليل الطيفي لألشعة فوق البنفسجية لها أنشطة مضادة للجراثيم وأظهر اختبار agnpsنانومتر. اثبتت الدراسة ان 9..6حجم ، غير منتظمة الشكل ، ومعظمها كروية بمتوسط متشتتة المركبة anova أنه ال توجد فروق ذات داللة إحصائية بينagno3 ،و بولوالنagnps في جميع البكتيريا التي تم اختبارها. اثبتت الدراسة ان الجسيمات ، curvularia lunata ،fusarium incarnatum ،aspergillus niger ،aspergillus flavusالنانوية لها نشاط مضاد ضدالفطريات aspergillus ochraceus وpenicillium sp وقد أظهر اختبار .anova و بولوالناختالفًا كبيًرا في النشاط المضاد للفطريات بين أيًضا أن هناك agnps بولوالن. يمكن استخدام بولوالنالمتواسطة بالبوليوان حيث أظهرت الجسيمات النانوية بوساطة البوليوالن نشاًطا مثبًطا أعلى من نشاط ا من نترات الفضة.أكثر أمانً هي والجزيئات النانوية بوساطة البوليوالن في صناعة األغذية و ، انتاج، أنشطة مضادة للميكروبات. بولوالن الجسيمات النانوية الفضية، : مفتاحيةالكلمات ال synthesis of pullulan mediated-silver nanoparticles (agnps) 89 1. introduction he antibacterial and antifungal properties of agnps have been used for many purposes, such as in biomedical and scientific applications, water purification, and food preservation [1]. this is because of their low toxicity to animal cells and high toxicity to microorganisms. nanoparticles have a broad spectrum of antibacterial and antifungal activities and have not been associated yet with microbial resistance [2]. they have the potential of being used against multi-drug resistant microbial strains. the synthesis of agnps using plant extracts, bacteria, fungi, yeasts and their antimicrobial activities has been widely investigated [3, 4] and there is a growing interest in the synthesis of nanoparticles from polymers such as polyester, cellulose, starch, dextran, alginate, and agar [2, 6]. the combined efficacy of synthesized aspergillus flavus nanoparticles and different antibiotics against multi-drug resistant bacteria has been reported [5]. however, there is still very little information available on pullulan-mediated nanoparticles and their antimicrobial activities. the synthesized and characterized pullulan-mediated nanoparticles and their antibacterial activities against escherichia coli, pseudomonas aeruginosa, listeria monocytogenes and against fungal isolates aspergillus spp. and penicillium spp. have been reported [6] and in addition there has been some study [2] on the activity of transparent nanocomposite films of pullulan and agnps against aspergillus niger, which has shown that the film can be used as an antifungal packaging material. aureobasidiu (a.) mangrovei s. nasr is a saprophytic black yeast-like fungus that was isolated from healthy leaves of avicinnia marina in iran [7]. the species has some resemblance to aurebasidium pullulans which is also a yeast-like fungus capable of producing pullulan. pullulan, an exopolysaccharide (eps), is a linear homopolymer with a chemical structure composed of maltotriose subunits interconnected with α-1,6 glucosidic linkages [8]. it is non-toxic, biodegradable, water soluble, non-carcinogenic, non-immunogenic and edible [9-12]. pullulan has been applied in various fields, ranging from food manufacturing to pharmaceutical applications, and even used as a source of edible monosaccharaides. pullulan is an excellent film former, producing a biodegradable film, which is heat sealable with good oxygen barrier properties [13]. as a result, pullulan film is sometimes referred to as “edible packaging.” coloring, flavoring, and other functional ingredients can be entrapped in the film matrix and are very stable. it has also been reported that pullulan can inhibit fungal growth in food [14]. pullulan polymer is exploited commercially in the food industry, cosmetics, and manufacturing industries [15]. with its high viscosity, pullulan is also a candidate for enhanced oil recovery [16]. the objective of this research was to extract pullulan from aureobasidium mangrovei, synthesize pullulanmediated agnps, characterize them and test their antibacterial activities against staphylococcus aureus, e.coli, p. aeruginosa, and bacillus cereus, and their antifungal activities against a. niger, a. flavus, a.ochraceus, curvularia lunata, penicillium spp., and fusarium incarnatum. 2. materials and methods the fungus was isolated from nerium oleander leaf at sultan qaboos university botanic garden (oman). it was identified using molecular techniques as a. mangrovei nasr. it was deposited at cbs, the netherlands, having an accession number cbs 142327 and a sultan qaboos university number, squ 30. it was cultured in yeast malt extract broth, placed in a shaker at a speed of 200 rpm and incubated at 25 °c for 4 to 5 days [14]. this is the second report of the existence of this species. to remove the fungal growth, the culture was centrifuged at 15000 g for 20 min. for the extraction of pullulan, six ml of cold ethanol was transferred to three ml of cell-free culture medium in a test tube and kept at 4 °c for 12 h. the precipitate was separated by centrifugation at 5000 rpm at 4 °c for 10 min. after removal of the residual ethanol, the precipitate was dissolved in distilled water and distributed in test tubes. the tubes were kept in the freezer at -30 °c for 3 days and then lyophilized to get dry pullulan powder. 2.1 characterization of pullulan the extracted pullulan was scanned using fourier transform infrared (ft-ir) spectroscopy [6]. it was compared with pullulan obtained from sigma, usa (number p4516). ft-ir spectra were recorded over a range of 4000-400 cm 1 . ultraviolet-visible spectroscopy was used to identify the different concentrations of the pullulan. 2.2 synthesis of pullulan-mediated agnps for the synthesis of pullulan-mediated agnps, three different concentrations of pullulan (1, 3 and 5%) were mixed with 1mm freshly prepared silver nitrate solution using a magnetic stirrer. the formation of agnps was recognized when the color turned brown [17]. the solutions were stored at room temperature (25 °c). primary characterization of synthesized silver nanoparticles was carried out by uv-vis spectroscopy. the stability of agnps was tested at different periods of time, 1.5 h, 3 days, 7 days and 14 days. the uv -vis absorbance spectrum of the solution was in the range of 300-700 nm; agno3 solution was used as a blank. to examine the possible functional groups of pullulan which are responsible for the reduction and stabilization of agnps, ft-ir spectrum measurement was used. dry agnps were prepared by lyophilization. then, a sufficient amount of potassium bromide powder was added and placed in a mortar with a small amount of agnps of about the tip t al-owasi, y. et al 90 of the micro spatula. the sample was crushed until it was uniformly distributed throughout the kbr. the mixture was placed in a stainless steel container and a hydraulic press was applied to produce a disk. the disk was put in the sample holder which was located in the sample compartment for scanning. ft-ir spectra were recorded at 4000-400 cm -1 . transmission electron microscopy (tem) was used to determine the size, shape, morphology and distribution of agnps. for the analysis of tem, a drop of agnp-containing aqueous solution was placed on a carbon-coated copper grid, and then the drop was allowed to air dry completely prior to the tem observations. at 300 kv of accelerating voltage, tem images of agnps were obtained using a transmission electron microscope [6]. 3. results and discussion 3.1 production of pullulan a. mangrovei had grown well in yeast malt extract broth after five days of incubation. the fungus produced pullulan together with melanin. this is the first report for this species to produce pullulan. many strains of a. pullulans reported in the literature produced melanin. pigment accumulation typically occurs late in culture growth, possibly associated with the formation of chlamydospore [9]. for commercial production, companies prefer to use strains which are non-melanin producers (mutant strains) or other non-pigment producers. however, pullulan can be purified of melanin by the addition of activated charcoal or hydrogen peroxide, sodium permanganate or other chemicals, but this makes pullulan more expensive. 3.2 extraction of pullulan pullulan is synthesized intracellularly and secreted into media by a. pullulans strains. most pullulan producing a. pullulans strains were reported from tropical countries. different strains have different abilities in pullulan production depending on their genetics and cultural conditions and pullulan production depends both on species and strain performance and the nature of the medium. the pullulan produced by different strains have ranged from 1.3 g/l to 29 g/l when harvested from a batch culture using stirred tank fermenter [18]. about 1.6 g/l of pullulan was extracted from a. mangrovei after five days of incubation. 3.3 characterization of pullulan by ft-ir analysis the ft-ir analysis of pullulan produced by a. mangrovei was compared to pullulan obtained from sigma. the strong absorption at 3435.75 cm -1 indicated that both the pullulans had some repeating units of –oh as in sugars (fig. 1). the other strong absorption at 2920.23 cm -1 indicated a -c-h bond, and the absorptions at 1633 cm -1 a -cooh bond, at 1383 cm -1 a c-oh bond, and at 1066 cm -1 the -c-o bonds in the ketone compounds. the extracted pullulan peaks and the standard sigma pullulan peaks were almost identical, which proves that our extracted compound from a. mangrovei was pullulan. our results were similar to those of previous studies [19]. figure 1. ft-ir of a) standard sigma pullulan and b) extracted pullulan. pp_smooth&baselinecorrected name description 4000 4003500 3000 2500 2000 1500 1000 500 88 70 72 74 76 78 80 82 84 86 cm-1 % t 3435.75cm-1, 76.77%t 1632.88cm-1, 82.22%t 1066.82cm-1, 82.61%t 1383.79cm-1, 84.12%t 2920.23cm-1, 84.36%t 2378.2 cm-1 1158.4 cm-1 mp_1 name description 4000 4003500 3000 2500 2000 1500 1000 500 75 30 35 40 45 50 55 60 65 70 cm-1 % t 3436.15cm-1, 44.77%t 2920.21cm-1, 53.80%t 1384.20cm-1, 56.94%t 1018.41cm-1, 58.49%t 1641.64cm-1, 58.85%t 1157.97cm-1, 59.32%t 580.24cm-1, 68.60%t 2082.85cm-1, 71.34%t 843.59cm-1, 71.62%t a b synthesis of pullulan mediated-silver nanoparticles (agnps) 91 3.4 characterization of agnps 3.4.1 uv –vis spectroscopy by the addition of pullulan into silver nitrate, agnps were synthesized by the reduction of ag + into ag 0 . the colorless solution turned to brown, which indicated the formation of agnps [17, 20]. the synthesis of agnps were tested by uv-vis spectroscopy. pullulan concentration (0.01%) formed agnps when mixed with agno3. a clear peak between 400-450 nm is an indication of agnps. the pullulan mediated agnps were tested for stability at 1.5 h, 3 days, 7 days and 14 days. the results showed that they were stable at room temperature (figure 2). figure 2. uv–vis spectra of agnps at different periods. 3.4.2 transmission electron microscopy (tem) tem was used to visualize the size and shape of the pullulan mediated agnps. it is evident from figure 3 that most of the synthesized particles were poly-dispersed, irregular in shape, and that most were spherical. the average diameter of the agnps was between 2-24 nm. the average size of the pullulan-mediated agnps was 9.76 nm; this figure was obtained from measuring 45 particles. it was found that the pullulan produced spherical agnps had a size of between 50-55 nm. [17], while in another study, the average size of the spherical agnps was reported to be between 240 nm [6]. figure 3. tem micrograph showing the size of synthesized agnps. a,b) 50 nm scale, c) 20 nm scale and d) 5 nm scale. al-owasi, y. et al 92 3.4.3 scanning electron microscope (sem) the surface morphology of the agnps was investigated using a sem. the micrographs in figure 4 show that the synthesized agnps had rough surfaces, and were spherical with uneven, irregular beads of different sizes. the results indicate that the reduction process takes place at the surface. the rough surface may be an advantage for the immobilization of enzymes [6]. the micrograph shows that the nanoparticles did not aggregate, but were dispersed as individuals. this means that they were stable [6]. figure 4. sem imaging of agnps a) 100 nm scale; b) 1 µm scale. 3.4.4 antibacterial activity of pullulan, agno3 and agnps pullulan has been reported to have some antimicrobial properties and has been used as a coating agent. in this study, pullulan, agno3 and agnps were tested against e. coli, s. aureus, b. cereus and p. aeruginosa obtained from the american type culture collection (atcc). figure 5 shows that pullulan, agno3, and agnps have antimicrobial activity against e. coli, s. aureus, b. cereus and p. aeruginosa but that the degree of inhibition, as measured by the average of inhibition zones, differs. agno3 showed better antimicrobial activities against e.coli , b. cereus and p. aeruginosa compared to pullulan, and agnps, although not against s. aureus. the anova test showed that there were no significant differences between agno3, pullulan and agnps against any of the bacteria tested. it has previously been reported that agnps can inhibit the growth of gram negative bacteria such as e. coli and p. aeruginosa [6], while other researchers [17] have reported that gram positive bacteria such as s. aureus can also be inhibited by the agnps. it has also been reported that [20] there was no antibacterial activity or inhibition when pullulan was tested on a film of s. aureus, l. monocytogenes, e. coli, and s. typhimurium, while other researchers [6] have found that only about 5% of e. coli and p. aeruginosa is inhibited by pullulan. our pullulan, which was extracted for the first time from a. mangrovei, showed better antibacterial activity against both gram negative and gram positive bacteria. figure 5. antibacterial activity of pullulan, agno3 and agnps (average diameter of the inhibition zones). synthesis of pullulan mediated-silver nanoparticles (agnps) 93 3.4.5 antifungal activity of pullulan, agno3, and agnps the antifungal activity of pullulan, agno3, and agnps was tested against c. lunata, f. incarnatum, a. niger, a. flavus, a. ochraceus and penicillium sp. obtained from sultan qaboos university biology department culture collection. figure 6 shows that pullulan, agno3, and agnps have antifungal activities against c. lunata, f. incarnatum, a. niger, a. flavus, a. ochraceus and penicillium. anova testing showed that there were significant differences between the anti-fungal effects of agno3, pullulan and agnps, where agno3 had a higher inhibitory effect compared to both the agnps and pullulan, and that agnps were more strongly inhibitory than pullulan.our results are similar to those of previous researchers [6] who showed that agnps inhibited penicillium sp. and aspergillus sp. others [21] have also found that agnps inhibit some fungal pathogens such as a. niger, a. flavus, penicillium sp. and curvularia sp., but their reducing agent was the leaf extract of cassia roxburghii and not pullulan. the pullulan-mediated agnps could be used as an antifungal agent in controlling various mycotoxigenic fungi such as a. flavus, which produces aflatoxin that causes liver cancer, a. ochraceus, which produces ochratoxin that causes kidney damage, and plant pathogens such as f. incarnatum and food spoilage fungi such as penicillium and rhizopus. figure 6. antifungal activity of pullulan, agno3, and agnps. conclusion pullulan-mediated agnps are of particular interest because of their ease of production, high antimicrobial activity, and ability to be incorporated into a diverse range of products. with the increasing number of antibioticresistant strains of bacteria and silver’s high toxicity to humans, the use of agnps as an antimicrobial agent is an exciting topic with a great deal of relevance to many fields of study and to industry. since only two papers have been published in using pullulan as reducing agent for the synthesis of nanoparticles, this study makes a contribution to this field. pullulan was extracted for the first time from a. mangrovei, which was isolated from the squ botanic garden. this species has shown better antibacterial and antifungal activities than other published strains of a. pullulans. conflict of interest the authors declare no conflict of interest. acknowledgement the authors would like to acknowledge the central analytical and applied research unit (caaru), department of chemistry at the college of science and the college of medicine, sultan qaboos university, for giving access to their facilities. references 1. rauwel, p., küünal, s., ferdov, s. and rauwel, e. a review on the green synthesis of silver nanoparticles and their morphologies studied via tem. advances in materials science and engineering, 2015, 2015, 682749. al-owasi, y. et al 94 2. pinto, r.j.b., almedia, a., fernandes, s.c., freire, c.s., silvestre, a.j., neto, c.p. and trindade, t. antifungal activity of transparent nanocomposie thin films of pullulan and silver against aspergillus niger. colloids and surfaces b biointerfaces, 2013, 103,143-148. 3. awwad, akl. m., salem, n.m. and abdeen, a.o. green synthesis of silver nanoparticles using carbo leaf extract and its antimicrobial activity. international journal of industrial chemistry, 2013, 4, 29. 4. krishnaraj, c., jagan, e.g., rajasekar, s., selvakumar, p., 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sciences, 2013, 2, 16-19. 20. morsy, m.k., khalaf, h.h., sharoba, a.m., el-tanahi h.h. and cutter, c.n. incorporation of essential oils and nanoparticles in pullulan films to control foodborne pathogens on meat and poultry products. journal of food science, 2014, 79, 675-84. 21. balashanmugam, p., balakumaran, m.d., murugan, r., dhanapal, k. and kalaichelvan, p.t. phytogenic synthesis of silver nanoparticles, optimization and evaluation of in vitro antifungal activity against human and plant pathogens. microbiological research, 2016, 192, 52-64. received 11 february 2019 accepted 9 june 2019 microsoft word biol050119-f.doc 4131squ journal for science, 10 (2005) © 2005 sultan qaboos university 31 effect of cumulus cell co-culture and protein supplement on success of in vitro fertilization and development of pre-implanted embryos in mice muhammad-baqir m-r. fakhrildin department of reproductive physiology; institute for embryo research and infertility treatment, university of baghdad, baghdad, iraq email:art_mbmrfd@yahoo.com تأثير وجود خاليا الركام المحضونة ومصدر بروتيني في الوسط الزرعي على نجاح االخصاب الخارجي وتطور األجنة قبل االنغراس في الفئران محمد باقر محمد رشاد فخر الدين مات يعتبر اخصاب البويضات وتطور األجنة الطبيعي من أهم المعايير التشخيصية ألمان المواد والمسـتلز :خالصـة cumulus(لذلك درسنا تأثير وجود خاليا الركام المحضنة . المستخدمة لألخصاب الخارجي ونقل األجنة في األنسان cells ( ومصدر بروتيني ضمن الوسط الزرعي على النسب المئوية لالخصاب الخارجي)in vitro fertilization; ivf (رانوالتطور الطبيعي للمراحل الجنينية األولية في الفئ. الزالة خاليا الركام، وقمست البويضـات الـى ) hyaluronidase(جمعت البويضات وعوملت بأنزيم الهيالورونديز حـاوي ) modified earl’s medium; mem(حضنت بويضات المجموعة األولى في وسـط . موعاتأربعة مج ) inactivated bovine amniotic fluid; 10%(على خاليا الركام ومجهز بالسائل األمينـوتي الخامـل لألبقـار كما حضنت . حاوي على خاليا الركام فقط ) mem(وحضنت بويضات المجموعة الثانية في وسط . كمصدر بروتيني كمصـدر بروتينـي %) 10(مجهز بالسائل األمينوتي الخامل لألبقار ) mem(بويضات المجموعة الثالثة في وسط يخلو من خاليا الركام والسائل األمينوتي الخامل ) mem( حضنت في وسط أما بويضات المجموعة الرابعة فقد. فقط ) paraffin oil(بويضات لغرض االخصاب الخارجي مع نطف نشيطة بوجود زيت البرافين ) 6-5(حضنت . لألبقار كـل سجلت النسب المئوية ل . ساعة) 20-18(لفترة ) co2( م بوجود غاز ثاني أوكسيد الكاربون ه 37بدرجة حرارة .من االخصاب الخارجي وتطور األجنة تحققت أفضل النتائج الخاصة بالنسب المئوية لالخصاب الخارجي وتطور األجنة الطبيعي من بويضـات المجموعـة انخفضت نتائج النسب المئوية لالخصاب الخارجي للمجموعتين الثانيـة . االخرى موعاتاألولى عند مقارنتها مع المج . على التوالي عند مقارنتها مع بويضات نتـائج المجموعـة األولـى ) p<0.05(نوي ومعنوي والثالثة بشكل غير مع نتائج االخصاب الخارجي وتطور األجنة الطبيعي من بويضات المجموعة الرابعة عنـد ) p<0.05(انخفضت معنوياً .مقارنتها مع بويضات المجموعة األولى muhammad-baqir m-r. fakhrildin 32 سائل األمينوتي لألبقار كمصدر بروتيني ضمن الوسط الزرعـي لذلك نستنتج أن وجود خاليا الركام المحضنة وال .لها تأثير هام على القدرة االخصابية للنطف والبويضات وتطور األجنة الطبيعي قبل انغراسها الحقاً في الفئران abstract: successful oocyte fertilization and normal embryonic development of mice were considered the most important diagnostic criteria for the safety of materials and tools used for human in vitro fertilization and embryo transfer (ivf-et). therefore, we studied the influence of cumulus cells co-culture and protein supplement within culture medium on percentages of in vitro fertilization (ivf) and normal development of early stages of mouse embryo later. oocytes were collected and treated with hyaluronidase to remove cumulus cells. oocytes were divided into four groups namely: group-1: oocytes incubated within modified earl’s medium (mem) supplied with 10% inactivated bovine amniotic fluid as a protein source and cumulus cells; group-2: oocytes incubated with mem supplied with cumulus cells only; group-3: oocytes incubated with mem supplied with 10% inactivated bovine amniotic fluid only; and group-4: oocytes incubated with mem free of both protein source and cumulus cells. for ivf, 5-6 oocytes were incubated with active spermatozoa under paraffin oil for 18-20 hours at 37° oc in 5% co2. percentages of ivf and embryonic development were then recorded. best results for ivf and normal embryonic development were achieved from oocytes of group-1 when compared to the other groups. as compared to group-1, the percentage of ivf for group-2 and group-3 were decreased insignificantly and significantly (p<0.002), respectively. significant (p<0.01) reduction in the percentages of ivf and normal embryonic development were reported in group-4 as compared to group-1. therefore, it was concluded that the presence of cumulus cells co-culture and bovine amniotic fluid as a protein source within culture medium may have an important role on the fertilizing capacity of spermatozoa and oocytes and normal development of pre-implanted mouse embryo later. keywords: mouse, fertilization, embryo, culture medium, ivf. 1. introduction n vitro fertilization (ivf) is a procedure that involves retrieving oocytes and spermatozoa from the female and male respectively, and placing them together in a laboratory dish to facilitate fertilization. fertilized eggs are then allowed to develop in vitro and after several days are transferred into a female’s uterus where implantation and embryo development can occur. a number of advances have been made concerning the laboratory aspects of ivf, and one of these advances was the development of better culture media for both fertilization and embryonic growth (yeung and ng, 2000). bavister (1995) reported that the programs of ivf use different types of culture media based on animal and human studies. however, culture media are classified into two types based on composition. the first one is a simple salt solution formulated with the addition of pyruvate, lactate, glucose and albumin. others are complex media such as ham’s f-10 which are suitable for long term serum-free cultures and contain nutrients such as vitamins, amino acids and other metabolites (mahadevan et al. 1997; duran, 2000). certainly, it is important to provide optimum constituents when using in vitro culture techniques to create more natural conditions, which has led to the development of several types of culture media and various additives to optimize fertilization and embryo development (bae and foote, 1980; motlik and fulka, 1981). efforts have been made to supplement the culture media with natural additives like serum (kane and headon, 1980; totey et al. 1993), follicular fluid (calvo et al. 1989), oviductal fluid i effect of cumulus co-culture and protein supplement 33 (zhu et al. 1994), human tubal fluid (maeda et al. 1996; osheroff et al. 1999), cumulus cells (hartshorne, 1989; xu et al. 1992; madan et al. 1994; watson et al. 1994), granulosa cells (motlik and fulka, 1981; vongpralub and koyanagi, 1994), and oviductal cells (minami et al. 1994; li et al. 2001). however, the use of bovine amniotic fluid as a constituent of culture medium for in vitro maturation, ivf and embryonic development has not been reported, although, amniotic fluid contains different electrolytes, non-protein and protein components (johnson and everitt, 1988). but, it was reported that the exact requirements for growing embryos through its different developmental stages are not fully known (yadav et al. 1998). the use of pre-implantation mouse embryo culture as a quality control and educational model for technicians to acquire necessary embryo handling skills for human ivf programs has been advocated (pike and alikani, 1990). more is known about the embryology of the laboratory mouse than that of any other mammal, and almost all mammalian embryological techniques were originally devised for, and practiced on, the mouse. even now, only few methods are possible on the mouse, and some other techniques may be less successful in other species (buehr, 1995). therefore, this study was designed to investigate the influence of cumulus cells co-culture and bovine amniotic fluid supplemented to the culture medium on the success of ivf and pre-implantation embryonic development in mice. 2. materials and methods 2.1 animals and superovulation regimen twenty four healthy, mothered mice (age: 15-16 weeks) of swiss albino strain were kept in an air-conditioned room at a temperature of (26+2) o c and exposed to 12-14 hour day light program (petter and pearson, 1971). females were intraperitoneally (ip) injected with 10 iu of urofollitrophin fsh-hp (metrodin, serono, italy). 72 hours after the first injection, the same females were injected ip with 10 iu of chorionic gonadotrophin (chorulon; intervet, holland). oocytes were flushed by using modified earl’s medium (mem) (earl’s balanced salts, icn flow, icn biomedicals inc., costa mesa, ca, usa) from both oviducts 16-18 hours after the last injection, and then treated with hyaluronidase (medi-cult, denmark) to remove cumulus cells. recovered oocytes were pippeted and washed two times with mem and classified into immature, mature and atretic depending on the presence of first polar body and morphological features. 2.2 cumulus cells preparation and culture cumulus cells were removed from collected oocytes by using hyaluronidase. cumulus cells were pooled and washed with mem twice. then, the cumulus cells were diluted and adjusted to a concentration of 1 x 105 cells/ml. cumulus cells were cultured according to the procedure reported in details by weiss and eckert (1989) with slight modifications. 2.3 collection and preparation of bovine amniotic fluid reproductive systems were obtained from pregnant bovine (10-12 weeks gestation) after slaughter directly, and then transferred to the laboratory within a 1-1.5 hour period. bovine amniotic fluid (baf) was collected and centrifuged (1200 g for 15 min. at 4 oc) to remove cells and debris. then, baf was inactivated at 56 oc for 30 min. and filtered by using millipore filter (0.22 µm; acrodisc-dll, gelman sciences). prepared baf was divided into aliquots (10 ml) and stored at – 4 oc for later use. muhammad-baqir m-r. fakhrildin 34 2.4 experimental design the present study was designed to examine the effects of cumulus cells co-culture and presence of 10% inactivated bovine amniotic fluid (baf) as a protein source within mem on percentages of ivf and normal development of pre-implanted mouse embryos later. accordingly, oocytes were divided into the following four groups including : group-1 (g-1): oocytes (no. = 108) were incubated with mem supplied with protein source and cumulus cells; group-2 (g-2): oocytes (no. = 112) were incubated with mem supplied with cumulus cells only; group-3 (g-3): oocytes (no. = 103) were incubated with mem supplied with protein source only; and group-4 (g-4): oocytes (no. = 113) were incubated with mem free of both protein source and cumulus cells. 2.5 sperm collection and function tests (sfts) spermatozoa were flushed from both vas deferens of male mouse with 1ml of sperm preparation medium (medi-cult, denmark). according to the procedure mentioned in-details by fakhrildin (2000), sperm function tests including sperm concentration, percentage of sperm motility, sperm grade activity and percentage of sperm viability were examined after one hour (table 1). then, vassal spermatozoa was adjusted to 5 x106 sperm / ml within sperm preparation medium. table 1. the sperm function tests of vassal spermatozoa after one hour incubation sperm function tests range sperm concentration ( x106 sperm/ ml) 26 38 percentage of sperm motility 68 76 sperm grade activity 2.5 3.5 percentage of sperm viability 80 88 2.6 in vitro fertilization technique for ivf, each 5-6 oocytes/0.5 ml of any group were incubated with active vassal spermatozoa (0.5 x106 motile sperm/0.1 ml) under paraffin oil (medi-cult, denmark) for 18-20 hour at 37 oc in 5% co2. the culture medium for each of four types was changed for in vitro developed embryos two times daily. percentages of ivf and embryonic development were recorded. 2.7 statistics data are presented as mean and standard error of mean (sem). the data were statistically analyzed by using chi-square test to compare the level of significance among different means of each group (spss data editor). 3. results 3.1 percentages of in vitro fertilization (ivf) the results of the present study show that the highest percentage of ivf for oocytes was obtained with mem supplied with cumulus cells co-culture and inactivated bovine amniotic fluid as a protein source (group-1). the percentage of ivf for oocytes of group-1 have either insignificant differences as compared to group-2, or significant (p<0.01) differences as compared to group-3 and effect of cumulus co-culture and protein supplement 35 0 10 20 30 40 50 60 p er ce nt ag e of iv f group 1 group 2 group 3 group 4 groups of oocytes figure 1. percentages of ivf for oocytes divided according to the presence of cumulus cells and/or protein source in culture medium. a: means significantly (p<0.01) decreased when compared to group-1. b: means significantly (p<0.03) decreased when compared to groups-2 and 3. group-4 (figure 1). however, there were insignificant differences in the percentages of ivf between oocytes of group-2 and group-3. the lowest percentage of ivf was recorded for the oocytes which were cultured with mem without the presence of cumulus cells co-culture and protein source (group-4) when compared to other groups (1, 2 and 3) of oocytes (figure 1). 3.2 percentages of progressive embryonic development the progressive development of pre-implanted embryos is presented in table 2. best embryonic development was recorded in the group-1 oocytes where more than 24 %, 31 % and 21 % of produced embryos were developed into 8 cells, 16 cells and 32 cells embryonic stages; respectively. meanwhile in the same embryonic stages, it was noticed that the lowest embryonic development occurred in oocytes of group-4. table 2. percentages of embryonic development produced from groups of oocytes, divided according to the presence of cumulus cells and/or protein source in culture medium percentages of embryonic development groups of ooytes ivf (%) no. of developed embryos 1 cell embryo 2 – cells embryo 4 – cells embryo 8 – cells embryo 16 – cells embryo 32 ce lls embryo group-1 57.24 62 1.61 9.68 12.90 24.19 30.64 20.98 group-2 45.33 51 7.84 29.41 23.53 21.57 9.80 7.85 group-3 39.70 41 4.88 9.76 21.95 21.95 26.83 14.63 group-4 32.69 36 15.79 28.95 26.32 21.05 7.89 0 a b muhammad-baqir m-r. fakhrildin 36 0 4 8 12 16 20 p er ce nt ag e of a bn or m al em br yo ni c de ve lo pm en t group 1 group 2 group 3 group 4 groups of oocytes figure 2. percentages of abnormal produced from groups of oocytes were divided according to presence of cumulus cells and/or protein source in culture medium a: means significantly (p<0.01) decreased when compared to groups-2 and 4. b: means significantly (p<0.05) decreased when compared to groups-2 and 4. in general, the oocytes of group-3 embryos developed into 8 cells, 16 cells and 32 cells embryonic stages better than the embryos which developed from oocytes of group-2 and group-4 (table 2). 3.3 percentages of abnormal embryonic development figure 2 shows the percentages of abnormal embryonic development produced from four different groups of oocytes. significant (p<0.01) reduction in the percentages of abnormal embryonic development was observed in the oocytes of group-1 and group-3 as compared to oocytes of group-2 and group-4. non significant differences were observed in the percentages of abnormal embryonic development produced from oocytes of group-1 and group-3. also, insignificant differences were found in the percentages of abnormal embryonic development between group-2 and group-4 oocytes. 4. discussion since the earlier works of steptoe and edwards in in vitro fertilization (ivf) (steptoe and edwards, 1978), numerous modifications have been introduced to the different stages of the technique. ivf and embryo transfer has become a widely accepted clinical method for the treatment of infertility, both for economic and academic purposes (diedrich et al. 1988). successful ivf requires appropriate preparation of sperm and oocyte, as well as culture conditions that are favorable to the metabolic activity of the male and female gametes (duran, 2000). because of the importance of the culture media for in vitro oocyte maturation, sperm preparation, in vitro fertilization and embryonic development (pike and alikani, 1990), considerable changes in composition and preparation of culture media, involving addition of the biological fluids and co-culture with granulose cells or oviductal cells or cumulus cells (maeda et al. 1996; conaghan et al. 1998), are necessary. the present study was designed to analyze the effects of supplementation of cumulus cells co-culture and inactivated bovine amniotic fluid (baf) as a protein source with culture medium on percentages of ivf and embryonic development. a b effect of cumulus co-culture and protein supplement 37 there are many reasons to select the baf as a protein source in the present study. the most important reason is that amniotic fluid contains several electrolytes, non-protein and protein components. the concentration of protein content within amniotic fluid is near 3 % (johnson and everitt, 1988). amniotic fluid is produced by the amniotic cells and is derived from maternal blood (langman, 1981; moore, 1988). therefore, some contents of amniotic fluid are similar to maternal serum including albumin, globulin, glucose, prolactin, prostaglandins, estrogens and progesterone (findlay, 1984; arici et al. 1999; yen and jaffe, 1999). the results of the present study showed that the highest percentage of ivf for oocytes were cultured with mem supplied with cumulus cells co-culture and 10 % inactivated baf as a protein source (group-1). the percentage of ivf for oocytes of group-1 have either insignificant differences as compared to group-2, or significant (p<0.01) differences as compared to group-3 and group-4 (figure 1). these results emphasize the major role of cumulus cells co-culture with the culture medium in success of ivf. also, our results are in agreement with different reports in the literature (bornslaeger and schultz, 1985; hartshorne, 1989; mori et al. 2000). it is suggested that the cumulus cells synthesize and secrete various substances like progesterone, polypeptides, cytokines, camp and map kinase which cause final maturation of oocyte, enhance fertilizing capacity of oocytes and spermatozoa and support in vitro development of early stages of embryos (kol and adashi, 1995; shimada et al. 2001; shimada and terada, 2002; su et al. 2002). in the present study, the use of inactivated baf didn’t have any species specific effect and improved the fertilizing capacity of both spermatozoa and oocytes in vitro (figure 1). possibly, the presence of several molecules in the 10 % inactivated bovine amniotic fluid may improve the physiology of sperm such as capacitation which is considered the first step for successful fertilization (osheroff et al. 1999). however, there are no reports or data to show the use of inactivated bovine amniotic fluid with constituents of culture media for ivf and embryonic development. the lowest percentage of ivf was recorded for oocytes that were cultured with mem without the presence of cumulus cells co-culture and protein source (group-4) when compared to other groups (1, 2 and 3) of oocytes (figure 1). it therefore appears that mem has no growth factors or amino acids or hormones or cytokines or any protein source, which is considered very important for ivf and embryonic development. indeed, the sub-optimal culture conditions are thought to contribute to these poor rates of development and consequently failure, following ivf (lane and gardner, 1997; conaghan et al. 1998). best embryonic development was recorded in the group-1 oocytes where more than 24 %, 31 % and 21 % of produced embryos were developed into 8 cells, 16 cells and 32 cells embryonic stages; respectively. meanwhile in the same embryonic stages, it was noticed that the lowest embryonic development was accrued from oocytes of group-4 (table 2). supplementation of the culture medium with both inactivated baf and cumulus cells co-culture may have a direct or synchronized effect to enhance in vitro development of the embryonic stages. the presence of somatic cell monolayer in the culture medium during in vitro culture of the developing embryo was found to be very important in enhancing its development potential, which provides the developing zygotes with a suitable environment, and secretes some growth factors, or autocrine factors or has paracrine effect and balanced electrolytes support further in vitro development (funahashi et al. 1997; canipari, 2000; duran, 2000; emery et al. 2001). the embryos that were produced from oocytes of group-3 developed into 8 cells, 16 cells and 32 cells embryonic stages were better than the embryos that were developed from oocytes of group-2 and group-4 (table 2). these results demonstrated the significant role of protein source to support progressive growth and embryonic development. in contrast, it was reported that there was no significant difference in the proportion of embryos that continued to develop between the protein-free and protein-supplemented culture media, but no blastocysts in the protein-free medium hatched and only those embryos in protein-containing medium hatched that were from the zona pellucida (pike muhammad-baqir m-r. fakhrildin 38 and alikani, 1990). the presence of cumulus cells with culture medium only did not improve embryonic development, possibly as a result of the release of toxic metabolites or reduction of o2 which led to rapid o2 deprivation of the embryo. however, it remains possible that the local concentration of o2 and lactic acid as well as a reduction in the partial pressure of o2 may cause irreparable damage to the embryos during incubation (barbehenn et al. 1974). significant (p<0.01) reduction in the percentages of abnormal embryonic development was observed from the oocytes of group-1 and group-3 as compared to oocytes of group-2 and group-4. also, non significant differences were observed in the percentages of abnormal embryonic development produced from oocytes of group-1 and group-3 (figure 2). these results indicate the importance and role of inactivated bovine amniotic fluid throughout progressive in vitro development of normal embryos, because baf have important nutrients such as hormones, electrolytes, albumin and glucose, as well as the ability to chelate toxic metal ions and pyrogens. graaff (2002) reported several beneficial functions of amniotic fluid for embryonic development that would ensure symmetrical growth, protection and consistent pressure and temperature. 5. conclusion 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barbiere, r.l., (eds.). w.b. saunders company, pennsylvania, usa. 4th edition. pp: 257-283. effect of cumulus co-culture and protein supplement 41 yeung, w.s.b. and ng, e.h.y. 2000. laboratory aspects of assisted reproduction. hkmj. 6: 163168. zhu, j., barrat, c.l.r., lippes, j., pacey, a.a., lenton, e.a. and cooke, i.d. 1994. human oviductal fluid prolongs sperm survival. fertil. steril. 61: 360-366. received 19 january 2005 accepted 30 june 2005 squ journal for science, 2019, 24(2), 139-146 doi:10.24200/squjs.vol24iss2pp139-146 sultan qaboos university 139 eventually pointed principally ordered regular semigroups g.a. pinto department of mathematics, sultan qaboos university, p.o. box 36, pc 123, alkhoud, muscat sultanate of oman. email: goncalo@squ.edu.om. abstract: an ordered regular semigroup, 𝑆, is said to be principally ordered if for every 𝑥 ∈ 𝑆 there exists 𝑥 ∗ = max{𝑦 ∈ 𝑆|𝑥𝑦𝑥 ≤ 𝑥}. a principally ordered regular semigroup is pointed if for every element, 𝑥, we have 𝑥 2 ≤ 𝑥. here we investigate those principally ordered regular semigroups that are eventually pointed in the sense that for all 𝑥 ∈ 𝑆 there exists a positive integer, 𝑛, such that (𝑥 𝑛)2 ≤ 𝑥 𝑛 . necessary and sufficient conditions for an eventually pointed principally ordered regular semigroup to be naturally ordered and to be completely simple are obtained. we describe the subalgebra of (𝑆,∗ ) generated by a pair of comparable idempotents 𝑒 and 𝑓such that 𝑒 0 = 𝑓 0. keywords: regular semigroup; strong dubreil-jacotin; principally ordered; naturally ordered; pointed principally ordered; green’s relations; completely simple. لترتيب األساسي لشبه الزمر العاديةلالتوجه النهائي بينتو ج.أ ∗𝒙 لعنصر ا 𝑺 ϶ 𝒙، مرتبة أساسا إذا وجد لكل 𝑺يقال إن شبه الزمر العادية المرتبة، :صلخمال = {𝒚 ∈ 𝑺 | 𝒙𝒚𝒙 ≤ 𝒙} .إلى مبدأ تتم اإلشارة 𝒙𝟐.ايلي: م 𝒙 ر شبه الزمر العادية إذا كان لكل عنص ترتيب ≤ 𝒙 في النهاية بمعنى أنه لكل هتوجنتحرى هنا عن شبه الزمر العادية المرتبة أساسا والتي . يكون ، بحيث𝒏عدد صحيح موجب، يوجد 𝑺 ϶ 𝒙عنصر (𝒙𝒏)𝟐 ≤ 𝒙𝒏 إلى مبدأ يتم الحصول على الشروط الضرورية والكافية في نهاية األمر يدعىالتي تم إنشاؤها بواسطة زوج قابل للمقارنة ∗,𝑺) (الجبر الجزئي ل ببساطة كاملة. لقد وصفنا شبه الزمر العادية لتكون مرتبة طبيعيا ترتيب 𝒆𝟎يكون و سأيديمبوتنت = 𝒇𝒐.. جرين، بسيط متكامل. ساسا، مرتب طبيعيا، مرتب وموجه أساسا، عالقاتجاكوتن القوي، مرتب أ-دوبريلشبه الزمر العادية، : مفتاحيةالكلمات ال 1. introduction n ordered regular semigroup, 𝑆, is said to be principally ordered if for every 𝑥 ∈ 𝑆 there exists 𝑥 ∗ = max{𝑦 ∈ 𝑆|𝑥𝑦𝑥 ≤ 𝑥}. the basic properties of the unary operation 𝑥 → 𝑥 ∗ in such semigroups were established in [1] and [2] and are listed in [3, theorem 13.26]. in particular, we recall for the reader’s convenience that, in such a semigroup, the following properties hold, and will be used throughout in what follows: (𝑃1) (∀𝑥 ∈ 𝑆) 𝑥 = 𝑥𝑥 ∗𝑥 (𝑃2) every 𝑥 ∈ 𝑆 has a biggest inverse, namely 𝑥 0 = 𝑥 ∗𝑥𝑥 ∗ (𝑃3) (∀𝑥 ∈ 𝑆) 𝑥 0 ≤ 𝑥 ∗ (𝑃4) (∀𝑥 ∈ 𝑆) 𝑥 ≤ 𝑥 ∗∗ in [4] we introduced the class of pointed principally ordered regular semigroups. we say that a principally ordered regular semigroup, 𝑆, is pointed, if the classes modulo green’s relations ℛ, ℒ, 𝒟 have biggest elements which are idempotent. in [4, theorem 1] we proved, in particular, that a principally ordered regular semigroup s is pointed if and only if 𝑥 2 ≤ 𝑥, for every 𝑥 ∈ 𝑆. in this paper we investigate a generalization of pointed principally ordered regular semigroups. a mailto:goncalo@squ.edu.om pinto, g.a. 140 2. eventually pointed principally ordered regular semigroups definition let s be a principally ordered regular semigroup. we say that s is eventually pointed if, for every 𝑥 ∈ 𝑆, there exists a positive integer, 𝑛, such that (𝑥 𝑛 )2 ≤ 𝑥 𝑛 , that is, 𝑥 2𝑛 ≤ 𝑥 𝑛. an immediate observation is that a pointed principally ordered regular semigroup is eventually pointed. simply take 𝑛 = 1. note that any finite ordered regular semigroup, 𝑆, is eventually pointed. in fact, there exists a positive integer power of each element 𝑆 that is an idempotent, and 𝑆 is eventually pointed. under the notation of the previous definition, we have that 𝑥 𝑛 ∙ 𝑥 𝑛 ∙ 𝑥 𝑛 = 𝑥 2𝑛 ∙ 𝑥 𝑛 ≤ 𝑥 𝑛 ∙ 𝑥 𝑛 = 𝑥 2𝑛 ≤ 𝑥 𝑛 from which we may conclude the following property (𝛼) (∀𝑥 ∈ 𝑆)(∃𝑛 ∈ ℤ+) 𝑥 𝑛 ≤ (𝑥 𝑛)∗ now, let us present examples that show that we are, in fact, in the presence of a new class of semigroups. example 1. consider mat2𝐵, the ordered regular semigroup of 2 × 2 matrices with entries in a boolean algebra 𝐵, and matrix multiplication, which can be seen in [1, example 13.1]). for the basic operations in 𝐵 we use the notation 𝑎 + 𝑏 (for 𝑎 ∨ 𝑏) and 𝑎𝑏 (for 𝑎 ∧ 𝑏). the subset mat2𝐵(0,1) where all the entries of the matrices are either 0 or 1, respectively the bottom and top element of 𝐵, is a semigroup for matrix multiplication. routine calculations allow us to say that mat2𝐵(0,1) is a principally ordered regular semigroup with hasse diagram: ( denotes idempotents) where [ 0 1 1 0 ] ∗ = [ 0 1 1 0 ] , [ 1 0 0 1 ] ∗ = [ 1 0 0 1 ] , [ 1 0 1 1 ] ∗ = [ 1 0 1 1 ] and [ 1 1 0 1 ] ∗ = [ 1 1 0 1 ] , [ 1 1 1 0 ] ∗ = [ 0 1 1 1 ] , [ 0 1 1 1 ] ∗ = [ 1 1 1 0 ] eventually pointed principally ordered regular semigroups 141 and, for every other element [ 𝑎 𝑏 𝑐 𝑑 ] ∈ mat2𝐵(0,1), [ 𝑎 𝑏 𝑐 𝑑 ] ∗ = [ 1 1 1 1 ]. for biggest inverses [ 0 0 0 0 ] 0 = [ 0 0 0 0 ] and for any other element in [ 𝑎 𝑏 𝑐 𝑑 ] ∈ mat2𝐵(0,1), [ 𝑎 𝑏 𝑐 𝑑 ] 0 = [ 𝑎 𝑏 𝑐 𝑑 ] ∗ . note that the element [ 1 1 1 0 ] in mat2𝐵(0,1) is such that [ 1 1 1 0 ] 2 = [ 1 1 1 0 ] [ 1 1 1 0 ] = [ 1 1 1 1 ] > [ 1 1 1 0 ], meaning that this principally ordered regular semigroup is not pointed. however, since it is a finite semigroup, it is eventually pointed. example 2. consider the set s = 0,a,1,b{ } with the following cayley table and hasse diagram: routine calculations allow us to conclude that, with the multiplication and partial order just defined, s is an ordered regular semigroup. in fact, it is a principally ordered semigroup, with 0∗ = 𝑏, 1∗ = 1, 𝑏∗ = 𝑏 and 𝑎∗ = 𝑎. note that s is not pointed since 𝑎2 = 1 is not comparable with 𝑎. as in the previous example, we can conclude that, since 𝑆 is a finite semigroup, 𝑆 is an eventually pointed semigroup. we can obtain this semigroup as a subsemigroup of mat2𝐵(0,1), in example 1. in fact, 𝑇 = {[ 0 0 0 0 ] , [ 0 1 1 0 ] , [ 1 0 0 1 ] , [ 1 1 1 1 ]} has the same cayley table and hasse diagram, denoting elements of t respectively, by 0, a, 1, b. alternatively, if we take a boolean algebra, 𝐵, and any element in it, 𝑥, different from 0 and 1, then 𝑈 = {[ 0 0 0 0 ] , [ 0 𝑥 𝑥 0 ] , [ 𝑥 0 0 𝑥 ] , [ 𝑥 𝑥 𝑥 𝑥 ]} with matrix multiplication and the cartesian order, we have the same cayley table and hasse diagram, and therefore the same ordered semigroup. example 3. consider the subset 𝐺 = {[ 0 1 1 0 ] , [ 1 0 0 1 ]} of mat2𝐵(0,1) described in example 1. obviously, it is a totally unordered group: 0 a 1 b 0 0 0 0 0 a 0 1 a b 1 0 a 1 b b 0 b b b pinto, g.a. 142 we have that [ 0 1 1 0 ] ∗ = [ 0 1 1 0 ] and [ 1 0 0 1 ] ∗ = [ 1 0 0 1 ], meaning that 𝐺 is principally ordered. however, it is not pointed since [ 0 1 1 0 ] 2 = [ 1 0 0 1 ] is not comparable with [ 0 1 1 0 ]. by a similar argument to the one used in example 1, we conclude that 𝐺 is eventually pointed. example 4. consider the principally ordered band, constructed in [4, example 1], 𝐿[2] = {(𝑥, 𝑦) ∈ 𝐿 × 𝐿|𝑦 ≤ 𝑥}, where 𝐿 is a lattice and the multiplication is defined by (𝑥, 𝑦)(𝑎, 𝑏) = (𝑥 ∨ 𝑎, 𝑦 ∧ 𝑏). the cartesian product with the cartesian order of 𝐿[2] and 𝑆 in example 2 is an infinite principally ordered regular semigroup that is eventually pointed, but not pointed. example 3 above provides an example of a principally ordered regular semigroup which is eventually pointed, that has a subgroup which is totally unordered and whose elements have finite order (one and two). this is always the case, as we can see in the next result, due to t. s. blyth. theorem 1. if 𝑆 is an eventually pointed principally ordered regular semigroup and if 𝐺 is any subgroup of s, then 𝐺 is totally unordered and every 𝑥 ∈ 𝐺 is of finite order. proof. for every 𝑥 ∈ 𝐺 there exists a positive integer, 𝑛, such that 𝑥 2𝑛 ≤ 𝑥 𝑛 . let 𝐺 + = {𝑥 ∈ 𝐺|1𝐺 ≤ 𝑥} be the positive cone of 𝐺. if 𝑥 ∈ 𝐺 +, then we have that 1𝐺 ≤ 𝑥 ≤ 𝑥 2 ≤ ⋯ ≤ 𝑥 𝑛 ≤ ⋯ ≤ 𝑥 2𝑛 ≤ ⋯ whence 𝑥 𝑛 = 𝑥 2𝑛 and so 𝑥 𝑛 is an idempotent in 𝐺. thus 𝑥 𝑛 = 1𝐺 , consequently 𝑥 = 1𝐺 and 𝐺 + = {1𝐺 }. the order in 𝐺 is then given by 𝑔 ≤ ℎ ⇔ 1𝐺 ≤ ℎ𝑔 −1 ⇔ ℎ𝑔−1 ∈ 𝐺 + = {1𝐺 } ⇔ ℎ = 𝑔. thus, 𝐺 is totally unordered. then, for every 𝑥 ∈ 𝐺, it follows from 𝑥 2𝑛 ≤ 𝑥 𝑛, that 𝑥 2𝑛 = 𝑥 𝑛 whence 𝑥 𝑛 = 1𝐺 and so 𝑥 is of finite order. several of the results in [4], or similar ones, can be obtained in this new class of eventually pointed principally ordered regular semigroups. for this reason, it may be necessary to provide a new proof, or adjust the existent one for pointed principally ordered regular semigroups. theorem 2. let 𝑆 be an eventually pointed principally ordered regular semigroup. if 𝑒 is a maximal idempotent of 𝑆, then 𝑒 is a maximal element of 𝑆. proof. let 𝑒 be a maximal idempotent of 𝑆 and consider any element 𝑥 in 𝑆 such that 𝑒 ≤ 𝑥. since, 𝑆 is eventually pointed, there exists a positive integer, 𝑛, such that 𝑥 2𝑛 ≤ 𝑥 𝑛. then, 𝑒 = 𝑒 𝑛 = 𝑒 … 𝑒 ≤ 𝑥 … 𝑥 = 𝑥 𝑛, and using (𝛼), 𝑒 = 𝑒𝑒 ≤ 𝑥 𝑛𝑥 𝑛 ≤ 𝑥 𝑛(𝑥 𝑛)∗ ∈ 𝐸(𝑆), whence 𝑒 = 𝑥 𝑛(𝑥 𝑛 )∗. now, 𝑥 𝑛 = 𝑥 𝑛(𝑥 𝑛)∗𝑥 𝑛 = 𝑒𝑥 𝑛 ≤ 𝑥𝑥 𝑛 = 𝑥 𝑛+1 ≤ ⋯ ≤ 𝑥 2𝑛 ≤ 𝑥 𝑛, from which we conclude that 𝑥 𝑛 ∈ 𝐸(𝑆) and consequently 𝑒 = 𝑥 𝑛. it follows that 𝑒𝑥 = 𝑥 𝑛𝑥 = 𝑥 𝑛+1 = 𝑥 𝑛 = 𝑒, and similarly 𝑥𝑒 = 𝑒. thus, 𝑥𝑒𝑥 = 𝑒𝑥 = 𝑒 ≤ 𝑥 gives 𝑒 ≤ 𝑥 ∗, whence 𝑒 = 𝑒𝑒 ≤ 𝑥𝑥 ∗ , which implies 𝑒 = 𝑥𝑥 ∗ and therefore 𝑥 = 𝑥𝑥 ∗𝑥 = 𝑒𝑥 = 𝑒 , meaning that 𝑒 is a maximal element of 𝑆. theorem 3. an eventually pointed principally ordered regular semigroup, 𝑆, has at most one maximal idempotent. proof. let 𝑒, 𝑓 be maximal idempotents of 𝑆. consider the element 𝑒𝑓 in 𝑆. since 𝑆 is eventually pointed there exists a positive integer, 𝑛, such that (𝑒𝑓)2𝑛 ≤ (𝑒𝑓)𝑛 . from (𝑒𝑓)𝑛 𝑒(𝑒𝑓)𝑛 = (𝑒𝑓)𝑛 𝑒𝑒𝑓(𝑒𝑓)𝑛−1 = (𝑒𝑓)𝑛𝑒𝑓(𝑒𝑓)𝑛−1 = (𝑒𝑓)2𝑛 ≤ (𝑒𝑓)𝑛 we obtain 𝑒 ≤ ((𝑒𝑓)𝑛 )∗ and similarly 𝑓 ≤ ((𝑒𝑓)𝑛)∗. using theorem 2, we have that both 𝑒 and 𝑓 are maximal elements of s and therefore 𝑒 = ((𝑒𝑓)𝑛)∗ = 𝑓. we recall that the natural order, ≤𝑛 , on the idempotents of a regular semigroup is defined by 𝑒 ≤𝑛 𝑓 ⇔ 𝑒 = 𝑒𝑓 = 𝑓𝑒 and that an ordered regular semigroup (𝑇, ≤) is said to be naturally ordered if the order extends the natural order, in the sense that if 𝑒 ≤𝑛 𝑓 then 𝑒 ≤ 𝑓. eventually pointed principally ordered regular semigroups 143 theorem 4 let 𝑆 be an eventually pointed principally ordered regular semigroup. the following statements are equivalent: (1) 𝑆 is naturally ordered (2) 𝑆 has a biggest idempotent (in fact, a maximal element), 𝜉, and 𝜉 = 𝑒 ∗ for every idempotent 𝑒 of 𝑆. proof. (1) ⇒ (2): by [1, theorem 13.29(3)] we have that, for every idempotent e of s, (𝑒𝑒 ∗)∗ is a maximal idempotent. thus, by theorem 3, we can conclude that s has a biggest idempotent, 𝜉, which by theorem 2 is a maximal element of 𝑆. from (1) and [1, theorem 13.28] we have that 𝑆 is a strong dubreil-jacotin semigroup and using [1, theorem 13.20], 𝑒 = 𝑒(𝜉: 𝑒)𝑒 for every idempotent 𝑒 of 𝑆. since, 𝑒𝜉 ≤ 𝜉, it then follows that 𝜉 ≤ 𝜉: 𝑒 ≤ 𝑒 ∗, whence 𝜉 = 𝑒 ∗, using the fact that 𝜉 is a maximal element of s. (2) ⇒ (1): let 𝑒 and 𝑓 be idempotents of 𝑆 such that 𝑒 ≤𝑛 𝑓, that is 𝑒 = 𝑒𝑓 = 𝑓𝑒. then, using (2), we have that 𝑒 ∗ = 𝜉 = 𝑓 ∗ , and therefore 𝑒 = 𝑓𝑒𝑓 ≤ 𝑓𝑒 ∗𝑓 = 𝑓𝜉𝑓 = 𝑓𝑓 ∗𝑓 = 𝑓, from which we conclude that s is naturally ordered. note that [4, theorem 5] states that a pointed principally ordered regular semigroup, s, is naturally ordered if and only if it has a biggest element, 𝜉, and 𝜉 = 𝑥 ∗ for every 𝑥 in 𝑆. corollary if 𝑆 is an eventually pointed principally ordered and naturally ordered regular semigroup, then green’s relations 𝒟 and 𝒥 coincide. proof. let 𝑥 be an arbitrary element of 𝑆. since 𝑆 is eventually pointed, there exists a positive integer, 𝑛, such that 𝑥 2𝑛 ≤ 𝑥 𝑛. by [1, theorem 13.27] we have that the unary operation 𝑥 → 𝑥 ∗ is antitone, whence (𝑥 𝑛)∗ ≤ (𝑥 2𝑛)∗. from theorem 4, 𝑆 has a biggest idempotent, 𝜉, which is, in fact, a maximal element of 𝑆, and therefore 𝜉𝜉𝜉 = 𝜉 implies 𝜉 ≤ 𝜉∗ whence 𝜉 = 𝜉∗. now, using (𝛼), 𝑥 2𝑛 = 𝑥 𝑛𝑥 𝑛 ≤ 𝑥 𝑛 (𝑥 𝑛)∗ ≤ 𝜉, whence 𝜉 = 𝜉∗ ≤ (𝑥 2𝑛)∗, and consequently 𝜉 = (𝑥 2𝑛)∗, which implies 𝑥 𝑛 ≤ (𝑥 𝑛)∗ ≤ (𝑥 2𝑛)∗ = 𝜉, from which we obtain 𝜉 = 𝜉∗ ≤ (𝑥 𝑛)∗ and therefore 𝜉 = (𝑥 𝑛 )∗. thus, 𝑥 2𝑛 = 𝑥 2𝑛(𝑥 2𝑛)∗𝑥 2𝑛 = 𝑥 𝑛𝑥 𝑛(𝑥 𝑛)∗𝑥 𝑛 𝑥 𝑛 = 𝑥 𝑛 𝑥 𝑛𝑥 𝑛 = 𝑥 3𝑛; that is, 𝑥 2𝑛 is an idempotent of 𝑆. therefore 𝑆 is a group bound and [5, theorem 1.2.20] allows us to conclude that green’s relations 𝒟 and 𝒥 coincide. in the presence of an identity element, 1, an interesting situation can be described. theorem 5. let s be an eventually pointed principally ordered regular semigroup with an identity element, 1, and consider 𝑇 = {𝑥 ∈ 𝑆|1 ≤ 𝑥}. for every 𝑥 ∈ 𝑇, there exists a positive integer, 𝑛, such that 𝑥 𝑛 = (𝑥 𝑛)∗ = (𝑥 𝑛 )∗∗ is an idempotent of 𝑆. proof. since 𝑆 is eventually pointed, for every 𝑥 ∈ 𝑇 there exists a positive integer, 𝑛, such that 𝑥 2𝑛 ≤ 𝑥 𝑛 . we have that 1 ≤ 𝑥 and 1 = 1 … 1 ≤ 𝑥 … 𝑥 = 𝑥 𝑛 whence, by (𝑃4), 1 ≤ (𝑥 𝑛)∗∗. then, (𝑥 𝑛)∗ ∙ 1 ∙ (𝑥 𝑛 )∗ ≤ (𝑥 𝑛)∗; that is, ((𝑥 𝑛)∗)2 ≤ (𝑥 𝑛)∗ and therefore, using (𝛼), (𝑥 𝑛)∗ = 1 ∙ (𝑥 𝑛)∗ ≤ (𝑥 𝑛)(𝑥 𝑛)∗ ≤ (𝑥 𝑛)∗(𝑥 𝑛)∗ = ((𝑥 𝑛)∗)2 ≤ (𝑥 𝑛)∗ which gives (𝑥 𝑛)∗ = (𝑥 𝑛 )(𝑥 𝑛)∗ , an idempotent of 𝑆. similarly (𝑥 𝑛 )∗ = (𝑥 𝑛)∗(𝑥 𝑛) , from which we obtain 𝑥 𝑛 = 𝑥 𝑛(𝑥 𝑛)∗(𝑥 𝑛)∗∗(𝑥 𝑛)∗𝑥 𝑛 = (𝑥 𝑛)∗(𝑥 𝑛)∗∗(𝑥 𝑛)∗ = (𝑥 𝑛)∗ allowing us to conclude that (𝑥 𝑛)∗ = (𝑥 𝑛)∗∗ and, therefore, 𝑥 𝑛 = (𝑥 𝑛)∗ = (𝑥 𝑛 )∗∗. in the special case where s is a pointed principally ordered regular semigroup, with an identity, 1, we have that the positive integer in the previous theorem is 𝑛 = 1. this means that, for these semigroups, we have 𝑥 = 𝑥 ∗ = 𝑥 ∗∗ for every element 𝑥 in 𝑆 such that 1 ≤ 𝑥. thus, we obtain the following corollary of theorem 5. corollary let 𝑆 be a pointed principally ordered regular semigroup with an identity element, 1, and consider 𝑇 = {𝑥 ∈ 𝑆|1 ≤ 𝑥}. for every 𝑥 ∈ 𝑇, 𝑥 = 𝑥 ∗ = 𝑥 ∗∗ is an idempotent of 𝑆. proof. it is an immediate consequence of theorem 5. from these results, we therefore obtain as a consequence [4, theorem 7]: theorem 6 let 𝑆 be a pointed principally ordered regular semigroup with an identity element, 1. the set 𝑆 ∗ = {𝑥 ∈ 𝑆|1 ≤ 𝑥} is a join semilattice in which 𝑥 ∨ 𝑦 = 𝑥𝑦. proof. we have, for every 𝑥 ∈ 𝑆, that 𝑥 ∙ 1 ∙ 𝑥 = 𝑥 2 ≤ 𝑥 , which implies that 1 ≤ 𝑥 ∗ and, therefore, 𝑆 ∗ ⊆ {𝑥 ∈ 𝑆|1 ≤ 𝑥}. conversely, for any 𝑥 ∈ {𝑥 ∈ 𝑆|1 ≤ 𝑥}, we obtain, by the corollary to theorem 5, that 𝑥 = 𝑥 ∗ , which means that {𝑥 ∈ 𝑆|1 ≤ 𝑥} ⊆ 𝑆 ∗. thus, 𝑆 ∗ = {𝑥 ∈ 𝑆|1 ≤ 𝑥}. pinto, g.a. 144 the fact that 𝑆 ∗ = {𝑥 ∈ 𝑆|1 ≤ 𝑥} is a join semilattice in which 𝑥 ∨ 𝑦 = 𝑥𝑦 follows, using the same argument as in [4, theorem 7]. example 5. in mat2𝐵(0,1) of example 1, [ 1 0 0 1 ] is the identity element and we have (mat2𝐵(0,1)) ∗ = {[ 1 0 0 1 ] , [ 1 0 1 1 ] , [ 1 1 0 1 ] , [ 1 1 1 1 ] , [ 0 1 1 0 ] , [ 1 1 1 0 ] , [ 0 1 1 1 ]} while {[ 𝑎 𝑏 𝑐 𝑑 ] ∈ mat2𝐵(0,1) |[ 1 0 0 1 ] ≤ [ 𝑎 𝑏 𝑐 𝑑 ]} = {[ 1 0 0 1 ] , [ 1 0 1 1 ] , [ 1 1 0 1 ] , [ 1 1 1 1 ]} this does not contradict theorem 6, since mat2𝐵(0,1) is not pointed. in [4, theorem 8] it is proven that any two-comparable 𝒟-related idempotents in a pointed principally ordered regular semigroup are mutually inverse. this heavily depends on the fact that in such a semigroup 𝑥𝒟𝑦 if and only if 𝑥 0 = 𝑦0. this is not necessarily true in eventually pointed principally ordered regular semigroups. to see this, let us present an example. example 6. in mat2𝐵(0,1) of example 1, we have that [ 1 0 0 1 ] and [ 0 1 1 0 ] are 𝒟 related, but [ 1 0 0 1 ] = [ 1 0 0 1 ] 0 ≠ [ 0 1 1 0 ] 0 = [ 0 1 1 0 ]. although the previous description of green’s 𝒟 relation is not true in our situation, we can prove a generalization of [4, theorem 8] to the wider class of ordered regular semigroups with biggest inverses. theorem 7. if 𝑆 is an ordered regular semigroup with biggest inverses such that 𝑒 and 𝑓 are comparable idempotents, for which 𝑒 0 = 𝑓 0, then 𝑒 and 𝑓 are mutually inverse. proof. let us assume without loss of generality that the idempotents 𝑒 and 𝑓 are such that 𝑒 ≤ 𝑓 and 𝑒 0 = 𝑓 0. then, 𝑒 = 𝑒𝑒𝑒 ≤ 𝑒𝑓𝑒 ≤ 𝑒𝑓 0𝑒 = 𝑒𝑒 0𝑒 = 𝑒 ⇒ 𝑒 = 𝑒𝑓𝑒 and 𝑓𝑒𝑓 ≤ 𝑓𝑓𝑓 = 𝑓 = 𝑓𝑓 0𝑓 = 𝑓𝑒 0𝑓 = 𝑓𝑒 0𝑒𝑒 0𝑓 = 𝑓𝑓 0𝑒𝑒𝑒𝑓 0𝑓 ≤ 𝑓𝑓 0𝑓𝑒𝑓𝑓 0𝑓 = 𝑓𝑒𝑓 ⇒ 𝑓 = 𝑓𝑒𝑓 which means that 𝑒 and 𝑓 are mutually inverse. in order to characterise, when an eventually pointed principally ordered regular semigroup is completely simple, we consider 𝐶 = {𝑥 ∈ 𝑆|𝑥 0 = 𝑥 ∗} the set of compact elements of 𝑆. theorem 8. let 𝑆 be an eventually pointed principally ordered regular semigroup. the following statements are equivalent: (1) 𝑆 is completely simple; (2) 𝑆 is naturally ordered and 𝐸(𝑆) ⊆ 𝐶; (3) 𝑆 has a biggest idempotent (in fact, a maximal element), 𝜉, and 𝜉 = 𝑒 0 for every idempotent 𝑒 of s. proof. (1) ⇒ (2): if 𝑆 is completely simple then, since ≤𝑛 reduces to equality, 𝑆 is trivially naturally ordered. we have, by theorem 4, that 𝑆 has a biggest idempotent, such that for every idempotent 𝑒 of 𝑆, 𝜉 = 𝑒 ∗. now, 𝑒 0 = 𝑒 ∗𝑒𝑒 ∗ = 𝜉𝑒𝜉 and 𝑒 0𝑒 0 = 𝜉𝑒𝜉𝜉𝑒𝜉 = 𝜉𝑒𝜉𝑒𝜉 = 𝜉𝑒𝑒 ∗𝑒𝜉 = 𝜉𝑒𝜉 = 𝑒 0 gives that 𝑒 ∗ = 𝜉 and 𝑒 0 = 𝜉𝑒𝜉 are idempotents such that 𝑒 0𝑒 ∗ = 𝜉𝑒𝜉𝜉 = 𝜉𝑒𝜉 = 𝑒 0 = 𝜉𝑒𝜉 = 𝜉𝜉𝑒𝜉 = 𝑒 ∗𝑒 0 that is, 𝑒 0 ≤𝑛 𝑒 ∗ and, since ≤𝑛 reduces to equality, 𝑒 0 = 𝑒 ∗, for every idempotent 𝑒 of 𝑆. therefore, we can conclude that 𝐸(𝑆) ⊆ 𝐶. eventually pointed principally ordered regular semigroups 145 (2) ⇒ (1): suppose now that 𝑆 is naturally ordered and 𝐸(𝑆) ⊆ 𝐶. assume that 𝑒 and 𝑓 are idempotents of 𝑆, such that 𝑒 ≤𝑛 𝑓 . thus, in particular, 𝑒 ≤ 𝑓 and also 𝑒 = 𝑒𝑓 = 𝑓𝑒. by theorem 4, 𝑆 has a biggest idempotent (in fact, a maximal element), 𝜉, such that 𝑒 ∗ = 𝜉 = 𝑓 ∗. since 𝐸(𝑆) ⊆ 𝐶 we have that 𝑒 0 = 𝑓 0, whence, by theorem 7, 𝑒 and 𝑓 are mutually inverse and, using the fact that 𝑒 ≤𝑛 𝑓, 𝑓 = 𝑓𝑒𝑓 = 𝑒𝑓 = 𝑒. hence, ≤𝑛 reduces to equality and 𝑆 is completely simple. (2) ⟹ (3): from theorem 4, 𝑆 has a biggest idempotent (in fact, a maximal element), 𝜉, and 𝜉 = 𝑒 ∗ for every idempotent 𝑒 of 𝑆. since 𝐸(𝑆) ⊆ 𝐶, we obtain that 𝜉 = 𝑒 ∗ = 𝑒 0. (3) ⟹ (2): by (3), 𝜉 is a biggest idempotent (in fact a maximal element) of 𝑆, such that 𝜉 = 𝑒 0 for every idempotent 𝑒 of 𝑆. by (𝑃3), we have that 𝜉 = 𝑒 0 ≤ 𝑒 ∗. since 𝜉 is a maximal element of 𝑆, we obtain 𝜉 = 𝑒 ∗ = 𝑒 0 and, by theorem 4, 𝑆 is naturally ordered and 𝐸(𝑆) ⊆ 𝐶. using theorem 7, we can prove as in [4, theorem 9] the following result in an eventually pointed principally ordered regular semigroup, under the weaker conditions of 𝑒 and 𝑓 comparable idempotents such that 𝑒 0 = 𝑓 0. theorem 9. let 𝑆 be an eventually pointed principally ordered regular semigroup. if 𝑒 and 𝑓 are idempotents of 𝑆 such that 𝑒 ≤ 𝑓 and 𝑒 0 = 𝑓 0, then the subalgebra 𝑇 of (𝑆,∗ ) generated by {𝑒, 𝑓} is a band having at most 10 elements. in the case where 𝑇 has precisely 10 elements it is represented by the hasse diagram. in which elements joined by lines of positive gradient are ℛ-related, those joined by lines of negative gradient are ℒ-related, and the vertical line also indicates ≤𝑛. example 7. consider in example 1 𝑒 = [ 0 0 0 1 ] and 𝑓 = [ 0 1 0 1 ] that verify 𝑒 ≤ 𝑓 and 𝑒 0 = [ 1 1 1 1 ] = 𝑓 0. this gives a simplified version of the structure presented in theorem 9, the four element set, with the induced order and matrix multiplication, 𝑇 = {[ 0 0 0 1 ] , [ 0 1 0 1 ] , [ 0 0 1 1 ] , [ 1 1 1 1 ]}. to obtain, precisely, the diagram in theorem 9, let us recollect that in [4, example 4] we obtained this diagram, in a pointed principally ordered regular semigroup, with a semigroup denoted by 𝐸(𝐵2 ). if we define, in the cartesian ordered set, 𝑇 × 𝐸(𝐵2 ), the cartesian multiplication, we easily obtain an eventually pointed principally ordered regular semigroup with a copy of the diagram in theorem 9. we just need to consider, for example, the cartesian product, cartesian order of {𝑒} by the band obtained in [4, example 4]. e e*= f * ef fe f ff * ee* e*e f *f e º =f º pinto, g.a. 146 conclusion in this paper we introduced a new class of ordered semigroups: eventually pointed principally ordered regular semigroups, as a generalisation of pointed principally ordered regular semigroups. examples showing that the classes are distinct were presented, and it was possible to prove several of the known results, or similar versions of them, in this class of semigroups, with new and adjusted justifications. conflict of interest the author declares no conflict of interest. acknowledgement i thank sultan qaboos university for providing facilities. references 1. blyth, t.s. and pinto, g.a. principally ordered regular semigroups, glasgow mathematics journal. 32 (1990) 349-364. doi:10.1017/s0017089500009435. 2. blyth, t.s. and pinto, g.a. idempotents in principally ordered regular semigroups, communications in algebra 19 (1991) 1549-1563. doi:10.1080/00927879108824220. 3. blyth, t.s. lattices and ordered algebraic structures, (springer 2005). doi:10.1007/b139095. 4. blyth, t.s. and pinto, g.a. pointed principally ordered regular semigroups, discussiones mathematicae 36 (2016) 101-111. doi:10.7151/dmgaa.1243. 5. higgins, p.m. techniques of semigroup theory (oxford science publications, 1992) doi:10.1007/bf02573500. received 29 may 2019 accepted 2 september 2019 microsoft word biol080603-f edited_checked.doc 17-23 squ journal for science, 14 (2009) © 2009 sultan qaboos university 17 pcr based detection of genetically modified soy in processed foods commercially available in saudi arabia ibrahim abdullah alaraidh department of biology, teachers college, king saud university, p.o.box 4341, riyadh 11491, saudi arabia. email: ibrahim1551@hotmail.com. تجات األغذية المتوفرة تجارياُ في المملكة نياُ في مثالمعدل وراعن الصويا pcr الكشف باستخدام الـ العربية والسعودية ابراهيم بن عبداهللا صالح العريض للكشف عن وجود األغذية المعدلة pcr)(في هذا البحث تم استخدام طريقة تفاعل سلسلة إنزيم البوليمريز :خالصة تم تطبيق هذه الطريقة للكشف عن وجود األغذية المعدلة وراثيا خصوصا . في أسواق المملكة العربية السعوديةوراثيا ومن ثم تم التأكد أن كل العينات تحتوي على فول الصويا من خالل . roundup ready soy (rrs)وجود جين الـ عينة غذائية من المفترض أن تكون 80تم فحص . ا في فول الصويالموجود أصالً) lectin gene(وجود جين الليكتين يثبت وجود فول الصويا المعدل وراثياً في منتجات األغذية مما وجد أن عينتين منهما معدلتين وراثيا . غير معدلة وراثيا شف عن هذا االكتشاف يدعم أهمية تطوير طرق كمية ونوعية للتحليل الروتيني للك. المملكة العربية السعوديةأسواقفي دليليكون قد المملكة أسواق وجود األغذية المعدلة وراثيا في إن. منتجات األغذية في أسواق المملكة العربية السعودية . هذه المنتجات بقصد أو بدون قصدتم توريد سواء دول الشرق األوسط في ا وجودهإمكانيةعن abstract: in this research, pcr (polymerase chain reaction) technique was applied to detect the presence of genetically modified soy (gmo) sold in the saudi arabian market. this method was applied to detect genetically modified soy (gm-soy), in particular the roundup ready soy (rrs). to confirm the presence of soy, samples were first tested for the existence of the soy specific lectin gene. a total of eighty samples were tested, out of which two samples tested positive as containing gm-soy. not surprisingly, the findings showed the existence of gm-soy in food products in saudi. this supports the necessity of developing precise quantitative and qualitative ways for routine analyses and detection of gmo products in the saudi arabian market. with the discovery of gm products in the saudi arabian market it would be of no surprise that other middle eastern nations also knowingly or unknowingly import gm crops. keywords : rr soybean, genetically modified organism, processed foods, soy, pcr. ibrahim abdullah alaridh 18 1. introduction owadays, utilizing genetically modified soys (gmos) as food and in food products has become common. many transgenic plants have been widely grown and sold in the global market since 1996 (james, 2003). maize and soy are the most cultivated gmos. they constitute a basic component of many prepared foods (gachet et al., 1999). particular labeling requisites have to be applied – in conformity with the european rules – to foodstuff which are not equivalent to a present food ingredient (regulation 1139/98). the saudi authorities have issued a legislation that imported food should be labeled if contains genetically modified materials indicating that that the product is genetically modified (regulation 1666). therefore, it is essential to use analytical methods to detect gmos in varied foods so as to investigate accordance with labeling requirements. we can establish a way of detecting gmos and gmo derived ingredients by examining molecules (dnas, rnas or proteins) which particularly targets the genes or sequences which were entered into the gmo. so far few ways have been developed for detecting proteins or rnas, whereas most of the ways developed for detecting gmos and derived ingredients concentrate on detecting dna (holst-jensen, 2001). this is because dna is a fairly stable molecule which allows its extraction from all types of tissue, and its analysis from processed and heat-treated food products (abdullah et al., 2006; anklam et al., 2002; holst-jensen, 2001; gachet et al., 1999; mathews & holder, 1990), and because of the uniqueness of dna in each kind of cell (wolf et al., 2000). the genetic information content of dna is greater than protein because of the degeneracy of the genetic code as one goes from dna to protein (wolf et al., 2000). in addition, when introducing a foreign gene into the dna of an organism it can be easily detected only at the dna level (heller, 2003). it was found that the pcr is suitable for analyzing food (james, et al., 2003; matsuoka et al., 2002; meyer et al., 1996; allmann et al., 1993) as it is the method selected for detecting gmos in food (yamaguchi et al., 2003; anklam et al., 2002; lipp et al., 2000; meyer, 1999; vollenhofer et al., 1999). this method includes a first amplification of certain soy sequences from plant dna. this is needed to differentiate between negative and positive results because of the inhibition in the amplification (forte et al., 2004). secondly it is necessary to amplify gmo-specific sequences represented by 35s promoter and nos terminator, to sift for the existence of any transgenic material in samples. after that the samples that contain are analysed for specific transgenic substances to determine the strain of gmo in them (lin et al., 2000) in this research, we characterize how a dna extraction technique is used. it is a method of screening and is construct-specific for detecting gmo in various food products which are found in saudi markets, supermarkets and grocery shops. 2. materials and methods 2.1 samples raw and processed products containing soy were purchased from supermarkets and grocery stores located in riyadh, saudi arabia. the certified reference materials containing 0%, 1%, 2%, and 5% gm-soy materials were obtained from the european reference materials (belgium). 2.2 dna extraction the dneasy plant kit (qiagen, hilden, germany) was used for extraction of dna from all samples of soy and its products due to its ease and rapid extraction methodology, and the crm standard is applied. 2.3 dna quantification the concentration and purity of the extracted dna was sampled using the gene quant spectrophotometer (amersham, usa) at 260 and 280 nm wavelength absorbance. n pcr based detection 19 2.4 primers used three pairs of primers as listed in table 1 were used in this study. these primers were the gm03/ gm04 primers for the amplification of a 118bp dna fragment for soy specific lectin gene, 35s1f/35s1r primers for the amplification of a 101bp dna fragment for 35s which is a marker for gmo content, and pro1/pro4 primers for the amplification of a 356bp dna fragment that indicates the gmo specific round-up ready soy. table 1 . primers used in this study 2.5 pcr reaction and product analysis amplification by polymerase chain reaction (pcr) was carried out in reaction mixture (25µl). pcr amplification was carried out in ready to go pcr beads (amersham bioscience, usa). reaction consisted of 50 temperature cycles of denaturation for 45 seconds at 94oc, annealing for 45 seconds at 60 oc, and extension for 25 seconds at 75 oc. final extension was performed at 72 oc for 7 minutes. the pcr products were analyzed by gel electrophoresis on a 2.0% agarose gel stained with ethidium bromide and photographed using a gel documentation system. a 100bp ladder (amersham, usa) was used as a size marker. 3. results and discussion in this study, analysis included three steps to define the nature of gmo samples. firstly, genomic dna extraction and amplification of certain soy sequences from plant dna (lectin gene) were performed, which is important in order to differentiate between positive and negative results because of the inhibition in the amplification (forte et al., 2004). secondly, the gmo-specific sequence represented by the 35s promoter was amplified. this was to sieve for the existence of any transgenic substance in the sample. thirdly, the samples that contained gmo were exposed to analysis of specific transgenic material (roundup readytm soy specific gene) to define the kind of gmo present (lin et al., 2000). electrophoresis through a 2% agarose gel (promega) was used to examine the pcr products. highly intensive dna bands were observed in the gel. it turned out that a high yield of genomic dna had been extracted from the samples. this was enough to be used as a template for pcr amplification of the concerned gene. 2 samples out of 80 soy samples (2.5%) were positive for the two introduced genetic elements, the promoter (p35s) and structural gene (rro) genes as shown in figures 1, 2 and 3. the classifications of the 2 positive gm-soy samples were as follows; a baby biscuit, and a cracker biscuit. in this research, all the positive samples were imported from abroad. the products were not labeled as containing positive gm-soy. a lectin gene primer targeting the endogenous gene of soybean was also used to confirm the presence of soy. primers oligonucleotides primers amplicon (bp) reference lectin 5’-gccctctactccacccccatcc-3’ 5’-gcccatctgcaagcctttttgtg 118bp meyer et al ., 1996 35s promoter 5'-att gat gtg ata tct cca ctg acg t-3' 5'-cct ctc caa atg aaa tga act tcc t-3' 101bp tengel et al., 2001 roundup ready 5'-tgg cgc cca aag ctt gca tgg c-3' 5'-ccc caa gtt cct aaa tct tca agt-3' 356bp tengel et al., 2001 ibrahim abdullah alaridh 20 figure 1. electrophoresis showing the detection of the specific bp lectin gene fragments in soy and soy products. lane 1: 100bp molecular marker, lane 2:chocolate, lane 3: baby biscuit, lane 4: milk powder, lane 5: spice powder, lane 6:biscuits, lane 7: toffee crunch, lane 8: crackers, lane 9: cake flour, lane 10: raw soy, lane 11: soy flour, lane 12: baby rusk . figure 2. gel electrophoresis showing the detection of the specific 101 bp 35s promoter in soy and soy products. lane 1: 100bp molecular marker, lane 2: negative control, lane 3: soy flour, lane 4: baby biscuit, lane 5: cracker. when the samples were analyzed, they generated enough dna of a quality to be amplified with the eucaryote-specific pcr. for the detection of lectin gene, agarose gel electrophoresis of the pcr amplified products from the samples resolved a band of 118 bp as observed in figure 1. however, no amplification occurred in soy sauce as it is very difficult to extract dna from oils and sauces. in addition, soy sauce is a fermented product and sometimes contains proteins from other sources for fermentation and not soy protein. consequently, we can say that detecting soy endogenous dna is difficult. other researchers have supported our observations. greiner et al., (2004) stated that out of soy margarine, soy sauce, soy and maize oil, no dna can be extracted. two kinds of pcr application using different sets of primers can be differentiated; the screening system and the specific system. as for the screening systems, they are not specific for one certain gmo. they detect commonly used elements in genetic engineering, for example promoters or terminators that contain the 35s promoter of camv (cauliflower mosaic virus) (figure 2), the (nos) terminator of agrobacterium tumefaciens or the kanamycin-resistance maker genes (nptii) (ahmed, 2002; shirai et al., 1998). only one certain gmo can be detected by very specific systems, such as the detection of the roundup ready soy (rrs) where the cp4epsps gene (5-enolpyrunylshikimate-3-phosphatesynthase from agrobacterium tumefaciens strain cp4) that isa pcr based detection 21 structure gene of inserted recombination in rrs) is detected as indicated by the primers pro1/pro4. they can allow quantification by using an emulative pcr method (studiers et al., 1999). figure 3. gel electrophoresis showing the detection of the specific 118 bp roundup ready soy gene fragments in soy and soy products. lane 1: 100bp molecular marker, lane 2: crm 2% roundup ready, lane 3: negative control, lane 4: baby biscuit, lane 5: cracker. 4. conclusion the pcr method and thermocycle has become a basic technique in life science laboratories. this method is capable of detecting target regions in different test samples using different conditions and primers. nowadays, detecting genetically modified organism (gmos) in food has an increasing importance. nonetheless, governments face many challenges, particularly in the fields of food labeling, international policy, regulation and safety testing. the importance of human health has to be taken more seriously in saudi arabia. as gmos are constantly produced, an urgent need of cooperation between the public, commerce and the government has to be addressed. thus a thorough national policy and food testing facility with the latest scientific instruments and trained personnel has to be established for this purpose, not only for saudi arabia but also as a centre for the whole gulf region. this facility need not be only for gmos, but should also be a testing and research facility that monitors all foodstuffs for meat contamination in terms of non-halal contamination and toxicity with general compliance by food manufacturers with internationally recognized food safety standards. moreover this facility or center should also produce and seek the advice of qualified and recognized individuals in terms of islamic law and legislation regarding food, and eventually guide the direction of food science in islamic countries. 5. references abdullah, t., radu, s., hassan, z. and hashim, j. k. 2006. detection of genetically modified soy in processed foods sold commercially in malaysia by pcr-based method. food chemistry, 98: 575-579. ahmed, f. 2002. detection of genetically modified organisms in foods. trends in biotechnology, 20: 215-223. allmann, m., candrian, u., holfelen, c. and luthy, j. 1993. polymerase chain reaction (pcr): a possible alternative to immunochemical methods ensuring safety and quality of food. zeits-chrift fur lebensmittel-untersuchung and forchung, 196: 248-251. anklam, e., gadani, f., heinze, p., pijnenpurg, h. and eede, g.v.d. 2002. analytical methods for detection and determination of genetically modified organisms in agricultural crops plantderived food products. european food research and technology, 214(1): 3-26. forte, v.t., pointo, a.d., martino, c., tantillo, g.m., grasso, g. and chena, f.b. 2004. a general multilex-pcr assay for the general detection of genetically modified soya and maize. food control, 16(6): 535-539. ibrahim abdullah alaridh 22 gachet, e., martin, g.g., vigneau, f. and meyer, g. 1999. detection of genetically modified organism (gmos) by pcr. a brief review of methodology available. trends in food science and technology, 9: 380-388. greiner, r., konietzny, u. and villavicencio, a.l.c.h. 2004. qualitative and quantitative detection of genetically modified maize and soy in processed foods sold commercially in brazil by pcr-based methods. food control, 10(8): 753-759. heller, k.j. 2003. part 3.7: detection of genetic modifications: some basic consideration. in k.n. heller (ed.), generally modified foods: method and detection (pp. 149-154).wiley-vch gmbh & co kgaa. holst-jensen, a. 2001. chapter 2 gmo detection methods and validation .<http://www.entransfood.com/workinggroups /wg4tqa/gmo%20detection%0methods%20using%20pcr% 20revew.htm> accessed o1.01.03. james, c. 2003. global status of commercialized transgenic crops:. isaaa briefs, 30. james, d., schmidt, a., wall, e., green, m. and masri, s. 2003. reliable detection and identification of genetically modified maize, soybean and canola by multiplex pcr analysis. j. of agric. food chemi. 2003. 51: 5829-5834. lin, h-y., chaing, j-w. and shih, y.-c. 2001. detection of genetically modified soy beans by pcr method and immunoassay kit .journal of food and drug analysis, 9(3): 160-166. lin, h.-y. and chiueh, l.-c. 2000. detection of genetically modified soy beans and maize by the polymerase chain reaction method. journal of food 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(ec) no. 1139|98 of the european council on the compulsory indication of the labeling of certain foodstuffs produced from genetically modified organism of particulars other than those provided for in direction 79|112|eec. official journal of european union, l159/4, 26.05.1998.<, http://europa.eu.int/eurlex/pri/en/oj/dat/ 1998/1_159/1_15919980603en00040007.pdf> accessed 01.12.03 regulation 1666. ministry of commerce, decision no. 1666 dated 15/9/1421h (10/12/2000). http://www.commerce.gov.sa/english/. shirai, n., momma, k., ozawa, s., hashimoto, w., kito, m. and utsumi, s. 1998. safety assessment of genetically engineered food: detection and monitoring of glyphosatetolerance soybeans. bioscience biotechnology and biochemistry, 62: 1461-1464. studer, e., rhyner, c., luthy, j. and hubner. 1999. quantitative competitive pcr for the detection of genetically modified soyabean and maize. european food research and technology, 207(3): 207-213. pcr based detection 23 tengel, c., schssler, p., setzke, e., baller, j., and speeger-haussels, m. 2001. pcr-based detection of genetically modified soyabean and maize in raw and highly processed foodstuffs. bio techniques, 31: 426-429. tengel, c., schssler, p., setzke, e., baller, j. and speeger-haussels, m. 2002. detection of genetically modified soyabean and maize in raw and processed foodstuffs. qiagen news, 2: 16-18. vollenhofer, s., burg, k., schmidt, j. and kroath, h. 1999. genetically modified organism in food – screening and specific detection by polymerase chain reaction. journal of agriculture food chemistry, 47: 5038-5043. wolf, c., burgener, m., hubner, p. and luthy, j. 2000. pcr-rflp analysis of mitochondrial dna: differentiation of fish species. lebensmittel-wissenshaft u technologie, 144-150. yamaguchi, h., sasaki, k., umetsu, h. and kamada, h. 2003. two detection methods of genetically modified maize and state of its import into japan. food control, 14(3): 201-206. received 3 june 2008 accepted 17 march 2009 photovoltaic cells and systems: 55-62 squ journal for science, 13 (2008) © 2008 sultan qaboos university on markov modulated mean-reverting price-difference models w. p. malcom*, lakhdar aggoun and mohamed al-lawati ** *national ict australia, canberra, australia;**department of mathematics and statistics, college of science, sultan qaboos university, p.o.box 36, pc 123 al-khoud, muscat, sultanate of oman, email: laggoun@squ.edu.om. نموذج مركوفى للفرق بين األسعار في سوق المال محمد اللواتيو مالكولم، األخضر عقون . ب.و طور نموذج يحتوي على سلسلتان من نوع مركوف تقوم بالتأثير على نموذج يقوم بدراسـة حركـة هذا البحث ي :خالصة غير معروفة لكن ذات تأثير علـى صيف أحداث السلسلتان من نوع مركوف تقوم بتو . للفرق بين األسعار في سوق المال . وتستعمل في هذا البحث طرق تغيير القياس لتقدير التوزيع الشرطي المتكرر. األسعار في سوق المال abstract: in this paper we develop a stochastic model incorporating a double-markov modulated mean-reversion model. unlike a price process the basis process x can take positive or negative values. this model is based on an explicit discretisation of the corresponding continuous time dynamics. the new feature in our model is that we suppose the mean reverting level in our dynamics as well as the noise coefficient can change according to the states of some finite-state markov processes which could be the economy and some other unseen random phenomenon. keywords: double-markov modulated mean-reversion model; filtering; smoothing. 1. introduction t he main contribution of this article is to further extend the primary ideas presented in elliott c. et al. (2005). the subject matter of our work is the dynamics that describe the difference between two prices, for example the prices of two different stocks. what we would like to do, is construct the dynamics which model price differences, and in addition to this, capture important but unseen random phenomena. to do this, we consider regime switching mean reversion. mean-reverting models are well known in quantitative finance and were introduced by vasicek. the extension of vasicek’s ideas to markov-modulated mean reversion has been investigated for interest rate models (see elliott r.j. et al., 1999). one common domain of application for price difference models is in the natural gas market. in the natural gas market the basis is the difference in the price of gas at two delivery points. the usual reference in the u.s.a. for a basis differential is nymex. for example, if the may henry hub price is 5 25$ . and the may nymex 55 mailto:laggoun@squ.edu.om w.p. malcolm, lakhdar aggoun and al-lawati mohamed price is then the basis differential for may nymex is 5 45$ . 0 20$ . to henry. the usual reference for canada is the price at the aeco facility. in this article we propose to model the basis as a mean reverting diffusion, { t x x t 0}= , ≥ . unlike a price process the basis process x can take positive or negative values. the new feature in our model is that we suppose the mean reverting level in our dynamics can change according to the state of the economy. the economy is modeled as a finite state markov chain and the economy can perhaps be in two states (’good’ and ’bad’), or possibly three states. our continuous time model is discretized and the results of elliott r.j. et al (2005), are adapted to obtain a recursive filter for the state of the economy given observations of { t z z t= , ≥ 0} x . in turn, this allows predictions to be made of the basis at the next time. if the observed basis is then higher or lower than the predicted value, it suggests one price is possibly higher than it should be and the other lower. consequently, a trading strategy can be implemented based on these predictions. 2. stochastic dynamics all models are, initially, on the probability space ( )f pω, , . write { 0 u }x x u t= , ≤ ≤ , for the basis (price difference) process. t x r∈ . suppose is a mean reversion level and l rα + ∈ is the rate-parameter, that is, a parameter determining how fast the level is attained by the process l x . x has dynamics: 0 0 ( ) t t u t x x l x duα= + − + wσ .∫ (1) where w is a standard wiener process, and rσ ∈ . remark 1. the dynamics at (1) exhibit a mean reversion1 character of the model when written in stochastic differential equation form: (2) ( ) t u dx l x dt dwα σ= − + t . ignoring the noise , if t dwσ t x l> then , while if ( ) t l xα − < 0 t x l< then , and so the right-hand side of (2) is continually trying to reach the level l . ( ) t l xα − > 0 now suppose that parameters and l σ are stochastic and can switch between different levels and 1 2 m l l … l, , , 1 n …σ σ, , , respectively. we assume here that these levels are determined by the states of two markov chains z and a , respectively. without loss of generality, we take the state spaces of our markov chains to be the canonical basis 1 2 { } of and the canonical basis of 1 2 { } n s f f … f= , , , nr , respectively. write m l e e … e= , , , mr ( ) 1 ( ) 1 ( / ( / j i k j k i s r k s k r p z e z e p p f f π , + , + ) ) = = = , = = =a a , 1 (3) ( ) 1 ( ) 1 1 [ ] [ ] j i j m s r s n i m r n p pπ , ≤ ≤ , ≤ ≤ ≤ ≤ ≤ ≤ π = , = . (4) 1 modelling a mean reversion process is widely used in finance, for example in interest rates models such as the vasicek model. this class of models assumes an (static) average value will be attained, not unlike the notion of an equilibrium state, or steady state of a dynamical system in the physical sciences 56 on markov modulated mean-reverting price-difference models write { 0 t u u }z u tσ= , , ≤ ≤z a . then (5) 1 1 1 k k k k k k z z m p m + + + = π + , = +a a 1+ . here, m and are martingale increments. the scalar-valued markov processes taking values and m 1 ml … l, , 1 n…σ σ, , , are obtained by { : ( ) } 1 { ( ) } 1 1 1 t t i m t z n t f i e i z lω ω ω ω σ = = : = = 〈 , 〉 = , 〈 , 〉 = . ∑ ∑ l s a a (6) here , 1 2 ( ) m l l … l ′= , , ,l 1 2 ( ) ; denotes an inner product and denotes an indicator function for the event . { }1 a a n …σ σ σ ′= , , ,s 〈⋅,⋅〉 what also we wish to impose is that the two markov chains z and are not independent, that is, information on the behavior of one conveys some knowledge on the behavior of the other. more precisely, we assume the dynamics: a (7) 1 1k k k k k z z + + ⊗ = ⊗ +p ma a 1+ . where ( )js ir,=p p denotes a mn mn× matrix, or tensor, mapping m n× into m n× and ( )1 1 / 1 1js ir k j k s k i k rp z e f z e f r s n i j m, + += = , = = , = , ≤ , ≤ , ≤ , ≤p a a . t t again is a martingale increment. the dynamics at (1) take the form 1k + m 0 0 ( ) t t u u x x z l x du wα= + 〈 , 〉 − + 〈 , 〉∫ s a . (8) remark 2. we defined z and as inherently discrete-time. here, we "read" a z and as the output of a sample and hold circuit, or cadlag processes. a what we wish to do now, is discretise the dynamics at (8) and then compute a corresponding filter and detector. we will use an euler-maruyama discretisation scheme to obtain discrete-time dynamics, although many other schemes can be used. for all time discretisations we will consider a partition, on the interval [0 ]t, and write ( ) 0 1 {0 }k k m t t … t t= , , , = . (9) this partition is strict, , regular and the 0 1 t t …< < 1t k k t t − ∆ = − are identical for indices . applying the eulermaruyama scheme to (8), we get, k 1 1 ( ) k k k t k t k k k k k k k x x z l x w w ax b z l c v α α + + = + 〈 , 〉∆ − ∆ + 〈 , 〉 − = + 〈 , 〉 + 〈 , 〉 . s s a a (10) here (1 ) t a α− ∆ , (11) t b α∆ , (12) 57 w.p. malcolm, lakhdar aggoun and al-lawati mohamed t c ∆ . (13) the gaussian process v is an independently and identically distributed (0 1)n , . our stochastic system now, under the measure , has the form: p 1 1 1 1 1 1 1 k k k k k k k k k k k k k k k z z m p p z z k x ax b z l c v + + + + + + + = π + = + ⊗ = ⊗ + = + 〈 , 〉 + 〈 , 〉 ⎧ ⎪⎪ ⎨ ⎪ ⎪⎩ p m s a a m a a a . . k ) (14) write 0 1 0 1 0 1 0 1 1 0 1 2 { } { } { } k k k k k k k k z z z … z … f x x … x g z z … z x … x … x σ σ σ = , , , , , , , = , , , = , , , , , , , , , , , a a a a a a 1. state estimation filters the approach we take to compute our filters is the so-called reference probability method. this technique is widely used in electrical engineering, (elliott et al., 1995 and more recently aggoun et al., 2004). we define a probability measure on the measurable space†p ( fω, , such that, under , the following two conditions hold : †p 1. the state processes z and are markov processes with transition matrices and and initial distributions and , respectively. a π p 0 p 0 p 2. the observation process x is independently and identically distributed and is gaussian with zero mean and unit variance. with defined, we construct , such that under the following hold: †p p p 3. the state processes z and are markov processes with transition matrices and and initial distributions and , respectively. a π p 0 p 0 p 4. the sequence 1 2 {v v …}, , , where 1 1 x ax b z l v c + + − − 〈 , 〉 = , 〈 , 〉sa (15) is a sequence of independently and identically distributed gaussian (0 1)n , random variables. write 1 1 22 ( ) exp( π )φ ξ ξ− . ξ ′ definition 1. for 1 2 …= , , , 1 1 ( ) ( ) k x ax b z l c x φ λ φ + − − 〈 , 〉 〈 , 〉 + = 〈 , 〉 s s a a (16) 0 0 1 k k λ λ = λ = , = .∏ (17) the "real world" probability is now defined in terms of the probability measure by setting p †p 58 on markov modulated mean-reverting price-difference models † tg k dp dp | = λ . lemma 1. under , the sequence is a sequence of independently and identically distributed random variables, where p 1 2{v v v …= , , } (0 1)n , 11 , ,k k k k k x ax b z l c ν ++ − − = sa . that is, under p , 1 ,,k k kx ax b z l c 1kν+ += + + sa (18) lemma 2. under the measure , the process p z remains a markov process, with transition matrix and initial distribution π 0p . the proofs of lemma 1 and 2 are routine. remark 1. the objective in estimation via reference probability is to choose a measure which facilitates and or simplifies calculations. in filtering and prediction, we wish to evaluate conditional expectations. †p under the measure , our dynamics have the form: †p 1 1 1 1 1 1 1 k k k k k k k k k k k k z z m p m z z x v + + + 1k+ + + + + = π + = + ⊗ = ⊗ + = ⎧ ⎪⎪ ⎨ ⎪ ⎪⎩ p m a a a a in what follows we shall use the following version of bayes' rule. 1 † 1 1 † 1 1 [ / ] ( (1)[ / ] [ / ] k k k k k k k k k k k e z f z e f e z f σ σ+ + + + + λ ⊗ ⊗ λ ⊗ = .=a aa ) 1 ] + note that † † 1 1 1 1 1 1 1 † 1 1 [ / ] [ / [ / ] m n m n k k k k r k k k r k r r k k e z f e f e z e f f e f + + + = = = = + + 〈 λ ⊗ , ⊗ 〉 = λ 〈 ⊗ , ⊗ 〉 = λ . ∑∑ ∑∑a a theorem 1. information state recursion. suppose the markov chain z and are observed through the unitdelay discrete-time dynamics at (10). the information state for the corresponding filtering problem is computed by the recursion: a † 1 1 1 1 ( ) [ / ] ( k k k k k k k k k z e z f zσ σ + + + − 1 ) − ⊗ λ ⊗ = γ ⊗pa a .a 1k + (19) here 1 1 1 2 1 1 1 diag{ }m n k k k …γ γ γ, , , + + + γ = , , , , (20) and (21) ( ) 1 , 1 1 k k r r k r x ax bl x c φ σ γ σ φ + + + − −⎛ ⎞ ⎜ ⎟ ⎝ ⎠= 59 w.p. malcolm, lakhdar aggoun and al-lawati mohamed proof of theorem 1 † 1 1 † 1 1 1 1 † 1 1 1 1 † 1 1 1 1 † 1 1 1 1( ( ( ) [ / ] [ / [ / ] [ / ] [ ) ) r k k k k k k m n k k k r r r m n k k k k r r r m n k k k k k r r r m n k r k k k r x ax bl c x z z e z f ] k e z e f e f f e z f e f e f e z f e f e f e σ σ φ σ λ φ + + + + = = + + = = 〈 + + = = 〈 = = + + − − ⊗ = λ ⊗ = λ 〈 ⊗ , ⊗ 〉 ⊗ = 〈 λ ⊗ , ⊗ 〉 ⊗ = λ ⊗ , ⊗ ⊗ = λ × ∑∑ ∑∑ ∑∑ ∑∑ a a a a 1 / ] k k k r r z f e f e f + ⊗ , ⊗ 〉 ⊗a 〉 r (22) hence † 1 1 1 1 † 1 1 1 1 1 1 1 1 1 1 1 1 1 ( ) [ / ] [ ( )/ ] ( ) ( ) m n r k k k k k k k r r r m n r k k k k k k r r m n r k k k r r r k k k z z e z f e f e e z f e f e z e f e f z σ γ γ γ σ σ , + + = = , 〈 〉 + − − = = , 〈 〉 + − − = = + − − ⊗ = 〈 λ ⊗ , ⊗ 〉 ⊗ f f= λ ⊗ + , ⊗ ⊗ = ⊗ , ⊗ ⊗ =γ ⊗ ∑∑ ∑∑ ∑∑ p m p p a a a a (23) the recursion given in theorem 1 provides a scheme to estimate the conditional probabilities for events of the form { : ( ) } k k r z e fω ω⊗ = ⊗a , given the information 1k f + . in practice, one would use the vector-valued information state , to compute an estimate for the state . in general two approaches are adopted; one computes either a conditional mean, that is ( k k zσ ⊗ a ) kkz ⊗ a 1 1 1 1 1 ( ) (1 1) { ( ) ( ) } k k k k k k k k m n m n z z … z e f e f … z e f e f σ σ σ ⊗ = 〈 ⊗ , , , 〉 × 〈 ⊗ , ⊗ 〉 ⊗ , ,〈 ⊗ , ⊗ 〉 ⊗ a a a a (24) or the so-called maximum-a-posteriori (map) estimate, that is 1 1 1 1 1 ( ) (1 1) argmax{ ( ) ( ) } k k k k k k k k m n m n z z … z e f e f … z e f e f σ σ σ ⊗ = 〈 ⊗ , , , 〉 × 〈 ⊗ , ⊗ 〉 ⊗ , ,〈 ⊗ , ⊗ 〉 ⊗ a a a a (25) marginal distributions for k z and k z are obtained by multiplying ( k k )z zσ ⊗ on the right-hand side with the 60 on markov modulated mean-reverting price-difference models n -dimensional row vector (1 1)…, , or on the left-hand side with the -dimensional column vector (1 , respectively. m 1)…, , 2. prediction/forecasting what we would like to do is to predict the difference x in the next time period, and with this information, develop a trading strategy. let us first compute the n -step predictor, where {0}n n∈ . lemma 3. ( -step predictor) n 1 1 1 1 1 1 [ / ] [ / ( ) ( ) 1 ( ) ( ) 1 n k n k k k k n k k k k n k k k k e z f e z f z z z z σ σ σ σ + + + + − + − = ⊗ ⊗ = ] 〈 ⊗ , 〉 γ = 〈γ , p p p p p a a a 〉 (26) proof of lemma 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 1 1 [ / ] [ / [ / ] [ / ] [ / [ / ] [ / ] ( ) ( ) 1 k n k n k k n k n k n k k n k n k k k k n k k n k n k n k k k n k k k k e z f e z f e z f e z f e m f e z f e z f z z σ σ + + + + − + − + + + − + − + + − + + − + + − + − + + ⊗ = ⊗ + = ⊗ = + = ⊗ = ⊗ ⊗ = 〈 ⊗ , 〉 p m p p p p p p p p a a a a a a a 1 ] ] 1 1k k k k k (27) recall now our discrete-time dynamics modeling a price difference process, viz x ax b z l c v + + = + 〈 , 〉 + 〈 , 〉 .sa the one-step prediction of the price difference is computed as follows: 11| 1 1 1 1 1 1 1 1 1 1 [ / ] [ / [ / ] [ / [ / ] (predictor 1) [ / ] ( )1 ( )1 1 k kk k k k k k k k k k k k k k k k k k k k n k k k n m e x fx e ax b z l c v f ax b e z l f c e v f ax b e z f l n ax b e z f l z ax b l z σ σ ++ + + − − − × − − × × = = + 〈 , 〉 + 〈 , 〉 = + 〈 , 〉 + 〈 , 〉 = + 〈 , 〉 = = + 〈π , 〉 ⊗ = + 〈π , 〉. 〈 ⊗ , 〉 s s a a a a ] ] k (28) remark 2. here the usual issue of map/conditional-mean-estimate is irrelevant, as the price difference is continuously-valued. 61 w.p. malcolm, lakhdar aggoun and al-lawati mohamed 3. trading strategies • the estimate is the predicted value of the basis at the next time , given observations 1| ˆ k k x + 1k + 0 1 k x x … x, , , . • if is greater than the observed difference 1| ˆ k k x + 1k x + , it suggests the higher price is too high and/or the lower price too low. • conversely, if is smaller than the observed difference 1| ˆ k k x + 1k x + , the higher price is possibly too low and/or the lower price too high. • these observations might suggest trading strategies. 4. acknowledgement aggoun, l. and malcolm, w.p. would like to gratefully acknowledge to have benefited from technical discussions with professor robert j elliott on the areas of modern quantitative finance, and malcolm w.p. would like to thank sultan qaboos university for their hospitality. 5. references aggoun, l., and elliott, r.j. 2004. measure theory and filtering: introduction with applications. cambridge series in statistical and probabilistic mathematics, cambridge university press, cambridge. elliott, c. elliott, r.j. and malcolm, w.p. 2005. commodity prices and regime switching bases, conference on stochastic modelling of complex systems, daydream island, queensland australia, 10-16, july 2005. elliott, r.j., aggoun, l. and moore, j.b. 1995. hidden markov models: estimation and control. springer-verlag, new-york. applications of mathematics no. 29. elliott, r.j. 1982. stochastic calculus and applications. springer-verlag, new-york. applications of mathematics no. 18. elliott, r.j., fischer, p. and platen, e. 1999. filtering and parameter estimation for a mean-reverting interest rate model, canadian applied mathematics quarterly, 7: 381-400. elliott, r.j. and kopp, p.e. 2005. mathematics of financial markets, 2nd edition, springer-verlag. received 25 march 2006 accepted 22 september 2008 62 2. stochastic dynamics write 1. state estimation filters 2. prediction/forecasting 3. trading strategies 4. acknowledgement squ journal for science, 2019, 24(2), 122-128 doi:10.24200/squjs.vol24iss2pp122-128 sultan qaboos university 122 zero-hopf bifurcation in the generalized stretch-twist-fold flow niazy h. hussein 1 * and azad i. amen 2 1 mathematics department, faculty of science, soran university, soran-erbil kurdistan region, iraq. mathematics department, college of basic education, raparin university, ranya, kurdistan region,iraq; 2 salahaddin university, basic education college, mathematics department, kirkuk road, erbil, iraq. college of science, knowledge university, erbil kurdistan region, iraq. *email: niazy.hussein@maths.soran.edu.krd abstract: a zero-hopf equilibrium in a three-dimensional system is an isolated equilibrium point which has a zero eigenvalue and a simple pair of purely imaginary eigenvalues. in general, for such an equilibrium, there is no theory for finding when some periodic solutions are bifurcated by perturbing the parameters of the system. in this work, we describe the values of the parameters for which a zero-hopf equilibrium occurs at the equilibrium points in the generalized stretch-twist-fold flow. thus, only one condition for parameters of the generalized stretch-twist-fold flow introduced in a system (eq. 1) is found for which the equilibrium point is a zero-hopf equilibrium. for this condition, we use the averaging method to provide the existence of a periodic solution, which bifurcates from the zero-hopf equilibrium point. the main result in this paper is theorem 1, which gives a periodic solution of the generalized stretch-twist-fold flow. keywords: stretch-twist-fold flow; zero-hopf equilibrium point; zero-hopf bifurcation; periodic solution; the averaging method. المعممالتدفق المطوي -إلتواء -متدادإفي يصفرال هوبف تشعب نو ازاد ابراهيم امي نيازي هادي حسين بسيط من القيم الذاتية العقدية البحتة. ال إن توازن هوبف الصفري في نظام ثالثي األبعاد هو نقطة توازن معزولة قيمتها الذاتية صفر ولها زوج :صلخمال الحلول الدورية عن طريق اضطراب معامالت النظام. نوصف، في هذا العمل، التوازن عندما يتم تشعب بعضتوجد طريقة نظرية، بشكل عام، لمثل هذا التواء التدفق المطوي المعمم. وبالتالي، تم ادخال شرط واحد فقط على -هوبف الصفري عند نقاط التوازن في تمدد قيم المعامالت التي يظهر فيها توازن هوبف الصفري. بالنسبة إلى هذا الشرط، ( تم ايجاده بحيث تكون نقطة التوازن هي توازن1تدفق المطوي المعمم في نظام )معادلة التواء ال -معامالت تمدد التي تقدم حالً دوريًا 1هوبف الصفري. النتيجة الرئيسية في هذه الورقة هي النظرية نستخدم طريقة المتوسط لتوفير وجود حل دوري يتفرع من نقطة توازن المعمم. التواء التدفق المطوي -لتمدد التدفق المطوي، نقطة توازن هوبف الصفري، تشعب هوبف الصفري، الحل الدوري ، طريقة المتوسط. -التواء -امتداد :مفتاحيةالكلمات ال 1. introduction s a special case of stokes flows, the stretch-twist-fold (stf) flow normally appears in dynamo theory. this flow was first formulated in the work of vainshtein and zel’dovich [1]. on the principle of this research, moffatt in [2] invented a particular quadratic flow to represent the stf action. there are also very extensive studies of the stf flow; one can see [3-8]. dependent on the stf flow, a generalized stretch-twist-fold (gstf) flow was suggested in [9] by jianghong and qigui. they added two extra parameters in the stf flow in order to further investigate the stf system. the parameters for which the hopf equilibrium point occurs in the gstf flow are described in [9]. the new parameter not only preserves the original dynamic properties but also has some novel characteristics. a mailto:niazy.hussein@maths.soran.edu.krd zero-hopf bifurcation in the gstf flow 123 now, in the following, the gstf system is considered �̇� = a1z − 8(b + 1)xy, �̇� = 11x2 + 3y2 + z2 + a2xz − 3c 2 �̇� = −a1𝑥 + 2𝑦𝑧 − a2𝑥𝑦, , } (1) where a1and a2 are real positive parameters and are associated with the ratios of intensities of the sft ingredients of the flow, and 𝑏, 𝑐 are real parameters added in the original stf flow which determines the bifurcations of the system. moreover, an over-dot indicates the derivative with respect to independent variable 𝑡. system (1) remains nonconservative anymore (𝛻 𝑉 = −8 𝑏 𝑦), and the original stf flow does not exhibit the hopf bifurcation, but the authors in [1] showed that system (1) has the hopf bifurcation, which is very interesting. they used the normal form theory for studying hopf bifurcations in detail. the authors in [9] proved that system (1) has no darboux first integral when a1 ≠ 0, 𝑏 = 0 and 𝑐 = ±1. in this work, our main goal is to study the existence of the zero-hopf equilibria; we put a suitable condition on the singular point to obtain a zero-hopf equilibrium point, and which gives the zero-hopf bifurcations in the gstf flow (1). this is described in proposition 1. generally, for this kind of equilibrium there is no theory to explain when it bifurcates some periodic solutions which move the parameters of the system. we then introduce a suitable rescaling of variables which transform the gstf system (1) into the normal form system; the condition for the existence of a periodic solution which bifurcates from the zero-hopf equilibrium is given by using the averaging method. this method will be given in section 4 also contains some basic results to obtain a periodic solution of three dimensional polynomial differential systems. this investigation provides a new results for a periodic solution of the gstf flow, which we have not found in the literature. whether or not a system has periodic solutions is very interesting and important in non-linear differential systems. the existence of periodic solutions for this kind of bifurcation in a 3d differential system has been widely addressed in [10-17]. actually, in [1] the authors investigate the hopf bifurcation of system (1). their results are more general than the present ones, but our results are more accurate for finding periodic solution produced from a zero-hopf equilibrium. the reason is that we follow the conditions of the averaging method which is described in theorem 2. these conditions clearly guarantee that there is a periodic solution of the given system. when the gstf system (1) possessing a zero-hopf equilibrium point at the origin of coordinates possess a zerohopf bifurcation, it produces some periodic solutions. for performing this, we consider 𝜖–perturbations of the values of the parameters for which new ones have a zero-hopf equilibrium. the small parameter 𝜖 is necessary to be used in the averaging method, and the analysis of a zero-hopf bifurcation will be executed with respect to it. this work is arranged as follows. in section 2, the equilibrium of system (1) is investigated. in section 3, the explicit parametric condition of existence of a zero-hopf equilibrium and a periodic solution of system (1) is given. section 4 explains the averaging method of the first order. in section 5, we give the proofs of the results presented in section 3, and we also describe the stability or instability of the periodic solution which is produced in such a zerohopf bifurcation of the gstf system (1). the last section concludes the work. 2. equilibrium the equilibria of system (1) for 𝑎1 ≠ 0 are all on the following surface of the ellipsoid (1 − 8 3 𝑏) 𝑥 2 + 𝑦2 + 𝑧2 = 𝑐2. (2) we obtain (2) by solving the following three equations a1z − 8(b + 1)xy = 0, 11x 2 + 3y2 + z2 + a2xz − 3c 2 = 0, −a1𝑥 + 2𝑦𝑧 − a2𝑥𝑦 = 0. for 𝑎1 = 0, the equilibria are the solutions of the following equations 8(b + 1)xy = 0, 11x2 + 3y2 + z2 + a2xz − 3c 2 = 0, 2𝑦𝑧 − a2𝑥𝑦 = 0. if 𝑦 = 0, the equilibria are a quadratic curve 11𝑥 2 + 𝑧2 + 𝑎2𝑥𝑧 − 3𝑐 2 = 0, 𝑦 = 0, if 𝑦 ≠ 0, then the two isolated points 𝐸+(0, 𝑐, 0) and 𝐸−(0, −𝑐, 0) are the equilibria. we are only interested in the case where 𝑎1 ≠ 0 and 𝑐 = 0. according to equation (2), these give us the origin of coordinates as the only equilibrium point of system (1). hussein, n.h. and amen, a.i. 124 3. statement of the main results if an isolated equilibrium point of a 3d autonomous differential system has a zero eigenvalue and a pair of purely imaginary eigenvalues then this kind of equilibrium point is called the zero-hopf equilibrium (also called a saddlenode hopf bifurcation). it comes out that its unfolding owns the rich dynamics in a small neighborhood of the origin. this means that, unfolding is used to describe the dynamics in small neighborhoods of the equilibria and their perturbations (see for instance, guckenheimer [18], guckenheimer and holmes [19], scheurle and marsden [20], kuznetsov [21], and the references therein). in some cases a zero-hopf bifurcation may lead to a local birth of “chaos” as can be found in the work of baldom´a and seara [22], and broer and vegter [23]. our goal in the next proposition is to find a condition in which a zerohopf equilibrium point takes the place of system (1). proposition 1. there is only a one-parameter family of system (1) in which the equilibrium point localized at the origin of coordinates is a zero-hopf equilibrium point. that is 𝑐 = 0. (3) we will prove this proposition in section 4. this condition is the only one-parameter family of system (1) which exhibits a zero-hopf equilibrium localized at the equilibrium point. the next theorem tells us there is a small amplitude periodic solution which bifurcates from a zero-hopf equilibrium point of system (1). theorem 1. let the vector given by (𝑎1, 𝑎2, 𝑏, 𝑐) = (�̃�1 + 𝜖 𝛼1, �̃�2 + 𝜖 𝛼2, �̃� + 𝜖𝛼3, 𝜖𝛼4 ) with 𝜖 > 0 a sufficiently small parameter. if 𝛼4 ≠ 0, and �̃� ≠ 3 4 . then system (1) has a zero-hopf bifurcation at the equilibrium point which localizes at the origin of coordinates, and when 𝜖 = 0, a limit cycle (periodic solution) is produced at this equilibrium. furthermore, a stability or instability of this limit cycle is the same as the equilibrium point of a planar differential system with the following eigenvalues ± 1 𝜔 √−6𝛼4 2 (3 + 4�̃�) . in section 4, the above theorem will be proved via the averaging method of first order. this method is explained briefly in the following section. 4. periodic solutions via the averaging method in this work, we use the averaging method to study a periodic solution of the gstf flow (1). the averaging method is a classical and developed tool to determine the behavior of the dynamics of non-linear differential systems, and in particular of their periodic orbits. this method has a long history which starts with the works of lagrange and laplace. an intuitive justification of the process was provided by them. the first formalization of this method is due to fatou [24]. bogoliubov and krylov [25], and bogoliubov [26], made important practical and theoretical contributions using this method. in the following, the basic results concerning he averaging theory of the first order can be summarized as follows theorem 2. consider the following two initial value problems: �̇� = 𝜖 𝑓1(𝑡, 𝑥) + 𝜖 2𝑓2(𝑡, 𝑥, 𝜖), 𝑥(0) = 𝑥0, (4) and �̇� = 𝜖 𝑔(𝑦), 𝑦(0) = 𝑥0, (5) where 𝑥, 𝑦, 𝑥0 ∈ ω is an open subset of ℝ 𝑛 , with 𝑡 ∈ [0, ∞). furthermore, we suppose that 𝑓1(𝑡, 𝑥) and 𝑓2(𝑡, 𝑥, 𝜖) are periodic of t-period in the variable 𝑡, and 𝑔(𝑦) is the averaged function of 𝑓1(𝑡, 𝑦) ∈ ω. we mean that 𝑔(𝑦) = 1 𝑇 ∫ 𝑓1(𝑡, 𝑦) 𝜋 0 𝑑𝑡. (6) suppose 1. 𝑓1, 𝜕𝑓1 𝜕𝑥 , 𝜕2𝑓1 𝜕𝑥2 , 𝑓2 and 𝜕𝑓2 𝜕𝑥 are all defined, continuous in ℝ+ × ω, and these expressions are bounded by a constant independent of 𝜖 ∈ (0, 𝜖0]. 2. t is a constant independent 𝜖, and 3. 𝑦(𝑡) belongs to ω on the interval of time [0,1/𝜖 ]. zero-hopf bifurcation in the gstf flow 125 then the following statements hold  on the time scale for 1 𝜖 , we have that 𝑥(𝑡) − 𝑦(𝑡) = 𝑂(𝜖), as 𝑡 → 0 $.  if p is an equilibrium point of the averaged system (5) such that 𝑑𝑒𝑡 ( 𝜕𝑔 𝜕𝑦 ) 𝑦=𝑝 ≠ 0. (7) then, there is a t-periodic solution 𝜙 (𝑡, 𝜖) for system (4) which is close to p and such that 𝜙 (𝑡, 𝜖) approaches to 𝑝, as 𝜖 approaches to zero. furthermore, the equilibrium point of averaging differential system (5) has the same stability or instability as the periodic solution 𝜙 (𝑡, 𝜖), and the equilibrium point with eigenvalues. actually, the equilibrium point 𝑝 has the stability behavior of the poincar´e map associated to the limit cycle 𝜙 (𝑡, 𝜖). the proof of the averaging method of the first order to determine periodic solutions can be found in the book of sanders and verhulst [27], see theorems 11.5 and 11.6. 5. proof of the main results proof of proposition 1: for 𝑎1 ≠ 0 and 𝑐 ≠ 0, system (1) has two isolated equilibria 𝐸± = (0, ± 𝑐, 0), which collide at the origin coordinates where 𝑐 = 0. the proof is made by calculating directly the eigenvalues at the origin coordinates. note that the linear part of system (1) has the following characteristic polynomial at the origin of coordinates 𝑝(𝜆) = 𝜆3 + 𝑎1 2𝜆 = 𝜆(𝜆2 + 𝑎1 2). putting that 𝑝(𝜆) = 𝜆(𝜆2 + 𝛿 2) = 0, where 𝛿 = 𝑎1 > 0, thus the proposition follows. proof of theorem 1: if we consider the 𝜖-perturbations (𝑎1, 𝑎2, 𝑏, 𝑐) = ( �̃�1 + 𝜖 𝛼1, �̃�2 + 𝜖 𝛼2, �̃� + 𝜖 𝛼3, 𝜖 𝛼4), with 𝜖 > 0 a sufficiently small parameter, then, system (1) becomes �̇� = (�̃�1 + 𝜖 𝛼1)𝑧 − 8(�̃� + 𝜖 𝛼3 + 1 )𝑥𝑦, �̇� = 11 𝑥 2 + 3𝑦2 + 𝑧2 + (�̃�2 + 𝜖 𝛼2)𝑥𝑧 − 3𝜖 𝛼4 2 �̇� = − (�̃�1 + 𝜖𝛼1)𝑥 + 2𝑦𝑧 − (�̃�2 + 𝜖 𝛼2)𝑥𝑦. , } (8) by the rescaling of variables (𝑥, 𝑦, 𝑧) = (𝜖 𝑋, 𝜖 𝑌, 𝜖 𝑍), system (8) in the new variables (𝑋, 𝑌, 𝑍) becomes �̇� = (�̃�1 + 𝜖 𝛼1)𝑍 − 8(𝜖 �̃� + 𝜖 2 𝛼3 + 𝜖 )𝑋𝑌, �̇� = 𝜖 𝑍2 + 𝜖 ( �̃�2 + 𝜖 𝛼2)𝑋𝑍 + 𝜖 ( 11 𝑋 2 + 3 𝑌2 − 3 𝛼4 2), �̇� = −(�̃�1 + 𝜖 𝛼1)𝑋 + 2𝜖 𝑌𝑍 − (𝜖 �̃�2 + 𝜖 2𝛼2)𝑋𝑌. } (9) now, the linear part at the origin of system (9) can be written in its real jordan normal form, namely when 𝜖 = 0, we shall transform the linear part at the origin of the differential equation (9) into its real jordan normal form, which is as ( 0 −𝜔 0 𝜔 0 0 0 0 0 ), where 𝜔 = �̃�1 > 0 . for doing this we use the linear change of variables (𝑋, 𝑌, 𝑍) → (𝑈, 𝑉, 𝑊) given by (𝑋, 𝑌, 𝑍) = 𝑃(𝑈, 𝑉, 𝑊), where 𝑃=( −1 0 0 0 0 1 0 1 0 ). (10) clearly, 𝑃−1 exists. then system (9) can be written in the new variables (𝑈, 𝑉, 𝑊) in the following �̇� = −𝑉 𝜔 + ( ( −8 �̃� − 8 )𝑈𝑊 − 𝑉 𝛼1)𝜖 − 8 𝜖 2𝑈 𝑊 𝛼3, �̇� = 𝑈 𝜔 + (𝑈 𝛼1 + 2 𝑊 𝑉 + 𝑈𝑊 �̃�2)𝜖 + 𝜖 2 𝑊𝛼2, (11) �̇� = ( 11 𝑈2 + 3 𝑊 2 + 𝑉 2 − 𝑈 𝑉�̃�2 − 3𝛼4 2 )𝜖 − 𝜖 2𝑈 𝑉𝛼2. to study the periodic solutions of system (11) when 𝜖 is too small, we use the following a class of cylindrical coordinates (𝑈, 𝑉, 𝑊) = (𝑟 𝑐𝑜𝑠 (𝜃), 𝑟 𝑠𝑖𝑛(𝜃), 𝑊), 𝑟 > 0. (12) hussein, n.h. and amen, a.i. 126 this is a topological change of variables in a deleted neighborhood of origin coordinates. �̇� = 𝜖 (2 ( 𝜖 𝛼2 − �̃�2)𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠 (𝜃) + (8 𝜖 𝛼3 + 8�̃� + 10)𝑐𝑜𝑠 2(𝜃) )𝑟𝑊, �̇� = 𝜔 + 𝜖𝛼1 + 𝜖( ( 10 + 8𝜖𝛼3 + 8�̃�) 𝑠𝑖𝑛(𝜃)\𝑐𝑜𝑠 (𝜃) + (�̃�2 + 𝜖𝛼2)𝑐𝑜𝑠 2(𝜃))𝑊, �̇� = −3 𝜖𝛼4 2 + 𝜖 ( 10𝑐𝑜𝑠2(𝜃) − (�̃�2 + 𝜖𝛼)𝑐𝑜𝑠 (𝜃)𝑠𝑖𝑛 (𝜃))𝑟 2 + 3𝜖 𝑊 2, where 𝜔 = �̃�1 > 0. this implies that there exists a small neighborhood of (𝑟, 𝑊) = (0, 0) such that �̇� ≠ 0 for all 𝜃 in this neighborhood. furthermore, we consider an equivalent system of (12) in the neighborhood of (𝑟, 𝑊 ) = (0, 0), introducing also 𝜃 as the new independent variable. thus, we obtain the following system 𝑑𝑟 𝑑𝜃 = 𝜖, 𝑓1,1 + 𝜖2 𝜔2 𝑓2,1(𝑟, 𝜃, 𝑊) + 𝑂(𝜖 3), 𝑑𝑊 𝑑𝜃 = 𝜖 𝑓1,2 + 𝜖 2 𝑓2,2(𝑟, 𝜃, 𝑊) + 𝑂(𝜖 3), } (13) where 𝑓1,1 = −𝑟 𝑊 𝜔 (8(𝑐𝑜𝑠(𝜃)) 2 �̃� + 10(𝑐𝑜𝑠(𝜃)) 2 − 2 − 𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃)�̃�2), 𝑓1,2 = 1 𝜔 ( −𝑟2 𝑐𝑜𝑠(𝜃)𝑠𝑖𝑛(𝜃)�̃�2 + 3𝑊 2 − 3𝛼4 2 + 𝑟2 + 10𝑟2 (𝑐𝑜𝑠(𝜃)) 2 ), 𝑓2,1 = (8(𝜔𝛼3 − �̃�𝛼1)𝑐𝑜𝑠 2(𝜃) + 𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠 (𝜃)�̃�2𝛼1 + 2𝛼1 − 𝑐𝑜𝑠(𝜃)𝑠𝑖𝑛(𝜃)𝛼2𝜔 − 10𝑐𝑜𝑠 2(𝜃)𝛼1)𝑟𝑊 + ( −160𝑐𝑜𝑠3(𝜃)𝑠𝑖𝑛(𝜃)�̃� + 20𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃) + 12𝑐𝑜𝑠2(𝜃) �̃�2 + 𝑐𝑜𝑠 3(𝜃) 𝑠𝑖𝑛(𝜃)�̃�2 2 + 8𝑐𝑜𝑠2(𝜃) �̃�2�̃� − 64𝑐𝑜𝑠 3(𝜃)�̃�2 𝑠𝑖𝑛(𝜃) − 16𝑐𝑜𝑠4(𝜃)�̃�2�̃� − 20 𝑐𝑜𝑠 4(𝜃)�̃�2 − 100𝑐𝑜𝑠3(𝜃) 𝑠𝑖𝑛 (𝜃) + 16 𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃)�̃�)𝑊 2𝑟, 𝑓2,2 = 3𝛼1𝛼4 2 + ( 3𝛼4 2𝑐𝑜𝑠2(𝜃)�̃�2 + 30𝛼4 2 𝑠𝑖𝑛(𝜃) 𝑐𝑜𝑠(𝜃) + 24𝛼4 2 𝑠𝑖𝑛 (𝜃)𝑐𝑜𝑠(𝜃)�̃�) 𝑊 + ( −𝛼1 + 𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃 )�̃�2𝛼1 − 10𝑐𝑜𝑠 2(𝜃)𝛼1 − 𝑐𝑜𝑠(𝜃)𝑠𝑖𝑛(𝜃)𝛼2𝜔)𝑟 2 − 3𝑊 2𝛼1 + (𝑐𝑜𝑠3(𝜃)𝑠𝑖𝑛 (𝜃)�̃�2 2 − 8𝑐𝑜𝑠4(𝜃)�̃�2�̃� − 8 𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃)�̃� − 80𝑐𝑜𝑠 3(𝜃) 𝑠𝑖𝑛(𝜃)�̃� − 100𝑐𝑜𝑠3(𝜃) 𝑠𝑖𝑛(𝜃) + 9𝑐𝑜𝑠2(𝜃)�̃�2 − 20𝑐𝑜𝑠 4(𝜃) �̃�2 + 8𝑐𝑜𝑠 2(𝜃)�̃�2�̃� − 10 𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃)) 𝑊 𝑟2 + ( −30 𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃) − 24𝑠𝑖𝑛(𝜃)𝑐𝑜𝑠(𝜃)�̃� − 3(𝑐𝑜𝑠(𝜃)) 2 �̃�2) 𝑊 3. hence, system (13) is transformed into the normal form with respect to the parameter 𝜖 in order to apply the averaging method. we now consider the averaging differential system of first order for system (13). using theorem 2, we note that all the assumptions of theorem 2 are satisfied for the differential system (13), where we put 𝑡 = 𝜃, 𝑇 = 2 𝜋, 𝑥 = (𝑟, 𝑊) ∈ (0, ∞) × ℝ, 𝑥0 = (𝑟0, 𝑊0) and 𝑓1(𝑡, 𝑥) = 𝑓1(𝜃, 𝑟, 𝑊) = [ 𝑓1,1 (𝜃 , 𝑟, 𝑊) 𝑓1,2 (𝜃 , 𝑟, 𝑊) ] now we denote 𝑔(𝑟, 𝑊) = (𝑔11 (𝑟, 𝑊), 𝑔12(𝑟, 𝑊)) and compute the integrals (6), i.e. the averaged functions with 𝑦 = (𝑟, 𝑊)𝑇 , 𝑔(𝑟, 𝑊) = [ 𝑔1,1 (𝑟, 𝑊) 𝑔1,2 (𝑟, 𝑊) ] = [ 1 2𝜋 ∫ 𝑓1,1𝑑𝜃 2𝜋 0 1 2𝜋 ∫ 𝑓1,2𝑑𝜃 2𝜋 0 ] = [ − 𝑟𝑊 𝜔 (3 + 4�̃�), 3 𝜔 (2 𝑟2 − 𝛼4 2 + 𝑊 2) ]. (14) therefore, the 𝑔11(𝑟, 𝑊), = 𝑔12(𝑟, 𝑊) = 0 has a unique real solution (𝑟 ∗, 𝑊 ∗) where (𝑟∗, 𝑊 ∗) = ( 1 √2 √ 𝛼4 2 ,0) ≠ 0. in addition, to compute the jacobian we have 𝜕𝑔(𝑟, 𝑊) 𝜕(r, w) = [ 𝜕𝑔1,1 𝜕𝑟 𝜕𝑔1,1 𝜕𝑊 𝜕𝑔1,2 𝜕𝑟 𝜕𝑔1,2 𝜕𝑊 ] = [ − 𝑊 𝜔 (3 + 4�̃�) − 𝑟 𝜔 (3 + 4�̃�) 12 r 𝜔 6 w 𝜔 ], that is, the jacobian matrix of (14) at the point (𝑟∗, 𝑊 ∗) takes the value | 𝜕𝑔(𝑟, 𝑊) 𝜕(r, w) | ( 1 √2 √ 𝛼4 2 ,0) = 6𝛼4 2(3 + 4 �̃� ) 𝜔2 , zero-hopf bifurcation in the gstf flow 127 which is different from zero where �̃� ≠ − 3 4 and 𝛼4 ≠ 0, and the eigenvalues at the solution (𝑟 ∗, 𝑊 ∗) are ± 1 𝜔 √−6𝛼4 2 (3 + 4�̃�) these eigenvalues are the same as given in (3). this shows that when �̃� < − 3 4 , (15) the periodic solution is unstable, and it has a stable manifold and an unstable manifold both formed by two cylinders. from the averaging theorm (theorem 2), the proof is deduced once we show that a periodic solution corresponding to (𝑟∗, 𝑊 ∗) produces a periodic solution which bifurcates from the origin of system (8) when 𝜖 = 0. theorem 2 guarantees that, for 𝜖 > 0 sufficiently small, there is a periodic solution corresponding to the point (𝑟∗, 𝑊 ∗) of the form (𝑟(𝜃, 𝜖), 𝑊(𝜃, 𝜖)) such that (𝑟(0, 𝜖), 𝑊(0, 𝜖)) → (𝑟∗, 𝑊 ∗) when 𝜖 approches to zero. so, the differential system (11) possess a periodic solution (𝑈(𝜃, 𝜖), 𝑉(𝜃, 𝜖), 𝑊(𝜃, 𝜖)) = (𝑟𝑐𝑜𝑠(𝜃), 𝑟𝑠𝑖𝑛(𝜃), 𝑊), (16) for 𝜖 > 0 sufficiently small. consequently, under the change of variables (10) the differntial system (9) posesses the periodic solution (𝑋(𝜃), 𝑌(𝜃), 𝑍(𝜃)) obtained from the relation (16). finally, for 𝜖 > 0 sufficiently small, system (8) possesses the periodic solution (𝑥(𝜃), 𝑦(𝜃), 𝑧(𝜃)) = (𝜖𝑋(𝜃), 𝜖𝑌(𝜃), 𝜖𝑍(𝜃)) tending to the origin of coordinates when 𝜖 approches to zero. then, it is the periodic solution which starts at the zerohopf equilibrium point located at the origin when 𝜖 is equal to zero. this completes the proof. conclusion in this article, we have considered the generalized stretch-twist-fold flow (gstf) system flow orginally suggested by jianghong and qigui. they added two extra parameters in the stf flow in order to further investigate the stf system. we have then described the values of the parameters for which a zero-hopf equilibrium occurs at the origin for this system. we showed that there is only one condition for parameters of this type of system (eq. 1) for which the equilibrium point is a zero-hopf equilibrium. moreover, we have used the averaging method of first order (see theorem 2) to determine a periodic solution, which bifurcates from the zero-hopf equilibrium point, see theorem 1. this theorem gives a periodic solution of the gstf. it follows from theorm 2 that any sufficiently small system has a periodic solution of period near 2π. clearly this periodic orbit tends to the origin of coordinates when tends to zero. therefore, this is the small amplitude periodic solution, which starts at the zero-hopf equilibrium. conflict of interest the authors delcare no conflict of interest. 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oscillations, publication 8 of ukrainian academy of sciences, kiev, 1934. 25. bogolyubov, n. on some statistical methods in mathematical physics, izdat. akad. nauk ukr. ssr, kiev. 1945. 26. sanders, j.a. and verhulst, f. averaging methods in nonlinear dynamical systems, in: applied mathematics science, vol. 59, springer, 1985. received 23 october 2018 accepted 31 january 2019 https://link.springer.com/journal/11071 squ journal for science, 2018, 23(2), 111-119 doi: http://dx.doi.org/10.24200/squjs.vol23iss2pp111-119 sultan qaboos university 111 preliminary assessment of utilization of al-jaif scoria (nw sana’a, yemen) for cement production ibrahim a. al-akhaly 1 *, ahmed m. al-anweh 2 and mohammed i. el-anbaawy 3 1 department of earth and environmental science, faculty of science, sana’a university; 2 amran cement plant, amran,yemen; 3 department of geology, faculty of science, cairo university. *email: ibnalakhaly@hotmail.com abstract: this paper presents the results of investigations on the potential industrial utilization of scoria, collected from al-jaif quarry, nw sana'a, yemen as a cement additive. scoria was chosen as a cement additive material due to its availability and low cost from the sana’a-amran volcanic field in yemen. the chemical composition of scoria was determined by x-ray fluorescence (xrf). the studied scoria is mainly composed of volcanic glass with a few zeolites (e.g. clinoptilolite) as revealed from petrographic investigation and x-ray diffraction (xrd). the scoria was added to the clinker in the range of 2, 4, 6, 8, 10 and 12% by weight. the fineness, surface area, water demand, setting time and compressive strength were conducted on scoria blended cement. according to experimental results, the high volcanic glass allows the addition of up to 12% scoria to the clinker to maintain a good potential of manufacturing blended cement. the results satisfy the european standard en requirements and confirm the viability of using scoria as a cement additive. keywords: scoria; pozzolan; cement; al-jaif; sana’a; yemen. سمنتالتقييم األولي الستخدام اسكوريا الَجائف )شمال غرب صنعاء، اليمن( في إنتاج األ االنبعاويإبراهيم عبدالحميد األكحلي، أحمد محمد العنوة ومحمد إبراهيم معها من َمخروط الَجائف والتي تم جَ ،هذه الورقة العلمية تَعرض نتائج التجارب المعملية حول إمكانية االستخدام الصناعي لالسكوريا:صلخمال قل خص ثمنها وتوفرها في حَ ر سبب سمنت ب صناعة األ عندَ ضافة ختيار االسكوريا كمادة م ناعة األسمنت. تم ا ضافة في ص م ركاني الستخدامها كمادة الب أن االسينية بين تشعة األالسينية. الدراسة البتروجرافية وحيود شعة فلراألتَ حديده باستخدام تَ ان البركاني. التركيب الكيميائي لالسكوريا تم مرَ عَ -نعاءصَ 12و8،01، 6، 4، 2 بإضافة االسكوريا إلى الكلنكر بنس ت، تم من الزيولي قليلة ركاني مع كمية ب شكل أساسي من زجاج االسكوريا المدروسة تتكون ب قاومة االن ضغَاطي ة لألسمنت المنتج والمخلوط باالسكوريا. اعتماداً عومة، مساحة السطح، ن سبة الماء الم ضاف، زمن الت صل ٪ وزناً. تم تحديد ن ب والم ٪ إلى الكلنكر مع احتفاظ األسمنت ٢١االسكوريا يمكن إضافة االسكوريا بنسبة تصل إلى على التجارب المعملية ونسبة الزجاج البركاني المرتفعة في ز صالحية استخدامها كمادة م المخلوط باالسكوريا بخواص ا ي عز ه.جيدة ت طابق م تطلبات المواصفات االوروبية، مم ضافة لألسمنت عند إنتاج ائف، صنعاء، اليمن.الجَ سمنت، أاسكوريا، بوزوالن، : مفتاحيةالكلمات ال 1. introduction he cement industry utilizes natural pozzolans (e.g. scoria) as substitutes for portland cement (pc) due to their environmental, economic and chemical advantages [1-4]. in this respect pozzolans lower costs and co2 emissions, and increase chemical resistance of cementacious materials through reduction of the alkali aggregate reaction. the manufacture of one ton of pc clinker consumes about 4 gj of energy, and releases nearly one ton of co2 to the atmosphere [5]. world pc clinker production is responsible for about 7% of the total co2 emissions [6-8]. for this reason, particular attention has recently been given to the exploitation of scoria in many countries, including turkey [9,10], syria [11,12] and yemen [13,14]. scoria can be utilized in several industrial applications including the manufacturing of lightweight concrete, as a source of pozzolan to manufacture portland-pozzolan cement additives, as a heat insulating material, in low cost fillers in paint, filter materials and absorbents, in architectural applications [15], for producing geopolymer mortar [16-18] and as a sand in pc mortar [19]. scoria is abundant in various parts of the world including turkey [9,10], syria [11,12], saudi arabia [15,21,22] and cameroon [16,17,19]. t mailto:ibnalakhaly@hotmail.com ibrahim a. al-akhaly et al 112 scoria is also abundant in yemen [13,14,20], where more than 9,000 km 2 of the country is covered with quaternary volcanic rocks [23] (figure 1). scoria is locally used in yemen in road construction as a sub -base material and there are several quarries operating on scoria deposits in nw sana'a where the sana'a-amran volcanic field covers a total area of some 1200 km 2 . whilst scoria has been used in industry worldwide for a long time, it has only had importance in yemeni industry for the last 6 years. however, yemen has an important potential reserve of 613 million m 3 [24] and about 500,000 metric tons are exploited annually [25]. figure 1. quaternary volcanic rocks in yemen [24]. the cement produced in yemen is almost entirely of pc, although an addition of up to 5% natural pozzolan is frequently used in most local cement plants. previous work has shown the possibility of using scoria in the production of blended cements in yemen [13]. the aim of the current research is to determine the potential industrial use of scoria from al-jaif (nw sana'a, yemen) as a cement additive material. the use of scoria as a construction material would provide both low cost cement and also a cleaner environment. this study is important not only for yemen but also for other countries of similar geological setting. 2. materials and methods 2.1. sample preparation more than 500 kg of bulk sample was collected from scoria pyroclastic deposits in the al-jaif volcanic cone, about 24 km nw of sana'a, yemen (figure 2). three sub-samples were selected from the bulk sample to represent its apparent lithological varieties. these sub-samples were prepared for thin section investigation. cutting and polishing processes were performed using an oil system. glue that hardens under uv light was used. to reduce the amount of sample, sampling was performed using the cone and quartering method and riffles, since sampling must have mineralogical, physical and chemical homogeneity. the sample was crushed and ground using a laboratory dodge jaw crusher, rod mill and ball mill to reduce their size to sieve no. 200 (74 μm) for mineralogical and chemical analyses, which were conducted in amran cement plant (acp) (amran/yemen). 2.2 chemical and mineral analysis chemical analysis of five samples of scoria was carried out of by unit model arl 9800 xp sim-seq xrf of quality laboratory of acp. this xrf device unit is manufactured by thermo electron corporation and uses rhtube and uniquant program. the preparation of powder pellets for analysis included crushing the samples using the jaw crusher, then grinding them to fine powder using the disk vibration mill. in this stage of sample preparation, about 6-7 ml of hexane (c6h14) were added to the crushed sample in order to decrease the temperature during the grinding. to investigate petrographical characteristics of the sample, thin sections of three representative samples were prepared and determined using the leica polarizing microscope. these thin sections were carried out in the preliminary assessment of utilization 113 geology department, faculty of science, cairo university, cairo, egypt. these investigations were supported by bulk mineralogical study using a philips xrd equipment model pw/1710 with monochromator cu-radiation (λ =1.542a o ) at 40 k.v., 35 m.a. and a scanning speed of 0.02 o /sec. the reflection peaks between 2θ = 2 o and 60 o , corresponding spacing (då) and relative intensities (peak areas) were obtained. the diffraction charts and relative intensities obtained were compared with icdd files that were carried out by the egyptian mineral resources authority (emra), cairo, egypt. figure 2. satellite image showing the location of the studied scoria field and the amran cement plant [26]. 2.3 test specimen preparation the clinker used for producing all types of cement (pc and scoria blended cement) was obtained from acp (amran/yemen) (figure 2). the clinker, scoria and gypsum were mixed to produce cement. a reference cement (pure pc) was produced by mixing pc clinker, 96%, and gypsum, 4% by weight. this mixture was then ground for 40 minutes in a laboratory-type ball mill. scoria blended cement samples were obtained by replacing 2, 4, 6, 8, 10 and 12% (by weight of clinker) of the pc clinker by scoria and mixing and inter-grinding. the gypsum content was kept constant in all cements at 4%. before the grinding operation, pc clinker, scoria and gypsum were crushed and sieved through a 9.5 mm sieve to maintain uniformity between the specimens through using the same feed size. pc clinker, scoria and gypsum were ground to fine powder using a ring crusher to obtain a blaine fineness of about 3200 cm 2 /gm. the gypsum was dried at 40°c prior to crushing whereas the scoria was dried at 110°c. 2.4 cement tests analyses of the chemical composition of the pc (reference specimen) and scoria blended cements were performed by the xrf. fineness analyses were performed in accordance with en 196-6 [27]. the fineness of the blended cement samples was determined by measuring the blaine fineness and amount of material retained on 45 μm and 90μm sieves after vacuum sieving. the following tests were carried out on the pc and blended materials: ibrahim a. al-akhaly et al 114 fineness, specific surface area by blaine instrument, normal consistency, setting time and compressive strength. the amount of water necessary for the cements to have normal consistency was determined according to en 196-3 [28]. pastes having normal consistency were then used to determine the setting time by conducting tests as described in this standard. preparation of cement mortar mixtures was completed according to en 196-1 [29]. in these tests, 450 ± 2 gm of cement and 1350 ± 5 gm of standard sand were used. scoria blended cement mortars were prepared with 225 cm 3 of water so that the water content of the scoria blended cement mortars were adjusted to have a w/c ratio of 0.5 as stated in the standards. the prepared mortars were poured into cubic shaped three-part mortar molds 7.06x7.06x7.06 cm 3 (surface area 50 cm 2 ). the mortar specimens of all cements used in the experiments were prepared in a laboratory environment at a room temperature of 20 ± 2 o c and 80 ± 4 % relative humidity. after being kept in a wet cabinet for 24 hours, the mortar specimens were demulded and kept in water until they were tested. compressive strength tests were performed by an automated strength testing machine in accordance with en 196-1 [29]. the compressive strength of the cubes was determined after 3, 7 and 28 days curing. three cube specimens were tested for each day for each type of cement. the reported values represent the average of three readings. 3. results and discussion 3.1 scoria composition al-jaif scoria is one of the natural pozzolan volcanic cones in yemen that formed during quaternary explosive eruptions. it has a highly porous structure which was formed by dissolved gases precipitated during cooling as the lava hurtled through the air. therefore, scoria consists of pyroclastic ejects, of irregular morphology, and has the basic composition of basalt. it is formed of vesicular fine to coarse fragments, reddish or black in color and light in weight. petrographic investigation shows that the scoria is mainly composed of volcanic glass with phenocrystals of olivine in the matrix and has hyalopilitic-porphyritic and vitrophyric-porphyritic textures with vesicles in the matrix (figure 3a). the vesicles are filled with secondary minerals (e.g. chlorite) (figure 3b). olivine is easily distinguished by color tone and y-cracks (figure 3c). figure 3. microphotographs of scoria sub-samples: (a) connected and isolated vesicles in reddish brown glassy groundmass, (b) the vesicles filled with chlorite, (c) cracked phenocrysts of altered olivine to iddengzite. the results of chemical analysis of the scoria sub-sample are given in table 1. chemical analysis indicates that sio2, al2o3, fe2o3, cao and mgo constitute its major contents. according to the xrf results, scoria shows basic composition due to the relatively low sio2 and high fe2o3 contents. the chemical composition of the scoria was compared with that of astm type i pc (table 1). chemical analysis indicates that scoria is mainly composed of sio2 (46.55 %); while the main oxide component of pc is cao preliminary assessment of utilization 115 (60-67 %). however, scoria also has cao (9.34 %), al2o3 (16.68 %) and fe2o3 (38.56 %). the content of na2o and k2o known as ‘alkalis’ was found to be higher in scoria (3.55 %) than in pc (≤ 1 %). the xrd pattern of scoria is given in figure 4. as stated before, scoria is an amorphous volcanic rock. xrd data (figure 4) indicates that, scoria consists mainly of glassy volcanic materials (of amorphous structure), with some crystalline mineral phases, e.g. labradorite, bytownite, pigeonite, augite, forsterite, magnetite, zeolite (clinoptilolite), calcite and caladonite, and with traces of clay minerals (mainly kaolinite and chlorite). table 1. chemical composition of the studied bulk scoria sample and astm type i pc. oxides scoria (mass, %) astm type i pc [30] (mass, %) sio2 46.55 17-25 al2o3 16.68 3.0-8.0 fe2o3 12.54 0.5-6.0 cao 9.34 60-67 mgo 7.82 0.5-4.0 k2o 0.86 0.5-1.3 na2o 2.69 0.5-1.3 so3 0.05 1.0-3.0 p2o3 0.36 tio2 2.09 loi 0.67 1.22 total 99.65 figure 4. x-ray diffraction chart of the scoria bulk sample. scoria can be considered a good component for the cement industry if it contains volcanic glass and high amounts of zeolite minerals [30]. the thin section studies show that scoria is mainly composed of volcanic glass, while the xrd analysis indicates the presence of a few zeolites mainly in the form of clinoptilolite mineral, establishing that the al-jaif scoria is a good additive for the cement industry. 3.2 cement properties chemical analyses of the control specimen and scoria blended cements are given in table 2. the chemical composition of the pc indicates that the cao/sio2 ratio is greater than 2 and the percent of mgo content is smaller than 5%. these values satisfy the main composition requirements imposed by the en 197-1 [32]. due to the scoria’s chemical composition, sio2, al2o3, fe2o3 and mgo contents increase and cao content decreases with increasing the scoria content ratio in the cement mixture (figure 5). ibrahim a. al-akhaly et al 116 physical and mechanical properties of pc and scoria blended cements are given in table 3. they have nearly the same water demand ratio. this was evidenced by the results of water demand of the investigated mortar mixes. therefore the scoria’s effect on the compressive strength of mortars could be considered marginal. a literature survey shows that the chemical composition, porosity and specific surface area of cement mixtures affect water demand [34]. the setting times of the pc and scoria blended cement mortars including 2, 4, 6, 8, 10 and 12% scoria content ratio were all close. table 2. chemical composition of the control (pc) and the scoria blended cements. standard after ghosh [33] astm type i pc [30] scoria (%) pc (%) oxides 12 10 8 6 4 2 20 ± 6 17-25 23.31 22.75 22.39 21.74 21.15 20.89 20.32 sio2 6 ± 2 3.0-8.0 7.12 6.82 6.61 6.37 6.06 5.86 5.58 al2o3 3 ± 2 0.5-6.0 3.96 3.99 3.67 3.41 3.33 3.08 2.98 fe2o3 62 ± 5 60-67 55.13 56.25 57.46 58.38 59.5 60.67 61.78 cao 3.5 ± 1.5 0.5-4.0 2.01 1.96 1.91 1.86 1.80 1.77 1.71 mgo 1.5 ± 1.2 1.0-3.0 2.09 2.10 2.19 2.22 2.15 2.42 2.26 so3 minor minor 0.60 0.54 0.50 0.45 0.41 0.36 0.31 tio2 0.7 ± 0.3 0.5-1.3 0.55 0.46 0.38 0.31 0.22 0.15 0.07 na2o minor minor 0.21 0.19 0.17 0.15 0.13 0.11 0.11 p2o5 minor minor 0.12 0.11 0.10 0.09 0.09 0.08 0.07 mno 0.7 ± 0.3 0.5-1.3 0.98 1.00 1.00 1.01 1.01 1.03 1.03 k2o table 3. physical and mechanical properties of the control and the blended cements. scoria (%) pc 12 10 8 6 4 2 35 36 36 37 36 37 38 3 days compressive strength (mpa) 42 43 43 44 44 45 46 7 days 48 50 51 53 54 55 57 28 days 1.2 0.8 1.2 1.2 1.2 1 0.9 90 μm fineness 13 11.2 12 12 12 9 11 45 μm 3310 3420 3340 3330 3290 3380 3300 blaine (cm 2 /gm) 70 70 60 70 60 60 60 initial setting time (min.) 140 130 130 120 130 130 140 final 29.2 29.2 29.2 29.2 28.8 28.8 28.8 water demand (%) the scoria blended cement mortars to be used for compressive strength testing were prepared to have a w/c of 0.5 as stated in en 196-1 [29]. table 3 shows the compressive strength values after 3, 7 and 28 days curing. the results of compressive strength development for all mortar mixes containing varying amounts of scoria are given in figures 6 and 7. as expected,all mortars show an increase in strength with curing time. mortar specimens containing pc have higher compressive strengths at any curing time compared to scoria blended cement mortars. also, it is seen that the compressive strength of scoria blended cement mortars decreases as the scoria content increases for all curing times. in en 197-1 [32], early strength (3 days) values should be greater than 10 mpa and standard strength (28 days) values should be between 42.5 mpa and 62.5 mpa. a literature survey shows that the compressive strength of a mortar is decreased by scoria content, due to the reduction of clinker content in the cement mixture [10-12]. however, according to comparison of the obtained results with the en 197-1 [32], the strength requirements were satisfied by the scoria blended cements up to 12% content. preliminary assessment of utilization 117 figure 5. relationship between major oxides and the scoria content in cements. figure 6. correlation between compressive strength of the pc and the scoria blended cement at different curing times. 30 35 40 45 50 55 60 0 5 10 15 20 25 30 c o m p r e s s iv e s tr e n g th ( m p a ) curing time (day) 12% scoria 10% s 8% s 6% s 4% s 2% s 0 % (pc control) ibrahim a. al-akhaly et al 118 figure 7. effect of the scoria content on compressive strength at different curing times. 4. conclusion this paper describes the potential use of scoria from al-jaif (nw sana'a, yemen) as an additive material to manufacture blended cement. the following conclusions were obtained: the studied scoria is mainly composed of amorphous silica (volcanic glass) and there are phenocrysts of olivine, plagioclase, pyroxene and a few of zeolite (clinoptilolite). it has a mainly hyalopilitic-porphyritic texture. 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المجموعات المتتابعة الخطوات سيموا . و.مانن و ر. م.م هذا البحث يناقش أداء فحص فاعلية مجموعات العوامل المتتابعة الخطوات حيث تحتوي الخطوة األولى : خالصة سيتم مناقشة فحص فاعلية العوامل دون إفتراض معرفة مسبقة إلتجاه تأثير العامل . على عدد متساو من العوامل أخيراً سيقارن أداء هذا الفحص بأداء الفحص ذو . االت، وهو عادة ما يتم إفتراضه في مثل هذه الح)سلباً أم إيجاباً( . المراحل العدة abstract: in this paper we evaluate the performance of step-wise group screening designs in which group-factors contain an equal number of factors in the initial step. a usual assumption in group screening designs is that the directions of possible effects are known a-priori. in practice, however, this assumption is unreasonable. we shall examine step-wise group screening designs without errors in observations when this assumption is relaxed. we shall consider cancellations of effects within group-factors. the performance of step-wise group-screening designs shall then be compared with the performance of multistage group screening designs. keywords: step-wise designs, group-factors, initial step, subsequent steps, cancellation of effects, screening efficiency. 1. introduction n scientific experimentations situations arise in which a large number of potentially important factors must be examined. in such situations there is often a need, due to limited resources, for an efficient method of factor screening. one such method, introduced by watson (1961), is the two-stage group screening. this method has been generalized to more than two-stages by li (1962) and patel (1962). the notion of step-wise group screening was introduced by patel and manene (1987) basing their method on the group testing procedure introduced by sterret (1957). odhiambo and manene (1987) considered step-wise group screening designs with errors in observations. manene (1997) extended step-wise group screening designs to what is called “two-type step-wise designs”. manene i m.m. manene and r.o. simwa 102 et al. (2002) further extended the two type step-wise group screening designs to multi-type step-wise group screening designs. a basic assumption in group screening is that the direction of all suspected effects are known or can be corrected a-priori. under this assumption, factor levels can be assigned in such a way that there is no cancellation of effects within a group-factor. in practice, however, this assumption is inadequate. mauro and smith (1982) considered the performance of two-stage group screening when the assumption of known effect direction is false. odhiambo (1986) generalized this approach and assessed the performance of multistage group screening when there is a non-zero probability of cancellation of effects within a group-factor. we shall use the approach, first suggested by mauro and smith (1982) and later used by odhiambo (1986), to assess the performance of step-wise group screening designs. the performance of step-wise group screening designs with cancellation of effects shall then be compared with the performance of multi-stage group screening designs. 2. assumptions suppose that f factors are to be screened for their effect on the response. for detecting the factors having major effect, it is usually adequate to assume a first-order linear model. 1 f u o i ui u i y xβ β ε = = + +∑ (2.1) where yu is the u th response, βo is a constant common to every response, ( )1i iβ ≥ is the linear effect of the ith factor in the uth run, and εu is the u th error term. in addition to equation (2.1) assumption, we shall assume that : (i) all factors have independently the same probability p1 of having a positive effect and the same probability p2 of having a negative effect. thus, the probability of a factor being active (defective) is 1 2p p p= + (ii) all active factors have the same absolute effect, 0,∆ ≥ that is , if factor is active 0, if factor is inactive . i i i β ∆ = ⎧ ⎨ ⎩ (iii) the screening procedure is performed without experimental errors. this means that we take εu = 0 in equation (2.1). these are basically the same assumptions made by mauro and smith (1982) and odhiambo (1986). suppose that it is desired to classify f factors as active or inactive using the step-wise group screening procedure. the initial step of this procedure consists of dividing the f factors into g first order group factors each of size k (f = kg). the first order group factors are then tested for their effect and those found to be effective are set aside. in step two we start with any effective first-order groupfactor and test factors within it one by one till we find an active factor. we set aside factors that are found to be inactive, keeping the active factor separate. in step three, the remaining factors are regrouped in a group, which is then tested for its effect. the test procedure carried out in step one and in step two is repeated successively in the subsequent steps till the analysis terminates with a test on a the performance of step-wise group screening designs 103 non-effective group-factor or with a group-factor of size one. this test procedure is performed on all group-factors found to be effective in the initial step. since there are no experimental errors, it is possible to use designs with the smallest number of runs in the initial step (i.e. the number of runs required to test g group-factors is g + 1), where the one extra run is the control run. this control run may be used at every step of the step-wise design. 3. the expected number of runs suppose that there are f factors divided into g group-factors in the initial step such that each group-factor contains exactly k-factors. let x denotes the number of factors with positive effects and y denotes the number of factors with negative effects contained in a group-factor of size k in the initial step. let p1 = probability that a factor chosen at random has a positive effect. p2 = probability that a factor chosen at random has a negative effect. then ( ) ( ) ( ) ,1 2 1 21 , 0 ! ! ! ! x y k x yk p p p p x y k x y k x yp x x y y − −− − + ≤ − −= = = ⎡ ⎢ ⎢ ⎢⎣ otherwise which is the trinomial distribution with parameters k1, p1, and p2. this distribution will subsequently be denoted by ( )1 2; ; ,, .x y p p kβ at any step of the step-wise design, a group-factor is active if it contains at least one active factor. however, an active group-factor will have a significant effect (i.e. will be effective) if and only if the factor effects do not cancel completely within the group-factor. let us define p* = p ( group at the initial step is active) and θ = p ( a group factor at the initial step is effective) then ( ) ( )1 2* 1 0, 0 1 1 k p p x y p p= − = = = − − − (3.1) and ( )1 p x yθ = − = = ( ) ( ) 2 1 2 1 2 1 1 1 ; ; , , k x k p p b x y p p k = − − − − ∑ p θ∗ ∗= − (3.2) where pθ θ∗ ∗= − (3.3) m.m. manene and r.o. simwa 104 is the probability of cancellation within an active group-factor at the initial step. let m denote the number of active group-factors and n denote the number of effective group-factors in the initial step. then, ( ) ( ) , 1 0,1, ..., 0 otherwise g mmg p p m g mp m m −⎛ ⎞ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ∗ ∗− = = = ⎧ ⎪ ⎨ ⎪⎩ (3.4) and ( ) ( )1 0,1, ..., 0 otherwise g n g p n n n g nnθ θ− = = = −⎧⎛ ⎞ ⎪⎜ ⎟ ⎨⎝ ⎠ ⎪ ⎩ (3.5) thus ( ) ( )andg p gε μ ε ν θ∗= = (3.6) let ( ),p x yk ∗ be the probability that a group-factor that has been identified as effective in the initial step contains exactly x factors with positive effects and y factors with negative effects for , 0, ..., ,x y k x y= ≠ . then ( ) ( )1 2; ;, ,k x y p p p x y θ ∗ β= ( ) ( )1 2 1 2 . 1 ! 1 0, ! ! x yk k x yp p p p x y x y x yθ − − = − − + ≠ ≠ (3.7) denote by ( )( ) ( ), , 0,1, 2,..., , , 0k x yr x y k x y x y kε = ≠ ≤ + < the expected number of runs required to classify as effective or non-effective factors within a group-factor that was found to be effective at the initial step if it contains x factors with positive effects and y factors with negative effects. if x ≠ 0 and y = 0, then ( )( ) ( )( ), ,reduces tok kx y x or rε ε which is actually the same as ( )k xrε given by patel and manene (1987). thus ( )( ),0 2 , 1, 2,...,1 1k x xk x x e r x x k x x k = + + − = + + (3.8) similarly if x = 0 and y ≠ 0, ( )( )0, 2 , 1, 2, ...,1 1k y yk y y r y y k y y k ε = + + − = + + (3.9) thus, ( )( ) ( )( )0, ,0 ,k kx x x yr r =ε = ε the performance of step-wise group screening designs 105 and that ( )( ) ( )( ), , .,k kx y y xr r x yε ε ≠= however, if x = y (i.e. the number of active factors with positive effects equals the number of active factors with negative effects), then the effects cancel completely and such a group-factor is dropped from further analysis in the initial step. thus ( )( ) 0, 0,1, 2,..., 2, k e r xx xk == (3.10) lemma 3.1 ( )( ) ( )1,2 713 29 7 18 9 3 1 k r k k k k ε = + − − − (3.11) proof there are two cases to consider, namely (i) the first active factor detected has a positive effect; (ii) the first active factor detected has a negative effect. considering case (i), the probability that the first factor tested has a positive effect is 1 / k and the probability that the (l + 1)-st factor tested is the first active factor and has a positive effect is ( ) ( ) 1 1 1 11 l w k w k w k − + π − − −= on average, we shall require 1 + 1 + ( )( )1 0,2k rε − tests to complete the test procedure if the first factor tested is active and has a positive effect, and ( ) ( )( )0,21 1 1kl rlε+ + + − + tests to complete the test procedure if the (l + 1) -st factor tested is the first active factor and has a positive effect. considering case (ii), the probability that the first factor tested has a negative effect is 2 / k and the probability that the (l + 1) – st factor tested is the first active factor and has a negative effect is ( ) ( ) 1 2 1 1 l w k w k w k l − + π = − − − . on the average we shall require 1 + 1 + ( )( )1 1,1k rε − tests to complete the test procedure if the first factor tested is active and has a negative effect, and ( ) ( )1 1,1 1 1 k ll r− ++ + + ε ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ tests to complete the test procedure if the (l + 1)-st factor tested is the first active factor and has a negative effect. it follows that m.m. manene and r.o. simwa 106 ( )( ) ( )( ){ } ( )( ) ( )( ) ( )( ) ( )( ){ } 3 1 11,2 0,2 1 11 0,2 1,1 11 1 1 1 1 11 2 1 1 1 1 1 2 k l k k w l kk l k w r r k w k lk w x l r r k − − = = −− + − + ε = + + ε π∑ − −− − + + + ε + + + ε + + ( ) ( ) ( )( ){ } 3 1 1 1,1 1 1 2 1 1 1 k l w k l k w l r k w k l − = − = − + π + + + ε∑ − − − (3.12) rewriting equation (3.12) and using results in equation (3.9) and equation (3.10) and expanding the resulting expression we obtain (3.11). this completes the proof of the lemma. lemma 3.2 ( )( ) ( )1,3 47 529 9 7 60 120 2 1 k r k k k k ε = + − − − (3.13) proof. we again consider the two cases highlighted in the proof of lemma 3.1 above. considering case (i), the probability that the first factor tested has a positive effect is 1 / k and the probability that the ( )1l + st factor tested is the first active factor and has a positive effect is ( ) ( )1 3 1 1 l w k w k w k l = − + π − − − . on average we shall need 1 + 1 + ( )( )1 0,3k r−ε tests to complete the test procedure if the first factor tested is active and has a positive effect, and ( ) ( )( )1 0,31 1 k ll e r− ++ + + tests to complete the test procedure if the (l + 1)-st factor tested is the first active factor and has a positive effect. for case (ii), the probability that the first factor tested has a negative effect is 3 / k and the probability that the (l + 1) – st factor tested is the first active factor and has a negative effect is ( ) ( )1 3 3 1 .lw k w k w k l = − + π − − − on the average we shall need 1 + 1 + ( )( )1 1,2k r−ε tests to complete the test procedure if the first factor tested is active and has a negative effect; and ( ) ( )( )1 1,21 1 k ll e r− ++ + + tests to complete the rest procedure if the (l + 1 )-st factor tested is the first active factor and has a negative effect. thus the performance of step-wise group screening designs 107 ( )( ) ( )( )( ) ( )( ) ( ) ( )( )( ) ( )( )( ) 4 1 11,3 0,3 1 11 0,3 1,2 31 1 1 1 1 3 1 1 1 1 k l k k w l kk l k w r r k k w k l x l r r k − − = = −− + − + ε = + + ε + π∑ − − − + + +ε + + ε+ ( ) ( ) ( ) ( )( )( ) 4 1 1 1,2 1 3 3 1 1 1 k l w k l l k w l r k w k l − = − + = − + π + + +ε∑ − − − + (3.14) using results in equation (3.9) and lemma 3.1 in equation (3.14), expanding the resulting expression and simplifying we obtain (3.13). this completes the proof of lemma 3.2. using the same argument as that used in the proof of lemma 3.1 and lemma 3.2, we obtain ( )( ) ( )1,4 37 497 11 14 45 90 3 1 k r k k k k ε = + − − − (3.15) ( )( ) ( )2,3 77 259 9 7 180 90 2 3 1 k r k k k k ε = + − − − (3.16) ( )( ) ( )1,5 107 1663 13 35 126 252 6 1 ke r k k k k = + − − − (3.17) ( )( ) ( )2,4 28 217 8 14 and 45 45 3 1 k r k k k k ε = + − − − (3.18) let 0sr denotes the number of tests required to analyse a group-factor of size k that is known to be effective. then ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) , 0 0 1 2 , 0 0 , ; ; , , k ko s kx ykx y k k k x y x y kx y r e r p x y b x y p p k r x y k θ ∗ = = + ≤= = ε = ∑ ∑ ε + ≤∑ ∑= (3.19) denote by rs the number of tests required to analyse all the factors in the n group-factors found to be effective in the initial step. then ( )0s sr ne r= let r be the total number of runs required to analyse the f factors under investigation, then 1 2r r r= + (3.21) where 1i f r k = + is the number of runs in the initial step. using (3.6), (3.19) and (3.20) in (3.21) and taking the expected value on both sides we obtain. m.m. manene and r.o. simwa 108 ( ) ( )( ) ( )1 2,0 01 ; ; , , k k k x y x y f f e r e r b x y p p k k k = = = + + ∑ ∑ ( x + y ≤ k) (3.22) theorem 3.1 let r denote the total number of runs required to classify as effective or non-effective all the f’ factors under investigation in a step-wise group screening experiment. then ( ) ( ) ( ) ( ) ( )4 1 2 1 1 ... 1 1 1 ! k j j j j k k k jf f r p p p k k j − = − − + ε ≈ + + − +∑ ⎡ ⎢ ⎣ ] ( ) ( )( 33 21 22 2 420 13 45 184 84 1 1 1 15120 kj j k f x k j j p p k k k p p j j k k −− + + − + + − + − + + ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ ( )( )( ) ( ) )43 2 2 21 221 3 94 435 1609 660 1 kk k k k p p p −+ − + − + + − where p1 is the a-priori probability of a factor being effective with positive effect and p2 is the a-priori probability of a factor being effective with negative effect (p = p1 + p2), and k is the size of the groupfactor at the initial step. proof. from (3.22) we have ( ) ( ) ( ) ( )1 2,0 01 ; ; , , k k k x y x y f f r e r b x y p p k x y k k k = = ε = + + + ≤∑ ∑ ⎡ ⎤⎣ ⎦ since p, the apriori probability of a factor being effective is usually small, the probability of having more than four effective factors in an effective group factor is negligible. we can thus assume that an effective group-factor will not have more than four effective factors. using this assumption we have ( ) ( ) 4 1 2 1 2 1 0; ; , , 1 1j f f jk j j r j b j p p k k k j j k= ε ≈ + + + + −∑ + + ⎡ ⎛ ⎞ ⎡⎢ ⎜ ⎟⎣ ⎝ ⎠⎣ ( ) ] ( ) ( ) ] 4 4 1 2 1 2, 1 1 ; 0; , , ; ; , ,k x y x y j p p k r b x y p p k = = +β + ε∑ ∑ ⎡ ⎤⎣ ⎦ ( )4,x y x y+ ≤ ≠ (3.23) now ( ) ( ) 4 4 1 2, 1 1 ; ; , ,k x y x y r b x y p p k = = ε∑ ∑ ⎡ ⎤⎣ ⎦ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (( ) 1 2 1 21,2 2,1 1 2 1 21,3 3,1 3 3 2 1 2 1; 2; , , 2;1; , , 1; 3; , 3;1; , , 2 420 13 45 184 84 1 15120 k k k k k k r b p p k r b p p k r b p p r p p k k p p k k k p p − ε + ε +ε + ε β − = + − + − ⎡ ⎤ ⎡ ⎤= ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤ ⎣ ⎦ ⎣ ⎦ ( )( )( )( ) ) ( ) 43 2 2 2 1 221 3 94 435 1609 660 1 4, , k k k k k p p p x y x y x y k − + − + − + + − + ≤ ≠ + ≤ (3.24) the performance of step-wise group screening designs 109 using (3.12), (3.14) and noting that ( )( ) ( )( ), ,k kx y y xr rε =ε and that p = p1 + p2 . the proof of the theorem follows from using results in equation (3.24) in equation (3.23) and simplifying the resulting expression. 4. expected number of active factors detected let ai denote the number of active factors within active group-factors declared non-effective in the initial step. then ai = (m – n)kp (4.1) denote by ( ),k x yε ι ⎡ ⎤ ⎣ ⎦ the expected number of active factors declared inactive from among the k factors within a group-factor which was classified as effective in the initial step if it contains x factors with positive effects and y factors with negative effects. obviously ( ) ( ), 0, 0k kx o ye ι = ε ι =⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ (4.2) and ( ) ( ), , ,k kx y y xi x yε ι = ε ≠⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ (4.3) to obtain ( ), , , , 1, 2, ..., , ;k x y x y x y k x y kε ι ≠ = + ≤⎡ ⎤⎣ ⎦ we consider the order in which the active factors occur for given x and y and the corresponding number of undetected active factors in each case. as an illustration, consider the case when x = 1 and y = 2. then the possible orders in which active factors appear are as indicated in table i using ‘‘ for negative effect and ‘+’ for positive effect. table 1. determining i(1,2) possibilities i(1,2) + + + 2 2 0 thus ( )1,2 2 1 4 2 x 0 x 3 3 3 kε ι = + =⎡ ⎤⎣ ⎦ (4.4) similarly ( )1,3 1 ,kε ι = ⎡ ⎤ ⎣ ⎦ ( ) ( ) ( )1,4 2,3 1,5 4 14 2 , , 5 5 3 k k kε ι = ε ι = ε ι =⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎣ ⎦⎣ ⎦ ⎣ ⎦ and ( )2,4 32 15 kε ι =⎡ ⎤⎣ ⎦ (4.5) let 0sa denote the number of undetected active factors in a group-factor of size k that were found to be effective in the initial step. then ( ) ( ) ( ),0 0 , k ko s k kx y x y a p x y x y k x y∗ = = ε = ε ι + ≤ ≠∑ ∑ ⎡ ⎤⎡ ⎤⎣ ⎦ ⎣ ⎦ (4.6) m.m. manene and r.o. simwa 110 denote by as the number of undetected active factors within the n group-factors of size k found to be effective in the initial step. further let a denote the total number of undetected active factors from among the f factors under investigation. then o s sne aα = ⎡ ⎤⎣ ⎦ (4.7) and i sa a a= + (4.8) thus [ ] [ ] [ ]sa a aιε = ε + ε (4.9) using results in equations (3.3), (3.6), (4.1), (4.6) and (4.7) in equation (4.9) we obtain [ ] ( ) ( ) ( )1 2,0 0 ; ; , , k k k x y x y f a fp x y p p k x y k k θ = = ∗ε = + ε ι β + ≤∑ ∑ ⎡ ⎤⎣ ⎦ (4.10) theorem 4.1 let a denote the total number of undetected active factors in a step-wise group screening design in which an active factor has either a positive effect or a negative effect with respective probabilities p1 and p2 (p1 + p2 = p). then ( ) ( )( ) ( ) ( )( )( )3 42 21 2 1 2a 1 2 4 1 3 1 6 k kk k fp fp p p p k p p pθ − −− −∗ε = + − + − −⎡ ⎤+⎣ ⎦ (4.11) where f is the number of factors under investigation, k is the size of each group-factor at the initial step and θ* is the probability of cancellation within a group-factor of size k. proof. equation (4.10) gives [ ] ( ) ( ) ( )1 2,0a ; ; , , . k k k x y x o y f fp x y p p k x y k k θ ι = = ∗ε = + ε β + ≤∑ ∑ ⎡ ⎤⎣ ⎦ if we assume that at an initial step a group-factor contains no more than four active factors and using equations (4.4) and (4.5) and simplifying we obtain equation (4.11). this completes the proof of theorem (4.1) . let a be the total number of active factors that are detected in a step-wise group screening design when cancellation is allowed. then, ( ) ( ) ( )( ) ( ) ( )( )( )3 42 21 2 1 2 a 1 2 4 1 3 1 6 k k fp k k fp fp fp p p p k p p pθ − − ε α = − ε − −∗≈ − + − + − + − ⎧ ⎫⎡ ⎤⎨ ⎬⎣ ⎦⎩ ⎭ (4.12) where fp is the expected total number of active factors among the f factors under investigation. when either 1 0p = or * 2 0,p θ= will also be zero and ( )e a fp= . 5. comparison of relative performance of step-wise group screening and sstage group screening (s = 2,3) to measure the efficiency of a step-wise group screening design, we need to obtain the efficiency of detecting active factors and the relative testing cost. let us define the performance of step-wise group screening designs 111 ( )100 a a fp φ ε = (5.1) as a percentage measure of the efficiency of a step-wise group screening strategy for detecting the active factors. as another measure of the efficiency of a step-wise group screening procedure we define the relative testing cost, ( )100 1 r r f ε ε = + (5.2) as the ratio, expressed as a percentage, of the expected number of runs required by step-wise group screening design to the number of runs required to test the factors individually. a large value of a φ or a smaller value of er indicates better performance on the average, but both measures should be considered in assessing the performance of a group screening strategy to ensure lack of conflict. only if one group screening design has both a large a φ and a smaller re than another screening strategy can the first be said to be definitely better than the second. expressions for ( )e r and ( )ae for the step-wise group screening design allowing for cancellations are given in theorem 3.1 and equation (3.17) respectively. odhiambo (1986) gave the corresponding expressions for an s-stage group screening design as ( ) 1 1 1 1 2 1 s r s j r s r r g g fj θ θ − = − − = ε = + + π +∑ (5.3) and ( ) ( )1 1 a 1 s s r r fp θ − ∗ = ε = − ∑ (5.4) respectively, where ( )1, 2, ..., 1jg j s= − is the number of the thj order roup-factors, ( )1, 2, ..., 1r r sθ = − is the probability that an thr order group-factor is effective and rθ ∗ is the probability of cancellation in an rth order group-factor (r = 1,2, …,s -1, s ≥ 2 ). table 2 shows the relative performance of step-wise group screening designs as compared with the two-stage group screening designs under different partitions of p’s. for both designs, for a particular value of p, if 1 2 / 2p p p= = , the minimum expected number of runs are slightly fewer and the efficiency in detecting effective factors is slightly lower than when 1 2 .p p≠ the difference in the minimum expected number of runs and in the efficiency in detecting effective factors increases as the difference between 1p and 2p becomes larger. it should be noted that 2 1 .p p p= − for all partitions, step-wise group screening has fewer runs than the corresponding two-stage group-screening design. step-wise group screening designs outperforms two-stage group screening designs for values of 0.08p ≥ for all partitions of p’s. that is for 0.8p ≥ step-wise group screening designs have both fewer number of runs and are more efficient in detecting active factors than the two-stage group screening designs. from table 3 we again observe that for the three stage group screening designs, the minimum expected number of runs for a particular value of p are slightly fewer when 1 2 / 2p p p= = and increases as the difference between increases 1p and 2p . also the efficiency in detecting effective m.m. manene and r.o. simwa 112 factors increases as the difference between 1p and 2p for fixed p increases. for all the partitions, step-wise group screening designs are more efficient in detecting active factors than three-stage group screening designs. step-wise group screening designs outperforms the three-stage group screening design for 0.05p ≥ . in both tables the horizontal lines indicate the beginning of a different partition. it should be noted that tables 2 and 3 are only for illustration and are not exhaustive. table 2. relative performance of step-wise and two-stage group screening designs for f =100 and specified values of p1 and p2. step-wise group screening two stage group screening p p1 p k φa φa k1 min.e( r) φ 0.001 0.0005 0.0005 46 5.56 99.94 32 7.25 99.98 0.002 0.00 0.001 33 7.49 99.89 23 9.80 99.95 0.004 0.00 0.002 23 10.29 99.79 17 13.37 99.90 0.005 0.002 0.0025 21 11.43 99.73 15 14.79 99.88 0.008 0.00 0.004 16 14.35 99.62 12 18.33 99.81 0.009 0.0045 0.0045 16 15.20 99.53 11 19.35 99.79 0.01 0.005 0.005 15 16.01 99.50 11 20.31 99.75 0.03 0.015 0.015 8 28.12 98.92 7 33.67 99.19 0.04 0.02 0.02 7 32.73 98.92 6 38.37 98.98 0.05 0.025 0.025 6 36.89 98.50 5 42.55 98.93 0.06 0.03 0.03 6 40.76 97.92 5 46.11 98.50 0.07 0.035 0.035 5 44.16 97.76 5 49.46 98.03 0.08 0.04 0.04 5 47.53 97.64 5 52.59 97.50 0.002 0.0012 0.0008 33 7.50 99.89 23 9.80 99.95 0.004 0.0024 0.0016 23 10.29 99.80 17 13.37 99.90 0.005 0.003 0.002 21 11.43 99.74 15 14.79 99.88 0.008 0.0048 0.0032 16 14.35 99.64 12 18.33 99.81 0.009 0.0054 0.0036 16 15.21 99.55 11 19.36 99.80 0.01 0.006 0.004 15 16.02 99.52 11 20.32 99.76 0.03 0.018 0.012 8 28.13 98.96 7 33.71 99.22 0.04 0.024 0.016 7 32.73 98.67 6 38.41 99.02 0.05 0.03 0.02 6 36.90 98.56 5 42.59 98.97 0.06 0.036 0.024 6 40.76 98.22 5 46.17 98.56 the performance of step-wise group screening designs 113 0.07 0.042 0.028 5 44.17 98.00 5 49.54 98.10 0.08 0.048 0.032 5 47.53 97.73 5 52.69 97.60 0.001 0.000 0.0009 46 5.57 99.98 32 7.27 99.99 0.002 0.0002 0.0018 32 7.52 99.96 23 9.83 99.98 0.004 0.0004 0.0036 23 10.34 99.92 16 13.43 99.97 0.005 0.0005 0.0045 21 11.50 99.90 15 14.87 99.96 0.008 0.0008 0.0072 16 14.44 99.86 12 18.45 99.93 0.009 0.0009 0.0081 15 15.30 99.85 11 19.48 99.93 0.01 0.001 0.009 15 16.11 99.81 11 20.47 99.91 0.03 0.003 0.027 8 28.26 99.61 6 34.15 99.78 0.04 0.004 0.036 7 32.85 99.50 6 39.02 99.63 0.05 0.005 0.045 7 37.02 99.35 5 43.23 99.61 0.06 0.006 0.054 6 40.80 99.25 5 47.07 99.46 0.07 0.007 0.063 5 44.26 99.23 5 50.72 99.29 0.08 0.008 0.072 5 47.62 99.15 5 54.19 99.10 table 3. relative performance of step-wise and three-stage group screening designs for f =100 and specified values of p1 and p2 step-wise group screening three stage group screening p p1 p2 k min. e(r) φa k1 k2 min. e(r) φa 0.002 0.001 0.001 33 7.49 99.98 70 8 5.59 99.57 0.004 0.002 0.002 23 10.29 99.79 44 6 8.22 99.35 0.005 0.0025 0.0025 21 11.43 99.73 40 6 9.34 99.17 0.008 0.004 0.004 16 14.35 99.62 30 5 12.30 98.85 0.009 0.0045 0.0045 16 15.20 99.53 28 5 13.18 98.75 0.01 0.005 0.005 15 16.01 99.50 27 5 14.04 98.58 0.03 0.015 0.015 8 28.12 98.92 16 4 27.22 96.18 0.04 0.02 0.02 7 32.73 98.62 12 3 32.36 95.22 0.05 0.025 0.025 6 36.89 98.50 12 3 36.89 94.63 0.06 0.03 0.03 6 40.76 97.92 12 3 41.05 92.95 0.07 0.035 0.035 5 44.16 97.76 12 3 44.90 91.24 0.08 0.04 0.04 5 47.53 97.64 12 3 48.47 89.55 m.m. manene and r.o. simwa 114 0.002 0.0012 0.0008 33 7.50 99.89 70 8 5.60 99.59 0.004 0.0024 0.0016 23 10.29 99.80 44 6 8.22 99.37 0.005 0.003 0.002 21 11.43 99.74 40 6 9.34 99.21 0.008 0.0048 0.0032 16 14.35 99.64 30 5 12.31 98.90 0.009 0.0054 0.0036 16 15.21 99.55 28 5 13.19 98.80 0.01 0.006 0.004 15 16.02 99.52 27 5 14.05 98.64 0.02 0.012 0.008 10 22.76 99.22 18 4 21.29 97.75 0.03 0.018 0.012 8 28.13 98.96 16 4 27.27 96.34 0.04 0.024 0.016 7 32.73 98.67 12 3 32.41 96.38 0.05 0.03 0.02 6 36.90 98.56 12 3 36.97 94.85 0.06 0.036 0.024 6 40.76 98.00 11 3 41.15 93.97 0.07 0.042 0.028 5 44.17 98.22 11 3 45.03 92.45 0.08 0.048 0.032 5 47.53 97.73 11 3 48.64 89.99 0.002 0.0002 0.0018 32 7.52 99.96 68 8 5.63 99.85 0.004 0.0004 0.0036 23 10.34 99.92 43 6 8.30 99.77 0.005 0.0005 0.0045 21 11.50 99.90 39 6 9.43 99.72 0.008 0.0008 0.0072 16 14.44 99.86 29 5 12.45 99.61 0.009 0.0009 0.0081 15 15.30 99.85 27 5 13.36 99.58 0.01 0.001 0.009 15 16.11 99.81 26 5 14.24 99.52 0.02 0.002 0.018 10 22.89 99.71 17 4 21.69 99.23 0.03 0.003 0.027 8 28.26 99.61 15 4 27.93 98.76 0.04 0.004 0.036 7 32.85 99.50 11 3 33.23 98.82 0.05 0.005 0.045 7 37.02 99.35 10 3 38.06 98.52 0.06 0.006 0.054 6 40.80 99.25 10 3 42.54 98.03 0.07 0.007 0.063 5 44.26 99.23 10 3 46.77 97.52 0.08 0.008 0.072 5 47.62 99.15 9 3 50.74 97.35 6. references li, c.h. 1962. a sequential method for screening experimental variables. jour. amer statist. assoc., 57: 455-477. manene, m.m. 1997. on two-type step-wise group screening designs. proceedings of the fifth scientific conference of the east, central and southern africa network of i.b.s., pp. 57-62 manene, m.m.; rotich, a.m. and simwa r.o. 2002. on multi-type step-wise group screening designs. bulletin of the allahabad mathematical society, 17: 59-78. the performance of step-wise group screening designs 115 mauro, c.a. and smith, d.e. 1982. the performance of two-stage group screening in factor screening experiments. technom., 24: 325-330. odhiambo, j.w. 1986. the performance of multistage group screening designs. commun. statist. theor. meth., 15 (8): 2467-2481. odhiambo j.w. and manene m.m. 1987. step-wise group screening designs with errors in observations. commun. statist. theor. meth. 16(10): 3095-3115. patel, m.s. 1962. group screening with more than two stages. technom, 4: 209-217. patel, m.s. and manene, m.m. 1987. step-wise group screening with equal prior probabilities and no errors in observations. commun. statist. simula. and computa, 16(3): 817-833. sterret, a. 1957. on the detection of defective members of large populations. annals of math. statist., 28: 1033-1036. watson, g.s. 1961. a study of the group screening method. technom, 3: 371-388. received 28 august 2004 accepted 5 october 2005 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 115-120 © 2003 sultan qaboos university synthesis and crystal structure of overcrowded non-photochromic organometallic fulgide shar saad al-shihry department of chemistry, college of science, king faisal university, p.o.box 1759, saudi arabia, email: sshihry@kfu.edu.sa. نية لمركب فولجايد عضو معدني مزدحم فراغياً غير فوتوكروميتحضير ودراسة األشعة السي شار سعد الشهري عند . فقط، وذلك عن طريق تكاثف شتوبe والمزدحم فراغياً على هيئة المشابه 7تم الحصول على مركب الفولجايد : خالصة وتم . 3ثنائي هيدرونفثالين -أ-8،1تق يحدث تحلق إلى المش ال) nm 366( األشعة فوق البنفسجية باستخدام 7تشعيع المركب . بواسطة تحليل األشعة السينية للبلورات7 فولجايد التثبت من تركيب abstract: pure e-isomer overcrowded organometallic fulgide 1 was obtained by using successive stobbe condensations between ketones and succinate diester. upon irradiation with uv light at (366 nm) it did not cyclise photochemically to the 1,8a-dihydronaphthalene derivative (1,8adhn) 8. the structure of 7 was confirmed by x-ray crystallographic analysis. keywords: fulgide, stobbe condensation, organometallic, crystal structure. 1. introduction f ulgides with aryl ring undergo ring-closure photochemically to give highly coloured tricyclic dihydronaphthalene derivatives (heller 1978). it was found that the preferred isomer was the e-isomer in sterically-hindered fulgide systems (hart and heller 1972; mccabe et al. 1993; liang et al. 2001). mccabe et al. (1993) synthesized the first organometallic fulgide 1, which was obtained as e-isomer 1. irradiation of 1 underwent e/z isomerization to z-isomer 2 rather than ring-closure, despite the introduction of donating groups on the ferrocenyl moiety scheme 1. o o o fe o o o fe1 2 uv scheme 1: e/z isomerization of fulgide 1. in the present work diphenylidene was introduced to the system to investigate whether or not photocyclization would occur, according to electrocyclization reaction, in agreement with woodward-hofmann rules (yokoyama 2000). 115 shar saad al-shihry 2. experimental general: melting points were recorded on a gallenkamp melting point apparatus and were uncorrected. nmr spectra were obtained in cdcl3 on a jeol 400 mhz with tms as internal reference; chemical shifts were expressed in δ (ppm). irradiation of the prepared fulgide in toluene at 366 nm for 48 hrs was carried out, using uv lamp (uv gl-58, 254/366 nml lamp, 50/60 hz), while uv–visible double beam spectrophotometer (shimadzu uv-1601pc) was used to follow up the irradiation effect. dimethyl (diphenylmethylene)succinate 4: a mixture of benzophenone (18.2 g, 0.1 moles), dimethyl succinate (17.5 g, 0.12 moles) and potassium t-butoxide (12 g, 0.1 moles) in toluene (200 ml) was stirred for 6 hours. work-up produced the half ester, which was esterified to give the diester as yellow crystals (17 g, 55% yield) m.p. 78-79ºc. 1h-nmr: 3.46 (2h, s, ch2 proton), 3.45 (3h, s, ch3o), 3.70 (3h, s, ch3o), 7.10-7.40 (10h, m, aromatic proton). ferrocenylethylidene(diphenylidene)succinic anhydride 7: stobbe condensation on an equimolar basis of dimethyl (diphenylmethylidene) succinate (10 g, 0.03 moles) and ferrocene (7.5 g, 0.03 moles) in toluene (200 ml) in the presence of potassium t-butoxide, followed by hydrolysis of the half ester gave the diacid, which cyclised with acetyl chloride. the solvent and acetyl chloride were removed and the residue was dissolved in dichloromethane and chromatographed on silica gel to give the fulgide 7 as black crystals from dichloromethane and petroleum ether (4.5 g, 28%). m. p. 234-235ºc 1h-nmr: 2.65 (3h, s, ch3), 4.34 (5h, s, cp’ and 1h, s, cp), 4.66 (3h, s, cp), 3.70 (3h, s, ch3o), 7.13-7.46 (10h, m, aromatic proton).found: c, 73.07; h, 4.39%. c29h22o3fe requires: c, 73.42; h, 4.64%. m/z, 474. 2.1 x-ray analysis a dark purple crystal with dimensions 0.483 x 0.260 x 0.188mm3 was placed and optically centered on the bruker smart ccd system at –80°c. the initial unit cell was indexed using a least-squares analysis of a random set of reflections collected from three series of 0.3° wide ω scans (25 frames/series) that were well distributed in reciprocal space. data frames were collected [mokα] with 0.3° wide ω-scans, 30 seconds/frame, 606 frames per series. five complete series were collected, including an additional partial, first 160 frames, run of the first series for decay purposes, with a crystal to detector distance of 4.94cm, thus providing a complete sphere of data to 2θmax=55°. a total of 30967 reflections was collected and corrected for lorentz and polarization effects and absorption using blessing’s method as incorporated into the program sadabs (blessing 1995 and sheldrick 1996) with 5041 unique [r(int)=0.0273]. 3. results and discussion stobbe condensation of benzophenone and dimethyl succinate in the presence of potassium tbutoxide in toluene and subsequent methylation of the condensation product gave dimethyl (diphenylmethylene)succinate 4. a second stobbe condensation using acetyl ferrocene yielded the half-ester, which was hydrolysed and cyclised using acetyl chloride, to afford solely fulgide 7 as dark purple crystals in 30% yield (scheme 2). irradiation of fulgide 7 reveals no changes in wavelengths of absorption bands located at λmax 392 and 544 nm ε 11300, 3940 dm3. ml-1. cm-1 respectively. this may indicate that there is neither e/z isomerisation, nor electrocyclic ring closure taking place in this specific fulgide, as normally seen in simple fulgides (yokoyama 2000) (scheme 3): the structure and stereochemistry of fulgide 7 was confirmed by x-ray crystallographic analysis which is shown in figure 1. of particular interest in this fulgide are the following features: • the phenyl rings and the ferrocenyl moiety are rotated from the plane of the anhydride ring. • the angle ct2-fe-ct1 is 177.46(8) and is less than the expected by 2.54°. 116 synthesis and crystal structure • the single bond c11-c12 (1.509 å) is longer than the single bond c10-c11 (1.457 å), while the single bonds c17-c18 and c17-c24 have almost the same length 1.489 and 1.484 å, respectively. selected bond lengths and angles are given in table 1. ph ph o ome ome o o oh ome o o ph ph ome ome o o ph ph fe me o or1 or o o ph ph fe ph ph 2)iii fe 7 o o o + i ii 3 4 5 r=h,r 1=me 6 r=h,r 1=h 1)i iv scheme 2 : reagents: i=t-butok, toluene, ii=meoh, h+, iii=koh, iv=ch3cocl. ph fe 7 o o o o ph o h o fe ph fe o o o x o ph o o fe h 8 scheme 3: irradiation of 7 shows neither e/z isomerization, nor ring closure. 117 shar saad al-shihry figure 1. the molecular structure of 7 with the atom-numbering scheme. hydrogen atoms are drawn as circles of arbitrary small radii for clarity. table 1 : selected bond lengths (å) and bond angles (º) for fulgide 7. _______________________________________________________________________________ fe(1)-ct2 1.647(2) fe(1)-ct1 1.661(2) c(10)-c(11) 1.457(2) c(11)-c(13) 1.371(2) c(11)-c(12) 1.509(2) c(13)-c(16) 1.474(2) c(16)-c(17) 1.367(2) ct2-fe(1)-ct1 177.46(8) c(9)-c(10)-c(11) 128.40(15) c(13)-c(11)-c(10) 123.08(14) c(13)-c(11)-c(12) 120.29(15) c(10)-c(11)-c(12) 116.63(14) c(11)-c(13)-c(16) 131.62(14) c(16)-c(13)-c(14) 105.84(13) c(17)-c(16)-c(13) 130.84(14) c(17)-c(16)-c(15) 121.73(14) c(16)-c(17)-c(24) 121.91(13) c(16)-c(17)-c(18) 122.11(14) structural determination and refinement: all crystallographic calculations were performed on a personal computer (pc) with dual pentium 450mhz processors and 256mb of extended memory. the shelxtl (sheldrick 1994) program package was now implemented, xprep, to determine the probable space group and set up the initial files. system symmetry and systematic absences 118 synthesis and crystal structure indicated the non-standard centrosymmetric space group p21/n (no.14). the structure was determined by direct methods with the successful location of nearly all atoms using the program xs (sheldrick 1990). the structure was refined with xl (sheldrick 1993). after the initial refinement difference-fourier cycle, additional atoms were located and input. after several of these refinement difference-fourier cycles, all of the atoms were refined isotropically, then anisotropically. hydrogen atoms were located directly from difference-fourier maps and input; these atoms were freely refined. centroids of the cp rings were calculated. the final structure was refined to convergence [∆/σ ≤ 0.001] with r(f)=3.91%, wr( )=9.52%, gof=1.060 for all 5041 unique reflections [r(f)=3.30%, wr( )=8.87% for those 4386 data with > 4σ( )]. a final difference-fourier map was featureless indicating the structure is therefore both correct and complete. 2f 2f of of the function minimized during the full-matrix least-squares refinement was σw( f f ) where w=1/[σ 2 o 2 c 2( ) +(0.0517*p)2of 2 +1.0474*p] and p=(max( ,0)+2* )/3. an empirical correction for extinction was attempted but found to be negative and therefore not applied. 2 of 2 cf crystal data for fulgide 7 empirical formula: c29 h22 fe o3 formula weight 474.32 temperature 193(2) k wavelength 0.71073 å crystal system monoclinic space group p2(1)/n unit cell dimensions a = 9.6446(10) å α= 90°. b = 12.0427(12) å β= 90.183(2)°. c = 19.1244(19) å γ = 90°. volume 2221.2(4) å z 4 density (calculated) 1.418 mg/m3 absorption coefficient 0.709 mm-1 f(000) 984 crystal size 0.13 x 0.210 x 0.424 mm3 theta range for data collection 2.00 to 27.50°. index ranges -12<=h<=12, -15<=k<=15, -24<=l<=24 reflections collected 30967 independent reflections 5041 [r(int) = 0.0273] completeness to theta = 27.50° 99.0 % absorption correction sadabs max. and min. transmission 1.000000 and 0.895124 refinement method full-matrix least-squares on f2 data / restraints / parameters 5041 / 6 / 392 goodness-of-fit on f2 1.060 final r indices [i>2sigma(i)] r1 = 0.0330, wr2 = 0.0887 [4386 data] r indices (all data) r1 = 0.0391, wr2 = 0.0952 largest diff. peak and hole 0.351 and -0.248 e. 4. acknowledgements the author would like to thank dr. j. fitteger, x-ray crystallographic facility, chemistry and biochemistry college park, university of maryland, usa, for carrying out the x-ray performance. 119 shar saad al-shihry references blessing, r.h. 1995. an empirical correction for absorption anisotropy. acta crystallographica. a51: 33-38. hart, r.j. and heller, h.g. 1972. overcrowded molecules. part vii. thermal and photochemical reactions of photochromic (e)and (z)benzylidene(diphenylmethylene)succinic anhydrides and imides. journal of the chemical society, perkin transactions, 1: 1321-1324. heller, h.g. 1978. the development of photochromic compounds for use in optical information stores. chemistry and industry, 18 march. 193-196. liang, y., dvornikov, a.s. and rentzepis, p.m. 2001. photochemistry of photochromic 2-indolylfulgides with substituents at the 1’-position of the indolylmethylene moiety. journal of photochemistry and photobiology a: chemistry, 146( 1): 83-93 (11). mccabe, r.w., parry, d.e. and saberi, s.p. 1993. organometallic fulgides. part 1. synthesis and photochemistry of ferrocenyl fulgides [ferrocenylethylidene (isopropylidene)succinic anhydrides]. journal of the chemical society, perkin transactions, 1: 1023-1029. sheldrick, g.m., 1996. sadabs ‘siemens area detector absorption correction’ university of götِtingen: göِttingen, germany. sheldrick, g.m., 1994. shelxtl/pc. version 5.03. siemens analytical x-ray instruments inc., madison, wisconsin, usa. sheldrick, g.m., 1993. shelxl93 program for the refinement of crystal structures. university of götِtingen, germany. sheldrick, g.m., 1990. phase annealing in shelx-90: direct methods for larger structures. acta crystallographica. a46: 467-473. yokoyama, y., 2000. fulgides for memories and switches. chem. rev. 100(5): 1717-1739. received 29 april 2003 accepted 24 june 2003 120 shar saad al-shihry department of chemistry, college of science, king faisal university, p.o.box 1759, saudi arabia, email: sshihry@kfu.edu.sa. 2. experimental dimethyl (diphenylmethylene)succinate 4: a mixture of benzophenone (18.2 g, 0.1 moles), dimethyl succinate (17.5 g, 0.12 moles) and potassium t-butoxide (12 g, 0.1 moles) in toluene (200 ml) was stirred for 6 hours. work-up produced the half es 2.1 x-ray analysis stobbe condensation of benzophenone and dimethyl succinate in the presence of potassium t-butoxide in toluene and subsequent methylation of the condensation product gave dimethyl (diphenylmethylene)succinate 4. a second stobbe condensation using acetyl scheme 2 : reagents: i=t-butok, toluene, ii=meoh, h+, iii=koh, iv=ch3cocl. microsoft word stat040225-arangeq-1.doc squ journal for science, 9 (2004) 53-66 © 2004 sultan qaboos university 53 recursive estimation of a discretetime lotka-volterra predator-prey model lakhdar aggoun department of mathematics and statistics, sultan qaboos university, p. o. box 36, alkhod 123, sultanate of oman, email: laggoun@squ.edu.om. فلتره للصائدة والمصطادة-التقدير الشرطي المتكرر لنموذج لوتكه األخضر عقون هذا المقال يعالج مسألة مهمة في اإلحصاء البيني وهي مسألة حساب التعداد الحيواني لنـوعين مـن : خالصة طلق سراحها من كل نوعية تؤخذ عينة عشوائية وتميز بإشارة خاصة ثم ي . الحيوانات وهي الصائدة و المصطادة وبعد فترة تؤخذ عينة عشوائية من القطيعين ويحصي منها األفراد المميزين باإلشارة الخاصة . داخل بقية القطيع ومن هذه المعلومات تستعمل طرق القياس لتقدير التوزيع الشرطي المتكـرر لمجموعـة الحيوانـات الصـائدة .والمصطادة abstract: in this paper, using hidden markov models, we estimate the number of individuals in a two-species (predator-prey) animal population using partial information provided by the so-called capture-recapture technique. random samples of individuals are captured, tagged in some way and released. after some time other random samples are taken and the marked individuals are observed. using this information, we estimate (recursively) the sizes of the two populations. also, using the expectation maximization (em) algorithm, the parameters of the model are updated. keywords: hidden markov models, predator-prey, capture-recapture, em algorithm. ams subject classification: 60j27, 93e11. 1. introduction ne of the first models to incorporate interactions between predators and preys was proposed in 1925 by the american biophysicist alfred lotka and the italian mathematician vito volterra . vito volterra (1860-1940) was a famous italian mathematician who retired from a distinguished career in pure mathematics in the early 1920s. his son-in-law, humberto d’ancona, was a biologist who studied the populations of various species of fish in the adriatic. volterra developed a series of models for interactions of two or more species. o lakhdar aggoun 54 alfred j. lotka (1880-1949) was an american mathematical biologist (and later actuary) who formulated many of the same models as volterra, independently and at about the same time. his primary example of a predator-prey system comprised a plant population and an herbivorous animal dependent on that plant for food. here we consider a discrete-time stochastic version of the lotka-volterra model. hidden markov models (elliott et al. 1995) have been used extensively in many areas of science and technology. in this paper we are extending the use of this powerful tools (see aggoun and elliott 1998 for a single species model) to estimate the hidden number of individuals in a multi-species animal population using partial information provided by the so-called capture-recapture technique (see seber 1982, for instance). two random samples of individuals one from the predator population and one from the prey population are captured, tagged or marked in some way, and then released. after allowing time for the marked and unmarked to mix sufficiently, two second simple random samples from both populations are taken and the marked ones are observed. at epoch write z for the prey population size, z for the number of marked and released preys, 1 k k zz == ∑ for the total number of captured and marked preys up to time k , r for the sample size, z for the number of available marked individuals for sampling and zy for the number of captured (or recaptured) marked individuals. similarly write x for the predator population size, x for the number of marked and released predators, 1 k k xx == ∑ for the total number of captured and marked predators up to time k , f for the sample size, x for the number of available marked predators for sampling and xy for the number of captured (or recaptured) marked predators. 2. model assumptions and recursive estimation all random variables are defined initially on a probability space ( )f pω, , . all the filtrations defined here are assumed to be complete. write ( )z xkg z z y r x x y f kσ= , , , , , , , ≤ , and ( , ) z x ky y y kσ= , ≤ . kx and kz represent the number of predators and preys, respectively, that are alive at time period k, then a (discrete time) lotka-volterra type model is: 1 1 1k k k k k kx x az x bx vσ+ += + − + (1) 1 2 1k k k k k kz z cz dz x wσ+ += + − + , where the parameters are defined by: a is the efficiency of turning predated preys into predators. b is the natural death rate of predators in the absence of food (preys), c is the natural growth rate of preys in the absence of predation, d is the death rate per encounter of preys due to predation, v and w are sequences of independent random variables with some (either discrete or continuous with finite supports) densities kφ and kϑ respectively and 1σ , 2σ are some positive real numbers. the random recursive estimation of a discrete-time 55 variables v and w indicate other sources of variations in the populations like death caused by old age, diseases, births etc. it is assumed here that kx and kz are random variables with binomial distributions with parameters ( )xk px , and ( )zk pz , respectively. the observed random variables z xk ky y, are assumed to have joint distribution: 1( ) x z k k k k k k k k kp y m y n g z z r x x f−= , = | , , , , , , ( ) (1 ) ( ) (1 )k kk k f m r nm nk k k k k k k k f r x x z z m n x x z z − −  = − −      (5) let 0 1λ = . for 1≥ and for suitable density functions χ , v write x zλ λ λ= , where 1 ( ) 1 (1 ) ( ) (1 ) ( ) 2 x xxx y y fx x x xf x x x x p p v x x σ χ λ φ − +− − − + = − − (6) 2 ( ) 1 (1 ) ( ) (1 ) ( ) 2 z zzz y y rz z z zr z v z z z p p w z z σ λ ϑ − +− − − + = − − (7) and 0 k k λ=λ =∏ . lemma 1. the process kλ is a g -martingale. proof. 1 1 1[ ] [ ] x z k k k k k ke g e gλ λ− − −λ | = λ | , so we must show that 1[ ] 1 x z k k ke gλ λ −| = . however using repeated conditioning it is enough to show that 1[ ] 1 z k ke gλ −| = , say. 2 1 1 2 1 1 2 ( ) 1 [ ] [ ( ) (1 ) ( ) 2 (1 ) ] ( )1 [ (1 ) [( ) ( )2 (1 ) ] ] ( )1 [ ( )2 z z k k k k k kk k z kk k k k k z k k k k y y rz k k k k k k r z k k k k zz z z kz zz yk k kz z zr z k k k y rk k k k k k k zk k zr z k k v z z z e g e w z z p p g v z z e p p e w z z g z z r g z v z e p w σ λ ϑ σ ϑ σ ϑ − − − + − +− − − +− − + − − − − + | = − × − | = − × − | , , , | = 1 0 (1 ) ] k kk k r z kz z k m r p g m − + − =   − |    ∑ lakhdar aggoun 56 2 1 2 1 0 2 1 2 1 2 1 2 ( )1 [ (1 ) ] ( )2 ( )1 [ ] ( )2 ( ) [ ] ( ) ( ) ( ) ( ) 1 ( ) kk k k k k zzk k z z z kz k k z k k k kz ik k k k k k k k k k k k k v z e p p g w v z ze g w i v z w e g w v z w w dv v u du w σ ϑ σ ϑ σ σ ϑ σ σ ϑ ϑ − +− − − = − − − = − |   = |    + = | + = = = ∑ ∫ ∫ a new probability measure q can be defined by setting | k k dq e g dp   = λ   . the point here is that: lemma 2. under the new probability measure q , kx , kx , x ky kz , kz and z ky are sequences of independent random variables which are independent of each other. further, kx has density kχ , kx has distribution 1 ( ) 2k bin x , , x ky has distribution 1 ( ) 2k bin f , , kz has density kv , kz has distribution 1 ( ) 2k bin z , and z ky has distribution 1 ( ) 2k bin r , . proof. we shall check the claim for the three processes kz , kz and z ky . for any integrable real-valued functions f , g and h and using a version of bayes’ theorem (see elliott et al. 1995) we can write: 1 1 1 1 2 1 [ ( ) ( ) ( ) ] [ ( ) ( ) ( ) ] [ ] [ ( ) ( ) ( ) ] ( ) 1 [ ( ) ( ) ( ) (1 ) ( ) 2 1[ ( ) ( ) (1 ) ] 2 kk k k z z k k k k z z k k k k k q k k k k k k z k k k k k zzz k k n k k k z zn k k y y rk kz k k k kk r k k e f z g z h y g e f z g z h y g e g e f z g z h y g v z e f z g z h y p p w z ze h y g z z r g z z λ σ ϑ − − − − − +− − − − λ | | = λ | = | = − − | , , , | 1 2 1 0 ] ( ) 1 [ ( ) ( ) ( ) (1 ) ( ) 2 1[ ( )( ) (1 ) ( ) (1 ) ] ] 2 kk k k k k k k k zzz k k n k k k z zn k k r km r m rk k k km m kr m k k k k v z e f z g z h y p p w rz z z zh m g mz z z z σ ϑ − − +− − + −− − = = −   − − |     ∑ recursive estimation of a discrete-time 57 2 1 0 2 1 1 1 1 ( ) 1 [ ( ) ( ) ( ) (1 ) ( ) 2 1[ ( ) ] ] 2 ( ) 1 [ ( )] [ ( ) ( ) (1 ) ] ( ) 2 [ ( )] [ ( )] [ ( kk k k k k kk k k zzz k k n k k k z zn k k r k kr m zzz k k n q k k k z z kn k k z q k q k k k k v z e f z g z h y p p w r h m g m v z e h y e f z g z p p g w e h y e g z e f z cz dz σ ϑ σ ϑ − +− − = − +− − − − − = −   × |     = − | = + − ∑ 2 2 1 1 1 2 1 1 1 1 2 2 1 1 1 2 ) ( ) ] ( ) [ ( )] [ ( )] ( ) ( ) [ ( )] [ ( )] ( ) ( ) [ ( )] [ ( )] [ ( )], k k k k k k k k k k k z q k q k k k k k k k k k k z q k q k k z q k q k q k x w v z cz dz x w g w e h y e g z f z cz dz x w v z cz dz x w dw e h y e g z f u v u du e h y e g z e f z σ σ σ ϑ σ σ σ − − − − − − − − − − + + − + × | = × + − + × + − + = = ∫ ∫ where k r m        = ( ) ! ! ! k k r m r m− . that is, under q the three processes are independent sequences of random variables with the desired distributions. using this fact we derive a recursive equation for the unnormalized conditional distribution of kz and kx given ky . for any measurable test function f consider: 1 1 [ ( ) ] [ ( ) ] [ ] q k k k k k k k q k k e f x z y e f x z y e y − − , λ | , | = . λ | (8) the denominator of (8) being a normalizing factor we focus only on the expectation under q in the numerator. write 1[ ( ) ] ( ) ( )q k k k k ke f x z y f x z q x z dxdz −, λ | = , , .∫ (9) theorem 1. the unnormalized conditional joint probability density function of the populations’ sizes given by the dynamics in (1) and (2) follows the recursion: lakhdar aggoun 58 1( ) ( ) ( ) ( )k k k kq x z a x z b u v x z q u v dudv−, = , , , , ,∫ (10) where 0 01 2 2 ( ) (1 ) (1 ) k k k k k k r f x z i ji jz xk k k z z x x j i z xa x z p p p p i jσ σ + − − = =    , = − −      ∑∑ ( ) (1 ) ( ) (1 ) x x z z k k k k k ky f y y r yj j i i x x z z − −× − − (12) 2 1 ( ) ( ) ( )k k k z v cv dvu x u avu bu b u v x z ϑ φ σ σ − − + − − + , , , = (13) (note we take 00 1= .) proof. in view of lemma 2 the left hand side of (9) is: 1 1 1 0 0 1 1 1 1 2 2 [ ( ) ] 1 1 2 2 2 [ (1 ) (1 ) ( )( ) (1 ) ( ) (1 ) ( ) ( ) ( ) ( k kk k k k k k k k x x z z k k k k k k q k k k k k r fz x x z x z i ji jz xk k q z z x x j i y f y y r y k k k k k k k k e f x z y z xe p p p p i j j j i if x z x x z z z z cz dz x v z v z x x λ ϑ σ σ φ − − − + + + − − = = − − − − − − = , λ | =    × − −      × , − − − − + − × ∑∑ ∫ 1 1 1 1 1 1 1 1 0 01 2 ) ( ) ( ) (1 ) (1 ) ] 2 (1 ) (1 ) ( )( ) (1 ) ( ) (1 ) ( k k k k k k k k x x z z k k k k k k k k k k k k i ji jz x z z x x k k r f x z i ji jz xk k z z x x j i y f y y r y k az x bx x x x p p p p dxdz y z x p p p p i j j j i if x z x x z z z v cv d σ σ χ σ σ ϑ − − − − − − − − + − − = = − − − + × − − λ |    = − −      × , − − − − + ∑∑ ∫ ∫ 1 2 1 ) ( ) ( )k k vu x u avu bu q u v dudvdxdzφ σ σ − − − + , comparing this last expression with the right hand side of (9) gives the result. recursive estimation of a discrete-time 59 remark 1. the normalized conditional joint density function of ( )k kx z, is simply ( ) ( ) k k q x z q u v dudv , ,∫ . the initial (normalized) probability density of 0 0( )x z, , prior to sampling, is 0 ( )π . , so 0 0( ) ( )q x z x zπ, = , . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 01 2 1 1 0 2 1 2 ( ) (1 ) (1 ) ( ) (1 ) ( ) (1 ) ( ) ( ) ( ) . x x z z r f x z jii j xz z z x x j i y f y y r y xzq x z p p p p i j j j i i x x z z z v cv dvu x u avu bu u v dudv σ σ ϑ φ π σ σ + −− = = − −    , = − −      × − − − − + − − + . ∑∑ ∫ and further estimates follow from (10). if the distribution of 0 0( )x z, is a delta function concentrated at ( )a b, say 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 01 2 1 1 2 1 2 ( ) (1 ) (1 ) ( ) (1 ) ( ) (1 ) ( ) ( ). x x z z r f x z jii j xz z z x x j i y f y y r y xzq x z p p p p i j j j i i x x z z z b cb dba x a aba ba σ σ ϑ φ σ σ + −− = = − −    , = − −      × − − − − + − − + ∑∑ 3. parameter revision here we shall assume, for simplicity, that the random variables v and w in our model are standard normal (means 0 and standard deviations 1). the em algorithm, (baum and petrie 1966, dempster et al. 1977) is a widely used iterative numerical method for computing maximum likelihood parameter estimates of partially observed models such as linear gaussian state space models. for such models, direct computation of the mle is difficult. the em algorithm has the appealing property that successive iterations yield parameter estimates with nondecreasing values of the likelihood function. suppose that we have observations 1 ky … y, , available, where k is a fixed positive integer. let { }pθ θ, ∈θ be a family of probability measures on ( )fω, , all absolutely continuous with respect to a fixed probability measure 0p . the log-likelihood function for computing an estimate of the parameter θ based on the information available in ky is 0 0 ( ) logk k dp l e y dp θθ            = | , and the maximum likelihood estimate (mle) is defined by ˆ argmax ( )klθθ θ∈θ∈ . lakhdar aggoun 60 let 0θ̂ be the initial parameter estimate. the em algorithm generates a sequence of parameter estimates { }jθ , 1j ≥ , as follows. each iteration of the algorithm consists of two steps: step 1. (e-step). set ˆ jθ θ= and compute ( )q θ θ, , where ( ) log k dp q e y dp θ θ θ θ θ            , = | . step 2. (m-step). find 1ˆ argmax ( )jj qθ θ θθ ∈θ+ ∈ , . using jensen’s inequality it can be shown (see theorem 1 in dempster et al. 1977) that the sequence of model estimates ˆ{ jθ , 1}j ≥ from the em algorithm are such that the sequence of likelihoods ˆ{ ( )}k jl θ , 1j ≥ is monotonically increasing with equality if and only if 1ˆ ˆj jθ θ+ = . sufficient conditions for convergence of the em algorithm are given in wu (1983). we briefly summarize them here: 1. the parameter space θ is a subset of some finite dimensional euclidean space rr . 2. 0ˆ{ ( ) ( )}k kl lθ θ θ∈θ: ≥ is compact for any 0ˆ( )kl θ > −∞ 3. kl is continuous in θ and differentiable in the interior of θ . (as a consequence of (1), (2) and (iii), clearly ˆ( )k jl θ is bounded from above). 4. the function ˆ( )jq θ θ, is continuous in both θ and ˆ jθ . then by theorem 2 in wu (1983), the limit of the sequence em estimates ˆ{ }jθ has a stationary point θ of kl . also ˆ{ ( )}k jl θ converges monotonically to ( )t tll θ= for some stationary point θ . to make sure that tl is a maximum value of the likelihood, it is necessary to try different initial values 0θ̂ . the model in (1) and (2) is determined by the parameters a , b , c and d which need to be updated as new information is obtained. these parameters are estimated using the expectation maximization (em) algorithm. maximum likelihood estimation of the parameters via the em algorithm requires computation of the filtered estimates of quantities such as ( ) 2 2 1 11 ki kt x z− −== ∑ , ( ) 2 1 11 kii kt x z− −== ∑ , ( ) 1 11 kiii kt x x z− −== ∑ , ( ) 2 11 kiv kt x −== ∑ , ( ) 11 kv kt x x −== ∑ , ( ) 2 1 11 ki ks x z− −== ∑ , recursive estimation of a discrete-time 61 ( ) 1 11 kii ks x z z− −== ,∑ ( ) 2 1 kiii ks z== ,∑ ( ) 11 kiv ks z z −== ∑ , 1 k k ku x== ∑ and 1 k k kv z== .∑ for m i … v= , , write 1 ( ) ( ) 1 [ ( ) ] [ ( ) ] [ ] m q k k k k km k k k k q k k e t i x dx z dz y e t i x dx z dz y e y − − λ ∈ , ∈ | ∈ , ∈ | = λ | , ( ) 1 ( )( ) [ ( ) ]m mk q k k k k kx z e t i x dx z dz yβ −, = λ ∈ , ∈ | , 1 ( ) ( ) ( )( ) 1 [ ] ( ) [ ] [ ] ( ) m m mq k k km k k k k q k k k e t y x z dxdz e t y te y q x z dxdz β− − λ | , | = = λ | , ∫ ∫ . for n i … iv= , , . 1 ( ) ( ) 1 [ ( ) ] [ ( ) ] [ ] n q k k k k kn k k k k q k k e s i x dx z dz y e s i x dx z dz y e y − − λ ∈ , ∈ | ∈ , ∈ | = λ | , ( ) 1 ( )( ) [ ( ) ]n nk q k k k k kx z e s i x dx z dz yη −, = λ ∈ , ∈ | , 1 ( ) ( ) ( )( ) 1 [ ] ( ) [ ] [ ] ( ) n n nq k k kn k k k k q k k k e s y x z dxdz e s y se y q x z dxdz η− − λ | , | = = λ | , ∫ ∫ . first we compute ml estimates of the parameters 1 2( )a b c dθ σ σ= , , , , , given the history in ky . now the expression for ( )q θ θ, is derived. to update the set of parameters from θ to θ , the following density is introduced 1 k k g dp dp θ θ γ = | = ,∏ 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 2 1 2 ( ) ( ) . ( ) ( ) k k k k k k k k k k k k k k k k k k k k x x az x bx z z cz dz x x x az x bx z z cz dz x σ φ σ ϑ σ σ γ σ φ σ ϑ σ σ − − − − − − − − − − − − − − − − − − + − − + = − − + − − + now 21 1 1 1 1 2 1 1 21 1 1 1 1 2 1 log log log ( ) 2 1 ( ) ( ) ( ) 2 k k k k k k k g k k k k k k k k k dp x x az x bx e y k k e y dp z z dz x cz e y r q θ θ θ θ θ σ σ σ θ θ θ σ        − − − −        =         − − − −     =   − − + | | = − − − | − + − − | + = , , ∑ ∑ lakhdar aggoun 62 where ( )r θ does not involve θ . to implement the m-step set the derivatives 0 q θ ∂ = ∂ . this yields ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2 2 1 1 1 1 1 ( 1) 1 ( ) 2 ( ) 1 ( iii ii k k i k iii ii v i k k k k iv i ii k k k iv iii i k k k iii k iii i iv i ii k k k k k i i iii k k k k k k k k k bt ta t t t t tb t t t ds s sc s s s s s sd s st e x x az x bx k θ σ − − − − = + − = , − − = , − − + = , − + = − = − − +∑ 21 2 2 2 1 1 1 1 1 ) 1 ( ) k k k k k k k k y e z z dz x cz y k θ σ                − − − −   =  | , = − + − | .∑ for any “test” function g , write 1 ( ) ( )[ ( ) ] ( ) ( )m mq k k k k k ke t g x z y x z g x z dxdz m i … vβ −λ , | = , , , = , , .∫ 1 ( ) ( )[ ( ) ] ( ) ( )n nq k k k k k ke s g x z y x z g x z dxdz n i … ivη −λ , | = , , , = , , .∫ theorem 1. for 1k ≥ , the unnormalized densities ( ) ( )mk x zβ , , ( ) ( )nk x zη , , m i … v= , , , n i … iv= , , are given by the following recursions. ( ) ( ) 1 2 2 1 ( ) ( ) 1 2 1 ( ) ( ) 1 ( ) ( )[ ( ) ( ) ( ) ( ) ] ( ) ( )[ ( ) ( ) ( ) ( ) ] ( ) ( )[ ( ) ( i i k k k k k k ii i k k k k k k iii i k k k k x z a x z b u v x z u v dudv b u v x z u v q u v dudv x z a x z b u v x z u v dudv b u v x z u vq u v dudv x z a x z b u v x z u β β β β β β − − − − − , = , , , , , + , , , , , = , , , , , + , , , , , , = , , , , , ∫ ∫ ∫ ∫ ∫ )v dudv recursive estimation of a discrete-time 63 1 ( ) ( ) 1 2 1 ( ) ( ) 1 1 ( ) ( ) ( ) ] ( ) ( )[ ( ) ( ) ( ) ( ) ] ( ) ( )[ ( ) ( ) ( ) ( ) ] ( ) ( k k iv i k k k k k k v i k k k k k k i k k x b u v x z uvq u v dudv x z a x z b u v x z u v dudv b u v x z u q u v dudv x z a x z b u v x z u v dudv x b u v x z uq u v dudv x z a x β β β β η − − − − − + , , , , , , = , , , , , + , , , , , = , , , , , + , , , , , , = ∫ ∫ ∫ ∫ ∫ ( ) 1 2 1 ( ) ( ) 1 1 ( ) ( ) 1 2 )[ ( ) ( ) ( ) ( ) ] ( ) ( )[ ( ) ( ) ( ) ( ) ] ( ) ( )[ ( ) ( ) ( i k k k k ii ii k k k k k k iii iii k k k k k z b u v x z u v dudv b u v x z uv q u v dudv x z a x z b u v x z u v dudv z b u v x z uvq u v dudv x z a x z b u v x z u v dudv z q x η η η η η − − − − − , , , , , + , , , , , = , , , , , + , , , , , = , , , , , + , ∫ ∫ ∫ ∫ ∫ ( ) ( ) 1 1 )] ( ) ( )[ ( ) ( ) ( ) ( ) ] iv iv k k k k k k z x z a x z b u v x z u v dudv z b u v x z vq u v dudv η η − − , = , , , , , + , , , , ∫ ∫ where ( )ka x z, and ( )kb u v x z, , , are given in (12) and (13) and kq is given recursively in (10). proof. first note that ( ) ( ) 2 21 1 1 i i k k k kt t x z− − −= + . therefore 1 ( ) 1 ( ) 1 2 2 1 1 1 [ ( ) ] [ ( ) ] [ ( ) ] i q k k k k k i q k k k k k q k k k k k k e t g x z y e t g x z y e x z g x z y − − − − − − = λ , | = λ , | + λ , | . the first expectation is simply 1 ( ) 1 0 01 2 [ ( ) ] 2 (1 ) (1 ) ( )( ) (1 ) ( ) (1 ) k k k k k k x x z z k k k k k k i q k k k k k r f x z i ji jz xk k z z x x j i y f y y r y e t g x z y z x p p p p i j j j i ig x z x x z z σ σ − − + − − = = − − λ , |    = − −      × , − − ∑∑ ∫ lakhdar aggoun 64 2 1 ( ) 1 ( ) ( ) ( ) . k k i k z v cv dvu x u avu bu u v dudvdxdz ϑ φ σ σ β − − − + − − + × , ∫ and 1 2 2 1 1 0 01 2 2 1 2 2 1 [ ( ) ] 2 (1 ) (1 ) ( )( ) (1 ) ( ) (1 ) ( ) ( ) ( ) k k k k k k x x z z k k k k k k q k k k k k k r f x z jii j xzk k z z x x j i y f y y r y k k k e x z g x z y xz p p p p i j j j i ig x z x x z z z v cv dvu x u avu bu u v q u v dudvd σ σ ϑ φ σ σ − − − + −− = = − − − λ , |    = − −      × , − − − − + − − + × , ∑∑ ∫ ∫ xdz using (12) and (13) yields the result. write 1 1 [ ( ) ] [ ( ) ] [ ] q k k k k k k k k k q k k e u i x dx z dz y e u i x dx z dz y e y − − λ ∈ , ∈ | ∈ , ∈ | = λ | , 1( ) [ ( ) ]k q k k k k kx z e u i x dx z dz yζ −, = λ ∈ , ∈ | , 1 1 [ ] ( ) [ ] [ ] ( ) q k k k k k k k q k k k e u y x z dxdz e u y ue y q x z dxdz ζ− − λ | , | = = λ | , ∫ ∫ , 1 1 [ ( ) ] [ ( ) ] [ ] q k k k k k k k k k q k k e v i x dx z dz y e v i x dx z dz y e y − − λ ∈ , ∈ | ∈ , ∈ | = λ | , 1( ) [ ( ) ]k q k k k k kx z e v i x dx z dz yξ −, = λ ∈ , ∈ | , 1 1 [ ] ( ) [ ] [ ] ( ) q k k k k k k k q k k k e v y x z dxdz e v y ve y q x z dxdz ξ− − λ | , | = = λ | , ∫ ∫ . to update the parameter from xp to xp , the following density is introduced 1 1 . 1 k kk x k x x xxk p x x g p x x dp p p dp p p − =    − | =     −    ∏ now recursive estimation of a discrete-time 65 1 log log log(1 ) log(1 ) ( ) ( ) x x k x k p p g k x x xk k p x x x dp e y p p pxu udp r p q p p           =  | | = + − + − + = , , ∑ where ( )xr p does not involve xp . to implement the m-step set the derivatives 0 x q p ∂ = ∂ . this yields 1 k x k up x = = . ∑ a similar argument yields: 1 k z k vp z = = . ∑ for any “test” function g , write 1[ ( ) ] ( ) ( )q k k k k k ke u g x z y x z g x z dxdzζ −λ , | = , , .∫ 1[ ( ) ] ( ) ( )q k k k k k ke v g x z y x z g x z dxdzξ −λ , | = , , .∫ theorem 2. for 1k ≥ , the unnormalized densities ( )k x zζ , and ( )k x zξ , are given by the following recursions. 1 1 ( ) ( ) ( ) ( ) ( ) 2 ( ) ( ) ( ) ( ) ( ) 2 k k k k k k k k k k k k x z a x z b u v x z u v dudv x q x z x z a x z b u v x z u v dudv z q x z ζ ζ ξ ξ − − , = , , , , , + , , = , , , , , + , ∫ ∫ proof. first note that 1k k ku u x−= + . therefore 1 1 1 1 [ ( ) ] [ ( ) ] [ ( ) ] q k k k k k q k k k k k q k k k k k e u g x z y e u g x z y e x g x z y − − − − = λ , | = λ , | + λ , | . the first expectation is simply lakhdar aggoun 66 1 1 0 01 2 2 1 1 [ ( ) ] 2 (1 ) (1 ) ( )( ) (1 ) ( ) (1 ) ( ) ( ) ( ) k k k k k k x x z z k k k k k k q k k k k k r f x z jii j xzk k z z x x j i y f y y r y k k k e u g x z y xz p p p p i j j j i ig x z x x z z z v cv dvu x u avu bu u v dudvdxdz σ σ ϑ φ σ σ ζ − − + −− = = − − − λ , |    = − −      × , − − − − + − − + × , . ∑∑ ∫ ∫ from which the result follows. remark. the above theorems do not require v and w to be gaussian. 4. references aggoun, l. and elliott, r.j. 1998. recursive estimation in capture-recapture methods, journal of science and technology, sultan qaboos university 3: 67–75. baum, l.e. and petrie, t. 1966. statistical inference for probabilistic functions of finite state markov chains, annals of the institute of statistical mathematics 37: 1554-1563. dempster, a.p., laird, n.m. and rubin, d.b. 1977. maximum likelihood from incomplete data via the em algorithm, jour. of the royal statistical society, b, 39: 1-38. elliott, r.j., aggoun, l. and moore, j.b. 1995. hidden markov models : estimation and control. applications of mathematics. vol. 29 springer-verlag, berlin-heidelberg-new york. lotka, a., j. 1925. elements of physical biology. baltimore: williams & wilkins co. seber, g.a.f. 1982. the estimation of animal abundance and related parameters. second edition. edward arnold. volterra, v. 1926. variazioni e fluttuazioni del numero d’individui in specie animali conviventi. mem. r. accad. naz. dei lincei. ser. vi, vol. 2. wu, c.f.j. 1983. on the convergence properties of the em algorithm, the annals of statistics 11, pp. 95103. received 25 february 2004 accepted 26 september 2004 microsoft word proofreading-comp040910-final.doc 63-75 squ journal for science, 10 (2005) © 2005 sultan qaboos university 63 the conditional fault-diameter of the k-ary n-cube khaled day and abderezak touzene department of computer science, college of science, sultan qaboos university, p.o. box 36, al-khod 123, sultanate of oman, email: kday@squ.edu.om, touzene@squ.edu.om. k-ary n-cubeالقطر المختل المشروط لشبكات خالد داي وعبدالرزاق توزان المختلة مع افتراض توزيعـات مشـروطة k-ary n-cubeنحصل في هذا البحث على قطر شبكات : خالصة . لنقاط الخلل حيث أننا نفترض أن لكل نقطة سليمة في الشبكة ما ال يقل عن نقطة مجاورة سـليمة مـن الخلـل وتحت الشرط المذكور لتوزيع نقاط الخلل ، ، 2n التي يساوي مقدار الربط فيها k-ary n-cube برهن أن شبكةن -kكما نستنتج أن القطر المختل المشروط لشـبكات .خلل بدون قطع االتصال بينها نقطة 4n-3 تتحمليمكن أن ary n-cubeمن هذه النتيجة أنه إذا وجد ما ال يزيد نستخلص. يساوي القطر في غياب أي خلل زائداً وحدتان وإذا كان لكل نقطة سليمة ماال يقل عن نقطة مجاورة سليمة ، k-ary n-cube نقطة خلل في شبكة الn4-3عن تبين في هذا البحـث . فالبد أن يكون هنالك طريق موصل خال من األعطال في الشبكة بين كل نقطتين سليمتين إلى مجموعـة k-ary n-cube بهذه النتيجة تنضم شبكة.وصل الخالي من األعطالكيفية بناء هذا الطريق الم والتي يساوي القطـر المختـل ) star-graph وشبكات hypercubeالتي تحتوي على شبكات (شبكات التوصيل .المشروط فيها القطر السليم زائداً وحدتان abstract: we obtain the conditional fault diameter of the k-ary n-cube interconnection network. it has been previously shown that under the condition of forbidden faulty sets (i.e. assuming each non-faulty node has at least one non-faulty neighbor), the k-ary n-cube, whose connectivity is 2n, can tolerate up to 4n-3 faulty nodes without becoming disconnected. we extend this result by showing that the conditional fault-diameter of the k-ary n-cube is equal to the fault-free diameter plus two. this means that if there are at most 4n-3 faulty nodes in the k-ary n-cube and if every non-faulty node has at least one non-faulty neighbor, then there exists a fault-free path of length at most the diameter plus two between any two non faulty nodes. we also show how to construct these fault-free paths. with this result the k-ary n-cube joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault diameter has been shown to be only two units over the fault-free diameter. keywords: fault-tolerance, multiprocessor systems, interconnection architectures, kary n-cube, torus. khaled day and abderezak touzene 64 1. introduction he node connectivity and the fault diameter have been used as measures of the fault-tolerance of interconnection networks. these measures however do not reflect the real resilience of these networks. it is true that when the number of faulty nodes is equal to the connectivity the network may become disconnected. however, this is very unlikely to happen since only very special fault distributions of these faults cause disconnection. for instance, in the k-ary n-cube, the nodeconnectivity is 2n and 2n faulty nodes may cause disconnection. but the network becomes disconnected only when all the 2n faults are adjacent to the same node which is very improbable. in an attempt to better quantify the fault resilience of a network, the concept of forbidden faulty sets has been introduced by esfahanian (1989). the idea is to assume that each node has at least one non-faulty neighbor. under this forbidden faulty set condition, the number of tolerable faulty nodes is significantly larger with a slight increase in the fault diameter. esfahanian (1989) has proven that for the binary n-cube, whose connectivity is n, 2n-3 nodes can fail (under the forbidden faulty set condition) without disconnecting the network. latifi (1993) has then showed that the corresponding conditional fault diameter increases only by 2 over the fault-free diameter. in rouskov et al. (1996) similar results for the star graph network have been established. latifi et al. (1994) have generalized this idea by assuming that each node has at least k non-faulty neighbors. similar results for the m-ary generalized n-cube network have also been obtained in wu (1998). it has been previously shown (day, 2004) that for k ≥ 4 and n ≥ 2, the k-ary n-cube, whose connectivity is 2n, can tolerate up to 4n-3 faulty nodes without becoming disconnected. the corresponding conditional node connectivity is therefore 4n-2. the result for the remaining small values of k and n has also been obtained in day (2004). we extend these results in this paper by showing that the conditional fault-diameter of the k-ary n-cube is equal to / 2 2n k⎢ ⎥⎣ ⎦ + . we therefore establish that the k-ary n-cube, like the hypercube and the star-graph, has conditional fault diameter equal to two plus the fault-free diameter. this paper is organized as follows: section 2 presents some notations; section 3 obtains some preliminary results useful for the derivation of the conditional fault diameter in section 4. section 5 concludes the paper. 2. notations the k-ary n-cube knq has n = k n nodes each of the form x = x n-1 x n-2 ...x 0 , 0 ≤ xi< k, for 0≤i<n. two nodes x = x n-1 x n-2 ... x 0 and y = y n-1 y n-2 ... y 0 in knq are connected if, and only if, there exists exactly one value of i, 0 ≤ i < n, such that xi = yi ± 1 (mod k) and xj = yj , for i≠j. it is shown in bose et al. (1995) that knq has degree 2n and diameter / 2n k⎢ ⎥⎣ ⎦ . given two nodes x = xn-1xn-2...x0 and y = yn1 y n-2 ...y 0 in q n k , we denote by d h (x,y) the hamming distance between x and y, i.e., the number of dimensions in which x and y differ. for the k-ary n-cube, d h (x,y) is not the length of a shortest path between x and y. the length of a shortest path between x and y is equal to the lee distance (bose et al. 1995) given by: d l (x,y) = σ i n = − 0 1 wi, where wi = min (|xi-yi|, k-|xi-yi|). the k-ary n-cube knq can be partitioned into k disjoint k-ary (n-1)-cubes. let , 1 k i nq − be the subgraph of knq containing all k nq nodes whose addresses are of the form x = i xn-2... x0. clearly, , 1 k i nq − t conditional fault-diameter of k-ary n cube 65 is a k-ary (n-1)-cube and the sub-graphs ,01 k nq − , ,1 1 k nq − ,…, , 1 1 k k nq − − form a partition of k nq . for any node a = a n-1 a n-2 ...a 0 in knq we denote by pa , 0 ≤ p < k, the node of the form pa = p a n-2 ... a 0 obtained from a by replacing its leftmost digit a n-1 by p. definition 1: the node-connectivity c(g) (or point-connectivity) of a graph g is the minimum number of nodes of g whose removal results in a disconnected or trivial graph. it has been shown in day and al-ayyoub (1997) that c( knq ) = 2n. definition 2: the fault-diameter fd(g) of a graph g is the maximum distance between any two nodes of g in the presence of at most c(g)-1 faulty nodes. it has been shown in day and al-ayyoub (1997) that fd( knq ) = / 2 1n k⎢ ⎥⎣ ⎦ + . definition 3: the conditional node connectivity cc(g) of a graph g is the minimum number of nodes of g whose removal results in a disconnected or trivial graph, provided that each of the remaining nodes has at least one adjacent node in g that is not removed. definition 4: the conditional fault diameter cfd(g) of a graph g is the maximum distance between any two nodes of g in the presence of at most cc(g)-1 faulty nodes, provided that each of the nonfaulty nodes has at least one non-faulty adjacent node in g. we use the abbreviation ffsc for denoting the forbidden faulty set condition which corresponds to the requirement that each non-faulty node must have at least one non faulty neighbor. 3. preliminary results in this section we present some preliminary results that will be used in the next section for the derivation of the conditional fault diameter of the k-ary n-cube. we start by the following result which has been proven in by day (2004): theorem 1. the conditional node connectivity of the k-ary n-cube for n ≥ 2 and k ≥ 4 is: cc( knq ) = 4n-2. we will denote by * k nq π (x,y) a minimum-length path between nodes x and y in knq . the following theorem established in by bose et al. (1995) about the existence of a complete set of node disjoint paths between any two nodes of the k-ary n-cube knq will be used in the next section for establishing the conditional fault diameter of knq . additional results about node disjoint paths in the k-ary n-cube can be found in day and al-ayyoub (1997). theorem 2. let x = x n-1 x n-2 ... x 0 and y = y n-1 y n-2 ... y 0 be two nodes in knq of hamming distance h = d h (x,y) and of lee distance l = dl(x,y). there are a total of 2n node-disjoint paths between x and y of which: 1) h paths have length l, 2) 2n-2h paths have length l+2, and 3) for each i such that wi > 0, there is a path of length l+k-2wi (h paths). in preparation for the proof of the conditional fault-diameter of the k-ary n-cube given in the next section, we present the corresponding result for the special case of the k-ary 2-cube (also called the k-torus). the k-torus is a wrap-around mesh which consists of k rows and k columns. each row and each column consists of a cycle of k nodes. there are four node-disjoint paths connecting any two khaled day and abderezak touzene 66 nodes of the k-torus. the connectivity of the k-torus is therefore equal to 4. any two nodes on the same cycle (row or column) are connected by two paths along the cycle. one is called the shortest path on the cycle and the other is called the longest path. we show that under the ffsc, the k-torus, whose connectivity is 4, can tolerate up to 5 faulty nodes without becoming disconnected. the conditional node connectivity of the k-torus is therefore 6. we also show that the conditional faultdiameter of the k-torus is equal to its fault-free diameter plus two. the proof of the following theorem consists of a lengthy manual construction of fault-free paths between any two non faulty nodes of the k-torus considering all possible relative locations of the source and destination nodes and those of the 5 faulty nodes. for brevity, we omit this lengthy construction here. interested readers can find it in touzene and day (2005). theorem 3. the conditional fault diameter of the k-torus under the ffsc is 2 / 2 2k⎢ ⎥⎣ ⎦ + . the next result states that it is always possible to construct between any two non-faulty nodes of k nq a fault-free path of length at most the diameter if the number of faults does not exceed two. this result will be used in the next section to prove the conditional fault diameter of knq . lemma 1. in knq , if k ≥ 4, n ≥ 2 and if there are two or less faulty nodes, then there exists between any two non-faulty nodes at least one fault-free path of length at most / 2n k⎢ ⎥⎣ ⎦ . proof. let x and y be any two distinct non-faulty nodes in knq . by theorem 2, there exist between x and y in knq a first set of h = dh (x,y) paths each of length dl (x,y) (which is at most / 2h k⎢ ⎥⎣ ⎦ ) and a second set of 2n-2h paths each of length d l (x,y)+2 (which is at most / 2 2h k⎢ ⎥⎣ ⎦ + ). hence we have in total 2n-h paths between x and y in knq each of length at most / 2 2h k⎢ ⎥⎣ ⎦ + . we distinguish the following cases: • if h = 1 then 2n-h = 2n-1 ≥ 3, and / 2 2 / 2 2 / 2h k k n k⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦+ = + ≤ (since n≥2 and k≥4). hence we have at least 3 paths each of length at most / 2n k⎢ ⎥⎣ ⎦ and at least one of these paths must be fault-free. • if h = 2 and n = 2, the result is derived from the proof of the fault-diameter of the 2-ary n-cube (k-torus) available in touzene and day (2005). • if h =2 and n ≥ 3 then 2n-h = 2n-2 ≥ 4 and / 2 2 2 / 2 2 / 2h k k n k⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦+ = + ≤ (since n≥3 and k≥4). hence we have at least 4 paths each of length at most / 2n k⎢ ⎥⎣ ⎦ , one of which must be fault-free. • if h ≥ 3 then at least one of the first set of h paths each of length at most / 2 / 2h k n k⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦≤ is fault-free. 4. the conditional fault diameter of the k-ary n-cube the following result establishes a lower bound on the conditional fault-diameter of knq . lemma 2. cfd ( knq ) ≥ / 2 2n k⎢ ⎥⎣ ⎦ + , for k ≥ 4, n ≥ 2. proof. let x and y be two nodes in knq at the maximum distance equal to the diameter / 2n k⎢ ⎥⎣ ⎦ . let z be a neighbor of y and let t be a neighbor of z other than y (see figure 1). assume that all 2n-2 neighbors of z other than y and t are faulty and that all 2n-1 neighbors of t other than z are faulty. notice that the former set of 2n-2 faults and the latter set of 2n -1 faults must be disjoint since k ≥ 4 conditional fault-diameter of k-ary n cube 67 (otherwise, if f were a faulty node appearing in both sets then z f t would form a cycle of length 3 which is impossible for k ≥ 4). assume there are no other faults. the total number of faults is therefore 4n-3. a path from t to x must first go through z then through y then from y to x in at least / 2n k⎢ ⎥⎣ ⎦ moves and, hence, will be of length of at least / 2 2n k⎢ ⎥⎣ ⎦ + . therefore, the conditional fault diameter satisfies: cfd ( knq ) ≥ / 2 2n k +⎢ ⎥⎣ ⎦ . now we establish an upper bound on the conditional fault-diameter of knq . lemma 3. cfd ( knq ) ≤ / 2 2n k +⎢ ⎥⎣ ⎦ , for k ≥ 4, n ≥ 2. proof . we proceed by induction on n. the induction basis (n = 2) is given by theorem 3. now we prove the result for n ≥ 3 assuming it is true for smaller n values. consider two arbitrary non-faulty nodes x = x n-1 x n-2 ...x 0 and y = y n-1 y n-2 ...y 0 in knq . assume the number of faulty nodes is at most 4n-3 and that the ffsc is satisfied. our aim is to show that it is always possible to find a fault-free path between x and y of length at most / 2 2n k⎢ ⎥⎣ ⎦ + . we distinguish the following cases: case 1. there exists m, 0 ≤ m < n, such that x m = y m = i (assume without loss of generality m = n-1), then both nodes x and y belong to the sub-graph ,1 k i nq − . case 1.1. ,1 k i nq − has at most 4(n-1)-3 = 4n-7 faults. by induction hypothesis there must exist a faultfree path from x to y in ,1 k i nq − of length at most [ ] [ ]/ 2 / 2( 1) 2 2k kn n− + ≤ + . case 1.2. ,1 k i nq − has more than 4n-7 faults. this means that there are at most 3 faults outside , 1 k i nq − . case 1.2.1. each of x and y has all its 2n-2 neighbors inside ,1 k i nq − faulty. there must exist at most one faulty node outside ,1 k i nq − . therefore either , 1 1 k i nq − − or , 1 1 k i nq + − is faultfree (notice i-1 and i +1 are modulo k). let x i-1 (respectively x i+1) denote the neighbor of x in , 11 k i nq − − (respectively , 11 k i nq + − ). similarly for y i-1 and y i+1 (see figure 2). since either , 11 k i nq − − or , 1 1 k i nq + − is fault-free, at least one of the two paths: x → x i-1 || * 1, 1 − − ik nq π (x i-1, y i-1) || y i-1 → y, or x → xi+1 || * 1, 1 + − ik nq π (x i+1, y i+1) || yi+1 → y yx z t 2n-2 faulty neighbors of z 2n-1 faulty neighbors of t x and y at distance / 2n k⎢ ⎥⎣ ⎦ figure 1. / 2 2n k⎢ ⎥⎣ ⎦ + is a lower bound of cfd ( k nq ). khaled day and abderezak touzene 68 is fault-free and is of length at most ( 1) / 2 2n k⎢ ⎥⎣ ⎦− + (since it is contained in a fault-free 1 k nq − subgraph except for two edges). the symbol || is used to denote path concatenation. case 1.2.2. x or y has a non-faulty neighbor inside ,1 k i nq − . x y x i-1 y i-1 x i+1 y i+1 1, 1 − − ik nq ik nq , 1− 1, 1 + − ik nq figure 2. path construction for case 1.2.1. figure 3. path construction for case 1.2.2.1. x y x i-1 y i-1 1, 1 − − ik nq ik nq , 1− x’x’ i-1 x y x i-1 y i-1 1, 1 − − ik nq ik nq , 1− y’y’ i-1 figure 4. path construction for case 1.2.2.3.1. conditional fault-diameter of k-ary n cube 69 assume it is x which has a non-faulty neighbor x’ inside ,1 k i nq − (case of y is similar). since there are at most three faulty nodes outside ,1 k i nq − , either , 1 1 k i nq − − or , 1 1 k i nq + − has at most one faulty node. assume , 11 k i nq − − has at most one faulty node (the other case is similar). case 1.2.2.1. x i-1 is faulty (hence x i-1 is the only faulty node in , 11 k i nq − − ). let x’ i-1 be the neighbor of x’ located in , 11 k i nq − − (see figure 3). by lemma 1, there exists at least one fault-free path π (x’ i-1,yi-1) of length at most ( 1) / 2n k⎢ ⎥⎣ ⎦− between x’ i-1 and y i-1 in , 11 k i nq − − . we have, therefore, a fault-free path: x → x’ → x’ i-1 || π (x’ i-1,yi-1) || yi-1 → y of length at most ( 1) / 2 3n k⎢ ⎥⎣ ⎦− + which is less than or equal to / 2 2n k⎢ ⎥⎣ ⎦ + since k ≥ 4. case 1.2.2.2. xi-1 is non-faulty and yi-1 is non-faulty. figure 5. path construction for case 1.2.2.3.2. x y x i+1 y i+1 ik nq , 1− 1, 1 + − ik nq x’ x’ i+1 x” x” i+1 figure 6. path construction for case 2. x y x j y i x ’ x ’ j y ’y ’ i πx πy x j+1 y j+1 x ’ j+1 y ’ j+1 y j-1 x j-1 jk nq , 1− 1, 1 + − jk nq ik nq , 1− khaled day and abderezak touzene 70 since there is at most one fault in 1, 1 − − ik nq , lemma 1 gives a path π ( x i-1,y i-1) of length at most ( 1) / 2n k⎢ ⎥⎣ ⎦− in 1, 1 − − ik nq yielding the path: x → x i-1 ||π ( x i-1,y i-1) || y i-1 → y of length at most ( 1) / 2 2 / 2n k n k⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦− + ≤ (since k ≥ 4). case 1.2.2.3. xi-1 non-faulty and yi-1 faulty (the only fault in 1, 1 − − ik nq ). case 1.2.2.3.1. y has a non faulty neighbor y’ in iknq , 1− . let y’ i-1 be the neighbor of y’ located in 1, 1 − − ik nq (figure 4). by lemma 1, there exists at least one fault-free path π (x i-1,y’ i-1) of length at most ( 1) / 2n k⎢ ⎥⎣ ⎦− from x i-1 to y’ i-1 in 1, 1 − − ik nq . therefore the path: x → x i-1 ||π (x i-1,y’ i-1) || y’ i-1 → y i-1 → y is fault-free and is of length at most ( 1) / 2 3n k⎢ ⎥⎣ ⎦− + ≤ / 2 2n k⎢ ⎥⎣ ⎦ + (since k ≥ 4). case 1.2.2.3.2. all neighbors of y in iknq , 1− are faulty. in this case y i+1 must be non-faulty (by the ffsc). we know that 1, 1 + − ik nq has at most 2 faulty nodes. if it has only one faulty node then it is possible to enter 1, 1 + − ik nq from x going directly from x to x i+1 or from x to x’ then to x’ i+1 requiring in both cases at most two moves (see figure 5). we can then use lemma 1 in 1, 1 + − ik nq to obtain a fault-free path of length at most ( 1) / 2n k− ⎢ ⎥⎣ ⎦ from x i+1 or from x’ i+1 to y i+1 and then make a final move from y i+1 to y. hence we have a fault-free path from x to y of length at most ( 1) / 2 3n k− +⎢ ⎥⎣ ⎦ which is at most / 2 2n k +⎢ ⎥⎣ ⎦ since k ≥ 4. 001 006 360 figure 7. an example of the 4n-2 node-disjoint paths in for 3 and 7.n kx yπ ∪ π = = 0,7 2q πx πy 3,7 2q x=000 060 010 x 3 =300 301 306 310 101 201 106 206 110 210 160 260 234 132 323 023 134 332 034 032 y 0 =033 043 y=333 334 343 232 133 233 123 223 143 243 100 200 7 3q conditional fault-diameter of k-ary n cube 71 if, however, 1, 1 + − ik nq has two faulty nodes, then x must have a second non-faulty neighbor x” inside ik nq , 1− (see figure 5), otherwise the total number of faulty nodes would include 2n-2 faulty neighbors of y inside iknq , 1− , 2n-3 faulty neighbors of x inside ik nq , 1− , two faults inside 1, 1 + − ik nq and one fault (namely y i-1) inside 1, 1 − − ik nq for a total of 4n-2 which exceeds 4n-3. let x” i+1 denote the neighbor of x” located in 1, 1 + − ik nq . at least one of the three nodes x i+1, x’ i+1 or x” i+1 must be non-faulty since there are only two faults in 1, 1 + − ik nq . let x* i+1 denote this non-faulty node. so it is possible to enter 1, 1 + − ik nq starting from x in at most two moves. we can then use lemma 1 in 1, 1 + − ik nq to obtain a faultfree path of length at most ( 1) / 2n k⎢ ⎥⎣ ⎦− from x* i+1 to y i+1 and then make a final move from y i+1 to y. hence we have in total a fault-free path from x to y of length at most ( 1) / 2 3n k⎢ ⎥⎣ ⎦− + which is at most / 2 2n k⎢ ⎥⎣ ⎦ + since k ≥ 4. case 2. x m ≠ y m for all m, 0 ≤ m < n. in this case, x and y differ in all n dimensions. let i = x n-1 and j = y n-1 (i ≠ j). we therefore have x ∈ ik nq , 1− and y ∈ jk nq , 1− . hence x and y are of the form: x = i xn-2 xn-3...x0 and y = j yn-2 yn-3...y0. assume without loss of generality that i, i+1, … j is the shortest path between i and j on the cycle 0, 1, 2, … k1. let xπ be the set of 2n-1 minimum-distance paths each joining either x to jx or any of the 2n2 neighbors x’ of x in iknq , 1− to its isomorphic node jx ' in jknq , 1− (see figure 6). the notations xπ (x, jx ) and xπ (x’, jx ' ) will be used to denote these 2n-1 paths of xπ . similarly, let yπ be the set of 2n-1 minimum-distance paths each joining either y to iy or any of the 2n-2 neighbors y’ of y in jknq , 1− to its isomorphic node iy ' in iknq , 1− . the notations yπ ( iy , y) and yπ ( iy ' , y’ ) will be used to denote these 2n-1 paths of yπ . the 4n-2 paths in x yπ ∪π are all minimum-distance paths. each is of length equal to d l (x, jx ) = d l ( iy ,y) which is at most / 2k⎢ ⎥⎣ ⎦ and they are all mutually node-disjoint. figure 7 illustrates the 4n-2 paths of x yπ ∪π for n = 3, k = 7, x = 000, and y = 333. these 4n-2 paths are mutually disjoint and therefore at least one of them must be completely fault-free (since the total number of faults is at most 4n-3). let π be this fault-free path and assume that π ∈ xπ (the case π ∈ yπ is symmetric). let x* denote the end node of *x located in jknq , 1− (i.e. x* is either jx or one of the 2n-2 nodes denoted jx ' ). from the previous discussion we have: |π | = d l (x, jx ) ≤ / 2k⎢ ⎥⎣ ⎦ . notice also that at most one of the sub-graphs lknq , 1− , 0 ≤ l < k, can possibly contain more than 4n-7 faulty nodes otherwise the number of faults would exceed 4n-3 since n ≥ 3 (by assumption of the induction step). case 2.1. jknq , 1− has at most 4n-7 faults. khaled day and abderezak touzene 72 we can build a path π || π (x*,y) of length at most / 2 2n k +⎢ ⎥⎣ ⎦ , where π (x*,y) is a fault-free path between x* and y in jknq , 1− of length at most ( 1) / 2 2n k− +⎢ ⎥⎣ ⎦ obtained using the induction hypothesis in jknq , 1− . case 2.2. if jknq , 1− has more than 4n-7 faults (hence at most 3 faults outside jk nq , 1− ). case 2.2.1. if yπ ( iy , y) is fault-free. in this case we can build a path: π (x, iy ) || yπ ( iy , y) of length at most / 2 2n k +⎢ ⎥⎣ ⎦ , where the path π (x, iy ) is a fault-free path of length at most ( 1) / 2 2n k⎢ ⎥⎣ ⎦− + between x and iy in iknq , 1− obtained using the induction hypothesis in iknq , 1− . notice here that the induction hypothesis applies in ik nq , 1− since the number of faults outside jk nq , 1− (hence inside ik nq , 1− ) is at most 3 which is less than 4(n-1)-2 (since n ≥ 3, by induction step assumption). furthermore, the ffsc is satisfied in iknq , 1− because it would take at least 2n-2 faults inside iknq , 1− to make all the neighbors of one of its nodes faulty which is not possible since 2n-2 > 3 (because n ≥ 3) and there are at most 3 faults in iknq , 1− . case 2.2.2. yπ ( iy , y) is faulty. case 2.2.2.1. 1* +jx is not faulty and 1+jy is not faulty. if d l (x,y) < / 2n k⎢ ⎥⎣ ⎦ , we can build a path: π || *x → 1* +jx || π ( 1* +jx , 1+jy ) || 1+jy → y of length at most / 2 2n k⎢ ⎥⎣ ⎦ + , where π ( 1* +jx , 1+jy ) is a fault-free path between 1* +jx and 1+jy of length at most ( 1) / 2n k⎢ ⎥⎣ ⎦− obtained using lemma 1 in 1, 1 + − jk nq . notice that there are at most three faults outside jknq , 1− and one of them is located on yπ ( iy , y), therefore there are at most two faults inside 1, 1 + − jk nq and hence lemma 1 applies in 1, 1 + − jk nq . if, however, d l (x,y) = / 2n k⎢ ⎥⎣ ⎦ , let ' 1x and ' 2x be neighbors of x in ik nq , 1− corresponding to minimum distance moves from x to y along two different dimensions (these neighbors exist since n ≥ 3). consider the 3 paths joining x to 1+jx , '1x to 1' 1 +jx , and '2x to 1' 2 +jx , corresponding to the sequence of moves i → i-1 → i-2 → … → j+1 in dimension n-1. these paths are node-disjoint and each is of length at most / 2 1k⎢ ⎥⎣ ⎦ + . therefore, it is possible to enter the sub-graph 1, 1 + − jk nq from x in at most / 2 2k⎢ ⎥⎣ ⎦ + moves (in fact if we had started with the edge x→ 1−ix then we would enter the sub-graph 1, 1 + − jk nq from x in at most / 2 1k⎢ ⎥⎣ ⎦ + moves). since in addition 1, 1 + − jk nq has at most two faults, lemma 1 can be used to go from one of the nodes 1+jx , 1'1 +jx or 1'2 +jx to 1+jy in at most ( 1) / 2n k⎢ ⎥⎣ ⎦− moves (in fact in at most ( 1 / 2 1n k⎢ ⎥⎣ ⎦− − moves if we had started with edge x → ' 1x or edge x → '2x since the initial move is a minimum distance move) and then from 1+jy to y yielding an overall path from x to y of length at most / 2 2n k⎢ ⎥⎣ ⎦ + . case 2.2.2.2. both 1* +jx and 1+jy are faulty. conditional fault-diameter of k-ary n cube 73 case 2.2.2.2.1. 1−jy is not faulty. in this case, the only faulty nodes outside jknq , 1− are 1* +jx , 1+jy and one node other than 1−jy on yπ ( iy , y). in this case we can build a path: π -1 || π ( 1−jx , 1−jy ) || 1−jy → y, of length at most / 2 2n k⎢ ⎥⎣ ⎦ + , where π ( 1−jx , 1−jy ) is a minimum distance fault-free path between 1−jx and 1−jy in 1, 1 − − jk nq (notice that there are no faults in 1, 1 − − jk nq in this case) and π -1 denotes the path obtained from π by removing its last 1−jx → x* edge. case 2.2.2.2.2. 1−jy is faulty. the only faulty nodes outside jknq , 1− are 1* +jx , 1+jy and 1−jy . in this case, y must have at least one neighbor y’ inside jknq , 1− which is not faulty (by ffsc). we can, therefore, build a fault-free path: π ( x, iy ' ) || yπ ( iy ' , 'y ) || 'y → y of length at most / 2 2n k⎢ ⎥⎣ ⎦ + where π ( x, iy ' ) is a minimum distance fault-free path between x and iy ' in iknq , 1− (notice that there are no faults in ik nq , 1− in this case). case 2.2.2.3. 1* +jx is not faulty and 1+jy is faulty. here 1+jy is faulty and we have at least one fault located on yπ ( iy , y) (condition of all sub cases under case 2.2.2). therefore, there is at most one other fault outside jknq , 1− . furthermore, node y must have at least one non faulty neighbor (by ffsc). we distinguish the following two sub-cases: case 2.2.2.3.1. some neighbor y’ of y inside jknq , 1− is not faulty. hence, at least one of the following two paths must be fault-free: π ( x, iy ' ) || yπ ( iy ' , 'y ) || 'y → y, (here |π ( x, iy ' )| ≤ ( 1) / 2n k⎢ ⎥⎣ ⎦− (by lemma 1) π || *x → 1* +jx ||π ( 1* +jx , 1' +jy ) || 1' +jy → 'y → y (all moves are minimum distance moves except for the two moves *x → 1* +jx and 1' +jy → 'y ). the length of each of these two paths is clearly at most / 2 2n k⎢ ⎥ +⎣ ⎦ . case 2.2.2.3.2. the neighbor 1−jy of y is not faulty. let 1' −jy and 1" −jy denote two neighbors of 1−jy inside 1, 1 − − jk nq . obviously 1' −jy and 1" −jy cannot be on the path yπ (y, iy ) since 1−jy is the only node on this path that is located in 1, 1 − − jk nq (this is justified by the fact that the paths in yπ are minimum distance paths). therefore, at least one of the following two paths must be fault-free and is of length at most / 2 2n k⎢ ⎥⎣ ⎦ + : π ( x, iy ' ) || yπ ( iy ' , 'y )-1 || 1' −jy → 1−jy → y π ( x, iy " ) || yπ ( iy " , "y )-1 || 1" −jy → 1−jy → y where π ( x, iy ' ) and π ( x, iy " ) are paths of length at most [ ]/ 2( 1) kn − obtained using lemma 1 in iknq , 1− . case 2.2.2.4. 1* +jx is faulty and 1+jy is not faulty. khaled day and abderezak touzene 74 if y has a non faulty neighbor other than 1+jy then the same sub-cases 2.2.2.3.1 and 2.2.2.3.2 apply for this case too. if, however, all the 2n-1 neighbors of y other than 1+jy are faulty, then for at least one of the 2n-2 neighbors '*x of *x inside jknq , 1− we must have both '*x and its neighbor 1'* +jx in 1, 1 + − jk nq non-faulty. otherwise, there will be at least 2n-1 (neighbors of y) plus 2n-2 (neighbors '*x of *x in jknq , 1− or their corresponding 1'* +jx in 1, 1 + − jk nq ) plus one ( 1* +jx ) faults for a total of 4n-2 faults which exceeds the number of faults 4n-3. in this case the path: π || *x → '*x → 1'* +jx ||π ( 1'* +jx , 1+jy ) || 1+jy → y is fault-free, where π ( 1'* +jx , 1+jy ) is a path of length at most ( 1) / 2n k− ⎢ ⎥⎣ ⎦ obtained applying lemma 1 in 1, 1 + − jk nq . the overall length would not exceed / 2 2n k +⎢ ⎥⎣ ⎦ if the length of π is strictly less than / 2k⎢ ⎥⎣ ⎦ . if however the length of π is at its maximum value / 2k⎢ ⎥⎣ ⎦ (i.e. x and y are diametrically opposite along dimension n-1) then a different path is needed. an alternative path can be built going first from x to a non faulty neighbor iy ' of iy following edges of a minimum distance path from x to iy inside iknq , 1− (this is possible making use of theorem 2 inside ik nq , 1− and remembering that x and y differ in all dimensions and that iknq , 1− contains at most one faulty node). in fact it is possible to find a non faulty neighbor iy ' of iy such that 1' +jy is also not faulty since we are left only with one fault outside jknq , 1− other than 1* +jx and 1−jy . the path can then continue going from iy ' to 1' +jy correcting the digit at dimension n-1 along the opposite direction of that followed along yπ ( iy ,y) (i.e. in the direction i → i-1 → i-2 … → j+1). going in this direction along dimension n-1 requires at most one extra move beyond the minimum distance since x and y are diametrically opposite along dimension n-1. the alternative path can be completed by the two moves from 1' +jy to 1+jy and then from 1+jy to y . the overall length of this alternative path would not exceed / 2 2n k⎢ ⎥⎣ ⎦ + since all moves are along minimum distance paths except possibly for the one extra move on the path from iy ' to 1' +jy (the opposite direction path) and the last move from 1+jy to y. theorem 4. the conditional fault-diameter of the k-ary n-cube is equal to / 2 2n k⎢ ⎥⎣ ⎦ + for k ≥ 4 and n ≥ 2. proof. derived from combining the results of lemma 2 and lemma 3. 5. conclusion we have contributed to the study of the fault-tolerance of the k-ary n-cube interconnection network by establishing its conditional fault-diameter under the ffsc (i.e., assuming that each nonfaulty processor has at least one non-faulty neighbor). we have shown that under this condition and for k ≥ 4 and n ≥ 2, the conditional fault-diameter of the k-ary n-cube is / 2 2n k⎢ ⎥⎣ ⎦ + . this means that if there are less than 4n-2 faults in the k-ary n-cube and if every non faulty node has at least one nonfaulty neighbor, then there is a fault-free path of length at most / 2 2n k⎢ ⎥⎣ ⎦ + between any two nonconditional fault-diameter of k-ary n cube 75 faulty nodes. we have shown how to construct these fault-free paths. with this result the k-ary n-cube joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault-diameter have been proved to be only two units over the fault-free diameter. 6. references bose, b., broeg, b., kwon, y. and ashir, y. 1995. lee distance and topological properties of k-ary n-cubes, ieee trans. computer, 44(8): 1021-1030. day, k. 2004. the conditional node-connectivity of the k-ary n-cube, journal of interconnection networks, 5(1):13-25. day, k. and al-ayyoub, a.e. 1997. fault diameter of k-ary n-cube networks, ieee trans. on parallel and distributed systems, 8(9): 903-907. esfahanian, a.h. 1989. generalized measures of fault tolerance with application to n-cube networks, ieee trans. on computers, 38(11): 1586-1591. latifi, s. combinatorial analysis of fault-diameter of the n-cube, ieee trans. on computers, 42(1): 27-33,1993. latifi, s., hegde, m. and naraghi-pour, m. 1994. conditional connectivity measures for large multiprocessor systems, ieee trans. on computers, 43(2): 218-222. rouskov, y., latifi, s. and srimani, p.k. 1996. conditional fault diameter of star graph networks, journal of parallel and dist. computing, 33: 91-97. touzene, a. and day, k. 2005. conditional fault-diameter of the torus, to appear in squ journal for science 10:53-63. wu, j. 1998. fault tolerance measures for m-ary n-dimensional hypercube based on forbidden faulty sets, ieee trans. on comp., 47(8): 888-893. received 10 september 2004 accepted 9 august 2005 microsoft word math060912_corrected.doc 79-93 squ journal for science, 11 (2006) © 2006 sultan qaboos university 79 the time evolution of a constant mass of air pollutant emitted by a point source m.h.a. hassan* and i.a. eltayeb** *the abdus salam international center for theoretical physics, p.o.box 586, miramare 11,34100 trieste, italy,**department of mathematics and statistics, college of science, sultan qaboos university, p.o.box 36, pc 123 al-khodh, muscat, sultanate of oman. بؤرة من التلوث أطلقت في الهواء من مصدر ثابت الزمني لطورالت الطيب عبدالرزاقو ابراهيمن حس عليمحمد حاج ، يقوم البحث بدراسة انتشـار التلـوث أطلقت بؤرة تلوث من مصدر ثابت على علو معين في وقت معين :خالصة طرق استعملت . ئية وشروط محلية ووقتية تحدد حالة االنطالقباستعمال نموذج رياضي يتكون من معادلة تفاضلية جز التحويالت الرياضية التكاملية إليجاد الحل كما تم تحديد الزمن الكلي النتشار التلوث الكلي واعتماد ذلك الزمن علـى . خواص بؤرة التلوث واالحوال الجوية المصاحبة abstract: the transient behaviour of a constant mass (i.e. a blob) of pollutant released from a point source at a height, h , above ground level at time 0t = is studied. the time dependent atmospheric diffusion equation in the presence of diffusion in both horizontal and vertical directions is used to model the problem. the model is found to be governed by an initial-boundary-value problem for the concentration of the pollutant. the solution is obtained in closed form using integral transform methods. the solution is illustrated graphically using appropriate numerical integrations. as time passes, the pollutant blob moves with a central point of accumulation of pollutant while the blob increases in volume to spread the pollutant around it. the motion of the accumulation point in space and time is strongly influenced by wind and gravity while the spread of the pollutant is governed by diffusion. the time taken by the blob to diffuse into space is estimated as a function of the parameters governing wind, gravity and diffusion. keywords: initial-boundary value problem, pollutant, diffusion equation, analytic solution, time-dependence, point source. m.h.a. hassan and i.a. eltayeb 80 1. introduction the study of the transport of small-size particulate matter under dry conditions has been of interest for many years because of its relevance to environmental and industrial applications (ragland and dennis, 1975; vogt, 1977; beiruti and alomshy, 1985; el-baz et al., 1990; keller and lambrecht, 1995; yoshikawa et al., 1996; spanomitsios, 2001). it is now known that under idealized conditions of stationary homogeneous turbulence the mean concentration of pollutants emitted from a point source takes the form of a gaussian distribution. for a comprehensive review which also includes a collection of gaussian-based formulae the reader is referred to pasquill and smith (1984), chatwin et al. (1996), and seinfeld, 1986). more realistic models have been proposed using the atmospheric diffusion equation. the two main factors affecting the spread of pollutants are the wind speed and the local diffusion coefficients. it is generally accepted that the two factors are not independent. as the wind speed varies, the interaction of the particles is influenced and the turbulence viscosity changes. a number of studies have investigated these two factors and their interrelationship using field data (vanderhoven, 1976; semetov et al., 1996) and experimental data (nguyenvanchi and saab, 1976; nagai, 2005). however, there is no general agreement, as yet, on the definite form of the dependence of wind and diffusion parameters on position. this is generally due to the fact that the two factors are not independent and as the wind depends on local circumstances as well as on the atmospheric boundary layer conditions the diffusion parameters will accordingly change with the wind conditions. the wind profile has sometimes been taken as logarithmic (van ulden and holtslag, 1985) or as a power law in the vertical distance, lin and hildemann (1996). the diffusion coefficients have also been assumed to have a number of different forms. whereas the wind speed is always assumed to vary with height, the diffusion coefficients are found to depend either on the height for large to moderate wind speeds (in excess of 10 m/s), (lin and hildemann, 1997), or depend on the distance along the wind for low wind speeds (about 2m/s), (sharan et al., 1996), or on both, (lin and hildemann, 1996). however, in most cases they are assumed to have a power law. the forms of the wind profile and the diffusion coefficients determine how complicated the study of that model of the atmospheric diffusion equation is. for the logarithmic wind profile the solution of the atmospheric diffusion equation can only be found by numerical integration and the same applies to the general power law profile, although certain special forms of the power law profile can possess analytical solutions (lin and hildemann, 1996). moreover, these solutions have been found only for steady forms of the atmospheric diffusion equation, (eltayeb and hassan, 2000; thompson, 1976; dumbauld and bowers, 1976, brian and lee, 1998). our purpose here is to study the transient evolution of a given mass of pollutant released from a point source with time. this problem has not received much attention in the literature. it requires the solution of the time dependent atmospheric diffusion equation as in an initial-boundaryvalue problem. such a problem is relevant to industrial accidents when an explosion releases a certain mass of pollutant into the atmosphere, (vogt, 1977), and it would be interesting to see how it spreads and how long it takes to diffuse away into the surroundings. in order to gain some insight into such a problem, we here study a simple model, as a bench mark for more realistic models, in which the wind speed and diffusion coefficients take simple forms that allow an analytical solution. the advantage of the analytical solution here is that it allows us to isolate the influences of the different factors affecting the solution. such basic factors are expected to remain qualitatively applicable for more realistic models. in section 2, we formulate the problem and in section 3 we find the solution. section 4 is devoted to a discussion of the results and some concluding remarks are made in section 5. 2. formulation of the problem consider a volume q of pollutant emitted at time 0=∗t from a point at a height h above ground level. we intend to study the distribution, ∗c , of pollutant concentration as it evolves with time in the presence of a uni-directional horizontal wind blowing with speed u . we take a cartesian system of coordinates the time evolution of a constant mass of air pollutant 81 ),,( ∗∗∗ zyxo such that ∗ox is horizontal and parallel to the direction of the wind, ∗oz is vertically upwards and ∗oy is horizontal and normal to ∗ox . accordingly the source is situated along the ∗z -axis. the governing equation is the time-dependent diffusion equation ( ). . , 0c c c c t ∗ ∗ ∗ ∗ ∗ ∂ + ⋅∇ = ∇ ⋅∇ − ∇ ∇⋅ = ∂ u d w u (2.1) in which u is the velocity, w ( ),0,0( w= ) is the settling velocity and d is the stress tensor. the settling velocity depends on the particle size and can be taken as a measure of the influence of gravity. the second term on the left-hand side of the first of (2.1) represents the advection of the particles by the local fluid motion. as we mentioned in the introduction above, the wind speed is, in general, a function of height, z∗ , but in order to make progress with the time dependent initial-boundary-value problem below, we shall assume that the wind speed is uniform so that ( ), 0, 0u=u (2.2) and a stress tensor, d , of the form 0 0 0 0 , 0 0 z γ β λ ∗ ⎛ ⎞ ⎜ ⎟= ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ d (2.3) in which γ , β and λ are constants. the stress tensor components in the horizontal may not be uniform but we believe that their variations for moderate wind speeds are smaller than those in the vertical direction. these assumptions about the wind speed and diffusion coefficients allow us to find an analytical solution that permits an analysis of the influences of the different components of diffusion as well as that of the wind speed in the process of diffusion and dispersion of the pollutant with time. we shall now proceed to transform the governing equation into a standard form using a scaling for both independent and dependent variables together with some transformations. define 2, ( / ) *, , , / / , / , / t t x u x y y z z b u a w c uc q λ λ γ λ β λ ν λ ∗ ∗ ∗ ∗ = = = = = = = = (2.4) and reduce (2.1) to ( ) 2 2 2 2 2 21 c c c c c c z b a t x z z x y ν ∂ ∂ ∂ ∂ ∂ ∂ + = + + + + ∂ ∂ ∂ ∂ ∂ ∂ (2.5) the initial condition of the problem is given by ( ) ( ) ( ) ( , , , 0)c x y z y x h zδ δ δ= − (2.6) since the pollutant is that released from the source, the solution must decay away from the source so that ( , , , ) 0, as , , ,c x y z t x y z t→ → ∞ (2.7) the condition at the top of the roughness layer where 0z z= should realistically be of the form 0/ 0 at c z c z zσ∂ ∂ + = = (2.8) where σ is a constant. here the first term represents reflection of the vertical flux of the pollutant. however, this condition makes the solution of the atmospheric diffusion equation very difficult and has not been used in many previous studies. most studies use either the condition 0/ 0 at c z z z ∗∂ ∂ = = (2.9) m.h.a. hassan and i.a. eltayeb 82 representing vanishing vertical flux at the top of the roughness layer so that the pollutant is perfectly reflected back into the region above the roughness layer, or the condition 00 at c z z= = (2.10) representing the vanishing of the concentration at the top of the roughness layer so that the pollutant falling to the top of the roughness layer is completely absorbed. here we find that the condition (2.10) permits an exact solution for all values of the thickness of the roughness layer, 0z . in the special case in which the thickness of layer is vanishingly small (ie. 0 0z → ) the boundary condition (2.9) will also lead to an exact solution. the general condition (2.8) will not be considered here. we shall then apply the condition 0( , , , ) 0c x y z t = (2.11) we are now required to solve the equation (2.5) subject to the initial condition (2.6) and the two boundary conditions (2.7) and (2.11). we make the transformation ( )/ 2 1/ 2 1/ 20( , , , ) , , , , 2 , 2x bu x y t e c x y t z h hνς ς ς ς−= = = (2.12) and reduce (2.5) to 2 2 2 2 2 2 1 1 4 u u u c u b u a t x b y ν ς ς ς ς ς ⎛ ⎞∂ ∂ ∂ ∂ ∂ = − + − +⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ (2.13) the boundary and initial conditions (2.11) can be written in terms of u as ( ) ( ) ( ) 0 / 2 0 / 2 (i) u( , , , ) 0 (ii) u( , , , 0) (iii) u( , , , ) 0, as , , , x b x b x y t x y e y x h e x y t x y t ν ν ζ ζ δ δ ζ δ ζ ζ ζ ζ − − = = − → → ∞ (2.14) the model then poses the initial-boundary-value problem (2.13) and (2.14). 3. the solution we adopt weber’s transform, in ς , defined by ( ) ( ) ( ) 0 , , , , , ,u x y p t u x y t h p dνς ς ς ς ς ∞ = ∫ (3.1) together with its inverse ( ) 2 20 ( , , , ) ( ) ( , , , ( ) ( )o o u x y p t h p u x y t pdp j p y p ν ν ν ς ς ς ς ∞ = +∫ (3.2) in which ( ) ( ) ( ) ( ) ( )o oh p j p y p j p y pν ν ν ν νς ς ς ς ς= − (3.3) here )(xjν and )(xyν are bessel functions of the first and second kinds with order ν and argument x . we note here that ( ) ( ) ( ) ( ) ( ) 1/ 20 0 0 0 0 22 2 2 2 2 0, , 2 , 1 0 dh p h p z d d d h p h p p h p d d ν ν ν ν ν ς ς ς ς πς ν ς ς ς ς ς ς ς = = − = ⎛ ⎞ + + − =⎜ ⎟ ⎝ ⎠ (3.4) the time evolution of a constant mass of air pollutant 83 the application of the weber transform (3.1) to equation (2.13) and the utilization of conditions (2.14), iii and (3.4) yields the equation 2 2 2 2 2 1 4 u u u b a p u t x y b ∂ ∂ ∂ ⎛ ⎞= + − +⎜ ⎟∂ ∂ ∂ ⎝ ⎠ (3.5) we next use the double fourier transform in x and y as defined by ( ) ( ) ( )2ˆ , , , , , , i x syu s p t u x y p t e dxdyωω π ∞ ∞ − + −∞ −∞ = ∫ ∫ % (3.6) and its inverse defined by ( ) ( ) ( )2 ˆ, , , , , , i x syu x y p t u s p t e d dsωω ω π ∞ ∞ + −∞ −∞ = ∫ ∫ % (3.7) the application of the double fourier transform to (3.5) and the use of (2.14),(iii) leads to 2 2 2 ˆ 1 ˆ 4 u p b as u t b ω ∂ ⎛ ⎞= − + + +⎜ ⎟∂ ⎝ ⎠ % % (3.8) the solution of the first order equation (3.8) in t is ( ) ( ) 2 2 21ˆ ˆ, , , , , , 0 exp 4 u s p t u s p p b as t b ω ω ω ⎧ ⎫⎛ ⎞= − + + +⎨ ⎬⎜ ⎟ ⎝ ⎠⎩ ⎭ % % (3.9) the application of the two transforms to (2.14),(ii) yields ( ) ( ) ( )10 0ˆ , , , 0u s p h h ph ν νω + =% (3.10) equations (3.9) and (3.10) then give ( ) ( ) ( )1 2 2 20 0 1ˆ ( , , , exp 4 u s p t h h ph p b as t b ν νω ω + ⎧ ⎫⎛ ⎞= − + + +⎨ ⎬⎜ ⎟ ⎝ ⎠⎩ ⎭ % (3.11) the solution now proceeds by inverting the two transforms (see duffy, 1994]). it is expedient to invert the fourier transforms first. this is carried out in a straightforward manner using standard tables: ( ) ( ) ( ) 2 2 1 2 0 0 1 1 , , , . . exp 4 4 42 x y u x y p t h h ph p t b bt atbt ν ν + ⎧ ⎫⎛ ⎞= − + − −⎨ ⎬⎜ ⎟ ⎝ ⎠⎩ ⎭ (3.12) the inversion of the weber transform gives ( ) ( ) ( ) 1 2 2 0 0 00 , , , exp , ; , , 4 4 42 h t x y u x y t f t h dp b bt atbt ν ς ς ς ν + ∞⎧ ⎫⎛ ⎞ = − + +⎨ ⎬⎜ ⎟ ⎝ ⎠⎩ ⎭ ∫ (3.13) in which ( ) ( ) ( ) ( ) 20 0 0 2 2 0 0 ( ) , ; , , tp h ph h p f t h pe j p y p ν ν ν ν ς ς ς ν ς ς −= + (3.14) the concentration ( , , , )c x y tς can now be written in closed form as m.h.a. hassan and i.a. eltayeb 84 0 5 10 15 20 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 p 0 2 4 6 -0.1 -0.05 0 0.05 0.1 0.15 p f (a) (b) i ii iii iv figure 1. a sample of representative profiles of the integrand ( )0 0, ; , ,f t hς ς ν as a function of the integration variable p when 5.0, 0.5h ν= = and 0 0.1, 0.0z b= = . in (a), the four curves are such that i (continuous) , ii ( discontinuous), iii (discontinuous-dotted) and iv ( dotted) refer to the pair 0( , )z z t− taking the values (0.1,0.1), (5.0,0.1), (0.1,10.0) and (10.0,1.0), respectively, while (b) represents 0 0.1z z− = and 0.01t = . ( ) ( ) ( ) 1 2 2 0 0 00 , , , exp ( , ; , , ) 4 42 h x t y c x y t f t h dp bt atbt ν ν ς ς ς ν ς + ∞⎧ ⎫−⎪ ⎪ = − −⎨ ⎬ ⎪ ⎪⎩ ⎭ ∫ (3.15) for all 2, , ( / 4), 0.x y z tς= > the dependence on the longitudinal distance x appears in the exponential factor outside the integral and is coupled only with the time and the diffusion coefficient in the same direction so that it is separated from the height and the diffusion coefficient in the vertical direction. a similar behaviour applies to the dependence on the lateral distance y . the dependence on the vertical distance 2( / 4)z ς= is more complicated; it is coupled with the parameters representing the height, 0h , the settling velocity, ν , and the roughness height, 0z and depends on the integral ( )0 0 0 , ; , ,i f t h dpς ς ν ∞ = ∫ (3.16) for non-zero values of the roughness height, as represented by 0ς , the integral (3.16) must be evaluated numerically. as the interval of integration is semi-infinite, the question of convergence of the integral must be addressed. since the integrand is an analytic function we have chosen to examine the nature of the function first before adopting a complicated automatic routine for its evaluation. an examination of the integrand ( )0 0, ; , ,f t hς ς ν shows that it is oscillatory with the period as well as decay rate depending crucially on the time t (see figure 1). it is bounded, possesses no singularities and decays to zero for all values of the relevant the time evolution of a constant mass of air pollutant 85 parameters. except for small times (i.e. 0.1t < ), the function decays to a negligible value for 10.0p . this makes it possible to limit the interval of integration to (0.0,10.0) except for small values of t . the integral is then evaluated using a nag subroutine which uses an adaptive integrator based on a method due to piessens et al.(1983). for very small values of t convergence is not good, as the integrand oscillates very rapidly and sometimes erratically until p increases to large values before it decays to zero. this is not a serious matter as we know that for very small times, the blob has not changed its shape much and is approximately in its original shape. the numerical integrations have shown excellent agreement with the analytical result (3.18) obtained for the case 0 0ς → below. it is always useful to identify any special cases where fully analytical solutions can be obtained in order to compare the numerical results with those particular cases in order to build confidence in the numerical results or to identify solutions which exhibit particular properties that are easily interpreted. in the present situation, we find two such cases. (i) 0 0ς = (no roughness height) here the integral (3.16) can be evaluated analytically by using the asymptotic forms of bessel functions in the integrand (3.14) to get ( )2 20 0 1 1 exp ( / 2 ) 2 4 v i h i h t t t ς ς⎧ ⎫= − +⎨ ⎬ ⎩ ⎭ (3.17) so that the concentration is given by ( ) ( ) 1 22 2 20 0 0 1 1 ( , , ) exp / / ( / 2 ) 2 42 h c x t h x t b y a i h t t tbt ν ν ς ς ς ς + ⎧ ⎫⎡ ⎤= − + + − +⎨ ⎬⎣ ⎦⎩ ⎭ (3.18) in which )(xiν is the modified bessel function with argument x and order ν . the expression (3.17) illustrates the complicated nature of the integral (3.16) as a function of ς and t and shows the complex nature of the interaction between vertical diffusion and gravity. the asymptotic behaviour of the modified bessel function ( )iν α shows that the solution decays to zero as t → ∞ . if we take the limit 0→t , we recover the initial condition (2.11),(ii). this solution was used to compare the results for small 0ς obtained using the numerical integration of the integral (3.16) to find excellent agreement. it can also be used to test the boundary condition (2.11), (i) demanding the vanishing of the concentration at the top of the roughness layer with the other relevant one of vanishing flux of concentration there. using the transformation (2.12), we have 1 / 2 02 , at x bc ue u z νς ζ ν ζ ζ ζ − − ⎡ ⎤∂ ∂= − =⎢ ⎥∂ ∂⎣ ⎦ (3.19) m.h.a. hassan and i.a. eltayeb 86 -2 -1 0 1 2 0 2 4 6 8 1.9 1.5 1 0.5 0.005 -2 0 2 4 6 0 5 10 15 0.2 0.15 0.1 0.01 0.05 0 5 10 15 0 5 10 15 20 0.001 0.001 0.01 0.02 0.03 0.042 0 5 10 15 0 5 10 15 20 0.015 0.01 0.005 0.0010.001 (a) z x (b) z x (d) (c) x figure 2. the contours of pollutant concentration when 05.0, 0.1, 0.5h z b= = = and 5.0=ν at different times: (a) 1.0=t , (b) 0.1=t , (c) 0.5=t , (d) 0.10=t . note the spread of pollutant upwind even for moderate values of t . when 0 0ζ → , the condition / 0c z∂ ∂ = at 0 0ζ = gives the condition ( ), , 0, 0u x y t = (3.20) which is identical with (2.14),(i) when 0 0ζ = . (ii) 0=b ( no longitudinal diffusion) as 0b → , the presence of the factor ( )2tx − in the exponential has the consequence that the solution decays to zero unless tx − is very small. we find that ( ) ( ) ( ) ( ) ( ) 2 1 2 0 0 2 20 0 0 ( ) , , ( ) exp 4 tph h ph h pyc x t x t e pdp at j p y p ν ν ν ν ν ν ς ς δ ς ς ς + ∞ −⎧ ⎫= − −⎨ ⎬ +⎩ ⎭ ∫ (3.21) it is noteworthy here that the delta function present initially remains in the solution at subsequent times and maintains the local nature of the distribution. this solution can be obtained by applying the weber and laplace transforms directly to (2.13) and (2.14) with 0=b . the solution (3.21) represents a mass of pollutant traveling as a front with uniform (dimensional) speed u and distributed vertically and laterally. the lack of spread of pollutant along the wind direction is due to the absence of diffusion in that direction. the time evolution of a constant mass of air pollutant 87 4. discussion the solution (3.15) gives the evolution of the mass of pollutant released from (0, 0, )h at 0t = for all subsequent times. the variation of the solution in the vertical direction is more complicated than those in the horizontal because of the interaction with gravity. furthermore, the horizontal variations in the wind direction are different from those in the lateral direction despite that the diffusion coefficients in both directions are uniform because of the interaction with the wind speed. this illustrates the crucial role played by diffusion and its interaction with the wind. the lack of wind speed in the presence of a uniform diffusion component in the lateral direction results in the concentration decaying exponentially on either side of the central plane 0y = . if we express the concentration (3.15) in the original quantities ,x y∗ ∗ and time t∗ ( ) ( ) ( ) 21 2 0 0 00 , , , exp 42 ( , ; , , ) x uth q y c x y t t tt f t h dp ν ν ς γ βλς γ ς λ ς ν + ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗∗ ∗ ∞ ∗ ∗ ⎧ ⎫−⎪ ⎪ = − −⎨ ⎬ ⎪ ⎪⎩ ⎭ ∗∫ (3.22) we see that the pollutant diffuses a distance ( )1/ 2o tβ ∗ on either side of the plane 0y = . in the direction of the wind, the pollutant travels in a front of thickness ( )1/ 2o tγ ∗ traveling with the speed of the wind u . in all cases, the volume of pollutant, in the central plane 0y = , moves in the direction of the wind diffusing both vertically and horizontally about a central point, at which the concentration is the highest. we shall refer to this as the point of accumulation. as time increases from 0, the mass of pollutant begins to diffuse in all directions. the dependence of the concentration on the parameters 0, ,h z ν is illustrated in figures 2-5 and table 1. the evolution of the mass of pollutant with time is illustrated in figure 2 for a given set of parameters. we note that the pollutant diffuses downwind as well as upwind and the location of the source is subject to pollution, albeit in decreasing concentrations, for quite some time after the release of the mass. in figure 3, the concentration is illustrated for different sets of the parameters at a given time. we note that the position of the height of the source influences the position of the accumulation point and the effect of increasing the roughness height, 0z , is to raise the level of the accumulation point. the point of accumulation is always situated at the centre of the pollutant mass and at a height mz . it moves horizontally with the flow speed, u , at all times so that its horizontal position mx t= . its downward motion is mainly due to the influence of gravity, as represented by ν (see also table 1). m.h.a. hassan and i.a. eltayeb 88 0 1 2 3 4 5 0 5 10 15 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 0 5 10 15 0.2 0.15 0.1 0.05 0.025 0 1 2 3 4 5 0 5 10 15 0.225 0.2 0.15 0.1 0.05 0.025 0 5 10 0 5 10 15 20 0.1 0.075 0.05 0.025 0.005 x z (a) (b) (d) (c) x x z figure 3. the contours of the concentration of pollutant at a fixed time, 2.0,t = for different sets of values of the pollutant parameters: (a) ,0.5=h 0 0.1,z = 0.5,ν = 0.1b = ; (b) 2.0,h = 0 0.1,z = 0.5,ν = 0.1b = ; (c) 05.0, 0.1,h z= = 0.1, 0.1bν = = ; (d) 5.0,h = 0 0.1,z = 0.1,ν = 0.5b = . note the marked horizontal spread of the pollutant volume as b is increased from 0.1 in (c) to 0.5 in (d). however, the speed with which it moves vertically is also affected by vertical diffusion and by the height of the initial point at h , as illustrated in figure 4. at the early stages of the evolution, the pollutant is still confined to a small volume and the influence of gravity is dominant. its rate of descent is relatively higher than at later times. when the pollutant has diffused and occupied a larger volume, its vertical speed downwards slows down and eventually decreases to zero and for large times it starts to move upwards. as the volume of pollution diffuses out in all directions, the value of the concentration at the accumulation point naturally decreases. the influence of gravity is now reduced and the accumulation point tends to rise with time. the height mz of the accumulation point is also dependent on 0z as the accumulation point maintains a certain distance above the top of the roughness layer. as time increases the pollutant spreads over a larger volume which is more extended in the vertical than in the horizontal direction due to the presence of the roughness layer and consequently the accumulation point moves up slowly with time (see figure 4). in the absence of longitudinal diffusion (i.e. when 0.0b = ) the volume of pollutant moves horizontally in the form of a vertical front with speed u and diffuses vertically due to the influence of the vertical diffusion. the time evolution of a constant mass of air pollutant 89 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0 0.5 1 1.5 2 z m t iii 1,ii,iv (a) i iii ii iv (b) c m t figure 4. the variation of the properties of the point of accumulation (i.e. the centre of the pollutant mass) with time for different values of the parameters for (a) the height mz and (b) the value of the concentration mc . the horizontal position of the accumulation point, mx t= for all times. the curves correspond to 0.5=h and are labeled such that i refers to 0.1,b = 0.1,0z = 0.5ν = , ii for 0.5,b = 0 0.1,z = 0.5ν = ; iii for 0.5,b = 0 0.5, 0.5z ν= = ; and iv for 00.5, 0.1, 0.1b z ν= = = . note the influence of the roughness height 0z in raising the level of the accumulation point. in figure 5, the distribution of the pollutant in the moving front is illustrated in the ( ,t z ) plane. we see that the vertical front also possesses an accumulation point whose height decreases with time. the expression (3.15) indicates that the concentration ( ), , , )c x y z t decays exponentially with time. however, at the accumulation point x t= and 0y = , the exponential factor outside the integral vanishes and the nature of decay becomes dependent on the integral (3.16). the rate of decay at the accumulation point is important because it can provide an estimate of the time the pollutant takes to diffuse out into space. in table 1 we give the time, 0t , it takes for the concentration at the accumulation point to reduce to 1.00x10 -4 (as compared with 1.00 at 0t = ) as a function of the parameters 0, , ,h z bν . this means that at time 0t , the scaled concentration ( ), , ,c x y z t is less than that value at every point in space. m.h.a. hassan and i.a. eltayeb 90 2 4 6 8 10 0 2 4 6 8 0.05 0.04 0.03 0.02 0.01 2 4 6 8 10 0 2 4 6 8 0.05 0.04 0.03 0.02 0.01 2 4 6 8 10 0 2 4 6 8 0.08 0.05 0.04 0.03 0.02 0.01 2 4 6 8 10 0 2 4 6 8 0.02 0.01 0.005 0.002 z z t t (a) (b) (c) (d) figure 5. the contours of the concentration in the zt − plane for the case of no horizontal diffusion ( 0=b ) when the mass is released from a height 5.0h = . the subfigures )()( da − correspond, respectively, to 5.0,1.00 == νz ; 5.0,5.00 == νz ; 1.0,1.00 == νz ; 0 0.5 , 0.1z ν= = , respectively. the concentration profile for any 0xx = , say, is obtained by drawing a vertical line at 0xt = and the intersection points of the line with the contours give the profile of the concentration with the vertical at the advancing front tx = at that instant. note that the point of accumulation moves down with a rate depending on the settling velocity in the same fashion as in the case 0≠b . the table shows that 0t is affected by variations in any one of the parameters 0, , ,h z bν . we note that the height of the accumulation point increases with time for moderate and large times for all the parameters 0, , ,h z bν . 5. concluding remarks a prescribed mass of pollutant particles is released from a point at time 0=t and its evolution has been investigated for all times. the gas ‘blob’ is subject to diffusion in both vertical and horizontal directions and the influence of gravity is also included. the uniform coefficients of diffusion in the wind and cross-wind directions are γ and β , respectively. the solution for the concentration as a function of both position and time has been obtained in closed form. the solution describes the transient movement of the mass of pollutant with time. the solution reduces to simpler forms in special cases where the solution can be obtained independently. the model used is a simple one with uniform wind speed and diffusion that is linear in height vertically and uniform horizontally. the solution obtained exhibits certain characteristics which we believe may apply qualitatively to more realistic models. the time evolution of a constant mass of air pollutant 91 table 1. the time taken for the maximum scaled concentration (c*u/q) to reduce to 1.00x10-4 for different values of the parameters. note that the position of the maximum concentration occurs on the line y = 0 , x = t. t0 zm b 0z ν h 372.00 281.00 293.00 222.00 215.00 170.00 182.00 143.00 232.00 176.00 159.00 120.00 128.00 101.00 96.00 75.54 48.75 38.92 57.04 46.31 12.02 10.41 20.29 17.62 33.26 26.75 35.96 29.26 8.69 7.52 13.92 12.54 0.2 0.5 0.2 0.5 0.2 0.5 0.2 0.5 0.2 0.5 0.2 0.5 0.2 0.5 0.2 0.5 0.1 0.1 0.5 0.5 0.1 0.1 0.5 0.5 0.1 0.1 0.5 0.5 0.1 0.1 0.5 0.5 0.1 0.1 0.1 0.1 0.5 0.5 0.5 0.5 0.1 0.1 0.1 0.1 0.5 0.5 0.5 0.5 5.0 2.0 the solution shows that: (1) the diffusion coefficient, γ , in the direction of the wind has a strong influence on the spread of the pollution along the wind direction. if 0γ = , the mass of pollutant moves as a vertical front of negligible xthickness with the speed of the wind and the pollutant can only diffuse vertically and in the cross-wind direction. for non-zero γ , the front has an x-thickness of ( )1/ 2o tγ ∗ about the location x ut∗ ∗= . (2) the extent of spread of the pollutant in the cross-wind direction extends a distance ( )1/ 2o tβ ∗ about the plane 0y = . m.h.a. hassan and i.a. eltayeb 92 (3) the concentration of pollutant is always maximum at the centre (where y = 0, x = t) but the actual value of this maximum decreases as time increases. also the centre moves horizontally with the flow but vertically it descends, for small times, in a manner determined by both gravity and diffusion and rises for moderate to large times. 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24: 1196-1207. vanderhoven, i. 1976. survey of wind-measurements of atmospheric diffusion under low wind-speed inversion conditions. nuclear safety 17: 223-230. vogt, s. 1977. forecast of atmospheric diffusion coefficients after hypothetical accidents at nuclearplants. atomkernenergie 29: 282-286. yoshikawa, y., kunimi, h and ishizawa, s. 1996. estimation of air quality by three-dimensional air simulation model – (effect of low-emission vehicles on air quality improvement in the greater los angeles area). jsme international j: b-fluids and thermal eng. 39: 647-652. received 12 september 2006 accepted 27 november 2006 microsoft word physc090211-f_edited_checked.doc 85-94 squ journal for science, 14 (2009) © 2009 sultan qaboos university 85 general screened coulomb potential : nonperturbative solutions *lalit kumar sharma, phillip monowe and samuel chimidza department of physics, university of botswana, gaborone, botswana, *email: sharmak@mopipi.ub.bw. تقريبيةحلول دقيقة غير: العام بالمسحجهد كولوم اللت كومار شارما ، فيليب موني وصامويل شيميدزا . باستخدام حلول دقيقة غير تقريبية بالمسحأوجدت طاقات الربط لعدة ذرات متفاعلة عن طريق جهد كولومب :خالصة .ات سابقةاسة توافقا تاما مع حسابوقد توافقت نتائج الدر ) r(ة مع تغير المسافة جيكما تم دراسة تغير الدالة المو abstract: using nonperturbative solutions, the binding energies for different atoms have been evaluated for the screened coulomb potentials. the variation of the wavefunction with distance r has also been studied. the results obtained are in excellent agreement with earlier calculations. keywords: nonperturbative solutions, screened coulomb potentials and binding energies. 1. introduction t is wellknown that there are some processes which although occurring outside the nucleus are dominated by distances which are small on the atomic scale (compton wavelength distances). in atomic photo-effect for example, pratt and tseng (1972) have argued that for a wide range of photo energies, electron compton wavelength distances are of primary importance. in such a case, the knowledge of screened wavefunction is desirable for including the effects of screening, at least for small distances r . furthermore, internal conversion (see e.g. singh and varshni, 1984), threshold pair production (see e.g. tseng and pratt, 1971) and single quantum annihilation (see e.g. tseng and pratt, 1973) phenomena are also characterized by small distances on the atomic scale. the normalization screening theory has been applied successfully to explain the anomalously large photodefect cross-section in molecular hydrogen (see e.g. cooper, 1974). there are many atomic and nuclear processes which are characterized by the behaviour of an electron wavefunction at the origin. one such phenomenon is the orbital electron capture, because in this process only the region of overlap between electron and nuclear wavefunction is involved. the screened coulomb potential also finds importance in atomic phenomena involving electronic transitions. it has been treated numerically and analytically by various workers using different methods, such as wkbj method (see e.g. schiff, 1968), the quantum defect method (see e.g. faridfathi and sever, 2007) and different types of perturbation methods. realizing the utility of the screened coulomb potential, several i lalit kumar sharma, philip monowe and samuel chimidza 86 variational calculations (see e.g. greene and aldrich, 1976, lam and varshni, 1971, roussel and o’ connel, 1974, harris, 1962) have been done and tables of energy as a function of screening parameters have been compiled. mcennan et al. (1976) used analytic perturbation theory for non-relativistic cases, while green and aldrich (1976) applied a non-perturbative approach to the problem. later mehta and patil (1978a), using an approximate and non-perturbative approach, considered a potential of the form: ( ) ( )β+ − = r ze rv 2 and found that s-wave energy level ( )βe , as a function of parameter β , has a singularity at the origin. these authors have studied the behaviour of the bound-state energy for this potential (a modified coulomb potential), as a function of the parameter β . it may be of interest that this potential may also serve as an approximation to the potential due to a smeared charge rather than a point charge, and may be pertinent potential for the description of mesonic atoms. when a classical charged two-particle system is influenced by a plasma sea, the coulomb potential is replaced by a static screened coulomb potential, the so-called debye potential (see e.g. lam and varshni, 1976), to explain the interaction. ray and ray (1980) obtained s -matrix, discrete energies and wavefunctions for the s states of an exponential cosine screened coulomb (ecsc) potential in ecker-weizel (ew) approximation. dutt (1979) and dutt et al. (1981) obtained bound s -state energies of an electron in ecsc potential by analytical method, using ew approximation. they further proposed an extension of ew approximation to treat the non-zero angular momentum bound-states of a class of screened coulomb potentials and obtained discrete energies for the yukawa potential. it may be of interest to note (see e.g. alhaidri et al, 2008) that screened coulomb potential also describes the shielding effect of ions embedded in plasmas. motivated by the growing importance of the screened coulomb potential, we have considered in this paper a general potential of the form ( ) ( )nrr ze rv 0 2 1 δ+ −= , (1) where 0δ is a screening parameter. the energy eigenvalues and wavefunctions for different values of n for the potential (1) have been obtained by an approximate and a non-perturbative approach. 2. calculation of eigenenergies the radial schrödinger equation with potential (1) can be written as ( ) ( ) ( ) ( )rrerr r ll rr z dr d r dr d r n =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + + −− 2 2 2 2 1 12 1 δ . (2) in equation (2), we have used atomic units (unit of length 2 2 0 me =α and unit of energy = 2 4me − ) and ( ) 00 δαδ n= . setting ( ) ( ) r rr r =ψ , equation (2) is transformed to ( ) ( ) ( )rerrv rd d eff ψψ =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +− 12 2 2 1 . (3) in equation (3), general screened coulomb potential 87 ( ) ( ) ( ) 21 2 1 1 r ll rr z rv n eff ++ + − = δ . (4) ( )rv eff1 may also be written in the form ( ) ( ) ( ) ( ) ( ) ( ) ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +−++ + + ++ − = − −− 2 1 2 1 2221 2 111ln2 1 1ln1 nnn n nn n eff rrr rll rr rz rv δδδ δ δδ δ . (5) as ( )rv eff2 tends to ( )rv eff 1 for 1< nrδ , i.e. ( ) 12 <<nrδ , and hence we can neglect terms of order ( )2nrδ or higher in the expansions of expressions involving ( )1 nrδ+ . thus, equation (3) with the help of equation (5) takes the form ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )rer rrr rll rr rz rd d nnn n nn n ψψ δδδ δ δδ δ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +−++ + + ++ −− − − − 2 1 2 1 222 1 2 2 111ln2 1 1ln12 1 . (6) further, setting ( ) ( ) 2 21 , 2 , na r e a r r e δ δ ψ φ − = − = (7) equation (6) becomes ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 12 1 2 2 2 2 1 1 2 2 2 2 2 2 2 2 1 2 1 ln 1 1 2 ln 1 1 1 1 . 2 2 n n n n n n n n n n z r rd d an r d r d r r r l l r r r r r n a n r r n a r r e r δφφ φ δ δ δ δ φ δ δ δ δ φ δ φ φ − − − − − − − + − + + + + ⎡ ⎤ + + − +⎢ ⎥ ⎣ ⎦ − + − = (8) now, a change of variable ( )nry δ+= 1ln along with the approximations ( ) ( )yyenr n n y φ δ δφ ′⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =′ − − 1 , lalit kumar sharma, philip monowe and samuel chimidza 88 and ( ) ( ) ( ) ( ) ( )[ ]yynnynyy ny ey nr yn n φφ δ δφ ′−−+′′− ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =′′ − − 11 21 , for 0,1 == ln (for the s states), transforms equation (8) to ( ) ( ) ( ) ( ) ( ) ( ) 02211 2 =+′+′+−′′− yzyyyayyyy φ δ φφφ . (9) in equation (9), terms involving 2δ (for the region 12 <<δ ) have been neglected. further, to observe the usefulness of the results with 1≠n in potential (1), the study is restricted to those processes which occur in the region 1≅r . thus from equation (8), ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2 1 1 3 2 2 2 2 1 0, 2 z y y y y y y y a y y y a y y y φ φ φ φ φ δ φ ′′ ′ ′ ′− − − + − + − + + = (10) for 2=n , and ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 21 3 2 2 2 2 1 0, z y y y y y y a y y a y ay y y φ φ φ φ φ δ φ ⎛ ⎞′′ ′ ′ ′− + − + + + −⎜ ⎟ ⎝ ⎠ − + = (11) for 1−=n 2.1 solutions for the case 1=n assuming ( )yφ to be of the form ( ) σφ + ∞ = ∑= i i i ycy 0 , (12) and substituting it in equation (9), one finds on equating the coefficients of like powers of y that 1=σ for s states and the ic ’s satisfy the following recursion relation ( )( ) ( )( )21 2 121 1 ++ ⎥⎦ ⎤ ⎢⎣ ⎡ −+++ =+ ii c z aii c i i δ . (13) if the series (13) is to terminate after a certain finite number of terms (i.e. 01 =+mc ), then ( )( ) 02121 =−+++ δ z amm m . (14) this expression is identical with the similar expression obtained by greene and aldrich (1976) for =z 1. equation (14) now determines the quantity ma and hence the energy. the wavefunction ( )rmlψ may now be written as general screened coulomb potential 89 ( ) ( )[ ]∑ = +− += m m m m ra ml rcer m 0 1ln σµ µψ , (15) where δ is replaced by a variational parameter µ as trial function. thus ( ) raml mrekr µµψ −= . the condition of normalization finally yields, δ22 4 mak = , where µ has been set such that 0=+ ma δ µ . now the expression (see e.g. greene and aldrich, 1976) ( ) ( ) ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + + −−= ∫ ∞ 22 2 0 2 1 12 1 r ll rr z rd d re nlm δ ψ ( )drrmlψ , (16) yields the following for the binding energy ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ −−== ∫ ∞ 42 ][ 2 1 0 1 δδ ψψ z drde sls , (17) where in the above relations the notations have the following meaning ( ) ( ) 22 2 2 1 12 1 r ll rr z rd d d nl + + + −−= δ , ( )ren ras s δψ δ += −− 1ln111 and ⎥⎦ ⎤ ⎢⎣ ⎡ −= 2 1 1 δ z a s . 2.2 solutions for the case 2=n again for 2=n in potential (1), ic ’s satisfy the relation ( ) ( )1 1 1 2 2 2 2 2 , with =0. 2 1 i i z a i i a c c i i δ σ+ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ + + − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦= + (18) this yields for s -states and for 0=m , δ z a =0 , ,1=m ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= 5 3 51 δ z a . (19) 2.3 solutions for the case 1−=n similarly for s -states and for 1−=n and 0=σ , the recursion relation is ( ) ( )( )21 2222 1 ++ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ +⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −++ =+ ii ca z aii c i i δ . (20) lalit kumar sharma, philip monowe and samuel chimidza 90 equation (20) yields δ z a =0 , and ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= 4 3 21 δ z a . (21) the above values of ma finally give the expression for the wavefunctions ( ) ( )[ ] σ δ δψ + = − ∑ += mm m n m ra ml rcer n m 0 1ln . (22) the wavefunctions given by equation (22) are only approximate and their resemblance to the exact wavefunctions depends on the extent to which ( )rv eff2 approximates ( )rv eff 1 in the approximation ( ) 1<<nrδ . 3. results and discussions (a) using equation (17) in table 1 the binding energy values (in kev) for 1=n and for different atoms with z ranging between 34 and 84 have been given. the values of the screening parameters chosen and the corresponding experimental values have also been depicted in the same table, while table 2 shows the binding energy values calculated for 1−=n . table 1. bound state energies e (kev) with 1=n as a function of z and δ z δ e present study with 1n = in potential (1) experimental (reference mehta and patil, 1978b) 34 0.09 -1.52 -1.27 39 0.095 -1.84 -1.70 44 0.100 -2.19 -2.21 49 0.120 -2.93 -2.79 54 0.130 -3.50 -3.46 59 0.135 -4.12 -4.20 64 0.16 -5.11 -5.02 69 0.18 -6.20 -5.94 74 0.20 -7.39 -6.95 84 0.22 -9.22 -9.31 general screened coulomb potential 91 table 2. bound state energies e (kev) with 1−=n as a function of z and δ z δ e present study with 1n = in potential (1) by dispersion relation (reference mehta & patil, 1978b) by perturbative approach (reference lyer, 1980) 34 0.09 -1.52 -1.30 -1.36 39 0.095 -1.84 -1.74 -1.55 44 0.100 -2.19 -2.25 -2.12 49 0.120 -2.92 -2.82 -2.80 54 0.130 -3.49 -3.45 -3.53 59 0.135 -4.11 -4.15 -4.44 64 0.160 -5.10 -4.92 -5.22 69 0.180 -5.81 -5.76 ---- 74 0.200 -7.37 -6.66 ---- 84 0.220 -9.20 -8.66 ---- (b) it should be noted here that the method of investigation used by us involves a minimum number of parameters and is quite straightforward as compared to the methods used by previous authors ( see e.g. greene and aldrich, 1976, rogers et al., 1970 and roussel and o’ connel, 1974). 4. conclusions (a) from table 1 it is seen that that the agreement between the calculated and the observed values is poor for lower values of z but it improves for higher values of z . (b) from table 2, the results on the binding energy values for 1−=n show a reasonably good agreement with the energy values obtained by iyer (1980). it may also be mentioned here that the screened coulomb potential (1) changes to a form considered by mehta and patil (1978a) for this value of n . the energy values obtained by us are comparable to those obtained in their study. (c) the potential considered in this paper is of general form, and the comparison of shapes obtained for the wavefunction ( )rmlψ for 1=n (figures 1 and 2) reveals that within the interior of the atom, i.e. 1<rδ , shapes of all the screened coulomb potentials are similar and correspond primarily to the coulombic form. this enhances the chances of possible use of ( )rmlψ as the trial wavefunctions. lalit kumar sharma, philip monowe and samuel chimidza 92 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 ψ m l ( r) r figure 1. unnormalised radial wave function ψml (r) for 1s state and for n = 1 of aluminium (z = 13). distances are in electron compton wavelengths. 0 0.5 1 1.5 0 0.1 0.2 0.3 0.4 0.5 ψ m l ( r) r figure 2. unnormalised radial wave function ψml (r) for 1s state and for n = 1 of gold (z = 79). distances are in electron compton wavelengths. general screened coulomb potential 93 (d) further, it is observed that there is a shift of maxima for 2=n towards origin for increasing values of z (figure 3). for the same value of n , however, magnitude of the wavefunction is found to fall-off rapidly with increase in r for higher values of z . 0 0.5 1 1.5 0.2 0.4 0.6 0.8 1 1.2 1.4 z = 13 z = 47 z = 79 r ψ m l ( r) figure 3. unnormalised radial wave function ψm l (r) for 2s state and for n = 2 of aluminium (z = 13), silver (z = 47) and gold (z = 79). distances are in electron compton wavelengths. (e) finally, we conclude with the remark that fairly satisfactory results of binding energies for the potential (1) can be obtained only for 1=n and that the utility of the results for the case 1≠n is restricted to the processes occurring in the region 1≅r . 5. references alhaidri, a.d., bahlouli, h. and abdelmonem. 2008. taming the yukawa potential singularity: improved evaluation of bound states and resonance energies. j. phys. a: math. theor. 41: 1-9. cooper, j.w. 1974. high energy dependence of the molecular-hydrogen photo ionization cross-section. phys. rev. a. 9: 2236-2237. dutt, r. 1979. bound s-state energies for the exponential cosine screened coulomb potential in ecker-weizel approximations. phys. lett. a. 73: 310-312. dutt, r., ray, a. and ray, p.p. 1981. bound states of screened coulomb potentials. phys. lett. a. 83: 6568. faridfathi, g. and sever, r. 2007. supersymmetric solutions of pt-/nonpt-symmetric and nonhermitian screened coulomb potential via hamiltonian hierarchy inspired variation method. j. math chem. 42: 289-291. lalit kumar sharma, philip monowe and samuel chimidza 94 greene, r.l. and aldrich, c. 1976. variational wave functions for a screened coulomb potential. phys .rev. a. 14: 2363-2366. harris, g.m. 1962. attractive two-body interactions in partially ionised plasmas. phys. rev. 125: 11311140. iyer, r.c. 1980. “ potential and scattering problems in quantum mechanics”. ph.d thesis, university of jabalpur, india. chapter 4. (unpublished). lam, c.s. and varshni, y.p. 1976. bound-state energies for the static screened coulomb potential. phys. lett. a. 59: 363-365. lam, c.s. and varshni, y.p. 1971. energies of s-state eigenstates in a static-screened coulomb potential. phys. rev. a. 4:1875-1881. mcennan, j., kissel, l. and pratt, r.h. 1976. analytic perturbation theory for screened coulomb potentials: non-relativistic case. phys. rev. a. 13: 532-562. mehta, c.h. and patil, s.h. 1978a. bound-states of the potential ( ) β+ −= r z rv . phys. rev. a. 17: 4346. mehta, c.h and patil, s.h. 1978b. nonperturbative approach to screened coulomb potentials. phys. rev. a. 17: 34-42. pratt, r.h. and tseng, h.k. 1972. behaviour of electron wave functions near the atomic nucleus and normalization screening theory in the atomic photoeffect. phys. rev. a. 5: 1063-1072. ray, p.p. and ray, a. 1980. continuum and discrete s-states for the exponential cosine screened coulomb potential by the ecker-weizel approximations. phys. lett. a. 78: 443-446. rogers, f.j., graboske, h.c. and harwood, d.j. 1970. bound eigenstates of static screened coulomb potential. phys. rev. a. 1: 1577-1586. roussel, k.m. and o’connel, r.f. 1974. variational solution of schrödinger equation for the static – coulomb potential. phys. rev. a. 9: 52-56. schiff, l.i. 1968. quantum mechanics, ch. 8. mcgraw-hill. (3rd edition). singh, d. and varshni, y.p. 1984. comparative study of the bound state of static coulomb and cut-off coulomb potentials. phys. rev. a. 29: 28952898. tseng, h.k. and pratt, r.h. 1971. exact screened calculations of atomic-field pair production and lowenergy screening. phys. rev. a. 4:1835-1843. tseng, h.k. and pratt, r.h. 1973. comments on screening and shell-ratio effects in single-quantum pair annihilation. phys. rev. a. 7:1423-1426. received 11 february 2009 accepted 24 may 2009 microsoft word biol030917.doc 17 squ journal for science, 9 (2004) 7 © 2004 sultan qaboos university 7 xanthotoxin and other furanocoumarins as phytoalexins in pastinaca sativa l. roots fatma m. al-barwani and elsadig a. eltayeb department of biology, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman, email: eatayeb@squ.edu.om. الباستيناكا ساتيفامالسانثوتوكسين والفيورانوكيومارينات األخرى كمركبات فيتو ألكسينية في جذور نبات فاطمة محمد البرواني والصادق عبداهللا الطيب السورالين، السانثوتوكسين، األيسوبمبينيلين، :أثبتت نتائج هذه الدراسة أن الفيورانوكيومارينات :خالصة ولكن وجدت الدراسة أن تركيز . الباستيناكا ساتيفامبتين توجد كمكونات طبيعية في جذور نبات األنجليسن والبيرقا هذه المركبات يزداد في الجذور المستحثة وتعتمد هذه الزيادة في التركيز على المستحث المستخدم وكذلك على يلن واأليسوبيرقابتين كمركبات مضادة باإلضافة لذلك فإن النتائج تثبت للمرة األولى وجود البيمبين. فترة الحضانة .الباستيناكا ساتيفامللفطريات منتجة طبيعياً في جذور نبات abstract: our results confirm the presence of the furanocoumarins psoralen, xanthotoxin, isopimpinellin, angelicin and bergapten as normal constituents of pastinaca sativa roots. however, the amounts of these compounds were increased in induced roots. the amount of increase in the induced roots varied depending on the inducing agent and time of incubation. in addition the results show for the first time the presence of pimpinellin and isobergapten as constitutive antifungal compounds in p. sativa roots. keywords: pastinaca sativa, angelicin, psoralen, isopimpinellin, bergapten, pimpinellin, isobergapten, antifungal compounds. 1. introduction any workers have reported elicitation of phytoalexins by various biotic factors. the most widely used and natural way for the induction of phytoalexin production is by fungal infection. in addition to biotic elicitors, salts of heavy metals and uv-light have commonly been used to elicit phytoalexins in many plants. different elicitors vary in their ability to induce phytoalexins depending on the plants induced and the phytoalexin produced. for example, ultraviolet radiation was found by mercier et al. (1993) to be the only m fatma m. al-barawani and elsadig eltayeb 8 elicitor effective in eliciting the accumulation of the carrot phytoalexin, 6-methoxymellein (1) in carrot root slices at cold storage temperatures, while edwards and strange (1991) in their test of the ability of various biotic and abiotic agents, found that uv light and heavy metals only resulted in low levels of accumulation in groundnut leaflets. on the other hand, wounding by detaching leaflets from plants and inoculation of groundnut (arachis hypogaea l.) leaflets with non-pathogenic fungi as well as naturally infected plants with major fungal pathogens resulted in the elicitation of phytoalexin response in groundnut with variation in the yield according to the challenging organism (subba rao and strange 1994). parsnips are known to contain at least six furanocoumarins namely, xanthotoxin (2), bergapten (3), isopimpinellin (4), angelicin (5), psoralen (6) and (7) imperatorin (johnson et al., 1973; berenbaum et al., 1984; desjardins et al., 1989; ekiert and gomólka, 2000). johnson and co-workers (1973), however, have established that xanthotoxin is a phytoalexin in parsnip roots by demonstrating its 20-fold induction in the roots inoculated with several fungi nonpathogenic to parsnip. in this study, phytoalexin induction in p. sativa was investigated using fungi and the abiotic elicitor cucl2. quantitative analysis using hplc was used to compare the effectiveness of these elicitors in inducing phytoalexins. time-course accumulation of phytoalexins was also followed by hplc. 2. materials and methods 2.1 plant material and fungi parsnip roots purchased from a local market (cultivar unknown) were surface sterilized in 1% sodium hypochlorite, and then rinsed twice with distilled water before use. dreschslera sorkiniana sacc. fusarium spp. and alternaria spp. were obtained from the college of agriculture, sultan qaboos university, muscat, oman. fungi were grown on petri dishes containing potato-dextrose agar medium and were incubated at 24 °c. spore suspensions were obtained by flooding cultures that produced spores or conidia with deionized water containing drops of tween-20 and gently scraping the surface. mycelial fragments were removed by passing the spore suspensions through layers of lens tissue and the density was adjusted to approximately 1.0 x 106 spores/ml with the aid of a haemocytometer. 2.2 chemicals the following standards were used for tlc and hplc analysis: isopimpinellin from carl roth (karlsruhe, germany); psoralen, xanthotoxin and bergapten from aldrich (sigma-aldrich chemie gmbh, steinheim, germany) and angelicin from sigma (sigma-aldrich chemie gmbh, steinheim, germany). only hplc grade solvents were used for hplc analysis. 2.3 induction of phytoalexins 2.3.1 chemical induction parsnip roots were chemically induced with a 50µl aliquot of 10mm cucl2 containing drops of tween-20, placed on the fresh slices of sterilized root in sterile petri dishes lined with moistened filter paper. the petri dishes were then sealed with para film and incubated in a humid environment at 24 ºc. the control slices received water containing drops of tween-20 but were otherwise treated in the same way. after 48 hr incubation, the slices were harvested for the determination of phytoalexin production. 2.3.2 biotic induction biotic induction was achieved by placing freshly sliced parsnip root disks on petri dishes containing a moistened filter paper. an agar inoculum plug (5mm diameter), mycelial side down, was then placed in the center core of each disk and incubated as above. inoculum plugs were cut from the growing margins of not more than 10 day-old cultures of a fungus. control slices received agar plugs without fungus (photo 1). phytoalexins in pastinaca sativa l. roots 9 photo 1. induction of pastinaca sativa root with 4 pathogenic fungi after 2 days incubation at 24ºc in a humid environment. 2.4 extraction and detection of phytoalexins induced and control parsnip slices were extracted twice overnight with methanol. the dried extracts were then dissolved in 100% methanol for phytoalexin analysis. a thin layer chromatography (tlc)-cladosporium bioassay was used for the detection and screening of phytoalexins. about 20 µl aliquot of the concentrated extracts were applied to tlc plates (si gel 60 f254, 20 x 20 cm). the plates were developed in either chloroform-methanol (97:3), or in toluene-ethyl acetate (1:1) and air dried. the developed tlc plates were sprayed with a dense spore suspension of dreschslera sorkiniana in a nutrient solution. the plates were then incubated at 24 °c in a moist chamber for 2-5 days. the antifungal inhibition zones were observed and the rf values calculated. the spore suspension nutrient solution was prepared by mixing 20 ml salt solution and 10 ml of 15 % glucose solution. 1 l of salt solution contained 7g kh2po4, 4g kno3, 3g nahpo4.2h2o, 1g mgso4.7h2o. 2.5 identification and quantification of phytoalexins after the tlc bioassay, using the above mentioned solvent systems, the regions of thin layer chromatograms corresponding to the inhibitory zones were scraped off and eluted with 100% methanol. identification of the antifungal compounds was carried out by co-tlc and co-hplc with authentic standards or by comparison of rf, rt values and uv spectra with literature. fatma m. al-barawani and elsadig eltayeb 10 o o oo o o o o o ome o o o ome o o o ome ome o o o o o o och2ch och2ch c(me)2 c(me)2 o oh o meo me o o o meo o o o meo ome o o o ome (6) psoralen (5) angelicin (2) xanthotoxin (3) bergapten (4) isopimpinellin (7) imperatorin (11) isoimperatorin (1) 6-methoxymellein (8) sphondin (9) pimpinellin (10) isobergapten figure 1. chemical structures of some phytoalexins phytoalexins in pastinaca sativa l. roots 11 2.5.1 thin layer chromatography purification of the eluted antifungal compounds was carried out on tlc plates (si gel 60 f-254, 20 x 20 cm). the chromatograms were developed at room temperature using the following solvent systems: a) chloroform: ethyl acetate (2:1). b) chloroform. c) toluene: ethyl acetate (1:1) following evaporation of the solvent, the thin layer plates were observed under uv light and the rf values were noted. compounds were identified from comparison of their rf values and fluorescence under uv light (254 nm) with standards run parallel to the samples. 2.5.2 hplc analysis a waters gradient system consisting of waters 626 pump, a model 600s system controller, a waters 717 plus auto-sampler and a waters in-line degasser was used for the separation and identification of antifungal compounds from the crude extracts or from the eluted tlc bands. for uv detection a waters 996 photodiode array detector was used at 254 nm. the gradient separations were carried out using a waters spherisorb ods-ii (3 µm) cartridge column (100 x 4.5 mm i.d.). solvent a was tetrahydrofuran-h2o (3.5:96.5) and solvent b was 100% meoh. the gradient profile was as follows: 0-20 min, 25% b in a (isocratic); 20-40 min, 25-45% b in a (linear gradient); 45-55 min, 45% b in a (isocratic). all standards and samples were dissolved in meoh and the injection volume was 10µl. peaks of sample and standard compounds were identified and compared by on-line uv detection at 254 nm. 2.6 antifungal activity 2.6.1 slide bioassay samples 25 µl of a series of concentration of the antifungal compounds dissolved in methanol were placed on a glass microscope slide within a circle of vaseline. these were left to dry before 50 µl of spore suspension was added. slides were incubated in a plastic container lined with moist tissue paper at 25 °c in the dark for 16 to 24 hr. spore germination and germ tube elongation were determined by microscopic observation. 2.6.2 paper-disk method paper discs (0.3cm diam.) were loaded with a known amount of the antifungal compound in absolute methanol (maximum volume, 20 µl). control disks were treated with 20 µl of methanol alone. in all cases, sufficient time was allowed for the methanol to evaporate before transferring the discs to agar surfaces. discs were arranged in potato dextrose agar (pda) petri plates, which had been inoculated with the test fungi. plates were incubated at 25 °c and diameters of inhibiting zones were measured after 20 hr. percentage inhibition was calculated as follows: 100{mycelial growth in treated/ mycelial growth in control × 100} ec50 values were calculated from the regression lines obtained from plots of concentration versus percent inhibition. 3. results 3.1 chemical induction strong antifungal zones on tlc were produced in both fungal and copper chloride treated parsnip root slices that were also present in the control slices. these compounds were identified by on-line uv detection (figure 2) and found to be the previously reported furanocoumarins xanthotoxin, isopimpinellin, angelicin and bergapten (desjardins et al., 1989; johnson et al., 1973; ekiert and gomólka, 2000). another fatma m. al-barawani and elsadig eltayeb 12 previously reported compound, sphondin (8) (rt 30) and two compounds which have not been reported from parsnip roots before, pimpinellin (9) (rt 41) and isobergapetn (10), (rt 43), were identified by their properties under uv light and by comparing their retention times and uv spectra with literature values (erdelmeier et al., 1985). however, isoimperatorin (11), earlier reported to be a constitutive component of parsnip roots was not detected in any of our samples, but another unidentified compound was detected at rt 37. surprisingly, psoralen was detected only in the control samples at very low concentration and was absent from the treated samples. figure 2. gradient hplc separation of furanocoumarins from pastinaca sativa root. separations were carried out using a waters spherisorb ods-ii (3 µm) cartridge column (100 x 4.5 mm i.d.). solvent a was tetrahydrofuran-h2o (3.5:96.5) and solvent b was 100% meoh. p: psoralen; x: xanthotoxin; a: angelicin; b: bergapten; ip: isopimpinellin. rt 29.9 sphondin; rt 43.2: isobergapten; rt 41.1: pimpinellin. quantitative hplc analysis indicated that the amounts of all of these compounds increased in the induced slices but at different levels (figure 3). the largest increase is in angelicin which increased by 34 fold in the chemically induced slices from 0.015 mg/g fresh weight in the control to 0.51 mg/g fresh weight followed by xanthotoxin which increased by 29 fold in the chemically induced slices from 0.05 mg/g fresh weight in the control to 1.48 mg/g fresh weight (table 1). table 1. increased furanocoumarin concentrations in pastinaca sativa l. root after 1 day induction with cucl2. mg/ g of fresh weight coumarin control test increase test/control psoralen 0.001 n.d.* xanthotoxin 0.051 1.475 29 isopimpinellin 0.033 0.392 12 bergapten 0.025 0.172 7 angelicin 0.015 0.51 34 * not determined phytoalexins in pastinaca sativa l. roots 13 control cucl2 0.00 0.25 0.50 psoralen xanthotoxin angelicin isopimpinellin bergapten fi gure 3: furanocoumarin content in pastinaca sativa l. root after one day incubation with cucl2. 1.0 1.5 treatment m g/ g f re sh w ei gh t 3.2 biotic induction parsnip roots inoculated with four different fungi resulted in increased levels of the furanocoumarins psoralen, xanthotoxin, isopimpinellin, bergapten and angelicin (figure 4). the five furanocoumarins were present in small amounts in control parsnip roots. both the amounts and proportions of the furanocoumarins varied with the type of elicitor used. the largest increase in furanocoumarin content was observed in parsnip roots inoculated with the fungus b. sorkiniana, while the smallest increase was in parsnip roots inoculated with alternaria spp. in all treatments, xanthotoxin was the major phytoalexin induced in parsnip roots and was the major constituent of the control roots. xanthotoxin, angelicin and psoralen were the major phytoaleins induced in parsnip roots by the fungus b. sorkiniana. treatment with copper chloride however, resulted in the accumulation of xanthotoxin and isopimpinellin as the major induced compounds, while psoralen was not detected in these discs. in addition, three other furanocoumarins, sphondin, pimpinellin and isobergapten were found in all treatments including the control but the amounts of these compounds were not determined. 3.3 time-course accumulation of phytoalexins changes in furanocoumarin content in parsnip root discs after induction with copper chloride solution over a period of six days are shown in figure 5. increase in furanocoumarin concentrations was observed from day 1 after induction. at this time, xanthotoxin and angelicin reached their maximum concentrations of 1.48 and 0.51 mg/g fresh weight respectively, followed by a rapid decline at day 2. while isopimpinellin and bergapten continued to increase to their maximum 0.60 and 0.26 mg/g fresh weight, respectively, at day 2. traces of psoralen were first observed at day 5, which increased to 0.052 mg/g fresh weight at day 6. xanthotoxin remained the dominant furanocoumarin throughout the experiments. figure 3. furanocoumarin content in pastinaca sativa l. root after one day incubation with cucl2 . fatma m. al-barawani and elsadig eltayeb 14 control alternaria bipolaris fusarium pythium cucl2 0 2 4 psoralen xanthotoxin angelicin isopimpinellin bergapten 5 6 7 8 9 10 el i ci tor m g/ g f re sh w ei gh t 0 1 2 3 4 5 6 7 0.00 0.25 0.50 0.75 1.00 1.25 1.50 psoralen xanthotoxin isopimpinellin bergapten angelicin days incubation time m g/ gr am f re sh w ei gh t figure 5. time course accumulation of furanocoumarin phytoalexins sativa l. roots induced with copper chloride. figure 4. furanocoumarin content in pastinaca sativa l. root treated with different elicitors elecicitors after 3 days incubation . phytoalexins in pastinaca sativa l. roots 15 3.4 antifungal activity three pathogenic fungi: alternaria spp. bipolaris spp. and fusarium spp. were tested for their sensitivity towards three antifungal compounds detected in p. sativa. the fungitoxic activity of the three compounds on the spore germination and the mycelial growth on agar plates are shown in table 2. all the tested furanocoumarins had relatively high ec50 values on both spore germination and mycelial growth of the tested organisms. the tested compounds inhibited spore germination of alternaria and bipolaris more effectively than mycelial growth of alternaria spp. but were most effective in inhibiting mycelial growth of fusarium spp. table 2. effective concentrations of furanocoumarins resulting in 50% inhibition of conidia germination and growth inhibition for three fungi. ec50 (µg/ml) conidia germination mycelial growth compound alternaria bipolaris alternaria fusarium xanthotoxin 1920 4320 5560 195 bergapten n.d.* 1920 6010 n.d.* angelicin 3460 n.d.* 6120 115 * not determined the high ec50 values of the furanocoumarins obtained here for mycelial growth of alternaria spp. are comparable to the values obtained by afek et al. (1995a and b) for celery. 4. discussion johnson et al. (1973) reported the production of xanthotoxin as a phytoalexin of pastinaca sativa roots inoculated with several fungi nonpathogenic to parsnip. this finding was confirmed in this study but the amounts of xanthotoxin reported here were larger than those reported by johnson and his co-workers. induction of parsnip roots with cucl2 in the present study resulted in an increase in the amounts of xanthotoxin by 29fold compared to 20fold. although xanthotoxin was found to be the major furanocoumarin component of parsnip root both constitutively (0.051 mg/g fresh weight) and cucl2 induced (1.47 mg/g fresh weight), the present study shows that xanthotoxin is not the only induced compound in parsnip roots. all other reported constitutive furanocoumarins of parsnip root, with the exception of psoralen and imperatorin, were found to increase similarly in the induced samples. the induced furanocoumarins are bergapten, isopimpinellin, angelicin and sphondin. a large increase in angelicin, psoralen, isopimpinellin and bergapten was also observed in parsnip roots inoculated with b. sorkiniana. this is therefore the first confirmation that psoralen, isopimpinellin, bergapten and angelicin are phytoalexins in parsnip roots with a similar effect to xanthotoxin. the large increase in furanocoumarins as a result of induction is in agreement with the earlier reports on the response of the umbelliferae to phytoalexin induction. for example, chaudhary et al. (1985) considered the linear furanocoumarins, psoralen (6), xanthotoxin and bergapten (7) to be phytoalexins of celery (apium graveolens) by reporting that diseased celery infected with the fungus sclerotinia sclerotiorum had greatly increased the levels of these compounds that are normally found in healthy celery (beier and oertli, 1983; chaudhary et al., 1985; ashwood-smith et al., 1986; trumble et al., 1990). similarly, al-barwani (2002) in her survey of phytoalexins in a number of umbelliferous species found that the majority of the species studied produce high levels of furanocoumarins as a result of induction. in many cases, the induced compounds were also found constitutively in small amounts in the untreated tissue. fatma m. al-barawani and elsadig eltayeb 16 the use of a gradient hplc separation of furanocoumarins with on-line uv detection and spherisorb ods ii (3 µm) column at the described gradient profile (erdelmeier et al., 1985) in this study has allowed the separation and identification of two more furanocoumarins in pastinaca sativa roots. these two compounds, pimpinellin and isobergapten were not quantified; hence their concentrations in the control and induced samples were not compared. whether they also act as phytoalexins in parsnip requires further investigation. variation in the amount and proportion of phytoalexins was observed in our study with p. sativa roots following treatment with various biotic and abiotic elicitors. the biotic elicitor, b. sorkiniana was found to be the most effective. parsnip roots induced with other fungi resulted in low levels of furanocoumarin accumulation while the heavy metal copper chloride was found to be less effective. time course studies of phytoalexin accumulation in p. sativa root showed variation in the rate of accumulation of the different compounds using the same non-specific elicitor, copper chloride. thus the major phytoalexins, xanthotoxin, and angelicin accumulated at day 1 while isopimpinellin and bergapten accumulated at day 2 after elicitation. this variation in the rate of accumulation of different phytoalexins of the same species was also observed elsewhere, e.g. in conium maculatum l. leaves following elicitation with cucl2 (al-barwani and eltayeb, 2004). in both species, psoralen was not detected until day 6 or 7 after elicitation. this was accompanied by a decrease in the levels of other coumarins. this is probably due to a decrease in the rate of transformation of psoralen (the presumed biosynthetic precursor of the other furanocoumarins) to other alkoxy-furanocoumarins. this was similarly observed in celery following elicitation with copper sulfate in cold conditions (beier and oertli, 1983). while the concentrations of xanthotoxin and angelicin in the induced roots of pastinaca sativa were found to be lower than their ec50 values on mycelial growth of alternaria and conidia germination of both alternaria and bipolaris, the concentrations of the two compounds were well above the concentrations required for 50% inhibition of mycelial growth of fusarium. thus, despite their high ec50 values, these compounds are induced in the umbelliferae at levels high enough to cause inhibition of both conidia germination and mycelial growth of some pathogenic fungi. however, it should be noted that the ec50 values were compared with the concentrations in the chemically induced tissues. since variation in the amounts of phytoalexins with the use of different elicitors was observed in the present study, the concentration of these compounds may be greater in infected tissue and thus play a role in disease resistance. to prove the role of these compounds in disease resistance, further studies are required to demonstrate that the substances are present at the right time, in the right place and in sufficient quantity to cause any observed inhibition of microbial colonization of plant tissue (mansfield, 2000). 5. acknowledgment f. al-barwani wishes to acknowledge the supervision of the late prof j. harborne under whose excellent guidance this work was partially done at the university of reading, u.k. 6. references afek, u., aharoni, n. and carmeli, s. 1995b. the involvement of marmesin in celery resistance to pathogens during storage and the effect of temperature on its concentration. phytopathology. 85: 1033-1036. afek, u., carmeli, s. and aharoni, n. 1995a. columbianetin, a phytoalexin associated with celery resistance to pathogen during storage. phytochemistry. 39: 1347-1350. al-barwani, f.m. 2002. phytoalexin induction in the umbelliferae. ph.d. thesis, university of reading, reading. uk. phytoalexins in pastinaca sativa l. roots 17 al-barwani, f.m., and eltayeb, e.a. 2004. antifungal compounds from induced conium maculatum l. plants. biochemical systematics and ecology, 32: 1097-1108. ashwood-smith, m.j., ceska, o., chaudhary, s.k., warrington, p.j. and woodcock, p. 1986. detection of furanocoumarins in plants and plant products with ultrasensitive biological photoassay employing a dna-repair-deficient bacterium. journal of chemical ecology. 12: 915932. beier, r.c. and oertli, e.h. 1983. psoralen and other linear furanocoumarins as phytoalexins in celery. phytochemistry. 22: 2595-2597. berenbaum, m.r., zangerl, a.r. and nitao, j.k. 1984. furanocoumarins in seeds of wild and cultivated parsnip. phytochemistry. 23: 1809-1810. chaudhary, s.k., ceska, o., warrington, p.j. and ashwood-smith, m. 1985. increased furanocoumarin content of celery during storage. journal of agriculture food and chemistry. 33: 1153 -1157. desjardins, a.e., spencer, g.f., plattner, r.d. and beremand, m.n. 1989. furanocoumarin phytoalexins. trichothecene toxins and infection of pastinaca sativa by fusarium sporotrichiodes. phytopathology. 79: 170-175. edwards, r. and strange, r.n. 1991. separation and identification of phytoalexins from leaves of groundnut (archis hypogaea) and development of a method for their determination by reversed-phase high-performance liquid chromatography. journal of chromatography. 547: 185-193. ekiert, h. and gomōlka, e. 2000. furanocoumarins in pastinaca sativa l. in vitro culture. pharmazie. 55: 618-620. erdelmeier, c.a.j., meier, b. and sticher, o. 1985. reserved-phase high-performance liquid chromatographic separation of closely related furanocoumarins. journal of chromatography. 346: 456-460. johnson, c., brannon, d.r. and kuć, j. 1973. xanthotoxin: a phytoalexin of pastinaca sativa root. phytochemistry. 12: 2961-2962. mansfield, j.w. 2000. antimicrobial compounds and resistance: the role of phytoalexins and phytoanticipins. in: mechanisms of resistance to plant diseases (slusarenko, a., fraser, r.s.s. and van loon l.c. eds.) pp. 325-370. kluwer academic publishers, netherlands. mercier, j., arul, j. and chantal, j. 1993. effect of uv-c on phytoalexin accumulation and resistance to botrytis cinerae in stored carrots. journal of phytopathology. 139: 17-25. subba rao, p.v. and strange, r.n. 1994 groundnut phytoalexins and disease resistance. in: handbook of phytoalexin metabolism and action, (danneil, m. and purkayastha, r.p., eds), pp 199-227. marcel dekker, new york. trumble, j.j., derecks, w., quiros, f. and beier, c. 1990. host plant resistance and linear furanocoumarin content of apium accessions. journal of economic entomology. 83: 519-525. received 17 september 2003 accepted 31 march 2004 microsoft word math040228 final version-f.doc squ journal for science, 9 (2004) 33-40 © 2004 sultan qaboos university 33 a new approach to the stabilization of the wave equation with boundary damping control boumediène chentouf and mohamed s. boudellioua department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al khod 123, muscat, sultanate of oman, email: chentouf@squ.edu.om.. إقرار معادلة موجة بنظام تحكم حدي مخمد بومدين شنتوف ومحمد صالح بودليوة يهتم هذا البحث بدراسة مسألة إقرار نظام مكون من معادلة موجة في مجال محدود مع شروط حدية :خالصة كانه أن حتى تتم عملية االقرار نقترح نظام تحكم مخمد ونبرهن أن هذا النوع من التحكم بإم .من نوع نومان وباإلضافة إلى ذلك ، نبرهن أن موضع االستقرار . يجعل حلول معادلة الموجة تتقارب نحو موضع إستقرار . يتعلق بالشروط األساسية فقط abstract: this paper deals with boundary feedback stabilization of a system, which consists of a wave equation in a bounded domain of n , with neumann boundary conditions. to stabilize the system, we propose a boundary feedback law involving only a damping term. then using a new energy function, we show that the solutions of the system asymptotically converge to a stationary position, which depends on the initial data. similar results were announced without proof in (chentouf and boudellioua, 2004). keywords: wave equation, neumann condition, boundary damping control, energy function, asymptotic behavior. 1. introduction et ω be a bounded open connected set in n having a smooth boundary γ = ∂ω of class 2c . given a partition ( )0 1,γ γ of γ , consider the following wave equation: ( ) ( ) ( ), , 0, in 0,tty x t y x t− ∆ = ω× ∞ (1.1) with neumann boundary conditions and initial conditions l boumediene chentouf and mohamed s. boudellioua 34 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 1 0 0 , 0, 0, , , ( ), 0, , , 0 , , 0 ,t y x t on y x t u t on y x y x y x z x υ υ ∂ = γ × ∞∂  ∂ = γ × ∞ ∂  = =  (1.2) where υ is the unit normal of γ pointing towards the exterior of ω and u is a feedback law to be determined. note that 1γ is supposed to be nonempty whereas 0γ may be empty. as in chentouf and boudellioua (2004), we propose a feedback depending only on a damping term, that is, ( ) ( ) ( ) ( ) ( )1, , , 0,tu t a x y x t x t= − ∈γ × ∞ (1.3) where ( )1a l∞∈ γ satisfies ( ) 0 0a x a≥ > for any 1x ∈γ . then, it is proved that the solutions of the closed loop system asymptotically tend towards a constant depending on the initial data 0 0andy z . there is a rich literature concerning the stabilization problem of the wave equation (see for instance bardos et al. (1992), chen (1979a, 1979b, 1981a, 1981b), komornik (1994), lax et al. (1963), lagnese (1988), lions (1988a, 1988b), morawetz (1975), quinn and russell (1977), triggiani (1975) and the references therein). in all references cited above, at least one of the following conditions is assumed to be satisfied: • the equation (1.1) involves also the displacement term y. • the stabilizing feedback law ( )u t contains not only a boundary dissipation term ty but also the boundary displacement y . • the first boundary condition in (1.2) involves the displacement term y (the boundary condition (1.2) is replaced for instance by 0 or 0 y y y υ ∂ = + = ∂ on ( )0 0,γ × ∞ . the main contribution of this paper is to provide an alternative proof of lagnese's result (1983) by means of a simple and direct method. the key idea of the proof is to introduce a new energy norm (see chentouf and boudellioua (2004) for similar systems and conrad et al. (2002) for one-dimensional wave equation). 2. preliminaries and well-posedness of the problem in this section, we study the existence and uniqueness of the solutions of the closed-loop system (1.1)(1.3). assume, without loss of generality, that for any ( )1,x a x a∈γ = , where a is a positive constant. then, consider the state space ( ) ( )1 2 ,h h l= ω × ω (2) equipped with the inner product a new approach to stabilization of the wave equation 35 ( )( ) ( ) ( )( ) 1 1 , , σ σ , h y z y z y y zz dx z dx ay d zdx ay dε ω ω γ ω γ = ∇ ∇ + + + + ∫ ∫ ∫ ∫ ∫ (2.1) where 0ε > is a constant to be determined. the first result is stated in the following proposition: proposition 1. the state space ( ) ( )1 2h h l= ω × ω endowed with the inner product (2.1) is a hilbert space provided that ε is small enough. proof of proposition 1. it suffices to show that the norm h ⋅ induced by the inner product (2.1) is equivalent to the usual one ( ) ( )1 2h lω × ω ⋅ , that is, the existence of two positive constants k and k such that ( ) ( ) ( ) ( ) ( ) ( ) ( )1 2 1 2 , , , h l h h l k y z y z k y z ω × ω ω × ω ≤ ≤ . (2.2) applying holder's inequality and using trace theorem adams (1976) (see also mikhaïlov (1980)) yield: ( ) ( )( ) ( ) ( )( )( ) 2 2 2 2 22 1 1 , 1 2 2 1 2 , h y z y mes z dx a c mes y y dx ε ε ε ω ω ≤ ∇ + + ω   + γ ∇ + + ∫ ∫ where 1c is a positive constant depending on ω (see adams (1976) or mikhaïlov (1980)). therefore (2.2) holds for a positive constant k depending on ( ) ( )1 and, ,a mes mesε γ ω . for the reverse inequality, we proceed as follows: ( ) ( ) ( ) ( ) ( )( ) 1 1 222 2 2 , σ 2 σ . h y z y z dx z dx ay d ay d z dx ε ε ε ω ω γ γ ω = ∇ + + + + ∫ ∫ ∫ ∫ ∫ (2.3) obviously for any 0,δ > , young's inequality yields ( )( ) ( ) ( ) 1 1 22 12 σ σ .ay d z dx a z dx a y dδ δ− γ ω ω γ ≥ − −∫ ∫ ∫ ∫ (2.4) combining (2.4) and (2.3), we get ( ) ( ) ( )( ) ( )( ) 1 222 2 2 1, 1 σ . h y z y z dx a z dx a a y dε δ ε δ− ω ω γ ≥ ∇ + + − + −∫ ∫ ∫ (2.5) furthermore, using a classical compactness argument, one can show the following generalized poincaré inequality: ( ) 1 2 2 2 2 σ ,y dx c y dx y dω ω γ   ≤ ∇ +    ∫ ∫ ∫ where 2 0c > depends on ω . this, together with (2.5), implies that boumediene chentouf and mohamed s. boudellioua 36 ( ) ( ) ( ){ } ( ) ( ) 2 2 2 21 2 2 1 , 1 , h y z a a c y a a y z dx a z dx ε δ ε δ ε δ δ − ω − ω  ≥ − + − − ∇ +    + − ∫ ∫ (2.6) for any aδ < . finally, applying again holder's inequality to the last term in (2.6), one can show the existence of a positive constant k depending on ,a δ and ( )mes ω such that the second inequality in (2.2) holds, provided that aδ < and ε satisfies the following condition ( ) ( ) ( ) 1 min , . a a a mes δ ε δ δ   <   − − ω  this concludes the proof of proposition 1. ■ we turn now to the formulation of the closed-loop system (1.1)-(1.3) in an abstract form on .h let ( ) ( ) ( ) ( ) ( )( ), , and , , , .tz t y t t y t z t⋅ = ⋅ φ = ⋅ ⋅ then, the closed loop system can be written as follows ( ) ( ) ( ) ( )0 0 0 , 0 , , t t t y z αφ = φ  φ = φ = (2.7) where a is an unbounded linear operator defined by ( ) ( ) ( ) ( ) ( )1 1 2 0 1 , ; ; , 0 on ; 0 on y z h h y l d a y y az υ υ  ∈ ω × ω ∆ ∈ ω   =  ∂ ∂ = γ + = γ  ∂ ∂  (2.8) and for any ( ) ( ), ,y z d a∈ ( ) ( ), , .a y z z y= ∆ (2.9) it is a simple task to check that the operator ,a− defined by (2.8)-(2.9), is maximal monotone. therefore, it follows from semigroups theory pazy (1983) (see also brezis (1992)) that: lemma 1. (i) the linear operator a generates a 0c semigroup of contractions ( )s t on ( ).h d a= (ii) for any initial data ( ) ( )0 0 0, ,y z d aφ = ∈ the system (2.7) has a unique strong solution ( ) ( ) ( )( ) ( ) ( )0, , ,tt y t y t s t d aφ = ⋅ ⋅ = φ ∈ for all 0t ≥ such that ( ) ( ), ty yφ ⋅ = ∈ ( ) ( )( )1 ; ;c h c d a+ +∩ . moreover, the function ( ) h t a tφ is decreasing. (iii) for any initial data ( )0 0 0,y z hφ = ∈ , the system (2.7) has a unique weak solution ( ) ( ) ( )( ) ( ) 0, , ,tt y t y t s t hφ = ⋅ ⋅ = φ ∈ such that ( ) ( ) ( )0, ;ty y c h+φ ⋅ = ∈ . a new approach to stabilization of the wave equation 37 3. asymptotic behavior in this section, we will show an asymptotic behavior result for the unique solution of (2.7) in the state space ( ) ( )1 2h h l= ω × ω . to do so, we shall first show the following lemma: lemma 2. the resolvent operator ( ) 1 :i a h hλ −− → is compact for any 0λ > and hence the canonical embedding ( ):i d a h→ is compact, where is equipped with the graph norm. proof of lemma 2. let ( ), ,f g h∈ . we seek ( ) ( ),y z d a∈ such that ( )( ) ( ), ,i a y z f g− = . equivalently, ( ) ( ) ( ) 0 1 1 2 , , 0, on , , on , ; . z y f y y f g y y ay af y h y l υ υ   = −  ∆ − = − + ∂ = γ ∂ ∂ + = γ∂ ∈ ω ∆ ∈ ω using lax-milgram theorem (see brezis (1992)), one can readily show that the above system has a unique solution and thus the operator ( ) 1i a −− exists and maps ( )intoh d a . finally, by using sobolev embedding, we deduce that ( ) 1i a −− is compact. the proof of lemma 2 follows then from the wellknown result of kato (1976). ■ the main result of this paper is: theorem 1 . for any initial data, ( )0 0 0, ,y z hφ = ∈ the solution ( ) ( ) ( )( ), , ,tt y t y tφ = ⋅ ⋅ of (2.7) tends in h to ( ), 0 ,c as t → +∞ where ( ){ } ( ) 1 1 1 0 0 σc a mes z dx ay d − ω γ = γ +∫ ∫ . proof of theorem 1. by a standard argument of density of ( )2d a in h and the contraction of the semigroup ( ),s t it suffices to prove theorem 1 for smooth initial data ( ) ( )20 0 0,y z d aφ = ∈ . let ( ) ( ) ( )( ) ( ) 0, , ,tt y t y t s tφ = ⋅ ⋅ = φ be the solution of (2.7). it follows from (ii) of lemma 1 that the trajectory of solution ( ){ } 0t t ≥ φ is a bounded set for the graph norm and thus precompact in h by virtue boumediene chentouf and mohamed s. boudellioua 38 of lemma 2. applying lasalle's principle, we deduce that ( )0ω φ is non-empty, compact, invariant under the semigroup ( )s t and ( ) ( ) [ ]0 0 as 10s t tωφ → φ → ∞ . in order to prove the strong stability, it suffices to show that ( )0ω φ reduces to ( ), 0c . to this end, let ( ) ( ) ( )0 0 0 0,y z d aωφ = ∈ φ ⊂ and ( ) ( ) ( )( ) ( ) ( )0, , ,tt y t y t s t d aφ = ⋅ ⋅ = φ ∈ the unique strong solution of (2.7). recall that it is well-known that ( ) h tφ is constant haraux (1991) and thus ( )( )2 0,hd tdt φ = i.e., 1 2 , σ 0.ha a z dγ< φ φ > = − =∫ (3.1) this implies that 0tz y= = on 1γ and therefore y is solution of the system system: ( ) ( ) ( ) 0 1 0 0 1 2 0, 0, on , 0, on , 0 ; , ; , tt t t y y y y y y y y z y h y l υ υ − ∆ = ∂ = γ ∂  ∂ = = γ ∂  = =  ∈ ω ∆ ∈ ω  (3.2) whereas tz y= is solution of the system ( ) ( ) 0 1 0 0 0, 0, on , 0, on , 0 ; 0 . tt t z z z z z z z z y υ υ − ∆ = ∂ = γ ∂  ∂ = = γ  ∂  = = ∆ (3.3) obviously, to deduce the desired result, it suffices to show that y = constant is the only solution of (3.2). to do so, we first use the standard holmgren's uniqueness theorem (see john (1982)) for the system (3.3) to conclude that 0z ≡ . thus the system (3.2) is reduced to the elliptic problem: 0, 0, on , y y υ ∆ =  ∂ = γ∂ which clearly yields that y ≡ constant. this, together with (3.1), implies the desired result. ■ a new approach to stabilization of the wave equation 39 remark 1. integrating with respect to x and t and using green formula for the closed loop system (1.1)(1.3), we obtain the following identity: 1 1 0 0σ σ.ty dx ay d z dx ay dω γ ω γ+ = +∫ ∫ ∫ ∫ furthermore, if the initial data ( )0 0,y z satisfies the additional condition 1 0 0 σ 0,z dx ay dω γ+ =∫ ∫ then the constant c of theorem 1 is zero, i.e., ( ) ( )( ) ( ), , , 0, 0ty t y t in h as t⋅ ⋅ → → +∞ . 4. acknowledgements the authors acknowledge the support of sultan qaboos university (grant ig/sci/doms/02/08). the authors are also grateful to the referees for their useful remarks and helpful suggestions. 5. references adams, r.a. 1975. sobolev spaces. pure and applied mathematics, vol. 65. academic press, new yorklondon. bardos, c., lebau, g., and rauch, j. 1992. sharp sufficient conditions for the observation, controllability and stabilization of waves from the boundary. siam j. control optim., 30(5): 10241064. brezis, h. 1992. analyse fonctionnelle, théorie et applications. paris: masson. chen, g. 1979a. energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain. j. math. pures appl., 58: 249-274. chen, g. 1979b. control and stabilization for the wave equation in a bounded domain. part i, siam j. control optim. 17: 66-81. chen, g. 1981a. control and stabilization for the wave equation in a bounded domain. part ii, siam j. control optim., 19: 114-122. chen, g. 1981b. a note on boundary stabilization of the wave equations. siam j. control optim., 19: 106-113. chentouf, b. and boudellioua, m.s. 2004. on the stabilization of the wave equation with dynamical control. in: proc. 16th international symposium on mathematical theory of networks and systems, 2004, leuven, belgium, 6 pages. conrad, f., o'dowd, g. and saouri, f.z. 2002. asymptotic behaviour for a model of flexible cable with tip masses. asymptot. anal., 30: 313-330. haraux, a. 1991. systèmes dynamiques dissipatifs et applications. paris. john, f. 1982. partial differential equations. (2nd edition) springer-verlag. kato, t. 1976. perturbation theory of linear operators. springer-verlag. komornik, v. 1994. exact controllability and stabilization. the multiplier method. masson, paris. lax, p.d, morawetz, c.s, and philips, r.s. 1993. exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle. comm. pure appl. math., 65: 447-486. lagnese, j. 1983. decay of solutions of the wave equation in a bounded region with boundary dissipation. j. diff. equ., 50: 163-182. lagnese, j. 1988. note on boundary stabilization of wave equations. siam j. control optim., 26(5): 1250-1256. boumediene chentouf and mohamed s. boudellioua 40 lions, j.l. 1988a. exact controllability, stabilization and perturbations for distributed systems. siam review, 30(1): 1-68. lions, j.l. 1988b. contrôlabilité exacte et stabilisation de systèmes distribués. 1, masson, paris. majda, a. 1975. disappearing solutions for the dissipative wave equations. indiana univ. math. j., 24: 1119-1133. mikhaïlov, v. 1980. equations aux dérivées partielles. mir, moscou 1980. morawetz, c.s. 1975. decay of solutions of the exterior problem for the wave equations. comm. pure appl. math., 28: 229-264. pazy, a. 1983. semigroups of linear operators and applications to partial differential equations. springer-verlag, new york. quinn, j.p., and russell, d.l. 1977. asymptotic stability and energy decay rate for solutions of hyperbolic equations with boundary damping. proc. roy. soc. edinburgh. 77: 97-127. rauch, j., and taylor, m. 1974. exponential decay of solutions to hyperbolic equations in bounded domain. indiana. univ. math. j., 24(1): 79-86. russell, d.l. 1978. controllability and stabilizability theory for linear partial differential equations: recent progress and open questions. siam review, 20(4): 639-739. triggiani, r. 1989. wave equation on a bounded domain with boundary dissipation: an operator approach. j. math. anal. appli., 137: 438-461. received 28 february 2004 accepted 18 december 2004 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 47-54 © 2003 sultan qaboos university a monte carlo method for low pressure radio frequency discharges lahouaria settaouti and abderrahmane settaouti department of electronics, university of sciences and technology, p.o.box 1505 oran, el-m’naouar, algeria, email: settaouti@yahoo.fr طريقة مونت كارلو لتفريغ تردد راديو تحت ضغط منخفض هوارية ستاوتى وعبدالرحمن ستاوتى إن االهتمام بالتفريغ تزيد الراديو إزداد كثيراً في األعوام األخيرة وذلك ألهميته في تقنيات اإللكترونيات الصغيرة : خالصة م بخصوصية التفريغ في غاز موجب التكهرب الذي يكثر استعماله في التطبيقات التكنولوجية في هذا الدقيقة وخاصة اإلهتما البحث نقدم بعض الخصوصيات المفصلة للبالزما تردد الراديو الموجودة عن طريق محاكاة مونت كارلو في غاز موجب . التكهرب abstract: there is increasing interest in glow discharges because of their importance to a large number of application fields, like the microelectronics industry, flat plasma display panel technology, the laser and light industry and analytical spectrochemistry. to improve the capabilities of rf glow discharges, a good understanding of the discharge physics is highly desirable. the typical calculated results include the radio frequency (rf) voltage, the electrical field distribution, the density of argon ions and electrons, the electron energy distribution function and information about the collision processes of the electrons with the monte carlo model. these results are presented throughout the discharge axis and as a function of time in the rf cycle. moreover, we have investigated how many rf cycles have to be followed before a periodic steady state is reached. keywords: monte carlo simulation, glow discharge, radio frequency, plasma. 1. introduction glow discharges are being used in many fields of application. they serve extensively as plasma processing devices in microelectronics, such as for ion etching, thin film deposition, and plasma treatment of surfaces, and they also find application as atomization excitation ionization sources in analytical chemistry (bogaerts et al 1995), (choi et al 1992), (wang et al 1997). a wide range of parameter space can be chosen to operate the plasma processes. by parameters here we mean those quantities that can be varied by changing not only the position of some external "knobs" (for example, pressure, current or voltage applied, and frequency), but also other quantities that cannot be varied as easily, such as electrode spacing and electrode area ratio. to attain better results in these application fields, a quantitative understanding of the glow discharge is required. the application of gas discharges in processing of materials for microelectronics has reached the point where it is not possible to achieve improvements purely on an empirical basis. theoretical investigations have recently reached a new level that promises to be a sufficiently good foundation for predictive models (nanbu, 2000), (yonemura et al 2001). however, in order to accomplish that goal, further experimental studies of the discharges and a wide range of data are required. on the other hand, plasma technological devices and processes are complex and it is necessary to have constant monitoring. a thorough physical understanding of such discharges, in particular of the spatial dependencies of plasma parameters as charged particle 47 lahouaria settaouti and abderrahmane settaouti densities and fluxes, electric field and electron temperature, in particular in the plasma and electrode sheath, is therefore desirable. theoretical study of glow discharge in the past has been mostly qualitative or semiquantitative in nature. rigorous approach to the problem requires functional solutions of the discharge equations which are difficult to obtain in analytic forms. an alternative is to use a large computer and solve the discharge equations numerically by means of some algorithms. consequently, there has been significant interest in developing models for these plasma based processes (gogolides, 1997), (denpoh et al. 2000). a validated process model has several benefits ranging from providing an understanding of mechanisms and in-process control to aid in equipment design. a current challenge in designing plasma processing tools is the development of computer models of rf discharges that can accurately describe non-equilibrium charged particle transport and plasma chemistry, yet execute quickly enough to make more realistic multidimensional simulations feasible. as in most areas of computational plasma and discharge physics, it is possible to describe the physical processes in the discharge with a variety of approaches. generally one uses either a fluid treatment (franklin, 1999), a kinetic scheme (loffhagen et al 2002), or a hybrid combining aspects of the fluid and kinetic schemes (garrigues et al. 2000). briefly, kinetic schemes solve for at least some of the species velocity distribution functions in both time and space whereas fluid models assume distribution functions. kinetic schemes are therefore intrinsically higher dimensional than fluid models since kinetic schemes involve solutions in velocity space as well as physical space and time. all other things being equal, kinetic schemes are generally much more costly computationally than fluid models because they provide more information. the monte carlo simulation has become increasingly important as a simulation tool particularly in the area of low temperature plasma physics. the motivation for the development of the computer simulation described in this paper has its basis in the need to quantitatively understand microelectronic plasma processing. 2. description of the model monte carlo methods as applied to gas discharge problems involve evaluating the percentage of a given species of particles emanating from a given source, after experiencing energy loss and gain and terminating in defined categories. its technique is realistic because a large number of particles is followed from the source throughout their life history. the fundamental physical concept is the mean free path or the mean free flight time, with the collision equations being formulated subject to the conditions such as the number density, and electric field intensity. the computing time for the monte carlo technique depends upon the number of test electrons released from the space of the interval and the number of collisions occurring while each electron travels the distance from the cathode to the anode. a simple group of electrons, typically 100-500, is randomly seeded between the electrode plates. the initial distributions of simulation particles are assumed to be maxwellian of 5 ev for electrons. the three dimensional motion of electrons between two successive collisions under the electric field is solved numerically with use of euler method. electron flight time between two successive collisions is determined by the electron collision cross-section with ar neutral particles. the scattering after all collisions is assumed to be isotropic. the secondary electron emission coefficient due to electrons flowing to the two electrodes is assumed to be zero. the distribution of the electric field is calculated from the solution of the one dimensional poisson's equation with the use of the electron and ion densities at the end of each time step. electron trajectories using the monte carlo method (helin et al 1996, settaouti et al 1999, nanbu, 2000, settaouti et al., 2001) for an rf parallel plate discharge in an electropositive gas (ar) while oscillating the applied electric field providing a time and spatially dependent electric field over many rf cycles are computed. the electrode system is assumed to consist of parallel plates with a diameter that is larger than the electrode separation. every electron, during its transit in the gas, performs a succession of free flights punctuated by elastic or inelastic collisions with atoms of gas defined by collision cross-sections. during the successive collisions 48 a monte carlo method for low pressure radio frquency discharges for every electron, certain information (velocity, position, etc.) is stored in order to calculate, from appropriate sampling methods, transport coefficients and macroscopic coefficients. the probability of collision and the nature of collision are simulated by comparison with computer generated random numbers. the probability of collision in the time step ∆t is       ∆− −= mt t p exp1 (1) tm is the mean flight time of an electron moving with a velocity v(ε), ( ) ( )εε vtnq tm . 1 = (2) in which v(ε) is the drift velocity of an electron. where qt is the total collision cross-section in m2, n the gas number density and ε the electron energy in ev. qt is a function of the electron energy. at t = 0 an electron observes a free flight time with a randomly selected angle of entry depending on the cosine distribution. the collision is simulated by comparing p with r1 at the end of each step, where r1 is a random number uniformly distributed between 0 and 1. when the electron undergoes a collision 1exp1 rt t p m ≥               ∆− −= (3) the nature of the collision is determined in the following way: p2,j is the probability that collision process j takes place, j = 1, 2, 3,... n, including momentum transfer, excitation, and ionization collisions. this leads to t i j q q p =2 ∑ = 12 jp nj pppp 222,21,2 ≤≤≤ jj ppprppp ,22,21,221,22,21,2 ....++≤≤++ − (4) determines the j-th collision process. the sum of the fractional probabilities is equal to unity, and the interval [0,1] is divided into segments with lengths corresponding to these fractional probabilities. a new random number r2 between 0 and 1 is generated, and the interval into which this random number falls, determines the type of collision that occurs. the new energy and direction after the collision depends upon the type of collision: for excitation, the excitation threshold energy e is given by: exceee −= 0 , where eexc is the excitation threshold and e0 is the electron energy before collision. for ionization, the total energy before collision is divided between the primary (original) electron and the secondary electron created in the ionization collision. for elastic collisions, the new kinetic energy of the electron is calculated by     −−= )cos1(210 χεε m m (5) which is deduced from the hard sphere model. χ is the scattering angle of the electron after collision, where m and m are the masses of electron and argon atom, respectively. after a collision the angles are determined by isotropic distribution. the assumption of isotropic scattering is a hypothesis which is consistent with the first order theory if, at the same time the total collision cross section is replaced by the momentum transfer cross section. the total number of electrons in the gap increases over many orders of magnitude, hence scaling is necessary to limit the number of simulation particles. when, the total number of simulation particles, exceeds the maximum allowable number of simulation particles, which is specified in the program input data, a statistical subroutine is introduced to choose a new group of larger particles to represent the old larger group 49 lahouaria settaouti and abderrahmane settaouti of smaller particles. the subroutine contains a weighing of velocity distribution of the old group, so that the new group is equivalent in phase space to the old group. in this simulation, the steady state is defined as that in which the electron and ion densities at the center of the bulk region stop increasing, when the initial densities are at least one order of magnitude smaller than the final densities. 3. results and discussion we present typical results of numerical simulations using a monte carlo method of rf plasmas sustained by an rf external source of 13.56 mhz and 200 v applied to the electrode at z = 0, in an argon model gas. the electrode system is assumed to consist of parallel plates with a diameter that is larger than the electrode separation. electrode separation and gas pressure used are 4 cm and 0.3 torr, respectively. the electron collision cross sections set of ar employed is that reported by delcroix (1960), christophorou (1971), huxley et al (1974) and vossen et al (1978). it is seen from figure 1 that the electric field in the first cycle oscillates with a period corresponding to the rf cycle. figure 2 shows that the mean electron energy in the first rf cycle is maximum when the electric field for this cycle is maximum, minimum where the electric field is minimum, and is almost spatially constant with small oscillation with the rf external field. 0.2 0.4 0.6 0.8 1.0 0.8 1.6 2.4 3.2 4.0 -100 0 100 e (v/cm) di sta nc e ( cm ) time (cycle) 0.2 0.4 0.6 0.8 1.0 0.8 1.6 2.4 3.2 4.0 0 15 30 ε (ev) d ist an ce (c m ) time (cycle) figure 1. temporal and spatial variations figure 2. temporal and spatial variations of the of the electric field for the first rf cycle. mean energy of electrons for the first rf cycle. the electric field in the first cycle oscillates with a period corresponding to the rf cycle. the electron density is low at the beginning of the avalanche growth but as time increases, the enhancement becomes greater, and oscillates with the change in the direction of the electric field (figure 3). when the applied electric field is sufficiently large, the electron accelerates to a high enough kinetic energy that makes inelastic collisions between the electron and the background gas occur. as the electron proceeds from the cathode to the anode, driven by the applied electric field, it undergoes many ionizing collisions in each of which an ion and another electron are formed. thus, we obtain an expanding cloud of electrons traveling toward the anode, known as electron avalanche, and a cloud of ions, almost stationary in the time scale of motion of the electron avalanche, remaining behind, and the space charge field distortion begins. 50 a monte carlo method for low pressure radio frquency discharges 0.2 0.4 0.6 0.8 1.0 0.8 1.6 2.4 3.2 4.0 1 ne (cm -3) distance (cm) tim e ( cyc le) 0 1 2 3 4 -60 -30 0 30 60 e (v/cm) 16t/25 17t/25 18t/25 19t/25 distance (cm) figure 3. temporal and spatial variations figure 4.1. electric field in argon discharge of the electron density for the first rf cycle. as a function of position for different times, and t is the rf cycle (third cycle). 0 1 2 3 4 -200 -100 0 100 200 300 e (v/cm) t/25 2t/25 4t/25 distance (cm) 0 1 2 3 4 -1000 0 1000 e (v/cm) 18t/25 19t/25 20t/25 21t/25 distance (cm) figure 4.2. electric field in argon discharge figure 4.3. electric field in argon discharge as a function of position for different times, as a function of position for different times, and t is the rf cycle (fourth cycle). and t is the rf cycle (fourth cycle). the space charge field distortion begins in the third cycle (figure 4.1), and in the beginning of the fourth cycle (figure 4.2), the field behind and ahead of the avalanche is enhanced, while in the bulk of the avalanche it is weakened by the space charge field. figures 4.3 and 4.4 show, the spatial and temporal evolution of the electric field during the fourth rf cycle, when the plasma is established. there are two distinct regions with respect to the flow of electron energy in a parallel 51 lahouaria settaouti and abderrahmane settaouti plate rf discharge; the bulk plasma and the sheaths. the electric field for the discharge is symmetric about the discharge mid-plane (in the parallel plate gap there are the sheath region, the bulk plasma and the sheath region). we also see from the figures 4.3 and 4.4 that the electric field in the sheath regions, adjacent to the electrodes, oscillates with significant amplitude with period corresponding to that of rf cycle. most of rf external electric field is absorbed in the sheath regions. as the cycle advances, electrons are pushed out of the right sheath and into the left one. the movement of electrons causes a modulation of sheath width. the sheaths are quite wide causing the discharge to behave capacitively. the apparent sheath thickness is 0.3 cm, (the sheath width was defined as the distance from the electrode to the edge region of the bulk plasma) and most of the voltage difference is concentrated in the sheaths. in the center and close to the electrodes the temporal modulation of electric fields is fairly well represented by a sinusoid with little dc bias.. the central bulk plasma is characterized by a weak electric field (few v/cm). at the times an electrode is cathodic, the plasma near the electrodes resembles the cathode fall of dc discharge in that there is a large voltage drop between the electrode and the bulk plasma in the center of the discharge. the calculated electric field (temporal and spatial variations) and sheath thickness compared with the measured values (sato et al 1990), (guo et al 1996), show good agreement. 0.2 0.4 0.6 0.8 1.0 0.8 1.6 2.4 3.2 4.0 -2000 -1000 0 1000 2000 e (v/cm) di sta nc e ( cm ) time (cycle) 0 1 2 3 4 100 101 102 103 104 105 106 107 108 109 1010 distance (cm) ne (cm -3) figure 4.4. temporal and spatial variations figure 5.1. electron density as a function of the electric field for the fourth rf cycle. of position for the fourth rf cycle. at the beginning of the growth of the avalanche, the electron density is low, and as time increases, the enhancement becomes greater and the electron density oscillate with the change in the direction of the electric field. when the plasma is established, electrons are contained in the plasma in part by the space charge fields. depending on the phase of the applied potential, electrons move toward either electrode. their movement affects the local field causing electrons to pile in the bulk sheath interface. the charged particle density profiles for argon are shown in figures 5.1 and 5.2. from figure 5.2 we see the positive ion density (due to the ionization) as a function of position. the central bulk plasma is characterized by a high density of electrons and positive ions, and the approximately equal densities of electrons and positive ions. the small peaks around the two sheath edges appear in the electron density. the positive ion density form an envelope around electrons, which move in and out of the sheath region. the agreement between, 52 a monte carlo method for low pressure radio frquency discharges the calculated charged particle density compared with the measured values (sato et al 1990), (guo et al 1996), is good. in figure 6, the profiles of the electron mean energy as a function of the distance show the different natures of the three regions in the discharge. the electron mean energy is low through the plasma bulk region and the relatively large modulations take place in sheath regions. the maximum in the electric field in the sheath regions create a maximum in the average electron energy shown in figure 6. here the secondary electron emission was assumed to be zero. indeed the maximum in the electric field is close to the maximum in energy, but not exactly at the same position in space or time because we do not assume local equilibrium with the field. the average electron energy is low in time and space in the bulk region, when the electric field is minimum. 0 1 2 3 4 100 101 102 103 104 105 106 107 108 109 1010 distance (cm) ne (cm -3) 0 1 2 3 4 0 2 4 6 8 10 ε (ev) distance (cm) figure 5.2. positive ion density as figure 6. the mean energy of electrons a function of position for the fourth as a function of position for the fourth rf cycle. rf cycle. 4. conclusion we have presented typical numerical results obtained using the monte carlo simulation code, and have shown the detailed properties of rf plasmas in argon gas which is sustained by an rf external source of 13.56 mhz and 200 v. the simulation results show that there are two distinct regions with respect to the flow of electron energy in a parallel plate rf discharge, the bulk plasma and the sheaths. the electric field is maximum in the sheath and minimum in the bulk region. the electric field in the sheath changes almost linearly from both electrodes to the edge region of the bulk plasma. the movement of electrons causes a modulation of sheath width. the sheaths are quite wide causing the discharge to behave capacitively. the discharge parameters are symmetric about the discharge mid-plane because we assumed that the geometry consists of parallel plates with a diameter that is larger than the electrode separation.. the model is in good qualitative agreement with experimental measurements. 53 lahouaria settaouti and abderrahmane settaouti references bogaerts, a., gijbels, r. 1995. the role of fast argon ions and atoms in the ionization of argon in a direct current glow discharge: a mathematical simulation. j. appl. phys. 78(11): 6427-6431. choi, s. w., lucovsky, g., bachmann, k. j. 1992. remote plasma enhanced chemical vapor deposition of gap with in situ generation of phosphine precursors. j. vac. sci. technol. b10(3): 1070-1073. christophorou, l. g., 1971. atomic and molecular radiation physics. wiley, new york. delcroix, j. l., 1960. introduction to the theory of ionized gases. wiley , new york. denpoh, k., nanbu, k. 2000. self consistent particle simulation of radio frequency cf4 discharge: effect of gas pessure. jpn. j. appl. phys. 39(part. 1., 5b): 2804-2808. franklin, r. n. 1999. the fluid model of the positive column of a discharge with negative ions at low pressure joining plasma and sheath. j. phys. d: appl. phys. 32: l71-l74. garrigues, l., heron, a., adam, j. c., boeuf, j. p. 2000. hybrid and particle in cell models of a stationary plasma thruster. plasma sources sci. technol. 9: 219-226. gogolides, e. 1997. a synthetic approach to rf plasma modeling verified by experiments: demonstration of a predictive and complete plasma simulator. jpn. j. appl. phys. 36(part. 1., 4b): 2435-2442. guo, x. m., zhou, t. d., pai, s. t., 1996. experimental study of spatial distribution of ar glow discharge plasma. phys. plasmas, 3(10): 3853-3857. helin, w., zuli, l., daming, l. 1996. monte carlo simulation for electron neutral collision processes in normal and abnormal discharge cathode sheath region. vacuum. 47(9): 10651072. huxley, l. g. h. and crompton, r. w., 1974. the diffusion and drift of electrons in gases. wiley, new york. loffhagen, d., sigeneger, f., winkler, r. 2002. study of the electron kinetics in the anode region of a glow discharge by a multiterm approach and monte carlo simulations. j. phys. d: appl. phys. 35: 1768-1776. nanbu, k. 2000. probability theory of electron-molecule, ion-molecule, molecule-molecule, and coulomb collisions for particle modeling of materials processing plasmas and gases. ieee trans. plasma science. 28(3): 971-990. sato, a. h., lieberman, m. a., 1990. electron-beam probe measurement of electric fields in rf discharges. j. appl. phys., 68(12): 6117-6124. settaouti, a., mimouni, a., 1999. monte carlo simulation of electron swarms in sf6 in uniform electric fields. the third international conference on computational aspects and their applications in electrical engineering, ''cataee'99''. october 19-20, 1999, philadelphia university, jordan. settaouti, a., aouabdi, l., 2001. monte carlo simulation of electron swarms in nitrogen in uniform electric field. 4th jordanian international electric & electronics engineering conference (jieeec'2001), april 16-18, 2001, amman, jordan. vossen, j. l., kern, w.,1978. thin film processes. academic press. inc. san diego (usa). wang, d. z., dong, j. q. 1997. kinetics of low pressure rf discharges with dust particles. j. appl. phys. 81(9): 38-42. yonemura, s., nanbu, k. 2001. electron energy distribution in inductively coupled plasma of argon. jpn. j. appl. phys. 40(part. 1, 12): 7052-7060. received 15 july 2002 accepted 17 april 2003 54 a monte carlo method for low pressure radio frequency discharges lahouaria settaouti and abderrahmane settaouti department of electronics, university of sciences references squ journal for science, 2019, 24(1), 1-10 doi: 10.24200/squjs.vol24iss1pp1-10 sultan qaboos university 1 assessment of heavy metal contamination in soil in and around sohar industrial port area, oman maha gharib al-jabri 1 , daniel moraetis 2 and reginald victor 1* 1 department of biology, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman; 2 department of earth sciences, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *email: rvictor@squ.edu.om abstract: the increase in the number of heavy metal emitting sources in industrial areas is a serious issue in pollution science. sohar industrial port (sip) area is located in the northern part of oman where different industrial activities like petrochemical production, metal processing, and waste disposal are prevalent. this study comprehensively identified the presence and quantities of heavy metals in the soils of sohar industrial port area and traced their origin to geogenic or anthropogenic sources. bulk geochemical and mineralogical analyses were carried out on all samples. environmentally available and bioavailable heavy metals were extracted by diethylenetriaminepentaacetic acid (dtpa) and were finally analyzed using inductively coupled plasma-optical emission spectrometry (icp-oes). the environmentally available metals that showed higher concentrations when compared to international standards were ni and cd. the geochemical evidence showed a strong geochemical signature of the ophiolite rocks in the soils as indicated by the significant correlation between cr and ni (p< 0.05). in addition, the cd content showed significant correlations with ni and cr (p< 0.05). other metals like pb and zn, possibly also were geogenic in origin, but with significantly elevated concentrations in samples close to a national highway (p< 0.05). the present study demonstrated the significance of understanding the geological framework of an industrial area, which is already imposing high background concentrations of cr, ni and cd, and also the possible anthropogenic impacts in the cases of pb and cd that exceeded internationally permissible limits. keywords: heavy metals; spatial distribution; sohar industrial port; oman. مقدار تلوث التربة بالمعادن الثقيلة حول ميناء صحار الصناعي في سلطنة عمان ريجنالد فكتورومها غارب الجابري، أدانيل موريتس ان ازدياد معدالت إنبعاث الكثير من المعادن الثقيلة في المناطق الصناعية يعتبر موضوع خطير في علم التلوث. تقع منطقة ميناء صحار :صلخمال تهدف هذهالصناعي في شمال سلطنة عمان حيث أن هنالك العديد من األنشطة الصناعية كانتاج البتروكيماويات،معالجة المعادن والتخلص من النفاياتز عي و لقد تم تحليل الدراسة الشاملة لتحديد أنواع وكميات المعادن الثقيلة في التربة المحيطة بميناء صحار الصناعي وتتبع المنشا الجيلوجي والبشري الصنا حليلها بواسطة استقراء وتم ت datpaكل العينات جيوكميائيا ومعدنيا. ان المعادن المتاحة بيئيا وبيولوجيا تم استخالصها بواسطة حامض وطريقة عاير الدولية. ان األدلة البالزما وطيف اإلنبعاثات الضوئية. لقد وجدنا تركيز النيكل والكادميم في عينات المعادن البيئية بانها كانت عالية بالمفارنة مع الم (. أما بالنسبة لمعدني p less than...0كروميم والنيكل )الجيوكميائية أظهرت وجود صخورأفيوليت في التربة والذي دل على ذلك اإلرتباط الكبير بين ال p less thanالرصاص والزنكل فربما لديهم منشأ جيولوجي ولكن بمقدار كثافة عالية في بعض العينات التي اخذت بالقرب من الطريق السريع القومي. ) عية تفرض خلفية عالية من تركيز الكروميم والنيكل والكادميم وتظهر احتمال اثر (. أظهرت الدراسة الحالية اهمية فهم اإلطار الجيولوجي بمنطقة صنا0... المنشأ البشري الصناعي في حالة الرصاص والكادميم االلذان فاق تركيزها المستوى الدولي المسموح به. معادن ثقيلة، التوزيع المكاني، ميناء صحار الصناعي، سلطنة عمان. : مفتاحيةالكلمات ال mailto:rvictor@squ.edu.om reginald victor et al 2 1. introduction oil is an interface for earth, water and air and is a key component of the ecosystem, and is exposed to several pollutants including toxic heavy metals generated by various natural and anthropogenic activities. this makes soil a source of pollution to living organisms, surface and groundwater, sediments and oceans. heavy metals can affect soil microbes and their associated activities, which play a significant role in the recycling of plant nutrients, detoxification of noxious chemicals, and the control of plant pests and plant growth [1,2]. among different contaminants, heavy metals are categorized as the most hazardous class of anthropogenic pollutants because of their persistence and toxicity [3,4]. the heavy metals of importance in soil with reference to potential hazards are cobalt (co), copper (cu), iron (fe), lead (pb), manganese (mn), aluminium (al), nickel (ni), cadmium (cd), arsenic (as) and zinc (zn) [5,6]. heavy metals in soil originate from natural sources like parent rocks, and anthropogenic activities including mining, other industrial activities, energy production, agriculture, vehicle exhausts, waste disposal, and coal combustion [7-13]. industrial activities are increasing rapidly all over the world. many studies have been conducted to assess heavy metal contamination in and around industrial areas, especially in the most industrialized countries [3,10]. the occurrence of heavy metals in soil at industrial sites depends on the type of the industry. metals contaminate soils through dust, spillage of raw materials, wastes, final products, fuel ash, accidents and fires [14]. in the last few years, industrialization in oman, especially in the north, has increased rapidly. sohar lies in the center of al-batinah region, in north oman. sohar industrial port (sip), sohar free zone together with sohar airport and the upcoming gulf cooperation council (gcc) rail network are prime areas for investment. sip in particular accommodates various types of highly polluting industries including metal processing, petrochemicals, power plants and a sewage treatment plant. in addition, it has high vehicular activity during working days. heavy metals generally are expected in the soil of such areas. so far, limited investigations have been conducted on the heavy metal concentrations in the soils of the sip area. al-rashdi and sulaiman [15] studied the heavy metal accumulation in the soils of farms west of the sohar industrial area and their results showed that the heavy metal concentrations in the soil were in the order of iron (fe) > aluminium (al) > nickel (ni) > zinc (zn) > chromium (cr) > cobalt (co) > copper (cu) > lead (pb). heavy metals in the surface sediments north and south of sohar industrial area studied by al-suely et al. [16] showed that the concentrations of chromium (cr), manganese (mn) and vanadium (v) were high in several areas while other elements were low. the present study is the first to investigate the heavy metals of the soil inside the sip area. its main objective is to identify the content of heavy metals in the soils around sip area and trace their origin. in addition to providing the baseline data on the soil concentrations of heavy metals in the sip area, this study is expected to provide a descriptive model for the investigation of heavy metals in the soils of other industrial areas in oman. 2. materials and methods sohar industrial port (sip) area, one of the most rapidly growing areas in sohar city, sultanate of oman, is approximately 240 km from muscat (figure1). it covers a total area of 123 km 2 and has three main clusters of activities: (a) petrochemical production, (b) metal processing, and (c) logistics such as power production and water supply. other activities include wastewater processing, water-cooling and cargo handling. the geology of the study area is comprised mainly of the allochthonous ophiolite nappe, like dunites and gabbro (seen in the west part of figure 1) and the quaternary deposits which cover most of the area. structurally, the ophiolite nappe has been covered by thick quaternary sediments. the quaternary deposits are mainly gravels and sands (either cemented or not) towards inland and sand and silt along with sabkha deposits in the coastal area downstream. the area is carved by numerous wedian supplying clastic material to coastal areas [17]. the study area was divided into a grid of 15 cells and each cell was 1.62 ×0.75 km in area around the port (figure 2). twenty-four surface soil samples were taken from the industrial area within the grid (sh1 sh24) and two from residential areas (sh25, sh26). in addition, two surface samples (b1, b2) were taken from the beach at the eastern and western limits of the port and two surface samples (c1, c2) were taken as controls at a distance of 2-5 km from the port. c1, c2 are considered to be the control areas because of their upstream position from sohar port and their similarity to the study area in the geochemical signature of the soils (mainly clasts from ophiolite nappe). five subsurface samples were also taken from selected locations (sh5, sh8, sh15, sh16, sh17) within the grid where surface samples were collected. the total number of soil samples collected were 35. the surface samples were taken at a depth of 0-10 cm using a spade and subsurface samples were taken by an auger at a depth of 60-80 cm. the surface samples were taken from three locations within a radius of 5 m within a cell and were mixed together to make up a composite sample. all samples were packed in labelled polyethylene bags. samples were transferred to the laboratory and then dried in the open air for about 72 h. the dried samples were sifted through a 2-mm sieve to remove large gravel, plant roots and other waste materials. then parts of the samples were ground using a pulverisette-5 planetary mill (fritsch, germany). the ground samples were sieved using a 315μm sieve and stored in labelled polyethylene bags. the electrical conductivity and ph were measured in a water to soil ratio of 2:1. the organic matter content was measured by the potassium dichromate method and the bulk chemistry was determined using x-ray fluorescence s assessment of heavy metal contamination 3 (xrf) with nilton xl3 from thermo scientific. the grain size distribution was measured by the bouyoucos method [18]. figure 1. study area geological map with sampling locations in and around sohar industrial port, “sh” refers to samples collected from industrial and residential areas, c refers to control and b to samples collected from the beach. the geological map was modified after bishimetal exploration co. ltd. [31] and the arabian peninsula map was supplied by the national survey authority oman (oman 2015). heavy metals were extracted using the us environmental protection agency (epa) 3050 extraction method [19] and were analyzed using inductively coupled plasma-optical emission spectrometry (icp-oes) (varian 710-es, usa). the analysis was done in triplicate and one spiked sample was analyzed for quality assurance. micronutrients were extracted using diethylenetriaminepentaacetic acid (dtpa) and the extracts were analyzed for heavy metals using icp-oes [20]. the results obtained from epa 3050 extraction methods were classified using cluster analysis based on similarity measures. 3. results the geology of the area is characterized by different sized loose sediments as shown in figure 1. sabkha, coastal sediments of clay and sand cover a large area. there are outcrops of ophiolite close to sites c1 and c2. the physical and chemical parameters along with the results of the grain size distribution are given in table 1. the xrf analysis showed that soils have a significantly positive correlation (p< 0.05) for cr and ni and significantly negative correlation (p< 05) for mgo and k2o (figure 2 a,b). the organic material was relatively low (<1%) in most of the samples except for those samples collected from sabkha deposits with vegetation cover as in sh14, sh18, and sh19 and a plantation of trees as in sh10. the samples with high organic content did not show correspondingly high heavy metal contents. the ph and electrical conductivity range from 7.78 to 8.99 and 50 μs/cm to 23 ms/cm respectively. the grain size was considered mainly fine in most of the samples except at the beach sites b1 and b2, where it was sandy. reginald victor et al 4 the concentrations of the environmentally available metals were extracted through epa 3050 procedure and the recommended international guidelines for soil quality are presented in table 2. the results of two factor anova for zones and gradients showed no significant differences of specific heavy metals within zones (f = 1.75 < f = 2.25; p = 0.13) and within gradients (f = 1.08 < f = 2.40; p = 0.38). in general, most of the metal concentrations were below the maximum concentrations recommended by the international guidelines for soil except for ni and cd, which were higher. the same results from epa 3050 procedure, fed into the cluster analysis showed that both cd and ni belong to the same cluster group along with cr. in addition, other heavy metals cluster into two other groups of pb, zn, cu, mo and v, al, fe and mn (figure 3). table 1. ph, electrical conductivity (ec), organic matter and soil texture for all samples. triplicates for organic matter and ec in 20% of the samples showed standard deviation less than 5% in the analysis. sampling code ph ec (us/cm) % soil organic matter % silt % clay % sand soil texture sh1 8.82 116 0.33 23.6 7.2 69.2 sandy loam sh2 8.87 46 0.87 29.6 5.2 65.2 sandy loam sh3 8.54 208 0.13 31.2 5.2 63.6 sandy loam sh4 8.13 7019 0.73 21.2 7.2 71.6 sandy loam sh5 7.78 6710 1.73 41.2 3.2 55.6 sandy loam sh6 8.55 138 0.73 35.2 7.6 57.2 sandy loam sh7 8.50 117 0.93 35.2 5.6 59.2 sandy loam sh8 7.88 6718 1.33 51.2 3.6 45.2 silt loam sh9 8.25 1094 1.27 33.2 5.6 61.2 sandy loam sh10 8.52 113 2.00 45.2 13.6 41.2 loam sh11 8.30 439 0.80 21.2 7.6 71.2 sandy loam sh12 8.68 72 1.27 25.2 7.6 67.2 sandy loam sh13 8.53 727 0.87 31.2 9.2 59.6 sandy loam sh14 7.87 23882 2.07 31.2 13.2 55.6 sandy loam sh15 7.90 4101 0.93 35.2 11.2 53.6 sandy loam sh16 7.97 6966 0.47 21.2 7.2 71.6 sandy loam sh17 7.97 8907 0.76 27.2 11.2 61.6 sandy loam sh18 8.70 13833 1.60 67.2 5.2 27.6 silt loam sh19 8.44 20112 2.07 71.2 15.2 13.6 silt loam sh20 7.86 2725 1.07 45.2 15.2 39.6 loam sh21 8.70 128 0.13 15.2 5.2 79.6 loamy sand sh22 7.91 2097 0.20 21.2 5.2 73.6 sandy loam sh23 7.95 7007 0.47 19.2 5.2 75.6 clay sh24 8.26 10890 0.93 51.6 23.6 24.8 loamy sand sh25 8.93 86 0.53 33.6 5.6 60.8 sandy loam sh26 8.17 2618 0.20 35.6 11.6 52.8 loam assessment of heavy metal contamination 5 c1 8.07 224 0.67 29.6 5.6 64.8 sandy loam c2 8.99 50 0.27 13.6 2.6 83.8 loamy sand b1 8.32 2889 0.13 1.6 1.6 96.8 sand b2 8.66 3103 0.47 1.6 1.6 96.8 sand table 2. summary of heavy metal concentration (mg/kg) with minimum, maximum, and mean ± standard deviation and international limits of heavy metals in soil (zhao et al., 2014). the small letters above the value in some results represent the first letter of international limits and mean that values exceed the limit . parameters al cd cr cu fe mn mo ni pb v zn minimum 5339 1.7 ch,g 52 9 11629 239 0.5 256.7 d,ch,cn,e u,g 0.7 17 24 maximum 10399 2.0 c h,g 103 g, cn 99 cn 15289 378 1.4 569 d,ch,cn,e u,g 8.0 33 405 ch,cn, eu,g mean 8343± 1333 1.8± 0.1 c h,g 70± 13 31± 18 13068± 939 339± 35 0.8± 0.2 397± 66 d,ch,cn,e u,g 2.2± 1.4 25± 3 56± 68 dutch soil guidelines d 12 380 190 200 210 530 720 chinese guidelines ch 0.3 200 100 50 300 250 canada guidelines cn 22 87 91 50 600 360 eurs eu 3.0 140 75 300 300 germany g 1.0 100 100 5.0 60 100 50 300 figures 2 (a,b). a. xrf analysis correlation between cr and ni (r 2 =0.43; df = 33; p<0.05), b. correlation between mg and k2o (r 2 =0.50; df =33; p <0.01). reginald victor et al 6 figure 3. dendrogram showing the clustering derived from the results of the environmentally available metals with epa 3050 method. the dtpa extraction was done for selected samples. at least one sample from each zone and gradient was chosen for analysis. the extraction was done for four metals, copper (cu), iron (fe), manganese (mn) and zinc (zn) which are important as micronutrients for plants. the concentration of metals among different samples was close to each other except for sh 25 where the concentration of zn was high. this also was shown in epa extraction. the results of dtpa extraction are presented in table 3. table 3. concentration of cu, fe, mn and zn in (mg/kg) extracted by dtpa for selected samples. sample code cu fe mn zn sh1 0.546± 0.005 1.532± 0.015 0.594± 0.005 3.063± 0.027 sh3 0.548± 0.004 3.036± 0.042 0.811± 0.011 1.770± 0.020 sh5 0.633± 0.009 1.455± 0.022 6.482± 0.036 1.828± 0.022 sh9 0.488± 0.011 1.558± 0.020 2.115± 0.031 0.743± 0.010 sh11 1.224± 0.019 2.949± 0.029 0.827± 0.009 1.511± 0.025 sh13 0.335± 0.001 1.893± 0.013 0.977± 0.008 1.071± 0.014 sh15 0.454± 0.007 1.895± 0.014 0.517± 0.004 0.622± 0.009 sh17 0.376± 0.003 3.220± 0.031 1.300± 0.008 0.982± 0.001 sh19 0.654± 0.004 0.189± 0.002 0.322± 0.002 0.856± 0.010 sh23 0.183± 0.002 1.934± 0.014 0.632± 0.003 0.567± 0.004 sh25 2.372± 0.008 2.910± 0.017 1.620± 0.002 31.679± 0.059 sh26 1.346± 0.003 2.535± 0.013 0.884± 0.005 0.490± 0.003 c1 0.948± 0.002 2.012± 0.012 0.938± 0.007 1.239± 0.001 c2 0.432± 0.004 1.034± 0.004 0.482± 0.003 0.693± 0.002 b1 0.241± 0.002 5.070± 0.046 1.828± 0.017 0.164± 0.002 assessment of heavy metal contamination 7 the spatial distribution of heavy metal concentration is shown in figures 5 a-d. the iso-concentration map of each metal is presented for the study area. the map has coordinates and contours. each contour indicates a different concentration displayed arranged in a different color as presented in the legend on the right side of the maps. the spatial distribution of cr and ni had similar trends. their concentration increased towards the coastline where there is industrial activity. in contrast, pb and zn decreased towards the coastline. 4. discussion the bulk chemical and physical analyses reflect the dry soil environment with low organic matter content and the lithology of the fine sediment alluvial fans. the low organic content is expected in the current climatic conditions. the high salinity and the high ph of several soil samples are attributed to the presence of sabkha deposits and the current coastline deposits such as those in samples sh14 to sh19. the absence of significant correlations between environmentally available metals and organic matter concentrations show that organic matter has little influence on the heavy metal contents in soils. eleven heavy metals were detected, namely al, cd, cr, cu, fe, mn, mo, ni, pb, v and zn. the mean concentrations of these heavy metals were compared with the international standards for industrial and agricultural soil quality of different countries because there are no national limits in oman for heavy metals in soil. the mean concentration of cd exceeded chinese and german limits and the mean concentration of ni exceeded all limits (dutch, chinese, canadian, european and german guidelines). zn and cr had mean concentrations below the standard limits, but the maximum concentrations were above several international standards. metal concentrations in soils below the standard limits usually indicate no influence of pollution on the soil environment and therefore can be ignored; concentrations above limits are deleterious to the environment [21]. the values of pb, zn and cd reported in this study are much lesser than those reported for other industrial areas [22-24]. in hong kong, li et al. [7] reported the concentrations of cr, ni, pb, zn and cd in urban soils close to an industrial area as 23.10 ±10.10, 12.4 ± 4.8, 94.60 ± 61.0, 125.0 ± 89.1, 0.62 ± 0.82 mg/kg respectively. in comparison, this study reported higher concentrations for cr, ni and cd, while pb and zn concentrations were lower. the clustering of cd, ni and cr in the same group (figure 3) suggests a common source of geogenic and/or anthropogenic contamination. correlation between cr and ni, (figure 2a) was significant (p< 0.05). the high correlation between cr and ni in both xrf analysis (figure 2a) and the epa 3050 leaching (figure 4a) suggest a significant geogenic origin such as in areas with ophiolite rocks [25, 26, 27]. the elevated concentration of the ni and cd when compared with most of the international guidelines could lead someone to conclude that this area is partly contaminated by anthropogenic activities. in addition, the negative correlation between mgo and k2o (figure 2b) confirms that the main factors controlling the geochemistry of the soils in sip are erosion and deposition of mafic and ultramafic material. the clustering of pb, zn, mo and cu (figure 3) is very common in areas rich in sulfides. sulfide deposits are widespread in the ophiolite outcrops of the northeastern flanks of the hajar mountains. the high concentrations of pb and zn in sample sh25 indicate anthropogenic impact due to the high number of vehicles plying the area. copper (cu), iron (fe), manganese (mn) and zinc (zn) were extracted by the dtpa method because of their importance as micronutrients for plants. the metals estimated by the dtpa method are low when compared with the acid digestion method. this is because the dtpa method targets available cations in the soil via chelation. the acid digestion method targets all metal forms including the available cations and those in compound forms. the results showed high concentrations of zn, and similar results were observed in epa 3050 extraction. the highest concentration of zn (31.679 ± 0.059 mg/kg) in sh 25 could be due the high vehicular traffic at this site. anyakora et al. [28] reported that zn in the soil adjacent to roads in africa was due to its release from car tires and lubricant oils. figures 4 (a,b). a. correlation between cr and ni, b. cr and cd derived from the soil acid digestion (epa3050). cr and ni correlation has an r 2 =0.53 and for mg and k2o is r 2 =0.50 reginald victor et al 8 figures 5 (a,b,c,d). spatial distribution of cr, ni, pb and zn concentration (mg/kg) presented as iso-concentration map with legend of different concentrations classified by colour codes. spatial distribution of heavy metals provides a simple and effective presentation of results in pollution investigations [29]. in addition, it is used to assess the origin of the possible sources and points of high metal concentrations [11]. the iso-concentration maps of cr and ni (figure 5) were generally similar suggesting that they originated from the same source, which is the ophiolite rocks as already demonstrated by the geochemical results. similarly, pb and zn showed an increase outside the sip towards a national highway thus indicating the contribution of heavy traffic (figure 5). however, within the sip, only sh 25 which has a lot of heavy vehicular traffic using diesel registered the highest concentration of pb and zn. many earlier studies have shown that pb and zn could originate from traffic emissions [7, 21, 23, 30], but these metals could also be released from the parent rocks. this study should prompt the decision makers to establish the baseline limits for heavy metals in the soils of industrial areas in oman. soil quality analysis for heavy metals should be an integral part of the environmental impact assessment (eia) protocols needed for establishing new industries. especially in the case of oman, heavy metals like cr, ni and cd should be considered in legislative and risk assessment studies because of their high concentrations in the natural environment. metals like pb, zn and cu could be released from geogenic sources, but extreme values, especially close to the roads should be carefully assessed for the anthropogenic impact. assessment of heavy metal contamination 9 5. conclusion the investigation of heavy metal content in sip soils showed that the concentrations of heavy metals are low when compared to international guidelines and standards except for ni and cd. however, the correlations of cr, ni and cd showed the geogenic origin of those heavy metals from the ophiolite. pb and zn fall in the same group with cu and mo and denote the possible geogenic origin from the erosion of sulfides deposits. the higher concentrations of pb and zn outside the sip, especially in sample sh25 towards a national highway, need further study on the roadside sediments to verify whether these are the products of anthropogenic soil impact or just the extreme outliers of the existing lithology. acknowledgement we would like to thank sohar port for their support during the collection of soil samples. departments of biology and earth 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technology, 2013, 7, 917-924. 29. yan, w., mahmood, q., peng, d., fu, w., chen, t., wang, y., li, s., chen, j. and liu, d. the spatial distribution pattern of heavy metals and risk assessment of moso bamboo forest soil around lead–zinc mine in southeastern china. soil and tillage research, 2015, 153, 120-130. 30. imperato, m. spatial distribution of heavy metals in urban soils of naples city (italy). environmental pollution, 2003, 124, 247-256. 31. bishimetal exploration co ltd.1992b. geological map of sur sheet, nf, 40-14f-i, scale 1:50,000. directorate general of minerals, oman ministry of petroleum and minerals, muscat. received 8 march 2018 accepted 8 october 2018 squ journal for science, 2019, 24(1), 47-56 doi: 10.24200/squjs.vol24iss1pp47-56 sultan qaboos university 47 petroleum hydrocarbon residues in surficial sediment samples from aden city coasts, yemen ibrahim a. al-akhaly 1 *, nabil a. al-shwafi 1 , basem y. al-matari 2 and eman i. siam 3 1 department of earth and environmental science, faculty of science, sana'a university, yemen; 2 maritime affairs authority, aden branch, yemen; 3 arab academy for science, technology and maritime transport, alexandria, egypt. *email:ibnalakhaly@hotmail.com. abstract: the environmental quality along aden coasts is affected by the anthropogenic pressure of aden city. field work has been carried out to investigate the occurrence of petroleum pollution along these coasts. to determine the status of aliphatic hydrocarbon (ah) (n-c10 to n-c34) and polycyclic aromatic hydrocarbon (pah) pollution in surface sediments, twenty seven surface sediment samples were collected in july and december 2014 and march 2015 and analysed for ahs and pahs by using gas chromatography–mass spectrometry (gc-ms) to determine their levels and sources. concentrations of ahs ranged from 6.25 µg/g at station 5 (goldmoor) to 41.05 µg/g at station 7 (al ghadir coast) with an average of 16.49 µg/g. concentrations of pahs were in the range between 0.37 µg/g at station 5 (goldmoor) and 16.30 µg/g at station 9 (oil harbor) with an average of 7.38 µg/g. the study showed that the levels of petroleum hydrocarbons (phs) in coastal sediments are low and within the allowed limits. the major sources of the pollution were petrogenic in origin, based on the indices of ahs and pahs. this pollution is a result of localized oil operations and/or heavy ship traffic in the gulf of aden. the results will be used to assess the ecosystem quality. environmental control is recommended to reduce the marine pollution of aden coasts. keywords: aden; coastal sediments; gulf of aden; petroleum pollution; yemen بقايا الهيدروكربونات النفطية في عينات رواسب سطحية مأخوذة من سواحل مدينة عدن، اليمن إبراهيم عبدالحميد األكحلي، نبيل عبده الشوافي، باسم يحيى المطري وإيمان إبراهيم صيام بالنشاط البشري في هذه المدينة. تم إجراء العمل الميداني للتحري عن التلوث النفطي على تتأثر نَوعية البيئة على ُطول سواحل مدينة عدن :صلخمال عينة من الرواسب السطحية في يوليو وديسمبر 72سواحل عدن لتحديد الهيدروكربونات النفطية األليفاتية والحلقية الملوثة في الرواسب السطحية، ُجِمعَت لتحديد مطياف الكتلة-رافي الغازجستخدام جهاز كروماتويدروكربونات النفطية األليفاتية والحلقية في تلَك العينات بام. تَمَّ تحليل اله7102ومارس 7102 20.12)جولدمور( و 2في المحطة رامجرام/جميكرو 5.72مستوياتها ومن ثَمَّ معرفة مصادرها. تركيز الهيدروكربونات األليفاتية تَراوَح ما بين 2..1. تركيز الهيدروكربونات الحلقية تَراوَح ما بين رامجرام/جميكرو 02.21)ساحل الغدير(، بِمتوسٍط ِمقدارهُ 2في المحطة رامجرام/جميكرو . هذه الدراسة رامجرام/جميكرو 1..2)ميناء النفط(، بِمتوسٍط ِمقدارهُ 9في المحطة رامجرام/جميكرو 1..05)جولدمور( و 2في المحطة رامجرام/جميكرو لمؤشرات يَنّت أن مستويات الهيدروكربونات النفطية الملوثة في الرواسب السطحية لسواحل عدن منخفضة وضمن الحدود المسموح بها. اِستناداً إلى ابَ ة المحلية و/أو حركة السفن الهيدروكربونية النفطية األليفاتية والحلقية فالمصادر الرئيسة لهذا التلوث ذات َمنَشأ نفطي. هذا التلوث ناتج عن العمليات النفطي من التلوث البحري في الكثيفة في خليج عدن. يُمكن استخدام هذه النتائج لتقييم نوعية النظام البيئي في منطقة الدراسة، كما نوصي بالمراقبة البيئية للحدّ .سواحل عدن عدن، الرواسب الساحلية، خليج عدن، التلوث البحري، اليمن.: مفتاحيةالكلمات ال 1. introduction oastal environments are considered to be places of high ecological risk due to complex biogeochemical processes and intensive human activities [1]. recently, due to rapid economic development, industrialization and urbanization, persistent organic pollutants such as ahs and pahs, have become highly concentrated in or near coastal areas [2]. c mailto:ibnalakhaly@hotmail.com ibrahim a. al-khaly et al 48 hydrocarbons are naturally occurring compounds which are important components of the sedimentary organic matter from coastal areas. their composition and distribution are significantly affected by human activities. petroleum hydrocarbons (phs) come from biogenic, petrogenic, and/or pyrogenic sources [3,4], and have received much attention due to their wide distribution in marine sediments [5]. phs enter the marine environment from many sources including industrial discharges, accidental spills, shipping activities, atmospheric fallout, and oil and gas exploration [6]. ahs and pahs are the major components of crude oil, which is one of the main pollutants in coastal environments. ahs are the most abundant components of organic material found in marine sediments [7,8]. a high concentration of ahs is a potential source of pollution and may cause adverse effects on ecosystems [9]. pahs are a wide group of compounds with two or more aromatic rings containing solely hydrogen and carbon [10]. ahs and pahs are environmental pollutants produced by pyrogenic, natural processes and/or anthropogenic activities [11,12]. pahs are also derived from crude oil and its derivatives [11,13]. the pollution of the marine environment by organic and inorganic pollutants in the gulf of aden and arabian sea is a major concern for all the countries in the region. the coastal waters of yemen are characterized by their high productivity making them a basic feeding and nursery ground for marine species [14]. more than 600 species of marine organisms have been recorded in yemeni waters [15]. however, the extent of pollution of the marine environment in the yemeni coastal area by persistent organic pollutants is largely unknown. untreated domestic wastewater, industrial wastewater, agricultural drain water, run-off during rainy periods, ship and boat traffic, oil transportation, oil spillage, and atmospheric fallout are all potential sources of pollution [16]. the gulf of aden is among the busiest tanker routes. most of the oil produced in the region is exported via sea and pipelines, while refineries producing for local consumption are located in the coastal area. the widespread oil pollution in the gulf of aden is therefore not surprising [17-20], so a chronic input of hydrocarbons into the sediments is to be expected. on the other hand, the gulf of aden is characterized by a high water temperature (> 25 ºc) and a surface water salinity varying between 33.70 to 37% [21], which provide favorable conditions for oil degradation [22]. the aims of this study are: (1) to evaluate the concentrations of ahs and pahs, and (2) to identify the sources of these pollutants in surface sediments collected along aden coasts, yemen. 2. study area aden city is located on the coast of the gulf of aden in the south of yemen. it is bounded by latitudes 12.70°12.90° n and longitudes 44.78°-45.08° e (figure 1). it is the economic capital of yemen and the second most important yemeni city after sana'a. aden is the largest coastal city and famous for transit trade, boat building, ship repairs and bunkering. before the closure of the suez canal in 1967, aden was the third largest bunkering port in the world. besides port related activities, major economic resources in the coastal zone are fisheries, maritime traffic, and oil and gas exploitation. crude oil is transferred by pipeline from the port to tankers. a large boat is available for transport of ship based garbage and oily waste, which is subsequently carried by lorries to a municipal landfill where it is burned. the port and entrance channel are dredged regularly and dredge spoil is dumped offshore [23]. 3. materials and methods twenty seven surface sediment samples were collected to cover the coastal area of aden, which is an area of intense industrial and urban activities. these samples were taken during july and december 2014, and march 2015 from nine selected stations (figure 1). the samples were collected using a stainless steel ekman's grab and kept frozen on dry ice until the time of analysis. just before analysis, the sediment samples were thawed, dried in an oven at 40 ̊c overnight and ground by an agate motor. because of the non-homogenous nature of these sediments, they were sieved through a 63µ sieve (silt and clay fraction). a reference sediment sample was collected from station 5 at goldmoor area which is far from any expected oil pollution and is a protected natural area (figure 1). the global positioning system (gps) was used to determine the coordinates of the sampling points. for the analysis of ahs and pahs,10 g of freeze-dried sediment was extracted with dichloromethane using an accelerated solvent extractor. the surrogates d8-naphthalene, d10-acenaphthene, d10-phenanthrene, d12-chrysene and d12perylene were added to the samples prior to extraction. concentrated extracts were fractionated with alumina/silica gel (80–100 mesh) column chromatography. target analyses were eluted from the column with 50 ml of pentane (aliphatic fraction) and 200 ml of 1:1 pentane–dichloromethane (pah/pcb/pesticide fraction). these fractions were then concentrated to 1 ml using kuderna–danish concentrator tubes, then the concentrated tubes heated in a water bath to between 60 °c to 70 °c [24,25]. in this way the ah and pah fractions were derived. the final determination was performed using gc-ms (a shimadzu gc2010 c.n. 1134102760 sa, with a split/splitless injector furnished with a 60 m × 250 mm × 25µm fused silica capillary with a chemically bonded gum phase db-wax). blank determinations were carried out by repeating the procedure with pre-extracted samples using a calibration with marib export blend crude oil, the detector response was 45.8 mv at 360 nm emission wavelength. the concentrations of the ah and pah were calculated three times (for july and december 2014 and march 2015) and the mean values were taken. petroleum hydrocarbon residues 49 figure 1. location map of the study area and selected sampling sites. to ensure an appropriate quality of analyses, matrix spikes, laboratory sample duplicates and laboratory blanks were processed with each batch of samples (10 samples/batch) as part of the laboratory internal quality control. standards and blanks were analyzed under the same conditions as the samples. the quality control procedures satisfied their acceptable ranges. the recoveries were between 78–103 % and 87–105 % for ahs and pahs, respectively. reproducibility of analyses was tested by triplicate analyses of sediment extracts; it ranged from 3 % to 10 % of relative standard deviation. standard reference materials (srms), provided by the national institute of standards and technology (nist) were analysed to monitor the performance of the analytical methods. the detection limit of ahs and pahs was 0.01 μg/g. concentrations value in the sample analysed are reported as micrograms/gram (μg/g) based on dry sediment weight. grain size analysis of the sediment was carried out using the combined dry sieve and pipette method [26]. percentage total organic carbon (%toc) was determined following the procedure of riley and chester [27], using the exothermic heating and oxidation of 1 g of milled dry sample with chromic acid. samples were extracted and analysed at the yemen standardization, metrology and quality control organization, sana'a, yemen. 4. results and discussion the results of pristane (pr), phytane (ph), squalane (sq) and ∑ahs concentrations in surface sediment samples from aden city coasts are presented in table 1. concentrations of pr range from 0.01 µg/g (station 4) to 0.05 µg/g (station 9), with an average of 0.03±0.02 µg/g (table 1, figure 2). the presence of pr in significant concentra tions supports the biogenic origin of hydrocarbons in surface sediment samples [28]. concentrations of ph range from 0.01 µg/g (station 4) to 0.04 µg/g (station 3), with an average of 0.03±0.01 µg/g (table 1, figure 2). table 1. pr, ph, sq, pr/ph, ucm, cpi and ∑ahs concentrations in surface sediment samples from selected aden city coastal locations (µg/g). station no. pr ph sq pr/ph ucm cpi ∑ahs 1 0.01 0.03 0.04 0.56 0.70 1.20 09.77 2 0.03 0.03 0.05 1.00 1.70 1.30 13.18 3 0.04 0.04 0.04 0.81 1.50 1.10 12.02 4 0.01 0.01 0.06 0.50 0.90 1.40 13.52 5 0.01 0.02 nd 0.67 0.40 0.60 06.25 6 0.04 0.03 0.08 1.56 1.70 1.50 10.31 7 0.04 0.02 0.07 1.40 1.90 1.70 41.05 8 0.04 0.03 1.00 1.40 2.00 1.70 31.50 9 0.05 0.03 1.10 1.36 2.10 1.90 10.79 average 0.03 0.03 0.31 1.03 1.43 1.38 16.49 stdev 0.02 0.01 0.46 0.41 0.61 0.39 11.67 nd = below detection of 0.001 µg/g ibrahim a. al-khaly et al 50 figure 2. concentrations of pristane, phytane, and squalane in surface sediment samples from nine stations along the aden city coast. the isoprenoids pr and ph are common components of crude oil. ph originates from petroleum hydrocarbons, but pr can be generated by biogenic processes in the absence of pollution by phs [5,29]. the ratio between pr/ph is used to determine the relative contribution of oil to sediment pollution, where values close to or < 1 indicate oil pollution, and values between 3 and 5 are characteristic of non-polluted sediments [3,29]. in this study, pr/ph ratios varied between 0.50 and 1.56, indicating petroleum pollution (table 1). similar results were reported at oil polluted locations such as the sfax in tunisia [30] and ushuaia bay in argentina [31]. concentrations of sq ranged from non-detected (nd) (station 5) to 1.10 µg/g (station 9), with an average of 0.31±0.46 µg/g (table 1, figure 2). sq, which is a major organic constituent in polluted surface sediment, was intimately correlated with anthropogenic sources of hydrocarbons [32]. this compound was encountered in all the aden coast sediment samples. this may help to indicate the nature of the pollution of these coasts. burns et al. [28] reported that high concentrations of sq in sediment samples indicate areas constantly subjected to chronic oil pollution. the concentrations of unresolved complex mixture (ucm) ranged from 0.40 µg/g (station 5) to 2.10 µg/g (station 9), with an average of 1.43±0.61 µg/g (table 1). the ucm represents components resistant to weathering and bacterial breakdown and its presence in chromatograms has frequently been taken as strong evidence for petroleum pollution in sediment samples [33]. the anthropogenic contribution of phs is evident from the presence of the ucm in all of the samples analysed (table 1). the ratio of odd to even carbon numbered n-alkanes is called the carbon preference index (cpi). the cpi for the sediment samples ranged from 0.60 µg/g (station 5) to 1.90 µg/g (station 9), with an average of 1.38±0.39 µg/g (table 1). it is the most common index for determination of the sources of ahs. cpi values < 3 indicate petrogenic hydrocarbon inputs to the sediments, while natural inputs have values > 3 [31,34-39]. the results of cpi of aden coastal sediment reflect that all samples are polluted with petrogenic hydrocarbons (cpi < 1.90). the linear regressions between ucm and cpi parameters show good significant correlation (r 2 =0.69) (figure 3). figure 3. relationship between ucm and cpi. the results of ∑ahs in surface sediment samples from aden coasts are given in table 1 and shown in figure 1. concentrations of ∑ahs ranged between 6.25 µg/g (station 5) to 41.05 µg/g (station 7), with an average of petroleum hydrocarbon residues 51 16.49±11.67 µg/g (figure 4). station 5 is taken as the background level for this study. little or no pollution is considered to exist when ∑ah concentration is <10 μg/g and sediments are considered polluted when the concentration is >100 μg/g [40]. hence, as all stations exhibited values < 41.05 µg/g, this clearly indicates that surface sediments in aden coasts are low polluted. figure 4. concentration of ∑ahs, ∑pahs and ∑phs in surface sediment samples from nine stations along aden coasts. concentrations of pahs in the sediment samples from some aden city coasts are summarized in table 2. the pahs consist of two groups: low molecular weight pahs (naphthalene, biphenyl, phenanthrene and anthracene) and high molecular weight (fluoranthene, pyrene, chrysene, benzopyrene and perylene). concentrations of ∑pahs in the sediments ranged between 0.37 µg/g (station 5) and 16.30 µg/g (station 9), with an average of 7.38 µg/g (table 2, figure 4). pah concentrations can be described as low pollution (<100 µg/g) or chronically polluted (>1000 µg/g) [41]. hence, aden's coastal sediments are low polluted with pahs (values ≤ 16.30 µg/g). the possible sources of pahs at station 9 were oil leakage, and the refinery, port area and shipping operations. similar conclusions were reached by [22,42,43]. the main sources of pahs in aquatic systems are pyrolytic or petrogenic sources [44,45]. pyrolytic pahs which are derived from combustion contain four or more aromatic rings, while petrogenic pahs derived from petroleum contain less than four aromatic rings [41,46]. table 2. concentration of pahs in sediment samples from some aden city coasts of yemen (in µg/g dry weight). station no. compounds 1 2 3 4 5 6 7 8 9 naphthalene 0.03 0.04 0.03 0.04 0.02 0.07 1.50 1.70 1.90 biphenyl 0.01 0.03 0.03 0.05 0.01 0.03 1.20 1.10 1.20 phenanthrene (phe) 0.08 1.00 0.09 0.09 0.06 0.10 1.10 1.20 1.30 anthracene (ant) 0.04 0.06 0.05 0.03 0.04 0.08 1.40 1.50 1.60 fluoranthene (flu) 0.03 0.06 0.05 0.04 0.03 0.07 1.20 1.30 1.40 pyrene (py) 0.05 0.09 0.08 0.07 0.07 0.08 1.30 1.50 1.70 chrysene 0.30 0.07 0.07 0.08 0.05 0.06 1.90 2.00 2.00 benzopyrene 1.00 1.50 1.30 1.20 0.09 1.30 2.50 2.70 2.90 perylene 0.08 1.30 1.40 1.10 nd 1.40 2.00 2.10 2.30 ∑pahs 1.62 4.15 3.10 2.70 0.37 3.19 14.10 15.10 16.30 flu/(flu+pyr) 0.38 0.40 0.38 0.36 0.30 0.47 0.48 0.46 0.45 ant/(ant+phe) 0.33 0.06 0.36 0.25 0.40 0.44 0.56 0.56 0.55 flu/pyr 0.60 0.67 0.63 0.57 0.43 0.88 0.92 0.87 0.82 nd= below detection of 0.01 µg/g in this study, to identify the possible sources of pahs, pah isomers of masses flu/pyr and flu/(flu+pyr) were used to differentiate between pyrolytic and petrogenic sources. all stations exhibited values of the flu/pyr ratio between 0.43 and 0.90. for flu/(flu+pyr) ratio, all station’s values ranged between 0.30 and 0.48. the flu/pyr and flu/(flu+pyr) ratios are useful indicators for evaluating the attribution of pah pollution in sediments [47]. if the flu/pyr ratio is higher than 1, pahs will have a pyrolytic source, but when the ratio is lower than one, their source is ibrahim a. al-khaly et al 52 from petroleum. moreover, if flu/(flu+pyr) > 0.50, a pyrolytic source from the combustion of a biomass or coal is indicated [46]. as shown in figure 5, the ratios of flu/pyr in all studied stations were < 1. this implies that the source of pahs in surface sediments could mainly pollution by petrogenic inputs. concentrations of total phs (∑phs) as the sum of ∑ahs and ∑pahs in the sediment samples are given in table 3, figure 4. these ranged from 6.62 µg/g (station 5) to 55.15 µg/g (station 7), with an average of 23.22 µg/g. a ∑phs concentration <10 µg/g indicates unpolluted sediments, whereas a concentration >500 µg/g shows that sediments are highly polluted [5,37]. hence aden's coastal sediments are low polluted with phs and station 5 is unpolluted. based on the results of the grain size distribution, surface sediments in all the sampling stations were characterized as sandy (table 3). figure 5. plots of the isomeric ratios a) ant/(ant+phe) versus flu/(flu+py) and b) flu/(flu+pyr) versus flu/py. figure 6. relationships between a) %toc and ∑pahs, b) %toc and ∑ahs c) %toc and ∑phs. petroleum hydrocarbon residues 53 table 3. ph, %toc and ∑phs concentration in surface sediment samples from some aden city coasts with their sediments type. station no. ph %toc ∑phs (µg/g) sediment type 1 8.01 0.07 11.39 medium sand 2 8.01 0.06 17.33 very fine sand 3 8.00 0.05 15.12 very fine sand 4 8.02 0.04 16.22 medium sand 5 8.03 0.04 06.62 coarse sand 6 7.80 0.06 13.50 fine sand 7 8.02 0.05 55.15 fine sand 8 7.93 0.07 46.60 fine sand 9 7.92 0.08 27.09 very fine sand average 7.97 0.06 23.22 stdev 0.07 0.01 16.73 the results of %toc and fine fraction in surface sediment samples of aden coasts is presented in (table 3). the %toc content in aden coast sediments ranged from 0.04% (stations 4 and 5) to 0.08% (station 9), with an average value of 0.06% (table 3). this would be considered low in organic matter (< 0.50 %) [48]. low values of %toc may be influenced by the ph. high ph values may contribute to low organic matter accumulation, while increasing anoxic degradation rates [49]. tongo et al. [49] observed a higher organic matter content in acidic sediment samples. in this study, the average ph was 7.97 (ranging from 7.80 to 8.03), which indicates an alkaline sediment. no significant correlation between %toc and grain size fractions was observed. in this study, the regression analysis was used to determine the relationship between the concentration of residual hydrocarbons (σpahs, σahs and σphs) and %toc in sediments (figure 6). the linear regressions between σpahs and %toc show weak positive correlation (r 2 =0.30) (figure 6a). mostafa et al. [14,50] demonstrated similar results of weak positive correlation of sediments from coastal areas. these studies and the present results, suggest that the distribution and concentration of ∑pahs in sediments are affected and related by direct input to marine environment, rather than by the type of the sediment found locally. no significant correlation between %toc and σahs or σphs were observed (figure 6 b and c). 5. conclusion surficial sediment samples from aden city coasts, yemen were analysed for ahs and pahs to determine the distribution, composition and source of organic matter in this coastal environment. ∑ahs concentrations ranged from 6.25 µg/g in station 5 to 41.04 µg/g in station 7 with an average value of 16.49 µg/g. ∑pahs concentrations ranged between 0.37 µg/g in station 5 and 16.30 µg/g in station 9 with an average value of 7.38 µg/g. the surface sediments in all the sampling stations were characterized as sandy. the concentration of %toc is not related to grain size, ∑ahs or ∑pahs. the concentration of ∑ahs, ∑pahs and ∑phs is not related to grain size or %toc. the observed sq, ucm, cpi, pr/pa ratio, flu/pyr ratio and flu/(flu+pyr) ratio indicate pollution by phs. the study shows that the levels of hydrocarbon in sediments of the aden coasts are low and within the allowed limits. the pattern of the distribution of pahs in the sediments appears to be governed mainly by their proximity to potential oil pollution sources. this study provides useful data for assessing the effect of marine petroleum pollution control measures from the perspective of human health. it is recommended that a continuous monitoring programme for the aden city coasts, yemen and red sea and gulf of aden region should be formulated and conducted, to ensure that the concentration of phs is within the base line level established in the present study. ibrahim a. al-khaly et al 54 acknowledgement the authors wish to express their sincere gratitude and appreciation to dr. hisham m. 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and barakat, a.o. distribution and characteristics of polycyclic aromatic hydrocarbons (pahs) in sediments of hadhramout coastal area, gulf of aden, yemen, journal of marine systems, 2009, 78, 1-8. received 24 april 2018 accepted 8 december 2018 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 145-151 © 2003 sultan qaboos university on group codes over elementary abelian groups adnan a. zain department of electronics and communications engineering, faculty of engineering, university of aden, p.o.box 7409, almansoora city, aden governorate, republic of yemen, email: aazain@gmx.de. بتدائية اال (abel)حول أنظمة التشفير المزمرة بواسطة زمر عدنان عبداهللا زین تقدم الورقة تعريفا لكل من مصفوفة التوليد و مصفوفة فحص التكافؤ ألنظمة التشفير المزمرة بواسطة الزمر االبتدائية من : خالصة تطوير النظرية , في هذا البحث, باستخدام ذلك تم. للزمرةةوهذه المصفوفات عناصرها تنتمي إلى الحلقات المتبلور, ) abel(نوع التي تعطي العالقة بين مصفوفة التوليد و مصفوفة فحص التكافؤ ألنظمة التشفير الخطية بواسطة الحقول المتناهية إلى نظرية جديدة أعلى : جديدة تمتلك خواص جيدة مثليعرض البحث شفرات ). abel(ألنظمة التشفير المزمرة بواسطة الزمر االبتدائية من نوع . والخاصية الحلقية, ذاتية االزدواجية, وقابلية االنفصال ) hamming(قيمة للمسافة abstract: for group codes over elementary abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group. we also lift the theorem that relates the parity check and the generator matrices of linear codes over finite fields to group codes over elementary abelian groups. some new codes that are mds, self-dual, and cyclic over the abelian group with four elements are given. keywords: codes over groups, elementary abelian groups, endomorphism rings. 1. introduction a group code of length n over an abelian group c a is a subgroup of , the n-fold direct product of . the rate is defined by na a )c(k cc a)( =k , where log x stands for cardinality. a group code c of length with rate and minimum hamming distance d is called a [ code. a linear code c over a field is also a group code over the additive group of . it has been shown by forney and trott (1993) that many of the important structural properties of codes over are associated with the additive and not the multiplicative group properties of . for an information set supporting group codes (forney, 1992) i.e. for group codes that are equivalent to systematic group codes over abelian groups, the notion of generator and check matrices was introduced in biglieri and elia (1993). in this paper, following biglieri and elia (1993), we present the formal definitions of a generator and parity check matrices over the endomorphism ring of the elementary abelian groups. based on this we generalize the well known theorem that relates the generator and parity check matrices of linear codes over fields to group codes over elementary abelian groups. some new codes, mds, self-dual, and cyclic over the abelian group with four elements, which cannot be obtained as linear codes over fields, are presented. n k h ],, hdkn f f f f the paper is organized as follows. section 2 contains the mathematical preliminaries. in section 3 the main theorem of the paper is proved. table 2 contains the generator matrices and the listing of the code words of the new codes. 145 adnan a. zain 2. preliminaries an elementary abelian group, denoted by , of order , where mpa mpq = p is a prime, is isomorphic to the direct sum of cyclic groups, , of order m pc p , written as . let be a generator for the i cyclic group. an arbitrary element can be written as times)( −⊕⊕≡ mcca ppp m k mp ax ∈β ig th .,,2,1 , , ,, 1 mizxgxx pihh m h k=∈⊕= = βββ (1) let mm pp aa →:ψ be an endomorphism of the group defined by the following mpa .,,2,1 , , )( ,, 1 mizgg pjijji m j i k=∈⊕= = ααψ (2) then ψ can be specified by the following m m× matrix over )( pgfz p ≡               = mmmm m m ,2,1, ,22,21,2 ,12,11,1 ][ ααα ααα ααα ψ k mmm k k (3) the action of ψ on any element , is given by the following expression mpax ∈β h m i hii m h mm gpxgxgxx ]} mod {[)()()( 1 ,, 1 ,11, ∑ = = ⊕=⊕⊕= αψψψ ββββ k (4) the endomorphism ring of denoted by is isomorphic to the matrix ring consisting of matrices over a finite field with mp a )( mpaend )( pm zm m m× p elements denoted by (mcdonald, 1974). )( pgf example 1: consider the group 2222 cca ⊕≡ . )()( 2222 zmaend ≡ . 2 2 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 ( ) , , , , , , , , , , , , , , 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 m z                               =                                                            1 1 , 1 1           2 2 10 01 11 01 10 11 ( ) , , , , , 01 10 10 11 11 01 gl z              =                           2 2 2 00 10 01 11 , , , (2 00 01 11 10 f g          = ≡                  )f the set , the set of endomorphisms, contains as a proper subset the set gl , the set of automorphisms, which contains a proper subset of the set that is isomorphic to the finite field with four elements, . the action of every endomorphism on the group elements is shown in table 1, where the first column contains the elements of the group against which are the images under the action of the underlying endomorphism. )( 22 zm )( 22 z 22 f )4(gf 146 group codes over elementary abelian groups table 1. list of and their actions on the group elements. )()( 2222 zmaend ≡ 00 00       10 00       01 00       00 10       00 01       11 00       10 10       10 01       01 10       01 01       00 11       01 11       10 11       11 01       11 10       11 11       00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 00 10 01 00 00 11 10 10 01 01 00 01 10 11 11 11 01 00 00 00 10 01 00 10 01 10 01 11 11 11 01 10 11 11 00 10 01 10 01 11 00 11 11 00 11 10 01 10 01 00 3. ( group codes ), kn a block of k message symbols kuuuu k21= , where u a , 1, 2, , ,mi p i k∈ = k , , , 2211 kxuxux = will be encoded into a codeword where , and these code words form a code. the first part of the codeword consists of the message itself: ,mpa∈ , 21 jn xxxx= kx kn ≥ ,ku== k followed by check symbols kn − . , ,1 nk xx k+ following the definition of systematic group codes presented by biglieri and elia (1993), the check symbols can be obtained as ).(,,2,1 ),( 1 knlxx iil k i lk −=⊕= = + kψ (5) in matrix notation the above can be written as ψ= ux (6) where is the generator matrix of the code given by ψ             =ψ ksi si si ψψψψψψ ψψψψψψ ψψψψψψ kk mmmmmm kk kk | | | | k2k100 2222100 1121100 (7) and iψ is the identity endomorphism that maps every element in the group onto itself while 0ψ is the zero endomorphism that maps every element on to the identity element of the group .e the parity check matrix η for the code can be obtained as follows )( nkn ×− 1 2 tr n x e x e x ex            η = η =            mm (8)             =η invksss invk invk ψψψψψψ ψψψψψψ ψψψψψψ kk mkmmmkmm kk kk | | | 0021 0022212 0012111 (9) where invψ is the endomorphism that maps every element on to its inverse. (this parity check matrix is different from the parity check matrix in biglieri and elia (1993)). 147 adnan a. zain now we are in a position to generalize the well-known result that relates the generator matrix and the parity check matrix for a linear code over finite fields. ),( kn theorem 1: for codes over an elementary abelian group the generator matrix ψ and the parity check matrix are related by ),( kn η mp a [ ]sktrtr ohh ×=ψ=ψ oo , where [ ]sko × is the matrix with all entries equal to 0ψ i.e. the zero endomorphism, and o denotes a composition of endomorphisms. proof: from equation (8) that defines h, we have [ ] 12 1 × =             =η=             η s tr n e e e e x x x x mm use equation (6) to substitute for in the above to obtain trx [ ] 1×=ψ strtr euh o using (7) and (9) in the above matrix equation, we obtain             =                                         −−−−−−             e e e u u u k ks k k i i i invksss invk invk mm k mkmm k k k mkmm k k o kk mkmmmkmm kk kk | | | 2 1 2s1s 22212 12111 00 00 00 0021 0022212 0012111 ψψψ ψψψ ψψψ ψψψ ψψψ ψψψ ψψψψψψ ψψψψψψ ψψψψψψ 1 2 11 21 1 0 0 12 22 2 0 0 11 2 0 0 1 1 ( ) ( ) | ( ) | ( ) | ( ) i i k inv k inv i k k i is s ks inv i k is i i u u u u u ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψ ψψ ψ ψ ψ ψ ψ ψ = =               ⊕     ⊕ k k m k k o m m k m m m k m k k m e e e             =             m 148 group codes over elementary abelian groups             =               ⊕⊕⊕ ⊕⊕⊕ == == e e e uu uu iis k i invlls k l ii k i invll k l m m ))}(({)}({ ))}(({)}({ 11 1 1 1 1 ψψψ ψψψ           =           ⊕ ⊕ e e vv vv sinvs inv mm )( )( 11 ψ ψ which yields           =                             −−−−−−             00 00 2s1s 22212 12111 00 00 00 0021 0022212 0012111 | | | ψψ ψψ ψψψ ψψψ ψψψ ψψψ ψψψ ψψψ ψψψψψψ ψψψψψψ ψψψψψψ k mkm k k mkmm k k k mkmm k k o kk mkmmmkmm kk kk ks k k i i i invksss invk invk that is . [ ]sktr oh ×=ψo in a similar way it can be proved that [ ]sktr oh ×=ψ o , hence the result. the class of codes over obtained using mpa ψ contains as a proper subclass the linear codes over gf . this can be illustrated using the following example. )( mp example 2: codes over and codes over gf . ),( kn 22a ),( kn )4( the matrix ψ with entries )()( 2222 zmaendij ≡∈ψ generates codes over denoted by the set ρ . ),( kn 22a the matrix ψ with entries )()( 2222 aendzglij ⊂∈ψ generates codes over denoted by the set ρ . ),( kn 22a ' the matrix with entries ψ )()( 22 2222 aendzglfij ⊂⊂∈ψ generates codes over denoted by the set ρ . this set coincides with codes over gf . ),( kn 22a '' ),( kn )4( clearly the following inclusion property holds, ''' ρ⊃ρ⊃ρ : based on example 2 we present, in table 2, three new (4,2,3) group codes and their binary images, where the codes belong to the set , and they do not belong to the set 'ρ ''ρ ; that means that they cannot be obtained as linear codes over gf . we also observe that these codes are self-dual, mds and two of them are also cyclic. )4( 149 adnan a. zain table 2: new (4,2,3) group codes over }3,2,1,0{}11,01,10,00{2222 ≡≡⊕≡ cca remarks binary image code generator matrix mds self-dual 00 00 00 00 00 10 01 11 00 01 11 01 00 11 10 10 10 00 10 11 10 10 11 00 10 01 01 10 10 11 00 01 01 00 11 10 01 10 10 01 01 01 00 11 01 11 01 00 11 00 01 01 11 10 00 10 11 01 10 00 11 11 11 11 0000 0123 0232 0311 1013 1130 1221 1302 2031 2112 2203 2320 3022 3101 3210 3333                                                               11 10 10 11 01 10 00 00 11 01 01 11 00 00 01 10 mds self-dual cyclic 00 00 00 00 00 10 10 11 00 01 11 10 00 11 01 01 10 00 01 11 10 10 11 00 10 01 10 01 10 11 00 10 01 00 11 01 01 10 01 10 01 01 00 11 01 11 10 00 11 00 10 10 11 10 00 01 11 01 01 00 11 11 11 11 0000 0113 0231 0322 1023 1130 1212 1301 2032 2121 2203 2310 3011 3102 3220 3333                                                               10 11 11 10 01 10 00 00 01 11 11 01 00 00 01 10 mds self-dual cyclic 00 00 00 00 00 10 11 01 00 01 01 11 00 11 10 10 10 00 11 10 10 10 00 11 10 01 10 01 10 11 01 00 01 00 10 11 01 10 01 10 01 01 11 00 01 11 00 01 11 00 01 01 11 10 10 00 11 01 00 10 11 11 11 11 0000 0132 0223 0311 1031 1103 1212 1320 2013 2121 2230 2302 3022 3110 3201 3333                                                               11 01 01 11 01 10 00 00 11 10 10 11 00 00 01 10 150 group codes over elementary abelian groups 4. conclusion in this paper, the formal definitions of a generator and parity check matrices over the endomorphism ring of the elementary abelian groups have been presented. the well-known theorem that relates the generator and parity check matrices of linear codes over fields were generalized to group codes over elementary abelian groups. new codes, mds, self-dual, and cyclic over the abelian group with four elements, which cannot be obtained as linear codes over fields, were also given. the algebraic framework motivates us to a further study of the class of group codes that are cyclic over elementary abelian groups especially over to cover the recently developed codes in ran and snyders (2000). 22 a references biglieri, e. and elia, m. 1993 construction of linear block codes over groups. ieee international symposium on information theory, san antonio, texas. forney, g.d. 1992 on the hamming distance properties of group codes. ieee trans. inform. theory, it-38: 1797-1801. forney, g.d. jr. and trott, m.d.1993 the dynamics of group codes: state space, trellis diagram, and the canonical encoders. ieee trans. inform. theory, it-39: 1491-1513. mcdonald, b.r. 1974. finite rings with identity. marcel dekker, new york, 1974. ran, m. and snyders, j. 2000. on cyclic reversible self-dual additive codes with odd length over . ieee trans. inform. theory, it-46: 1056-1059. 22z received 5 february 2002 accepted 3 september 2003 151 on group codes over elementary abelian groups adnan a. zain department of electronics and communications engineering, faculty of engineering, university of aden, p.o.box 7409, almansoora city, aden governorate, republic of yemen, email: aazain@gmx.de. abstract: for group codes over elementary abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group. we also lift the theorem that relates the parity check and the keywords: codes over groups, elementary abelian groups, endomorphism rings. references squ journal for science, 2019, 24(1), 23-35 doi: 10.24200/squjs.vol24iss1pp1-23-35 sultan qaboos university 23 preparation and characterization of acidic, basic and hydrophobic dehydrated carbons and their capability for methylene blue adsorption el-said i. el-shafey*, syeda n.f. ali, haider al-lawati, saleh n. al-busafi department of chemistey, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *email: elshafey@squ.edu.om. abstract: dehydrated carbon (dc) was prepared from date palm leaflets via sulfuric acid treatment. dc was functionalized via amide coupling using ethylene diamine (eda) and propylene diamine (pda) to produce basic dehydrated carbons (bdcs): bdc-eda and bdc-pda, respectively, and using ethylamine (ea) and aniline (an) to produce hydrophobic dehydrated carbons (hdcs): hdc-ea and hdc-an, respectively. surface areas were found low, between 6.7-16 m 2 /g with mesoporosity domination. ftir shows that –cooh content on dc almost disappeared after surface functionalization. faster adsorption of methylene blue with larger adsorption capacity was found on hdcea than other adsorbents because of stronger hydrophobic interaction forces. keywords: dehydrated carbon; acidic; basic; hydrophobic; methylene blue. إمتزاز الميثيلين االزرق ىتحضير وتوصيف الكربون المنزوع المياه الحمضي والقاعدي والكاره للمياه وقدرتهم عل البوصافيالسعيد إبراهيم الشافعي ، سيده ناهيج فرقان علي ، حيدر اللواتي و صالح من سعف النخيل عن طريق المعالجة بحمض الكبريتيك. وقد تم إضافة مجموعات سطحية بواسطة (dc)تم تحضير الكربون منزوع المياه :صلخمال -bdc و bdc-pdaالنتاج الكربون القاعدي منزوع المياه (pda)وبروبيلين ثنائي األميد (eda)اقتران األميد مستخدما ايثيلين ثنائي األميد eda وتم ايضا استخدام أمين االيثيل(ea) واالنيلين(an) النتاج الكربون الكاره للمياهhdc-ea و hdc-anأن مساحة سطح . بينت الدراسة متر 67و 7.6الكربون كانت منخفضة وتتراوح بين 2 إختفاء مجموعات /جم وتغلب عليها المسامية المتوسطة. وبينت دراسة االشعة تحت الحمراء بعد عملية تحوير السطح وظيفيا. وأظهرت الدراسة أيضا أن امتزاز الميثيلين االزرق كان (dc)الكربون منزوع المياه الكربوكسيل من علي سطح وذلك لوجود قوي تجاذب كارهة للماء. hdc-eaاالسرع واالكثر سعة علي الكربون الكاره للمياه .الميثيلين االزرق ،الكاره للمياه ،القاعدي ،الحمضي ،الكربون المنزوع المياه : مفتاحيةالكلمات ال 1. introduction ulfuric and phosphoric acids, as dehydrating agents, are capable of carbonizing celluloses and hemicelluloses via the removal of water [1,2]. hanzawa and satonaka, in their early studies, prepared chars from raw materials such as filter papers, saw-dust and mandarin orange peel using sulfuric and phosphoric acids [3,4]. the carbon was named as “shitsujunkasseitan” (moistened active charcoal) and later as “suikakasseitan” (hydrated active charcoal) [3,4]. in recent studies, carbon produced by dehydration was called “chemically prepared” [5] or “chemically carbonized” [6] and “dehydrated carbon” [7]. different agricultural resources have been utilized for the production of dehydrated carbon (dc) using sulfuric acid, including flax shive [8], rice husk [5], peanut shell [9] and date palm leaflets [1,3,10]. phosphoric acid has also been utilized to produce dehydrated carbon from date palm leaflets [1,11]. previous studies have shown that dc, prepared by sulfuric acid treatment, is acidic and possesses a high content of acidic functional groups (carboxylic, lactonic and phenolic) with low phzpc [2,10]. dc is cheaply prepared [10] and due to its high carboxylic content it can be functionalized directly via amide coupling. on the other hand, activated carbon is costive as it requires high energy to prepare and an oxidation step to insert carboxylic groups on its surface before surface functionalization [12]. s el-said ibrahim el-shafey et al 24 in this study, dc was prepared from date palm leaflets using sulfuric acid dehydration/oxidation followed by surface functionalization using amines and diamines to produce hydrophobic and basic dehydrated carbons, respectively. dc and functionalized dcs were surface characterized and tested for methylene blue (mb) adsorption in terms of kinetics and equilibrium. 2. materials and methods 2.1 materials chemicals used were of analytical grade. dry date palm leaflets (phoenix dactylifera l.) were collected from a local farm in muscat. the leaflets, after cleaning with deionized water, were dried and cut to small pieces (1 cm length) before use in dehydrated carbon preparation. 2.2 dehydrated carbon preparation and surface functionalization an amount of 50 g of concentrated sulfuric acid was added dropwise with constant stirring to a mixture of 25 g of clean dry leaflets and ~ 200 ml deionized water. the mixture was left to carbonize at 200 ˚c in an oven for 8 hours. the dc produced was left to cool and residual acid was filtered in a buchner funnel. the dc was washed several times with deionized water until the wash water showed no change in methyl orange color, indicating that the dc had become acid free. the dc was allowed to dry to constant weight at 120 ˚c. after cooling in a desiccator, it was kept in a well-closed polyethylene jars. amide coupling surface functionalization follows a method published earlier for oxidized activated carbon [12]. ethylene diamine (1,2-diaminoethane), eda, and propylene diamine (1,3-diamino propane), pda, were immobilized on the surface of dc to produce basic dehydrated carbons (bdcs) as follows. a mixture of 15 g dry dc and 100 ml of 25 % thionyl chloride in toluene was kept under reflux for 6 hours at 70 ˚c, during which time -cooh groups were converted to -cocl groups. residual reagents were allowed to evaporate using a rotary evaporator. the sample was dried at 85 ˚c for 2 hours in an oven, followed by reacting with 100 ml (0.75 m) eda or pda at 90 ˚c for 24 hours under reflux. on completion of the reaction, nitrogen-containing functional groups were immobilized on the dc surface via amide coupling. for the preparation of hydrophobic dehydrated carbons (hdcs), 15 g of dry dc was allowed to undergo reflux with 200 ml of 50 % thionyl chloride in toluene at 70˚c for 6 hours in a 250 ml round bottomed flask. the product was allowed to cool and the solvents were dried using a rotary evaporator. after evaporation, 100 ml ethylamine (ea) or aniline (an) were immediately mixed with the carbon and the mixture was left under reflux for 2 hours at 90 o c. the carbons were purified via soxhlet extraction with 150 ml acetone for 6 hours, followed by washing with deionized water. residual amines or diamines were removed via washing using 1 m hcl. another washing using 1 m naoh was carried out to deprotonate amine groups. finally, the carbons were washed with deionized water to remove residual base. the carbons were left to dry at 70 ˚c in an oven under vacuum (0.1 atm) until constant weight was obtained. bdcs produced using eda and pda are referred as bdc-eda and bdc-pda, respectively, and hacs produced using ea and an are named hdc-ea and hdc-an, respectively. a schematic illustration for surface functionalization of dc is shown in figure 1. figure 1. schematic representation of dc surface functionalization. preparation and characterization of acidic 25 2.3 surface characterization the surface area of dehydrated carbons was measured using asap 2020 (micrometrics, usa) via nitrogen adsorption at 77 k with degassing at 70 ˚c for 24 hours under vacuum. higher degassing temperature was avoided to prevent possible changes on the carbon surface structure. apparent density was determined using a standard method [13]. x-ray powder diffraction was conducted using a philips pw 1830 generator with a philips pw 1050 powder goniometer (philips, usa) and copper kα as the incident radiation. scanning electron microscopy (sem) was carried out using a jeol/eo jsm 5600 with 20 kv accelerating voltage. using acetanilide as a reference, chn analysis was carried out using a euro ea 3000 elemental analyzer (eurovector, italy). infrared analysis was carried out using a ftir spectrometer spectrun bx, berkin elmer, (germany). surface zero point of charge (phzpc) was determined following the procedure of moreno-castilla et al. [14]. quantification of carboxyl, lactone, phenol and carbonyl groups on the carbon surface was carried out using boehm titrations [15]. surface basicity was determined following a method published earlier [12]. cation exchange capacity (cec) was determined following the procedure of a standard method [16]. thermogravimetric analysis was conducted using sdt q600 simultaneous dsc-tga apparatus (ta instruments, usa) under nitrogen in a flow rate of 100 ml/min with a heating rate of 20 ˚c/min from room temperature to 785 ˚c. zeta potential was determined as a function of ph using a surpass tm electrokinetic analyzer (uk) as follows. ~ 0.05 g of carbon was mixed with 0.001 m kcl solution (prepared in co2-free water). the ph was adjusted using drops of 0.05 m of naoh and 0.05 m hcl. 2.4 adsorption of methylene blue a stock solution of mb (1000 mg/l) was prepared in deionized water. standard and test solutions were prepared by suitable dilution in deionized water. kinetic and equilibrium studies were conducted at 25 ˚c with ph 7.0 as initial ph. initial ph was adjusted using drops of 0.1 m hcl or 0.1 m naoh before carbon mixing. in the kinetic study, 0.1 g of carbon was added to 50 ml of mb (100 mg/l) at 25 ˚c. at different periods of time, an aliquot of supernatant was withdrawn for analysis and the adsorption process was followed for ~60 hours under mechanical agitation (100 rpm/min). for the equilibrium study, 0.05 g of carbon was mixed with 25 ml of mb solution (10–700) mg/l at 25 ˚c under mechanical agitation (100 rpm/min) until the equilibrium was reached. residual mb concentration was determined using a varian/cary/50 conc uv-visible spectrophotometer at λmax 665 nm with deionized water as blank. all the experiments and analysis were carried out at least twice. 3. results and discussion 3.1 surface area and porosity the adsorption desorption isotherms of nitrogen at 77 k, shown in figure 2, exhibit characteristics of both type i and type iv isotherms according to the classification of sing et al. [17], but with more dominant characteristics of type iv and a larger extent of mesoporosity [18]. based on the iupac classification, the adsorption isotherms show an h3 hysteresis loop type (figure 2). figure 2. nitrogen adsorption isotherms at 77 k on dc and modified dcs. total surface area (sbet) was calculated using the bet equation [19]. according to the gurvich rule [20], total pore volume (vt) can be determined from the amount of nitrogen adsorbed at a high relative pressure such as p/p o = 0.98. micropore volume (vmicro) and mesopore surface area (smeso) were estimated using the t-plot method [20] taking el-said ibrahim el-shafey et al 26 into consideration the theoretical thickness of the adsorbed nitrogen layer (t) on carbon black [21] as a reference isotherm (eq.1). it is more appropriate to use that reference isotherm for carbon-like adsorbents [12,20,22,23]. t= 0.88(p/po) 2 + 6.45(p/po) + 2.98 a o (1) smeso is determined from the slope of the straight line, but vmicro is determined from its intercept. the micropore surface area (smicro) can be determined from eq. 2 [20,24] while mesopore volume (v meso) can be estimated from eq. 3, [12,25]. smicro= sbet smeso (2) vmeso =vt-vmicro (3) fig. 3 figure 3. pore size distribution of dc and functionalized dcs. (dc) )bdc-eda) )bdc-pda) )hdc-ea) )hdc-an) preparation and characterization of acidic 27 table 1. surface textural properties of dc and functionalized dcs. carbon sbet (m 2 /g) bet-c vt (ml/g) d (a o ) smeso (m 2 /g) smicro (m 2 /g) vmicro (ml/g) vmeso (ml/g) apparent density (cm 3 /g) dc 11.55 48.29 0.431 149.1 10.59 0.963 0.0002 0.0428 0.190 bdc-eda 10.727 270.4 0.0472 176.1 6.985 3.74 0.00164 0.04557 0.254 bdc-pda 9.884 104.8 0.0319 125.8 8.496 1.388 0.0006 0.0305 0.230 hdc-ea 6.717 308.5 0.0166 98.85 4.74 1.977 0.0009 0.0157 0.290 hdc-an 15.82 98.21 0.0408 103.3 14.58 1.245 0.0005 0.0403 0.289 during dc preparation, as water evaporates, sulfuric acid concentrates carbonizing the leaflets via the dehydration of cellulose and hemicelluloses with partial fragmentation to lignin and partial oxidation to the surface [8,10]. the surface area of dc and modified dcs is low, as presented in table 1, unlike activated carbon [12]. similar low values of surface area were reported previously for dehydrated carbons prepared via sulfuric acid treatment from flax shive (19 m 2 /g) [8], rice husk (66 m 2 /g) [26] and date palm leaflets (24 m 2 /g) [27]. the low surface area of dc is related to the higher content of carbon-oxygen hydrophilic groups that occupy a large fraction of its surface, restricting the adsorption of the non-polar nitrogen molecules [10]. the surface area of bdc-eda, bdc-pda and hdc-ea is slightly decreased as a result of surface functionalization. this is probably because the chemically-immobilized chains block, or limit to some extent, the access of nitrogen molecules to some active sites on their surfaces. for hdc-an, a slight rise in surface area was noticed. the anilide groups on its surface perhaps provided some active sites for nitrogen adsorption. mesoporosity dominates the surface texture of dc and functionalized dcs (table 1). in a previous study [12], the surface area of activated carbon was high (823 m 2 /g). however, on surface functionalization, it was tremendously decreased [12]. pore size distribution was investigated using the barrett–joyner–halenda (bjh) model for mesopores and the horvath–kawazoe (hk) model for micropores [12,28] showing bimodal pore structure (micro and meso), figure 3. dc and modified dcs possess different ranges of mesopores with a common peak at ~ 38 a˚ and limited microporosity. as shown in figure 2, nitrogen adsorption on dc and modified dcs show h3 hysteresis type with no plateau at high p/p˚ values. thus, vt values are, to an extent, unreliable [19,20] and thus, the parameters associated with vt including d, vmeso and pore size distribution may not be accurate [19,20]. the apparent density is generally low ranging between 0.19 0.29 cm 3 /g (table 1). 3.2 x-ray powder diffraction and sem the general structure of dehydrated carbons is amorphous, with a common peak at 2θ of 22˚ which can be related to amorphous silica [10,30]. the x-ray diffraction pattern of dc as representative of all dcs is presented in figure 4. sem micrographs of carbons (figure 5) show that dc and modified dcs keep to some extent the fibrous features of the plant morphology with wide pores on their surfaces. the sem photographic method of identifying pores depends on the sections selected for imaging. in addition, the currently achievable resolution levels make the characterization of most micropores in carbons difficult [29]. figure 4. x-ray diffraction of dc. 3.3 ftir the broad band between 3400 – 3000 cm -1 , figure 6, for dc corresponds to -oh stretching vibration. other functionalized dcs show weak and broad bands, in the same region, that can be related to n-h stretching vibrations in el-said ibrahim el-shafey et al 28 amide and amines on bdcs, and to amide on hdcs. the bands in that region are broad probably because of hbonding involved among those groups [31]. figure 5. sem photographs of dc and functionalized dcs. the bands at 2920 and 2850 cm -1 refer to c-h asymmetric and symmetric stretching vibration in the –ch2 group, respectively. a strong band at ~1700 cm -1 for dc indicates the presence of –coo on its surface. this band almost disappeared for bdcs and hdcs as a result of amide coupling. the bands between 1600-1540 cm -1 correspond to c=o and the skeletal c=c aromatic vibrations in all carbons [31]. the band that appears at 1460 cm -1 for dc refers to c-h bending vibration for the –ch2 group. the small band that appears around 1440 cm -1 for functionalized dcs refers to c−n stretching vibrations in amine and amide groups in bdcs, and amide in hdcs. however, such a band is not (dc-eda) (dc-pda) (dc-ea) (dc-an) (dc) preparation and characterization of acidic 29 available for dc (figure 6). the bands between 1400–1000 cm −1 are assigned to the o−h bending and c−o stretching vibrations such as phenols, ether, ester and carboxylic acids [31]. figure 6. ftir of dc and functionalized dcs. 3.4 surface chemical characterization chn analysis, presented in table 2, shows a high content of elemental carbon for dc. however, after surface functionalization, a decrease in carbon content is observed except for hdc-an. nitrogen content is higher for bdcs than hdcs and is the minimum for dc. the high nitrogen content on bdcs is attributed to the presence of amide and amine groups immobilized on their surfaces. dc shows more carboxylic and cec with lower phzpc than functionalized dcs, indicating the acidic nature of dc (table 2). although there is no significant variation of lactone, phenol and carbonyl groups after surface functionalization, the carboxyl content and cec were clearly decreased by surface functionalization. phzpc values for bdcs fall within an alkaline range, but for hdcs it is around neutrality (table 2). bdcs possess more surface basicity than other carbons because of the presence of amine groups immobilized on their surfaces. table 2. surface chemical properties of dc and functionalized dcs. as shown in figure 7, as ph increases, zeta-potential becomes more negative because of oh deposition on the carbon surface [32]. the ph of the isoelectric point (phiep) for dc is the lowest (~ 3). this is related to the deprotonation of carboxylic groups, which are abundant on dc, and which mainly occur in the ph range of 2-6 [33]. surface functionalization has led to a decrease in carboxylic group content and accordingly, zeta-potentials of hdcs and bdcs have become less negative than dc. phiep shifts to higher values of 6.2, 5.6, 6.5 and 6.8 for hdc-ea, hdc-an, bdc-eda and bdc-pda, respectively (figure 7). the shifts in phiep are related to the decrease in surface acidity. carbon phzpc cec (meq/ 100 g) surface functionality (meq/g) surface basicity (meq/g) chn analysis (%) carboxyl lactone phenol carbonyl c h n dc 3.24 87.1 2.45 0.23 0.82 1.65 0.36 51.72 4.24 0.52 bdc-eda 7.7 23.0 0.62 0.21 0.86 1.234 1.52 44.3 4.17 6.15 bdc -pda 7.6 16.5 0.63 0.23 0.83 0.927 1.9 46.73 4.47 5.82 hdc-ea 7.03 21.4 0.61 0.22 0.81 0.824 0.23 45.71 4.29 3.65 hdc-an 6.82 26.3 0.62 0.24 0.82 0.88 0.19 64.03 4.22 4.87 el-said ibrahim el-shafey et al 30 figure 7. zeta-potentials of dc and functionalized dcs in 0.001 m kcl solution. 3.5 thermogravimetric analysis figure 8 (a&b) shows the thermogravimetric analysis (tga) and differential scanning calorimetry (dsc) of carbons, respectively. in the range of 50-150 ˚c, the decrease in wt % is associated with the loss of physisorbed water. the weight loss ranges between 3.6 % for hdc-an and 8.5 % for dc. dc and bdcs possess higher moisture content than hdcs because of the h-bonding between water molecules and c-o groups on dc, or amine groups on bdcs. hdcs possess less moisture than dc, probably because of their surface hydrophobicity. figure 8. (a) tga and (b) dsc of dc and functionalized dcs. between 150-785 o c, dc shows a steady weight loss of about 40.7 % with maximum weight loss at 425 ˚c, reaching an overall weight loss of 49.2 % at 785 ˚c. in that temperature range, both co and co2 break away as volatiles [34,35]. co evolves from the decomposition of carbonyl, ethers, lactone and anhydrides; however co2 evolves from the decomposition of carboxylic, lactone and anhydrides [34,35]. between 250 450 o c, bdc-eda and bdc-pda show broad peaks in the range of 250-785 ˚c with maximum weight loss of 40.2 and 43.0 %, respectively. in that temperature range, amide surface groups on both carbons b reak away [12]. in a previous study, thermal decomposition between 290-310 ˚c was ascribed to amide groups on amide functionalized carbon [36]. between 250-780 ˚c, a weight loss of 42.7 and 40.5 % was observed for hac-ea and hac-an, respectively, with maximum weight loss taking place between 250 and 450 ˚c. this can be related to the loss of amide functionalities together with co and co2. the relatively high temperature for the decomposition of immobilized functional groups suggests that surface functionalization is of covalent nature [37]. )a) )b) preparation and characterization of acidic 31 3.6 methylene blue adsorption in the kinetic experiment, hdcs and bdcs show the fastest and the slowest mb adsorption, respectively (figure 9). pseudo first and pseudo second order kinetic models [38] were tested for the adsorption kinetic data, equations 4 and 5. log(qe-qt) = log qe – k1t/2.303 (4) t/qt =1/k2qe 2 + t/qe (5) where k1 and k2 are rate constants for pseudo first and second order models, respectively. qt is the amount of mb adsorbed per gram of adsorbent (mg/g) at time t. the initial adsorption rate is calculated from k2 using eq. 6 [38]. h = k2qe 2 (6) the pseudo second order model, presented in figure 10, better fits the adsorption data with high r 2 values than the pseudo first order model, table 3, suggesting a mechanism of sharing or exchange of electrons between the carbon surface and mb molecules [38]. the values of k2 and initial rate h follow the order: hdcs> dc> bdcs (table 3). the mechanism of interaction of mb with the carbon surface depends mainly on the surface nature of the carbons. hdcs exhibit strong hydrophobic interaction with mb molecules. dc is negatively charged at ph 7 and, thus, interacts with the cationic mb molecules via electrostatic forces. mb adsorption on bdcs involves h-bonding between amine groups on bdcs and mb molecules. figure 9. kinetics of methylene blue adsorption on dc and functionalized dcs at 25 ˚c. (initial ph 7.0). figure 10. pseudo second order model application for methylene blue adsorption on dc and functionalized dcs at 25 ˚c. (initial ph 7.0). el-said ibrahim el-shafey et al 32 table 3. kinetic models’ parameters of methylene blue adsorption on dc and functionalized dcs. carbon pseudo second order model pseudo first order model rate const k2 (g/mg / hr) initial adsorption rate, h (mg/g/hr) qe (mg/g) r 2 k1 (hr -1 ) qe (mg/g) r 2 dc 0.0056 7.41 36.36 0.9987 0.0912 34.51 0.9144 bdc-eda 0.0047 5.85 35.09 0.9972 0.0795 32.98 0.9066 bdc-pda 0.0048 5.01 32.47 0.9982 0.0949 39.78 0.8271 hdc-ea 0.0223 89.3 63.29 0.9999 0.117 36.67 0.9221 hdc-an 0.0130 8.18 25.13 0.9995 0.0679 21.03 0.9464 equilibrium adsorption data follow well the l-type adsorption isotherm (figure 11). the equilibrium adsorption data were tested for the langmuir and freundlich equations (eqs.7and 8). ce/qe = 1/b.q + ce/q (7) log qe = log k + 1/n log ce (8) where k (l 1/n mg 1-1/n /g) and 1/n are freundich constants which are considered to be relative indicators of adsorption capacity and adsorption intensity, respectively. q and b are the langmuir constants which are related to the monolayer adsorption capacity (mg/g) and the relative energy of adsorption (l/mg), respectively. figure 11. methylene blue adsorption on dc and functionalized dcs at 25 ˚c. (initial ph 7.0). the equilibrium adsorption data better fit the langmuir model (figure 12) with high r 2 values than the freundlich model indicating the formation of a monolayer of mb molecules on carbon surfaces at equilibrium (table 4). maximum uptake (q) follows the order: hac-ea> dc > bdc-eda > bdc-pda > hdc-an. [39] used a dimensionless factor, rs, eq. 9, to indicate the favorability of an adsorption system. rs is the separation factor which is a direct function of the langmuir constant b. rs = 1/(bco +1) (9) rs values indicate the shape of the isotherm: rs >1 (unfavorable), rs = 1 (linear), 1>rs>0 (favorable) and rs = 0 (irreversible) [39]. as presented in table 4, rs values are all between 0 and 1 indicating ‘favorable adsorption’. strong binding between the mb and hdc-ea, in particular, shows the lowest rs values. mb adsorption onto the different carbons involves different dominating adsorption forces depending on the nature of the carbons’ surfaces. hdc-ea shows the largest mb adsorption capacity involving strong hydrophobic interactions between the ethyl chains on its surface and mb molecules. although hdc-an shows a high adsorption rate of mb, its adsorption capacity is the lowest. this is probably due to a steric effect provided by the immobilized anilide groups on hdc-an [12]. on the preparation and characterization of acidic 33 other hand, dc is acidic and negatively charged at ph 7. it adsorbs the mb (cationic dye) dominantly via electrostatic attraction. bdcs probably involves h-bonding (between the amine groups on mb and -nh2 groups on bdcs surface) and hydrophobic forces involving the ethylene and propylene chains and mb molecules. figure 12. langmuir adsorption isotherm for the adsorption of methylene blue on dc and functionalized dcs at 25 ˚c (initial ph 7). table 4. equilibrium parameters for methylene blue adsorption on dc and modified dcs. adsorbent langmuir constants separation factor, rs r 2 freundlich constants r 2 q (mg/g) b (l/mg) 1/n k dc 196.1 0.0372 0.029-0.73 0.9989 0.482 12.9 0.8803 bdc-eda 153.8 0.0252 0.038-0.80 0.9989 0.468 9.60 0.9214 bdc-pda 133.3 0.0262 0.026-0.62 0.9990 0.453 8.99 0.9260 hdc-ea 294.1 0.0626 0.016-0.61 0.9997 0.475 23.8 0.8941 hdc-an 34.36 0.0447 0.022-0.69 0.9998 0.310 5.40 0.8488 the low surface area of dc and functionalized dcs is not the main factor of mb adsorption. however, the surface chemistry that involves different interaction forces with mb has the most influence on mb adsorption. in our previous study, hydrophobic activated carbon by ethylamine surface area (9.9 m 2 /g) showed better performance in mb removal than activated carbon surface area (823 m 2 /g) [12]. hdc-ea, in this study (surface area 6.7 m 2 /g) shows faster adsorption of mb and larger adsorption capacity (294 mg/g) than activated carbon (surface area 823 m 2 /g) with an adsorption capacity of 270 mg/g for mb [12]. in other studies, the adsorption capacity of mb was 47.6 and 126.9 mg/g on activated carbon developed from ficus carica bast [40] and that developed from biomass waste by h2so4 activation, respectively [41]. the adsorption capacity of mb on activated carbon in those studies is still lower than that of hdc-ea in this study. 4. conclusion dc and modified dcs, in this study, possess low surface area. dc is 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qaboos university 54 magnetization dynamics in a perpendicular anisotropy free layer under a spin torque effect with crossed polarization nafeesa rahman and rachid sbiaa* department of physics, college of science, sultan qaboos university, p.o. box 36, al-khoud, pc 123, muscat, sultanate of oman. *email: rachid@squ.edu.om. abstract: the transfer of spin angular momentum from a spin polarized current provides an efficient way of reversing the magnetization direction of the free layer of the magnetic tunnel junction (mtj), and while faster reversal will reduce the switching energy, this in turn will lead to low power consumption. in this work, we propose a design where a spin torque oscillator (sto) is integrated with a conventional magnetic tunnel junction (mtj) which will assist in the ultrafast reversal of the magnetization of the free layer of the mtj. the structure formed (mtj stacked with sto), will have the free layer of the mtj sandwiched between two spin polarizer layers, one with a fixed magnetization direction perpendicular to film plane (main static polarizer) and the other with an oscillatory magnetization (dynamic polarizer). the static polarizer is the fixed layer of the mtj itself and the dynamic polarizer is the free layer of the sto. keywords: magnetic random access memory; spin transfer torque; magnetization reversal; magnetic tunnel junction; spin torque oscillator. دراسة حركة المغنطة المغناطيسية في العينات ذات المغنطة العمودية بتأثير عزم إلكترونات التيار الكهربائي نفيسة عناية الرحمان و رشيد سبيع في االنعكاس فائق السرعة لمغناطيسية الطبقة ( mtj)عند دمجه مع تقاطع النفق المغناطيسي التقليدي ( sto)سيساعد مذبذب عزم الدوران :صلخمال احداها ذات اتجاه مغنطيسي ثابت . محصورة بين طبقتين مستقطبتين mtjطبقة حرة من ( stoمكدسة بـ mtj)سيكون للهيكل المكون . mtjالحرة من نفسها mtjمستقطب الثابت هو الطبقة الثابتة من ال(. مستقطب ديناميكي)واآلخر مع مغنطة تذبذبية ( مستقطب ثابت رئيسي)عمودي على مستوي فيلم .stoوالمستقلب الديناميكي هو الطبقة الحرة من .اإللكترون دوران، المغناطيسي نفقيالجهاز ال، تبديل المغناطيس عزم الدوران، تدور نقل، الوصول العشوائي المغناطيسية ذاكرة :مفتاحيةالكلمات ال 1. introduction pin transfer torque (stt) in magnetic heterostructures gives rise to several dynamical processes that are not accessible with a magnetic field alone [1-5]. two such magnetic heterostructures are the magnetic tunnel junction (mtj) and a spin torque oscillator (sto). both mtj and sto comprise a magnetic free layer (fl), a magnetic reference layer (rl) and a non-magnetic layer between them. the use of mtj in random access memory (ram) application leads to magnetic ram (mram). when the damping is overcome by the spin angular momentum the magnetization of the free layer could be reversed between its two equilibrium states. this is the principle of writing in s mailto:rachid@squ.edu.om magnetization dynamics in a perpendicular anisotropy free layer 55 stt-mram. magnetic tunnel junction with perpendicular magnetic anisotropy has experienced strong growth in the past 10 years and has a good potential for the future growth of low power consumption and high-density stt-mram [6-16]. in stt-mram, the magnetic state of an mtj is switched by applying a spin-polarized current through the junction. the magnetization switching of the free layer of the mtj occurs only when the current density exceeds the threshold current, also known as the critical current or, more specifically, critical current density, jc = ic/a (where ic is the critical current and a is the area of the mtj). at a given current (i ≥ ic), the minimum pulse width needed to switch the magnetization is defined as the switching time ts. the goal of low power magnetic memory involves reducing the critical current as well as switching time of the mtj. an sto exhibits self-sustained magnetization oscillations, which are made possible through the compensation of magnetic damping by the transfer of spin angular momentum from a spin-polarized current [17-23]. when magnetization dynamics are induced in the active layer, the magnetoresistance of the device becomes time-varying, thereby generating a microwave signal. thus, an sto has the capability of converting a direct current into a microwave signal, by utilizing the spin transfer torque (stt) in ferromagnetic multilayer systems. more recently, and to store more data in a magnetic nanowire, it has been discovered that spin torque could also move domain wall, leading thus to different magnetic states [24-36]. an sto which is a spintronic device is fabricated without any semiconductor material [37]. it is a nanoscopic and ultra-tunable microwave signal generator. the microwave signals emitted by an sto can vary in frequency from hundreds of mhz to 40 ghz. the frequency of emission is a function of the magnitude and direction of the dc spin-polarized current. if in addition to the spin-polarized current, an external magnetic field is applied, then the frequency generally increases with the applied magnetic field because the magnetic oscillations are precessional: the larger the net effective magnetic field, the greater the torque acting on the spins, and the higher the frequency of precession. the frequency of emission is also a function of the strength and angle of the applied magnetic field. in this paper a technique is presented, wherein a spin torque oscillator with an optimal frequency is integrated with a conventional mtj to realize a real-time device known as a “spin transfer oscillator magnetic tunnel junction” (stomtj), which will form the basis for low power magnetic memory [38-40]. in our proposed methodology, a stomtj nanostructure is formed by stacking an sto and an mtj vertically, separated by a spacer. the magnetization of fl of mtj, if aligned parallel or antiparallel with respect to its own fixed layer magnetization corresponds to binary bit 1 and binary bit 0 as shown in figure 1(a). the sto used in the stomtj device is a trilayer structure comprising a magnetic fl, a magnetic rl and a nonmagnetic layer between them. the magnetization direction of the fl initially in-plane can be changed under a polarized electric current while the direction of the rl magnetization is unchangeable and aligned in the z-direction. the simulation results of such an sto are enumerated elsewhere [41]. the spin-polarized d.c current injection is capable of inducing oscillations in the free layer of the sto. the free layer of the sto acts as a resonance-inducingpolarizer, effectively reducing the critical current of the mtj in the stomtj device. this reduction of the critical current can improve the performance of the mtj leading to low power magnetic memory. the magnetization reversal of the free layer of mtj results from the contribution of two polarizers as shown in figure 1(b), where the magnetizations mp1 and mp2 are considered to be a static polarizer and dynamic polarizer, respectively. the rl and the non-magnetic layer of the sto are not shown in fig 1(b) for simplicity. 2. theoretical model in the first case, an mtj is simulated as shown in fig. 1 (a). the magnetization direction of the fl (m) can be changed under a polarized electric current while the direction of the rl magnetization (mp) is unchangeable and aligned in the z-direction. the dynamics of the magnetization of the free layer in the presence of spin-polarized current is obtained by solving the llgs equation given by eq. 1. d𝐦 dt = γ[𝐦 × 𝐇𝐞𝐟𝐟 ] + 𝛼 (𝒎 × 𝑑𝒎 𝑑𝑡 ) (1) in eq. 1, γ is the gyromagnetic ratio, 𝛼 is the damping constant, 𝐦 is the normalized magnetization of the free layer. the effective field heff can be expressed by 𝑯𝒆𝒇𝒇 = 𝑯𝒔 + 𝑯𝒌 + 𝑯𝒆𝒙 + 𝑯𝑺𝑻 (2) in eq. 2, hs is the magnetostatic field, hk is the magnetic anisotropy field, hex is the exchange field and hst is the spin transfer torque field given by eq. 3. 𝐇𝐒𝐓 = −𝐻𝑆𝑇 (𝒎 × 𝒎𝒑) (3) in eq. 3, mp is a vector with polarization direction of the reference layer, hst is given by eq. 4 where j is the current density (j= i/a), t is the thickness of the ferromagnetic layer under stt, 𝜀 is the spin polarization efficiency, ms is the saturation magnetization, e is the electron charge and ħ is the reduced planck constant. rahman, n. and sbiaa, r. 56 𝐻𝑆𝑇 = ħ𝜀 𝐽 2𝑒𝑀𝑠𝑡 = ħ𝜀𝑖 2𝑒𝑀𝑠𝑡𝐴 (4) 3. results and discussion case 1: mtj simulation without dynamic polarizer. for solving eq. 1, the free layer of the device mtj, with a size of 30 × 30 × 2 nm 3 and discretization of 3 × 3 × 2 nm 3 was considered. the polarization vector mp is in the positive z-direction following the orientation of the magnetization of the perpendicular polarizer. the free layer saturation magnetization (ms), spin current polarization (p), the anisotropy field (hk) and exchange stiffness constant (a) were fixed to 600 ka/m, 0.6, 900 mt and 410 12 j/m, respectively. by exploring magnetization dynamics at different values of current, the critical current (ic) was found to be 0.2 ma with switching time (ts) of 0.5 ns, as shown in figure 2. as can be easily understood, a current with magnitude more than the critical current ic led to a decrease in the mtj switching time. figure 1. (a) the sketch of the p-mtj and (b) the sketch of the p-mtj with two spin polarizer layers. case 2: mtj simulation with dynamic polarizer. in the second part of this study, the magnetization dynamics of the free layer shown in figure 1 (b) was investigated. in this scheme, the free layer magnetization m was under two spin-transfer torque fields. the first one was hst1, from the main static polarizer (mp1), with a fixed magnetization direction, which was taken in the positive zaxis (out-of-plane). the second stt field hst2 was from the second polarizer layer (mp2) which is the free layer of an sto here considered to be a dynamic polarizer. its magnetization, given by eq. 5, is oscillating at a characteristic frequency depending on the intrinsic properties of the sto and applied current. in eq. 5, ms is the saturation magnetization of the free layer of the dynamic polarizer, f is its oscillation frequency and θ is the angle between the out of plane axis (z-axis) and its magnetization vector. the spin torque efficiency from the polarizer mp2 was fixed to 0.3. 𝒎𝑝2 = 𝑀𝑠 (𝑠𝑖𝑛𝜃cos(2𝜋𝑓𝑡)�̂�𝒙 + 𝑠𝑖𝑛𝜃𝑠𝑖𝑛(2𝜋𝑓𝑡)�̂�𝒚 + 𝑐𝑜𝑠𝜃�̂�𝒛) (5) the second stt field hst2 was obtained by substituting eq. 5 in eq. 3. the magnitude of the hst2 is given by equation 4. for the sto-mtj device shown in figure 1 (b), the magnetization dynamics were explored at different values of current. the critical current (ic) was found to be 0.1 ma with switching time (ts) of 0.5 ns, as shown in the figure 3. the spin-polarized d.c current injection is capable of inducing oscillations in the free layer of the sto. the magnetization of the dynamic polarizer was oscillating at 7 ghz and θ = 85º. without the dynamic polarizer, the magnetization of the free layer of mtj was precessing and then going back to its initial magnetization state. it is important to note that for the current value i = 0.1 ma, the switching of the free layer magnetization m with only the main polarizer, similar to an mtj device only, was not possible, as shown in fig. 4(a). with the dynamic polarizer, the precessing m was in synchronization with mp2, and the resonance condition was achieved leading to magnetization reversal as shown in figure 4(b). (a) (b) magnetization dynamics in a perpendicular anisotropy free layer 57 figure 2. time domain plot of the three normalized components of the magnetization (mx, my and mz, respectively represented in green, purple and pink) with respect to time for i = 0.2 ma. figure 3. time domain plot of the normalized component of the magnetization mz for i = 0.1 ma. figure 4. the trajectory of magnetization vector for i = 0.1 ma (a) without dynamic polarizer and (b) with dynamic polarizer oscillating at f = 7 ghz. in comparison to magnetization switching by ferromagnetic resonance (fmr) and stt-fmr, the resonance in the sto-mtj device is without the use of a.c. current ir.f. the dynamic magnetization mp2 has a microwave component (b) (a) rahman, n. and sbiaa, r. 58 at the fmr frequency and the associated stt drives m into resonance. thus, the driving force of the magnetic precession in stt–fmr in a magnetic tunnel junction device is the oscillating mp2 associated with an applied spinpolarized d.c current id.c. the frequency of the oscillating mp2 can be tuned by adjusting the sto’s fixed and oscillating layers’ properties such as their spin polarization, thickness, anisotropy field and saturation magnetization. the area of the sto and magnitude of the current passing through it will be the same as the mtj device. an mtj as shown in figure 1 is made of ultra-thin films with a thickness of 2 nm or less. in general, the insulator layer and the magnetic layer are made of mgo and cofeb alloy respectively. to validate the design discussed above, two similar mtjs were considered. the first mtj was left as it was and an sto could be engineered on top of the second mtj to form a stacked stomtj device. the first mtj and the stomtj device were electrically characterized to know the critical current. the scheme discussed above is applicable only if the magnetization of the free layer of the mtj exhibits precessional motion without the dynamic polarizer. for the simulated stomtj device shown in figure 1(b), the critical current found was ic = 0.1 ma. the simulations were repeated for different frequencies of the dynamic polarizer. it was found that the magnetization m switches even for 8 ghz as shown in figure 5. from the results shown in figure 6, the switching probability ps of the free layer magnetization has a maximum at an optimal frequency range of 7 ghz to 8 ghz. the free layer magnetization can be reversed from one state to the other at a frequency close to the mean frequency f s. this result offers a frequency-based switching of the free layer magnetization. by adding the dynamic polarizer mp2 oscillating within an optimal frequency range, it is possible to switch the magnetization of a memory layer in an mram device. for better functionality of the device memory, a narrow distribution of switching probability is required. it is important that the switching happens only at one characteristic frequency. figure 5. time domain plot of the normalized component of the magnetization mz for i = 0.1 ma figure 6. switching probability of the free layer magnetization versus the frequency of the dynamic polarizer for spinpolarized current value i = 0.1ma. the applied current duration is 2 ns. magnetization dynamics in a perpendicular anisotropy free layer 59 4. conclusion in summary, we have simulated the stomtj device which can be used to attain a low power magnetic memory. the free layer magnetization switching with lower current becomes possible as reported in figure 3 where the switching probability reaches a maximum when the oscillating polarizer mp2 is added. a good comparison of the switching process in the mtj with and without dynamic polarizer is shown. the assist mechanism shown can help reduce high current density without compromising the diameter of the mtj. conflict of interest the authors declare no conflict of interest. acknowledgement the authors would like to thank sultan qaboos university for the financial support under the grant 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magnetization reversal dependence on magnetic properties of a spin torque oscillator with in-plane anisotropy free layer and orthogonal polarizer, current applied physics, 2014, 14, 1521. 39. sbiaa, r. magnetization reversal driven by a spin torque oscillator, applied physics letters, 2014, 105, 092407. 40. sbiaa, r. frequency selection for magnetization switching in spin torque magnetic memory, journal of physics: d, applied physics, 2015, 48, 195001. 41. rahman, n. and sbiaa, r. thickness dependence of magnetization dynamics of an in-plane anisotropy ferromagnet under a crossed spin torque polarizer, journal of magnetism and magnetic materials, 2017, 439, 95. received 4 august 2019 accepted 3 october 2019 microsoft word biol041017-finalproof.doc 5043squ journal for science, 10 (2005) © 2005 sultan qaboos university 43 circulating hormone levels in hatchlings of green turtle, chelonia mydas, from ras al-hadd reserve, oman a. y. a. alkindi department of biology, college of science, sultan qaboos university, p.o. box 36, al-khod 123, sultanate of oman, email:aakindy@squ.edu.om مستويات الهرمونات البالزمية في السالحف الخضراء الفاقسة للتو باستخدام حاضنة مخبرية للبيض الذي جلب من محمية رأس الحد بسلطنة عمان عبدالعزيز بن يحيى الكندي تمت دراسة معدالت الهرمونات البالزمية المتمثلـة فـي هرمونـات التكـاثر مـن األسـترادايول و :خالصة ن و الجونادوتروبين في السالحف الخضراء التي فقست للتو و التي تم جمعها بطريقة عشوائية من التستوسيرو 16و قد تمت حضانة البيض باستخدام حاضنة معملية بعد ، خمسة أعشاش من منطقة راس الحد بسلطنة عمان -30نتاج الذكور و مئوية إل 27º-26ساعة من جمع البيض من األعشاش، و قد كانت درجة حرارة الحاضنة 31º و قد وجـد أن . مئوية إلنتاج اإلناث وتم التعرف على نوع الجنس بالفحص المباشر ألنسجة أعضاء التكاثر إال أن معامل (p<0.001)الفروق اإلحصائية بين درجة الحرارة و التستوسيرون ذات داللة إحصائية موجبة كان سالبا، وكان معامل االرتباط بين مستويات هرمـون ، يول االرتباط بين درجة الحرارة و هرمون األسترادا lh وفيما يخص اإلناث فانه لم يوجد معامل ارتباط بين درجة . ودرجة الحرارة ضعيفا، هذا فيما يخص الذكور لم يكن ممكنا قياسه في كل من الجنسين، و سيتم نقاش fshكما أن هرمون. الحرارة و أي من تلك الهرمونات .تائج وأهميتها في هذا البحثهذه الن abstract: post-hatching levels of plasma estradiol (e2), progesterone (pro), testosterone (t), luteinizing hormone (lh), follicle-stimulating hormone (fsh) and thyroxine (t4) were monitored in hatchlings of green turtle, chelonia mydas immediately after emergence. eggs were collected at random from 5 nests. the eggs were placed in incubators 16 hr after oviposition set at 26-27oc for male producing hatchlings and at 30-31oc for female producing hatchlings. blood was collected after sacrifice. chemiluminescence immunoassay was used for determination of plasma hormone levels, using beckman coulter access-2-immunoassay and reagents (beckman coulter, inc.). sex was determined from histological examination of gonads. in males, plasma t levels were positively correlated with temperature (rho = 0.67, p<0.001). a.y.a. alkindi 44 however, plasma e2 levels were negatively correlated but not strongly with temperature (rho = -0.396, p<0.05) and there was a weak correlation between plasma lh levels and temperatures (rho = 0.38, p<0.05). also in the males, there was no correlation between temperature and either plasma pro or t4 levels. in females, there was no correlation between temperature and any of the hormones. in addition, there was no significant difference in plasma concentrations of t, pro, lh or t4 between sexes. however, plasma e2 concentration was significantly higher in males (p<0.05). fsh was undetectable in plasma from both sexes. the significance of these findings will be discussed. keywords: circulating hormone, hatchilings, green turtle. 1. introduction n many reptiles including turtles, sex determination depends on incubation temperature. in chelonian embryos with temperature–dependent sex determination (tsd), the thermosensitive period (tsp) takes place in the middle third period of incubation (yntema and mrosovsky, 1982; wibbels et al. 1991, a, b; desvages et al. 1993). in the olive ridley (lepidochelys olivacea) tsp was about 7 days (day 20-27 of the incubation period) at a male or female promoting temperature (merchant-larios et al. 1997). the rate of gonadal growth was faster at female promoting temperature than at male promoting temperature. during the critical stages of tsp, there is a rapid differentiation in the steroidogenic tissues as well as differential expression of steroidogenic enzymes (thomas et al. 1992; fleming et al. 1999; rhen et al. 1999). moreover, sex steroid hormones and particularly estrogens are essential in controlling sex determination (crews et al. 1994; crews, 1996; lance, 1997; wibbels et al. 1998). administration of exogenous estrogens to the red-eared slider turtle (trachemys scripta) was capable of changing males to females during tsp despite the temperature effect (crews et al. 1991). administration of exogenous aromatase inhibitor, the enzyme that is responsible for estrogen biosynthesis, can override the female–promoting incubation temperature that resulted in male hatchlings (crews et al. 1994; wibbels and crews, 1994). rhen et al. (1999) reported that incubation temperature could influence sex steroid levels 6 weeks after hatching in the red-eared slider turtle. temperature may be transduced into steroid signals for controlling gonadal differentiation. steroidogenic factor 1 (sf-1) regulated steroidogenic enzymes expressed during tsp in red-eared slider turtle (fleming et al. 1999; fleming and crews, 2001). this report represents a preliminary investigation on monitoring plasma sex steroids, gonadotropins and thyroxine in the green turtle hatchlings immediately after emergence. such findings are valuable in understanding the physiological and hormonal status in the green turtles, and provide important preliminary information for future conservation programs of these animals at ras al-hadd reserve, oman. 2. methods 2.1 study area ras al-hadd reserve (between 22o 32 n and 59o 45 e and 22o 14 n and 59o 48 e) is a 45 km coastal strip on the gulf of oman and the arabian sea with over 20 major sandy beaches that extend from al-jarama bay to ras ar ruays. the first 4 km in the northern section of the reserve is located on the gulf of oman while the rest (approx. 41 km.) is located on the arabian sea. i circulating hormone levels in hatchings of green turtle 45 2.2 egg collection eggs were collected randomly within 1 km area from 5 different nests immediately after oviposition from ras al hadd reserve-oman in january and may 2003. each nest was excavated and eggs were taken out. the eggs were then transported in plastic buckets with damp sand from ras alhadd to the department of biology at sultan qaboos university (squ) and placed in the incubators about 16 hr after oviposition. 2.3 method of incubation each egg was incubated singly in 600 ml plastic container according to the method of mrosovsky (1988), with some modifications. each container had a plastic cover 10 cm in diameter. the upper part of the container was punched (eight holes in each container, 2.5 mm in diameter). each egg was placed at the center of the container on top of sponge foam surrounded by vermiculite. in each container, 65 ml of distilled water was added to moisten the foam. additional 65ml of distilled water was added to the vermiculite on day 20 of incubation. the eggs were placed in precision scientific incubators (thermo forma, marietta, oh, usa) adjusted to run at different temperatures. eggs incubated at 30-31oc produced females while eggs incubated at 26-27oc produced males. uncovered containers containing distilled water were placed at the bottom of the incubators in order to provide humidity for the eggs. two mercury thermometers with 0.1°c graduation were placed inside the incubators at the center of each shelf to ascertain temperature accuracy. daily temperature readings were quickly taken when the incubator was opened. on the outside of the incubator a temperature gauge was checked to make sure that there was no significant fluctuation between daily temperature readings. 2.4 fixation and tissue processing hatchlings were sacrificed and the gonads were dissected along with the adjacent kidneys. they were fixed in 10% buffer formaline and then processed for light microscope according to the method of mrosovsky, (1988). 2.5 blood collection blood samples were collected from the hatchlings approximately 24h after hatching. the hatchlings were sacrificed and plasma was obtained from the blood samples. 2.6 determination of plasma steroid concentrations chemiluminescence immunoassay was used for the determination of plasma steroids, fsh, lh and t4 levels using a beckman coulter access 2 immunoassay system and reagents. (beckman coulter, inc., usa). the technique detects the emission of light due to the occurrence of a chemical reaction. it involves the release of energy in the form of photons as the electrons move from the excited state to the ground state. 2.7 statistical methods the non-parametric mann-whitney u test was used to compare the differences of hormone levels between the sexes while spearman correlation was used to test the correlation between the hormones values. (p< 0.05) was considered significant. a.y.a. alkindi 46 male (n=32) female (n=12) t e s t o s t e r o n e ( nm ol /l ) 4.5 4.0 3.5 3.0 2.5 figure 1. box plots of plasma testosterone levels in hatchlings of the green turtles chelonia mydas incubated in laboratory under constant temperature. boxes represent the middle 50% of the observations. horizontal lines inside the boxes represent the median. observations beyond the vertical lines are outliers. table 1. plasma hormone levels and the incubation temperature of hatchlings – green turtles, chelonia mydas. (*significant at p< 0.05) hormone values sex and number mean ±sem incubation temperature oc testosterone (nmol/l) f = 12 m = 32 3.57 ± 0.081 3.41 ± 0.069 f = 16 30 15 ± 0.28 m = 39 27 19 ± 0.18 estradiol (nmol/l) f = 11 m = 36 0.18 ± 0.03 0.27 ± 0.02* “ progesterone (nmol/l) f = 12 m = 34 11.16 ± 1.77 10.08 ± 0.88 “ luteinizing hormone (iu/l) f = 11 m = 30 0.15 ± 0.04 0.27 ± 0.05 “ thyroxine (pmol/l) f = 9 m = 16 45.20 ± 3.16 52.90 ± 4.27 “ 3. results p, t, lh and t4 plasma values were not significantly different between sexes (figs. 1-5). however, e2 levels were significantly higher in males over females (p<0.05) (fig. 2). fsh levels were undetectable in both sexes. hormone values are reported in table 1. circulating hormone levels in hatchings of green turtle 47 male (n=36) female (n=11) e st r a d io l (n m ol /l ) .7 .6 .5 .4 .3 .2 .1 0.0 44 5 15 13 figure 2. box plots of plasma estradiol levels in hatchlings of the green turtles chelonia mydas incubated in laboratory under constant temperature. see fig 1 for explanation. male (n=16) female (n=9) t h y r o x in e (p m ol /l ) 100 80 60 40 20 0 figure 3. boxplots of plasma thyroxine levels in hatchlings of the green turtles chelonia mydas incubated in laboratory under constant temperature. see fig 1 for explanation. in the female hatchlings, there was no correlation between plasma levels of e2, pro, t, lh and t4, and the incubation temperature. there was also no correlation between the hormone levels. in male hatchlings, incubation temperature was positively correlated with plasma t levels (rho= 0.67, p=<0.01) but there was a weak negative correlation with plasma e2 levels (rho= -0.4, p=<0.05). as the incubation temperature increased there was a decrease in plasma e2 levels. also, there was a weak a.y.a. alkindi 48 male (n=34) female (n=12) pr o g e st e r o n e (n m ol /l ) 30 20 10 0 26 53 figure 4. boxplots of plasma progesterone levels in hatchlings of the green turtles chelonia mydas incubated in laboratory under constant temperature. see fig 1 for explanation. correlation between incubation temperature and plasma lh concentration (rho = 0.380, p<0.05). there was no correlation between incubation temperature and plasma p, and t4 levels. light microscopic studies indicated that in the female the gonadal medulla was degenerative while the cortex was well developed with the appearance of the primary follicles. male (n=30) female (n=11) l h (i u /l ) .8 .6 .4 .2 0.0 17 29 figure 5. boxplots of plasma lh levels in hatchlings of the green turtles chelonia mydas incubated in laboratory under constant temperature. see fig 1 for explanation. circulating hormone levels in hatchings of green turtle 49 4. discussion plasma levels of steroids (e2, pro and t) gonadotropins (fsh and lh) and thyroxine (t4) were analyzed shortly after hatching in relation to the incubation temperature in the green turtles collected from ras al-hadd, oman. the results indicate that there is no clear pattern in the hormonal levels of the male and female hatchlings 24 hr after emergence. the lack of specific differences in hormone values may indicate that these hatchlings are still in their transitional stage of gonadal development and may take sometime before any conclusive difference in hormonal levels can take place. on the other hand, the histological sex differences clearly show that in the males, the gonadal tissue cortex is degenerative while the medulla is well developed with distinct appearance of the seminiferous tubules. in the female gonadal tissue the medulla is degenerative while the cortex is well developed with the appearance of the primary follicles. the values of plasma hormone levels in the females did not show any correlation with the incubation temperature. however, in males the incubation temperature was positively correlated with t and lh levels but negatively correlated with e2. also, pro, t4 levels were not correlated with the incubation temperature. fsh levels were not detected in both sexes. there was no significant difference in hormone levels between the sexes except e2 levels, which were higher in males over the females. these results indicate that there was no conclusive evidence that the incubation temperature had any lasting influence on steroidogenesis immediately after emergence in the green turtles. rhen et al. (1999) reported that the incubation temperature in the red-eared slider turtles trachemys scripta, a species with tsd, had lasting effects on the sex–steroid levels even six weeks after hatching. plasma thyroxine levels did not show any correlation with the incubation temperature and there was no significant difference between the sexes. in the snapping turtle (chelydra serpentina) plasma t4 levels from hatchlings emerging from eggs incubated at 21.5oc average 220% that of turtles emerging from eggs incubated at 30.5oc (o’steen and janzen, 1999). however, o’steen and janzen, (1999) added triiodothyronine to the eggs during mid-incubation and that may have altered the natural values of t4 in the embryo. in the present study carried out in both sexes, t4 levels did not show any correlation with the incubation temperature. a comprehensive investigation on the relationship between stages of tsp and the steroidogenic pathways must be investigated before drawing any conclusion on the effects of incubation temperature on the hormone levels in the hatchlings of a tsd species like the green turtles. 5. acknowledgement the author would like to acknowledge the technical assistance provided by mr. matar al-maani and mr. sultan alsiyabi during the course of this study. 6. references crews, d., bull, j.j and wibbels, t. 1991. estrogen and sex reversal in turtles: a dosedependent phenomenon. gen. comp.endocrinol. 81: 357-364. crews, d. 1996. temperature-dependent sex determination: the interplay of steroid hormones and temperature. zool. sci. 13: 1-13. crews, d., bull, j.j., skipper, j.k., tousignant, a. and wibbels, t. 1994. temperaturedependent sex determination in reptiles: proximate mechanisms, ultimate outcomes, and practical applications. dev. genet. 15: 297-312. a.y.a. alkindi 50 desvages, g., girondot, m. and pieau, c. 1993. sensitive stages for the effects of temperature on gonadal aromatase activity in embryos of the marine turtle dermochelys coriacea. gen. comp. endocrinol. 92: 54-61. fleming, a., and crews, d. 2001. estradiol and incubation temperature modulate regulation of steroidogenic factor 1 in the developing gonad of the red-eared slider turtle. endocrinology. 142: 1403-1411. fleming, a., wibbels, t., skipper, j.k and crews, d. 1999. developmental expression of steroidogenic factor 1 in a turtle with temperature-dependent sex determination. gen. comp. endocrinol. 116: 336-346. lance, v. a. 1997. sex determination in reptiles: an update. am. zool. 37: 504-513. merchant-larios, h., ruiz-ramirez, s., moreno-mendoza, n. and marmolejovalencia, a. 1997. correlation among thermosensitive period, estradiol response, and gonad differentiation in the sea turtle lepidochelys olivacea. gen. comp. endocrinol. 107: 373-385. mrosovsky, n. 1988. pivotal temperatures for loggerhead turtles (caretta caretta) from northern and southern nesting beaches. can. j. zool. 66: 661-669. o’steen, s. and janzen, f.j. 1999. embryonic temperature affects metabolic compensation and thyroid hormones in hatching snapping turtles. physiol. biochem. zool. 72(5): 520-533. rhen, t., willingham, e., sakata, j.t. and crews, d. 1999. incubation temperature influences sex-steroid levels in juvenile red-eared slider turtles, trachemys scripta, a species with temperature-dependent sex determination. biology of reproduction. 61: 1275-1280. thomas, e. o.,light, p., wibbels, t. and crews, d. 1992. hydroxysteroid dehydrogenase activity associated with sexual differentiation in embryos of the turtle trachemys scripta. biology of reproduction. 46: 140-145. wibbles, t. and crews, d. 1994. putative aromatase inhibitor induces male sex determination in a female unisexual lizard and in a turtle with tsd. j. endocrinol. 141:295-299. wibbels, t., bull, j.j. and crews, d. 1991(a). synergism of temperature and estradiol: a common pathway in sex determination. j. exp. zool. 260:130-134. wibbels, t., bull, j.j. and crews, d. 1991(b). chronology and morphology of temperaturedependent sex determination. j. exp. zool. 260: 71-381. wibbels, t., cowan, j. and leboeuf, r. 1998. temperature-dependent sex determination in the red-eared slider turtle, trachemys scripta. j. exp. zool. 281: 409-416. yntema, c.l., and mrosovsky, n. 1982. critical periods and pivotal temperatures for sexual differentiation in loggerhead sea turtles. can. j. zool. 60: 1012-1016. received 17 october 2004 accepted 10 june 2005 squ journal for science, 2020, 25(1), 17-25 doi:10.24200/squjs.vol25iss1pp17-25 sultan qaboos university 17 distribution of nutrient salts and chlorophyll-a in surface water along the gulf of aden and arabian sea coast, yemen ibrahim a. al-akhaly*, nabil a. al-shwafi and shehab a. al-kabsh faculty of petroleum and natural resources, sana’a university, yemen. *email: ibnalakhaly@hotmail.com abstract:the distribution of inorganic nutrient salts (ammonium, nitrite, nitrate, phosphate and silicate) and phytoplankton chlorophyll-a (chl-a) were investigated in the gulf of aden and along the arabian sea coast, yemen. seventy two surface water samples were collected during cruises in august 2014 and january 2015. the sampled area extends from as suqayyah in the west of the gulf of aden to hawf in the east. the study showed that the average values of nutrient salts (μg/l) in waters collected in august 2014 and january 2015 were 0.83 and 0.60, 10.98 and 10.03, 16.41 and 14.73, 10.36 and 8.76, and 29.72 and 22.67 for ammonium, nitrite, nitrate, phosphate and silicate, respectively. the average values of chl-a (mg/m 3 ) in august 2014 and january 2015 were 0.26 and 0.21, respectively. the results showed that nitrate levels were very high but those of ammonium very low. this may reflect the oxidation of ammonia to nitrite and then nitrate, leading to a very favorable ratio of ammonia and nitrate values. the low levels of dissolved inorganic nitrogen (din)compounds, (ammonium, nitrite, and nitrate), phosphate, silicate and chl-a indicated that the southern coast of yemen is not in a eutrophic condition. the highest nutrient salt values were in the eastern part of the study area, and may have resulted from water originating from the indian ocean and upwelling. statistical analysis to seek correlations between nutrient salts and chl-a show very good to excellent correlation, which may be due toconstant coastal environment. keywords:arabian sea; gulf of aden; nutrient salts; chlorophyll-a; yemen. ، اليمنبحر العربوخليج عدن لساحل في المياه السطحية أ-والكلوروفيل ةالمغذيلمحا األ توزيع إبراهيم األكحلي، نبيل الشوافي و شهاب الكبش وبحر أ للعوالق النباتية في ساحل خليج عدن -وكلورفيل ،النتريت، الفوسفات، السليكات(األمونيا )تم دراسة توزيع األمالح المغذية غير المعضوية :صلخمال ، وتمتد منطقة جمع العينات من ساحل السقية 7102ويناير 7102عينة من المياه السطحية خالل رحالت بحرية في أغسطس 27في اليمن، تم جمع العرب عينات المياه غرب خليج عدن إلى ساحل حوف بمحافظة المهرة في الشرق. وأظهرت هذه الدراسة أن متوسط قيم األمالح المغذية )ميكروجرام/لتر( في ،األمونيالـ 2..77و 70.27، .2..و .01.0، 02.20و 20..0، 01.10و .01.0، 1..1و 0..1كانت 7102ويناير 7102التي جمعها في أغسطس أ )ملغ/م-النترات، الفوسفات والسليكات على التوالي، ومتوسط قيم الكلورفيلو النتريت 0 على التوالي. 1.70و .7كانت 7102ويناير 7102( في أغسطس يا إلى النتريت ثم كما أظهرت النتائج أن قيم النترات مرتفعة، لكن قيم األمونيا منخفضة مقارنة بالظروف البيئية الطبيعية. وهذا ربما يعكس أكسدة األمون روجين غير العضوية الذائبة )األمونيا، النتريت النترات، مما أظهر عالقة جيدة جداً بين قيم األمونيا والنترات. وتشير المستويات المنخفضة لمركبات النيت ، وبالتالي فالمياه السطحية في ساحل خليج إغناء بالمغذياتأ إلى أن الساحل الجنوبي لليمن ليس في ظروف -والنترات( والفوسفات والسليكات والكلورفيل جزء الشرقي من منطقة الدراسة، وقد يكون هذا ناتج عن المياه التي عدن وبحر العرب في ظروف بيئية طبيعية. وكانت أعلى قيم لألمالح المغذية في ال أ ارتباطاً جيداً جداً إلى ممتازاً بينهما، وقد يكون بسبب -مصدرها المحيط الهندي وعملية الرفع، وأظهر التحليل اإلحصائي بين األمالح المغذية والكلورفيل البيئة الساحلية المستقرة. .أ، اليمن-بحر العرب، خليج عدن، األمالح المغذية، كلورفيل: مفتاحيةالكلمات ال ibrahim a. al-akhaly et al 18 1. introduction he most overwhelming feature of the gulf of aden and arabian sea coastal regions affecting every aspect of the present day physical, biological and socio-economic environment is the fact that the area is a desert. the yemen coast is characterized by a narrow coastal plain between the gulf of aden and the mountain range that parallels the shoreline [1]. the yemen coastal region is influenced by two distinct monsoon seasons. the months of april and may, and september and october are transitional months as global pressure patterns re-adjust to the changing incoming solar energy [2]. the climate of the yemen coast and nearby waters is dominated by hot and extremely arid conditions characteristic of the arabian peninsula [3]. consequently, the present work was undertaken to study the nutrient salts and chl-a in the gulf of aden and arabian sea coastal areas by different cities within yemen. therefore the results of these investigations could be considered to be a pilot for further similar studies in the coastal waters of the gulf of aden and arabian sea. the high primary productivity, due in part to upwelled nutrients, supports a feed web which ultimately sustains the fish community. the seasonality of the monsoon wind and the upwelling can see seasonal periodicity throughout the food web [4]. among the components of waste water most likely to have an impact on the marine ecosystem are nutrients, organic matter and microorganisms. several literature reports have described the occurrence of eutrophication as a result of high concentrations of nutrient chemicals in coastal waters [5-7]. eutrophication is a process driven by enrichment of water by nutrients, especially compounds of nitrogen and/or phosphorus, leading to increased growth, primary production and biomass of algae, changes in the balance of organisms, and water quality degradation. the consequences of eutrophication are undesirable if they appreciably degrade ecosystem health and/or the sustainable provision of goods and services [8]. the phenomenon of eutrophication due to nutrient inputs from land-based pollution sources is a major environmental problem and the geographical distribution of eutrophication in the different seas occurs in densely populated areas characterized by intensive economic activities [9]. there are good reasons to believe that eutrophication can, in the near future, become a common hazard in marine coastal areas in many parts of the world. such a process would have damaging effects on both inshore fisheries and recreational facilities. monitoring major nutrient levels, therefore, is important to assess the degree of pollution and/ or the quality state of water resources [6,10-12]. riley et al., [13] reported that, the range of nutrient concentrations in marine water under normal environmental conditions are as follows (μg/l): nitrate, 1.0-120; phosphate, 1.0-160; ammonia, 0.0-50 and nitrite, 0.2 30. coastal waters have higher concentrations of nutrient salts and chl-a than the open sea waters [14,15]. the present study aimed to determine inorganic micronutrient salts (din, phosphate and silicate) and chl-a variation along the coastal area of the gulf of aden and arabian sea, yemen. 2. materials and methods seventy two surface sea water samples were collected using a clean plastic bucket from the surface (0.90 m) at 12 stations (figure 1) for nutrient salt and chl-a analysis and transferred to cleaned 100 ml polyethylene bottles which had been prewashed with 10% hydrochloric acid. at the time of sampling, the sample bottles were rinsed twice with the sampled water, and then filled with it. for nutrient salt analysis, samples were filtered through whatman gf/c millipore filter papers (0.47μm) and frozen (−20 °c). once in the laboratory, the samples were allowed to thaw for 24 hours prior to determination of dissolved nutrients [16]. the phytoplankton standing crop as chl-a was extracted with 90% acetone. the measurements of dissolved nutrient salts and chl-a were performed using a shimadzu double beam spectrophotometer uv-150-02, following the methodology of strickland and parsons [17]. double distilled water and/or deionized water was used for dilution of samples. blank determinations were carried out for each group of samples on a monthly basis. the concentrations of the nutrient salts and chl-a were measured three times and the mean values were taken. correlation matrices were estimated to show the relationship between nutrient salt concentrations and chl-a. these analyses were applied to interpret the data and to obtain better information about the surface water of the studied stations. 2.1 study area the gulf of aden and arabian sea is dominated by the indian ocean monsoon system (figure 2). from january to march the northeast monsoon blows in a south western direction. between may and september, the south west monsoon generates winds which blow onshore and replace surface waters by cooler nutrient-rich water from deeper layers. this upwelling has limited the growth of coral reefs but triggers high primary production which supports the region’s rich pelagic fish stocks [18,19]. mean surface water temperature in the gulf of aden and arabian sea coastal area is about 24.44 o c in summer (august) and about 26.60 o c in winter (january). t distribution of nutrient salts and chlorophyll-a 19 figure 1. map of gulf of aden and arabian sea showing the sampling stations. figure 2. gulf of aden and arabian sea climatological quikscat wind speed (m/s) for january and august, ne and sw monsoon [20,21]. 3. results and discussion 3.1. nutrient salts 3.1.1. din (ammonium, nitrite and nitrate) ammonium is the major nitrogenous product of the bacterial decomposition of organic matter containing nitrogen, and is an important excretory product of invertebrates and vertebrates. as for the utilization of nitrogenous materials, nh4 is the preferred inorganic source because of its ease of uptake and incorporation into amino acids (nassimilation). the present study shows that august 2014 had the higher values of ammonium, ranging between 0.65 and 0.95 μg/l with an average of 0.83±0.10 μg/l, whereas january 2015 had lower values of ammonium, ranging between 0.33 to 0.85 μg/l with an average of 0.60±0.17 μg/l (table 1 and figure 3). the level of ammonium during august 2014 and january 2015 was relatively low; this may be attributed to the increase in its consumption rate by phytoplankton. however, generally, the concentrations of ammonia during august 2014 were mostly higher than those of january 2015 (figure 4). the available ammonium may have been the decomposition product of organic material. nitrite concentrations during august 2014 ranged from 9.55 to 13.60 μg/l with an average of 10.98± 1.52 μg/l, whereas the concentrations in january 2015 ranged from 8.50 to 12.60 μg/l with an average of 10.03±1.42 μg/l (table 1 and figure 3). the average values for the different locations of nitrite in january 2015 were slightly lower than the average values in august 2014 (figure 4). ibrahim a. al-akhaly et al 20 table 1. mean concentration of nutrient salts and chl-a at selected stations in the gulf of aden and arabian sea coast surface water during august 2014 and january 2015. station no. location name month nitrite (µg/l) nitrate (µg/l) ammonium (µg/l) phosphate (µg/l) silicate (µg/l) chl-a (mg/m 3 ) 1 as suqayyah aug. 2014 9.55 14.33 0.65 8.80 20.40 0.10 jan. 2015 8.50 12.25 0.33 7.00 18.30 0.09 2 khor-omair aug. 2014 9.60 14.50 0.70 8.85 20.60 0.12 jan. 2015 8.60 12.50 0.40 7.30 18.60 0.09 3 aden aug. 2014 9.63 14.60 0.72 8.95 20.80 0.09 jan. 2015 8.65 12.55 0.45 7.65 19.00 0.11 4 shuqrah aug. 2014 9.80 14.65 0.80 9.50 21.00 0.14 jan. 2015 8.90 12.70 0.50 8.00 20.30 0.10 5 ahwar aug. 2014 9.83 14.80 0.83 10.30 25.30 0.13 jan. 2015 9.50 13.00 0.53 8.30 20.30 0.13 6 balhaf aug. 2014 10.25 15.30 0.83 10.50 27.80 0.20 jan. 2015 9.56 13.50 0.55 8.50 20.55 0.12 7 al-mukalla aug. 2014 10.30 15.65 0.85 10.75 30.00 0.33 jan. 2015 9.80 14.30 0.61 9.30 21.00 0.20 8 qusayír aug. 2014 11.53 17.00 0.90 11.00 33.40 0.37 jan. 2015 10.30 15.50 0.66 9.50 23.50 0.25 9 ras sharwin aug. 2014 11.76 17.30 0.93 11.30 35.60 0.36 jan. 2015 10.50 16.53 0.73 9.55 25.80 0.30 10 haswayn aug. 2014 12.35 19.00 0.93 11.30 37.40 0.40 jan. 2015 11.00 17.40 0.81 9.70 26.20 0.33 11 al-muhyfif aug. 2014 13.50 19.50 0.92 11.50 40.00 0.43 jan. 2015 12.50 18.00 0.80 10.00 28.30 0.37 12 hawf jan. 2014 13.60 20.30 0.95 11.55 44.30 0.45 aug. 2015 12.60 18.50 0.85 10.30 30.20 0.40 minimum aug. 2014 9.55 14.33 0.65 8.80 20.40 0.09 jan. 2015 8.50 12.25 0.33 7.00 18.30 0.09 maximum aug. 2014 13.60 20.30 0.95 11.55 44.30 0.45 jan. 2015 12.60 18.50 0.85 10.30 30.20 0.40 average aug. 2014 10.98 16.41 0.83 10.36 29.72 0.26 jan. 2015 10.03 14.73 0.60 8.76 22.67 0.21 std aug. 2014 1.52 2.16 0.10 1.07 8.39 0.14 jan. 2015 1.42 2.35 0.17 1.11 4.03 0.12 the present data of nitrite was similar to that recorded off the hadramout coast; 10.34-13.50 μg/l [4]. a very strong to excellent positive correlation was recorded between nitrite and ammonium (r = 0.84 on august 2014 and = 0.94 on january 2015) (table 2). nitrate is the final oxidation product (nitrification) of other nitrogen compounds in toxic seawater having a high redox potential. the nitrate form is generally considered the most stable and predominant din in oxygenated sea water [22]. its concentration during august 2014 ranged from 14.33 to 20.30 μg/l with an average of 16.41±2.16 μg/l, whereas the concentration during january 2015 ranged from 12.25 to 18.50 μg/l with an average of 14.73±2.35 μg/l (table 1 and figure 3). the distribution of nitrate showed that the concentration during august 2014 was higher than that in january 2015 (figure 4). in addition, it was observed that the concentration of ammonium was less than that of nitrate. this relates to the fact that the rate of nitrification is mostly similar to that of denitrification, or due to the oxidation of ammonium to nitrite and nitrate either chemically or biologically. distribution of nutrient salts and chlorophyll-a 21 table 2. correlation coefficients of nutrient salts and chl-a. nitrite nitrate ammonium phosphate silicate chl-a nitrite 1.00 nitrate 0.99 0.97* 1.00 ammonium 0.84 0.94* 0.84 0.97* 1.00 phosphate 0.86 0.92* 0.85 0.94* 0.98 0.98* 1.00 silicate 0.97 0.97* 0.97 0.99* 0.91 0.96* 0.94 0.92* 1.00 chl-a 0.93 0.96* 0.93 0.99* 0.90 0.96* 0.93 0.94* 0.97 0.98* 1.00 r = 0.86 for august 2014 r = 0.92* for january 2015 figure 3. average concentrations of nutrient salts in the gulf of aden and arabian sea coast surface water during august 2014 and january 2015. the present data for nitrate was similar to that previously recorded on the hadramout coast; 17.30-20.90 μg/l [4]. an excellent positive correlation was recorded between nitrate and nitrite (r = 0.99 in august 2014 and = 0.97 in january 2015) and a very strong to excellent positive correlation was recorded between nitrate and ammonium (r = 0.84 in august 2014 and = 0.97 in january 2015) (table 2). lower din concentrations were detected in as suqayyah and high concentrations were detected in hawf. the average values of nitrate concentrations of 16.41 and 14.73 μg/l for august 2014 and january 2015, respectively, were much higher than the average contents of nitrate, of 10.98 and 10.03 μg/l for the same period, respectively, while the concentration of ammonium was fifteen and tenfold less than those recorded for nitrate and nitrite, respectively. based on these results, the abundance of nitrogen species in the study area is principally in the order nitrate > nitrite > ammonium. this reflects the preferred uptake of the din species by phytoplankton organisms in their n-assimilation. 3.1.2. reactive phosphate phosphorus plays a major role in biological metabolism; it is an essential nutrient element in photosynthesis and other processes in plants. phosphate concentrations in august 2014 ranged from 8.80 to 11.55 μg/l with an average of 10.36±1.07 μg/l, whereas concentrations in january 2015 ranged from 7.00 to 10.30 μg/l with an average of 8.76±1.11 μg/l (table 1 and figure 3). the average value of phosphate in august 2014 was higher than the average value in january 2015 (figure 4). lower phosphate concentrations were detected in as suqayyah and higher concentrations were detected in hawf (figure 4). a very strong to excellent positive correlation was recorded between phosphate and other nutrient salts (r ≥ 0.85) and chl-a (r ≥ 0.93) (table 2). ibrahim a. al-akhaly et al 22 the present data for phosphate was similar to that previously recorded for the hadramout coast; 10.30-11.20 μg/l [4]. figure 4. spatial distribution of inorganic nutrient salts and chl-a at selected stations in the gulf of aden and arabian sea coast surface water during august 2014 and january 2015. 3.1.3. reactive silicate silicate is one of the major mineral constituents in sea water. it is a good indicator of fresh water dispersion and of the potential for diatoms [23]. silicate concentration in august 2014 ranged from 20.40 to 44.30 μg/l with an average of 29.72±8.39 μg/l, whereas the concentration in january 2015 ranged from 18.30 to 30.20 μg/l with an average of 22.67± 4.03 μg/l (table 1). the average value of silicate in august 2014 was higher than the average value in january 2015 (figure 3). lower silicate concentrations were detected in as suqayyah and actually high concentrations were detected in hawf (figure 4). the concentration of silicate in the present study revealed high levels (>18 μg/l). probably, during august, the dissolution of diatom skeletons by increasing temperature, up-welling and sandstorms are responsible for high levels of silicate. the average concentrations of silicate were higher than those of the other nutrient salts. this means that silicate is not a limiting factor for phytoplankton growth in the stations studied. an excellent positive correlation was recorded between silicate and other nutrient salts (r ≥ 0.91) (table 2). the present data for silicate was similar to that previously recorded on the hadramout coast; 20.30-40.50 μg/l [4]. distribution of nutrient salts and chlorophyll-a 23 the coastal areas of the gulf of aden and arabian sea exhibit comparatively high values of nutrient salts, indicating the probable effects of upwelling. upwelling of variable intensity is reported to occur along the se coasts depending mainly upon influencing factors like wind stress, and acceleration of the vertical movements due to the changing current regime [24]. spatial distribution of surface nutrient concentrations showed high concentrations of ammonium, nitrite, nitrate, phosphate and silicate in the east of the study area but lower concentrations to the west during both cruises (figure 4). 3.2. chlorophyll-a (chl-a) marine phytoplankton play a central role in the planktonic food web and biogeochemical cycling in the global ocean. primary production by phytoplankton is consumed or decomposed to support other trophic levels, including the fish we harvest, or is exported to deeper waters [25]. chl-a is the main pigment that can be used for the determination of phytoplankton biomass [26], and it is used as a trophic state indicator. chl-a concentration in august 2014 varied between 0.09 and 0.45 mg/m 3 with an average of 0.26±0.14 mg/m 3 , whereas the concentration in january 2015 varied between 0.09 and 0.40 mg/m 3 with an average of 0.21±0.12 mg/m 3 (table 1). the average value of chl-a in august 2014 was higher than the average value in january 2015 (figure 5). figure 5. minimum, maximum and average concentrations of chl-a in the gulf of aden and arabian sea coast surface water during august 2014 and january 2015. nutrient concentrations decline from east to west in the gulf of aden and along the arabian sea coast. the highest concentrations were recorded in station 12 and lower concentrations were encountered in station 1surface water (figure 4). generally, during january 2015 levels of chl-a were lower than those recoded during august 2014 (figure 4). the present data for chl-a was similar to that recorded previously on the hadramout coast, with 0.23-0.34 mg/m 3 [4], and semi-similar to that recorded in the aegean sea, with 10-0.80 mg/m 3 [27] and 0.03-0.70 mg/m 3 [28], but lower than that reported by khomayis [29] in the coastal waters of jeddah city, red sea (0.02-10.16 μg/l) and higher than that reported by ignatiades et al., [30] in the north and eastern mediterranean sea (0.01-0.15 μg/l).the study values indicate that the production potential of the gulf of aden and arabian sea coast is low. the reason why higher concentrations were noticed at station 12 (hawf) may be due to the intense upwelling and the advection of the upwelled water of the somali region brought into this area due to the intensification of the somali current, a part of which flows northwards into the area further north along the coast of oman. the distribution of chl-a also follows exactly the same pattern as that of the nutrient salts, indicating a higher productivity due to the blooming of phytoplankton in areas rich in nutrient salts, and showing a direct relationship between the two as illustrated in table 2. the results show a relationship between phytoplankton and nutrients salts; this is confirmed by the excellent positive correlation between chl-a and nutrient salt concentration (r ≥ 0.93) (table 2). in general, the high values of chl-a in the coastal area investigated are undoubtedly due to the rich supply of din, phosphate and silicate; these nutrient salts contribute to the growth of phytoplankton, expressed by the high levels of chl-a, which has ledto a eutrophication process in the gulf of aden and arabian sea coasts. the levels of din, phosphate, silicate and chl-a indicate that, the gulf of aden and arabian sea is in a eutrophic condition. the general trend of temporal distribution of nutrient salts and chl-a showed slightly higher values during august 2014 than january 2015. the data in this work clearly demonstrate the oligotrophic nature of the gulf of aden and arabian sea coasts. ibrahim a. al-akhaly et al 24 conclusion the distributions of nutrient salts and chl-a during august 2014 and january 2015 cruises in the gulf of aden and arabian sea coasts have been investigated. the content of nitrate through the study period is higher than the content of ammonium. this observation may reflect the oxidation of ammonium to nitrite and then to nitrate which may justify the very good relation between ammonium and nitrate concentrations. based on the results, the abundance of nitrogen species in the study area is principally in the order: nitrate > nitrite > ammonium. this reflects the uptake preferable of the inorganic nitrogen species by phytoplankton organisms in their n-assimilation. the concentrations of nutrient salts and chl-a during august 2014 are higher than observed concentrations during january 2015. the spatial distribution of nutrients affects the distribution of phytoplankton, as confirmed by the chl-a data in the gulf of aden and arabian sea coasts (between 0.09-0.45 mg/m 3 ). hence, surface seawater in gulf of aden and arabian sea coast maintains normal environmental conditions. the results of these investigations could be considered as pilot for further similar studies in the coastal waters of gulf of aden and arabian sea. conflict of interest the authors declare no conflict of interest. acknowledgements we thank the anonymous reviewers for helpful comments and constructive criticisms to improve the manuscript. references 1. ba-sumaid, a.a. effects of masila oil terminal on coastal fauna m.sc. thesis, dep. biology, fac. sci, sana’a university, 1997, 133p. 2. naval oceanography command detachment. 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eutrophication based on nutrient concentration scales. marine pollution bulletin, 1992, 24(5), 238-43. received 7 october 2019 accepted 20 november 2019 photovoltaic cells and systems: science and technology, special review (2000) 227-245 © 2000 sultan qaboos university 227 evolution of axial-field electrical machines abdullah al-badi, adel gastli, hadj bourdoucen and joseph jervase electrical, electronics and computer engineering department, college of engineering, sultan qaboos university, p.o. box 33, al khod 123, muscat, sultanate of oman. تطور اآلالت الكهربائية ذات المجال المغناطيسي المحوري عبداهللا البادي ، عادل القصطلي ، حاج بوردوسن ، جوزيف جيرفيس هذه الورقة عبارة عن استعراض لآلالت الكهربائية ذات المجال المغناطيسي المحوري ، و هي تعتبر :خالصة لك قرص فارادي المشهور ، كما تعرض هذه الورقة األشكال أساساً إلختراع اآلالت الكهربائية وخير مثال على ذ المختلفة لهذه اآلالت و فوائدها و خصائصها مثل الكفاءة العالية و النسبة العالية لطاقتها مقارنة بالوزن وتتم أيضا تبر مناقشة الفوارق بين هذا النوع من اآلالت و اآلالت االصطالحية ذات المجال المغناطيسي القطري حيث يع النوع القرصي ذو اإلثارة المغناطيسية الثابتة والمجال المغناطيسي المحوري من أفضل التصاميم من حيث الشكل و .االنسجام و القوة و الخصائص الكهربائية يتوقع مستقبالً استخدام هذه اآلالت في كثير من المجاالت نظرا لخصائصها و فوائدها المتميزة التي تنعدم في .الصطالحية ذات المجال المغناطيسي القطرياآلالت ا abstract: this paper is a review of axial-field electrical machines, which were at the origin of the invention of electrical machines such as the famous faraday’s disk. the different configurations of the axial-field machines are presented along with their advantageous key steady state characteristics such as high efficiency and high power to weight ratio. the differences between axial-field machines and conventional radial-field machines are discussed. the disc-type axial-field electrical machines with permanentmagnet excitation seem to be among the best designs in terms of compactness, suitable shape, robustness, and electric characteristics. axial-field machines are expected to be used in a large number of applications in the future owing to their special features and distinct advantages compared to conventional radial-field machines. al-badi, gastli, bourdoucen and jervase contents 1. introduction 228 2. classification of axial-field machines 230 3. differences between axial-field and conventional machines 231 4. main configurations of axial-field machines 231 4.1 faraday disk 231 4.2 printed circuit board motors 231 4.3 axial-field electromagnetic differential induction motor 232 4.4 axial-field machines with yokeless armature core 233 4.5 single-phase axial-field and induction motors 234 4.6 disc-armature d.c. motor 234 4.7 multi-stage axial-field permanent-magnet with water-cooled 234 4.8 double-disc alternator with a.c.-side excitation 236 4.9 axial flux interior permanent magnet synchronous motor 237 4.10 torus machine 237 4.10.1 properties of the torus machine 241 4.10.2 modes of operation of the torus machine 241 4.10.2.1 d.c. generator 241 4.10.2.2 a.c. generator 241 4.10.2.3 brushless d.c. motor 241 5. applications of the axial-field machines 242 5.1 auxiliary power units 242 5.2 wind-power generator 242 5.3 electric scooter drive 242 5.4 water-cooled ev drive 243 5.5 high speed generator driven by a gas turbine 243 5.6 adjustable-speed pump drive 243 5.7 coreless-winding axial-field permanent-magnet generator 243 6. conclusions 243 7. references 244 1. introduction an electrical machine is an electromagnetic energy conversion device. it translates its input electrical power into an output mechanical power. electrical machines have been available and working for nearly a century (bose, 1986). during this period many extensive efforts have been made by researchers worldwide to develop and improve design, configuration and performance of electrical machines. nowadays, electrical machines are found in various physical topologies. they may be categorized according to their conductor geometry and field orientation (see figure 1) as : 1. radial-field machine, where the conductor is axial and the airgap flux is radial. 2. axial-field machine, where the conductor is radial and the airgap flux is axial. 3. linear machine, where the mutually perpendicular flux and the conductors are arranged along a linear path. the history of electrical machines shows that the earliest machines were of the axial-field type. based on the principle of electromagnetic induction, faraday invented the faraday disk in 1832, which is also called the homopolar machine. because of the strong magnetic force existing between the stator and the 228 evolution of axial-field electrical machines rotor, these machines were soon replaced by radial-field machines (chan). these radial-field machines have been and are still used to a large extent. one example of a popular axial-field machine is the printed circuit servomotor (chan, 1983 and hanitsch, 1987). as mentioned above, one drawback of the axial-field design is the strong magnetic force between its stator and rotor. this problem may be alleviated by using a sandwich configuration with a stator placed between two rotors or a rotor sandwiched between two stators (see figures 2b and 2c respectively). a study of axial-field machines reveals that high electrical power to weight ratios have been achieved as shown by the works of chan (1983), hanitsch (1987), campbell (1974a), spooner et. al. (1990a) and spooner et. al. (1990b). there is reason to believe that axial-field machines will be used in the future in a large number of applications where their special features offer distinct advantages (chan, 1983, spooner et al, 1990a, profumo et al, 1997, caricchi et al, 1998b, 1997, herdzak et al, 1996a, 1996b, 1997, 1998, chalmers et al, 1999, huang et al, 1999, madlena et al, 1996, panuza et al, 1996, bailey et al, 1990, eastman et al, 1995 and rahman, 1995). some potential applications of the axial-field machines include car heater blower, radiator cooling fan, auxiliary power unit, windpower generator, electric vehicle, high speed generator driven by a gas turbine, adjustable-speed pump drive, lawnmower motor, and others. 229 end plates rotor pole piece commutator coil side end connectors axial-field machine (a) secondary primary x stator rotor y 3 φ winding aluminum (conductors) cut along xy and enroll radial-field machine linear machine (b) (c) figure 1. different types of electrical machines: (a) axial filed, (b) radial field and (c) linear machines. al-badi, gastli, bourdoucen and jervase this paper examines first the overall construction, development, and principle of operation of axialfield machines, then compares the different configurations, steady state characteristics and applications of various axial-field machines. 2. classification of axial-field machines in theory, each type of radial-field machine will have an analogous axial-field machine (chan, 1983). therefore, an axial-field machine can operate as a d.c. machine as well as an a.c. synchronous or induction machine. figure 2 shows the topology of the magnetic circuit of the axial-field machine. these machines can be constructed in one of the following ways in correspondence with the design of the magnetic circuit: 1. single stator and single rotor (one airgap), as shown in figure 2(a). 2. central-stator machine (double airgaps), as shown in figure 2(b). 230 φ φ φ φ φ (a) (b) (c) figure 2. topology of the magnetic circuit of axial flux machine ( φ is the flux). evolution of axial-field electrical machines 231 3. central-rotor machine (double airgaps), as shown in figure 2(c). 4. multi-disc machine (multiple airgaps). machines constructed using a single stator/rotor experience a strong magnetic pull between the stator and rotor and therefore, the sandwich configuration appears much more viable. of the two types of sandwich construction available, the central-stator machine produces more torque per length of stator conductor, since both the working surfaces of the stator core are used. in axial-field machines, the electromagnetic torque is a function of the machine outer diameter (spooner and chalmers, 1992). the multi-stage arrangement is suited to overcome the restriction on the machine diameter and to meet the torque required at the machine shaft. 3. differences between axial-field and conventional machines axial-field machines differ from conventional machines in the following: 1. the airgap flux is axial in direction and the active current carrying conductors are radially positioned. 2. the stator and the rotor cores are of the disc type. 3. a higher percentage of the stator winding produces torque. this is due to the fact that the stator winding is wound in a toroidal configuration. thus, the two working surfaces of the core are both active for the electromechanical energy conversion such as in the torus machine. 4. the two rotating discs (in the central-stator machine) act naturally as fans, thereby removing heat produced by copper and iron losses. this can be accomplished by means of holes positioned near the mechanical shaft so that the air flows radially through the machine airgaps. this machine configuration, therefore, permits an exploitation of active materials than in conventional machines. 5. axial-field machines can be designed to possess high power to weight ratios with more saving in the core material especially if permanent magnets are used. they have also a larger diameter to length ratio. 6. floor space required for manufacturing and assembly line is significantly reduced for the axial-field machine (caricchi et al, 1998a). 7. the short axial length of the axial-field machine results in a larger diameter than that of the radial-field machine and hence a higher inertia for the same power rating. this limits their application to systems requiring slow response. 4. main configurations of axial-field machines 4.1 faraday disk based on the principle of electromagnetic induction, faraday (1832) illustrated that if a copper disk is rotated in an axially magnetic field, with sliding contact and brushes mounted at the rim and at the center of the disk, a voltage will be present at the brushes. such a machine is commonly known as the faraday disk (nasar, 1996) or the homopolar generator and is shown in figure 3. the device is also capable of operating as a motor. 4.2 printed circuit board motors in 1958, f. h. raymond and j. henry-baudot invented the first printed-circuit-board (pcb) d.c. motor (knights, 1975). the armature had a disk shape. the motor is lighter and shorter than a conventional type but slightly larger in diameter. it has a short time constant which results in a very fast response and low rotor inertia. these advantages derive mainly from the fact that the armature has no iron in it. the pcb armature (rotor) has conductors that are stamped from a sheet of copper, welded together and placed on a disc. the conductor segments are then joined with a commutator at the center of the disk. the disk armature is located between two sets of permanent magnets mounted on ferromagnetic end plates. al-badi, gastli, bourdoucen and jervase the magnets are circular in shape with magnet faces parallel to the printed armature. this arrangement provides axial flux through the armature. when current from a supply is passed through the armature conductors, they generate a field, which interacts with the permanent-magnet field to produce the torque needed for the armature. the pcb motor's special geometry, high power to weight ratio, and very high pulse torque, have led to their use in a variety of applications. typical applications of pcb motors are in machine tools, computer peripheral equipment, ultra-violet recorder drivers, large control valves, etc… the schematic representation of a pcb motor is shown in figure 1a. 232 s power electronic interface n ω φ + _ v copper disk magnet conducting shaft brush figure 3. faraday disk or homopolar machine. 4.3 axial-field electromagnetic differential induction motor the basic layout of this type of machine comprises a single stator and two squirrel-cage rotors as shown in figure 4. these rotors are mounted on two individual shafts and may rotate independently. the two surfaces of the stator core and the rotors have slots. the coils of the stator winding are placed in slots and wound in a toroidal fashion around the stator core. both rotors carry a squirrel-cage winding. since the excitation of the machine is from the stator winding currents, the airgaps must be reduced as much as possible in order to produce adequate airgap flux density. the machine has been used to drive the wheels of an electric vehicle by performing the function of both the engine and the differential (caricchi et al, 1995a and profumo et al, 1997). cage rotor stator figure 4. single converter-fed motor having one stator and two rotors evolution of axial-field electrical machines 4.4 axial-field machines with yokeless armature core the basic construction of this machine is that its armature is sandwiched between two rotor cores. the armature consists of a number of teeth; each is made of a packet of laminations. the laminated teeth are held together in position by two endplates where the armature winding is located (see figure 5). end plate figure 5. armature core note the absence of the yoke in the armature core. as a result, a considerable saving in the core material and a significant increase in the power/weight ratio of the machine are achieved (chan, 1983 and leung, 1980). one way to construct the stator is to insert the teeth laminations into one endplate. the stator winding is then wound in place before the second endplate is placed in position on to the other end of the teeth lamination. the side view lamination of the armature core is shown in figure 6. 233 endplate laminated tooth figure 6. the side view lamination of the armature core. al-badi, gastli, bourdoucen and jervase 4.5 single-phase axial-field induction motors single-phase axial-field induction motors may have distinct advantages in the field of small power domestic applications such as fans, pumps, etc… firstly, the flat shape is a desirable configuration for such applications. secondly, the rotor may be integrated with the rotating part of mechanical load. the axial force between the rotor and the stator is not so severe in the small power range and therefore, a thrust bearing can withstand it (chan, 1983). 4.6 disc-armature d.c. motor this is an axial airgap machine with a permanent-magnet field system. the permanent-magnets are fixed to mild steel endplates by epoxy resin adhesive. the armature consists of two double layer windings. the active conductors running radially so that the complete armature is disc shaped. the coil ends are connected to the commutator and epoxy resin is added to give the whole armature rigidity (campbell, 1972, 1974b and corbet, 1976). this motor can have two different types of design. in the first design (see figure 7), the armature is free from iron, the windings being encapsulated in epoxy resin. as a result, all losses due to hysteresis or eddy currents are eliminated. however, with the addition of running clearance on either side of the disc, this leads to a large airgap. as any reduction in the airgap length would reduce the magnet length also, it was decided to incorporate the flux return ring in the armature for the second type of design. with this new arrangement (see figure 8), the inherent high efficiency of the first design has been sacrificed. eddy-current and hysteresis losses have been introduced into the armature and a thrust bearing is now unavoidable between rotor and stator. the disc-armature d.c. motors are basically similar to printedcircuitboard (pcb) motors. the difference is in the shape of the permanent-magnet and in the armature design. the shape of the pole segments in disc-armature d.c. motor gave a more uniform airgap flux density than the circular pole in pcb. moreover, the armature design of the disc-armature motor allows it to sustain much larger overload currents, which leads to a much greater reliability (campbell, 1974b). magnets commutator armature disc before windings are resin encapsulated gearbox support plate brake drum brushes magnets figure 7. disc armature d.c. motor. 4.7 multi-stage axial-field permanent-magnet with water-cooled ironless stator for some applications, lightness and long-term overload capability are of crucial significance. a totally enclosed construction of the motor is required where the machine must operate in a hostile environment. to meet such conditions, direct cooling of the stator winding must be used and may be achieved using an ironless stator. the space normally occupied by the core becomes a water duct, which removes heat directly from the stator winding. in principle, the winding coils in an ironless stator may have 234 evolution of axial-field electrical machines 235 ri 2 a trapezoidal shape, but these have significant end-winding length. much higher values of torque per unit loss are achieved by means of winding coils of rhomboidal shape as illustrated in figure 9. mild steel ring commutator armature (showing winding magnets mild steel ring figure 8. disc armature motor with a flux return ring. optimum values of inclination angleα lie between 60 to 70 degrees and the ratio of the outer radius to the inner radius is between 1.45 and 1.65 (caricchi et al , 1995b). multi-stage designs provide a solution for higher ratings when there are limits on acceptable machine diameter. in a multi-stage axial flux machine, if is the number of stages, then the machine has stator windings and rotor discs. the rotors share a common mechanical shaft whereas the terminals of the three-phase windings may be connected either in series or in parallel. a two-stage arrangement of the machine is shown in figure 10. or ir n n ( +n )1+ )1 (n ro active side end winding α ri figure 9. rhomboidal coil shape for machine with ironless stator. al-badi, gastli, bourdoucen and jervase flux path cooling ductironless winding coil epoxy body external rotor mechanical couplingintermediate rotor magnet figure 10. cross section of two-stage axial-field permanent magnet machine with ironless water cooled stator winding 4.8 double-disc alternator with a.c.-side excitation the rotor of this machine consists of a central hub interconnecting two rotor "paddles" which are circumferentially displaced with respect to each other by one pole pitch as shown in figure 11. the stator core is a strip-wound laminated cylinder concentric with the rotor hub and located between the paddles. the field coil surrounds the hub but is separate from it and stationary. “the path for the main flux is axially along the hub, radially along one paddle and axially across the air gap into the stator core; dividing in the core, it passes circumferentially in both directions through one pole pitch, then axially across the second air gap into the second paddle, radially through the paddle and completes at the hub (evans et al, 1983a)". this arrangement produces directly a brushless machine with a rotating robust steel assembly. rotor paddles central hub stator core figure 11. the arrangement of the magnetic circuit. 236 evolution of axial-field electrical machines 4.9 axial flux interior permanent magnet synchronous motor this machine is realized by one stator and two rotors, the stator core is built using a ring structure with slots. the polyphase windings are symmetrically mounted in the slots on each stator surface. the permanent magnets are mounted inside the rotor disc. this motor has the following characteristics (evans et al, 1983a) • the machine is quite robust because the rotor permanent magnets and the stator windings are located inside the iron structure. • the effective air gap is small thus, the value of the inductances will be large enough to allow the operation in the flux-weakening region. • the resultant torque has two terms: one due to field excitation and the other due to saliency. shaft engine air-outlet rotor disk magnet shaft air-inlet stator dowel stator winding stator core figure 12. torus machine cross-section. 4.10 torus machine axial flux machines with permanent magnets have not found widespread commercial application previously, partly because suitable permanent magnets of high coercivity and remanence have not been available. by using high-energy permanent magnets such as neodymium-iron-boron (nd-fe-b), high values of the flux density in the airgap can be obtained even with relatively large airgap length. sintered nd-fe-b magnets have a remanence, br, in excess of 1t, recoil permeability approximately equal to that of 237 al-badi, gastli, bourdoucen and jervase air, and a coercivity of about 800a/mm. this fact has opened up application opportunities for axial-field machines. such a machine allows the arrangement of a slotless-designed stator winding, which has the advantage of relatively short-end winding, resulting in low copper losses and consequently, increased efficiency. in umist (university of manchester institute of science and technology) several 2.5 kw axial-field, slotless, toroidal-stator, permanent-magnet machines have been built and tested and have demonstrated all aspects of the steady-state capability and performance in the generating and motoring modes (spooner et al, 1990a, 1990b, 1991). this type of configuration was called torus. the name torus was proposed by spooner and chalmers (1990b, 1992), to indicate the toroidal nature of both the stator winding and the stator core. torus brings further improvements over earlier designs, because it employs comparatively new magnetic material (nd-fe-b) that has the necessary remanence, together with a coercivity, that permits a slotless winding to be used (spooner and chalmers, 1992). torus is an axially compact electrical machine suitable for the development of compact integrated designs. the basic layout is shown in figure 12, the machine has similarities with several other configurations proposed in recent years including the permanent-magnet axial-field machine investigated by campbell (1974c) and slotless-disc alternator proposed by evans and eastham (1983b). for a machine to deliver high power from a small space, it must have: (a) high magnetic and electric loadings. (b) intensive cooling to remove the losses. (c) low impedance to avoid pull-out. the use of the sintered neodymium-iron-boron magnets enables a high magnetic loading to be achieved. the rotor discs act naturally as fans and so good cooling of the stator winding is ensured even with a high electric loading. the values of the phase self and mutual inductances are low because the magnetic gap is large and the slot leakage is absent. moreover, with the high magnetic loading, the required emf could be generated using a small number of winding turns and so the inductance and the resistance are low. the core is a toroid wound from thin electrical steel strip; the quantity of steel used is quite small. it works at high flux density in the tangential direction but a rather low flux density axially. these features lead to low iron loss. the torus machine is a double-sided, axial-field, disc-type, permanent-magnet, brushless machine. it has a simple toroidal, strip-wound stator core that carries a slotless toroidal winding which may have any chosen number of phases, as illustrated in figure 13. figure 13. toroidal stator with 11-phase winding. the experimental 6-pole machine is shown in figure 14. the a.c. output of the machine is fed through rectifiers that are mounted on the stator casing. it can be seen that the casing forms a well-ventilated heat sink for mounting the electronic components. the machine has been designed to provide a flat-topped emf 238 evolution of axial-field electrical machines wave to avoid excessive ripple in the output voltage. a large number of phases raises the frequency of the output ripple so that filtering can be performed with a small passive component. for brushless d.c. motor operation, additional electronic components are required which may be fixed to the casing. in the stator the copper losses have two component, loss due to the flow of current in the windings and eddy current loss due to the main airgap field passing through the conductors. the copper losses are removed by conduction into the iron core and by the heat transfer to the air flowing between the stator and the rotor. figure 14. experimental 2.5 kw torus machine with outer rotor disk removed, mounted on a 4 kw induction motor. the rotor comprises two discs carrying six axially polarized magnets, as illustrated in figure 15. figure 15. six-pole inner rotor for 2.5 kw experimental machine. typical flux paths are indicated in figure 16. the rotor discs may be mounted directly on the shaft of the coupled machine, eliminating the need for a coupling and separate bearings. moreover, the flywheel and ventilation fan may be eliminated. the rotor suffers no significant losses because the torus machine is excited by permanent magnets. each phase in the armature consists of a pair of coils wound on the core at positions separated by 180 mechanical degrees as shown in figure 17. the two coils are connected in opposition so that no flux tends 239 al-badi, gastli, bourdoucen and jervase to pass around the core when current flows. torus has a very small stator leakage and relatively small mutual inductances because of the slotless configuration and the large effective airgap compared to a conventional machine with slotted stator. 240 shaft rotor disc magnet stator core air gap figure 16. principal flux paths (shown as dotted lines). the active conductor lengths are the radial portions facing the magnets. the axially directed endwinding lengths are relatively short, yielding low resistance compared with the end-winding resistance of a normal machine. the slotless armature windings are also known as airgap windings. mmf . figure 17. arrangement of a phase winding. evolution of axial-field electrical machines 241 4.10.1 properties of the torus machine the salient feature of the torus machine can be summarised as follows: 1. torus machines have short axial length and high power to weight ratio. the overall arrangement of torus is compact and suitable for mechanical system integration. 2. the slotless airgap winding gives low values of mutual and leakage inductances because the effective airgap is necessarily large and slot leakage is absent. 3. owing to the large effective airgap length, the magnets are less prone to demagnetisation. 4. vibration, flux ripple and high-frequency rotor losses owing to stator slotting are eliminated. 5. the absence of slots leads to a low-noise machine with negligible cogging torque. 6. saturation and iron losses of stator teeth are absent. 4.10.2 modes of operation of the torus machine the machine may be operated as an a.c. generator or its output may be rectified for generating d.c. power. it may also operate as a motor via suitable switching circuits. 4.10.2.1 d.c. generator the torus arrangement is well suited for use as a low-voltage d.c. generator with low voltage ripple. the a.c. output of the machine is fed through rectifiers, which may be mounted on the stator casing, which act as a well-ventilated heat sink. the magnet shape may be made close to the arc shape; as a result, the phase emf is a flat-topped wave. the magnitude of the ripple voltage appearing across the bridge rectifier depends on the machine number of phases and on the impedance of the load. for 11-phase, 6-pole machine, 3000 r.p.m. generator, the ripple frequency in the rectified d.c. output is 1650 hz so that filtering can be easily performed. the ripple voltages may be filtered by means of a capacitor connected across the machine terminals. a permanent magnet is a constant excitation field system so that the output of an isolated permanentmagnet generator exhibits its natural voltage regulation characteristics. this may be overcome by several alternative methods (chalmers et al, 1997): 1. adjusting the drive speed to the generator. 2. designing the machine to have low series impedance. since a slotless winding is used thus providing low values of phase self and mutual inductances because the magnetic gap is large and the slot leakage is absent. 3. adding a voltage regulator. 4. utilising magnetic saturation within the design so that on load, the armature reaction mmf simply reduces the degree of saturation (wu et al, 1995). 5. adjusting the total induced emf by mechanically adjusting the angular displacement between the rotor disks (chalmers et al, 1997). 4.10.2.2 a.c. generator reduction of the harmonic content of the generated open circuit voltage in torus generator is achieved by the shaping of the magnet thickness and relative displacement of the rotor disks by a small angle (chalmers et al, 1997). 4.10.2.3 brushless d.c. motor any axial-field d.c. machine may be operated as a brushless d.c. motor in the same way as a cylindrical machine using a variable-frequency inverter to feed currents into the stator windings in synchronism with the rotor speed. the inverter is fired according to information obtained from the rotor position sensor and so, performs the same function as the brushes and the commutator in a d.c. motor. in al-badi, gastli, bourdoucen and jervase these types of machines there is little scope for field weakening by the usual technique of phase advancing the stator currents. 5. applications of the axial-field machines axial-field machines are particularly appropriate for the development of compact integrated designs owing to their disc-shape. some potential applications of the axialfield machine include the following: 5.1 auxiliary power units using the torus configuration a number of auxiliary power units for military applications have been developed in association with dornier gmbh (chalmers et al, 1997). 5.2 wind-power generator the torus generator can be direct coupled to a wind turbine allowing the elimination of the gearbox. this brings about reduced nacelle weight and noise, and improved reliability and efficiency. these considerations led to the proposed use of direct-coupled torus generators for small-scale stand-alone generating systems in remote areas. 10 kw stand-alone wind/photovoltaic generating system prototypes have been constructed. figure 18 shows the layout of a system that uses a wind turbine-driven permanentmagnet machine and a photovoltaic array as power generating units (stiebler and okla, 1992, caricchi et al, 1994a, chalmers et al, 1996, 1999). 242 single-phase or three-phase pwm inverter load wind generator double input single-output dc-to-dc converter photovoltaic figure 18. layout of the wind-photovoltaic system. the principal features of the system are: 1. the permanent-magnet wind generator is directly driven and has high torque to weight ratio and high efficiency. 2. the double-input, single-output, d.c.-d.c. converter, combines the power generated by the wind and photovoltaic array with high efficiency. 3. the d.c.-d.c. converter is used for charging a storage battery and supplying the user a.c. load via a voltage source inverter. 5.3 electric scooter drive an axial-field slotless permanent-magnet motor was used as motor-in-wheel drives for an electric vehicle to replace the 3hp two-stroke engine in a standard production scooter. the motor drive arrangement uses a microprocessor-controlled igbt power converter, which is fed by a lead-acid battery. the motor was evolution of axial-field electrical machines 243 supplied from a 96 d.c. voltage via a microprocessor-controlled igbt power electronic interface consisting of a bi-directional d.c.-d.c. converter and a current-regulated pwm inverter. the use of a bi-directional converter allows suitable control of both motoring and regenerative braking operations and also for onboard battery charging from the main supply (caricchi et al, 1994b). 5.4 water-cooled ev drive the arrangement with a water-cooled ironless stator is particularly suitable for direct-coupled wheel drives demanding high torque density. the motor construction could be totally enclosed to provide protection against the environment. a single-stage demonstrator machine was first developed and tested to prove the principle, and a two-stage machine was then designed for the application in an innovative city car. the power loss within the winding is removed by assisted circulation of cooling water. this results in a relatively low over-temperature between the inlet and the outlet of the cooling duct (fenocchi, 1995). 5.5 high speed generator driven by a gas turbine high speed enables a high power output to be obtained from a relatively small and lightweight machine, and allows the generator to be directly coupled to a gas-turbine engine. a prototype machine was driven at 60,000 r.p.m. by a small gas turbine engine. the generator is rated at 50 kva. the machine could be used in an electric vehicle with suitable batteries as the electrical power source for the traction motors. moreover, the machine could be used also as a small stand-alone generator set (fenocchi, 1995). 5.6 adjustable-speed pump drive the design and construction of a 3 nm, 2800 r.p.m., slotless, axial-field machine prototype using ferrite permanent-magnets for application in adjustable speed pump drives, was reported by caricchi et al,( 1998a). this prototype drive possesses several advantages over the conventional three-phase induction motor such as, higher efficiency, compactness and lightness. furthermore, it was shown that the manufacturing cost of the prototype, on a large scale, can be as low as that of an induction machine drive having the same power rating (for low power ratings) (caricchi et al, 1998a). 5.7 coreless-winding axial-field permanent-magnet generator with power output at 400 hz in the design of power generation aboard aircraft and on ships, significant efforts have been made to ensure that lightness and compactness are as high as possible. a coreless-winding axial-field permanent-magnet generator with power output at 400 hz, 3000 r.p.m. prototype has been designed and tested. because of the use of an ironless winding placed in a high frequency rotating field, the eddy-current loss is a serious problem. this can be quite easily solved by using conductor arrangements based on litz wires or multitier construction of the conductors (caricchi et al, 1998b). 6. conclusions axial-field machines have been presented and discussed. they offer an alternative to the conventional radial-field machines. their main advantages over the conventional machines are: • they can be designed (using permanent magnets) to possess a higher power-to-weight ratio. • they have a larger diameter-to-length ratio. • they have a planar and adjustable airgap. • their magnetic circuit topology can be easily varied so that many different types of axial field machines may be designed. axial-field electromagnetic differential induction motors are a promising solution for electrical cars because they can behave in the same way as an electro-magnetic differential supplied by a single set of al-badi, gastli, bourdoucen and jervase 244 inverters. the machines can have both higher efficiency and power density compared with two individual motors. disc-type electrical machines with permanent-magnet excitation appear to be the best design in terms of compactness, suitability in shape, robustness, and superior electrical characteristics. because the axial-field machines can be designed to possess high power to weight ratio, they are more suitable for use in aircrafts. their relatively flat shape makes them also suitable for ceiling-fan motors, radiator cooling fans, etc…the possibility of using an ironless rotor in the axial-field machine makes it appropriate for applications with fast response and low inertia. moreover, the prospect of separating the stator and the rotor makes the axial-field machine design suitable for sealed and screened machines, such as domestic pump motors and wheel-directly-coupled motors for electric vehicles. finally, reductions in the cost of high-field permanent magnets are expected to open-up several applications for the axial-field machines. 7. 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no. 3, march 1975, pp.199-202. leung, w. s. and chan, c. c. 1980. a new design approach for axial-field electrical machines. ieee transactions on power apparatus and systems, vol.pas-99: 1679-1685. madlena, m., gair, s., canova, a. and profumo, f. 1996. torque control of a bdc axial field drive motor with open and closed slot configuration. proc. of the ieee international symposium on industrial electronics, vol. 2, pp. 837-843. nasar, syed a. 1996. electric energy systems. prentice-hall, inc., new jersey, 1996. panuza, f., beszedics, g., toriser, w., wawra, m. and w. winkler. 1996. an electric vehicle for recreational areas and local traffic. southcon/96, conference record, pp. 281-283. profumo, f., zheng, z. and tenconi, a. 1997. axial flux machine drives: a new viable solution for electric cars. ieee transactions on industrial electronics, 44: 39-45. rahman, m., yoo, k. and lim, k. 1995. performance of an axial-field pm disc motor under impresses current waveforms. proc. of international conference on power electronics and drives systems, vol. 2, pp. 651-656. spooner, e., chalmers, b. j., el-missiry, m. m. and kitzmann, i. 1990. the design of an axial-field, slotless, toroidal-stator, permanent-magnet machine for starter/alternator application. universities power engineering conference aberdeen, pp.171-174. spooner, e. and chalmers, b. j. 1988. toroidally-wound, slotless, axial-field, permanent-magnet, brushless-dc motors. proc. int. conf. on electrical machines, pisa, italy, vol. iii, pp.81-86. spooner, e. and chalmers, b. j. 1990. toroidal-stator, permanent-magnet machine for small scale power generation. proc. int. conf. on electrical machines, cambridge, usa, vol. iii, pp. 1053-1058. spooner, e., chalmers, b. j., el-missiry, m. m.,wei, w. and renfrew, a. c. 1991. motoring performance of the toroidal permanentmagnet machine torus. proc. 5th iee int. conf. on electrical machine and drives, pp. 36-40. spooner, e. and chalmers, b. j. 1992. torus-a slotless, toroidal-stator, permanent-magnet generator. iee proc. b, 139: 497-506. stiebler, m. and okla, o. 1992. a permanent magnet toroid wind generator. icem92, manchester, pp. 10431047. wu, w., spooner, e. and chalmers, b. j. 1995. design of slotless torus generators with reduced voltage regulation. iee proceedings b, 142: 337-343. received 30 january 2000 accepted 3 july 2000 245 evolution of axial-field electrical machines abdullah al-badi, adel gastli, hadj bourdoucen and joseph jervase êøæñ çáâáçê çáßåñèçæíé ðçê çáãìç� úèïçááå çáèçïí ¡ úçïá çáþõøáí ¡ í contents classification of axial-field machines differences between axial-field and conventional machines 4.main configurations of axial-field machines axial-field electromagnetic differential induction motor axial-field machines with yokeless armature core single-phase axial-field induction motors disc-armature d.c. motor multi-stage axial-field permanent-magnet with water-cooled ironless stator double-disc alternator with a.c.-side excitation axial flux interior permanent magnet synchronous motor 4.10 torus machine 4.10.1 properties of the torus machine 4.10.2 modes of operation of the torus machine 5. applications of the axial-field machines 7. references microsoft word biol080413-f edited_checked_ref.doc 1-7 squ journal for science, 14 (2009) © 2009 sultan qaboos university 1 an electrophoretic study of ldhisozyme distribution in developing embryonic and adult tissues of the toad bufo arabicus intisar ambusaidi, taher ba-omar, saif al-bahri and aisha al-shihi department of biology, college of science, sultan qaboos university, p.o.box 36, postal code 123, muscat, sultanate of oman, email: taher@squ.edu.om. في مراحل نمو جنين وأعضاء الضفدع العربي البالغldhدراسة استشرادية لتوزيع ايسوزوم انتصار امبوسعيدي، طاهر باعمر، سيف البحري وعائشة الخياط باستخدام طريقة االستشراد للنظر في الفروقات االيسوزيمية المتوقع ldhتم دراسة الكتات الديهايدروجينيزات :خالصة تم تحليل الشكل التعبيري اليسوزومات . في مراحل نموه المختلفةعضاء جنين الضفدع العربي جميع أفي وجودها تم مالحظة خمسة ). page(ير الشكل غمتال الالكتات الديهايدروجينية باستخدام هالم البولي اكريالمايد االستشرادي غير لسالب قويا، اما مراحل نمو الجنين شاط القطب ا في خمسة أعضاء للضفدع العربي البالغ حيث كان نldhايسوزومات مرحلة االخصاب الى (16-1 في مراحل الجنين من ldhفاظهرت االيسوزمات االجابية أوال، حيث ظهرت اربعة وذلك بداية نشاط العضالت ويزداد كثافة عند التقدم 17زوم الخامس فقد ظهر في مرحلة ، أما االيسو)ن الذيليمرحلة تكو .43 الى مرحلة 17ل النمو ابتداءا من مرحلة في مراح abstract: lactate (ldh) dehydrogenases were studied by electrophoresis to investigate the possibility of isozymic differences in different stages and organs of b. arabicus embryos, tadpoles and adults. the expression pattern of lactate dehydrogenase (ldh) isozymes was analysed using nondenaturing discontinuous polyacrylamide gel electrophoresis (page). five ldh isozymes were observed in five different adult tissues. the most cathodal isozyme, ldh-5 (a4), showed the strongest activity. all embryonic stages tested displayed the anodic isozymes first. four ldh isozymes were present in the stages 1-16 (fertilized egg-tail bud stage). the first appearance of the fifth isozyme was detected in stage 17 when the muscular response started. this isozyme showed gradual increase in intensity from stage 17 to stage 43. keywords : toad, embryos, tadpoles, skeletal muscle, ldh, bufo arabicus. intisar ambusaidi et al 2 1. introduction or a range of animal groups, ‘model’ species are now well characterized in terms of the morphology and molecular biology of their embryonic and early larval stages. for anuran amphibians, the best characterized species is xenopus laevis. however, if we are to understand the ways in which development has diverged within animal groups, and adapted to different environments (gilbert, 2001), we need to examine both morphology and molecular expression in a variety of related species. molecular analysis provides additional information on species identity in areas where mixed genetic types are present (simovich and sassman, 1986). during cell differentiation, genes play an important role in metabolism, so multilocus isozymes constitute probes for investigating the mechanisms of spatial and temporal gene regulation in different stages of development (philipp et al., 1979). thus the study of isozymes provides considerable insight into the structure and function of metabolic enzymes. lactate dehydrogenase (ldh) is considered a suitable system for studying several metabolic, genetic and ecological features (coppes, 1990; ropson et al., 1990; almeida-val et al., 1992). in most vertebrates, ldh is a tetrameric enzyme composed of two kinds of subunit polypeptides, a and b (appella and markert, 1961). ldh isozyme patterns are species and tissue specific and their expression patterns vary during development and several studies have been conducted on the electrophoretic distribution of ldh in amphibians (mathews, 1975; harintz and diehl, 1999). this study aims to investigate the ontogeny of the enzyme lactate dehydrogenase (ldh) in some tissue of the bufo arabicus embryos, tadpoles and adults. 2. materials and methods embryos and tadpoles of stages 1-18, 21-25, 29, 31, 35, and 43 (ba-omar et al. 2004) were obtained by induced fertilization. adult toads were killed by pithing and the following tissues were collected skeletal muscle, heart, liver, lung and stomach (ambusaidi, 2002). the embryos and tadpoles were first washed in distilled water, then frozen in liquid nitrogen and stored at -70 ºc (beis et al. 1992). the adult organs were dissected out, kept in ice, and washed with distilled water prior to the protein extract being prepared. with slight modifications, the method of markert et al. (1998) was used to analyse ldh isozymes. thawed embryos and tadpoles were homogenized in 250-500 µl of sterile de-ionized water in an ice bath with a tissue tearor (biospec products, usa) for 3-5 minutes depending on the sample size. the same procedure was used for adult organs using 1.0 ml of sterile de-ionized water. the homogenate was then centrifuged at low speed (x 2000g) in a microcentrifuge (eppendorf 5402, germany) for 15 minutes at 4º c. the supernatant was then taken and centrifuged at high speed (x 16000g) for 30 minutes at 4ºc. the resulting supernatant was removed for ldh analysis by electrophoresis on a polyacrylamide gel. ldh isozymes were separated using non-denaturing discontinuous polyacrylamide gel electrophoresis following the method of markert et al (1998). ldh isotrol (sigma co, usa) was used as a marker. ldh isozyme activity was visualized by incubating the gel at 37° c in the dark, in a reaction mixture specific for ldh, consisting of 20 ml 0.35 m tris-hcl (ph 8.0), 80 ml de-ionized water, 2 ml nicotinamide adenine dinucleotide (sigma co, usa) (10 mg/ml), 2 ml nitro-blue tetrazolium (sigma co, usa) (10 mg/ml), 0.1 ml phenazine methosulphate (sigma co, usa) (10 mg/ml) and 2 ml of (3.0 m) lactic acid syrup (bdh co, uk) until bands appeared after about 15 minutes. to determine whether any enzyme activity resulted from the activity of alcohol dehydrogenase, control gels were incubated in the absence of the substrate (lactate). 3. results the electrophoretic pattern of the ldh isozymes of the toad b. arabicus was distinctly different from those of the ldh isotrol standards from human tissue (figure 1 lane m). the bands revealed by ldh specific stain were due to ldh activity. in the absence of a lactate substrate, no bands appeared. this confirms that the observed bands were produced by ldh activity and not by alcohol dehydrogenase or impurities (figures 14). f an electrophoretic study of ldh-isozyme 3 cathode _ m sm h li lu s anode + figure 1. electrophoretic patterns of ldh of b. arabicus adult from different tissues. marker (m), skeletal muscle (sm), heart (h), liver (li), lungs (lu) and stomach (s). _ m 1 2 3 4 5 6 7 8 9 + figure 2. electrophoretic patterns of ldh of b. arabicus embryos (stages 1-9). the numbers at the top refer to the developmental stages of b. arabicus embryos. marker (m). ldh-5 (a4) ldh-3 (a2b2) ldh-2 (a1b3) ldh-1 (b4) ldh-4 (a3b1) intisar ambusaidi et al 4 3.1 electrophoretic pattern of ldh in adult tissues ldh activity was detected in all tissues examined. five distinct bands appeared on the polyacrylamide gel and these were numbered from 1-5 in their order of migration from the cathode to the anode (figure 1). the most cathodic band was the homotetramer isozyme ldh-5 (a4) and the most anodic band was the homotetramer isozyme ldh-1 (b4). the three intermediate heterotetramers from cathode to anode were ldh-4 (a3b1), ldh-3 (a2b2) and ldh-2 (a1b3). all five isozymes ldh-5 to ldh-1 were observed in all adult tissues examined and the most cathodic isozyme (ldh-5 a4) showed the strongest activity. in skeletal muscle and liver (figure 1 lanes sm and li respectively) the most cathodal isozyme (ldh-5 a4) predominated and appeared as a very broad band, especially in skeletal muscle, followed by ldh-4 (a3b1). the other isozymes [ldh-3 (a2b2), ldh-2 (a1b3) and ldh-1 (b4)] were only indicated by faint bands, especially in the skeletal muscle. the heart displayed all five bands with high intensity coloration (figure 1 lane h). ldh-1 (b4) was highly intense in the heart (figure1 lane h) and secondly in the stomach (figure 1 lane s), but it was only faintly indicated in skeletal muscle (figure1 lane sm) and liver (figure 1 lane li). 3.2 ontogeny of ldh in developing bufo arabicus all embryonic stages tested displayed first the anodic isozymes (figures 2, 3, and 4). a gradual increase in the expression of more cathodic isozymes was observed in the embryos and tadpoles at various developmental stages. stages 1-16 (fertilized egg-tail bud stage) showed four stained bands: ldh-1 (b4), ldh-2 (a1b3), ldh3 (a2b2) and ldh-4 (a3b1). ldh-3 showed the lowest activity, while ldh-1 (b4) showed the highest activity (figure 2 lanes 1-9; figure 3 lanes 10-16). the first appearance of the fifth isozyme band was in stage 17 (figure 3 lane 17). this isozyme showed a gradual increase in intensity from stage 17 to stage 43 (figure 3 lane 17; figure 4 lanes 21-43). this electrophoretic pattern persisted to stage 43 (figure 4 lane 43). it is apparent that band 5 [ldh-5 (a4)] was the strongest, followed in intensity by bands 4, 1, 3 and 2. no differences could be observed in stages 29 43 regarding the number and intensity of bands (figure 4 lanes 29 43). _ m 10 11 12 13 14 15 16 17 18 + figure 3. electrophoretic patterns of ldh of b. arabicus embryos (stages 10-18). the numbers at the top refer to the developmental stages of b. arabicus embryos. marker (m). an electrophoretic study of ldh-isozyme 5 _ m 21 22 23 24 25 29 31 35 43 + figure 4. electrophoretic patterns of ldh of b. arabicus embryos and tadpoles (stages 21-25, 29, 31, 35 and 43). the numbers at the top refer to the developmental stages of b. arabicus embryos and tadpoles. marker (m). 4. discussion the ontogeny of lactate dehydrogenase (ldh) expression in the toad b. arabicus, embryos, tadpoles and some adult organs, shown by electrophoresis gives a five-band pattern. the expression of ldh genes is not tissue-specific in b. arabicus since all five isozymes appeared in all organs examined, although the isozyme a4 predominated in skeletal muscle and the liver. similar observations were also reported by hranitz and diehl, (2000) in their study of b. woodhousii fowleri. the isozyme a4 always predominated in skeletal muscle, confirming its metabolic role in reducing pyruvate during the anaerobic glycolysis. vonwyl (1983), in a study of x. l. laevis, x. vestitus, x. borealis and x. wittei, claimed that the multibanded pattern of ldh isozymes or the presence of secondary isozymes facilitates the identification of the species and contributes strongly to a species specific pattern . b. arabicus exhibits anodal bands in early embryonic stages (stages 1-16). moyer et al., (1968), kunz (1973) and vonwyl (1983) showed that the species they studied are characterized by the appearance of anodal bands in oocytes and early embryonic stages. in b. arabicus, the first appearance of the fifth isozyme (ldh-5, a4) was at stage 17, which coincides with the onset of muscular contraction. this can be explained by the synthesis of the a4 homotetramer isozyme at this stage. according to kunz (1973), the ldh pattern from the newly fertilized egg to early tail bud (stages 1-24) is the same and a change is observed at stage 25, when isozyme ix appears and this may be correlated with the onset of contractility. moyer et al. (1968) indicated that clear evidence of the new isozyme was found around stage 19 when the heart starts beating. basu et al., (1992) claimed that the initial predominance of b4 over a4 in fish up to the onset of muscular contraction (stage 17 in b. arabicus of ontogenesis) indicates that cell differentiation of the heart and kidney takes place earlier and retarded expression of a4 may indicate that skeletal muscular cell differentiation and activity is somewhat delayed during ontogenesis. on the other hand, goldberg et al., (1969) described the intisar ambusaidi et al 6 predominance of b subunits in early embryonic stages of lake and brook trout, with a gradual increase in the activity of a-containing isozymes as they develop. it seemed to be that ldh isozyme composition of unfertilized and cleavage embryos revealed that more b subunits than a subunits had been synthesized prior to or during these development stages. it is possible that the synthesis of different isozymes is mediated by preformed stable mrna during the process of oogenesis. goldberg et al., (1969) indicated that at gastrulation, the increase in proportion of ldh-5 suggests that new mrna synthesis takes place providing more a subunits for tetramer assembly at a time when the synthesis of many molecules is accelerated in embryos. in b. arabicus, it is possible that new synthesis of mrna takes place when muscular contraction starts (stage 17) which provides more a subunits for the synthesis of the homotetramer ldh-5 (a4). 5. references ambu-saidi, i. 2002. staging of bufo arabicus. m.sc. thesis. sultan qaboos university, oman. almeida-val, v.m., paula-silva, m.n., caraciolo, m.c., mesquita, l.; farias, i.p. and val, a.l. 1992. ldh isozymes in amazon fish-iii. distribution patterns and functional properties in serrasalmidae (teleostei: ostriophysi). comp. biochem. physiol. 103b: 119-125. appella, e. and markert, c.l. 1961. dissociation of lactate dehydrogenase into subunits with guanidine hydrochloride. biochem. biophys. res. commun. 6: 171-176. ba-omar, ta; ambu-saidi, i.; al-bahri, s. and al-khayat, a(2004). embryonic and larval staging of the toad bufo arabicus. zoo .mid. east. 32: 47-55. basu, s.k., ganguly, s., sarkar, s.k. and basu, t.k. 1992. ontogenetic and comparative analysis of ldh isozymes in the three species on indian major carp. ind. j. exper. biol. 30: 90-93. beis, a., lazou, a. and kontogianni, e. 1992. changes in plasma membrane protein composition during early development of the frog rana ridibunda. cellular and molecular biol. 38: 513-523. coppes, z.l. 1990. divegence of duplicate genes in three scianid species (perciformes) from the south coast of uruguay. comp. biochem physiol. 96b: 33-39. coppes, z.l. 1984. isozymes of lactate dehydrogenase in fishes of the superorder acanthopterygii: an update. comp. biochem. physiol. 97b: 1-8. gilbert, s.f. 2001. ecological developmental biology: developmental biology meets the real world. develop. biol. 233:1-12. goldberg, e., cuerrier, j.p. and ward, j.c. 1969. lactate dehydrogenase ontogeny, paternal gene activation and tetramer assembly in embryos of brook trout, lake trout and their hybrids. biochemical genetics. 2: 335-350. hranitz, j.m. and diehl,w.j. 2000. allozyme variation and population genetic structure during the life history of bufo woodhousii fowleri (amphibia: anura). biochem. syst. and ecol. 28: 15-27. kaplan n, o. 1964. lactate dehydrogenase: structure and function. brookhaven symp. biol. 17: 131-153. kunz, y.w. 1973. changes in lactate dehydrogenase isozyme pattern during the development of xenopus laevis ( daudin). rev. suisse zoo. 80(2): 431-446. markert, c.l., amet, t.m. and goldberg, e. 1998. human testis-specific lactate dehydrogenase-c promoter drives over expression of mouse lactate dehydrogenase-1 cdna in testes of transgenic mice. j. exp. zoo. 282: 171-178. mathews, t.c. 1975. biochemical polymorphism in populations of the argentine toad bufo arenarum. copeia. 3: 454-465. moyer, f.h., speaker, c.b. and wright, d.a. 1968. characteristics of lactate dehydrogenase isozymes in amphibians. ann. n. y. acad. sci. 151: 650-669. philipp, d.p., childers, w.f. and whitt, g.s. 1979. evolution of patterns of differentialgene expression: a comparison of temporal and spatial patterns of isozyme locus expression in two closely related species an electrophoretic study of ldh-isozyme 7 (northern large mouth bass, micropterus salmoides salmoides and small mouth bass, m. dolomieui). j. exp. zoo. 210: 473488. ropson, i.j., brown, d.c. and powers, d.a. 1990. biochemical genetics of fundulus heteroclitus (l). vi. geographical variation in the gene frequencies of 15 loci. evolution. 44: 16-26. simovich, m.a. and sassaman, c.a. 1986. four independent elecrophoretic markers in spade foot toads. j. heredity. 77: 410-414. vonwyl, e. 1983. expression of the lactate dehydrogenase genes of the xenopus species and interspecies hybrids during early development. comp. biochem. physiol. 76b: 17-21. received 13 april 2008 accepted 22 june 2009 photovoltaic cells and systems: 33-41 squ journal for science, 13 (2008) © 2008 sultan qaboos university stability and persistence of synchronization in a system with a diffusive-time-lag coupling adu a.m. wasike school of mathematics, university of nairobi, p.o. box 3019700100 nairobi, kenya, email: aduwasike@yahoo.com. اإلعاقة الزمنيةىشار المزدوج ذاستقرار وثبوت التوافق في نظام االنت واًسك .م.أدو أ و قد تـم اسـتخدام . درسنا في هذه الورقة التوافق في إطار المتنوعات الال متغيرة لألنظمة ذات اإلعاقة الزمنية :خالصة يجاد نتائج عامة عـن خواص الزائدية الطبيعية و ثبوتها في األنظمة الحركية ذات البعد الال متناهي في فضاءات باناخ إل .التوافق و ثباته abstract: we study synchronization in the framework of invariant manifold theory for systems with a time lag. normal hyperbolicity and its persistence in infinite dimensional dynamical systems in banach spaces is applied to give general results on synchronization and its stability. keywords: normal hyperbolicity; synchronization; robustness; lyapunov numbers. 1. introduction s ynchronization phenomena of oscillators and diffusively coupled oscillators has been a subject of great interest by physicist, engineers, and mathematicians, see for instance (afraimovich, et.al., 1986; chow and liu, 1997; fujisaka and yamada, 1983; hale, 1997; wasike, 2002; wasike, 2003; wasike and rotich (2007). basic to the study of synchronization, two fundamental questions are of interest. the first is to do with the stability of the synchronization state of the system and the second is its robustness. robustness of the synchronization state is its ability to be insensitive to small perturbations in the system that generates it. the two questions have been done for diffusively coupled systems without a time lag in the coupling. normal hyperbolicity and the generalized lyapunov exponents have been used to establish conditions for the stability and persistence of synchronization manifold for lattice dissipative systems each with a compact global attractor, see for example (chow and liu, 1997; wasike, 2002; wasike, 2003; josica, k, 2000; wasike and rotich, 2007). the subject of stability and persistence of synchronization in a system with a diffusive-time-lag coupling has received less attention. grasman and jansan (1979) have studied synchronization in oscillators coupled in only one variable with a time lag in which phase differences have been used to detect synchrony. numerical 33 adu a.m. wasike results have also been used to determine the lyapunov exponents in order to exhibit stability of the synchronization manifold, see for instance (pyragas, 1998; rossoni, 2005). to the best of my knowledge, no rigorous mathematical results in the framework of robustness of invariant manifolds for delay differential equations have been reported. this is how we approach this problem. we set the problem in the framework of dynamical systems and then consider the two aspects of synchronization based on invariant manifold theory for systems with a time lag. for the theory of invariant manifold for systems with a time lag, see for instance halanay (1967), kurzweil (1967). normal hyperbolicity is exactly the right condition for persistence of invariant manifolds (see bates et. al., 1998). in particular, we shall apply the theory of normally hyperbolic invariant manifolds for semiflows in banach spaces as defined in bates et al., (1998, 1999, 2000). this approach will enable us to compare the rate of growth in the transversal direction to the synchronization manifold and that along the manifold. this is our road map. most of the definitions and terminologies will be given in § 2 while in § 3 we present the main results on the robustness of a synchronization manifold where normal and tangential growth rates are compared. in § 4 we give an example of an all-to-all coupled system. §5 is the conclusion. 2. definitions and terminologies let [ ]( , 0 xn mx c r= − ) be the space of continuous functions from [ ], 0r− to endowed with the usual supremum topology. consider the following system x n m ( ) ( ) ( ) ( ) 1 2 , , , , t t t t x t f x y y t f x y = = (1) where [ ]( ) [ ]( ) ( ) ( ), 0 , , , 0 , , ,n m tx c r y c r x x tθ θ∈ − ∈ − = + ( ) ( ) [ ], , 0ty y t rθ θ θ= + ∈ − , m 1 2: , : nf x f x→ → are continuous functions defined on x to and , respectively. n m let ( ) ( ) ( ) , , , 1 2 .t tt t t t f x y f x y f x y = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ for any ( ),c s ,xϕ ϕ ϕ= ∈ equation (1) has a unique solution ( ) ( )( ), , ,x t y tϕ ϕ which is continuous for and coincides with t r≥ − ϕ on [ ], 0 .r− let ( )( ) ( ) ( )( ) [ ], , , 0tt t x rϕ θ θ ϕ θ= ∈ − and assume all solutions are uniquely defined for , then is a semigroup on 0t ≥ ( )t t 0c .x suppose that the system in equation (1) is dissipative, then there exists a global attractor . a the following definition is motivated by the works of halanay (1967) and also kurzweil (1967). 2.1 definition. system (1) is synchronized for y with respect to x, if there exists a map 1c : ,mh c→ where n is the dimension of x and [ ]( ), 0 , ,mc c r= − with m the dimension of y such that the graph of h denoted graph (h), is invariant and globally attracting. 34 stability and persistence of synchronization in this case, for any ( ),c s xϕ ϕ ϕ= ∈ has ( ) ( )( ) 0t ty h xϕ ϕ− → as ;t → ∞ exponentially. in particular, if ,aϕ ∈ then ( )s chϕ ϕ= and ( ) ( )( )t ty h x ϕϕ = for all and this h is unique (see halanay 1967; p. 209). 0,t ≥ in case, equation (1) is mutually synchronized if h is invertible. m n= for the system with ( ){ }, :d x y x y= = ) invariant, for example, in coupled identical systems or any system symmetric with respect to d, the synchronization occurs for h = i. in this case, the diagonal in x that consists of the set of functions ( ,c sϕ ϕ ϕ= for which c sϕ ϕ= is an invariant set for equation (1). in many applications, we are interested in local synchronization. we are interested in the local attractivity of graph (h); that is, the graph of (h) is exponentially attracting in the neighbourhood of d, ( ) ( )( ) ( ) ,t s ct ty h x ke hαϕ ϕ ϕ ϕ−− ≤ − where ,k α are positive constants. 2.2 definition. suppose equation (1) is locally synchronized with map h. the synchronization is stable if for any 1c 0,∈> there is a 0δ > such that for any 11 2 1 1 , , c f f f f δ− < and 12 2 c f f δ− < , the system ( ) ( ) ( ) ( ) 1 2 , , t t t t x t f x y y t f x y = = , (2) is locally synchronized with map and h 1c h h− <∈ see (bates et .al ;1998 p. 119). 3. main results: robustness of a synchronized manifold let us recall some of the invariant manifold theory for infinite dimensional systems in a banach space. let x represent a banach space with norm ⋅ ⋅ in subspaces the same norm symbol is used. the notation ⋅ ⋅ will be reserved for the linear operator norm l ≡ sup ( ){ }: 1, ,lx x x d l= ∈ ( ) } where means the domain of the operator l. ( )d l( ){min : 1,m l lx x x d l= = ∈ for any ,xϕ ∈ there is a unique solution ( ),z t ϕ to equation (1) that defines a semiflow on x ; that is, 1c ( ),tt z tϕ ϕ= is continuous on [ )0, x∞ × , and for each is and 0, :tt t x x≥ → 1c ( ) (t s t st t t )ϕ ϕ+= for all and , 0t s ≥ , .xϕ ∈ 35 adu a.m. wasike suppose, for system (1), there exists a smooth connected invariant manifold m = graph that is, for each consider the linearization of equation (1) along ( ) ;h x⊂ ( )tt m m⊂ 0.t ≥ m ( ) ( )( ), ,tz t a z t zϕ= (3) where ( ,z t )ϕ is the solution of equation (1) with ( )0,z mϕ ϕ= ∈ and ( )( ),a z t ϕ is jacobian of f at ( ), .z t ϕ let be the linearized semiflow associated with equation (3). ( )tdt m m is said to be normally hyperbolic if the following are satisfied: (h1) the tangent bundle of x restricted to m splits into two continuous subbundles , m c stx x x= ⊕ where cx is the tangent bundle of m and sx is transversal to cx . the superscripts c and s stand for “center”, and “stable”, respectively. (h2) this splitting is invariant under that is, for each ;tdt m m∈ and if , and 0,t ≥ ( )1 tm t m= ( ) ( ) , , t t pp x p c sm dt m dt m = = , then ( ) 1 : p ptp m mdt m x x→ and is an isomorphism from ( )tpdt m p mx onto 1 p mx , where p mx denote the fibers for the vector bundles , ,px p c s= at .m m∈ (h3) there exists and 0 0t ≥ ( )0,1λ ∈ such that for all and 0t t≥ ,m m∈ ( ) ( ){ }{ }min 1,inf : , 1 . t x s m t c c c c m dt m dt m x x x x λ< ∈ = (4) for this definition see bates et al., (1998, 1999). a few remarks on the above definition of normal hyperbolicity are useful. remark. inequality (4) suggests that near contracts in the direction of, tm m t∈ smx , and at a rate greater than that on m. furthermore (4) suggests that for an invariant splitting to persist we need both ( ) 1tsdt m < and ( ) ( ){ }inf : , 1 1,t t c c c csdt m dt m x x x xm< ∈ = < (5) 36 stability and persistence of synchronization to be satisfied, see for instance bates et al. (1998, pages 124 and 11, respectively). 3.1 generalized lyapunov-type numbers for the purpose of calculation it will prove convenient to phrase inequalities (5) and (6) more quantitatively in terms of rates of growth. by the equivalence of norms, ( ){ } ( ), 1inf : .m cxt c c c tcdt m x x x dt m=∈ ≤ (6) thus inequality (6) reduces to ( ) ( ) 1. t s t c dt m dt m < (7) let us now compare the growth bounds of the two semigroup operators. the growth bound of the linear operator is a real number ( )tcdt m 0ω defined by {0 inf 1cmω ω= ∃ ≥ such that ( ) , t t for t (8) c cdt m m e ω≤ }0 .≥ this is the same as ( ) ( )0 0 1 inf ln lim ln ,tct t dt m dt m t ω > → ∞ = = tc (9) see for instance diekmann et al (1995, p. 470). we also know that the ( )tsdt m satisfies ( ) ttsdt m m es α≤ (10) for where and 0,t ≥ 0sm > α are real constants. without loss of generality, we can take cm and sm each equal to 1. this is possible by the use of the next lemma. lemma 3.1 the spaces cmx and , s mx for all can be renormed so that in equations (8) and (10) ,m m∈ cm and sm can be taken to be 1. proof . define a new norm ′⋅ on smx by ( ) 0 sup t ts t x e dt m xα− ≥ ′ = for .smx x∈ clearly, x x ′≤ and by equation (10) ,sx m x′ ≤ so ⋅ and ′⋅ are equivalent norms on smx . let ′⋅ be the operator norm on smx equipped with ′⋅ . then for smx x∈ and 0τ ≥ ( ) ( ) ( ) ( ) ( ) . 0 0 sup sup sup t t t t t t t s s s t tt t s t t tt s t t dt m x e dt m dt m x e dt m x e e dt x e x e α α α α α α + − ≥ − −+ ≥ − ≥ ′ = = ′= ≤ (11) 37 adu a.m. wasike hence, ( ) ttsdt m x e α′ ≤ for 0.τ ≥ the proof for cmx is similar. we now define some generalized lyapunov exponents for semiflows. 3.2 definition. the generalized lyapunov exponents for m m∈ are defined as follows ( ) ( ) 1 lim sup ln ,ts t m dt t α → ∞ = m (12) and ( ) ( ) ( )( ) ln lim sup ln . t s t t c dt m m m dt m β → ∞ = (13) the generalized lyapunov exponents were introduced for the study of normally hyperbolic invariant manifolds in finite dimensional systems, see for instance (chow and liu, 1997; fenichel, 1971; hirsch et al., 1977; wiggins, 1994). no similar results exist for semiflows. the results we have are: theorem 3.3 consider system (1). suppose the graph (h) is invariant. if ( ) 0mα < for graph (h), then graph (h) is attracting, and hence equation (1) is locally synchronized. m ∈ theorem 3.4 suppose that graph (h) is locally synchronized. the synchronization is stable if and for all graph (h). 1c ( ) 0mα < ( ) 1mβ < m∈ proof. the proof makes use of equations (9), (10) and lemma 3.1. we have that ( )mα α= and ( ) 0 .m α β ω = for the stability of the synchronized manifold, we require that inequality (5) be satisfied. this requirement translates to for all ( ) 0mα < .m m∈ for persistence, inequality (7) implies that ( ) 1.mβ < 4. example: synchronization of all-to-all coupled systems in this part, the theorems are applied to the study of synchronization of all-to-all coupled systems. let ( ) ( )( ) ,z t g z t= (14) ,dz ∈ be a dissipative processes and a be the attractor. consider the coupled system ( ) ( ) ( )( ) ( )( ) ( ) ( ) ( )( ) ( )( ) 1 2 1 1 2 1 2 2 , . z t k z t r z t g z t z t k z t r z t g z t = − − + = − − + (15) let [ ]( , 0 , x .d dx c r= − ) equation (15) subject to ( )1 1, xϕ ϕ ϕ= ∈ has a unique solution which coincides with ( ) ( )1 2, , , 0z t z t tϕ ϕ ∀ ≥ , ϕ on [ ], 0 .r− 38 stability and persistence of synchronization equation (15) is synchronized if its solution belongs to a compact inertial manifold ,km m⊂ ( ){ }1 1 1 1, .m xϕ ϕ ϕ ϕ= ∈ = to show synchronization, we show that m is attracting; that is, ( ) ( )1 2, , 0 as t . for this purpose, we need to study the semiflow tangential and transversal to .m we thus make the change of variables z t z tϕ ϕ− → .→ ∞ ( ) ( ) ( ) ( ) ( ) ( )1 2 1 2, 2 2 . z t z t z t z t w t y t − + = = (16) with the transformation (16) in equation (15), we get ( ) ( ) ( )[ ] ( ) ( )) ( ( ) ( )( )[ ] ( ) ( ) ( )[ ] ( ) ( )) ( ( ) ( )( )[ ] 1 , 2 1 . 2 w t k w t r w t g w t y t g y t w t y t k y t r y t g w t y t g y t w t = − − + + + − − = − − + − + + (17) synchronization is equivalent to the fact that ( ){ }, 0w t ϕ = is attracting. by the linearization of equation (15) along ( ){ }, 0w t ϕ = ; that is, along ( )( ), ( ) ,kw t y t m m∈ ⊂ equation (17) becomes ( ) ( ) ( )[ ] ( )( ) ( ) ( ) ( ) ( )[ ] ( )( ) ( ) 0 0 , , z z w t k w t r w t d g y t w t y t k y t r y t d g y t y t = − − + + = − − + (18) where is the jacobian of ( )( 0zd g y t ) ( )( )g z t at ( )( )0y t , the solution is obtained from ( ) ( ) ( )[ ] ( )( ) .y t k y t r y t g y t= − − + notice that there is a continuous invariant splitting ,s cx x⊕ where ( )( ) ( ){ } ( )( ) ( ){ } , , ( , ) | , 0 , , , ( , ) | , 0 . s c x w t y t y t x w t y t w t ϕ ϕ ϕ ϕ ϕ ϕ = = = = let us now look at the attractivity of sx . clearly ( ) ,td s w t i eλ= where sλ satisfies the characteristic equation , is the fundamental matrix solution of the first equation in equation (18); that is, ( ) ( ): 1 rsh k e λλ λ −= + + = 0 ( ) ( ) ( )[ ].w t k w t r w t= − − + by the variation-of-constants formula, the solution ( ,w t )ϕ to the first equation in equation (18) is given by ( ) ( ) ( ) ( ) ( ) ( )( ) ( )1 1 00, 0 0 t zw t w t w w d g y w d .ϕ ϕ τ τ τ − −= + τ⎡ ⎤⎣ ⎦∫ by the gronwall's inequality ( ) ( ) ( )( )( )00 ., 0 z d st d g y i d w t e τ λ τ ϕ ϕ −∫ ≤ 39 adu a.m. wasike let mλ and mλ be the maximum and minimum lyapunov exponents of the trajectory defined by then for as we require ( ) ( )( ) ( )0 .zy t d g y t y t= ( ), 0w t ϕ → ,t → ∞ ( ){ }max 0.sm reλ λ+ < since all roots of for have negative real parts (see for instance bose; 1986), this would mean ( ) 0sh λ = 0k > ( )max , .sm mre k kλ λ λ< = > indeed ( )2 2 , 2 2 , 0, 1, 2, .......s krk i r m kre m mλ π π π π= − + + = + = by theorem 3.2 ( ){ },w t ϕ 0= is attracting and the coupled system is locally synchronized. the solution ( ,y t )ϕ of the second equation in equation (18) is given by ( ) ( ) ( ) ( ) ( ) ( )( ) ( )1 1 00, 0 0 t zy t y t y y d g y y dϕ ϕ τ τ τ − −= + τ for ⎡ ⎤⎣ ⎦∫ 0,t ≥ where ( ) , ct c dy t i e λ λ= satisfies the characteristic equation ( ) ( ): 1c rh k e 0λλ λ −= + − = , is the fundamental matrix solution of the second equation in (18) that is, ( ) ( ) ( )[ ].y t k y t r y t= − − indeed ( )( ) ( )2 2 1 , 2 2 1 , 0,1, 2, .....krc i r m kre m mk π π π πλ + + + = + + == − for persistence we have ( ){ } ( ){ }max re min re ,s mmλ λ λ λ− ≤ − c (19) where cλ satisfies the characteristic equation whose roots except ( ) 0ch λ = 0λ = lie to the left of the complex plane(see for instance bose, 1986). equation (19) gives .mmk λ λ> − by theorem 3.3, the synchronization manifold is robust. 5. conclusion time delay in the coupling does not always destabilize synchronization states of similar systems with delay 0.r = 6. references afraimovich, v.s, verchev, n.n. and riabonvich, m.i. 1986. stochastic synchronization of oscillations in dissipative systems. radio phy. quantum electron. 29: 31-45. bates, p.w., lu, k., zeng, c. 1998. existence and persistence of invariant manifold for semiflows in banach spaces, mem. amer. math. soc. 135(645): 305-317. 40 stability and persistence of synchronization bates, p.w., lu, k., zeng, c. 1999. persistence of overflowing manifolds for semiflows, comm. pure appl. math. lii: 983-1046. bates, p.w., lu, k., zeng, c. 2000. invariant foliations near normally hyperbolic invariant manifolds for semiflows, trans. amer. math. soc. 352(10): 4641-4676. bose, f.g. 1986. stability conditions for the general linear difference-differential equation with constant coefficients and one constant delay. j. math. anal. appl. 140:136-176. chow, s.n. and liu, w. 1997. synchronization, stability and normal hyperbolicity. resenhas ime-usp}. 3: 139-158. chow, s.n. 2000. lattice dynamical systems, dynamical systems springer. 1822: 1-99. diekmann, o., van gils, s. a.,verduyn lunel, s.m. and walther, h.-o. 1995. delay equations. springer-verlag, berlin, heidelberg, new york. fenichel, n. 1971. persistence and smoothness of invariant manifolds for flows. ind, univ. math. j., 21(3): 193-225. fujisaka, h. and yamada, t. 1983. stability theory of synchronized motion in coupled-oscillator system. prog. theor. phys. 69: 32-47. grasman, j., and jansan, m.j.w. 1979. mutually synchronized relaxation oscillators as prototypes of oscillating systems in biology. j. math. biology 7: 171-197. halanay, a. 1967. invariant manifolds for systems with time lag, differential equations and dynamical systems. academic press. 199-213. hale, j. 1997. diffusive coupling, dissipation and synchronization j. dyn. differ. equ. 9:1-52. hale, j.k, and verduyn lunel. 1993. introduction to functional differential equation; springer-verlag: new york. henry, d. 1983. geometric theory of semilinear parabolic equations, lecture notes in mathematics. no. 840, springer-verlag: berlin. hirsch, m.w., pugh, c.c., shub, m., invariant manifolds. lecture notes in mathematics vol 583. springer-verlag: berlin, heidelberg, new york, 1977. josica, k. 2000. synchronization of chaotic systems and invariant manifolds, nonlinearity 13: 1321-1336. kurzweil, j. 1967. invariant manifolds for flows, differential equations and dynamical systems. academic press. 431-468. pyragas, k. 1998. synchronization of coupled time-delay systems: analytical estimations physical review e. 53(3): 3067-3071. rossoni, e., chen, y., ding, m., feng, j. 2005. stability of synchronous oscillations in systems of hh neurons with delayed diffusive and pulsed coupling. phys. review e. 71: 819-823. wasike, a.a.m. 2002. periodic solutions of systems of delay differential equations indian journal of mathematics, 44(1): 95-117. wasike, a.a.m. 2003. synchronization and oscillator death in diffusively coupled lattice oscillators international journal of mathematical science, 2(1): 67-82. wasike, a.a.m., rotich, k.t. 2007. synchronization, persistence in diffusively coupled lattice oscillators sultan qaboos university journal of science, 12(1): 41-52 . wiggins, s. 1994. normally hyperbolic invariant manifolds in dynamical systems. springer-verlag: berlin, heidelberg, new york. received 12 september 2007 accepted 31 may 2008 41 microsoft word math080902-f edited_checked-f3.doc 61-69 squ journal for science, 14 (2009) © 2009 sultan qaboos university 61 incidence matrices of x-labeled graphs and an application w.s. jassim department of mathematics, college of education saadah, saadah – yemen, email: email: wadhahjassim@yahoo.co.uk. مع تطبيق x-المحمولة بعناصر المجموعة الوقوع للبيانات مصفوفات جاسم . وضاح س بعض التحسينات على تعريف مصفوفات الوقوع للبيانات الموجهة من أجل أن تكون أكثر ب قمنافي بحثنا هذا :خالصة . نكولص–ه التحسينات استطعنا وصف برنامج لخوارزمية بهذ . x –مة للبيانات المحمولة بعناصر المجموعة ءمال abstract: in this work, we have made some modifications to the definition of the incidence matrices of a directed graph, to make the incidence matrices more suitable for x – labeled graphs. the new incidence matrices are called the incidence matrices of x – labeled graphs, and we have used the new definition to give a computer program for nickolas` algorithm . keywords: incidence matrix, directed graph, x -labeled graph, spanning tree, cyclomatic number. 1. introduction n abdu (1999), nickolas described an algorithm to change two core graphs of one type of branch points to core graphs with two or more types of branch points. since incidence matrices of directed graphs do not deal with labeled graphs, from this point we worked to make the incidence matrices to be more suitable for x – labeled graphs. this work is divided into three sections. in section 1, we give basic concepts about free groups and graphs. in section 2, we give the definition of the incidence matrices of x – labeled graphs, and some definitions and results on incidence matrices of x – labeled graphs. in section 3, we apply the concept of incidence matrices of x – labeled graphs to give a computer program for nickolas` algorithm. 1.1 basic concepts: let f be a group and x be a subset of f . then we say that f is a free group on x , if for any group g and any mapping : ,f x g→ there is a unique homomorphism : f gψ → , such that )()( xfx =ψ for all x x∈ . two free groups f and k are called isomorphic if and only if f and k have the same rank. i w.s. jassim 62 if a graph γ is a collection of two sets, ( ) ( )( )is not empty setv vγ γ and ( )e γ , called the set of vertices and edges respectively of the graph γ ,together with two functions : ( ) ( ), : ( ) ( )i e v t e vγ → γ γ → γ , we say that the edge e joins the vertex ( )i e to the vertex ( )t e . the vertex ( )i e is called the initial vertex of e and ( )t e is called the terminal vertex of e . moreover for each e in ( )e γ there is an element ee ≠ in ( )e γ , which is called the inverse of e , such that )()(),()( eietetei == and ee = . a subgraph ω of a graph γ is a graph with ( ) ( )v vω ⊆ γ and ( ) ( )e eω ⊆ γ such that, if )(ω∈ ee , then )(eiω , )(etω and e have the same meaning in γ as they do in ω . if ω ≠ γ , then we call ω a proper subgraph. a component of a connected graph γ is a maximal connected subgraph of γ . the number of edges incident with the vertex v is called the degree of the vertex v and denoted by ( )d v . the vertex v is called a branch point if 3)( ≥vd . now let f be a group and x be a subset of f . then the graph ( , )f xγ is called the cayley graph of the group f with respect to x , if ( , )f xγ has vertex set f and set of edges ( ){ }, : , ,f x w x w f x x× = ∈ ∈ such that the initial vertex of the edge ( ),w x is ( ), ,i w x w= the terminal vertex of the edge ( ),w x is ( ),t w x wx= and x is the labeled of the edge ( ),w x . the inverse edge of ( ),w x is ),( 1−xwx . the quotient graph or cayley coset graph ( , ) /f x hγ for a subgroup h of f has set of vertices { : , }hw w f h f∈ ≤ and set of edges {( , ) : , }hw x w f x x∈ ∈ such that an edge ( , ) ( , ) /hw x f x h∈γ takes the vertex hw to hwx . it is also denoted by ( )hγ . the core of a coset graph )(hγ is the smallest subgraph containing all cycles. it is denoted by ( )h∗γ . for example, if f is a free group on generators a and b , then ( )f∗γ : a b the number of cycles in ∗γ ( )h is called the cyclomatic number and the cyclomatic number of ∗γ ( )h is the minimal number of edges that we can delete to make a tree. the rank of the finitely generated subgroup h of a free group on x is the cyclomatic number of ∗γ ( )h and denoted by ( )r h . definition 1.1 a consistent graph is a directed x – labeled graph γ on { , }x a b= , such that no reduced path in γ with labeled 1−aa , aa 1− , 1−bb or bb 1− ever occurs in consistent graphs. therefore ( , )f xγ , ( )hγ and ( )h∗γ are consistent graphs. now if ( )h∗γ has vertices of degree 2, 3, 4, then as in [5] we can reduce the degree of the vertices into vertices of degree 2 and 3 only, by isomorphic embedding of f into a free group k on { },u v , via the map : f kθ → with 21 )(,)( vbuva == − θθ and taking the graph into a new set of labels },{ vu . incidence matrices of x-labeled graphs 63 proposition 1.2: if ( )h∗γ has vertices of degree 2, 3 only, then # ( ( )) ( ) 1 2 br h r h ∗γ = + , where # ( ( ))br h∗γ is the number of branch points in ( )h∗γ . proof: ( ) 2 # ( ( ))d v e h∗= γ∑ . ( ( ) 2) 2(# ( ( )) # ( ( )))d v e h v h∗ ∗− = γ − γ∑ , and the number of edges in the spanning tree of ( )h∗γ = # ( ( )) 1v h∗γ − . therefore we have the following : ( ( ) 2)d v −∑ = (the number of edges in )(h∗γ the number of edges in the spanning tree of ( )h∗γ 1). since ( )r h = the number of edges in )(h∗γ the number of edges in the spanning tree of ( )h∗γ , so ∑ − )2)(( vd = )1)((2 −hr )1( , and also 2)( −vd ) = int 0 1 pobranchaisv otherwise if ⎩ ⎨ ⎧ . thus ∑ =− )2)(( vd ))((# hbr ∗γ . therefore 12 ))((# )( + γ = ∗ hbr hr . definition 1.3: for any two branch points u and v in )(h∗γ , we say that u and v are neighboring branch points if they are connected by a (reduced) path which does not contain any branch point. definition 1.4: the product of core graphs )(* hγ and )(* kγ is the graph )(~)( ** kh γ×γ with set of vertices ))}(()),((:),{())(())(( **** kvvhvuvukvhv γ∈γ∈=γ×γ and edges })),((),()),((),(:)),,{(( ** xykeyvheyuyvu ∈γ∈γ∈ . if ∗γ (h), )(k∗γ and )(* kh ∩γ are the core graphs of the finitely generated subgroups ,h k and kh ∩ respectively of a free group f on },{ bax = and )(~)( ** kh γ×γ is the product of core graphs )(* hγ and )(* kγ defined above, then )(* kh ∩γ may identified with a core of a connected component of )(~)( ** kh γ×γ and )(* hγ has only four types of branch points as follows: b – sources b – sinks a – sources a sinks 2. incidence matrices of x –labeled graphs in this section we will give the definition of incidence matrices of x – labeled graphs and some definitions and results related to it. as we know there are two types of matrices to describe graphs, which are called adjacency (or vertex incidence) matrices and incidence matrices. recall that the incidence matrices of w.s. jassim 64 directed graphs γ are without loops and with n vertices and m edges ( i.e. it is mn × matrices ][ ijx , where mjni ≤≤≤≤ 1,1 ) such that : ⎪ ⎩ ⎪ ⎨ ⎧ =− = = )(1 0 )(1 ji ji ji ij evif ewithincedencenotisvif eivif x τ all edges e in x – labeled graphs ( )),(~)(),,(),(),( …khxfhh ∗∗∗ γ×γγγγ are labeled 1−∪∈ xxx and the incidence matrices of directed graphs do not deal with the labels of edges, so we will put more conditions on the incidence matrices of directed graphs as below. definition 2.1: let γ be any x – labeled graph without loops ( where },{ bax = ) , then the incidence matrix of the x – labeled graph γ is an mn × incidence matrix ][ ijx , where mjni ≤≤≤≤ 1,1 ) with ijx entries such that xxlabelese ewithincident xxlablese ande notisv andei v if v if if x x x j j j j i j i i ij ∈ ∈ = = ⎪ ⎩ ⎪ ⎨ ⎧ = − )( )( 0 1 τ n.b. incidence matrices of x – labeled graphs γ will be denoted by )(γxm . now if },{ bax = and the x –labeled graph γ has loops with labeling a or b , then choose a mid point on all edges labeled a or b to make all of them two edges labeled aa or bb respectively. therefore in the rest of this work we will assume that all x – labeled graphs γ are without loops. definition 2.2: let )(γxm be an incidence matrices of x – labeled graphs γ . if )(γxm does not contain any row ir with non zero entries ijx and ikx in 1−∪ xx such that ikij xx = , then )(γxm is called a consistent incidence matrix of x – labeled graphs γ . now let )(γxm be an mn × incidence matrix ][ ijx of x – labeled graphs γ and let ir and jc be a row and a column in )(γxm respectively. if ijx is a non – zero entry in the row ir , then ir is called an incidence row with the column jc at the non – zero entry ijx 1−∪∈ xx and if xxij ∈ , then the row ir is called the starting row ( denoted by ))( jcs of the column jc and the row ir is called the ending row ( denoted by )( jce ) of the column jc if 1−∈ xxij . if the rows ir and kr are incident with column jc at the non – zero entries ijx and kjx respectively, then we say that the rows ir and kr are adjacent. if jc and hc are two distinct columns in )(γxm such that the row ir is incident with the columns jc and hc at the non – zero entries ijx and ihx respectively (where 1, −∪∈ xxxx hij ), then we say that jc and hc are adjacent columns. for each column c there is an inverse column denoted by c such that )()(),()( cscececs == and cc = . the degree of a row ir of )(γxm is the number of the columns incident on ir and is denoted by )deg( ir . if incidence matrices of x-labeled graphs 65 the row ir is incident with at least three distinct columns jc , hc and kc at the non – zero entries, then the row ir is called a branch row. if the row ir is incident with only one column jc at the non zero entry ijx 1−∪∈ xx and all other entries of ir are zero, then the row ir is called isolated row. a scale in )(γxm is a finite sequence of form kkk rcrcrcrs k ,,,,,,, 121 112211 − ∈ −− ∈∈= … , where ,1≥k ,∓∈= jj rcs j =∈ )( and kjcsrce jjj j ≤≤== ++ ∈ 1),()( 11 . the starting row of a scale kkk rcrcrcrs k ,,,,,,, 121 112211 − ∈ −− ∈∈= … is the starting row 1r of the column 1c and the ending row of the scale s is the ending row kr of the column 1−kc and we say that s is a scale from 1r to kr and s is a scale of length k for 21 −≤≤ kj . if )()( sess = , then the scale is called closed scale. if the scale s is reduced and closed, then s is called a circuit or a cycle. if )(γxm has no cycle, then )(γxm is called a forest incidence matrix of x – labeled graph γ . two rows ir and kr in )(γxm are called connected if there is a scale s in )(γxm containing ir and kr . moreover, )(γxm is called connected if any two rows ir and kr in )(γxm are connected by a scale s . if )(γxm is connected and forest, then )(γxm is called a tree incidence matrix of x – labeled graph γ . let ω be a subgraph of γ , then )(ωxm is called a subincidence matrix of )(γxm , if the set of rows and columns of )(ωxm are subsets of )(γxm and if c is a column in )(∆xm . then )(),( cecs and c have the same meaning in )(γxm as they do in )(ωxm . if )()( γ≠ω xx mm , then )(ωxm is called a proper subincidence matrix of )(γxm . a component of )(γxm is a maximal connected subincidence matrix of )(γxm . if )(ωxm is a subincidence matrix of )(γxm , and every two rows ir and kr in )(γxm are joined by at least one scale s in )(ωxm , then )(ωxm is called a spanning incidence matrix of )(γxm , and )(ωxm is called a spanning tree of )(γxm if )(ωxm is a spanning and tree incidence matrix. the inverse of )(γxm is an incidence matrix of 1−x labeled graph γ . now by direct calculations and the definition above, we can prove the following results. lemma 2.3: if )(γxm is a tree incidence matrix of x – labeled graph γ with n rows, then )(γxm has n – 1 columns. lemma 2.4: if )(γxm is an incidence matrix of x – labeled graph γ with n rows and m columns, then mr n i i 2)deg( 1 =∑ = , where ni ≤≤1 . corollary 2.5: if )(γxm is a finite incidence matrix of x – labeled graph γ , then )(γxm has even number of rows of odd degree. lemma 2.6: the cyclomatic number ))(( γxmc of a finite incidence matrix of x – labeled graph γ is equal to r k+#c-# , where c# , r# and k are the number of columns, the number of rows and the number of components of )(γxm respectively. corollary 2.7: if )(γxm is a connected incidence matrix of x – labeled graph γ with r rows and c columns, then 1##))(( +−=γ rcmc x . w.s. jassim 66 3. an application of incidence matrices of x – labeled graphs in this section we will represent the core graphs )(h∗γ of finitely generated subgroups h of a free group f generated by },{ bax = in the form of incidence matrices of core graphs ))(( hm x ∗γ and then we will describe nickolas` algorithm (nickolas, 1985) in the form of incidence matrices of x – labeled graphs, but before that we give some results and definitions that will be used in the rest of the paper. since the core graphs )(h∗γ of finitely generated subgroups h of a free group f generated by },{ bax = are x – labeled graphs, they may be represented by incidence matrices of x – labeled graphs γ which are denoted by ))(( hm x ∗γ . lemma 3.1: let ))(( hm x ∗γ be an incidence matrix of a core graph )(h∗γ of a finitely generated subgroup h of a free group f generated by },{ bax = with n rows of degree two and three only and m columns , then 1 2 )))(((# )))((( + γ =γ ∗ ∗ hmbrhmc xx , where )))(((# hmbr x ∗γ is the number of branch rows of ))(( hm x ∗γ . proof: since ∑ = = n i i mr 1 2)deg( , so ∑ −=− )(2)2)(deg( nmri . but ∑ ∗γ=− )))(((#)2)(deg( hmbrr xi and nmhmc x −=−γ∗ 1)))((( . therefore 1 2 )))(((# )))((( + γ =γ ∗ ∗ hmbrhmc xx . corollary 3.2: let ))(( hm x ∗γ be an incidence matrix of a core graph )(h∗γ of a finitely generated subgroup h of a free group f generated by },{ bax = with n rows of degree two and three only, then ( )r h = 1 2 )))(((# + γ∗ hmbr x . definition 3.3: let ))(( hm x ∗γ and ))(( km x ∗γ be the incidence matrices of core graphs )(h∗γ and )(k∗γ respectively, of a finitely generated subgroup h of a free group f generated by },{ bax = . the product of ))(( hm x ∗γ and ))(( km x ∗γ is the incidence matrix ))((~))(( kmhm xx ∗∗ γ×γ of x – labeled graph of the product of )(h∗γ and )(k∗γ with set of rows vuv :),{( and u are rows in ))(( hm x ∗γ and ))(( km x ∗γ respectively } and set of columns :),{( ji cc ic and jc are columns in ))(( hm x ∗γ and ))(( km x ∗γ ,respectively} , and they have the same non – zero entries 1−∪∈ xxx . lemma 3.4: let ))(( hm x ∗γ and ))(( km x ∗γ be the incidence matrices of core graphs )(h∗γ and )(k∗γ respectively, of a finitely generated subgroup h of a free group f generated by },{ bax = . then incidence matrices of x-labeled graphs 67 the incidence matrices of the product )(~)( kh ∗∗ γ×γ (denoted by ))(~)(( khm x ∗∗ γ×γ ) is the same as the product ))((~))(( kmhm xx ∗∗ γ×γ . proof: by the definition of the product of core graphs and definition 3.3 the result follows. lemma 3.5: let ))(( hm x ∗γ be defined as above and have 2n branch rows. if all branch rows of ))(( hm x ∗γ are of one type b – sources, say , then there are at least n rows with only two non – zero entries axbx ikij == − ,1 and all other entries are zero. proof: since all possibilities of scales joining two neighboring branch rows are 654321 ,,,,, ssssss such that 122111 + = kkk ijijiji rcrcrcrs ; where 1i r is the starting row of the column 1j c at the non – zero entry bx ji =11 and 1+kir is the ending row of the columns kjc at the non – zero entry 1 11 −= ++ ax kk ji , 122112 + = mmm ijijiji rcrcrcrs ; where 1i r is the starting row of the column 1j c at the non – zero entry bx ji =11 and 1+mir is the ending row of the column mjc at the non–zero entry ax mm ji =+1 , 122113 + = ttt ijijiji rcrcrcrs ; where 1i r is the starting row of the column 1j c at the non – zero entry bx ji =11 and 1+ti r is the ending row of the columns kj c at the non–zero entry bx tt ji = +1 ; 12114 + = ggg ijiiji rcrrcrs ; where 1i r is the starting row of the column 1j c at the non – zero entry ax ji =11 and 1+gir is the ending row of the columns gj c at the non–zero entry 1 1 −= + ax gg ji , 12115 + = hhh ijiiji rcrrcrs ; where 1i r is the starting row of the column 1j c at the non–zero entry ax ji =11 and 1+tir is the ending row of the columns kjc at the non zero entry ax tt ji = +1 , and 12116 + = ddd ijiiji rcrrcrs ; where 1i r is the starting row of the column 1j c at the non – zero entry 1 11 −= ax ji and 1+tir is the ending row of the columns kjc at the non–zero entry 1 1 −= + ax tt ji . since ))(( hm x ∗γ is a consistent incidence matrix of x – labeled graph γ , so the scales 54321 ,,,, sssss and 6s must contain rows fir with a non – zero entries 1−= bx vf ji , and ax uf ji = or 1−= ax uf ji only and all other entries are zero. also ))(( hm x ∗γ has 2n branch rows and all of them are of one type b – source row, so suppose that ))(( hm x ∗γ has 1s scales of type 1s , 2s scales of type 2s , 3s scales of type 3s , 4s scales of type 4s , 5s scales of type 5s and 6s scales of type 6s . therefore we have nssssss 3654321 =+++++ )1( . since each branch row ir of ))(( hm x ∗γ has exactly one non – zero entry axij = , and the scale of type 2s ending with the row mir at the non zero entries ax mm ji = , scales of types 4s starting with the row 1ir at the non – zero entry ax ji =11 and scales of types 5s starting and ending with the rows 1i r and hi r at the non – zero entries ax ji =11 and ax hji =1 respectively. therefore ))(( hm x ∗γ has 2 4 5 2 2)2 (s s s n+ + = . hence from (2) we have 2 4 5 32 ( )s s s n+ + < . from (3) and (1) we have nsss >++ 631 , since each of the scales 31 , ss and 6s has at least one row with non – zero entries 1−= bxij and axiz = , and all other entries are zero. w.s. jassim 68 nickolas [5] gave an algorithm to change core graphs )(h∗γ and )(k∗γ of two finitely generated subgroups h and k of a free group f generated by },{ bax = , which have only one type of branch points , b – sources,say, into new core graphs with two or more types of branch points. therefore we will represent nickolas` algorithm in the form of incidence matrices of x –labeled graphs in order to give a computer program to change the type of branch points of core graphs with only one type of branch points into two or more types of branch points. now let ))(( hm x ∗γ and ))(( km x ∗γ be incidence matrices of x –labeled core graphs )(h∗γ and )(k∗γ respectively, such that ))(( hm x ∗γ and ))(( km x ∗γ have branch rows of one type, b – sources, say, then we will use the representation of nickolas` algorithm to change ))(( hm x ∗γ and ))(( km x ∗γ into two incidence matrices of x –labeled core graphs ))(( hm kx ∗γ and ))(( km kx ∗γ with two types or more of branch rows, after k – times . the steps are given below: 0) delete all zero columns and zero rows if they appear; )0∗ if the branch rows are not of one type, then stop. otherwise, change the non – zero entries to make all branch rows of type b – sources by reversing the labeling of the columns and then proceed to step 1; 1 ) if ir is the ending and the starting row of the columns jc and kc at 1−= bxij and bxik = respectively and all other entries of ir are zero, and tr is the ending row of the column kc , then add tr and ir to a new row tr ′ , and if there is no such a row ir , then proceed to step ii; ii ) if gi rr , and tr are rows such that ir is the ending and the starting row of the columns jc and kc at 1−= bxij and axik = respectively, and gr is the ending row of the columns kc and hc at 1−= ax gk and 1−= bx gh respectively and all other entries of ir and gr are zero, and also tr is the starting row of the column hc at bxth = , then add it rr , and gr to have a new row tr ′ , and if there is no such rows, then proceed to step iii; iii ) if ir is the ending and the starting row of the columns jc and kc at 1−= bxij and axik = respectively and all other entries of ir are zero, and tr is the ending row of the column kc at 1−= axtk , then add tr and ir to have a new row tr ′ , and if there is no such a row then return to step 0 above. note: in the program of the above algorithm we will consider 1−a and 1−b as a− and b− respectively and then will represent a and b by 1 and 2 respectively. the representation of nickolas` algorithm in the form of incidence matrices of x –labeled graphs is well defined, which means the representation of nickolas` algorithm satisfying the following conditions: 1) at each step of the representation of nickolas` algorithm, we get consistent incidence matrices of x – labeled graphs because step i is applied to non – branch rows ir and tr to give a non – branch row tr ′ with non – zero entries 1−′ = bx jt and ax ht =′ or 1− ′ = ax ht , so step i always gives consistent incidence matrices of x –labeled graphs . also step ii is applied on non – branch rows of ))(( hm x ∗γ which do not contain non – branch rows ir with non – zero entries 1−= bxij and bxih = so step ii always gives, either non – branch incidence matrices of x-labeled graphs 69 rows tr ′ with non – zero entries 1− ′ = ax jt and 1− ′ = bx ht or a branch row with non – zero entries 1− ′ = bx ht , ax jt =′ and 1− ′ = ax lt . while step iii is applied on non – branch row ir with non – zero entries 1−= bxij and axik = , and the row tr which is either a non – branch row with non – zero entries 1−= axtk and bxth = or axth = , or tr is a branch row of type b – sources , so when we apply step iii either we have a non branch row tr ′ with non zero entries 1− ′ = bx jt and bx ht =′ or 1− ′ = bx jt and ax ht =′ , or tr ′ is a branch row with non – zero entries 1−′ = bx jt , bx ht =′ and ax lt =′ . therefore step iii always gives consistent incidence matrices of x –labeled graphs. 2) the representation of nickolas` algorithm preserves the number of branch rows in ))(( hm x ∗γ , because it is applied on non – branch rows, so apply steps i, ii and iii reduce the non – branch rows only and then the number of branch rows in ))(( hm x ∗γ will be still the same as before and the type of branch rows may change only. 3)the representation of nickolas` algorithm preserves the number of branch rows in ))((~))(( kmhm xx ∗∗ γ×γ , because each row in ))((~))(( kmhm xx ∗∗ γ×γ comes from the product of two rows ir and tr in ))(( hm x ∗γ and ))(( km x ∗γ respectively and the removed rows are non – branch rows which contain a non zero entries 1−= bxij , and ))(( hm x ∗γ and ))(( km x ∗γ have no branch row with non –zero entry 1−= bxij . therefore whatever happens to ))(( hm x ∗γ and ))(( km x ∗γ , then will happen to the maximum connected submatrix of ))((~))(( kmhm xx ∗∗ γ×γ . 4) each time we return to step ∗0 of the representation of nickolas` algorithm, we must apply one of the steps 1, 2 or 3 , because if step 1 and 2 do not apply , the step 3 must apply by lemma 3.5. 5) in each time we return to step ∗0 we have fewer rows ; this comes from reducing at least two rows to a single row. 6) the algorithm must stop after a finite time, because each time we reduce the total number of rows by at least one row, and then we have at least two different types of branch rows of ))(( hm x ∗γ and ))(( km x ∗γ . 4. references abdu, k.a. 1999. representing core graphs and nickolas`s algorithm. m.sc .thesis, baghdad university. lyndon, r.c. and schupp, p.e. 1977. combinatorial group theory. ergebniss vol. 89, berlin – heidelberg – new york, springer. magnuss, w., karrass, a. and soliter, d. combinatorial group theory. new york. john wiley and sons inc 1966. nickolas, p. 1985. intersecton of finitely generated free groups. bull. austral. math. soc. 31: 339 – 349. sarvatius, b. 1983. a short proof of a theorem of burns. math. 71: 551 – 565. received 2 september 2008 accepted 29 april 2009 microsoft word phys041017_corrected.doc squ journal for science, 11 (2006) 95-101 © 2006 sultan qaboos university 95 specific heat of dy.40 cu.37 y.23 amorphous alloy at low temperatures k.a. mohammed department of physics, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, email: kadhimm@squ.edu.om. في درجات الحرارة الواطئة dy.40 cu.37 y.23يكة الحرارة النوعية للسب كاظم احمد محمد تم في هذا البحث دراسة الحرارة النوعية في درجات الحرارة الواطئة للسبيكة العشوائية المغناطيسية :خالصة dy0.40cu0.37y0.23 2 في مدى درجات الحرارة k 50 إلى k .ة في الحرارة إذ تم حساب المساهمة المغناطيسي النوعية وتغيرات االنتروبي المغناطيسي ودرجة حرارة التحول في الطور المغناطيسي والعزم المغناطيسي k 28 مساوية تقريبا إلى tmأظهرت الحرارة النوعية المغناطيسية قمة عريضة مرتكزة عند درجة حرارة، .المؤثر كانت . والمقاسة من التأثرية المغناطيسيةk 23.5المساوية إلى وtf أعلى من قيمة tmإن قيمة . متبوعة بتأثير شوتكي من قيمة االنتروبي المغناطيسي 84 % مساوية تقريبا إلى tm إلى k 0قيم االنتروبي المغناطيسي المحسوبة بين عناصر تتفق تصرفات هذه السبيكة العشوائية مع تصرفات السبائك العشوائية المكثفة لل. العظمى المحسوبة نظريا .األرضية النادرة abstract: the low temperature specific heat of the magnetic dy0.40cu0.37y0.23 amorphous alloy have been investigated in the temperature range 2 to 50 k. the magnetic contributions to the specific heat, magnetic entropy changes, ordering temperatures and the effective magnetic spin have been estimated for this magnetic amorphous alloy. the magnetic specific heat show broad anomaly at a certain temperature, tm of about 28 k. the value of tm is higher than tf (=23.5 k) determined from low field ac susceptibility measurements. the magnetic entropy changes between 0 k and tm are estimated to be 84 % of the maximum theoretical value. the behaviors of this amorphous alloy agree quit well with those of condensed rare earth amorphous systems. keywords: specific heat, amorphous alloys, dysprosium amorphous alloys. 1. introduction rystal field effects are likely to be well-defined in amorphous rare earth (re) alloys. the topological disorder in this amorphous alloy results in a competition in sign exchange interactions together with random uniaxial crystal fields with the local easy axis of magnetic anisotropy varying from site to site (coey, 1978; harris et al., 1979). the low temperature specific heat of rare earth magnetic amorphous alloys appears to posses intrinsic features such as the well defined sharp anomaly in the low field ac susceptibility at a certain c k.a. mohammed 96 temperature, tf, which is a function of the magnetic element, a broad maximum in the specific heat at a temperature, tm, and specific heat linear term in t at low temperatures. moreover, characteristics contributions to the specific heat are expected in the paramagnetic phase resulting from the crystal field excitations. the low temperature specific heat results of some rare earth metals and alloys show another contribution to the specific heat arising from the hyperfine nuclear magnetic effects (garoche et al., 1980). measurements of the specific heat of pr21ag79, sm21ag79 and lu21ag79 amorphous alloys reported by (garoche et al., 1980) are characterized by a large and nearly temperature independent term down to very low temperatures. these behaviors have been attributed to the low energy crystal field excitations associated with the distribution of the asymmetry parameter of the crystalline electric field effects. values of the magnetic entropy changes, which have been usually estimated between 0 k and tf and tm are usually less than the maximum magnetic entropy expected theoretically. this means that effective spin value is less than the maximum value expected for pure metals and there is still considerable amount of magnetic order even at temperatures higher than tf and tm. the specific heat and ac susceptibility of the amorphous gdxcu0.37y0.63-x (0<x<0.63) have been studied at low temperature (mohammed et al., 1986). this investigation showed the spin glass nature for x<0.35 for gd. the magnetic amorphous dy0.40cu0.37y0.23 alloy exhibits low cusp in its low field ac susceptibility as shown in figure 1, indicating spin glass phase transition to the paramagnetic phase (del moral et al.,1986). theoretical calculations of debye temperature, lattice specific heat and the spin glass ordering temperatures in the magnetic re0.33cu0.67, re0.33al0.67 and re0.33ag0.67 amorphous alloys have been reported (mohammed et al., 1994). spin glass like behavior and low temperature specific heat have been investigated for bulk amorphous erxni1-x (x=0.33, 0.50 and 0.80) alloys prepared by high rate direct current sputtering (hattori et al., 1995). the specific heat parameters of the magnetic er-cu-y and ho-cu-y amorphous alloys had been investigated in the temperature range 0 k to 50 k (mohammed k. a. to be published). 2. experimental procedure the phase diagram of the crystalline binary cu-y alloys shows that the deepest eutectic point occurs at about 33 at % cu. it has been reported (rainford et al., 1982). that a 37 at % cu is marginally better for glass formation than 33 at % cu. accordingly, copper proportion was fixed at 37 at % in this sample. prior to preparing ribbons in the amorphous state polycrystalline alloys were prepared by melting together appropriate quantities of dy, cu and y of 99.99% nominal purity, which were supplied by rare earth products ltd. the alloys were prepared in an arc furnace in a high purity (99.999%) reduced argon atmosphere. the alloy was turned and remelted many times to promote homogeneity. the loss in the total mass after alloying was less than 0.1 %. the production of the amorphous ribbons method was the well tried melt spinning technique, which is quite similar to that described by liebermann et al. (1976). in this method typically about half a gram of an alloy is melted by rf induction in a quartz crucible and immediately expelled under pressure onto a rapidly rotating massive copper wheel, which cools the melt sufficiently rapidly for amorphous samples to be produced. the crucible was about 5 to 10 cm long and 9 to 10 mm in diameter with an orifice of about 1mm diameter at its bottom end. high purity (5n) argon gas at pressure of 5 to 10 psi was used to force the molten stream through the hole in the bottom of the tube. specific heat of dy.40 cu.37 y.23 amorphous alloy 97 figure 1. the ac susceptibility, χ versus temperature, t [reference 5]. the space between the orifice and the surface of the copper wheel was between 1 and 3mm. the diameter of the copper wheel was 15 cm and the optimum speed of rotation was found to be approximately 4000 to 6000 rpm. the amorphous nature of the ribbons was checked by studying the x-ray diffraction using cukα radiation. normally no evidence of crystallite was observed. on the matter of testing samples for amorphicity, it is perhaps of interest to point out that we have found that in nearly every case an amorphous ribbon can sustain a sharp 180o bend without fracture whereas the same operation will break ribbons with any trace of crystalline. this has been used to test the amorphicity of the very long length of ribbon required to form a satisfactory sample for heat capacity measurement. the heat capacity was measured using a modified adiabatic continues heating technique from 4.2 k to 50 k while the heat pulse technique has been used in the temperature range 1.5 k to 7 k. the accuracy of the measured temperature and the heat capacity were better than ± 3 mk and 1 % respectively (lanchester et al.,1987). 3. results and discussion the total specific heat results, cp, of the magnetic dy0.40cu0.37y0.23 amorphous alloy are shown in figure 2 as cp versus temperature, t. figure 2 also includes specific heat results of the non-magnetic lu0.40cu0.37y0.23 amorphous alloy for comparison (mohammed et al., 1987). it is clear that there is no sharp transition in cp at the ordering temperature, as observed in crystalline dy metal and alloys (lounassma et al.,1966). k.a. mohammed 98 figure 2. the specific heat cp versus temperature, t. the total specific heat cp of the amorphous magnetic alloys can be written as ; p e l mc = c +c +c (1) where ce, cl and cm represent the electronic, lattice and magnetic terms respectively. cm forms the major part of cp for magnetic materials below their critical temperatures. an acceptable method to estimate values of the nonmagnetic terms ce and cl is to use experimentally measured specific heat results of a similar but non-magnetic material (lounassma et al.,1966). therefore, the specific heat of the non-magnetic lu0.40cu0.37y0.23 amorphous alloy can be considered to be the best alloy to represent the non-magnetic terms in the specific heat of the magnetic dy0.40cu0.37y0.23 amorphous alloy. fortunately, the experimental results of the reference materials do not need to be corrected for the atomic mass difference between the magnetic and non magnetic crystalline alloys because the average atomic weights are very similar and the difference does not affect the accuracy of such calculations. the magnetic contribution to the specific heat can now be obtained simply by subtracting the specific heat of the non-magnetic lu0.40cu0.37y0.23 amorphous alloy from the total specific heat cp of the amorphous dy0.40cu0.37y0.23 alloy, i.e.; ( ) ( )m p dy-cu-y lu-cu-yc =c c p− (2) specific heat of dy.40 cu.37 y.23 amorphous alloy 99 figure 3. the magnetic specific heat, cm versus temperature, t. figure 4. cm / t versus temperature, t. k.a. mohammed 100 values of cm for this alloy are shown in figure 3 as cm versus t. this excess specific heats have been attributed to the magnetic effects in this magnetic alloy. it is clear that cm shows clearly broad maximum centered at tm=28±1 k. the value of tm is about 1.1 times higher than the value of tsg(=23.5 k)_ obtained from the low field ac susceptibility results (del moral et al.,1986). values of cm/t versus t are shown in figure 4. the magnetic entropy changes, sm, in the magnetic systems are usually related to the magnetic specific heat, cm, through the following relation. m m c s c dt t = ∫ (3) where c represents the molar fraction of the magnetic metal in the alloy. the magnetic entropy changes, sm(tm), in the alloy between 0 k and tm have been determined by integrating the smooth cm results between 0 k and tm respectively. moreover, the magnetic entropy changes (per mole) are theoretically related to the magnetic spin, j, of the magnetic element in the magnetic systems through another relation, which is ( )ln 2 1ms r j= + (4) where r is the gas constant. the numerically estimated values of the magnetic entropy changes, sm(tm), between 0 k and tm are shown in table 1 together with the expected maximum entropy values obtained from equation (4) for j=15/2 for dy ions. the ratio sm(tm)/sm(max) is equal to about 84 % . this indicates that the effective spin value is equal to about 6.3 rather than 15/2 in this alloy and the that there is still a considerable amount of magnetic order even at temperatures higher than tf and tm. this is very similar to the results of (hattori et al.,1995) for the magnetic amorphous erxni1-x system, which shows magnetic entropy changes of about 45 % to 60 % of the theoretical maximum values with an effective spin value less than the 15/2 expected for er ions. the results of the low temperature specific heat of the amorphous dy-cu-y alloy agree quite well with reported results for other magnetic amorphous systems such as pr21ag79, sm21ag79 and lu21ag79 amorphous alloys (garoche et al.,1980), gd-y-cu (mohammed et al., 1986), tb-y-ni (mohammed,1998), er-ni (hattori et al., 1995), gd-cu (mohammed, 2002) and er-cu-y and ho-cu-y (mohammed, to be published). table 1. specific heat parameters of the magnetic dy.40cu.37y.23 amorphous alloy. dy.40cu.37y.23 calculated parameters value ref. tf (k) 23.5 [del moral, 1986] tm (k) 28 ± 1 tm / tf 1.1 sm (tm) (j/mol,k) 19.5 ± 1 spin (j) 15/2 effective spin 6.3 sm(max) = rℓn (2j+1) 23.56 sm(tm) / sm(max) % 84 ± 2 this study 4. conclusion the specific heat of the magnetic dy0.40cu0.37y0.23 amorphous alloy has been investigated in the temperature range 2 to 50 k. the total specific heat does not show any clear changes at the ordering temperature, tf, of the phase transition but the magnetic specific heat exhibits broad anomaly centered at tm of about 28±1 k. the value of tm is 1.1 higher than tf determined from susceptibility measurements for the same alloy. the maximum magnetic entropy changes expected theoretically, sm(max), is calculated using the relation r ln(2j+1) specific heat of dy.40 cu.37 y.23 amorphous alloy 101 for the spin value, j = 15/2 for a mole of dy ions. the ratio of sm(tm)/sm(max) is equal to about 84 %. this gives an effective spin value equal to about 6.3 rather than 15/2. 5. acknowledgment the experimental part has been done at the physics department southampton university (u.k.) the author would like to thank the magnetism group at southampton for their help with these measurements. 6. references coey j. m.d. 1978. amorphous magnetic order. j. appl. phys.49: 1646-1652. del moral a., arnaudas j.j. and mohammed k.a. 1986. spin glass parameter of re-cu-y alloys (re=rare earth). solid state commun.58: 395-398. garoche p., fert a., veyssie j.j. and boucher b. 1980. specific heat of rare earth amorphous alloys. j. magn. magn. mater. vol. 15-18:1397-1398. harris r., plischke m. and zuckermann m.j. 1979. new model for amorphous magnetism. phys. rev. lett. 31: 160-162. hattori h., fukamichi k., suzuki k., aruga-katori h. and goto t. 1995. spin-glass-like behaviour and low-temperature specific heat of amorphous erxni1-x random magnetic anisotropy system. j. phys. : condens. matter. 7: 4193-4205. lanchester p.c. and mohammed k.a. 1985. apparatus for heat capacity measurements of amorphous metals. j. phys. e : sci. instrum.18: 581. liebermann h. and graham, c., jr 1976. production of amorphous alloy ribbons and effect apparatus parameters on ribbon dimensions. ieee trans. magn. 12: 921-923. lounasmaa o.v. and sundstrom l.j. 1966. specific heat of gadolinium, terbium, dysprosium, holmium and thulium metals between 3 and 25 k. phys. rev. 150: 399-412. mohammed k.a. and lanchester p.c. 1986. the low temperature specific heat of gd-cu-y metallic glasses. j. magn. magn. mater. 60: 275-284. mohammed k.a. and lanchester p.c. 1987. the low temperature specific heat of lu-cu-y metallic glasses. j. magn. magn. mater. 65: 15-20. mohammed k.a. 1994. the low temperature specific heat and spin glass ordering temperature of rexcu1-x, rexag1-x and rexa11-x metallic glasses. j. edu. and sci. 22: 57-63. mohammed k.a. 1998. the specific heat and ac susceptibility of tbmetallic glasses. raf. jour. sci. 9: 84-89. mohammed k.a. 2002. the specific heat and ac susceptibility of gd.33cu.67 metallic glass. j. abhath alyarmouk : “pure sci. & eng.” 11: 183-191. rainford b.d., samadian v., begum r.j., lee e.w. and burke s.k. 1982. crystal field splittings in dilute amorphous rare earth alloys. j. appl. phys. 53: 7725-7727. received 17 october 2004 accepted 28 february 2006 squ journal for science, 2019, 24(2), 71-77 doi:10.24200/squjs.vol24iss2pp71-77 sultan qaboos university 71 nutritive value of spirulina as livestock feed in the sultanate of oman osman mahgoub 1 *, hafidh al-mahrouqi 2 , sadeq al-lawatia 1 and rabea al-muqbali 1 1 department of animal and veterinary sciences, college of agricultural and marine sciences; 2 agricultural experiment station, p.o. box 34, pc 123, muscat, alkhoud, sultan qaboos university, sultanate of oman. *email: osmanhgob@squ.edu.om. abstract: a study was carried out to evaluate the nutritional value of spirulina (arthrospira platensis) to determine its potential use for feeding livestock in oman. spirulina was grown in wooden cubicles and harvested after 10 days. one batch of spirulina was dried by centrifugation (cs) and the other was dried in an oven without centrifugation (ncs). samples were analyzed for dry matter (dm) and proximate chemical components. an in vitro assessment was carried out to measure gas production and in vitro dm degradability of spirulina. the dm was 56.1 and 57.1% in cs and ncs, respectively. the proximate composition for cs and ncs as a percentage of dm, respectively was: 60.8 and 62.5 for crude protein (cp); 0.97 and 1.05 for ether extract (ee); 6.35 and 7.55 for ash. the cs and ncs contained: 0.25 and 0.37% dm acid detergent fiber (adf) and 1.03 and 1.92 % dm neutral detergent fiber (ndf), respectively. the gross energy (cal/g dm) was 5730 and 5629 in cs and ncs, respectively. the cs produced more in vitro gas (73 and 71 ml/200mg dm) from 12 hr until the end of the experimental period (96 hr) compared to the ncs (51 and 48 ml/200mg dm), respectively. the cs had significantly higher metabolizable energy (me) (approximately 12 mj/kg dm) than ncs (about 9 mj/kg dm). cs had significantly higher (81 and 79%) organic matter digestibility (omd) than ncs (61 and 58%). the cs had significantly higher short chain fatty acids (scfa) (1.7 and 1.6 µmol) than ncs (1.2 and 1.1 µmol). it was concluded that spirulina is an excellent source of protein and can be used after drying as a potential animal feed. there was little effect of the method of drying of spirulina on its chemical composition or digestibility. keywords: oman; spirulina; chemical composition; in vitro digestibility. القيمة الغذائية لطحالب السبيرولينا كعلف للمواشي في سلطنة عمان عثمان محجوب ، حافظ المحروقي ، صادق اللواتيا ، ربيع المقبالي في عمان. لقد تم أجريت دراسة لتقييم القيمة الغذائية للسبيرولينا )ارثروسبيرا بالتينسيس( لتحديد مدى كفاءة استخدامها كعلف للماشية :صلخمال تخدام فرن زراعة السبيرولينا في احواض خشبية وتم حصادها خالل عشرة ايّام. تم تجفيف السبيرولينا بطريقتين االولى بالطرد المركزي والثانية بإس اس كمية الغاز ومدى تحلل المواد تجفيف. تم بعد ذلك تحليل العينات لحساب المواد الجافة، والبروتين، والكربوهيدرات، والدهون. كما تم مختبريا قي ٪ في المجففة بالطرد المركزي والفرن على التوالي . كما أعطت التحاليل النسب التالية للمواد ١,٦٥و ١,٦٥الجافة بها. كمية المواد الجافة كانت ٦,١,، الرماد ٥٦,١و ,,٦,، مستخلص اإليثر ٦٦,,و ٦٦,,البروتين الخام -الكيميائية للمجففه بالطرد المركزي والمجففة بالفرن على التوالي: على التوالي. إجمالي الطاقة (ndf٪ ),,٥٦و ,,٥٦و نسب ألياف (adf ٪ ),,٣,و ٦,١,كذلك احتوت العينات على نسب ألياف ٪٦١١,و (cal/g dm) ٥ملغ ، من ,,,مل/ ٥,و ,,على التوالي. العينات المحصودة بالطرد المركزي أنتجت كمية غاز مختبريا ,,,١و ,,,١كانت, ملغ . الطاقة ,,,مل / ٨٦و ١٥ساعه( مقارنة مع العينات المجففة بدون طرد مركزي والتي أنتجت كمية غاز ,,ساعه وحتى نهاية فترة التجربة ) ى التوالي وكذلك نسبة هضم ميجاجول/كغ( عل ,ميجاجول/كغ ( ) ,٥االيضية للعينات المجففة بالطرد المركزي كانت اعلى من المجففة بالفرن ) ٪( للعينات المجففة بالفرن. كما كانت أيضا اعلى في كمية األحماض ١٦و ٥,٪( لعينات الطرد المركزي مقارنة ب),,و ٦٥المواد العضوية ) ار ان السبيرولينا مصدرا ميكرومول( على التوالي. خلصت الدراسة الى اعتب ٥،٥و ,،٥ميكرومول( مقارنة ب) ,،٥و ,،٥الدهنية قصيرة السلسلة ) جيدا للبروتين لتضمينه في العليقة الحيوانيه مع وجود تأثير بسيط في طريقة التجفيف على التركيب الكيميائي والهضم. .مختبريا هضم المواد العضوية ، التركيب الكيميائي،عمان، سبيرولينا: مفتاحيةالكلمات ال mahgoub, o. et al 72 1. introduction pirulina (arthrospira platensis) as named by stizenberger in 1852 is a prokaryotic cell-type blue green algae presently classified under the genus arthrospira [1]. arthrospira platensis’s cells are transparent and connected to one another forming a filament in non-heterocyte spiral form. the cell walls are easily digested in a moist environment or in the presence of certain enzymes. this is because the thick gelatinous cell walls are made of complex structure sugars. the cell walls have a diameter ranging between 1-12 mm and their length ranges between 3 to 20 mm [2]. spirulina can grow in a variety of habitats like brackish water, hot springs, freshwater, desert, and seawater. richmond [3] reported that spirulina can grow well in fresh water with an alkaline ph in hot springs and lakes. nutrient uptake by microalgae such as spirulina does not depend only on the nutrients distributed within the growth medium but also on the physical factors affecting their growth such as salinity [4]; ph [5]; light intensity and temperature [6]. it also depends on biotic factors such as initial density, which is a major factor influencing growth. if the initial density is set up higher, the higher growth can be achieved and the more nutrient removal takes place [7]. spirulina platensis has been considered a suitable natural antioxidant and immune-stimulant for humans and animals with few side effects [8-10]. spirulina is edible and a highly nutritious potential feed resource for several animal species. it contains a high level of protein [9] and all essential amino acids, vitamins, minerals, carotenoids and fatty acids [11]. although spirulina did not produce consistent positive effects on growth in chickens, with high levels resulting in declined growth, it can be used for vitamin and mineral supplementation and lowering egg cholesterol [11]. spirulina can compose up to 20% ruminants’ diets due to their ability to digest unprocessed algae especially as a suspension in water [11, 12]. it increases microbial protein production and by-pass protein by reducing protein rumen degradability [11]. spirulina feeding improved body condition score and increased milk yield in dairy cows [13, 14]. panjaitan et al. [15] found out that spirulina improved microbial crude protein production, efficiency of microbial crude protein and feed intake of cattle consuming low protein forage and that it could also be fed safely at higher levels of nitrogen intake. bezerra et al. [16] reported that spirulina feeding produced higher live weights and average daily gains in lambs. holman et al. [11] also reported that dietary spirulina supplementation increased lamb live weight and improved body condition and conformation, although the difference in average daily gain was not statistically different. el-sabagh [17] reported that spirulina supplementation improved final live body weight, daily live weight gain, feed intake and feed conversion ratio in lambs. they recommended that spirulina could be incorporated in fattening lamb’s diets as an antioxidant, immune-stimulant and growth promoter feed additive. shimkiene et al. [18] have shown that pregnant ewes receiving spirulina deliver up to 4% heavier lambs with subsequent higher weight gains compared to pregnant ewes receiving no spirulina. the current study aimed to evaluate the nutritional value of spirulina species as a livestock feed. this was achieved by determining the chemical composition and in vitro digestibility of spirulina. 2. materials and methods 2.1 growing spirulina the experiment was conducted in an open area in the agricultural experimental station (aes) of sultan qaboos university, muscat, oman by culturing spirulina in wooden tanks (400 × 400 cm by 15 cm deep) lined with clear polythene sheets (figure 1a). kosaric medium used as a control was prepared [19] with minor modification using commercial fertilizer (g l -1 ): 5.0 nahco3, 0.25 nacl, 0.1 cacl2, 0.2 mgso4.7h2o, 0.221 urea, 0.07 h3po4, 0.242 koh, 0.02 feso4.7h2o and 0.5 mll -1 of trace metals solution composed of the following (g l -1 ): 2.86 h3bo4, 1.81 mncl2.4h2o, 0.22 znso4.7h2o, 0.08 cuso4.5h2o, 0.01 moo3, and 0.01 cocl2.6h2o (sukumaran et al., 2014). urea was added to the culture medium using fed-batch methods (pulse fertilization) [20]. the fed batch methods were invented to feed the culture with from smaller to increasingly larger amounts. at the premature period, the fed batch method is known to introduce and adapt the culture slowly to the specific nutrient. without this step, the culture could collapse due to medium stress. spirulina culture was added after the chemicals had been added to the water. the spirulina was harvested after 10 days when it had reached its highest density. the spirulina was harvested by the filtration method by using nylon cloth (figure 1b). the cells on the cloth were rinsed several times in tap water to remove traces of growth medium prior to drying. 2.2 in vitro gas production rumen liquor was collected into a pre-warmed thermo flask at 39 °c from a fistulated goat before it was offered the morning feed and strained using a cheese cloth. the incubation procedure was carried out as reported by menke and steingass [24] using 120 ml calibrated transparent glass syringes fitted with silicon tubes. the 200 mg (n=3) samples were carefully dropped into syringes and thereafter, 30 ml inoculums containing strained rumen liquor and buffer. the buffer (g/l) containing 9.8 nahco3 + 2.77 na2hpo4 + 0.57 kcl + 0.47 nacl + 2.16 mgso3 7h2o + 16 cacl2. 2h2o (1:4 v/v) was dispensed under continuous flushing with co2. incubation was carried out at 39±1°c and the volume of the gas production was measured at 3, 6, 9, 12, 15, 18, 21, 24, 48, 72, and 96 hr. the average volume of s nutritive value of spirulina 73 gas produced from the blanks was deducted from the volume of gas produced per sample against the incubation time and from the graph. metabolizable energy (me) and organic matter digestibility (omd) were calculated according to the methods of menke and steingass [24] as: me (mj/kg dm) = 2.20 + 0.136*gv + 0.057*cp + 0.0029*cf; omd (%)= 14.88 + 0.889*gv + 0.45*cp + 0.651*cf. the short chain fatty acids (µmol) was estimated according to the equation of getachew et al. [25] as: 0.0239*gv -0.0601. 2.3 statistical analysis data obtained on in vivo digestibility and in vitro gas production parameters were subjected to one-way analysis of variance using the analysis of variation model in spss [26] pc package. multiple comparison tests used tukey’s multiple-range test on spss [26]. 3. results and discussion 3.1 spirulina cultivation the current experiment proved that spirulina could be cultivated very well under oman’s weather conditions. spirulina grew well and reached a high density after 10 days. the open system used in the current study appeared to be suitable for growing spirulina under local conditions. the requirements for growing spirulina are within reach and the procedures may be adopted by omani farmers. therefore, spirulina offers an excellent potential high protein source for feeding livestock in oman. it will be an excellent product under saline conditions. this is of significant national importance as large areas of omani land and water resources are becoming progressively salinized especially in the al batinah plains due to low rainfall and sea water seepage. 3.2 chemical composition of dried spirulina the proximate chemical analyses of the cs and ncs are given in table 1 with the contents expressed as a % of dm. the dm for both spirulina species ranged between 56 and 57%. the high moisture contents in spirulina should be taken into consideration during storage and processing. drying would be an excellent option of processing to reduce moisture for better storage and incorporation of livestock feeds. figure 1. growing (a) and collecting (b) spirulina in wooden frames at the agricultural experiment station in sultan qaboos university. 3.3 chemical analyses of spirulina the spirulina samples were dried in two ways: by centrifugation at 7,500 rpm (cs) and without centrifugation in (ncs). the dried spirulina was analyzed according to the standard methods of the aoac [21]. dry matter was determined by drying in an oven for 24 h at 80 ºc (method 934.01). crude protein (cp) was determined using a foss tecator kjeltec 2300 nitrogen/protein analyzer (method 976.05). lipids (essential fatty acids and photosynthetic pigments) and ether extract (ee) were determined by soxhlet extraction of the dry sample, using petroleum ether (method 920.39). ash was determined by ashing samples in a muffle furnace at 500 ºc for 24 hr (method 942.05). acid detergent fiber (adf) was determined using cetyltrimethyl ammonium bromide (ctab) and 1n h2so4 as described by roberston and van soest [22]. neutral detergent fiber (ndf) was determined using sodium sulphite and b a a a mahgoub, o. et al 74 sodium lauryl sulphate as described by van soest et al. [23]. adf was expressed with ash whereas ndf was expressed without ash. gross energy (ge) was measured using a bomb calorimeter. table 1. chemical composition of spirulina dried in two different ways. spirulina dm (%) cp (%dm) ee (%dm) ash (%dm) adf (%dm) ndf (%dm) gross energy (cal/g) centrifuged spirulina (cs) 56.08 60.84 ± 0.25 0.97 ± 0.06 6.35 ± 0.03 0.25 ± 0.30 1.03 ± 0.15 5730 non-centrifuged spirulina (ncs) 57.06 62.48 ± 1.25 1.05 ± 0.00 7.55 ± 0.06 0.37 ± 0.36 1.92 ± 0.18 5629 the cp content was 61% for cs and 62% for ncs. this value falls within the range of 60-70% of cp reported by holman and malau-aduli [11]. this cp content in spirulina is excellent compared to other plant sources such as sbm (44%) and animal sources such as fish meal (60%). spirulina is more edible compared to fish meal and contains all essential amino acids, vitamins, minerals, carotenoids, fatty acids [11]. it is readily digestible by ruminants and it increases microbial protein production and by-pass protein by reducing protein rumen degradability [27, 11]. moreover, spirulina protein contains a balanced composition of amino acids with concentrations of essential amino acids such as methionine and tryptophan similar to that of casein, depending on the culture used [27]. the lipid (ee) contents in cs and ncs were 0.97 and 1.05%. this level is very low compared to the 4-16% dm reported by habib et al. [27] and holman and malau-aduli [11]. the reason behind this low lipid content compared with reports in the literature was explained by vonshak et al. [4], in that salt-adapted cells had a modified biochemical composition with a reduced chlorophyll content, and increased carbohydrate content which might affect lipid levels. however, low fat levels are recommended for ruminant rations as high fat levels negative ly influence rumen fermentation. the ash content was 6.4 and 7.6%, for cs and ncs, respectively. habib et al. [27] and holman and malau-aduli [11] reported a comparable range of 3-11% dm. spirulina's ash was reported to contain all the essential minerals (about 7% of total weight) depending on the media. it should be noted that high ash content in non-conventional feeds poses a problem for using them in high proportions in mixed pelleted feeds. cs and ncs had an adf content of 0.25 and 0.37% dm and an ndf content of 1.03 and 1.92% dm in the cs and ncs, respectively (table 1). a special value of spirulina is that it is readily digested due to its low fiber content or absence of cellulose in its cell walls [27]. about 85% of its protein is digested or assimilated after 18 hours [28]. this explains the low level of energy in spirulina. the gross energy (cal/g dm) in the current study was 5730 and 5629 for cs and ncs, respectively. holman and malau-aduli [11] reported a gross energy of 1504 kj/100 g. this implies that spirulina should be used mainly as a protein supplement to a high fiber diet for ruminants due to its extremely low fiber content. 3.4 in vitro digestion of spirulina the gas volume produced by spirulina over 96 hr is given in figure 2. the centrifuged spirulina produced a total in vitro gas of 39.7 ml whereas the non-centrifuged spirulina produced a total of 31.2 ml (figure 2). the difference between the two types started to be significant from 12 hr and continued until the end of the experimental period at 96 h. this total gas production is very low compared to that of forages. for instance, kamalak et al. [29] reported much higher gas volumes (40-80 ml at 96 hr) for wheat straw, barley straw, alfalfa hay and maize silage. gas production by fermentation largely arises from the carbohydrate fraction of forage. this is because ash and fat produce no gas and protein produces very little [30]. drying spirulina by centrifugation resulted in higher gas production indicating that spirulina dried by this method is more digestible. this may be explained by its cell walls being easily digested in a moist environment or in the presence of certain enzymes. this is because of the lack of cellulose in its thick gelatinous cell walls which are made of complex structure sugars. the cell walls have a diameter ranging between 1-12 mm and their length ranges between 3 and 20 mm [2]. the cs in the current study had significantly higher me (9.13 mj/kg dm) than the ncs (8.25 mj/kg dm) (table 2). high energy levels in spirulina indicate its excellent potential as a livestock feed. tobias marino et al. [31] reported that me levels followed the same pattern of gas production which is similar to the findings of the current study. nutritive value of spirulina 75 figure 2. in vitro gas production pattern from spirulina dried by cs or ncs. the cs had higher odm (67.86%) than ncs (61.37%) and me (9.1 and 8.25 mj/kg) (table 2). calculations indicated that the cs had higher short chain fatty acids (scfa) than ncs (0.59 and 0.41 µmol), respectively (table 2). this adds to the value of spirulina as a potential livestock feed if it has been properly processed. table 2. gas production parameters of spirulina dried by centrifugation (cs) and non-centrifuged spirulina (ncs). me (metabolizable energy) = 2.20 + 0.136*gv + 0.057*cp + 0.0029*cf (menke & steingass, 1988) omd (organic matter digestibility) = 14.88 + 0.889*gv + 0.45*cp + 0.651*cf (menke & steingass, 1988) scfa (short chain fatty acids) = 0.0239*gv -0.0601 (getachew et al., 1999) means on the same row with similar denoting letters do not differ significantly (p>0.05) conclusion in general, the findings of the current study supported published reports that, based on chemical composition and digestibility, spirulina proves to be an excellent non-conventional feedstuff especially as a protein source. drying of spirulina by centrifugation improved its quality. conflict of interest the authors declare no conflict of interest. acknowledgement the technical help of animal science students hussein al-madhani and waleed al-madhani during the experimental period is acknowledged. this study was supported by a sultan qaboos university internal grant no. ig/agr/anvs/15/01. 20 30 40 50 60 70 80 0hr 3hr 6hr 12hr 24hr 48hr 72hr 96hr g a s vo lu m e ( m l) time of incubation cs ncs parameter cs ncs mean sd mean sd total gas (ml) 39.7 1.65 31.2 1.65 me (mj/kg) 9.13 0.275 8.25 0.079 odm (%) 67.86 1.796 61.34 1.119 scfa (µmol) 0.59 0.048 0.41 0.030 mahgoub, o. et al 76 references 1. castenholz, r.w. subsection iii, order osciilatoriales. in: j. t. stanley, m. p. bryant, n. pfenning and j.g. holt (eds.). bergey’s manual of systematic bacteriology, 1989, 3,1771-1775. 2. salleh, b. pengenalan alam tumbuhan. dewan bahasa dan pustaka, kuala lumpur, 1987, 47-59. 3. richmond, a. spirulina. in: micro-algal biotechnology. borowitzka, m. a. and borowitzka, l. y. 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satellite symposium, 1999. 26. statistical packages for social sciences (spss). version 16, spss inc., illinois, usa. 2007. 27. habib m.a.b., parvin, m., huntington, t.c. and hasan m.r. a review on culture, production and use of spirulina as food for humans and feeds for domestic animals and fish. fao fisheries and aquaculture circular. no. 1034 fao, rome, 2008, pp. 33. 28. sasson, a. micro biotechnologies: recent developments and prospects for developing countries. biotec publication 1/2542, 1997, pp. 11-31. place de fontenoy, paris. france. united nations educational, scientific and cultural organization (unesco). 29. kamalak, a., canbolat, o., gurbuz y. and ozay, o. comparison of in vitro gas production technique with in situ nylon bag technique to estimate dry matter degradation. czech journal of animal science, 2005, 50(2) 60-67. 30. robinson, p.h. and getachew. g. university of california ce: a practical gas production technique to determine the nutritive value of forages: the uc davis approach, 2000 (available from: https://www.researchgate.net/publication/265997062_uc_ce_a_practical_gas_production_technique_to_deter mine_the_nutritive_value_of_forages_the_uc_davis_approach [accessed jun 06 2018]. 31. tobias marino, c., hector, b., mazza rodrigues, p.h., oliveira borgatti, l.m., marques meyer, p., alves da silva, e.j. and ørskov, e.r. characterization of vegetables and fruits potential as ruminant feed by in vitro gas production technique. livestock research for rural development, 2010, 22, article #168. last accessed 18.06.2017.from http://www.lrrd.org/lrrd22/9/mari22168.htm received 25 june 2018 accepted 3 january 2019 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 121-130 © 2003 sultan qaboos university analysis of fire data in oman k.s. al-jabri, a.w. hago, a.s. alnuaimi and s. al-mahrooqi department of civil and architectural engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email: aljabri@squ.edu.om. رائق في سلطنة عمانتحليل بيانات الح علي النعيمي و سعود المحروقي، عبد الواحد هجو ،خليفة الجابري الماضية في سلطنة اإلحدى عشرة سنة تهـدف هذه الدراسة لتوضيح مشــكله حـوادث الحرائق ومسبباتها خالل :خالصـة لضعف في المباني الموجودة وللتقليل من عمـان من اجل استخدام البيانات في تحسين سبـل مكافحة الحرائق و اكتشاف نقاط ا الحرائق و مسبباتها و زيادة أمن تخص مناسبةكما يمكن تقديم توصيات . امكانـيه حدوث الحرائق في المناطق التي تكثر فيها لدفاع المدني و في هذا البحث تم جمع البيانات الخاصة بالحرائق من المديرية العامة ل. الخ........ الوعـي الجماهيري و التعليم عشرة اإلحدىو تتضمن البيانات أعداد الحرائق بالسلطنة خالل . و من مكتبة جامعة السلطان قابوس ) قسـم العالقـات العامة ( وقد أوضحت الدراسة الزيادة المطردة في حوادث . كما تتضمن تقسيم الحرائق ألنواعها المختلفة و إحصائياتها . الماضيةسـنة . كما ناقشت مسبباتها المحتملة و الطرق الممكنة للتحكم في حدوثها. الماضيالحرائق خالل العقد abstract: the aim of this study is to illustrate the problem of fire accidents in the sultanate of oman and their causes in order to find out how the existing data could be used as a base to improve fire resistance, to detect the weak points (vulnerability to fire) in existing structures, and to minimize fire occurrences in places where it is high. this will also provide useful recommendations with regard to fire safety including causes, people’s awareness and education, etc. fire data in oman were collected from two sources: the directorate general of civil defence (public relations department) and sultan qaboos university library. the collected data represent the number of fires in oman during the last decade. it also includes fire distribution by type and averages. the analysis shows that there is a linear increase in the number of fire accidents in the last decade with time. many factors are included as potential sources, which are explained in the paper, and suggestions are made for possible control. keywords: analysis, fire safety, dwelling, farms, fatality, financial loss, fire. 1. introduction s ince the discovery of fire, mankind has realized its power and is still searching for sensible ways to minimize its occurrence and the destruction which it might cause. the risk of fire exists in every building and it is accepted that absolute safety from fire is impossible. over the centuries fire safety regulations have been introduced in many countries with two main objectives: • to reduce the loss of life and ensure the safety of the occupants and those in the neighboring buildings. • to minimize the financial losses both in the property and its neighbourhood, medical costs, interruption to business, etc. active and passive fire prevention measures have been implemented in many countries to prevent fire occurrence. regulations insist that such measures must strictly be followed in order to minimize the risk of fire. this can be achieved either by early detection of fire or by allowing ample time for safe evacuation of occupants and for the fire brigade to fight the fire safely. however these measures cannot provide complete immunity against the risk of fire. 121 k.s. al-jabri, a.w. hago, a.s. alnuaimi and s. al-mahrooqi analyzing existing fire accident data and identifying the causes of fire accidents is of great importance in improving fire resistance techniques and methods. also this can help in detecting the weak points in fire safety regulations and thereby help in developing strategies for minimizing fire occurrences particularly in places where they are high. this, in turn, will provide better understanding of fire safety including causes, people’s awareness and education. this paper presents an analysis of fire accidents in the sultanate of oman during the past eleven years (1990-2000). the major fire types studied in this paper are: dwelling fires, farm fires and vehicle and equipment fires, while other minor fire types are referred to as “other fires”. financial losses in rial omani (r.o.), saved properties and the number of deaths and injuries caused by fire are the essential elements of fire data collected. because of the random nature of its occurrence (i.e. fire does not happen in the same pattern and in the same manner unless through arson), the average number of occurrences per month is reported and fire causes are discussed, and some solution measures are proposed. 2. fire safety regulations in the sultanate of oman the sultanate of oman is located in the south east corner of the arabian peninsula and has an estimated population of 2 million and an area of 309,000 km2. in the last three decades and due to the discovery of oil, oman has witnessed considerable and rapid development in all aspects of life. this was accompanied by an increase in the number of dwellings and commercial and industrial buildings in different regions. the number of vehicles and road users has also increased significantly. fire accidents in oman are not as high as in many other countries. this is due to less congestion in towns, and the use of non-combustible construction materials. yet people do not have enough knowledge concerning fire safety. fire statistics (annual reports, 1990-2000) within the sultanate of oman reveal that in the last decade there were over 17500 fire accidents and nearly 750 deaths and injuries caused by fire. beside loss of life, there is an estimated cost of nearly r.o. 100 million for damage to property. fire safety regulations in the sultanate of oman are set up by the directorate general of civil defense. these regulations are implemented by the different organizations throughout the country. from fire safety perspective, the civil defense has the following objectives: • reducing the risk of fire in buildings and other premises as well as in petrol and service stations. • reducing the risk of fire when transporting, handling and storing hazardous materials. • increasing fire safety awareness among the public through seminars, exhibitions, public media and visits to schools to explain the fire safety regulations, fire prevention measures and precautions to be taken in the event of fire. • preparing and issuing fire safety code of practice in collaboration with directorate general of standards and measurements as a national health and safety code of practice in the country. each organization has the freedom to prepare and implement its own fire safety policy in accordance with the national health and safety code of practice. however, a regular inspection is carried out by civil defense inspection teams to residential, commercial and industrial premises to ensure compliance with fire safety regulations. also, approval from the civil defense authority must be obtained prior to the commencement of the construction of any building, especially multistorey residential and commercial buildings and industrial premises. 3. recorded fires in oman the total number of fires from 1990 to 2000 is shown in figure 1. it can be seen that the total average number of fires per year reached almost 1068. the number of fires was 903 and 927 in 122 analysis of fire data in oman 1990 and 1991, respectively. the number of fires increased slightly until 1995 and declined by 11% in 1996. however, in 1998 the number of fires recorded reached 1251 fires, 903 927 1100 1108 1066 1070 951 1011 1251 1136 1203 500 700 900 1100 1300 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 year n um be r of f ir es figure 1. recorded fire accidents in oman. 0 100 200 300 400 500 600 1989 1991 1993 1995 1997 1999 2001 year dwelling farm othervechicle n um be r of f ir es figure 2. the number of fire types in oman. which is 27.8% more than in 1990 and the highest ever recorded. in 1999, the number of fires decreased by 9.2% comparatively, whereas in 2000 it dropped by only 3.8%. it may be seen from figure 1 that the total number of fires at the end of the decade is to some extent more than those at the beginning. this increase in the number of fires may be attributed to the increase in the number of residential, commercial and industrial buildings. this is depicted in table 1, which shows the number of building permits in the muscat region during the last decade (department of building permits, 2000). a breakdown of the different types of fires is shown in figure 2 and will be discussed in the following sections. 4. dwelling fires during the last decade there was a general decrease in dwelling fires as can be seen in figure 2. the percentage of dwelling fires in the year 2000 was 28.3% of the total number of fires in that 123 k.s. al-jabri, a.w. hago, a.s. alnuaimi and s. al-mahrooqi year, compared to 53.9% in 1999, indicating a drop of 25.6%. although the general trend during the 1990-2000 period was a decrease in fires, some minor variations were observed. the highest number of dwelling fires occurred in 1992 with 490 fires and the lowest was in 1997 with 314 fires. the decline in dwelling fires may be attributed to many reasons. the most likely reason may be the increase in the public educational level during the last decade. it is well known that education plays an important role in reducing the risk of fire by increasing public awareness of fire safety. the second reason is probably due to the directorate general of civil defense playing a major role in increasing public awareness of the risk of fire among the public, school children and government sectors through lectures, seminars, tv programs and fire safety exhibitions. table 1: number of building permits in muscat region (excluding industrial buildings). year number of building permits 1991 1940 1992 2263 1993 2079 1994 2126 1995 1865 1996 1700 1997 1905 1998 1951 1999 1552 2000 1475 total 18856 5. farm fires as can be seen in figure 2, there was a gradual increase in farm fires. in 1990 the number was 129 fires, which contributed to 14.3 % of the total number of fires. in 1991 and 1992, this number had doubled. the highest number of farm fires was recorded in 1998, when there were 410 fires. this gradual increase in the number of farm fires, despite developments in farming methods and waste disposal techniques, may be due to the lack of awareness among farmers and workers. based on civil defense information, many farmers still burn the dry waste from farms near trees and other grasses which has the effect of increasing the possibility of fire. many farmers are careless when they burn farm waste particularly in windy weather. also, the majority of farmers are still hiring unskilled cheap labor, many of whom are illiterate and lack the basic knowledge regarding fire safety in farms. in addition, many of these laborers are smokers, which in turn increases the possibility of fire. moreover, leaving dry grasses in the sun makes them vulnerable to fire. observations show that many farm fires occur in summer when the temperature is very high, reaching above 50 °c. for these reasons, farmers are still lacking in awareness with respect to fire safety in farms. this matter needs to be addressed seriously by the fire safety authorities. 6. vehicle and equipment fires the number of vehicle and equipment fires is also shown in figure 2. like farm fires, there is also a gradual increase in the number of vehicle and equipment fires. the lowest number of fires recorded was 147 in 1990, while the highest was 218 in the year 2000. the increase may be attributed to the following reasons: • negligence: many drivers and passengers do not dispose of cigarettes properly in cars. • arson for revenge or compensation. • lack of regular maintenance particularly in summer, which increases the risk of electrical faults. 124 analysis of fire data in oman • the majority of drivers do not keep fire extinguishers in their cars and even if they do many of them do not know how to use them properly. 7. other fires other fires are defined as fires which occur in companies, garages and workshops. from figure 2 the lowest number of such fires was 140 in 1991 which increased to 302 in the year 2000, showing a substantial increase. this is probably due to the fact that many of the companies and factories are not complying with fire safety regulations, which has an influence on increasing the risk of fires in these places. the other reason is that in the last ten years the number of industrial regions has increased quite rapidly and consequently the chances of fire risk have also increased. 8. average number of fire distribution by type the distribution of percentages of fire types is shown in figure 3. it may be seen that although there was a reasonable decrease in the number of dwelling fires since 1990, it still represents the highest percentage (36%) in comparison with other fire types. this is due to the increase in the number of residential, commercial and industrial buildings which was constructed in the last ten years. from table 1 it may be seen that the total number of building permits (excluding industrial buildings) issued by muscat municipality in the muscat area was 18856 (department of building permits). the farm, vehicle and equipment and other fires contributed, respectively, to 24%, 22.7% and 17.3 % of the total average percentage. dwelling 36% farm 24% vehicle 17% others 23% figure 3. the average number of fire types in oman (1990-2000). 9. financial losses this section concentrates primarily on the financial losses in the properties and premises. the estimated total financial losses in fire accidents in oman in the last decade were r.o. 57.4 million. as can be seen in figure 4, the lowest losses have been recorded during the period from 1990 to 1998. for instance, in 1990 the financial losses reported was r.o 0.798 million. in 1995 the financial losses were r.o. 1.903 million. after that, it dropped significantly to r.o 0.629 million in 1997. however, in 1999 and 2000 financial losses increased considerably. the financial losses were estimated at r.o. 22.6 and 25.4 million for 1999 and 2000, respectively. this increase is due to fire accidents in large factories. it is clear that the increased number of industrial regions has contributed significantly to the increased value of financial losses. 125 k.s. al-jabri, a.w. hago, a.s. alnuaimi and s. al-mahrooqi therefore, in an industrial region, factories should comply very strictly with the fire safety rules and fire fighting units should be made available in the vicinity of industrial estates. 0.798 1.072 1.108 0.76 0.677 1.903 0.908 0.629 1.465 22.599 25.482 0 5 10 15 20 25 30 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 year fi na nc ia l l os se s (m ill io ns r .o .) figure 4. financial losses due to fire (in million r.o.). 10. saved properties figure 5 shows the value of saved property (in millions r.o.) in the last ten years. the total value of property, which has been saved by the civil defense was estimated at r.o. 281.906 million, with 43.3% of the total property saved in 1990 and 1991. this means that almost more than two thirds of the total saved property happened in these two years. then it decreased considerably between 1993 and 2000, despite the increase observed in the saved properties in 1995 and 1999. 60.88 61.24 38.268 10.8 32.124 10.696 9.127 13.566 36.679 8.526 0 10 20 30 40 50 60 70 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 year v al ue o f s av ed p ro pe rt y ( m ill io n s r .o .) figure 5. the value of saved property due to fire (in million r.o.). 126 analysis of fire data in oman 11. fire causalities figures 6 and 7 show that the total number of deaths in the last 11 years was 167 and the number of the injuries was 563, which is more than three times the number of deaths. the lowest number of deaths and injuries per year was recorded in 1990 as 4 and 32, respectively. however, the largest number of deaths was recorded in 1993 and 1994, and the largest number of injuries was in 1994 and 2000. one of the main causes was the inhalation of smoke, particularly carbon monoxide. moreover, many deaths and injuries could have been prevented if people had had early warning and had been able to escape quickly. it has been observed that the shorter the time interval between the start and discovery of the fire, the lower the death or the injury rate is. 32 35 52 47 72 34 53 59 51 48 80 0 10 20 30 40 50 60 70 80 1990 1992 1994 1996 1998 2000 year n um be r of in ju ri es figure 6. the number of injuries due to fire. 4 12 14 28 35 11 9 10 13 9 22 0 10 20 30 40 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 year n um be r of d ea th s figure 7. the number of deaths due to fire. 127 k.s. al-jabri, a.w. hago, a.s. alnuaimi and s. al-mahrooqi 12. monthly fires the average monthly fires during the last decade are presented in figure 8. the lowest percentage of fires was between november and january (during winter) while the highest was in april, may and june (summer season). the highest percentage recorded was in may, which accounted for about 12% of the overall average. however, the lowest number of fire accidents was in november which is estimated to be 7% of the total average. it should be noted that the months of may to july are usually the hottest months of the year in the sultanate of oman. the rise in fire accidents during summer may be due to the following reasons: 1. electrical supply is overloaded due to the excessive use of air conditioning. this causes electrical faults which in turn increase the risk of fire. 2. irregular maintenance of cars may also lead to a higher risk of fire. 3. the fierce heat from the sun and the lack of rain during the summer may lead to fires in dry grassland. 0 20 40 60 80 100 120 140 ja nu ar y f ab ru ar y m ar ch a pr il m ay ju ne ju ly a ug us t s ep te m be r o ct ob er n ov em be r d ec em be r a ve ra g e n u m b er o f f ir es month figure 8. the average number of monthly fires (exc. 93). 26 23 13 11 8 6 4 3 2 2 1 1 0 5 10 15 20 25 30 a ve ra ge p er ce nt ag e (% ) a rs on e le ct ric al fa u lts o th er re a so n s p la yi n g ch ild e rn s m o ki ng b u rn in g w as te s co ok in g t eh n ic al d ef ec ts in ce ns e v eh ic le s g a s le a ka g e w el di ng figure 9. the main fire causes in oman. 128 analysis of fire data in oman 13. average number of fire causes in oman it can be seen from figure 9 that according to the data of the directorate general of civil defense arson is the main cause of fire in oman, contributing to 26 % fires. electrical faults come in second place by 23 % of the total percentage. the percentage of fires caused by children playing was evaluated by 11 % of the whole percentage. estimates of the percentage of fires caused by smoking and burning waste were about 8 % and 6 %, respectively. 14. conclusions analysis of fire data collected in oman from 1990 to 2000 is very important in helping to minimize fire occurrence. from the results obtained the following conclusions were drawn: a) the increase in the total number of fires in oman may be attributed to the increase in the population and the increase in the number of residential, commercial and industrial buildings. this increase is not matched by a corresponding compliance with safety regulations. b) although there has been a gradual decrease in dwelling fires during the last decade, they still record the highest percentages followed by farm fires. c) the gradual increase in the number of farm fires, despite developments in farming methods and waste disposal techniques, may be due to the lack of awareness among farmers and workers, which needs to be considered seriously by the fire safety authorities. d) the gradual increase in vehicle and equipment fires may be attributed to negligence, arson and lack of regular maintenance. e) the number of fires in factories and workshops has increased owing to the fact that many companies and factories are not maintaining a strict enough observance of fire safety regulations. f) financial losses have increased quite considerably owing to the increase in the number of industrial areas, which is not matched by corresponding compliance with safety regulations. g) the main causes of deaths were linked to smoke inhalation. h) the highest number of fires was recorded in the summer between april and july because of the overloading of the electrical supply and dry leaves and grasses catching fire in the hot dry weather. i) according to civil defense statistics the main causes of fires in oman are arson and electrical faults. 15. recommendations in order to minimize the risk of fire accidents in buildings, the following points may be considered as recommendations based on the study made in this paper: a) use of fire retarding materials in the construction of buildings, warehouses, workshops, etc. b) proper disposal of farm and industrial wastes. c) annual inspection of buildings and vehicles to ensure compliance with safety regulations. d) establishment of fire safety management policy throughout the country. e) increase in the use of the media for public awareness to fire safety. f) increase in the awareness of children of fire safety at home, school and in the community. g) strict implementation of fire safety regulations in all factories and workshops. h) proper installation of fire fighting systems in labour accommodation barracks, especially those built from combustible materials. 16. acknowledgement the authors would like to thank the directorate general of civil defense for providing the data for this research. thanks are also extended to muscat municipality for providing some of the data needed in the research. 129 k.s. al-jabri, a.w. hago, a.s. alnuaimi and s. al-mahrooqi references the annual reports from 1990 to 2000, general directorate of civil defense, royal oman police, sultanate of oman. department of building permits, general directorate of technical affairs, muscat municipality, sultanate of oman, 2000. received 6 november 2001 accepted 2 december 2003 130 analysis of fire data in oman k.s. al-jabri, a.w. hago, a.s. alnuaimi and s. al-mahrooqi department of civil and architectural engineering, college of engineering, sultan qaboos university, p.o.box 33, al khod 123, muscat, sultanate of oman, email: aljabri@squ.edu.om. 2. fire safety regulations in the sultanate of oman total photovoltaic cells and systems: 1-11 squ journal for science, 13 (2008) © 2008 sultan qaboos university behaviour of thermal degradation of some poly (4-amino-2,6pyrimidinodithiocarbonate) metal complexes hussein m. al-maydama*, ali el-shekeil**, ashour al-karbouly** *department of chemistry, faculty of science, sana'a university, p.o.box 12286, sana'a, yemen, email:hmaydama@yahoo.com; **department of chemistry, faculty of science, applied science university, amman, jordan. . )بريمدين ثنائي ثايوكاربامات-2، 6امينو-4 (لبعض معقدات المعادنسلوك التحلل الحراري ن مانع الميدمه، علي جمعان الشكيل وعاشور الكربولييحس ــة دد :خالص ل لمتع ت والنيك د والكوبل دات الحدي راري لمعق ل الح لوك التحل ري س م تح و-4[ت ائي -2،6-امين دين ثن بريم باستخدام طريقة . درجه مئوية لكل دقيقة في وجود النيتروجين10بالتحليل الحراري ألحجمي عند معدل تسخين ] ثايوآاربامات ريدفيرن التكاملية تم تقدير البيانات الحرآية للخطوات المتعاقبة للتحلل المتتابع الملحوظ في منحنيات التحليل الحراري -آوتس قدات الثالث درست بالمقارنة الن منحنيات التحليل الحراري ألحجمي و منحنيات عملية التحلل الحراري في هذه المع. لحجميأ تمت مناقشة الثبات الحراري لتحرر فتات الجسيمات . التحليل الحراري ألتفاضلي تبين االختالف في سلوك التحلل الحراري وآما تم األخذ في . ه الكهربية والحجم األيوني عند الخطوات المتعاقبة للتحلل المتتابع لهذه المعقدات على أساس تأثير ا لسالبي . منسجم في البيانات الحرآيةالاالعتبار التباين في الثبات الحراري واالختالف غير abstract: the thermal decomposition behaviour of the fe(ii), co(ii) and ni(ii) complexes of poly[4-amino-2,6-pyrimidinodithiocarbamate] has been investigated by thermogravimetric analysis (tga) at a heating rate of 10°c min-1 under nitrogen. the coats-redfern integral method is used to evaluate the kinetic parameters for the successive steps in the decomposition sequence observed in the tga curves. the processes of thermal decomposition taking place in the three complexes are studied comparatively as the tga and dta curves indicate the difference in the thermal decomposition behaviour. the thermal stabilities for the release of the fragments at the successive steps in the sequential decomposition of these complexes are discussed in terms of electronegativity and ionic size effects. the difference in thermal stability and the inconsistent variation in the kinetic parameters of these complexes are considered. keywords: polydithiocarbamate complexes; thermal behaviour; kinetic parameters; thermal stability. 1 hussein m. al-maydama et al. 1. introduction o ver many decades, the thermal behaviour and properties of various types of materials and the thermal parameters of their degradation processes have been reliably widely studied by using the well-established thermal analysis methods (tg, dtg, dta, dsc). as these methods allow determination of the chemical steps of the investigated degradation, the kinetic parameters for each step have been estimated by some methods (brown et al 1980) and (brown 2001). the evaluation of the kinetic parameters has been often performed by processing the data of a single thermogravimetric curve (tg curve) recorded at a certain heating rate and atmospheres (under nitrogen or air flow). some recent examples concerning the thermal and thermo-oxidative degradation of polymers or polymeric material, metal complexes, medicinal plant leaves and thermoplastic starch obtained by thermoanalytical methods (tg, dtg, dta, dsc) have been reported (martns et al 2003; kim et al 2003; giurginca and zaharescu 2003; gonzalez et al 2000; chang et al 2000; el-naggar et al 1997; zidan 2001; gad 2004; alawadi et al 2008; wang et al 2004; bora 2000 and mano et al 2003). the kinetic parameters evaluated for the successive steps in the decomposition sequence of these materials are based on considering a reaction order model for the kinetic analysis of a single tg curve data. in our previous studies (el-shekeil et al 1997; el-shekeil et al 1998 and el-shekeil et al 1999) a comparative study from the point of view of the dc electrical conductivity and its change with temperature variation (300-500 k) was illustrated for the polymer-metal complexes under investigation in the present work. as a result the activation energies worked out for different temperature segments were explained. the thermal analysis results (tga and dta) were invoked only to monitor the loss of adsorbed water in order to study its effect (i.e. the role of adsorbed water) on the dc electrical conductivity at 300 – 500 k range. this adsorbed water effect study (el-shekeil et al 1999) concludes that the water attaches itself to specific but nonequivalent points on the polymer chain. this attachment causes the localization of the n and/or s electron pairs and the creation of quantum quasi-particles; solitons and polarons. the release of this adsorbed water by temperature results in the release of quasi-particles. hence, the increase of temperature excites the electrons from the soliton’s level to the conduction band. these electrons either contribute to the number of the conductivity carriers or combine with the positive holes. the fast mechanism decrease the number of the conductivity carriers, which could be the reason for the exothermal phenomenon observed. the higher the released number of adsorbed water molecules, the higher the number of conductivity carriers, and as a result the higher the conductivity values. in this work, we present a comparative study of some polymer-metal complexes of a particular ligand with various metals. this study is based on the point of view of the thermogravimetric analysis (tga) and its thermal parameters at a certain condition (i.e. heating rate of 10°c min-1 under nitrogen). the chosen organic polymer, poly[4-amino-2,6-pyrimidinodithiocarbonate] (ppt),which is rich in electrons due to the existence of nitrogen and sulphur atoms, acts as a polymer ligand forming the desired complexes via coordination with the metal ion of the 3d-transition elements fe(ii), co(ii), ni(ii). the processes of thermal degradation taking place in these polymer-metal complexes have been investigated by thermal analysis methods (tg, dtg, and dta). the coats-redfern integral method (coats and redfern. 1964) has been used to determine the associated kinetic parameters for the successive steps in the decomposition sequence. although these three polymer-metal complexes are identical in terms of the ligand type around the metal ions of fe(ii), co(ii) and ni(ii), the difference in thermal decomposition behaviour and that in thermal stability are clearly observed. therefore, information concerning the thermal decomposition behaviour, thermal stability, mechanism and kinetics of the investigated degradation process obtained from the tg curves recorded for the three conducting polymer-metal complexes at a certain condition (i.e. heating rate of 10°c/min and nitrogen flow) has become of interest to be studied comparatively. our first attempt similar to this pattern of study has recently been published (al-maydama et al 2006) for four conducting polymer-metal complexes of fe(ii), co(ii), ni(ii) and zn(ii) with polydithiooxamide ligand. 2 behaviour of thermal degradation 2. experimental 2.1 synthesis of polymer complexes and physical analysis the details of the synthesis, physical measurements, characterization and identification as well as the dc electrical conductivity of the three conducting polymer complexes of interest (ppt-fe, ppt-co and ppt-ni) and their structure, shown in structure 1, can be found in previous publications (el-shekeil et al 1997; el-shekeil et al 1998 and el-shekeil et al 1999). 2.2 thermal analysis the tga thermograms (tg and dtg) and dta curves were obtained by using shimadzu, thermogravimetric analyzer, tga-50, and dta-50, respectively, at a heating rate of 10°c min-1 under nitrogen flow and heating programme 20 – 1000°c. 2.3 methods from the tga curves (tg, dtg) recorded for the successive steps in the decomposition process of these polymer complexes it was possible to determine the following characteristic thermal parameters for each reaction step: initial point temperature of decomposition (ti) is the point at which dtg curve starts deviating from its base line. final point temperature of decomposition (tf) is the point at which dtg curve returns to its base line. peak temperature, i.e. temperature of maximum rate of weight loss (tdtg) is the point obtained from the intersection of tangents to the peak of dtg curve. n n n h 2 s s c nh n m c l c l h 2o h 2o y h2 o m = fe, co, ni y = 2.5, 2, 1 structure 1 weight loss at the decomposition step (∆m) is the amount of mass that extends from the point ti up to the point tf on the tg curve. the material released at each step of the decomposition is identified by attributing the weight loss (∆m) at a given step to the component of similar weight calculated from the molecular formula of the investigated complexes and comparing that with literatures of relevant compounds considering their temperature. this may assist identifying the mechanism of reaction in the decomposition steps taking place in the polymer complexes under study. activation energy (ea) of the decomposition step: the integral method used is the coats-redfern equation (coats and redfern. 1964) for reaction order n ≠1, which when linearised for a correctly chosen curve yields the activation energy from the slope; 3 hussein m. al-maydama et al. log 1 a 2 a a e1 (1 ) 2 log 1 (1 ) e e 2.303 n zr rt t n q r α − ⎡ ⎤⎡ ⎤− − = − −⎢ ⎥⎢ ⎥−⎣ ⎦ ⎣ ⎦ t where: α = fraction of weight loss, t = temperature (k), n = order of reaction, z = pre-exponential factor, r = molar gas constant, q = heating rate and ea = activation energy. a plot of log ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − −− − )1( )1(1 2 1 nt nα versus 1/t gives the slope from which activation energy (ea) was determined. order of reaction (n) is the one for which a plot of the coats-redfern expression gives the best straight line n among various trial values of n that are examined, i.e., by trial and error for various trial values of n, estimated by the horovitz-metzger method (horovitz and metzger 1963). 3. results and discussion the tga (tg and dtg) and dta curves recorded for the ppt-fe, ppt-co and ppt-ni complexes (i.e., poly-4-amino-2,6-pyrimidinodithiocarbamate-fe(ii), co(ii) and ni(ii) complexes) are given in figures 1 and 2. these curves, which characterize and compare the thermal decomposition behaviour of the complexes under study at the heating rate of 10°c min-1 under nitrogen, generally show consecutive steps for almost uninterrupted weight losses in the sequential decomposition of these three polymer complexes (i.e. no clear plateau between the steps on tg curves) over the experimental temperature range (20–1000°c). therefore, the maximum rate temperature of weight loss (tdtg) is determined only for some steps in the decomposition sequence that their dtg plot shows a maximum rate of weight loss, and the peaks tdta are observed only for some steps in the dta curves. in general, it is observed that the sequence of decomposition that takes place in these complexes starts with dehydration of adsorbed water followed by the release of coordination water, then bonded chlorine and then fragments of the backbone. this seems like a four-step decomposition process. however, close examination of the tg and dtg curves (figure 1) reveals a three-step decomposition process for ppt-fe(ii) at the 20-564°c range and a six-step process of decomposition for ppt-co(ii) at the 25-897°c and ppt-ni(ii) at the 30-728°c range. the difference in the thermal decomposition behaviour of these three complexes can be seen more clearly in their tga and dta curves (figures 1 and 2). table 1 compares the characteristic thermal and kinetic parameters determined or evaluated, from the tga curves, for each step in the decomposition sequence of the complexes. it can be seen clearly (table 1) that the weight losses obtained from the tga curves and that calculated for the corresponding molecule or molecules are in good agreement as is the case for all of these complexes. as the composition of the final decomposition products (i.e. final residue) of these three complexes are not proved, thermal decomposition with ill-defined final states are considered for these complexes. the activation energies (ea) are calculated from the slopes of the best fit straight lines, which regress satisfactorily (0.9924 ≤ r2 ≤ 0.9998) for using the best values of reaction order (n) in the plots of the coats-redfern equation (coats and redfern. 1964). the first-steps of decomposition in the tg curves at the 20-95°c, 25-96°c and 30-90°c range with temperatures of maximum rate of weight loss (tdtg) in the dtg curves (figure 1) at 43°c, 48°c and 55°c, and the associated exothermic peaks (tdta) in the dta curves (figure 2) at 52°c, 47°c and 54°c indicate the loss of two and half molecules, two molecules and one molecule of adsorbed water in the fe, co and ni-polymer complexes , respectively. this corresponds well with weight losses data for fe (obs. 11.46%, theor. 11.49%), co (obs. 9.20%, theor. 9.33%) and ni-polymer complex (obs. 5.01%, theor. 4.9%). the temperature ranges reported (al-maydama et al 2006; donia et al 1990; donia et al 1992 and donia et al 1997) for releasing adsorbed water in some metal complexes are in good agreement with that mentioned above. the activation energies determined for these reactions in the polymer complexes of fe, co and ni are 84.2 kj mol-1, 84.6 kj 4 behaviour of thermal degradation mol-1 and 84.1 kj mol-1, respectively. these three complexes show very close values of activation energy, temperature-range and reaction order for the dehydration reactions as summarized in table 1. table 1. characteristic parameters of thermal decomposition (10°c min-1) for a; fe(ii), b; co(ii) and c; ni(ii) polymer complexes. tga peak comp. step wt. loss % obs. (theor.) ti/°c tf/°c tdtg tdta n ea/ kj mol -1 heat/ j reaction 1 11.46 (11.49) 20 95 43 52 2.5 84.20 -0. 245 2.5h2o (ads) 2 27.11 (27.28) 190 442 378 306, 423 0.5 46.16 -0.719, 1.05 [2h2o (coor) + 2cl] a 4 41.86 (41.87) 442 564 480 474, 546 598 2.1 335.44 0.285, 0.118 1.92 [89.1% of bba] phase transfer final residual weight; (found 19.57%, cal. 19.36%) 1 9.20 (9.33) 25 96 48 47 2.5 84.6 -0.0897 2 h2o (ads) 2 2.31(2.33) 99 146 119 2.2 124.72 -25% of 2h2o (coor) 3 7.01 (7.0) 148 255 199 0.8 51.65 -75% of 2h2o (coor) 4 18.40 (18.36) 258 471 301 3 96.29 2cl 5 31.13 (31.11) 485 586 515 515 597 3.5 578.05 7.07 1.20 [ 65.2% of bb] phase transfer b 6 3.40 (3.34) 826 897 868 833 2 1103.46 0.94 [7% of bb] final residual weight; (found 28.55%, cal. 28.53%) 1 5.01 (4.9) 30 90 55 54 2 84.10 0.44 h2o (ads) 2 4.73 (4.9) 90 150 113 111 2.2 112.8 0.15 h2o (coor) 3 4.97 (4.9) 155 227 210 0.6 68.99 h2o (coor) 4 19.28 (19.27) 229 350 271 265 3 209.05 0.69 2cl 5 14.81 (14.97) 350 518 452 1.4 84.15 0.66 [ 29.9% of bb] c 6 35.19 (35.11) 518 728 650 551 674 2.4 235.95 0.80 1.52 [ 70.1% of bb] final residual weight; (found 16.01%, cal. 15.95%) abb; backbone components (i.e. organic ligand around the metal) in this dehydration process, the ease of adsorbed water desolvation (20°c ≤ t ≤ 96°c) in these complexes suggests the weak interaction of water, i.e. water plays little or no role in the lattice forces and occupies the crystal voids (donia et al 1997 and byran 1982). the small differences in the tdtg values (43, 48 and 55°c), the exothermic peaks with small differences in the tdta values (52, 47 and 54°c) and the activation energies of almost similar values (84.2, 84.6 and 84.1 kj mol-1 for the fe, co and ni complexes, respectively) suggest that 5 hussein m. al-maydama et al. the adsorbed water in these complexes may be identical. the shape and the strength of the dehydration dtg peaks indicate that the rate of dehydration in these complexes is almost similar. figure 1. tga and dtg the heating rate of 10°c °c min-1 a b r . c mograms of the ppt complexes of fe (a), co (b) and ni (c) in nitrogen at the 6 behaviour of thermal degradation in the tg curves (figure 1), continuous and slow bleed of weight losses are observed at the 190-442°c, 99-255°c and 90-227°c ranges for the polymer complexes of fe, co and ni, respectively. these ranges are in good agreement with the temperature ranges reported (al-maydama et al 2006; donia et al 1997; donia and elboraey 1993) for the release of coordinated water molecules in some complexes of fe, co and ni metals. the second-step (190-442°c) of fe-complex occurs with a broad and weak peak tdtg at 378°c and two broad exothermic peaks (tdta) at 306°c and 423°c. as a result, the weight loss of 27.11% indicates that the ppt-fe complex continuously loses its two molecules of coordination water along with the two chlorine atoms (theor. 27.28%) in one step. this step seems to be due to a complete overlapping of two consecutive steps, as the two consecutive dta peaks (306°c and 423°c) indicate. at the 99-255°c range, the ppt-co complex loses its two molecules of coordination water in two steps, i.e. second and third steps. the second-step (99-146°c) of a weak and broad tdtg (119°c) indicates the loss of 25% of the two water molecules (obs. 2.31%, theor. 2.33%), while the third-step (148-255°c) of a very weak and broad tdtg (199°c) indicates the loss of the remaining 75% of the two water molecules (obs. 7.01%, theor. 7.0%). the 90-227°c range in the ppt-ni complex is for the second and third steps as the complex loses one molecule of its coordination water at each step. the second-step (90-150°c) of a broad tdtg (113°c) and a small exothermic peak tdta (111°c) corresponds to the first molecule of coordination water (obs. 4.73%, theor. 4.90%), and the third-step (155227°c) of a very weak and broad tdtg (210°c) is assigned to the second water molecule (obs. 4.97%, theor. 4.90%). hence, the ppt-ni complex shows more clearly the loss of two coordination water molecules in two steps; one molecule in each step. the activation energies of the second-step reactions are calculated for the polymer complexes of fe (46.16 kj mol-1), of co (124.72 kj mol-1) and of ni (112.8 kj mol-1), while for the third-step reactions the activation energies 51.65 kj mol-1 and 68.99 kj mol-1 are determined for the complexes of co and ni, respectively. the weight loss (18.40%) at the fourth-step (258-471°c) of a very weak and broad tdtg (301°c), and the weight loss (19.28%) at the fourth-step (229-350°c ) of a large and strong tdtg (271°c) and a broad exothermic peak tdta (265°c) are assigned to the release of two chlorine atoms in the ppt-co (theor. 18.36%) and ppt-ni (theor. 19.27%) complexes, respectively. the temperatures reported (al-maydama et al 2006; donia et al 1992; donia et al 1997; donia and el-boraey 1992 and donia 1993) for the release of chlorine in some complexes of nickel (270°c, 315°c, 220-374°c, 217-291°c ) and in that of cobalt (300°c, 340°c, 300-400°c) are in accordance with that obtained. the activation energies calculated for the release of these two chlorine atoms in the complexes of co and ni are 96.29 kj mol-1, and 209.05 kj mol-1, respectively. as preceded, the complex of cobalt and that of nickel both lose their two coordination water in two overlapping or consecutive steps. the slow rate of releasing the water molecules, temperature range, order of reaction and activation energy observed for the two steps in complex of cobalt and in that of nickel are somewhat comparable (table 1). this reflects similarity in the kinetic and nature of the activated molecule of these two complexes at the transition-state reaction. in the contrary, although the cobalt and nickel complexes lose their two chlorine atoms in one step at about nearly close temperature ranges with similar order of reaction, the activation energies associated with this reaction in the two complexes are vastly incomparable. this is because of various kinetic and nature of both complexes at the transition-state, i.e. their activated molecules are of different reaction nature. hence, slow elimination of the chlorine atoms with a lower activation energy (96.29 kj mol-1), and the rapid one with a higher activation energy (209.05 kj mol-1) are observed for the cobalt and nickel complexes, respectively on the other hand, if the initial temperatures (ti) concerning the release of the coordination water and then the chlorine atoms (table 1) are taken as a measure of the thermal stabilities of these complexes, the iron complex (190°c) show a higher thermal stability than those of cobalt and nickel, i.e. on the basis of ti values, the thermal stability of these complexes follows the order: fe> co> ni. this can be discussed in terms of the repulsion among electron pairs in the valence shell of the central ion. iron, cobalt and nickel ions in the investigated complexes have multiple bonding (six bonds) in their valence shells. but due to the higher electronegativity of nickel than that of cobalt and iron, the space occupied by a bonding pair in the valence shell of nickel is greater than that of cobalt and iron. this leads to a higher repulsion between the bonding pairs in the 7 hussein m. al-maydama et al. valence shell of nickel (smallest ionic size, i.e. ni < co < fe), which in turns alter the bond angles from those of ideal octahedral, giving a lower stability (moeller 1982 and malik et al 1998 ). for this reason, the complex of ni loses its coordinated water and bonded chlorine more rapidly than the others as indicated by the apparently strong peaks (tdtg) at 113°c and 271°c, respectively. a figure 2. dta and drdt heating rate of 10°c °c mi b c n a thermograms of the ppt complexes of fe (a), co (b) and ni (c) in nitroge at the n-1. 8 behaviour of thermal degradation 9 the third-step (442-564°c) of a large and strong tdtg (480°c) and two very weak and broad successive endothermic peaks with a tdta of 474°c and 546°c is due to a complete breakdown of the ppt-fe backbone structure. the weight loss found (41.86%) is attributed to the elimination of 89.1% of the backbone components (theor. 41.87%). the final residual weight found (19.57%) corresponds to an ill-defined final decomposition product (theor. 19.36%). the activation energy calculated for this step is 335.44 kj mol-1. the large and strong endothermic peak (tdta) at 598°c which does not correspond to any weight loss in the tg curve may be due to some change in the crystalline structure of the final residue. the complete decomposition of the ppt-co backbone structure occurs at the fifth-step (485-586°c) of a large and strong tdtg (515°c) and a large and strong endothermic peak with a tdta of 515°c. at this stage, the weight loss found (31.13%) in thetg curve indicate the elimination of 65.2% of the backbone (theor. 31.11%). this leaves the deposition of a residue of an ill-defined compositom (theor. 31.87%) that corresponds to the residual weight found (31.95%) in the tg curve at the end of this step. the small endothermic peak (tdta) at 597°c which does not correspond to any weight loss in the tg curve may be due to some change in the ructure st tof the residual deposit. however, the weight loss (3.40%) at the small sixth-step (826-897°c) with a dtg of 868°c and a large and broad endothermic peak (tdta) of 833°c is assigned to the decomposition of the residual deposit (i.e. residue) by losing 7% of the backbone components or 10.48% of the residue (theor. 3.34%). the final decomposition product of an ill-defined composition found and calculated are 28.55% and 28.53%, respectively. the activation energies calculated for the fifth and sixth-step are 578.05 kj mol-1 and 1103.46 kj mol-1, respectively. in the tga curve (figure 1c), it can be seen clearly that a complete breakdown of the ppt-ni backbone structure takes place in two consecutive steps, i.e. fifth and sixth-step. at the fifth-step (350-518°c) of a broad exothermic peak (tdta) at 452°c, the ppt-ni complex loses 29.9% of its backbone components (theor. 14.97%) at slow rate corresponding to the weight loss found (14.81%). the weight loss found (35.19%) at the sixth-step (518-728°c) of a very large and broad tdtg (650°c) with a very broad exothermic peak tdta (674°c) indicates the rapid loss of the remaining 70.1% of the backbone components (theor. 35.11%). the final decomposition product of an ill-defined composition (theor. 15.95%) corresponds to the residual weight found (16.01%) in the tg curve at the end of this step. the irregular shape of the dtg curve in the (518-728°c) range and the endothermic peak (tdta) at 551°c indicate more than one reaction took place in the sixth-step. the activation energy determined for the fifth and sixth-step are 84.15 kj mol-1 and 235.95 kj mol-1, respectively. at the stage after the release of coordination water and chlorine the iron, cobalt and nickel ion in the complexes are converted from multiple bonding (six bonds) to lower bonding (two bonds) in their valence shells. in consequence, it is noteworthy that the situation here may be inverted with lower coordination numbers, where the repulsion between electron pairs is decreased. therefore, the electronegativity of the central metal ion becomes the predominant factor in the stability (donia et al 1992). this is evident in the complete decomposition of the backbone structure of the iron, cobalt and nickel complexes, if the initial temperature (ti) of the complete backbone decomposition is used as a measure of the thermal stability. this can be discussed as follows: 1) in the case of iron and cobalt complexes, the complete decomposition of their backbone structure that takes place rapidly in one single step suggests a higher thermal stability (485°c) for cobalt than that for iron (437°c). this is also confirmed by the values of the maximum rate temperature of weight loss (tdtg) at 515°c and 480°c determined for the backbone decomposition in the cobalt and iron complexes, respectively. the small thermal stability difference (48°c) between the backbone decomposition in cobalt and that in iron, and also the small difference (35°c) between the values of their tdtg may be attributed mainly to the higher electronegativity of cobalt than that of iron. 2) unlike the iron and cobalt complexes, the nickel complex shows two initial tem eratures (350°cp and 518°c) indicating two thermal stabilities for the two successive steps in the decomposition of the backbone.the lower thermal stability (350°c) may be related to the strain that the backbone structure of nickel experiences more due to the smaller ionic size of nickel relative to that of cobalt and iron. this interpretation is confirmed by the tg weight loss (14.81%), which relieves the strain in the backbone by the decomposition of about 30% of the hussein m. al-maydama et al. backbone components (14.97%), and consequently one more step of a higher temperature range (518-728°c) is required for the completion of the backbone decomposition. the higher thermal stability (518°c) due to the completion of the backbone decomposition with a higher ay be attributed to the higher electronegativity of nickel than that of cobalt. al-a al-m .nist.. 001. introduction to thermal analysis. techniques and applications, 2nd edition, kluwer academic publishers, london. . solid tatechemistry of druge, academic press, new york, london. chang, t.c., yang, c.w., wu, k.h., and chiu, y.s. 2000. organic-inorganic hybid materials 3 coat don te thermal polymorphic tdtg of 650°c can be attributed to the higher electronegativity of nickel than that of iron and cobalt, proving the predominant roll of the electronegativity in the stability. the higher thermal stability difference (135°c) between the complete and the partial decomposition of the backbone in both complexes of cobalt and nickel, respectively, reflects the strain in the backbone angles may be due to mainly the smaller ionic size and partially the higher elecronegativity of nickel than those of cobalt. however, the small thermal stability difference (33°c) between the completion of the backbone decomposition in the complex of nickel and the complete backbone decomposition of cobalt m 4. conclusion the thermal properties of these three metal-complexes were investigated and the activation energy of each step in the decomposition sequences was determined by using costs-redfern expression. the almost similar kinetic parameters and the tdta values of the dehydration suggest that adsorbed water molecules in these complexes are identical. the activation energies of the two coordinated water in the cobalt and nickel complexes are of close values, indicating similar kinetic and decomposition reactions nature of the activated complexes at the transitionstate. however, the differences in the activation energies values for the release of the two chlorine atoms and that for the backbone structure distraction are due to different kinetic and nature of the activated complexes decomposition reactions at the transition-state. although the three complexes are of a particular ligand with a variety of metals, their tga curves exhibit various and not identical decomposition reactions. this may be attributed to the various metals and not to the particular ligand. 6. references wadi, n.a., shuaib, n.m., abbas, a., el-sherif, a.a., el-dissouky, a. and al-saleh, e. 2008. synthesis, characterization, and biological activity of n1-methyl-2-(1h-1,2,3-benzotriazol-1-y1)3-oxobutanethioamide complexes with some divalent metal (ii) ions. bioinorganic chemistry and application. vol. 2008, article id 479897, 10 pages. doi:10.1155/2008/479897. aydama, h., a, khalid, m.a. and al-karbouly, a. 2006. thermal degradation behaviour of some polydithiooxamide metal complexes. ecl. quim., sao paulo, 31(1): 45-52. bora, m.n. 2000. thermophysical properties of some medicinal plant leaves 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complexes containing m diethyldithiocarbamate ligand., synth react inorg met-org chem, 31(3): 457-469. ived 30 april 2008 11 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 83-95 © 2003 sultan qaboos university effect of mechanical injury and low temperature storage on the accumulation of glycoalkaloids in the tubers of 7 varieties of potato (solanum tuberosum l.) grown in oman elsadig a. eltayeb*, sana salem al-sinani* and i. a. khan** *department of biology, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman; email: eatayeb@squ.edu.om, **department of crop science, college of agriculture, sultan qaboos university. تأثير جروح وإصابات درنات البطاطس وتخزينها في درجات حرارة منخفضة على تراآم األلكالويدات السكرية في درنات أنواع من البطاطس التي تزرع في سلطنة عمان7 الصادق عبداهللا الطيب ، سناء سالم السناني وإقرار خان أثيرات البيئية مثل التخزين تحت البطاطس األلكالويدات في درناتتمت دراسة صناعة وتراآم لقد : خالصة آنتيجة لبعض الت وجدت الدراسة أن . درجة حرارة منخفضة أو آنتيجة للجروح أو أي إصابة للدرنات وهو ما يمكن أن يحدث أثناء النقل والتخزين حرارة منخفضة يزيد من التخزين في درجة آما وجدت الدراسة أن . األلكالويداتالجروح واإلصابات عموما تزيد من ترآيز .م4ºم آان أآبر منه في درجة حرارة 10ºترآيز في درجة األلكالويدات ولكن مستوى الترآيز abstract: tubers from 7 potato varieties were analyzed for their rates of glycoalkaloid accumulation in response to stresses of three types of mechanical injury and low temperature storage. mechanical injuries were found to greatly stimulate glycoalkaloid accumulation in both peel and flesh of tubers. the extent of glycoalkaloid accumulation appears to depend on variety, type of mechanical injury, and storage period. most of the injury-stimulated glycoalkaloid accumulation occurred within 7 and 14 days after treatment. cutting the tubers resulted in the highest content of glycoalkaloids both in flesh and peel up to levels that exceeded the upper safety limit of 200 mg/kg fw. injury stimulated α-solanine accumulation in stored potato tubers is more than α-chaconine, resulting in a decrease in the α-chaconine: α-solanine ratio. when tubers were stored at low temperature, the rate of glycoalkaloid accumulation was found to be independent of the glycoalkaloid level at harvest. the greatest increase in total glycoalkaloid content of the seven varieties was found after two weeks of storage at both 4 ºc and 10 ºc. further storage at these temperatures resulted in a decrease in the rate of glycoalkaloid accumulation in most of them. at 10 ºc glycoalkaloid content tended to increase more rapidly than at 4 ºc. the α-solanine content of the tubers showed an increase following low temperature storage. keywords: potato, solanum tubersum , glycoalkaloids, chaconine, solanine, hplc, mechanical injury and low temperature storage. 1. introduction p otato, a member of the solanaceae family, is consumed by millions of people every day. the potato tuber contains natural bitter-tasting steroidal toxicants, known as glycoalkaloids (ga) (smith et al. 1996). the principal glycoalkaloids found in potato tubers are α-solanine and αchaconine (dale et al. 1998; sotelo and serrano, 2000). 83 mailto:eatayeb@squ.edu.om elsadig a. eltayeb, sana salem al-sinani and i.a. khan glycoalkaloids are thought to function in the chemical defense of the plant, as nonspecific protectors or repellents against potential pest and predators (roddick, 1989). they are found throughout the potato plant with the highest levels observed in those parts of the plant with high metabolic rates (van gelder, 1990). tubers have much lower glycoalkaloid content than foliage and the distribution is not uniform, with higher levels found in the periderm and cortex decreasing markedly towards the pith (dale et al. 1998). the majority of current commercial varieties have been reported to have their average ga content below 150 mg/kg fresh weight (fw) (van gelder, 1990). concentrations in the range 10-150 mg/kg fw are regarded as acceptably low, while glycoalkaloid concentration exceeding 200 mg/kg fw gives a bitter taste and can cause gastroenteric symptoms, coma, and even death (gregory, 1984). consequently potato tubers containing >200 mg glycoalkaloids kg-1 fresh weight exceed the limit recommended for food safety and should be withdrawn from sale (percival and dixon, 1994). the total glycoalkaloid level in potato tubers is controlled by genetic as well as environmental factors (dale et al. 1998). potato grown in oman is faced with varying degrees of heat stress. breeders have been screening potato varieties adapted to local conditions (khan et al. 2001, 2002). potato glycoalkaloids represent a threat not only to certain microbial pathogens and herbivores, but also to man if excessive quantities are inadvertently ingested (morris and lee, 1984). because of the importance of glycoalkaloids in the quality of potatoes and their resistance to disease, the present investigation was undertaken with a view to finding out the accumulation rate of glycoalkaloids in tubers exposed to postharvest stress such as mechanical damage and low temperature storage. although the nature and relative concentrations of glycoalkaloids are genetically determined, the total concentrations are certainly influenced by environmental factors during the growing period (friedman and mcdonald, 1997). elevated glycoalkaloid levels may be caused by adverse growing conditions such as prolonged cold, extreme heat, too much water, too little water, too much sunshine, or too little sunshine (friedman and mcdonald, 1997). also glycoalkaloids, which are usually present at low levels in commercial potatoes, may accumulate as a result of continued biosynthesis. environmental and storage factors may influence glycoalkaloid formation (friedman and mcdonald, 1997). more glycoalkaloid concentrations were reported as a result of storage at lower temperatures than at higher temperatures by griffiths et al. (1997). any injury or damage to the potato plant or tuber is thought to result in glycoalkaloid accumulation. thus disease or insect attack to the plant as well as rough tuber handling during harvest or distribution will initiate glycoalkaloid synthesis (maga, 1994). 2. experimental potato samples: seed tubers of 7 exotic potato varieties were harvested in mid march 2000 and cold-stored up to mid october 2000. the plants were grown in two periods: the first from mid-november 2000 to mid-february 2001 and the second from mid-december 2000 to midmarch 2001 at the agricultural experiment station, sultan qaboos university, muscat, oman. the plants were grown in sandy loam soil of 49% sand, 34% silt and 12% clay. fertilizer was added as n:p:k in the ratio of 2:1:1 with n given as 224 kg ha-1. irrigation was scheduled according to evapotranspiration data, which was averaged for 90 days at about 51 m3d-1ha-1. during that period the total precipitation was 30 mm and the average day temperature was 31°c (overall average temperature was 21°c). the average relative humidity was 62% and the average day-length was 12.5 hours, with average total radiation of 16 cal./hr.cm2 (186 w/m2). the average net solar radiation was 7 cal./hr.cm2 (81.75 w/m2). 84 effect of mechanical injury and low temperature storage supplies: α-solanine and α-chaconine standards were obtained from sigma chemical co., st. louis, mo, usa. acetonitrile was hplc grade from bdh laboratory supplies (poole, u.k.). the water used was deionized and further purified using the milli-q purification system from millipore corp. (bedford, ma, usa). all other solvents and chemicals used were of standard analytical grades (bdh laboratory supplies, poole, uk). chemical analysis: tuber α-solanine and α-chaconine content was determined using an improved version of hplc procedure described by hellenas et al. (1995). 12 tubers of uniform size and without greening or fungal infection were collected from each of the 18 varieties, cleaned, weighed, and peeled with a domestic potato peeler. peels of 2 mm thickness were removed and the ratio of peels to total weight was recorded. alkaloid extraction and clean up: the extraction method was a modification of that used by hellenas et al. (1995). details are as follows: samples (10 g) of peel and flesh were mixed with 20 ml of water/acetic acid/sodium bisulphate (nahso3), 95:5:0.5 (v/v/w), for five minutes using a blender (moulinex, france). the mixture was diluted to a final volume of 50 ml with the same solvent, and was then vacuum filtered through a whatman no. 1 filter paper. the sample was cleaned up by centrifuging at 5000g (6500 rpm) for 10 minutes in centrikon t-124 centrifuge (kontron, italy). a seppak classic c18 extraction cartridge (waters corporation, milford, ma, usa) was conditioned by the passing through of 5 ml of acetonitrile, followed by 5 ml of the water/acetic acid/nahso3 solvent, and a 10 ml sample of the tuber extract was then passed through followed by 4 ml water/acetonitrile, 85:15 (v/v), for washing. the glycoalkaloids were eluted from the cartridge with 4 ml of the acetonitrile/0.022m potassium phosphate buffer, ph 7.6, 55:45 (v/v), and the volume was finally adjusted to 5 ml with the same solvent. high performance liquid chromatography (hplc): α-solanine and α-chaconine were separated and quantified using an hplc apparatus consisting of a waters 626 pump, a waters 717 plus autosampler, a waters 996 photodiode array (pda) detector, and controlled with millennium 32 software. the analytical column was a 250 x 4.6 mm id supelcosiltm lc-nh2 5 µm (supleco park. bellefonte, pa, usa). the mobile phase was acetonitrile/0.022 m potassium dihydrogenphosphate (kh2po4) buffer, ph 4.7, 75:25 (v/v) pumped at a flow rate of 1.0 ml min-1. the column effluent was monitored for uv absorption at 200 nm wavelength and 0.05 aufs sensitivity. the volume of the injected samples was 20 µl. the retention times for α-chaconine and α-solanine were approximately 7 minutes and 10 minutes, respectively. α-solanine and αchaconine concentration in sample extracts were quantified by comparing the peak areas with those of injected known amounts of pure standards. recovery of glycoalkaloids (sigma) that were added to samples averaged (93%). mechanical damage: potato tubers of each variety without any mechanical and pathological injuries were randomly selected and hand washed prior to treatments. four treatments including controls and three types of mechanical injuries on potato tubers were arranged. there were three replicates. the mechanical injury treatments included dropping, puncturing with a nail and cutting. dropping was done by dropping each tuber 6 times from a height of 2 m, cutting was done by cutting lines 1 cm deep and 1 cm apart into tubers (6 lines/tuber) and puncturing was done by making a hole of 3 mm diameter to the depth of 1 cm with two holes cm-2 (max. 10 holes tuber-1). zero time samples were taken from each variety. tubers were sampled immediately and after 7, 14 and 21 days of storage. peel and flesh were separated and analyzed for their glycoalkaloid content. temperature: tubers from each variety were randomly selected and hand washed prior to treatments. three replicates from each variety were stored at the following temperatures: constant 4 ºc for 0, 2, 4, 6 weeks, constant 10 ºc for 0, 2, 4, 6 weeks, variable: a) 3 weeks at 4 ºc followed by 3 weeks at 10 ºc and b) 3 weeks at 10 ºc followed by 3 weeks at 4ºc. peel and flesh tissues were separated and analyzed for their glycoalkaloid content. 85 elsadig a. eltayeb, sana salem al-sinani and i.a. khan figures and statistical analysis: figures were prepared using the computer software graphpad prism version 2.01, which has a statistical package for the analysis of data in the graph. 3. results and discussion 3.1 dropping figure 1 and tables 1-3 show the results of dropping on the glycoalkaloid contents of whole tubers, peel and flesh of potato tubers after 3 weeks of storage. the total glycoalkaloid (tga) content of four of the treated varieties increased significantly as a result of dropping while the remaining three turbo, l. clair and spunta varieties were less sensitive to this treatment and their total glycoalkaloid content decreased by 43, 86 and 176 mg/kg fw, respectively. most of the glycoalkaloid accumulation occurred within 2 weeks after treatment with some further increase after 2 weeks (table 2). with l. rosseta, aida, and atlas varieties, however, the rate of glycoalkaloid accumulation decreased after this period for the rest of the varieties treated. aida atlas clair diamant rosseta spunta turbo 0 250 500 750 1000 1250 1500 at harvest 1 week dropping 2 weeks dropping 3 weeks dropping varieties t g a m g/ kg f re sh w ei gh t figure 1. effect of dropping on the accumulation of glycoalkaloids in the tubers from 7 potato varieties grown in oman. l. rosseta and atlas were the most sensitive to the dropping treatment, as after three weeks their tubers contained 4.6 times and 2.3 times glycoalkaloid as before treatment. diamant and aida showed a slight increase of 1.7 times and 1.3 times respectively. after one week of storage, the total glycoalkaloid content in the flesh of the dropping treated potatoes was 11 times higher than before treatment for l. rosseta, 8 times higher for diamant, 3 times for spunta and atlas. the flesh total glycoalkaloid content of l. clair increased from 0 to 34 mg/kg after one week of the dropping treatment. the flesh glycoalkaloid content of all varieties decreased during the last two weeks of the treatments. this decrease coupled with high tuber tga indicates that the glycoalkaloid synthesis was stimulated and 86 effect of mechanical injury and low temperature storage continues in the peel during this period. with the exception of atlas, the flesh glycoalkaloid content of most of the dropping treated potatoes remained below the upper safety limit of 200 mg/kg fw. higher glycoalkaloid content was detected in the peel tissue than in the flesh (table 2). the extent of glycoalkaloid accumulation depends on the cultivar and duration of storage. the relative α-solanine content of the dropping treated potato tubers increased after 3 weeks to between 35 41% (α-chaconine content 59 65%) compared to that of 19 29% α-solanine before treatment (71 81% α-chaconine). this synergy is still considered high (table 3). because it has been demonstrated that the maximum synergy was exhibited between 60:40 and 40:60 (αsolanine: α-chaconine) ratios (fewell and roddick, 1993), these authors also reported that as little as 10-20% of either glycoalkaloid in the mixture is sufficient to initiate a marked synergism, especially chaconine, which suggests a significant saving in metabolic cost by the plant through the operation of the synergism. table 1: tga levels (mg/kg fresh weight) in the tubers of 7 potato varieties grown in oman after 3 types of injury. cutting puncturing dropping 1 wk 2 wks 3 wks 1 wk 2 wks 3 wks 1 wk 2 wks 3 wks f p f p f p f p f p f p f p f p f p diamant 117 323 254 680 206 603 113 310 101 340 156 406 113 266 123 367 50 348 turbo 92 377 92 316 110 295 90 57 92 166 36 254 30 194 41 171 36 165 l. rosseta 208 727 237 322 165 616 91 539 50 532 36 464 76 208 155 504 134 750 l. clair 82 255 204 484 213 522 31 346 64 266 60 206 34 44 76 311 26 293 spunta 161 434 233 474 124 67 45 31 85 253 55 270 132 258 62 222 75 213 aida 279 369 219 555 228 562 122 555 161 393 93 422 26 118 124 494 191 442 atlas 250 435 326 541 381 572 157 203 285 469 301 1126 208 556 149 397 412 774 f = flesh, p = peel, tga = the sum of a-solanine and a-chaconine. table 2: percentage peel and flesh tga of 7 potato varieties grown in oman after 3 types of injury. cutting puncturing dropping % flesh ga % peel ga % flesh ga % peel ga % flesh ga % peel ga 1 wk 2 wk 3 wk 1 wk 2 wk 3 wk 1 wk 2 wk 3 wk 1 wk 2 wk 3 wk 1 wk 2 wk 3 wk 1 wk 2 wk 3 wk variety 27 27 26 73 73 74 27 23 28 73 77 72 30 25 13 70 75 87 diamant 20 22 27 80 78 73 61 36 12 39 64 88 13 19 18 87 81 82 turbo 22 42 21 78 58 79 14 8 7 86 92 93 13 24 15 87 76 85 l. rosseta 24 30 29 76 70 71 8 22 22 92 78 78 43 20 8 57 80 92 l. clair 27 33 65 73 67 35 57 25 17 43 75 17 34 22 26 66 78 74 spunta 43 28 29 57 72 71 18 29 18 82 71 82 18 20 30 82 80 70 aida 36 38 40 64 62 60 44 38 21 56 62 79 27 27 35 73 73 65 atlas 27 27 26 73 73 74 27 23 28 73 77 72 30 25 13 70 75 87 3.2 cutting after one week of treatment all of the cut potatoes contained higher glycoalkaloid content than the control ones; however, after three weeks of storage the rate of glycoalkaloid accumulation decreased in the diamant, turbo, l. rosseta, and spunta varieties. some varieties showed an increase in glycoalkaloid content after one week of storage reaching 744 mg/kg in l. rosseta, 225 mg/kg in turbo, 196 mg/kg in diamant, 159 mg/kg in atlas, 154 mg/kg in aida, and 132 mg/kg in spunta, whereas a decrease in total glycoalkaloid content of l. clair was observed after one week of treatment. (figure 2 and tables 1-3). 87 elsadig a. eltayeb, sana salem al-sinani and i.a. khan table 3: chaconine: solanine ratio in the tubers of 7 potato varieties grown in oman after 3 types of injury. cutting puncturing dropping chaconine: solanine ratio chaconine: solanine ratio chaconine: solanine ratio variety 1 wk 2 wks 3 wks 1 wk 2 wks 3 wks 1 wk 2 wks 3 wks diamant 59:41 63:37 65:35 53:47 59:41 57:43 52:48 68:32 62:38 turbo 64:36 73:27 60:40 69:31 65:35 66:34 81:19 64:36 60:40 l. rosseta 60:40 46:54 61:39 51:49 60:40 64:36 53:47 67:33 59:41 l. clair 65:35 69:31 65:35 66:34 85:15 67:33 71:29 74:26 71:29 spunta 68:32 65:35 79:21 88:12 75:25 87:13 61:39 61:39 64:36 aida 67:33 70:30 64:36 73:27 61:39 69:31 94:06 63:37 65:35 atlas 62:38 60:40 60:40 72:28 62:38 62:38 66:34 67:33 61:39 aida atlas clair diamant rosseta spunta turbo 0 250 500 750 1000 1250 at harvest 1 week cutting 2 weeks cutting 3 weeks cutting varieties t g a m g/ kg f re sh w ei gh t than turb time treat resp in to figure 2. effect of cutting on the accumulation of glycoalkaloids in the tubers from 7 potato varieties grown in oman. after one week of treatment, the content of glycoalkaloid in l. rosseta was 5 times higher before treatment while it was 4 times higher for diamant and only two times higher for o. varieties continued to accumulate glycoalkaloids after three weeks l. clair and atlas 1.8 s, aida 1.6 times. l. rosseta and diamant were the most sensitive varieties to the cutting ment and showed the highest increase in total glycoalkaloid contents of 5 times and 4 times ectively, whereas spunta and aida were the least sensitive which showed the lowest increase tal glycoalkaloid of 1.5 times as before the treatment. 88 effect of mechanical injury and low temperature storage most of the glycoalkaloid accumulation in the flesh occurred within 2 weeks of treatment, although there was further increase after 3 weeks, but that was rather small in turbo, l. clair, aida and atlas. however, the glycoalkaloid level in the flesh of diamant and l. rosseta started to decrease after 3 weeks of storage (table 1). the highest increase in glycoalkaloid accumulation was recorded for the flesh of l. clair, as its total glycoalkaloid increased from 0 to 213 mg/kg fw after 3 weeks of the cutting treatment. this was followed by l. rosseta, which contained 29 times as much glycoalkaloid, 18 times for diamant and 6 times for spunta after 2 weeks. after 3 weeks, the flesh tga content of atlas was 5 times higher than before treatment, 3 times for turbo and 2.3 times for aida. in general, after the cutting treatment, the flesh of most of the seven varieties (except turbo) contained total glycoalkaloid content, which was well above the upper safety limit of 200 mg/kg fw. cutting also stimulated glycoalkaloid synthesis and accumulation in peels of potato tubers. after one week peels from the cut potatoes of l. rosseta contained 4 times as much glycoalkaloid as before treatment and twice as much for turbo, but after 2 weeks they contained 4 times tga for diamant and 1.1 times for spunta. after 3 weeks aida peels contained 1.4 times tga content as before the treatment, 1.3 times for l. clair and 1.2 times for atlas. the effect of the cutting treatment on the relative content of α-solanine was similar to that of the dropping treatment. 3.3 puncturing after one week of treatment, puncturing stimulated synthesis and accumulation of glycoalkaloid in the tubers of most of the potato varieties with the exception of l. clair and spunta, where the tga content decreased by 28 mg/kg fw and 386 mg/kg fw, respectively. after a further 3 weeks of storage, an increase in the total glycoalkaloid content was recorded for diamant, turbo, and atlas, but the total glycoalkaloid content for l. rosseta and aida decreased. the total glycoalkaloid content of the punctured potatoes was found to be 3.3 times as much tga for l. rosseta and 1.4 times for aida after one week, whereas it was 2.7 times for atlas, 2.3 times for diamant, and 1.2 times for turbo after three weeks. this indicates that l. rosseta and atlas were the most sensitive to the puncturing treatment, while turbo was the least sensitive. after one week the flesh total glycoalkaloid content of the punctured potatoes was 11 times higher than before treatment for l. rosseta, whereas after 2 weeks it was 3 times higher for turbo, and 1.6 times for aida. after 3 weeks, the flesh total glycoalkaloid content of diamant was 11 times higher than before treatment and 4 times for atlas. although puncturing greatly stimulated glycoalkaloid synthesis and accumulation in the flesh of most of the varieties, the flesh total glycoalkaloid content of these varieties was still below the upper safety limit of 200 mg/kg fw with the exception of atlas, which had tga content higher than the upper limit of food safety after the treatment (tables 1-3, figure 3). the tga accumulation that was stimulated in the peels by the puncturing treatment after one week was 3 times higher for l. rosseta and 1.4 times for aida, but after 3 weeks it was 2.5 times higher for atlas, twice for diamant, and 1.2 times for turbo. the relative content of α-solanine of the punctured potato tubers increased after 3 weeks to be between 31-43% (corresponding to a relative α-chaconine content between 57-69%) compared to that of 19-29% α-solanine before treatment (corresponding to 71-81% α-chaconine). our results show that the extent of glycoalkaloid accumulation depends on variety, type of mechanical injury and duration of storage. following treatment, the flesh and peel of most of the mechanically injured potatoes contained higher total glycoalkaloid content than the control. these results agree with the conclusions made by wu and salunkhe (1976) from three cultivars; ahmed and muller (1978) from two cultivars; olsson (1986) from a range of cultivars; and of dale et al. (1998). this increase could be attributable to either localized synthesis in response to damage 89 elsadig a. eltayeb, sana salem al-sinani and i.a. khan triggered by some form of elicitor or to diffusion or transfer of synthesized glycoalkaloids from the damaged areas. aida atlas clair diamant rosseta spunta turbo 0 250 500 750 1000 1250 1500 at harvest 1 week puncturing 2 weeks puncturing 3 weeks puncturing varieties t g a m g/ kg f re sh w ei gh t figure 3. effect of puncturing on the accumulation of glycoalkaloids in the tubers from 7 potato varieties grown in oman. injury stimulated glycoalkaloid accumulation in flesh and peels occurred within 7-14 days after treatment, which is consistent with previously reported work (wu and salunkhe, 1976). of the three treatments, cutting the tubers appeared to be the most effective as it resulted in the highest total glycoalkaloid content in both flesh and peel of potato tubers. cutting greatly stimulated glycoalkaloid synthesis and/or accumulation in the flesh of most potato varieties to very high and unsafe levels of much more than 200 mg/kg fw. puncturing and dropping also stimulated glycoalkaloid synthesis and accumulation in the flesh but to a lesser extent than cutting and to tga levels that do not exceed the upper safe limit. glycoalkaloid accumulation in the flesh after the puncturing and dropping treatments was higher than in the peel, which indicates that puncturing and dropping caused more injury and as a result more glycoalkaloid accumulation in the flesh than in the peel. glycoalkaloid accumulation as a result of dropping seems to depend on the severity of the damage as well as damage susceptibility of the variety. dropping damage during harvest and storage operations can result in various types of injury including bruising, shattering, cracking and splitting leading to glycoalkaloid accumulation. there was a wide variation between varieties in their susceptibility to the types of injury tested in this work. of the seven varieties, l. rosseta was the most sensitive to all three types of injury treatments. however, diamant was highly sensitive to the cutting treatment, whereas spunta and aida were the least sensitive to this treatment. l. clair and spunta were insensitive to the puncturing treatment, while atlas was highly sensitive to it. atlas was more sensitive to the 90 effect of mechanical injury and low temperature storage dropping than the cutting treatment, whereas turbo was insensitive to the dropping while l. clair and aida accumulated glycoalkaloid to a lesser extent than the other varieties in response to dropping. the observed low increase is probably attributable to the severe tissue reaction and cell death throughout the tuber in response to severe damage. no relationship was found between the initial total glycoalkaloid levels and the extent of glycoalkaloid accumulation after injury treatment. for example, l. rosseta, which had the lowest initial total glycoalkaloid content (< 200 mg/kg fw) was the most sensitive to the three types of injury and accumulated glycoalkaloid content to levels of more than 200 mg/kg fw, and spunta, which had very high initial total glycoalkaloid content of more than 200 mg/kg fw, was least sensitive to both puncturing and dropping, and was the least sensitive of the seven varieties to the cutting treatment in which it accumulated only 1.5 times as much glycoalkaloid as that before treatment. these results disagree with those previously reported by sinden and webb (1972) and olsson (1986) where the resulting high total glycoalkaloid contents were more common in cultivars with inherently high contents than in those cultivars with low contents. 3.4 chaconine: solanine ratio differences between varieties in respect of their α-chaconine: α-solanine ratios are in table 3. the cultivar appears to be the principal significant factor in determining the chaconine: solanine ratio. generally, all types of injury increased the relative content of α-solanine in the tubers of all varieties tested to be between 31%-43% (corresponding to α-chaconine content 5769%) compared to that of 19-29% α-solanine (corresponding to 71-81% α-chaconine) before treatment. this indicates that the injury stimulated α-solanine synthesis and/or accumulation in tubers more than α-chaconine, possibly indicating a conversion of starch to sugar following tuber stress. as a result a higher proportion of reducing sugars such as galactose is more freely available compared with rhamnose resulting in the sequential addition of monosaccharide units to the aglycone in favor of α-solanine production (percival, 1999a; b). alterations in the relative proportions of glycoalkaloids as a result of injury may influence toxicity more than absolute total glycoalkaloid concentrations, with consequential implications for the overall recommendation of 200 mg/kg fw for food safety (percival, 1999a; b). this ratio appears enough for obtaining maximum synergy as reported by roddick (1996). potato tissue injuries in commercial harvesting, grading, shipping, and storage practice may not be as severe as those produced in this study; however, our results indicate that the three types of mechanical injury (cutting, puncturing, and dropping) stimulated glycoalkaloid synthesis and accumulation in both peel and flesh. 3.5 effect of storage at 4 ºc results in table 4 show that cultivar, storage time, and storage temperature affect the tga content of the potato tubers of the seven varieties tested. at harvest the total glycoalkaloid contents of all seven varieties were higher than the recommended maximum level of 200 mg/kg fw, except for the total glycoalkaloid content of l. rosseta, which was slightly below that maximum. immediate postharvest storage of potato tubers at 4 ºc for a period of 6 weeks resulted in a significant increase in total glycoalkaloid of the tubers. tga levels increased to the highest levels after 2 weeks of storage at 4 ºc, with tga concentration reaching 740 mg/kg fw in spunta, followed by total glycoalkaloid content of 660 and 620 mg/kg fw in diamant and l. rosseta respectively. aida was the only variety to show a decrease in total glycoalkaloid content after two weeks of storage at 4 ºc with total glycoalkaloid content decreasing from 494 mg/kg to 424 mg/kg. further storage at 4 ºc resulted in a decrease in the rate of glycoalkaloid accumulation in all of the seven varieties and the total glycoalkaloid content was found to be below the upper safety limit for aida and atlas, but the concentrations of the other varieties remained above that safety limit. 91 elsadig a. eltayeb, sana salem al-sinani and i.a. khan table 4: tga levels in the tubers of potato varieties grown in oman stored at different temperatures. 4 ºc 10 ºc variable temperature storage period (weeks) storage period (weeks) variety 0 2 4 6 0 2 4 6 at harvest 4-10 ºc 10-4 ºc diamant 244 660 489 614 244 1120 477 616 244 577 455 turbo 245 424 243 283 245 611 476 329 245 63 178 l. rosseta 192 620 407 354 192 912 463 547 192 955 454 l. clair 405 580 332 481 405 1114 444 442 405 508 389 spunta 464 740 446 668 464 73 527 565 464 636 80 aida 494 424 264 83 494 393 397 104 494 311 218 atlas 526 648 91 26 526 60 516 1521 526 530 482 these results agree in principle with previously reported studies (griffiths et al. 1997) of six other cultivars stored at 4 ºc, whose total glycoalkaloid content increased after 6 weeks of storage. the relative α-solanine content of the potato tubers after two weeks of storage at 4 ºc increased slightly to between 21%-34% compared to that of 19%-29%, however, it slightly decreased again after 6 weeks to between 13 %-31 % of the total glycoalkaloid content (table 5). table 5: chaconine: solanine ratio in the tubers of 7 potato varieties grown in oman stored at low temperatures. 4 °c 10 °c variable temperature chaconine: solanine chaconine: solanine chaconine: solanine variety 2 wks 4 wks 6 wks 2 wks 4 wks 6 wks 4 – 10 °c 10 – 4 °c 2 wks diamant 76:24 67:33 74:26 82:18 63:37 71:29 73:27 66:34 76:24 turbo 78:22 71:29 76:24 87:13 67:33 79:21 64:36 81:19 78:22 l. rosseta 70:30 71:29 81:19 78:22 67:33 69:31 84:16 57:43 70:30 l. clair 79:21 77:23 80:20 83:17 71:29 79:21 76:24 79:21 79:21 spunta 69:31 70:30 73:27 50:50 72:28 66:34 74:26 81:19 69:31 aida 72:28 68:32 87:13 72:28 71:29 45:55 74:26 53:47 72:28 atlas 66:34 61:39 69:31 46:54 67:33 67:33 67:33 70:30 66:34 3.6 effect of storage at 10 ºc: storage at 10 ºc for a period of 6 weeks resulted in high increases in the tga content of diamant, l. rosseta, l. clair, and turbo. the tga content of these varieties increased rapidly in the first two weeks of storage, reaching 1120 mg/kg fw in diamant, 1114 mg/kg fw in l. clair, 912 mg/kg fw in l. rosseta and 611 mg/kg fw in turbo. thereafter, the rate of glycoalkaloid accumulation in the tubers dropped but tga levels remained above the recommended safety limit in all varieties. in spunta and atlas, great decreases in total glycoalkaloid concentrations were observed during the first two weeks of storage at 10 ºc, but upon continued storage the total glycoalkaloid content increased again to 101 mg/kg fw higher than at harvest in spunta and 996 mg/kg fw higher in atlas. however, after 6 weeks of storage the only variety with tga levels below the upper safety limit was aida (table 4). 92 effect of mechanical injury and low temperature storage the effect of storage at 10 ºc for 6 weeks on α-solanine content was similar to that of storage at 4 ºc during the first two weeks (table 5). it is also of interest to note that at either constant storage temperature there was no relationship between tga concentration at harvest and the rate of accumulation in response to temperature, and that varieties which have previously been shown to accumulate lower glycoalkaloid in response to injury treatments also appear to be the least sensitive to storage temperature and length of storage time. 3.7 storage at 10 ºc prior to storage at 4 ºc: as can be seen in table 4, storage for a period of three weeks at 10 ºc prior to three weeks at 4 ºc resulted in a decrease in tga content of all of the seven varieties as compared to those of the tubers stored continuously at 10 ºc, but the tga content in these tubers remained above the maximum recommended level except that of turbo and spunta. if these results are compared to that of tubers placed immediately at 4 ºc, a fluctuation between varieties is observed. the effect of this treatment on α-solanine content of the tubers varied widely between varieties to be between 19% for spunta and 47% for aida compared to that of 19%-29% αsolanine before treatment (corresponding to 71%-81% α-chaconine). 3.8 storage at 4 ºc prior to storage at 10 ºc: the results of storage for a period of three weeks at 4 ºc prior to three weeks at 10 ºc fluctuated between the seven varieties. for example, the tga content of diamant, turbo, and spunta was lower than those of tubers stored continuously at 4 ºc, but it was higher for l. rosseta, l. clair, aida, and atlas. if these results are compared with those of tubers placed immediately at 10 ºc, a fluctuation between varieties is also observed. storage of 3 weeks at 4 ºc prior to 3 weeks at 10 ºc resulted in a decrease in the tga content of diamant, turbo, l. clair, and atlas to levels lower than those of tubers stored immediately at 10 ºc, and the reverse is observed for l. rosseta, spunta, and aida. this treatment increased the relative α-solanine content to between 24%-36% (corresponding to α-chaconine content 64%-76%) compared to that of 19%-29% α-solanine before treatment, indicating better synergy for the protection of the tuber. our results indicate that the rate of glycoalkaloid accumulation in potato tubers is dependent both on variety and storage temperature and demonstrate that selection of new varieties based solely on tga content at harvest is insufficient to ensure consumer safety. these results are consistent with the results reported by griffiths et al. (1997). tubers placed immediately at 10 ºc storage can, as in the case of diamant, l. rosseta, l. clair, and turbo rapidly accumulate high glycoalkaloid levels, while aida tubers did not accumulate glycoalkaloid in response to this treatment. the highest rate of accumulation was observed in diamant, l. clair and l. rosseta varieties stored at 10 ºc for 2 weeks. prior storage at 4 ºc reduces the magnitude of this effect in the varieties diamant, turbo, l. clair, and atlas. storage at 10 ºc prior to storage at 4 ºc decreased the glycoalkaloid accumulation in all varieties to levels lower than those obtained for samples stored continuously at 10 ºc. continuous storage of potato tubers at 4 ºc stimulated glycoalkaloid synthesis rapidly, but to a lesser extent than in those stored continuously at 10 ºc. this glycoalkaloid accumulation was observed in most of the varieties except in aida, whose tga content decreased in response to this treatment. the greatest increase was found after 2 weeks of storage at 4 ºc, again with the highest being for diamant and l. rosseta. prior storage at 10 ºc was found to reduce the magnitude of the effect of storage at 4 ºc for diamant, turbo, l. clair, and spunta. storage at 4 ºc prior to storage at 10 ºc reduced the rate of glycoalkaloid accumulation in diamant, turbo, and spunta to levels lower than those obtained for tubers stored continuously at 4 ºc. this indicates that the transfer of tubers stored for 3 weeks at 10 ºc to colder storage conditions results in lower glycoalkaloid accumulation rates than those placed in similar 93 elsadig a. eltayeb, sana salem al-sinani and i.a. khan conditions soon after harvest, which is in agreement with conclusions reported by griffiths et al. 1997. this may offer a viable strategy for maintaining low levels of total glycoalkaloid in these varieties. exposure of potato tubers to stress such as mechanical injury and low temperature storage appears to increase the total glycoalkaloid levels in both peel and flesh of potatoes, the magnitude of the effect being dependent on the variety, treatment and duration of exposure. l. rosseta was the most sensitive of the seven varieties, whereas aida was the least sensitive to the three types of stress treatments. the cultivars that did not accumulate glycoalkaloid rapidly in response to low temperature (e.g. aida) were the most stable and least sensitive to stress caused by mechanical injury, while in almost all cases the observed increases in total glycoalkaloid levels exceeded the maximum levels currently judged to be safe for human consumption (200 mg/kg fw). 4. acknowledgements we wish to acknowledge the excellent technical assistance from ms fatma al-siyabi for her valuable help with the hplc and mr. khamis al-habsi for growing the potato plants. sana s. al-sinani wishes to acknowledge scholarship from the ministry of education, sultanate of oman. references ahmed, s.s., and muller, k. 1978. effect of wound-damages on the glycoalkaloid content in potato tubers and chips. lebensm.-wiss. u.-technol. 11: 144-146. dale, m.f.b., griffiths, d.w. and bain, h. 1998. effect of bruising on the total glycoalkaloid and chlorogenic acid content of potato (solanum tuberosum) tubers of five cultivars. j. sci. food agric. 77: 499-505. fewell, a.m., and roddick, j.g. 1993. interactive antifungal activity of the glycoalkaloids α-solanine and α-chaconine. phytochemistry. 33: 323-328. friedman, l., and mcdonald, g.m. 1997. potato glycoalkaloids: chemistry, analysis, safety, and plant physiology. crit. rev. in plant sci. 16: 55-132. gregory, p. 1984. glycoalkaloid composition of potatoes: diversity and biological implications. am. potato j. 61: 115-122. griffiths, d.w., bain, h. and dale, m.f.b. 1997. the effect of low temperature storage on the glycoalkaloid content of potato (solanum tuberosum) tubers. j. sci. food. agric. 74: 301-307. griffiths, d.w., dale, m.f.b. and bain, h. 1994. the effect of cultivar, maturity and storage on photo-induced changes in the total glycoalkaloid and chlorophyll contents of potatoes (solanum tuberosum). plant sci. 98: 103-109. hellenas, k.e., branzell, c., johnsson, h. and slanina, p. 1995. high levels of glycoalkaloids in the established swedish potato variety magnum bonum. j sci. food aric. 68: 249-255. khan, i.a., deadman, m.l. and al-habsi, k.a. 2001. screening potato varieties for cultivation in arid regions: effect of planting date on emergence of imported and locally produced seed. squ j. sci. res.-agricultural sciences. 6: 41-46. khan, i.a, deadman, m.l. and al-habsi, k.a. 2002. screening potato varieties for cultivation in arid regions: effect of planting dates on yield potential. squ j. sci. res.agricultural sciences. 7: 53-57 maga, j.a. 1994. glycoalkaloids in solanaceae. food reviews international. 10: 385-418. morris, s.c., and lee, t.h. 1984. the toxicity and teratogenicity of solanaceae glycoalkaloids, particularly those of the potato (solanum 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traditional and modern medicine. plenum press. new york. sinden, s.l., and webb, r.e. 1972. effect of variety and location on the glycoalkaloid content of potatoes. am. potato j. 49: 334-338. smith, d.b., roddick, j.g. and jones, j.l. 1996. potato glycoalkaloids: some unanswered questions. trends in food science and technology. 7: 126-131. sotelo, a., and serrano, b. 2000. high-performance liquid chromatographic determination of the glycoalkaloids α-solanine and α-chaconine in 12 commercial varieties of mexican potato. j. agric. food chem. 48: 2472-2475. van gelder, w.m.j. 1990. chemistry, toxicology, and occurrence of steroidal glycoalkaloids: potential contaminants of the potato (solanum tuberosum l.). in: poisonous plants contaminating edible plants. rizc, a-f. m., ed. crc press. boca raton, florida, 1990, 117-156. wu, m.t., and salunkhe, d.k. 1976. changes in glycoalkaloid content following mechanical injuries to potato tubers. j. am. soc. hort. sci. 101: 329-331. received 13 january 2003 accepted 3 september 2003 95 effect of mechanical injury and low temperature storage on the accumulation of glycoalkaloids in the tubers of 7 varieties of potato (solanum tuberosum l.) grown in oman elsadig a. eltayeb*, sana salem al-sinani* and i. a. khan** *department of biology, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman; email: eatayeb@squ.edu.om, **department of crop science, college of agriculture, sultan qaboos university. ????? : ??? ??? ????? ????? ?????? ???????????? ?? ????? ??????? ?????? ???? ????????? ??????? ??? ??????? ??? ???? ????? ?????? ?? ?????? ?????? ?? ?? ????? ??????? ??? ?? ???? ?? ???? ????? ????? ????????. ???? ??????? ?? ?????? ????????? ????? ???? ? experimental results and discussion these results agree in principle with previously references microsoft word math060211.doc 19-40 squ journal for science, 12 (1) (2007) © 2007 sultan qaboos university 19 a knowledge-induced operator model m.a. choudhury*, s.i. zaman** and yaqoub al-nassar*** *department of economics and finance, college of commerce and economics, sultan qaboos university, p.o.box 20, al khod 123, muscat, sultanate of oman and school of business, cape breton university, sydney, nova scotia, canada, email: masud_choudhury@capebretonu.ca, department of mathematics and statistics, college of science, sultan qaboos university, p.o.box 36, alkhod 123, muscat, sultanate of oman, **email: zaman@squ.edu.om,*** department of mechanical engineering, king fahad university of petroleum and minerals, dhahran, saudi arabia. لمعرفةانموذج الدالة منتجة زمان و يعقوب الناصر . أي.تشاودوري ، س. م.م وفي العلوم اإلجتماعية تقوم نظم التعليم بدراسة تعقيدات نظم . نظم التعليم في مقدمة التحقيقات التحليلية في العلوم :خالصة يات تعتمد طرق في علوم الرياض. أو علم الرموز" مكمل األخر"وعندما يرتبط بعبارات المنطق يطلق عليه اسم . الكلمات في هذه الورقة سوف يتم التوصل إلى أن النظام التعليمي يتخطى . النظام التعليمي على المنطق الرسمي أو تحليل األنظمة وأفاق المعرفة هذه ستفسر بتفاعل واسع يؤدي إلى تكامل يتبعه . زمان ومكان التحقيقات العلمية ليصل إلى أفاق المعرفة في هذه الورقة أيضاً سيتم ايجاد توصيف . مكاملة ما بين الوحدات والمجموع في نظم الكلماتتطور مستمر يعتبر عملية والنتيجة هي تشكيل تعميم رياضي . رياضي لخواص العمليات المنتجة للمعرفة في نظم الكلمات في ضوء علم المعرفة م استعمالها تلخص خواص التفاعل والتكامل وهذه الدالة التي ت. لظاهرة التعليم، وهذا التعميم يعتمد على احدى الدوال . المعالجة أي التجهيلكما تمت بعد ذلك دراسة الحالة . والتطور في نظام التعليم abstract: learning systems are in the forefront of analytical investigation in the sciences. in the social sciences they occupy the study of complexity and strongly interactive worldsystems. sometimes they are diversely referred to as symbiotics and semiotics when studied in conjunction with logical expressions. in the mathematical sciences the methodology underlying learning systems with complex behavior is based on formal logic or systems analysis. in this paper relationally learning systems are shown to transcend the space-time domain of scientific investigation into the knowledge dimension. such a knowledge domain is explained by pervasive interaction leading to integration and followed by continuous evolution as complementary processes existing between entities and systemic domains in world-systems, thus the abbreviation iie-processes. this paper establishes a mathematical characterization of the properties of knowledge-induced process-based world-systems in the light of the epistemology of unity of knowledge signified in this paper by extensive complementarities caused by the epistemic and ontological foundation of the text of unity of knowledge, the prime example of which is the realm of the divine laws. the result is formalism in mathematical generalization of the learning phenomenon by means of an operator. this operator summarizes m.a. choudhury, s.i. zaman and yaqoub al-nassar 20 the properties of interaction, integration and evolution (iie) in the continuum domain of knowledge formation signified by universal complementarities across entities, systems and subsystems in unifying world-systems. the opposite case of ‘de-knowledge’ and its operator is also briefly formalized. keywords: learning systems, epistemology, topology, evolutionary set, functional, dynamic continuity, knowledge-induced operators and variables, knowledge flow. 1. introduction he objective of this paper is to formulate an analytical methodology and model of knowledge induction premised on systemic unity of knowledge. such a model premised on the epistemology of unity of knowledge is found to apply to theoretical conception and positive perspectives relating to a vast domain of epiphenomena. furthermore, if we can formulate the model by means of a mathematical ‘operator’ based on the underlying episteme of unity of knowledge, such an operator can be used to develop well-defined mappings for generating the objective criteria for all socio-scientific problems. we undertake this task in this paper. along the passage of developing our detailed model and operator of the relationally learning topological system we introduce important concepts and explain them in detail. these important concepts are of the social wellbeing function and the interactive, integrative and evolutionary (iie) learning processes across continuity and continuums. 1.1 definition of the operator the operator developed in this paper means a summarized way of depicting and bringing together the function and application of systemic unity of knowledge to bear upon sets of learning relations by the use of the operator. the operator is thereby a concept imbued in a mathematical form to explain, quantify and measure the implications of unity of knowledge relating to the problem under investigation. our operator is thus a conceptual-quantitative functional form that generalizes the functions of unity of knowledge as relational epistemology underlying all learning entities intraand intersystems. the singular axiom of our methodology is unity of knowledge both in its epistemological and ontological sense of existence and quantification of a unified worldview of entities intraand intersystems. this choice of the axiom is premised on the historical permanence of the search for unity in the sciences and world-systems in reference to the most reduced totality of laws that can overarch all systemic explanations. the prime example of such an axiom is the episteme of unity of knowledge in the divine laws. another example of the search for unity of knowledge from the sciences is the classical contribution on the unity of science by neurath et al. (1970). in this revolutionary work the role of ethics as relational learning is explained well by edel [p. 285 in neurath et al (1970)]: “causal-explanatory approaches look for the conditions and contexts of the occurrence of moral phenomena, experiences and processes. in whatever terms these phenomena be described, there is always the question of relating them, as they occur, to other phases of life and internal economy of the individual and to the other phases of operation of the society at a given point of development of its history and culture.” 1.2 rationale for the topological method used the topological method used in the study of the epistemology, ontological and applicative nature of the operator as conceptual-quantitative functional form imputed on a general body of socio-scientific problems is found to be the most suitable one for studying relationally learning entities of ‘every’ world-system. the word ‘every’ and ‘everything’ are used to convey a generalized theory of unity of relationally learning entities within and across entities and their sub-systems in the domain of learning. such a totality of knowledge flows and knowledge-induced variables characterizing entities intraand intersystems is defined by the generalized understanding of topological mappings that universalize continuously relational learning among all such entities. t aknowledge-induced operator model 21 when certain entities do not learn due to the absence of relational continuity attained by the topological mappings, such entities are enclosed within their own universe as a segmented domain of study. now once again, the persistence of differentiated entities caused by their systemic independence and individualism means, continuity of such entities within their own domain of differentiation and methodological individualism. hence there is continuity of the relational worldview for both cases treated in this paper. first, there is continuity of the relationally unifying entities of their world-systems. secondly, there is continuity of the differentiated entities in their own and disjoint world-systems. the topological method applied to both kinds of world-systems in this context generalizes the methodology of unity of knowledge to explain such ‘everything’ (barrow, 1990). the conceptual, quantitative and applied perspectives of the unified worldview explained through the operator have serious implications on a scientific way of exclaiming the powerful methodology of unity of knowledge. some limited applications of the methodology of unity of knowledge to constructed and estimated models are brought out. but for reason of space, a full development of the applied content cannot be divulged in the paper and the technical appendix. the reader may refer elsewhere for this interest [choudhury (2004, 2006a), choudhury & hossain (2006) forthcoming, johannessen (1998), xuemoue and dinghe (1999)]. 2. principal definitions at the very outset we define some of the foundational terms and concepts used in this paper to establish the methodological background of the knowledge-induced operator. some definitions appear by reference to the literature; others are original contributions by the authors in the field of relationally learning systems under unity of knowledge. 2.1 epistemology what is the epistemology of unity of knowledge used here? epistemology means theory of knowledge and its study explains the foundations and structure by which knowledge is derived, classified and disseminated. in the case of unity of knowledge epistemology becomes the field of studying relational unification between multidimensional and multivariate entities that learn by interaction leading to integration between them and thereafter evolving to subsequent phases of knowledge flows arising from the level of experiences encountered in the previous phases of learning. thus knowledge flows get forward lagged. the scientific research program of unity of knowledge has a singularly strict axiom. that is the axiom of epistemology of unity of knowledge that springs from the premise of the unified laws of ‘everything’. the epistemology of the unified laws leads to a worldview of relational unity of knowledge in the systemic sense. the epistemological premise is formally used to establish the ontological model of unity of knowledge. finally, generically formulated ontological model of unity of knowledge explaining relational unity of knowledge between variables and their systems leads to its application through data simulation. empirical consequences, application and inferences follow from such a methodological treatment of the relationally learning iieprocesses emanating from the epistemological origins of oneness in the ontological model. the search thereby is for the unique and universal foundations of the epistemological and ontological text of laws. these are firstly established in the absolutely unified nature of such laws (e.g. the divine laws). secondly, the unity of relationally unified learning systems is reflected in ‘everything’ of diverse world-systems. thirdly, the totality of such unified laws and their causation generated by relational unification in world-systems reproduces unity of being in the problem at hand between and within entities and their sub-systems. the socio-scientific and historical search for such a law leads straight to the foundations of oneness of god, which is the established premise of the divine laws. hence the ensuing concepts and quantitative systems are premised on this epistemology and ontology of relational unity of knowledge as the axiom to be found in the fundamental epistemology. such a precept of unity of the divine laws is referred to as tawhid in the qur’an. in every other epistemic reasoning, for example in the ghaia notion of a relational worldview, the epistemological m.a. choudhury, s.i. zaman and yaqoub al-nassar 22 premise is human reason ( primavesi, 2000). in aquinas (1946) the notion of oneness of god is a speculative metaphysical concept. 2.2 uniqueness and universality in the introduction we have pointed out the meaning of ‘everything’ in the context of the methodological generalization of the epistemology of unity of knowledge and the role of the operator as a conceptualquantitative generalized functional form to explain this context of systemic unity. we now go on to extend this idea to the concept of uniqueness and universality in spaces that are induced by relational learning, and hence must be explained by probability limits ( plim) taken over domains of interaction, integration and evolutionary (iie ) learning between the entities and their functions as topological relations. 2.2.1 universality a formal definition of universality and uniqueness that endows it with a generalized methodology is given below ( wiener, 1961): let pn be a proposition. pn is extended to all numbered propositions ‘n’ if the following properties of pn hold: pn is proved true for n = 1 if pn is true then pn+ 1 is true therefore pn is true for all positive integer n. furthermore, if ‘n’ is a real number then too the above conditions abiding establish the extended inductiveness of the proposition pn. 2.2.2 uniqueness the relationally learning methodology of unity of knowledge is unique. the definition of uniqueness follows by virtue of the relationally learning methodology that remains permanent in explaining unity of knowledge in ‘every’ world-system (issues and problems) in the sense of universality. the methodology of unity of knowledge thus explains both learning by relational unity as well as ‘de-knowledge’ (differentiated relations). thus issues and problems under investigation may be diverse but their socio-scientific treatment remains unique in the methodology of unity of knowledge. choudhury (1998, pp. 20) writes, “the unification of knowledge under a unique set of universal laws that apply equally within and between systems, given the perceived differences in the specifications of the problems underlying the systems, is the essence of the worldview.” we note then that in connection with the concepts of paradigms and scientific revolutions, the concept of the worldview means reduction of all paradigms and scientific revolutions to a unique praxis of theory. this core of all theories that enables the interdisciplinary systems to get linked up is premised on unity of knowledge. when the premise of unity of knowledge is identified as having a vaster explanatory and applicative power than do specific theories on an ever-expanding class of issues and problems under investigation, we then prove the universality and uniqueness of such a super paradigm. we have then discovered a socio-scientific revolution. 3. formalizing epistemological concepts by means of probabilistic topology when translated into probability language, the concept of universality and uniqueness are formalized as follows: let { }ijθ ∈(t, s) denote a space of learning parameters. { }ijθ are treated as knowledge flows, being premised on the unity of relational systems as defined under the epistemology of (t, s). here i denotes numbered interaction intraand interentities and sub-systems; j denotes numbered entities or their sub-systems. such knowledge flows are derived from the epistemology of unity of knowledge as the reference law (t ). they are mapped into learning possibility by the ontological mapping (s). hence (t, s) denotes the fundamental epistemology (foundation of knowledge). aknowledge-induced operator model 23 with the above definition we now reframe the definition of universality given above, as follows: =θ plimij ∪i ∩j { }ijθ the postulate, issue or the problem, pn(θ ) is proved true for a certain number n = 1. if pn+1 (θ ) is proved true on the assumption that pn(θ ) is true, then it is true for all n. therefore pn(θ ) is true for every knowledge-induced configuration ))(;()( θθθ nijij pkk ⊆ existing in continuum. thus due to the positive monotonic continuous relationship between θ and ))(;( θθ npk , and between { }ijθ and ))}(;({ ijnijij pk θθ , probability functions and limits apply to all the class of functions defined over these domains, if and only if θ ∈ (t, s) in the sense of probability limit taken over relationally learning processes between entities intraand intersystems. within the above formalization, uniqueness is characterized by the application of the universal topology (t, s) to the learning domain ))}(;(,{ θθθ npk and all its specific sub-domains of issues and problems, ))}(;(,{ ijnijijij pk θθθ . ⊆))}(;({ ijnijij pk θθ ))(;( θθ npk is therefore true in the general case of θ being knowledge flows denoting relational unity of knowledge. what is true of ))(;( θθ npk with respect to the given pn(θ ) is equally true of )( ijijk θ with respect to the application of )( ijnp θ i, j defined as above. this result is readily proved by noting that monotonically positive and continuous mappings over sub-domains of a topology (t, s) form topological sets (maddox, 1970). hence such a function defined on }{θ applies to its components }{ ijθ and vice versa. it is likewise the case for ))(;( θθ npk and ))(;( ijnijij pk θθ . more along these lines can be read in the recent contributions by choudhury (2005), choudhury and zaman (2006) and shakun (1988). an example of normed positive monotonic transformation on the domain ))}(;(,{ ijnijijij pk θθθ and the domain ))}(;(,{ θθθ npk is a probability measure (halmos, 1974). let such a probability measure be denoted by µ (.) operating on the domains shown here that can be enclosed in (.). thus, plim }{ ijθ = θ ⇒ plim )()( θµθµ =ij is a normed density function of θ. a similar normed probability density function ν maintains, plim )}({ ijijk θ = k(θ ) ⇒ plim ))(())(( θνθν kk ijij = . all probability limits are taken over interaction and entities. such measures can be extended by matrix transformations over interconnecting systems of entities. over still more complex interacting, integrating and m.a. choudhury, s.i. zaman and yaqoub al-nassar 24 evolutionary domains of learning, tensors can be used ( fandlge ′ , 1961; choudhury, 2006a,b). any further normed and positively monotonic and continuous transformations of these functions will behave in the same way (henderson and quandt, 1971 p. 20). 4. formulation of the knowledge-centered methodology to address our stated objective we now formulate the methodology of unity of knowledge. (t, s) was defined above as the epistemological core of unity of knowledge. it comprises the irreducible concept, hence the universality and uniqueness of the divine laws. (t, s) is the topology of the complete, perfect and absolute stock of knowledge from which emanate flows of knowledge, },{ ijθθ . the stock by its very concept of completeness and absoluteness is never changed, as it recycles back the flows into itself continuously across processes of learning (iie-processes). thus (t, s) remains the exogenous source of knowledge in every relationally learning problem. on the other hand, the derived ))}(;(,{ θθθ npk and its sub-spaces are permanently endogenous in nature in the relationally learning systems of unity of knowledge. { }θ ∈ (t, s) denotes an open set of knowledge flows emanating from the epistemology of the unchanging knowledge stock t. the very property of topology makes t an open set containing its members, which too are open. thus even at this early stage of the paper the process-oriented nature of learning, and thereby the impossibility of optimization as opposed to simulation to occur among the relations generated by knowledge flows, is established (choudhury and korvin, 2001). complexity signified by non-linearity caused by the topological mappings becomes the general rule of relationally learning systems as opposed to linearity of relations in differentiated systems that mutate or reflect the preferences of methodological individualism. we deal with this issue of ‘de-knowledge’ briefly later on in this paper. s denotes a mapping from t ‘into’ the domain of knowledge flows. this mapping was identified earlier by the example of the ontology of the prophetic guidance in islam. we denote the direction of the epistemic mappings as, { }θ→→ )(tst following up on the properties of topology (maddox, 1970; robertson and robertson, 1966),{ }θ forms an open subset contained within a subset of t, denoted by s(t ) . thus for a particular knowledge value pertaining to a range of interaction i, say iθ , we write, ti ∈∈ }{θθ the following case holds as well: tii ∈≠∩ φθ besides, ii θ∩ (as also the previous intersection property) is under the impact of dynamic iθ values. thus, ii θ∩ forms an open subset of t. in the more general sense with say i number of interaction and j entities in their systems (variables) we have, tijii ∈∩∪ }{θ (1) also the complement of { }θ , say { }cθ ∈ t. since t is complete as the stock of knowledge, therefore{ }cθ also forms an open subset of t. we can therefore write, { } { } tcii ∈=∩ φθθ (2) aknowledge-induced operator model 25 in reference to our earlier characterization of the universality and uniqueness properties of (t, s), this specific topology cannot be probabilistic in nature because of its irreducible and complete nature that enables it to contain ‘every’ sub-systemic sets. that is (t, s) determines all the functions and processes ensuing as knowledgeinduced systems of entities. but such sub-systemic members of the topology, as in the case of },{ ijθθ and },{ c ij c θθ and likewise, )}(,)({ ijijkk θθ and )}(,)({ c ij c ij cc kk θθ are all probabilistic in nature because of their openness and incompleteness in learning (‘de-learning’) spaces within the topologies defined by (t, s). expression (2) now assumes plimij transformation, as was noted earlier. the symbolization of plim (.) over interaction and systems of entities is subsumed in this notation. in expression (2), i denotes the number of interaction taken in the set of interactions i across entities contained in the set of entities a in their sets of systems denoted by s. as was explained earlier relational learning is identical with interaction that lead to integration and are followed by further evolutionary learning (iie-process). thus implicitly, each knowledge flow }{ iθ spans (i, a, s). that is knowledge-flows occur over interaction, integration and evolution. (i ∈ i) of entities (a) in their sub-systems (s). both intra-systemic and inter-systemic iie-processes are implied. these iie-processes lead to the formation of { }iθ , i = 1, 2,… the idea of the iie-process is further brought out in figure 1. interactive, integrative and evolutionary (iie) learning processes: { }θ→→ )(tst → {x(θ )} new }{ * in θ values etc. in continuum social wellbeing function /generalized topological mapping simulation )( inθ sw = f(x* )( * in θ , * in θ ) = h(t) subject to circular causation in the multiple {x* }),( ** inin θθ variables. …………………………………………… continuity of the relationally learning iie processes : }{ * in θ { }θ→→ )(tst → continuity across continuums x* )( in θ ↓ simulation )( inθ sw = f(x* )( * in θ , * in θ ) = h(t) subject to circular causation in the multiple {x* }),( ** inin θθ variables figure 1. the string relation of unity of knowledge and it’s implications. any temporary phase of learning is characterized by a given level of interaction converging to integration followed by evolution, whereby a subsequent phase of similar learning emerges from recalling of (t, s) and a fresh knowledge flow is derived from (t, s). such process-oriented phases carry onwards fresh knowledge flows m.a. choudhury, s.i. zaman and yaqoub al-nassar 26 that are learned out of the experience of previous probability limiting domains of )}(,)({ ijijkk θθ and )}(,)({ cij c ij cc kk θθ over (i, a, s). we write in the probability limiting sense of relational learning with the simplified case of i denoting interaction only over n-rounds: { } .}..,,{,lim 21* nnnp iini ini ∈= → θθ (3) this probability limiting property can be further extended across entities and systems. the result will then be, { } .}..,,{,lim 21* ,,,, nnnp iisiainsai iss iaa ini ∈= → → → θθ (4) here, ni ∈ {n1, n2, …}, ai ∈ {a1, a2,…}, si ∈ {s1, s2,…}. the probabilistic nature of relational learning across evolutionary phases (processes) signifies that evolutionary dynamics is intrinsic in knowledge-induced systems of entities. the properties of the knowledge stock (t ) and flow )(θ shown in expressions (1) and (2), are also true for the extended system of relations shown in expression (4). thus both (t, s) and its derived knowledge flows comprise topologies (maddox, 1970). the property of the mapping s maintains the topological nature of learning in unity of knowledge derived from the core of t and of the knowledge induction of systemic variables, {x )( iθ } and their topological relations. let x )( iθ denote the knowledge-induced vector variables. because of the properties in expressions (3) and (4) we can write, ini p → lim {x )( iθ } = x * )( * in θ , ni ∈ {n1, n2, …} (5) iss iaa ini p → → → lim {x )( ,, saiθ } = x * )( * ,, iii sanθ (6) for, ni ∈ {n1, n2, …}, ai ∈ {a1, a2,…}, si ∈ {s1, s2,…}. i denotes the totality of the interaction domain, i = {n1, n2, …, ni, …}; a denotes the totality of the agents domain, a = {a1, a2,…, ak …}; s denotes systems s = {s1,s2,…, sl ,…}. 5. the social wellbeing expression (w(.)) we have now defined a mapping from t to )( iθ by s and from )( iθ to {x )( iθ }, say by w. because of the irreducible nature of t, this being the complete topology and because all other sets are proper subsets of (t, s) as topologies in their own, we refer to the self-referencing nature of these topologies as a property of unity of knowledge derived from the fundamental root of (t, s). aknowledge-induced operator model 27 we define a functional map w characterized by all the properties of topological mapping defined on the (x* )( * in θ , * in θ ) domain and which carry the probabilistic transformation as, w = w(x* )( * in θ , * in θ ) (7) with s(t ) = * in θ (8) s(t ) is taken as a proper and open subset of t. furthermore, x* )( * in θ = f1 )( * inθ , (9) because of the jacobian inversion of x* )( * in θ in terms of * in θ denoted by the non-vanishing function 1f . therefore, 1−w exists as a result of jacobian inversion by the non-vanishing of 1f . hence by composite mapping ‘ο ’ we write, sw = f(x* )( * in θ , * in θ ) = h(t ) (10) sw is a continuously differentiable function of t mapped into a proper open subset of {x* )( * in θ , * in θ }. the sets of {x* )( * in θ , * in θ } in terms of the open topological set }{ * in θ and their functional relations comprise topologies as proper open subsets of the complete topology t. yet it is not necessarily true that 1−w (x )( * in θ ) = * in θ , because there can be multiple probability limiting values in the mapping between * in θ and x )( * in θ , causing perturbation sets to appear in the domains of these variables. recursive and discursive learning also causes such consequences in social systems. such learning processes are current themes of sociology (.), philosophy (whitehead, 1978) and the process worldview of economics (georgescu-roegen, 1961; boulding, 1971). they have also entered the study of science as process in recent times (prigogine, 1980; hull, 1988). the essential point underlying all these is the relational viewpoint of learning systems. yet it is true that socio-scientific disciplines despite their search for relational processes (thayer-bacon, 2003) have not been able to develop a cogent methodology (sztompka, 1991) in the field of unity of knowledge. the problem lies in the fundamental epistemology of received socioscientific reasoning. epistemologies are over-determined in mainstream sciences, even in those with social meaning (resnick and wolff, 1987). contrarily, our methodology of unity of knowledge in the study of processual world-system issues in this paper is premised on a unique and universal epistemology that cannot thereby accept overdetermination of competing epistemologies. the meaning of expression (10) is now particularized from the generalized form of this topological mapping over its domain into a social wellbeing function (w(.)). such a function is central for evaluating the degree to which the domain of the function has been relationally unified as a participatory social system. social wellbeing function defined on the knowledge space of the compound mapping, { }θ→→ )(tst → {x(θ )} has an intermediary function that causes further mappings of this kind to emerge from each completed learning iie-process. this generates θ -values in continuum. the function w post-evaluates a process of relational learning experience subject to the circular causation between the variables of the domain. m.a. choudhury, s.i. zaman and yaqoub al-nassar 28 6. the formal nature of interactive, integrative and evolutionary learning: circular causation the following characterization of the relational learning process gives an explicit epistemological background of learning consequences mentioned above in the probabilistic sense and its ontological form (methodological formulation). the meaning of ontology used is of the engineering category as opposed to being of a metaphysical nature (gruber, 1993). figure 1 as a whole points out the simulation nature of probabilistic learning defined by the epistemology and ontology of (t, s) on the (θ, x(θ )) domain. in figure 1, }{ * in θ denotes new }{ * in θ values in continuum of relational learning. the probabilistic nature is carried across in such a simulative and topological space of evolutionary learning over the domain (θ , x(θ )). despite this open nature of the learning domain there always comes about temporary evolutionary equilibriums in every phase of the simulative relational learning over iieprocesses (grandmont, 1989). consequently, there is temporary boundedness in the probability limiting values of the domain variables. such evolutionary equilibriums are only expectational in nature, in the sense that the core of equilibrium cannot be attained, as learning continuously shifts the expectational equilibrium along the path of evolutionary equilibriums (choudhury, 2006c; thurow, 1996). probability limits of expectational equilibriums that do not attain the core equilibrium but are deflected away by relational learning across processes in continuum can be explained by the measure theoretic understanding of probability measure. we have explained the measure-theoretic implication of probability limit equilibriums earlier in this paper. iie-processes continue across continuums post-evaluation of unity of knowledge by the simulation of social wellbeing function taken over iie processual domains of relational learning. 7. dimensionality of the social wellbeing function in learning spaces finally, the matter of dimensionality of w needs to be addressed in this section. w by definition is the positive monotonic measure of unity of knowledge attained by relational learning along the iie-processes and circular causation between the variables of the domain of the w-function. w can assume various forms. as a complex non-linear function of the domain variables in any one system (e.g. economy) w represents one objective function in a vector of variables of this system. when w is compounded with multiple social wellbeing indices (ws say, s = 1, 2,….n ) of similar relationally learning types then, ∏ =′ ′ =′≠= n ss ss nsswww 1, ...,2,1,][ . each ws has similar character of relational unity of knowledge both between their individual domains and across domains, as diverse but relationally learning systems in unity of knowledge interact, integrate and evolve. finally, if the objective is to explicate inter-systemic iie-processes, as for example in the case of specifically interdependent securities within a portfolio of financial securities, then w assumes matrix characterization denoted by [.] here (jean, 1970). now, ...,2,1,,][ =′= ′ ssww ss , which will include the identity case of ss ′= , with wss = ws. besides, the interdependent variables across circular causation processes of relational learning will also be expressed interactively. according to figure 1, we now have a simulation problem of the social wellbeing objective criterion over θ -variables. once again, θ -variables are understood in the sense of plimij }{ ijθ , as mentioned earlier in this paper. the dimensional issue of w-function is now established as dimw = n in the case of n variables within a system or compounded system of sub-systems of variables and dimw = nn × in the case of matrix system. the dimensionality of the circular causation variables is as follows: aknowledge-induced operator model 29 dim(variables ; dimw = n ) = nn × variables and equations, respectively. dim(variables ; dimw = 2n ) = 22 nn × number of variables and equations. matters of actually estimating such systems with policy and instrumental revisions to the estimated dynamic coefficients of such a simulation system, as implicated in figure 1, is beyond the scope of this paper. the interested reader may refer to choudhury and hossain (2006 forthcoming). a simple empirical version of the simulation problem is given in technical appendix 2. 8. implications of the methodology of relational learning in unity of knowledge in the social sciences it can be noted from figure 1 and the implications of the positive monotonic and continuously differentiable property of the probability measure-theoretic transformation over the domains of the learning sets (i.e. over phases of iie-processes between entities and their sub-systems) that these entities and systems learn recursively between processes in a circular causal way. that is along a history of such evolutionary learning processes that recursive share experiences forward and backward both over time and continuums. in the social sciences as an example, the recursive learning across iie-processes in the mode of circular causation conveys how s(t ) generates { }θ values and the resulting measure-theoretic functional forms denoted in general by say (.)f . now the social wellbeing function w appears as one such evaluative criterion of the positive monotonic, continuously differentiable function over its domain that evaluates the degree of unification attained by circular causation interrelations between the included domain variables (vectors) and systems (matrices). this kind of plethora of circular causations between interactions, entities and their systems signify relational unity of knowledge between them. they are extended further over learning iie-processes and convey the moral and ethical nature of the entire methodology. the knowledge flows are representations of the moral and ethical values in the socio-scientific studies. they are further endogenously extended by relevant state and policy variables. such extended domains of the variables learn perpetually over time and space along the iieprocesses. all such variables are influenced by the epistemology emanating from t → s(t ). 9. the knowledge-induced operator we now set up the following expression in view of expression (1) to mean interaction (i ∈ i ) among entities with integration (∩a ) across systems (systemic integration = ∩s). thus we write these properties together as, (∪i ∩a ∩s)[w(x* )( * inθ , * in θ )] as, i here any function or variable within the operator would be carried over interactions i ∈ i, i being the totality of interaction domain, and across the totality of systems s and the totality of agents a. a s, i means the number of agents (a) in s number of systems that go through numbered interaction in the interaction set i. the dynamic continuity of knowledge-flows }{ * in θ , and their monotonically positive effect on [w(x* )( * in θ , * in θ )] as, i is expressed as, * in d d θ {∪i (∩a ∩s)[w(x* )( * inθ , * in θ )] as, i } > 0. (11) m.a. choudhury, s.i. zaman and yaqoub al-nassar 30 note that we have changed f to w in order not to add yet another new symbol. note also that w(x* )( * in θ , * in θ )as, i being continuously differentiable over {x* )( * inθ , * in θ } as, i , means (∪i ∩a ∩s)[w(x* )( * in θ , * in θ )] as, i is also continuously differentiable in the same open sets of variables defined in their epistemology denoted by t → s(t ). because of the above properties of the continuously differentiable functions the differentiation as shown in expression (11) exists over values of {x* )( * in θ , * in θ }as, i. [w(x* )( * inθ , * in θ )] as, i is thus differentiable around the limiting knowledge-induced variables {x* )( * in θ , * in θ }as, i as a series by taylor’s theorem. now by dropping the specificity of the limiting values, {x* )( * in θ , * in θ }, we define the knowledge-induced operator as the interactive (i), integrative (i) and evolutionary (e) – thus the iie-process in the form given by, id d θ {( sai ∩∪ )[.] a s, i } > 0 (12) this operator summarizes the entire idea of unity of knowledge in terms of its application to relational unity of knowledge that is derived from the epistemic core, (t, s). this is signified by the fact that any included function and its variables within [.] is monotonically positive transformation in the iie relational learning processes. this is the principle of pervasive and continuous complementarities in the relationally learning system of unity of knowledge as derived from the epistemology of (t, s). in the case of the differentiated system of ‘de-knowledge’ cθ (mathematical complementation as opposite of θ ) de-learns, but [.] is still positive monotonic and continuously differentiable in terms of cθ . contrarily, this is not the case in non-(t, s) epistemic cores. in the case of neoclassical economic theory the variables of the objective function enclosed by [.] remain marginal substitutes of each other and complementarities between them are problematic (holton, 1992). now cθ is derived from the realm of individualism, the ego, which is a matter of the ontological origins of knowledge as perceived in the liberal order (heidegger, 1988; minogue, 1963). consequently, by the concept of ‘de-knowledge’ in neoclassical economic theory the sign of expression (12) will be negative. in the special case of the social wellbeing function w(x ),)( ii θθ in [.] we get the following result: id d θ { ( sai ∩∪ )[w(x ),)( ii θθ ] a s, i } > 0, (13) where , ∩a s = ∩a ∩s ; a = {a1, a2,…, ai …} ; s = {s1, s2,…, si ,…}; i = {n1, n2 , …, ni, …} and i = 1,2,…… the properties of w-function in terms of the variables and θ-values were given earlier. all the notations were defined. in the language of social theory expression (13) signifies that integration resulting from interand intrasystem interaction are continuously evolved under the impact of new sequences of knowledge values }{ iθ derived from the epistemology t → s(t ). the operator conveys many knowledge-induced properties all at once. that is, there are extensive interactions (i ) in generating knowledge flows. these interactions lead to integration across agents and systems aknowledge-induced operator model 31 in terms of the knowledge flows (i ). the interactively formed integration then evolves continuously by the passage of knowledge flows into more of the same kind of processes circularly in continuously differentiable sequences (e ). the higher is the positive value of the operator (d/dθi)[.] a s, i > 0 in reference to w(.), the more integrated becomes the system and the more capable it is of evolving to higher levels of complementarities that are formed by interrelations between the entities with systemic diversity (choudhury, 2000). the above kind of densification of knowledge and the iie-process define the continuously learning character of the system (13) as defined by (d/dθi)[.] a s, i > 0. in other words, existence of complementarities across diversity is the sure sign of realizing unity within diversity through the iie-process (see technical appendix 1). the expression within [.] can be of specific types, though this operator is capable of examining the three attributes of interaction, integration and evolution (iie-process) across all possible complementary networks of diverse systems, agents, variables and their intraand intersystemic interrelations. let a denote the set of entities as agents and variables together with their relations ; s denote systems of agents and variables together with their relations and i denote the total number of interaction within which {x(θi),θi} are generated and then acquire their limiting values as shown earlier. in this way, expressions (1) (13) have already been built into the operator. a note on the continuously positive value of (d/dθi)[.] a s, i > 0 needs to be explained. three particular kinds of learning can constrain the continuously evolutionary nature of this operator in the iie-processes. firstly, when the learning has lags between the iie-processes particular knowledge values iθ in }{ iθ across a s, i are temporarily halted from evolution. then we do not have evolutionary equilibriums with punctuated limiting iθ (grandmont, 1989). secondly, when iθ = constant, then learning ceases. the result conveys neoclassical marginal substitution between alternatives at the optimal and steady-state point of equilibrium resource allocation. now all novelty of learning is lost (shackle, 1971). the variables cannot participate and therefore cannot complement in any social interrelationship. thirdly, the ideal case is of continuously learning, which is a phenomenon of symbiotic socio-scientific world-systems (yolles, 1998). 10. an application w = w(x* )( * in θ , * in θ ) as the social well-being function describes complementarities between the vectors of knowledge flows and their induced variables. functional relations of such paired complements signify relational learning in systemic unity of knowledge. this is the meaning of interaction (i.e. participation). the diversities of interrelations lead to integration (complementarities). next the creative evolution of w(.) is caused by the evolutionary epistemology of {θi}, and hence of {x(θi),θi)}and {w(x(θi),θi)} over iie-processes. the social wellbeing function as a criterion signifying degrees of complementarities attained establishes the spirit of unity of knowledge. such a social criterion contrasts sharply with the neoclassical economic meaning of social welfare. the latter is based on marginal substitution between variables and agents, and hence between systems. the neoclassical principle of marginal substitution imparts the causal relationship between the axioms of methodological individualism, competition and independence in an optimal state of resource allocation with scarcity of resources. the undp has presented a specific form of a wellbeing index. world development report writes as follows with regards to the human development while addressing the topic of poverty alleviation in developing countries (world bank, 2000, p.7): "there is no hierarchy of importance. the elements are deeply complementary. each part of the strategy affects underlying causes of poverty addressed by the other two." the report then carries on (p.19): "one approach to addressing comparability is to define a multidimensional welfare function or a composite index. an alternative is to define a poor as anybody who is poor in any of the dimensions without attempting to estimate tradeoffs among the dimensions." m.a. choudhury, s.i. zaman and yaqoub al-nassar 32 the stand of the world bank and undp on the complementary social approach to poverty alleviation is the newest well-thought out methodology of socio-economic development. it requires a framework of theorizing and application to poverty alleviation, entitlement and empowerment formation and institution-market interaction that can be addressed by the principle of pervasively complementary relations across diversity of issues and problems. so far the world bank and the undp have not come up with another model of the type we are prescribing in the framework of unity of knowledge with the social wellbeing function as a quantitative measure of complementarities between the knowledge-induced variables. 11. implications on complexity systemic interaction, integration and evolution under a continuum of knowledge-flows and their induced socio-scientific variables lead to networking. networking may be either over orderly domains of knowledge or over chaotic domains of ‘de-knowledge’. in the case of equilibrium dynamics of the punctuated type conveyed by the knowledge-induced operator of expression (12) yields the following result (we have the specificity of i ∈ i in expression (12)): θd d {( sai ∩∪ )[w(x ),)( θθ ] a s, i } > 0, for )( ** θεθθ <− (14) )( *θε is an arbitrarily small quantity based on *θ induction. the knowledge-induced form has a similar property: | x(θ ) – x*( *θ )| )( *θη< where )( *θη is an arbitrarily small quantity defined around x*( *θ ) based on *θ . the limiting values {(x )},)( θθ as, i , and thereby {[w(x )]),( θθ as,i }, are probabilistic in nature. this signifies the incompleteness of learning from the perfect state of knowledge and knowledge-induced forms at any given iie-process relating to the problem under investigation in the dynamically (iie) learning socioscientific space. equivalently the expressions, )( ** θεθθ <− and | x(θ ) – x*( *θ )| )( *θη< establish the continuity of the variables and function relating to, {( sai ∩∪ )[w(x(θ ), θ)] a s, i } note that because of the topological nature of the mappings that occur between the knowledge-flows and their induced forms, diverse forms of the distance functions can be defined, depending upon the incomplete nature of learning with evolutionary equilibriums. in the simplest case with linearity in the learning process such distances are metric in nature. in the complex case they can be extended to higher dimensions, such as in banach space (choudhury, 1993). aknowledge-induced operator model 33 12. a brief note on ‘de-knowledge’ relations in the light of the (t, s)-methodology the formalism for the case of ‘de-knowledge’ experience of differentiated world-system of methodological individualism is also addressed by the same universal and unique episteme of (t, s), but as a consequence that is disjoint of relational learning in unity of knowledge. the ‘de-knowledge’ character is conveyed by the continuously evolutionary processes that cause differentiation instead of integration out of interaction in mutations. such mutative social processes reflect social darwinism (dawkins, 1976). the circular causation processes now define temporary bundles of interactive social organisms that share in their over-determined epistemologies, but subsequently cause plethora of mutations by competition, conflict and independence between the present generations and their parents. methodological individualism following subsequently from the early temporary interactive processes becomes the permanent character of the mutated world-system (buchanan, 1971, 1999). 13. ‘de-knowledge’ operator in the above-mentioned case when learning ceases with iθ = constant, we have the case of a ‘deknowledge’ operator. we now replace all the variables by the ones induced by ‘de-knowledge’. the ‘deknowledge’ connotation of the variables-domain is depicted by (x ),)( ccc θθ . previously, cθ was defined as the opposite (mathematical complementation of θ ). now two cases arise: firstly, when the problem objective is one of optimization as opposed to simulation of continuous relational learning then, θ ′d d {( sai ∩∪ ) [w(x )],)( ccc θθ as, i } = 0 (15) for )( ** ccc θεθθ =− and |x )( cc θ – x )( ** cc θ | = )( *cθη , here, * refers to the whole of cθ and x c , as the case may be, in the probability limiting sense. secondly, for the ‘de-knowledge’ system, cd d θ {( sai ∩∪ )[w( cx )( cθ , cθ )] as, i } = 0 (16) for 0* =− cc θθ and for | cx )( cθ – x )( ** cc θ | = )( *cθη . in other words, in the language of social sciences in the case of ‘de-knowledge’ methodology the methods of optimization and steady-state equilibriums pertaining to the problem under investigation replace the simulation (continuously learning) methodology of the knowledge-induced iie-process. the concept of ‘deknowledge’ conveyed in the optimal and steady-state equilibrium case is the end of learning in (15) and evolutionary non-convergence and hence a de-unified system in (16). all these conditions are taken in the probabilistic sense of evolutionary equilibrium into order or disorder, respectively. the symbol plim is not explicitly repeated. only expression (13) conveys complexity with knowledge in the probabilistic sense. this is distinct from the non-learning though convergent order of expression (16). in this regard stewart (1989, p. 55) writes: “…. simple systems behave in simple ways, complicated systems behave in complicated ways. between simplicity and complexity there can be no common ground.” m.a. choudhury, s.i. zaman and yaqoub al-nassar 34 14. conclusion from the knowledge-centered methodology a vast number of conceptions and possibilities can be investigated in cases where complementary relations of pervasive types replace the neoclassical postulate of marginal substitution. the knowledge-centered worldview and methodology thus mark a substantive revolutionary scientific shift in terms of the epistemology of unity of knowledge and its induced relational forms as vectors, matrices and tensors of variables and their complex transformations. daly (1992) has incisively argued that the concept of complementarities between human capital and natural capital against the orthodox neoclassical concept of ‘marginal substitution’ between goods, resources and productive factors marks the rise of a new and powerful economic paradigm. the reality in socio-scientific matters that we see today is that of extensive interdependence between various domains of human activity (sztompka, 1991). when we address the topic of human ecology (hawley, 1986), constitutional economics (buchanan, 1999, reprinted), political economy of globalization (henderson, 1999), poverty alleviation and equality (sen, 1986), money and real economic activities (choudhury, 1997) and we can go on in this list, we essentially address the topic of interaction, integration and their further evolution (iie) by learning in unity of knowledge. this forms the body of complexity phenomena in which the human world realistically dwells. we have addressed such a problem of complexity but with probabilistic determination in generalizing the iie-process model that can be cogently summarized in the knowledge-centered operator. the operator is shown to summarize the entire model and implications of the relationally learning processes called the iie-processes. these are evaluated for the attained degree of unity of systemic knowledge by reference to the fundamental epistemology of unity of knowledge. we have introduced the critical evaluation function for this criterion and called it substantively as the social wellbeing function. this has been developed at length. while in this paper we have formulated our methodology and the model of relationally learning systems of knowledge-flows and their knowledge-induced variables and forms, the same epistemology of unity of knowledge is capable of explaining the mathematical complementation (opposite) of knowledge – ‘deknowledge’. the uniqueness and universality of t is shown to explain both truth (knowledge) and falsehood (‘de-knowledge’) due to the topological property of completeness of both of these in t. t thereby contains the set }{θ and its mathematical complementation (opposite) }{ cθ . likewise, the methodology of }{ cθ is extended to its cognitive forms and relational functions. the primal difference between these two evolutionary kinds of systems is this: while }{θ generates complementary relations out of diversity, }{ cθ generates marginal substitution, independence and methodological pluralism along its evolutionary path of darwinian mutations. ‘global’ complementarities and hence a relational precept of reality becomes increasingly impossible in the latter case. technical appendix 1: mathematical results relating to knowledge-induced operator some results related with the operator of the knowledge-centered methodology can be derived as follows. for mathematical details see maddox (1970): let *1θ be the limiting value of the sequence of interactions, {1,2,…n1} and * 2θ be the limiting value of the sequence of interactions, {n1 + 1,…n2}, etc. thus, ∪i = {1, 2, …, n1, n1+1, …, n2,….} (a1) consequently, we obtain for {1, 2,…, n1}, {n1+1…, n2}……… ↓ ↓ aknowledge-induced operator model 35 the values of θ (i, a, s), such as, *θ (1, a, s), *θ (2, a, s)…….. (a2) that is, )},({)},,({lim * sasaip i i θθ =∪ ∞→ (a3) likewise, ** ),( )},({lim θθ =∩ sap sasa (a4) over all possible a and s. we can re-write expression (a3) and (a4) as, * ),( )},,({limlim θθ =∩∪ ∞→ saipp saiisa (a5) in this way, expression (12) in the text is established in the limiting sense. furthermore, it can be shown that, * ),( )},,({{limlim θθ =∩∪ ∞→ saipp saisai (a6) this can be readily proven by starting in the same way as (a1) (a5) but commencing with the limits over a and s and then taking the limit over i. note however that, expression (a6) although mathematically correct, it does not convey the correct picture on the methodology pertaining to how knowledge-flows are formed first by interaction, which then lead to integration (intersection) across a, s. finally, from the result that x( *θ ) is monotonically related with *θ -values and all these categories form topologies of their own, we extend the results (a5) and (a6) to the case of {x( *θ )} and their functional relation like {w(x( *θ ), *θ )}. technical appendix 2: a simple estimation of the learning model the simple example given below was done by hossain et al. (2006) using the θ -induced model for the problem of effects of globalization on the health illness of the labor force in the united states. the empirical summary is given below. table 1 shows how the ordinal values have been assigned discursively in respect to the ratio (xi/x ) of specific ith-industry injury and illness (xi) compared to the total incidence across all industries (x). with the assigned values on social wellbeing determined by noting the spread of the incidence of total illness and injury by industries and the given industrial incidence of total illness and injury the cross-section regression involving seven industries is run for the years 1992 and 2002 separately. the estimated slope coefficient α of the estimated equation θ = a + α log x, signifies the sensitivity of a percentage change in the incidence value of illness and injury x, on the change in worker wellbeing ranked by numerically assigned values of θ. the log in the estimated equation above is taken to base. m.a. choudhury, s.i. zaman and yaqoub al-nassar 36 table 1. assigned ordinal worker wellbeing values by industry-specific illness and injury, u.s. 1992, 2002 (1000 of workers under incidence). 1992 industries (i) ordinal values of worker wellbeing (θ i ) total illness & injury by industries (xi thousands) (xi / x ) in % agriculture forestry & fishing 10.2 47.116 2.0212 mining 11.5 22.972 0.9986 construction 8.2 209.564 8.9800 manufacturing 2.0 623.568 26.7500 transportation & public utilities 8.0 224.654 9.6373 wholesale & retail trade 2.1 590.144 25.3161 finance, insurance & real estate 10.0 60.415 2.5917 services 2.5 552.665 23.7083 total incidence x 2331.098 e. a higher negative value of α corresponds to a higher wellbeing level and vice-versa. table 2 gives the estimation results. 2002 industries (i) ordinal values of worker wellbeing (θ ) total illness & injury by industries (xi thousands) (xi /x ) in % agriculture forestry & fishing 10.1 31.52 2.1947 mining 8.5 11.355 0.7906 construction 7.1 163.641 11.3941 manufacturing 4.0 280.005 19.4963 transportation & public utilities 7.0 168.632 11.7416 wholesale & retail trade 2.0 372.192 25.9152 finance, insurance & real estate 10.0 36.689 2.5546 services 2.0 372.159 0.2591 total incidence x 1436.193 source: bureau of labor statistics, u.s.a., 1992, 2002 aknowledge-induced operator model 37 table 2. sensitivity of ordinal worker wellbeing values to incidence of illness and injury by industries, u.s.a. 1992, 2002. 1992 industries (i) ordinal values of worker wellbeing (θi ) estimated values of worker wellbeing ( }îθ agriculture forestry & fishing 10.2 10.53 mining 11.5 12.64 construction 8.2 6.16 manufacturing 2.0 2.96 transportation & public utilities 8.0 5.96 wholesale & retail trade 2.1 3.13 finance, insurance & real estate 10.0 9.80 services 2.5 3.32 2002 industries (i) ordinal values of worker wellbeing (θi ) estimated values of worker wellbeing ( }îθ agriculture forestry & fishing 10.1 8.89 mining 8.5 11.07 construction 7.1 5.37 manufacturing 4.0 4.23 transportation & public utilities 7.0 5.31 wholesale & retail trade 2.0 3.62 finance, insurance & real estate 10.0 8.57 services 2.0 3.62 source: bureau of labor statistics, u.s.a., 1992, 2002 the estimated equations relating the levels of worker wellbeing iθ by industrial sectors to total incidence of illness and injury by industries in cross-sectional regression are given below for the years 1992, 2002 separately. the α-sensitivity parameters are shown in the estimated equations. estimated equations year 1992: the estimated regression equation on cross-sectional data on illness and injury over industries is, θ = 21.820 – 2.930 log x (a7) t-stats (9.754) (-6.890) r-square = 0.888 ; dw = 3.280 the a and α estimates are confident at the 5% level of significance. the sensitivity indicator is m.a. choudhury, s.i. zaman and yaqoub al-nassar 38 xd xd d ∆θ θ α %/ )(log 930.2ˆ ==−= that is, with one percentage decline in the rate of incidence the worker wellbeing increases by 2.930. year 2002: the estimated regression equation on cross-sectional data on illness and injury over industries as shown: θ = 16.263 – 2.136 log x (a8) t-stats (6.247) (-3.944) r-square = 0.777 ; dw = 3.285 the a and α estimates are confident at the 5% level of significance. the sensitivity indicator is xd xd d ∆θ θ α %/ )(log 136.2ˆ ==−= that is with one percentage decline in the rate of incidence the worker wellbeing increases by 2.136. comparison of the estimated values of α between 1992 and 2002 shows a decrease in worker wellbeing between these years. the decrease in this value of α implies that a decline in incidence of illness and injury did not sufficiently increase the ordinal value of worker wellbeing in the year 2002 compared to that in 1992. the resulting effect of this slack in the α-sensitivity values from a potential one is measured in the following way. the increase in incidence as a result of the deterioration of the sensitivity parameter α between 1992 and 2002 equals 0.794. that is, the sensitivity parameter could have been potentially improved by this value for the sensitivity parameter to be at least equal to the 1992-estimated α-value (this is the slack). because of this slack in the sensitivity parameter, worker wellbeing declined (absolute value) from –2.930 in 1992 to –2.136 in 2002. this adversely affected the ordinal value of worker wellbeing by an estimated 0.794×log 1463.193 (= x ) = 5.7869 in the year 2002 based on the logarithmic value of the total incidence over all industries, which equals log 1463.193. 15. references aquinas, t. 1946. the existence of god in things, the infinity of god, “the eternity of god, the unity of god, of god’s knowledge, in summa theologiae. 1: 1-11, 30-34, 40-45, 46-48, 72-86, new york, ny: benziger brothers, inc. barrow, j.d. 1990. theories of everything, the quest for ultimate explanation, oxford university press, oxford, england. boulding, k.e. 1971. economics as a moral science, in f.r. glabe ed. boulding collected papers vol 3, association of university press, boulder, co. buchanan, j.m. 1971. the bases for collective action, general learning press, new york, ny. buchanan, j.m. 1999. the domain of constitutional economics, in the collected works of james m. buchanan, the logical foundations of constitutional liberty, vol. 1: 377-395 liberty press, indianapolis, in. choudhury, m.a. 1993. unicity precept and the socio-scientific order, university press of america, lanham, maryland. choudhury, m.a. 1997. money in islam, london, eng: routledge. aknowledge-induced operator model 39 choudhury, m.a. 1998. studies in islamic social sciences, london, england: macmillan & new york, ny: st. martin’s press. choudhury, m.a. 2000. the qur’anic model of knowledge: the interactive, integrative and evolutionary process, in his the islamic world view, chapter 3, london, england: kegan paul international. choudhury, m.a. 2004. explaining the qur’an, a socio-scientific inquiry, lewiston, new york: the edwin mellen press. choudhury, m.a. 2005. learning systems, kybernetes: international journal of systems and cybernetics, 33:1, 2004. choudhury, m.a. 2006a forthcoming. science and epistemology in the qur’an 5: the qur’anic principle of complementarities applied to social and scientific themes,lewiston, new york: the edwin mellen press. choudhury, m.a. 2006b. generic title, science and epistemology in the qur’an, 5 volumes, lewiston, new york: the edwin mellen press. choudhury, m.a. 2006c forthcoming. islamic economics and finance: where do they stand?, proceedings of the sixth international conference on islamic economics, finance and banking, jeddah, saudi arabia: islamic development bank. choudhury, m.a. and hossain, m.s. 2006. forthcoming. evolutionary epistemology and development planning, lewiston, new york: the edwin mellen press. choudhury, m.a. and korvin, g. 2001. knowledge-induced socio-scientific systems, international journal of sustainability in higher education, 3:1. choudhury, m.a. and zaman, s.i. 2006. forthcoming. learning sets and topologies, kybernetes: international journal of systems and cybernetics, 35: 3-7. daly, h. 1992. from empty-world economics to full-world economics, in r. goodland, h. daly, s. el-serafy and b. von droste eds. environmentally sustainable economic development: building on brundtland, paris, france: unesco, pp. 29-38. dawkins, r. 1976. the selfish gene, new york: oxford university press, 1976. edel, a. science and the structure of ethics, in neurath, o. carnap, r. and morris, c. eds. foundations of the unity of science, chicago, ill: university of chicago press.pp. 277-369. gel’fand, i. 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والهرمونات التناسلية وخزعة ال بمتالزمة خاليا سرتولي الوحيدة *** و ظاهر حميد برا** ، محمد باقر رشاد فخر الدين*ناسو سليمان قهرمان سائل المنوي ومستويات الهرمونات التناسلية وحجـم الخصـية وقطـر تحديد معايير ال ) 1(تهدف هذه الدراسة الى :خالصة مـن المرضـى المصـابين بالالنطفيـة )testicular biopsies (النبيبات المنوية اعتماداً على عدد من الخزع الخصـوية . التناسـلية تقييم تأثير التدخين على تراكيز الهرمونـات ) 2(، و )non-obstructive azoospermia; noa(الالانسدادية تم اختيار المرضى وفق فحوصات السائل المنوي بطريقة النبذ المركزي ). noa(مريضاً مصاباً بـ ) 34(تضمنت الدراسة )centrifugation ( كذلك اسـتخدمت ورقـة معلومـات . وتراكيز الهرمونات التناسلية وفحص الخزعة التشخيصية للخصية لمتالزمة خاليا سرتولي ) noa(دراسة ان متوسط عمر المرضى المصابين بـ أظهرت نتائج هذه ال .تفصيلية عن المرضى بينت معايير . سنوات 4-2منهم يعانون من فترة عقم ) % 47.05(سنة، وان نسبة ) 33.875(هو ) noa-scos(الوحيدة فـي حجـم ) p>0.05(وية ظهرت فروقات غير معن . السائل المنوي تقييماً طبيعياً كما ورد في تقرير منظمة الصحة العالمية ارتفاعاً غير طبيعياً للمرضى ) fsh(سجلت تراكيز هرمون . الخصية وقطر النبيبات المنوية بين الخصيتين اليمنى واليسرى في تراكيز الهرمونات التناسلية بين المرضى المدخنين ) p>0.05(لم تظهر فروقات معنوية ). noa-scos(المصابين بـ المرضى اللذين يعـانون مـن مجاميع ان اجراء خزعة الخصية يكون مفيداً للتشخيص والتمييز بين نستنتج. وغير المدخنين )noa .( هناك حاجة الجراء دراسة اضافية لتوضيح أسباب المرض واتجاهاته وادارته في المرضى المصابين بـ)noascos.( abstract: the aims of this study were (i) to determine the seminal fluid parameters, levels of serum reproductive hormones, testicular size and diameter of seminiferous tubules depending on multiple testicular biopsies from non-obstructive azoospermic (noa) patients, and (ii) to assess the effect of smoking on concentrations of serum reproductive hormones. thirty four noa patients were involved in the present study. the selection of patients was based on an average of 2 pelleting seminal analysis, reproductive hormones profile and diagnostic testicular biopsy. a detailed questionnaire was used to obtain a thorough history from the patients. naso. s. qhraman, muhammad-baqir m.r. fakhridin and dhaher h. bra 2 the results of this study showed that the mean age of noa patients with sertoli cell only syndrome (scos) was 33.875 years, and 47.05 % of noa patients have had 2-4 years duration of infertility. macroscopic examination of seminal fluid appeared to have normal values as reported by who. non-significant (p>0.05) difference was observed for testicular size and diameter of seminiferous tubules between right and left testis. high and abnormal concentrations of serum fsh were registered for noa patients with scos. however, non-significant (p>0.05) differences were reported for concentrations of serum reproductive hormones between smokers and non smokers. in conclusion, testicular biopsy is the useful and predictable diagnostic tool for noa patients with scos. further studies are needed to explain the etiology, management and prognosis of noa patients with scos. keywords: azoospermia, sertoli cell, hormones, testicular biopsy. 1. introduction zoospermia defined as a complete absence of sperm in the ejaculate, is present in about 1% of all men (marmar, 2001) and in about 10-15% of infertile men (jarrow et al., 1989). azoospermia is one of the causes of male infertility factor that can be detected by seminal analysis (hendin et al., 1998). non-obstructive azoospermia (noa) is considered the major contributor to azoospermia, and may be classified into several categories based upon testicular histopathological changes including sertoli cell only syndrome (scos) (marmar, 2001). sertoli cell-only syndrome (scos) (so-called germ cell aplasia) is a condition in which the sperm producing-cells are no longer present in the testicles. in complete germ cell aplasia, the tubules are reduced in diameter and contain only sertoli cells but no other cells involved in spermatogenesis (nistal et al., 1990; anniballo et al., 2003). scos also can be focal with a variable percentage of tubules containing germ cells (sigman and howards, 1998). the testicular biopsy is a useful adjunct in the male infertility evaluation because it can provide a more precise clinical diagnosis, and assist in treatment selection for several infertility disorders. testicular biopsy is most useful in differentiation between obstructive and non-obstructive azoospermia (turek et al., 1995). abnormalities of seminiferous tubule architecture and cellular composition can be assessed and categorized into several patterns that aid in therapeutic decision-making (turek, 2000). in addition, physical examination should note testicular size and consistency, secondary sex characteristics, including body habitus, hair distribution, gynecomastia, consistency of the epididymis, presence of a varicocele and masses on digital rectal examination. the initial hormonal evaluation should include measurement of serum testosterone and fsh levels (sigman and howard, 1998). therefore, the aims of this study were (i) to determine the seminal fluid parameters, levels of serum reproductive hormones (including fsh, lh, testosterone and prolactin), testicular size and diameter of seminiferous tubules (st) depending on multiple testicular biopsies from non-obstructive azoospermic (noa) patients, and (ii) to assess the effect of smoking on concentrations of serum reproductive hormones. 2. subjects, materials and methods 2.1 subjects this study was carried out on non-obstructive azoospermic (noa) patients who complained from primary infertility and attended the infertility clinic at azadi general hospital, kirkuk governorate. the total number of noa patients involved in this study was 34. the study extended from october, 2004 to october, 2005. selection of azoospermic patients was based on diagnosis of azoospermia in which at least two standard semen samples were found to be devoid of sperm cells and the absence of spermatozoa. azoospermia was confirmed by a study of the sediment after centrifugation of semen at 2500 rpm for 10 minutes (sperm pelleting) (hendin et al., 1998). a evaluation of seminal fluid parameters 3 the time interval between the two consecutive semen samples was not less than 7 days and did not exceed three months (who, 1999). the clinical data of noa patients with scos are shown in table 1. the criteria applied for patient selection were proper history taking, physical examination and reproductive hormones levels assessment. each patient should have a report of histological examination of a diagnostic testicular biopsy. table 1. clinical data of noa patients with scos * involved in this study parameters data age (year) 33.875 + 0.802 duration of infertility (range: > 1.0 – 13.0 year) < 2 year 6 (17.54 %) 2 – 4 years 16 (47.05 %) 5 – 6 years 3 (8.82 %) 7 – 8 years 2 (5.88 %) 9 – 10 years 2 (5.88 %) > 10 years 5 (14.70 %) seminal fluid parameters liquefaction time (min.) 29.76 + 0.98 volume (ml) 2.467 + 0.16 viscosity normal (leave the pipette as droplets) ph 7.931 + 0.024 * number of patients: 34. 2.2 laboratory tests 2.2.1 seminal fluid collection and analysis semen samples were collected by masturbation after 3 to 5 days of abstinence into a dry, clean and sterile petri dish labeled with the name and age of the patient, period of abstinence and the time of collection. the specimens were placed in the incubator at 37°c to allow the semen liquefaction (silverberg and turner, 2001). the specimen was examined in detail macroscopically and microscopically including semen liquefaction time, volume viscosity, ph and sperm concentration. because of the fluctuation of semen parameters, each patient had at least two seminal fluid analyses. who criteria for normal semen values were applied (who, 1999). 2.2.2 hormonal assay a blood sample was drawn and collected in a clean, disposable plastic tube. concentrations of serum fsh, lh, prolactin and total testosterone were measured using minividas apparatus (vidas 12, 1992, biomerieux company, france), through an enzyme linked fluorescent assay (elfa) technique. 3. open diagnostic testicular biopsy 3.1 procedure the procedure applied for open diagnostic testicular biopsy was described by qhraman (2006). however, open diagnosed testicular biopsy was performed under general anesthesia. the testis should be held with the ventral testicular side facing the surgeon, the skin held tightly and the epididymis held between the left-hand index and the middle finger to fix the testicle and keep the epididymis away from the operation. after incising naso. s. qhraman, muhammad-baqir m.r. fakhridin and dhaher h. bra 4 the skin, the dartos muscle was incised, the edges dissected away from the tunica vaginalis and separated with small retractors. a tiny incision was made in the tunica albugenia and a small piece of the protruded testicular tissue was taken with a fine pair of scissors and placed in bouin's solution to preserve it. the cut edges of tunica albugenia were sutured with fine 2 or 3 zero chromic cat gut, leaving one side of the thread long to be held with artery forceps and used as a means of retraction as the first biopsy was taken from the middle zone. after the three biopsies, the tunica vaginalis was sutured separately by cat gut in a way that prevented any possible bleeding which might lead to hematoma and infection. when the testes were small, only two or even one biopsy was taken. the samples were sent for histopathological examination. 3.2 preparation the sections for histopathology the method for the preparation of histological sections for histopathology was slightly modified from work done by bancroft and stevens (1982), and mentioned by qhraman (2006) in detail. 3.3 histological assessment of spermatogenesis histological evaluation was done for the prepared specimens. germ cell elements were quantitatively assessed. at least 15 transverse sections of seminiferous tubules were examined in each biopsy to see the size and proportion of tubules in the biopsy. the diameter of seminiferous tubules was measured using an ocular micrometer. the diameter of at least 12 sections of seminiferous tubules was measured for each slide. the seminiferous tubules (st) with or without germ cells were observed, number, type, distribution, localization; and morphology of germinal epithelium within the seminiferous tubules were observed. sertoli cells, leydig cells, degenerating cells, tubular diameter and thickness of tubular basement membrane, all were checked. the pattern of sertoli cell-only syndrome, characterized by seminiferous tubules occupied by sertoli cells only with absence of germ cells was recorded. 4. statistical analysis computerized statistical analyses were performed using spss (statistical package of social science, version 12). frequency distribution, percentage and mean ± standard error of the mean (sem) for selected variables were calculated. paired student t-test and one way anova test were used to assess the statistical significance of the difference in the means of different groups. p value less than 0.05 was considered statistically significant (sorlie, 1995). 5. results thirty four noa patients with mean age 33.8 years, and duration of infertility (1 – 13 years) were involved in the present study (table 1). from same table, 47 % of noa patients with scos (noa-scos) have 2-4 years duration of infertility while the lowest percentages (10.41%) were recorded for 5-6 years and 7-8 years durations of infertility. macroscopic parameters of seminal fluid observed normal values (table 1). varicocele and orchidopexy were the most common risk factors affecting noa-scos (figure 1). evaluation of seminal fluid parameters 5 0 1 2 3 4 5 6 7 8 9 10 va ric oc ele mu m ps / o rc hi tis in gu in al he rn ia dr ug h ist or y or ch id op ex y ch em ot he ra py risk factors p er ce nt ag es o f r is k fa ct or s figure 1. percentages of noa with scos complaining from different risk factors for a sample of 34 patients. non-significant (p>0.05) differences for testicular size and diameter of seminiferous tubules were reported between right and left testis of noa-scos. the mean testicular size and diameter of seminiferous tubules were 3.143 cm and 118.756 µ ; respectively (table 2). table 2. mean testicular size and diameter of seminiferous tubules (rt, lt and mean within both testes)* of noa patients with scos for a sample of 34 patients (data are means + sem). testes parameters * right left mean within both testes testicular size (cm) 3.188 + 0.114 3.097 + 0.123 3.143 + 0.146 diameter of seminiferous tubules (µ) 125.879 + 3.27 123.784 + 2.93 118.756 + 3.79 * non-significant (p>0.05) difference. higher levels of serum fsh, lh and prolactin were observed in noa-scos, and combined with low level of serum testosterone as compared to normal ranges of who report (figure 2), although, non-significant (p>0.05) differences for concentrations of serum fsh, lh, testosterone and prolactin were obtained between smokers and non smokers patients (figure 3). naso. s. qhraman, muhammad-baqir m.r. fakhridin and dhaher h. bra 6 0 5 10 15 20 25 fsh lh testosterone prolactin types of reproductive hormones s er um h or m on e le ve ls figure 2. mean serum levels of fsh (miu/ml), lh (miu/ml), testosterone (ng/ml) and prolactin (ng/ml) of noa patients with scos for a sample of 34 patients. (data are means + sem). 0 5 10 15 20 25 30 fsh lh testosterone prolactin types of reproductive hormones m ea n se ru m h or m on e le ve l smokers non-smokers ns ns ns ns figure 3. mean serum levels of fsh (miu/ml), lh (miu/ml), testosterone (ng/ml) and prolactin (ng/ml) of noa patients with scos divided according to smoking habit for a sample of 34 patients. (data are means + sem). * non-significant (p>0.05) difference. evaluation of seminal fluid parameters 7 6. discussion thirty four non-obstructive azoospermic patients (mean age: 33.87 years) complaining from scos (noascos patients) were enrolled in this study. medical and surgical history, seminal fluid parameters, reproductive hormonal profile and histopathological features of testicular biopsies were evaluated. in the present study, the highest percentage (47.05 %) of noa-scos patients had 2-4 years duration of infertility. however, there was gradual reduction in the percentages of noa-scos patients as duration of infertility progressed. several explanations for this result may be relevant. the start of infertility treatment after one year of marriage causes accumulation of infertile patients throughout the first two years of treatment. while other causes reduce numbers of noa-scos patients including increased years of infertility without fecundation and hope, then an increased psychological stress and financial cost. furthermore, increase in age of noa-scos patients combined with failure of medical management may also be relevant. in relation to the risk factors associated with noa-scos patients, varicocele has the higher frequency of those assessed. who (1992) found a non-significant difference in the occurrence of azoospermia among infertile males with or without varicocele. tulloch (1995) considered varicocele as the most common identifiable cause of male subfertility. however, pasqualotto et al., (2003) observed a common association between azoospermia and varicocele as a result of generalized impairment in sperm production. the results of this study indicate that the mean testicular size (3.143 cm) for noa-scos patients was within the lower limit of the normal range (mcannich, 2000). since seminiferous tubules (sts) form the 80-85 % of the testicular mass (heath and young, 2000) reduced testicular size, in our study, may be attributed to seminiferous tubules (sts) that are either destroyed or empty of different spermatogenic cells. sharif (2000) reported that the small testicular volume may suggest an impairment of sts especially if the small volume is associated with raised fsh concentration. a reduced bilateral testicular size associated with normal ejaculate volume and raised concentration of circulating fsh, is considered to be a reliable indicator of germinal epithelial damage and non-obstructive azoospermia (battaglia et al., 2001). from testicular biopsies, the mean diameter of seminiferous tubules (sts) (118.756 + 3.79 µ m) revealed a significant reduction in diameter as compared to normal diameter of sts range (150-200 µ m) (junqueira et al., 2003). the diagnosis of scos is made when a single biopsy is histologically empty (except for sertoli cells) while seminiferous tubules and no other pathological findings. although there are many cases of non-obstructive azoospermia that have been classified as scos, 100% occurrence of scos is very rare indeed (silber et al., 1995). sigman and howards (1998) noticed that the diameter of sts is reduced and may show some thickening of the tubular basement, in addition to slightly elevated serum fsh (leifke et al., 1997). many authors mentioned that the testicular histology in case of complete scos will show normal leydig cells, no germ cells and narrow tubules (behre and bergmann, 2003). a non-significant (p>0.05) difference was found in the diameter of sts between right and left sides. a similar result was reported by other researchers (turek, 2000). regarding the macroscopic results of seminal fluid parameters in the present study, normal means were obtained according to the criteria of who (1999). most seminal fluid is produced from male accessory glands which are affected by level of testosterone. in turn, macroscopic parameters of seminal fluid are highly affected by testosterone concentration (martini, 2001). in the present work, results of the hormonal profile indicated that low levels of serum testosterone are associated with elevation of serum lh. these results are correlated with results of macroscopic parameters of seminal fluid, indicating normal leydig cell function (behre and bergmann, 2003). sigman and howards (1998) mentioned that the leydig cells are present, usually normal but on occasion are found to be reduced in size and number. in the present study, investigation of the hormonal profile for noa-scos patients showed elevation of serum gonadotropins and prolactin as compared to the normal criteria of who (1999). leifke et al. (1997) observed that infertile men with scos have highly elevated serum fsh relating to the degree of histological damage, and extremely low levels of inhibin b (hu and huang, 2002). however, elevated serum fsh associated with normal or low serum testosterone is consistent with primary testicular failure (hauser, 1995). marked elevation of serum fsh to greater than two times the upper limit of normal is diagnostic of abnormal naso. s. qhraman, muhammad-baqir m.r. fakhridin and dhaher h. bra 8 spermatogenesis. therefore, a diagnostic testicular biopsy is not necessary in patients with markedly elevated fsh (jarrow et al., 2002). the mild elevation in level of serum prolactin observed in noa-scos patients leads to reproductive dysfunction. hyperprolactinemia causes low testosterone secretion and leads to disorder of spermatogenesis (biller, 1999). however, pre-testicular causes are endocrine abnormalities that adversely affect spermatogenesis that are relatively rare and account for 1 % of azoospermia (jarrow et al., 1989). non-significant (p>0.05) differences in hormonal profiles were observed between smokers and nonsmokers noa-scos patients. light to moderate cigarette smoking causes permanent and undetectable damage for functions of endocrine cells. however, the results of this study are similar to the results of some authors and contrast to others. many studies have assessed the association between smoking and a variety of male reproductive hormone levels with some conflicting results (istvan et al., 1995). while it is likely that smoking alters male hormone levels, the relationships are not well characterized (stillman et al., 1986). cigarette smoke contains several chemical agents, many of which are carcinogenic or mutagenic (kunzle et al., 2003). these agents affect the production and function of normal sperm by reduction in testosterone concentration in testicular tissue as a consequence of impaired leydig cell function by direct effect of inhaled nicotine and carbon monoxide on testicular tissue (zavos et al., 1999). in conclusion, the open testicular biopsy was found to be practical, informative and valuable diagnostic tool for noa patients. more studies are needed to explain the etiology, management and prognosis of noa patients with scos. 7. references anniballo, r., ubalid, f. and tesarik, j. 2003. functional status of the sertoli cells in azoospermic men. fertil. steril, 79: 237-238. bancroft, j.d. and stevens a. 1982. theory and practice of histological techniques. 2nd edition. churchill, livingston, london. pp. 110-111. battalgia, c., giuliani, s., regnani, g. and modgar, i. 2001. intratesticular doppler flows, seminal plasma nitrites/nitrates and nonobstructive sperm extraction from patients with obstructive and non-obstructive azoospermic. fertil. steril, 75: 1088-1094. behre, h.m. and bergmann, m. 2003. primary testicular failure. in: endocrinology of male reproduction. www.endotext.com. biller, b.m. 1999. hyperprolactinemia. int. j. fertil, 44: 74-77. hauser, r. 1995. fertility in cases of hypogonadotropic azoospermia. fertil. steril, 63: 631-636. heath, t.w. and young, b. 2000. male reproductive system. in: functional histology. horne, t. 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(eds.), lange medical book / mcgraw-hill, beirut, lebanon. 15th ed.; pp. 750-787. world health organization (who) 1992. the influence of varicocele on parameters of fertility in a large group of men presenting to infertility clinic. fertil. steril, 57: 1289-1293. world health organization (who) 1999. who laboratory manual for the examination of human semen and sperm cervical mucus interaction. 4th ed.; new york; cambridge university press; pp. 4-59. zavos, p.m., zarmakoupis, c.n. and zarmakoupis zavos, p.n. 1999. the impact of cigarette smoking on human reproduction: its effects on female and male fecundity. mid. east fertil. soci. j, 4: 94-101. received 25 july 2006 accepted 31 october 2006 microsoft word chem040209.doc squ journal for science, 9 (2004) 19-23 © 2004 sultan qaboos university 19 isolation of aristolochic acids from aristolochia bracteolata and studies of their antioxidant activities saleh al-busafi, munir al-harthi and bushra al-sabahi department of chemistry,college of science, sultan qaboos university, p. o. box 36, al-khod 123, muscat, sultanate of oman, email: saleh1@squ.edu.om. ودراسـة انشـطتها المضـادة أريستولوكيا براكتيوالتا إستخالص أحماض االريستولوكيك من نبات لألكسدة صالح البوصافي ، منير الحارثي و بشرى الصباحي أريسـتولوكيا براكتيوالتـا لتركيب ألجزيئ ألحما ض أألريستولوكيك من نبـات ا إستخالص وكشف : خالصة إلـى mo(vi) لمركبات الطبيعيه قد تم تقيمها بناء علـى قـدرتها إلختـزال األنشطه ألمضاده لألكسده لهذه ا .mo(v) أ -د أكثر نشاطا من فيتامين ج بينما حمض أريسـتولوكيك -لدراسه أظهرت أن حمض أريستولوكيك ا .مماثل لنشاط فيتامين ج abstract: the isolation and structural elucidation of aristolochic acid-a and aristolochic acid-d from omani aristolochia bracteolata plant is reported. antioxidant activities of these two natural products were evaluated for their capacity to reduce mo(vi) to mo(v). the study revealed that aristolochic acid-d is more active than vitamin c while aristolochic acid-a has activity similar to vitamin c. keywords: aristolochia bracteolata; aristolochic acid-a; aristolochic acid-d; antioxidant activities and omani plants. 1. introduction ristolochia bracteolata is a climbing perennial plant with cordate leaves and dark-purple tubular flowers with unpleasant smell (ghazanfar, 1991). traditionally, the plant has been used to treat wounds and for snakebites. the genus aristolochia is a source of aristolochic acid, which has been evaluated in china for the treatment of wounds and infectious diseases; it was found to be useful for promoting wound healing in ulcers, burns, and scalds (jiangsu, 1977). recently, aristolochic acids, present in aristolochia plants, have been shown to be nephrotoxic in rats (matsuo, et al., 2003). a family of aristolochic acids have been isolated from aristolochia argentina (priestap, 1987), and from aristolochia indica (kupchan et al., 1968). aristolactam alkaloids and amides were isolated from aristolochia a saleh al-busafi, munir al-harthi and bushra al-sabahi 20 kankauensis (tian-shung wu et al., 1994) and from aristolochia auricularia (houghton et al., 1990). aristolochic acid-a was isolated from the root of aristolochia bracteata from sudan (mohamed et al., 1999). magnoflorine and aristolochic acid-a were isolated from a. bracteata from saudi arabia (el tahir et al., 1991). both compounds were found to induce contractions in the isolated pregnant rat uterus and stimulated the isolated guinea pig ileum. n-acetylnornuciferine and aristololactam were isolated from a. bracteata from india (chakravarty, et al., 1988). aristolochic acid-a was characterized as the principal tumer-inhibitory principle (kupchan et al., 1968). in recent years, the antioxidative action of natural products received much attention, due to their possible role in disease prevention (aruoma, 1998). in the course of continuing search for natural products with antioxidant properties from omani plants we report herein the isolation and elucidation of two aristolochic acids (1, 2) from n-butanol extract of a. bracteolata leafs and stems and their antioxidant activities relative to vitamin c. the antioxidant activities were tested using the reduction of phosphomolybdenum complex system (prieto, et al, 1999). aristolochic acid-a (1) aristolochic acid-d (2) o o oh o no2 ome h h h h h 12 4 5 6 7 8 9 10 3 o o oh o no2 ome h ho h h h 12 4 5 6 7 8 9 10 3 2. results and discussion 2.1 isolation and structural elucidation of aristolochic acids 1 and 2 isolation of the two compounds was carried out by a standard column chromatography with silica gel (0.13-0.25 mm, 60-120 mesh). the principal product was aristolochic acid-a (1), which was eluted with a mixture of chloroform-methanol (95% : 5%). elution with increasing polar mixtures of chloroformmethanol (88% : 12%) yielded aristolochic acid-d (2). aristolochic acid-a (1) separated from methanol as dark-red solid with melting point of 260-265 ˚c. the mass spectrum ([m]+at m/z 341) establishes the molecular formula as c17h11no7 with fragment ions at 327 [m-ch2] +, 281 [m-ch2-no2] +, 253 [m-ch2-no2-co] +, 237 [m-ch2-no2-co2] +, 207 [m-ch2-no2co2-och2] +. ultraviolet (uv) absorptions at 218, 227, 255, and 312 nm suggest a highly conjugated system. the infrared (ir) spectrum showed the presence of hydroxyl group (strong broad signal at 2850 – 3579 cm-1), carbonyl group (sharp signal at 1714 cm-1), nitro group (signals at 1345 cm-1 symmetric stretch and at 1517,1594 cm-1 asymmetric stretch). the 1h nuclear magnetic resonance (1h nmr) spectrum of 1 showed signals for an aromatic methoxyl group at δ 4.04 (3h, s) and for methylenedioxy group at δ 6.47 (2h, s). three mutually coupled aromatic protons appeared at δ 7.32 (1h, d, j=8.1hz), 7.79 (1h, t, j=8.2 hz), δ8.66 (1h, d, j=8.4 hz); the signals were assigned to h-7, h-6 and h-5 respectively as revealed by 1h1h correlation spectroscopy (1h-1h cosy) and compared to literature values (tian-shung wu et al., 1994). two singlets at δ 7.75 and 8.47 (each 1h) were assigned to h-2 and h-9 respectively. the position of 8ome was deduced from nuclear overhauser effect (noesy spectrum) which showed h-7 (δ 7.32) to be within noe distance from the 8-ome. isolation of aristolochic acids 21 table 1. nmr spectral data of aristolochic acids 1 and 2. aristolochic acid-a (1) aristolochic acid-d (2) position 1h data (ppm) 13c data (ppm) 1h data (ppm) 13c data (ppm) 1 119.4 118.0 2 7.76, s 112.4 7.69, s 112.6 3 146.34 145.7 4 147.06 145.7 4’ 117.6 117.0 5 8.62, d, j 8.4 119.2 8.06, d, j 2.4 104.1 5’ 130.4 132.1 6 7.79,t, j 8.2 132.0 158.4 7 7.32, d, j 8.1 109.5 6.84, d, j 2.4 100.0 8 156.68 161.5 8’ 115.8 112.3 9 8.47, s 119.3 8.36, s 112.6 10 146.34 145.7 10’ 117.1 117.0 c=o 168.7 168.9 -och2o6.43, s 103.0 6.40, s 102.7 ch3o4.04, s 56.7 3.98, s 56.6 aristolochic acid-d (2) was obtained as brown solid with melting point range of 280-288 ºc. the structure of 2 was inferred from its mass spectrum ([m-2]+ at m/z 355) which establishes the molecular formula as c17h11no8 with fragment ions at 327 [m-och2] +, 281 [m-och2-no2] +, 277 [m-2oh-no2], 207 [m-ch2-no2-co2-och2o] +. uv absorptions at 225, 245, 289, and 364 nm show a close resemblance to that of 1. the ir spectrum showed the presence of hydroxyl group (strong broad signal at 2720 – 3691 cm-1), carbonyl group (at 1702 cm-1), nitro group (signals at 1517 cm-1). the aromatic region of the 1h nmr spectrum of 2 contained two doublets at δ 6.84 (1h, d, j=2.4 hz) and 8.06 (1h, d, j=2.4 hz) attributed to h-7 and h-5 respectively. the small j value suggests a meta coupling system. the low frequency signal of h-7 at δ 6.84 is due to the shielding effect of the ortho hydroxyl and methoxyl groups. two singlets at δ 7.69 and 8.36 (each 1h) were assigned to the c-2 and c-9 protons. the 1h nmr spectrum showed the presence of methoxyl group at δ 3.98 (3h, s) and methylenedioxy group at δ 6.40 (2h, s). the position of 8-ome was deduced from a noesy spectrum which showed h-7 (δ 7.32) to be within noe distance from the 8-ome. the nmr spectral data of aristolochic acid-a (1) and aristolochic acid-d (2) are summarized in table 1. 2.2 antioxidant activities of aristolochic acids 1 and 2 the phosphomolybdenum method is based on the reduction of mo(vi) to mo(v) by the antioxidant compound and the formation of a green phosphate/mo(v) complex with a maximal absorption at 695 nm. the assay was successfully used to quantify vitamin e in seeds (prieto et al., 1999) and measuring antioxidant activity of the sage polyphenols (yinrong et al, 2001). the method is simple and independent of other antioxidant measurements commonly employed. our value for vitamin c (a695 = 1.625) at a concentration of 5 mm, was well comparable with the reported molar absorption coefficient of vitamin c [ε = (3.4 ± 0.1) x 103 m-1 cm-1] (prieto et al., 1999). the results in table 2 show that the antioxidant activity of aristolochic acid-a (1) is almost equal to that of vitamin c. on the other hand, aristolochic acid-d (2) has better antioxidant activity than vitamin c. saleh al-busafi, munir al-harthi and bushra al-sabahi 22 this high antioxidant activity of aristolochic acid-d (2) is presumably due to the presence of the hydroxyl group at c-6. table 2. antioxidant activities of aristolochic acids 1 and 2 relative to vitamin c. compound am a aristolochic acid-a (1) 1.03 aristolochic acid-d (2) 1.20 vitamin c 1 a am , activity relative to vitamin c on a molar basis. 3. experimental 3.1 general the uv spectra were obtained with a varian model cary 50 conc spectrophotometer. the ir spectra were obtained as kbr discs with a nicolet model magna 560 spectrometer; absorption bands are recorded in wave number (cm-1). the 1h nmr and 13c nmr spectra were recorded at 400 mhz using bruker spectrometer in dmso-d6. chemical shifts are expressed as δ values (ppm) downfield from tms. thin-layer chromatography (tlc) was carried out on merck f254 silica gel plates (0.2 mm thickness) with mobile phase chcl3 – meoh, (80 : 20) and spots were detected under uv 254 nm. melting points were recorded using gallen kamp apparatus. electron impact mass spectroscopy (eims) was performed on a shimadzu gcms qp5050 spectrometer. 3.2 plant material aristolochia bracteolata was collected from mazara, wilayat of quraiyat, sultanate of oman in 2001 and was authenticated by specialists in the department of biology, sultan qaboos university. 3.3 extraction and isolation 450 g of shade dried powdered leafs and stems of a. bracteolata was repeatedly extracted with methanol at room temperature. the combined extract was concentrated under reduced pressure to get 45 g of greenish viscous material which was first partitioned between hexane/h2o, then etoac/h2o and finally n-butanol/h2o to give a hexane extract, an ethyl acetate extract and n-butanol extract. the concentrated nbutanol extract (23 g) was chromatographed over a silica gel column and eluted with chloroform then with chloroform-methanol mixture. aristolochic acid-a (1) (40 mg) was isolated from chloroform-methanol mixture (95% : 5%) fractions. aristolochic acid-d (2) (20 mg) was isolated from chloroform-methanol mixture (88% : 12%). 3.4 evaluation of antioxidant activity the antioxidant activity of aristolochic acids was evaluated by the phosphomolybdenum method according to the procedure of prieto et al. (1999). an aliquot of 0.1 ml sample solution (5 mm in meoh) was combined in a 4-ml vial with 1 ml of reagent solution (0.6 m sulfuric acid, 28 mm sodium phosphate and 4 mm ammonium molybdate). the vials were capped and incubated in a water bath at 95 ºc for 90 min. after the samples had cooled to room temperature, the absorbance of the mixture was measured at 695 nm against a blank. the antioxidant activity was expressed relative to that of ascorbic acid. 4. acknowledgements this research was supported by sultan qaboos university grant number ig/sci/chem/03/01. the authors are grateful to salem al-saidi, department of chemistry, sultan qaboos university for ei-ms isolation of aristolochic acids 23 spectra, and to wafa al-shuaily, department of chemistry, sultan qaboos university for the nmr spectra. the authers wish to thank dr. hisham kader for helpful discussions. 5. references aruoma, o.i. 1998. free radicals, oxidative stress, and antioxidants in human health and disease. j. am.oil chemists’ soc., 75: 199-212. chakravarry, m.; chaudhuri, c.; achari, b. and pakrashi, s.c. 1988. studies on indian medicinal plants. part 90. n-acetylnornuciferine and other constituents of aristolochia bracteata. planta med., 54(5): 467-468. el tahir, k.e. 1991. pharmacological actions of magnoflorine and aristolochic acid-1 isolated from the seeds of aristolochia bracteata. int. j. pharmacogn, 29(2): 101-110. ghazanfar, s.a. 1992, an annotated catalogue of the vascular plants of oman. scripta bot. belg. 2:20 houghton, p.j. and ogutyeren, m. 1990. aristolochic acids and aristolactams from aristolochia auricularia. phytochem., 30(1): 253-254. jiangsu. 1977. new medicine college. encyclopedia of chinese materia medica, 1: 294. kupchan, s.m. and merianos, j.j. 1968. the isolation and structural elucidation of novel derivatives of aristolochic acid from aristolochia indica. j. org. chem., 33(10): 3735-3788. matsuo, s.; yuzawa, y.; hanaki, s.; morita, y.; mizuno, m.; maruyama, s. and liu, m. 2003. the nephrotoxicity of aristolochia manshuriensis in rats is attributable to its aristolochic acids. clinical and experimental nephrology, 7(3): 186-194. mohamed, o.a.; wang, z.; yu, g.; khalid, h.e. and abu-elrish, b.i. 1999. determination of aristolochic acid-a in the roots and rhizomes of aristolochia from sudan and china by hplc. zhongguo yaoke daxue xuebao, 30(4): 288-290. priestap, h.a. 1987. minor aristolochic acids from aristolochia argentina and mass spectral analysis of aristolochic acids. phytochem., 26(2): 519-529 prieto, p.; pineda, m. and aguilar, m. 1999. spectrophotometric quantitation of antioxidant capacity through the formation of a phosphomolybdenum complex. anal. biochem., 269: 337-341. tian-shung wu; li-fei ou and che-ming teng. 1994. aristolochic acids, aristolactam alkaloids and amides from aristolochia kankauensis. phytochem., 36(4): 1063-1068. yinrong, lu and foo, y.l. 2001. antioxidant activities of polyphenols from sage (salvia officinalis). food chem., 75: 197-202. received 9 february 2004 accepted 22 november 2004 microsoft word biol090331-f edited_corrected.doc 15(2010) 9-17 squ journal for science, © 2010 sultan qaboos university 9 a comparison of the physiological age of adult resting versus flying culex quinquefasciatus (diptera: culicidae) d.m. roberts department of biology, college of science, sultan qaboos university, p.o. box 36, postal code 123, muscat, sultanate of oman, email: derekmr@squ.edu.om. وهو في طور السكون مقارنة بحالة الطيران) الكيولكس كيوينكويفاسيا(مقارنة بين العمر الفسيولوجي للبعوض سديريك روبرت وجد في هذه الدراسة إن نسبة ذآر ، هناك معلومات قليلة عن العمر الفسيولوجي للبعوض وهي في حالة السكون :خالصة ولكن عند اإلناث وجد أن هناك % 76وفي حالة الطيران % 75في حالة السكون هي البعوض آيومكس آوينكيفاسياتص وهو حيث وجد أن نسبة اإلناث في طور السكون والتي لم يتم .فرق بين العمر الفسيولوجي في حالة السكون مقارنة بحالة الطيران وجدت نسبة عالية من اإلناث التي تم تغذيتها بالمقارنة %. 82 آانت نسبتها في حالة الطيران واإلناث التي % 51تغذيتها آانت في حالة السكون % 21(ولدرجة أقل عند وضعها للبيض ) في حالة الطيران % 4في حالة السكون مقارنة ب % 28( على الدم ر على إن غالبية الذآور واإلناث قد دخلوا في حالة السكون طوال اليوم حيث لم يتم العثو ) في حالة الطيران % 14مقارنة ب أي منهم بعد الغروب وآانت أعلى نسبة في الصباح الباآر قبل شروق الشمس إن المجموعات الطائرة آانت تكثرفي الصباح تبين االختالف الجغرافي الكبير في هذا النوع من حيثالباآر وتقل عند الغروب وهذه الدراسة مختلفة عن الدراسات السابقة . لمداريةالحشرات التي تعيش في المناطق ا abstract: relatively little is known about the physiological age of resting mosquitoes. in this study, culex quinquefasciatus had a similar proportion of resting males (75%) as in the flying population (76%), but among the females, there were significant differences between the physiological age of the resting and flying populations. the proportion of unfed resting females (51%) made up a significantly smaller proportion than in the flying female group (82%). by contrast, in the resting group, there were much higher proportions of blood-fed (28% compared with 4%) and to a lesser extent gravid (21% compared with 14%) females. of the blood-fed females, most of the resting individuals were freshly blood-fed. both males and females entered the resting traps throughout the day (but none were collected after sunset), with the main peak around dawn. the flying population showed two circadian peaks: a larger peak at dawn and smaller peak after sunset. this indicates a different pattern from that shown in other studies and demonstrates the significant geographic variation within this pan-tropical species. keywords: culex quinquefasciatus, mosquitoes, circadian activity, resting, flight activity. d.m. roberts 10 1. introduction he female mosquito has up to 8 gonotrophic cycles, each averaging 4 4.5 days (birley and rajagopalan, 1981; chandra et al., 1996), although subra (1981) found this varied on different cycles. during each of these cycles, the female needs to find a blood meal, digest the blood meal and develop its eggs, and then find somewhere to oviposit the eggs. its behaviour thus changes during different stages of the cycle and its need for somewhere to rest will thus similarly change. although there have been many studies of circadian flying activity in cx. quinquefasciatus from different parts of the world , there have been few studies of resting behaviour and particularly the effect of physiological age on this behaviour. by emptying artificial resting-site traps at different times of the day, the resting behaviour of the mosquitoes was compared with their circadian flight activity, studied using suction traps. a further experiment investigated how easily each group of resting mosquitoes were disturbed and thus left the trap during the day. 2. materials and methods two suction traps and 10 resting-site traps were placed in a suburban garden, at least 10 m apart, in the town of al-khod on the batinah coast of oman. all the mosquitoes collected were identified as cx. quinquefasciatus and no other mosquito species were found in the urban area. this is probably because there was no surface water within 10 kilometres of the site and no rain during the collecting period (or for many months beforehand). thus virtually the only available breeding waters were in the septic tanks of the surrounding houses, which are the major breeding sites for cx. quinquefasciatus. each suction trap had a 33 cm fan sucking air through a wire net cone and depositing the insects into a jar containing ethanol. the artificial resting sites each consisted of a thick plastic bag with dimensions of 85 (h) x 50 (l) x 24 (w) cm. each bag was black internally and light-proof, thus fitting morris’ (1981) ideal characteristics of a resting trap. the traps were attached to trees, so that their open tops were about the same height above ground (1.5 m) as the suction trap entrances. the resting-site bags were emptied by rapidly repeatedly sweeping a net through the bag, until no more mosquitoes emerged. although cx quinquefasciatus is present throughout the year, due to the extreme climatic conditions of oman with daytime temperature over 40 oc for 5 months of the year, the mosquitoes were only sufficiently abundant for the experiments for 3 months during the winter. in the first two experiments, which were run consecutively in feb. 2004, both suction traps (to monitor the flying insects) and resting traps were emptied 7 times a day to give 7 daily samples: late night = 23.00h to 6.00 h (7 h); early dawn = 6.00 h (which was 1st light with < 100 lux) to 6.30 h (0.5 h); late dawn = 6.30 h to 7.00 h (by which time, the light intensity was > 100,000 lux) (0.5 h); day = 7.00 h to 18.00 h (11 h); early sunset = 18.00 to 18.30 h (0.5 h); late sunset = 18.30 h (sunset) to 19.00 h (0.5 h); and early night = 19.00 h to 23.00 h (4 h). in the second experiment, the two sunset catches (early + late) were combined, due to their very small size. the first experiment had 15 replicates (i.e. 15 consecutive days), but the other 3 experiments using resting traps were reduced to 10 replicates each due to the large mosquito catches. in the third experiment (early march 2004), 10 resting traps were left for 24h and only emptied after dawn (7.00 h), while a further 10 resting traps were emptied at sunset each day (18.30 h), in order to see whether a particular mosquito group (sex/ physiological age or blood-fed stage) was more sensitive to mechanical disturbance by wind during the day. all the female mosquitoes were dissected under an insect saline solution (8.5g nacl / l) in order to identify their physiological state. they were divided into unfed, blood-fed and gravid. the blood-fed females were further subdivided by the stage of oocyte development into type i, ii, iii and iv (type v being gravid). initially, the unfed and blood-fed individuals were also divided into nulliparous and parous. however, for logistical reasons, half the mosquitoes were not dissected until a year later, by which time they had deteriorated too much to permit separation by age. t a comparison of the physiological age of adult resting versus flying 11 3. results table 1. composition of the mosquito catch in the suction traps (flying insects) and the resting traps. flying insects (suction trap) resting insects total % catch total % catch males 18,334 76 % 8,184 75 % females 5,666 24 2,748 25 unfed 4,656 c 82 %* 1,392 a 51 %* bloodfed 249 d 4 766 b 28 gravid 761 e 14 589 b 21 bloodfed 1 67 h 27 %** 279 f 36 %** bf 2+3 89 gh 36 266 f 35 bf 4 93 g 37 221 f 29 * % of females ** % of bloodfed. different letters (after the totals) show they are significantly different in tukey test for 1-way anova. in the suction traps, flying mosquitoes showed a much greater level of activity in the males (making up 76% of the catch, table 1) than in the females. males, however, were mainly restricted to a large dawn and smaller sunset peak, while the females had smaller peaks, due to a higher level of activity throughout the night (figure 1). 0 0.5 1 1.5 2 2.5 3 3.5 0 2 4 6 8 10 12 14 16 18 20 22 24 time a bu nd an ce ( lo g1 0+ 1) fig.1 figure 1. circadian activity of flying males and females. males; _____ females. d.m. roberts 12 0 0.5 1 1.5 2 2.5 0 2 4 6 8 10 12 14 16 18 20 22 24 time a b u n d an ce (l o g 10 +1 ) fig 2 figure 2. circadian activity of flying females. unfed; ---blood-fed; ______ gravid. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 2 4 6 8 10 12 14 16 18 20 22 24 time a b u n d an ce (l o g 10 +1 ) fig 3 figure 3. circadian activity of flying blood-fed females. _____ stage 1; ---stage 2+3; stage 4. a comparison of the physiological age of adult resting versus flying 13 0 0.5 1 1.5 2 2.5 3 3.5 0 2 4 6 8 10 12 14 16 18 20 22 24 time a b u n d an ce ( lo g 10 +1 ) fig 4 figure 4. circadian resting activity of males and females. males; _____ females. 0 0.5 1 1.5 2 2.5 0 2 4 6 8 10 12 14 16 18 20 22 24 time a b u n d an ce (l o g 10 +1 ) fig 5. figure 5. circadian resting activity of female groups. unfed; ---blood-fed; ____ gravid. among the flying females, most (82%) were unfed (table1) and showed the activity pattern above (figure 2), but the small numbers of gravid and very small (4%) numbers of blood-fed females had their activity d.m. roberts 14 largely restricted to the large dawn and smaller sunset peaks. when the blood-fed females were subdivided by their physiological age, the freshly blood-fed (stage 1) were significantly less abundant (p = 0.018 in a 1-way anova) than the stage 4 females. in addition, they differed from the others by having activity throughout the night, but no sunset peak (figure 3). the resting mosquitoes had virtually the same sex ratio (75% males) as the flying ones (76% table 1). both males and females had a similar pattern of entering the resting traps at dawn (figure 4). small numbers continued to enter during the day, with the females in this group being almost entirely unfed (figure 5), but at night the traps did not attract mosquitoes. among the females, only 51% were unfed (table 1), but there was a significantly (p < 0.0001 on a 2-way anova) greater proportion of blood-fed females (28%) and to a lesser extent gravid females compared with the flying population. the blood-fed resting females, compared with those flying, had a significantly greater (p = 0.025) proportion of freshly blood-fed (stage 1 oocytes) females (tukey test in table 1). table 2. comparison of resting mosquitoes collected at dawn and at dusk. dawn collection sunset collection total total % of dawn catch males 10,295 7,422 72 % females 2,158 1,760 82 unfed 1,014 941 92 % bloodfed 539 296 55 gravid 605 523 86 bloodfed 1 157 37 23 % bf 2+3 214 163 76 bf 4 168 96 57 when resting mosquitoes were left until sunset before being collected (table 2), the number declined to 82% of the dawn catch for the females and 72% for the males. among the females, the decline was greatest among the blood-fed (45% had gone by sunset), with only a very small decrease (8%) for the unfed flies. among the blood-fed females, the biggest decrease was in the freshly fed (stage i) females. 4. discussion when considering the activity patterns of male and female cx quinquefasciatus, both had two peaks: before sunrise and after sunset. the females, however, had much more extensive activity than the males and were active throughout the night. they even showed some activity during the daytime. both sexes had their main peak at dawn and a much smaller sunset peak. a similar result was found in laboratory studies by jones (1982), and also for studies on the cx quinquefasciatus sibling species: cx molestus forskal and cx pallens coquillet (shinkawa et al., 1994) and cx pipiens l. (caglar et al., 2003). however, other studies have shown considerable variation in the circadian activity of cx quinquefasciatus, although most were limited to biting catches and therefore represent only a small part of the female population. some studies have found that biting activity of cx quinquefasciatus was greatest in the early part of the night (gowda and viayan, 1993; khan et al., 1997; pipitgool et al, 1998), while others found activity greatest after midnight (brunhes, 1975; subra, 1981; vanamail and ramaiah, 1991; ramasamy et al, 1994; chandra, 2001). in still other studies, however, two peaks of activity were recorded. for example mahanta et al. (1999) found peaks around 19.00 and 23.00h; yee and foster (1992) found peaks at 23.00h and before dawn, while sucharit et al. (1981) found three peaks. a comparison of the physiological age of adult resting versus flying 15 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 2 4 6 8 10 12 14 16 18 20 22 24 time a b u n d an ce (l o g 10 +1 ) fig 6. figure 6. circadian resting activity of blood-fed females. stage 1; _____ stage 2+3; --- stage 4. the fact that gravid females, which are likely to be looking for oviposition sites, had dawn and sunset peaks corresponds to the results of oviposition behaviour observations by hayes and downs (1980) and subra (1981). however, other studies have shown considerable differences from this pattern. thus beehler et al. (1993) found that oviposition occurred mainly within 2 hours after sunset, but extended up to midnight. suleman and shirin (1981) found a midnight peak, while panicker et al. (1981) found a peak after midnight. these variations observed by different workers in different parts of the world, when studying the flight, biting and oviposition cycles of cx quinquefasciatus are likely to be due to the pantropical distribution of the species, with resulting racial genetic variations in different regions, and they demonstrate the importance of regional studies when trying to understand the ecology of the vector of filariasis and viral diseases. the resting females, when compared with the active flying population, had a significantly higher proportion of blood-fed individuals, especially those freshly blood-fed with stage 1 oocytes, showing their need to rest while digesting the meal. there was also a greater proportion of resting gravid females than in the active population, but many non-fed females were also collected. the fact that all the female stages were present in large numbers in these outdoor resting sites contrasts with other studies. thus subra (1970), studying an area of traditional huts, found a high proportion of freshly fed resting females inside the huts, but outside resting sites (wells) mainly had non-fed and gravid females. from this, he concluded that the mosquitoes mainly fed indoors and remained resting indoors to digest their meal. they then moved outdoors to lay their eggs and remained outdoors until ready to blood-feed again. similar conclusions were made by service (1963) and kulkarni and rajput (1988). however, in the present urban study, where all houses have window mosquito netting and airconditioning, endophagic feeding would be more normal and thus a high proportion of the resting females outdoors were freshly fed. tuno et al. (2003) considered that non-fed mosquitoes rested near their host before deciding whether to blood-feed and this could partly account for the large numbers of resting non-fed females collected in this study. this would lead to a cycle in which females rested before feeding (making up 51% of the resting females), but after blood-feeding still spent most of their cycle resting while their eggs developed (28% blood-fed and 21% gravid). when the resting traps were emptied at sunset, rather than dawn, the decline in population was greatest among the freshly blood-fed, showing that they were more likely to be disturbed and move on to a better resting d.m. roberts 16 site, whereas the unfed and gravid females were much less likely to be disturbed from their resting behaviour. this disturbance is most likely due to the wind, since the traps were in deep shade and so unlikely to get hot during the winter months. male mosquitoes were much more abundant than females in both the resting traps (75%) and among the flying population (76%), although emerging cx quinquefasciatus have an equal sex ratio. schreiber et al. (1993) found a lower ratio of 61% resting cx. quinquefasciatus to be male. he concluded that the males were less active than the females and that his traps were close to the breeding sites. however in this study with abundant breeding sites, it is more likely that the resting traps were more attractive to the males and, by observation, the males swarmed around the suction traps, which thus collected more males than females 5. acknowledgements i thank sultan qaboos university for providing research facilities. 6. references abu hassan, a., narayanan, v. and salmah, m.r.c. 1993. observations on the physico-chemical factors of the breeding habitats of culex quinquefasciatus say, 1823 (diptera: culicidae) in towns of north western peninsular malaysia. ann. med. entomol., 2: 1-5. beehler, j.w., webb, j.p. and mulla, m.s. 1993. spatial and circadian oviposition patterns in an urban population of culex quinquefasciatus. j. am. mosq. control assoc., 9: 385-388. birley, m.h. and rajagopalan, p.k. 1981. estimation of the survival and biting rates of culex quinquefasciatus (diptera: culicidae). j. med. entomol., 18: 181-186. brunhes, j. 1975. la filiarose de bancroft dans les sous-region malgache (comores-madagascar-reunion). memoires orstom, 81: 1-212. caglar, s.s., alten, b., bellini, r., simsek, f.m. and kaynas, s. 2003. comparison of nocturnal activities of mosquitoes (diptera: culicidae) sampled by new jersey light traps and co2 traps in belek, turkey. j. vector ecol., 28: 1-11. chandra, g., seal, b. and hati, a.k. 1996. age composition of the filarial vector culex quinquefasciatus (diptera: culicidae) in calcutta, india. bull. entomol. res,. 86: 223-226. chandra, g. 2001. man biting activity of filarial vector culex quinquefasciatus. j. comm. dis., 33: 53-57. chavasse, d.c., lines, j.d., ichimori, k. and marijani, j. 1995. mosquito control in dar es salaam. i assessment of culex quinquefasciatus breeding sites prior to intervention. med. vet. entomol., 9: 141-146. gowda, n.n. and viayan, v.a. 1993. biting density, behaviour and age distribution of culex quinquefasciatus say in mysore city, india. s.e. asian j. trop. med. public hlth., 24: 152-156. hayes, j. and downes, t.d. 1980. seasonal changes in an isolated population of culex pipiens quinquefasciatus (diptera: culicidae): a time series analysis. j. med. entomol., 17: 63-69. jones, m.d.r. 1982. coupled oscillators controlling circadian flight activity in the mosquito, culex pipiens quinquefasciatus. physiol. entomol., 7: 281-289. khan, s.a., narain, k., dutta, p., handique, r., srivastava, v.k. and mahanta, j. 1997. biting behaviour and biting rhythm of potential japanese encephalitis vectors in assam. j. comm. dis., 29: 109-120. kulkhani, s.m. and rajput, k.b. 1988. day-time resting habitats of culicine mosquitoes and their preponderance in bastar district, madhya pradesh, india. j. comm. dis., 20: 280-286. mahanta, b, handique, r., dutta, p., narain, k. and mahanta, j. 1999. temporal variations in biting density and rhythm of culex quinquefasciatus in tea agro-ecosystem of assam, india. s.e. asian j. trop. med. public hlth., 30: 804-809. a comparison of the physiological age of adult resting versus flying 17 menon, p.k.b. and rajagopalan, p.k. 1980. relative importance of different types of breeding habitats in contributing to the population of culex pipiens fatigans in pondicherry. indian j. med. res., 71: 725733. morris, c.d. 1981. a structural and operational analysis of diurnal resting shelters for mosquitoes (diptera: culicidae). j. med. entomol., 18: 419-424. panicker, k.n., bai, m.g. and viswam, k. 1981. observations on the oviposition rhythm of some mosquitoes. indian j. med. res., 74: 388-391. pipitgool, v., waree, p., sithithaworn, p. and limviroj, w. 1998. studies on biting density and biting cycle of culex quinquefasciatus, say in khon kaen city, thailand. s.e. asian j. trop. med. public hlth., 29: 333-336. ramasamy, m.s., kulasekera, r., srikrishnaraj, k.a. and ramasamy, r. 1994. population dynamics of anthropophilic mosquitoes during the northeast monsoon season in the malaria epidemic zone of sri lanka. med. vet. entomol., 8: 265-274. roberts, d.m. and irving-bell, r.j. 1997. salinity and microhabitat preferences in mosquito larvae from southern oman. j. arid environ., 37: 497-504. schreiber, e.t., walton, w.e. and mulla, m.s. 1993. mosquito utilisation of resting sites at an urban residence in southern california. bull. soc. vector ecol., 18: 152-159. service, m.w. 1963. the ecology of the mosquitoes of the northern guinea savannah of nigeria. bull. entomol. res,. 54: 601-632. shinkawa, y., takeda, s., tomioka, k., matsumoto, a., oda, t. and chiba, y. 1994. variability in circadian activity patterns within the culex pipiens complex (diptera: culicidae). j. med. entomol., 31: 49-56. sinha, v.p. 1976. further observations on the physico-chemical factors of the breeding places of culex quinquefasciatus say = fatigans wied. mosq. news, 36: 358-360. subra, r. 1970. etude ecologiques sur culex pipiens fatigans wiedemann, 1828, (diptera, culicidae) dans une zone urbaine de savane soudanienne ouest-africaine. dynamique des populations preimaginales. cah. orstom serie entomol. med. parasitol., 8: 353-376. subra, r. 1981. biology and control of culex pipiens quinquefasciatus say, 1823, (diptera: culicidae) with special reference to africa. insect sc. applic., 1: 319-338. subra, r. 1982. the distribution and frequency of culex pipiens quinquefasciatus say 1823 (diptera: culicidae) breeding places on the kenya coast in relation to human sociological factors. j. trop. med. hygiene, 85: 57-61. sucharit, s., harinasuta, c., surathin, k., deesin, t., vutikes, s. and rongsriyam, y. 1981. some aspects of biting cycles of culex quinquefasciatus in bangkok, thailand. s.e. asian j. trop. med. public hlth., 12: 75-78. suleman, m. and shirin, m. 1981. laboratory studies on oviposition behaviour of culex quinquefasciatus say (diptera: culicidae): choice of oviposition medium and oviposition cycle. bull. entomol. res,. 71: 361-369. tuno, n., tsuda, y., takagi, m. and swonkerd, w. 2003. preand postprandial mosquito resting behaviour around cattle hosts. j. am. mosq. control assoc.,19: 211-219. vanamail, p and ramaiah, k.d. 1991. biting periodicity index of culex quinquefasciatus and its relationship with microfilaria periodicity in pondicherry. indian j. med. res., 93: 379-383. yee, w.l. and woodbridge, a.f. 1992. diel sugar-feeding and host-seeking rhythms in mosquitoes (diptera: culicidae) under laboratory conditions. j. med. entomol., 29: 784-791. received 31 march 2009 accepted 30 january 2010 squ journal for science, 2019, 24(2), 129-138 doi:10.24200/squjs.vol24iss2pp129-138 sultan qaboos university 129 connected components of the hurwitz space for the symmetric group of degree 7 haval m. mohammed salih soran university, faculty of science, mathematics department-kawa st, soran, erbil, iraq; university of raparian, college of basic education, department of mathematic, ranya, kurdistan region of iraq. email: haval.mahammed@soran.edu.iq. abstract: the hurwitz space ℋr in(g) is the space of genus g = 0 covers of the riemann sphere ℙ1 with r branch points and the monodromy group g. let g be the symmetric group s7. in this paper, we enumerate the connected components of ℋr in(s7). our approach uses computational tools, relying on the computer algebra system gap and the mapclass package, to find the connected components of ℋr in(s7). this work gives us the complete classification of primitive genus zero symmetric group of degree seven. keywords: monodromy groups; braid orbits; connected components. 7من الدرجة زمرة تناظريةفضاء هيوريتز للمكونات المتصلة لال فال م. محمد صالحه ℋr,gالفضاء الهوروتيزي :صلخمال a (g) هي نوع من غالف في الفضاء الريمانيℙ1 مع نقاط تفرع𝑟 والزمرة المونودرومية. g حيث𝐺 زمرة تناظرية 𝑆7 المكونات المتصلة ل ددع، ن. في هذا البحثℋr in(s7) . ستخدم االدوات الحاسوبية باالعتماد على نظام الجبر الحاسوبي نطريقتنا فيgap وحزمة mapclass المكونات المتصلة ب على للعثورℋr in(s7) من الدرجة السابعة. للزمرة تناظريةتصنيفات الجنس الصفرية يعطنا.هذا العمل المكونات المتصلة. و مدارات بريد ،المنودروميةة زمر: مفتاحيةالكلمات ال 1. introduction et us start this section by the following definition: a primitive genus 𝑔 system is a triple (𝐺, ω, (𝑥1, … , 𝑥𝑟 )) where ω is a finite set of size 𝑛 and 𝐺 is a primitive subgroup of 𝑆𝑛 such that 𝐺 =< 𝑥1, … , 𝑥𝑟 > (1) ∏ 𝑥𝑖 𝑟 𝑖=1 = 1 (2) 2(𝑛 + 𝑔 − 1) = ∑ 𝑖𝑛𝑑 𝑥𝑖 𝑟 𝑖=1 (3) where 𝑥𝑖 ∈ 𝐺\{1}. for 𝑥 ∈ 𝐺 define 𝑖𝑛𝑑 𝑥 = 𝑛 − 𝑜𝑟𝑏 (𝑥), 𝐹𝑖𝑥 𝑥 = {𝑤 ∈ ω |𝑥𝑤 = 𝑤}, 𝑓(𝑥) = |𝐹𝑖𝑥 𝑥| and 𝑜𝑟𝑏(𝑥) = 1 𝑑 ∑ 𝑓(𝑥 𝑖 )𝑑−1𝑖=0 , where 𝑑 is the order of 𝑥 in 𝑆𝑛 . these conditions (1), (2) and (3) are equivalent to the existence of the branched cover 𝜇: 𝑋 → ℙ1, where 𝑋 is a riemann surface of genus 𝑔. the number of holes is called the genus, and μ is a meromorphic function where ℙ1 = ℂ⋃{∞} is the riemann sphere. let 𝐶𝑖 be a non-trivial conjugacy class of 𝑥𝑖 . then the set 𝐶 = {𝐶1, … , 𝐶𝑟 } in 𝐺 is called the ramification type of the cover 𝜇. note that the trivial conjugacy class contains only the identity element. in this paper, we classify primitive genus 0 systems for 𝑆7. it is clear that there are seven primitive groups of degree 7. in [1], we classified all those groups except 𝑆7. now we are going to classify the group 𝑆7 by using the computer algebra system gap. all together give the complete classification of primitive genus 0 groups of degree 7. l mailto:haval.mahammed@soran.edu.iq mohammed salih, h.m. 130 braid orbits can be interpreted as saying interesting things about components of the moduli space of curves ℳ𝑔 [3] and equivalence classes of branched covers of the riemann sphere ℙ1. the full details of the following results and concepts can be found in [1-11]. let 𝐶1, … , 𝐶𝑟 be non-trivial conjugacy classes of a finite group 𝐺. the set of generating systems (𝑥1, … , 𝑥𝑟 ) of 𝐺 with 𝑥1 … 𝑥𝑟 = 1 and such that there is a permutation 𝜋 ∈ 𝑆𝑟 with 𝑥𝑖 ∈ 𝑆𝜋(𝑖) for 𝑖 = 1, … , 𝑟 is called a nielsen class and denoted by 𝒩(c), where 𝐶 = (𝐶1, … , 𝐶𝑟 ). each nielsen class is the disjoint union of braid orbits, which are defined as the smallest subsets of the nielsen class closed under the braid operations (𝑥1, … , 𝑥𝑟 ) 𝑄𝑖 = (𝑥1, … , 𝑥𝑖+1, 𝑥𝑖+1 −1 𝑥𝑖 𝑥𝑖+1, … , 𝑥𝑟 ) (4) for 𝑖 = 1, … , 𝑟. we denote by or, the space of subsets of ℂ of cardinality r. definition 1.1 let 𝐵 ∈ 𝑂𝑟 and 𝑏0 ∈ ℙ 1 ∖ 𝐵. we call a map 𝜑: 𝜋1(ℙ 1 ∖ 𝐵, 𝑏0) → 𝐺 admissible if it is a surjective homomorphsim, and 𝜑(𝜃𝑏 ) ≠ 1 for each 𝑏 ∈ 𝐵. here 𝜃𝑏 is the conjugacy class of 𝜋1(ℙ 1 ∖ 𝐵, 𝑏0). definition 1.2 let 𝐵 ∈ 𝑂𝑟 and 𝜑: 𝜋1(ℙ 1 ∖ 𝐵, ∞) → 𝐺 be admissible. then we say that two pairs (b, φ) and (b̅, φ̅) are a-equivalent if and only if 𝐵 = �̅� and �̅� = 𝑎 ∘ 𝜑 for some a ∈ a. let [b, φ]a denote the a-equivalence class of (𝐵, 𝜑). the set of equivalence classes [𝐵, 𝜑]𝐴 is denoted by ℋ𝑟 𝐴 (𝐺) and is called the hurwitz space of 𝐺-covers. lemma 1.3 let 𝐶 be a fixed ramifcation type in g, and the subset ℋ𝑟 𝑖𝑛 (𝐶) of ℋ𝑟 𝑖𝑛 (𝐺) consist of all [𝐵, ∅]𝐴 with 𝐵 = {𝑏1, … , 𝑏𝑟 }, ∅: 𝜋1(ℙ 1\𝐵, ∞) → 𝐺 and ∅(𝜃𝑏𝑖 ) ∈ 𝐶𝑖 for i = 1, … , r. then ℋ𝑟 𝐴(𝐶) is a union of connected components in ℋr a(g). under the bijection from lemma 2.2, the fiber in ℋ𝑟 𝐴 (𝐶) over b0 corresponds the set 𝒩 a(c). this yields a one to one correspondence between components of ℋ𝑟 𝐴 (𝐶) and the braid orbits on 𝒩 𝐴(𝐶). in particular, ℋ𝑟 𝑖𝑛 (𝐶) is connected if and only if there is only one braid orbit. proof. for a proof see [2]. 2. computing indexes and labeling conjugacy classes in this paper, we discuss two methods for computing index as follows: method one (via fixed points) let g be a group acting on a finite set ω of size 𝑛. if 𝑥 ∈ 𝐺, define the index of x by 𝑖𝑛𝑑 𝑥 = 𝑛 − 𝑜𝑟𝑏 (𝑥) where 𝑜𝑟𝑏 (𝑥) is the number of orbits of < 𝑥 > on ω. also 𝐹𝑖𝑥 𝑥 = {𝜔 ∈ 𝛺 |𝑥𝜔 = 𝜔}, 𝑓(𝑥) = |𝐹𝑖𝑥 𝑥|. furthermore, 𝑜𝑟𝑏 (𝑥) = 1 𝑑 ∑ 𝑓(𝑥 𝑖 )𝑑−1𝑖=0 where x has order d.we discussed this method in detail in [2]. method two (via cycle types) as we know that 𝑖𝑛𝑑 𝑥𝑖 is the minimal number of 2-cycles needed to express 𝑥𝑖 as a product. we will label the fourteen nontrivial conjugacy classes of s7 as atlas notation by: table 1. non trivial conjugacy classes of 𝑺𝟕. type conjugacy class ind 2a (1,2)𝑆7 1 2b (1,2)(3,4)𝑆7 2 2c (1,2)(3,4)(5,6)𝑆7 3 3a (1,2,3)𝑆7 2 3b (1,2,3)(4,5,6)𝑆7 4 4a (1,2,3,4)𝑆7 3 4b (1,2,3,4)(5,6)𝑆7 4 5a (1,2,3,4,5)𝑆7 4 6a (1,2,3)(4,5)(6,7)𝑆7 4 6b (1,2,3)(4,5)𝑆7 3 6c (1,2,3,4,5,6)𝑆7 5 7a (1,2,3,4,5,6,7)𝑆7 6 10a (1,2,3,4,5)(6,7)𝑆7 5 12a (1,2,3,4)(5,6,7)𝑆7 5 connected components of the hurwitz space 131 3. algorithm to achieve connected components of ℋ𝑟 𝑖𝑛 (𝐺), we need to perform the following steps: step 1: select the primitive group 𝑆7 by using the gap code [7] : primitive group ( 7, 7 ). step 2: find all ramification types that satisfy equation (3) for given 𝑆7, degree 7 and genus 0. step 3: remove those types which have zero structure constant from the character table of 𝑆7 via the following equation. 𝑛(𝐶1, … , 𝐶𝑘 ) = |𝐶1||𝐶2|…|𝐶𝑘| |𝐺| ∑ 𝜒(𝑥1)𝜒(𝑥2)…𝜒(𝑥𝑘) 𝜒(1)𝑘−2𝜒∈𝐼𝑟𝑟(𝐺) (5) with equation (5), we compute the number of k-tuples (𝑥1, … , 𝑥𝑘 ) of elements 𝑥𝑖 in the conjugacy class 𝐶𝑖 of a group 𝑆7 such that 𝑥1𝑥2 … 𝑥𝑘 = 1. in other words, we remove those types which don’t satisfy equation (2). step 4: for the remaining types, that pass equation (1) which are called generating types. step 5: for the generating types, compute braid orbits by using mapclass package. now we perform the above steps by using the program described in [12], but with a few modifications to it. that is, we remove the condition of affine type in that program. in this paper we only consider primitive groups. 4. results in this paper, we use the algorithm which is presented in section 3 to compute braid orbits on nielsen class. an application of the algorithm is the classification of the primitive genus zero systems for 𝑆7. that is, we find the connected components ℋr in (c) of s7-curves x, such that g(x/s_7) = 0. in our situation, the computation shows that there are exactly 1071 braid orbits of primitive genus 0 systems of degree 7. the degree and the number of the branch points are given in tables 2 and 3. the detail of the table 1 exists in [10]. table 2. primitive genus zero systems: number of components. degree # group iso types #rts # comp’s r = 3 # comp’s r = 4 # comp’s r = 5 # comp’s r = 6 # comp’s total 7 5 154 179 61 67 10 317 table 3. primitive genus zero systems: number of components. degree # group iso types #rts # comp’s r = 3 # comp’s r = 4 # comp’s r = 5 # comp’s r = 6 # comp’s r =7,8,9,10,11,12 # comp’s total 7 1 632 171 183 172 113 61,31,14,6,2,1 754 theorem 4.1 up to isomorphism, there exist exactly 6 primitive genus zero groups of degree seven. the corresponding primitive genus zero groups are enumerated in table 4 and tables 2-3. lemma 4.2 the hurwitz spaces, ℋ𝑟 𝑖𝑛 (𝐶) are connected if 𝐺 = 𝑆7 and 𝑟 ≥ 5. proof. it follows from the fact that the nielsen classes 𝒩(𝐶) are the disjoint union of braid orbits but we have only one braid orbit for 𝑆7 and 𝑟 ≥ 5. from lemma 1.3, we obtain that the hurwitz spaces ℋ𝑟 𝑖𝑛 (𝐶) are connected. lemma 4.3 the hurwitz spaces, ℋ𝑟 𝑖𝑛 (𝐶) are disconnected if 𝐺 = 𝑆7 and 𝑟 ≤ 4. proof. since we have at least two braid orbits for some type 𝐶 for 𝑟 ≤ 4 and 𝐺 = 𝑆7 and the nielsen classes 𝒩(c) are the disjoint union of braid orbits. from lemma 1.3, we obtain that the hurwitz spaces ℋ𝑟 𝑖𝑛 (𝐶) are disconnected. mohammed salih, h.m. 132 table 4. primitive genus zero systems of 𝑺𝟕. ramification type number of orbits length of largest orbit ramification type number of orbits length of largest orbit (4a,5a,6c) (4a,5a,10a) (4a,5a,12a) (4a,4b,6c) (4a,4b,10a) (4a,4b,12a) (4a,4a,7a) (4a,3b,6c) (4a,3b,10a) (4a,3b,12a) (4a,6a,6c) (4a,6a,10a) (4a,6a,12a) (6b,5a,6c) (6b,5a,10a) (6b,5a,12a) (6b,4b,6c) (6b,4b,10a) (6b,4b,12a) (6b,4a,7a) (6b,3b,6c) (6b,3b,10a) (6b,3b,12a) (6b,6a,6c) (6b,6a,10a) (6b,6a,12a) (6b,6b,6c) (3a,6c,6c) (3a,10a,6c) (3a,10a,10a) (3a,12a,6c) (3a,12a,10a) (3a,12a,12a) (2c,5a,6c) (2c,5a,10a) (2c,5a,12a) (2c,4b,6c) (2c,4b,10a) (2c,4b,12a) (2c,4a,7a) (2c,3b,10a) (2c,3b,12a) (2c,6a,6c) (2c,6a,10a) (2c,6a,12a) (2c,6b,7a) (2b,6c,6c) (2b,10a,6c) (2b,10a,10a) (2c,12a,6c) (2c,12a,10a) 1 2 3 4 4 4 1 2 3 1 3 1 2 6 7 5 12 9 9 3 6 4 4 6 4 3 9 1 2 1 2 2 1 3 1 2 4 3 2 1 1 1 1 1 1 3 4 3 3 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (3a,6b,4a,4b) (3a,6b,4a,3b) (3a,6b,4a,6a) (3a,6b,6b,5a) (3a,6b,6b,4b) (3a,6b,6b,3b) (3a,6b,6b,6a) (3a,3a,4a,6c) (3a,3a,4a,10a) (3a,3a,4a,12a) (3a,3a,6b,6c) (3a,3a,6b,10a) (3a,3a,6b,12a) (3a,3a,2c,6c) (3a,3a,2c,10a) (3a,3a,2c,12a) (3a,2c,4a,5a) (3a,2c,4a,4b) (3a,2c,4a,3b) (3a,2c,4a,6a) (3a,2c,6b,5a) (3a,2c,6b,4b) (3a,2c,6b,3b) (3a,2c,6b,6a) (3a,2c,2c,5a) (3a,2c,2c,4b) (3a,2c,2c,3b) (3a,2c,2c,6a) (2c,4a,4a,4a) (2c,6b,4a,4a) (2c,6b,6b,4a) (2c,6b,6b,6b) (2c,2c,4a,4a) (2c,2c,6b,4a) (2c,2c,6b,6b) (2c,2c,2c,4a) (2c,2c,2c,6b) (2b,4a,4a,5a) (2b,4a,4a,4b) (2b,4a,4a,3b) (2b,4a,4a,6a) (2b,6b,4a,5a) (2b,6b,4a,4b) (2b,6b,4a,3b) (2b,6b,4a,6a) (2b,6b,6b,5a) (2b,6b,6b,4b) (2b,6b,6b,3b) (2b,6b,6b,6a) (2b,3a,4a,6c) (2b,3a,4a,10a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 141 64 69 210 348 168 153 12 20 18 48 50 44 20 10 16 30 42 27 13 75 105 48 39 15 32 13 11 32 88 188 102 16 56 84 16 36 40 96 52 44 150 248 118 114 395 620 282 247 33 30 (2c,12a,12a) (2a,6c,7a) (2a,10a,7a) (2a,12a,7a) (4a,4a,4a,4a) 2 1 1 1 1 1 1 1 1 16 (2b,3a,4a,12a) (2b,3a,6b,6c) (2b,3a,6b,10a) (2b,3a,6b,12a) (2b,3a,2c,6c) 1 1 1 1 1 34 102 85 75 35 connected components of the hurwitz space 133 (6b,4a,4a,4a) (6b,6b,4a,4a) (6b,6b,6b,4a) (6b,6b,6b,6b) (3a,4a,4a,5a) (3a,4a,4a,4b) (3a,4a,4a,3b) (3a,4a,4a,6a) (3a,6b,4a,5a) (2b,2c,2c,5a) (2b,2c,2c,4b) (2b,2c,2c,3b) (2b,2c,2c,6a) (2b,2b,4a,6c) (2b,2b,4a,10a) (2b,2b,4a,12a) (2b,2b,6b,6c) (2b,2b,6b,10a) (2b,2b,6b,12a) (2b,2b,2c,6c) (2b,2b,2c,10a) (2b,2b,2c,12a) (2a,4a,5a,5a) (2a,4a,4b,5a) (2a,4a,4b,4b) (2a,4a,4a,6c) (2a,4a,4a,10a) (2a,4a,4a,12a) (2a,4a,3b,6c) (2a,4a,3b,10a) (2a,4a,3b,12a) (2a,4a,6a,5a) (2a,4a,6a,4b) (2a,4a,6a,3b) (2a,4a,6a,6a) (2a,6b,5a,5a) (2a,6b,4b,5a) (2a,6b,4b,4b) (2a,6b,4a,6c) (2a,6b,4a,10a) (2a,6b,4a,12a) (2a,6b,3b,5a) (2a,6b,3b,4b) (2a,6b,3b,3b) (2a,6b,6a,5a) (2a,6b,6a,4b) (2a,6b,6a,3b) (2a,6b,6a,6a) (2a,6b,6b,6c) (2a,6b,6b,10a) (2a,6b,6b,12a) 1 2 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 72 176 640 1008 15 44 23 34 65 35 48 22 18 72 60 52 198 140 124 60 40 36 12 39 80 12 16 20 23 38 12 26 34 21 10 62 119 188 48 49 41 54 90 42 59 77 36 28 144 112 100 (2b,3a,2c,10a) (2b,3a,2c,12a) (2b,2c,4a,5a) (2b,2c,4a,4b) (2b,2c,4a,3b) (2b,2c,4a,6a) (2b,2c,6b,5a) (2b,2c,6b,4b) (2b,2c,6b,3b) (2b,2c,6b,6a) (2a,2c,3b,4b) (2a,2c,3b,3b) (2a,2c,6a,5a) (2a,2c,6a,4b) (2a,2c,6a,3b) (2a,2c,6a,6a) (2a,2c,6b,6c) (2a,2c,6b,10a) (2a,2c,6b,12a) (2a,2c,2c,6c) (2a,2c,2c,10a) (2a,2c,2c,12a) (2a,2b,5a,6c) (2a,2b,5a,10a) (2a,2b,5a,12a) (2a,2b,4b,6c) (2a,2b,4b,10a) (2a,2b,4b,12a) (2a,2b,4a,7a) (2a,2b,3b,6c) (2a,2b,3b,10a) (2a,2b,3b,12a) (2a,2b,6a,6c) (2a,2b,6a,10a) (2a,2b,6a,12a) (2a,2b,6b,7a) (2a,2b,2c,7a) (2a,2a,6c,6c) (2a,2a,10a,6c) (2a,2a,10a,10a) (2a,2a,5a,7a) (2a,2a,12a,6c) (2a,2a,12a,10a) (2a,2a,12a,12a) (2a,2a,4b,7a) (2a,2a,3b,7a) (2a,2a,6a,7a) (2b,2b,3a,6n,4a) (3a,3a,3a,4a,4a) (3a,3a,3a,6b,4a) (3a,3a,3a,6b,6b) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 25 22 50 80 36 28 125 176 84 65 24 12 11 20 9 8 48 31 29 12 10 8 33 28 27 60 47 42 14 30 21 19 27 20 17 42 14 12 12 10 7 12 10 8 14 7 7 2396 163 606 1827 (2a,2b,3a,2c,3b) (2a,2b,3a,2c,6a) (2a,2b,2c,4a,4a) (2a,2b,2c,6b,4a) (2a,2b,2c,6b,6b) (2a,2b,2c,2c,4a) (2a,2b,2c,2c,6b) (2a,2b,2c,2c,2c) (2a,2b,2b,4a,5a) (2a,2b,2b,4a,4b) (2a,2b,2b,4a,3b) 1 1 1 1 1 1 1 1 1 1 1 249 197 400 976 2256 276 612 168 760 1264 600 (2a,2a,2a,2c,7a) (2a,2a,3a,3a,7a) (2a,2a,3a,2c,6c) (2a,2a,3a,2c,10a) (2a,2a,3a,2c,12a) (2a,2a,2c,4a,5a) (2a,2a,2c,4a,4b) (2a,2a,2c,4a,3b) (2a,2a,2c,4a,6a) (2a,2a,2c,6b,5a) (2a,2a,2c,6b,4b) 1 1 1 1 1 1 1 1 1 1 1 49 49 132 85 92 196 296 156 100 486 684 mohammed salih, h.m. 134 (2a,2b,2b,4a,6a) (2a,2b,2b,6b,5a) (2a,2b,2b,6b,4b) (2a,2b,2b,6b,3b) (2a,2b,2b,6b,6a) (2a,2b,2b,2c,5a) (2a,2b,2b,2c,4b) (2a,2b,2b,2c,3b) (2a,2b,2b,2c,6a) (2a,2b,2b,3a,6c) (2a,2b,2b,3a,10a) (2a,2b,2b,3a,12a) (2a,2b,2b,2b,6c) (2a,2b,2b,2b,10a) (2a,2b,2b,2b,12a) (2a,2a,4a,4a,5a) (2a,2a,4a,4a,4b) (2a,2a,4a,4a,3b) (2a,2a,4a,4a,6a) (2a,2a,6b,4a,5a) (2a,2a,6b,4a,4b) (2a,2a,6b,4a,3b) (2a,2a,6b,4a,6a) (2a,2a,2b,2c,10a) (2a,2a,2b,2c,12a) (2a,2a,2b,2b,7a) (2a,2a,2a,5a,6c) (2a,2a,2a,5a,10a) (2a,2a,2a,5a,12a) (2a,2a,2a,4b,6c) (2a,2a,2a,4b,10a) (2a,3a,3a,3a,3a,4a) (2a,3a,3a,3a,3a,6b) (2a,3a,3a,3a,3a,2c) (2a,2b,3a,3a,3a,4a) (2a,2b,3a,3a,3a,6b) (2a,2b,3a,3a,3a,2c) (2a,2b,2b,3a,3a,4a) (2a,2b,2b,3a,3a,6b) (2a,2b,2b,3a,3a,2c) (2a,2b,2b,2b,3a,4a) (2a,2b,2b,2b,3a,6b) (2a,2b,2b,2b,3a,2c) (2a,2b,2b,2b,2b,4a) (2a,2b,2b,2b,2b,6b) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 540 2115 3080 1248 1223 615 880 414 330 513 405 364 972 690 612 131 336 182 190 519 948 438 447 160 144 196 108 105 105 216 180 1456 4788 1872 3350 9441 2967 6608 17164 5174 12316 30099 8658 21824 51336 (2a,2a,2c,6b,3b) (2a,2a,2c,6b,6a) (2a,2a,2c,2c,5a) (2a,2a,2c,2c,4b) (2a,2a,2c,2c,3b) (2a,2a,2c,2c,6a) (2a,2a,2b,5a,5a) (2a,2a,2b,4b,5a) (2a,2a,2b,4a,6c) (2a,2a,2b,4b,4b) (2a,2a,2b,4a,10a) (2a,2a,2b,4a,12a) (2a,2a,2b,3b,5a) (2a,2a,2b,3b,4b) (2a,2a,2b,3b,3b) (2a,2a,2b,6b,6c) (2a,2a,2b,6b,10a) (2a,2a,2b,6b,12a) (2a,2a,2b,6a,5a) (2a,2a,2b,6a,4b) (2a,2a,2b,6a,3b) (2a,2a,2b,6a,6a) (2a,2a,2b,3a,7a) (2a,2a,2b,2c,6c) (2a,2a,2a,2b,4a,3b) (2a,2a,2a,2b,4a,6a) (2a,2a,2a,2b,6b,5a) (2a,2a,2a,2b,6b,4b) (2a,2a,2a,2b,6b,3b) (2a,2a,2a,2b,6b,6a) (2a,2a,2a,3a,6b,5a) (2a,2a,2a,3a,6b,4b) (2a,2a,2a,3a,6b,3b) (2a,2a,2a,3a,6b,6a) (2a,2a,2a,4a,4a,4a) (2a,2a,2a,6b,4a,4a) (2a,2a,2a,6b,6b,4a) (2a,2a,2a,6b,6b,6b) (2a,2a,2a,2c,4a,4a) (2a,2a,2a,2c,6b,4a) (2a,2a,2a,2c,6b,6b) (2a,2a,2a,2c,2c,4a) (2a,2a,2a,2c,2c,6b) (2a,2a,2a,2c,2c,2c) (2a,2a,2a,2b,3a,6c) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 324 252 120 192 84 72 328 592 252 952 215 206 291 444 204 720 545 487 265 388 183 148 98 228 2304 2076 7530 11796 5508 4818 3900 6720 3132 2991 1296 4428 12000 29802 1560 3828 8772 992 2376 672 1836 (2a,3a,5a,6c) (2a,3a,5a,10a) (2a,3a,5a,12a) (2a,3a,4b,6c) (2a,3a,4b,10a) (2a,3a,4b,12a) (2a,3a,4a,7a) (2a,3a,3b,6c) (2a,3a,3b,10a) (2a,3a,3b,12a) (2a,3a,6a,6c) (2a,3a,6a,10a) (2a,3a,6a,12a) (2a,3a,6b,7a) (2a,3a,2c,7a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 16 17 30 27 27 7 15 16 10 18 10 12 21 7 (3a,3a,3a,2c,4a) (3a,3a,3a,2c,6b) (3a,3a,3a,2c,2c) (2b,3a,3a,4a,4a) (2b,3a,3a,6b,4a) (2b,3a,3a,2c,4b) (2b,3a,3a,2c,6b) (2b,3a,3a,2c,2c) (2b,2b,3a,4a,4a) (2b,2b,3a,6b,6b) (2b,2b,3a,2c,4a) (2b,2b,3a,2c,4a) (2b,2b,3a,2c,2c) (2b,2b,2b,4a,4a) (2b,2b,2b,6b,4a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 272 612 133 418 1285 412 1038 286 876 5935 748 1721 474 1712 4296 connected components of the hurwitz space 135 (2a,2c,5a,5a) (2a,2c,4b,5a) (2a,2c,4b,4b) (2a,2c,4a,6c) (2a,2c,4a,10a) (2a,2c,4a,12a) (2a,2c,3b,5a) (2a,3a,3a,6b,5a) (2a,3a,3a,6b,4b) (2a,3a,3a,6b,3b) (2a,3a,3a,6b,6a) (2a,3a,3a,3a,6c) (2a,3a,3a,3a,10a) (2a,3a,3a,3a,12a) (2a,3a,3a,2c,5a) (2a,3a,3a,2c,12a) (2a,3a,3a,2c,3b) (2a,3a,3a,2c,6a) (2a,3a,2c,4a,4a) (2a,3a,2c,6b,4a) (2a,3a,2c,6b,6b) (2a,3a,2c,2c,4a) (2a,3a,2c,2c,6b) (2a,3a,2c,2c,2c) (2a,2b,4a,4a,4a) (2a,2b,6b,4a,4a) (2a,2b,6b,6b,4a) (2a,2b,3a,4a,5a) (2a,2b,6b,6b,6b) (2a,2b,3a,4a,4b) (2a,2b,3a,4a,3b) (2a,2b,3a,4a,6a) (2a,2b,3a,6b,5a) (2a,2b,3a,6b,4b) (2a,2b,3a,6b,3b) (2a,2b,3a,6b,6a) (2a,2b,3a,3a,6c) (2a,2b,3a,3a,10a) (2a,2b,3a,3a,12a) (2a,2b,3a,2c,5a) (2a,2b,3a,2c,4b) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 26 38 56 20 11 14 21 525 996 462 468 108 135 120 210 300 168 105 238 587 1335 136 366 108 384 1232 3196 355 7752 690 349 315 1085 1763 828 754 252 220 220 350 536 (2b,2b,2b,6b,6b) (2b,2b,2b,2c,4a) (2b,2b,2b,2c,6b) (2b,2b,2b,2c,2c) (2a,3a,4a,4a,4a) (2a,3a,6b,4a,4a) (2a,3a,6b,6b,4a) (2a,3a,6b,6b,6b) (2a,3a,3a,4a,5a) (2a,3a,3a,4a,4b) (2a,3a,3a,4a,3b) (2a,3a,3a,4a,6a) (2a,2a,6b,6b,5a) (2a,2a,6b,6b,4b) (2a,2a,6b,6b,3b) (2a,2a,6b,6b,6a) (2a,2a,3a,6a,5a) (2a,2a,3a,6a,4b) (2a,2a,3a,6a,3b) (2a,2a,3a,6a,6a) (2a,2a,3a,5a,5a) (2a,2a,3a,4b,5a) (2a,2a,3a,4b,4b) (2a,2a,3a,4a,6c) (2a,2a,3a,4a,10a) (2a,2a,3a,4a,12a) (2a,2a,3a,3b,5a) (2a,2a,3a,3b,4b) (2a,2a,3a,3b,3b) (2a,2a,2a,4b,12a) (2a,2a,2a,4a,7a) (2a,2a,2a,3b,6c) (2a,2a,2a,3b,10a) (2a,2a,3a,6b,6c) (2a,2a,3a,6b,6a) (2a,2a,3a,6b,12a) (2a,2a,2a,3b,12a) (2a,2a,2a,6a,6c) (2a,2a,2a,6a,10a) (2a,2a,2a,6a,12a) (2a,2a,2a,6b,7a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10128 1248 2880 748 156 589 1782 4455 145 350 172 216 1267 2352 1098 975 170 236 126 82 131 302 548 82 120 123 156 264 105 168 49 108 90 360 325 286 72 108 75 7 147 (2a,2b,2b,2b,2b,2c) (2a,2a,3a,3a,4a,4a) (2a,2a,3a,3a,6b,4a) (2a,2a,3a,3a,6b,6b) (2a,2a,3a,3a,3a,5a) (2a,2a,3a,3a,3a,4b) (2a,2a,3a,3a,3a,3b) (2a,2a,3a,3a,3a,6a) (2a,2a,2b,3a,3a,5a) (2a,2a,2b,3a,3a,4b) (2a,2a,2b,3a,3a,3b) (2a,2a,2b,3a,3a,6a) (2a,2a,2b,2b,3a,5a) (2a,2a,2b,2b,3a,4b) (2a,2a,2b,2b,3a,3b) (2a,2a,2b,2b,3a,6a) (2a,2a,3a,3a,2c,4a) (2a,2a,3a,3a,2c,6b) (2a,2a,3a,3a,2c,2c) (2a,2a,2b,3a,4a,4a) (2a,2a,2b,3a,2c,4a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14448 1398 4588 12600 1260 2640 1260 1422 2795 4952 2418 2197 5530 8896 4191 3671 1688 4044 1020 3150 2824 (2a,2a,2a,2b,3a,10a) (2a,2a,2a,2b,3a,12a) (2a,2a,2a,2b,2c,5a) (2a,2a,2a,2b,2c,4b) (2a,2a,2a,2b,2c,3b) (2a,2a,2a,2b,2c,6a) (2a,2a,2a,2b,2b,6c) (2a,2a,2a,2b,2b,10a) (2a,2a,2a,2b,2b,12a) (2a,2a,2a,2a,4a,6c) (2a,2a,2a,2a,4a,10a) (2a,2a,2a,2a,4a,12a) (2a,2a,2a,2a,5a,5a) (2a,2a,2a,2a,6b,6c) (2a,2a,2a,2a,6b,10a) (2a,2a,2a,2a,6b,12a) (2a,2a,2a,2a,3a,7a) (2a,2a,2a,2a,2c,6c) (2a,2a,2a,2a,2c,10a) (2a,2a,2a,2a,2c,12a) (2a,2a,2a,2a,4a,7a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1500 1402 2340 3456 1620 1296 3564 2650 2327 864 800 784 1110 2592 2100 1872 343 864 600 576 686 mohammed salih, h.m. 136 (2a,2a,2b,3a,2c,6b) (2a,2a,2b,3a,2c,2c) 1 1 6744 1860 (2a,2a,2a,2a,4b,5a) (2a,2a,2a,2a,4b,4b) (2a,2a,2a,2a,6a,5a) 1 1 1 2160 3648 1050 (2a,2a,2b,2b,4a,4a) (2a,2a,2b,2b,6b,4a) (2a,2a,2b,2b,6b,6b) (2a,2a,2b,2b,2c,4a) (2a,2a,2b,2b,2c,6b) (2a,2a,2b,2b,2c,2c) (2a,2a,2a,3a,3a,6c) (2a,2a,2a,3a,3a,10a) (2a,2a,2a,3a,3a,12a) (2a,2a,2b,2b,2b,5a) (2a,2a,2b,2b,2b,4b) (2a,2a,2b,2b,2b,3b) (2a,2a,2b,2b,2b,6a) (2a,2a,2a,3a,4a,5a) (2a,2a,2a,2b,4a,4b) (2a,2a,2a,2a,2a,4a,5a) (2a,2a,2a,2a,2a,4a,4b) (2a,2a,2a,2a,2a,4a,3b) (2a,2a,2a,2a,2a,4a,6a) (2a,2a,2a,2a,2a,6b,5a) (2a,2a,2a,2a,2a,6b,4b) (2a,2a,2a,2a,2a,6b,3b) (2a,2a,2a,2a,2a,6b,6a) (2a,2a,2a,2a,2a,2c,5a) (2a,2a,2a,2a,2a,2c,4b) (2a,2a,2a,2a,2a,2c,3b) (2a,2a,2a,2a,2a,2c,6a) (2a,2a,2a,2a,2a,2b,6c) (2a,2a,2a,2a,2a,2b,10a) (2a,2a,2a,2a,2a,2b,12a) (2a,2a,2a,2a,2a,2a,7a) (2a,2a,2a,2a,2b,2b,5a) (2a,2a,2a,2a,2b,2b,4b) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6320 11628 39288 4880 11268 3080 864 850 808 10215 15408 7182 6066 1205 4744 9500 17600 8640 8160 27750 45120 21060 19080 9000 13440 8480 5040 12960 10000 9120 2401 38300 59264 (2a,2a,2a,2a,6a,4b) (2a,2a,2a,2a,6a,3b) (2a,2a,2a,2a,6a,6a) (2a,2a,2a,2a,3b,5a) (2a,2a,2a,2a,3b,4b) (2a,2a,2a,2a,3b,3b) (2a,2a,2b,2b,3a,3a,3a) (2a,2a,2a,3a,4a,4b) (2a,2a,2a,3a,4a,3b) (2a,2a,2a,3a,4a,6a) (2a,2a,2a,3a,2c,5a) (2a,2a,2a,3a,2c,4b) (2a,2a,2a,3a,2c,3b) (2a,2a,2a,3a,2c,6a) (2a,2a,2a,2b,4a,5a) (2a,2a,2b,2b,2b,2b,2b) (2a,2a,23a,3a,3a,3a,3a) (2a,2a,2b,3a,3a,3a,3a) (2a,2a,2a,2a,2a,2a,2b,5a) (2a,2a,2a,2a,2a,2a,2b,4b) (2a,2a,2a,2a,2a,2a,2b,3b) (2a,2a,2a,2a,2a,2a,2b,6a) (2a,2a,2a,2a,2a,2a,3a,5a) (2a,2a,2a,2a,2a,2a,3a,4b) (2a,2a,2a,2a,2a,2a,3a,3b) (2a,2a,2a,2a,2a,2a,3a,6a) (2a,2a,2a,2a,3a,3a,3a,3a) (2a,2a,2a,2a,2b,3a,3a,3a) (2a,2a,2a,2a,2b,2b,3a,3a) (2a,2a,2a,2a,2b,2b,2b,3a) (2a,2a,2a,2a,2b,2b,2b,2b) (2a,2a,2a,2a,2a,3a,3a,4a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1536 756 756 1080 1728 750 48859 2516 1260 1290 1365 2040 1026 744 2710 260848 12207 25860 142500 226560 106920 92880 73125 126720 60750 56160 92880 183252 336372 593244 1016904 87840 connected components of the hurwitz space 137 table 5. primitive genus zero systems of 𝑺𝟕. (2a,2a,2a,2a,2b,2b,3b) (2a,2a,2a,2a,2b,2b,6a) (2a,2a,2a,2a,2b,3a,5a) (2a,2a,2a,2a,2b,3a,4b) (2a,2a,2a,2a,2b,3a,3b) (2a,2a,2a,2a,2b,3a,6a) (2a,2a,2a,2a,3a,3a,5a) (2a,2a,2a,2a,3a,3a,4b) (2a,2a,2a,2a,3a,3a,3b) (2a,2a,2a,2a,3a,3a,6a) (2a,2a,2a,2a,2a,3a,6c) (2a,2a,2a,2a,2a,3a,10a) (2a,2a,2a,2a,2a,3a,12a) (2a,2a,2a,2a,2b,2c,4a) (2a,2a,2a,2a,2b,2c,6b) (2a,2a,2a,2a,2b,2c,2c) (2a,2a,2a,2a,3a,2c,4a) (2a,2a,2a,2a,3a,2c,6b) (2a,2a,2a,2a,3a,2c,2c) (2a,2a,2a,2a,2b,4a,4a) (2a,2a,2a,2a,2a,6b,4a) (2a,2a,2a,2a,2b,6b,6b) (2a,2a,2a,2a,3a,4a,4a) (2a,2a,2a,2a,3a,6b,4a) (2a,2a,2a,2a,3a,6b,6b) (2a,2a,2a,2b,2b,2b,4a) (2a,2a,2a,2b,2b,2b,6b) (2a,2a,2a,2b,2b,2b,2c) (2a,2a,2a,2b,2b,3a,4a) (2a,2a,2a,2b,2b,3a,6b) (2a,2a,2a,2b,2b,3a,2c) (2a,2a,2a,2b,3a,3a,4a) (2a,2a,2a,2b,3a,3a,6b) (2a,2a,2a,2b,3a,3a,2c) (2a,2a,2b,2b,2b,2b,3a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 27756 23760 20250 33696 16062 14304 9825 18432 8910 8796 6480 5625 5280 18816 44064 12096 11040 26448 7056 23128 61836 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(2a,2a,2a,3a,3a,3a,2c) (2a,2a,2b,2b,2b,3a,3a) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 244020 78000 172920 442720 131760 317920 772200 221760 83360 231840 581040 72960 172800 47040 46656 37500 43560 676830 1275960 2283120 3954720 638400 1682100 514080 1202880 2978640 866880 525000 880160 408240 362880 11656 34695 11910 88254 (2a,2a,2a,2a,2a,2a,2a,2a,3a,3a) (2a,2a,2a,2a,2a,2a,2a,2a,2b,3a) (2a,2a,2a,2a,2a,2a,2a,2a,2b,2b) (2a,2a,2a,2a,2a,2a,2a,2a,2a,4a) (2a,2a,2a,2a,2a,2a,2a,2a,2a,6b) (2a,2a,2a,2a,2a,2a,2a,2a,2a,2c) (2a,2a,2a,2a,2a,2a,2a,2a,2a,2a,3a) (2a,2a,2a,2a,2a,2a,2a,2a,2a,2a,2b) (2a,2a,2a,2a,2a,2a,2a,2a,2a,2a,2a,2a) 1 1 1 1 1 1 1 1 1 4798080 8749440 15355040 4515840 11430720 3386880 33339600 59270400 228191040 conclusion here, we compute braid orbits on nielsen class with the aid of the computer algebra system gap and mapclass package. a result of the algorithm is that it gives the complete classification of the symmetric group 𝑆7 up to braid actions and diagonal conjugations. the computation shows that there are exactly 754 braid orbits of s7. as a consequence of lemma 1.3, we find the connected components ℋ𝑟 𝑖𝑛 (𝑆7) of 𝑆7-curves 𝑋, such that 𝑔 = 0. so we have 754 connected components ℋ𝑟 𝑖𝑛 (𝑆7) of the symmetric group of degree seven. acknowledgments the author would like thank the anonymous referees, whose comments and suggestions helped to improve the manuscript. mohammed salih, h.m. 138 references 1. volklein, h. groups as galois groups an introduction to cambridge studies in advanced mathematics, volume 53, cambridge university press, cambridge, 1996. 2. mohammed salih, h. finite groups of small genus. 2014, ph.d. thesis, university of birmingham. 3. michael, d.f. and volklein, h. the inverse galois problem and rational points on moduli spaces. mathematical annual, 1991, 290(4), 771-800. 4. frohardt d., guralnick, r. and magaard k. genus 0 actions of groups of lie rank 1. in arithmetic fundamental groups and noncommutative algebra (berkeley, ca, 1999), proceeding symposium in pure mathematics, 2002, 70, 449-483. 5. frohardt, d. and magaard, k. composition factors of monodromy groups. american mathematical society, providence, ri, annals of mathematics, 2001, 154(2), 327-345. 6. frohardt, d., guralnick, r. and magaard, k. primitive monodromy groups of genus at most two, journal of algebra, 2014, 417, 234-274. 7. the gap group. gap-groups, algorithms, and programming, version 4.6.2, 2013. 8. guralnick, r and john, g. thompson. finite groups of genus zero. journal of algebra, 1990, 131(1), 303-341. 9. magaard, k., shpectorov, s. and wang, g. generating sets of affine groups of low genus. in computational algebraic and analytic geometry, contemporary mathematics, american mathematical society, providence, ri, 2012, 572, 173-192. 10. mohammed salih, h. connected components of ℋ𝑟 𝑖𝑛 (𝐺). sultan qaboos university journal for science, 2017, 22(2), 106-113. 11. neubauer, m. on solvable monodromy groups of fixed genus. 1989. ph.d. thesis, university of southern california. 12. guralnick, r. and john, g.t. finite groups of genus zero. journal of algebra, 1990, 131(1), 303-341. received 16 january 2019 accepted 12 june 2019 microsoft word stat020824-neweq-f.doc squ journal for science, 9 (2004) 41-51 © 2004 sultan qaboos university 41 optimal control of switching linear systems ali benmerzouga department of mathematics and statistics, college of science, sultan qaboos university, p. o. box 36, al khod 123, muscat, sultanate of oman, email: aliben@squ.edu.om التبديلية التحكم األمثل للنظم الخطية علي بن مرزوقة ). 1997( بإستخدام إقتران مراقبة محدود من طرف بن مرزوقة ادليةلقد أعطي حلين للنظم الخطية التب : خالصة في هذه الدراسة نتطرق إليجاد سلسلة المراقبة أو التحكم المثالية التي . لكن الحلول المقدمة هناك لم تكن الوحيدة بإستعمال النظام المـأخوذ مـن تجزئـة النظـام ) أو قريبة منها (ومة إلى نهاية معلومة تنقل النظام من بداية معل بإستخدام طريقة البرمجة المتحركة و نتحصل علـى الحـل األمثـل و . المتواصل مع تقليل إقتران كلفة التشغيل بين صعوبة الحسابات كذلك ن ). 1997(الوحيد لكل من الطريقتين التعدادية و الجديدة المذكورتين في بن مرزوقة . و نعطي عددها للطريقة المعدلة في هذه الورقة abstract: a solution to the control of switching linear systems with input constraints was given in benmerzouga (1997) for both the conventional enumeration approach and the new approach. the solution given there turned out to be not unique. the main objective in this work is to determine the optimal control sequences {ui(k) , i = 1,..., m ; k = 0, 1, ..., n -1} which transfer the system from a given initial state x0 to a specific target state xt (or to be as close as possible) by using the same discrete time solution obtained in benmerzouga (1997) and minimizing a running cost-to-go function. by using the dynamic programming technique, the optimal solution is found for both approaches given in benmerzouga (1997). the computational complexity of the modified algorithm is also given. keywords : controllability; bilinear systems; dynamic programming; switching linear systems; optimization. 1. introduction ne of the most important objectives of dynamical systems in control theory is to find the optimal control u(t). most of the work done is primarily in the area of control and analysis of continuous bilinear systems described as o ali benmerzouga 42 1 ( ) ( ) ( ) m i i i dx t = u t a x t dt = ∑ , (1.1) where ( ) nx t ∈ r , ia are n n× matrices, [ ]: 0,iu ∞ →u where ⊆u r . the work that has been done in bilinear systems considers the control u(t) as a scalar belonging to a compact set u such that ( )u t δ≤ . the case where ( )u t takes just two values as an on-off system ( )( )i.e., 0 1u t or= is given by benmerzouga (1985, 1997). a discrete solution to the continuous dynamical system is given in benmerzouga (1997). for both the conventional enumeration approach and the new approach, the solution found was not unique. most of the work and emphasis in this case has been on the structural aspects of bilinear systems as given in aslanis (1983) where ( ) 2x t ∈ r and ( ) {0, 1}u t ∈ . tarn, et al. (1973) tested the controllability of discrete bilinear systems. goka, et al. (1973) gave necessary and sufficient conditions for the controllability of a class of discrete bilinear systems. all the work done in discrete bilinear systems considers the control ( )u t as a scalar belonging to a compact set u such that ( )u t δ≤ . the case where ( )u t takes just two values as an on-off system ( )( )i.e., 0 or 1u t = as shown by benmerzouga (1985), has had limited treatment. the major focus in this work is to determine optimal control sequences ( ){ }, 1,...,iu t i m= which transfer the system from a given initial state 0x to a specific target state tx (or to be as close to it as possible). in both the conventional enumeration approach and the new approach treated in benmerzouga (1997), the properties of the discrete solution, which is derived by sampling (or discretizing) the continuous solution of the continuous dynamical system described by equation (1.1), are conserved and used in this paper. the solution found by benmerzouga (1997) steers the system from an initial state 0x to a final state tx through more than one path. that is due, of course, to the performance index used. the only criterion used in benmerzouga (1997) is the magnitude of the gap between the final state nx and the target state tx . there was no restriction whatsoever on how much it would cost to steer the system from the initial state to the final state. hence, there are no restrictions on the paths which are found to be optimal. a dynamic programming technique is used to find the optimal path through which the control sequence will steer the system. various studies and algorithms used are described in section 2. the cost-to-go function and the dynamic programming approach used in the modified algorithm are given in section 3. section 4 includes the step-by-step procedure used to solve the problem optimally by using dynamic programming and the computational complexity of the modified algorithm. finally some concluding remarks are given in section 5. 2. dynamics of switching control systems the dynamics of switching control systems can be studied for both continuous and discrete time systems as mentioned in benmerzouga (1985) and (1997). the emphasis, in this paper, is mainly about discrete time systems obtained by sampling (or discretizing) a continuous system given by equation (1.1). this choice is made because of the following two main reasons that were mentioned in benmerzouga (1997): (i) most control algorithms are implemented on a digital computer, and (ii) when discretizing a continuous system the discrete system obtained will have a non-singular characteristic matrix. for more switching linear systems 43 details see wismer and chattergy (1978). such ground will make the computations of the switching controls much easier, as will be shown in the subsequent sections. 2.1 solution of the continuous switching system as stated earlier, the dynamics of the continuous switching system is given by equation (1.1) in addition to the constraints, ( ) ( ) 0i j u t . u t = , i j ,≠ and ( ) 1 , m i i 1 u t = = ∑ (2.1) where m is the number of systems that can be used when steering the system from the initial state 0x to the target state tx . the solution of such a dynamical system, with only one active system, in the interval [ ]0,t is ( ) (0) ( (0) is given)b tx t = . x , x .e (2.2) where the n n× matrix b is equal to any of the given state matrices isa ′ , depending on which control ( )iu t is equal to 1, i.e., which system is actually on or active. (for more details see brockett (1970), kailath (1980) and sandell and athans (1974)). 2.2 the discrete solution for the switching system the discrete solution of the switching system is obtained by sampling (or discretizing) the continuous solution given by equation (2.2). since the initial state ( )0x is given, then the discrete solution of the switching system at each stage k is given by the following difference equation: ( 1) ( ) 0, 1, 1b tx k + = . x k , k = ..., n .e ∆ − (2.3) since there are m systems in the above dynamics, and since the initial state 0x is given, and in view of the details given by benmerzouga (1997), the discrete time solution of the switching system with a single state matrix is now completely defined by the difference equation 1 ( 1) ( ) ( ) m ii i x k + = u k . . x k ,p = ∑ (2.4) where ip are n n× matrices and have the same definitions and properties given in benmerzouga (1997). having the discrete solution of the switching system given by (2.4), the main purpose of this work is to find a computationally efficient approach that will optimally steer the system from an initial state 0x to a target state tx (or to be as close as possible). in addition to that, we should find the optimal control sequence ( ){ }, 1, 2,..., , 0,1,..., 1iu k i m k n= = − that will achieve such goal in a given number of steps. therefore, the first objective is to minimize the total running gap (or cost) accumulated when steering the system from an initial state 0x to the target state tx in a given number of steps and the second objective is to find the optimal control sequence ( ){ }, 1, 2,..., , 0,1,..., 1iu k i m k n= = − . the accumulated gap (or costs) can be computed using different measures depending on the system we are actually using. this measure could be a distance, a quadratic form, or something different that will quantify and measure the cost. the form of the gap (or cost) used in this work and how to minimize it are described in detail in section 4. ali benmerzouga 44 3. previous methods since equation (2.4) gives the discrete solution of the switching system, the main purpose of the previous methods is only to minimize the gap (or cost) between the final state of the system ( )x n and the target state tx , when steering the system from an initial state 0x to the target state tx in a given number of steps. in addition to that, the control sequence { ( ) } n 1 i k = 0 u k that will achieve this goal in a given number of steps has to be found. the gap (or cost) used as a criterion for optimality is given by 2 [ ( )] ( ) .tg x n = x nx − (3.1) 3.1 method 1: the conventional method by using the conventional enumeration approach, all the states at all stages are computed and stored in order to reach the last stage as shown on figure 3.1. | | | (p1) 3.x(0) | … | | (p1) 2.x(0) | | … | | | p2(p1) 2.x(0) | … | p1.x(0) | | | … | | | p1.p2.p1.x(0) | … | | p2.p1.x(0) | | … | | | (p2) 2.p1.x(0) | … x(0) | | | | … | | | (p1) 2.p2.x(0) | … | | p1.p2.x(0) | | … | | | p2.p1.p2.x(0) | … | p2.x(0) | | | … | | | p1.(p2) 2.x(0) | … | | (p2) 2.x(0) | | … | | | (p2) 3.x(0) | … --------------------------------------------------------------------------------------------------------------------------- x(0) | x(1) | x(2) | x(3) | … figure 1. all possible stages and states for k =3 and n = 2. switching linear systems 45 when solving example 5.1 in benmerzouga (1997), the final cost was obtained by two different control sequences, namely, ( ) ( ) ( )( ) ( )0 , 1 , 2 0,1,1u u u = and ( )1,1, 0 , respectively. in addition to that, the solution to the conventional problem was found to be not unique. the value of the terminal cost, namely. ( ) ,g x n   is found to be equal to zero through two different trajectories. all the details of the computations are fully executed and presented in benmerzouga (1997). 3.2 method 2: the new approach the new approach description, mathematical development and solution are completely given in detail in benmerzouga (1997). when solving the same example, the minimum gap (or cost) was found to be equal to 1 and is given by two different paths through the two different control sequences (0, 1, 1) and (1, 1, 0). this is exactly what we obtained in subsection 3.1. it was shown is benmerzouga (1997) that the new approach is much better than the enumeration method from the storage and computations point of view and from the very simple way used to get the control sequence corresponding to the minimum final cost. as we can see in the previous two methods we are getting more than one control sequence as a solution. in other words, there is more than one trajectory to steer the system from an initial state 0x to a final state nx . the question that remains open is which of the above paths is really the best to go through from a cost point of view. this is will be fully explained and illustrated in the next section. 4. the cost-to-go function the performance index used in benmerzouga (1997) was basically focusing on the smallest terminal or final cost ( )g x n   and not on the smallest overall running cost. the procedure used in benmerzouga (1997) was kind of memoryless of what is happening between steps and through those trajectories. the only objective in benmerzouga (1997) was to pick the path with minimum terminal cost and not the overall running cost. this was the main reason for having more than one path as solutions to the problem. the performance index used in this analysis is the one that minimizes the total running cost incurred while steering the system from the initial state 0x to the target state tx in a given number of steps, n , or the one that will give the minimum cost-to-go when being as close as possible to the target state tx . the cost-to-go function is defined by the recurrent formula given by ∑ − = += 1 0 )]([)](),([ n k nxgkxkufv , (4.1) where v is the final running cost, ( )u k is the control sequence which takes the values 0 or 1 and ( ) ( ),f u k x k   , and ( )g x n   are given by ( ) ( ) ( ) ( ) ( ) 2 , , t t t tf u k x k x x k x x k x x k= − = − −           (4.2) ( ) ( ) ( ) ( ) 2 . t t t tg x n x x n x x n x x n= − = − −           (4.3) equation (4.1) has a structure that requires the use of a dynamic programming approach for its minimization. more details about dynamic programming are given in dreyfus and law (1977). all the criteria, structures and restrictions, mentioned in benmerzouga (1997), are conserved and used in this paper. ali benmerzouga 46 4.1 the modified algorithm this modified algorithm is built on the basis of the details of the algorithm provided in benmerzouga (1997). as mentioned earlier, one of the objectives in this work is to steer the system from an initial state 0x to a target state tx (or as close as possible) in a given number of stages, n , with minimum running cost (or distance) and not a minimum terminal cost. therefore the required steps are: step 1: given the number of stages n and an initial state 0x , a matrix ( ),s i j is generated which will contain all different values of ( )z n , where i is the space dimension and j the number of states at stage n . this step is the same as step 1 in the old algorithm given by benmerzouga (1997). step 2: when searching for the minimum running distance it is necessary to go back from z space to x space using the relationship ( ) ( )k .x k b z k= . hence it is necessary to compute the matrix kb . step 3: compute ( ) ( )k .x k b z k= , namely, the transformation from z-space to x-space for each k . step 4: compute all possible costs (or performance indices) at each stage k. step 5: store all the computed costs in the matrix ( )cm ,i j as shown in table 4. step 6: find the final running cost on each path by adding up the costs of all the previous stages. step 7: given the rank, ( )j , of the minimum running cost, a binary representation is generated to get the optimal control sequence ( ){ }and, 0,1,..., 1 1,..., .iu k k n i m= − = the above algorithm not only makes the computations tractable, but it also facilitates the way to get the optimal control sequence to reach the final target for the problem. therefore, given an initial state of the system 0x , a target state tx , and a number of steps n , the algorithm will give us the optimal state and its corresponding sequence ( ){ }and, 0,1,..., 1 1,..., .iu k k n i m= − = without loss of generality, the dynamic programming approach and the overall running costs criteria are used for the two methods given in the previous section. the computations are carried out for the following bilinear example: example 4.1 the same example used in benmerzouga (1997) is to be used here. let 1p and 2p be 2 × 2 matrices, x0 and tx be 2 × 1 vectors, and the number of stages, n , equals to 3. . = x ,= x , = p , = p t21      −             −       −− 1 1 1 1 01 10 11 01 0 4.2 method 3: the dynamic programming technique applied to the conventional problem now we need to use the dynamic programming approach to the conventional problem by minimizing the cost-to-go function given in (4.1) and not only the terminal cost. in order to compute the intermediate switching linear systems 47 running cost, a complete enumeration and computation of all costs for all the possible states at all stages has to be performed as it is shown in table 1. by using the recurrent formula given by equation (4.1), the costs-to-go from one stage to the next one, namely, f[u(2), x(2)], f[u(1), x(1)] and f[u(0), x(0)], will lead to the optimal solution for this case and its optimal control sequence. the results of the different computations are summarized in table 2 (a)-(c). the sequence that generates the optimal path when using dynamic programming is unique and it is equal to (u1(0), u1 (1), u1 (2)) = (0, 1, 1). since we are using a bilinear system the other control sequence is just the complement to this one, i.e., (u2 (0), u2 (1), u2 (2)) = (1, 0, 0). as we can see from table 2 (c), we have just one single optimal path with a minimum running cost of 5. 4.3 method 4: the dynamic programming technique applied to the new approach given the data obtained using subsection 4.2 and by using the dynamic programming technique, the minimum distance is found to be equal to 1 through a unique control sequence (0, 1, 1) with a minimal overall running cost of 5. knowing the structure of the new approach and how the data and the computations are to be handled and stored, a useful new data is obtained and stored. this data is used to find the corresponding value of ( )z k in our original x-space as shown in table 3. the latter one is going to be used to compute the running costs. this is done by using just one extra matrix, namely, b , until an initial state is obtained. this can be done without any extra storage, except for a matrix ( ),cm i j that is used to store different distances at each stage, where i is the number of paths and j is the number of stages. the matrix ( ),cm i j is given in table 4. table 1. the complete computational and sequence picture, when n = 3. xt ─ x(0) f[u(0), x(0)] xt ─ x(1) f[u(1), x(1)] xt ─ x(2) f[u(2), x(2)] xt ─ x(3) g[x(3) ] -2 3 13 0 0 0 -2 3 13 -2 0 4 -3 4 25 -1 1 4 0 1 1 0 -1 1 0 0 0 -3 0 9 0 0 0 0 2 4 -1 2 5 0 -1 1 -2 2 8 by localizing the rank of the minimum final running cost in the matrix ( ),cm i j , a binary representation is given to that rank in order to find the optimal control sequence ( )iu k . as we can see ali benmerzouga 48 from table 4 the final cost is equal to 1 and its rank in the ( ),cm i j matrix is 3. the only thing left is to get the binary representation of rank 3j = to get the optimal control sequence ( )iu k , which is equal to (0,1,1) and of course it is unique. table 2 (a). the different paths, gaps, combinations of ( )iu k , and minimum gaps when n = 3. x(2) f [u(2), x(2)] v2 u(2) 1 1 4 4 0 2 1 9 10 0 -1 0 1 1 1 -1 -1 4 5 1 table 2 (b). the different paths, gaps, combinations of ( )iu k , and minimum gaps when n = 3. x(1) f [u(1), x(1)] v1 u(1) 1 -2 13 17 1 -1 1 0 1 1 table 2 (c). the minimum running cost. x(0) g[u(0), x(0)] v u(0) 1 1 4 5 0 by using the dynamic programming approach, the following is observed: (i) in methods 3 and 4 we ended up with the same final results, namely, the minimum distance is unique, equal to 1 and obtained through the unique control sequence (0, 1, 1), (ii) when applying the dynamic programming approach directly to the original problem, all the states have to be computed and stored and (iii) when applying the dynamic programming to the new approach that is devised in benmerzouga (1997), just half of the states have to be computed and stored and the optimal control sequence is obtained by using a very simple combinatorial approach. 4.4 the complexity of the modified algorithm the complexity of the modified algorithm can be traced back to the continuous system given by equation (1.1). the parameter n , which is the state space of the system and k , which is the number of stages desired, and all types of computations and comparisons done at each stage must be fully taken into account and used to find the complexity of the whole procedure. switching linear systems 49 table 3. the different values of ( )z n and ( )x n , their corresponding ranks and the minimum gaps when n = 3 and m =2. z(3) x(3) g[x(3)] rank 1 1 1 -1 8 0 -2 -1 -1 2 1 1 1 0 0 -1 5 2 -1 -1 -1 1 0* 3 -2 -1 -1 2 1 4 3 2 2 -3 25 5 -1 -1 -1 1 0* 6 2 1 1 -2 13 7 proposition 4.1: the complexity of the above procedure is of order 32k n , where n is the state space of the system and k is the number of stages involved. proof: first of all, the transition matrix given in equation (1.1) is found by using the eigenvalue and eigenvector methods for both state matrices ( ), 1, 2ia i = . this is a very classical method used in diagonalizing matrices. for more details see gerald and wheatley (1994). this step requires ( )3 210 2n n+ number of computations. the next step involves propositions 4.2 and 4.3 given in benmerzouga (1997). secondly, the computations of different states for every stage requires ( )32kn n+ number of computations for computing the matrices ( )q k for all stages and ( )( )32 1k n n− + number of computations to find all states at all stages. for more details about the complexity of this step see gerald and wheatley (1994). thirdly, we go from the new z-space to the old x-space ( ) 3 21 2kk n n − +  computations are required. fourthly, the number of computations needed to get the performance index ( )g x n   is ( )2 3 1 k n − and finally the number of comparisons involved to find the smallest distance is 2k . in summary, to obtain the complete complexity figure, all of the above has to be taken into account. hence the complexity of the above procedure is equal to ( ) ( )3 2 12 3 8 2 2 2 .k k kk n n n++ + + + + ali benmerzouga 50 therefore the complexity of our optimal control problem is of order ( )32k n . this number is quite large when both k and n are large. table 4. ( ),cm i j matrix : all the different distances using the running cost ||xt –x(1)|| 2 ||xt –x(2)|| 2 ||xt –x(3)|| 2 rank j final cost 0 4 8 0 12 0 4 1 1 5 0 1 5 2 6 0 1 0 3 1 ** 13 9 1 4 23 13 9 25 5 47 13 4 0 6 17 13 4 13 7 30 5. concluding remarks this work presents two new ways of solving a switching control problem for discrete time systems, namely, a dynamic programming technique applied to the original problem and a dynamic programming technique applied to the new approach. the discrete time system is obtained by sampling (or discretizing) the continuous time system. the same restrictions are maintained as in benmerzouga (1997). the same results were obtained when applying the dynamic programming technique to both the conventional enumeration and the new approach when solving example 4.1. but when using the conventional enumeration approach and the dynamic programming approach applied to the conventional enumeration approach, all the states at each stage have to be computed and stored. on the other hand just half of the states have to be computed and stored with the new approach and the dynamic programming applied to the new approach. the nice thing about the dynamic programming technique when applied to both the original problem and the new approach, it manages to optimally steer the system from the initial state 0x to the target state tx and gives us the cheapest path possible. on the other hand, when solving the original problem directly or by using the new approach, there was no concern on how much it would cost us in order to reach a prespecified target tx or to be as close as possible. also, all the good properties about the new approach mentioned in benmerzouga (1997) are kept untouched and are added to all the nice and powerful characteristics known about the dynamic programming approach. economically speaking, the savings are huge when adopting this modified algorithm. the savings are made in the number of computations, the storage required and in the overall cost to go from the initial state 0x to the target state tx . all of these put together, have made this work much more efficient than the work given in benmerzouga (1997). when the number of steps is small the procedure is not computationally difficult. finally, when applying the dynamic programming technique to the original problem and to the new approach the performance is basically the same for a small number of steps. but when the number of steps increases applying dynamic programming to the new approach will take over all the way. in other words, the computations and storage involved in the procedure will be cut down by at least 50 % as shown in switching linear systems 51 benmerzouga (1997). in addition to the above, another important ingredient that improves the efficiency of the algorithm when applied using the dynamic programming approach to the new approach is the hasslefree way to determine the control sequence ( ){ }, 0,..., 1 ,u k k n= − which is complicated and not easy when finding it in the conventional enumeration approach. a modified algorithm, corresponding to the dynamic programming approach when applied to the new approach that is given in benmerzouga (1997) was developed. the computer simulations showed that the obtained modified algorithm performed successfully in computing the optimal control sequences ( ){ }, 0,..., 1 ,u k k n= − . the modified algorithm was shown to perform adequately when the number of steps increases. 6. acknowledgement thanks are due to anonymous referees for their many helpful suggestions. 7. references aslanis, j.t. 1983. analysis of switched linear systems in the plane, m.sc. thesis, department of systems engineering, case western reserve university, cleveland, usa. benmerzouga, a. 1985. the control of switched linear systems, m.sc. thesis, department of systems engineering, case western reserve university, cleveland, usa. benmerzouga, a. 1997. using switching linear systems to reach a pre-specified target. sultan qaboos university journal for scientific research -science and technology, 2: 69-76. brockett, r.w. 1970. finite-dimensional linear systems, wiley, new york. dreyfus, s.e. and law, a.m. 1977. the art and theory of dynamic programming, academic press, new york. gerala, c.f. and wheatley, p.o., 1994. applied numerical analysis. addison-wesley, new york. goka, t., tarn, t.j. and zaborszky, j. 1973. on the controllability of a class of discrete bilinear systems, automatica, vol. 9, pp. 615-622. pergamon press. kailath, t. 1980. linear systems, prentice hall, new jersey. sandell, n.r. and athans, m. 1974. modern control theory, massachusetts institute of technology. tarn, t.j., elliott, d.l. and goka, t. 1973. controllability of discrete bilinear systems with bounded control, ieee transaction on automatic control, ac-18: 298-301. wismer, d.a. and chattergy, r. 1978. introduction to nonlinear optimization, elsevier science publishing co. inc. received 19 february 2002 accepted 31 march 2004 introduction science and technology, special review (2000) 281-310 © 2000 sultan qaboos university 281 a comprehensive review of boundary integral formulations of acoustic scattering problems s.i.zaman department of mathematics & statistics, college of science, sultan qaboos university, p. o. box 33, al khod 123, muscat, sultanate of oman. عادالت التكاملية المحددة لمسائل االرتدادات الصوتية مراجعة شاملة للم سيف االسالم زمان وبشكل عام ،تشكلت . تمت مراجعة شاملة لكل تطورات المعادالت التكاملية المحددة لمسائل االرتدادات الصوتية : خالصة و هذه .أو الثنائي البسيط ليرإما باستعداد التكوين النظري فيلير والثانية باستخدام جرين األولى بمعادلة : المسألة بطريقتين إن الحاجة لتكوين معادالت . راجعة تظهر و تفسر المساهمات األساسية في هذا الموضوع في األربعة عقود الماضية مال الت ن الطريقة التقليدية لتكوين المعاد أل نسبهظهرت ) نيومان أو ديرشليت ( قوية و متطورة لمسألة االرتدادات الخارجية لمسألة االرتدادات الداخلية ) الترددات األيجينية (تعطي حال وحيدا في أرقام األمواج الصوتية و التي تعود للقيم األيجينية إن . كلما ازداد تردد الصوت أخر كما و أن االرتباط يكون اكثر كفاءة كلما كبرت أرقام األمواج بمعنى . المناظرة لها من النوع الثاني و التي تعتبر أكثر فردهولمزلتي تمت مناقشتها هنا تعطي معادالت التكامل ل تكوين معادالت التكامل و ا و على الرغم من ذلك فان المعادالت التكاملية و التي تتعلق . ة للعمليات الحسابية من النوع األول من هذه التكامالت ءممال . ثيل للمصفوفة النهائية تم تناول الموضوع بطريقة مبررة بالنواة المنفردة بقوة و التي تنتج شروطا صعبة في التم . هناك قائمة مهمة تفيد الباحثين و تشمل المراجع المهمة في الموضوع abstract: this is a review presenting an overview of the developments in boundary integral formulations of the acoustic scattering problems. generally, the problem is formulated in one of two ways viz. green’s representation formula, and the layer-theoretic formulation utilizing either a simple-layer or a double-layer potential. the review presents and expounds the major contributions in this area over the last four decades. the need for a robust and improved formulation of the exterior scattering problem (neumann or dirichlet) arose due to the fact that the classical formulation failed to yield a unique solution at (acoustic) wave-numbers which correspond to eigenvalues (eigenfrequencies) of the corresponding interior scattering problem. moreover, this correlation becomes more pronounced as the wave-numbers become larger i.e. as the (acoustic) frequency increases. the robust integral formulations which are discussed here yield fredholms integral equations of the second kind which are more amenable to computation than the first kind. however, the integral equation involves a hypersingular kernel which creates ill-conditioning in the final matrix representation. this is circumvented by a regularisation technique. an extensive useful list of references is also presented here for researchers in this area. s. i. zaman contents 1. introduction 282 1.1 boundary condition 285 2. background theory 286 2.1 helmholtz surface potentials 286 2.2 surface 287 2.3 properties of helmholtz potentials and their derivatives 288 2.4 helmholtz formulae 291 2.5 differentiated helmholtz formula 292 2.6 layer-theoretic formula 293 2.7 connection between the interior and exterior problems 295 3. improved integral equation formulations 297 3.1 brundrit 297 3.2 panich 299 3.3 copley 299 3.4 schenck 300 3.5 kussmaul 301 3.6 burton and miller 301 3.7 ursell and jones 302 3.8 piaszczyk and klosner 304 3.9 zaman 305 4. conclusion 306 5. acknowledgment 307 6. references 307 1. introduction the main purpose of this review is to give the general mathematical public an overview of the developments that occurred in the field of boundary integral methods for acoustic scattering problems. here, we are mainly concerned with the acoustic wave. the study of wave propagation in solids and fluids is very important in many branches of physics and engineering. we concentrate mainly on the area of time-harmonic acoustics. acoustic problems like assessing and reducing the noise produced by aircrafts, vehicles, household appliances and machines in general have been of major concern and interest to industry. scattering problems (or radiation problems) in mathematical physics are concerned with finding the solution of the helmholtz equation, ∇ (1) 022 =+ φφ k in an exterior domain. in the process of finding this solution, the integral equation method is very convenient. the helmholtz equation (or the reduced wave equation) arises when we seek steady-state solutions of the scalar wave equation for monochromatic (single frequency) sources. to give a general idea, consider a typical scattering problem: an incident wave with harmonic time-dependence is intercepted by a bounded scatterer. consequently, reflected and diffracted waves are produced which travel outwards from the scattering region, the propagation of the waves being described by the wave-equation, ),( 1 ),( 2 2 2 2 tp tc t ∂ φ∂ =φ∇ p (2) 282 a comprehensive review of boundary integral where c is the speed of propagation and φ is as defined in (3) below. it may also be regarded as the excess pressure at in the exterior domain and at time t. let us suppose that the wave-length of the source radiation is λ which corresponds to a frequency c/λ hz, and assume that steady state has been reached so that all waves present have harmonic time-dependence of this frequency. we can then write, p (3) 3321 ),,(;)();( ℜ∈==φ − xxxet ti ppp ωφ where φ is a complex function in the spatial co-ordinates and ω = kc. the constant k is the wave-number, defined as k = 2π/λ is a dimensionless quantity. by substituting (3) in equation (2) we see that φ is a solution of the helmholtz equation given in (1). the problem as described above is generally speaking a diffraction problem. such problems occur widely in acoustics, electromagnetic theory, hydrodynamics etc. it is very important to know how the incident wave field is modified by the scatterer. another type of scattering problem arises when the sources are actually on the scattering surface. in such situations one needs to know how the surface modifies the radiation characteristics of the source. as far as the mathematics is concerned, these two classes of problems are almost similar. for diffraction problems it is convenient to regard the total wave-function φ t at any point as being made up of two parts : a known incident wave φ inc , and a scattered wave φ sc which is to be determined (the time factor e-iωt is omitted), so we have scinct φφφ += . the incident wave is simply the wave-function that would exist in the absence of the scattering surfaces, and the scattered part is a wave diverging from the scattering region. a radiation condition is necessary for the scattered wave in order to ensure that it represents a diverging wave. at the boundary of the scatterer, conditions are imposed on the total wave φt , or its normal derivative or possibly a linear combination of the two, and the mathematical problem is to find an exterior wave-function which satisfies these boundary conditions and is such that the scattered wave obeys the radiation conditions. in reality the shape of the scatterer is usually arbitrarily shaped . this demands a numerical method of solution especially if the solution is needed in the midfrequency range. and as such, it is convenient to reformulate the problem as an integral equation. integral equations have been used extensively in formulating diffraction problems for analytical solution. the integral equations cannot usually be solved exactly in closed form, although the formulation very often provides a very useful basis for asymptotic analysis. during this century much effort has been concentrated on developing new alternatives, such as numerical techniques, to deal with the mathematical modelling of the problems. time-harmonic acoustic scattering problems are among the engineering problems for which the boundary element methods (bem) have already been shown to yield powerful numerical techniques. as we will see later, the fundamental feature of the integral equation method is one of shifting the problem of solving a domain equation to a boundary equation which is usually an integral equation of the second kind. by applying bem numerical techniques the solution is achieved, at least as an approximation. the advantages of the bem technique are that: only the boundary of the region (i.e. the surface scatterer) needs discretisation; the explicit calculations of results at domain points i.e. in the region; the possibility of using continuous and discontinuous elements in the mesh; and the capability of modelling infinite domains by discretisation of the internal boundary (surface of the scatterer only). during the latter half of the seventies, the appearance of texts like jaswon and symm (1977) and brebbia (1978), on integral equations and their numerical solutions by discretisation, proliferated the popularity of integral equation methods among the engineering community. later on, brebbia et al (1984) broadened the range of applications of bem. the basic ideas of the bem are not new to acoustic and structural engineers. since 1960s several integral equation methods have been used. in acoustics, these include, shaw and friedman (1962), banaugh and goldsmith (1963), chen and schweikert (1963), copley (1967). the bem was first applied to general transient elastodynamics in 1968 by cruse and rizzo (1968). since then some more 283 s. i. zaman dynamic applications emerged such as niwa et al (1976), domínguez (1978), manolis and bescos (1981), and cole et al (1978). bem is best suited when dealing with unbounded regions. in domain-based numerical methods, such as finite element method (fem) there are well known disadvantages. the use of integral equation methods presents many advantages, notably in that the meshing region is reduced by one dimension i.e. from the infinite domain exterior to the body (scatterer) to its finite surface, and the sommerfeld radiation condition at infinity is automatically satisfied. however, there is a well-known drawback in that the standard integral equation formulations obtained from the green’s representation formula, for time-harmonic acoustics, fail to have a unique solution at frequencies corresponding to the eigenfrequencies of the adjoint associated interior problem. this is not a physical drawback and nor indeed does it appear when the problem is represented by partial differential equations, but comes up entirely as a result of a deficiency of the integral equation representation. we shall look into this in detail later. over the last thirty years several techniques have been proposed to circumvent these fictitious eigenfrequencies. indeed the existence and uniqueness of solutions of the radiation problem, i.e. the exterior neumann boundary value problem for the helmholtz wave equation, has been proved for all values of wave-numbers by leis (1958). however, this matter is still one of the main areas of research in the bem. for acoustic problems, some of the most promising techniques have been proposed by panich (1965), schenck (1968), kussmaul (1969), burton and miller (1971), ursell (1973) and jones (1984,85). more recently, zaman (1994) proposed a technique using a modified hybrid layer potentials, based on the theory of potentials. let us first consider the equations governing acoustics. the propagation of small amplitude acoustic waves through a fluid medium is as described by the linear wave equation given in (2), where φ is a velocity potential and c is the velocity of sound in the medium. when the motion is considered to be timeharmonic, the function φ may be represented as in (3), where φ is a reduced velocity potential and ω is the angular frequency, and thus equation (2) reduces to the helmholtz equation (1), where k is the wave-number as defined before. 284 u let ρo, po be the density and pressure, respectively, of the fluid at rest. at time t, the excess pressure and the particle velocity, denoted by p and , are related by newton’s equation of motion, p to ∇−= ∂ ∂u ρ (4) usually we describe a sound field in terms of a velocity potential φ by u =∇φ (5) hence the excess pressure, after substituting (5) in (4), is t p o ∂ φ∂ −= ρ (6) and consequently by using (3), the velocity potential φ is related to the acoustic pressure p by p = -iω ρoφ (7) ρo is assumed constant here. helmholtz equation (1) is in fact the governing equation of a steady-state sound wave propagation problem. the acoustic scattering problem seeks the solution of this equation in the exterior region where the solution satisfies some boundary conditions. a comprehensive review of boundary integral 1.1 boundary conditions there are basically two types of scattering surfaces which yield two different types of boundary conditions. one condition is for perfectly soft scatterers and the other for perfectly hard scatterers. at the surface of a soft scatterer the excess pressure p is zero which in view of (7) gives 0)( =ptφ for all on the boundary (8) p at a perfectly hard or rigid scattering surface the incoming wave is completely reflected i.e. no part of the wave enters the surface which means that the normal component u . n of the particle velocity vanishes at the surface and hence, from (5), 0)( = ∂ ∂ p n tφ for all on the boundary (9) p the condition (8) is a form of homogeneous dirichlet boundary condition and the condition (9) is a form of homogeneous neumann condition. in order to determine the exterior solution uniquely, it is not sufficient to have the boundary condition on the surface only. but from the physical point of view it is essential that the scattered wave be entirely outgoing. in order to ensure this, we have to impose a radiation condition: i. in three dimensions, ∞→r lim [ ] 0)/( =−∂∂ scsc ikrr φφ ii. in two dimensions, ∞→r lim ( )[ ] 0/21 =−∂∂ scsc ikrr φφ (10) where r is the length of the vector measured from a fixed origin in the scattering region to a general field point. this condition was first expressed formally by sommerfeld (1949), and later by kupradze (1965), atkinson (1949), rellich (1943) and wilcox (1956). p let us now collate all the above and consider the mathematical statement of the general scattering problem. we have seen how time-harmonic wave problems in acoustics and indeed in diffraction, can be reduced to finding solutions of helmholtz equation, and we have also considered some of the more appropriate boundary conditions, (8) and (9). in scattering problems, wave-functions are sought in exterior domains, which satisfy not only boundary conditions at the surface of the scatterer but also the radiation condition at infinity. the surface boundary conditions are usually of three main types: (i) φ = f for the dirichlet problem, (ii) f= n∂ ∂φ for the neumann problem, (iii) f=h n + ∂ ∂ φ φ for the robin problem n is the outward normal to the surface and f, h are given functions. in the diffraction case, where the total wave is expressed as the sum of incident and scattered waves, we have seen that appropriate boundary conditions are often homogeneous. so the diffraction problem reads: 285 s. i. zaman (i) solve ∇ 2φ t + k 2φ t = 0 in the exterior region, where (ii) φt = φinc + φsc , (iii) with φt = 0 or 0= ∂ ∂ n tφ or 0=+ ∂ ∂ t t h n φ φ on the boundary. (iv) with φ sc satisfying the radiation condition in (10) it is more convenient and appropriate to work in terms of the scattered wave rather than the total wave. bearing in mind that scinct φφφ += , the diffraction problem reads: (i) solve in the exterior region 0 inc 22 =+∇ scsc k φφ (ii) with sc φφ −= [ dirichlet ] or nn sc ∂ ∂ −= ∂ ∂ φφ inc [neumann] or       + ∂ ∂ −=+ ∂ ∂ inc inc sc sc h n h n φ φ φ φ [robin] (11) on the boundary (iii) with φsc satisfying the radiation condition in (10). in a radiation-only situation, the problem is similar. here the solution behaves like a scattered wave satisfying the radiation condition, hence the problem to can be specified in the form (11), with the incident wave terms replaced by given functions describing the surface properties of the sources and the scatterer. analytical solutions to typical scattering problems are seldom obtainable. surface shapes and specified normal velocities are quite general. even asymptotic approximation methods (large or small k) are usually inappropriate because the solutions of interest are often those for which the wavelength of the source radiation is comparable with the size of the scatterer. as such, numerical approach is the only logical option. although for an elliptic equation (i.e. helmholtz equation) it is natural to think in terms of either finite difference method or finite element method (fem), there are some basic difficulties, one of which is that the region of interest is at infinity. on the other hand, the boundary element method (bem) is appropriate for this problem. 2. background theory before considering different integral equation formulations for the interior as well as the exterior helmholtz problems (acoustic scattering problems for instance), it will be worthwhile looking into the definitions of simple-layer and double-layer helmholtz potentials, and also investigating their properties. 2.1 helmholtz surface potentials consider a domain −b bounded by a closed surface ∂b, and let σ be a density function defined on ∂b. the simple-layer and double-layer potentials are defined as follows: simple-layer : ∫∂= bkk dyyyxgxl )(),()( σσ (12) 286 a comprehensive review of boundary integral double-layer : dyyyx n g xm b y k k )(),()( σσ ∫∂ ∂ ∂ = (13) where lk and mk are the simple and double-layer potential operators, x and y are positions in three dimension. the integration is performed at y∈∂b, ny is the outward normal at y and x is any other point either in the interior , exterior b−b + or on the boundary ∂b. gk(x, y) is the free-space green’s function for helmholtz equation, i.e., ( )yxyxgk k −−=+∇ πδ4),()( 22 (14) where δ is the dirac delta function and gk satisfies the radiation condition in (10). when the time factor e -iωt is included, gk represents the effect experienced at x of a point y (or vice-versa) radiating into free space in either two or three dimensions, more precisely, it represents the potential at x generated by a unit point source at y (and vice-versa). in three dimension, this function is gk (x, y) = yx e yxik − −− (15) the free space green’s function is closely related to the corresponding functions for laplace’s equation (k = 0), in that they possess the same singularity for | x – y |=0. this may readily be seen by expanding the functions for small | x – y |< ε, where ε is very small. so we find that in three dimensions, as | x – y |→ 0, )1(),()1( 1 ),( 0 oyxgoyx yxg k +=+− = (16) it is this weak singularity which is responsible for the continuity properties of the surface potentials, particularly the jump properties as the point x crosses the surface ∂b. because the singularity is the same for helmholtz potentials as for the more familiar potentials associated with laplace’s equation, the properties can be obtained as in classical potential theory (kellogg, 1929; günter, 1967). 2.2 surface it is clear from the definitions (12) and (13) of the potentials that whether or not the integrals exist and indeed whether or not they define the operatorss lk and mk, depends on three interrelated factors: (i) the behaviour of the layer or the surface density function σ, (ii) the singularities of the kernel functions, viz. gk and n g k ∂ ∂ , (iii) the nature of the surface ∂b. the development of classical potential theory followed two paths. russian workers (günter, 1967) built up the theory based on the concept of the lyapunov surface, whereas kellogg (1929) in his classic work introduced the idea of a regular surface. for these two types of surface slightly different conditions are required on σ in order to establish the existence of the potentials. in the present review we will not delve into details of these two types of surfaces. however let us look into the definitions of these surfaces. 287 s. i. zaman a lyapunov surface s satisfies the following three conditions (smirnov, 1964; günter, 1967): (i) a tangent plane exists at every point of the surface s. (ii) ∀x ∈ s, ∃ε > 0 such that s ∩{y | |x – y| < ε} intersects lines parallel to the normal at x in at most one point. it is self-evident that if this property holds for any given ε it also holds for any smaller ε. (iii) if , where are normals at )ˆ1n 1ˆ(cos 0 1 .n−=θ 0 ˆ,ˆ nn s∈10 , xx , then θ satisfies the hölder condition, θ α ≥− 10 xxa where a, α are constants, and 0 < α ≤ 1. as a result of condition (ii), the portion of the surface within the sphere may be represented in terms of a tangent-normal system of coordinates centred around the point .0x kellogg’s regular surface : the definition is in several parts (müller, 1969), (i) a curve is regular if it is continuous, has finite number of continuously differentiable arcs, has no double points and has finite length. (ii) a regular surface element is a point-set such that, for at least one cartesian coordinate system (x, y), it can be represented in the form z = f(x, y) , (x, y) ∈ h where f is continuously differentiable in h, and h is a finite closed area of the x-y plane which is bounded by a regular curve. the x-y plane would usually be the tangent plane at some representative point in the surface element. (iii) a regular surface is a point set which can be divided into a finite number of regular surface elements. (iv) a surface is closed if each of the edges of every regular surface element belongs to two surface elements. (v) a point is regular relative to a regular surface if there exists a decomposition of the surface into regular surface elements so that the point does not belong to an edge. it is regular relative to a curve if the curve is continuously differentiable at that point. (vi) a curve or surface is called ‘smooth’ if all its interior points are regular points. (vii) a regular region is a compact point set bounded by a finite number of closed regular surfaces such that no two of the surfaces have a point in common. if ∂b= u and each ∂bib∂1 n i= i is a lyapunov surface, then provided x is not on an edge or vertex of ∂b, it can be shown that lk and mk exist for all other x∈ℜ 3 provided σ is hölder continuous over ∂b. the existence and continuity of the normal derivative of mk requires that the source density σ ∈ c (2), (burton, 1973; colton and kress, 1983). 2.3 properties of helmholtz potentials and their derivatives let the potentials be defined on closed surfaces bounding the regular regions. the surfaces are assumed to be regular in the sense of kellogg. and also assumed to be ‘smooth’ in the sense described above. the helmholtz potentials are analytic functions of x∈ −b or x∈ b+, the behaviour for x∈ ∂b will depend on the local nature of the surface in the neighbourhood of x. the simple-layer potential, lk , and the double-layer potential, mk, are clearly the solutions of helmholtz equation, both in and b −b +. however, they define different solutions in the interior and exterior regions. at the boundary the potentials exhibit various irregularities due to the singularity of gk. the existence everywhere of lk and mk is assured if σ is merely continuous (günter, 1967). kellogg (1929) showed that the assumption σ ∈ c (2) is sufficient to ensure the existence (and continuity) of the derivative, and this is the condition we are imposing. the 288 a comprehensive review of boundary integral 289 ib∂ immediate consequence of (16) is that the jump and continuity properties of the helmholtz potential at the boundary parallel to those of the laplace potential at the boundary. for the smoothness condition on the boundary ∂b= , we merely require that each ∂bni=1u i be a lyapunov surface. we also require that σ be hölder continuous over the boundary i.e. σ satisfies the following inequality ++ ∈ b , ∂ 0,10;)()( 2121 >≤<−<− ayyayy βσσ β for any y1 ≠ y2 on the boundary. before we can review the continuity properties of the potentials at the boundary, we must understand the difference between the limiting value and the direct value of the integrals defining the potentials i.e. limiting values : , are on the normal line at x∈∂b ±±± → ∈ ± bxxlk xx ;)(lim σ ±x direct value : lkσ (x) for x ∈ ∂b subject to the conditions described above, the simple-layer potential lk has the following properties: a. it exists and, is continuous and differentiable everywhere in b + ∪ and satisfies the helmholtz equation i.e. −b byylk k ∂ℜ∈∀=+∇ \;0)()( 322 σ and it also satisfies the radiation condition (10). b. it exists and is continuous on the boundary despite the singularity (16), as this is essentially a weak singularity. also, its value at x in ∂b is continuous with its neighbouring values in and in i.e. −b+b bxxlxlxl k xx kk xx ∂∈== − → + → −+ ;)(lim)()(lim σσσ where . −b− ∈xx c. there exists two distinct normal derivatives at x in ∂b, one on each side of ∂b. we use the convention that n −+ ∂∂∂∂ xkxk nlnl /,/ x + , nx both increase moving away from ∂b. at any point x± in b + ∪ −b on the normal line through x in ∂b we have, ∫∂ ±± ± ′= ∂ ∂ b k x k dyyyxgx n l )(),()( σ σ where gk ′(x±, y) denotes the derivative of gk in the direction of the normal passing through x ± keeping y fixed (jaswon and symm, 1977). but at the initial point x, ∫∂ ±± ∂∈∂ ∂ +−= ∂ b x k x k bxdyyyx n g xx n l ;)(),()(2)( σπσ σ s. i. zaman which yields the jump, bxx n l n l x k x k ∂∈−= ∂ ∂ + ∂ ∂ −+ ;)(4πσ σσ since, 0= ∂ ∂ + ∂ ∂ −+ x k x k n g n g . for the double-layer potential mk, the treatment is similar, subject to the same conditions. here are the properties: a. it exists, and is continuous and differentiable everywhere in b + ∪ −b and satisfies the helmholtz equation ( ) bxxmk k ∂ℜ∈∀=+∇ \;0)( 322 σ and in b+ it satisfies the radiation condition (10). b. it exists on ∂b even though there is a singularity as |x y|→ 0 , which is essentially a weak singularity and consequently for x ∈ ∂b ∞< ∂ ∂ =∫∂ dyyyxn g xm b y k k )(),()( σσ however, its value at x in ∂b is not continuous with its neighbouring values in b+∪b , i.e. bxxmxxm kk xx ∂∈+±=± →± ;)()(2)(lim σπσσ so the jump is, bxxxmxm k xx k xx ∂∈−=− + →+ − →− ;)(4)(lim)(lim πσσσ c. normal derivatives are continuous i.e. 0)()( = ∂ ∂ + ∂ ∂ − − + + x n m x n m x k x k σσ . here are some more useful notations, )(xm tk σ ≡ [ ])(xln kx σ ∂ ∂ , which is the normal derivative at x of the simple-layer potential ; and nkσ (x) ≡ [ ])( xm n kx σ ∂ ∂ , 290 a comprehensive review of boundary integral 291 m kmwhich is the normal derivative at x of the double-layer potential. note that is the transpose of , hence the symbol. the derivative with respect to n t k x in [ ] ∫∂ ∂ ∂ ∂ ∂ = ∂ ∂ b y k x k x dyy n yxg n xm n )( ),( )( σ cannot be taken inside the integral sign because 0;)1( 1 ),( 3 2 ≅−+ − ≅ ∂∂ ∂ yxo yx yx nn g yx k consequently the kernel of nk becomes hyper-singular i.e. non-integrable. we shall look into some integral equation formulation of scattering problems which involve such hyper-singular kernels. this poses numerical complications which require special treatments. rêgo silva et al (1992,1993) used hadamard’s finite part integration in their treatment of the hyper-singular kernel. 2.4 helmholtz formulae these are integral representations of the scattering problem derived from a variant of green’s second theorem. they also utilize the helmholtz potentials defined above. when the field point of the representation is allowed to approach the surface, we get integral equations connecting the boundary values of the wave-function and its normal derivative. the representation utilizes green’s second theorem: let φ1, φ2 be any scalar functions with continuous second derivatives in a domain s ∪ ω, where s is the boundary of the domain. then we have, [ ]dvds nns ∫∫ ω ∇−∇=     ∂ ∂ − ∂ ∂ 1 2 22 2 1 1 2 2 1 φφφφ φ φ φ φ (17) if both φ1, φ2 satisfy helmholtz the equation in ω, then (17) takes the form, 012 2 1 =      ∂ ∂ − ∂ ∂ ∫ dsnns φ φ φ φ (18) we get the helmholtz formulae by replacing φ1 by any solution of the helmholtz equation φ(x), regular in ω, and φ 2 by gk(x, y). so, applying this to an exterior wave-function φ + in b+ which satisfies the radiation condition (10), and to the free space green’s function gk, we get, ++ ∂ + + ∈=         ∂ ∂ − ∂ ∂ ∫ bxxdyynyxgyxn g y b y k y k ;)(4)(),(),()( πφ φ φ (19a) s. i. zaman as x → x ∈ ∂b, due to ‘jump’ in the double-layer potential we have bxxdyy n yxgyx n g y b y k y k ∂∈=         ∂ ∂ − ∂ ∂ + ∂ + +∫ ;)(2)(),(),()( πφ φ φ (19b) and, as x → w ∈ , due to further ‘jump’ of the double-layer potential we have, −b − ∂ + + ∈=         ∂ ∂ − ∂ ∂ ∫ bwdyynywgywn g y b y k y k ;0)(),(),()( φ φ (19c) the boundary equation (19b) is known in the literature as the surface helmholtz equation (she), which in operator form becomes bxxx n lxm y kk ∂∈=         ∂ ∂ − + + + ;)(2)()( πφ φ φ for the dirichlet boundary condition we have bxxxmx n l k y k ∂∈−=         ∂ ∂ ++ + ;)(2)()( πφφ φ which is fredholm integral equation of the first kind with φ + given on the boundary. for the neumann condition we have bxx n lxmx y kk ∂∈         ∂ ∂ =+− + ++ ;)()()(2 φ φπφ which is fredholm integral equation of the second kind with ∂φ+⁄∂ny given on the boundary. a similar application of green’s second theorem to an interior wave-function φ in −b gives the following:       ∈− ∂∈− ∈ =         ∂ ∂ − ∂ ∂ −− − + ∂ − −∫ bxx bxx bx dyy n yxgyx n g y b y k y k ;)(4 ;)(2 ;0 )(),(),()( πφ πφ φ φ (20a,b,c) 2.5 differentiated helmholtz formula we can construct integral representations of the derivatives of φ in either the interior or exterior domains by differentiating the helmholtz representations for φ presented above. for the wave function in the interior, 292 a comprehensive review of boundary integral            ∈         ∂ ∂ − ∂∈         ∂ ∂ − ∈ =         ∂ ∂ − ∂ ∂ ∂ ∂ − − − + ∂ − −∫ bxx n bxx n bx dyy n yxgyx n g y n x xb y k y k x ;)(4 ;)(2 ;0 )(),(),()( φ π φ π φ φ (21a) for an exterior wave-function,            ∈         ∂ ∂ ∂∈         ∂ ∂ ∈ =         ∂ ∂ − ∂ ∂ ∂ ∂ + − − − ∂ − −∫ bxx n bxx n bx dyy n yxgyx n g y n x xb y k y k x ;)(4 ;)(2 ;0 )(),(),()( φ π φ π φ φ (21b) 2.6 layer-theoretic formula since both lkσ and mkσ are radiating wave functions in b +, it would be convenient to express the exterior solution of the helmholtz equation by means of layer potentials. exterior dirichlet problem (edp): we seek a solution in the form of a simple-layer potential (22a) +∈= bxxlx k ;)()( σφ and by continuity across the boundary the corresponding boundary equation becomes bxxlx k ∂∈= ;)()( σφ (22b) this is a fredholm integral equation of the first kind for the surface density σ in terms of the prescribed boundary value of φ . alternatively, we seek a solution in the form of a double-layer potential (23a) +∈= bxxmx k ;)()( µφ and by using the jump properties the boundary equation becomes bxxmxx k ∂∈+= ;)()(2)( µπµφ . (23b) this is a fredholm integral equation of the second kind for µ in terms of the prescribed boundary value of φ. 293 s. i. zaman exterior neumann problem (enp): we seek a solution in the form (22a) and then differentiate in the direction of the normal at x, taking the limit towards x ∈ ∂b, to get the boundary equation bxxmxx n t k x ∂∈+−= ∂ ∂ ;)()(2)( σπσ φ . (24a) this is a fredholm integral equation of the second kind for σ in terms of the prescribed boundary value of ∂φ ⁄∂n. alternatively, seeking a solution in the form (23a), differentiate in the direction of the normal at x, taking limit towards x ∈ ∂b, gives the boundary equation bxxnx n kx ∂∈= ∂ ∂ ;)()( µ φ (24a) this is a (non-fredholm) integral equation of the first kind for µ in terms of the prescribed boundary value of ∂φ ⁄∂n. as noted before, the nk operator has a hypersingular kernel. hadamard’s finite-part integration (hadamard (1923); rêgo silva et al 1992), treatment is required here. a formulation along this line has been proposed by jin (1993). interior dirichlet problem (idp): simple-layer form gives −∈= bxxlx k ;)()( σφ the boundary equation takes the form bxxlx k ∂∈= ;)()( σφ (25a) alternatively, the double-layer formulation gives −∈= bxxmx k ;)()( µφ the boundary equation takes the form bxxmxx k ∂∈+−= ;)()(2)( µπµφ (25b) interior neumann problem (inp) : applying the neumann condition to the simple-layer formulation above yields, bxxmxx n t k x ∂∈+= ∂ ∂ ;)()(2)( σπσ φ (26) also, by applying the neumann condition to the double-layer formulation above yields bxxnx n kx ∂∈= ∂ ∂ ;)()( µ φ (27) 294 a comprehensive review of boundary integral note that (24a) which refers to enp is the transpose of (25b) which refers to idp. also note that (23b) which refers to edp is the transpose of (26) which refers to inp. the discussion on this connection follows. 2.7 connection between the interior and exterior problems integral equation formulations for helmholtz problems (acoustic) in the exterior region repeatedly make reference to the related interior problem. as suggested in the introduction that there may be no physical connection between the two regions (e.g. the surface may be perfectly rigid), nevertheless the integral equation formulations for the two regions often have similar integral operators. burton (1973) gives a very clear analysis of this. when the wave-number k takes certain discrete values, the interior problems with homogeneous boundary conditions have non-trivial solutions. these values of k are the eigenvalues of the interior problem and the corresponding non-trivial solutions are the eigenfunctions. it may be shown (burton, (1973) that these eigenvalues must be real. at these values the corresponding integral equation governing the exterior case breaks down i.e. it may either fail to yield a unique solution or it may be insoluble for the given inhomogeneous term. zaman (1994) gives a detailed treatment of this. it is shown that the exterior neumann (dirichlet) problem breaks down whenever the wave-number k equals the eigenvalue of the interior dirichlet (neumann) problem. let us look at the situation briefly here: let, kd = { wave-numbers k  interior dirichlet problem has non-trivial solutions}, kn = { wave-numbers k  interior neumann problem has non-trivial solutions}. homogeneous dirichlet case : inserting the boundary condition φ = 0 into the boundary equation (20b) and writing the resulting equation in operator form, we find that ∂φ ⁄∂n satisfies bxx n lk ∂∈=    ∂ ∂ ;0)( φ (28) now inserting the same boundary condition into the (differentiated) boundary equation (21b) and writing the resulting equation in operator form, we get, ( ) bxx n mi tk ∂∈=    ∂ ∂ +− ;0)(2 φ π (29) where i is the identity operator. it is clear that the boundary values of ∂φ ⁄∂n satisfy both (28) and (29) simultaneously. suppose k∈kd . then the interior homogeneous dirichlet problem has non-trivial solutions, i.e. φ ≠ 0 in , even though φ = 0 on the boundary. so it follows from (20c) that ∂φ ⁄∂n ≠ 0 on ∂b implying that (28) and (29) have non-trivial solutions. this result has an important implication on the exterior neumann formulations. −b homogeneous neumann case : inserting the boundary condition ∂φ ⁄∂n = 0 into the boundary equation (20b) and then writing the result in operator form we get ( ) bxxmi k ∂∈=+ ;0)(2 φπ (30) now, inserting the same boundary condition in the (differentiated) boundary equation (21b) and writing the result in the operator form we get 295 s. i. zaman bxxn k ∂∈= ;0)(φ (31) clearly the boundary values of φ satisfy both (30) and (31) simultaneously. let k∈kn , the interior homogeneous neumann problem has non-trivial solutions i.e. φ ≠ 0 in −b even though ∂φ ⁄∂n = 0 on ∂b. therefore it follows from (20c) that φ ≠ 0 on ∂b, suggesting that (30), (31) have non-trivial solutions. this result has an important implication to the exterior dirichlet formulation. let us now consider how the above phenomena affect different formulations of the exterior problems. we look at first the layer-theoretic formulations. homogeneous dirichlet case: inserting φ = 0 into (25a, 25b) and writing the equations in operator form we get, bxxlk ∂∈= ;0)(σ (32) bxxmi k ∂∈=+− ;0)()2( µπ (33) it is noted that (32) is mathematically identical to (28) but that (33) is the transpose equivalent of (29). this suggests that (32) and (33) have non-trivial-solutions whenever (28) and (29) do respectively. homogeneous neumann case: inserting ∂φ ⁄∂n = 0 into (26b, 27b) and writing in operator form we get, (34) bxxmi tk ∂∈=+ ;0)()2( σπ bxxn k ∂∈= ;0)(µ (35) again we note that (35) is mathematically identical to (31) but that (34) is the transpose equivalent of (30). this suggests that (34) and (35) have non-trivial solutions whenever (30) and (31) do respectively. connection with exterior problems: suppose we seek a solution of the exterior neumann problem using a simple-layer formulation +∈= bxxlx k ;)()( σφ taking the normal derivative and inserting the neumann condition with ∂φ ⁄∂nx prescribed on ∂b, we get, bxx n xmi x t k ∂∈∂ ∂ =+− ;)()()2( φ σπ (36) this boundary equation has a unique solution if the homogeneous equation (37) bxxmi tk ∂∈=+− ;0)()2( σπ has only the trivial solution (zaman, 1994). however, since (37) is mathematically identical to (29), it has non-trivial solutions for wave-numbers k∈kd i.e. enf fails to yield unique solution for these wavenumbers. arguing similarly it can be shown that edf fails to give unique solution if k∈kn . also, by using the helmholtz formula we arrive at the same conclusion. however a distinction can be drawn between the 296 a comprehensive review of boundary integral layer-theoretic formulation and the helmholtz formula. the inhomogeneous equation (36) is insoluble because the free term ∂φ ⁄∂nx is not orthogonal to the eigenfunctions of the homogeneous adjoint equation. by contrast, the helmholtz formula which yields at least non-unique solutions since the free term satisfies the compatibility condition [cf. fredholm alternative]. zaman (1994) gives an interesting illustration of this connection between the interior and the exterior problems with reference to a spherical surface. jaswon (1963) is one of the early significant works on integral equation methods in potential theory. it presents the ground work for most of the subsequent works in this area. this peculiar defect and hence a drawback in the classical formulation led several workers to propose alternative formulations in order to circumvent this. this phenomenon has been known for at least fifty years (lamb, 1945). in the next chapter we will look at those proposals which made significant contribution to the development of the integral equation formulations of helmholtz problem. 3. improved integral equation formulations the formulations discussed at the end of the previous chapter are known as the classical integral equation formulations. they were defective in that those formulations fail to yield a unique solution at certain critical values of the wave-number k, which are the eigenvalues of the corresponding homogeneous interior problem. we discuss below some of the significant propositions which improve this situation. 3.1 brundrit brundrit (1965) in his paper presented a proposal, utilizing a layer potential i.e. indirect formulation, and developed a numerical method, which did not suffer from the effect of critical wave-numbers. considering the problem of hard acoustic scattering by a fixed obstacle of boundary ∂b, he proposed that the scattered wave be represented as (38) +∈= bxxlx k ;)()( σφ this is a classical formulation. applying the neumann boundary condition, it is noted that the source density σ satisfies the boundary equation bxx n xmi tk ∂∈∂ ∂ =+− ;)()()2( φ σπ (39) however, the corresponding homogeneous equation (40) bxxmi tk ∂∈=+− ;0)()2( σπ has non-trivial solutions at any failing (characteristic) values of k which are also the eigenvalues of the corresponding interior dirichlet problem. therefore the general solution of (39) may be written in the form * jσ ∑+ j jjo c *σσ at any choice of k, where σo is a particular solution, and cj ’s are arbitrary constants. brundrit noted that the non-trivial eigensolutions of (40) are the boundary-values of ∂φ ⁄∂n, for the interior dirichlet eigensolutions, which satisfy simultaneously 297 s. i. zaman bxx n lk ∂∈=    ∂ ∂ ;0)( φ bxx n mi tk ∂∈=    ∂ ∂ +− ;0)()2( φ π as a result of using direct formulation, which yield bxxlcxcl j jkj j jjk ∂∈== ∑∑ ;0)()( ** σσ consequently, bxxlxlcxlxcl ok j jkjok j jjok ∂∈=+=      + ∑∑ ;)()()()( ** σσσσσ brundrit further noted that by continuity of a simple-layer potential and by uniqueness, the wave-function generated by the eigensolutions of (40) must vanish identically in the exterior i.e. +∈== ∑∑ bxxlcxcl j jkj j jjk ;0)()( ** σσ therefore he argued that component of a general solution of (39) would make no contribution in the exterior. * jσ alternatively, we can utilise the non-trivial eigensolutions to generate an exterior potential, *jσ v(x) = +∈ bxxl jk ;)( *σ for each j. using (40) bxxmix n v j t k ∂∈=+−=∂ ∂ + ;0)()2()( *σπ where (+) signifies that the normal points are into the exterior. since, ∂v/∂n+ = 0 for each j , it follows, by uniqueness that v vanishes identically in the exterior i.e. +∈= bxxl jk ;0)( *σ and by continuity v(x) = bxxl jk ∂∈= ;0)( *σ 298 a comprehensive review of boundary integral for each j. therefore as noted by brundrit, the component of the general solution does not make any contribution in the exterior domain. * jσ nevertheless, brundrit overlooks the fact that the boundary integral equation (39) has no solution whenever k coincides with any of the critical values, since the eigenfunctions of the corresponding adjoint equation of (40) are not orthogonal to the inhomogeneous term in (39). note that brundrit’s approach can also be formulated by helmholtz formula which yields a consistent non-unique solution. 3.2 panich by using layer potentials, panich (1965) initially proposed [ ] +∈+= bxxmlx kk ;)()( σµφ (41) where µ is a complex constant, chosen to be +i if ℜ(k) ≥ 0, see burton (1974, 1976). accordingly, σ satisfies the following boundary equation, [ ] bxxnmix n k t k ∂∈++−=∂ ∂ ;)(2)( σµπ φ (42) since (42) contains a hypersingular operator nk , which is non-compact, panich proposed replacing (41) by the hybrid layer-potential (43) [ ] +∈+= bxxlmlx okk ;)()( σµφ where the subscript o denotes putting k = 0 in the definition of lk. therefore σ satisfies [ ] bxxlnmix n ok t k ∂∈++−=∂ ∂ ;)(2)( σµπ φ (44) writing [ ] ooookok lnlnnln +−= and using the identity [ ][ ]imimln totooo ππ 22 −+= the boundary equation (44) takes the form { }[ ] bxximlnnmix n t oook t k ∂∈−+−++−=∂ ∂ ;)(4)()(2)( 22 σπµπ φ (45) here, all the operators are weakly singular and hence compact. this is one of the earliest examples of the regularization technique for weakening the singularity of the kernel. using fredholm theory, colton and kress (1983) deduced that (45) has a unique solution for all non-negative real k provided ℑ(µ) > 0 . however, numerical implementation is very expensive and cumbersome due to the application of the product of matrix approximations to the operators. 3.3 copley the proposal by copley (1967) utilised the helmholtz formula at points in the interior region i.e. 299 s. i. zaman − ∂ ∈=         ∂ ∂ − ∂ ∂ ∫ bxdyynyxgyxn g y b y k y k ;0)(),(),()( φ φ thus avoiding the singularity problem. the idea was originally proposed by kupradze (1965). in operator form, −∈    ∂ ∂ = bxx n lxm kk ;)()( φ φ (46) which is a functional relation between φ and ∂φ ⁄∂n on ∂b, involving the non-singular kernel gk . this becomes an integral equation of the first kind for φ in terms of ∂φ ⁄∂n. copley calls it the interior helmholtz integral relation. he proves two uniqueness theorems: i. if (46) holds ∀ x ∈ , then the solution of the functional equation is unique. −b ii. if the surface ∂b is axisymmetric and (46) holds for all x along the axis of symmetry in , then the solution is unique. −b copley proposed a scheme for enforcing (46) at a finite number of points {x1, x2, x3,..} denoted by x, in . however a bad choice of x∈ −b could cause an interference with the interior eigenfunctions , which satisfies φ̂−b [ ] −∈      ∂ ∂ =+ bxx n lxmi kk ;)( ˆ )(ˆ2 φ φπ (47) a typical bad choice is when x lies on a nodal surface of eigenfunctions . these nodal surfaces are such that (x) = 0 i.e. (47) is the same as (46). if this is true for the choice x then the eigenfunctions will also satisfy (46), thereby causing an interference. cunfare et al (1989) suggested a linear combination of (46) and its normal derivative, but as the points in x do not lie on ∂b the normal derivative operation cannot be well defined. it is also noted that any numerical implementation of this fails as the number of such points increases, which is detailed in the next proposition. further it can be shown that any numerical scheme based on (46) has undesirable characteristics as the number of points increases as we shall see in the next proposition. copley solved some axisymmetric radiation problems but noted that his method fails to give accurate results for bodies which are not sufficiently smooth. fenelon (1969) obtained results for acoustic radiation by a finite cylinder, using copley’s approach. φ̂ φ̂ φ̂ 3.4 schenck this method (schenck, 1968) utilizes the surface helmholtz equation [see eq. (19b) of previous section], supplemented by the interior helmholtz relation i.e. [ ] bxx n lxmi kk ∂∈    ∂ ∂ =+− ;)()(2 φ φπ (48a) 300 a comprehensive review of boundary integral −∈    ∂ ∂ = bxx n lxm kk ;)()( φ φ (48b) schenck showed that for any k there is only one solution to (48a) which also satisfies (48b) for all points in the interior region. discretisation of (48a) and of (48b) for only a few points in gives a non-square system of linear equations, which is then solved by a least-square method. this method is better known in literature as the combined helmholtz integral equation formulation (chief). for lower ranges of values of k, successful applications of chief have been reported (amini and harris, 1990; seybert et al, 1984, 1985, 1986, 1987). seybert et al have used chief successfully to model radiation and scattering problems using quadratic isoparametric elements. however, the major drawback of the schenck method is that there is no way of knowing how many interior points are needed and where best to locate them. if a point is placed on a nodal surface of an interior eigenfunction, the method will still fail for the reason given before. no criterion has yet been reported which enables one to isolate these “bad” interior points. however, since this method is relatively simple to implement, it is often successfully used in practice for modest values of k (amini and harris, 1990; seybert and rangarajan, 1987). −b 3.5 kussmaul this proposal utilizes hybrid layer-potentials. kussmaul (1969) proposed for a scattered wave, (49) [ ] +∈+= bxxmlx kk ;)()( σµφ it is a superposition of a simple-layer and a double-layer distribution over the boundary. zaman (1994) proposed an adaptation of this method and successfully obtained some numerical results for higher k. the hard boundary condition on (49) yields [ ] bxxnmix n k t k ∂∈++−=∂ ∂ ;)(2)( σµπ φ (50) this proposition is analogous to the mixed potential used by brakhage and werner (1965) and leis (1958,1962,1965) in their treatment of the dirichlet problem. the constant µ is chosen to be +i if ℜ(k) ≥ 0 and –i if ℜ(k) < 0. this choice ensures the uniqueness of the solution of the equation (50). since the operator nk is non-compact, so the operator on the right-hand side of (50) becomes non-compact, and as a result, fredholm theory cannot be applied to deduce whether or not a solution exists. kussmaul uses a regularization technique, which, by eliminating the non-compactness, enables him to prove the existence of solution. due to the complexity of the regularization technique few numerical implementations have been reported. kirkup and henwood (1992) used this method to compute solutions of some acoustic radiation problems. 3.6 burton and miller this proposition is the direct analogue of the indirect formulation of panich (1965). burton and miller (1971) proposed a linear combination of the surface helmholtz equation (19b) and its normal derivative (21b), which in operator notation takes the form, [ ] ( )[ ] bxx n milxnmi tkkkk ∂∈∂ ∂ ++=++− ;)(2)(2 φ παφαπ (51) 301 s. i. zaman where α is an arbitrary coupling parameter. it is proved (burton and miller, 1971; tzu-chu, 1984) that if α is chosen to be a complex constant with ℑ(α) > 0 , then the homogeneous equation [ ] 02 =++− φαπ kk nmi , (52) has only the trivial solution φ = 0 for real values of k, ensuring that (51) has a unique solution for all wavenumbers. harris (1989), in a similar way to tzu-chu (1984), extends the uniqueness proof to the case where α is taken to be a function of x, i.e. for the condition ℑ(α(x)) > 0, ∀x∈∂b it is proved that (52) has only the trivial solution. this result is used in the study of the conditioning of the formulation. analytically, the proposal is undoubtedly elegant. nevertheless, it suffers from a numerical drawback due to the involvement of the non-compact (i.e. hypersingular) integral operator nk. to resolve this problem burton (1974), following panich (1965), regularizes nk to obtain the regularized burton and miller formulation (rbm): { }[ ] ( )[ ] bxx n milxl ximnnlxmi t kok ookok ∂∈ ∂ ∂ ++= −+−++− ;)(2)( )(4)()()(2 22 φ πα φπαπ where all the integral operators are weakly singular and compact. the choice of α(x) is such that ℑ(α(x)) > 0 for k > 0. the main drawback of rbm is having to compute the product of operators (by multiplying their matrix approximations) which proves to be very expensive and cumbersome. the reason for the regularized version is twofold. firstly to establish the uniqueness of solution using classical fredholm theory, and secondly to make it amenable to numerical treatment despite its complexities. however it seems possible to compute a direct approximation to nk. terai (1980) gives an approximation to nk for a flat boundary element, and stallybrass (1967) introduced a pointwise variational principle to approximate nk, which meyer et al (1978, 1979) utilized in order to show that ∫∫ ∂∂ ⋅=∂∂ ∂ b yxk b yx k dynnyxgkdyyx nn g ),(),( 2 2 which may be used in [ ] bxdynnyxgxkdyxy nn g xn b yxk b yx k k ∂∈⋅+−∂∂ ∂ = ∫∫ ∂∂ ;),()()()()( 2 2 φφφφ the second integral on the right-hand-side is weakly singular and the first integral can be interpreted in the sense of cauchy principal value. amini and harris (1990) gave a comparison between the rbm and the direct burton and miller form. reut (1985) has developed a burton and miller formulation which is called composite normal derivative overlapping relation (condor), based in part upon terai (1980). 3.7 ursell and jones ursell (1973, 1978) noted that gk(x, y) can be replaced by any fundamental solution to the helmholtz equation in the exterior domain b+ which satisfies the radiation condition. so we have a modified green’s function g(x, y) = gk(x, y) + γ(x, y) (53) 302 a comprehensive review of boundary integral where γ is an analytic wave function in b+. using this in the classical formulation (layer-theoretic or helmholtz formula) with (53) replacing the classical free-space green’s function, and applying the hard boundary condition, the boundary equation takes the form, [layer-theoretic]: bxdyyyx n g xx n b x ∂∈ ∂ ∂ +−= ∂ ∂ ∫∂ ;)(),()(2)( σπσ φ (54) [helmholtz]: ∫∫ ∂∂ ∂∈      ∂ ∂ +−=         ∂ ∂ b yb y bxdyyyx n g xdyy n yxg ;)(),()(2)(),( φπφ φ (55) now, if −⊂∈=γ+ ∂ γ∂ bsxyxyx n r ;0),(),( γ where γ is a complex constant such that ℑ(γ) > 0 and sr is a sphere enclosed entirely within ∂b, then ursell (1973) shows that the solutions to (54) and (55) are unique. ursell noted that γ(x, y) may be chosen to be an infinite series of spherical wave-functions, which converges quickly for small k but slowly as k increases. jones (1974) proposed a modification to this by replacing the infinite series with a finite one, i.e. γ (56) ∑∑ = = ψ= m m m n mnmnmn yxbyx 0 0 )()(),( ψ where xx n mxmmn xx n mxmmn pkrhx pkrhx φθ φθψ sin)(cos)()( cos)(cos)()( =ψ = the point x has the spherical coordinates ( xxxr φθ ,, ). the functions are the spherical hankel functions of the first kind and are the associated legendre functions. )( xm krh n mp supposing, k = { ki 0 < k1< k2 < k3 …} jones showed that if k < km+2 then (54) and (55) have unique solutions provided that the bmn’s are real and non-zero. kleinmann and kress (1983) suggested that bmn be chosen so as to minimize the condition number of the resulting integral operator. the major drawback of this method is that for an arbitrary surface one does not know how large to take m since k is usually unknown. also it is known (burton, 1974) that the number of elements in k less than a given k is proportional to k3, and so for a moderately large k we have to take a considerably large number of terms. consequently γ(x, y) becomes very costly. as such there has been little or no report of its implementation in practical problems. 303 s. i. zaman 3.8 piaszczyk and klosner this approach (piaszczyk and klosner, 1984) is similar to chief, but it uses she (19b) together with the exterior helmholtz relation +∈    ∂ ∂ += bxx n lxmx kk ;)()()( φ φφ (57) naturally φ is not known for points in b+ , and for hard scattering ∂φ ⁄∂n only is known on ∂b. therefore it is supposed that there exists some function z(x) which gives a simple impedence relationship bxx n xzx ∂∈ ∂ ∂ = ;)()()( φ φ (58) using (57) and (58), one can compute φ for a few points in b+. utilizing these values and a suitable discretisation of she, an overdetermined system for φ in ∂b can be formed. using a least-squares procedure one can solve this system of linear equations and find φ on ∂b. then one can recompute φ in b+ and repeat the process until a convergence criterion is satisfied. the proposal is analytically sound since a uniqueness proof is presented. however this method also suffers from a major drawback in that it requires the solution of an over-determined system at each iteration, which is very costly from a computational point of view. also the rate of convergence depends on the choice z(x) and it is doubtful whether or not the iteration process will converge at all (cunefare et al, 1989). although, the problems which the classical formulations faced are circumvented analytically by the improved approaches, the implementations have been very difficult. rêgo silva et al (1993) presented a numerical implementation of a hypersingular boundary element formulation for acoustic radiation problems. here, burton and miller formulation in (51) is used. it is argued that in the hypersingular integral operator nk the behaviour of the integral is determined by conditions at small r = x yfor which ( ) ( )      + ∂∂ ∂ =     +         + ∂ ∂ ∂ ∂ =         ++ ∂ ∂ ∂ ∂ −+= ∂∂ ∂ −− −−− r oyx nn g r onn n r n r r ennikr n r n r rkikr r yx nn g yx o xy yx ikr xy yxyx k 1 ),( 1 3 1 13 1 ),( 2 3 22 3 2 clearly the convergence conditions of the integral in nk are the same as those of the normal derivative of a double-layer of a harmonic (laplace) potential (with k = 0), given by the lyapunov-tauber theorems (courant and hilbert, 1989). following guiggini et al (1992), the method of hadamard’s (1952) finite part was used here to evaluate the hypersingular integral i.e. ( )∫ +−→ ∂∂ ∂ εε φ ε ses yx k dyyx nn g y ),()(lim 2 0 here x ∈ eε ∈ s. here sε is the surface exterior to s of a small sphere of radius ε around a point x ∈ s, and eε is the subregion of s lying inside the small sphere. according to hadamard’s definition, the shapes of sε 304 a comprehensive review of boundary integral and eε must be preserved while ε → 0. more so, the shape of eε must be consistent with the shape of sε throughout the limiting process. 3.9 zaman another method (zaman, 1994; jaswon and zaman, 1993) proposed forms an adaptation of the kussmaul (1969) formulation. analogous to kussmaul formulation (48), a superposition of a simple and a double-layer potential is used. the formulation (48) is improved by introducing an internal fictitious surface ∂b*, similar and similarly situated to the given surface ∂b, i.e. for each y ∈∂b there is a corresponding y*∈∂b* such that y*= ϑy, where ϑ is a real constant such that 0 < ϑ ≤ 1. the solution of the helmholtz equation in the infinite region exterior to the surface ∂b is represented by a superposition of layer potentials with a coupling parameter η, [ ] 10,;)()( ≤<∂∪∈γ+= + ϑσηφ ϑ bbxxlx kk (59) where **** ,;)(),()( * bybbxyyx n g x b y k k ∂∈∂∪∈∂ ∂ =γ + ∂∫ σϑ ϑ is a continuous distribution of modified dipole sources on ∂b* for each ϑ. in (59) the parameter η is chosen to be iϑ -1 so that the coupling parameter eventually takes the form +i. this formulation is called modified layer formulation (mlf). this is a hybrid potential distribution except that the dipole components are located away from the surface. it may be regarded as a classical simple-layer formulation with the freespace green’s function gk replaced by the modified green’s function ),(),(),( * * yx n g yxgyxg y k kk ∂ ∂ += η which satisfies in x the equation ( )yxyxgkyxg kk −−=+∇ πδ4),(),( 22 . note that gk has the same singularity behaviour as that of gk when |x y| ≈ 0. the hard acoustic boundary condition (neumann) applied to (59) yields bxdyyyx n g xx n b x k ∂∈ ∂ ∂ +−= ∂ ∂ ∫∂ ;)(),()(2)( σπσ φ (60) where *** * 2 ,;),(),(),( bybxyx nn g yx n g yx n g yx k x k x k ∂∈∂∈ ∂∂ ∂ + ∂ ∂ = ∂ ∂ η relation (60) is a fredholm integral equation of the second kind for σ in terms of the given term ∂φ ⁄∂n on the left hand side. also, significant in (60) is that the only singularity in the kernel is the weak singularity of ∂gk ⁄∂nx, which presents no computational havoc. zaman (1996, 1997) presents arguments 305 s. i. zaman 306 concerning the uniqueness of the solution of (60) and also presents some illustrative works on potential theory applied to a spherical surface. the formulation (59) and the corresponding boundary equation (60) are utilized numerically to find some test results comparing the analytical and numerical results for a sphere, cube and cylinder. the radiation problem of a pulsating and oscillating sphere is also performed numerically. finally the scattering problem from a sphere is performed. it is found that ϑ ≅ 0.5 yields the best agreement with the analytical result. detailed numerical treatment of the problem is discussed in zaman (1994). 4. conclusion the purpose of this review has been to investigate different improved boundary integral formulations of scattering / radiation problems designed to overcome the shortcomings of classical formulations. a host of boundary element methods (bem) has emerged over the last couple of decades for the numerical implementations of the formulations. numerical aspects of the applications are discussed in many publications. for numerical implementation, one way is the discretisation (zaman, 1994) process with the collocation method applied to the surface divided into geometrical shaped-elements? with constant on each element, which resulted in a set of several linear equations. the other way is the surface interpolation (harris, 1989) process which involved spline-interpolation with parametric rectangular or triangular mappings. burton (1976) suggested that the surface should first be divided into a few surface regions, each of which is mapped parametrically on to a rectangle using bicubic b-spline interpolation. this procedure allows the surface integrals to be expressed as sums over unit square elements and thus leads to a large reduction in the number of quadrature weights needed. the set of linear equations are then solved by a gaussian-elimination process (zaman, 1994) or otherwise. the mlf formulation (zaman, 1993, 1994) has been applied to regular axisymmetric bodies as test problems with promising numerical results and its engineering feasibility is still being looked at. there are many papers (burton and miller, 1971; wilton, 1974; wait, 1973; van buren, 1970; brebbia et al, 1991; bannerjee and butterfield, 1981; ingber and hickox, 1992) dealing with the feasibilities of other formulations. atkinson (1976) gives a very useful survey of numerical methods for the solution of boundary integral formulations. brebbia (1978) gives a good text for bem. for getting round the problem of fictitious interior eigenvalues, which we come across when wave-numbers are large, shaw and huang (1989) suggested an embedding approach. the mathematical formulations of the problem is reviewed. the factors governing the choice of integral equation formulation were threefold: 1. the integral equation must be numerically stable over the required range of wave-number, preferably without user intervention. 2. the integral equation reliable for all surface shapes including long slender bodies. 3. the formulation efficient in the use of computer time. acoustic shields, screens or barriers are sometimes used as a means for reduction of noise from machines, engines or roads. for determining mathematical model for an acoustic shield, the main property to take into account is that the shield is a thin structure and so its vibratory motion can become coupled to the acoustic field. thus a shield is equivalent to a discontinuity in the sound pressure field. due to its topology, the shield is termed a shell. kirkup (1990, 1991, 1992) and kirkup and henwood (1992) give a detailed study of this. the purpose of their study was to extend the bem for the solution of 3-d acoustic radiation problems to acoustic-vibratory systems involving vibratory bodies and thin acoustically coupled shells. the collocation method is applied resulting in a method termed boundary and shell element method (bsem) which is noted to be a useful generalisation of the traditional bem. the method was implemented for general 3-d problems in a fortran subroutine absemgen. the subroutine is applied to test problems. due to numerous recent applications of boundary element methods involving hypersingular integrals, some research has been carried out on developing new sophisticated elements in order to satisfy their existence, as alternatives to the simple but time-consuming discontinuous elements (rêgo silva, et al 1993). a comprehensive review of boundary integral 307 splines c1,α elements, and b-splines c2 elements, are among the most promising options. nevertheless, further developments regarding their efficient computational implementation are still required. problems such as fluid/structure or soil/structure interaction are of importance to many physical and engineering applications, and have been receiving considerable attention as to their numerical modelling. some approaches discretise the structure using fem. however, bem can also be an efficient alternative for these modellings. 5. acknowledgement the facilities provided by the department of mathematics and statistics, sultan qaboos university, are gratefully acknowledged by the author. also, a warm gratitude from the author goes to professor ibrahim a. eltayeb, sultan qaboos university, for his encouragement and advice throughout this project. 6. references amini, s. and harris, p. j. 1990. a comparison between various boundary integral formulations of the exterior acoustic problems, comp. meth. appl. mech. and eng., 84(1): 59-75. atkinson, f. v. 1949. on sommerfeld’s radiation condition, philosophical magazine, 40: 645-651. atkinson, k.e. 1976. a survey of numerical methods for the solution of fredholm integral equation of the second kind, siam, philadelphia, pa. banaugh, r. p. and goldsmith, w. 1963. diffraction of steady acoustic waves by surfaces of arbitrary shapes, journal of acoustical society of america, 35: 1590-1601. bannerjee, p. k. and butterfield, r. 1981. boundary element methods in engineering science, mcgraw hill, london, uk. brakhage, h. and werner, p. 1965. über das dirichletsche außenraumproblem für die helmholtzsche schwingungsgleichung, archiv. der math, 16 (english translation): 325-329. brebbia, c. a. 1978. the boundary element methods for engineers, pentach press, plymouth, uk. brebbia, c. a., telles, j. c. f. and wrobel, l. c. 1984. boundary element techniques, springer-verlag, berlin. brebbia, c. a., rêgo silva, j. j. and partridge, p. n. 1991. computational formulations, boundary element in acoustics, , comp. mech. publications, southampton & elsevier applied sciences, london, pp13-60. brundrit, g. b. 1965. a solution to the problem of scalar scattering from a smooth bounded obstacle using integral equations, quarterly journal of mechanics and applied mathematics, 18(4): 473-489. burton, a. j. and miller, g. f. 1971. the application of integral equation methods for numerical solution of exterior boundary value problems, proceedings of the royal society london, a232: 201-210. burton, a. j. 1973. the solution of helmholtz equation in exterior domains using integral equations, npl report nac30, national physical laboratory, middlesex, uk. burton, a. j. 1976. 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(english translation) kupradze, v. d. 1965. potential methods in the theory of elasticity, israel program for scientific translations, jerusalem. lamb, h. 1949. hydrodynamics, 6th ed., dover. leis, r. 1958. über das neumannssche randwertproblem für die helmholtzsche schwingungsgleichung, arch.rat. mech. & anal., 2: (english translation), 101-113. leis, r. 1962. über die rand wertantgaben des außenraumes zur helmholtzschen schwingungsgleichung, arch.rat. mech. & anal., 9: (english translation), 21-44. leis, r. 1965. zur dirichletschen randwertaufabe des außenraumes der schwingungsgleichung, math. zeit., 90: (english translation), 205-211. manolis, g. d. and bescos, d. e. 1981. dynamic stress concentration studies by boundary integrals and laplace transform, international journal for numerical methods in engineering, 17: 573-599. meyer, w. l., bell, w. a., zinn, b. t. and stallybrass, m. p. 1978. boundary integral solutions of three dimensional acoustic radiation problems, journal of sound and vibration, 59(2): 245-262. a comprehensive review of boundary integral 309 meyer, w. l., stallybrass, m. p. and zinn, b. t. 1979. prediction of the sound field radiated from axisymmetric surfaces, j. acoust. soc. am., 65(3): 631-638. müller, c. 1969. foundations of the mathematical theory of electromagnatic waves, springer-verlag. niwa, y., kobayashi, s. and fukui, t. 1976. applications of the integral equation method to some geomechanical problems, numerical methods in geomechanics, asce, usa, pp120-131. panich, i. o. 1965. on the question of solvability of the exterior boundary value problem for the wave equation and maxwell’s equation, uspekhi mat. nauk. 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f., soenarko, b., rizzo, f. j. and shippy, d. j. 1984. application of boundary integral equation method to sound radiation problem using an isoparametric element, asme trans. journal of vib. acoustic stress reliability des., 106: 413-420 seybert, a. f., soenarko, b., rizzo, f. j. and shippy, d. j. 1985. an advanced computational method for radiation and scattering of acoustic waves in three dimensions, j. acoust. soc. am., 77: 362-368. seybert, a. f., soenarko, b., rizzo, f. j. and shippy, d. j. 1986. a special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions, j. acoust. soc. am., 80(4): 1241-1247. seybert, a. f. and rangarajan, t. k. 1987. the use of chief to obtain unique solution for acoustic radiation problem, j. acoust. soc. am., 81(5): 1299-1306. shaw, r. p. and friedman, m. b. 1962. diffraction of a plane shock wave by a free cylindrical obstacle at a free surface, proceedings of the 4th us national congress of 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soc., 74: 117-125. ursell, f. 1978. on the exterior problem of acoustics ii, math. proc. camb. phil. soc., 84: 545-548. van buren, a. l. 1970. a test of the capabilities of chief in the numerical calculation of acoustic radiation from arbitrary surfaces, nrl report 7160. wait, r. 1973. finite-element-type solution of integral equations, ministry of defence research report, jan., dundee, uk. wilcox, c. h., 1956. a generalisation of theorems of rellich and atkinson, proc. amer. math. soc., 1: 271-276. wilton, d. t. 1974. a numerical approach to some problems in acoustic radiation, ministry of defence research report, apr., dundee, uk. zaman, s. i. 1994. integral equation formulations of exterior acoustic scattering problems, ph.d. thesis, city university, london, uk. zaman, s. i. 1996. a proof of kussmaul formulation of acoustic scattering valid for all wave-numbers, math. research memorandum no. 4/96, city university, london, uk. s. i. zaman zaman, s. i. 1997. an uniqueness argument for the kussmaul type formulation of acoustic scattering problem, proc. first uk conference on boundary integral methods, university of leeds, uk, pp134-142. received 31 january 2000 accepted 24 june 2000 310 s.i.zaman ãñçìúé ôçãáé ááãúçïáçê çáêßçãáí� contents introduction therefore he argued that �component of a general solution of (39) would make no contribution in the exterior. alternatively, we can utilise the non-trivial eigensolutions � to generate an exterior potential, for each j. using (40) � 3.2 panich by using layer potentials, panich (1965) initially proposed 3.3 copley thus avoiding the singularity problem. the idea was originally proposed by kupradze (1965). in operator form, (46) 3.4 schenck 3.5 kussmaul 3.6 burton and miller 3.7 ursell and jones 3.9 zaman acknowledgement microsoft word stat090428-f edited_corrected.doc squ journal for science, 15(2010) 87-100 © 2010 sultan qaboos university 87 filtering and m-ary detection of markov modulated mean reverting model lakhdar aggoun*, mohamed al-lawati* and w.p. malcolm** *department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, postal code 123, muscat, sultanate of oman, email: laggoun@squ.edu.om. **australian national university, canberra australia, email: malcolm@maths.anu.edu.au. نموذج مركوفي للفرق بين األسعار في سوق المال مالكولم. ب.و و األخضر عجون، محمد اللواتي هذا البحث يطور نموذج يحتوي على سلسلتان من نوع مرآوف تقوم بالتأثير على نموذج يقوم بدراسة حرآة للفرق :خالصة في سعار صيف أحداث غير معروفة لكن ذات تأثير على األ تقوم بتو السلسلتان من نوع مرآوف .ألسعار في سوق المال ابين .وتستعمل في هذا البحث طرق تغيير القياس لتقدير التوزيع الشرطي المتكرر. سوق المال abstract: in an earlier paper we developed a stochastic model incorporating a double-markov modulated mean-reversion model. the model is based on an explicit discretisation of the corresponding continuous time dynamics. here we discuss parameter estimation via the technique of m-ary detection. keywords: double-markov modulated mean-reversion model, filtering, m-ary detection, continuous-time dynamics. mathematics subject classification. 60g35, 62m05, 62m20, 91b30, 91b70. 1. introduction he model we developed in malcolm et al. (2004) is a stochastic model incorporating a double markov modulated mean reversion model. unlike a price process the basis process can take positive or negative values. this model is based on an explicit discretization of the corresponding continuous time dynamics. in that model we suppose the mean reverting level in our dynamics as well as the noise coefficient can change according to the states of some finite-state markov processes which could be the economy and some other unseen random phenomenon. in this paper we wish to discuss -ary detection for this model. the term -ary detection is used in electrical engineering to describe sequential hypothesis testing for more than two candidate model hypotheses. here we are interested in model-parameter hypotheses. in effect our formulation is something like a discrete and finite version of the em algorithm by baum and petrie (1966), dempster et al. (1977) where, rather than considering an uncountable collection of model parameter sets in the space of all admissible models, we consider a finite collection in this space. t lakhdar aggoun, mohamed al-lawati and w.p. malcolm 88 we assume that we have a list of candidate models, from which to choose, describing the model dynamics over time. these candidate models will be denoted by , . let be a simple random variable denoting a specific model, with states indexed by . we assume that is taking on values in the canonical basis of . we suppose is an indicator random variable such that , that is if and only if hypothesis holds. here is the usual inner product. we shall be interested in computing the posterior probabilities , where denotes information contained in some observation process. it will be shown that this problem separates into a pure filtering component and a pure estimation component. in the context of -ary detection, this is known as the separation theorem (poor 1988). this paper is organized as follows. in §2 & §3 we recall the model dynamics as well as the construction of a new probability measure under which all processes are independent. in §4 m-ary detection filters are derived. in §5 & §6 our results are adapted to continuous time dynamics. 2. stochastic dynamics all models are, initially, on the probability space ( )f pω, , . write { 0 }ux x u t= , ≤ ≤ , for the basis (price difference) process. tx r∈ . suppose l is a mean reversion level and rα +∈ is the rate-parameter, that is, a parameter determining how fast the level l is attained by the process x . x has dynamics: 0 0 ( ) t t u tx x l x du wα σ= + − + .∫ (2.1) here w is a standard wiener process, and rσ ∈ . remark 1. the dynamics at (2.1) exhibit a mean reversion1 character of the model when written in stochastic differential equation form: ( )t u tdx l x dt dwα σ= − + . (2.2) ignoring the noise tdwσ , if tx l> then ( ) 0tl xα − < , while if tx l< then ( ) 0tl xα − > , and so the right side of is continually trying to reach the level l. now suppose that parameters l and σ are stochastic and can switch between different levels 1 2 ml l … l, , , and 1 n…σ σ, , respectively. we assume here that these levels are determined by the states of two markov chains z and respectively. without loss of generality, we take the state spaces of our markov chains to be the canonical basis 1 2{ }ml e e … e= , , , of mr and the canonical basis 1 2{ }ns f f … f= , , , of nr respectively. 1 modeling a mean reversion process is widely used in finance, for example in interest rates models such as the vasicek model. this class of models assumes an (static) average value will be attained, not unlike the notion of an equilibrium state, or steady state of a dynamical system in the physical sciences. filtering and m-ary detection of markov 89 write (2.3) (2.4) write . then (2.5) here, and are martingale increments. the scalar-valued markov processes taking values 1 ml … l, , and 1 n…σ σ, , , are obtained by (2.6) here 1 2( )ml l … l ′= , , ,l , 1 2( )n…σ σ σ ′= , , ,s , 〈⋅,⋅〉 denotes an inner product and { }1 a denotes an indicator function for the event a . what also we wish to impose is that the two markov chains z and be not independent, that is, information on the behavior of one conveys some knowledge of the behavior of the other. more precisely, we assume the dynamics: (2.7) where js ir ⎛ ⎞ ⎜ ⎟,⎝ ⎠ =p p denotes a mn mn× matrix, or tensor, mapping into and again 1k +m is a martingale increment. the dynamics at (1) take the form (2.8) remark 2. we defined z and as inherently discrete-time. here, we "read" z and as the output of a sample and hold circuit, or cadlag processes. • what we wish to do now, is discretise the dynamics at (8) and then compute a corresponding filter and detector. lakhdar aggoun, mohamed al-lawati and w.p. malcolm 90 • we will use an euler-maruyama discretisation scheme to obtain discrete-time dynamics, although many other schemes can be used; see, for example, numerical solution of stochastic differential equations by kloeden and platen (1992). for all time discretisations we will consider a partition, on some given time interval [0 ]t, and write (2.9) this partition is strict, 0 1t t …< < , and regular, the 1t k kt t −∆ = − are identical for indices k . applying the euler-maruyama scheme to (8), we get, (2.10) here the gaussian process v is an independently and identically distributed (0 1)n , . our stochastic system now, under the measure p , has the form: (2.11) write 3. state estimation filters the approach we take to compute our filters is the so-called reference probability method. this technique is widely used in electrical engineering, see elliott et al. (1995) and more recently aggoun and elliott (2004). we define a probability measure †p on the measurable space ( )fω, , such that, under †p , the following two conditions hold. 1. the state processes z and are markov chains initial distributions 0p and 0p respectively. 2. the observation process x , is independently and identically distributed and is gaussian with zero mean and unit variance. with †p defined, we construct p , such that under p the following hold: filtering and m-ary detection of markov 91 3. the state processes z and are again markov chains with initial distributions 0p and 0p respectively. 4. the sequence v, where (3.1) is a sequence of independently and identically distributed gaussian (0 1)n , random variables. write . definition 1. for 1 2 …= , , , (3.2) (3.3) the "real world" probability p , is now defined in terms of the probability measure †p by setting † tg k dp dp | = λ . lemma 1. under p , the sequence v, is a sequence of independently and identically distributed (0 1)n , random variables, where . that is, under p , (3.4) lemma 2. under the measure p , the process z remains a markov process, with transition matrix π and initial distribution 0p . the proofs of lemma 1 and 2 are routine. remark 1. the objective in estimation via reference probability is to choose a measure †p which facilitates and/or simplifies calculations. in filtering and prediction, we wish to evaluate conditional expectations. under the measure †p , our dynamics have the form: (3.5) in what follows we shall use the following version of bayes' rule. lakhdar aggoun, mohamed al-lawati and w.p. malcolm 92 (3.6) note that the following result is proven in malcolm et al. (2008). theorem 1. information state recursion. suppose the markov chains z and are observed though the unitdelay discrete-time dynamics at (2.10). the information state for the corresponding filtering problem is computed by the recursion: (3.7) here , (3.8) and (3.9) the recursion given in theorem 1, provides a scheme to estimate the conditional probabilities for events of the form , given the information up to time k+1. in practice, one would use the vector-valued information state , to compute an estimate for the state . in general two approaches are adopted; one computes either a conditional mean, that is (3.10) or the so-called maximum-a-posteriori (map) estimate, that is (3.11) marginal distributions for the markov chains are obtained by multiplying on the right with the n -dimensional row vector (1 1)…, , or on the left with the m -dimensional column vector (1 1)…, , respectively. 4. m-ary detection filters filtering and m-ary detection of markov 93 to denote a specific model hypothesis for the discrete-time dynamics given at (2.5), (2.7) and (2.10) we write, (4.1) here . using the simple random variable , as before, we are interested to compute the detector expectation (4.2) here the sigma algebra is taken as generated by a model with parameter set , and similarly the radonnikodym derivative , is constructed according to . further, to make a clear distinction between the filter information state defined for specific model , and the corresponding un-normalised detector probability for model , we write, respectively theorem 2 (m-ary detection filter) the m-ary detection filter for the model hypothesis is computed by the recursion proof: lakhdar aggoun, mohamed al-lawati and w.p. malcolm 94 the expectation in the last line of the calculation is the normalized probabilities are computed by the normalized one step predictor information state, that is, for the model hypothesis and the event , we compute here is the information state for the filter computed earlier. since we need the normalised form of the expectation at (4.2), the -ary detector has the form: 5. continuous-time dynamics we consider here a continuous time markov chain . again we use the canonical representation of an arbitrary markov chain. that is, without loss of generality we take the state space for to be the set , whose elements are column vectors with unity in the position and zero elsewhere. the key benefit of this representation is that it admits the dynamics: filtering and m-ary detection of markov 95 here is a -martingale and is a time invariant rate matrix, whose elements are the infinitesimal intensities of . to denote an element of the matrix at row and column , we write . here denotes an inner product. now we consider the continuous-time dynamics (5.1) under the state and observation process dynamics have the form: let where is given by equation (5.1). then the ‘real world’ probability is defined via under the dynamics have the form: notation: suppose is any -adapted process and we wish to estimate . using bayes’ rule (elliott et al. 1995) 6. continuous-time detection schemes state estimation filters with lakhdar aggoun, mohamed al-lawati and w.p. malcolm 96 then . -ary detection filters the process z takes values on a canonical basis of matrix-valued indicator functions, each of which jointly indicates a particular model hypothesis, and a particular value taken by the state process. filtering and m-ary detection of markov 97 the corresponding normalized detection probabilities are computed, for example, by write (6.1) define the process , defined by equation ( 6.1) satisfies the dynamics the symbol in the previous equation denotes a point-wise matrix product, where for two matrices of the same dimensions, the point-wise product is lakhdar aggoun, mohamed al-lawati and w.p. malcolm 98 write recalling the numerator in bayes’ rule, we note that so, by computing the numerator in bayes’ rule, we can readily compute the normalizing denominator . the matrix quantity , defined at (6.1), is an un-normalized conditional expectation, so, the corresponding normalized conditional expectation is computed by to recover the normalized -ary detection probabilities from the quantity , one computes the corresponding normalized detection probabilities are computed, for example, by write (6.1) define the process , defined by equation ( 6.1) satisfies the dynamics filtering and m-ary detection of markov 99 the symbol in the previous equation denotes a point-wise matrix product, where for two matrices of the same dimensions, the point -ise product i write recalling the numerator in bayes’ rule, we note that so, by computing the numerator in bayes’ rule, we can readily compute the normalising denominator . the matrix quantity , defined at (6.1), is an un-normalized conditional expectation, so, the corresponding normalized conditional expectation is computed by to recover the normalized -ary detection probabilities from the quantity , one computes 6. references aggoun, l. and elliott, r.j. 2004 measure theory and filtering: introduction with applications. cambridge series in statistical and probabilistic mathematics. baum, l.e. and petrie, t. 1966 statistical inference for probabilistic functions of finite state markov chains. annals of the institute of statistical mathematics, 37: 1554-1563. lakhdar aggoun, mohamed al-lawati and w.p. malcolm 100 demp, a.p., laird, n.m. and rubin, d.b. 1977 maximum likelihood from incomplete data via the em algorithm. jour. of the royal statistical society b 39: 1-38. elliott, c., elliott, r.j. and malcolm, w.p. 2005 commodity prices and regime switching bases, conference on stochastic modelling of complex systems, daydream island, queensland australia 10-16 july. elliott, r.j., aggoun, l. and moore, j.b. 1995 hidden markov models: estimation and control. springer-verlag, new-york. applications of mathematics no. 29. elliott, r.j. 1982 stochastic calculus and applications. springer-verlag, new-york. applications of mathematics no. 18. elliott, r.j., fischer, p. and platen, e. 1999 filtering and parameter estimation for a mean-reverting interest rate model, canadian applied mathematics quarterly, 7: 381-400. elliott, r.j. and kopp, p.e. 2005 mathematics of financial markets, 2nd edition, springer-verlag. kloeden, p.e. and platen, e. 1992. numerical solution of stochastic differential equations springerverlag, new-york. applications of mathematics no. 23. malcolm, w.p., aggoun, l., and al-lawatia, m. 2008. on a markov modulated mean reverting finance model. journal of science and technology, sultan qaboos university. 13: 55-62 . poor, h. 1988. an introduction to signal detection and estimation, springer-verlag, new york. received 28 april 2009 accepted 8 december 2009 endocrine, physiological and histopathological responses of fish and their larvae to stress with emphasis on exposure to crude science and technology, special review (2000) 73-113 ©2000 sultan qaboos university 73 dirhodium(ii) carbenes : the chiral product cascade *gregory h. p. roos, **conrad e. raab and *said al-hatmi * chemistry department, college of science, sultan qaboos university, p.o. box 36, al-khod 123, muscat, sultanate of oman ** department of drug metabolism , merck and co., inc., ry80r -104, p. o. box 2000, rahway, new jersey 07065, usa. نسج الناتج الكايرالي) . ٢(كاربينات دايروديم راب ، وسعيد الحاتمي. روس ، و كونراد أ. جريجوري هـ أحد الطرق . شهدت العشر سنوات الماضية توسعاً كبيراً في طرق تحضير المركبات الكايرالية :خالصة استنباط طرق . ات الديازو المحضرة من مركب ) ٢(الهامة في هذا المجال هو استعمال كاربينات دايروديم جديدة باستعمال العوامل المساعدة الموجهة أدت إلى تحضير عدد من المركبات الغير راسمية عبر قنوات هذه . واإلضافة األروماتية الحلقية وخالفه c-xمختلفة مثل إضافة البروبان الحلقي واإلدخال من نوع دة التي تؤدي إلى تحضير مركبات عالية النقاء لمتماكب النبذة القصيرة تتعرض بإختصار للعوامل المساع .ضوئي abstract: the last decade has witnessed enormous growth in the spectrum of highly efficient asymmetric synthetic transformations. one prominent example of this progress is the application of dirhodium (ii) carbenes generated from diazo precursors. innovative construction of ‘designer’ catalysts has played a integral role in extending the breadth of the synthetic cascade of non-racemic products now available through the range of cyclopropanation, c-x insertion, aromatic cycloaddition-rearrangement, and ylide-based reaction types. this review deals briefly with an overview of the important catalytic systems and maintains as its primary focus the cascade of diverse optically enriched products that flow from their applications. roos, raab, and al-hatmi 74 contents 1. introduction 74 1.1 the need for asymmetric synthesis 74 1.2 carbene reactions 74 2. generation of dirhodium(ii) carbenes 75 2.1 diazo compounds 75 2.2 metal-catalysed diazo decomposition 76 2.3 dirhodium(ii) catalysts 76 3. reaction products from dirhodium(ii) carbenes 80 3.1 cyclopropanes and cyclopropenes 80 3.2 intermolecular processes 81 3.3 intramolecular processes 87 3.4 insertion products 92 3.4.1 carbon-hydrogen insettion products 94 3.4.2 heteroatom-hydrogen insertion products 100 3.5 aromatic cycloaddition and substitution products 101 3.6 ylide cascade products 104 4. conclusion 105 5. references 106 1. introduction 1.1 the need for asymmetric synthesis the world around us is chiral. most organic compounds are chiral. the chemistry of perfumes, nutrients, pesticides, and pharmaceuticals involves chiral compounds whose physiological or pharmacological properties depend upon their recognition by chiral receptors. public opinion and associated legislation surrounding the pharmaceutical industry demands, especially since the thalidomide disaster (figure 1), the preparation and testing of enantiopure compounds. this has, in part, caused asymmetric synthesis to become the single greatest “growth industry” within organic chemistry over the past 25 years. once the important factors that control reaction stereoselectivity were recognized, development has exploded throughout the arena of organic synthesis (ager and east, 1996; gawley and aubé, 1996; seyden-penne, 1995). of the handful of approaches to asymmetric synthesis, catalysis has the advantage over stoichiometric synthesis with chirons (enantiomerically pure substrate fragments) or chiral auxiliaries (temporary enantiomerically pure attachments), particularly in terms of large-scale or industrial processes. catalytic asymmetric reactions have been the subject of research investigations for many years and, particularly over the last decade, the number of catalytic asymmetric processes (some giving enantioselectivities of greater than 99%) has burgeoned (brünner and zettlmeier, 1993; jacobsen et al, 1999). whilst broad scope and high enantioselectivity are important for any catalytic asymmetric transformation, they alone are not necessarily sufficient to ensure that a process will become widely used, especially on industrial scale. to reach this goal, the process additionally needs to be economical and easy to perform. for this reason, many of the new wave of catalysts are either already commercially available, or are designed for easy or in situ preparation. 1.2 carbene reactions the general group of transformations referred to as “carbene reactions” forms a versatile class of transition metal catalysed processes. these reactions are characterised by the involvement of a transition dirhodium(ii) carbenes: the chiral product cascade metal stabilized carbene that is formed from the decomposition of a diazo compound in the presence of the transition metal catalyst. further reaction of the carbene may follow a number of pathways including insertion and addition reactions, as well as ylide generation. recent investigations have focussed on the development of catalysts that control the selectivity of what had traditionally been thought of as nonselective reactions of “free carbenes”. of these, dirhodium catalysts have emerged as arguably the most versatile for a wide range of stereoselective transformations (doyle et al, 1993a, 1994a, 1996a, 1997a, 1998a, 1998b, 1998c, 1999; ene and doyle, 1998; ye and mckervey, 1994; roos and raab, 1997). given the rapid growth within this area of endeavor, this review seeks to place these developments in context via the published literature through mid-1999. the specific focus is on homochiral catalysts and therefore excludes chiron-based syntheses, and only pertinent examples of diastereoselectivty via chiral auxiliaries are covered. previous reviews have tended to focus on details of catalyst development or of subsequent reaction type that the carbene undergoes. outside of essential introductory material, this review seeks primarily to highlight the wealth of diverse enantiomerically enriched chiral products that are available via the numerous highly chemoselective, regioselective, and stereoselective transformations brought about by dirhodium(ii) catalyst systems. some of these have a high potential for commercial adaptation. readers seeking further details on access to diazo compounds, catalyst design and preparation, as well as mechanistic aspects are referred to the alternative specialist reviews cited throughout. 75 n n o o oo h n n o o oo h (r)-thalidomide sedative (s)-thalidomide teratogenic figure 1. thalidomide enantiomers 2. generation of dirhodium(ii) carbenes 2.1 diazo compounds diazo compounds are derivatives of diazomethane, and as such have stabilities and reactivities that reflect their substituents. generally, the stabilities of diazo compounds towards diazo decomposition are increased by electron withdrawing substituents, and decreased by electron donating substituents (figure 2). for this reason, the most widely employed diazo compounds for metal catalysed reactions are diazocarbonyl compounds. numerous synthetic methodologies are now available for the synthesis of diazo compounds and these have been reviewed by regitz and maas (1986) and doyle et al (1998a). roos, raab, and al-hatmi 2.2 metal-catalysed diazo decomposition since diazo decomposition is an acid promoted process, transition metal complexes that are effective catalysts for diazo decomposition are of necessity lewis acids (doyle, 1986). their catalytic activity depends on the metal centre being coordinatively unsaturated, which allows them to react as electrophiles with diazo compounds. z y o n2 o z o n2 r r n2 r increasing stability increasing reactivity z, y = r, or, nr2 r = alkyl, aryl, h figure 2. relative stability/reactivity of diazo substrates in the generally accepted mechanism for catalytic diazo decomposition, electrophilic addition of the catalyst to the diazo compound causes the loss of dinitrogen from a diazonium ion adduct 1 to produce a metal-stabilized carbene 2 (scheme 1). the electrophilic carbene is transferred to an electron-rich substrate (s:) to form the product of the carbene reaction (scr2), with release of the transition metal catalyst to complete the catalytic cycle. 2.3 dirhodium(ii) catalysts a wide range of other metals such as copper, cobalt, palladium, ruthenium, osmium, iron, nickel, and zinc have been employed with varying success in catalytic systems (roos and raab, 1997; doyle et al, 1998a). rhodium, and more specifically dirhodium(ii) complexes have proven to be the most effective and versatile catalysts for diazo decomposition (maas, 1987; padwa and krumpe, 1992; davies, 1993a; padwa and austin, 1994; ye and mckervey, 1994; doyle, 1995a). generally, rhodium-mediated carbene reactions proceed under much milder conditions than is common for classical synthetic methodology with copper(ii) catalysts (padwa and austin, 1994). 76 lnm lnm cr2 n2 lnm cr2 scr2 n2 r2c n2 2 1 s: scheme 1. cycle for transition-metal catalyzed diazo decomposition dirhodium(ii) carbenes: the chiral product cascade their versatility arises from the large variety of bridging ligands that can be coordinated to the dirhodium(ii) skeleton, and in their marked influence on reactivity and selectivity. dirhodium(ii) catalyst complexes are divided into two major groups, those bridged with carboxylate ligands and those bridged with carboxamidate ligands. it is through the tuning of these ligands that particular catalysts are able to provide appropriate chemical properties as well as specific reactivity and selectivity profiles for desired transformations. the dirhodium(ii) catalysts are based on the parent dirhodium(ii) tetraacetate, rh2(oac)4 3, first introduced by paulissenen et al (1973). since that time, this has been the single most widely used catalyst for metal carbene transformations. rh2(oac)4 3 possesses four bridging acetate ligands and has d4h symmetry, leaving one vacant axial coordination site on each metal for carbene attachment (boyar and robinson, 1983). a multitude of dirhodium(ii) catalysts is available by replacement of the acetate ligands with other carboxylate or carboxamidate ligands. many of these catalysts have unique properties or synthetic uses (doyle et al, 1998a, 1998b). 77 rh2(acam)4 5rh2(pfb)4 4rh2(oac)4 3 o rh rh ch3 oo o o ch3 o o o ch3 ch3 o rh rh ch3 on o n ch3 n n o ch3 ch3 h hh h o rh rh c3f7 oo o o c3f7 o o o f7c3 c3f7 rh rh o o r3 r2 r1 6 rh rh o o n s o o h z 7 8 rh rh o o nh r o o r = phch2, tbuz = h, no2, ome, me tbu [rh2(tbsp)4], nc12h25 [rh2(dosp)4] dirhodium(ii) perfluorobutyrate, rh2(pfb)4 4, is the most reactive dirhodium(ii) catalyst, and its selectivity in diazo decomposition reactions is often correspondingly poor (doyle et al, 1993b). in contrast, dirhodium(ii) carboxamidates such as rh2(acam)4 5, which have two nitrogen and two oxygen donor atoms at each rhodium, with the two nitrogens arranged cis to each other (a [2,2-cis] configuration) roos, raab, and al-hatmi (ahsan et al, 1986) are less reactive than the dirhodium(ii) carboxylates in diazo decomposition, but are often more selective in the subsequent carbene reactions (doyle et al, 1989a,b; doyle et al, 1991a). homochiral dirhodium(ii) carboxylate catalysts 6 for asymmetric carbene reactions were simultaneously developed in three laboratories (brunner et al, 1989; kennedy et al, 1990; hashimoto et al, 1990; roos and mckervey, 1992) from enantiomerically pure carboxylic acids. more recent refinements have demonstrated highly successful prolinate 7 (mckervey and ye, 1992; davies et al, 1993b, 1996; doyle et al, 1996b) and phthalimide 8 derivatives (hashimoto et al, 1994; watanabe et al, 1995, 1996a). a recent report (buck et al, 1998) has employed parallel array techniques to screen rapidly for novel carboxylate catalysts. in contrast to the dirhodium(ii) carboxylates, the rhodium(ii) carboxamidates allow placement of an inducing chiral centre adjacent to nitrogen in closer proximity to the axial carbene centre. a series of more than twenty structurally varied homochiral dirhodium(ii) carboxamidates derived from chiral cyclic amide ligands has been developed by doyle and co-workers (doyle, 1994b, 1996a). in general, dirhodium(ii) carboxamidate catalysts based on chiral 2-oxopyrrolidine 9 (doyle et al, 1993c, 1994c) 2oxazolidinone 10 (doyle et al, 1993d, 1995b), n-acylimidazolidinone 11 (doyle, 1995c, 1996c, 1997b; roos et al, 1998), and 2-azetidinone 12 (doyle et al, 1996d) ligands, especially those bearing pendant carboxylate groups, afford the highest levels of enantioselectivity. dirhodium(ii) complexes 13 bearing chiral phosphate ligands derived from binaphthol have been reported to provide moderate enantioselectivities in a number of carbene reactions (mccarthy et al, 1992; pirrung and zhang, 1992). in addition, estevan et al (1995) prepared a novel set of c2-symmetric catalysts 14 bearing two cis carboxylate ligands along with two orthometallated phosphine ligands. x h z coorh z z coorh zh roocch n2 + rh2l4 x h z x roocch2x ylide generation insertion cyclopropanation cyclopropenation z x = sulphides, amines, halides, ethers = c-h, n-h, o-h, si-h, s-h z = alkyl, aryl, vinyl, or' z = alkyl, vinyl z x chcoor co2r aromatic cycloaddition scheme 2. diversity of metal carbene reactions 78 dirhodium(ii) carbenes: the chiral product cascade 9 a a = co2ch2ph; rh2(4s-bnaz)4 b a = co2ch2chme2; rh2(4s-ibaz)4 o rh rh on o n n n o a h a a = co2me, r = ch3; rh2(4s-macim)4 b a = co2me, r = ph; rh2(4s-mboim)4 c a = co2me, r = phch2; rh2(4s-mpaim)4 d a = co2me, r = phch2ch2; rh2(4s-mppim)4 e a = co2me, r = c-c6h11ch2; rh2(4s-mchim)4 o rh rh on o n n n o n a h o r a a = co2me, r = h; rh2(4s-meox)4 b a = co2me, r = ch3; rh2(4s-threox)4 c a = ch2ph, r = h; rh2(4r-bnox)4 d a = ipr, r = h; rh2(4r-ipox)4 e a = ph, r = h; rh2(4r-phox)4 a a = co2me; rh2(5s-mepy)4 b a = co2ch2cme3; rh2(5s-nepy)4 c a = co2(ch2)17me; rh2(5s-odpy)4 d a = conme2; rh2(5s-dmap)4 10 o rh rh on o n n n o a h o rh rh on o n n n o o a h h r 11 12 p rhrh o parc o o o r1 r2 x 14 x = h, f, ch 3, cf3 o o p oo rh rh 13 a. rh2(s-bnhp)2(hco3)2 b. rh2(r-bnhp)4 79 roos, raab, and al-hatmi 80 -r* -r* r*o o n2 mln x r*o o x * (a) ro o n2 mln* x ro o x * (b) r*o o n2 mln* x r*o o x * (c) scheme 3. approaches to asymmetric synthesis with metal carbene 3. reaction products from dirhodium(ii) carbenes the metal-carbenes resulting from the diazo decomposition of α-diazocarbonyl compounds by a transition metal catalyst, are versatile electrophilic reagents. dirhodium(ii) catalysed diazo decompositions provide the greatest versatility in subsequent carbene reactions, and provide many synthetically useful transformations. this includes interand intramolecular reactions as diverse as cyclopropanation, cyclopropenation, insertion, aromatic cycloaddition, and ylide generation (scheme 2). as a result, the range of stereoselectively generated product types is large. researchers in this area have tested a variety of fundamental approaches to the asymmetric production of chiral compounds via dirhodium(ii)-catalysed reactions (scheme 3). thus, (a) diastereoselective reaction of achiral catalysts with diazo substrates containing chiral auxiliaries, (b) enantioselective reaction between chiral catalysts and achiral substrates, and in a few instances (c) a double diastereoselective approach with both chiral catalyst and substrate have been used. for the purpose of orderly classification, the range of product molecules has been grouped according to the reaction type via which they are generated. 3.1 cyclopropanes and cyclopropenes due to their biological significance and synthetic utility, cyclopropanes and cyclopropenes are extremely important target molecules (rappoport, 1987; binger and büch, 1987; baird, 1988; salaün, 1989). they are often present as structural sub-units in natural and non-natural products (rappoport, 1987; burke and grieco, 1979; hudlicky et al, 1985; ho, 1988; burgess and ho, 1994), are frequently used as mechanistic probes to elucidate reaction pathways (suckling, 1988; silverman et al, 1993; newcomb and chestney, 1994; caldwell and zhou, 1994; husbands et al, 1994), and are increasingly valuable as synthetic intermediates (wong et al, 1989; davies, 1991; reissig, 1995). dirhodium(ii) carbenes: the chiral product cascade cistrans + rh2l4 + z coorz coor n2chcoor z (1) since the availability of enantiomerically pure cyclopropanes is critical to many applications, a number of useful methods for their enantioselective synthesis have been developed. these include the cyclopropanation of chiral bicyclic lactams to give optically pure diand trisubstituted cyclopropanes; highly diastereoselective simmons-smith cyclopropanation of chiral auxiliary-derivatised allylic ethers; enantioselective simmons-smith cyclopropanation of allylic alcohols using diethylzinc that is coordinated with chiral ligands; and enzymatic resolutions of meso-cyclopropanes. in the field of asymmetric synthesis, cyclopropanation of electron-rich olefins by catalytic diazo decomposition of α-diazocarbonyl compounds with chiral catalysts equation 1, particularly copper and rhodium, has become an attractive and important route to optically active cyclopropanes (maas, 1987; doyle, 1993a, 1998a, 1998d; ye and mckervey, 1994, singh et al, 1997). cyclopropanation may either be performed intermolecularly or intramolecularly. a successful example of the former is the commercial synthesis (by the “sumitomo process”) of optically pure cilastatin 15, an in vivo stabiliser of the antibiotic imipenem (doyle, 1995a). generally it has been found that copper-based systems are the better catalysts for intermolecular cyclopropanation with traditional diazoacetates, whilst dirhodium catalysts provide the better results in intramolecular variants (roos and raab, 1997; doyle et al, 1998a). 81 s cooh nh2 hooc nh o h3c h3c 15 1716 o n o chn2 o o n ph ch3 o chn2 o 3.2 intermolecular processes initial attempts at asymmetric intermolecular cyclopropanations by means of chiral auxiliaries bonded to diazoacetates were largely unsuccessful (equation 1, z = chiral auxiliary). chiral n(diazoacetyl)oxazolidinones 16 and 17 underwent rh2(oac)4 catalysed cyclopropanation of styrene in roos, raab, and al-hatmi good yield but with low diastereoselectivity (doyle et al, 1990). high diastereoselectivities in the catalytic cyclopropanation of diazo compounds bearing chiral auxiliaries have only been achieved in select cases (davies et al, 1993c; doyle et al, 1993e). these reports now include diastereomeric excesses of up to 97% in the dirhodium(ii) octanoate catalysed cyclopropanation of styrenes and vinyl ethers with (r)pantolactoneand (s)-lactate-substituted vinyldiazomethane 18 with (table 1) (davies et al, 1993c, 1997a) these workers (davies et al, 1998a) have shown that appropriate choice of vinyldiazo substituent allows facile subsequent transformation of the cyclopropyl products to 2,3-dihydrofurans with high asymmetric induction. table 1. diastereoselective intermolecular cyclopropanation with vinyldiazoacetates containing chiral auxiliaries. r + ph n2 co2x rh2(ooct)4 ch2cl2 42-92% co2x r ph 18 a x = o o b x = co2et ch3 19 r diazo de, % abs. config. ph ph pclc6h4 pmeoc6h4 aco eto ph 18a 18a 18a 18a 18a 18a 18b 89 97 >95 >95 90 92 67 (1r,2r) (1r,2r) (1r,2r) (1r,2r) (1s,2s) this methodology has been extended to diene systems, furans (davies et al, 1996b) to give 8oxabicyclo[3.2.1]octan-3-ones and pyrroles (davies et al, 1997b) to give tropanes (scheme 4).the fundamental reaction sequence has allowed the preparation of the oxabicycles 20-22 and a series of 2βacyl-3β-aryltropanes 23 (davies et al, 1994a, 1996c), which are important building blocks in further synthesis. 82 dirhodium(ii) carbenes: the chiral product cascade x = chiral auxiliary o r3 r2 + n2 co2x otbs r1 rh2(ooct)4 r3 co2x otbs r1 r2 o 75-95% de n r1 boc + n2 co2x r2 rh2(ooct)4 co2x r2 r1 n boc 53-80% de o me o h o me o h me co2me h o h o 20 21 22 coet r1 n r x 23 scheme 4. diastereoselective synthesis of oxabicyclooctanones and tropanes enantioselective approaches have surveyed two distinct types of homochiral dirhodium(ii) carboxylates. brünner et al (1989) used carboxylate ligands of the type r1r2r3ccoo, as in catalysts 6 (substituents varied from h, me, and ph; to oh, nhac, and cf3) and kennedy et al (1990) persued the chiral prolinate derivatives 7 (z = h). they found that enantioselectivities in the cyclopropanation of styrene with ethyl diazoacetate were less than 12% ee and 30% ee respectively. more recently, davies et al (1993b, 1996b, 1997) have used modified prolinate catalysts with vinyldiazoacetates to achieve enantioselectivities of ≥90%, with correspondingly high diastereoselectivities (table 2). it has further been shown that with suitably fuctionalised vinyldiazoacetates, the cyclopropyl products can afford cyclopentenes with high stereoselectivity (davies et al, 1998b). a recent catalyst, based on an axially 83 roos, raab, and al-hatmi table 2. dirhodium(ii) prolinate catalyzed intermolecular cyclopropanation with vinyldiazoacetates r + ph n2 co2me catalyst pentane 40-90% co2me r ph r ee, % with rh2(tbsp)4 ee, % with rh2(dosp)4 ph pclc6h4 pmeoc6h4 aco eto nbu et ipr 90 89 83 76 59 >90 >95 95 98 >97 90 95 93 dissymmetric biphenyl, does as yet not appear to offer any significant advantages over existing examples (ishitani and achiwa, 1997). 84 co2me ph ph co2me ph co2h co2me ph nh2.hcl co2me ph co2me co2h ph co2me nh2.hcl ph co2me 72% 43% 94% 78% 66% a d b c d a: rucl3/naio4 b: k2co3, me2so4 c: lioh, meoh d: net3, dppa, tbuoh; [(ch3)3coco]2o; naoh/h2o/thf; hcl/etoac scheme 5. stereoselective synthesis of cyclopropaneamino acids dirhodium(ii) carbenes: the chiral product cascade 85 ph + ph n2 co2me rh2l4* 7 (z = c12h25) 79% co2me ph ph h 94% ee co2me co2meph h h nhch3 h cl cl sertraline scheme 6. enantioselective synthesis of the antidepressant sertraline the vinyl functionality that exists in the cyclopropane offers a number of opportunities for further transformations. one generally useful application is for the stereoselective synthesis of cyclopropaneamino acids (scheme 5) (davies et al, 1993b, 1996b). this approach has been utilised in a recent synthesis of the antidepressant sertraline (scheme 6) (corey and grant, 1994). (2) ewg r3 r4 r5 r2 x r6 r1r3 x r2 r1 ewg r4 r6r5 ewg = electron-withdrawing group r1 r6 r5 r4 r3 r2 + ewg n2 x the extension of asymmetric vinylcarbenoid cyclopropanation to dienes affords a good general entry into seven-membered rings equation 2 (davies et al, 1994b). the stereoselectivity that occurs results in a strong preference for the formation of cis-divinylcyclopropanes, and the subsequent cope rearrangement follows with a predictable stereochemical outcome. roos, raab, and al-hatmi 86 me me co2me n2 ph me co2me ph me co2me ph 90% ee [rh2(s-tbsp)4] 96% ee [rh2(s-dosp)4] 90% ee [rh2(s-tbsp)4] 98% ee [rh2(s-dosp)4] scheme 7. enantioselective cycloheptatriene synthesis this methodology, which represents a formal [3 + 4]-cycloaddition, has been well exploited by davies et al (1994b) (scheme 7) (table 3). table 3. enantioselective synthesis of bicyclo[3.2.1]octadienes co2me n2 r2 r1 + catalyst 66-98% co2me r2 r1 r1 r2 ee % with rh2(s-tbsp)4 ee % with rh2(s-dosp)4 ph me ch=ch2 h co2et h h h h h h h me otbs 75 83 91 63 10 64 42 93 92 93 although the dirhodium(ii) carboxamidate catalysts 9-12 are able to provide substituted cyclopropanes with reasonable levels of enantioselectivity, they suffer the drawback of poor dirhodium(ii) carbenes: the chiral product cascade diastereoselective when diazoacetates are employed, with mixtures of transand cis-adducts being formed (table 4) (doyle et al, 1993d; müller et al, 1995; watanabe et al, 1996b). diastereoselectivity can only be effectively induced when sterically demanding diazo esters can be employed. the most noteworthy recent examples have been reported with the catalysts rh2(4s-ibaz)4 12b (doyle et al, 1996d) and rh2(s-ptpi)4 (kitagaki et al, 1997) where enantioselectivities of up to 95% have been achieved in selected systems. the situation has been somewhat improved by the discovery that methyl phenyldiazoacetate 24 is an excellent substrate for intermolecular cyclopropanation (table 5) (davies et al, 1996d; doyle et al, 1996b). homochiral dirhodium(ii) carboxamidates, in particular 9a, have proven to be exceptional catalysts for highly enantioselective intermolecular cyclopropenation (table 6) (doyle et al, 1994d). since the cyclopropene products can be quantitatively reduced to cis-cyclopropanes, this provides an alternative route to these products in high enantiomeric purity. table 4. dirhodium(ii) carboxamidate catalyzed intermolecular cyclopropanation n 87 cph tr ci 2chco2r rh2l*4 9-12 ph h co2r h h ph o2r h ans s + r catalyst trans yield % (de %) cis yield % (de %) d-menthyl et l-menthyl et d-menthyl et cyc-(c6h11)2ch et et rh2(5s-mepy)4 rh2(5s-mepy)4 rh2(4s-phox)4 rh2(4s-phox)4 rh2(4r-bnox)4 rh2(4r-bnox)4 rh2(4s-ibaz)4 rh2(4s-ibaz)4 rh2(4s-macim)4 57 (31) 56 (58) 27 (40) 34 (24) 67 (34) 46 (8) 34 (77) 36 (47) 43 (30) 43 (88) 44 (33) 73 (72) 66 (57) 33 (62) 54 (13) 66 (95) 64 (73) 57 (37) 3.3 intramolecular processes because of geometric constraints, intramolecular cyclopropanations of unsaturated diazocarbonyl compounds can produce only one fused bicyclic cyclopropane (the cis isomer). tanimori et al (1997) have reported a chiral auxiliary approach to intramolecular cyclopropanation of a diazoacetate in their synthetic route to the carbocyclic moiety of the anti-hiv agent carbovir equation 3. this is, however, a rare diastereoselective approach, since the dirhodium(ii) carboxamidate catalysts 9-12 have proven to be roos, raab, and al-hatmi most efficient and selective for reactions of diazoacetates and diazoacetamides (doyle et al, 1995c, 1997c, 1998d). table 5. enantioselective intermolecular cyclopropanation with phenyldiazoacetate r ph cat r phr1 2 + n2 co2me alyst 1 r2 co2me 24 r1 r2 catalyst ee of z, % ph pclc6h4 pmepc6h4 eto nbuo nbu ph ph h h h h h h ph me rh2(s-tbsp)4 rh2(s-tbsp)4 rh2(s-tbsp)4 rh2(s-dosp)4 rh2(s-dosp)4 rh2(s-dosp)4 rh2(s-tbsp)4 rh2(s-tbsp)4 87 85 88 66 64 77 97 85(e), 81(z) table 6. enantioselective intermolecular cyclopropenation coxh r ch2cl2 rh2l4*, 9an2chcox+r r x yield % ee % ch(oet)2 ch2ome ch2ome tbu ch2ome tbu ome otbu oet oet nme2 nme2 42 52 73 85 22 47 ≥ 98 78 69 57 ≥ 94 89 88 dirhodium(ii) carbenes: the chiral product cascade (3) o co2r* n2 rh2(oac)4 ho n n n n oh nh2 co2r* o major isomer (de 72%) carbovirr* = ( r)-pantolactone ( )n (4) 26: n = 1,2 z = o, n-tbu 25: n = 1,2 z = o, n-tbu rh2l4*, (s)or (r)-9a ch2cl2 z o r1 r2 n( ) z o chn2 r1 r2 excellent enantioselectivities have been reported in a series of allylic diazoacetates 25 (n = 1, z = o) catalysed by rh2(5s-mepy)4 (s-9a), and rh2(5r-mepy)4 (r-9a) to give fused cyclopropyl lactones 26 (n = 1, z = o) equation 4 (doyle et al, 1991b, 1995c, 1996e). cyclopropanation of homoallylic diazoesters 25 (n = 2, z = o) (martin et al, 1992a) and n-tert-butyldiazoacetamides 25 (n = 2, z = n-tbu) equation 4 (doyle et al, 1994e) proceeded with moderate to high enantioselectivities with the same catalysts. it has further been shown that enantioselectivities obtained in the catalysed cyclopropanation of allylic diazoacetates 27a-g to give the cyclopropyl γ-lactones 28a-g, were largely dependant on the position of vinylic substitution (table 7) (doyle et al, 1995c). as is shown in table 7, careful selection of the catalyst becomes necessary in order to optimise the enantioselectivity (doyle et al, 1995d, 1997c). application of the enantiomeric catalysts to the cyclopropanation of these allylic diazoacetates provide the cyclopropyl lactone products with the same enantiomeric excesses, but with the opposite absolute configurations. a recent contribution to the area by martin and hillier (1998) has investigated the complimentarity of chiral diazoacetates and chiral catalysts in a form of double diastereodifferentioncyclopropanation. several pharmacologically important molecules have been synthesized through the use of the above methodology, using either of the enantiomeric catalysts 9a. as outlined in scheme 8, martin et al (1992b, 1993) synthesized trisubstituted cyclopropanes as conformationally restricted peptide isosteres for renin 29 and collagenase inhibitors, and rogers et al (1995) have synthesizes presqualene alcohol 30. in addition, the products of these cyclopropanation reactions may serve as synthetic precursors to cischrysanthemic acid (mukaiyama et al, 1983) and the pheromone r-(-)-dictyopterene c (schotten et al, 1986). with homoallylic diazoacetates 31 (n = 2, r4 = h) (martin et al, 1992a; doyle et al, 1995c) and allylic diazopropionates 31 (n = 1, r4 = me) (doyle and zhou, 1995e), there is a moderate reduction in the enantioselectivity with a similar selection of dirhodium catalysts (table 8). 89 roos, raab, and al-hatmi table 7. enantioselective intramolecular cyclopropanation of allylic diazoacetates r rh r o h 90 o ch o refluxch2cl2 2 r1 n2 3 27a-g 28a-g o r2 r3 r1 2l4* 27 r1 r2 r3 catalyst yield % (ee %) config. a b c c d e e f f g h me h h h ph ph pr pr h h me h h ph h h h h ipr h h me me h h h h h h 9a 9a 9a 11d 9a 9a 11d 9a 11d 9a 75 (95) 89 (98) 72 (7) 75 (89) 70 (≥94) 78 (68) 61 (96) 93 (85) 83 (95) 85 (≥94) (1r,5s) (1s,5r) (1r,5s) (1s,5r) (1r,5s) (1r,5s) (1r,5s) (1r,5s) (1r,5s) (1r,5s) analogous intramolecular cyclopropanation of n-allyl diazoacetamides 32 (n = 1) (doyle et al, 1995c, 1996f) and n-tert-butyl-n-homoallylic diazoacetamides 32 (n = 2) (doyle et al, 1994e) to give the cyclopropyl lactams have progressively been refined to high yielding, highly enantioselective processes (table 9). o n2 o me h o me o h h h o me h h ho (5) rh2l4* 7 (z = c12h25) 93% ee heat although diazoacetates and diazoacetamides generally undergo dirhodium(ii)-catalysed intramolecular cyclopropanation with high enantiocontrol, the same is not true for diazoketones. here the best results were obtained from copper-based catalysts (doyle et al, 1997d). the davies group has demonstrated the applicability of their formal [3 + 4]-cycloaddition in an intramolecular example as part of a synthesis of 5-epitremulenolide equation 5 (davies and doan, 1996e). dirhodium(ii) carbenes: the chiral product cascade outside of two very recent preliminary reports from the doyle group (doyle et al, 1999b, 1999c), no widespread success with intramolecular cyclopropenation has been developed. these reactions often produce unstable fused cyclopropenes that undergo ring opening to vinylcarbenes that can react by a number of pathways, often giving rise to multiple products (padwa et al, 1991, 1993). n2ch o o r2 r1 n2ch o o rh2(5s-mepy)4 9a o o h h r1 r2 >94% ee>94% ee o o h h me o n o h r1 r2 o n h o h n oh oh sn hme oh h 29 renin inhibitor 30 presqualene alcohol scheme 8. applications of enantioselective intramolecular cyclopropanation 91 roos, raab, and al-hatmi table 8. enantioselective intramolecular cyclopropanation of homoallylic diazoacetates and allylic diazopropionates r 92 rr rh2l4* o o 2 3 r4 r1 31 o o r4 n2 r1 r2 3 ( )n ( )n ch2cl2 n r1 r2 r3 r4 cat. yield % (ee %) 2 2 2 2 2 2 1 1 1 h me h ph h h me h h h me ph h et h me npr ph h h h h h me h h h h h h h h h me me me 9a 9a 9a 9a 9a 9a 10a 10a 10a 80 (71) 74 (77) 73 (88) 55 (73) 80 (90) 76 (83) 81 (71) 62 (85) 65 (78) 3.4 insertion products catalytically generated metal carbenes have been shown to be capable of highly versatile insertion into carbon-hydrogen and heteroatom-hydrogen bonds equation 6. x h lnm cr2 r2c h x + + mln (6) although generally indiscriminate, the advent of dirhodium(ii) catalysts provided the required element of control to make these highly attractive c-c bond-forming processes (maas, 1987; doyle, 1986, 1995a; ye and mckervey, 1994; nefedov et al, 1992; padwa and krumpe, 1992). although the dirhodium(ii) carbenes: the chiral product cascade mechanism of the transition metal catalysed c-h insertion reactions has been the subject of considerable speculation (taber, 1991; doyle, 1992), there is general agreement that insertion occurs through a metal carbene intermediate. doyle and co-workers have suggested the mechanism depicted below as a suitable model for the c-h insertion process (scheme 9) (doyle et al, 1993b). table 9. enantioselective intramolecular cyclopropanation of n-allyl and n-homoallylic diazoacetamides r rr r rh2l4* n r4 o 2 3 1 32 n r4 o n2 1 r2 r3 ( )n ( )n ch2cl2 n r1 r2 r3 r4 cat. yield % (ee %) 1 1 1 1 1 2 2 2 2 2 h me h pr h h me h et h h me pr h h h me et h h h h h h me h h h h me h me me me me tbu tbu tbu tbu tbu 10a 10a 11d 11d 11d 9a 9a 9a 9a 9a 40 (98) 91 (94) 88 (95) 93 (92) 84 (44) 60 (60) 75 (75) 94 (90) 62 (67) 87 (78) 93 c hb c hb a h a d rh2l4 h e + a c rh2l4 h e d cb h ed scheme 9. proposed mechanism of c-h insertion roos, raab, and al-hatmi 3.4.1 carbon-hydrogen insertion products although examples of dirhodium(ii) catalysed intermolecular c-h insertion reactions are known, they generally lead to multiple products and require highly electrophilic catalysts in order to minimise competitive reactions such as formal carbene dimer formation. the yields and regioselectivities of these reactions are highly dependant on the catalyst employed (demonceau et al, 1981, 1984). 94 34 n2 oo or* oh 33 r* = rh2(oac)4 o co2r* meo o scheme 10. diastereoselective route to (+)-estrone methyl ether intramolecular c-h insertion reactions of diazocarbonyl compounds are more effective and selective, and they have become synthetically relevant, with the dirhodium(ii) carboxylates and carboxamidates 7-12 as the catalysts of choice (doyle 1994a, watanabe et al, 1995; doyle and mckervey, 1997a, anada and hashimoto, 1998a). two diastereoselective approaches are worthy of note. both groups have used 1-naphthylborneol 33 esters as the chiral auxiliary for asymmetric induction in ch insertion reactions (taber et al, 1987, 1998; wee and liu, 1996). taber and co-workers achieved diastereoselectivities of 83:17-92:8, which corresponds to enantiomeric excesses for the hydrolysed ester of 66 to 84%. this procedure was extended to a synthesis of (+)-estrone methyl ether 34 (scheme 10). wee and liu (1996) used this auxiliary in the c-h insertion reactions of diazomalonamides equation 7. enantioselective adaptations have been a more recent development. the mckervey group (mckervey an ye, 1992; kennedy et al, 1990; doyle and mckervey, 1997a) and others (hashimoto et al, 1990, 1994; anada and hashimoto, 1998a, 1998b) have utilised dirhodium(ii) carboxylates derived from n-protected amino acids (catalysts 7 and 8 respectively) to catalyse the enantioselective c-h insertion of diazoketone derivatives. enantioselectivities in the c-h insertion reactions of α-diazo-β-ketosulphones catalysed by 7 (z = h) were low (~12% ee), although yields were high kennedy et al, 1990). with a series of methyl diazo ketones 35, the same catalyst yielded the corresponding chromanones with enantioselectivities (for the major cis isomers) of 62-82% ee equation 8 (mckervey an ye, 1992). taber and co-workers have very recently published a preliminary report on the preparation of a new type of chiral catalyst 36 (enantiomeric m and p) that has backbone chirality. whilst this design strategy may dirhodium(ii) carbenes: the chiral product cascade have potential, the initial intramolecular c-h insertions with a diazoketone only afforded an enantioselectivity of 36% (taber et al, 1999). 95 r r*o o n2 o n pmp pmp = pmeoc6h4 r* = 33 n rr*o2c o pmp rh2(oac)4 n r o pmp r = nhex 45% ee (r) r = chex 98% ee (s) r = ph 79% ee (s) (7) r = ch3, ph, ch=ch2 o n2 ch3 o r o o ch3 r (8) 35 major cis 62-82% ee rh2l4* 7 (z = h) ch2cl2 hashimoto and co-workers obtained enantiomeric excesses of 24-76% ee in the intramolecular c-h insertion reactions of α-diazo-β-keto esters 37 catalysed by catalysts of type 8, to yield β-keto esters 38 equation 9 (hashimoto et al, 1990). more recent results with this catalyst line have afforded good enantioselective routes to azetidinones (anada and hashimoto, 1998b) and 2-pyrrolidones (anada and hashimoto, 1998a). these successes are exemplified by their syntheses of intermediates for trinem βlactam antibiotics 39 and a typical gabab receptor agonist (r)-(-)-baclofen 40 (scheme 11). p rh rh ph php ph ph o o cf3 o o cf3 (m)-36 p rhrh ph ph p ph ph oo cf3 oo cf3 (p)-36 roos, raab, and al-hatmi 96 n n on 2 o meo2c on o meo2c h h nh ro h h o o n2meo2c o r no2 rh2l4* 8 n meo2c o no2 r 82% ee ho2c nh2.hcl rh 40 84% ee r = pclc 6h4 n ho h h o ome co2r 39 trinem antibiotics (r)-(-)-baclofen rh2l4* 8 scheme 11. applications of enantioselective intramolecular c-h insertion dirhodium(ii) carbenes: the chiral product cascade doyle and co-workers have applied the homochiral dirhodium(ii) carboxamidate catalysts to the enantioselective carbon-hydrogen insertion reactions of diazoesters and diazoamides (doyle et al, 1993c, 1995b, 1996c). an early application of rh2(5s-mepy)4 9a was in the diazo decomposition of alkyl diazoacetates such as 41 to give the corresponding γ-lactones 42 in high yield, since insertion into a c-h bond α to an ether oxygen is a facile process equation 10 (doyle et al, 1991c). with primary alkyl diazoacetates other than 41, c-h insertion reactions catalysed by rh2(mepy)4 proceed with enantioselectivities that are < 70% ee. however, the introduction of 2-oxoimidazolidine catalyst variants 11 has led to enhanced enantioselectivities and excellent regiocontrol (doyle et al, 1994f, 1995f-h; müller and polleux, 1994; bode et al, 1996). for example, use of rh2(4s-mppim)4 11d provided γ-lactones 44 from diazoacetates 43 derived from primary alcohols equation 11. this methodology provided facile access to a series of naturally occuring lignans, for example (-) enterolactone 45, (+)-arctigenin 46 and (+)-isodeoxypodophyllotoxin 47 (bode et al, 1996). a = me, ph, c5h11, ch=ch2 38 24-76% ee37 (9) o coor a rh2l4* 8 ch2cl2 a coor n2 o (10) 91% ee 89% ee 87% ee r = me et bn 62-73% ch2cl2 rh2l4* 9a 4241 o o ro o o ro n2 (11) 96% ee 95% ee 89% ee 92% ee 94% ee r = et ibu bn mmeobn 3,4-(meo)2bn 62-73% ch2cl2 rh2l4* 11d 4443 o o r o o r n2 97 roos, raab, and al-hatmi o o 98 47 o o ome omemeo o 46 ho ome o ome ome o o ho ho 45 this methodology has been applied to the c-h insertion reactions of secondary cycloalkyl diazoacetates 48, where diastereoselectivity in the formation of cisand trans-fused bicyclic lactones 49 and 50 is a critical control feature (table 10) (doyle et al, 1994f). use of rh2(5s-mepy)4 9a or rh2(4smeox)4 10a produced insertion products with a high degree of enantiocontrol, but levels of diastereocontrol were far lower. in the formation of the more strained fused cyclopentyl lactone, only the cis diastereomer is formed, but the levels of enantioselectivity are lower than those obtained with the larger ring-sizes. however, both high enantiocontrol and almost complete stereocontrol were achieved in the latter with the catalyst rh2(4s-macim)4 11a (table 10) (doyle et al, 1994f). investigation of the enantioselective c-h insertion reactions of tertiary cycloalkyl diazoacetates 51a,b catalysed by rh2(5s-mepy)4 9a and rh2(4s-bnox)4 10c have been carried out equation 12 (müller and polleux, 1994). in contrast to the secondary cycloalkyl analogues above (table 10), both enantioselectivities and yields obtained in the formation of the bicyclic lactones 52a,b were poor, although only cis products were observed. again, rh2(4s-macim)4 led to greatly improved results (doyle et al, 1995f). high levels of enantioand diastereocontrol have been achieved with cisor trans-4alkylcyclohexyldiazoacetates (doyle et al, 1994f; müller and polleux, 1994), and with 2-adamantyl diazoacetate (doyle et al, 1995b) in the formation of lactones 53-55 respectively. ch3 o o chn2 rh2l4* 9a ch2cl2 o o ch3 h (12) 51 a n = 1 b n = 2 52 a 85% ee b 90% ee doyle and co-workers have described the use of rh2(5r-mepy)4 r-9a in the c-h insertion reactions of glycerol derived diazoacetates for the convenient synthesis of pure 2-deoxyxylolactone (scheme 12) (doyle et al, 1994g). the success of this reaction is probably based on the ether oxygen’s dirhodium(ii) carbenes: the chiral product cascade electronic activation of adjacent c-h bonds (adams et al, 1989; wang and adams, 1994). in the absence of the ether oxygen, enantioselectivities in the c-h insertion reactions of alkyl diazoacetates remain high, but diastereocontrol with rh2(mepy)4 catalysts tends to be relatively low. 99 h o h3c o h h 54 95% ee o 3c o h h 53 98% ee 55 98% ee o o h table 10. diastereoand enantioselective intramolecular synthesis of fused bicyclic lactones ch rh o o o o n2 ( )n 2l4* ch2cl2 o h h ( )n o h h ( )n 48 a n = 1 b n = 2 c n = 3 d n = 4 49 a-d 50 a-d 46 cat 49:50 49 % ee 50 % ee a a b b b c d 11a 9a 11a 9a 10a 11a 11a 100:0 100:0 99:1 75:25 55:45 99:1 99:1 89 40 97 97 96 96 97 65 91 95 61 59 dirhodium(ii) carboxamidate catalysed c-h insertion reactions of diazoacetamides derived from cyclic amines have been shown to afford β-lactam products preferentially, with a high degree of enantiocontrol equation 13 (doyle and kalinin, 1995i). roos, raab, and al-hatmi rh2l4* (r)-9a ch2cl2 67% n h o n chn2 o 97% ee (13) o c ch or 100 ro ro hn2 o rh2l4, (r)-9a 2cl2 65-81% o o h h ro o o h h or ro + r = me, 97% ee r = bn, 94% ee 93% 7% r =bn h2 pd(oh)2/c 83% o o h oh h ho 2-deoxyxylolactone cl cl oh scheme 12. enantioselective synthesis of 2-deoxyxylolactone 3.4.2 heteroatom-hydrogen insertion products the insertion of transition metal carbenes, particularly those derived from dirhodium(ii) carboxylate catalysts, into a variety of nucleophilic heteroatom-h bonds have provided novel routes to the synthesis of many synthetically relevant compounds (ye and mckervey, 1994; doyle et al, 1998a). of these, insertion into o-h, n-h and si-h are the most prominent. asymmetric variants of these reactions are, outside of those that are conducted on enantiomerically pure substrates, still in their infancy. of the asymmetric variants reported, the diastereoselective chiral auxiliary approach has shown the most success. recently, moody and co-workers reported the rh2(oac)4 catalysed intermolecular o-h insertion reactions of chiral auxiliary-bearing diazoacetates with simple alcohols, with diastereomeric excesses of up to 53% being attained (table 11) (aller et al, 1995; miller et al, 1999). to date the n-h insertion reactions reported have shown disappointing levels of asymmetric induction (< 50% ee), and much more research is required before this becomes a useful synthetic tool (aller et al, 1996; garcia et al, 1996). on the other hand, si-h insertion has shown greater promise. the landais group (landais, 1997) has provided the most significant results via a chiral auxiliary approach (landais et al, 1994a, 1994b; bulugahapitiya et al, 1997) equations 14, 15. three groups have independently reported initial successful results in an enantioselective approach with chiral dirhodium dirhodium(ii) carbenes: the chiral product cascade catalysts, rh2(5s-mepy) 9a (buck et al, 1996; bulugahapitiya et al, 1997) and rh2(s-dosp)4 7 (davies et al, 1997c). the best results equation 16 were obtained with vinyldiazoacetates. 101 ch n2 o o menthyl et3sih rh2(oac)4 2cl2 siet3 o o menthyl (14) dr = 72:28 et n2 o o h o o phme2sih rh2(oac)4 ch2cl2 75% et o o h o o phme2si h (15) dr = 85:15 r1 r2 n2 co2r3 rh2l4* 7 phme2sih r1 r2 co2r3 sime2ph l = (s-dosp) ee 77-95% l = (5s-mepy) ee 52-72% (16) 3.5 aromatic cycloaddition and substitution products transition metal catalysed carbene addition to aromatic rings may be considered a special class of cyclopropanation reaction. the high-yielding dirhodium(ii) catalysed intramolecular reactions of αdiazocarbonyl compounds form the fused bicyclic cycloheptatrienes such as 56 this was reduced to the bicyclodecanone 57 with a determined enantiomeric excess of 33% equation 17 (kennedy et al, 1990). asymmetric success has also been observed using chiral dirhodium(ii) phosphates 13a and have yielded enantioselectivities of up to 60% ee equation 18 (mccarthy et al, 1992). 5756 (17) ch2cl2 80% 93% 33% ee o n2 o o h pd/c, h2rh2l4* 7 (z = h) roos, raab, and al-hatmi table 11. diastereoselective intermolecular o-h insertion by chiral auxiliary-bearing diazoacetates ph n2 o or* roh or h 2o rh2(oac)4 ph o or* h or(h) r* roh yield % dr (major config) meoh 95 52:48 h2o meoh iproh 84 75 82 50:50 54:46 (s) 62:38 (s) h2o meoh iproh tbuoh 79 63 85 40 66:34 (r) 72:28 (r) 68:32 (r) 76:24 (r) h2o iproh 85 71 75:25 (s) 71:29 (r) h2o iproh tbuoh 98 82 37 66:34 (r) 74:26 (r) 75:25 (r) 102 so2n(chex)2 ipr ph ph the only diastereoselective approach to aromatic cycloaddition involves the recent novel use of a chiral diol auxiliary as a tether between the aromatic substrate and the diazo reagent (sugimura et al, 1998). this has provided entry into a series of potentially useful tropilidenes as chirons for further synthesis equation 19. dirhodium(ii) carbenes: the chiral product cascade o ch3 n2 ch3 o 60% ee 80% yield (18) catalyst 13a rh2(oac)4 ch2cl2 o o r o (19)o o o r o o r n2 o intramolecular aromatic substitution by metal carbenes represents a formal c-h insertion with tremendous potential for asymmetric synthesis via chiral catalysis. although not many reports have appeared, there is evidence of early success. the hashimoto group has exploited their amino acid phthalimide catalysts 8 to good effect in the synthesis of a range of indanones (table 12) (watanabe et al, 1995, 1996a). table 12. enantioselective intramolecular aromatic substitution 103 o n2 r2 r1 rh2l4* 8 ch2cl2 r1 o r2 58 r1 r2 58 yield % 58 % ee me et npr allyl me h h h h co2me 75 86 74 70 87 88 95 98 88 93 roos, raab, and al-hatmi the same workers have exploited this protocol in the synthesis of the aspartate receptor antagonist fr 115427 (scheme 13) (watanabe et al, 1996a). 104 come o n2 co2me me me o co2me rh2l4* 8 ch2cl2 87%, 93% ee me 2me co2me nh.hcl 59 scheme 13. synthesis of antagonist fr 115427 via intramolecular aromatic substitution 3.6 ylide cascade products metal carbenes derived from α-diazocarbonyl compounds are electrophilic enough to add to heteroatoms and form ylides equation 20. these then may undergo a wide range of reactions including [2,3]-sigmatropic rearrangements, [1,2]-insertion (stevens rearrangements), hydride elimination, and dipolar cycloaddition (doyle and forbes, 1998e; doyle et al, 1998a). this diverse reactivity, along with their often-competitive initial formation, has contributed to the relatively barren landscape in terms of their dirhodium-catalysed asymmetric synthesis. successful asymmetric adaptation is only a very recent achievement, and is so far restricted to oxonium ylide systems. r (20)+ r2 x r3 x r2o r1 r3 r r1 o rh2l4 o o (21) co2me n2 o ch2cl2 o co2me rh2l4* 6, 8, 13a dirhodium(ii) carbenes: the chiral product cascade the initial examples were provided by the mckervey group who exploited a tandem ylide formation-[2,3]-sigmatropic rearrangement sequence to produce benzofuranone derivatives with up to 60% ee equation 21 (mccarthy et al, 1992; pierson et al, 1997). dirhodium(ii) carboxamidate catalysts were used in initial studies of catalytic asymmetric tandem ylide formation-cycloaddition (doyle and forbes, 1998e; suga et al, 1998). however, these only produced ee values of < 30%. very recent developments have produced the first examples with ee values approaching synthetically useful levels. thus diazo ketoesters were induced to give intramolecular cycloadducts with ee’s up to 53% equation 22 (hodgson et al, 1997). the hashimoto group has taken this development further with diazo ketones in the intermolecular cycloaddition to afford bridged bicyclic skeletons in good yield and high enantioselectivity equation 23 (kitigaki et al, 1999). 105 n2 co2r o o (ch2)n rh2l4* 7 (z = nc12h25) o o co2r (ch2)n (22) the doyle group has provided the best enantioselective (ee up to 88%) example of ylide formation[1,2]-insertion in their report on the decomposition of 1,3-dioxane diazoacetates equation 24 (doyle et al, 1997e). ph o o rh n2 co2memeo2c 2l4* 8 o o ph co2memeo2c (23) 51-78% yield 70-92% ee o ome me o chn2 o me rh2l4* 11d ch2cl2 86%, 81% ee o o me me me (24) 4. conclusion over the past decade, the reports of chiral dirhodium(ii) catalyst systems and their applications to asymmetric synthesis have burgeoned. as this technology is applied to a greater diversity of reaction systems, it seems inevitable that the spectrum of dirhodium(ii)-carbene chemistry will continue to roos, raab, and al-hatmi 106 expand. given the wide range of non-racemic products that can be targeted in this way, these developments auger well for asymmetric organic synthesis and the industries that depend thereon. note added in proof the readers’ attention is drawn to the following noteworthy contributions which have appeared since original submission. doyle et al (1999d) – intramolecular addition to remote furans; davies and panaro (1999) improved d2-symmetric 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dirhodium(ii) carbenes80 3.2 intermolecular processes81 3.3 intramolecular processes87 introduction 1.1 the need for asymmetric synthesis the world around us is chiral. most organic compounds are chiral. the chemistry of perfumes, nutrients, pesticides, and pharmaceuticals involves chiral compounds whose physiological or pharmacological properties depend upon their recognition by chiral re reaction products from dirhodium(ii) carbenes 3.2 intermolecular processes initial attempts at asymmetric intermolecular cyclopropanations by means of chiral auxiliaries bonded to diazoacetates were largely unsuccessful (equation 1, z = chiral auxiliary). chiral n-(diazoacetyl)oxazolidinones 16 and 17 underwent rh2(oac)4 r r ph r 3.3 intramolecular processes because of geometric constraints, intramolecular cyclopropanations of unsaturated diazocarbonyl compounds can produce only one fused bicyclic cyclopropane (the cis isomer). tanimori et al (1997) have reported a chiral auxiliary approach to intramolec ph x me pr heteroatom-hydrogen insertion products the insertion of transition metal carbenes, particularly those derived from dirhodium(ii) carboxylate catalysts, into a variety of nucleophilic heteroatom-h bonds have provided novel routes to the synthesis of many synthetically relevant compounds (ye r* conclusion note added in proof squ journal for science, 2019, 24(2), 95-108 doi:10.24200/squjs.vol24iss2pp95-108 sultan qaboos university 95 flora, life-forms and biological spectrum of muscat governorate neelam sherwani department of biology, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat sultanate of oman. email: sherwani@squ.edu.om. abstract: the present study evaluated the floristic diversity and biological spectrum of muscat governorate, sultanate of oman. heterogeneity of geology, topography and climatic conditions create a diverse array of habitats across the 3,500 km 2 study area, supporting a range of vegetation types. floristic studies were conducted across 42 sites spread across various habitats such as sand dunes, alluvial plains, gravel plains, wadis, saline dunes, coastal areas, farms and plantations. a total of 264 species belonging to 183 genera and 54 families of angiosperm were documented during sampling the vegetation from different wilayats of the governorate. maximum number of species belonged to family fabaceae (14%), followed by poaceae (12%), asteraceae (9%), apocyanaceae and convolvulaceae (3.66% each), boraginaceae, euphorbiaceae, zygophylaceae (3% each). the biological spectrum was represented almost equally by therophytes and chamaephytes (30% each), followed by phanerophytes (19%), hemicryptophytes (13%), geophytes (4%), liana (3%), and helophytes (1%). the dominance of therophytes and chamaephytes reveals a thero-chamaephytic phytoclimate for the area. different habitats are characterized by specific plant assemblages, but some species such as acacia tortilis, prosopis cineraria, tetraena quaterense, dipterygium gluacum, aerva javanica, due to their broad ecological tolerance and adaptations, inhabit more than one habitats, while some species are just confined to certain parts of a single habitat. keywords: biological spectrum, flora, habitats, phytoclimate. الحياة النباتية والطيف البيولوجي لمحافظة مسقط نيالم شروني هذه الدراسة لتقييم تنوع الحياة النباتية والطيف البيولوجي لمحافظة مسقط ، سلطنة عمان، إن عدم التجانس الجيولوجي وإختالف سمات سطح :لخصمال 0033الدراسة التي امتدت إلى األرض وإختالف المناخ خلق مجموعة متنوعة من المناطق الطبيعية لمجموعة متنوعة من أنواع النباتات المختلفة في منطقة نوع من 462موقع بيئي مختلف كالكثبان الرملية ، الكثبان المالحة، المناطق الساحلية والمزارع. وتم رصد 24كلم مربع. لقد تمت دراسة النباتات في ط. لخصت الدراسة إلى أن أكثر أنواع النباتات تنتمي عائلة من النباتات كاسيات البذور في مختلف واليات محافظة مسق 02جنس و 380النباتات تنتمي إلى %(، العائلة 0.66%(، العائلة المحمودية )0.66%(، العائلة الدفلية )9%(، العائلة اإلستراسيا )34%( تتبعها العائلة النجيلية )32إلى العائلة البقولية ) %( 03و ) therophytes%( 03ن الطيف البيولوجي تمثل تقريبا بالتساوي ما بين )% لكل عائلة(. إ0الحمحمية، العائلة الغربيونية والعائلة القديسية ) chamaephytes ( 39ويلي ذلك )%phanerophytes ( 30و )%hemicryptophytes ( 2و )%geophytes ( 0و )%liana ( 3و )% helophytes إن هيمنه .therophytes وchamaephytes المنطقة. إن الموائد )الموطن الطبيعي( المختلفة تتميز هذه المجموعة على تعكس هيمنة dipterygium gluacumو tetraena quaterenseو proposis cinerariaو acacia tortilisبتجميع نباتات محددة إال أن بعض األنواع كـ في حين إن هذه الخاصية ال تتوفر لبعض األنواع التي تتقيد ببيئة تستوطن مناطق مختلفة نسبة لقدرتها على التحمل و التكيف البيئي aerva javanicaو .محددة ، الموطن الطبيعي و المناخ النباتي.تنوع النباتات ،الطيف البيولوجي: الكلمات المفتاحية 1. introduction ocated in the northeast corner of oman, along the coast running north of the hajar mountain range, muscat is the capital city of oman. muscat features hot and arid climatic conditions with an average annual rainfall of about 100 millimetres per year [1]. spanning across an area of 3,500 km 2 , muscat governorate is comprised of six provinces called wilayats, namely muttrah, bawshar, seeb, al amerat, muscat and quriyat. different type of rocks and sediments makes the surface geology of muscat governorate, which are mixture of samail ophiolite, carbonates, limestones and tertiary sandstones. l mailto:sherwani@squ.edu.om sherwani, n. 96 the surface sediment materials in general, are dense mixture of clay, gravel, silt, sand, and rock fragments [2,3]. heterogeneity of geology, topography and climatic conditions create a diverse array of habitats ranging from mud flats, saline dunes, sabkhas, khawrs, sand dunes, alluvial plains, gravel plains, wadis and khabrah supporting a range of vegetation types. generally, the floristic composition of a region and the biological spectrum, which is the percent representation of the number of species belonging to each life form [4], is influenced by the climate and nature of the substrate material [5] and their distribution is closely associated with the topography of the region [6]. the life forms are manifestations of the total adaptation of their perennating organs [7], and has evolved as a direct response to the prevailing environment [8-10], and are representations of flora adaptations to specific ecological conditions [11] and act as an indicator of nature of existing environmental conditions [12,13]. according to life form’s system [7], the harsher the climatic conditions, the more protected are the renewing buds. arid zones represent harsh environmental conditions [14] and in these extreme habitats, the biological spectrum shifts towards the more protected life-form classes such as therophytes, as they are the only one capable of better survival due to their short vegetative seasons and they survive under unfavourable seasons in the form of seeds. the biological spectra of a typical desert flora is represented mainly by therophytes and chamaephytes [6]. in view of the climate change, with a predicted increase of 1 to 2 °c in the maximum temperature for the entire country of oman through 2040 [15] and predicted 40% less rainfall for northern coastal area by 2040 [15], oman is likely to experience a decrease in water resources due to climate change. oman ranked 28 th in terms of in global climate risk index 2018, the floristic diversity and biological spectrum is expected to be affected. recent tropical cyclones has also caused substantial damage to the coastal areas like muscat. with rapid phase of urbanization, infrastructure development and industrialization going on, and muscat, being the capital city of oman, the floristic diversity is under threat. urbanization affects floristic diversity directly through habitat loss and fragmentation and indirectly due to human behavior [16-19]. being an arid zone ecologically, such zones are fragile, usually highly specialized, with high degree of endemism. oman has a high percentage of endemics, with 78 plant species being strictly endemic to oman, 48 species near endemic and 63 species regional endemic to the arabian peninsula [20]. many of these species are rare, threatened, and endangered. a slight change in climatic conditions will cause havoc on these species. the floristic diversity overall in oman and specially in capital city muscat is under threat due to its limited water resources, climatic change, population growth and urbanization, thus there is a need to document the total flora, various life forms and species distribution across various habitats. no previous study has highlighted the biological spectrum and plant life forms in this area. therefore, the present study was conducted to analyse the vegetation of the muscat governorate in terms of floristic composition, life-form, and habitat and to prepare a biological spectrum to infer the existing phytoclimate of the area. 2. materials and methods study area muscat governorate is located in the northeast corner of oman, latitude 23.5859 °n, and longitude, 58.4059 °e bordered by gulf of oman on its north (figure 1). the western al hajar mountains range dominate the landscape of muscat. its area is about 3,500 km 2 . muscat governorate has a hot arid climate, with long and very hot summers and warm winters. temperature reaches as high as 49 °c in summer. the hottest month is june with an average temperature of 35 °c, january is the coldest month with an average temperature of 21 °c. the muscat governorate is comprised of six provinces called wilayats, namely muttrah, bawshar, al seeb, al amerat, muscat and quriyat. samail ophiolite is mainly exposed around muscat and mutrah wilayat [21], surface geology of al amirat is composed of aeolian sand, alluvial fans, dolomite and limestone. sand, clay and silt are found in bawsher, with coastal dunes, alluvial sand, silt and khabrah found in seeb [2]. a checklist of angiosperm species growing in muscat governorate was generated based on the results of four years (2014-2018) intensive study. field surveys were an important part of the study, regular field surveys were conducted across 42 sites (figure 1), scattered along different habitats . specimen of all the species of trees, shrubs, herbs and climbers found in these sites were collected and identified. in the field, the plant species were documented, collected and field notes were taken so as to have information on the plant’s habit, leaves, stem and floral parts and habitat. accession numbers were assigned to each specimen along with locality data. the specimens were identified using related taxonomic books, [22-26] and compared with herbarium specimens from herbarium, college of science, squ. life forms of species were evaluated, relying on the location of the regenerative buds and the shed parts during the unfavorable season [7]. flora, life-forms and biological spectrum 97 figure 1. map of site of collections from muscat governorate. 3. results a total of 283 species were recorded from different habitats in the governorate of muscat, representing 196 genera and 49 families (table 1). the families with the highest number of species recorded was leguminosae with 42 species (14%). figure 2. number of species per family recorded from muscat governorate. sherwani, n. 98 other families represented were poaceae with 36 species (12%), asteraceae with 27 species (9%), apocyanaceae and convolvulaceae with 11 species each (3.66%), boraginaceae, euphorbiaceae, zygophylaceae with 9 species each (3%), caryophyllaceae and polygonaceae with 8 species each (2.6%), solanaceae with 7 species (2.3%), cleomaceae with 6 species (2%), followed by capparaceae and phyllanthaceae with 5 species each (1.6%), brassicaceae, cyperaceae, lamiaceae, malvaceae and resedaceae with 4 species each (1.3%) (figure 2). convolvulus with 6 species was the largest genus in terms of number of species in the study area, followed by launea and cleome with 5 species each. figure 3 shows the biological spectrum or the life form spectrum of the given 264 species in the study area. the vegetation of muscat governorate showed almost equal percentage of therophytes (30%) and chamaephytes (30%), followed by that of phanerophytes (19%), hemicryptophytes (13%), geophytes (4%), liana (3%), and helophytes (1%). the therophytes and chamaephytes together constitute 60% of the life-forms. figure 3. biological spectrum of life-forms of plant species recorded from muscat governorate. figure 4. percentage of the studied species by life-span. [category name] [percentage] therophytes 30% phanaerophytes 19% hemicryptophytes 13% liana 3% geophytes 4% helophytes 1% annuals 37% perrenials 63% l i f e s p a n p e r c e n t a g e annuals perrenials flora, life-forms and biological spectrum 99 life span wise, 105 species were annuals (37%) and 159 were perennials (63%), figure 4. study of the dominant families in terms of species richness revealed that fabaceae has high percentage (77%) of perennials and astereaceae family has high percentage (67%) of annuals. distribution studies of the species along varied habitats (table 1) showed that different habitats are characterized by specific plant assemblages, but some species can be found in more than one habitat. gravel and rocky terrain habitat: the highest species density was concentrated in the gravel and rocky terrain habitat (136 species), here the life-form composition is dominated by small trees, woody chamaeophytes and therophytes. perennial phanaerophytes such as acacia tortilis, prosopis cineraria, prosopis juliflora (introduced and naturalized), zizyphus spina-christi, and chamaeophytes such as heliotropium bacciferum, euphorbia larica are the permanent features of the plant cover in this habitat and therophytes such as launea intybatea and cenchrus setigerus are common. alluvial plains and disturbed areas: here the vegetation is characterized by chamaeophytes such as convolvulus virgatus, fagonia indica, amaranthus viridus, tephrosia appollinea, chrozophora oblongifolia, pulicaria glutinosa and therophytes such as tribulus terrestris, tribulus arabica, cenchus ciliaris, pennisetum setaceum, tetreana simplex. a total of 78 species was found in this zone. sand dunes: in dunes, with 55 species, the life-form composition is typical of the desert flora, characterized by low carbonate content substrate. sand dunes are mainly colonized by chamaeophytes such as dipterygium glaucum, calligonum commosum and cyperus conglomeratus. wadi: in wadis, the life-form composition is dominated by dense stands of helo-geophytes such as phragmatis australis and typha domingensis in wadi beds, margins of wadi are colonized mainly by species such as acacia tortolis, prosopis cineraria, prosopis juliflora. annuals such as centurea pseudosinaica and plantago ovata are common on dried wadi beds. coastal area with the least number of species (27) are dominated by perennial, low growing halophytic chamaephytes such as suaeda aegyptiaca, sphaerocoma aucheri, tetraena quaterense and cornoluca monocantha. the vegetation stands usually are species poor, as cover of one particular species is frequently seen over a larger area. avicenia marina is a typical mangrove species found in the intertidal zone. 4. discussion the floristic data clearly indicate that despite having a dry arid climate, muscat governorate is home to a rich diversity of plants and these plant species are very much associated with aridity and drought. fabaceae, poaceae and asteraceae were the dominant families in terms of number of species. these families show high compatibility with arid and semiarid environmental conditions. similar results were observed in hema faid region of ha’il province, saudi arabia [27], in tabuk province, north saudi arabia [28], in hafer albatin region, northeastern saudi arabia [29]. generally, the vegetation type and the biological spectrum of a given area reflects an apparent relationship to its surrounding environment [30-32]. the biological spectrum in the present study ranged from therophytes, chamaephytes, phanerophytes, hemicryptophytes, geophytes, liana and helophytes. therophytes and chamaephytes were the dominate forms, the dominance of the therophytes and chamaephytes may be attributed to the hot dry climate, geological factors and the topography [33-35]. therophytes are associated with a dry climate [36,37], and are characteristics vegetation type of desert flora, as influenced by microclimate and soil conditions [38]. the therochamaephytic spectrum has been assiociated with other desert climates observed in the neighbouring countries such as taif, saudi arabia [39], hail region of saudi arabia [40], wadi al-jufair, saudi arabia [35], toor al-baha district, lahej governorate, yemen, [41]. generally, a sparse vegetation cover with scattered small trees, dwarf shrubs and mainly annuals represent a typical desert flora, as the sandy soil of these regions is characterized by low soil organic carbon and low structural stability, a high nutrient leaching and degradation due to erosion [42]. diverse habitats are zones of microenvironments at local scales, each habitat supporting a characteristic type of vegetation. as the species distribution is generally limited by its ecological amplitude, [43] climate and habitat filtering, generating species pools, [44], where species adjust their metabolism [45] and produce functional traits as result of adaptation to the microclimates found under variable habitats [46]. analysis of the present study reveals that highest species concentration was found in gravel rocky terrain, here the life-form composition is dominated by small trees, woody chamaeophytes and therophytes. scattered xerophytic vegetation of dwarf chamaeophytes, perennial herbs, and small trees are features of water limited sand dunes habitat with soils low in organic carbon, phosphorus and low water retaining capacity. similar results were observed by [47] in al kharj region, saudi arabia. the psammophytic vegetation of the sand dunes exhibit specific ecological adaptation, sending out long roots to catch hold of the slightest moisture available. wadi beds are usually rich floristically [48], where the access to water creates a favourable microclimate and microhabitat, for many species to flourish. the availability of annuals or perennials in a wadi mainly depends on the amount of rainfall received during the year [49]. perennials helophytic tall grasses are the common representative species in wadis. similar results were observed in wadi hegiya [50]. halophytic perennial chamaephytes with reduced succulent leaves predominate the coastal vegetation, with mostly chenopodiales and members of zygophyllaceae being the dominant feature at many coastal locations, similar sherwani, n. 100 results were observed in coastal area of al-uqair, saudi arabia [51]. reduced leaf area is an indicator of severe environmental stress [52]. reduced leaf area and fleshy leaves, under salinity stress is a common phenomenon associated with most of the coastal halophytes [53]. under selective pressures at a given habitat, the ecological strategies are limited which results into communities having species with similar functional traits and life form composition [54]. lying in the arid zone, oman already suffers from aridity, water paucity and salinity , and being vulnerable to climatic change, with a predicted 1-2 ˚c rise in average temperature over the next 30 years [55], erratic patterns of precipitation and raised sea levels, all these factors are expected to exert considerable physiological constraints and affect biodiversity [56]. in view of the above threats, with high degree of endemism, many threatened species, lack of enough in situ protected areas for plant conservation, lack of enough restoration programs, urban sprawl affecting biodiversity, documentation of the species is necessary and important. conclusion the heterogeneity of environmental conditions, surface geology and topography across diverse habitats lead to variation in the distributional pattern of plant species in the studied area. species were morphologically and physiologically adapted to the varied environmental conditions across different habitats, through selection on their functional traits by environmental filters, generating species pools. each habitat acts as a microenvironment where specific abiotic stress leads to similar responsive characteristics among the co-existing species, thus similar life-form composition. based on the work, the phytoclimate of the area, based on raunkiaer’ s system of classification, has been described as thero-chamaephytic phytoclimate. table 1. flora, life forms, life span and habitat of plants recorded from muscat governorate. (names follow apg 1v classification). key, ph : phanerophyte; ch: chamaephyte; he: hemicryptophyte; ge: geophyte; he: helophytes th: therophyte; li :liana; ann: annual; per: perennial; coa : coastal; al-p : alluvial plains, roadsides, dun: dunes; wad : wadi’s; gr-roc : gravel, rocky terrain, mountains; far : farms and plantations. family species life-form life span habitat coa alp du n wa d g r r oc far 1. acanthaceae avicenia marina hl per x 2. blepharis ciliaris ch per x 3. ecbolium viride ph per x x 4. aizoaceae aizoon canariense he ann x x 5. gisekia pharnaceoides he ann x 6. trianthema portulacatrum he ann x 7. amaranthaceae achyranthus aspera ch an/p x 8. aerva javonica ch per x x x 9. amaranthus graecizans th ann x x 10. amaranthus hybridus th ann x x 11. amaranthus viridus th ann x x 12. anabasis setifera ch per x x x 13. arthrocnemum macrostachyum ch per x 14. atriplex farinose ch per x 15. atriplex leucoclada ch per x 16. chenopodium album th ann x x 17. chenopodiastrum murale th ann x x 18. cornoluca aucheri th ann x 19. cornoluca monocantha ch per x x 20. digera muricata th ann x 21. halothamnus bottae ch per x x 22. hamada salicornica ch per x x x flora, life-forms and biological spectrum 101 23. pupalia lappacea ch per x x 24. salsola drummondii ch per x 25. caroxylon imbricatum th ann x x x 26. seidlitzia rosmarinus ch per x x 27. suaeda aegyptiaca ch per x x x 28. suaeda vermiculata ch per x 29. apiaceae ammi majus th ann x 30. apocyanaceae adenium obesum ph per x 31. calotropis procera ph per x x 32. caralluma edulis ch per x 33. glossonema varians he ann x 34. leptadenia pyrotechnica ph per x x x 35. nerium oleander ph per x x 36. pentatropis nivalis li per x x x 37. pergularia tomentosa li per x 38. periploca aphylla ch per x 39. rhazya stricta ch per x x 40. arecaceae nanorrhops ritchieana ph per x 41. phoenix dactylifera ph per x x 42. asparagaceae asparagus racemosus li per 43. aristolochiacea e aristolochia bracteolata li per x x 44. asphodelaceae aloe inermis ch per x 45. asphodelus tenuifolius ge ann x x 46. asteraceae ageratum conyzoides th ann x 47. bidens pilosa th/c h ann x x 48. calendula arvensis th ann x 49. carthamus tinctorius th ann x 50. centaurea puedosinaica th/c h ann x x 51. conyza bonariensis th ann x x 52. dyssodia tenuiflora th ann x x 53. echinops spinosissimus ch per x x 54. eclipta alba th ann x 55. eclipta prostrata th ann x x 56. flaveria trinervia th ann x x 57. iphiona aucheri ch per x x 58. iphiona horrida ch per x x 59. iphiona scabra ch per x x 60. launea capitata th ann x x 61. launea intybacea th ann x 62. launea massauensis th ann x 63. launea nudicaulis ch per x 64. launea procumbens ch per x x 65. pluchea dioscoridis ch per x x 66. pulicaria glutinosa ch per x x x 67. pulicaria jaubertii ch per x x 68. pulicaria schimperi th ann x 69. reichardia tingitana th ann x sherwani, n. 102 70. senecio flavus th ann x 71. sonchus oleraceus th ann x x x 72. vernonia cinerea th ann x 73. bignoniaceae tecomella undulata ph per x 74. boraginaceae arnebia hispidissima th ann x x 75. echiochilon persicum ch per x 76. heliotropium bacciferum ch per x x x 77. heliotropium calcareum ch per x x x 78. heliotropium kotschyi ch per x 79. heliotropium longiflorum ch per x 80. brassicaceae anastatica hierochuntia th ann x x 81. diplotaxis harra th ann x 82. physorrhynchus chamerapistrum ch per x x x 83. sisymbrium irio th ann x 84. capparaceae cadaba farinosa ph per x 85. capparis cartilaginea ph per x 86. capparis spinosa ph per x x 87. capparis decidua ph per x 88. maerua crassiflolia ph per x 89. caryophyllacea e cometes surattensis he ann x 90. herniaria mascatensis he per x x 91. polycarpaea repens he per x x 92. silene conoidea th ann x x 93. silene linearis th ann x 94. spergula fallax he ann x 95. sphaerocoma aucheri ch per x 96. vaccaria hispanica he/ th ann x 97. cleomaceae cleome austroarabica ch per x 98. cleome brachycarpa ch per x x 99. cleome gynandra th ann x 100. cleome rupicola ch per x x 101. cleome scaposa th ann x 102. dipterygium glaucum ch per x x x 103. convolvulaceae convolvulus arvensis ch per x x 14. convolvulus cephalopodus ch per x x 105. convolvulus fatmensis ch per x 106. convolvulus glomeratus ch per x x x 107. convovulus prostratus ch per x x x 108. convovulus virgatus ch per x x 109. cressa cretica ch per x x 110. cuscuta planiflora li ann x x x 111. seddera glomerata ch per x x 112. cucurbitaceae citrullus colocynthis he ann x 113. corallocarpus epigaeus li per x 114. cucumis prophetarum li ann x x 115. cyperaceae cyperus conglomeratus ge per x 116. cyperus laevigatus ge per x flora, life-forms and biological spectrum 103 117. cyperus rotandus ge per x x 118. fimbristylis ferruginea he per x 119. euphorbiaceae andrachne telephoides he per x 120. chrozophora oblongifolia ch per x x x 121. euphorbia arabica th ann x x 122. euphorbia hirta th ann x x x 123. euphorbia indica th ann x x 124. euphorbia larica ch per x x 125. jatropha integerrima ph per x 126. ricinus communis ph per x x 127. juncaceae juncus rigidus ge per x x 128. lamiaceae lavendula subnuda ch per x x 129. leucas inflata th ann x x 130. ocimum forskaolii ch per x x x 131. salvia aegyptiaca ch ann x x 132. fabaceae acacia ehrenbergiana ph per x x 133. acacia nilotica ph per x 134. acacia tortolis ph per x x x 135. alhagi graecorum ch per x x 136. argyrolobium roseum he ann x x 137. astragalus fatmensis he ann x 138. astragalus tribuloides th ann x x 139. astragalus vogelii th ann x 140. caesalpinea bonduc ch per x 141. caeslapinea pulcherrima ch per x 142. crotalaria aegyptiaca ch per x x x 143. crotalaria persica ch per x 144. hippocrepsis constricta th ann x x x 145. indigofera arabica he per x x 146. indigofera coerulea ch per x x 147. indigofera intricata ch per x x x 148. indigofera oblongifolia ch per x x x 149. lotus garcini ch per x 150. lotus schimperi he ann x x 151. medicago sativa ch per x 152. melilotus indicus th ann x 153. prosopis cineraria ph per x x x x 154. prosopis juliflora ph per x x 155. rhynchosia minima li per x 156. rhynchosia pulverulenta li per x x 157. pseudolotus vilosus he ann 158. senna holosericea ch per x x x x 159. senna obtusifolia ch ann x 160. senna italica ch per x sherwani, n. 104 161. taverniera glabra ch per x x 162. taverniera spartea ch per x 163. tephrosia appollinea ch per x x x 164. tephrosia nubica ch per x x 165. tephrosia purpurea ch per x 166. lythraceae ammannia baccifera th ann x 167. lawsonia inermis ph per x x x 168. malpighiaceae acridocarpus orientalis ph per x x 169. malvaceae abutilon fruticosum ch per x x 170. abutilon pannosum ph per x x 171. malva parviflora th ann x x x 172. menispermacae cocculus pendulus li per x 173. moraceae ficus carica ph per x x 174. ficus cordata ph per x x x 175. moringaceae moringa peregrina ph per x x 176. myrtaceae myrtus communis ph per x 177. nyctaginaceae boerhavia diffusa th ann x x 178. boerhavia elegans ch per x x 179. orobanchaceae cistanche phelypaea ge-p per x 180. oxalidaceae oxalis corniculata th ann x 181. phyllanthaceae andrachne aspera he per x x 182. andrachne telephoides he per x x 183. phyllanthus maderaspatensis th ann x 184. phyllanthus niruri th ann x 185. phyllanthus rotandifolius th ann x 186. plantaginaceae plantago major th ann x 187. plantago ovata th ann x 188. poaceae aeluropus lagopoides he per x 189. aristada adscensionis th ann x x 190. arundo donax ch per x 191. cenchrus ciliaris he per x x x 192. cenchrus setigerus he per 193. chloris barbata th ann x x x 194. chloris gayana he ann x 195. chloris virgata th ann x x 196. cymbopogon schoenanthus he per x x 197. cynodon dactylon ge per x x 198. dactyloctenium aegyptium th ann x 199. desmostachya bipinnata th ann x 200. dichanthium foveolatum he per x 201. digitaria ciliaris th ann 202. echinochloa colona th ann x x 203. eragrostis cilianensis th ann x x 204. halopyrum mucronatum th per x 205. hyparrhenia hirta he ann x x flora, life-forms and biological spectrum 105 206. lasiurus scindicus he per x x 207. panicum turgidum he per x x 208. pennisetum divisum he per x 209. pennisetum setaceum he per x x 210. phalaris minor th ann x x 211. phragmites australis hl/ge per x 212. saccharum ravennae ch per x 213. setaria verticillata th ann x 214. sporobolus ioclados ge per x 215. sporobolus spicatus ge per x x x 216. stipagrostis uniplumis he per x x 217. typha domingensis hl/ge x 218. polygalaceae calligonum comosum ph per x x 219. polygala erioptera th ann x 220. polygala irregularis th ann x 221. polygala mascatensis ch per x 222. pteropyrum scoparium ph per x x 223. rumex pictus th ann x 224. rumex vesicarius th ann x 225. portulacaceae portulaca grandiflora th ann x 226. portulaca oleraceae th ann x 227. primulaceae anagallis arvensis th ann x 228. ranunculaceae ranunculus muricatus th ann x 229. resedaceae ochradenus arabicus ch per x x x 230. ochradenus aucheri th ann x x 231. oligomeris linifolia th ann x x 232. reseda aucheri th ann x x 233. rhamnaceae ziziphus spina-christi ph per x x 234. rubiaceae plocama aucheri ch per x x 235. rutaceae haplophyllum tuberculatum ch per x x 236. salvadoraceae salvadora persica ph per x x x 237. sapindaceae dodonaea viscosa ph per x 238. scrophulariacea e schwienfurthia imbricata ch per x x 239. schwienfurthia papilionacea th ann x x 240. solanaceae datura innoxia th ann x 241. datura metel th ann x x x 242. hyoscymus gallagheri ch per x x 243. lycium shawii ph per x x 244. physalis minima th ann x 245. solanum incanum ch per x 246. solanum nigrum th ann x sherwani, n. 106 247. tamaricaceae tamarix aphylla ph per x x 248. tamarix mascatensis ph per x x 249. tiliaceae corcorus depressus he per x x x 250. corcorus trilocularis th ann x 251. typhaceae typha domingensis hel per x 252. typha angustata hel per x 253. urticaceae forsskalea tenacissima th ann x x 254. verbenaceae lantana camara ch per x 255. phylla nodiflora ch per x 256. vitex agnus castus ph per x 257. zygophyllaceae fagonia bruguieri ch per x x 258. fagonia indica ch per x x 259. seetzenia lanata he per x x 260. tribulus arabicus he per x x 261. tribulus pentandrus he per x 262. tribulus terrestris he ann x x 263. tetraena quaterense ch per x x x x 264. tetraena simplex he ann x x x conflict of interest the author declares no conflict of interest. acknowledgement the author would like to thank the herbarium unit at sultan qaboos university for access to herbarium plant specimens for comparison and identification. references 1. gunuwardhana, l.n., and al rawas, g.a. trends in extreme temperature and precipitation in muscat, oman. proceedings of the international association of hydrological sciences, 2014, 364, 57-63. 2. el-hussain, i., saad, m.g., deif, a., mohamed, a.e.m. and ezzelarab, m. seismic liquefaction potential in muscat, sultanate of oman. journal of earth science climate change, 2018, 9, 451. 3. hoffmann, g., meschede, m., zacke, a. and al kindi, m. field guide 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847940. received 12 february 2019 accepted 13 may 2019 microsoft word ersc090209 edited_checked.doc 25-43 squ journal for science, 14 (2009) © 2009 sultan qaboos university 25 multiphase mineral inclusions in ferrikaersutite megacrysts : implications for postmagmatic alteration of the kaersutite host sobhi nasir department of earth sciences, college of science, sultan qaboos university, email: sobhi@squ.edu.om. للكيرسوتيت الحاوي دالئل على التغيرات الصهرية : في بلورات فريكيروسيتيت خشنة المعادن مكتنفات متعددة صبحي نصر وجدت مكتنفات أولية وثانوية لمعادن متعددة وبدون بقايا للمحاليل ضمن بلورات خشنة من الفريكيروسيتيت ضمن : خالصة تحتوي المكتنفات علـى معـادن المجنتيـت، والهماتيـت، . حقل براكين حرات الشام ذات العصر الكينوزوي في سوريا تتكـون معـادن . تم تكوين بلورات الكيرسوتيت من صهير باسانيتي مائي فـي العمـق . والبسودوبروكيت والبيرويتيت ـ . ينالسليكات في المتكنفات من األوليفين، والبالجيوكليز، والفلوجوبيت، والهورنبلند، والكلينوبيروكسـين واألرثوبيروكس تكون معدن الماجنتيـت . تكونت معادن السليكات من الصهير المتداخل والمالئ للكسور والتشققات في معدن الكيرسوتيت أدت التغيـرات افـي . تغيرات على حرارة منخفضـة إلىوالبروتيت من خالل التبلور الصهيري والذي تعرض بعد ذلك ن الهماتيت والليمونيت وكذلك نواج التجوية الدقيقة الحجم والمتكونـة المراحل المتأخرة القريبة من السطح الى تكون معاد من نواتج غنية بالسليكا والحديد، والسليكا والمجنسيوم واأللمنيوم، والسليكا والحديد واأللمنيوم، والسليكا واأللمنيوم ،والسليكا بعد صهيرية المرافق للمرحلة الما ية محكوما بالتغير لقد كان تركيب نواتج التجو . والتيتانيوم واأللمنيوم والحديد والكالسيوم .للكيروسوتيت على حرارة منخفضة من خالل أسطح التشقق والكسور abstract: primary and secondary multiphase mineral inclusions, without preserved fluid are found in ferrikaersutite megacrysts from the cenozoic harrat ash sham volcanic field in sٍyria. mineral phases in the inclusions are magnetite, hematite, pseudobrookite and pyrrhotite. the kaersutite megacrysts formed from a hydrous basanitic melt at depth. silicate minerals in the inclusions are olivine, plagioclase, phlogopite, hornblende, clinoand orthopyroxene. these silicate minerals crystallized from melt penetration and infillings of veins and fractures in the kaersutite. magnetite and pyrrhotite inclusion formed through magmatic crystallization which was followed by low temperature alteration and re-equilibration. late stage near-surface alteration resulted in the formation of hematite, limonite and fine-grained weathering products which comprise high-fe-si-, si-mg-al-, si-fe-al-, si-aland si-ti-al-fe-ca-rich alterations. the composition of these late stage alteration products was governed by low-temperature postmagmatic alteration of kaersutite along cleavage planes and fractures. sobhi nasir 26 keywords: harrat ash sham, inclusion, kaersutite megacryst, sulphide, iron oxides, alteration. 1. introduction ron-oxide, sulphide, silicate solid, and melt inclusions have been reported from minerals (e.g. olivine and pyroxene) in igneous rocks of diverse compositions with different cooling histories (e.g. larocque et al., 2000; török et al., 2003; zajacz and szabó, 2003; halter et al., 2004a b; hongfu et al., 2006; laubier et al 2007). such inclusions in minerals of igneous rocks provide important information on the composition and evolution of magmatic systems (e.g. andersen and neumann, 2001; frezzotti, 2001). however, the composition of solid and melt inclusions in minerals may be controlled by the composition of the host phenocryst and can be affected by processes such as volatile dissociation, oxidation, partial re-equilibration, alteration, and reaction with their host during cooling. upper mantle xenoliths and megacrysts of kaersutite as well as clinopyroxene, orthopyroxene and spinel can be found in lava flows and ejecta of the cenozoic harrat ash sham volcanic field of jordan and syria. the kaersutite megacrysts are single crystals and contain multiphase solid inclusions. in this paper, we describe several generations of primary and secondary multiphase solid inclusions in kaersutite megacrysts that occur in quaternary basaltic rocks from the harrat ash sham volcanic field, syria. we present textural observations and compositional data of these inclusions and discuss the possible processes which have formed and modified these inclusions. 2. geologic setting the cenozoic harrat ash sham volcanic field is a segment of a widespread volcanic province in the northwestern part of the arabian peninsula (figure 1) which consists of several volcanic fields that are locally called "harrats" (camp and roobol, 1992; nasir, 1994). the harrat ash sham volcanic field is noteworthy due to abundant mafic and ultramafic xenoliths, xenocrysts and megacrysts (nasir, 1992; nasir et al., 1992; nasir, 1995; nasir and safarjalani, 2000; al-mishwat and nasir, 2003). the emplacement of the harrat ash sham lava was controlled by rifting related to the opening of the red sea. k-ar age dating indicates that most of the volcanism occurred before 14 + 1.6 ma ago (ilani et al., 2001) compositionally the lavas are mainly alkali olivine basalts and basanites (nasir, 1994; lustrino and sharkov, 2006; krienitz et al., 2006; shaw et al., 2007). in southern syria there were three episodes of volcanism – in the miocene, pliocene and quaternary. these three episodes are petrographically and geochemically indistinguishable (mouty et al., 1992). however, kaersutite megacrysts and mafic and ultramafic xenoliths of lower crustal and upper mantle origin are most common in the quaternary lavas and are scarce in the miocene-pliocene alkali olivine basalts. the petrography and mineral chemistry of these xenoliths are described in detail by nasir (1992) and nasir and safarjalani (2000). the dominant megacryst phases in the harrat ash sham volcanic field are al-clinopyroxene, ferroan spinel (pleonaste) and kaersutitic amphibole (nasir, 1995). pressure-temperature estimations (e.g. 2 pyroxenes ca in orthopyroxene thermometers, ca in olivine barometers) suggest that the megacrysts and maficultramafic xenoliths crystallised at temperatures of 900-1050°c and pressures of 12-15 kbar i.e. in the upper mantle near the crust-mantle boundary (nasir, 1992; nasir and safarjalani, 2000). 3. methods the samples in this study were collected from the pyroclastic component of the quaternary alkali-olivine basalt of the dhanoon volcano in the harrat ash sham volcanic field (figure1). three megacrysts (m1, m2, and m3) were selected for this study. these specimens contain abundant round to oval-shaped silicate, sulphide, and oxide inclusions. the inclusions were screened by means of transmitted and reflected light microscopy as well as with back-scattered electron imaging (bse). mineral analyses were then carried out on representative inclusions at universität stuttgart using a cameca sx100 electron microprobe. operating conditions were: 15 kv accelerating i multiphase mineral inclusions in ferrikaersutite megacrysts 27 voltage, 10 to 15 na beam current, 1 to 5 µ electron beam size, and integration time of 20 seconds on peak and on background per analysed element. the standards applied were: corundum (al), albite (na), wollastonite (ca, si), mgo (mg), orthoclase (k), rhodonite (mn), hematite (fe), barite (ba), rutile (ti), nio (ni), cr2o3 (cr), coo (co), sphalerite (zn) and chalcopyrite (cu, fe, s). the raw data were corrected using the pap procedure. no aqueous fluid inclusions were observed in the investigated samples. figure 1. location map relating to the investigated megacrysts of the harrat ash sham volcanic field. 4. petrography amphibole megacrysts occur as black and hypidiomorphic crystals ranging between 5 x 3 x 3 cm and 10 x 5 x 5 cm in size (figure 2a, b). most amphibole megacrysts are characterised by numerous inclusions that are distributed irregularly or in patches or are aligned in planes. the inclusions are often bleb-like, rounded, rod-like, elongated or globular (figures 3a 4a 5a). in case of elongated inclusions, the long axes of rods are oblique to the (110) cleavage planes of the host amphiboles (figure 4a). in many cases, minute veins containing the same mineral phases as the inclusions connect inclusions (figures 3c d f and 4a b f). furthermore, sealed cracks connecting the inclusions are also present. these cracks are often curved and not related to the cleavage planes of the amphibole. the identified inclusion phases comprise various sulphide, oxide and silicate minerals as well as silicateand/or ferich alteration products. the alteration products are variable in size and shape (figures 3-5). they occur as birefringent cryptocrystalline aggregates of presumably silicate minerals (e.g. clay, chlorite) and/or iron hydroxides (limonite) filling the spaces between daughter crystals. sobhi nasir 28 oxide minerals are magnetite, pseudobrookite, and hematite. pyrrhotite is the major sulphide phase, occurring as rounded or rod like blebs that typically form isolated rounded inclusions. small amounts of chalcopyrite appear together with pyrrhotite in inclusions of sample m3. figure 2a. photomicrograph showing representative kaersutite megacrysts. figure 2b. scanned image of polished sections showing the distribution of inclusions (black points) within the analyzed samples m1, m2 and m3. small crystals of clinopyroxene, orthopyroxene, amphibole, phlogopite, olivine, and plagioclase also occur in the silicateand/or iron-rich alterations (figures 3a to f, 4d, e and 5c, d). the kaersutite megacrysts are divided into three types considering the textural arrangement of the inclusions: (1) megacryst type a (sample m1; globules a-e in figure 3): this type contains mostly spherical and rounded inclusions. the size of the inclusions is usually between 100-200 µ, but may occasionally reach up to 300 µ. the megacryst is dominated by magnetite and pyrrhotite inclusions. interconnecting veins and annealed fracture planes are common (figure 3a to f). the interfaces of these veins with the host kaersutite are irregular. very fine-grained aggregates of plagioclase, orthopyroxene, clinopyroxene, phlogopite, amphibole and hematite have been identified multiphase mineral inclusions in ferrikaersutite megacrysts 29 in these veins. fe-richand/or silicate-alterations are widespread in cores of larger magnetite, hematite and pyrrhotite grains. figure 3. back scattered electron (bse) image of type a inclusions (samplem1). (a) rounded inclusions. (b) ironoxide globule within kaersutite (mt, magnetite; mtex, magnetite exsolution, hm, hematite). black areas at the surface of iron oxides are empty voids (v). clinopyroxene (cpx) is present as rims surrounding iron oxides. rounded pyrrhotite (po) inclusions with a rim of magnetite. clinopyroxene and sa2 and ia crosscut the inclusion (# 1, 2; table 6-7). (d) iron-oxide globule surrounded by phlogopite (phl), plagioclase (pl) and orthopyroxene (opx) at the bottom. at the top: inclusion rich in ia (# 3; table 6) and iron oxide surrounded by plagioclase, orthopyroxene and sa3. (e) rounded magnetite inclusion bounded by plagioclase orthopyroxene and tschermakitic hornblende (thbl). (f) magnetite inclusion with voids and bounded by pyrrhotite and plagioclase. a vein cross-cuts the kaersutite and the inclusion. the vein is filled with orthopyroxene, plagioclase, magnetite, hematite, ferrokaersutite (fkst). (2) megacryst type b (sample m2; globule a-f in figure 4) contains inclusions of pyrrhotite, magnetite, hematite, pseudobrookite, clinopyroxene and orthopyroxene. most of these inclusions have elongated, rod-like outlines ranging in length from 50 to 100 µ, and occur along parallel planes. interconnecting veins and annealed fracture planes are common (figure 4a to f). the veins and fractures are filled with fine-grained aggregates (e.g. chlorite and/or clay minerals). sobhi nasir 30 (3) megacryst type c (sample m3; globules a-f in figure 5) contains globular inclusions. these inclusions occur as isolated globules within the kaersutite, as well as several globules arranged along cleavage planes of kaersutite. some globules are associated with open voids (figure 5a, b). most blebs of this type have a droplet shape and range in length from 100 to 1200 µ. meniscus-shaped boundaries of silicate alteration assemblages are common in open voids (figure 5b). the inclusion phases comprise pyrrhotite, chalcopyrite, a ni-co-s solid solution phase, magnetite, pseudobrookite, hematite, clinopyroxene, olivine and fine-grained alteration products. along rims and cracks, pyrrhotite is partly replaced by limonite (figures 4c and 5f). in megacryst m3, empty voids occur associated with hematite inclusions (figure 5c, d). the shape of hematite and magnetite in these inclusions is rounded and bleb-like. the interior of hematite drops in m3 is often frothy and impregnated by minute holes (figure 5b, e). similar frothy hematite globules in olivine were observed by larocque et al. (2000), who interpreted these structures as due to degassing phenomenon. figure 4. photomicrographs of inclusions in kaersutite (type b) sample m2. (a) oriented inclusions with rod-like outlines in kaersutite. the inclusions appear black due to a high content of oxides. individual inclusions are interconnected by veinlets containing the same phases (black arrows) or curved crack plans (white arrow). transmitted light 1 polar. (b) bse image showing inclusions containing sulphides (white) and silicate alteration (black) in kaersutite. a planar veinlet (upper left to lower right) is interconnecting several inclusions. (c) pyrrhotite (po) globule partly replaced by limonite (lm). small amounts of magnetite (mt) are additionally present. (d) detail of (b) showing a globule composed of slightly exsolved magnetite, hematite (hm) and sa2. (e) inclusion containing hematite, pseudobrookite (pb) and small amounts of sa (greyish colour). bse image. (f) detail of (b) showing inclusions containing sa1 and hematite. inclusions are interconnected by a veinlet containing the same phases as the inclusions. multiphase mineral inclusions in ferrikaersutite megacrysts 31 5. chemical compositions of kaersutite and the inclusion phases 5.1 silicate minerals the kaersutite host crystals are homogeneous in composition (# 61 to 63, table 1). no significant chemical zoning has been detected even on the centimeter scale. mössbauer spectroscopy indicates that all fe in the kaersutite is fe3+ (nasir and al-rawas, 2006). thus, they are ferrikaersutite according to the nomenclature of leake et al. (1997). the composition of the kaersutite megacrysts is similar to that of the associated group i and ii xenoliths. amphibole re-crystallisation on small void walls can be easily recognised by a slight change in colour. the bleached kaersutite seams around inclusions are characterised by very low or no fe3+ (# 64, table 1) according to the calculated formulae. two additional varieties of amphibole were identified within the inclusions. the first variety which is al2o3-rich and tio2-poor occurs in inclusion m1-e (# 65, table 1). it is a tschermakitic hornblende according to the nomenclature of leake (1997). the second variety is a ferro-kaersutite, and occurs in inclusion m1-f (# 66, table 1). this amphibole is tiand fe-rich and mg-poor. figure 5. photomicrographs of inclusions in kaersutite (type c) sample m3. (a): black drop-like hematite-rich inclusions in kaersutite. the hematite inclusions are partly linearly arranged along cleavage planes of the amphibole host. transmitted light, 1 polar. (b) detail of (a). the bse image shows frothy hematite droplets (white) and silicate alteration (dark gray) in an open cavity. meniscuses and rounded voids in the alteration indicate the presence of fluid during the settlement of the melt. (c) open cavity in kaersutite partly filled by silicate alteration (sa4) and clinopyroxene crystals (cpx). possible reaction of sa4 with the kaersutite host is indicated by a bleached seam around the inclusion. (d) open cavity filled by silicate alteration with (oxidised) olivine and clinopyroxene crystals and by voids. plane polarised transmitted light. (e) detail of (b) showing frothy hematite with tiny voids (irregular black) and trevorite (trev, intermediate grey reflectance). plane polarised reflected light. (f) at the top: inclusion of magnetite (mt) with tiny inclusion of a ni-co-fe-s phase sobhi nasir 32 solid solution (white spots) and irregular inclusions of silicate alteration (sa1). silicate alteration (sa2) is also present at the exterior of the inclusion. lower half: globules with pyrrhotite (partly replaced by limonite) coexisting with ia. plane polarised reflected light. phlogopite (mg# (mg/(mg + fe) = 0.94) occurs only in inclusion m1-d (# 67, table 1). in comparison to phlogopite in associated group i xenoliths, it shows lower contents of al2o3, tio2, and na2o and higher mgo content. olivine up to 0.8 mm occurs in sample m3. this mineral is reddish in colour as if oxidized to fine-grained iddingsite. however, microprobe analyses still yield compositions close to olivine (# 68 and # 69 in table 6). variations in fe and mg content suggest a zoning of the former olivine. the chemistry of olivine is relatively similar to olivine in host basalt and associated group ii xenoliths (table 1). table 1. representative electron microprobe analyses of amphibole, phlogopite and olivine. fe2o3/feo ratio determined by mössbauer (# 61,62,63) or according to holland & blundy (1994) (# 64,65,66). krs: subcalcic kaersutite, thbl: tschermacitic hornblende, fkrs: ferro-kaersutite, phl: phlogopite, ol: olivine. i, ii, bas: representative mineral analyses from group i and ii xenoliths and basalts from the same area (nasir, 1992, 1995). multiphase mineral inclusions in ferrikaersutite megacrysts 33 clinopyroxene is diopsidic in composition (wo45-46en33-42 fs10-19) in inclusions m1-b and m1-c (figure 5 b-c # 53-54, table 2) whereas that from inclusions m2-e and m3-c (figures 4e and 4c, # 55-56) is augitic (wo36-42en 46-53fs9-10) according to the pyroxene nomenclature of morimoto et al. (1988). the mg# of clinopyroxenes from megacrysts m1 (# 53-54) varies between 0.68 and 0.71, which is lower than the mg# of pyroxenes from host basalts and associated xenoliths (0.8-0.92). however, clinopyroxenes from inclusions m2 and m3 are similar in their mg# (0.82-0.85) to mg# (0.8-0.83) of host basalt and group ii xenoliths from the same area (nasir, 1992). orthopyroxenes were detected only in inclusions m1 (d, e, f) and m2-d (# 57 to 60, table 2). the mg# of this mineral is variable (0.81-0.92). orthopyroxene from inclusion m2-d (# 60) is poor in al2o3 (3.91 wt.%) compared with those from m1(# 57 to 59, table 2). the orthopyroxenes in the inclusions of megacryst m1 have mg# of 0.81 to 0.85, which is similar to the mg# of orthopyroxenes from associated megacryst and group ii xenoliths from the same area, while orthopyroxene from megacryst m2 (#60, table 2) is similar in mg# (0.92) to clinopyroxenes from associated group i xenoliths. plagioclase occurs only in inclusions d, e, and f (figure 3d) of the megacryst m1 (# 70 to 72, table 3). the plagioclase compositions (an73-75) are similar in all inclusions. the an-content of this plagioclase is higher than the an-content in the host basalt (an 40-50). 5.2 iron oxide minerals magnetite occurs in four compositional varieties: type (1) magnetite coexists mostly with pyrrhotite (samples m1 and m2) and shows exsolution lamellae of another type of magnetite (type 2). type1 magnetite is poor in al2o3 and mgo (#20, 27, table 4) whereas the lamellae (type 2) show higher al and mg contents (# 21 and 28, table 4). type 3 magnetite, without exsolution lamellae, coexists mostly with hematite, sulphide, ia and/or sa (# 25, 29, 33, table 4). the chemical composition of this type of magnetite is variable. type 4 magnetite coexists with hematite. it is enriched in nio and coo, and may even reach trevorite composition (# 30, table 4). primary magnetite is altered to hematite along individual cracks, particularly near open cracks or cavities (figures 3d, f, 4b, f). a representative analysis of a pseudobrookite occurring in sample m2 and m3 is given in table 4 (# 34-35). according to the calculated formula, it contains no fe2+ but a significant karooite (mgti2o5) and lesser tielite (al2tio5) component. three types of hematite have been identified. type 1 hematite occurs in iron alteration (ia) and/or silica alteration (sa) (# 36, 42, table 4) and shows only minor amounts of the ilmenite component in comparison to type 2 hematite, which is associated with magnetite (# 37, 41; table 4). type 3 hematite occurs in blebs of sa inclusions and is close to the end-member composition (# 45, table 4). 5.3 sulphide minerals pyrrhotite is the principal sulphide phase in the inclusions. in the structural formula normalised to one sulphur, the cation total ranges between 0.88 and 0.93 (# 46 to 50, table 5). in samples m1 and m2, pyrrhotite mostly occurs as single-phase inclusions (54) or ni-co-fe-s phase solid solution (33 wt.% nio and 18 wt.% coo; # 52, table 5) occurs as tiny (up to 5 µm in size) inclusions in magnetite. chalcopyrite associated with ni poor pyrrhotite was observed only in m3 (# 51, table 5). the sulphide compositions resemble those reported from sulphides in clinopyroxene megacrysts and sulphide inclusions of type-i xenoliths from several localities globally (figure 6) (zajacz and szabó, 2003). 5.4 alteration phases tables 6 and 7 summarize the electron microprobe data for the different alterations phases in the inclusions. two main types of alteration products are found: iron-rich alteration (ia) and silicate alteration (sa). analyses of sa and ia show low and variable anhydrous totals of 74 to 92 wt.% and 85 to 97 wt.% respectively. similar observations were made by stimac and hicmott (1996) and larocque et al. (2000) on comparable iron-rich inclusions. these authors attributed such low totals to the frothy nature of the inclusions. sobhi nasir 34 another and more probable reason for obtaining low totals in the microprobe analyses could be the volatile content in the alteration products of the inclusion (e.g. churikova et al. 2007). the silicate minerals (e.g. hornblende, pyroxene, phlogopite and plagioclase) are altered to fine grained products (“clay minerals and/or chlorite”), particularly in sample m2. 5.4.1 iron-rich alteration (ia) ia is associated with magnetite, hematite, or pyrrhotite inclusions. it shows high fe2o3total (80-89 wt.%), low mgo (0.23.3 wt %), and variable sio2 (12-19 wt%), cao (0.16-2.4 wt%), tio2 (0.02-0.2 wt%) contents, and contains appreciable nio (0.1-0.9 wt%). contents of alkali oxides (0.02-0.1 wt.%) are negligible (table 6). hurai et al. (1998) and larocque et al. (2000) observed similar compositional ranges for high iron glass inclusions in olivine megacrysts (table 6). however, the ia compositions in table 6 do not look like they were originally silicate melts or glasses, but are most probably iron hydroxides. figure 6. bulk sulphide compositions plotted in (a) cu-fe-(ni+co) system. (b) fe-(ni+co)-cu system. the stability field of monosulphide solid solution (mss) at 1100°c based on experimental studies by kullerud et al. (1969). (c) bulk sulphide compositions compared to compositions of sulphides in type i xenoliths and clinopyroxene megacrysts (zajacz and szabó, 2003). 5.4.2 silicate alteration (sa) the anhydrous total of sa always shows a clear deficit compared to 100% total, which is attributed to alteration of silicate minerals to hydrous phases (e.g. chlorite and/or clay minerals). during this alteration, the original composition was modified. the extent of this compositional modification is difficult to assess. four groups of sa compositions have been identified (table 7). the first (sa1) is associated with hematite and contains 41 to multiphase mineral inclusions in ferrikaersutite megacrysts 35 48 wt.% sio2 with some mgo and al2o3 as sole constituents of importance. cao is only present in subordinate amounts in sa1 (# 6 ,7; table 7). in contrast, sa occurring with magnetite (sa2) contains 36 to 44 wt.% sio2, higher al2o3 and lower mgo content. in addition, 3.7 to 7.8 wt. % of fe2o3total are present in sa2 (# 8 to 11, table 7). other oxide components are subordinate. both alteration products (sa1 and sa2) are comparable in composition to clay minerals (e.g. saponite and/or vermiculite) and thus could be mainly composed of such phases. sa3 was found mainly in m1 inclusions. it is represented by a fe-al-rich alteration product with a composition similar to fe-rich chlorite and/or chloritic alteration in terms of its fe2o3(29-42 wt.%), al2o3(19-22 wt. %), and sio2-content (21-26 wt.%). mgo, cao, tio2, mno, and alkalis are minor and range between 0.01 and 2.8 wt. % each (# 12 to 14, table 7). brownish-coloured silicate alteration (sa4) is present in open cavities and at the rims of inclusions of sample m3. under reflected light, this alteration shows abundant reddish internal reflections pointing to the presence of fe3+-rich minerals. sa4 is similar in composition to the kaersutite host. remarkable is the relatively high content of tio2 in sa4, ranging between 5.4 and 6.2 wt.% (# 15 to 19, table 7). the main chemical variability of sa4 concerns the fe2o3 content ranging between 13.9 and 20.0 wt. %. 6. discussion kaersutite crystallizes from mafic and ultramafic melts at medium pressures, somewhat below 10 kbar, high temperatures (>950oc) and moderate oxygen fugacity (oba, 1997; ernst and liu, 1998). hops et al., (1992) proposed a model of megacryst formation from localized melt segregations within the lithosphere. boettcher and o'neil (1980) and ionov et al., (1997) presented evidence that metasomatism of upper mantle lherzolite by aqueous fluids rich in tio2, k2o and feo is responsible for the production of kaersutite. conformably, studies of mantle xenoliths from jordan and syria show that the formation of the harrat ash sham volcanic field over the last 40 million years was accompanied by extensive mantle metasomatism (altherr et al 1990; nasir ,1992; nasir and safarjalani, 2000). henjes-kunst et al. (1990) showed that the lithospheric mantle beneath the arabian peninsula formed from the same source as the overlying juvenile crust – at about 700 ma. henjes-kunst et al. (1990) identified two metasomatic events in the sub-continental lithosphere, the second of which they related to mantle processes connected to the formation of the red sea. the megacryst suite of the harrat ash sham volcanic field comprises large unzoned single grains of clinopyroxene, orthopyroxene, spinel and kaersutite. these megacrysts have a limited range of compositions (nasir, 1995). major and trace-element partitioning in the kaersutite megacrysts indicates that they equilibrated with their host magmas (nasir, 1995). the monomineralic nature of the megacrysts suite, their large size and homogeneity, and their uniform composition suggest crystallization from a hydrous melt. the megacryst assemblages are interpreted as high-pressure phenocrysts associated with the formation and partial crystallization of a hydrous basanitoid melt at depth. the abundant presence of kaersutite and its association with other phases implies the formation of a hydrous melt at a depths estimated to be 40-50 km (nasir and safarjalni, 2000). (this hypothesis is very testable by comparing ree and trace element patterns of megacrysts with basanite ree and trace element patterns). the mineral composition of primary minerals (magnetite, pyrrhotite) of the inclusions in the three kaersutite megacrysts are extremely heterogeneous both in terms of phase compositions and phase proportions. the inclusions lack a visible melt and fluid phase (i.e. h2o, co2). however, the former presence of a fluid phase may be assumed because of the regular presence of one or more deformed cavities (voids) within most inclusions (figures 3-5). the formation of solid inclusions in these kaersutites as manifested by the typical round to oval shapes could be due to trapping of melt residue from the basanitoid magma which may have penetrated the fractured kaersutite during crystallisation. the spherical shape of some magnetite inclusions and some negative crystal-shaped oriented inclusions suggests their enclosure during the growth of the host amphibole. formation of some inclusions contemporaneous with the growth of kaersutite is an attractive explanation because of the parallel arrangement of the long axes of inclusions (figure 4) which may represent former kaersutite growth planes as proposed by andersen et al. (1987) and zajacz and szabó (2003). however, from the textural descriptions and the bse images (figures 3 to 5) it appears that most inclusions are secondary in origin, i.e. trapped along cracks in kaersutite after it had already crystallised. (could rod-like inclusions reflect exsolution phenomenon?). sobhi nasir 36 some inclusions are interconnected by veins containing the same assemblages as the inclusions. these veins are interpreted as former cracks that partly exploited kaersutite cleavage planes. sub-parallel fractures combined with breaks along the cleavage divide the crystals into small fragments. in sample m3 a suite of inclusions can be observed ranging from ovoid droplets in open voids to rounded inclusions completely enclosed by amphibole (figure 5a). this observation suggests that the trapping of some of the inclusions occurred in open cracks. an additional argument for a secondary origin of most inclusion is that the host kaersutite was not in chemical equilibrium with the trapped melt. in most globules, the host amphibole-inclusion interface is not smooth but irregular and shows an intimate interlocking of silicates with kaersutite (figures 3d, e, f, and 4c, e, c). the irregular interfaces of the inclusions and veins with the host kaersutite which show resorption and melting of the host, might be connected with the infiltration and thermal effect of the basalt. table 2. representative electron microprobe analyses of pyroxenes. fe2o3/feo ratio determined from stoichiometry cpx, opx: representative clinopyroxene and orthopyroxene megacrysts, respectively from the same area (nasir, 1995). bas.: representative clinopyroxene from associated basalt (nasir, 1995), i, ii: representative clinopyroxene and orthopyroxene from group i and ii xenoliths from the same area (nasir, 1992). multiphase mineral inclusions in ferrikaersutite megacrysts 37 table 3. representative electron microprobe analyses of plagioclase. the texture of the rods and globules in the kaersutite resembles the anorthosite-calcite rods within kaersutite megacrysts described by wallace (1977) and the sub-parallel tubular voids in labradorite phenocrysts described by gutmann (1974). wallace suggested that the rods are large elongate fluid inclusions that resulted from the growth of gaseous "bubbles" on the crystal contemporaneously with the crystal growth. he interpreted the anorthoclase and calcite as secondary filling of rods in the kaersutite. gutmann (1974) suggested that the tubular voids in labradorite resulted from nucleation of a gas phase. the pyroclastic breccia of harrat as sham volcanoes, including dhanoon volcano, were the results of multiphase volatile-rich explosive eruptions (nasir and safarjalani, 2000). during eruption the kaersutite megacryst was broken up and veins and fractures were filled by melts from which silicate minerals crystallized. the kaersutite host crystals are homogeneous in composition, which implies that there were no reactions between kaersutite and the invading melt. most analyses of kaersutite, pyroxene, and olivine show them to be relatively similar in their chemistry to those in host basalt and associated group ii xenoliths, which supports the argument that most of the silicate minerals were formed through crystallisation from invading melt. however, a few analyses of silicate minerals (e.g., hornblende # 65-66, table 1, phlogopite # 67, table 1 and clinopyroxene #53-54, table 2) show them to have compositions remarkably different from the minerals of the host basalt and upper mantle xenoliths. their occurrence may reflect open system differentiation, recrystallization and/or localized decompression melting inside the inclusions which could generate mineral paragenesis different from that sobhi nasir 38 of the host basalt. mt: magnetite, mtex.: magnetite exsolution lamellae, pb: pseudobrookite, hm: hematite 1 to 4: type of magnetite, i-iii: type of hematite. fe2o3/feo ratio determined from stoichiometry. sa and ia are extremely heterogeneous both in terms of composition (tables 6-7) and included phase proportions. the ia are dominated by hematite and limonite, while the sa are dominated by chloritic phase and some other clay minerals (sa1-3), and/or kaersutite alteration (sa4). silicate alteration may represent vein-fillings crystallized from an invading melt and/or they may have formed by alteration of silicate minerals with the last, h2o-rich melt fraction. this suggests variable growth histories and/or more probably low temperature latemagmatic or subsolidus alterations of kaersutite, iron oxides and infilling silicates along the cleavage planes (figure 5), fractures (figure 6a, b, and d) and around sulphide inclusions (figure 4). magnetite is altered to hematite along cracks and cavities (figures 23, f, 5b, f). this well known martitic alteration of primary magnetite was obviously a post-trapping process. the presence of ni-rich magnetite (trevorite) inclusions in hematite may reflect such an oxidation reaction: magnetite (ss) + o2 => hematite + trevorite. table 4. representative electron microprobe analyses of iron-oxides. multiphase mineral inclusions in ferrikaersutite megacrysts 39 table 5. representative electron microprobe analyses of sulfides. po: pyrrhotite, cp: chalcopyrite, mss: ni-co-s monosulfide solid solution. table 6. representative electron microprobe analyses of iron-rich alteration (ia) in inclusions from kaersutite megacryst in comparison to high-iron glass in igneous xenoliths from the carpathians (hurai et al., 1998) and in volcanic rocks from the philippines, mexico, usa and japan (larocque et al., 2000). globule*: (a to f) refers to figures 2 to 4. c: average of 6 samples from hurai et al. (1998). pj: average of 26 samples from larocque et al. (2000). sobhi nasir 40 after formation of the host kaersutite, circulating fluids may have interacted with pre-existing inclusions. in this way, the original chemical signature of the inclusions would be lost. alteration processes such as zeolitization of the volcanic tuff (e.g., dwairi, 1998; ibrahim and hall 2004) and post-magmatic deutric iddingsitization of olivine in the host basalt and associated xenoliths is a widespread phenomenan in the harrat ash sham volcanic field (e.g., nasir and mahmood, 1991). tio2-rich silicate alteration (sa4) is present at inclusion rims of sample m3. the composition of this alteration is similar to that of the kaersutite host (# 15 to 19, table 7). the composition of the participating ti-rich silicate alteration (sa4) was probably produced by decompression melting of the kaersutite host. table 7. representative electron microprobe analyses of silicate alteration (sa). at present there seems to be no way to derive the true composition of the original precursor of the ia and/or sa because of the observed variable alterations and variable phase compositions and ratios. 7. conclusions in this paper we describe different types of primary and secondary multiphase solid inclusions in ferrikaersutite megacrysts occurring in quaternary alkali basalts from dhanoon volcano, syria. the inclusion compositions reported include silicates, sulphides, oxides, fe-richand/or silicate-alteration products. magnetite crystallised most probably from a fe-rich melt in the early phases of inclusion growth. in a later phase, pyrrhotite, hematite, trevorite, and pseudobrookite crystallized. secondary inclusions were trapped along cracks in kaersutite after crystallizaton. textures, solid mineralchemistry as well as iron-rich and silicate alterations indicate that the original compositions of the inclusions phases were further modified by low-temperature post-magmatic deutric alteration of inclusion minerals. late stage, nearsurface alteration formed limonite and fine-grained sheet silicates possibly due to interaction with the last, h2orich, melt and/or circulating fluids. multiphase mineral inclusions in ferrikaersutite megacrysts 41 8. acknowledgements s. nasir is indebted to the german academic exchange service (daad) for financial support, which enabled his residence for two months at universität stuttgart. thanks for thomas theye and h.-j. massonne for their help with the electron microprobe analysis. the author is grateful to martin okrusch, robert stern and ghaleb jarar who made constructive suggestions to improve the manuscript. thanks are also due to j. touret for his help with finding fluid inclusions in polished section. 9. references al-mishwat, a., nasir, s. 2003. composition of the lower crust of the arabian plate: a xenolith perspective. lithos, 72: 45-72. altherr, r., henjes-kunst, f. and baumann, a. 1990. asthenosphere versus lithosphere as possible sources for basaltic magmas erupted during formation of the red 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e., szabó, c. and szakal, a. 2003. sr-barite droplets associated with sulfide blebs in clinopyroxene megacrysts from basaltic tuff (szentbekkalla: western hungary). lithos, 66: 275-289. wallace ,c. 1977. anorthoclase-calcite rodding within kaersutite xenocryst from the kakanui mineral breccia, new zealand. am. mineral. 62: 1038-1041. zajacz, z., and szabó, c. 2003. origin of sulfide inclusions in cumulate xenoliths from nograd-gomِorِ volcanic field pannonian basin (north hungary/south slovakia). chem. geol. 194: 105-117. received 9 february 2009 accepted 7 april 2009 microsoft word math040908-f.doc 77-92 squ journal for science, 10 (2005) © 2005 sultan qaboos university 77 realization in generalized state space form for 2-d polynomial system matrices *m.s. boudellioua and **b. chentouf department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, al-khod 123, sultanate of oman, email: *boudell@squ.edu.om, **chentouf@squ.edu.om. تحقيق مصفوفات كثيرات الحدود الممثلة للنظم ثنائية البعد في شكل مجال الحاالت العام محمد الصالح بودليوة و بومدين شنتوف في هذه الورقة يتم تقديم طريقة مباشرة لتحويل مصفوفة نظام عامة عناصرها كثيرات حدود ثنائية البعد :خالصة التحويل يحافظ على الخاصيات الهامة بما فيها البنية الصفرية لمصفوفة النظام هذا . إلى شكل مجال الحاالت العام مع تحديد طبيعـة (zero coprime system equivalence)وتبين الورقة أن هذا التحويل هو تكافؤ . األصلية .المصفوفة الناتجة عن هذا التحويل وطبيعة مصفوفات التحويل نفسه abstract: in this paper, a direct realization procedure is presented that brings a general 2-d polynomial system matrix to generalized state space (gss) form, such that all the relevant properties including the zero structure of the system matrix are retained. it is shown that the transformation linking the original 2-d polynomial system matrix with its associated gss form is zero coprime system equivalence. the exact nature of the resulting system matrix in gss form and the transformation involved are established. keywords: 2-d systems, system matrix, generalized state space form, zero coprime system equivalence, invariant polynomials, invariant zeros, grobner bases. 1. introduction tate space models play an important role in the theory of 1-d finite-dimensional linear systems. in recent years attempts have been made toward extending the state space representation to more general systems, e.g. time-delay systems or systems described by partial differential equations. another extension from 1-d to 2-d is the discrete linear state space model which has a number of variants as given by givone and roesser (1972), attasi (1973) or fornasini and marchesini (1976). one of the limitations of these models is that they can only be used to describe 2-d proper transfer functions. in other words, they are suitable only for the representation of northeast quarter plane 2-d systems. several authors have suggested a generalized state space description for 2-d systems. zak s m.s. boudellioua and b. chentouf 78 (1984) suggested a generalized model based on roesser’s model while kaczorek (1988) proposed a model based on that of fornasini-marchesini. the natural description of a system is not necessarily in a state space form, and it is often desirable to reduce such a description into a simpler but equivalent form. the reduction of an arbitrary 2-d polynomial system matrix to 2-d generalized state space (gss) form was first studied by pugh et al. (1998). their algorithm involves the application of a two stage reduction procedure which includes the removal of factors from certain matrices to ensure that the transformations linking the original system matrix with the final gss form are polynomial. the method does not give a priori the form of neither the resulting 2-d gss system matrix nor the transformation linking it to the original 2-d polynomial system matrix. in the present work, we present a direct and simple procedure for the realization of a 2-d polynomial system matrix by an equivalent 2-d polynomial system matrix in gss form. the exact nature of the resulting gss system matrix and the transformation linking it with the original system matrix will be given. the transformation linking the original system matrix to its corresponding gss form is shown to be zero coprime system equivalence. this type of equivalence has been studied by levy (1981), johnson (1993) and pugh et al. (1996) and has been shown by pugh et al. (1998) to provide the connection between all least order polynomial realizations of a given 2-d transfer function matrix. 2. 2-d system matrices and system equivalence consider the 2-d system matrix in the general form: ( ) ( ) ( )( ) ( ) , , , , , t s z u s z p s z v s z w s z = − ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ (2.1) where t(s,z), u(s,z), v(s,z) and w(s,z) are respectively r×r, r×n, m×r and m×n polynomial matrices with t(s,z) invertible, in which case the system matrix in (2.1) is said to be regular. the transfer function matrix of the system matrix in (2.1) is given by g(s,z) = v (s,z)t-1(s,z)u(s,z) +w(s,z) (2.2) a special case of (2.1) is obtained from the system described by the following 2-d generalized state space discrete equations (kaczorek 1988), ex(i + 1, j + 1) = ( ) ( )1 21 1, ,a x i j a i jx+ + + + ( ),a x i j + b1u(i + 1, j) + b2 u(i, j + 1) + b0 u(i, j), (2.3a) y(i, j) =cx(i, j) + du(i, j) (2.3b) where x(i,j) is the state vector, u(i,j) is the input vector, y(i,j) is the output vector, 1 2 1 2, , , , , ,e a a a b b b , c and d are constant real matrices of appropriate dimensions and e may be singular. then, taking the 2-d z-transform of (2.3a) and (2.3b) and assuming zero boundary conditions yields ( ) ( ) ( ) 1 2 0 1 2 0 0, ,, b b b x s z d y s zu s z sze sa za a s z c − − − + + = − −− ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦⎣ ⎦⎣ ⎦ (2.4) the polynomial matrix over [ ],s zr , realization in generalized state space form 79 ( ) 1 2 0 1 2 0, sze sa za a sb zb b p s z c d − − − + + = − ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ (2.5) in (2.4), is a system matrix in gss form and the corresponding transfer function is given by g(s,z) = c(sze sa1 za2 a0) -1(sb1 + zb2 + b0) + d (2.6) definition 2.1 two polynomial matrices p1(s,z) and s1(s,z) of appropriate dimensions, are said to be zero left coprime if the matrix [p1(s,z) s1(s,z)] (2.7) has full rank for all (s,z) ∈ c 2. similarly, p2(s,z) and s2(s,z), of appropriate dimensions, are said to be zero right coprime if the matrix ( ) ( )2 2, , tt tp s z s s z⎡ ⎤⎣ ⎦ (2.8) has full rank for all (s,z) ∈ c 2. following the results of youla and gnavi (1979), it follows that the polynomial matrices p1(s,z) and s1(s,z) are zero left coprime if and only if there exist zero right coprime polynomial matrices x(s,z) and y (s,z) of appropriate dimensions satisfying the bezout’s relation p1(s,z) x(s,z) + s1(s,z)y (s,z) = i (2.9) one immediate result given by sontag (1980) is that a necessary and sufficient condition for the matrices p1(s,z) and s1(s,z) to be zero left coprime is that the matrix in (2.7) is unimodular equivalent to the matrix [ i 0 ]. similar results can be stated for zero right coprime matrices. definition 2.2 given a p×q polynomial matrix p(s,z), the ith order invariant polynomial φi(s,z) of p(s,z) is defined by : ( ) ( ) ( ) ( )1 , 1 ,, 1 min , 0 i ii d s z if i t d s zs z if i p q φ − ≤ ≤ ≤ ≤ ⎧ ⎪ = ⎨ ⎪ ⎩ (2.10) where t is the normal rank of ( ) ( )p , d , 1,s z s z = , d0(s,z) =1 and di(s,z) is the greatest common divisor of all the ith order minors of the given matrix p(s,z). as in 1-d case, the zero structure of 2-d systems is a crucial indicator of the system behavior. zerz (1996) has shown that the controllability and observability of a system is connected to the zero structure of the associated polynomial matrix. however, unlike the 1-d case, the zero structure of a multivariate polynomial matrix is not completely captured by the invariant polynomials. therefore the following concept of invariant zeros as given by pugh and el-nabrawy (2003) is introduced. definition 2.3 given a p×q polynomial matrix p(s,z), the ith order invariant zeros of p(s,z) are the elements of the variety v r (i i [p]) defined by the ideal [ ]pii generated by the ith order minors of m.s. boudellioua and b. chentouf 80 p(s,z). definition 2.4 let p (m,n) denote the class of (r+m)×(r+n) polynomial matrices where m, n are fixed positive integers and r>min(m, n). two polynomial system matrices p1(s,z) and p2(s,z) are said to be zero coprime equivalent if there exist polynomial matrices s1(s,z), s2(s,z) of appropriate dimensions such that ( ) ( ) ( ) ( )2 1 2 1, , , ,s s z p s z p s z s s z= (2.11) where p1(s,z), s1(s,z) are zero left coprime and p2(s,z), s2(s,z) are zero right coprime. pugh et al. (1996) and pugh and el-nabrawy (2003) have shown that zero coprime equivalence exhibits fundamental algebraic properties amongst its invariants: lemma 2.1 (pugh et al. 1996) suppose that two polynomial matrices p(s,z) and q(s,z)∈ p (m, n), are related by zero coprime equivalence and let [ ] [ ] [ ]1 2, , , p p p hφ φ φ… ,where h min= [ ] [ ]( ),p pr m r n+ + , denote the invariant polynomials of ( ),p s z and [ ] [ ] [ ]1 2, , , q q q kφ φ φ… , where [ ] [ ]( ),q qk min r m r n= + + , denote the invariant polynomials of q(s,z), then [ ] [ ] ( )for 0,1, , 1, 1p qh i i k ic i max k hφφ − − = − −= … (2.12) where [ ] [ ] { }1, 1 for any 1, \ 0p qj j ij c rφ φ < ∈= = lemma 2.2 (pugh and el-nabrawy 2003) suppose that two polynomial matrices p(s,z) and q(s,z) ∈ p (m,n),are related by zero coprime equivalence and let [ ] for 1, , pji j h= … [ ] [ ]( )min ,p pr m r n= + + denote the ideal generated by the j×j minors of p(s,z) and [ ],qii for [ ]( )1, , min qi k r n= = +… denote the ideal generated by the i×i minors of q(s,z). then [ ] [ ] 0, , ,p qh i k ii i i h− −= = … (2.13) where ( ) [ ]min 1, 1 and for any 1 in case or ., ph ih h k i h i i h i k−= − − > = < < a basic transformation proposed for the study of 2-d systems is zero coprime system equivalence given by levy (1981) and johnson (1993). this transformation, based on zero coprime equivalence is characterized by the following definition. definition 2.5 two polynomial system matrices p1(s,z) and p2(s,z) ∈ p (m,n), are said to be zero coprime system equivalent if they are related by the following ( ) ( ) ( )1 , 0 , , m m s z x s z i s s z ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ( ) ( ) ( ) ( ) ( )2 1 1 1 1 , , , , , t s z u s z v s z w s z p s z − ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ realization in generalized state space form 81 ( ) ( ) ( ) ( ) ( )1 2 2 2 2 , , , , , t s z u s z v s z w s z p s z = − ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ( ) ( ) ( )2 , , 0 , n n s z y s z i s s z ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ (2.14) where p1(s,z), s1(s,z) are zero left coprime and p2(s,z), s2(s,z) are zero right coprime and m(s,z), n(s,z), x(s,z) and y(s,z) are polynomial matrices of appropriate dimensions. the transformation of zero coprime system equivalence is an extension of fuhrmann’s strict system equivalence from the 1-d to the 2-d setting and has been shown by levy (1981), johnson (1993) and pugh et al. (1996, 1998) to preserve important properties of the system matrix p(s,z) and plays a key role in certain aspects of 2-d systems theory. lemma 2.3 (johnson 1993) the transformation of zero coprime system equivalence preserves the transfer function and in the sense described in lemma 2.1, the invariant polynomials of the matrices: • ti(s,z), i = 1, 2. • pi(s,z), i = 1, 2. • [ti(s,z) ui(s,z)], i = 1, 2. • ( ) ( ), , 1, 2, . tt t i it s z v s z i− =⎡ ⎤⎣ ⎦ the following lemma is a direct consequence of lemmas 2.2 and 2.3. lemma 2.4 the transformation of zero coprime system equivalence preserves, in the sense described in lemma 2.2, the invariant zeros of the matrices given in lemma 2.3. 3. realization in 2-d generalized state space form let ( ) ( ) ( ) [ ], ,r m r np s z s z+ × +∈ r be a 2-d polynomial system matrix given by (2.1). first write p(s,z) as ( ) 0 0 0 1 0 2, 0,0 0,1 0,2 , 0 0 , p q i j p q i j p q i j p s z p s z p s z p s z p s z p s z = = = = + + + +∑∑ … (3.1) where pi,j , i = 0, 1, ..., p and j = 0, 1, ..., q are (r + m)× (r + n) real constant matrices. now construct the block matrices ( )( ) ( )1 , 1 1 0 r n pq r n pq q q e e e e + − + − = ⎡ ⎤ ⎢ ⎥ ⎢ ⎥⎣ ⎦… (3.2a) where , 1, 1, 1, 2, ,, .j p j p j je p p p j q−= =⎡ ⎤⎣ ⎦ … (3.2b) ( )( )( )0 0,01 ,r n pqa diag i p+ −= − − , (3.3) m.s. boudellioua and b. chentouf 82 ( ) ( ) ( ) ( )( ) ( )( ) ( )( ) ( ) ( ) ( ) 1 , 1 1 , 1 1 ,0 1,0 1,0, 1 0 0 0 r n p q r n pq r n p r n pq p r n p p pr m r n p q a i p p p + − + + − + − + + − −+ + − = − − − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ , (3.4) and ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) 1 , 1 2 1 , 2, 2, 1 2,1 0 0 r n p q r n p r n p q r n p r n pq q q i a a a a + − + + − + − + − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ (3.5a) where ( ) ( )( )2, o,, 10 1, 2, , .,j jr m r n pa p j q+ + −= − =⎡ ⎤⎣ ⎦ … (3.5b) theorem 3.1 let the matrices e, a0, a1 and a2 be as constructed in (3.2a), (3.3), (3.4) and (3.5a), respectively. then the [(r +n)pq +2m]×[(r +n)pq +m+n] polynomial system matrix is in gss form (2.5):] ( ) 1 2 0 0 , 0 0 0 m n n m sze sa za a z q s z z i i − − − − − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (3.6) where ( ),0n nn r n pq r m nz i⎡ + + + − ⎤⎣ ⎦ = ⎡ ⎤ ⎣ ⎦ and ( ),0 t m mm r n pq m z i ⎡ + − ⎤⎣ ⎦ = ⎡ ⎤ ⎣ ⎦ is related to the original system matrix p(s,z) by the following : ( ) ( ) ( ) ( )1 2, , , ,s s z p s z q s z s s z= (3.7) where ( ) ( )( ) ( )( ) ( ) ( ) ( ) 1 1 , 1 , 2 , 1 2 , , , , 0 0 0 , , 0 0 0 0 , r n pq r r n pq m r r m qm n r m n m m r m n r n y y i s s z s s z y v wi i + − + − + + = = − ⎡ ⎤ ⎢ ⎥⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎢ ⎥⎣ ⎦ (3.8) 1 2 , tp q j p q j q j j r ny s z s z z i − − − − − +⎡ ⎤= ⊗⎣ ⎦ (3.9) where j = 1, 2, . . . , q and ⊗ denotes the matrix kronecker product. proof. the matrix q(s,z) in (3.6) can be represented in the form realization in generalized state space form 83 ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 0 0 0 0 0 0 0 0 0 , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p r n p r n p r n p r n p r n q q m n n m i zi i q s z i zi q q q q z z i i + + + + + − − = − − − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (3.10) where 1 ,1 ,0 1,1 10 1,1 1,0 0,1 0,0 0 0 0 0 0 , r n r n r n r n p p p p i si i q si szp sp szp sp szp sp zp p + + + + − − − = − + + + + + ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (3.11) , 1, 2, 1, 0, 0 0 0 0 0 0 0 0 2, 3, , 0 0 0 0 ,j p j p j j j j q j q szp szp szp szp zp− = = + ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ … (3.12) and ( ) ( )( ), , 10 0, t n n m mn p r n n m p r n rz i z i+ − − + += =⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ (3.13) and the matrix s2(s,z) can be written as m.s. boudellioua and b. chentouf 84 ( ) 1 1 2 1 1 1 2 2 2 2 2 , 0 p q r n p q r n q r n p q r n p q r n q r n r n n s z i s z i z i s z i s z i s s z z i i v w i − − + − − + − + − − + − − + − + + = − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ (3.14) from which it can be easily verified that ( ) ( ) ( ) ( ) ( )( ) ( )( )1 , 1 , 1 2 , , 0 0 , , , , 0 0 r n pq r r n pq n m n r m n n t u s s z p s z q s z s s z v w + − + − + + ≡ − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥= ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ (3.15) lemma 3.1 the matrices in (3.7), q(s,z) and s1(s,z) are zero left coprime and p(s,z) and s2(s,z) are zero right coprime. proof. the matrix [ q(s,z) s1(s,z) ] is given by ( ) ( ) ( ) ( ) ( ) 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 p r n p r n p r n rp r n p r n q q m n n m m i zi i i zi i q q q q z z i i i + + + + + − − − − − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ (3.16) it can be easily seen that the minor obtained by deleting the columns( )( )1r n pq+ − 1,+ ( ), r n+… pq from the matrix in (3.16) is equal to ±1. realization in generalized state space form 85 similarly, the matrix ( ) ( )2 , , p s z s s z ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ is given by ( ) 1 2 1 2 , , 0 p r n p r n r n n r n p s z y y s i s i i v w i − + − + + − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ (3.17) it is clear that the matrix in (3.17) contains a block identity matrix ir+n, and therefore it has the highest order minor which is equal to 1. theorem 3.2 if p(s,z) is an arbitrary (r+m)×(r+n) polynomial system matrix over [ ]s,zr given by (2.1) and q(s,z) is the corresponding [(r+n) pq+2m]×[(r+n) pq + m + n] 2-d system matrix in gss form (3.6), then p(s,z) and q(s,z) are zero coprime system equivalent. proof. the result follows immediately from theorem 3.1 and lemma 3.1. 4. example consider the system matrix ( ) [ ]2 2, ,p s z s z×∈ r given by ( ) ( ) ( ) ( ) ( ) , , , , , t s z u s z p s z v s z w s z ≡ − ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ (4.1) where t(s,z) =(z2 + 1)s2 (2z2 z 3)s + z2 4z + 1, (4.2a) u(s,z) =(z2 z)s2 (z2 2)s + z2 – z, (4.2b) v(s,z) = (z + 2)s2 + (z2 z)s + 4z + 1, (4.2c) w(s,z) =(2z2 z)s2 + 5zs + z2 z + 3 (4.2d) here r = m = n = 1 and p = q = 2. using maple, the transfer function of the system matrix p(s,z) is given by : m.s. boudellioua and b. chentouf 86 [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 2 2 3 2 4 4 3 2 3 4 3 2 4 3 3 2 , 1 2 3 4 1 2 3 2 4 4 2 6 13 2 4 2 2 3], [ p g s z z s z s z z z z z s z z z z s z z z s z z z s z z z z − = + − − − + − + × − + − + − + − − − − + + − + + + − − + ⎡ ⎤ ⎣ ⎦ (4.3) the invariant polynomials of p(s,z) are computed as : [ ] [ ] ( ) ( ) ( ) ( ) 1 4 3 2 4 4 3 2 3 2 4 3 2 2 4 3 2 4 3 2 1 2 2 3 8 8 4 2 16 13 12 3 2 24 13 11 5 14 3, p p z z z z s z z z s z z z z s z z z z s z z z z φ φ = = − + + + − + + − + − + + + + − + − + + + − + − + (4.4) the reduced grobner bases of the ideals generated by the minors of the matrices in lemma 2.2 associated with p(s,z) are given by : matrix order of i minors ideal generated by the i i× minors ( ) ( ), ,t s z u s z⎡ ⎤⎣ ⎦ 1 8 7 6 5 4 3 2 7 6 5 4 3 2 2 11 32 39 2 19 4 4 16 3 6 35 98 137 50 27 10 , z z z z z z z z s z z z z z z z − + − + − − − + + − + − + − − + ( ) ( ) , , t s z v s z− ⎡ ⎤ ⎢ ⎥ ⎢ ⎥⎣ ⎦ 1 8 6 5 4 3 2 7 6 5 4 3 2 17 35 22 103 29 114 9 179880 1879 1563 37934 93203 202249 68516 12719 102237 , z z z z z z z s z z z z z z z + − + + − − − + − + − + − − + ( ),p s z 1 1 realization in generalized state space form 87 ( ),p s z 2 ( ) ( ) ( ) ( ) 4 3 2 4 4 3 2 3 4 3 2 2 4 3 2 4 3 2 2 2 3 8 8 4 2 16 13 12 3 2 24 13 11 5 14 3 z z z z s z z s z z z z s z z z z s z z z z z + + − + + + − + + − + − + + + + − + − + + − + − writing p(s,z) in the form (3.1), ( ) 0 ,0 0 ,1 0 ,2 1,1 1,21,0 2 ,0 0 0 0 1 0 2 1 0 1 1 1 2 0 0 1 0 4 1 1 1 , 1 3 4 1 0 1 3 2 1 0 2 1 0 0 1 5 1 0 1 0 0 1 2 0 p p p s z s z s z s z p p p s z s z s z p s z p − = + + − − − − − + + + − + + ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ 2 ,1 2 ,2 2 1 2 21 1 1 1 0 2 s z s z p p + ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦ (4.6) and constructing the 10×10 polynomial system matrix in gss form q(s,z) corresponding to (3.6) gives ( ) ( ) ( )( ) ( ) 4 4 2 1 1 1 0 0 0, , , 0 0 1, , 0 0 1 0 t i zi q q zt s z u s z q s z zv s z w s z ≡ − −⎡ ⎤ ⎢ ⎥−⎡ ⎤ ⎢ ⎥≡⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎢ ⎥ ⎢ ⎥⎣ ⎦ (4.7) where 2 2 1 2,1 2,0 1,1 1,0 0,1 0,0 1 0 0 0 1 0 3 4 1 2 4 1 5 3 2 i si q szp sp szp sp zp p s s s sz sz s z s z sz s sz sz z sz z − ≡ + + + + − − = − + − + − + − − − − + ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (4.8) (4.5) m.s. boudellioua and b. chentouf 88 2,2 2,2 2 2,2 1,2 0,2 0 0 0 0 0 0 0 0 0 0 2 0 2 q szp szp zp sz sz sz sz z sz sz z ≡ = + − − + − ⎡ ⎤ ⎢ ⎥⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥ ⎣ ⎦ (4.9) and 1 1z z= is the fourth column of i4. the matrices e, a0, a1 and a2 corresponding to (3.2a, 3.3, 3.4 and 3.5a) are given by 6,2 6,2 6,2 6,26,4 6,4 2,2 1,2 2,1 1,12 1 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 0 1 1 0 0 2 1 0 1 1 1 5 e p p p pe e ≡ ≡ = − − − − − ⎡ ⎤⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ , (4.10) 6 0 0,0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 3 i a p − − − − = −− − − − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ −⎡ ⎤ ⎢ ⎥≡ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ , (4.11) 4,4 4,2 4,2 1 2,4 2,2 2 2,4 2,0 1,0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 3 2 0 0 0 0 2 0 0 0 a i p p ≡ = − − − − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ , (4.12) realization in generalized state space form 89 2,2 2,2 2 2,2 4,4 4 2,2 2,2 2,2 2 2 2,4 2,4 2,2 2,2 2,2 2,2 2,2 2,1 2,2 0,2 2,2 0,1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 4 1 0 0 0 1 0 0 4 1 i i i a a a p p ≡ ≡ = − − − ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ − −⎢ ⎥⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ (4.13) by virtue of theorem 3.1 and theorem 3.2, the polynomial matrix p(s,z) in (4.1) and the corresponding system matrix in gss form q(s,z) in (4.7) are related by the zero coprime system equivalence transformation s1(s,z)p(s,z) = q(s,z)s2(s,z), where ( ) 6,1 6,1 1 2,1 2,1 0 0 1 0 , 0 0 0 1 s s z = ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ , (4.14) and ( ) ( ) ( ) ( ) 2 2 2 2 2 2 0 0 0 0 0 , 0 1 0 0 1 2 4 1 2 5 3 0 1 sz sz z z s s s z s z s z z s z z z s sz z z = + − + − − − + + − + ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ , (4.15) in fact it can be easily verified that m.s. boudellioua and b. chentouf 90 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 6,1 6,1 1 2 2,1 2,1 0 0 , , , , , , 0 0 , , t s z u s z s s z p s z q s z s s z v s z w s z = ≡ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ −⎣ ⎦ (4.16) where t(s,z), u(s,z), v(s,z) and w(s,z) are given by (4.2a), (4.2b), (4.2c) and (4.2d), respectively. the matrices q(s,z), s1(s,z) are zero left coprime and the matrices p(s,z), s2 (s,z) are zero right coprime since the matrices [ q(s,z) s1(s,z) ] and ( ) ( )2 , , p s z s s z ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ have respectively a 10×10 and a 2×2 minor which is equal to 1. the transfer function of the system matrix q(s,z) is given by : [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] ( ) 1 2 2 2 2 3 2 4 4 3 2 3 4 3 2 4 3 3 2 , 1 2 3 4 1 2 3 2 4 4 2 6 13 2 4 2 2 3] , [ q p g s z z s z z s z z z z z s z z z z s z z z s z z z s z z z g s z − = + − − − + − + × − + − + − + − − − − + + − + + + − − + = ⎡ ⎤ ⎣ ⎦ (4.17) and the invariant polynomials of q(s,z) are : [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] ( ) ( ) ( ) [ ] 1 2 3 4 5 6 7 8 9 1 4 3 2 4 4 3 2 3 10 4 3 2 2 4 3 2 2 1 2 2 3 8 8 4 2 16 13 12 3 5 14 3 , q q q q q q q q q p q p z z z z s z z z s z z z z s z z z z φ φ φ φ φ φ φ φ φ φ φ φ = = = = = = = = = = = − + + + − + + − + − + + + + − + − + = (4.18) realization in generalized state space form 91 the reduced grobner bases of the ideals generated by the minors of the matrices in lemma 2.2 associated with q(s,z) are given by: matrix order i of minors ideal generated by the i × i minors 1, , 8i = … 1 [ t(s,z) u(s,z) ] 9 8 7 6 4 3 2 7 6 5 4 3 2 2 11 32 39 2 19 4 4, 16 3 6 35 98 137 50 27 10 z z z z z z z z s z z z z z z z + + − + − + − − − − + − + − − + 1, , 8i = … 1 ( ) ( ) , , t s z v s z− ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ 9 8 6 5 4 3 2 7 6 5 4 3 2 17 35 22 103 29 114 9, 179880 1879 1563 37934 93203 202249 68516 12719 102237 z z z z z z z s z z z z z z z + − − + − + − + − − + − + + − ( ),q s z 1, , 9i = … 1 ( ),q s z 10 ( ) ( ) ( ) ( ) 4 3 2 4 4 3 2 3 4 3 2 2 4 3 2 4 3 2 2 2 3 8 8 4 2 16 13 12 3 2 24 13 11 5 14 3 z z z z s z z z s z z z z s z z z z s z z z z + + − + − − + + + − + − + + + + + + + + − + − (4.19) which is in accord with lemmas 2.3 and 2.2. 5. conclusions in this paper, a new direct reduction procedure to obtain a realization in gss form for an arbitrary 2-d polynomial system matrix has been presented. the numerical operations required to determine the gss form are simple. the exact connection between the original system matrix with its corresponding gss form has been set out and shown to be zero coprime system equivalence. the zero structure of the original polynomial system matrix is preserved making it possible to analyze the polynomial system matrix in terms of its associated gss form. the resulting 2d system matrix may be larger in size than the one obtained by the algorithm used by pugh et al. (1998), however, the method presented in this paper has the advantage of providing a priori both the final 2-d system m.s. boudellioua and b. chentouf 92 matrix in gss form and the transformation relating it to the original polynomial system matrix. to reduce the size of the resulting system matrix while preserving its gss form, a constant zero coprime system equivalence transformation may be used. 6. acknowledgment the authors wish to express their thanks to sultan qaboos university (oman) for their support in carrying out this research work and to the anonimous reviewers for their helpful comments. 7. references attasi, s. 1973. systemes lineaires a deux indices, technical report 31, iria. fornasini, e. and marchesini, g. 1976. state space realization theory of two-dimensional filters, ieee trans. autom. control ac-21, 4: 484-492. fuhrmann, p.a. 1977. on strict system equivalence and similarity, int. j. control 25(1): 5– 10. givone, d.d. and roesser, r.p. 1972. multidimensional linear iterative circuitsgeneral properties, ieee trans. computers ac-21, 10: 1067-1073. johnson, d.s. 1993. coprimeness in multidimensional system theory and symbolic computation, phd thesis, loughborough university of technology, uk. kaczorek, t. 1988. the singular general model of 2-d systems and its solution, ieee trans. autom. control 33, 11: 1060-1061. levy, b.c. 1981. 2-d polynomial and rational matrices and their applications for the modelling of 2-d dynamical systems, phd thesis, stanford university, usa. pugh, a.c. and el-nabrawy, e.m.o. 2003. zero structures of n-d systems, proceedings mediterranean conference on control and automation, rhodes (greece). pugh, a.c., mcinerney, s.j., m. hou and hayton, g.e. 1996. a transformation for 2-d systems and its invariants, in proceedings of the 35th ieee conference on decision and control, kobe (japan). pugh, a.c., mcinerney, s.j., boudellioua, m.s., johnson, d.s. and hayton, g.e. 1998. a transformation for 2-d linear systems and a generalization of a theorem of rosenbrock, int. j. control, 71(3): 491-503. pugh, a.c., mcinerney, s.j., boudellioua, m.s. and hayton, g.e. 1998. matrix pencil equivalents of a general 2-d polynomial matrix, int. j. control, 71(6): 1027-1050. sontag, e.d. 1980. on generalized inverses of polynomial and other matrices, ieee trans. autom. control ac-25(3): 514-517. youla, d.c. and gnavi, g. 1979. notes on n-dimensional system theory, ieee trans. circuits and systems cas-26(2): 105-111. zak, s.h. 1984. on state-space models for systems described by partial differential equations, in proceedings of the 33rd ieee conference on decision and control, las vegas (usa). zerz, e. 1996. primeness of multivariate polynomial matrices, systems and control letters 29: 139-145. received 8 september 2004 accepted 20 july 2005 squ journal for science, 2019, 24(1), 11-17 doi: 10.24200/squjs.vol24iss1pp11-17 sultan qaboos university 11 preliminary investigations of allelopathic effects and herbicide-based eradication of mesquite (prosopis juliflora) salim s. al-abdali, azan s. al-dhuhli, hassan a. al-reasi* department of biology, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *email: alreasi@squ.edu.om. abstract: velvet mesquite, locally known as al-ghaf bahri (prosopis juliflora), is a well-known invasive alien plant species in several regions around the world, including oman, with various environmental effects. the allelopathic effect of p. juliflora leaves and seed pods on native ghaf (p. cineraria) and a crop species, mung bean (vigna radiata) was demonstrated. results indicated that p. juliflora extracts have inhibitory effects on seed germination and seedling growth of both species, particularly on p. cineraria when exposed to pod extracts. for eradication experiments, three herbicides (tribenuron methyl, clethodim and 2,4-d & mcpa) were investigated to determine their inhibitory properties on seed germination, and on the growth and development of young seedlings of p. juliflora. generally, germination time (gt50, time required for 50% of seeds to germinate) and germination percentage (%) indicated that only 2,4-d & mcpa treatment showed a significant effect on inhibiting seed germination and stopping seedling growth relative to the other two herbicides. the effect of 2,4-d & mcpa was supported by significant reduction in above-ground fresh biomass. the data clearly illustrate the potential negative effects of p. juliflora on other plant species and its tolerance of herbicide treatment. on a farm scale, limited application of 2,4-d & mcpa on young p. juliflora seedlings would be recommended as an effective way to limit further spread and distribution and consequently to successfully eliminate this invasive alien plant. keywords: invasive alien species (ias); prosopis juliflora; allelopathic effect; eradication; herbicides. األعشاب مبيداتب لقضاء عليهاوا التضاد الكيميائيب (المسكيت) الدخيلة لنباتاتا تأثيرالتقصي األولي ل سالم صالح العبدلي وعزان سعيد الذهلي وحسن علي الريسي البيئية باألضرار المعروفة الدخيلة النباتات أنواع من نوع هو( prosopis juliflora) البحري الغاف باسم محليًا المعروف أو المخملي المسكيت :صلخمال وحوافظ أوقرون بذور الغاف أوراق لمستخالصاتالتضاد الكيميائي تأثير إثبات تم. عمان سلطنة ذلك في بما العالم حول المناطق من العديد في المختلفة إلى النتائج أشارت(. vigna radiata) بقلة الماش أو اللوبياء الخضراء وهو المحاصيل وأحد أنواع( p. cineraria) المحلي الغاف على كل من البحري عند تعرضها لمستخالصات الحوافظ أو المحلي الغاف خاصة النوعين، لكال البادرات ونمو البذور إنبات تعمل على تثبيط البحري الغاف مستخلصات أن لمنع دي وإم سي بي أي( -٢,٤كليثوديم ووتريبينورون )ميثيل ال تم فحص ثالثة مبيدات عشبية فيما يتعلق بتجارب القضاء على الغاف البحري، .القرون ونسبة (البذور من٪ ٠٥ إلنبات لنسبة الالزم الوقت ،gt50) اإلنبات أشارت نتائج وقت بشكل عام،المسكيت. نبتات أو شتالتنمو وتطور و إنبات البذور شتالت المسكيت نمو ووقف البذور إنبات في تثبيط فعالً تأثيًرا كان المبيد الوحيد الذي لديه (دي وإم سي بي أي-٢,٤المبيد العشبي ) أن إلى )٪( اإلنبات . (دي وإم سي بي أي-٢,٤للمبيد العشبي ) التأثير الفعال دعم الخضراء )السيقان واألوراق( الحيوية الكتلة في الكبير اإلنخفاض. اآلخرين بالمبيدين مقارنة المزارع، مستوى على .األعشاب وكذلك مقاومتها لمبيدات األخرى نباتيةال األنواع على البحري للغاف المحتمل السلبي التأثير بوضوح نتائج الدراسة توضح الغاف البحري إنتشار لوقف ات المسكيت الصغيرةرشجيلى ع (دي وإم سي بي أي-٢,٤للمبيد العشبي )المحدود التطبيق الموضعي المفيد من قد يكون .ى هذا النبات الدخيلوالمساهمة في القضاء الناجح عل ، تأثير التضاد الكيميائي، إزالة شجرة المسكيت، مبيدات األعشاب.دخيلةاألنواع ال :مفتاحيةالكلمات ال salim s. al-abdali et al 12 1. introduction nvasive alien species (ias), according to the convention on biological diversity, is defined as “a species that is established outside of its natural past or present distribution, whose introduction and/or spread threaten biological diversity”. such species can be introduced to their new habitats accidently or deliberately and are considered to be a global environmental concern. for example, an ias may compete with some native species, disturb food webs, degrade habitats and introduce parasites and/or diseases [1]. prosopis juliflora (sw.) dc, commonly known as velvet mesquite, is a well-known alien invasive plant species worldwide, including in oman where it is locally called al-ghaf bahri. p. juliflora belongs to the fabaceae family and it is native to central america and south america [2]. our field observations indicated that this plant produces copious pods, each of which contains 8–15 seeds. in india, where it is considered an exotic species, p. juliflora flowers twice a year (february-march and august-september) [2]. this would contribute significantly to its rapid spread and distribution particularly in the invaded habitats. p. juliflora was probably introduced into the tropics for a variety of purposes including slowdown of deforestation [3] and into oman for slowing down desertification, for shading and as an ornamental plant. the species has adapted to arid climates and various soil types with a wide range of alkalinity and salinity [2] and is thought to tolerate drought better than other native prosopis species such as p. cineraria in oman [4]. people in areas densely invaded by p. juliflora have discovered many benefits of this ias. for example, they use its wood for fuel and timber, sweet pods as fodder for livestock and woody stems for making charcoal [5, 6]. nevertheless, p. juliflora is a growing threat to ecosystems and their biodiversity [4, 6]. for example, native herbaceous vegetation and native tree diversity under a canopy of p. juliflora-trees and in nearby areas tend to be much reduced [7], suggesting the production of allelochemicals. plant allelopathy refers to the ability of one plant species to influence the seed germination and/or growth of another species through release or secretion of allelochemicals [8]. studies have demonstrated that p. juliflora reduces seed germination percentage of the native ghaf species (p. cineraria) when their seeds are planted together [4]. although leaves of p. juliflora are reported to contain a variety of chemicals including alkaloids, flavonoids, hydrocarbons, steroids, tannins and waxes [9], limited studies have been conducted to examine the allelopathic effects of different parts of the plant. because of the potential threat to native flora diversity and possible effects on invaded farmlands, the concerned authorities (e.g. the ministry of environment and climate affairs and the ministry of agriculture and fisheries) have launched a national campaign for mesquite eradication. eradication of p. juliflora is a challenging task since it is spreading rapidly due to its production of a massive amount of seeds. the pods or seeds can be transported or dispersed by a variety of mechanisms including livestock and flooding of the wadis or dry valleys. according to ilukor et al. [7], flooded areas which are likely to be rich in groundwater are usually more prone to p. juliflora invasion, relative to drylands. there are several management approaches to controlling the rapid growth and spread of p. juliflora, but with wide variability in effectiveness. for example, the national campaign for mesquite eradication is heavily employing a mechanical approach of uprooting adult trees as well as younger seedlings followed by burning of the dry biomass. on a cost-effective basis it is a practical option; however, this approach can facilitate distribution and germination of the seeds buried in the soil if suitable conditions are provided (i.e. enough moisture). targeting seeds and new seedlings using chemical approaches (e.g. herbicides) is another option to eradicate p. juliflora. understanding the sensitivity of omani native species to allelochemicals of p. juliflora may help to protect omani native plants and to manage this ias especially in the invaded agricultural lands. therefore, the first objective of this study is to determine the effect of extracts of leaves and seed pods of p. juloflora on seed germination and seedling growth of one native omani plant species (p. cineraria) and on that of a crop species, mung bean (vigna radiata). moreover, an important feature of p. juliflora is its ability to produce enormous amounts of seeds with a relatively long dormancy period allowing them to withstand various harsh environmental conditions. thus, the second objective of this study is to investigate seed germination and seedling growth of p. juliflora when exposed to three agricultural herbicides as an alternative approach for eradication, specifically for use on farmlands. 2. materials and methods 2.1 sample collection and processing seedpods of p. cineraria and p. juliflora were collected from liwa and saham (al-batinah north governorate, oman) from different trees during 2016. additional p. juliflora seedpods were gathered from the squ botanical garden. seeds of v. radiata were purchased from a local hypermarket. fresh leaves from p. juliflora trees were obtained from saham. prior to experimentation with the seeds, they were subjected to the seed viability float test. briefly, a 250-ml glass beaker was filled with distilled water and then 100 p. cineraria or p. juliflora seeds were poured into the water and left undisturbed for about 15-20 minutes. after that, the floating and sunken seeds were counted and the viability percentages were calculated (ranging between 92-97%). floating seeds are unlikely to germinate while sunken seeds are considered viable. to break dormancy, micropyles of p. cineraria seeds were scratched against sand paper to improve water imbibition into the seed. i allelopathic and eradication prosopis juliflora 13 2.2 preparation of aqueous extracts of p. juliflora leaves and seed pods the fresh green leaves were exposed to sunlight until they became dry. then seedpods (with seeds) and leaves were separately ground to powder mechanically using a grinder. a wide range of concentrations of leaf and seedpod extracts were prepared, based on observations of the presence of copious amounts of leaves and pods under the canopies of these trees. hence, 2.5, 5.0, 10.0 and 15.0 grams of powdered leaves or pods were weighed out and soaked in 100 ml of distilled water for 24 hours at room temperature. the solutions were filtered through a 2 mm mesh sieve to get rid of undissolved large particles and then centrifuged at 3500 rpm for 15 minutes. the resulting supernatants were dark greenish and yellowish to brownish for leaf and pod extracts, respectively. aqueous extracts were stored in conical flasks and refrigerated at 4°c until performing exposures. 2.3 seed germination and seedling root growth measurements of p. cineraria and v. radiata the exposures to observe seed germination of p. cineraria or v. radiata were performed in petri dishes, with five separate treatment levels for leaf and pod extracts (control, 2.5, 5.0, 10.0 and 15.0 grams/100 ml). one cotton pad was placed in each petri dish and then a small amount (~ 10 ml) of each of the extracts was added for wetting the cotton pads. distilled water was used as control. then10 seeds of p. cineraria or v. radiata were put in each petri dish and the dishes were placed in the dark. after 7 days, the petri dishes were observed by counting the number of geminated seeds and measuring the length of radicle or embryonic root of each seedling. three replicates were done for each concentration of the extracts. 2.4 eradication experiments of p. juliflora 2.4.1 preparation of herbicide exposure solutions three herbicides (tribenuron methyl, clethodim and 2, 4-d & mcpa which is a mixture of 2,4dichlorophenoxyacetic acid and 4-chloro-2-methylphenoxyacetic acid) were purchased from a local shop for agricultural materials and chemicals. following the manufacturers’ recommendations, herbicide exposure solutions were prepared by dissolving 0.3 g, 1.0 ml and 15.0 ml of tribenuron methyl, clethodim and 2, 4-d & mcpa, respectively, in 1000 ml of distilled water. 2.4.2 effect of herbicide on seed germination seeds of p. juliflora were randomly selected for 4 treatments (control, tribenuron methyl, clethodim, and 2, 4-d & mcpa) and 20 seeds were placed in each petri dish fitted with a filter paper. the seeds were incubated in distilled water (control) or herbicide solution for 24 hours. pots were prepared using potting peat (klasmann potgrond h 70 blocking substrate, netherlands) and irrigated using distilled water, and 5 treated seeds were then planted in each pot. the pots were watered and observed for seed germination on a daily basis for 12 days. the data were used to calculate germination time (gt50 in days required for 50% of the seeds to germinate) and germination percentages (%). 2.4.3 effect of herbicide on seedling growth a further sample of p. juliflora seedlings were germinated and allowed to grow for 14 days, and were then randomly divided into 4 treatment groups (control, tribenuron methyl, clethodim, and 2, 4-d & mcpa) with 10 seedlings taken for each treatment. next, the prepared herbicide solutions (as tested above for seed germination experiments) were sprayed on the seedlings while control seedlings received distilled water as spray. changes in the seedlings were observed daily. after 5 days, above-ground fresh biomass was measured by cutting the shoots and leaves from each exposed seedling. the fresh biomass was determined with an analytical balance and expressed in grams. 2.5 statistical analyses the number of germinated seeds and length of radicles of p. cineraria and v. radiata, their times to germinate (gt50) and germination percentages (%) were processed, graphed and analyzed for descriptive statistics using microsoft excel software, as was the above-ground fresh biomass of p. juliflora. the values were reported as mean ± standard error (se). in addition, sigmastat software was employed to perform one-way analysis of variance (anova) or the non-parametric kruskal-wallis anova to detect differences between the control and treatments and among treatments. after significant anova or kruskal-wallis anova, post hoc multiple comparisons were carried out using tukey’s test or dunn's method. all statistical analyses were established at the significance level of p = 0.05. 3. results and discussion 3.1 effect of p. juliflora extracts on seed germination and seedling root growth measurements of p. cineraria and v. radiata the allelopathic effect of leaf and pod extracts of p. juliflora on seed germination and length of radicle or embryonic root growth of the native ghaf (p. cineraria) and mung bean (v. radiata) was demonstrated (figure 3.1). seed germination of p. cineraria exhibited concentration-dependent inhibition for the pod extract (figure 3.1). seeds salim s. al-abdali et al 14 of p. cineraria failed to germinate at the highest tested concentration (15 g/100 ml) of p. juliflora pod extract (figure 3.1). similar numbers of germinated seeds were recorded for both control (extract-free) and all treatments of p. juliflora leaf extract (figure 3.1). neither leaf extracts nor pod extracts of p. juliflora had an effect on the germination of v. radiata seeds (figure 3.1). figure 1. effect of leaf and pod extracts of the ias, mesquite (p. juliflora) on the seed germination of the native ghaf (p. cineraria) and mung bean (v. radiata). the values are means ± se of n = 3 replicates. capital letters are for leaf extract exposures and lower case letters are for pod extract exposures. different letters indicate significant differences and asterisks indicate significance between the action of leaf and pod extracts (p ≤ 0.05). ng: no germination. both species (p. cineraria and v. radiata) showed significant reduction of growth and/or development of their embryonic roots or radicles (fig. 3.2) with both extract types of p. juliflora. while the effect was more pronounced in the case of p. cineraria even at low concentration levels, increased reduction in radicles of v. radiata was noticed with increased extract concentration (fig. 3.2). generally, both species (the native ghaf and mung bean) suffered similarly from both extracts especially at higher concentrations, at which root growth and development was completely inhibited (fig. 3.2). figure 2. effect of leaf and pod extracts of p. juliflora on the growth of embryonic roots of p. cineraria and v. radiata seedlings. the values are means ± se of n = 10-40 seedlings. capital letters are for leaf extracts and lower case letters are for pod extracts. different letters indicate significant differences and asterisks indicate significance between the action of leaf and pod extracts (p ≤ 0.05). relative to the crop species (mung bean), data suggest the native ghaf is likely to be more affected by the allelochemicals released by the ias even at lower environmentally-relevant levels (e.g. 2.5 grams/100 ml). earlier studies [4] have suggested the presence of allelochemicals from observations of the germination percentage of the native ghaf species (p. cineraria) being greatly reduced when grown together with the ias (p. juliflora). in addition, field surveys [5, 7] have reported that native flora diversity under dense p. juliflora-trees tends to be much reduced. the adverse impact of the invasion of arid grazing lands by p. juliflora has also been demonstrated [10]. in oman, p. cineraria is a native woody species that provides shade and nutrients for livestock plus other ecosystem services. soil of areas densely-impacted with p. juliflora would be expected to be contaminated by allelochemicals, thus negatively impacting the germination as well as the development and growth of the native species. moreover, prosopis species have detrimental effects on crop yield or productivity. for example, extracts of p. juliflora flowers, leaves and pods affected germination and seedling growth of important cereals such as common wheat (triticum aestivum) and corn (zea mays) [11]. in the present study, despite the fact that the crop species (v. radiata) appeared to tolerate the action of allelopathic substances for seed germination (fig. 3.1), radicle length of its seedlings was markedly affected (fig. allelopathic and eradication prosopis juliflora 15 3.2). water extracts of dry leaves of p. juliflora inhibited germination and delayed the growth of bermuda grass [12], an important species in tropical and subtropical pastureland. field surveys have shown that both annuals and perennials in the arid lands are negatively affected by the presence of p. juliflora, although this depends on the density and extend of canopy [13]. in the current study, a substantial drop in seed germination of p. cineraria was observed, especially when exposed to seedpod extract (fig. 3.1). the pronounced effect of pod extract may indicate that seed pods of p. juliflora act as a storage site or reservoir for allelochemicals. alleochemicals work individually or in combination to inhibit or reduce germination and growth of the native plant species [9]. further studies are needed to quantify and characterize the individual substances or mixtures from different parts of p. juliflora and identify which would be responsible for the observed reduction in growth and germination of other plant species. figure 3. germination time (gt50) and percentage (%) for seeds p. juliflora after exposure to 3 herbicides. the values are means ± se of n = 6-15 replicates. different letters indicate statistical significant differences (p ≤ 0.05). nd: not determined because seeds exposed to 2, 4-d & mcpa did not germinate even after 12 days. figure 3.3 shows gt50 (the time required for 50% of the exposed p. juliflora seeds to germinate) and germination percentage. the seeds in the control had the lowest mean gt50 of 5.3 days while those of the clethodim treatment had a significantly higher mean gt50 of 10.4 days (fig. 3.3). compared to the control, there was slightly higher mean gt 50 value of about 5.9 for tribenuron methyl, but it was not statistically significant (fig. 3.3). no gt 50 was calculated for the 2, 4-d & mcpa treatment because no seed germinated even after 12 days (i.e. the duration of the experiment). clearly, there is an inverse relationship between the gt50 and the germination rate. in other words, the lower gt50 values indicate higher germination rates and vice versa. the measurement of gt50 seems plausible to illustrate inhibition of seed germination by the herbicides. indeed, gt50 has been employed to study plant germination under various environmental conditions [14-16]. despite the fact that the investigated herbicides are usually applied on the seedlings, one objective of the study was to explore an effective way to eradicate p. juliflora by targeting seeds. it is not clear how clethodim and 2,4-d & mcpa delayed and inhibited seed germination, respectively. however, it is likely that seed germination and seedling development are affected by the same mechanisms. for example, clethodim acts as inhibitor of acetyl coenzyme a (coa) carboxylase and 2,4-d & mcpa produces an action mimicking growth hormone auxins [17, 18]. interestingly, an increase in auxin biosynthesis was reported to enhance seed dormancy via abscisic acid stimulation [19]. figure 4. above-ground fresh biomass for 14-day old seedlings of p. juliflora exposed to the 3 herbicides. the values are means ± se of n = 5 replicates. different letters indicate statistically significant differences at p ≤ 0.05. salim s. al-abdali et al 16 for germination percentages, p. juliflora seeds in the herbicide-free condition (i.e. control) scored 100% germination after 12 days (fig. 3.3). germination did not differ much between the control and the tribenuron methyl treatment (fig. 3.3). relative to the control and tribenuron methyl treatments, the clethodim treatment had a very low germination percentage, with only 17% of the seeds germinated after 6 days and about 67% of them germinated after 12 days (fig. 3.3). after exposure to the 2, 4-d & mcpa treatment, seeds failed to germinate during the duration of the experiment (fig. 3.3). with the exception of exposure to 2, 4-d & mcpa, the above-ground fresh biomass of the 14 day old of p. juliflora seedlings did not appear to be affected by the herbicides (fig. 3.4). on average, seedlings in the control, tribenuron methyl and clethodim treatments had statistically similar above-ground fresh biomasses of 0.25, 0.23 and 0.24 g, respectively. on the other hand, the above-ground fresh biomass of p. juliflora seedlings treated with 2,4-d & mcpa dropped by more 50% percent (less than 0.1 g on average) relative to that of the control. while p. juliflora seeds and seedlings exhibited tolerance to tribenuron methyl and clethodim, 2,4-d & mcpa was the most powerful in inhibiting seed germination and stopping seedling growth of this ias. the latter herbicide is a mixture of two active chemical ingredients (2,4-dichlorophenoxyacetic acid and 4-chloro-2-methylphenoxyacetic acid) and which probably act additively or synergistically to result in complete inhibition of seed germination and delay of seedling growth. tribenuron methyl and 2,4-d & mcpa are herbicides for controlling broad-leaved weeds by inhibition of acetolactate synthase and mimicking growth hormones auxins [17], respectively. on the other hand, clethodim is a selective herbicide for narrow-leaved weeds and grasses and works as inhibitor of acetyl coenzyme a (coa) carboxylase [17, 18]. herbicides have been used in controlling mesquite for quite a long time [20]. in general, one disadvantage of the chemical approach for controlling alien invasive plant species and weeds is the emergence of resistant individuals. for example, some weeds have already been shown to have resistance to tribenuron methyl and clethodim [17, 20]. interestingly, neither herbicide was effective for controlling p. juliflora, although clethodim did influence seed germination significantly in the present study. p. juliflora has been reported to tolerate several adverse environmental conditions such as copper-contaminated soils [21] as well as drought. for instance, p. juliflora exhibited a higher tolerance to drought conditions relative to native prosopis species (e.g. p. cineraria) [4]. this feature seems to play a major role in the widespread distribution of this ias in habitats with highly variable environmental conditions. conversely, few resistant weeds have been reported for auxin-like herbicides (e.g. 2,4-d & mcpa) [17]. in this study, 2,4-d & mcpa worked very well for controlling seedling growth of p. juliflora, but this does not make it a better chemical option for controlling mesquite particularly in the wild or open areas. largescale application of such powerful herbicides would be associated with detrimental consequences on the native flora. on the farm scale, localized application of 2,4-d & mcpa on young p. juliflora seedlings may be recommended as an effective way to limit further spread and distribution. however, the use of pesticides including herbicides in agriculture may be generally associated with effects such as herbicide accumulation and residuals in produce. for example, residues of 2,4-d have been detected at levels of up to 0.030 mg/l in marketable watermelon [22]. 4. conclusion the study aimed to quantify the germination and growth of the native ghaf species (p. cineraria) and mung bean (v. radiata) when exposed to water extracts of leaves and seed pods of the ias (p. juloflora) and to investigate the effectiveness of 3 agricultural herbicides to stop seed germination and seedling growth of p. juliflora. while seed germination of v. radiata was not affected by the extracts, seedling growth of native ghaf and mung bean was substantially reduced by both leaf and pod extracts, emphasizing earlier reports of the negative effects of this ias. seeds and seedlings of p. juloflora did not appear to be affected by the herbicides tested, except by 2, 4-d & mcpa which would be effective for restricted use on agricultural lands for successful elimination of this ias. acknowledgement the research work is part of final year project course at the department of biology, squ. the authors appreciate the support they received from the department and thank the technical staff for facilitating the experimental trials. references 1. allendorf, f.w. and lundquist, l.l. introduction: population biology, evolution, and control of invasive alien species. conservation biology, 2003, 17, 24–30. 2. orwa, c., mutua, a., kindt, r., jamnadass, r. and anthony, s. prosopis julifloraagroforestry database: a tree reference and selection guide version 4.0. world agroforestry centre, kenya, 2009. 3. mwangi, e. and swallow, b. prosopis juliflora invasion and rural livelihoods in the lake baringo area of kenya. 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(lolium rigidum) populations. australian journal of agricultural research, 2007, 58, 711–718. 19. liu, x., zhang, h., zhao, y., feng, z., li, q., yang, h. q., luan, s., li, j. and he, z-h. auxin controls seed dormancy through stimulation of abscisic acid signaling by inducing arf-mediated abi3 activation in arabidopsis. proceedings of the national academy of sciences of the united states of america, 2013, 110, 15485–15490. 20. bovey, r.w. and mayeux jr., h.s. effectiveness and distribution of 2,4,5-t, triclopyr, picloram, and 3,6dichloropicolinic acid in honey mesquite (prosopis juliflora var. glandulosa). weed science, 1980, 28, 666–670. 21. victor, r., pillay, a. and al-minji, s. copper tolerance to germination in mesquite, a potential tree species for restoring mined-lands in oman. journal of agriculture, food, and environmental sciences, 2007, 1, 19–23. 22. culpepper, a.s., sosnoskie, l.m., shugart, j., leifheit, n., curry, m. and gray, t. effects of low-dose applications of 2,4-d and dicamba on watermelon. weed technology, 2018, 32, 267–272. received 1 st july 2018 accepted 15 november 2018 squ journal for science, 2020, 25(1), 1-9 doi:10.24200/squjs.vol25iss1pp1-9 sultan qaboos university 1 effect of smokeless tobacco product, afzal, on the reproductive hormones and gonadal pathology of wistar rats nawal m. al-mukhaini 1 , taher a. ba omar 1 *, elsadig a. eltayeb 1 , aisha h. al khayat al-shehi 1 , jamila al-belushi 1 , nafila al-riyami 2 , romulo cipriano 2 and kawther al-adawi 3 1 department of biology, college of science, sultan qaboos university, p.o. box 36, pc 123, muscat, sultanate of oman; 2 clinical biochemistry, sultan qaboos university hospital. p.o. box 38, pc 123, muscat, sultanate of oman; 3 pathology department, college of medicine and health sciences. p.o. box 35, pc 123, muscat, sultanate of oman. *email: taher@squ.edu.om abstract: afzal is a common smokeless tobacco product (stp) in oman, and it is believed to contain toxins that may affect the reproductive hormones and hence reproductive function. this study assessed the effect of afzal on the gonads of wistar rats. in order to assess gonad toxicity induced by this stp, an aqueous extract of afzal was added to drinking water to be administrated orally to wistar albino rats (n = 72) classified as young (4 weeks old) and adult (20 weeks old) of both genders weighing between 60-80 g and 150-240 g respectively for 8 weeks. the rats were divided into 3 groups; control (received distilled water instead of afzal extract), low-dose (received 3 mg nicotine/kg body weight/day) and high-dose (received 6 mg nicotine/kg body weight/day). at the termination of the study, the rats were euthanized and their blood samples and ovaries were collected for biochemical and histopathological investigations. testosterone and estradiol hormones showed a significant decrease (p<0.05( in afzal-treated groups (low and high doses) compared with the control. histopathological findings revealed the damaging effects manifested as a reduction in the number of the germ cells with deformed organization and in fatty and fibrous degenerations in testes and ovaries. afzal was found to have adverse effect on the reproductive hormones and gonadal pathology in wistar rats of both genders, and hence users of afzal need to consider the risk associated with its frequent use. keywords: smokeless tobacco product; afzal; wistar rats; reproductive hormones, testes; ovaries; testosterone; estradiol. غير مدخن، أفضل، على هرمونات وأمراض الغدد التناسلية لجرذان ويسترالثير منتج التبغ ـأت نوال المخيني، طاهر باعمر، الصادق الطيب، عائشة الخياط، نفيلة الريامي، جميلة البلوشي، كوثر العدوي و رومولو سيبريانو أفضل أحد أنواع التبغ غير المدخن بسلطنة عمان ويعتقد باحتوائه على سموم قد تؤثر على هرمونات التناسل والتي بدورها تؤثر على يعد :صلخمال مستخلص منتج وظائف التناسلية. تهدف هذه الدراسة الى تقييم تأثير مادة افضل على أعضاء التناسل لدى فئران التجارب من نوع ويستر. تم إضافة محلول ال 72أسابيع( وبالغين )بعمر 4( بتصنيف صغار )بعمر 27لمياه الشرب ليتم استهالكه عن طريق الفم بواسطة الفئران من نوع ويستر األمهق )عدد=أفضل وتلقت ماء مجموعات: التحكم ) 3أسابيع. تم تقسيم الفئران إلى 0جم على التوالي لمدة 742-052جم و 02-02أسبوع( من كال الجنسين بأوزان تتراوح من ملجم نيكوتين/كجم من 0ملجم نيكوتين/كجم من وزن الجسم/يوم( والجرعة المرتفعة )وتلقت 3مقطر بدال من محلول أفضل( ، الجرعة المنخفضة )وتلقت الكيمياء الحيوية وفحص تم قتل الحيوانات بطريقة إنسانية ، وأخذ عينات من الدم والخصى والمبايض لعمل تحاليل وزن الجسم/ يوم(. بنهاية الدراسة انخفاض أوضحت تحاليل الهرمونات وقد التستوستيرون واإلستراديول لجميع مجموعات الفئران. تم تحليل مستويات هرمون األنسجة لتطور المرض. و ولوحظ أن هذا االنخفاض لتحكم. في مستويات التستوستيرون واإلستراديول في كال المجموعتين المعالجتين بأفضل مقارنةً بمجموعة اp<0.05) كبير ) محلول. الهرموني يتناسب طردياً مع زيادة تركيز محلول األفضل وقد تأثرت به جميع مجموعات الفئران )صغار/بالغين ، ذكور/إناث( التي تلقت هذا ظيم في الخاليا الجرثومية التناسلية و تحلل دهني وكشفت نتائج التحاليل النسيجية المرضية التأثيرات التناسلية المتضررة على شكل نقص عدد وتشوه بالتن لفئران وليفي في كل من الخصى والمبايض. وفي الختام ، فقد أظهر منتج التبغ أفضل تأثيره على هرمونات التناسل وسبب أشكال مرضية بكال الجنسين ر المرتبطة به مع االستخدام المتكرر.التجارب من نوع ويستر ، ولذلك فإن على مستخدمي أفضل األخذ بعين االعتبار المخاط التوستوستيرون ، اإلستراديول.منتج التبغ غير المدخن ، أفضل ، هرمونات التناسل ، فئران ويستر ، الخصى ، المبايض ، : مفتاحيةالكلمات ال mailto:taher@squ.edu.om nawal m. al mukhaini et al 2 1. introduction fzal is a smokeless tobacco product (stp) which contains toxins and heavy metals. tobacco consumption has always been associated with stress induction [1]. physiological and behavioral responses appear as a result of stress exposure [2]. hormone secretion during stress may directly affect gonadal sex steroids such as corticotrophin releasing hormone (crh). a stressor can induce corticosteroid secretion and may affect pituitary responsiveness to gonadotrophin releasing hormone (gnrh) [3]. additionally, stp extract leads to oxidative stress which causes tissue damage and apoptosis [4]. nicotine, a major component of tobacco, is considered to cause a high incidence of infertility [5]. acute nicotine administration results in a rise in the plasma glucocorticoid levels [6] via the release of adrenocorticotropic hormone (acth) from the pituitary gland [7]. nicotine has shown negative effects on both testosterone and estradiol levels in both genders of adult wistar albino rats [8]. tobacco use inhibits spermatogenesis and causes decreased steroidogenesis in men and anti-estrogenic effects in women [9-11]. male users of stps have exhibited some infertility findings such as reduced semen volume, sperm count, sperm motility and increased frequency of abnormal spermatozoa [12]. decreased sperm count, sperm viability and sperm motility have also been reported in rats treated chronically with stp extract [13,14]. stp users place it inside the mouth for a period of time and the tobacco-saliva mixture formed most likely ends up in the systemic circulation. systemic exposure to the harmful ingredients of stps probably occurs from direct oral absorption or from swallowed saliva or tobacco particulate matter in the digestive tract [15]. previous chemical analysis of afzal has shown that it is contaminated with some hazardous substances such as heavy metals [16], high nicotine, nitrate/nitrite, other anions [17] and tobacco-specific nitrosamines (tsnas) [18]. among those are some reproductive toxins including nicotine, and several metals, especially chromium (cr), arsenic (ar), cadmium (cd) and lead (pb) [19]. the present study was undertaken to evaluate afzal’s reproductive toxicity by assessing its effect on sex hormone (testosterone and estradiol) levels and the morphological changes of testes and ovaries in wistar rats. 2. materials and methods this study has been approved by sultan qaboos university animal ethics committee (squ/aec/2013-14/6). wistar albino rats (n =72) both young (4 weeks old) and adult (20 weeks old) of both genders weighing between 60-80 g and 150-240 g respectively were obtained from the small animal house at sultan qaboos university. the rats were housed in cages at room temperature (23±2 ºc) and a relative humidity of about 60% for 12 hour dark / light cycles and given water and a normal pellet diet ad libitum. they were acclimatized for a week prior to the experiment and randomized according to their weight. a single sample of afzal weighing 4 kg was purchased personally by the investigators from one source in order to maintain uniformity for chemical and toxicological investigations. this paper presents the results of the toxicological tests. the sample was labelled with the date of purchase and the product was kept refrigerated at 4 °c in plastic bags until analysis. the rats were treated with aqueous afzal extract mixed with drinking water for 8 weeks. afzal extracts were freshly prepared every week according to the modified method of pramanik [13]. the amount in grams needed for each group was calculated according to their weekly weight measurements, and with reference to the lethal dose of nicotine (ld50)[20]. extracts were placed in a shaker for 1 hour at 37 ºc and then filtered twice using filter paper (whattman no.1) through a buchner funnel. the resulting concentrated extracts were diluted with the normal drinking tap water in the ratio of 1:30 ml of the concentrated extract to the tap water. the rats were divided into 3 groups of 24 each; the control group received distilled water mixed with the drinking water, a low-dose group received 3 mg nicotine/kg body weight/day and a high-dose group received 6 mg nicotine/kg body weight/day. blood samples for nicotine/cotinine detection and sex hormone tests were collected in week 2, from the tail vein (1ml), and at sacrifice day (end of week 8) by means of cardiac puncture. at the day of sacrifice, the animals were anaesthetized by intramuscular injection of ketamil/xylazil-20 and the blood samples and the gonads, testes and ovaries, were collected and dissected out respectively. serum was separated by centrifugation at 3000 rpm for 20 min. (cl3 or-centrifuge, thermo scientific, uk) and was stored at -80 °c until the analysis. before hormonal testing, the serum samples were subjected to a verification analysis to prove afzal consumption by the animals through nicotine/cotinine gc/ms analysis [21]. for nicotine/cotinine analysis, the serum samples from the control and afzal-treated groups were analyzed by gc/ms using the method of broadway et al., [21]. the extraction solvent was prepared using 1 ml of dichloromethane and 1 ml of 1:1 petroleum ether (ethyl ether). another solution used was prepared by making a 2:1 ratio of solvent to serum. the solution samples were left at room temperature in a shaker and then allowed to settle. the clear upper layer was collected by pipette aspiration. the solution was placed in another test tube for evaporation using a nitrogen stream at room temperature. one ml of methanol was added to the test tube of the nicotine suspension. the contents of the test tube were kept in a vial for general screening run by gc-ms analysis (perkin a effect of smokeless tobacco product 3 elmer clarus 600 gc system, usa) looking for the nicotine/cotinine peak. this operation was performed under conditions as described in a previous work [17]. sex hormone levels of testosterone and estradiol were estimated using the serum samples. estradiol (ref 33540) and testosterone (ref 33560) were assayed using immunoassay by an automated unicel™dxi 600 (beckman coulter, usa) analyzer used in the biochemistry laboratory, sultan qaboos university hospital. this analytical method used antigen-antibody reactions (immune complexes) to detect or measure the specific hormones in the serum samples of the rats [22, 23]. quality control standards for estradiol and testosterone were maintained in the analyzer, and the calibration data updated automatically daily. for estradiol, they were as follows: r-value 0.99, accuracy or recovery coefficient 110%, with the analytical range of the lower limit of detection and the highest calibrator value being 73-17,621 pmol/l. those for testosterone were: r-value 0.98, the accuracy or recovery coefficient 105%, with the lower limit of detection and the highest calibrator value being 0.35-55.5 nmol/l. the system uses a six-point calibration curve, controls, and 10 replicates of the zero calibrator in multiple assays. the six calibration levels were 0.0, 0.5, 1.5, 4.0, 8.0 and 16.0 ng/ml. the calibrators were prepared gravimetrically from testosterone/estradiol and a buffered bovine serum albumin (bsa) matrix. an assay calibration curve was prepared and measured daily, and from it, the amount of the analyte in the sample was determined. testes and ovaries were fixed in karnovsky fixative, dehydrated in a series of acetone and embedded in resin. semi-thin sections (0.5 µm), stained with toluidine blue, and ultra-thin sections (70 nm) were cut using ultramicrotome (reichert-jung, canada). the ultra-thin sections were collected on grids, and stained with uranyl acetate and lead citrate according to the method of boozola and russell [24]. they were then screened under a transmission electron microscope (jeol jem-1230, japan). data were expressed in standard error of the mean (sem). the significance of differences in the mean between control and treated animals was determined using one way anova (analysis of variance) and followed by multiple comparison tests for observed means, least significant difference (lsd) and duncan post-test, using ibm-spss statistics-version 21 software. p values <0.05 were considered significant. 3. results the serum of afzal-treated wistar rats showed several peaks for nicotine and/or its secondary metabolites (figure 1). the nicotine peak was obvious in the serum samples collected in both week 2 of treatment and at the termination of study. this is a clear verification of the ingestion of afzal by the tested rats. levels of testosterone and estradiol hormones in serum samples of 8 weeks afzal-treated rats showed significant differences (p <0.05) compared with those of the control groups (figure 2). testosterone of the control group (34.58 nmol/l ± 22.32) was higher than both the low dose group (14.36 nmol/l ±11.51) and the high dose group (3.69 nmol/l ±1.24). the control level of testosterone was approximately 9 fold higher than that of high dose and 2.4 fold higher than that of low dose groups. similarly, the estradiol of the control group (0.288 nmol/l ±0.07) was higher than both the low dose group (0.133 nmol/l ±0.03) and the high dose group (0.045 nmol/l±0.02). figure 1: gc/ms chromatography showing the peak of nicotine (with asterisk and the spectrum mass of 84 m/z) seen in the serum of afzal-treated rats only, while the control serum samples did not show peaks. nawal m. al mukhaini et al 4 a b figure 2. sex hormone levels in 8 weeks afzal treated rats’ serum samples and their control counterpart groups. a. testosterone hormone, b. estradiol hormone. all treated groups were significantly different from the control, p <0.05, in the two hormone levels (* asterisks: refer to significant differences compared with the control). values are expressed on the top of each bar as the mean ± sd, and animals were 8/group. a b figure 3. micrographs of 8 weeks treated adult male rat testes of the control (a) and afzal-treated (b) groups. the control group shows compact seminiferous tubules within the testicular capsule which is composed of tunica vaginalis (tv), tunica albuginea (ta) and tunica vasculosa (ts) with the interstitial cells of leydig (arrow head) (scale bar =200µm). the treated low dose group shows a sertoli cell engulfing the apoptotic cells (ap) and forming multiple vacuoles, and their microtubules (arrowhead) exhibiting their intercellular communications (scale bar =2µm). red blood cells (rbc), seminiferous tubules (st), lipid droplets (f), nucleus (n), myoid cells (m), vacuoles (v). 34.580 ±22.323 * 14.3575 ±11.514 * 3.685 ±1.248 0 10 20 30 40 control low dose high dose t e st o st e ro n e ( n m o l/ l) afzal treatment (8 weeks) 0.2875 ±0.066 * 0.1325 ±0.029 * 0.045 ±0.022 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 control low dose high dose e st ra d io l (n m o l/ l) afzal treatment (8 weeks) effect of smokeless tobacco product 5 a b figure 4. micrographs of 8 weeks afzal-treated adult male rat testis. (a) shows seminiferous tubules of a rat treated with the low dose showing degenerating germ epithelia and nuclear pyknosis (arrowheads). the lumen of the right tubule shows exfoliated germ cell and fat, while the lumen of left tubule shows a lower number of spermatids than in that on the right (scale bar =1.0mm). (b) shows a high–dose treated rat showing sertoli cells with prominent nuclei engulfing the deformed spermatid cell. sertoli cells show a large amount of fat droplets in the cytoplasm and many cellular extensions (arrowheads) (scale bar =2µm). lipid droplets (f), nucleus (n), primary spermatocytes (ps), spermatids (sm) and spermatozoa (sz), vacuoles (v), seminiferous tubule basement membrane layer (bl), and lumen of seminiferous tubule (l). a b figure 5. micrographs of 8 weeks afzal-treated adult female rat ovaries. (a) shows the control with primary follicle (pf), secondary follicle (sf) and graafian follicle (gf) (scale bar = 1.0mm). (b) shows a low dose treated rat with impaired development of ovarian follicles with plenty of fat droplets accumulating in the follicular cell of zona granulosa cytoplasm along with multiple intracellular vacuolations (arrow head) and some surrounding deformed follicles (star) (scale bar = 1.0mm). primary oocyte (o1), zona granulosa (zg), theca interna (ti), theca externa (te), blood vessels (bv), follicular antrum (fa), secondary oocyte (o2), cumulus oophorus (co), corona radiata (cr), zona pellucida (zp), germinal epithelial layer (ge), basement membrane (bm), apoptotic cells (ap), vacuoles (v). nawal m. al mukhaini et al 6 a b figure 6. micrographs of 8 weeks afzal-treated adult female rat ovaries. (a) shows a low dose treated rat with degenerated atretic follicle (brackets) with high lipid droplets within the follicular granulosa cells (scale bar = 5µm). (b) shows a high dose treated rat with atretic follicles (star) with many vacuolations and lipid droplets. it also shows loss of granulosa cells, some with apoptotic and pyknotic nuclei (arrow head). the stroma shows the large increase of fibroblast activity (scale bar = 1.0mm). theca externa (te), blood vessels (bv), follicular antrum (fa), germinal epithelial layer (ge), follicular granulosa cells (fc), fat tissue or droplet (f), vacuolations (v), fibroblast cells (fb) and collagen fibers (c). the control group showed normal features of testicular tissue with their seminiferous tubules containing germinal epithelial layers (figure 3a). the testicular capsule is composed of different layers which are; tunica vaginalis (inner layer) (figure 3a), tunica albuginea (middle layer) and tunica vasculosa (inner layer). fat tissues can be seen within the interstitial spaces. testes of the adult wistar rats treated with afzal for 8 weeks in both low and high doses groups showed degeneration and damage (figure 3b and figure 4a and b). the low dose afzal-treated rats showed fatty degeneration occupying the majority of the interstitial spaces (figure 3b and figure 4a). moreover, some seminiferous tubules showed small and deformed lumen and fat tissue between the germ cells, which may affect spermatogenesis. some seminiferous tubules showed deformations in their lumen and their walls (figure 4a). these deformations include indentations of nuclei, loss of cell-to-cell contact and multiple vacuoles in the cytoplasm and some apoptotic cells (figure 3b). the high dose group showed similar degeneration of spermatogenesis stages and focal disorganization of seminiferous tubules with marked depletion of the spermatogenic cell populations (figure 4b). moreover, the degenerated seminiferous tubules showed the exfoliation of damaged germ cells in the lumen with fat tissue. some seminiferous tubules lacked spermatids and secondary spermatocytes. the control group showed normal covering of the ovaries by a thick connective tissue capsule (figure 5a). the ovarian cortex showed the presence of the developing follicles, and a vascular interstitial space. the cortex exhibited various developing oocytes. the low dose showed impaired development of ovarian follicles (figure 5b and figure 6a). the follicles contained lipid droplets and vacuolations. some ovarian follicles showed apoptotic characteristics (figure 5b). other degenerated atretic follicles were also observed (figure 6a). in the high dose group, tissues of adult female rats showed different forms of atretic follicles (figure 6b). some of those follicles appeared as cystic-like structures. secondary follicles showed loss of normal granulosa cells arrangement and some displayed a deformed antral cavity, and apoptotic and dark small (pyknotic) nuclei. other degenerating ovarian follicles and cells exhibited various vacuolations and lipid droplets in their cytoplasm (figure 6b). generally, the high dosage group showed fatty degeneration and loss of the usual organization, and large spaces between the cells reflecting the loss of cell junctions. gametes are vulnerable organs which showed stp associated tissue damage [12, 14]. tobacco use leads to oxidative stress which has been established as one of the causes of male infertility [25]. oxidative stress in testes was found to be increased in stp treated wistar rats when compared with tobacco smoke or nicotine [26]. stress induces impairment in the pituitary function causing the release of gnrh, which may affect gonadal secretion of sex steroids, such as corticotrophin releasing hormone (crh) and corticosteroids [3]. effect of smokeless tobacco product 7 afzal is contaminated with some hazardous substances such as heavy metals, [16] high nicotine, [17] and some carcinogens (tsnas) that might cause reproductive toxicity [18]. several metals found in afzal, especially cr, ar, cd and pb, are considered to be reproductive toxins [19]. it has been suggested that nicotines act as a central nervous system stimulant and also interferes with endocrine secretion of gonadotropins (fsh and lh) and prolactin from the pituitary and causes a feedback decrease in testosterone level [27, 28]. nicotine has been reported to have a dose-dependent deleterious effect on the sperm characteristics. aprioku and ugwu found that smoking or nicotine treatment results in testicular degeneration, deficiency of male sex hormone and reduction in sperm count [26]. thus the low sperm count would probably be a result of the decrease in, or absence of, androgens and fsh, which steer the process of spermatogenesis. additionally, it has been claimed that nicotine can cause a high incidence of female reproductive disorders [29]. a similar conclusion was that nicotine exerts a reproductive dysfunction affecting the female sex hormones [1]. it has also been observed that nicotine administration can cause an elevation in plasma glucocorticoid levels by releasing (acth). [6,7] our study is in agreement with the above findings. chromium has been detected in afzal samples [16] and it has been found that exposure to this metal affects and alters both male and female reproductive organs and their function in wistar rats. [30-31] in addition, a significant decrease in estradiol levels was found to occur due to cr treatment of female wistar rats for 6 months [31]. in this study the testosterone level was found to be significantly lower in the afzal-treated group (p <0.05). some studies attributed the relationship of tobacco use and nicotine in inhibiting the spermatogenesis and causing decreased steroidogenesis [9]. the findings of this study are in agreement with yamamoto et al., [32] and oyeyipo et al., [33]. it has been established that nicotine administration decreases the level of testicular androgenic enzymes along with plasma testosterone and sperm counts [32-33]. furthermore, the fertilization ability of sperm has been found to be impaired due to tobacco use [32]. additionally, galam et al., reported that nicotine alone affects male fertility and causes significant reduction of sex hormones [14]. those results are in agreement with the high nicotine levels found in afzal and its effects in impairing the reproductive organs in male rats. testes of wistar rats displayed the damaging effects of exposure to cr, which caused membrane damage and lipid peroxidation in testes [30]. the membrane damage was attributed to the alteration of the proportions of cholesterol and phospholipid in the membrane structure. the results of this study confirm the finding that sex hormones are negatively affected by the presence of tobacco or its products. moreover, our results clearly show that the administration of the aqueous extract of afzal to adult male rats induced variable pathological changes in the testes. the present investigation has revealed that some of the seminiferous tubules appeared devoid of sperm, most probably due to alteration or inhibition of the process of spermatogenesis, and such changes may be dependent on the stage in the process at which the tobacco extract exerts its effect [34]. apoptosis, disorganization, marked loss of spermatogenic cells and maturation arrest in the seminiferous epithelia of rats treated with afzal were all clearly manifested. afzal also caused degeneration of spermatocytes at various stages of maturation. these features and other degenerative changes in seminiferous tubules and spermatocytes are in agreement with reports on the testes of vitamin a-deficient rats and testes of mice exposed to halogenated diamines [35]. in females, the levels of the sex hormone estradiol were found to be significantly decreased in the afzal-treated group. tanko and christiansen reported similar tobacco anti-estrogenic effects in women [11]. some studies attribute this effect to the main tobacco alkaloid, nicotine, and some to cr toxicity, both of which were abundant in afzal. [8, 31]. nicotine has been found to exert a negative effect on both testosterone and estradiol levels in adult wistar albino rats [8]. nicotine has adverse effects on female sex hormones by mediating the reproductive dysfunction [1]. however, it was also found that a significant decrease in estradiol levels in female wistar rats occurred due to cr treatment for 6 months [31]. extracts from stps have been reported to induce oxidative tissue damage and apoptosis [4]. our findings in assessing afzal’s toxicity in ovarian tissues are in line with those of kilinc et al. [4] and iranloye and bolarinwa [29]. stress and chronic tobacco use are associated with the disturbance of body lipid patterns [1]. an effect of lipid disturbance has also been observed as fat accumulation within the surrounding follicular cells in ovarian tissues of afzal treated groups. conclusion the present study has shed light on the adverse health consequences associated with afzal in wistar rats, including impaired functional and structural outcomes for the main reproductive organs (testes and ovaries). functionally, the sex hormone (testosterone and estradiol) levels showed significant decrease due to afzal treatment compared to the control groups. structurally, the degenerated features of testicular and ovarian tissue were evident in this study. the main destructive features are reduction in the germ cells population with fatty and fibrous degeneration in testes and ovaries. it can be concluded that the frequent administration of afzal causes significant reduction in the testosterone and estradiol levels and may lead to a compromised reproductive activity in afzal users. nawal m. al mukhaini et al 8 conflict of interest the authors declare no conflict of interest. acknowledgement we would like to acknowledge the help of mr. sultan al-maskari and mr. badr al-ruquishi from the animal house at sultan qaboos university for their valuable assistance in animal care during the study period. references 1. abd el mohsen, m.m., fahim, a.t., motawi, t.m.k. and ismail, n.a. nicotine and stress: effect on sex hormones and lipid profile in female rats. pharmacological research. 1997, 35(3), 181-187. 2. millan, m.j. stress and endogenous opioid peptides. modern problems in pharmacopsychiatry. 1981, 17, 49-67. 3. rivier, c., rivier, j. and vale, w. stress-induced inhibition of reproductive functions. science. 1986, 231, 607609. 4. kilinc, m., okur, e., kurutas, e.b., guler, f.i. and yildirim, i. the effects of maras powder (smokeless tobacco) on oxidative stress in 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administration on weight and histology of some vital visceral organs in female albino rats. nigerian journal of physiological sciences. 2009, 24(1), 7-12. 30. dey, s.k. and roy, s. effect of chromium on certain aspects of cellular toxicity. iranian journal of toxicolgy. 2009, 2(4), 260-267. 31. trif, a., petrovici, s., dumitrescu, e. and muselin, f. dynamics of female sexual hormones after six months exposure to potassium dichromate (cr vi). animal biology and animal husbandry international journal of the bioflux society. 2010, 2(1), 15-19. 32. yamamoto, y., isoyama, e. sofikitis, n. and miyagawa, i. effects of smoking on testicular function and fertilizing potential in rats. urological research. 1998, 26(1), 45-8. 33. oyeyipo, i.p., raji, y., emikpe, b.o. and bolarinwa, a.f. effects of oral administration of nicotine on organ weight, serum testosterone level and testicular pathology in adult male rats. nigerian journal of psychological sciences. 2010, 25(1), 81-86. 34. gambo, i.m., galam, n.z., adamu, g., louis, a.o., habeeb, a.a., bello, m.m., bello, n., rabiu, a.m. and odeh, s.o. the effect of aqueous leave extract of nicotiana tabacum (tobacco) on some reproductive parameters and micro-anatomical architecture of the testis in male albino wistar rats. journal of natural sciences research. 2013, 3(5), 137-143. 35. galaly, s.r., hozayen, w.g., amin, k.a. and ramadan, s.m. effects of orlistat and herbal mixture extract on brain, testes functions and oxidative stress biomarkers in a rat model of high fat diet. beni-suef university journal of basic and applied sciences. 2014, 3, 93-105. received 23 september 2019 accepted 9 december 2019 https://www.beckmancoulter.com/wsrportal/page/itemdetails?itemnumber=33540#2/10//0/25/1/0/asc/2/33540//c_%2fconsumable%20ifu|cis|setting%20sheet/0/0/techdoc/1/ https://www.beckmancoulter.com/wsrportal/page/itemdetails?itemnumber=33540#2/10//0/25/1/0/asc/2/33540//c_%2fconsumable%20ifu|cis|setting%20sheet/0/0/techdoc/1/ https://www.beckmancoulter.com/wsrportal/page/itemdetails?itemnumber=33560#2/10//0/25/1/0/asc/2/33560//c_%2fconsumable%20ifu|cis|setting%20sheet/0/0/techdoc/1/ https://www.beckmancoulter.com/wsrportal/page/itemdetails?itemnumber=33560#2/10//0/25/1/0/asc/2/33560//c_%2fconsumable%20ifu|cis|setting%20sheet/0/0/techdoc/1/ photovoltaic cells and systems: science and technology, special review (2000) 157-183 © 2000 sultan qaboos university 157 intelligent systems for active program diagnosis haider ali ramadhan and khalil shihab department of computer science, college of science, sultan qaboos university, p. o. box 36, al khod 123, muscat, sultanate of oman. أنظمة البرمجه الذكية للتحليل الفوري حيدر علي رمضان و خليل شهاب يتناول هذا البحث دراسة تحليلية و مقارنة النظمة البرمجة الذكية القادرة على اكتشاف االخطاء :خالصة و الوسائل , كما يتناول البحث طبيعة المعالجة الذكية للبرنامج في هذه االنظمة . المنطقية في البرنامج كما يطرح البحث السبل البديلة للتغلب على السلبيات . عملية المعالجة لضرورية ل المستخدمة لتمثيل المعلومات .الموجودة في االنظمة الحالية abstract: intelligent program diagnosis systems are computer programs capable of analyzing logical and design-level errors and misconceptions in programs. upon discovering the errors, these systems provide intelligent feedback and thus guide the users in the problem-solving process. intelligent program diagnosis systems are classified by their primary means of program analysis. the most distinct split is between those systems that are unable to analyze partial code segments as they are provided by the user and must wait until the entire solution code is completed before attempting any diagnosis, and those that are capable of analyzing partial solutions and providing proper guidance whenever an error or misconception is encountered. this paper gives an overview of the field and then critically compares work accomplished on several closely related active diagnosis systems, emphasizing such issues as the representation techniques used to capture the domain knowledge required for the diagnosis, ability to handle the diagnosis of partial code segments of the solutions, features of the user interfaces, and methodologies used in conducting the diagnosis process. finally the paper presents a detailed discussion on issues related to active program diagnosis along with various design considerations to improve the engineering of this approach to intelligent diagnosis. the discussion presented in this paper tackles the issues referred above within the context of discover, an intelligent system for programming by discovery. keywords: intelligent programming systems, knowledge representation, program debugging, software development, user programming. haider ali ramadhan and khalil shihab contents 1. introduction: automatic program debugging 158 1.1 the background 158 1.2 a general model of program debugging 159 2. active versus passive debugging 160 2.1 advantages of active debugging 161 2.2 the implementation of active debugging 161 3. survey of approaches 162 3.1 post-event systems 162 3.1.1 specification-based analysis 162 3.1.2 trace analysis 163 3.1.3 model-answer analysis 163 3.2 in-event analysis 164 3.2.1 greaterp 164 3.2.2 gil 166 3.2.3 bridge 166 3.2.4 discover 168 3.2.5 a summarized comparative analysis 172 4. model-tracing based diagnosis 173 4.1 critiquing model-tracing 174 4.1.1 what goals and plans in discover stand for 174 4.1.2 is discover an intelligent diagnosis and tutoring system? 175 4.1.3 production systems and model-tracing 175 4.2 discover approach to model-tracing 176 4.3 improving the engineering of model-tracing 176 4.3.1 explicit planning mechanism 177 4.3.2 plan-based model-tracing 177 4.3.3 rules versus plans 178 4.4 immediacy of feedback 179 4.4.1 the need for flexible interaction 179 4.4.2 the interaction style of discover 180 5. conclusion 181 6. references 181 1. introduction : automatic program debugging 1.1 the background over the past twenty years, the area of user programming has undergone a major change in perspective and direction. in the beginning, the emphasis was centered on the needs of the users in trying to learn programming and problem-solving. intelligent programming systems developed for this purpose targeted the design and the planning sides of programming, which embodied an instruction-oriented paradigm. users were led through a structured manner, embarking on well-defined tasks, and even designing and implementing their programs according to a model of good practice or ideal solution. this model was critical because it facilitated automated diagnosis when bugs were introduced by the users. this approach of instruction-oriented paradigm appeared to embody a clean, top-down, and reliable software engineering practice, since it aimed to get the design and specification error-free from the beginning. unfortunately, in 158 intelligent systems 159 reality, it also acted as a straight-jacket in many situations for novice users. examples of these systems include (bonar, 1992; anderson, 1990; reiser, 1992; murray, 1986; johnson, 1980). subsequently and due to limitations associated with the above approach to automatic debugging, and in general with the difficulty in coming up with automatic debuggers which would cater for more than small and toy programs, the efforts in this area shifted to the software maintenance side of user programming. discovery programming environments along with support for visual techniques were the focal point of this new direction. efforts invested in this direction seemed to claim that helping the users to understand the dynamic behavior of programs and algorithms during execution could be proven to be more effective in teaching programming to novice users. the result of this direction created a shift from automated debuggers to software visualization. ever since, much of research in user programming has been polarized toward these two opposite domains: intelligent programming systems and discovery programming environments. the intelligent systems concentrated mainly on helping novices in acquiring programming skills through a series of problem solving situations. most of these systems ignored the significance of incorporating visualization and discovery features which would also help the users in compiling effective programming knowledge. discovery systems, on the other hand, concentrated mainly on helping the users in building correct programming knowledge through visual and discovery environments. these systems neglected the issue of supporting intelligent diagnosis and tutoring through which novices can transform their knowledge into programming skill. examples of these systems include agentsheets (repenning, 1996), see (baecker, 1990), tango (stasko, 1992), zeus (brown, 1992), and tpm (eisenstadt, 1993). recently, another improvement on the general lines discussed above has emerged. this recent direction emphasizes the incorporation of visualization and discovery features into intelligent program debuggers in order to come up with guided programming environments, which may hopefully help novice users in building both the programming knowledge and the problem-solving skill. a solid practical example of such recent direction is exhibited by the discover system (ramadhan, 1992a, 1992b, 1997, 1998, 1999a, 1999b, 2000a, 2000b). empirical evaluations of the system seem to support the usefulness of this direction. with the advancement in the internet computing and web development, teaching user programming over the web is becoming a very promising direction. world societies will become more reliant on proficiency in programming, so that teaching it quickly and effectively will become more important. with the growth of distance learning technology, access to learning systems is expected to grow, and the lessons learnt from teaching programming have the potential to be applied to other areas such as medical diagnosis and circuit design and layout. among the three general programming paradigms mentioned in the above discussion, this paper deals with only two types of systems: (1) automatic program debuggers, and (2) guided discovery programming systems. discovery programming environments with no support for automatic program diagnosis are not covered in our analysis. it is important to note here that due to difficulty encountered in the development of systems for automatic program diagnosis, very little progress has been reported in this interesting area especially in recent years. it is for this reason that most of the systems mentioned in this paper are the ones developed some considerable time ago. however, it is the methodology embodied in these systems that constitutes the core of this paper and not the systems themselves. we have also put considerable effort in suggesting better design directions to improve the engineering of new systems for program diagnosis. 1.2 a general model of program debugging before describing specific systems that support automatic program diagnosis, it is worth looking at a general model of program diagnosis. this will facilitate characterizing and comparing various approaches and systems that have been developed in this area. an automatic program diagnosis and debugging system is a computer based program capable of analyzing programming solutions and providing intelligent feedback, and thus supporting problem-solving haider ali ramadhan and khalil shihab 160 domains. the program diagnosis methodologies discussed in this paper are basically specializations of the following general model. task specifications are mapped to the code provided by the user. this mapping process allows the task of program debugging to be decomposed into smaller and simpler steps. when decomposition is no longer possible, the diagnostic critic looks for discrepancies between code and specifications and interprets these as bugs. when intelligent tutoring is also supported by the system, this information from the critic is passed over to the tutorial expert that interacts with the user model and provides tutorial interactions and instruction. the task specifications are precise criteria for successful completion of the debugging task. the following methods of task specifications have been used by the automatic program debugging systems indicated: • model-answer programs (reference solutions): laura (adam, 1980), aurac (hashmer, 1983), talus, bridge, and discover. • input/output pairs: bip (barr, 1976). • goals to be achieved (specified in some special language or format): proust, bridge, greaterp, gil, aurac, mycroft (goldsein, 1974), and discover. • the expected trace: pds6 (shapiro, 1983). • constraints on program output: mycroft. the diagnostic critic compares task specifications and program code for discrepancies that can be interpreted as bugs. the following indications have been used to flag the detection of bugs: • mismatch between plan templates and student code: proust, discover. • inability to synthesize student code (simulate the ideal student): greaterp, gil. • differences between expected and actual execution traces: bip, pds6. • inability to verify program specifications: talus, aurac. • inability to satisfy a list of program requirements: bridge. • violations of output constraints: mycroft. 2. active versus passive debugging automatic program diagnosis and debugging systems can be classified by their primary means of program analysis. the most distinctive split is between those systems that are unable to analyze partial code segments as they are provided by the user and must wait until the entire solution code is completed before attempting any diagnosis, and those that are capable of analyzing partial solutions. the former perform post-event analysis while the later perform in-event analysis. systems using post-event analysis can be further divided according to their methods of isolating and localizing errors into (1) those using specification based analysis, such as proust, pudsy (lukey, 1980) and aurac, (2) those using trace-based analysis, such as pds6, (3) those using i/o based analysis, such as bip, and (4) those using model-answer based analysis, such as laura and talus. systems using in-event analysis can be further divided according to their methods of reasoning about the user into those supporting active analysis and those supporting passive analysis. systems using passive analysis do not trace the intentions of the user or his design decisions while being developed and require him to explicitly request the automatic debugging of his code segments. these systems localize errors in the user programs either by looking for surface structural forms (plans) (rich, 1986) or by accounting for differences between forms and actual code segments, as in the case of bridge. generally speaking, these systems rely on some sort of pre-stored requirements for a complete solution, and hence are classified in our taxonomy under model-answer based systems. it is worth noting here that systems which rely on preintelligent systems 161 stored requirements for a successful solution cannot solve the problems themselves, and hence cannot reason about the solutions and designs provided by the users (see section 2.2). on the other hand, systems using active analysis perform automatic debugging by implementing model-tracing (anderson, 1990). through this approach, these systems subdivide tasks into smaller steps that must be solved one at a time. the user’s design decisions are traced as he develops the solution. during each step taken by the user, these systems check to see if the user is following a design path known to be correct or buggy. buggy paths are pruned as soon as they are detected by giving the user intelligent feedback and allowing him to try again. examples of such systems include greaterp, gil and discover. these systems tend to be quite directive. however, through rich interaction and flexible immediate feedback, these systems detect very specific bugs and misconceptions. there is some overlap in these categories. discover performs model-tracing, but relies on a prestored model answer (the reference solution) to represent its knowledge about the ideal user. aurac performs specification based analysis to match code segments with the library of program clichés, but then later on uses its model-answer algorithm to conduct data-flow analysis. 2.1 advantages of active debugging several advantages of the active approach to automatic program debugging can be outlined as follows: • very specific errors can be diagnosed and feedback can be given in proper context of the error, hence the users can be explicitly guided in the process of acquiring problem-solving skills. • systems using this approach are capable of analyzing partial solutions as they are provided by the user and therefore have access to all intermediate states, hence they work with more information than systems that are capable of only analyzing complete solutions. this in turn provides these systems with the capability of reasoning about the programming process itself and thus generates very specific explanations and advice. • the impact of multiple bugs on the diagnosis process is minimized. many of the post-event based systems such as proust, talus, aurac and laura have to deal with disentangling multiple bugs which require them to generate all possible alternative treatments of these bugs and pick the best from among them. systems using active analysis simply prevent the user from making multiple bugs and explain each bug immediately. therefore, the code never contains more than one bug at a time. in addition to cognitive justifications, (see anderson, 1982), this approach greatly simplifies the engineering and the implementation of automatic program diagnosis. despite these advantages, this approach to automatic program diagnosis tends to be very directive. in addition, such approach ignores the issue of providing the user with some chance to detect and correct bugs on his own, since the user is not allowed to go wrong. however, these disadvantages can be overcome by supporting a more flexible style of user interaction while still retaining close ties to model-tracing. this was successfully accomplished by the discover system through (1) supporting an ability to give delayed feedback by increasing the grain size of automatic diagnosis to a complete program statement, not just a single word or symbol, and (2) allowing the user to do limited backtracking by giving him some chance to delete previously entered code and restart, while in full interaction with the system (see section 4 for more detail). 2.2 the implementation of active debugging one way to implement model-tracing, active program debugging is to provide the system with a set of problem solving rules (a production system) that allow it to model the user by generating possible steps that a user might take while solving a given problem. thus, while the user is working, the system simulates the steps that an ideal user could take in completing the program. in addition, this approach also models possible errors that the user makes at each step on the basis of pre-known bugs and misconceptions stored in a library. by comparing the user’s actions (partial solution steps) to the set of possible correct actions and haider ali ramadhan and khalil shihab 162 the set of buggy actions, the system can determine whether the user is moving on a correct solution path or showing evidence of bug. this combination of correct and buggy sets of rules is referred to as the student model, while the process of comparing the user’s actions to the ones generated by these rules is referred to as model-tracing. both gil and greaterp follow this model. discover followed a different approach in implementing model-tracing. in this approach the system is provided with a pre-stored reference solution that represents the ideal solution, but with no account for possible and common bugs. the system much like laura, talus, aurac and bridge, applies various heuristics and pattern matching techniques to match steps taken by the user with parts of the reference solution. the system analyzes the surface code provided by the user without much specific knowledge about the problem to be solved or about how to design and construct an algorithm. therefore, unlike production based systems, systems that rely on pre-stored reference solution cannot solve the problems themselves. since these systems rely on manipulating the surface code, it is possible to describe to the user what the next step in the solution is but it is not possible to reason about why the step is appropriate. however, this problem can be bypassed to some extent by incorporating hand-coded explanations for each reference solution. in fact, by augmenting each complete step in the reference solution with a handcoded explanation that simulates the reasoning process, it becomes possible for discover to describe to the user quite specifically why each of his actions is appropriate or not. 3. survey of approaches as described above, automatic program debugging and tutoring systems can be classified by their primary means of program analysis. the most distinctive split is between those debugging systems that are unable to analyze partial code segments as they are provided by the user and must wait until the entire solution code is completed before attempting any automatic debugging or tutoring, and those that are capable of analyzing partial solutions. the former perform post-event analysis while the letter perform inevent analysis. 3.1 post-event systems post-event analysis systems are characterized by their inability to diagnose partial, incomplete solution steps. these systems also lack rich interaction with the user and require him to sufficiently understand both the detailed knowledge of the syntax and the semantics of the language constructions (programming knowledge), and the process of relating these constructs along with their semantics to come up with correct programs (algorithmic or programming skill). the remainder of this section examines some of these systems in more details. 3.1.1 specification-based analysis automatic debugging systems that perform specification-based analysis are provided with a high-level description of the goals of the user’s code and they check to see to what extent these goals are satisfied by the user’s code. examples of such systems include proust, aurac, pudsy, and mycroft. proust uses stored plan templates to match against parsed student code. the program specification is expressed as a sequence of task goals. proust stores a plan library that associates task goals with plan templates. plan templates are associated with the expected code in the user’s plan that they can match against. proust infers the intentions of the student program statements by matching each statement to some part of a plan. when all goals are achieved, proust fully determines the intentions of the student program. when more than one plan matches a statement, proust uses heuristics to select the one that expects the fewest bugs in the student program. by using heuristics, proust avoids impractical exhaustive search. aurac attempts to match segments of the student program written in solo against a library of clichés. because of the simplicity of the solo domain, aurac manages to store programming clichés that would match most segments of the student program. partial matching of the clichés to the code, is treated as a intelligent systems 163 candidate bug. in the final stage, the system uses data flow analysis to detect such errors as unused bounded variables. aurac is also capable of recognizing some simple algorithms. by making sure that the high-level goals specified by a model algorithm for a given algorithm are satisfied by the student code, aurac can determine if the code is logically correct. the system checks each line of the code against sample lines from an algorithm. when all lines of a given algorithm are found, aurac states that the code is correct. pudsy uses a specification as the high-level description of the correct code, and matches the output of the student program against a specification. pudsy breaks the code into smaller logical chunks. the system then relates each chunk to a particular task in the problem, using a record of tasks associated with the highlevel description of the program’s goals. in the first pass, pudsy looks for local clues that suggest bugs in chunks, such as redundant assignments. in the second pass, pudsy figures out low-level assertions about the values of variables on exiting each chunk and then transforms these low-level assertions into a high-level description. the description is then matched against a specification. on mismatch between specification and description, pudsy examines the assertions built so far and determines the code segment responsible for discrepancies between specification and description. mycroft examines the side effects produced by a program. the domain is drawing simple pictures in logo and the side effects are lines drawn and changes to the turtle state. like pudsy, mycroft uses a specification as the high-level description of the correct code, and matches the output of the student’s code against a specification. the specification describes the relationships between the components of the shapes drawn. on finding a mismatch between the drawing and the specification, mycroft determines the bug to be in the code that produced the drawing. 3.1.2 trace analysis systems that perform trace analysis engage in a debugging dialogue with the user. pds6 is an example of such a system. the system interactively debugs prolog programs by monitoring program execution. the system builds a tree of the calling sequence of the procedures involved. it then asks the user questions about the desired and actual behavior of the procedures. by comparing actual program execution with the desired execution, pds6 can determine the buggy procedure. the system relies heavily on an ‘oracle,’ typically the user, to answer questions about the expected behavior of the program. 3.1.3 model-answer analysis debugging systems that perform model-answer based analysis attempt to match pre-stored, possibly parsed, model programs to the parsed student code. examples of such systems include laura, talus and ruth’s system (ruth, 1973). laura analyzes the surface code of the student program. the system transforms the student program written in fortran and the model program into graphs and then normalizes these graphs. normalization transforms the graphs into a standard form. an example of transformation used might be if the same variable is used for two different purposes then a new variable is generated. this makes the matching process easier. any discrepancies discovered between these graphs during the matching process are considered to be bugs. talus debugs programs in lisp by reasoning about the computational semantics of the programs. recursive programs are compared to model programs. these programs act both as specifications and sources for correcting the buggy code. an inductive proof of equivalence is constructed to compare student and reference programs. where the proof would fail, the student program is altered with code from the reference program. talus applies various heuristics to pair reference functions with student functions and to pair formal variables with actual variables. the system simplifies the student code using a sequence of program simplification transformations. this process transforms the programs into if-normal forms, which then facilitates algorithm recognition and bug detection by reducing the variability of the programs. talus detects bugs by generating and evaluating verification conditions that are required for the inductive proofs haider ali ramadhan and khalil shihab 164 that establish the functional equivalence of each student function to its paired function. when the proof would fail, talus knows that a bug has been discovered. ruth’s system uses ‘generative semantic grammars’ to represent plans, and student programs are parsed in terms of the grammar. this method is similar to syntactic analysis in natural language processing. the system analyzes simple sorting programs with this approach and a grammar similar to an augmented transition network (atn). the system uses the grammar to translate a given algorithm into the program submitted by the student. if the translation fails, then the program is considered to be incorrect. the system also uses the same grammar to generate the problems in the first place. 3.2 in-event analysis automatic program debugging systems which diagnose partial solutions as they are provided by the user perform in-event analysis. the systems normally emphasize rich interactions and a visible user interface. these systems allow the user to explore the problem-solving process through an interactive exploration of programming functions, concepts and plans. the user is not required to have extensive programming knowledge and programming skill to be able to explore programming in these systems. the user learns by trying out his hypotheses which are represented by the fragments of knowledge he might have about programming, and it is up to the system to guide him in acquiring new knowledge and new skill. these systems can be further divided according to their methods of reasoning about the user into those using active analysis, such as greaterp, gil and discover, and those using passive analysis, such as bridge. interactive approach and immediacy features are two main characteristics which differentiate active systems from passive ones. through rich interactions and immediate feedback, active systems bring affordance into users’ knowledge of perception and action. users are expected to perceive and manipulate the dynamic behavior of the program and its unfolding computation with less effort and accelerate the debugging task. hence, these systems can reduce the mental overhead and help the users in putting more emphasis on program understanding, debugging and problem-solving. the remainder of this section examines in more detail these four fully implemented systems that perform in-event analysis. these examples are intended to show that every one of these automatic program debugging and tutoring systems is limited due to its inability either to support sufficiently large grain size of automatic debugging, as in the case of greaterp, or to support active debugging of partial solution steps as they are provided by the user, as in the case of bridge. a more critical analysis of the lisp tutor vs. discover is covered in the last section of this paper. 3.2.1 greaterp greaterp (the lisp tutor) uses production rules to synthesize code for both an ‘ideal’ and a ‘buggy’ novice lisp programmer. the student’s design decisions are traced as the student develops the program. this approach is called the model tracing approach to automatic program debugging. as each lisp symbol in the student program is entered, greaterp decides what rule would have to fire to duplicate the input. if the duplicating rule is in the ‘expert’ set then greaterp does nothing, but if the duplicating rule is in the ‘buggy’ set then greaterp gives the student a short tutorial on his misconception. in this way, the system always checks to see if the student is following a design path of an ideal model. buggy paths are pruned as soon as they are discovered. the system is based on a cognitive model which suggests that mistakes by the student should be flagged as soon as they are encountered. anderson (1990) argues that there is considerable psychological evidence that humans learn better with immediate feedback (an important learning assumption of the act* theory of skill acquisition), and that this approach increases the possibility that the student will be able to relate the advice to the current issue (context) rather than getting advice at a much later stage. the system is very directive and interventionist. computational advantages of such an approach are that it reduces the usual combinatorics associated with mal-rules to decide whether or not each new lisp intelligent systems 165 token is a legal or illegal continuation of the program, and that it eliminates the problem of multiple bugs. the problem of deciding which bug to tutor does not even arise, because the tutor simply prevents the student from making multiple bugs. though of course, it cannot prevent the user from entertaining multiple misconceptions about a single symbol. the disadvantage of this approach is that the student is highly constrained in the solutions that can be developed. the student must conform to the task decomposition and coding sequence that greaterp enforces. the latest version of greaterp attempts to overcome some of the problems cited above by varying the nature of the tutorial interaction. the new system has employed a problem compilation approach to provide the student with more control over the coding process in two ways: by relaxing the constraint on , input order, so that the student can generate code in any order he wants instead of the left-to-right, top-tobottom manner, and by giving the student control over when feedback is presented. this student controlled feedback is achieved by delaying feeding each unit of code to the tutorial engine as it is generated. instead, the code is buffered and submitted to the tutor at the student’s request. however, the debugging of the user program is carried out in the same way: the system scans the code in a top-to-bottom, left-to-right manner, stops at the first error encountered, and ignores the rest of the solution. this transition to the student-controlled interaction makes the new system, like bridge, a passive system that waits for the novice to request automatic analysis of his code, and thus loses the rich interaction with him. by doing that, this new system loses very important features: the ability to monitor the novice’s progress on the solution path, determine when he shows evidence of errors within their proper and immediate context and decide when to guide him in what to say during interactive tutoring. in principle, there is no reason why a model-tracing system should stick to a single-symbol based immediate feedback. one possible alternative would be to increase the grain size of automatic debugging to a full program statement or even to a block of statements, not just a single lisp symbol. this would not only provide the system with an ability to delay its interactive feedback but would also allow the user to backtrack and delete some previously entered code and restart. thus the system would support a more flexible style of interaction while preserving strong ties to the cognitive principles of model-tracing and immediate feedback. when two design paths leading to alternate implementations overlapped, greaterp, in its old version, could not determine which design path was being followed. now through problem compilation approach, greaterp can search multiple alternative branches down in the goal tree when it needs to disambiguate some responses. in the current version, discrepancies between predicted implementations and expected implementations can be explained either in terms of an incorrect design path being assumed, or in terms of a bug in the student’s program. by doing that, greaterp follows a similar approach to interpreting discrepancies as that of proust: either the wrong plan has been chosen to interpret the program, or the plan is correct but the student’s program has a bug. the student interacts with the system mainly through a structure editor. this feature aids automatic debugging by eliminating certain low-level syntax errors, such as balancing parentheses, and trapping and immediately remedying others, such as quoting a function call. this feature also ensures that both the system and the student know explicitly which part of the problem is being coded, since this is always done by replacing one of the place-holding parameters in the partially completed code. in this way, the student knows most of the time what goals and subgoals need to be satisfied. besides the code-level interaction, the system also supports a planning mode. this mode is used by the system when the knowledge of the student’s design and planning decisions becomes very difficult to be derived from the code entered by the student. the mode is also used when the system suspects that the student is having some difficulty in planning or when the student requests help. interactions at the planning-level are supported by multiple choices from the menus. this feature simplifies the task of automatic debugging even more, since in this way plans are more easily recognized than trying to derive them from step-by-step coding. haider ali ramadhan and khalil shihab 166 3.2.2 gil it is worth noting that the other model-tracing system, gil, does not defer judgment. any errors are immediately pointed out and the feedback is presented to the user as soon as a single erroneous token is encountered. however, gil has one clear advantage over greaterp. the system incorporates a visual programming environment which allows the user to observe in a graphical manner how lisp lists are constructed. the newer version of gil extends its functionality even more. this is achieved by augmenting the guided, visible environment with a free, visible environment. by doing that, this newer version has clearly followed a path similar to that already taken by the discover system. like discover, this recent version of gil synthesizes a free programming environment with a guided programming environment. this is implemented in two phases. during the first phase (the free programming phase), the users are encouraged to explore the graphical programming environment to build a mental model of simple lisp functions. users build a program by connecting together objects that represent program constructs into a graph, rather than by defining lisp functions in their traditional text form. however, the environment is not as dynamic as that of discover’s. gil does not evaluate individual steps taken by the users during their exploration, and hence does not allow the users to see the immediate effects of their actions in relation to the behavior of lisp functions. for example, when the user selects the ‘cons’ icon from the menu, gil displays a box with ‘cons’ written in it along with two branches coming out from the box. here the user is expected to provide two arguments that go with the selected function. after filling the two branches with appropriate arguments, the user does not get to see how the selected function is applied to the arguments. the system just displays the partially completed graph. it would be nice if gil could allow the users to see the dynamic behavior of the partially completed graph. during the second phase (the guided phase), gil’s users solve simple programming problems under the intelligent guidance of the system. to be able to trace the user’s solution, the system requires the user to specify his next step by selecting graphical icons from the menu that correspond to lisp functions. concerning model-tracing, gil analyzes each and every single lisp symbol provided by the user. however, gil has one important advantage over both discover and the lisp tutor: it allows more flexibility than working on a program in top-down, left-to-right order. this is accomplished by supporting both forward and backward reasoning, and thus allowing the user to choose the part of the problem on which to work. 3.2.3 bridge bridge is a programming environment intended to understand student design and partially complete programs. the system provides the user with intermediate design languages that allow him to talk about his plans and intentions directly. by doing that, the system avoids the process of deriving student intentions using complicated techniques such as partial matching based on a bug catalog used in the proust system, or partial matching based on a reference solution used in discover, or a process model of the student’s decision making used in greaterp and gil. bridge supports the user in an initial informal statement of a problem solution, later refinement of that solution, and final implementation of the solution as programming language code. this is done in three phases. in phase one, the user constructs a set of stepby-step instructions for other people. each phrase represents a goal and corresponds to one programming plan. in the next phase, the user matches these phrases to programming plans and builds a program using a representation of these plans. in phase three, the user matches these plans to actual programming language constructs of pascal and builds a solution to the original problem. as an example of this goal-plan-code matching during theses three phases, consider the following simple problem. write a program to get an integer from the user and output the result of multiplying the integer by 10. to solve this problem correctly, the user is expected to provide the following four goals which represent one way to solve the problem: setup the memory variables for the integer and its result (g1) intelligent systems 167 ask the user to enter an integer (g2) multiply the integer by 10 (g3) output the result on the display (g4) once the goals are provided, the user can now select the plans which would satisfy the above goals, i.e. plans that would implement the goals. here is one possible scenario: declare num1 and resultnum (p1) input num1 (p2) resultnum = num1 * 10 (p3) output resultnum (p4) finally, the user matches these plans to actual programming language constructs of pascal and builds a solution to the original problem. after the user finishes building a natural language solution to the problem, the system builds a symbolic representation of the natural language version of the program. in this representation, bridge notes the order of each plan, and compares the representation with a list of requirements for a correct solution to the problem. the first requirement that the student fails to satisfy becomes the subject of the tutor’s remarks. in other words, bridge compares the required plans and their ordering in a pre-stored list of requirements against the plans supplied by the user in his solution. whenever a mismatch occurs in this comparison, the system presents the user with a hind. only when all the plans in the requirements list are satisfied is the user allowed to move to the next phase. the system also supports some aspects of supportive environments (microworlds), especially in the second phase. this is accomplished by highlighting each plan during execution, animating data flow with floating value plans and highlighting the corresponding program statements, written during the first phase using the intermediate design language of the system. the advantages of providing a language for intermediate representations to allow the student to express his planning actions are obvious: (1) it provides the student with specific mental models with which to conceptualize the problem-solving process, and (2) it separates out the two activities of planning and coding, and thus reduces the cognitive load and allows focusing on one level of problem-solving at a time. this feature also reduces the engineering cost of automatic debugging, since the system does not need to infer the plans from the code using complex pattern matching: the student spells them out to the system through menu selections. the driving force behind the design of the bridge system was the desire of its developers to come up with an interactive learning programming environment that would overcome (1) the lack of rich interaction found in the proust system, and (2) the rigidity and restricting directiveness found in greaterp. the current implementation of the system, however, is not as interactive as it is liked to be seen. the system has no capability of actively reasoning about the novice user while he develops the solution. during the first phase, novices are expected to select a plan that correctly goes with a goal statement and to relate these plans together in a correct order. this pre-assumes that the user possesses adequate algorithmic skill to be able to accomplish this task. when the user requests automatic debugging of his solution, the system steps through the code and presents the user with its feedback. by doing that, bridge resembles the latest version of greaterp (the student-controlled version). an interesting extension to the system would be to make it capable of explicitly guiding the novice in the process of selecting programming plans to go with the goals and organizing these plans in a required order. the important assumption underlying the system is that teaching plans to novices will improve their ability to comprehend and write programs. there is very little evidence to suggest that this method is the only way that can provide a basis for the kind of outcome that bonar (1992) hopes. experiments looking at using plans across different tasks and programming languages have demonstrated that other knowledge structures play an equal or even greater role in programming comprehension and generation than plans (gilmore et al, 1988). the evaluation of bridge focuses on informal reports of the problems encountered haider ali ramadhan and khalil shihab 168 during interactions with the system and, therefore, provides neither a good insight into its effectiveness for novice programming nor an account on the usefulness of the plan-based approach to the design of learning environments. in the second phase, novices are required to select a plan and then select a corresponding pascal construct that best implements that plan. one of the difficulties of this approach is that the mapping from a plan to a piece of code, such as an assignment, or vice versa is neither easy for nor clear to the novices. here is an assumption that the novice user already knows enough about these plans to be able to successfully select from them the most appropriate one for the next mapping task. interestingly, bonar (1992) reports that the second phase was the most problematic in that the novices found it quite difficult to translate their plan-based solutions into pascal programs. this appears to suggest that knowing plans only might not be adequate to explain the performance of novice programmers. rather, what appears to be important is the conceptual knowledge and understanding of how different programming plans are used. one possible way to simplify this task would be to provide novices with a microworld-like, plan-based environment through which they can ‘discover’ themselves how different plans are used. 3.2.4 discover like gil, discover is an intelligent programming environment which synthesizes free with guided programming and supports software visualization (mukherjea et al, 1994; stasko et al, 1992; price, 1993; baecker et al, 1997; anjaneyulu, 1992) and immediacy of feedback. the system is designed to help novices acquire both programming knowledge and programming skill. this is accomplished in two phases: • in the first phase, the exploratory phase, the system helps novices through visualization and immediacy features to explore the dynamic behavior of programming statements and of the underlying notional machine to build a robust mental model of language execution and machine behavior. • in the second phase, the guided phase, novices put together program statements and language constructs, explored in the first phase, to solve problems under the intelligent guidance of discover. the interface of the discover system (shown in figure 1) was designed to facilitate the comprehension of large quantities and activity options that normally characterize discovery systems. the interface appears to a user as a collection of seven windows. the four windows on the left side of the interface, namely the memory space, the input space, the output space and the algorithm space, represent the components of the programming machine (ramadhan, 2000b). the interface is designed to expose the users to whatever is being manipulated and experienced, and hence brings them closer to the language and the machine. by doing that, the system brings the affordance into the users’ knowledge of perception and action. the visual model of the notional machine, through visualisation and immediacy features, is expected to help the users perceive and manipulate the dynamic behavior of the program and its unfolding computation with less effort and accelerate the debugging task. by allowing the users to have such visual view of program behavior within an integrated and coherent image of the programming machine, the system can reduce the mental overload on the novice users, hence more emphasis can be put on program understanding, debugging and problem solving. in short, interactions in discover among the program, the language and the machine are designed to produce an environment which makes it effortless for users to examine a program, figure out its effects and connections, and to relate problem solving with the properties of the machine they are interacting with. it may be argued that the interface with its multiple windows and various forms of feedback messages may increase the cognitive overload on the novice users during learning programming. we are aware of this point. during our pilot evaluations, summarized in the last section of this paper, we paid special attention to the comments made by the users on the usefulness of the display and its organization. we did not find any serious concerns on the novices’ side regarding the interface. we also have no reason to suspect that the interface layout is somewhat confusing to novices or distracting them while using discover. in fact, it is worth noting that the entire left portion of the interface represents one logical intelligent systems entity which nicely integrates its four components and provides a high-level image of the underlying programming machine. the programming language of the system is a simple pseudo-code based and algorithm-like language. at present, the language has no provision for functions, procedures, recursion and complicated data structures such as records, arrays and lists, thus focusing users’ attention on basic programming concepts and simplifying the learning process. programming concepts supported include create, put, read in, write out, while-end-while and if-istrue-isfalse. the naming of these concepts was drawn from the results of several well organized empirical experiments which studied the effects of pseudo-code as a programming language (vessey, 1985; boehm-davis, 1987; curtis, 198; dyck, 1987; mayer, 1985). figure 1: the interface it may be claimed that the language is very simple and that more functionality needs to be supported by the language to orientate novices to modern programming environments. we accept this argument and note that there is no reason why discover’s language should not be scaled up to support advanced users. this can be done by supporting advanced programming features such as procedures, functions and recursion, and more abstract data structures such as arrays, records, pointers, sets and files. in fact, it would be interesting to see in future versions of discover visual representations of advanced data structures such as lists and trees in the memory space of the system. having said that, it is our firm conviction that environments designed for beginner and intermediate programmers should avoid the temptation of including complicated functions and structures found in modern commercial languages such as support for visual applications, device interfacing, parallel programming and network support. clearly, with this advanced functionality, the environment would no longer be suitable for novice programmers. the selections in the concepts menu, shown in the top right-most position of the screen, contain the beginning of phrases. each phrase corresponds to one programming concept. when the user selects a concept, its corresponding name is inserted into the editor window and all the user has to do is to complete it by typing in its parameter part (e.g. the names of memory cells to be created). a template showing the 169 haider ali ramadhan and khalil shihab correct syntax for the selected concept is also inserted in the window next to the concepts menu. once a concept is completed it appears in the algorithm space window, where the code so far entered is stored. during the free phase, users can either load pre-written example programs or type in their own programs and visually observe the dynamic behavior of the language and the machine. for the later option, the system interprets each and every statement immediately after it is completed and visually shows its effects on the components of the notional machine. the user can also disable this interactive execution of his statements. in this case, the user can type his program and request the execution at any point by selecting the run option from the debug menu. syntax errors in the programs are trapped by the syntaxdirected editor and reported in the message window. figure 2 shows the visual execution of a program loaded by the user. 170 figure 2: visual execution of a program in both phases, the system visually executes the currently encountered statement and instantly shows the c the aim of the guided phase is to teach the novice how to compose and co-ordinate programming concepts and statements to solve programming problems under the intelligent guidance of the system and thus build effective problem-solving skills. the user has to build his solution to the current problem by properly putting together programming concepts. once a concept is completed and accepted by the syntaxdirected editor it is passed to the intelligent component of discover for automatic diagnosis. in doing so, discover attempts to model the steps taken by the user by evaluating his actions and responses. discover analyzes the surface code of the completed statement (partial solution code) without much specific knowledge about the problem to be solved or about how to design and construct an algorithm (i.e. discover cannot solve the problem itself). during the guided phase, users select from the problems menu the problem to be solved. for each problem, a statement is presented in the problem description window. hanges that take place in the memory space, input space or output space windows. in addition, each statement of the program is visually highlighted during the execution to show the user how the control flows from one statement to another, and how the highlighted statement affects the current state of the underlying notional machine. figure 3 shows an example of interacting with the novice user during the intelligent systems guided phase. this figure also shows how different programming concepts affect the components of the visible notional machine during execution in a manner which clearly shows possible causes and effects. this figure shows the user interaction while attempting to solve the ending value averaging problem. in this example, the user has failed to accumulate the numbers read by the program for the averaging purpose. the system detects this misconception and considers this step as a deviation from the solution path, and hence decides to interfere by guiding the user toward the expected step. for more detail regarding the diagnosis process, see (ramadhan, 1997). much like bridge, discover relies on a pre-stored reference solution (the ideal student model) for a given problem and applies various heuristics and pattern matching techniques to match the solution code provided by the novice with the reference solution in order to spot errors and misconceptions. however, like greaterp and gil, discover is a model-tracing based system, capable of interactively analyzing partial solution code and providing immediate feedback on failure. the system explicitly guides the novice in the process of putting together programming concepts to solve the given problem. discover monitors the novices actions, not on a symbol-by-symbol basis as it is done in greaterp, but on a complete statement-by-statement basis. as long as each statement represents a correct goal on a solution path, discover continues guiding the novice towards the final goal, reasoning about the goals already satisfied and hinting at the goals that still remain to be satisfied. unlike greaterp and gil, however, discover (1) utilizes goals and plans (not a production system) to represent the domain expertise, (2) does not keep an account, at least currently, of common error patterns (the buggy model), and (3) supports an ability to give delayed feedback by increasing the grain size of automatic debugging to a complete programming statement (not just a single symbol or token) and an ability to do limited backtracking by giving the user some chance to delete previously entered code and restart. see (ramadhan, 1997) for more description on how discover represents the reference solution and how it implements the diagnosis process. in the sections to follow, we present a more detailed discussion on various design issues incorporated in active program diagnosis systems along with suggestions for improving their engineering. as mentioned earlier, this discussion is presented in the context of the system discover. 171 figure 3 : a message from the intelligent component haider ali ramadhan and khalil shihab 172 3.2.5 a summarized com he four systems included in the in-event analysis category. an o 3. table 1: comparative analysis systems parative analysis this section provides a short analysis of t bjective and comparative evaluation of learning environments requires a set of standards to measure the effectiveness of the systems. to compare the features of these systems reviewed above, we use the following three design principles as criteria for our analysis: 1. systems should help the users in avoiding learning a mass of detailed syntax of the programming language being explored. 2. systems should assist the users in exploring the programming experience interactively through supporting various immediacy features. users should become active learners: forming their own hypotheses, exploring their own questions, and drawing their own conclusions. systems should assist the users in problem-solving through supporting automatic diagnosis with flexible immediate feedback on individual errors. table 1 shows the correspondence between the criteria established above and the four systems surveyed in the previous subsections. criteria 1 criteria 2 criteria 3 l isp tutor fair excellent good bridge exc ellent good fair gil fair ex cellent good dis cover exc ellent excellent good egarding the first cr th th being d, it has been claimed that r iterion, namely e scope of e language explore simplicity is among the most important characteristics that a programming language intended for novices should have (du boulay et al, 1981). three types of simplicity have been proposed: functional, logical and syntactic simplicity. the language should be kept functionally simple by giving it small set of basic instructions that are easy to understand; it should be kept logically simple by giving it instructions that are suited to the problems of interest to the novices, so that they can tackle and solve these problems by short and simple programs; and it should be kept syntactically simple, i.e. the rules for writing instructions should be uniform and have well chosen names. the names of the basic instructions are important as novices tend to make inferences about the language from these names. examples of these names are load and store instructions used in the assembler language that have real world connotations. both the lisp tutor and gil require the users to have a good command of the lisp language. because of high abstraction involved in the syntax and semantics of the lisp commands, constructs, and functions, users are faced with greater mental overhead when learning to program using the lisp language. discover and bridge use a pseudo-code like language which puts more emphasis on programming concepts and less emphasis on detailed syntax and abstract data types and constructs. regarding the pseudocode language, it has been noted that comprehension of programs depend both on the language used and on the task for which the language is used (du boulay et al, 1981). thus, even if the underlying algorithms are identical, creating the internal representation from one language may be more difficult than creating that representation from another language. in addition, it has been reported that the reason why it may be less difficult to create internal representations using pseudo-code language could be that it lessens the 'translation distance' from the documentation format to the program code. on the second criterion, namely the scope of the interaction, discover, gil and the lisp tutor provide highly interactive environments. all these three systems implement program diagnosis using model-tracing methodology, by which they monitor the actions of the user as he moves along the solution intelligent systems 173 the third criterion, namely flexibility of the immediate feedback, bridge falls behind the other 4. model-tracing based diagnosis model-tracing, used in the lisp tutor and gil, simply expresses the fact that the novice user is made to fol one of the rules in the ideal user mode short, the main features of model-tracing based diagnosis and tutoring are the following: • shows an • of checking low-level syntax of the • that it responds to every step (e.g. a single lisp symbol) the user through this approach to automatic diagnosis and tutoring, a model-tracing system can (1) diagnose very path, automatically analyze partial solutions for semantic errors and misconceptions, and offer guidance whenever he deviates from a correct solution path. bridge is not as interactive as it should be. the system has no capability of actively reasoning about the novice user while he develops the solution. as it was mentioned in section 3.2.3, the user builds his solution in a passive-like mode. when the user requests automatic debugging of his solution, the system steps through the code and presents the user with its feedback. an interesting extension to the system would be to make it capable of explicitly guiding the novice in the process of selecting programming plans to go with the goals and organizing these plans in a required order. finally, on three systems, as shown in table 1. the system has no capability of actively reasoning about the novice user while developing the solution, and hence the feedback is not immediate. discover, gil and the lisp tutor do support immediate feedback on errors. however, the grain size of automatic diagnosis in discover is not confined to a single language token or command, as in gil and the lisp tutor, but to a complete statement and expression. this feature gives the user some opportunity for self-correction and provides a larger context for tutorial instruction; hence its feedback is considered to be more flexible. low the system’s model quite closely. a model-tracing based system analyzes each and every step of the user’s solution to determine whether it is on a correct path toward a solution or indicates a misconception. in the lisp tutor and gil, the user’s step is analyzed by comparing it with the rules currently considered by the system, which represent the ideal user model. if the step taken by the user is one that can be produced by executing l, the rule is applied and the user is considered to be moving on a correct solution path. in this case, the system remains silent in the background and permits the user to continue. alternatively, if the user’s step cannot be produced by the ideal model, the system considers its buggy model, which represents general patterns of errors. misconceptions are flagged and diagnosed when the user’s step is produced by one of the rules of the buggy model. here the system interrupts and offers advice associated with the buggy rule. in this way, the system understands each step the user takes to build his program. it is this combined use of the ideal and buggy models, together called the generic model, which defines the model-tracing methodology: the system traces out the path currently taken by the user through the generic model and insists that the user stay on a correct path. in the system constantly monitors partial steps taken by the user and intervenes whenever he evidence for a misconception by deviating from a solution path. the interface in these systems tries to eliminate the problem language being learned (e.g. via the use of structure editors), and thus reduces the mental overhead associated with problem-solving. the interface is highly active in provides. specific errors and misconceptions, and provide clear advice and explanation within proper and immediate context, (2) explicitly guide the user in the process of organizing different programming concepts and statements, and (3) simplify the engineering of automatic diagnosis by preventing multiple bugs and errors. haider ali ramadhan and khalil shihab 174 anderson’s (1990) work on model-tracing and immediate feedback has strongly argued that these advantages make it worthwhile to incorporate this approach in the design of intelligent diagnosis and tutoring systems. his well documented empirical evaluations of the effectiveness of model-tracing and immediate feedback in procedural domain indicate that users learn procedures more quickly than conventional tutoring when provided with a model-tracing based environment. students can more easily utilize feedback and explanations when the system, the lisp tutor, supports the capability of automatically tracing, analyzing and reasoning about their partial solution steps that led to the error. anderson has also shown that such a tutoring strategy can prevent long episodes of counter-productive floundering by interactively trapping errors and correcting them as they show up in their proper context during the performance of a task. similar results have also been reported by reiser (1992) on his model-tracing, interactive, graphical lisp tutoring system gil. 4.1 critiquing model-tracing despite the achievement of the model-tracing based methodology to intelligent diagnosis, the approach suffers several drawbacks and shortcomings. first, by restricting the user to a symbol-by-symbol based top-to-bottom coding order, model-tracing hinders the opportunity for experimentation that might lead to a clearer understanding of the problem and thereby does not allow the users to explore and discover new strategies nor does it allow them to detect and correct their own errors and misconceptions. the main driving force behind model-tracing based systems is the detection of deviations from the ideal user model. these systems reject any other correct approach to solving a problem if it differs from the path currently followed by the system (nwana, 1991; wegner, 1987). second, the success of model-tracing based systems depends heavily on the extent of their modeltracing knowledge, which includes the number of correct rules in the ideal user model and the number of the mal-rules in the buggy user model (wegner, 1987). for example, the production system of the lisp tutor currently contains more than 1200 rules, more than half of which are mal-rules (anderson, 1990). production systems, despite their many advantages, impose several computational problems when utilized to support model-tracing based diagnosis and tutoring, especially of large problems, see section 4.3.2. third, the important programming activity of debugging is taken away from the user since modeltracing based systems, in principle, do not permit floundering (nwana, 1991; wegner, 1987). as a consequence, such systems may weaken the user’s personal motivation and sense of discovery. to address these issues, we have designed a prototype system called discover. the system uses a different implementation of model-tracing, supports an improved engineering of model-tracing based diagnosis, and provides a slightly more flexible style of tutorial interaction (e.g. than the lisp tutor) while preserving close ties to the underlying cognitive modeling of the model-tracing based diagnosis. before moving on, it is very important to clarify points that have to do with the terminology used to describe discover’s approach to automatic diagnosis, intelligent tutoring and knowledge representation. 4.1.1 what goals and plans in discover stand for there has been a great deal of work with programming ‘plans’. this includes formal definition (rich, 1986), empirical investigation (soloway, 1984), and implementation in ai systems (johnson, 1990). the plan notation has been developed to characterize aspects of language independent knowledge (information) about programming and to characterize language dependent knowledge used by novices and experts to implement programming problems (bonar, 1992). in this paper, we focus on plans as a tool for coding and matching syntactic templates that correspond to the low-level syntactic code objects in the discover’s language. this implies that plans here are language dependent. moreover, the plans presented and used in this paper reflect only the actual implementation of the code provided by novices, and not the possible implementation of the underlying knowledge of novices. the plans used in this research are thus neither (1) characterized to be the plans that were derived from a psychological theory of programming plans that was developed at yale, or the plans intelligent systems 175 that were developed at mit for the automatic programming project (rich, 1986), nor (2) characterized to have any sort of structures in them. concerning the ‘goals,’ johnson (1990) points out that goals are the principal requirements that must be satisfied if a solution is to meet the problem specification. these goals are used to represent the intentions of the programmer. a goal statement consists of a name of a type of goal followed by arguments. in short, johnson argues that goals describe what the programs must do, while plans describe how these programs are supposed to do it. in this paper, the term ‘goal’ is used to indicate the programming concept that the user is expected to select while solving a programming problem. so for example, when we say that the next goal is to initialize cell num, what we mean is that the user is expected to select a put concept from the menu to store a value in cell num. in this paper, goals are used as a planning tool for enabling novices to break down the problem in smaller steps, and each corresponds to the concept in a single program statement. in short, goals are mapped to programming concepts, which in turn are mapped to single statements. whereas in the original goal-and-plan literature, goals are mapped to plans, which are mapped to structures, which in turn are mapped to multiple statements, or possibly single statements. 4.1.2 is discover an intelligent diagnosis and tutoring system? instead of using a production system to perform automatic diagnosis and tutoring, discover uses a reference solution to trace all the possible solution paths needed to guide the tutoring process. the reference solution is represented in terms of a proust-like goal-and-plan tree, except (1) that it includes explicit relationships to constrain user steps on a solution path, and thus allows discover to preserve strong ties with the model-tracing paradigm, and (2) it is encoded procedurally. in the current implementation, the reference solutions (goal-and-plan trees) that guide automatic diagnosis in discover are generated by hand, and manually coded as a set of procedures, where a procedure represents a goal or subgoal, which in turn calls other procedures that represent the plans. in short, at present there is no explicit representation of knowledge in the system. it could be argued that this approach neither makes discover a knowledge-based system nor an intelligent debugging system, and hence a better term to characterize discover would be ‘an automatic diagnosis system’. while we agree with the first criticism, we argue that discover is more than an automatic diagnosis system. since the system currently has no student model and good courseware, we do not claim that it is a complete its. the plans in the reference tree have provision for associating a feedback message with user behavior. the system through these hand-coded explanations is capable of generating highly specific tutorial-like messages, and thus simulating some of the functionality of an its. by supporting that, discover is more than just a diagnosis system. 4.1.3 production systems and model-tracing in this paper, we argue that a production system is not the most efficient way to represent the domain expertise needed to implement model-tracing. model-tracing requires the system to be capable of interactively tracing all the possible paths that a user might decide to follow. to accomplish this, a production system needs to follow several branches simultaneously, and thus keep several rules active at one time. this is true even when a model-tracing system, such as the lisp tutor, is only capable of handling a very small grain size of modeling (e.g. single lisp symbol). in this paper, we argue that for a model-tracing system to be able to handle larger grain sizes of diagnosis (e.g. a complete program statement), the computational cost associated with time and space becomes too high. it is important to note the context for the discussion that follows. the critique is of production rules as used in model-tracing systems like the lisp tutor. it is not a critique of production systems in general. in short, the discussion that follows does not attempt to devalue the modular and expressive nature of production systems, but the way these systems are used to handle model-tracing in the domain of computer programming. haider ali ramadhan and khalil shihab 176 4.2 discover approach to model-tracing like the lisp tutor and gil, discover analyzes each and every step of the user’s solution to determine whether it is on a correct path toward a solution or indicates a misconception. however, the grain size of automatic diagnosis in discover is not confined to a single language token or command, but to a complete statement and expression. this feature gives the user some opportunity for self-correction and provides a larger context for tutorial instruction. to consider a simple example, suppose the user is expected to compute the average by generating ‘put total/count in average’ statement in discover language. discover will not diagnose individual parameters and tokens that make up this expression and will wait until the user submits the completed statement as his current step by hitting the return key. even if the user selects an entirely different concept than the one expected by the system, for example ‘read’ instead of ‘put’ in this case, the system will immediately recognize the bad selection but will not flag an error and thus give the user some opportunity for self-correction. in discover, the user’s step is analyzed by comparing it with the goals and plans of the reference solution, and not rules. if the step taken by the user is the one that can be matched with one of the plans (e.g. with the syntactic templates of plans) that are currently considered by the system, the plan is applied (e.g. the plan’s template is matched with the code object in the user’s statement) and the user is considered to be moving on a correct solution path. in this case, the system permits him to continue. alternatively, if the user’s step cannot be matched with any of the plans currently considered by the system, the system interrupts and offers a feedback message that attempts to explain the misconception in relation to its current context. in short, discover relies on its explicit planning mechanism (discussed in the next section) to trace the user’s planning and design decisions during problem-solving. as each complete statement in the user’s program is entered, discover checks to see if the user is following a correct design path. incorrect paths are pruned as soon as they are detected and the user is allowed to try again. if the user cannot determine how to proceed, discover can assist him and if necessary can provide the next correct step. 4.3 improving the engineering of model-tracing several alternative design principles can be proposed to tackle some of the pitfalls associated with the model-tracing approach, as it is implemented in the lisp tutor and gil, while preserving close ties to the underlying cognitive modeling on which it is based. one approach would be to support the following features and capabilities: 1. increasing the grain size of automatic analysis and tutoring to handle a complete expression and statement, rather than a single token, and thus delaying the feedback until the whole statement is submitted will give the user some flexibility for self-correction of errors. this approach will also provide the system a larger context for automatic diagnosis. this larger context in turn will enable the system to support a more flexible mode of tutorial interaction. 2. supporting an explicit planning (though low level) mechanism through which the information about the user’s planning and design actions are provided to the system naturally and voluntarily using a menu during all stages of the problem-solving process and not only in response to the lisp tutor like interventionist dialogue, which occurs at the last stage of the diagnosis process (e.g. when the system fails to determine the user’s planning decisions) will not only provide the user with an opportunity to decompose the problem into smaller steps, but will also simplify the computational cost involved in the automatic diagnosis process. 3. representing the ideal model using some other knowledge representation formalism that is more practical in terms of implementation and less expensive in terms of cost associated with time and space than the production system currently used in the lisp tutor and gil. intelligent systems 177 4.3.1 explicit planning mechanism to model the problem-solving process, discover utilizes an explicit planning mechanism. through this mechanism, discover, like bridge and gil, explicitly requires the novice user to select programming concepts from a menu. these selections externalize and represent the user’s design actions. in this way, the information about the user’s overall planning decisions is provided to the system by the user naturally while solving a problem. in other words, the information about the user’s goals (e.g. programming concepts to be selected in this case) needed to monitor his progress on a solution path is provided nonintrusively as an integrated part of problem-solving. the novice is presented with a menu of programming concepts that represent high-level goals. the novice solves the problem by selecting these concepts and putting them together in their proper positions. selecting a read in concept, for example, indicates to the system that the novice’s current goal is probably to get a value or an input from the user. through this mechanism, the system always gets the information needed to trace the novice’s actions in building the program. this approach greatly simplifies the problems associated with the automatic diagnosis of the solution. the system does not need to establish goals (programming concepts) because the novice spells them out for it. thus, the time spent by the system in diagnosing the errors could be certainly reduced, since the uncertainty in what path the novice would take is greatly minimized. the system compares the concept selected by the novice, which represents his current goal, with the one expected by the system (considered in the reference solution) and generates feedback without relying on a bug catalog. this mechanism, however, does not eliminate the plan-recognition problem. the representation of discover’s reference solution resembles the goal-and-plan tree of spohrer (1985). for each goal, there is number of plans that may be applied to implement and satisfy that goal. although the novice tells the system what goal he wants to pursue (i.e. what concept he wants to select), the system still needs to recognize the plans (i.e. code objects) used by the novice to properly implement the selected goal. 4.3.2 plan-based model-tracing a frequently used strategy in representing domain knowledge is to use a set of problem solving rules. each rule contains a description of a particular problem situation and a step to take in that situation, basically an action-oriented approach (clancy, 1987). a combination of these rules makes up what is known to be the production system. a production based system traces a user’s solution by matching each partial step provided by the user against the conditions of the rules in its problem solving model. gil and lisp tutor are the classic examples of programming tutoring systems that follow this approach. production systems, despite their advantages, are not the most efficient way (e.g. in terms of computational costs associated with time and space (anderson, 1990) to implement model-tracing (discussed in the next section). these systems have to consider a very large number of rules at any point during diagnosis process to be able to trace all possible next steps that the novice might follow. moreover, to cope with the problem of nondeterminism, these systems have to be used nondeterministically (i.e. more than one rule active at once) to be able to trace multiple paths before disambiguating information is encountered. the inability of these production systems to easily handle a larger grain size of modeling, for example a complete programming expression or statement (see next section), while supporting model-tracing, greatly contributes to their weaknesses. theoretically, there is no reason why a production system cannot handle larger grain sizes of modeling. in practice though, this would require a large increase in the number of rules, as will be shown shortly. in fact, it is for this reason that the systems based on such representation force a particular interpretation of the novice’s behavior on the novice (e.g. single-symbol based tutoring), rather than waiting until the novice generates enough of the solution step (e.g. complete statement), which in turn will enable the system to establish an adequate context for dealing with ambiguity. therefore, to increase the grain size of tutoring, a model-tracing system needs to depart somehow from using production systems as its driving force during the process of automatic diagnosis and tutoring. haider ali ramadhan and khalil shihab 178 implementing a production system also has high computational cost both in terms of space and time. problems tend to become more costly as they become larger even if they involve the same underlying knowledge. this is because the working memory of the production system tends to increase, as does the nondeterminism. in terms of time, a production based tutoring system becomes very slow when trying to simulate the user dynamically and interactively in order to trace and guide him. running the production system through an off-line compiler would solve the computational cost associated with time, but would increase the computational cost associated with space. because when the system is run ahead of time to produce the trace tree, it is necessary to follow every branch at an or-node so that later the system can trace the user down any possible branch. this requires exhaustively searching the trace tree for possible alternatives in the user solution, and also results in very large structures needed to store the trace tree. additionally, it is also an onerous task to develop complete production systems that also include a good set of buggy rules to model possible misconceptions and errors (nwana, 1991). discover uses a different approach to implementing a model-tracing based tutoring. instead of developing a complete production system with all the necessary mal-rules in it, discover uses a reference solution to trace all the possible solution paths needed to guide the diagnosis process. currently, the system has no knowledge of what bugs and misconceptions are likely to occur in the novice program. the system relies on its explicit planning mechanism to trace the user’s high-level goals and utilizes pattern matching and heuristics to trace the user’s plan-oriented actions. through this approach, discover detects and diagnoses very specific bugs when they arise in their immediate and proper context. the reference solution is represented in terms of a proust-like goal-and-plan tree, except that it includes explicit relationships to constrain user steps on a solution path, and thus allows discover to preserve strong ties with the model-tracing paradigm. in addition, plans in the reference tree also have provision for associating a feedback message with user behavior. goals represent different programming concepts which the novice needs to have in his solution and the plans represent the correct implementation of goals. thus plans are used to indicate the textual structure that the user code must have and the goalsubgoal structure of the code. variability as well as constraints over the user solution are represented using and/or clauses in the reference tree. it is this representation coupled with pattern matching which makes discover capable of supporting more variability (e.g. than the lisp tutor and gil) and larger grain sizes of modeling. for a detailed description of the representation mentioned here, see (ramadhan, 1997). 4.3.3 rules versus plans it is not easy for a rule-based system to allow the type of variability supported by discover, while at the same time handling active diagnosis and tutoring. the following discussion illustrates this point. consider the following function call in the case of the lisp tutor ( + (cdr list1) (cdr list2)), where the function cdr is used to return the remaining part of the list after stripping the first argument, e.g. applying the function cdr to the list (‘a b c d’) will return the list (‘b c d’). since the ordering of arguments to the function + is not important, the system allows the user to code the two arguments in either order. thus, when the goal is set to code the first argument, there are two candidate productions, each of which codes cdr. when the user types cdr, the context is not large enough to make it possible for the system to determine which argument the user is coding. this ambiguity could be resolved only in the next cycle when the next symbol is typed. however, to postpone resolution for a cycle, it would be necessary for the production system to follow both possible branches. that requires matching the user’s next step to the subgoal of each production, and thus increasing the amount of pattern matching required. moreover, even this simple variability that concerns the typing of the arguments in any order, as long as the ordering is unimportant, becomes very costly when the number of arguments grows larger than two. currently, the lisp tutor easily handles different unimportant orderings of arguments as long as the number of arguments is not greater than two. this requires only two productions to keep track of the two arguments, one checks for the ‘list1’, in our simple example, and the other for the ‘list2’. when the number of arguments is 4, for example, the number of different orderings becomes 4! (24 orderings). this implies intelligent systems 179 that the production system either has to have four productions, each with 4 matching components, or 24 different productions. in both cases, 24 different matchings are required. in addition, these productions have to follow at least 4 branches at the same time to be able to resolve the ambiguity, which in turn increases the computational cost involved. had we decided to represent discover’s knowledge using a rule-based approach, the same problems would have made the attempt to handle larger grain sizes of modeling very difficult to implement. in the case of discover, only 4 plans are required to check the unimportant ordering of 4 different arguments. for example, consider the following statement put (num1*4) + (num2*3) + (num3*7) + (num4*8) in newnum. since the entire statement is submitted at once, the first plan verifies the existence of the argument (num1*4) in the statement, regardless of its order. this is done by making sure that the pattern (num1*4) does exist in the statement. the second plan verifies the existence of the pattern (num2*3), and so on. since these patterns are hand coded in the reference solution, only one matching operation is required per plan. for example, the following plan (expressed in pop-11 programming language) member(“ (num3*7)”, statement) would be enough to make sure that the user has indeed included this argument in his statement. this would have been impossible had discover allowed the user to enter only one single symbol or token at a time. of course, the production system could incorporate this approach in its implementation (e.g. requires expected patterns to be hand coded in its rules to reduce the amount of matching components). but then, this would make the system become more or less discover-like, hand coded reference solution, which in turn would make the system lose its ability to synthesize the solution and simulate the user. 4.4 immediacy of feedback to develop the novice’s programming skill, a program diagnosis system must be able to trace the novice’s actions and determine when he diverges from a correct solution path so that it can offer suggestions or criticism on individual steps, rather than being limited to advice on complete solution step. by following the novice’s actions while trying to put programming concepts together, the system can respond to the underlying misconceptions that motivated the behavior rather being restricted to comments concerning the surface form of the whole solution. this requires, besides model-tracing, support for immediate feedback on both failure and success. 4.4.1 the need for flexible interaction the principal features of the lisp tutor’s interaction style can be summarized as follows: • the system insists that the novice stay on a correct solution path and immediately flags errors. the system reacts to every symbol the novice types and provides immediate feedback as soon as the novice deviates from the solution path. • the system does not allow the novice to backtrack and delete previously entered code. • the system uses a menu-based dialogue to track planning decisions and behaviors when it fails to trace them nonintrusively. • the system forces the novice to enter the code in a left-to-right, top-to-bottom manner. this implies that the next piece of code or the next step on a solution path is decided by the system and not by the novice. occasionally though, the user is given some freedom in dealing with arguments whose ordering is not important, or even with functions which have the same underlying functionality, such as cons, append and list. while each of these features has pedagogical justification and close ties to the underlying cognitive modeling, there is no reason why some of these features, especially the first two, cannot be improved to support a more flexible style of tutorial interaction while preserving a close relationship to the modelhaider ali ramadhan and khalil shihab 180 tracing approach. some amount of self-detection and correction of errors may lead to a clearer understanding of the problem and a better explanation of the programming process by the novice and certainly is something that users using the lisp tutor have said they wanted (anderson, 1990). providing immediate feedback upon every single lisp symbol is also extremely undesirable and restricting in situations where not enough context has been established for the novice to understand why his solution is wrong. 4.4.2 the interaction style of discover discover supports a more flexible style of tutorial interaction that is based on improving the first two features of the lisp tutor’s interaction style mentioned above. this is achieved by increasing the grain size of automatic tutoring and by providing novices with some opportunity for self-correction of errors. the principal features of discover’s interaction style can be summarized as follows: • the system reacts to every complete programming statement and expression, not to a single symbol, and provides immediate feedback as soon as the novice wanders off the correct solution path. • the system supports limited backtracking by allowing novices to delete previously entered code (e.g. parts of the statement currently being completed). • the system supports an explicit planning mechanism to trace the intentions and high-level goals of the novices. novices externalize their planning decisions by choosing form a menu of programming concepts rather than through a dialogue. • the system requires the novice to enter the code in a top-to-bottom manner. by increasing the grain size of tutoring to a complete statement and expression, discover provides novices with some opportunity for self-correction and also a larger context for instruction. since the grain size of tutoring is confined to a single symbol, the lisp tutor finds it difficult to explain why a novice’s action is wrong at the point which the misconception is first manifested because there is not enough context. to consider an example, compare a novice who provides (append x y) where (cons x y) is better for appending the contents of the two lists x and y in a single list returned by the system. it would become easier to explain the choice after the complete statement has been provided rather than after ‘(append’ has been entered. in the case of discover, this problem does not arise. if the novice provides, for example, ‘read 5 in num’ where ‘put 5 in num’ is more appropriate, the system explains the choice after the complete statement has been typed in rather than immediately after ‘read’ has been selected. this allows discover to generate more appropriate explanations and advice that can derive mapping, generalization and coordination that exist between similar programming concepts. for example, in the case of ‘read’ instead of ‘put’, discover informs the novice that it would be better in normal cases where getting an input from the user is not required to use the ‘put’ concept for assigning values to cells. this explanation would not become possible to generate if discover could not wait to see whether the novice indeed wanted to read 5 and not some other values in cell ‘num’. discover also supports limited backtracking by allowing novices to delete previously entered parameters and operators of the statement currently being completed. unfortunately, at present the backtracking is confined to the current statement only. the novice can also cancel the selection of a concept and select a new one that best represents his next goal. for example, if the novice selects the ‘read’ concept where ‘while’ is expected and realizes after completing the selected concept, but before submitting it, that he made an error, he can backspace over the statement. the system would ignore the selection without considering it a deviation from a solution path. this gives the novice some opportunity for self-correction. in fact, there are cases in which the novice may be confused about what goals and plans are appropriate in the current situation and would realize only if he is given a little more time to self-correct. this is not possible with the classical version of the lisp tutor. intelligent systems 181 5. conclusion in this paper we have presented an overview of the field of intelligent program diagnosis and critically compared work accomplished on four closely related active diagnosis systems while emphasizing such issues as the representation techniques used to capture the domain knowledge required for the diagnosis, ability to handle the diagnosis of partial code segments of the solutions, features of the user interfaces, and methodologies used in conducting the diagnosis process. several design considerations to improve the engineering of active approach to intelligent diagnosis were proposed. in particular, we have argued in this paper that the model-tracing based active approach to automatic program diagnosis has several advantages when compared to other approaches. these advantages include (1) the ability for diagnosing very specific errors and providing specific feedback within proper context, (2) the ability to analyze partial solution steps as they are generated by the users and hence reason about the problem solving process, and (3) the ability to minimize the impact of multiple bugs on the diagnosis process. despite these advantages, we have also argued that this approach to automatic diagnosis tends to be very directive and that some alternative design decisions need to be incorporated into this approach to make it support a more flexible style of user interaction. alternatives proposed include (1) supporting an ability to give delayed feedback by increasing the grain size of diagnosis to a complete program statement, not just a single word or token, (2) allowing the users to do limited backtracking by giving them some chance to delete previously entered code and restart, and (3) departing from production system when representing the expertise needed for automatic diagnosis. these alternative design issues were successfully incorporated in the implementation of discover. with the rapid growth in the web development and distance learning technology, we hope to develop a web version of discover using some internet programming languages such as java to introduce programming concepts and problem-solving to novice users all over the world. the language supported by the system can also vary to cover other languages used in some popular applications such as the scripting language used in the spreadsheets calculations, sql language used in the database applications, and the html language used in the web applications. 6. references adam, a. and laurent, j. 1980. laura: a system to debug student programs. journal of artificial intelligence, 15: 75-122. anderson, j. 1982. acquisition of cognitive skill. psychological review, 89: 369-6. anderson, j. 1990. cognitive 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animation and multi-view editing, proceedings of the 1991 ieee workshop on visual languages, japan, pp. 4-9. clancy, w. 1987. qualitative student models. annual review of computer science, 1: 381-450. curtis, b. 1988. experimental evaluation of software documentation formats. journal of systems and software, 9: 141. haider ali ramadhan and khalil shihab 182 davies, s. 1992. cognitive models of programming and the design of support for learning. proceedings of the nato workshop on cognitive models and intelligent environments for learning programming, italy. du boulay, j.b.h., o'shea, t. and monk, j. 1981. the black box inside the glass box: presenting computing concepts to novices. international journal of man-machine studies, 14: 237-249. dyck, j. 1987. learning and comprehension of basic and natural language computer programming by novices, ph.d thesis, university of california, santa barbara, usa. eisenstadt m. 1993. software visualization as a pedagogical tool, instructional science, vol. 21: 335-364. gilmore, d. and green, t. 1988. programming plans and programming expertise. journal of experimental psychology, 40a: 69-92. goldsein, i. 1974. understanding simple picture programs. phd thesis, mit. hashmer, t. 1983. an empirically-based debugging system for novice programmers. phd thesis, the opend university, uk. johnson, w. 1990. understanding and debugging novice programs. artificial intelligence and learning environments, clancey and soloway (eds.), mit/elsevier. lawrence, a. empirically evaluating the use of animations to teach algorithms. ieee symposium on visual languages, st. louis. lieberman, h. 1984. seeing what your programs are doing. international journal of man-machine studies, 21: 311-331. lukey, f. 1980. understanding and debugging programs. international journal of man-machine studies, 12: 42-71. mayer, r. 1981. the psychology of how novices learn computer programming. computing surveys, 13: 121-141. mayer, r. 1985. learning in complex domains: a cognitive analysis of computer programming, in psychology of learning and motivation, bower (ed.), 19: 89-130, academic press, usa. miller, j. 1982. intelligent tutoring for programming tasks. technical report, texas instruments. mukherjea, s. and stasko, j. 1994. toward visual debugging: integrating algorithm animation capabilities within a source-level debugger, acm tochi, vol. 1: no. 3 (sept. 1994), pages 215-244. murray, w. 1986. automatic program debugging for intelligent tutoring systems. phd thesis, texas university, austin, 1986. nwana, h. 1991. an approach to developing intelligent tutors. proceedings of the 6th international peg conference on knowledge based environments for teaching and learning, italy. price, b. a. 1993. principled taxonomy of software visualization. journal of visual languages and compuling, 4(3): 211-266. ramadhan, h. 1992a. intelligent vs. unintelligent programming systems for novices. proceedings of the ieee 15th international conference on computer applications and systems, usa. ramadhan, h and du boulay, b. 1992b. programming environments for novices. du boulay and lemut (eds.), cognitive models and intelligent environments for learning programming, spring verlag. ramadhan, h. 1997. improving the engineering of model-tracing based approach to intelligent program diagnosis and tutoring, iee journal of software engineering, 144(3): 149-161. ramadhan, h. 1997. model tracing based approach to intelligent program diagnosis. squ journal of science & technology, 2: 65-76. ramadhan, h. 1999a. active vs. passive systems for automatic program diagnosis, proceedings of international conference on hci (hci’99), pp 345-351, munich, germany. ramadhan, h. 1999b. improving the engineering of immediate feedback for model-tracing based program diagnosis, proceedings of international conference on hci (hci’99), pp 352-358, munich, germany. ramadhan, h. 2000a. discover: an intelligent system for discovery programming , journal of cybernetics & systems, vol. 31: 87-114. ramadhan, h., brusilovsky, p., and deek, f. 2000b. incorporating software visualization in the design of intelligent diagnosis systems for user programming, journal of artificial intelligence review, 01: 1-24. reiser, b. 1992. making process visible: scaffolding learning with reasoning-congruent representations. proceedings of the 2nd conference on intelligent tutoring systems (its ’92), montreal. repenning, a. 1996. domain-oriented design environments: making learning a part of life, communications of the acm, 9: 56-72. rich, e. 1986. characterization of plan-based program analysis approaches to debugging. personal communication, april, 1986. ruth, g. 1973. analysis of algortihm implementations. technical report, mit project mac tr 130, mit. shapiro, e. 1983. algortihmic program debugging. mit press, mit. intelligent systems soloway, e. 1984. empirical studies of programming knowledge. ieee transactions on software engineering, september, 1984. stasko j. and patterson c. 1992. understanding and characterizing software visualization systems, proceedings of the 1992 ieee workshop on visual languages, usa, pp. 3-10. spohrer, j. 1985. a goal/plan analysis of buggy pascal programs. human computer interaction, 1(2): 163:207. vessey, i. 1985. expertise in debugging computer programs: a process analysis. international journal of manmachine studies, 23: 459-494. wegner, e. 1987. artificial intelligence and tutoring systems, morgan kaufmann publishers, usa. received 22 september 1999 accepted 3 july 2000 183 intelligent systems for active program diagnosis haider ali ramadhan and khalil shihab contents 1. introduction: automatic program debugging 158 6. references 181 introduction : automatic program debugging conclusion 6. references microsoft word biol080506-f edited_checked.doc 9-15 squ journal for science, 14 (2009) © 2009 sultan qaboos university 9 integumentary histology of the amphibious blenny, isteblennius edentulus (forester and schneider, 1801) taher ba-omar and maisoon m. al-riyami department of biology, college of science, sultan qaboos university, p.o.box 36, alkhod 123, muscat, sultanate of oman, email: taher@squ.edu.om. دراسة أنسجة جلد سمكة البليني البرمائية استبلينيوس ايدينتولوس طاهر باعمر وميسون الريامي بواسطة المجهـر الضـوئي والمجهـر الماسـح استبلينيوس ايدينتولوس تم دراسة جلد سمكة البليني البرمائية :خالصة ، وكذلك وجود نتؤوات شبيهة ببصمة االصبع فـي الجلد أدمة الدموية تحت األوعيةتم مالحظة عدد كبير من . االلكتروني باالضافة الى وجود ) التنفس(الطبقة الطالئية الخارجية للجلد، وتقوم هذه النتؤوات بزيادة المساحة الالزمة لتبادل الغازات لبطنـي هذه المسامات في الجانب الظهري للسمكة مقارنة بالجانب ا إعدادمسامات جلدية صغيرة حيث تم مالحظة زيادة . أن الجلد سميك في الجانب الظهري مقارنة بالجانب البطنيإلى هنا اإلشارةوتجدر abstract: the skin of the amphibious blenny, istiblennius edentulus, was studied using both light and scanning electron microscopy. rich vascularisation was found immediately below the epidermis and the dermis. surface epithelial cells displayed microridges in a fingerprint-like pattern. it was speculated that this increased surface area may aid in the adhesion of mucous secretions as well as to increase the surface area for gas exchange. the number of pores on the dorsal side (6.3x103 per mm2) was significantly higher than that on the ventral side (4.3x103 per mm2). the thickness of the skin on the dorsal side was measured at 31.6±10.0µm and that on the ventral side was 32.9 ± 7.8µm. keywords : blenny; istiblennius edentulus; pores; skin epithelia. 1. introduction eleost fish, the most diverse group within the vertebrates, exploit a wide range of habitats. some families such as the blennidae (blennies), pholidae (gunnels), stichaeidae (prickle-backs), gobiidae (gobies), t taher a. ba omar and maisoon m. al-riyami 10 gobiesolidae (clingfishes) and cottidae (sculpins) have colonized the intertidal zone (gibson, 1986). these groups utilize the intertidal zone either as a primary habitat or as a feeding ground when it is submerged (moyle and cech, 1988). in this environment they are exposed to daily variations in temperature, oxygen (po2), carbon dioxide (pco2), ph and salinity (bridges, 1988). they have therefore evolved a range of structural and physiological adaptations. these include small body size resistance to wave action scales firmly attached or totally absent, the development of mucus and the use of specialized pectoral fins for substrate attachment (gibson, 1986). because gills collapse under their own weight in air, and so are not well suited to aerial respiration (withers, 1992), structural adaptations have evolved to facilitate aerial respiration. these include modifications of the gills, the use of the skin as a gas exchange surface, special respiratory structures in the mouth and gut and, also, true lungs (moyle and cech, 1988). some forms exploit the relatively high levels of oxygen in air to compensate for low levels in water. several histological studies have been conducted on the skin of various species of air-breathing fish (mittal and munshi, 1971; brown et al. 1992; al-khadomiy and hughes, 1988; yokoya and tamura, 1992; suzuki, 1992 ; zhang et al 2000 and ba-omar and al-riyami, 2007). in this study, we describe the skin structure of i. edentulus, using light and scanning electron microscopy and compare it to adaptations in fishes exploiting a similar niche. 2. materials and methods specimens of istiblennius edentulus (figure 1) were collected from the rocky shores of the gulf of oman in muscat, oman and transported to the laboratory alive where they were kept in a saltwater aquarium. the fish were killed by freezing and then cut into three portions; front, middle and back. each portion was then further divided into dorsal and ventral halves. representative subsamples were fixed in 40% buffered formalin and processed for light microscopy. other subsamples measuring 4 mm2 were fixed in 3% glutaraldehyde (two days) followed by a two-hour immersion in phosphate buffer (ph 7.3) and then dehydration through an ethanol series. tissue samples were then dried in a critical point drier (samdripvt 3b) and coated with gold using a jeol jfc-1100 e ion sputter. the samples were examined with a jeol jms-840a scanning electron microscope. using sem micrographs exposed at a magnification of x2000, the number of pores on the surface of the epithelial cells per unit area, other than openings of mucous cells, was counted. the thickness of the skin on the dorsal and ventral sides was measured using the scale bar from the micrograph. an analysis of variance (anova) was performed to detect significant differences in the number of pores on both dorsal and ventral sides and also to measure the thickness of the skin of both dorsal and ventral sides. paired t-tests were performed to detect significant differences in the number of pores in the dorsal and ventral sides and the thickness of the skin. data on the number of pores and the thickness of the skin were log transformed. microsoft excel was used for the statistical analysis. 3. results 3.1 light microscopy the skin of i. edentulus does not possess scales. it displays the familiar three layers: epidermis, dermis and hypodermis (figure 2). the epidermis consists of stratified squamous epithelium and contains large numbers of mucous cells which are spheroidal in shape (figure 2). the dermis is made up of bundles of collagen fibers. the hypodermis lies between the dermis and the body musculature and consists of loose connective and adipose tissues (not visible in sections due to solution by xylene). blood capillaries, together with pigment cells, are seen throughout the integument. pigment cells are elongated and have dendritic processes that radiate from the central cell body (figure 2). the capillaries are more common on the dorsal side than on the ventral side of the fish. integumentary histology of the amphibious blenny 11 figure 1. the amphibious blenny, i. edentulous. figure 2. light micrograph through the skin of i. edentulus from the dorsal side. epidermis (e), dermis (d), hypodermis (h), muscles (m), pigment cells (p), mucous cell (arrow). (h and e) x200. 3.2 scanning electron microscopy the epidermal cells that cover the skin surface possess closely-spaced microridges displaying a fingerprint-like pattern (figure 3). the boundaries between the epidermal cells are clearly defined where several pores are visible at their junctions. in many cases, mucous cells can be seen in the vicinity of the pores. other pores which extend deep into the integument were observed on the surface of epithelial cells (figure 4). unlike the light microscopic preparations, sem micrographs clearly show pigment cells with their pigment granules. blood capillaries are also clearly visible and can be seen running close to the epidermis and penetrating down through the dermis (figure 5). taher a. ba omar and maisoon m. al-riyami 12 figure 3. scanning electron micrograph of the dorsal surface of the skin showing fingerprint-like appearance of the microridges. the opening of mucous cells (m) and the pores (arrows) are visible. scale bar =10µm. figure 4. scanning electron micrograph of the ventral surface of the skin showing pores (arrows). scale bar = 100µm not at all clear. figure 5. scanning electron micrographs of the skin showing blood vessels (b), hypodermis (h), mucous cells (m) and pigment granules (p). scale bar =10µm. integumentary histology of the amphibious blenny 13 3.3 measurements and statistical analysis paired ttest showed that there is a significant difference in the number of pores in the dorsal and the ventral side of the body (t = 3.519; p = 0.012). pores are significantly more abundant in the dorsal side (6.3 x103 pores/mm2± 0.8 ) than in the ventral side (4.3 x10 3 pores/mm2 ± 1.1) (table 1). table 1. maximum, minimum, mean and standard deviation with 95% cl of the number of pores on the surface of the skin (x1000 per mm square) in the different parts studied, where n = 5. the average thickness of the skin on the dorsal side is 31.6 µm ±10.0 and that of the ventral side is 32.9µm ±7.8 (table 2). anova and paired t-test have shown that there are no significant differences in the thickness of both the dorsal and ventral side (f = 0.07, t = 0.335, p > 0.05) table 2. maximum, minimum, mean and standard deviation with 95% cl of the thickness of the skin in the different parts studied, using sem where n = 5. 4. discussion in amphibious fish, the integument must provide a viable interface between both air and water. while it has been indicated (salih and al-jaffary, 1980) that the hypodermis is the principal layer of fish integument, this study has shown that the skin of the amphibious blenny, i. edentulus has a poorly developed hypodermis. in this species the epidermis is composed of stratified squamous epithelium and large numbers of mucous cells while the dermis is the dominant layer and contains bundles of layered collagen fibers. the hypodermis, which is the thinnest layer, is made up of loose connective tissues and adipose tissues. gas exchange in air breathing fishes generally does not occur across the gills but, across other vascularized surfaces, including the skin, buccal, branchial or opercular mucosa, stomach and intestine (withers, 1992). the skin is particularly important in aerial respiration (salih and al-jaffery, 1980) and is adapted by an increased density of cutaneous capillaries (mittal and munshi, 1971). using such criteria, the air breathing fishes can be classified into three groups according to the structure of the skin: those in which the blood capillaries are subepithelial in position: those in which the capillaries are more numerous in the subepithelium and may even extend into the epithelium, and those in which the capillaries are mostly epithelial in position (yokoya and tamura, 1992). mittal and munshi (1971) suggested that the cutaneous blood capillaries are typically in the dermis and not the epidermis. the only vertebrates reported to have epidermal capillaries are some of the gobioid fishes and several semi-terrestrial amphibians (kent, 1987). brown et al. (1992) showed the location of the capillaries just below the epidermis in the rock skipper alticus kiri and suggested that they may perform an important function in gas exchange. the skin of i. edentulus location dorsal ventral front middle back maximum 7.0 6.0 7.1 5.9 6.6 minimum 5.0 3.4 5.2 3.7 3.1 mean 6.3 4.3 6. 1 5.1 4.8 sd 0.8 1.1 1.1 0.8 1.4 location dorsal ventral front middle back maximum 48.0 43.3 41.7 51.5 42.7 minimum 20.9 21.8 25.1 18.5 19.0 mean 31.6 32.9 31.5 33.6 32.1 sd 10.0 7.8 6.5 12.4 8.7 taher a. ba omar and maisoon m. al-riyami 14 is richly vascularized, and the blood capillaries are similarly present immediately below the epidermis and the dermis, thus also suggesting a role in gas exchange in this species. the most effective surface for gas exchange in the skin would seems to be the thinner and the more vascularized regions. mittal and munshi (1971) proposed that the capillaries of the skin, located within 500 µm of the surface, are competent for the exchange of gases by diffusion. the skin of i. edentulus with a thickness of 18.5 – 51.5 µm is likely to permit vascular gas exchange through diffusion. since there is no significant difference in the thickness of the skin across the body, the entire skin of the fish would facilitate gas exchange with equal efficiency. the surface view of the skin under sem illustrated epithelial cells with invaginations and elevations that form fingerprint-like patterns. a similar pattern is seen in the skin of coho salmon, oncorynchus kisutch, and has been described as ‘microridges’ (hawkes, 1974). microridges were also reported in the gill filaments of the air breathing fish, saccobamchus fossilis (hughes and mittal, 1973) and the swamp mud eel, monopterus cuchia (munshi et al. 1989). the probable function of microridges is to increase the surface area for gas exchange. however, hughes and munshi (1973) suggested that the microridges do not extend far above the general epithelial surface, and might well be more important for providing a surface of adhesion for the mucous layer. there are two developmental pathways for the epidermis of vertebrates, one related to keratinization and the other to mucogenisis. this duality in developmental potential is open to environmental adaptation. keratinization cell types usually occur predominantly in terrestrial animals, whereas mucous producing cells are found in amphibians and aquatic forms (suzuki, 1992). the presence of large number of mucous cells in the epidermis of i. edentulus is an adaptation to its rocky habitat (mittal and banorjee, 1975). since the skin is devoid of scales, unlike typical fishes, mucous cells serve to protect the skin against mechanical injury in the rock pool habitat. they also play a role in slowing desiccation by evaporation in air (mittal and banorjee, 1975). furthermore, with respect to cutaneous respiration, the maintenance of wet surfaces is essential to preserve the functional morphology of diffusion membranes (yokoya and tamura, 1992). in i. edentulus mucous cells discharge their secretions onto the surface of the skin through openings located at the junctions of epithelial cells. in addition to the openings of mucous cells, other pores were found to extend deep into the skin and may function to reduce the air-blood distance. the dorsal side of the fishes possesses larger number of pores and higher levels of vascularization than the ventral side. this suggests that higher rates of gas exchange may take place across the dorsal surface, which is consistent with it being the area most in contact with air. like blood capillaries, pigment cells are present just below the epidermis and the dermis. they have dendritic processes that extend from the central cell body. this organization enables changes in the colour such as are found in chromatophores. consequently it can be deduced that pigment cells have both photoprotective and camouflage functions. 5. references al-kadhomy, n.k. and hughes, g.m. 1988. histological study of different regions of the skin and gills in the mudskipper, boleophthalmus boddarti with respect to their respiratory function. j. mar. biol. assn. uk, 68: 413-422 ba-omar, t.a. and al-riyami, m.m. 2007. scanning electron microscopy of the fish istiblennius edentulus skin . microsc and microanal 13: 282-283 bond, c.e. 1979. biology of fishes. saunders college publishing, new york. pp358-370. bridges, c.r. 1988. respiratory adaptation in intertidal fish. am .j .zoo, 28:79-96. brown, c.r, gordon, m.s. and martin, k.l. 1992. aerial and aquatic oxygen uptake in the amphibious red sea rockskipper fish, alticus kiri (family blennidae). copeia. 4:1007-1013. eckert, g., randall, d., and augustin,g. 1988. animal physiology, mechanisms and adaptation. 3rd ed. w.h freeman and company, new york. pp483-496. fishelson, l. 1975. observations on the behavior of the fish meiacanhus nigrolineatus smith-vaniz (blenniidae) in nature (red sea) and captivity. aus. j. mar. and freshwater 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inc. new jersy. p45. munshi, i.s.d., hughes, g.m., gehr, p. and weimbel, e.r. 1989. structure of the air breathing organs of a swamp mud eel monopterus cuchia. japan j. icthyol. 35: 453-465. salih, m.s. and al-jaffary, a. 1980. morpholgical study of boleophthalmus dentus, with reference to its feeding habits, 1:habitat, external features and integument. bull. biol. res. 149: 147-158. suzuki, n. 1992. fine structure of the epidermis of the mudskipper, periophthalims modestus (gobiidae). japan j. icthyol. 38: 379-395. withers, p.c. 1992. comparative animal physiology. saunders college publishing, new york. pp 608-614. yokoya, s. and tamura, o.s. 1992. fine structure of the skin of the amphibious fishes, boleophthalamus pectinirostris and priophthalmus cantonensis, with special reference to the location of blood vessels. j. morphol. 214: 287-297. zhang, j., taniguchi, t., takita, t. and ali, ab. 2000. on the epidermal structure of boteophthalmus and scartelaos mudskippers with reference to their adaptation to terrestrial life. ichthyol. res., 47(4): 359-366. received 6 may 2008 accepted 29 june 2009 microsoft word ersc090726-f -edited_corrected_20oct2010.doc 54-41 squ journal for science, 15 (2010) © 2010 sultan qaboos university 41 lithofacies attributes of a transgressive carbonate system : the middle eocence seeb formation, al khoud area, muscat, oman. *osman salad hersi and abdulrahman al-harthy department of earth sciences, college of science, sultan qaboos university, p.o. box 36, postal code 123, muscat, sultanate of oman, *email: oshersi@squ.edu.om. دراسة تكوين السيب في منطقة الخوض بسلطنة عمان : خصائص ومميزات السحنات الصخرية في فترة طغيان البحر كمثال لهذا النظام الكربوناتي عثمان صالد حرزي و عبدالرحمن الحارثي حيث ،ترة طغيان البحرثناء فأوسط يوسين األ اإلعهدن في ّو و الذي تكم، 600سماآة تكوين السيب حوالي تبلغ :خالصة يتالف تكوين السيب من خمس . محافظة مسقطمتداد الساحلي لمنطقة الباطنة واإلترسبت هذه السحنات الصخرية الجيرية على تتميز هذه . من الجرف القاريوحدات متراصة تمثل بنية تراآمية للسحنات الجيرية المترسبة في المياه البحرية الضحلة قدم تكونت األالطبقات بمعنى ان ، في عمق المياه مع الطبقات االقل عمراَا مطردًازديادإا على ترسبات تمثل حتوائهإالطبقات ب قدم تمثل تراآمات يكثر فيها التقاطع الطبقي و هي األ والوحدة االولى . عمقأي مياه ترسبت فا بينما االحدث في مياه ضحلة جًد مما يوحي ) grainstones(او منعدم تماما ) packstones( و قليلة النسيج الطينيتتكون من طبقات جيرية غنية باالحافير تتكون من الوحدة الثانية . شاطئية ذات طاقة هيدروليكية عالية بسبب حرآات المد والجزران هذه الوحدة تكونت في بيئة النسيج الطيني بدرجات متفاوتة دالة على طبقات غير متمايزة تكثر فيها المنخربات الكبيرة و العقد الكلسية و تحتوي على تتكون من طبقات جيرية ذات سماآة متوسطة الى الوحدة الثالثة .الخيران ذات طاقة هيدروليكية متوسطةترسيب في بيئة و توجد بهذه الوحدة ) grainstones(او منعدم تماما ) packstones( آبيرة و هي غنية باالحافير و قليلة النسيج الطيني كثر فيها التقاطع الطبقي و البنيات الرسوبية المقعرة و يو . سات من الكونجلومرات محصورة أفقيا في نطاقات معينةعد مما يدل داللة قاطعة على انها تكونت في االجزاء الضحلة ) hummocky and swaley cross-stratificiation(المحدبة ة بالوحدة الثانية من حيث ه فهي شبيالوحدة الرابعةأما . بشدة االعاصيرالقاري والذي آانت تعتريه فترات تمتازالجرف من فهي عبارة عن سحنات جيرية يغلب الوحدة الخامسةو اخيرا . السحنة اال انها ترسبت في نطاق أعمق من الجرف القاري آبيرة زيادة علىا يعطي مؤشرمع وجود آميات من حبيبات الكورتزمما المنخرباتنسبة قليلة من وبهانييعليها النسيج الط ن ترسيب تكوين السيب بدأ من أعاله يؤآد أنفة الذآر بالطريقة المذآورة ن تتابع الوحدات األإ .في عمق مياه الجرف القاري .في فترة طغيان البحرالقاري لى مناطق عميقة في الجرف إبيئة شاطئية ضحلة abstract: the seeb formation (middle eocene) is an about 600 m thick transgressive carbonate succession deposited in the batina and muscat coastal region of oman. the formation consists of five informal, but distinct units, and their stacking architecture suggests a deepening-upward, shallow marine depositional setting. unit i is characterized by crossbedded, sandy, bioclastic packstones to grainstones deposited in a high energy beach-toosman salad hersi and abdulrahman al-harthy 42 intertidal environment. unit ii consists of indistinctly bedded, nodular, bioclastic (mainly larger foraminifera) packstones and wackestones deposited in a lagoonal environment. unit iii is defined by medium to thickly bedded, bioclastic packstones to grainstones and subordinate, laterally confined conglomerates. prominent sedimentary structures in unit iii include hummocky and swaly cross-stratificiation, erosional surfaces, dewatering-induced deformations and laterally amalgamating beds. this unit represents sub-tidal sand shoals deposited in a storm-dominated shelf (between the fair-weather wave-base and storm-base). unit iv is extensively burrowed, nodular, bioclastic wackestone to rudstone which is similar to unit ii in many aspects. unit iv was deposited on the basinward side of the unit iii sand shoals below the reach of the storm-generated waves and currents. the uppermost unit v is characterized by poorly-cemented bioclastic (large foraminiferal) rudstones with clay and silt-size quartz matrix. bioclasts are generally intact with no apparent reworking. deposition of unit v is also envisaged as a low-energy, outershelf environment. keywords: seeb formation, middle eocene, carbonate platform, muscat and lithofacies. 1. introduction he seeb formation belongs to the tertiary sequence of northern oman and is well exposed along the eastern coastal strip of the batina region and the governorate of muscat, oman. nolan et al. (1990) have proposed the name seeb formation for a thick carbonate sequence previously correlated with the dammam formation that occur in much of the arabian peninsula (steineke et al, 1958). however, the batina coast (including the muscat region) where the formation is best developed appears to have been separated from the main arabian carbonate platform during deposition of the coeval dammam formation by the uplifted hinterland of omani mountains. a recent publication by beavington-penney et al. (2006) has made further biostratigraphic dating, mainly based on larger foraminifera of the formation, confirming its middle eocene age. however, the sedimentological attributes and the stacking nature of the various lithostratigraphic units of the formation need further consideration in order to better understand the interplay between the sedimentation and relative sea level changes. spectacular outcrop exposures occur within a few kilometers of the campus of sultan qaboos university (squ, figure 1) and recent geological visits to the area acknowledged new sedimentologic attributes and lithostratigraphic architecture for the seeb formation. this work presents the preliminary results on the lithostratigraphic evolution of the seeb formation based mainly on field observations. 1.1 previous work the earliest works on the tertiary sequence of the batina coast include powers et al. (1966), glennie et al. (1974), racz (1979), warrak (1986) and hughes-clarke (1988). these authors commonly adopted a stratigraphic nomenclature imported from coeval sedimentary sequences in saudi arabia (i.e., umm radhuma, russ and dammam formations. a stratigraphic revision by nolan et al. (1990) has changed this practice by proposing new stratigraphic terms of jafnayn, rusayl and seeb formations, in ascending order, for the lower tertiary strata of the batina & muscat coastal regions (figure 2). later researchers have adopted this new nomenclature (e.g., béchennec, 1992; racey, 2001; beavington-penney, 2002; beavington-penney et al, 2006). the type section documented by nolan et al. (1990, p. 507) is a “roadside section along the main nizwa to muscat road through wadi rusayl …”. despite the proximity and easy access of the section, nolan et al. (1990) apparently reiterated a description given by crawford (1982) in an unpublished report. nolan et al. (1990) stated that at the type locality, the formation is 356 m thick, including a middle 145 m-thick portion concealed. thus, descriptions given by the proponents of the type section are insufficient and incomplete. the most recent work on the seeb formation is a phd thesis by beavington-penney (2002); this work has been summarized in a publication by beavington-penney et al. (2006). the latter work gives a fair description of the various lithofacies attributes of the formation and effect of intensive bioturbation on the cyclicity of these shallow marine t lithofacies attributes of a transgressive carbonate system 43 carbonates. the major theme of beavington-penney et al. (2006) work is obliteration of cyclic sedimentation by the then marauding organisms (bioretexturing) and creating acyclicity in the major central portion of the formation. a recent abstract by salad hersi et al. (2008) has, however, claimed that, although intense bioturbation is common in significant portions of the formation, the original cyclicity is still preserved and discernible. this point is further discussed in this paper. figure 1. location of the studied area and sections (1, 2 and 3). section 1 lies along the squ-waha al ma’rifah institute, section 2 is the al-khoud road-cut and section 3 is the along wadi al-khoud, north of al-khoud village. 2. geologic background the batina-muscat coast lies on the eastern coastal margin of the north oman mountains. the geological evolution of the sedimentary cover of north oman is well preserved and exposed in this region. the exposed rock succession spans from precambrian to recent. the pre-tertiary rocks are well exposed along deeply cut wadis occurring on the flanks of the mountains (e.g., jabal akhdar). the oldest rocks in the area include a slightly metamorphosed, thick (>1.8 km) sequence of precambrian age (e.g., mistal, hajir, mu’aidin and kharous formations, (mann and hanna, 1990)). a long period of tectonic disturbances, erosion and nondeposition elapsed before the onset of deposition of a very thick, carbonate-dominated succession of late paleozoic (permian) to late cretaceous age (the arabian carbonate platform associated with the tethys ocean, (robertson and searle, 1990)). these platformal sediments, commonly called as hajar supergroup, are punctuated by prominent stratigraphic breaks and further subdivided into groups (e.g., akhdar, sahtan, kahman, wasia and aruma groups, (see for instance figure 4 of robertson and searle, 1990, p. 9)). convergent plate tectonic movement and closure of the tethys ocean in late cretaceous heralded obduction of the oceanic crust osman salad hersi and abdulrahman al-harthy 44 (semail ophiolites) onto the platform carbonates (michard et al., 1989). following the orogenic upheaval related to the emplacement of the semail ophiolite in the campanian, widespread deposition of maastrichtian to tertiary dominantly marine sediments occurred over much of northern oman. however, presence of autochthonous iron-stained conglomerates (al-khod conglomerates) and laterites that occur below these marine sediments suggest that some areas were raised above sea-level and exposed to subaerial weathering. by late maastrichtian to eocene times, the batina-muscat coastal region lying east of the oman mountains was largely submerged under shallow sea (nolan et al. 1990, béchennec, 1992). the region was later (miocene and afterwards, i.e., post-late alpine culmination collapse, (hanna, 1992)) affected by uplifting of the paleogene to ?oligocene sedimentary sequence of the region. figure 2. stratigraphic chart showing the various late paleocene to oligocene lithostratigraphic units in the study area. note the interfingering nature of the rusayl – seeb contact. the seeb formation is divided into five informal units (i to v) and it is unconformably overlain by the mam (muaskar al murtafa’ reefs). 3. lithostratigraphic attributes of the seeb formation the seeb formation conformably overlies the rusayl formation but is unconformably overlain by the informal unit of mu’askar al murtafa’ (“mam”) reefs (figures 2 and 3). although there is no section that shows a complete sequence of the formation, its thickness is conservatively estimated to about 600 m. this thickness is much more than that proposed by nolan et al (1990) from the type section but comparable to that reported by beavington-penney (2002) and beavington-penney et al (2006). the formation can be lithostratigraphically divided into five units (i to v, figures 2 and 3). these units can be easily traced in the lithofacies attributes of a transgressive carbonate system 45 study area south of sultan qaboos university but may be promoted to formal members if they prove to be regionally mappable. this is part of the objectives of a longer term research program but we present here a preliminary and brief description that highlights the internal lithostratigraphic subdivision and attributes of the formation. 3.1 contacts of the formation the seeb formation conformably overlies the middle eocene rusayl formation. the contact between the two formations is well exposed in section 2 (figures 1, 4 and 5a). the uppermost portion of the rusayl formation consists of bioclastic wackestone interbedded within the dominant shaly facies of the formation. this interbedding suggests recurring changes in the depositional environment until it became dominated by the marine realm that deposited the basal beds of the seeb formation. moreover, the lower part of the seeb formation consists of shale horizons that are lithologically similar to the shales of the rusayl formation. thus, the contact separating the two formations is considered conformable. based on field observations close to the type section of the formation, the lowermost part of the seeb formation appears to laterally merge with the uppermost beds of the rusayl formation. the upper contact of the formation is not exposed in any of the studied sections. however, the small hills just south of the sultan qaboos university (in close proximity of locality 1) terminate with a recessive area filled by poorly cemented foraminiferal rudstone (unit v, as defined here) capped by a ferruginous hardground surface (figure 5b) and overlain (within a sand-covered flat area about 50 meters wide) by massive coral framestones of the oligocene mam reefs. 3.2 lithostratigraphic units 3.2.1 unit i unit i is the lowest lithologic unit of the formation overlying the rusayl formation. it is well exposed in sections 2 and 3 where it is about 50 m thick in section 2. the unit may be thicker than that since it is dissected (at locality 2) by a fault (figure 4). at locality 3, about 40 meters constituting the upper part of the unit are exposed; the lower part and lower contact are concealed under the bed of the stream of wadi al-khod. the upper boundary of the unit is sharp (figure 5c and 5d) and erosional to irregular. unit i is characterized by light yellowish brown (beige), sandy, bioclastic packstone to grainstone. these rusayl-like shales are present (figure 5c). the unit is thick to medium beds, cross-bedded and locally vertically burrowed. the cross beds include low angle, trough, tabular and bipolar (herringbone) sets (figure 6a, b). dewatering structures that disrupt the bedding are present in the unit (figure 6c). rare, poorly preserved desiccation cracks are observed in finegrained packstone lithofacies in section 3. pebble size vein quartz clasts are disseminated in the lower part of the unit but rare in its upper part. the framework grains are dominated by biocalsts that include larger foraminifera (e.g., nummulites, alveolina, miliolids and rotalids), gastropods, bivalves, algae and echinoids (figure 6d). intraclasts and peloids (most likely micritized bioclasts) are also present. the mollusk clasts are commonly leached-out and replaced by calcite spar; however, their original occurrence is preserved by micrite envelopes (figure 6d). a thin (~15 cm thick), laterally discontinuous layer of rhodolithic bindstone lies at the top of the unit; this is particularly well exposed in loc. 3. its lateral discontinuity is mainly due to erosion. the rhodolith is formed by encrusting, calcareous red algae. 3.2.2 unit ii unit ii is well exposed with a complete thickness of about 40 m in sections 2 and 3. the upper contact of the unit is sharp and abrupt as exposed in loc. 3 and (figure 7a). the unit is characterized by light brown to light pink, indistinctly bedded, nodular, bioclastic packstones and wackestones. prominent sedimentary structures include intense bioturbation obliterating all pre-existing structures (figure 7b). this intense bioturbation (or ‘bioretexturing’, the term of beavington-penney et al, 2006) is responsible for the amalgamation of the beds. such amalgamation has resulted in the massive and indistinct bedding (figure 5d) that characterizes the unit. osman salad hersi and abdulrahman al-harthy 46 unit ii is highly fossiliferous (figure 7c) with nummulites (figure 7d), alveolina and coralline red algae being the most common fossils. other fossils include miliolids, gastropods, bivalves and echinoids with less than 2% quartz grains scattered in the unit. figure 3. hypothetical stratigraphic log for the seeb formation with lithologic descriptions of the five units that constitute the formation. the cycles shown for unit iv are not to their actual scale. lithofacies attributes of a transgressive carbonate system 47 figure 4. stratigraphic log of section 2 (al-khoud road-cut) showing the rusayl – seeb contact and descriptions of the lower three units that are exposed along the section. note the fault that lies within unit i. the upper contact of unit iii is not exposed. 3.2.3 unit iii unit iii is exposed in sections 2 and 3 although its upper contact is covered. the exposed thickness is in the range of 40 to 50 m thick. the lower contact is sharp with an abrupt lithofacies change from the burrowed packstones of unit ii to the well-bedded, non-burrowed facies of unit iii (figure 8a). unit iii is dominated by thin, medium and thick bedded, medium-grained, bioclastic packstone to grainstone lithofacies. subordinate, laterally confined, quartz-rich (vein quartz) conglomerates are also present in the unit. the lateral extension of osman salad hersi and abdulrahman al-harthy 48 the conglomeratic layers is in the range of a meter to 10-m scale with a thickness of a few tens of centimeters. their matrix is calcareous sand similar to the most common packstone / grainstone lithofacies. sandand pebblesize extraclasts (quartz) are also locally disseminated in the unit. moreover, intervals of burrowed bioclastic packstones are seldom interbedded with the dominant packstone / grainstone facies. bioclasts present in the unit include broken pieces of foraminifera, mollusk and algae. prominent sedimentary structures in the unit include hummocky and swaly cross-stratificiation, erosional surfaces, dewatering-induced internal deformation, amalgamation and lenticular bedding (figure 8b and 8c). figure 5. outcrop exposures showing (a) the jafnayn – rusayl – seeb sequence with formational boundaries demarcated with thick black lines (loc. 2); (b) a hardground surface with ferruginous nodules (arrows) replacing bioclasts. this surface most likely indicates the top of the seeb formation (~ 250m northwest of loc. 1, close to squ); (c) unit i of the seeb fm. exposed in loc. 2. note the rusayl-like layers (s & arrow heads) with the unit; (d) unit ii of the seeb fm. also exposed in loc. 2. the upper contact with unit iii is also exposed here. 3.2.4 unit iv unit iv is the thickest unit and constitutes the bulk of the formation. although a complete thickness of the unit has not been observed, it is estimated to be in the range of 300 m thick. it is widely exposed in a roughly east-west oriented strip along rusayl industrial zone, wahat al-ma’rifa technical institute and the hilly terrain lying north of localities al-khod road-cut (loc. 2) and wadi al-khod (loc. 3). lithofacies attributes of a transgressive carbonate system 49 figure 6: sedimentary structures and microfacies attributes of unit i. (a) tabular x-bedding; (b) bidirectional, tabular x-bedding (herringbone x-bedding); (c) deformation of the layers due to dewatering (hammer = 33 cm, pencil ~ 10 cm), and the bars on the card in c are in cm); (d) thin section photomicrograph showing bioclastic grainstone (f = foraminifera, e = echinoid, a = alveolina, r = red algae). the unit is dominated by grey-weathering, light yellowish brown, thickly to massively bedded, extensively burrowed, nodular, bioclastic wackestone, floatstone to rudstone. it is lithologically similar to unit ii in terms of color, nodularity, fossil content and intense bioturbation. bioclasts include larger foraminifers, gastropods, echinoids, algae, corals and bivalves. this unit has been discussed in great detail in the work of beavingtonpenney (2002) and beavington-penney et al (2006). the intense bioturbation that had obliterated almost all of the previously existing textures and structures led beavington-penney et al (2006) to conclude that the unit lacks the rhythmic sedimentation common in shallow marine carbonates. they documented that this “thick package of nodular, indistinctly bedded lagoonal sediments, which consists largely of one facies type, shows no evidence of hiatus surfaces (such as hardgrounds and subaerial exposure) or cyclicity (i.e., shallowing upward cyclothems)(see beavington-penney et al 2006, p. 1155). contrary to these authors’ assertion of acyclic package for this part of the formation, this study documents that the unit is indeed cyclic with meter-scale rhythmic sedimentation. the thorough bioturbation which revamped the original sediments destroyed most of the internal texture and structure within each cycle and beavington-penney et al’s (2006) bio-retexturing is confined within the limits of individual cycles. each cycle is commonly characterized by (i) a basal, poorly cemented, burrowed, clay-rich, bioclastic rudstone, (ii) a middle part (the thickest within a cycle) of highly bioturbated (typical bioosman salad hersi and abdulrahman al-harthy 50 retexturing), bioclastic packstone and (iii) an upper part of bioclastic packstone, grainstone or rudstone lithofacies (figures 8d and 8e). the clay content decreases from the base to the top. such stacked cycles form the bulk of the unit and are well exposed in the study area. fossils in the basal part are commonly intact, large foraminifers, including long (> 1 cm) fusiform alveolina and discoidal nummulites. the top of each cycle forms a resistant ledge above its lower more recessive portion (figure 8d). the bioclasts within these cap rocks are dominated by crustose red algae with common mollusk fragments and foraminifers are also common. figure 9a shows the contact between unit iv and unit v which is irregular to wavy at this locality 1. the bed below the contact is the uppermost biclastic grainstone bed which defines the top of unit iv. however, the overall contact with unit v is of transitional nature, marked by interbedding of nodular bio-retextured facies with typical unit v facies (see below). figure 7. (a) outcrop exposure showing the sharp contact between unit i and unit ii (loc. 3). (b) a view highlighting the nodular texture of unit ii (hammer = 33 cm). (c) close-up view of unit ii showing scattered larger foraminifera tests in the unit (coin is ~1.5 cm in diameter). (d) thin section photomicrograph of unit ii showing a grainstone lithofacies rich in nummulites and other fossil fragments. 3.2.5 unit v unit v defines the highest lithofacies of the seeb formation and ranges about 100 m in thickness. it is characterized by thickly bedded, light to medium brown, poorly-cemented, clay-rich bioclastic rudstones (marls with excessively abundant foraminifera, figure 9b). due to their recessive nature, they commonly occur the eastwest trending lowland area between the mam reefs and the seeb industrial zone. the dominant larger foraminifera shells are commonly intact and imbricated; they are represented by nummulites, discocyclina and lithofacies attributes of a transgressive carbonate system 51 asselina. besides high clay content, the matrix also contains silt-size quartz grains (figure 9c). the road-cut at the northern entrance of the road to wahat al-ma’rifah is an excellent reference example for this unit. its upper boundary is not exposed and a ferruginous hardground surface close to loc. 1 (figure 5b) marks the top of the unit (and of the formation). above this unit, there is a short covered zone which is followed by sandy conglomerate lithofacies which becomes interbedded with the oligocene “mam” reefs. figure 8. (a) field view of the sharp contact separating unit ii from unit iii (loc. 3). (b) hummocky cross stratification that commonly occurs within unit iii (loc. 3). hammer (in all pictures) is 33 cm. photos d & e are from unit iv and show textural appearance of the unit. the unit is the thickest among all units of the formation and is characterized by rhythmically stacked cycles. (d) single cycle defined by a basal, recessive, muddy / marly rudstone to flaostone lithofacies followed by highly burrowed (bio-retextured) packstone grading into more resistant, cleaner bioclastic packstone / grainstone / rudstone lithofacies. (e) close-up view of the basal burrowed facies with significant amount of larger foraminifera (arrows) including nummulites and fusiform alveolina. 4. depositional setting the lithofacies attributes and vertical succession of various units that constitute the seeb formation suggest that deposition took place in a rising relative sea level scenario on a ramp carbonate platform. the lowest osman salad hersi and abdulrahman al-harthy 52 unit i is envisaged to have accumulated in a transgressive (retrograding), high energy, shallow marine setting, particularly a beach environment. this is indicated by the presence of low-angle and bipolar cross stratifications, and the absence of mud and vertical burrows in the lithofacies (jones and desrochers, 1992; pemberton and mcewan, 1992). the overlying unit ii was deposited in a lagoonal environment where deposit feeding organisms produced intensive mixing of the sediments, thus producing this uniform package of sediments. the lagoon was sheltered from wave energy by being deep on one hand and by basin-ward sub-tidal sand shoals that have produced unit iii. the latter accumulated between a fair-weather wave base and storm wave base as suggested by the dominant hsc and scs structures (tucker and wright, 1990). local tidal channels connected to the shallower parts of the platform may have transported the clastic pebbles associated with unit iii during occasional stormy events. the fore-shoal (basin-ward) depositional site was a quiet zone, allowing accumulation of the very thick, cyclic unit iv (mid shelf). occurrence of the fusiform alveolina and discoidal nummulites at the base of the cycles suggests a depth increase (racey, 2001; beavington-penney et al. 2006) whereas the topcycle packstone / grainstone lithofacies indicates gradual shallowing. the packstone / grainstone lithofacies may either be due to basin-ward extension of unit iii (sand flats) during relative sea level drop or simple shoaling due to increased in-situ carbonate productivity. this unit gave way to an outer-shelf setting where deposition of the topmost unit v took place. the presence and proliferation of intact, larger foraminiferal tests and the high clay / silt content underscores a low energy depositional environment (racey, 2001). the late eocene was a period of sea level fall in arabia in which many parts of the arabian shelf was exposed, developing an unconformity at the eocene – oligocene contact (nolan et al., 1990; haq and al-qahtani, 2005). such an unconformity most likely separates the middle eocene seeb formation from the oligocene “mam” reef deposits of the region. figure 9. (a) outcrop exposure showing the contact between unit iv and unit v (loc. 1). the contact is irregular with clear lithologic change across it. the lower part of unit v consists of interbeds of unit iv and unit v lithofacies (salad hersi et al., 2008). (b) close-up view of unit v showing prolific larger foraminifera tests (nummulites, asselinas and discocyclinas) commonly dispersed throughout the unit (hammer in both a and b is 33 cm long). (c) a thin section photomicrograph showing larger discocyclina (d) and nummulites (n) tests. lithofacies attributes of a transgressive carbonate system 53 5. conclusions the seeb formation is a middle eocene sedimentary succession deposited in a shallow marine setting along the eastern margin of the oman mountains. it is very thick (up to 600 m) and well exposed in the muscatbatina coast region. the lower contact of the formation is conformable with the underlying rusayl formation. presence of limestone beds in the upper part of the rusayl formation and rusayl-like shale beds within the lower part of the seeb formation suggest temporal alternations of the rusayl and seeb depositional environments. field study of the formation (supported by petrographic analysis) allowed recognition of five units that constitute the formation. unit i consists of medium to coarse-grained, sandy, bioclastic packstone to grainstone with well preserved low angle, trough, tabular and bipolar cross bedding. this is followed by thickly bedded, extensively burrowed, bio-retextured bioclastic packstone (unit ii). the bioturbation obliterated most of the original sedimentary structures, as well as depostional textures. the third unit (unit iii) is characterized by well-bedded, medium grained, sandy, bioclastic packstone to grainstone with hummocky and swaly cross stratification. subordinate pebble-size vein quartz conglomerates locally occur, occupying meterto decameterlong channelized zones. minor burrowed intervals also occur. the fourth unit is the thickest of all units reaching as high as 300 m thick. its lithology is more or less similar to that of unit ii, but shows prominent rhythmic sedimentation. however, the bio-retexturing has obliterated any pre-existing sedimentary structures within the boundaries of each cycle. the last and the fifth unit (unit v) of the formation is defined by poorly cemented, foraminiferal rudstone. it can be simplified as marls teaming with larger foraminifera tests dominated by nummulites, discocyclina and asselina. the upper contact of the formation with the overlying oligocene “mam” reefs is not exposed. however, a hardground surface with ferruginous infillings below the mam reef outcrops is considered to represent the upper surface of the seeb formation. the sedimentologic attributes and the stacking nature of the various units of the formation indicate that deposition took place in a deepeningupward shallow marine basin. unit i represents sandy shoreline deposits that pass basinward into a protected lagoonal deposits of unit ii. the latter was protected by subtidal sand shoals of unit iii lying seaward that accumulated between the fair-weather wave-base and storm base. unit iv was deposited below the storm base allowing deposit feeders to flourish and rampage the sediments, producing the extensive bioturbation that characterizes this unit. the uppermost unit v was deposited in an outershelf setting as suggested by the dominance of flat foraminifers (e.g., nummulites, discocyclina and asselina). 6. acknowledgements we wish to thank the referees for their constructive comments leading to an improvement in the paper. we also extend our thanks to mr. hilal al-zidi and mr. hamdan al-zidi, technicians of the department of earth sciences, sultan qaboos university, for their support in the thin section preparations. 7. references bechennec, f., roger, j., le metour, j., and wyns, r. 1992. geological map of seeb (1:250 000) with explanatory notes. min. of petroleum & minerals, sultanate of oman. 104 p. beavington-penney, s.j. 2002. characterization of selected eocene nummulites accumulations. phd thesis, university of wales, cardiff. 393pp. beavington-penney, s.j., wright, v.p. and racey, a. 2006. the middle eocene seeb formation of oman: an investigation of acyclicity, stratigraphic completeness, and accumulation rates in shallow marine carbonate settings. journal of sedimentary research, 76:1137-1161. glennie, k.w., bouef, m.g.a., hughes-clarke, m.w., moody-stuart, m. pilaar, w.f.h., and reinhardt, b.m. 1974. the geology of the oman mountains. verhandelingen van ket knoninklijk nederlands geologisch minjbouwkundig genootschap. 31. osman salad hersi and abdulrahman al-harthy 54 haq, b.u. and al-qahtani, a.m. 2005. phanerozoic cycles of sea-level change on the arabian platform. geoarabia, 10(2): 127-160. hughes-clarke, m.w. 1988. stratigraphy and rock unit nomenclature in the oil producing area of interior oman. journal of petroleum geology, 11: 5-60. jones, b. and desrochers, a. 1992. shallow platform carbonates. in: walker, r.g. and james, n.p. (eds), facies models: response to sea level changes. geological association of canada, 277-301. mann, a. and hanna, s. 1990. the tectonic evolution of pre-permian rocks, central and southern oman mountains. in: robertson, a.h.f., searle, m.p., and ries, a.c. (eds): the geology and tectonics of the oman region. geol. soc. london, sp. publ. 49: 307-325. michard, a., le mer, o., goffe, b. and montigny, r. 1989. mechanisms of the oman mountains obduction ont the arabian continental margin, reviewed. bull. soc. geo. france, 2: 241-252. nolan, s.c., skelton, p.w., clissold, b.p., and smewing, j.d. 1990. maastrichtian to early tertiary stratigraphy and palaeogeography of the central and northern oman mountains. in: robertson, a.h.f., searle, m.p., and ries, a.c. (eds): the geology and tectonics of the oman region. geol. soc. london, sp. publ. 49: 495-519. pemberton, s.g. and maceachern, j.a. 1992. trace fossils facies models: environmental and allostratigraphic significance. in: walker, r.g. and james, n.p. (eds), facies models: response to sea level changes. geological association of canada, 47-72. powers, r.w., ramirez, l.f., redmond, c.d., and elberg, e.l. 1966. geology of the arabian peninsula: sedimentary geology of saudi arabia. united states geological survey porfessional paper 560d, 147 p. racey, a. 2001. a review of eocene nummulite accumulations:structure, formation and reservoir potential. journal of petroleum geology, 24(1): 79-100. racz, l. 1979. paleocene carbonate development of ras al hamra, oman. bulletin centre recherche exploration et production elf-aquitaine, 3: 767-779. robertson, a.h.f. and searle, m.p. 1990. the northern oman tethyan continental margin: stratigraphy, structure, concepts and controversies. in: robertson, a.h.f., searle, m.p., and ries, a.c. (eds): the geology and tectonics of the oman region. geol. soc. london, sp. publ. 49: 3-25. salad hersi, o., al-harthy, a., al-sayigh, a. and abbasi, i.a. 2008. new insights on the sedimentology and depositional setting of the middle eocene seeb formation in the al-khod area, sultanate of oman. scientific research abstracts, sultan qaboos university, p.80. tucker, m.e. and wright, v.p. 1990. carbonate sedimentology. blackwell scientific publications. oxford. 482 pp. warrak, m. 1986. structural evolution of the northern oman mountain front, al-ain . in: symposium on the hydrocarbon potential of intense thrust zones. ministry of petroleum and mineral resources, uae and opec, abu dhabi, 375-431. received 26 july 2009 accepted 28 august 2010 endocrine, physiological and histopathological responses of fish and their larvae to stress with emphasis on exposure to crude science and technology, special review (2000) 1-30 ©2000 sultan qaboos university 1 endocrine, physiological and histopathological responses of fish and their larvae to stress with emphasis on exposure to crude oil and various petroleum hydrocarbons a.y.a al-kindi*, j.a brown** and c.p. waring *** * department of biology, college of science, sultan qaboos university, p.o. box 36 al-khod 123, muscat, sultanate of oman ** school of biological sciences, hatherly laboratories, university of exeter, ex4 4ps. u.k. ***school of biological sciences, university of portsmouth, king henry building, king henry i street, portsmouth, hampshire, po1 2dy, u.k. االستجابات الهرمونية والفيزيولوجية والتركيبية لألسماك ويرقاتها للضغوط البيئية مع التركيز على .العديدةآثار تعرضها للبترول الخام ومشتقاته عبدالعزيز بن يحيى الكندي وآن براون وكولن وارنج اجعة االستجابات الهرمونية والفيزيولوجية لألسماك التي تتعرض ألنواع عديدة من الضغوط والعوامل تم مر : خالصة الفيزيائية والكيميائية مع التركيز على أثر البترول الخام ومشتقاته في هذا الصدد، وقد تم تشخيص كيميائية ذه الحيوانات لهذه المشتقات البترولية، كما تم الهيدروكربونات البترولية وقدرتها على تسميم األسماك ووسائل تعرض ه استقصاء أثر البترول الخام ومشتقاته على عوامل هرمونية عديدة في الدم كالتغيرات في تركيز األدرينالين والنورأدرينالين والكورتيزوالت والثيرويدات وهذه هرمونات مهمة في ابراز أثر الضغوط المحيطة عامة على األسماك كما تم استقصاء أثر مشتقات البترول على سكر الدم والوظائف األيونية واألسموزية وأكسجين . ية منها خاصة والكيمائ الدم ونسبة الخاليا الحمراء والهيموجلوبين باإلضافة إلى التغيرات التركيبية الناتجة عن تعرض األسماك ألنواع عديدة .من البترول الخام ومشتقاتها المختلفة abstract: various endocrine and physiological responses of fish exposed to forceful physical and chemical stimuli are reviewed with emphasis on the effects of crude oils and their hydrocarbon constituents. the chemistry and toxicity of petroleum hydrocarbons are examined and methods for experimental exposure of fish to crude oil and petroleum hydrocarbons are considered. a variety of blood-borne parameters recognized as reliable tools in determining the relative severity of stress in fish are reviewed. the effects of stress and petroleum hydrocarbons on endocrine responses including changes in plasma al-kindi, brown, and waring catecholamines, corticosteroids, and thyroid hormones are reviewed. the physiological responses: changes in plasma glucose, osmotic and ionic regulation, blood oxygen, hematocrit and hemoglobin concentration are explored, and histopathological effects of crude oil on fish are reviewed. recent studies of the effects of petroleum hydrocarbons on fish larvae are considered and the increased sensitivity of the early life stages of fish are highlighted. contents 1. introduction 2 1.1 the fish stress response 2 1.2 petroleum hydrocarbons 3 1.3 exposure of fish to petroleum hydrocarbons 4 1.4 experimental exposure methods 4 2. endocrine responses to stress and their induction in fish exposed to petroleum hydrocarbons 5 2.1 plasma catecholamines 5 2.2 plasma cortisol 6 2.3 plasma thyroid hormones 8 2.4 endocrine interactions during stress 9 3. physiological responses to stress in fish 10 3.1 carbohydrate metabolism and plasma glucose 10 3.2 osmotic and ionic regulation 10 3.3 endocrine systems and ionic and osmotic regulation during stress 11 3.4 blood oxygen 12 3.5 hematocrit and blood hemoglobin concentration 13 4. histopathological effects of crude oil and petroleum hydrocarbons on fish 13 4.1 gill histopathology 14 4.2 liver histopathology 15 4.3 kidney histopathology 15 5. effects of petroleum hydrocarbons on fish larvae 15 6. conclusions and future research 17 7. references 17 1. introduction 1.1 the fish stress response developing an accurate knowledge of the stress responses in fish is a crucial element for better understanding of the problems related to the well-being and survival of fish when exposed to forceful physical and chemical stimuli. a variety of blood-borne parameters have been recognized as reliable tools in determining the relative severity of stress in fish (mazeaud and mazeaud, 1981; barton, 1988; brown et al 1990; waring et al 1992; pickering, 1993a,b; alkindi et al 1996). these physiological indicators have been measured in a range of fish species to evaluate the trauma inflicted on fish by various stressors (mazeaud et al 1977; giesy et al 1988; folmar, 1993; pickering, 1993a,b). identifying stress responses can be achieved by determining the changes in plasma catecholamines (mazeaud et al 1977; mazeaud and mazeaud, 1981; barton, 1988; tang and boutilier, 1988; gingerich and drottar, 1989; aota et al 1990) and plasma corticosteroids (donaldson, 1981; sumpter et al 1986; thomas and rice, 1987; pickering and pottinger, 1989; whitehead and brown 1989; waring et al 1992; foo and lam, 1993; mazur and iwama, 1993; alkindi et al 1996). these primary (endocrine) responses to stress are more immediate than the induced secondary (metabolic) responses (barton and toth, 1980; 2 endocrine, physiological and hispatological responses of fish 3 mazeaud and mazeaud, 1981). the stress responses of fish have been reviewed recently by wendelaar bonga (1997). this review will highlight aspects of the fish stress response applicable in understanding the effects of petroleum hydrocarbons and then review the literature describing histopathological effects of hydrocarbons in fish. 1.2 petroleum hydrocarbons crude oils and their water-soluble fractions are a major source of pollution in the marine environment. studies have estimated that the quantity of crude oils and their constituent hydrocarbons, which enter the marine environment, is in the range 2 to 20 million tons per annum (solangi, 1980; neff, 1990). the main sources of petroleum hydrocarbon pollution are oil spills, oil-tanker washings and offshore production which generates produced waters (dey et al 1983; neff, 1990; steinhauer et al 1994; syvertsen, 1996). massive volumes of crude oil have been released into the marine environment as a result of large oil spills. for example, the exxon valdez spill released 258,000 barrels (maki, 1991), ixtoc i 475,000 metric tons (jernelov and linden, 1981), the iraqiiranian war is estimated to have resulted in the release of 6 million barrels, the gulf war, 7-11 million barrels (alam, 1993) and the braer oil spill, 85,000 tons (ritchie and o'sullivan, 1994). various changes occur when oil is spilled at sea. these encompass bacterial degradation, photooxidation, evaporation, emulsification, dissolution, dilution by spreading, clustering to form tar-balls and formation of the water-soluble fraction (wsf) and water-accommodated fraction (waf) (dey et al 1983; neff, 1990; ehrhardt et al 1992). ultimately, much of the spilled oil penetrates into the bottom sediment. it appears that the attraction between hydrocarbons and sediment is greater than the separation forces and the loss of hydrocarbons is significantly reduced after attachment to sediment (moore and dwyer, 1974; hyland and schneider, 1976; neff, 1990; i.c.e.s. 1991; steinhauer et al 1994). petroleum residues may thus persist in sediment of beaches for 20 years after an oil spill (vandermeulen and singh, 1994). crude oils are complex mixtures containing literally thousands of organic and a few inorganic compounds. most crude oils contain the same major classes of compounds but the amounts of each compound are different (neff, 1990). aromatic hydrocarbons based on the benzene ring may constitute 20% of the total hydrocarbon content of crude oil. crude oils usually have higher concentrations of monocyclic aromatic hydrocarbons such as benzene and toluene than dicyclic aromatics such as naphthalenes or polycyclic aromatic hydrocarbons (anderson et al 1974). the abundance of aromatic hydrocarbons in crude oil is usually inversely related to their molecular weight; one-ring (benzene) to the three-ring (phenanthrene) compounds comprise at least 90% of the total aromatic hydrocarbons present in petroleum (neff, 1979, 1985, 1990). aromatic hydrocarbons with methyl substitutions of one or more rings are more toxic than less substituted compounds, but tend to be less water-soluble, and thus less abundant in the wsf of crude oil (anderson et al 1974; neff, 1990). there are at least two pathways by which petroleum hydrocarbons can be taken into fish, firstly via the gills (evans, 1987) and secondly via the gut with food or with the seawater drunk for volume regulation (lee et al 1972; stegeman, 1977). the rate of hydrocarbon uptake will be affected by exposure concentration, the molecular weight of the hydrocarbons and the amount of lipid in the fish, which depends on the species, age, season and reproductive state as well as feeding rate and oxygen uptake (neff et al 1976; falk-petersen et al 1982; rice, 1985). retention of hydrocarbons in the animal tissues will depend upon the partitioning of hydrocarbons between the exposure water and the tissue lipids (neely et al 1974). binding of hydrocarbons to tissue lipids is probably by lipophilic interaction (stone, 1975). thus, hydrocarbons remain exchangeable and when the animals are returned to hydrocarbon-free seawater, the lipid/water partition coefficients for the hydrocarbons will permit their gradual release from the tissues to the water (neff et al 1976). the longer tissue retention time and the more toxic effects have been indicated for aromatic hydrocarbons with more than one ring and methyl-substitutions (i.e. naphthalene, methylnaphthalenes and higher molecular weight pahs) (anderson et al 1974; morrow, 1974; morrow et al 1975; neff et al 1976; falk-petersen et al 1982; neff, 1990) are probably due to their lipophilic interaction with animal tissue. tetramethyl-benzene and 1and 2methylnaphthalene were absorbed in the highest concentrations by english sole exposed to crude oil in sediment al-kindi, brown, and waring 4 (mccain et al 1978). lipophilic interaction of hydrocarbons with lipids could lead to the accumulation of aromatic hydrocarbons in the structural lipids of membranes and disturb the membrane function (payne et al 1978; mckeown and march, 1978; solangi, 1980; zbanyszek and smith, 1984). 1.3 exposure of fish to petroleum hydrocarbons during an oil spill, transient high levels of petroleum hydrocarbons in the seawater phase are followed by a decline as natural processes such as evaporation, photooxidation and biodegradation occur. the acute toxic effects of an oil spill are most likely caused by soluble low molecular weight aromatic hydrocarbons such as benzenes, toluene and naphthalene. acute toxicity has been reported to be inversely related to the molecular weight of aromatic hydrocarbons (mcauliffe, 1977; neff, 1990), but chronic effects are always attributed to four and five-ring polycyclic aromatic hydrocarbons (neff, 1990). compared to monocyclic aromatics, naphthalene appeared to be accumulated to a greater extent by fish (falkpetersen et al 1982) and retained for longer periods of time following exposure, thus making naphthalenes probably the most acutely toxic aromatic hydrocarbon (morrow, 1974; morrow et al 1975; neff et al 1976; falkpetersen et al 1983, falk-petersen and kjorsvik, 1987; neff, 1990). in oil-polluted marine waters, concentrations of total hydrocarbons are usually substantially less than 1 ppm (malins and hodgins 1981; neff 1990). acute short-term laboratory studies (1-96h) have investigated the effects of high concentrations of petroleum hydrocarbons, generally above those ordinarily encountered after most major oil spills (mazmanidi and kovaleva, 1975; thomas et al 1980; kiceniuk and khan, 1987; davison et al 1992; alkindi et al 1996) while chronic studies, lasting for several months have used lower exposure concentrations of petroleum hydrocarbons, generally in the sublethal ppb range (mazmanidi and kovaleva, 1975; hawkes, 1977; payne et al 1978; whipple et al 1978; khan et al 1981; woodward et al 1981; fletcher et al 1982; khan, 1987; davison et al 1993; stephens et al 2000). the heavy fractions (i.e. polycyclic aromatic hydrocarbons and n-alkanes) of crude oil persist in sediment for long periods of time and benthic fish will be particularly exposed to these hydrocarbons (steinhauer et al 1994). 1.4 experimental exposure methods there are several routes through which fish may be exposed to crude oils and their products. experimental approaches have included exposure of fish to a dietary intake of petroleum hydrocarbons via contaminated food (gruger et al 1977; leatherland and sonstegard, 1978; carls and rice, 1987). sediment contaminated with crude oil has been employed for chronic exposure of fish to petroleum hydrocarbons for up to several months in some cases (mccain et al 1978; fletcher et al 1981, 1982; khan, 1991a; truscott et al 1992; tahir et al 1993; khan et al 1994). fish exposed to the water-accommodated fraction (waf) of crude oils and their constituents have been the subject of several investigations (anderson et al 1974; mckeown and march, 1977, 1978, prasad, 1987, 1988, 1991), but the most widely used experimental approach has involved exposure of fish to the water-soluble fraction of crude oils or their products (thomas and rice, 1975, 1987; hawkes, 1977; smith and cameron, 1979; korolev et al 1980; solangi, 1980; thomas et al 1980; engelhardt et al 1981; eurell and haensly, 1981; solangi and overstreet, 1982; khan and kiceniuk, 1984, 1988; tilseth et al 1984; zbanyszek and smith, 1984; moles et al 1985; hellou et al 1986; carls and rice, 1987; hellou and payne, 1987; kiceniuk and khan, 1987; rice et al 1987; khan, 1990; ehrhardt et al 1992; davison et al 1992, 1993). generally, the preparation of the wsf of crude oil is achieved by low energy mechanical mixing of crude oil with water followed by a period of separation of oil from the water phase (anderson et al 1974; shaw, 1977). the difference between wateraccommodated and water-soluble fractions is mainly dependent on their preparation. a high energy vigorous mixing of oil with water may form an emulsion that will not separate and which will yield a wateraccommodated fraction rather than a water-soluble fraction of crude oil, but with low energy gentle mixing, emulsions are less likely to form and the wsf of crude oil will not contain the water-accommodated fraction. endocrine, physiological and hispatological responses of fish 5 several studies have employed the water-soluble fraction of crude oil that has been prepared by a variety of flow-through systems (hellou et al 1986; kiceniuk and khan, 1987; khan and kiceniuk, 1988; khan, 1990) or prepared in a contained system to supply a static test system (anderson et al 1974; rice et al 1976; gruger et al 1977; tamra and karinen, 1977; moles et al 1979; solangi and overstreet, 1982; thomas and rice, 1987). the preparation of a wsf using a flow-through system is usually accomplished by dropping or spraying water onto a layer of crude oil on top of a water layer, and water, containing the wsf of crude oil, is then drawn from the bottom of the water layer (moles and rice, 1983). the advantage of a flow-through system is that it can achieve a constant concentration of petroleum hydrocarbons in the prepared wsf. another advantage of this system is that spraying provides some form of aeration, which maintains a constant supply of oxygenated water containing the wsf of crude oil (moles and rice, 1983; moles et al 1985). however, after an oil spill, the immediate transient high concentrations of petroleum hydrocarbons will probably decline, subsequently so that a flowthrough system of producing a wsf of crude oil with constant hydrocarbon levels does not mimic an oil spill. nevertheless, oil in water was detectable one month after the braer oil incident, particularly in areas near the wreck (ritchie and o'sullivan, 1994). for a static testing system of the effects of the wsf of crude oil, low energy mixing of crude oil with water is achieved by gently mixing, followed by a period of total separation of the oil phase from the water phase which will be used in the static test system (anderson et al 1974; gruger et al 1977; moles et al 1979; thomas and rice, 1987; alkindi et al 1996). the main advantage of this approach is the ease of producing the wsf of crude oil. however, changes in the composition of the wsf during the experimental exposures are unavoidable. furthermore, it is usually impractical to produce large volumes of the wsf of crude oil by this method. 2. endocrine responses to stress and their induction in fish exposed to petroleum hydrocarbons 2.1 plasma catecholamines the chromaffin tissue of the head kidney, the homologue of the adrenal medulla of higher vertebrates, synthesizes, stores and secretes three hormones: adrenaline, noradrenaline and dopamine (mazeaud and mazeaud, 1981; randall and perry, 1992). the three hormones exist in different proportions depending on the species (mazeaud et al 1977; mazeaud and mazeaud, 1981; folmar, 1993; pickering, 1993b). the relative amounts of circulating adrenaline and noradrenaline, the main catecholamines involved in fish responses to stress, vary from one species to another (mazeaud et al 1977; mazeaud and mazeaud, 1981; gingerich and drottar, 1989; hathaway and epple, 1989). catecholamine synthesis involves hydroxylation of a precursor molecule (tyrosine) into l-dopa then deamination of l-dopa to form dopamine. noradrenaline is produced by further hydroxylation of dopamine and adrenaline is then produced by methylation of noradrenaline (jonsson and nilsson, 1983). catecholamines are stored within granules in chromaffin cells. the chromaffin cells are innervated by preganglionic cholinergic fibres of the sympathetic nervous system which stimulate catecholamine release into circulation (nilsson et al 1976). a rapid and dramatic increase in circulating catecholamines can occur in response to a variety of physical stressors such as forced swimming and handling (mazeaud et al 1977; hughes et al 1988; vijayan and moon, 1994) and forceful exercise (butler et al 1986; primmett et al 1986; tang and boutilier, 1988; wood et al 1990). these responses are likely to be a reflection of the oxygen status of the fish. plasma catecholamines are elevated in response to hypoxia (mazeaud et al 1977; ristori and laurent, 1989; aota et al 1990; perry et al 1991; perry et al 1993), and this may explain the similar rise caused by chemical stressors such as anaesthetics (gingerich and drottar, 1989; hathaway and epple, 1989; iwama et al 1989). while the above stressors are known to cause various physiological changes, few studies have investigated the effects of petroleum hydrocarbons on endocrine pathways responsive to stress. however, alkindi et al (1996) found that wsf-exposed flounders had elevated plasma noradrenaline concentrations while plasma al-kindi, brown, and waring 6 adrenaline concentrations were unaffected. this was most likely a response to the profound decline in the blood oxygen content of these flounder (alkindi et al 1996). when released in response to stressful conditions, catecholamines enhance the survival of fish by exerting a variety of beneficial effects such as mobilizing energy reserves and increasing oxygen carrying capacity. catecholamines stimulate glycogenolysis and gluconeogenesis, and consequently increase blood sugar providing an animal with a readily available energy source to deal with stressful conditions (mazeaud and mazeaud, 1981; morata et al 1982; ristori and laurent, 1985; suarez and mommsen, 1987; sheridan and mur, 1988; wright et al 1989; pickering 1990; wood et al 1990; wendelaar bonga, 1997). adrenaline stimulates glycogenolysis by increasing levels of intracellular cyclic amp, which then activates glycogen phosphorylase and causes the breakdown of glycogen to glucose (morata et al 1982; van raaij et al 1995). there is also evidence to suggest the involvement of catecholamines in the mobilization of free fatty acids (waring et al 1996b) though results are inconsistent (see review by wendelaar bonga, 1997) catecholamines have a stimulatory action on cardiovascular function (randall and perry, 1992; perry and bernier, 1999), increasing heart rate (wahlqvist and nilsson, 1977; satchell, 1991) stroke volume (wood and shelton, 1980; mazeaud and mazeaud, 1981; pennec, 1987), blood pressure (wahlqvist and nilsson, 1977; wood and shelton, 1980) and branchial blood flow (capra and satchell, 1977; butler and metcalfe, 1983; stagg and shuttleworth, 1984). elevated branchial blood flow has been suggested to increase gaseous exchange at the branchial surface (booth, 1979), although this adaptive response needs to be balanced against a non-adaptive increase in water permeability of the gills (bennett and rankin, 1987). catecholamines have been reported to have a beneficial effect on the oxygen carrying capacity of fish by causing various physiological responses. catecholamines stimulate a rapid release of red blood cells from the spleen into the bloodstream (kita and itazawa, 1989; perry and kinkead, 1989). furthermore, catecholamines have been reported to affect red blood cell ph of some species of fish (nikinmaa, 1986; primmett et al 1986) and cause red blood cell swelling (nikinmaa, 1983; nikinmaa et al 1984; ling and wells, 1985; fuchs and albers, 1988; wood, 1991; perry and thomas, 1993). under conditions of forceful exercise, anaerobic metabolism of the white muscle will cause metabolic acidosis that results in the decrease of plasma ph which will reduce red blood cell ph causing a decrease in oxygen carrying capacity of the hemoglobin by means of the root effect. catecholamines can counteract this effect, particularly in salmonid fish, by stimulating h+ excretion from red blood cells, hence restoring intracellular ph which results in maintenance of the oxygen carrying capacity of the cells. simultaneously, na+ and clmove into the cells, causing osmotic swelling, which ultimately decreases the organic phosphate concentration of the red blood cells, and consequently, again increases the affinity of hemoglobin for oxygen (paajaste and nikinmaa, 1991; wood, 1991; perry and thomas, 1993). in contrast to the salmonids it seems that fish with high hypoxia tolerance (eg carp, tench, eels) do not rely on this mechanism (see review by jensen et al 1993). in addition, in the rainbow trout, oncorhynchus mykiss, adrenaline may directly affect the oxygen affinity of at least one of the hemoglobin components of red blood cells (falcioni et al 1991). in contrast to the salmonids it seems that fish with high hypoxia tolerance (eg carp, tench, eels) do not rely on this mechanism 2.2 plasma cortisol cortisol is the major corticosteroid hormone secreted by the interrenal tissue found in the ‘head kidneys’ of fish (chester jones et al 1969; donaldson, 1981; fryer, 1975; idler and truscott, 1972; matty, 1985; nichols and weisbart, 1984). during stress, a corticotrophin releasing factor (crf) released from the hypothalamus stimulates the anterior pituitary, pars distalis, to secrete adrenocorticotrophic hormone, acth (fryer and peter, 1977). subsequently, acth stimulates the synthesis and release of cortisol from the interrenal tissue. cortisol has been recognized as a reliable indicator of stress in fish (mazeaud et al 1977; barton and toth, 1980; donaldson, 1981; barton, 1988; waring et al 1992; waring et al 1996a: mcdonald et al 1993; pickering, 1993b). cortisol is released in fish in response to a wide variety of stress stimuli. cortisol has been reported to increase in response to physical stressors such as handling (sumpter et al 1986; thomas and robertson, 1991; melotti et al 1992; waring et al 1992; barry et al 1993; foo and lam, 1993), physical disturbance and exercise endocrine, physiological and hispatological responses of fish 7 (zelnik and goldspink, 1981; barton et al 1986; flos et al 1988; white and fletcher, 1989; mcdonald et al 1993) and capture or confinement (davis and parker, 1986; sumpter et al 1986; davis and parker, 1990; melotti et al 1992). elevation of plasma cortisol has also been reported in response to environmental chemical stressors such as acid (brown et al 1984; barton et al 1985; jones et al 1987; edwards et al 1987; goss and wood, 1988; whitehead and brown, 1989; brown et al 1989), aluminum (goss and wood, 1988; whitehead and brown, 1989; brown and whitehead, 1995; waring et al 1996a), and many other pollutants (swift, 1981; gluth and hanke, 1984) and prolonged exposure to anaesthesia (strange and schreck, 1978). however, exposure of rainbow trout and chinook salmon to brief anaesthesia did not change the plasma cortisol (strange and schreck, 1978; iwama et al 1989). cortisol has been widely used to assess the state of health in fish exposed to stress (mazeaud and mazeaud, 1981; pickering, 1993b). changes in the concentration of plasma cortisol, however, depend upon the nature of the stress stimuli, the duration of the stress, the magnitude and severity of the stress (barton and toth, 1980; pickering et al 1982; davis and parker, 1983; gluth and hanke, 1984) and the species under investigation (davis and parker, 1983, 1986; waring et al 1992). nevertheless, since increased concentrations of plasma cortisol constitute part of the generalized stress response (mazeaud et al 1977), a release of cortisol in fish exposed to petroleum hydrocarbons might be expected. so far only a few studies have examined plasma cortisol in fish exposed to petroleum hydrocarbons. generally, exposure of fish to crude oils and their derivatives caused elevated plasma cortisol concentrations (dimichele and taylor, 1978; thomas et al 1980; lopez et al 1981; thomas and rice 1987). the wsf of crude oil increased plasma cortisol in juvenile coho salmon after 48 h exposure (thomas and rice, 1987), and the wsf of fuel oil caused a 50-fold increase in the circulating cortisol concentration of stripped mullet after 1 h followed by a recovery to resting levels 6 h after oil addition (thomas et al 1980). exposure to individual petroleum hydrocarbons and other oil products similarly increased plasma cortisol; fish exposed to naphthalene exhibited an increase in serum cortisol (dimichele and taylor, 1978). exposure of rainbow trout to crude oil caused an initial elevation of plasma cortisol (engelhardt et al 1981). an elevated concentration of plasma cortisol in wild eels, caught at field sites, persisted for at least 8 months after an oil spill (lopez et al 1981). the wsf of omani crude oil caused a significant elevation in plasma cortisol concentrations in exposed flounders, pleuronectes flesus (alkindi et al 1996). increased cortisol secretion in response to acute stress presumably enhances survival. an adaptive role of cortisol has been suggested to be linked to mobilization of energy reserves through its catabolic functions (mazeaud et al 1977; barton et al 1985; jones et al 1987; goss and wood, 1988; brown et al 1989; whitehead and brown, 1989; pickering, 1990; thomas and robertson, 1991; waring et al 1992; barry et al 1993; bollard et al 1993). cortisol administration to fish has been commonly reported to cause hyperglycemia (leach and taylor, 1980; davis et al 1985; barton et al 1987; van der boon et al 1991; vijayan et al 1991). similarly, administration of cortisol to hypophysectomised eels resulted in a dramatic increase in plasma glucose (chan and woo, 1978a). in contrast to these observations, however, cortisol treatment caused hypoglycemia in american eels (foster and moon, 1986) and administration of cortisol to rainbow trout to achieve plasma concentrations similar to those occurring during stress did not induce hyperglycemia (andersen et al 1991). the hyperglycaemic effects of administered cortisol have been suggested to result from the inhibitory effects of the hormone on glucose oxidation and utilization in peripheral tissues (gill and khanna, 1975; van der boon et al 1991). this may be accompanied by stimulated gluconeogenesis. cortisol can directly provide the free amino acids for gluconeogenesis via stimulation of protein catabolism (lidman et al 1979; marshall adams et al 1985) with elevation of circulating amino acids in some species (chan and woo, 1978a), but not apparently in fundulus heteroclitus (leach and taylor, 1982), or may act indirectly by inhibiting protein synthesis (reviewed by van der boon et al 1991). in gluconeogenesis, free amino acids act as precursors for glucose synthesis and the regulation of this process in the liver is suggested to be mediated by cortisol (lidman et al 1979; murat et al 1981). the gluconeogenic action of cortisol was supported in studies by vijayan et al (1994) when a corticosteroid antagonist inhibited the increased alanine gluconeogenesis in cortisol-treated fish. contradictory results have also been reported concerning the effects of cortisol on liver glycogen. administration of cortisol caused an increase in liver glycogen content (chan and woo, 1978a; lidman et al al-kindi, brown, and waring 8 1979; leach and taylor, 1982). on the other hand, decreased glycogen content in the liver in response to elevated cortisol has been reported (barton et al 1986; foster and moon, 1986; vijayan and leatherland, 1989; soengas et al 1992). increased blood fatty acid concentrations in parallel with an elevation in plasma cortisol have been reported (dave et al 1979; white and fletcher, 1989; waring et al 1992) and a role of cortisol in lipid-mobilization has been proposed (lidman et al 1979; sheridan, 1987). changes in blood glucose and free fatty acid compositions are probably significant actions by which cortisol increases the availability of energy and the readiness of fish to survive stress. however, there are significant species differences in the mechanisms involved in achieving this and the mode of action of catecholamines and cortisol in individual species (see wendelaar bonga, 1997). cortisol appears to have beneficial effects on ionoregulatory balance in both freshwater and seawater fish (parwez and goswami, 1985; laurent and perry, 1990; madsen, 1990; barton and iwama, 1991; bisbal and specker, 1991). the mechanism by which cortisol influences ion balance and its interaction with other hormones has been the subject of many investigations (mccormick 1995). cortisol stimulation of salt uptake is thought to be via increased gill na+-k+-atpase activity (pickford et al 1970; forrest et al 1973; dange, 1986; langhorne and simpson, 1986; madsen, 1990; bisbal and specker, 1991). however, in some experiments cortisol had no apparent effect on this enzyme (langdon et al 1984; redding et al 1984). linked to the elevated na+-k+atpase, cortisol has been shown to cause chloride cell proliferation (perry and wood, 1985; laurent and perry, 1990; madsen, 1990) and increase the area of the chloride cell, which is in contact with the external media and therefore concerned with ion transport (laurent and perry, 1990). cortisol could thus play a role in the reduction of ionic imbalance in stressed fish. 2.3 plasma thyroid hormones thyroxine (t4) is synthesized in the thyroid follicles by iodination of tyrosine (matty, 1985). the thyroid gland primarily secretes l-thyroxine in response to thyroid stimulating hormone (tsh) released from the pituitary (eales and brown, 1993). tsh release from the pituitary is regulated by a hypothalamic hormone, thyrotrophin releasing hormone (trh) and thyrotrophin release inhibiting factor (tif) and /or negative feedback inhibition by t4 (leatherland, 1982; matty, 1985; eales, 1990; eales and brown, 1993). over 99% of t4 binds to plasma proteins called thyroglobulins (eales, 1990; rousset and mornex, 1991). free t4 enters cells of peripheral tissue (brain, liver, gill, kidney, heart and muscle) and is then deiodinated to form triidothyronine, (t3) by l-thyroxine 5’monodeiodinase (mdi), the enzyme responsible for peripheral conversion of t4 to t3 (eales, 1990; leatherland et al 1990; byamungu et al 1992; maclatchy and eales, 1990, 1992; eales et al 1993a,b). eales and brown (1993) suggest that in teleosts the ‘peripheral model’ of plasma t3 regulation by mdi activity predominates over the ‘central model’ via the hypothalamic-hypophyseal-thyroidal axis. thus, for example, exogenous t4 or tsh will raise plasma t3 concentrations despite massive increases in plasma t4. similar trends also occur in nature during parr-smolt transformation (eales and brown, 1993). a physiologically viable model is that the thyroidally-secreted t4 is a relatively inactive prohormone converted peripherally via mdi and that the hypothalamic-hypophyseal-thyroidal axis merely ensures adequate t4 secretion (eales, 1985, 1990; eales and brown, 1993). thus all t3 in teleosts may be generated peripherally and t3 represents the active thyroid hormone at the level of target cells (plisetskaya et al 1983; eales, 1990; eales and brown, 1993). stressors such as physical disturbances and environmental toxicants including petroleum hydrocarbons have been reported to affect thyroid function but responses have been inconsistent (osborn and simpson, 1972; brown et al 1978; leatherland and sonstegard, 1978; pickering et al 1982; plisetskaya et al 1983; brown et al 1984; leatherland, 1985; brown et al 1989; whitehead and brown, 1989; brown et al 1990; sinha et al 1991; alkindi et al 1996; johnston et al 1996; waring et al 1996a; waring and brown, 1997). reduced plasma t4 concentrations were observed in flounder exposed to the wsf of crude oil but plasma t3 concentrations were unaffected (alkindi et al 1996). stress has been reported to alter the t3:t4 ratio (osborn and simpson, 1972; brown et al 1978). if thyroid hormones have biological significance in stressed fish, then potential physiological benefits lie in their potential roles in regulating osmoregulation, growth and metabolism. endocrine, physiological and hispatological responses of fish 9 thyroid hormones have been suggested to have significant hypo-osmoregulatory effects on fish adapted to seawater. t4 treatment reduced the elevation of plasma na + in fish transferred from freshwater to seawater, whereas treatment with thiourea (a thyroid hormone antagonist) resulted in a significant increase in plasma na+ concentrations in fish transferred to seawater (knoeppel et al 1982; leatherland, 1985). subsequent studies suggested that conversion of t4 to t3 was essential for the osmoregulatory action of thyroid hormones (leloup and lebel, 1993). potential iono and osmo-regulatory effects of thyroid hormones reflect their possible effects on gill na+-k+-atpase activity. gill na+-k+-atpase activity increased concomitantly with an elevation in plasma t4 (dickhoff et al 1977; folmar and dickhoff, 1979; sullivan et al 1983; boeuf and prunet, 1985). however, in other experiments administration of thyroid hormones did not affect the gill na+-k+-atpase activity (dickhoff et al 1977; saunders et al 1985; dange, 1986) and t3 treatment decreased gill na +-k+-atpase activity of freshwater rainbow trout (omeljaniuk and eales, 1986). part of the explanation for such differences may reflect the interaction of thyroid hormones with other hormones, such as cortisol and growth hormone, in determining na+-k+-atpase activity (dange, 1986; see review by mccormick, 1995). t4 administration did not increase na+-k+-atpase activity in seawater-acclimated tilapia by itself but did act synergistically when administered with cortisol (dange, 1986). however, there was no apparent synergistic action of t4 with cortisol in increasing chloride cell number or gill na+-k+-atpase activity in rainbow trout (madsen, 1990). thyroid hormones affect various aspects of metabolism. effects of thyroid hormones on carbohydrate and lipid metabolism have been reported (leatherland, 1982; plisetskaya et al 1983) and thyroid hormones may play a role in a stress-related mobilization of glucose in fish. thyroxine treatment caused hyperglycemic effects in some cases (chan and woo, 1978b). however, other studies observed hypoglycemic responses to thyroid treatment (murat and serfaty, 1970). closely related significant elevations of plasma t4 and glucose induced by disturbance stress were reported (himick and eales, 1990). it has also been shown that injection of glucose caused elevation of both plasma glucose and t4 (himick and eales, 1990). treatment of fish with low doses of thyroid hormones has been reported to stimulate protein synthesis whereas, treatment with high doses of thyroid hormones appeared to cause catabolic effects (medda and ray, 1979; matty et al 1982). the outcome of the various metabolic impacts of thyroid hormones in determining the growth of fish has varied in studies so far. thyroid hormone administration has been reported to accelerate fish growth (higgs et al 1979; saunders et al 1985; woo et al 1991) and, in support of this concept, elevated concentrations of plasma t3 were found in periods of rapid growth (mckenzie et al 1993). however, in other studies thyroid supplementation did not affect growth (leatherland et al 1987; gannam and lovell, 1991; soengas et al 1992). the apparent inconsistencies in these experiments may partially reflect the interaction of thyroid hormones with other hormones such as growth hormone and cortisol. thyroid hormones treatment was found to promote the anabolic effects of growth hormone (e.g. lower liver glycogen and higher serum cholesterol) in rainbow trout (fagerlund et al 1980; farbridge and leatherland, 1988). on the other hand, growth hormone treatment significantly elevated the plasma t3 concentration of rainbow trout (farbridge and leatherland, 1988; maclatchy and eales, 1990) indicating an increased peripheral conversion of t4 to t3. thyroid hormones may play a significant role in fish behaviour. for example, increased concentrations of plasma thyroxine were associated with migration of juvenile yellow american eels (castonguay and dutil, 1990). the level of motor activity of migrant atlantic salmon was also suggested to be determined by thyroidal status (youngson and webb, 1993). sublethal exposure of coho salmon to arsenic decreased thyroxine concentrations which coincide with decreased migration of smolts (nichols et al 1984). 2.4 endocrine interactions during stress stress-induced increases in plasma cortisol in rainbow trout were closely correlated with elevations in growth hormone (pickering et al 1991). stress was also reported to increase plasma growth hormone in immature rainbow trout (takahashi et al 1991). this stimulation of both cortisol and growth hormone release is important as cortisol has been found to facilitate the actions of other hormones, for example, growth hormone and thyroid hormones (dange, 1986; madsen, 1990). thus, growth hormone stimulation of gill na+-k+-atpase activity and chloride cell number was enhanced by cortisol treatment (madsen, 1990). al-kindi, brown, and waring 10 chronic stress in fish is often associated with a suppression of growth (reviewed by wendelaar bonga, 1997). for toxic stress the distinction of direct toxic effects and those resulting from the integrated hormonal stress responses may be difficult to determine. the influence of hormonal factors is further complicated by the multiplicity of endocrine systems affecting growth. pickering (1993a) reviewed the integrated hormonal control of growth (gonadal steroids, the thyroid axis, the hpi axis, growth hormone and catecholamines) in relation to stress-induced growth suppression. it has become clear in recent years that the aspects of the two components of the primary endocrine responses to stress (hypothalamic-pituitary-interrenal (hpi) axis and the hypothalamic-sympathetic-chromaffin cell axis) are in reality components of an integrated response to stress and these two components influence one another. activation of the hpi axis, acth treatment and increased plasma cortisol resulting from cortisol implants have each been found to result in increased chromaffin stores of catecholamines and their release into circulation (reid et al 1996). this implies that chronically stressed fish may be more able to generate a catecholamine response to stress. furthermore, elevated plasma cortisol concentrations have been reported to elevate the internal population of adrenoreceptors (reid et al 1992) potentially enhancing physiological responses to the circulating catecholamines. 3. physiological responses to stress in fish 3.1 carbohydrate metabolism and plasma glucose many teleost fish rely primarily on protein and lipid sources for energy and they are considered to possess poor enzyme system for utilization of carbohydrates (cowey and sargent, 1979; walton and cowey, 1982). in these species, amino acids such as arginine and lysine have been shown to be more effective than glucose in stimulating insulin release (higuera and cardenas, 1986; petersen et al 1987; suarez and mommsen, 1987). however, carbohydrate metabolism increases in states of high energy demand such as stress. in stress, blood glucose is elevated as a result of both glycogenolysis and gluconeogenesis (suarez and mommsen, 1987; wendelaarbonga, 1997). stress has been described as an energy drain with energy that might be utilized in growth being diverted to catabolic utilization (barton and schreck, 1987; pickering, 1990; mcdonald et al 1993). mobilization of readily available energy in the form of glucose is suggested to enhance the survival of fish (barton and iwama, 1991; pickering, 1993b). it is perhaps not surprising, therefore, that elevation of plasma glucose has been recognized as part of a generalized stress response in fish (mazeaud et al 1977). increased plasma glucose has been widely reported in fish exposed to physical stressors such as handling and confinement (mazeaud et al 1977; davis and parker, 1990; melotti et al 1992; waring et al 1992; barry et al 1993; foo and lam, 1993), exercised fish (zelnik and goldspink, 1981; barton et al 1986; flos et al 1988; white and fletcher, 1989; waring et al 1992; mcdonald et al 1993) and fish exposed to pollutants (gluth and hanke, 1984; edwards et al 1987; jones et al 1987; goss and wood, 1988; whitehead and brown, 1989; alkindi et al 1996). petroleum hydrocarbons have been reported to increase plasma glucose in various fish species (dimichele and taylor, 1978; thomas et al 1980; zbanyszek and smith, 1984; aabel and jarvi, 1990; alkindi et al 1996), with dose-related responses in mullets exposed to the wsf of fuel oil (thomas et al 1980). however, rainbow trout exposed to bunker c oil showed an unusual decrease in blood glucose concentrations which was attributed to a malfunction of glucose reabsorption by the renal tubules (mckeown and march, 1977, 1978). 3.2 osmotic and ionic regulation the regulation of the internal body fluid composition is essential for normal cellular functions in all organisms. in both seawater and freshwater there is a large osmotic gradient between the extracellular fluid of an aquatic organism and its environment (eddy, 1981; giesy et al 1988). maintaining a relatively constant internal environment, independent of the external environment, is achieved via the combined actions of the gills, gut and kidneys (eddy, 1981; mccormick, 1995; fuentes and eddy, 1997). the ionic and osmotic concentrations of the body fluid of marine teleost fish are approximately one third those of seawater. the endocrine, physiological and hispatological responses of fish 11 continuous outward osmotic movement of water is counteracted by drinking seawater, while the continuous influx of salts (sodium and chloride) is balanced by active efflux of salt via branchial chloride cells (eddy, 1981). in contrast, the body fluids of freshwater fish are more concentrated than the surrounding environment and consequently there will be an influx of water and an outward salt diffusion. freshwater fish excrete this excess water by production of copious volumes of hypotonic urine and salt losses are compensated for by active uptake via the gills (eddy, 1981; mcdonald and rogano, 1986). although highly simplified, this description of the ionic and osmotic-regulatory processes in both marine and freshwater fish may provide the basis for discussion of the osmoregulatory imbalances in stressed fish. disturbed plasma osmolarity and electrolyte concentrations have been recognised as a significant effect of stress in fish (mazeaud et al 1977; thomas et al 1980; engelhardt et al 1981; haux et al 1985; robertson et al 1987; goss and wood, 1988; brown et al 1990; waring et al 1992; barry et al 1993; wendelaar bonga, 1997). failure to maintain ionic and osmotic balance within certain limits may cause the death of stressed fish (stegeman and sabo, 1976; mcdonald, 1983). altered plasma osmotic and ionic concentrations have been reported in response to physical stressors such as handling and transport (barton et al 1985; robertson et al 1987; davis and parker, 1990; waring et al 1992; barry et al 1993; waring et al 1996b), and pollutant stress (swift 1981; stagg and shuttleworth, 1982; gluth and hanke, 1984; edwards et al 1987; jones et al 1987; goss and wood, 1988; allen, 1994) including exposure to petroleum hydrocarbons. petroleum hydrocarbons have been reported to have profound effects on plasma na+, k+ and cl concentrations with increases in fish exposed to crude oil in seawater, while concentrations of these ions decreased in fish exposed to crude oil in freshwater (morrow, 1974; engelhardt et al 1981; baklien et al 1986). however, decreased plasma chloride concentration in marine fish have also been reported (payne et al 1978; fletcher et al 1979; kiceniuk et al 1980) while no change in plasma cloccurred in the antarctic fish, pagothenia borchgrevinki, exposed to the wsf of fuel oil (davison et al 1992, 1993). moreover, exposure to the wsf of crude oil had no effect on plasma na+ and cl concentrations of flounders (alkindi et al 1996). sediment containing aliphatic hydrocarbons had no effect on plasma clconcentrations of winter flounder pleuronectes americanus (payne et al 1995). interestingly, brauner et al (1999) found that wsf contaminated water had no effect on plasma na+ and k+ concentrations in hoplosternum littorale (a teleost from the amazon), whereas crude oil exposure via the diet caused significant reductions in the plasma concentrations of these ions. reported changes in concentrations of plasma divalent ions in response to petroleum hydrocarbons are also inconsistent. plasma ca2+ concentrations were decreased in rainbow trout exposed to bunker c oil solution in seawater (mckeown and march, 1977), but flounders exposed to dispersed crude oil in seawater showed an elevation of plasma concentrations of both ca2+ and mg2+ (baklien et al 1986) while no significant changes in plasma ca2+ and mg2+ were observed in marine cunners, tautogolabrus adspersus, chronically exposed to weathered crude oil (fletcher et al 1979). changes in plasma osmolality of fish exposed to crude oil were generally in line with those to be expected from the change in monovalent ions in the particular group of experimental fish (mckeown and march, 1977, 1978; engelhardt et al 1981). thus, osmolality was increased in seawater mullets acutely exposed to the wsf of fuel oil (thomas et al 1980), however, there was no change in the plasma osmolarity of an antarctic fish pagothenia borchgrevinki in response to the wsf of fuel oil (davison et al 1993) or in flounders exposed to the wsf of crude oil (alkindi et al 1996). ionic and osmotic disturbances in fish exposed to petroleum hydrocarbons suggest specific types of gill damage such as increased permeability to ions or a deceased activity of ion pumps/exchange mechanisms (mckeown and march, 1977, 1978; wong and engelhardt, 1982). in line with this concept, gill na+-k+-atpase activity was reduced in pacific staghorn sculpin exposed to refinery wastewater (boese et al 1982). 3.3 endocrine systems and ionic and osmotic regulation during stress catecholamines, released as part of the generalized stress response, have been reported to increase branchial water permeability and cause branchial vasodilation, and may, partially explain stress-related weight loss in seawater fish and a gain in weight by stressed freshwater fish (mazeaud et al 1977). the branchial effects al-kindi, brown, and waring 12 of catecholamines would probably lead to disturbances in plasma ions with elevated plasma catecholamines in freshwater fish, leading to a decrease in the concentration of plasma ions and elevated catecholamines in seawater fish, increasing the concentration of plasma ions (mazeaud et al 1977; mazeaud and mazeaud, 1981; isaia, 1984; wendelaar bonga, 1997). however, injection of freshwater-adapted eels with adrenaline, noradrenaline or dopamine did not significantly change plasma osmolarity, na+ or cl(epple and kahn, 1985). cortisol is a major stress-related hormone and is reputed to directly affect osmoregulation. since stress frequently causes changes in plasma osmolarity in fish, the role of cortisol is of interest. cortisol is suggested to stimulate ion movement by increasing gill na+-k+-atpase activity (pickford et al 1970; forrest et al 1973; dange, 1986; madsen, 1990; bern and madsen, 1992; mccormick, 1995). in this connection, cortisol has been observed to increase the number of chloride cells (perry and wood, 1985; laurent and perry, 1990) and increase their apical area (laurent and perry, 1990). thyroid hormones may also affect the osmoregulation of teleost fish via their effects on na+-k+-atpase activity, but this is still far from conclusive. 3.4 blood oxygen the internal respiratory status of fish is determined by the combined processes of branchial gas transfer and blood gas transport. ventilatory water flow and lamellar blood perfusion, together with the diffusive properties of the gill epithelium collectively, determine branchial gas transfer. blood gas transport is affected by numerous factors including the blood oxygen carrying capacity and homodynamic variables such as cardiac output and regional blood flow distribution (perry and wood, 1989). during stress, plasma catecholamines may be elevated and the increase in catecholamines generally enhances the oxygen carrying capacity of fish. this is particularly evident during hypoxia (mazeaud et al 1977; ristori and laurent, 1989; aota et al 1990; perry et al 1991, 1993) and hypercapnia (perry et al 1989). for example, catecholamines stimulate a rapid release of red blood cells from the spleen into the bloodstream (kita and itazawa, 1989; perry and kinkead, 1989). furthermore, catecholamines have been reported to increase red blood cell ph (nikinmaa, 1986; primmett et al 1986) and to increase the oxygen affinity of hemoglobin. catecholamines may also enhance the oxygen carrying capacity via their homodynamic effects, stimulation of hyperventilation and by increasing branchial gaseous exchange. the respiratory status of fish has been an area of major interest in studying the effects of pollutants on fish (patten, 1977; johnstone and hawkins, 1980; gluth and hanke, 1984; malte, 1986; malte and weber, 1988; davison et al 1993). blood oxygen decreased in rainbow trout exposed to aluminum (malte, 1986), acid (malte and weber, 1988) or copper (wilson and taylor, 1993). alkindi et al (1996) found reduced blood oxygen content in wsf-exposed flounders. this hypoxia may have been the cause of the elevated plasma noradrenaline concentrations. the antarctic fish, pagothenia borchgrevinki, exposed to the wsf of fuel oil were much less tolerant of low levels of ambient oxygen than non-exposed fish (davison et al 1993) and markedly elevated their rate of oxygen consumption during pollutant exposure (davison et al 1992). similarly, juvenile american shad exposed to the wsf of crude oil were less tolerant of lower levels of dissolved oxygen (tagatz, 1961). reduction in oxygen uptake has been reported as a serious symptom of petroleum toxicity in a variety of fish species (devries, 1977; prasad, 1987; davison et al 1993). reduced oxygen uptake was observed in sculpin exposed to naphthalene (devries, 1977) and in carp exposed to crude oil (prasad 1987). however, increased oxygen uptake was observed in cod exposed to a simulated oil slick (johnstone and hawkins, 1980). brauner et al (1999) found elevated breathing frequency in the air breathing teleost hoplosternum littorale exposed to crude oil. the respiratory effects of petroleum hydrocarbon may be related to their histopathological effects on gills, which are discussed later in this review. interestingly, gagnon and holdway (1999) found altered gill metabolic enzymes in atlantic salmon (salmo salar) exposed to the water accommodated fraction of crude oil and dispersed crude oil. also, some recent work has shown that crude oil exposure or exposure to its wsf reduces the growth rate of fish (christiansen and george, 1995; gundersen et al 1996). endocrine, physiological and hispatological responses of fish 13 3.5 hematocrit and blood hemoglobin concentration changes in hematocrit (% packed erythrocytes) and blood hemoglobin concentrations have been widely reported as indicators of stress in fish (fletcher, 1975; thomas et al 1980; engelhardt et al 1981; haux et al 1985; goss and wood, 1988; aabel and jarvi, 1990; davison et al 1992, 1993). physical stressors such as handling and transport and pollutant stressors have been reported to increase hematocrit and blood hemoglobin concentrations (fletcher, 1975; yamamoto et al 1980; swift, 1981; barton et al 1985; jones et al 1987; goss and wood, 1988; alkindi et al 1996), although some studies of stressed fish have reported decreased hematocrit and blood hemoglobin concentrations (hattingh and van pletzen, 1974; davis and parker, 1990; mazur and iwama, 1993) or no significant change in these parameters (haux et al 1985). crude oils and their products have been reported to affect blood hemoglobin concentration and hematocrit. hematocrit initially increased after exposure of flounder to a 50% dilution of the wsf of omani crude oil (alkindi et al 1996), dab and english sole to oil-contaminated sediment (mccain et al 1978; tahir et al 1993), pacific staghorn sculpin to petroleum refinery wastewater (boese et al 1982) and antarctic fish (pagothenia borchgrevinki) to fuel oil (davison et al 1992, 1993). similarly, hemoglobin concentrations were increased in rainbow trout exposed to the wsf of a mixture of aromatic hydrocarbons (zbanyszek and smith, 1984), and in atlantic salmon exposed to an oil slick, and in english sole exposed to oil-contaminated sediment (mccain et al 1978). however, hematocrit was decreased in sculpin exposed to petroleum hydrocarbons (devries, 1977). hematocrit and blood hemoglobin concentrations were also dramatically reduced (by ~50%) in flounder exposed to a 50% solution of the wsf of crude oil (resulting in exposure to approximately 6ppm aromatic hydrocarbons) (alkindi et al 1996). adding further confusion to the discussion of the haematological effects of petroleum hydrocarbons, there have been several studies in which no significant changes in either hematocrit and/or hemoglobin concentrations were found. the hematocrit of cunners, tautogolabrus adspersus (payne et al 1978; kiceniuk et al 1980) and atlantic salmon (aabel and jarvi, 1990) and the hematocrit and hemoglobin of longhorn sculpin (khan, 1991a) were unaffected after chronic exposure to crude oil. hematocrits and blood hemoglobin concentrations were also unchanged in hoplosternum littorale exposed to the wsf of crude oil (brauner et al 1999) and hematocrit was not affected in winter flounder exposed to sediment contaminated with oil-base mud (payne et al 1995). the apparent contradictions in haematological effects of petroleum hydrocarbons are likely to reflect a combination of differences in the level of petroleum hydrocarbons to which the fish have been exposed, any resultant gill damage, the length of time of exposure and species differences in sensitivity and catecholamine responses. in relation to the last of these factors, it is clear that fish possess a splenic reservoir of erythrocytes which when released (under catecholamine stimulation) significantly elevates hematocrit and blood hemoglobin concentrations (yamamoto et al 1980; kita and itazawa, 1989; yamamoto and itazawa, 1989; pearson and stevens, 1991). reduction of splenic weight, an indication of the release of erythrocytes into general circulation by splenic contraction, has been recognized as a useful index of stress in fish. decreased splenic weight has been reported in fish exposed to crude oils and their derivatives (payne et al 1978; kiceniuk et al 1980). however, splenic weight was unchanged in other studies of fish exposed to petroleum hydrocarbons (khan, 1991a; davison et al 1993; payne et al 1995). 4. histopathological effects of crude oil and petroleum hydrocarbons on fish petroleum hydrocarbons have been reputed to cause a variety of histopathological effects in fish. malins (1982) reviewed the structural effects of petroleum hydrocarbons on marine fish and reported hepatocellular vacuolisation, increased liver rough endoplasmic reticulum (rer), gill damage (for example, epithelial lifting, chloride cell damage and fusion of the secondary lamellae), hyperplasia of the olfactory epithelium, degeneration of olfactory mucosal tissue and development abnormalities (for example, misfit of the lower jaw into the upper jaw, missing premaxillary bones and failure of the jaw to fully differentiate, absence of the branchiostegal membranes and reduced cephalization). al-kindi, brown, and waring 14 4.1 gill histopathology copious mucous secretion from the gills with hyperplasia and hypertrophy of mucus-producing epithelial cells are widely reported histopathological effects of crude oils and their products (hawkes, 1977; solangi, 1980; engelhardt et al 1981; lopez et al 1981 haensly et al 1982; solangi and overstreet 1982; khan and kiceniuk, 1984, 1988; khan, 1987; prasad, 1988, 1991; davison et al 1993). aside from increased mucous secretion, petroleum hydrocarbons have been reputed to have several other pathological effects on the gills. these include separation of respiratory epithelium, lamellar curling and hyperplasia, fusion of adjacent secondary lamellae and hemorrhaging of gill filaments (blanton and robinson, 1973; hawkes, 1977; solangi, 1980; engelhardt et al 1981; malins and hodgins, 1981; woodward et al 1981; haensly et al 1982; solangi and overstreet, 1982; khan and kiceniuk, 1984; alkindi, 1995). in some studies, gill damage and hemorrhaging from gill filaments could account for the decline in the number of circulating red blood cells (alkindi et al 1996), but few studies have included both physiological and histological approaches. a further change in gill histology reported in some studies was a proliferation of chloride cells in fish exposed to crude oil and its various fractions (solangi, 1980; engelhardt et al 1981; lopez, 1981). such an event could result from endocrine responses which have already been discussed. gills have been observed to be sensitive to crude oil or its wsf even at relatively low concentrations. coho salmon and starry flounder exposed to about 100 ppb of the wsf of crude oil for five days developed gill lesions which included loss of surface cells or the first two or three layers of the mucous cells, exposing immature mucous cells (hawkes, 1977). in addition, increased levels of parasite infection were observed in the gills of these fish. the extent of parasitic infection of the gills of oil-treated sculpin and cod was about 17-fold greater than that of control fish (khan, 1990) and chronic exposure of longhorn sculpin (khan, 1991a) and flounder (khan, 1991b) to oil-contaminated sediment increased parasite infection. an increased number of monogenoid parasites in the gills of cod exposed to the wsf of crude oil (approximately 30-80 ppb) occurred alongside other changes in gill morphology such as epithelial hyperplasia at the interlamellar bases and an increased number of mucus-secreting cells (khan and kiceniuk, 1988). such events could reflect the well-known immunosuppressive action of an activated corticosteroid response (see wendelaar bonga, 1997). at higher concentrations, 70% of the exposed fish showed lesions such as epithelial hyperplasia and lamellar curling. similarly, lamellar curling and swelling (edema) with ruptured afferent and efferent blood vessels, increased necrotic debris and extensive deterioration of the gill structure were all observed in rainbow trout exposed to bunker c oil mixed in seawater (mckeown and march, 1977, 1978) or the wsf of crude oil (prasad 1988; khan and kiceniuk, 1988). however, payne et al (1995) reported no gill histopathological changes in winter flounder exposed to sediment contaminated with oil-base mud, apart from a very mild hyperplasia of the gill tips in fish exposed to the lowest hydrocarbon level. chronic exposure to oil-shale water caused a graded increase in the diffusion distance of the gills of rainbow trout, which was proportional to the pollutant concentration. increased diffusion distance was attributed to swelling of the lamellae and epithelial cell hypertrophy (johnson, 1983). increased branchial diffusion distance has also been attributed to elevated mucous secretion in the antarctic fish, pagothenia borchgrevinki, exposed to the wsf fuel oil (davison et al 1993). fish living in the vicinity of drilling platforms which may be exposed to high levels of petroleum hydrocarbons were reported to show hyperplasia of gill epithelium (grizzle, 1986). once into production, coastal and marine platforms in many areas of the world currently discharge the waste ‘produced water’, contaminated with ppm levels of hydrocarbons, into the marine environment. here it will be heavily diluted and subject to rapid degradation, but effects on fish living in the vicinity of the platforms is of interest. in a recent study, turbot juveniles were exposed for up to 6 weeks to dilutions of a north sea oil platform ‘produced water’ using dilutions to mimic the likely concentration close to the discharge point to the likely concentration at several kilometers from discharge (stephens et al 2000). in turbot exposed to 1% or 0.1% produced water (likely to occur close to the discharge point) for 6 weeks ~50% gill lamellae were fused at their tips which appeared to develop after a curling and sticking at their tips. as a result, respiratory and/or ionoregulatory processes were likely to be disturbed in these fish. the higher concentration of produced water (1%) resulted in a similar endocrine, physiological and hispatological responses of fish 15 proportion of fused lamellae within 3 weeks. lower concentrations, however, did not cause a significant development of fusion. 4.2 liver histopathology increased cellular vacuolization, rer proliferation and glycogen depletion have been widely reported in the liver of fish exposed to petroleum hydrocarbons (hawkes 1977; dimichelle and taylor, 1978; mccain et al 1978; sabo et al 1978; whipple et al 1978; solangi, 1980; solangi, and overstreet, 1982; kiceniuk and khan, 1983; khan and kiceniuk, 1984). according to sindermann (1982), increased vacuolization in liver cells reflects an increased hepatic lipid content in fish exposed to petroleum hydrocarbons. however, eurell and haensly (1981) suggested that vacuole formation was not directly related to lipid accumulation; after 14-21 days of exposing atlantic croaker, micropogon undualatus to 5% wsf of crude oil, liver lipids were lower in exposed fish than in controls, although at 10% wsf, lipid content was increased. since vacuolization in liver cells was a consistent response, it did not appear to be closely related to an increased lipid content. also, exposure of sculpin to naphthalene did not appear to cause histological damage in the liver (devries, 1977). marty et al (1999) found evidence of increased incidence of hepatic necrosis in pacific herring (clupea pallasi) sampled from oiled sites in alaska and suggested that this may have resulted from a crude-oil associated increase in viral disease prevalence. vacuolization and increased rer have been observed not only in the liver but also in a variety of other organs. the intestine of petroleum-exposed chinook salmon revealed a presence of irregular cellular inclusions in the columnar cells of the intestinal mucosa, increased vesicle density in the cytoplasm near the luminal surface of the columnar cells and cytoplasmic changes of the basal cells of the mucosa. moreover, membrane bound vesicles containing fine granular material filled the luminal half of the intestine columnar cells and increased rer, as in the liver, has also been observed (hawkes et al 1980; haensly et al 1982). 4.3 kidney histopathology there have been relatively few histopathological studies of fish exposed to the wsf of crude oil (solangi, 1980; haensly et al 1982). in two studies shrinkage of renal tubules and epithelial separation from basement membranes suggested loss of functional renal tubules in fish exposed to the wsf of crude oil (solangi, 1980), while dilation of the bowman’s space and hypertrophy of the glomeruli were observed in kidneys of the plaice (pleuronectes platessa) collected from oil spill areas (haensly et al 1982). 5. effects of petroleum hydrocarbons on fish larvae the early life stages of marine fish appear to be more sensitive to hydrocarbons than adult fish (stene and lonning, 1984; carls and rice, 1988; marchini et al 1992). the greatest embryonic sensitivity to pollutants such as the wsf of crude oil may be very early in the development of an embryo when damage to a few precursor cells could potentially result in extensive damage as the embryo develops (moore and dwyer, 1974; rosenthal and alderdice, 1976; carls and rice, 1988). however, studies often indicate that fish eggs are, in fact ,more resistant to dissolved petroleum hydrocarbons than larvae (see carls and rice, 1988). these variations in resistance to hydrocarbons may reflect differences in the bioaccumulation of hydrocarbons by eggs and larvae: embryonic tissues may accumulate substantially less hydrocarbons (which may tend to partition in the yolk) than accumulation by larval tissues (carls and rice, 1988). moore and dwyer (1974) estimated that fish larvae may be ten times more sensitive to soluble aromatic hydrocarbons (ranging from 0.1 ppm to 1.0 ppm) than adult fish. this high sensitivity has been suggested to reflect a possible reduction in detoxifying capacity, their high surface area in contact with the environment and their limited mobility (rice, 1985). petroleum hydrocarbons have been reported to affect the survival of fish larvae (linden, 1976; kuhnhold et al 1978; falk-petersen et al 1985; tilseth et al 1984; carls, 1987; edsall, 1991; marchini et al 1992; alkindi et al 1996). exposure to weathered crude oil caused high mortality in larvae of the baltic herring al-kindi, brown, and waring 16 (linden, 1976). similarly, petroleum hydrocarbons such as polycyclic aromatic hydrocarbons (i.e. naphthalene and 1,3-dimethylnaphthalene) and cyclic alkanes were found to be toxic to rainbow trout alevins (edsall, 1991) and exposure of cod larvae or pacific herring larvae to the wsf of crude oil affected survival (falk-petersen et al 1983; carls, 1987). exposure to benzene derivatives also reduced the survival of larval and juvenile fathead minnow with larvae being more sensitive than juveniles (marchini et al 1992). crude oils and their hydrocarbon derivatives have been reported to cause morphological and developmental abnormalities in fish larvae (lindcn, 1976; lonning, 1977; smith and cameron, 1977, 1979; cameron and smith, 1980). exposure of pacific herring larvae to crude oil caused enlargement of the pericardial cavity, failure in development of branchiostegal membranes and erosion of pectoral fins (smith and cameron, 1977), and abnormal mouth development (smith and cameron, 1977, 1979). exposure to crude oil caused cellular disruption manifested in intercellular membrane breakdown, irregular and non-membrane bound intracellular spaces in brain and muscle tissues and swollen mitochondria ‘some with damaged cristae’ in pacific herring larvae (cameron and smith, 1980). exposure of three marine species of larvae to crude oil and aromatic hydrocarbons caused abnormally bent notochords, poor differentiation of the head region and protruding eye lenses (lonning, 1977). an ultrastructural study of plaice larvae exposed to crude oil showed irregular and degenerating muscle tissue (falk-petersen and kjorsvik, 1987). these morphological abnormalities can exert dramatic impacts on larval fitness. a completely normal mouth and normal swimming are essential for feeding while well developed fins are important for swimming and avoidance of predators (smith and cameron, 1977). exposure of fish larvae to petroleum hydrocarbons has been reported to affect their swimming ability (linden, 1975; smith and cameron, 1977; tilseth et al 1984; carls, 1987). rice (1985) described the pattern of behaviour of larvae exposed to high levels of the wsf of crude oil as a brief burst in activity followed by deep narcosis and, ultimately, death. this pattern of rapidly reduced swimming ability was confirmed in turbot larvae exposed to 25% to 50% of the wsf of crude oil, although there was good survival (over a 6h experimental period) in 25% and 33% wsf (alkindi, 1995; stephens et al 1997). reduced swimming ability is a widely reported effect of oil hydrocarbons on fish larvae (linden, 1975; smith and cameron, 1977; tilseth et al 1984; carls, 1987). reduction in swimming ability and deep narcosis of larvae will seriously cripple their ability to feed and to avoid predators. baltic herring larvae exposed to crude oil showed abnormal swimming behaviour characterized by vigorous swimming up to the surface followed by a slow sinking to the bottom (linden, 1975). petroleum hydrocarbons have also been reported to affect the metabolism of fish larvae (eldridge et al 1977; serigstad and adoff, 1985). depressed oxygen uptake may cause impaired growth and development (eldridge et al 1977; kuhnhold et al 1978; serigstad and addof, 1985; tilseth et al 1984; carls, 1987; marchini et al 1992). moles et al (1981) found that the growth rate of coho salmon fry was inversely related to increasing concentrations of naphthalene and toluene. direct exposure to crude oil caused a reduction in the length of larvae of the baltic herring (linden, 1976), pacific herring (smith and cameron, 1977; carls, 1987) and cod (tilseth et al 1984). ingestion of crude oil in the diet also resulted in a reduced body length of pacific herring larvae (carls, 1987). exposure to benzene derivatives also reduced the growth of fathead minnow larvae (marchini et al 1992) and post-yolk sac larvae of pacific herring exposed to benzene showed decreased growth even though they ingested more food than unexposed larvae (eldridge et al 1977). however, exposure to the wsf of crude oil caused a rapid reduction in feeding of pacific herring larvae (carls, 1987). oil-induced reduction in growth may represent the result of a diversion of energy to the well-established detoxification processes (eldridge et al 1977; kuhnhold et al 1978) as well as effects on feeding and oxygen uptake (see above). very few studies have investigated the resultant endocrine stress responses of larvae exposed to petroleum hydrocarbons. a concentration and time-related increase of whole body t4 and t3 content of turbot larvae exposed to the wsf of crude oil was reported (stephens et al 1997). increased whole body cortisol content (a measure of de novo synthesis and release of cortisol) has also been observed in fish larvae exposed to petroleum hydrocarbons (ramsay, 1991; alkindi, 1995; stephens et al 1997). endocrine, physiological and hispatological responses of fish 17 6. conclusions and future research endocrine responses of fish exposed to petroleum and related hydrocarbons are not well established. cortisol has been investigated more than any other stress-related hormone but so far responses are not well established (alkindi et al 1996). there is a need for further dose-related studies on the effects of petroleum hydrocarbons on plasma cortisol and other hormones. there is also a need to establish the ability of fish to adapt to chronic exposure to petroleum hydrocarbons. chronic exposures may ‘down-regulate’ the corticosteroid response, which has been observed in response to other chronic stressors (wendelaar bonga, 1997). crude oil and their products have been reported to affect osmotic and ionic balances of a wide variety of fish species but the responses have not been entirely consistent. analysis of the ionoand osmo-regulatory processes are required to more clearly determine the impact of petroleum hydrocarbons. morphological alterations caused by exposure of fish to individual petroleum hydrocarbons and to model hydrocarbon mixtures or to whole crude oil have been observed by investigators both in laboratory and field studies, but investigators often report the structural effects of toxicants without investigating potential functional abnormalities. there are relatively few integrated studies of morphological and physiological events. the evaluation of the hypothalamic neurosecretory hormones during petroleum-induced stress should be explored in future studies. we can obtain a more complete picture by examining not only the peripheral aspects but also the central control as 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aromatic hydrocarbons on some haematological parameters of rainbow trout, salmo gairdneri richardson, during acute exposure. j. fish biol. 24: 545-552. zelnik, p.r. and goldspink, g. 1981. the effect of exercise on plasma cortisol and blood sugar levels in the rainbow trout, salmo gairdneri r. j. exp. biol. 19: 37-43. received 9 december 1999 accepted 11 june 2000 30 endocrine, physiological and histopathological responses of fish and their larvae to stress with emphasis on exposure to crude oil and various petroleum hydrocarbons a.y.a al-kindi*, j.a brown** and c.p. waring *** 1.1 the fish stress response 2 1.2petroleum hydrocarbons 3 1.3 exposure of fish to petroleum hydrocarbons 4 1.4 experimental exposure methods 4 endocrine responses to stress and their induction in fish exposed to petroleum hydrocarbons 5 2.1plasma catecholamines 5 2.2plasma cortisol 6 2.3plasma thyroid hormones 8 2.4endocrine interactions during stress 9 physiological responses to stress in fish 10 3.1carbohydrate metabolism and plasma glucose 10 3.2osmotic and ionic regulation 10 3.3endocrine systems and ionic and osmotic regulation during stress 11 3.4blood oxygen 12 3.5hematocrit and blood hemoglobin concentration 13 histopathological effects of crude oil and petroleum hydrocarbons on fish 13 4.1gill histopathology 14 4.2liver histopathology 15 4.3kidney histopathology 15 references 17 introduction 1.1 the fish stress response 1.2petroleum hydrocarbons 1.3 exposure of fish to petroleum hydrocarbons 1.4 experimental exposure methods endocrine responses to stress and their induction in fish exposed to petroleum hydrocarbons 2.1plasma catecholamines 2.2plasma cortisol 2.3plasma thyroid hormones physiological responses to stress in fish 3.1carbohydrate metabolism and plasma glucose 3.2osmotic and ionic regulation 3.3endocrine systems and ionic and osmotic regulation during stress 3.4blood oxygen 3.5hematocrit and blood hemoglobin concentration histopathological effects of crude oil and petroleum hydrocarbons on fish 4.1gill histopathology 4.2liver histopathology 4.3kidney histopathology conclusions and future research references brown, j.a., edwards, d. and whitehead, c. 1989. cortisol and thyroid hormone responses to acid stress in the brown trout, salmo trutta l. j. fish biol. 35: 73-84. brown, s.b., eales, j.g., evans, r.e. and hara, t.j. 1984. interrenal. thyroidal and carbohydrate responses of rainbow trout, salmo gairdneri, to environmental acidification. can. j. fish. aquat. sci. 41: 36-45. epple, a. and kahn, h.a. 1985. exogenous catecholamines do not affect osmoregulatory parameters in the intact eel. j. exp. zool. 234: 485-488. gannam, a.l. and lovell, r.t. 1991. effects of f leatherland, j.f. 1982. environmental physiology of the teleost thyroid gland: a review. env. biol. fish. 7: 83-110. photovoltaic cells and systems: squ journal for science, 9 (2004) 67-86 © 2004 sultan qaboos university 67 on regression estimators using extreme ranked set samples hani m. samawi*, ahmed y.a. al-samarraie* and obaid m. al-saidy** *department of statistics, , yarmouk university, pc 211-63, irbid, jordan, email: hsamawi@yu.edu.jo, **department of mathematics and statistics, college of science, sultan qaboos university, al-khod, p.o. box 36, pc 123, sultanate of oman. حول تقديرات اإلنحدار باستخدام العينات القصوى المرتبة هاني سماوي، أحمد السامرائي و عبيد السعيدي االنحدار قد استخدم لتقدير الوسط الحسابي للمجتمع للمتغير المعتمد )ص( في حالتين. أسلوب خالصة : س( معلوماً وفيي الحالية النانيية عنيدما يكيون في الحالة األولى عندما يكون الوسط الحسابي للمتغير المساعد المستقل ) . أيضا فيي الحالية النانيية لقيد اسيتخدمنا طريقية العينية المتدوجية لتقيدير الوسيط الحسيابي للمتغيير المسيتقل م غير معلو .(1996)س(. لقد تحققنا من أداء الطريقتين باستخدام العينات القصوى المرتبة كما جاء في بحث سماوي وتمالءه ) م عرض الناحية النظرية والرقمية بواسطة المحاكاة والتطبيق في هذا البحيث. ولقيد أظتيرت النتيانه أنيح فيي حالية لقد ت التوتيعيات المتمانليية فيان طريقيية اسيتخدام العينييات القصيوى المرتبيية لتقرييرات االنحييدار هيي اكنيير فعاليية ميين طريقيية العينات المرتبة العادية والعينات البسيطة. abstract: regression is used to estimate the population mean of the response variable, y , in the two cases where the population mean of the concomitant (auxiliary) variable, x , is known and where it is unknown. in the latter case, a double sampling method is used to estimate the population mean of the concomitant variable. we invesitagate the performance of the two methods using extreme ranked set sampling (erss), as discussed by samawi et al. (1996). theoretical and monte carlo evaluation results as well as an illustration using actual data are presented. the results show that if the underlying joint distribution of x and y is symmetric, then using erss to obtain regression estimates is more efficient than using ranked set sampling (rss) or simple random sampling (srs). keywords: extreme ranked set sample, ranked set sample, relative efficiency, regression estimators, two-phase sampling. 1. introduction in many experimental situations the response variable y is related to a non-stochastic concomitant variable, x . for instance, let y be the bilirubin level in jaundice babies who stay in neonatal intensive mailto:hsamawi@yu.edu.jo hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 68 care and let x be the weight of the baby at birth. by obtaining simultaneous observations on x and y , we can use information contained in the x-measurements to estimate the mean value of .y this can be done by using either ratio estimation or regression estimation. herein, we are interested in the regression estimation method used to obtain increased precision in estimating the population means or totals of the variable of interest, y , by taking advantage of its correlation with the auxiliary variable x . the two cases where the mean, x  , of x is known and where it is unknown are considered. in many cases the sampling units in a study are easier ranked than actually quantified. mcintyre (1952) proposed to use the mean of n units obtained from a ranked set sample (rss) to estimate a population mean. patil et al. (1993) compared the precision of ranked set sampling with the regression estimator. they showed that using rss is superior to regression estimator under srs in most of the cases. yu and lam (1997) used the rss regression estimation method to estimate the population mean and showed that using rss provides a more efficient estimator than using srs. for more details on rss see, for example, kaur et al. (1995) and patil et al. (1999). samawi et al. (1996) investigated the use of extreme ranked set sampling (erss) in reducing the ranking error and in improving the precision in estimating the population mean in the case of a symmetric underlying distribution. they showed that if the underlying distribution is the uniform distribution, then the highest magnitude of the relative savings occur when only the extreme ordered units are measured with equal proportion. however, in the case of other unimodal symmetric distributions the highest gain is achieved when the units possessing the middle rank are measured. for this reason, yanagawa and chen (1980) did not consider the uniform distribution while investigating various symmetric distributions to develop a better ranked set sample estimator of the population mean. as in samawi et al. (1996) we obtain an extreme rank set sample by first choosing r independent sets, each of which contains r bivariate elements drawn randomly from an infinite population. rank the elements in each set with respect to one of the variables y or x . suppose that the ranking is done on the variable x . from the first set an actual measurement is taken of the x element with the smallest rank, together with the value of y associated with this smallest element of x . from the second set an actual measurement is taken of the element with the largest rank of x , together with the associated y value. from the third set an actual measurement is taken of the element with the smallest rank of x , together with the associated y value, and so on. in this way we obtain the first 1r  measured elements using the first 1r  sets, together with the associated values of the y variable. the choice of the thr  element from the thr  (i.e., the last) set depends on whether r is even or odd : (a) if r is even the largest ranked x element is measured, together with the value of the associated variable y . erssa will denote such a sample. (b) if r is odd we measure the median of x , together with the value of variable y associated with the median of x . erssb will denote such a sample. the cycle may be repeated m times until n rm bivariate elements have been measured. in this paper we propose to use erss to improve the precision of the two methods of regression estimation. we study the properties of these estimators and compare them under different settings. in section 2, we obtain the regression estimator of the mean of y using extreme ranked set sampling when x is known. the mean and variance of the estimator are derived. comparisons between the various estimators are discussed in terms of efficiencies. in section 3, we obtain the regression estimator using extreme ranked set sampling when x  is unknown using a double sampling method. again, we derive the mean and variance of the estimator and some comparisons between the various estimators are discussed in terms of efficiencies. an illustration of the methods using real data about the bilirubin level in jaundice babies is given in section 4. on regression estimators using extreme ranked set samples 69 2. regression estimators when  x is known like ratio estimation, linear regression estimation of the mean is designed to increase the precision of the estimator by using an auxiliary variable x that is correlated with y . when the relationship between y and x is examined, it may be found that although the relation is approximately linear, the line does not go through the origin. this suggests that an estimator based on the linear regression of y on x is better than an estimator that is based on the ratio of the two variables. 2.1 regression estimator using srs let  ,i ix y , 1, 2,...,i n be a bivariate random sample from   ,f x y and assume that  i y i x iy x       (2.1) where and x   y are the means of x and y respectively, and for a fixed i x , the 's i  , 1, 2,...,i n are i.i.d. with mean zero and variance  22 2 1y    , where  is the correlation coefficient between x and y . when the population mean x  is known, the regression estimator of the mean of y is given by:  ˆreg xy y x    , (2.2) where 1 i x x n   , 1 i y y n   ,      2 ˆ ii i i x x y y x x        , and n m r . when the joint underlying distribution of  ,x y is assumed to be a bivariate normal, the regression estimator regy is an unbiased estimator for y  and its variance is given by     2 2 1 1 1 3 y reg v ar y n n           (2.3) (see tikkiwal (1960) or sukhatme and sukhatme, 1970.) however, if the assumption of the linear relationship in (2.1) is invalid, then the srs regression estimator in (2.2) is in general a biased estimator of y . 2.2 regression estimator using rss consider a bivariate rss where the relationship between     and i ki k y x is       y xi ki k i ky x       , and1, 2,..., 1, 2,..., .i r k m  (2.4) then the regression estimator regy based on rss as in yu and lam (1997) is given by  ˆreg rss rssxy y x    . (2.5) hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 70 using basic properties of conditional moments, yu and lam (1997) showed that under (2.4), regy is an unbiased estimator of y  and its variance is     2 2 2 2 1 1 y rss reg zr z var y e n s               , (2.6) where,   1 rss i k i i z z mr   ,       x xki ki x z   , and    2 2 1 rsszr i k k i s z z rm   . again, if the assumption of the linear relationship is invalid, the rss regression estimator in (2.5) is in general a biased estimator for  y . 2.3 regression estimator using erss assuming that both variables, x and y , have symmetric underlying distributions, let     , i jk i jk x y be respectively, the i th smallest value of x and the corresponding value of y obtained from the j th sample and the k th cycle. then regressing   i jk y on  i jk x we have      , y y x ijki jki jk x y x           (2.7) where 1, ; 1, 2,..., / 2i r j r  and 1, 2,..., ,k m when r is even,  1, , 1, 2,...,i r j  1 2 r  and 1, 2,...,k m when r is odd, and ijk  has the same distributional assumptions as in (2.1). in what follows we discus in details the case when r is even. the case when r is odd is similar and it will only be presented in the numerical results. when the population mean  x is known, we have the difference estimator,  da erssa x erssay y x    (2.8) where,       / 2 1 1 2 1 1 1 m r erssa j k r jk k j y y y n      ,       / 2 1 1 2 1 1 1 m r erssa j k r jk k j x x x n      , and  is a constant to be determined. under the assumption of symmetric underlying distribution functions of x and y , erssa y and erssa x are unbiased estimators for  y and x  respectively, see samawi et al. (1996). therefore, it can easily be shown that da y is an unbiased estimator of . y  furthermore,        2var var 2 var varyda erssa erssa erssa x y x x y        where, on regression estimators using extreme ranked set samples 71     1 2 var x erssa x n   ,     1 2 var y erssa y n   ,     1 2 1 var x x  ,     1 2 1 var y y  and n r m . note that by the symmetry of the underlying distributions,    1 2 2 n x x   and [1] [ ] 2 2 ny y   , see samawi et al. (1996). since for any value of  , ad  is an unbiased estimator of y  , the optimal value of  can be obtained by minimizing the variance of ad  . doing so gives * y x      as the optimal value of  . however, *  is unknown but can be estimated by              2 2 1 1* 2 2 1 1 1 1 , rm erssa erssai jk i jk rm k j i a i jk i jkrm k j i erssai jk k j i x x y y c y x x                1i  and r , where         2 2 1 1 erssai jk i jk rm erssai jk k j i x x c x x      . now, define the errsa regression estimator for y  as  ˆereg erssa a x erssay y x    . (2.9) then using basic properties of conditional moments, we have the following theorem: theorem 2.1: under (2.2) and assuming that the underlying marginals distributions of x and of y are symmetric, the regression estimator of y  as defined in (2.9) has the following properties: (a)  e yereg y (b)     22 2 2 y 1 1 e erssy ereg z z var e n s                 where,      / 2 1 2 1 2 1 1 1 , m r erss j k r jk k j z z z n      and       / 2 / 22 2 2 1 2 1 2 1 1 1 1 e m r r z erss erssj k r jk k j j s z z z z n                 , with hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 72     , xi jk i jk x x z     1, ; 1,..., / 2i r j r  and 1,..., ,k m proof: to prove theorem 2.1, we first show that (1)  ˆa   and (2)      2 2 2 1 1 ˆ | e a rm erssai jk k j i var x x x       proof of (1): from the definition of     / 2 11 ˆ rm a i jk i jk j ik c y    , we have that ˆ[ ( | )] x y a e e x      / 2 1 1 [ ( | )] i jk i jk m r x y k j i e e xyc    . since   / 2 / 2 [ ] ( ) ( ) ( ) ( ) 1 1 1 1 | ( ) , 0 and 1, m r m r y i jk y i jk x i jk i jk i jk k j i k j i e y x x c c x             then it clear that     / 2 / 2 ( ) ( ) 1 1 1 1 ˆ( ( | )) [ ( ( ))] [0 0] ( ) . i jk i jk m r m r x y a x y i jk x x i jk k j i k j i x e e x e x e xc c e                      proof of (2): similarly, since   / 2 2 2 [ ] ( ) / 2 21 1 ( ) 1 1 1 | and , ( ) m r y i jk e i jk m r k j i i jk erssa k j i var y x c x x           then   2/ 2 2 ( ) [ ] / 2 21 1 ( ) 1 1 ˆ | ( | ) . ( ) m r e a i jk i jk m r k j i i jk erssa k j i var x c var y x x x            proof of theorem 2.1 (a): using (2.7) and the proof of (1), we have that     xyeeye eregyxereg               / 2 [ ] 1 1 1 1 ˆ 1 ˆ , 1 ˆ y ereg y erssa a x erssa m r y i jk a x erssa k j i m k y y x a x erssai k k j i e y x e y x x e y x x rm e x x x rm                                         y erssa x x erssax x         . on regression estimators using extreme ranked set samples 73 therefore,   ,ereg ye y  and hence eregy is an unbiased estimator of y  . proof of theorem 2.1 (b): using properties of conditional moments,      ereg x y ereg x y eregvar y e var y x var e y x        . first note that,     ˆ x y ereg x y erssa a x erssavar e y x var e y x x           and from the proof of part (a),   yereg μ xye  , then   0x y ereg x yvar e y x var        . also,               2 ˆ ˆ ˆ 2 , , x y ereg x y erssa a x erssa x y erssa x erssa y a erssa a x erssa e var y x e var y x x e var y x x var x cov y x x                         but,        r/2 r/2 [ ] ( ) [ ] 1 j 1 i 1 j 1 i ( ) ˆ 1 , 1 ( erssa a x erssa m m x erssa i jk i jk i jk k k x erssa i jk cov y , β x x x cov y c y x rm x c var rm                       r/2 [ ] 1 j 1 i r/2 2 ( ) 1 j 1 i | ), 1 , 0, m i jk k m x erssa e i jk k y x x c rm            therefore,                 xvarxexyvarexyvare ayerssaxxerssayxeregyx  ˆ 2 , and from the proof of (2) above,       / 2 x [ ]2 1 1 2 2 x / 2 2 ( ) 1 1 1 ( ( ) m r x y ereg y i jk k j i e x erssa m r i jk erssa k j i e var y x e var y rm e x x x                                   . hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 74 clearly this implies that,       / 2 2 x 2 1 1 2 2 2 x / 2 2 2 ( ) 1 1 1 / {( ) ( )} / m r x y ereg e k j i erssa x x e m r i jk x erssa x x k j i e var y x e rm x e x x                                         and hence,     2 2 2 x 2 1 1 . y erss ereg e z var y e n s z                   2.4 comparison with naïve estimators using theorem (2.1) and the above results, the relative precision of the erss regression estimator, ereg y , relative to the erss naive estimator, erss y , is           1 2 22 2 2 , 1 1 e y erss ereg erss ereg y erss var y nrp y var n s                    (2.10) whereas the relative precision of erss regression estimator, y ereg relative to the rss naive estimator rssy is given by           2 1 2 22 2 1 ,y y 1 1 i e r y rss i ereg rss ereg erss y var ry rp y var s                    . (2.11) for the variances of the naïve rss and erss estimators, see for example samawi et al. (1996). as it is known that    erss srsvar vary y , samawi et al. (1996), we only compare ereg y to erss y and rss y . using (2.10), ereg y has the a greater precision than erss y whenever  1 2 2 2 2 1 2 1 1 y erss y z e z s                              . on regression estimators using extreme ranked set samples 75 therefore, the regression method of estimating y  based on erss is most preferable if  is large. similarly, from (2.11), ereg y has a greater precision than rss y whenever   1 2 2 1 2 2 2 1 1 1 2 1 i e r y i erss y z r z s                              . 2.5 comparisons with regression estimators 2.5.1 comparisons with srs regression estimator we consider the relative precision of our proposed erss regression estimator relative to the srs regression estimator. table 2.1 presents the relative precision when  ,x y has a bivariate normal distribution with a correlation coefficient of zero. from the table we see that the relative precision is always greater than 1 when 0  . since the relative precision as given in (2.12) is independent of , the erss regression estimator is always superior to the srs regression estimator, regardless of the value of  . table 2.1. relative precision of erss regression estimator relative to the srs regression estimator.   when, 0erg regrp y y   /m r 4 5 6 7 8 1 1.771401 1.396518 1.282631 1.213074 1.17554 4 1.054236 1.043639 1.038408 1.032832 1.02938 8 1.023997 1.019787 1.017815 1.015426 1.01390  1 1 1 1 1 2.5.2 comparisons with rss regression estimator finally, we consider the relative precision of our proposed erss regression estimator relative to the rss regression estimator, as presented by yu and lam (1997). following, yu and lam (1997), since erss y does not utilize any information on the concomitant variable x , it is fair to compare erss regression estimator, ereg y , with the regression estimator, reg y , based on a srs, (see hedayat and sinha, (1992)) and with the regression estimator, reg y based on rss. when the sample is drawn from a bivariate normal population the relative precision of ereg y relative to reg y is hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 76       2 2 1 1 3, 1 e reg ereg reg ereg erss z var y nrp y y var y z s            . (2.12) and the relative precision of ereg y relative to re g y is       2 2 2 2 1 , 1 r e rss zreg ereg reg ereg erss z z svar y rp y y var y z s                     . (2.13) table 2.2 presents the relative precision for a bivariate normal distribution with zero correlation coefficient. the table shows that the relative precision is always greater than 1 when 0  . since the relative precision given in (2.13) is independent of  , we can again conclude that the erss regression estimator is always superior to the rss regression estimator regardless of the value of  . table 2.2. relative precision of erss regression estimator relative to the rss regression estimator   when, 0erg regrp y y   /m r 4 5 6 7 8 1 1.096072 1.038646 1.029965 1.018206 1.015733 4 1.008527 1.004899 1.004976 1.003545 1.003144 8 1.003801 1.002274 1.00236 1.001684 1.001516  1 1 1 1 1 2.6 evaluation of departure from the linearity assumption generally, if the assumption of the linear relationship in (2.7) is invalid, the erss regression estimator is a biased estimator. in such a case, we define the relative precision to be the ratio of the mses of the estimators compared. as in yu and lam (1997), we evaluate the performance of the regression estimator under the departure from the linearity assumption by using plackett’s class of bivariate distributions with fixed marginal distribution functions  f x and  g y . the joint cdf is given by                   1/ 2 2 , , 4 1 , 2 1 s x y s x y f x g y x y f x g y               1 1, if if     where        , 1 1s x y f x g y      and the parameter  governs the dependence between x and y . on regression estimators using extreme ranked set samples 77 table 2.3. relative precision of erss regression estimator relative to erss naive estimator when the linearity assumption is violated (bold numbers indicate rp < 1). r = 4 y n(  ,1 ) m u ( 0,1 ) m x  1 4 8 1 4 8 n( ,1 ) 0.05 1.3437 1.4061 1.5112 1.2469 1.3043 1.3604 0.3 0.9467 1.0188 1.0351 0.9099 1.0178 1.0343 1 0.8878 0.9735 0.9897 0.8741 0.9786 0.9909 3 0.9444 1.0183 1.0382 0.914 1.0149 1.0294 10 1.1241 1.2085 1.2466 1.0167 1.1686 1.1649 u( 0,1 ) 0.05 1.3481 1.4636 1.4963 1.3333 1.4565 1.4647 0.3 0.9589 1.0303 1.0452 0.9511 1.0305 1.0464 1 0.9127 0.9913 0.9919 0.8908 0.9839 0.9929 3 0.9717 1.0289 1.0316 0.9411 1.0255 1.0438 10 1.1652 1.1947 1.2164 1.1018 1.1886 1.2483 r = 5 y n( ,1 ) m u ( 0,1 ) m x  1 4 8 1 4 8 n( ,1 ) 0.05 1.3485 1.3797 1.4031 1.2057 1.2991 1.2878 0.3 0.9692 1.0241 1.0395 0.975 1.0261 1.0355 1 0.9305 0.9836 0.9959 0.9336 0.9833 0.9962 3 0.9473 1.0165 1.0262 0.9627 1.0261 1.0336 10 1.1455 1.1612 1.1627 1.0535 1.1489 1.1671 u( 0,1 ) 0.05 1.3668 1.3565 1.3876 1.3086 1.4015 1.4203 0.3 1.0039 1.0363 1.0383 0.9848 1.036 1.0529 1 0.9452 0.9885 0.9937 0.9508 0.9884 0.9956 3 0.9973 1.0291 1.028 0.9834 1.0306 1.0387 10 1.1845 1.1734 1.2056 1.1509 1.2088 1.2089 the reason for choosing this class of bivariate distributions is that it covers the full range of dependence: (a)    ygxf  10 (b) 1   x and y are independent (c)    f x g y     . in general, the relationship between x and y is not linear. however, their relationship might be close to linear when  is close to 0 or  and their marginal distributions are the same and symmetric if hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 78  is close to 0. for a more detailed description of plackett’s distribution and its random generation, see johnson (1987), (p. 191-197). first, we fix the set size r to be 4 and 5, and examine m = 1, 4, 8. five types of dependence from strongly negative to strongly positive corresponding to  = 0.05, 0.3, 1, 3, 10, and two marginal distributions, normal ( , 1), uniform (0,1), are considered here. table 2.3 gives the relative precision of the erss regression estimator relative to the erss naive estimator based on simulations of size 100,000. the main conclusions from table 2.3 are: 1. clearly, if both x and y have symmetric marginal distributions and  is 0.05 or 10, the erss regression estimator is superior to the erss naive estimator since the plackett’s distribution in these cases is close to a bivariate distribution with linearly related marginal. 2. the efficiency decreases as the value of  increases from 0.05 to 1, and starts to increase as  increases from 1 to 10 for any given value of m and for r = 4 and 5. 3. for any fix  and any value of r, we note that as m increases the efficiency increases. in general when  is close to 1, the performance of the erss regression estimator is poor. this may be due to the fact that when  is close to 1, the two variables x and y are independent. 3. regression estimators when x  is unknown in this section, we discuss how to obtain the extreme ranked set sample regression estimator by using the method of double sampling (or two-phase sampling), when  x is unknown. 3.1 regression estimation using two-phase sampling the regression estimators ereg , reg  and reg  involve the population mean x  of the concomitant variable x , which is usually unknown in practical settings. if x  is unknown, the method of double sampling can be used to obtain an estimate of x  . this involves the drawing of a large random sample of size ,n which is used to estimate x  . a sub-sample of sizeis then selected from the n  original ( n ) selected units to study the primary characteristics of y . under an extreme ranked set sampling setting,phase sampling is srs and the second -. note that the first rmn  and mrn 2  phase sampling is erss. let x  be the sample mean of x based on mr 2 observation of x in the first-phase. clearly, x  is an unbiased estimator for x  . if erss is the second phase sampling, the double sampling regression estimator of the population mean y  is defined as  ˆ ,eds erssa a erssay y x x    (3.1) where, on regression estimators using extreme ranked set samples 79   / 2 [1`]2 1 [ ]2 1 1 1 m r erssa j k r jk k j y y y n      ,   / 2 (1)2 -1 ( )2 1 1 1    m r erssa j k r jk k j x x x n = , 2 1 1 m r jk k j x x nr      , ˆ a  is as in (2.9) and n mr . again, using basic properties of conditional moments, we have the following theorem. theorem 3.1: assume that the model in (2.7) is satisfied and that the underlying marginals distribution functions of y and x are symmetric. then the double sampling regression estimator for y  defined in (3.1) has the following properties: (a)  eds y  , (b)       2 2 2 2 2 2 1 1var y n s rn                     e erssy y eds z , where,   jk i , erss and 2 s ee as in section 2 and x x x      . proof of theorem 3.1: from the proof of theorem 2.1, we have (1)  ˆae   and (2)      2 2 2 1 1 ˆ | e a rm erssai jk k j i var x x x       . proof of (a):     xyeeye edsyxeds               / 2 [ ] 1 1 1 1 ˆ 1 ˆ , 1 ˆ , y eds y erssa a erssa m r y i jk a erssa k j i m k y y x a erssai k k j i e y x e y x x x e y x x x n e x x x x n                                  then by the proof of part (1) of theorem 2.1, we have that      x .y eds y erssa x erssae y x x x         hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 80 since erssax is an unbiased estimator for x  (under the symmetry assumption, see samawi et al. (1996)) and x is also an unbiased estimators for x  , then    ( | ) { x } ,x y eds y x erssa x erssa ye e y x e x x          and hence eds y is an unbiased estimator of y  . proof of theorem 3.1 (b): similar to the proof of theorem 2.1,        .xyevarxyvareyvar edsyxedsyxeds  first from the proof of part (a) above,     ˆ x y eds x y erssa a erssavar e y x var e y x x x          . from (1) we know that       xxxye erssaxerssayeds  x . also,               2 ˆ ˆ ˆ 2 , . x y eds x y erssa a erssa x y erssa erssa y a erssa a erssa e var y x e var y x x x e var y x x x var x cov y x x x                       similar to the proof of theorem 2.1, we can show that   xxxycov erssaaerssa ˆ ,  = 0, and hence                 xvarxxexyvarexyvare ayerssaxerssayxedsyx ̂ 2 ,                 2 2 2 2 x / 2 2 2 ( ) 1 1 2 2 2 x 2 x 1 1 . x erssa x x e e m r i jk x erssa x x k j i erss y e x x e rm x z z e rm rm s z                                                           .x }x{ 2 2 2 mr var xxvarxyevar x x erssaxerssayxedsyx      on regression estimators using extreme ranked set samples 81 therefore,       2 2 2 2 2 x 2 1 1 . erssy y eds e z z v ar y e n s rn z                      for the double sampling regression estimator ds based on srs, sukhatme and sukhatme (1970) showed that, when  ,x y follows a bivariate normal distribution, ds y is an unbiased estimator of y  with variance   2 2 21 1 11 3 yds r var n r n r n            . 3.2 relative efficiency again since erss y did not use any information on the concomitant variable x , we can compare the two-phase erss regression estimator, eds y , to the two-phase regression estimator ds y based on srs, and to the two-phase regression estimator rds y based on rss. the relative precision of eds y relative to ds y when  ,x y has a bivariate normal distribution (see tikkiwal, 1960) is             2 2 2 2 2 2 1 1 1 1 3 , 1 1 e ds eds ds eds erss r var r n r rp var rs                                  (3.2) and the relative precision of eds y relative to rds y is               2 2 2 2 2 2 2 2 1 1 , 1 1 r e rss rds eds rds eds erss rsvar y rp y y var y rs                                         . (3.3) 3.3 numerical comparison assuming that  ,x y has a bivariate normal distribution, we compute various expressions for the relative efficiencies obtained in the previous section. the set sizes examined are r = 4, 5, 6, 7 and 8 with cycles of m = 1, 4, 8 and  . a simulation size of 100,000 is used to evaluate the values of    2 2 eerss s    and    2 2 rrss s    . in the case of double sampling, note that the hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 82 relative precision is less than the relative precision of the case when x  is known. this is due to the extra variation introduced when estimating the mean x  . table 3.1 shows the relative precision of eds y relative to ds y for an underlying bivariate normal distribution. from the table we see that all the relative precision values are at least 1 indicating again in precision when using erss instead of srs. the main conclusions from table 3.1 are: 1. when ranking is done on the variable x , the relative precision is best at 0  . the efficiency increases as the value of  decreases from .99 to 0. 2. for a fixed value of the set size, r , we note that as m increases the efficiency converges rapidly to 1. 3. the efficiency decreases with increasing set size  r , for any given value of m . 4. for a given value of r , there is no change in the efficiency when the cycle is repeated more than 8, (efficiency stability). this may be due to the fact that when the sample size is large enough to represent the population, the ranking has less impact on the regression estimator. 5. the double sampling erss regression estimator is always superior to the double sampling srs regression estimator no mater how large the correlation coefficient,  is. table 3.1. the relative precision of double sampling erss regression estimator relative to double sampling srs regression estimator.   when, 0eds rdsrp y y   /m r 4 5 6 7 8 1 1.63416 1.34607 1.24611 1.19055 1.15995 4 1.04718 1.03945 1.03428 1.03009 1.02665 8 1.02100 1.01802 1.01588 1.01399 1.01269  1 1 1 1 1   when, 0.9eds rdsrp y y   /m r 4 5 6 7 8 1 1.3124 1.189 1.1501 1.1206 1.1029 4 1.0226 1.0212 1.0197 1.0186 1.0176 8 1.0100 1.0096 1.0093 1.0087 1.0082  1 1 1 1 1 table 3.2 presents the relative precision under the assumption of an underlying bivariate normal distribution. again, the table shows that the relative precisions are all at least 1. we also note that the double sampling erss regression estimator is always slightly better than the double sampling rss regression estimator no mater how large the correlation coefficient,  is. on regression estimators using extreme ranked set samples 83 table 3.2. the relative precision of double sampling erss regression estimator relative to double sampling rss regression estimator.   when, 0eds rdsrp y y   /m r 4 5 6 7 8 1 1.02771 1.00935 1.00749 1.0046 1.00405 4 1.00192 1.00111 1.0011 1.00079 1.00071 8 1.00081 1.00053 1.00052 1.00035 1.00034  1 1 1 1 1   when, 0.9eds rdsrp y y   /m r 4 5 6 7 8 1 1.0083 1.0063 1.0047 1.0029 1.0025 4 1.0008 1.00064 1.00061 1.0004 1.0004 8 1.0003 1.0002 1.0002 1.0002 1.0002  1 1 1 1 1 4. application to bilirubin level in jaundice babies we illustrate the methods discussed above using real data on bilirubin level in jaundice babies who stay in neonatal intensive care. hyper bilirubinemia is defined as a total serum bilirubin above 1.5 mg/dl while neonatal jaundice is defined as yellowish discoloration of skin and sclera and it occurs if bilirubin level is more than 5 mg/dl. (see nelson et al., 1994). jaundice is observed during the first week of life in approximately 60% of term infants (from 37 to less than 42 completed weeks) and 80% of pre-term infants (less than 37 completed weeks) (see nelson et al., 1994). neonatal jaundice is a common problem in full-term infants (42 completed weeks or more (294 days or more)) and pre-term babies. it is possible that the generally accepted levels are too high and may produce some high tone hearing loss. most experts accept that 18.82 mg/dl to 20 mg/dl should not be exceeded in full-term babies, who are less than three days of age, but that a mature baby can tolerate levels of up to 21.18 mg/dl or 22.35 mg/dl by the fifth day without evidence of damage. pre-mature babies are probably more susceptible and 17.64mg/dl should not be exceeded. since most cases of neonatal jaundice appear on the second day of life and most of normal newborn babies leave the hospital after 24 hours of life, our primary concern will be on babies staying in neonatal intensive care. physicians are interested in jaundice because of its importance and risk on hearing, brain and death. it will be really helpful to the physicians if we can estimate the populations mean of the amount of bilirubin in the blood for jaundice pre-term, mature, and full term babies. however, estimating the population mean can be expensive and time consuming. therefore, there is a need for a sampling scheme which can give more accurate population mean estimates with a smaller sample size, and hence results in saving money and time. all babies who appear significantly jaundiced on clinical examination should have their plasma bilirubin estimated. this is done in a laboratory test that needs about half an hour or more to find the level of bilirubin in the blood. this test is expensive and time consuming. however, by using the regression estimator calculated based on extreme rank set sample, we will show that the population mean of plasma bilirubin for babies who stay in neonatal intensive care, can be estimated with more precision without measuring all units. hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 84 4.1 data collection the data were collected by samawi and al-sagheer (2001) from five hospitals in jordan. these hospitals are al-qawasmeh hospital, prince rahma hospital, irbid specialty hospital, ibin al-nafies hospital, and queen zein al-sharaf hospital. the data were limited to deliveries in the first six months of 1997. herein, we find the population mean estimate for the bilirubin level for neonatal jaundice. jaundice is measured by the level of bilirubin in the blood. this level is determined via a blood test (tsb). the unit of measurement is mg/dl. the test is conducted on neonatal infants twice daily during the period of the neonatal in the intensive care. one hundred and twenty cases are included in the study. the weight at birth is taken as the concomitant variable. since ranking on the concomitant variable x (weight) is easier and measuring x is less expensive than ranking and measuring y (tsb), we will rank on the variable x . 4.2 parameters the following are the exact population values of the data:  x  2 87. ,  x  0 71. , 120 1 344.73 i i x   , 120 2 1 1049.62 i i x   ,  y  1118. ,  y  5 08. , 120 1 1341.06 i i y   , y i i 2 1 120 18062 12    . , xy i   1 120 3877 27. ,   0 06. . 4.3 using erss, rss and srs erss and rss and srs sampling methods are used to obtain the samples shown in table 4.1. the following results are obtained from the samples: 1) based on the erss sample, the regression estimate is ˆ 11.46 y   , with   675.0ˆ  ereg arv and the naïve estimate is 47.11erssy with 634.0)(ˆ erssyarv . 2) based on the rss sample the regression estimate is 44.11ˆ y with  ˆ 0.685regvar   and the naïve estimate is 81.11rssy with 560.0)(ˆ rssyarv . 3) based on the srs sample, the regression estimate is ˆ 11.67 y   with   962.0ˆ  reg arv and the naïve estimate is 42.11srsy with 746.0)(ˆ rssyarv . note that    ˆ ˆreg eregvar y var y also    reˆ ˆg eregvar y var y . for the data at hand, the naïve estimators are doing better than the regression estimators. this may be due to the fact that the correlation between the weight and tsb is very small. although this is only an illustration of the computations, the results confirm our earlier conclusions:  , , 1.42ereg regeff y y  ,  re, , 1.01ereg geff y y  . on regression estimators using extreme ranked set samples 85 table 4.1. the drawn samples. erss rss srs cycle wt tsb wt tsb wt tsb 1 2.83 6.67 2.83 6.67 2.83 6.67 3.50 11.94 2.45 8.71 2.45 8.71 1.50 8.51 4.15 2.06 1.80 16.94 3.45 8.00 3.45 8.00 3.00 5.50 2 2.00 10.94 2.00 10.94 2.50 10.58 2.60 16.76 2.50 16.60 2.50 19.79 1.50 5.90 2.75 5.60 2.75 5.60 3.50 12.59 3.50 12.59 3.50 12.59 3 1.95 15.76 1.95 15.76 4.40 16.60 3.70 12.28 3.40 8.00 3.70 12.82 2.50 25.12 3.25 5.60 2.85 15.20 3.00 6.90 3.00 6.90 2.70 14.20 4 1.80 22.94 1.80 22.94 3.00 22.94 3.60 7.20 2.70 14.20 2.00 10.94 1.90 8.00 2.70 15.47 2.50 15.19 3.70 5.50 3.70 5.50 2.50 10.58 5 2.45 13.76 2.45 13.76 2.45 13.76 3.30 9.53 3.10 12.30 3.15 7.80 1.95 15.76 2.83 6.67 1.95 15.76 4.40 10.94 4.40 10.94 1.90 11.88 6 2.50 12.76 2.50 12.76 3.25 5.60 3.60 16.46 3.20 11.60 3.20 11.60 1.85 9.20 2.60 22.52 2.60 22.52 3.15 11.53 3.15 11.53 3.15 11.53 7 2.75 5.60 2.75 5.60 4.45 2.06 2.85 15.20 2.45 8.71 2.45 13.76 1.75 8.53 2.30 18.29 1.75 8.53 3.6 16.46 3.60 16.46 2.20 7.60 8 2.00 11.00 2.00 11.00 3.40 8.00 3.50 11.94 2.70 7.45 2.85 13.94 3.00 5.90 3.25 8.90 3.65 7.50 2.60 22.52 2.60 22.52 1.80 16.94 9 2.70 7.45 2.70 7.45 2.70 7.45 3.75 8.20 3.40 16.50 3.40 16.50 1.50 5.90 3.50 22.12 3.10 10.18 3.40 16.50 3.40 16.50 2.10 14.59 10 1.20 8.76 1.20 8.76 3.20 11.60 3.85 14.27 2.50 7.06 3.85 14.27 3.00 12.3 3.20 8.53 3.20 8.53 3.30 3.30 3.30 3.30 3.00 5.50 hani m. samawi, ahmed y. al-samarraie and obaid m. al-saidy 86 5. references hedayat, a.s. and sinha, b.k. 1992. design and inference in finite population sampling. new york: wiley. kaur, a., patil, g.p., sinha a.k. and taillie, c. 1995. ranked set sampling: an annotated bibliography. environmental and ecological statistics 2: 25-53 johnson, m.e. 1987. multivariate statistical simulation. new york: wiley. mcintyre, g.a., 1952. a method of unbiased selective sampling, using ranked sets. australian j. agricultural research 3: 385-390. nelson, w.e. behrman, r.e., kliegman, r.m. and vanghan, v.c. 1994. textbook of pediatrics. 4th edn. w. b. saunders company harcourt barance jovanovich, inc. patil, g.p., sinha, a.k. and taillie 1999. ranked set sampling: a bibliography. environmental and ecological statistics. 6 (1): 91-98. patil, g.p., sinha, a.k. and taillie 1993. relative precision of ranked set sampling: comparison with regression estimator. environmetrics. 4 (4): 399-412. samawi, h.m. and al-sagheer, o.a. 2001. on the estimation of the distribution function using extreme and median ranked set sampling. biom. j. 43 (3): 357-373. samawi, h.m., mohmmad, s. and abu-dayyeh, w. 1996. estimating the population means using extreme ranked set sampling. biom. journal. 38: 577-586. sukhatme. p.v. and sukhatme, b.v. 1970. sampling theory of surveys with applications. ames: iowa state university press. tikkiwal. b.d. 1960. on the theory of classical regression and double sampling estimation. journal of the royal statistical society, series b 22: 131-138. yanagawa, t. and chen, s.h. 1980. the mg procedure in ranked set sampling: comparision with the regression estimator. yu, p.l.h. and lam, k. 1997. regression estimator in rank set sampling. biometrics, 53: 1070-1080. received 12 march 2004 accepted 15 december 2004 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 153-165 © 2003 sultan qaboos university step-wise group screening designs with unequal a-priori probabilities and errors in observations m.m. manene department of mathematics, university of nairobi, p.o. box 30197, nairobi, kenya, email: mathuon@iconnect.co.ke. السابقة غير المتساوية واألخطاء في المالحظاتاالحتماالتتصاميم الغربلة التدريجية للمجموعات ذات مانين. م.م السابقة غير المتساوية بداللة عدد التجارب المتوقعة يهتم هذا البحث بأداء طرق الغربلة التدريجية ذات االحتماالت : خالصـة السابقة لالحتماالتالمثلى لتصاميم الغربلة التدريجية الطريقة إيجاد الخاطئة ، وفيها يتم وعـدد الحد األقصى المتوقع للقرارات دالة التكاليف المناسبة وإيجاد إيجادوامل المعتلة والمالحظات القابلة للخطأ ، وفيها أيضاَ يتم المتساوية لحالة معرفة اتجاه العغير .متها الصغرىحجم المجموعة التي تجعل جملة التكاليف في قي abstract: the performance of step-wise group screening with unequal a-priori probabilities in terms of the expected number of runs and the expected maximum number of incorrect decisions is considered. a method of obtaining optimal step-wise designs with unequal a-priori probabilities is presented for the case in which the direction of each defective factor is assumed to be known a priori and observations are subject to error. an appropriate cost function is introduced and the value of the group size which minimizes the expected total cost is obtained. keywords: step-wise, designs, group-factors, initial step, subsequent steps, expected number of runs, incorrect decisions, cost function. 1. introduction t here are investigations where a large number of factors needs to be examined. in such a situation we have to run an experiment to identify the influential factors. the group screening procedure aims at reducing the size of the experiment, thus conserving resources. the method of group testing was first introduced by dorfman (1943), who proposed that instead of testing each blood sample individually for the presence of a rare disease, blood samples be pooled and analysed together. watson (1961) considered two stage group screening designs with and without errors in observations and with equal prior probabilities. in the same paper, he laid down the device of using different group sizes when prior probabilities differ. li (1962) and patel (1962) generalized watson's method to more than two stages. both these authors considered multistage groupscreening designs with equal prior probabilities and without errors in observations. ottieno and patel (1984) extended the idea of two stage group screening with unequal prior probabilities to include situations when no prior information is available so that no natural partitioning can be assumed. odhiambo and patel (1986) generalized this approach to multi-stage designs. the group testing procedure first considered by sterrett (1957) has been extended by manene (1985), patel and manene (1987), odhiambo and manene (1987) and manene (1997) in what they have called step-wise group-screening designs and they have approached the problem from the 153 m.m. manene point of view of designs of experiments. they have considered the cases when all factors are defective with equal prior probabilities. in this paper, we shall extend group screening designs considered by odhiambo and manene (1987) to the case when factors are defective with unequal prior probabilities. 2. assumptions and design structure we shall assume that there is a single response variable of interest y, which is related to a set of f factors through the first order linear regression model 0 1 f u j u j y x j uβ β ε = = + +∑ (2.1) where is the u response, uy th 0β is a constant term common to every response; is the linear effect of the ( 1j jβ ≥ ) thj factor, is the level of the 1= ±u jx thj factor in the u run, th uε is the u error term. further, we shall assume that it is possible to partition the th f factors into a fixed number of groups, such that the group contains factors. the factors will be partitioned into groups of unequal sizes by selecting a set of numbers g thi ik { }1 2 .... ; o 1g ip p p p≤ ≤ ≤ < < and identifying as the probability that a factor belonging to the group is defective. thus ip thi ip s′ and will be variables. this is a generalization of natural partitioning, when ik s′ ip s′ are actual probabilities. thus, in addition to model (2.1), we shall make the following assumptions; (i) the total number of factors, f , can be divided into a fixed number of group-factors in the ' g ' initial step such that 1 g i i f k = = ∑ where k is the number of factors in the i group factor. i th (ii) the errors are independent normal with means zero and variance 2σ (known). (iii) all the factors in the group-factor have independently the same probability thi ip (variable) of being defective. (iv) a defective factor within the group-factor has a positive effect thi i∆ . the approach here is rather similar to the use of diffuse prior distributions in bayesian inference. the step-wise group-screening experiment is performed in steps as follows: in the initial step, the f factors are divided into groups such that the group contains factors ( ) these groups are called group factors. these group-factors are then tested for significance. those that are declared non-defective are set aside. in step two, we start with any groupfactor that is declared defective in the initial step and examine the factors within it one by one till a factor is declared defective. we set aside factors which are declared non-defective, keeping the factor declared defective separate. the remaining factors are then tested in a group. this is done for all group-factors declared defective in the initial step. the test procedure carried out in the initial step and in step two is repeated in subsequent steps successively till the analysis terminates with a group-factor declared non-defective or with a group-factor of size one. g thi ik =1,2,..., .i g in testing the significance of the group-factors in the initial step, we shall use the orthogonal main effects plans of the type given by placket and burman (1946). for testing the significance of individual factors and group-factors in the subsequent steps we shall use non orthogonal designs to simplify computations. 154 step-wise group screenin designs 3. expected number of runs suppose that f factors are divided into a fixed number of group-factors in the initial step such that the i group-factor is of size . the group-factors are tested in ' 'g ' 'gth 1 g i i i k k f =   =    ∑ ( ) ( ) ( ) 4 mod 1, 2, 3, 4 r g g g g h h = + − = + = 4 (3.1) runs. in the subsequent steps, factors within the defective group-factors are tested as explained earlier. let be the estimate of the main effect of the i group-factor in the initial step, with ˆig th iδ effective factors each with effect ( )0; 1 ....,i i kδ∆ > = , 2, i i h . then and var . ( )i ie g δ= ∆ ( ) 2ˆ /ig gσ= + define a random variable w by i ˆ /i iw g g hσ= + (3.2) then ( )i ie w u iδ= and var ( ) 1iw = , where /i i σu g h= ∆ + (3.3) consider the hypothesis h u0 : i i 0δ = alternative u 0i iδ = . let iiα be the level of significance for testing the i group-factor in the initial step and denote by th ( )ii,i iuii δ απ the power function of the test. then ( ) ( )( )ii ii ii, 1i i i iu zδ α φ α δπ = − − u (3.4) where ( ).φ denotes the standard normal distribution function and ( )iiz α satisfies ( )( )ii ii1 zα φ α= − (3.5) thus if i0 for 0i ,δ µ= = then ( )ii ii ii0,α απ = and if 0iδ ≠ and 1 /σ∆ is large, then (ii i iu )ii,δ απ tends to 1. let denote the probability that the i group factor is declared defective in the initial step. then * iiπ th ( ) (*ii ii ii 0 1 i ii i ki ki i i i i i k p p u δδ δ ), ,δ α δ − =   π = − π    ∑ (3.6) where ip is the probability that a factor in the group-factor in the initial step is defective. define a random variable u such that thi i ( ) * ii1 with probability 0 otherwise 1, 2,...i u i g  π =  = (3.7) then ( ) *iiie u = π (3.8) 155 m.m. manene in the subsequent steps, we shall use non-orthogonal designs. let 'ip be the probability that a factor chosen at random from the group factor containing thi iδ defective factors that has been declared defective in the initial step is defective. then ( )1* * 1 1 ' / , / 1 i i i i i k i k i i ii i i ii i i ii i ii ii i k p p p q pδ δ δ δ µ α δ − − + = −  = π π = π π −  ∑ (3.9) where ( ) (1 ii 1 1 1 1 i i ii i k ki ii i i i i ii i k p p δδ δ ),δ µ α δ −−+ = −  π = − π −  ∑ (3.10) let siα be the probability of declaring a non-defective factor from the group-factor in the initial step as defective and thi siγ be the probability of declaring a defective factor as defective in the subsequent steps. further let iβ + be the probability that a factor chosen at random from the group-factor in the initial step is declared defective in the subsequent steps if the group-factor was declared defective in the initial step. thi then ( ) ( ) ** * ii ii ' 1 ' / / si i si ii i si si si ii ii p p p β γ α γ α α β + + + = + −  = − π + π π =  iπ (3.11) where ( ) * * ii iii si si sii pβ γ α α += − π + π  (3.12) let *siα be the probability of declaring a non-defective factor from the i group-factor in the initial step group-factors is declared defective at any step but on testing individual factors within it, no factor is declared defective due to errors in observations. obviously th * siα will take different values at different steps. however for simplicity in algebra, we shall assume *siα to be of uniform value, say *iα . denote by ( )*jkp j the probability that exactly j factors from the group-factor in the initial step that has been declared defective in the subsequent steps. thi then ( ) ( ) ( ) ( ) * * * * * * 1 1 1 1 ; 0 1 1 ; 1, 2,......., i i j i k i ii k k j i ii i ii j p j k j k j β β β −     − − − =   π    =    − = π   (3.13) let be the expected number of runs required to declare exactly factors defective from the initial step group-factor which has been declared defective. then following odhiambo and manene (1987), ( )* ik e r thi j 156 step-wise group screenin designs ( ) ( ) ( ) ( ) ( )( ) ( ) 2 * * i for =0 2 1 1 1 1 1 1 1 for =1,2,.....,k 1 i i ii i k j i i i i i i i i i i k j j k jjk kj j j e r j j j k k j j k k k j k j j k k α ξ     1 j + −  = + + − + − − +  + + − + + − −       − −−  − (3.14) where *iα is as already defined and 0iξ = if * 0iα = and 1 otherwise. let sir be the number of runs required to analyse the group-factor once it has been declared defective in the initial step. then thi ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) * * 1 * * * 1* * * * 1* * * * ** 1 1 1 2 1 1 1 1 1 1 1 1 1 1 i i i i i i i k si k j k j k i i ii i ii ii k i i i i ii i k k i ii i i i ii i e r e r p j k k k k k β ξ β ξ β β β β α β β β β β = + + =    = − − − − − +    π π     + + + − − −   π       + − − − − − − +  π    ∑ *2 *2 i i iβ (3.15) using (3.13) and (3.14). if sr is the number of runs required to analyse all the group factors declared defective in the initial step, then ( 1 g )s i s i ir u e r = = ∑ (3.16) theorem 3.1: the expected total number of runs in a step-wise group screening design with (fixed) group-factors in the initial step such that the group-factor is of size is given by g thi ( )1, 2,....,ik i g= ( ) ( ) ( ) ( ) ( ) ( ) 1** * 1 * * * 1 1 * ** * 1 1 1 ** 1 1 2 1 1 1 2 1 1 1 1 i i i g k i i i i g g i i i ii i ii i g g gk i ii i i i i g k i i i i e r h f g k k k k k k α β β ξ α β 2 ii i iβ α α ξ α β + = = = = = = = β   = + + − − − −     − + − − + π      − − − − + −   − − ∑ ∑ ∑ ∑ ∑ ∑ ∑ where * *, iiβ α and iξ are as defined earlier. proof : in the initial step we require 1 r g h= + runs ( )1,2,3,4h = . the number of runs 157 m.m. manene required in the subsequent steps is ( ) 1 g s i s i ir u e r = = ∑ with ( ) ( ) 1 g s i i e r e u e r = si   =     ∑ (3.17) the theorem then follows on using (3.8) and (3.15) in (3.17), simplifying and noting that ( ) ( )i se r r e r= + . corollary 3.1 : for large values of i s σ ′∆ and small values of ,ip s , the expected number of runs in a step-wise group screening design with group-factors in the initial step, the groupfactor being of size is approximately equal to g thi ( 1, 2,......,ik i g= ) ( ) ( ) ( )( ) ( ) g * 1 g g 2 1 1 1 2 1 11 1 1 2 1 i si i i i i i i i ii i ii i i i g h k p k k k k k p ξ α α α α = = =  − + + − − + − +    + + − ∑ ∑ ∑ proof : if i s σ ′∆ are large, then π ≈ ( )* 1 1 ,ikii ii i iiqα− − π ≈ 1 ( ) ( )*1 and 1 1 1 iksi i si i si ii ip qγ β α α α ≈ ≈ − + − −  further if ip s′ are small, then ( ) ( )1 1 1ikii i ii i i iiq k pα α α− − ≈ − + up to order ip . the corollary then follows on using these approximations in the expression for given in theorem 3.1. ( )re 4. calculation of the expected number of incorrect decisions we shall consider the same cases of incorrect decisions as were considered by odhiambo and manene (1987) i.e. (i) declaring defective factors as non-defective in the initial step (ii) declaring defective factors as non-defective in subsequent steps (iii) declaring non-defective factors as defective in the subsequent steps let denote the expected number of factors declared defective from the group-factor that is declared defective in the initial step. then ( ) ik e j thi ( ) * 1 ik i i i ii e j k k iβ β + + = π (4.1) where * */ iii iβ β + = π let d be the number of factors declared defective in the subsequent steps. then 158 step-wise group screenin designs g 1 i ii i d k uβ + = = ∑ (4.2) where u is as defined in (3.7). i let ( )0ip be the probability that a factor chosen at random from the initial step groupfactor declared non-defective, is defective. then thi ( ) ( ) ( )0 *1 / 1i i ii iip p += −π −π (4.3) let ip + be the probability that a factor from the i group factor is non-defective given that it is declared defective. then th ( )1 /i si i ip pα β ++ ′= − (4.4) theorem 4.1 : let rm be the number of defective factors declared defective in a step-wise group screening design with initial group-factors, the factors in the i group-factor of size being defective with a priori probability g th ik ( )1, 2,.....,ip i g= . then ( ) g i=1 r i i ie m k p i siγ += π∑ proof : the expected total number of factors declared defective in the subsequent steps is given by ( ) ( ) g g * 1 1 i i ii i i e d k e u kβ + = = iiiβ + = =∑ ∑ π (4.5) the probability that a factor which is declared defective from the group-factor, is defective is given by 1 thi ip +− . therefore ( ) ( ) ( ) ( ) g 1 g * 1 g * 1 1 1 r i i ii i i sii i i i ii si i e m k p e u k p k p β β α γ + + = + = = = −  ′ ii = − − π = π ∑ ∑ ∑  i i (4.6) as required. let denote the expected number of defective factors declared non-defective in the initial step. ii then ( ) ( ) ( ) g 0 1 g 1 1 1 i i i i i ii i i e u k p k p = + =   = −    = −π ∑ ∑ (4.7) theorem 4.2 : in a step-wise group screening design with errors in observations and unequal apriori probabilities, the expected number of defective factors declared non-defective in the subsequent steps is given by ( ) g 1 1 .s i i ii si i i k p γ = = π −∑ 159 m.m. manene proof : the expected total number of defective factors in all the group-factors in the initial step is equal to . therefore g 1 g i i i k p = ∑ ( ) ( ) ( ) 0 1 1 1 1 1 g g s i i i i i r i i g i i ii si i i e k p u k p m k p γ = = + =   = − − −    = π − ∑ ∑ ∑ (4.8) this completes the proof. theorem 4.3 : let um be the number of non-defective factors declared defective in the subsequent steps. then ( ) ( ) g * 1 u i si ii i i e m k pα ii + = = π − π∑ proof : the total number of factors declared defective in the subsequent steps is g 1 i ii i k uβ + = ∑ . thus g 1 u i ii i im k u pβ + + = = ∑ which implies that ( ) ( ) g 1 g * 1 u i i ii i i si ii i ii i e m e k u p k p β α + + = + =   =     = π − π ∑ ∑ (4.9) theorem 4.4 : let i be the expected total number of incorrect decisions in a step-wise group screening design with group-factors in the initial step such that the group-factor of size contains factors with a-priori probability of being defective g thi ik ip ( )1, 2i g= ,....., . then ( ) g g g * 1 1 1 i i ii si i si ii i ii i i i i kp k p k pγ α+ + = = = = − π + π − π∑ ∑ ∑ proof : the expected total number of incorrect decisions is given by ( ) ( ) ( ) ( ( ) g g g * 1 1 1 g g g * 1 1 1 1 1 i s u i i ii i i ii si i si ii i ii i i i i i i i ii si i si ii i ii i i i i i i e m k p k p k p k p k p k p γ α γ α + + = = = + + = = = = + + = −π + π − + π − = − π + π − π ∑ ∑ ∑ ∑ ∑ ∑ )+π (4.10) using (4.7), (4.8) and (4.9). this completes the proof. corollary 4.1: 160 step-wise group screenin designs ( ) ( ) ( )( ) ( ){ } g g 1 1 g 1 , 1 ,i i i i i i si ii ii ii i i k k i si ii i i ii i ii ii i ii ii ii i max i k p k p k q q k p γ φ α α α φ α φ α = = = = − π + + − π − π ∑ ∑ ∑ , proof : ( ) ( ) ( ) g g g * 1 1 1 g 1 i i i i ii si i si ii i ii i i i i i r u i i k p k p k p k p e m e m γ α+ + = = = = = − π + π − = − + ∑ ∑ ∑ ∑ π (4.11) hence i will take its maximum value when ( )re m is minimum and is maximum. but takes its maximum value when ( ue m ) )(e m r iii+π is replaced by ( ),ii ii iiφ απ . that is ( ) ( g 1 ,r i si i ii ii i min e m k p )iiγ φ α = = π∑ (4.12) ( ue m ) will take a minimum value when *iiiπ is replaced by its maximum value and ii+π is replaced by its minimum value. that is when *iiπ is replaced by ( ) ( ){ }1 ,i iiki ik kii i i ii i iq qα φ+ − π α ), and is replaced by ii +π ( ), .ii ii iiφ απ thus ( ) ( ) ( ) ({ } g 1 1 ,i ik ku i si ii i i ii i ii ii i ii ii ii i max e m k q q k pα α φ α φ α = = + − π − π∑ (4.13) the result follows on using (4.12) and (4.13) in (4.11). corollary 4.2 : for large i σ ∆ and small 'ip s ( ) g 1 1i si ii i ii i i i max i k p p kα α α = ≈ − + −  ∑ proof : for large i σ ∆ and small ( )' , , 1, 1 and 1iki ii i ii ii si i i ip s s q kφ α γπ ≈ ≈ ≈ − p . the result follows immediately on replacing these values by their approximations in the expression for max i given in corollary 4.1. 5. optimum sizes of initial group-factors in relation to total cost we define the expected total cost( )c as a linear function of the expected number of runs and the expected number of incorrect decisions and obtain the sizes of the group-factors so that the expected total cost is minimum. let c be the cost of inspection per run and c be the loss for each incorrect decision made. then the expected total cost is given by 1 2 ( )1 2 maxc c e r c i= + 161 m.m. manene we shall only discuss the case when 'i s σ ∆ are large and 'ip s are small. for simplicity we shall only consider the special case when ( )* *, 1, 2,...,si s and i gα α α= = = =ii iα α iα . theorem 5.1 : if *, andii i si s i * ,α α α α α α= = = then for large 'i s σ ∆ and small 'ip s , the value of which minimizes the expected total cost is given by ik 1 1 / g g i i i i i i i k f g h g g g h = =   = − +    ∑ ∑ i i (5.1) where ( ) ( )( ){ } ( )* 1 2 1 2 1 1 1 2 1 i i s i s i g c p c pα α α α α i − = − − − + + − and ( )( ) ( ) (*1 2 1 1 3 ; 1, 2,..., g . 2i i s i s i i h c p c p iα α α α α = + − − − − =    ) proof : the problem is to minimize ( )1 2c c e r c max i= + subject to ( ) ( ) g 1 i ii 0 ; 1, 2,..., i i i k f k i = = > = ∑ g that is to minimize ( ) ( ) ( )( ) ( ) ( ) g g 2 1 1 1 g g * * 1 1 g g 2 2 1 1 1 1 1 1 1 3 1 2 2 1 i s i i i i 2 i i s i i s i i i i s i s i i s i i i i i c c h g f p k p k p k p c f k p k p α α α α α α α α α α α = = = = = =  = + + − − + −   + − − − −     + − + −    ∑ ∑ ∑ ∑ ∑ ∑ (5.2) subject to ( ) ( ) g 1 i ii 0 ; 1, 2,..., i i i k f k i = = > = ∑ g using corollaries (3.1) and (4.2) noting that * *i 1, , andii i si s iξ α α α α α α= = = = . using the method of lagrange multipliers, let 162 step-wise group screenin designs ( ) ( ) g 1 2 g 1 2 1 , ,....., , max i i f k k k c e r c i k fλ λ =   = + +     ∑ − where λ is the lagrange multiplier. assuming continuous variation in , the critical value of is obtained from the equations ik ik / 0 ; 1, 2,..., , and / 0if k i g f λ∂ ∂ = = ∂ ∂ = (5.3) the theorem follows immediately on solving equations (5.3). 6. examples of screening plans the screening efficiency of step-wise group screening design with unequal group sizes can be measured in terms of the minimum expected total cost. a small value of indicates better performance on the average. examples of group screening plans which minimize the expected total cost are given in table 1 below. the corresponding values of and max ( )c )(c ) (e r i are also given. table 1 : optimum group-sizes obtained by minimizing expected total cost ( , when and for selected unequal apriori probabilities. the minimum given is a relative figure using c (the cost of observing a run) as the unit. )c * *, and , for 100ii i i si s fα α α α α α= = = = ( )c 1 ( ) * 2 1a 3, 13, 0.05 , : 3 : 5 , 0.035i s ih g c c p pα α α= = = = = = ≤ = . i ip ik 1 2 3 4 5 6 7 8 9 10 11 12 13 0.008 0.009 0.010 0.013 0.015 0.017 0.020 0.022 0.025 0.027 0.030 0.033 0.035 17.088 15.024 13.372 9.942 8.418 7.252 5.940 5.265 4.454 4.014 3.463 3.013 2.755 total 100.000 ( ) 28.577, 0.770, 29.039.e r max i min c= = = ( ) 26.739e r = the corresponding value of min when incorrect observations are not considered. ( ) * 2 1b 4, 20, 0.05, : 3 : 5 , 0.100i s ih g c c p pα α α= = = = = = ≤ = . 163 m.m. manene i ip ik 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.040 0.045 0.050 0.053 0.055 0.060 0.062 0.065 0.070 0.075 0.078 0.080 0.082 0.085 0.087 0.090 0.092 0.095 0.098 0.100 9.565 8.337 7.354 6.853 6.550 5.880 5.642 5.313 4.827 4.403 4.179 4.037 3.902 3.712 3.592 3.423 3.316 3.164 3.020 2.931 total 100.000 ( ) 51.422, 1.545, 52.349e r max i min c= = = ( ) 49.219e r = . the corresponding value of min when incorrect observations are not considered. from the two tables it is easily seen that when a cost function involving both and max ( )e r i is used, the number of runs increases. it should be noted that these tables are just an illustration. the values of 'ip s used are not unique; neither is the ratio c 2 1: .c references dorfman, r. 1943. the de1ection of defective members of large populations, annals of mathematical statistics, 14: 438 -440. li, c.h. 1962. a sequential method for screening experimental variables. jour. arner statistical assoc. 57: 455-477. manene, m.m. 1985. further investigations of group screening designs: step-wise designs; ph.d. thesis submitted to university of nairobi. manene, m.m. 1997. on two type step-wise group screening designs, proc of fifth scientific con£. of eastern. central and southern africa network of i. b.s., 57 –62. odhiambo, j.w. and manene, m.m. 1987. step-wise group screening designs with errors in observations. comm. in statistics theor. meth. 16(1 0): 3095-3115. odhiambo, j.w. and patel, m.s. 1986. on multistage group screening designs. comm. in statistics theor. meth. 15(5): 1627-1645. ottieno, j.a.m. and patel m.s. 1984. two stage group screening designs with unequal apriori probabilities. comm in statistics theor. meth. 13(6): 761-779. patel, m.s. 1962. group screening with more than two stages; technometrics, 4: 209-217. 164 step-wise group screenin designs patel, m.s. and manene, m.m. 1987. step-wise group screening with equal prior probabilities and no errors in observations, comm. in statistics simula_and comguta, 16(3): 817-833. placket, r.l. and burman, j.p 1946. the design of optimum multifactor experiments. biometrika, 33: 305-325. sterret, a. 1957. on the detection of defective members of large populations, annals of mathematical statistics. 28: 1033-1036. watson, g.s. 1961. a study of the group screening method, technometrics, 3: 371-388. received 30 december 2002 accepted 20 november 2003 165 step-wise group screening designs with unequal a-priori probabilities and errors in observations department of mathematics, university of nairobi, p.o. box 30197, nairobi, kenya, email: mathuon@iconnect.co.ke. êõçãíã çáûñèáé çáêïñíìíé ááãìãæ� ã.ã. ãçäíä 3. expected number of runs theorem 3.1: the expected total number of runs in a step-wise group screening design with � (fixed) group-factors in the initial step such that the � group-factor is of size � is given by proof : in the initial step we require � runs �. the number of runs required in the subsequent steps is calculation of the expected number of incorrect decisions proof : the total number of factors declared defective in the subsequent steps is �. proof : and � proof : the problem is to minimize total total references squ journal for science, 2019, 24(1), 36-46 doi: 10.24200/squjs.vol24iss1pp36-46 sultan qaboos university 36 radiometric surveys for detection of uranium in dhofar region, sultanate of oman narasimman sundararajan 1 *, bernhard pracejus, salah alkhirbash, talal k. al-hosni, a. ebrahimi, ali al lazki 2 and 3 musallam al-mushani 1 department of earth science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman; 2 petroleum development of oman (pdo), muscat, sultanate of oman; 3 ministry of commerce and industry, muscat, oman, *visvid12@squ.edu.om. abstract: the proterozoic basement of the dhofar region of the sultanate of oman might be considered as a potential source of uranium mineralization like other proterozoic basins of the world, which collectively contribute 30%-40% to the global production. uranium exploration assumes great importance in this part of the world and therefore geochemical and geophysical exploration for uranium was initiated. initial, random sampling of the study area with gamma ray spectrometry as well as in situ xrf (xray florescence) analysis indicated the presence of around 30-40 ppm of uranium. since gamma ray spectrometry results in the calculation of the heat produced during radioactive decay of potassium (k), uranium (u) and thorium (th) within the rocks in the study area, measurements were acquired along eleven traverses of varying length from 100-250 m at a traverse interval of 20 m and sampling interval of 10 m. individual plots of the concentrations of radioelements such as u, k and th have shown favorable anomalous radioactive sources. besides this, uranium to thorium (eu/eth) and uranium to potassium (eu/k) ratio plots have been presented and the alteration zones associated with uranium mineralization through all traverses have been identified. further, the generated composite ternary image based on the combination of k, th and u from gamma ray spectrometry determines different relative amounts of radioelements and paves the way for deciphering the level of radioactivity in the study area. however, there seems to be no presence of strong uranium anomalies in the near surface of the limited study area. as the study area is heavily faulted, the depth to concealed subsurface fault structures is estimated to be around 64 m based on hartley spectral analysis of total magnetic anomaly (line-6). keywords: gamma ray spectrometry; xrf analysis; uranium; potassium; thorium. ، سلطنة عمانكشف عن اليورانيوم في منطقة ظفارلمسوحات اإلشعاعية للا ابراهيمي ، مسلم المعشني حسين لخرباش، طالل الحوسني، عالناريسمان ساندرجان، برنارد براسيس، صالح ا ساس التابعه لحقب البروتيروزوي في منطقة ظفار بسلطنة عمان مصدراً محتمالً لتمعدن اليورانيوم مثل أحواض عتبر صخور األت :صلخمال تفقد بدأ ستكشاف اليورانيوم من أهمية كبيرة ،إنظرا لما يمثله .٪ في اإلنتاج العالمي03-٪ 03البروتيروزويك األخرى في العالم والتي تسهم بنسبة قياس طيف بواسطة أوضحت النتائج األولية والعشوائية لمنطقة الدراسة .الجيوكيميائية والجيوفيزيائية لليورانيوم في هذه المنطقة ستكشافيهاإل الدراسات حساب الحرارة الناتجة دنتج عنتوبما أن أشعة جاما .جزء في المليون من اليورانيوم 03-03حوالي نسب ن وجود ع الشعة السينيه أشعة جاما وكذلك تحليل صخور منطقة الدراسة ، فقد تم الحصول على القياسات على طول أحد في ( th)والثوريوم ( u)، واليورانيوم ( k)اإلشعاعي للبوتاسيوم تحللأثناء ال قد أظهرت المؤاشرات الفردية لمواد و. م 03ألخذ العينات يبلغ رقم وفا 03 ةعرضيوبمسافات م 053 033من ةل متفاوتاطوابمسار او مقطع عشر / eu)باالضافة الى ذلك، تم عرض نسبة اليورانيوم إلى الثوريوم (.شاذه) على تواجد مصادر مشعة مناسبه غير طبيعية thو kو uاإلشعاع مثل تركيز eth ) ونسبة اليورانيوم إلى البوتاسيوم(eu / k )وعالوة .(المقاطع)ليورانيوم من خالل جميع المسارات وتم تحديد مناطق التحويل المرتبطة بتمعدن ا أشعة جاما كميات نسبية مختلفة من اإلشعاعات وتمهد الطريق لفك شفرة طيفمن uو thو kالقائمة على الجمع بين على ذلك ، تحدد الصورة الثالثية اليورانيوم القوية في المنطقة القريبة من منطقة الدراسة جود شذوذ لنسب ومع ذلك ، يبدو أن هناك عدم و .مستوى النشاط اإلشعاعي في منطقة الدراسة م استناداً إلى التحليل 40يقدر بحوالي تحت السطح المخفية هذه التصدعات، فإن عمق صدع بشكل كبيرتوبما أن منطقة الدراسة تعرضت لل .المحدودة (.4الخط )الطيفي لهارتلي من الشذوذ المغناطيسي الكلي .، ظفار، عمانشعة السينية، يورانيومشعة جاما، تحليل األأ: مفتاحيةالكلمات ال radiometric surveys for detection of uranium 37 1. introduction ranium is a strategically important mineral having wide applications in the field of energy (electricity) and other industrial research and development (r and d) sectors. this futuristic resource is very important for developing countries, hence the government of oman is keen to evaluate its resources. the proterozoic basement of the dhofar region of oman might be a potential source of uranium mineralization in the light of the global production of uranium (30%-40%) coming from proterozoic basins, especially from canada, australia and kazakhstan. spectrometry is a well-established analytical technique that has been widely used in r and d for elemental composition analysis. a relatively recent development has been the availability of sophisticated digital instrumentation, which can be transported to field sites and used for both direct and in situ non-destructive analysis of samples. their non-destructive analysis, multi element capability, speed of operation and access to valuable samples are further major advantages of field-portable spectrometers [1]. gamma ray spectrometry is a surveying technique that allows the calculation of the heat produced during radioactive decay of uranium (u), thorium(th) and potassium(k) within rocks [2]. many natural elements have radioactive isotopes, but only u, th and k decay series produce sufficient energy and intensity to be measured by γ-ray spectrometry. these decay series have the greatest intensity for the energy ranges of 1.37-1.57 mev for potassium (40k), 1.66-1.86 mev for uranium (238u) and 2.41-2.81 mev for thorium (232th) [2]. gamma rays are used to determine the quantities of these elements in rocks; alpha and beta components of decay produce much more heat than gamma rays, especially so the alpha decay of uranium [3]. spectrometric surveying will allow better constraint of resources estimation and help to target drilling. airborne gamma ray spectrometry is a major geologic mapping strategy in different environments, such as mineral, environmental, hydrocarbon and even ground water investigations [4-6]. in geothermal investigation, gamma ray spectroscopy could be used to determine radiogenic heat producing rocks that are often targets for geothermal exploration and production [7]. geochemical and geophysical surveys in the search for metallic ores [8] have been carried out around the world with the help of gamma ray spectrometry. an in-situ field gamma ray study with a portable gamma ray spectrometer using a sodium iodide detector was carried out by grasty [9] to analyze lithological variations by assessing the concentration of radioelements. in our investigation, a bgo super rs-230 spectrometer was used to measure the concentrations of these radioactive elements in the dhofar region of the sultanate of oman. the study was also substantiated by random sampling of both gamma ray spectrometry and by geochemical analysis of samples acquired by xrf from the study area. the results of gamma ray spectrometry and xrf were correlated to highlight the salient features of the entire investigation. 2. uranium occurrence the major types of uranium deposits are grouped according to their respective geological setting [10-13]. unconformity-related deposits occur in the immediate vicinity of major unconformities separating igneous basement and overlying clastic sediments. metasediments near the area are usually faulted and brecciated and are the locus of the main mineralization. igneous environments not only include intrusive rocks per se, but also the vein deposits (granite related and stock works), pegmatites containing rare metals (sn, ta, nb, li, and rees), volcanic and caldera-related deposits, as well as hematite breccia complex deposits (associated with a near surface explosive events involving boiling processes). in metamorphic deposits, the uranium enrichment can be derived and concentrate in metamorphosed rock. however, metasomatic processes (e.g., na metasomatism) lead to a re-distribution of uranium via leaching, transport, and mineralization in the form of disseminations within structurally deformed rocks (precambrian shields). with the exception of phosphorites (marine, and of continental-shelf origin), sedimentary uranium deposits show the significance of carbon (coal and hydrocarbons) in capturing uranium by absorbing it on lignite, organic matter in black shales (also carbonaceous pyritic shales) and sandstone deposits (medium to coarse-grained continental fluvial or marginal marine sediments under reducing conditions and occasionally quite c-rich; categorized into roll-front, tabular, basal channel, and tectonic/ lithologic deposits). while the geological environment of some archaean to early palaeoproterozoic quartz pebble conglomerate deposits with detrital uraninite could also be classified as metamorphic environments, they also clearly indicate reducing conditions (anoxic atmosphere, prevalence of hydrocarbons at least during overprinting). in addition, hydrocarbons occasionally also enrich uranium. two-thirds of the world's production of uranium comes from kazakhstan, canada and australia, and mostly comes from proterozoic rocks [14]. the athabasca basin (canada) accounts for 30% of the world’s high grade uranium production [15]. the surface of the basin consists of mainly sandstone sediment varying from 100 to 1000 meters in depth. the uranium ore is mostly found at the base of this sandstone, at the point where it meets the basement [15]. in australia, queensland is the largest producer of uranium [16]. kazakhstan has also been an important source of uranium for more than 50 years. new investigations to evaluate uranium contents are occurring in india, uzbekistan and many other countries around the world. jordan is the only country in the middle east that has a confirmed availability of uranium [17]. u http://en.wikipedia.org/wiki/sandstone http://en.wikipedia.org/wiki/uranium_ore n. sundararajan et al 38 the history of uranium exploration began during early 1980s in the sultanate of oman, wherein [18-20] a number of target areas have been identified. in our study, a couple of sites were selected on the basis of prevailing radiation which prompted further investigation using geophysical and geochemical methods. accordingly, the gamma ray spectrometry investigation was carried out to trace the uranium concentration in addition to in situ xrf measurements. subsequently, a detailed story based on vlf-em survey has been carried out. according to forbes et al. [21], in southwestern oman (some 300 km west of our site), there are indications of high radiation in oil well logs which intersect the shales of the andhur formation. the carbon content of these shales could have acted as a preconcentrating medium for uranium, while faults intersecting such formations then presented the pathways for migrating fluids [21]. 3. gamma ray spectrometry the most obvious technique to explore uranium deposits is the radiometric method, as it directly records the decay of the isotopes of these elements. all rocks and soils are naturally radioactive, containing various proportions of those radioactive elements [22]. their natural decay produces a variety of radiation (alpha, beta, and gamma) at specific energy levels. only gamma ray radiation has adequate energy to be useful for geological mapping and exploration [22]. thus, gamma ray spectrometry aids in measuring concentrations of the individual radioactive elements u, th and k as the basis for mapping rocks and soils by virtue of their characteristic radioactivity signatures [23,24]. the spectrometry data processing techniques mostly are qualitative, illustrating radioelements (u, th and k) in the form of maps and related ratios to decipher the potential of radioactive regions. these maps of the elements viz. u, th and k show the individual concentrations of their levels in order to understand the activity ratio of the three radioelements [2 and 25]. maps of the ratio of uranium/thorium (eu/eth) and uranium/potassium (eu/k) represent the alteration zones associated with uranium mineralization and other reducing environments which may be favorable indications for uranium mineralization. further, a high uranium and eu/th ratio can often indicate that an area has undergone multiple phases of remobilization and concentration [26 and 27]. the composite ternary image represents clearly different relative amounts of the radioelements (u, th and k) in three different colors, wherein the intensity of each color is proportional to a specific concentration. the concentration of different radioelements varies among different rock types and can be estimated through a gamma ray spectrometer measurement and mapping of the rocks. when the normal radioelement signature of the rocks is disrupted by a mineralized system, corresponding radioelement anomalies may provide direct exploration guidance [7]. 4. geology of the study area the study area spreads over an area of 0.35 km 2 (dhofar region) and encompasses the utm of easting 757580.61 to 758112.08 and northing 1868379.43 to 1869328.01 (figure 1(a)). in this study, the focus is on the relatively young sub-horizontal layers of tertiary micritic (eozl) and lacustrine (oaq) limestones including calcretes (surficial deposits) that are cross-cut by mineralised fault systems (veins). geological map and vertical profile (the green arrow indicates the approximate position of the investigated site (figure 1(b) and table 1); the yellow line on the map corresponds to the location of the profile) in figure 1(b), modified after the geological map of oman w of salalah (courtesy ministry of commerce and industry, 2013). table 1. overview of the geological rock units of the study area label age (ma) stratigraphic unit formation description qcx-z 24 quaternary / slope colluvium eozl 92 tertiary zalumah micritic limestones oaq 94 tertiary ashawq lacustrine limestones eay 105 tertiary aydim bioclastic limestones edm2-3 110 tertiary dammam bioclastic limestones edm1 113 tertiary andhur shale and intercalated limestones ers 120 tertiary rus chalky dolomitic limestone and marl radiometric surveys for detection of uranium 39 the area is heavily faulted (striking ne-sw, figure 1(b)). some of these faults have already been identified as the places of uranium enrichment [18-20]. since many of the limestone samples of the area have u levels below the detection limit of our equipment (portable xrf: < 1 ppm), we can rule out a general unfocussed disseminated uranium enrichment of the rocks. rather, the fault systems must have acted as fluid conduits for circulating waters scooping up uranium from deeper formations and carrying it to higher levels along the fault plane and also distributing it near the surface. possible sources for the observed u anomalies are: the crystalline proterozoic basement of the arabiannubian shield outcropping west of salalah [27], igneous continental basement and carbonaceous shales, which appear in the underlying andhur formation (edm1; figure 1(b) and table 1) and which occur much higher up in the section (several kilometers above the basement, although precise information regarding depth is not available for this location). figure 1. (a) location of study area and geophysical traverses. the map was produced with simpledemviewer for mac (version 4.4.9), aster gdem data (product of meti and nasa), qgis (version 2.0.1-dufour) under gnu general public license (b) geological map (the green arrow indicates the approximate position of the investigated site and the yellow line corresponds to the location of traverses (c) geological profile (s-n) near the investigation site [28]. (b) (c) (a) n. sundararajan et al 40 5. data acquisition measurements were recorded along 11 traverses, 20m apart and at station interval of 10m. the number of measurements along each line varied as the area is irregular in shape. the gamma ray spectrometry recorded close to, or slightly higher than, the background level along all these traverses (figure 1(c)). total magnetic field was also recorded along all these traverses at the same measurement interval and the results are available in the literature [28]. it may be noted that there were isolated elevated readings of uranium concentrations in the range 30-40 ppm on random sampling near to the study area. the recorded data, viz., radioelement dose (ngy/h), u, th and k, are displayed as contour images in order to decipher the distribution of these elements in the study area. figure 2 represents the radioelement dose while figures 3a, 3b and 3c illustrate the concentrations of u, th and k respectively. figure 2. contour image of radioelement dose (ngy/h) recorded by gamma ray spectrometer. the ratio maps of (eu/eth) and (eu/k) are shown in figure 4. in addition, in situ geochemical analysis in the field as well as of rock samples analyzed in the laboratory was carried out by a handheld niton xl3t 950 xrf analyzer (thermo scientific), used in geochemical survey to directly examine anomalies indicated out by a gamma ray spectrometer. the device is equipped with an sdd goldd+ detector and an ag-anode x-ray tube; the excitation voltage is 50 kv (200 ma, 2 watt). the instrument auto calibrates on activation. figures 5a and 5b represent the composite ternary image which was generated by combining three sets of the data pertaining to k, th and u from gamma ray spectroscopy and xrf analysis respectively. the equivalent uranium ratio composite (eu, eu/eth and eu/k) image is shown in figure 6. as reported in the geology section above, the study area is heavily faulted. the hartley spectral analysis of total magnetic anomaly of line-vi is presented to decipher the depth to the concealed fault. the method is briefly described hereunder. the hartley transform of the total magnetic anomaly (t(x)) can be defined as [29] 𝐻(𝑤) = ∫ 𝑇(𝑥) +∞ −∞ 𝑐𝑎𝑠 (𝑤𝑥)𝑑𝑥 (1) radiometric surveys for detection of uranium 41 (a) (b) (c) figure 3. contour image of concentration in ppm of (a) uranium (b) thorium and (c) potassium recorded by gamma ray spectrometer. n. sundararajan et al 42 where 𝑐𝑎𝑠 (𝑤𝑥) = cos(𝑤𝑥) + sin(𝑤𝑥) (2) is a 45 degrees phase shifted sine wave. h(𝑤) = e(𝑤) + 𝑂(𝑤) (3) where e(𝑤) 𝑎𝑛𝑑 𝑂(𝑤) are the even and odd components of the hartley transform h(𝑤). the amplitude spectrum is given by a(𝑤) = √(e(𝑤) ∗ e(𝑤) + o(𝑤) ∗ o(𝑤) (4) (a) (b) figure 4. contour image of the ratio of (eu/th) and (eu/k) expressed in ppm. radiometric surveys for detection of uranium 43 the hartley transform is identical to the well-known 1-d fourier transform and yields the same amplitude spectrum as that of fourier amplitude, but with a 45 degree phase shifted spectrum. in the case of traverse vi, the hartley spectra [30] was computed and shown in figure 7, which represents the wave number versus the log amplitude spectra of the total magnetic anomaly in which the slope of the least square fitted straight line results approximate depth. (a) figure 5. composite ternary image derived from (a) gamma ray spectrometry and (b) xrf analysis. 6. results and discussion the abundance of the examined radioelements u, th and k varies significantly with the lithology of the study area (figure 3a, b and c) reflecting the presence of rocks such as lacustrine limestones, bioclastic limestones, micritic limestones, shale units with intercalated limestones and chalky dolomitic limestones and marls. further, it may be noticed from figure 3a that an elevated uranium concentration exists along traverses l5 to l8 and also in traverse l10. the ratio of equivalent uranium to thorium (figure 4a) and the ratio of eu/k (figure 4b) marginally differ in the concentration of uranium wherein elevated levels of uranium are visible along traverses l0, l4-l7 and l10 in figure 4a, whereas traverses l0, l5-l7 and l10 show similar elevated levels of u in figure 4b. the composite ternary image (b) n. sundararajan et al 44 from gamma ray spectroscopy (figure 5a) simultaneously displays the radioelement concentrations, although a spatial shift of uranium away from an inferred line of the observed th anomalies exists since u is more mobile than th. similarly, a ternary diagram of th and sr shows a clear separation between u and th in the geochemical analysis (figure 5b). in addition, the composite ternary image of the equivalent uranium map (figure 6) substantiates such a separation of the observations seen from figure 5a and 5b. however, the results do not reveal any strong uranium anomalies. on the other hand, the spectral analysis of the total magnetic anomaly pertaining to line -vi indicates the depth to the subsurface fault as being around 60 m, and this cover of the fault may explain the difficulty in locating a distinctive radiogenic anomaly. figure 6. equivalent uranium concentration (ppm) image map. figure 7. hartley spectral analysis of total magnetic anomaly of line-vi indicating the depth to subsurface fault. radiometric surveys for detection of uranium 45 7. conclusion the gamma ray spectroscopic measurements recorded in the study area have shown the concentrations of radioelements particularly uranium as being only close to ambient noise values, and sporadically a little more in the range 30-40 ppm. however, within this range, a spatial shift of uranium away from an inferred line of the observed th anomalies was observed since uranium is more mobile than thorium. this sort of separation between uranium and thorium is further supported by the geochemistry. the combined geophysical and geochemical study in an area of less than one third square km did not reveal any strong uranium anomalies but it does not rule out the possibility of uranium mineralization sites elsewhere in the region. an airborne gamma ray spectroscopic study may yield a clearer picture of the dhofar region in the sultanate of oman. acknowledgement the authors wish to record their sincere thanks to sultan qaboos university for the 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geochronology of the neoproterozoic crystalline basement of salalah, dhofar, sultanate of oman. precambrian research, 2006, 145(3), 182-206. 28. béchennec, f. le métour, j. platel, j.p. roger, j. geological map of the sultanate of oman (1:250000, gis version), explanatory notes. ministry of petroleum and minerals, directorate general of minerals, sultanate of oman, muscat, 1993. 29. sundararajan n, pracejus b, alkhirbash s, alhosni tk, ebrahimy a. and m. al-mushani. magnetic mapping for delineating structures favorable to uranium mineralization in dhofar region, sultanate of oman. international journal of earth and environmental science, 2017, 127, 2-9. 30. bracewell, r.n. fourier transform and its applications, mcgraw hill book co, 1986. 31. sundararajan n, al-garni ma, ramabrahmam g. and srinivas y. a real spectral analysis of the deformation of a homogeneous electric field over a thin bed a hartley transform approach. geophysical prospecting, 2007, 55, 901-910. received 16 november 2017 accepted 23 september 2018 photovoltaic cells and systems: 24-33 squ journal for science, 16 (2011) © 2011 sultan qaboos university 24 surface morphology of cus thin films observed by atomic force microscopy anuar kassim*, ho soon min*, lim kian siang* and saravanan nagalingam** *department of chemistry, faculty of science, university putra malaysia, 43400, serdang, selangor, malaysia,**faculty of science, university tunku abdul rahman, 31900, kampar, perak, malaysia, email: soonminho@gmail.com. النحاس بواسطة مجهر القوة الذرية شكل السطح الخارجي لغشاء رقيق من كبريتيد أنور قاسم ، هو سون مين ، ليم كييان سيانق و سارافانان ناقالينقام في حُض حبمط اىثبرثبرك ببسخعمبهمه مبزيخيذ اىىحبص عيى سطح سجبج مجٍز ترقيق أغشيتىقذ حم حزسيب :ملخص ىقذ حمج دراست ذراست أثز سمه اىخزسيب اىسطحي عيى اىشنو اىخبرجي ىيغشبء اىزقيق. ى. حٍذف ٌذي اىُرقت حزسيب ميميبئي أقصز مذة حميشث بشنو فيألغشيت اىخي حنُوج . إن ااىزقيقت بُاسطت مجٍز اىقُة اىذريتٌيئت اىسطح اىخبرجي ىألغشيت يغطي مو اىسطح. أمب األغشيت اىخي حنُوج وخيجت ىشمه مثيفَىٍب شنو خبرجي جي مخىبسق َمبوج خبىيت مه اىشقُقخبر ي َشنيً يعخمذان َجذ أن سمل اىغشبء اىخبرج ىذا. ىم حخمنه مه حغطيت مو اىسطحأعطج أغشيت اىسخُن دقيقتحزسيب حجبَس . عيى سمه اىخزسيببشنو أسبسي abstract: cus thin films were deposited onto microscope glass substrates using the chemical bath deposition method in the presence of tartaric acid as a complexing agent. the objective of this paper was to study the influence of the deposition time on the morphology of thin films. the surface morphology of the thin films was investigated using atomic force microscopy. the thin films deposited for the shortest time were found to be uniform, without cracks and with a dense surface morphology covering the entire substrate surface area. however, the films prepared for 60 min and above indicated incomplete coverage of the material over the substrate surface. the surface roughness and film thickness values that were observed depended mainly on the deposition time. keywords: surface roughness; film thickness; thin films; copper sulphide; chemical bath deposition method. 1. introduction opper sulphide thin films have been used in photo thermal conversion, solar cells, electro conductive electrodes and microwave shielding coatings. the copper sulphide thin films have been deposited using various methods such as spray pyrolysis (nascu et al. 1997), successive ion layer adsorption and reaction method ( zhuge et al. 2009), photochemical deposition ( podder et al. 2005), electrodeposition ( anuar et al. 2002) and chemical bath deposition ( gadave and lokhande, 1993). the chemical bath c surface morphology of cus thin films 52 deposition method is considered to be a cheap method to produce various chalcogenide thin films such as as 2 s 3 (mane et al. 2004), mns2 (anuar et al. 2010a), in2s3 (asenjo et al. 2010), fes (anuar et al. 2010b), cdse (gopakumar et al. 2010), pbs (seghaier et al. 2006), sns (guneri et al. 2010), cd0.5zn0.5se (kale et al. 2007) and cubis 2 (sonawane et al. 2004) thin films. the chemical bath deposition method is based on the controlled precipitation from solution of a compound on to a suitable substrate. the substrate is immersed either in an alkaline or acidic solution containing the metal ion, chalcogenide source and complexing agent (such as ammonia, ammonium sulphate, sodium citrate, triethanolamine, disodium ethylenediaminetetraacetate and sodium tartrate). the present work reports the preparation and physical characterization of cus thin films onto microscope glass substrates using the chemical bath deposition method. the chemical bath contains copper sulfate and thiourea which provide cu 2+ and s 2 ions, respectively. it is the first time we report the influence of deposition time ranging from 30 to 180 min on the cus thin film in the presence of tartaric acid solution. the thin films were analyzed using atomic force microscopy. 2. materials and methods microscope glass slides were used as the substrate during the deposition process. the substrates were first cleaned in ethanol then ultrasonically washed with distilled water. finally, substrates were dried in an oven at 90 °c. copper sulfate, thiourea, tartaric acid and hydrochloric acid of analytical reagent grade were used as received. deionized water (alpha-q millipore) with a resistivity of 18.4 mωcm was used as the solvent. aqueous solutions of copper sulfate, thiourea and tartaric acid were separately prepared before t h e experiment. 20 ml of copper sulfate (0.125 m) and 20 ml of tartaric acid (0.125 m) were mixed in a beaker. during the deposition process, the tartaric acid served as a complexing agent to chelate with cu 2+ to obtain complex solution. then, 20 ml of thiourea (0.125 m) was added and the ph of the solution was adjusted to ph 1.5 by addition of hydrochloric acid using the ph meter. the substrates were immersed vertically into the solution. then, the deposition was conducted at 80 °c. the beaker was not stirred during the thin films deposition. after completion of film deposition (30 180 min), the deposited films were washed with distilled water and dried in air for further characterization. the surface morphology, thickness and surface roughness were examined b y recording atomic force microscopy images with a q-scope 250 in contact mode with a commercial si3n4 cantilever. values of root mean square (rms) roughness were calculated from the height values in the atomic force microscopy images using the commercial software. 3. results and discussion atomic force microcopy (afm) has been proved to be a unique, convenient and versatile technique to analyze surface morphology, film thickness and grain size. the three-dimensional and two-dimensional afm images of copper sulfide thin films deposited at different deposition times in an area of 20µm x 20 µm were as shown in figure 1(a), 2(a), 3(a), 4(a), 5(a), 6(a) and figure 1(b), 2(b), 3(b), 4(b), 5(b), 6(b), respectively. significantly, the microstructures of the thin films changed depending on the deposition time. it can be observed that there are many pinholes on the copper sulphide thin films deposited for 60 min and above. the afm images indicate these samples were found to cover the surface of the substrate incompletely. the reduction of the deposition time is an effective method to diminish the pinholes on the copper sulphide thin films. anuar kassim, et al. 52 ( a ) ( b ) figure 1. 3-dimesional (figure 1a) and 2-dimensional (figure 1b) afm image of cus thin films deposited for 30 min. as the deposition time decreases to 30 min, the surface morphology of the thin films becomes more homogeneous. from the afm image, it is found that these thin films (figure 1a, 1b) are uniform, without cracks, with dense surface morphology and covering the entire substrate surface area. surface morphology of cus thin films 52 ( a ) (b) figure 2. 3-dimesional (figure 2a) and 2-dimensional (figure 2b) afm image of cus thin films deposited for 60 min. anuar kassim, et al. 52 (a) (b) figure 3. 3-dimensional (figure 3a) and 2-dimensional (figure 3b) afm image of cus thin films deposited for 90 min. these films also indicate that grains are very small in size (0.5 µm) with no well-defined grain boundaries. for the films deposited for a longer deposition time, the grain size increased compared to the sample deposited for 30 min and indicates an agglomerated morphology. it is observed that the film formation is surface morphology of cus thin films 52 irregular and the sizes of the grains are dissimilar to each other (0.6-2 µm), indicating the non-uniformity in the grains produced at these deposition times. based on the afm image analysis, the films deposited for the longest deposition time (180 min) show less particles compared to other films. table 1 shows the dependence of the thickness of the copper sulfide thin films on the deposition time. the deposition time was varied from 30 to 180 minutes to obtain copper sulfide thin films with different thicknesses (65.6 to 608.9 nm). based on table 1, we can conclude that thicker films are formed for the films prepared for 60 min. table 1. thickness variation versus deposition time of the copper sulphide thin films. time thickness (nm) 30 98.9 60 608.9 90 356.4 120 461.2 150 80.7 180 65.6 root mean square (rms) roughness defined as the standard deviation of the surface height profile from the average height, is the most commonly reported measurement of surface roughness (jiang et al. 2005). the surface roughness values of 7.48 and 31.91 nm were observed for the films prepared for 30 and 60 min, respectively indicating that the surface roughness increases with increasing deposition time up to 60 min. according to the surface roughness (table 2), the films deposited for 180 min have a smoother surface while the films prepared for 60 min have a rougher surface. we observed that the surface roughness depends on the deposition time. the surface roughness is unavoidable due to three-dimensional growth of the films. table 2. surface roughness variation versus deposition time of the copper sulphide thin films. time rms (nm) 30 7.48 nm 60 31.91 90 12.38 120 31.18 150 2.90 180 2.41 4. conclusions here, we showed the results of atomic force microscopy of the cus thin films prepared using the chemical bath deposition technique. the influence of the deposition time on the morphological properties of thin films was investigated. the thin films deposited for the shortest time were found to be uniform, without cracks and with a dense surface morphology covering the entire substrate surface area. however, the films prepared for 60 min and above indicated incomplete coverage of material over the substrate surface. the surface roughness and film thickness values were found to depend mainly on the deposition time. anuar kassim, et al. 03 (a) (b) figure 4. 3-dimensional (figure 4a) and 2-dimensional (figure 4b) afm images of cus thin films deposited for 120 min. surface morphology of cus thin films 03 (a) (b) figure 5. 3-dimensional (figure 5a) and 2-dimensional (figure 5b) afm images of cus thin films deposited for 150 min. anuar kassim, et al. 05 (a) (b) figure 6. 3-dimensional (figure 6a) and 2-dimensional (figure 6b) afm images of cus thin films deposited for 180 min. surface morphology of cus thin films 00 5. acknowledgement the authors would like to thank the department of chemistry, university putra malaysia for the provision of laboratory facilities and mosti for the national science fellowship. 6. references anuar, k., zainal, z., hussein, m.z., saravanan, n. and haslina, i., 2002. cathodic electrodeposition of cu 2 s thin film for solar energy conversion. sol. energy mater. sol. cells, 73: 351-365. anuar, k., ho, s.m., atan, s. and saravanan, n., 2010. x-ray diffraction and atomic force microscopy studies of chemical bath deposited fes thin films. studia ubb. chemia, 3: 5-11. anuar, k., abdullah, a.h., ho, s.m. and saravanan, n., 2010. influence of deposition time on the properties of chemical bath deposited manganese sulfide thin films. av. quim., 5: 141-145. asenjo, b., guilln, c., chaparro, a.m., saucedo, e., bermudez, v., lincot, d., herrero, j. and gutirrez, m.t., 2010. properties of in2s3 thin films deposited onto ito/glass substrates by chemical bath deposition. j. phys. chem. solids, 71: 1629-1633. gadave, k.m. and lokhande, c.d., 1993. formation of cuxs films through a chemical bath deposition process. thin solid films, 229: 1-4. gopakumar, n., anjana, p.s. and vidyadharan, p.k., 2010. chemical bath deposition and characterization of cdse thin films for optoelectronic applications. j. mater. sci., 45: 6653-6656. guneri, e., ulutas, c., kirmizigul, f., altindemir g., gode f. and gumus, c., 2010. effect of deposition time on structural, electrical and optical properties of sns thin films deposited b y chemical bath deposition. appl. surf. sci., 257: 1189-1195. jiang, t., hall, n., ho, a. and morin, s. 2005. quantitative analysis of electrodeposited thin film morphologies by atomic force microscopy. thin solid films, 417: 76-85. kale, r.b., lokhande, c.d., mane, r.s. and han, s.h., 2007. cd0.5zn0.5se wide range composite thin films solar cell buffer layer application. appl. surf. sci., 253: 3109-3112. mane, r.s., todkar, v.v. and lokhande, c.d., 2004. low temperature synthesis of nanocrystalline as2s3 thin films using novel chemical bath deposition route. appl. surf. sci., 227: 48-55. nascu, c., pop, i., ionescu, v., indrea, e. and bratu, i., 1997. spray pyrolysis deposition of cus thin films. mater. lett., 32: 73-77. podder, j., kobayashi, r. and ichimura, m., 2005. photochemical deposition of cuxs thin films from aqueous solutions. thin solid films, 472: 71-75. seghaier, s., kamoun, n., brini, r. and amara, a.b., 2006. structural and optical properties of pbs thin films deposited b y chemical bath deposition. mater. chem. phys., 97: 71-80. sonawane, p.s., wani, p.a., patil, l.a. and seth, t., 2004. growth of cubis 2 thin films by chemical bath deposition technique from and acidic bath. mater. chem. phys., 84: 221-227. zhuge, f.w., li, x.m., gao, x.d., gan, x.y. and zhou, f.l., 2009. synthesis of stable amorphous cu2s thin film b y successive ion layer adsorption and reaction method. mater. lett., 63: 652-654. received: 16 february 2010 accepted: 1 st may 2011 microsoft word ers060824.doc 7-17 squ journal for science, 12 (1) (2007) © 2007 sultan qaboos university 7 a procedure to correct errors in depth estimation from slope hale slope method fitian r. al-rawi and ali m. al-rahim* department of geology, college of science, baghdad university, iraq, *email: alial_rahim@yahoo.com. ق باستخدام طريقة الميل ونصف الميل أسلوب لتصحيح األخطاء عند تقدير العم فتيان رشيد الراوي و علي مكي الرحيم تحري لتقدير النسبة المئوية لألخطاء المحتملة عند حساب عمق المصدر المسبب للمجال المغناطيسي عند ىجر :خالصة استخدمت . 1949 عام فيز لمبتكرة والتي اقترحها بيترخطوط عرض مختلفة باستخدام طريقة الميل ونصف الميل ا ) درجة 90من صفر إلى ( مجموعة من النماذج المتمثلة بالقواطع السميكة التي لها أعماق وزوايا ميل مغناطيسي مختلفة تتراوح .لحساب النسبة المئوية لألخطاء مع القيم المختلفة للميل وقد عرض أسلوب لتصحيح هذه األخطاء في تقدير العمق المحسوبة بين قيم موجبة وسالبة لنفس زاوية الميل عند األعماق المختلفة وهذه قد خلقت صعوبات لوضع النسبة المئوية لقد وجدت عالقة بين المسافة . ة ومن ثم التغلب على هذه المشكلةصيغة تخص العامل المستخدم لتعديل قيم األعماق المقدر تم رسم خطين مستقيمين من هذه العالقة وقد . قيقية والمحسوبةحاألفقية عند نقطة التماس ومركز أقصى ميل مع األعماق ال يحدد موقع نقطة التقاطع الفرق بين القيم الحقيقية والمحسوبة وهذا أما يضاف أو . طعت في نقطة معينة لكل زاوية ميلتقا يقي فان مقدار وفي حالة حساب العمق للمصدر في العمل الحق. يطرح من العمق المحسوب للحصول على العمق الحقيقي قيمة التصحيح سوف تقدر من خالل تحديد نقطة التقاطع بين العمق المحسوب والمسافة األفقية ومن ثم يحسب الفرق عن إن كل زاوية ميل لها عالقتها الخاصة المتمثلة بالخط المائل وان . الخط المائل للعمق الحقيقي المخصص لزاوية الميل . عمق الحقيقي النقطة التقاطع تستخدم لتقدير abstract: the novel method named slope half slope for depth estimation of the causative magnetic field proposed by peters (1949) has been investigated to determine the possible percent errors in depth estimation to magnetic sources situated at different latitudes. a sequence of models represented by thick dykes with various depths and with different values of field inclination (0 to 90°) has been used to estimate the percentage errors for the different inclination values. a procedure to correct the errors in depth estimate has been discussed. the calculated percent errors range between positive and negative values for the same angle of inclination at various depths. this raises difficulties to use a formula concerning the factor to adjust the estimated depths and to overcome this problem. therefore, a new approach has been adopted to correct the estimated depth values. a relationship between the horizontal distance at the tangential point and center of the maximum slope with the actual and estimated depths is found. two straight lines are plotted from this relation and they are intersected at a certain point for each inclination value. the location of this point defines whether the difference between the fitian r. al-rawi and ali m. al-rahim 8 actual and the estimated depth values will be added to or subtracted from the estimated depth to get the actual depth. in real depth determination, the correct value is determined by defining the intersect point between the estimated depth and the horizontal distance and then calculating the difference from the actual slope line for the assigned inclination angle. each inclination angle has its own relation and intersected point that can be used to determine the actual depth. keywords: magnetic depth estimation, slope method, correction procedure, percent errors in depth estimation, percent errors with inclinations. 1. introduction uch is written on the variety and relative merit of methods for estimating the depth to the source of magnetic anomalies. since the magnetometer is primarily a tool for subsurface mapping and detection, it follows that determination of the depth as well as edges of bodies is important in its application to geological exploration and search. several methods have been developed to estimate the magnetic depth (reynolds 1998, telford et a1. 1990). the number keeps growing with continual development of new algorithms (li. 2003). in most cases, depth may be estimated by visual inspection. several rules of thumb, modeling (i.e. calculation of assumed source and comparison with observation, gay, 1963, stanley, 1977), measured gradient techniques (naudy, 1971, atchuta et al. 1981, ku and sharp, 1983), spectral analysis techniques (spector and grant, 1970, bhattacharya, 1971) and various computer -oriented pr ocedures (thompson, 1 982), have been used. a given anomaly could have an infinite number of possible sources and source depths, but the realistic models that are assumed usually produce maximum depth estimates. riddel (1975) has summarized the results of applying the various empirical relations given by half width rule method, peters rule, tiburg rule, hannel rule, thalen rule and slope distance rule. he stated that peters rule gave the calculated heights above the ore body that agree reasonably well with the nominal terrain clearances. the subject of depth estimation for magnetic sources has been discussed recently by li (2003). the shape of the magnetic anomaly has a relation to the depth between the level of measurements and source. this property enables one to determine the approximate depth to the source independent of any other information concerning the source. the characteristic of anomaly wavelength, or width, as a function of depth will allow rapid and easy interpretation of anomalies of interest. peters’ slope half-slope method (peters, 1949) is one of the earliest magnetic estimate technique. the method depends on the horizontal distance between two parallel lines that pass through the maximum and minimum of an anomaly and have a slope equal to one half the maximum horizontal gradient of the anomaly. the depth to the top of the body is proportional to the horizontal distance. each of these horizontal distance measurements when multiplied by an empirical-determined factor equals the depth to the top of the anomaly source. the slope is multiplied by a factor between 0.5 and 1.5 depending upon whether the source is a thin or thick dyke. the slope method is a "direct" estimate that is roughly proportional to depth (breiner, 1994). this method was improved by the bean ratio method (bean, 1966) by introducing a regional slope thus removing the effect of a local regional field. the depth estimates derived from any of the techniques described are seldom more accurate than 10 percent of the actual depths and sometimes as poor as 50 percent (breiner, 1994). in theory, most of the estimates are maximum estimates so that the real source will actually be at a shallower depth. although peters' method was published in 1949, it is still being used because the relation between depth and slope of the anomaly is easy to perform. the problem in the application of such empirical relation is the factor value that should be used and the role of inclination angle of the magnetic field i.e. at what latitude are the magnetic measurements carried out. the purpose of the present paper is to determine the percentage errors in m a procedure to correct errors in depth estimation 9 depth estimation by applying this method and to overcome this problem by adopting a new proposed and applicable treatment procedure for different inclination angles as a correction to the estimated depths. 2. percentage errors in depth estimation the procedure followed in the calculation of the percentage error is through using models of thick dykes, having various depth values at every 10 degrees of magnetic inclination and with constant other parameters, in addition to inclination of 45°. these angles give the effect of inclination angle on the shape of the magnetic anomaly from the equator to the north pole (figure 1). calculations are based on a ready used computer program issued by geophysical software solution pty. ltd-pdyke copyright 2002-2005. slope half-slope method with a factor of 0.625 is applied to magnetic anomalies due to these models and depth is estimated for each model (figure 2). peters' rule gives the depth as 5/8 of the horizontal distance between the points on the side of an anomaly where the slope is half of the maximum slope (sheriff 1980). then, the estimated depths are compared with the actual depth values of the sources as in the models. the percentage errors for the various models are calculated. they show great discrepancies in certain profiles and with large variation for the same inclination at different depths of the source. plots of the percentage errors against inclination values are prepared (figure 3). they show that the percent errors are minimum around inclination 45 degrees and they increased toward the equator and the pole. the problem arising in the plots is that the percent errors are ranging between positive and negative values, so for the same inclination angle, changing the factor will not solve the problem and at the same time does not reduce the errors for other inclination values. however, care should be taken when choosing the maximum slope and in turn the points at the tangent of the half slope. the estimated depth values are very sensitive to the measurement of the appropriate horizontal distances that will be multiplied by the factor which in fact depends upon the distance scale of the magnetic profile. many procedures have been tried by the authors to solve this problem, without success. one solution is found and presented by this study that can be followed to treat the estimated depths at various inclinations and it considered a procedure of depth correction. the adopted procedure uses the advantage of the relation between the depth of causative source and the maximum slope of the anomaly and the slight change in shape of the anomaly and amplitude at different depths. plots between the actual and estimated depths against the horizontal distances between the tangential points of the half-slope line and the center of the maximum slope gives two straight lines intersecting at a certain point (figure 4). these intersection points are characteristic of each inclination angle because they vary in position for the various inclinations or latitudes. it is easy to notice the gradual and regular changes in their positions as one moves from inclination zero to inclination 90°. these plots can be used to adjust the estimated depth values for the specified inclination angle. a line projected from the point of intersection between the estimated depth value and the above mentioned horizontal distance (x) on figure 2 on the plotted straight line of the actual depth will determine the difference in depth value that should be added to or subtracted from the estimated value. the difference for points above the intersection position of the two straight lines will be subtracted while those below are to be added. this procedure is then applied to known depths of thirty models (figure l). it gives approximately 100% of the actual depth value after correction is applied to the estimated depth. in normal magnetic interpretation of field data the actual source depth of the causative magnetic body does not known unlike the models. this means that the intersection point obtained from the relation of the actual and estimated depths against the horizontal distance(x) will not be defined. therefore as a rule of thumb, the vertical projection from the point of intersection of the estimated depth with horizontal distance will be either to the right or to the left of the straight line of the slope of the actual depth for the assigned inclination angle in figure 4. here, the slope line in figure 4 of the actual depth fitian r. al-rawi and ali m. al-rahim 10 for each inclination angle is considered as a standard relation that can be used to obtain the difference value. if the intersection point is to the right of the straight line of actual depth in the plot of figure 4, the difference value should be added, while the difference should be subtracted if the point lies to the left of the straight line. figure 1. total magnetic intensity profiles due to vertical thick dyke sources with the mentioned body parameters for inclination from 0° to 90°. a procedure to correct errors in depth estimation 11 figure 2. procedure of depth estimation of magnetic source adopted in the present paper. fitian r. al-rawi and ali m. al-rahim 12 figure 3. the variation of percentage errors for depth estimation against different inclination angles of the magnetic field calculated for dyke like models. 3. application of the procedure application of peters' method is accompanied by certain errors that may give serious discrepancies in the estimated depths of the magnetic anomalies. these results can be greater or smaller than the actual values by 30%, depending on the inclination values of the magnetic field and source depth (figure 3). the proposed procedure of correction requires : a) applying the slope half-slope method carefully on the actual magnetic profile and then estimating the depth of the magnetic source, b) measuring the horizontal distance (x) between the tangential point of the half-slope and center of maximum slope as illustrated in figure 2, c) converting the depth and distance values to an appropriate scale to fit the given scale of figure 4 and d) defining the point of intersection of the estimated depth value with the horizontal distance on figure 4 by using the assigned inclination angle. this point is used with the assigned inclination angle of the plot to project a vertical line on the straight line drawn for the actual depth to determine the difference value. figure 5 shows an example of the procedure followed in calculating the correction values for two cases having estimated depths of 512.8 and 580m and horizontal distances of 440.4 and 492.2m, respectively, for an inclination angle of 60°. the difference value of 12.8m is subtracted from the estimated depths of 512.8 while the value of 20 m is added to the estimated depth 580m. the final corrected depths are 500 and 600 which are the actual depths of the dyke models. these values are subtracted for the first case and added to the second case depending on the position of the intersection point which is to the left or the right of the line, respectively. the scale used in the plot here represents a unit distance and can be adjusted with the magnetic profile scale by multiplying or dividing the profile scale to fit with the plots of any given figure. a procedure to correct errors in depth estimation 13 figure 4. a plot the horizontal distance between the points of the half slope tangent and the central points of maximum slopes against actual depths of the model and the estimated depths by slope-half slope method. fitian r. al-rawi and ali m. al-rahim 14 figure 5. illustration of the procedure followed to correct the estimated depth obtained by the present method. (actual slope-line for inclination 60°). 4. field example the published magnetic anomaly of the vertical component over the pima copper mine in arizona is considered here to check the above procedure of depth estimation. this anomaly had been analyzed by gay (1963) and reinterpreted by kara et al. (2003) through using displacement of the maximum and minimum by upward continuation. the adopted procedure in the present paper is applied to the total magnetic intensity of this anomaly (figure 6). the slope half-slope method gives an estimated depth of 61.5 m for the source of this anomaly. then this value is corrected by using the above nomographs of figure 4. the corrected value is 4m which is subtracted from the estimated value and the final determined depth is 63.5m. an illustration of the procedure followed in determining the correct value is shown in figure 1. the location of the intersect point between the estimated depth of 61.5m and horizontal distance of 13m is above (to the left) of the slope line for inclination 60°, so the value is subtracted. this value resembles nearly the depth value of the ore body which is 64m obtained by drilling (gay 1963). this depth value is so near to the actual depth value and more acceptable than the values of 69.8m and 13m given by gay (1963) and kara et al. (2003) respectively. 5. conclusions, discussion and recommendation depth estimated by slope half-slope method accompanied serious errors in model applications which should be considered in any calculation of magnetic source depths. here, the profiles are too smooth and there are no difficulties in selecting the best lines for the maximum and half-slopes and therefore, care should be given to field data. any slight change in the measured distances will create great effects in the calculated depth values and in turn produce wrong results and these depend upon the used distance scale. therefore, one should consider the subjective errors to avoid such mistakes. with these cautions, the method still has big errors in low and high latitudes and required correction to those estimated depths. the question is whether the estimated value is larger or smaller than the actual depth. the answer is too difficult because no one knows the actual depth of the magnetic source. the proposed procedure given in the present paper provides an easy solution to this problem a procedure to correct errors in depth estimation 15 and can define the positive or negative difference values and at the same time it will be very useful in magnetic interpretations. figure 6. total magnetic anomaly taken from kara et al. (2003) used as an example in depth estimation by applying the present procedure. (estimated depth = 67.5 m). figure 7. illustration of the procedure used to calculate the difference between the estimated value and the actual value from the intersection point between the estimated depth and the horizontal distance for the field example. fitian r. al-rawi and ali m. al-rahim 16 although the present procedure uses certain plots and mostly works with recent days done by computer, it can be translated in future to certain equations that make application so simple. understanding the procedure is one of the tasks and the steps of calculation can be followed by the illustrations given in figures 5 and 7. the present procedure can be recommended since depth estimation for magnetic sources is still a problem. the correct depth will assist the interpreter to obtain a constraint parameter that will give a good model fitting because magnetic interpretation includes many variables, which complicate the final results. determination of the correct depth is very useful as a forward step in magnetic interpretation. 6. references atchuta, rao, d, ram babu, h.v. and sankor narayan, p.v. 1981. interpretation of magnetic anomalies due to dikes: the complex gradient method. geophy. 46: 1572-1578. bean, r.j. 1966. a rapid graphical solution for the aeromagnetic anomaly of the twodimensional tabular body. geophy. 3l: 963-970. bhattacharya, b. 1971. analysis of a vertical dyke infinitely deep, striking north by fourier transform. pure and appl. geophys. 89: 963-970. breiner, s. 1994. applications for portable magnetometers. practical gcophysics ii tor the exploration geologist. compiled by richard van blaricom. northwest mining association. p. 313-345. gay, s.p. 1963. standard curves for interpretation of long tabular bodies. geophys. 28: 161-200. geophysical software solutions pty.ltd. (http://www.geoss.com.au). kara. i., ozdemir, m. and kanli, a.i. 2003. magnetic interpretation of horizontal cylinders using displacement of the maximum and minimum by upward continuation. jour. of the balkan geophysical society. 6: 16-20. ku, c.c. and sharp, j.a. 1983. werner deconvolution for automated magnetic interpretation and its refinement using marquardt's inverse modeling. geophys. 48: 754-774. li xiong, 2003. on the use of different methods for estimating magnetic depth. the leading edge. p10901099. naudy, h. 1971. automatic determination of depth on aeromagnetic profiles. geophys. 36: 717-722. peters, l.j. 1949. the direct approach to magnetic interpretation and its practical application. geophys. 14: 290-320. reynolds, j.m. 1998. an introduction to applied and environmental geophysics. wiley and sons. riddell, p.a. 1975. magnetic observations at the dayton iron deposit, lyon county, nevada. soc. of exploration geophysics' mining geophysics. i, case histories, p.418-428. roest, w.e. and verhoef, j. 1992. magnetic interpretation using 3-d analytic signal. geophys. 57: 116125. sheriff, r.e. 1980. encyclopedic dictionary of exploration geophysics. soc. of exploration geophysicists, 4th ed. 266p. spector, a. and grant, f.s. 1970. statistical models for interpreting aeromagnetic data. geophys. 35: 293302. stanley, j.m. 1977. simplified magnetic interpretation of the geologic contact and thin dike. geophys. 42: 1236-1240. telford, w.m., geldart, l.p. and sheriff, r.e. 1990. applied geophysics. cambridge uni. press. a procedure to correct errors in depth estimation 17 thompson, d.t. 1982. euldph – a new technique for making computer-assisted depth estimates from magnetic data. geophys. 47: 3l-37. received 24 august 2006 accepted 5 march 2007 photovoltaic cells and systems: 45-56 squ journal for science, 16 (2011) © 2011 sultan qaboos university 45 spectral analysis of magnetic anomalies due to a 2-d horizontal circular cylinder: a hartley transforms technique mansour a. al-garni department of geophysics, faculty of earth sciences, king abdulaziz university, jeddah, saudi arabia, email: maalgarni@kau.edu.sa. التحليل الطيفي للشواذ المغناطيسية الناتجة من اسطوانة أفقية ذو مقطع دائري ثنائية األبعاد: تقنية محوالت هارتلي عبدهللا القرنيمنصور الناتجة من اسطوانة أفقٌة ذو مقطع دائري ثنائٌة المغناطٌسٌةلشواذ العمودي تخدام محول هارتلً للتحلٌللقد تم اس :صخمل لقد تم حساب تبر محول هارتلً كوسٌلة بدٌلة للتحلٌل الطٌفً على غرار التحلٌل الطٌفً باستخدام محول فورٌر.ٌع األبعاد. ع كما انه تم استخدام مثال مصطن العمق الى مركز األسطوانة األفقٌة باستخدام معادلة رٌاضٌة بسٌطة كدالة فً التردد. الطرٌقة المقترحة بنجاح على شاذة هنه قد تم تطبٌق هذإى ذلك ففة الضا. باإلومدى صالحٌتها التقنٌة هلتوضٌح خطوات هذ تأثٌرمن بلدة كارٌمناغار، الهند. لقد تمت دراسة تٌت مأخوذة من مانغامبالً بالقربماغنٌ -حقلٌة على شرٌط من الكوارتز لطرٌقة المقترحة على مثال الشاذة ن نتائج اأكما .لثقةظهرت مستوى عال من اأو المقترحةالشوشرة العشوائٌة على الطرٌقة الحقلٌة أظهرت تطابقا مع نتائج الطرق األخرى المنشورة. abstract: the spectral analysis of the vertical effect of magnetic anomalies due to a 2-d horizontal circular cylinder is presented using hartley transform. hartley transform is an alternative approach to the famous complex fourier transform. the depth to the center of the horizontal cylinder can be computed by a simple equation as a function of frequency. a synthetic example has been used to illustrate this technique and the validity of this approach has been proved by applying it to real data of a narrow band of quartz-magnetite in mangampalli near karimnagar town, india. the noise analyses were tested on the technique and showed a high level of confidence. the results of the field example are in good agreement with the ones published in the literature. keywords: hartley transform; magnetic; 2-d horizontal cylinder. 1. introduction he hartley transform (hartley, 1942) has gained an importance in the field of geophysics in the last decade (bracewell, 1983; villasenor and bracewell, 1987; saatcilar et al. 1990; saatcilar and ergintav, 1991; t mailto:maalgarni@kau.edu.sa mansour a. al-garni 68 sundararajan 1995, 1997; sundararajan et al. 2007). the importance of this transform has been ignored not because of the complexity of the transform but because scientists have been overwhelmed by the complex algebra concept (sundararajan et al. 2007). the hartley transform is purely real and exactly equivalent to the fourier transform (bracewell, 1983; rajan, 1993; sundararajan, 1995). the significance of this transform is that it requires no assumptions to be made, unlike the fourier transform (mohan and seshagiri rao, 1982). the hartley and fourier transforms provide two numbers, having the same information at each frequency, which represent a physical oscillation in amplitude and phase. sundararajan and brahmam (1998) used the hartley transform to interpret gravity anomalies caused by slab-like structures. sundararajan et al. (2007) used the hartley transform to interpret the deformation of a homogeneous electric field over a thin bed. in this paper, the hartley transform approach is used to estimate the causative target parameters of a 2-d horizontal circular cylinder from its magnetic anomaly. this approach is applied first to a theoretical example to illustrate the method and then applied to the vertical magnetic anomaly over a narrow band of quartz-magnetite in mangampalli near karimnagar town, india, to demonstrate the applicability of the method. figure 1. geometry of the 2-d horizontal circular cylinder. 2. the magnetic effect of a horizontal cylinder the vertical magnetic effect of a buried horizontal circular cylinder extending infinitely in the horizontal direction along the y-direction, with its normal section parallel to the x-z plane, is considered. the coordinate system origin is taken on the ground surface such that the z-axis coincides with the diameter (figure 1). hence, the vertical magnetic effect at a point p on the surface can be expressed as follows (mohan et al. 1982).       2 2 2 2 2 sin 2 cosh x x h v x k x h              (1) where 2 2 ,k r i r is the radius of the cylinder, i is the magnetization intensity, is the polarization angle, and h is the depth to the center of the cylinder. 3. hartley transform of the magnetic effect the hartley transform of the real function v(x) is defined by hartley (1942) as: http://www.sciencedirect.com/science?_ob=articleurl&_udi=b6vfc-3v5m2bf-5&_user=1366817&_coverdate=05%2f31%2f1998&_rdoc=1&_fmt=full&_orig=search&_cdi=6007&_sort=d&_docanchor=&view=c&_acct=c000052384&_version=1&_urlversion=0&_userid=1366817&md5=6ccad01ca7dfc2377ad689c7207313f3#b6 http://www.sciencedirect.com/science?_ob=articleurl&_udi=b6vfc-3v5m2bf-5&_user=1366817&_coverdate=05%2f31%2f1998&_rdoc=1&_fmt=full&_orig=search&_cdi=6007&_sort=d&_docanchor=&view=c&_acct=c000052384&_version=1&_urlversion=0&_userid=1366817&md5=6ccad01ca7dfc2377ad689c7207313f3#b7 http://www.sciencedirect.com/science?_ob=articleurl&_udi=b6vfc-3v5m2bf-5&_user=1366817&_coverdate=05%2f31%2f1998&_rdoc=1&_fmt=full&_orig=search&_cdi=6007&_sort=d&_docanchor=&view=c&_acct=c000052384&_version=1&_urlversion=0&_userid=1366817&md5=6ccad01ca7dfc2377ad689c7207313f3#b8 spectral analysis of magnetic anomalies 69      h v x cas x dx      (2) where        cos sin 2 sin / 4cas x x x x        (3) is the kernel which represents a phase-shifted sine wave of 45° and hence takes the harmonics of both cosine and sine functions. the frequency ω has the same physical significance as in the case of the fourier transform. by analogy with the real and imaginary components of the fourier transform, the hartley transform may be expressed in terms of its even and odd components as:      h e o    (4) where           cos 2 h h e v x x dx           (5) and           sin 2 h h o v x dx            (6) where      h v cas x        (7) and        cos sin 2 sin / 4cas x x x x          (8) hence the amplitude and phase spectra can be expressed, respectively, as:       2 2 a e o    (9)       1 tan o e              (10) numerically, the amplitude a(ω) is equivalent to the fourier amplitude; however, the phase-shifted    differs by 45o from that of fourier phase   f   . therefore,   4 f      (11) alternately, the amplitude a(ω) and phase-shifted    can be computed as:       2 2 2 h h a       (12)           1 tan h h h h                   (13) mansour a. al-garni 6: substituting for v(x) in equation (1) into equation (2), the even and odd components of the hartley transform for the vertical magnetic effect of the horizontal circular cylinder infinitely extending in the horizontal direction can be easily evaluated as:   sin h e k e       (14)   cos h o k e       (15) therefore, the hartley transform   h  (sum of the even and odd components), amplitude  a  and phaseshifted    of the horizontal circular cylinder infinitely extending in the horizontal direction can be given, respectively, as:    sin cos h h k e         (16)   h h a k e      (17) 2     (18) 4. parameters evaluation at two successive frequencies i  and 1i   ,   i h h i i a k e      (19)   1 1 1 i h h i i a k e         (20) where 2 / n x   is the fundamental frequency expressed in radian per unit length, n is the total number of samples and x is the station interval. at 1i  and dividing equation (19) by equation (20), one can obtain:       2 1 1 2 2 1 h a e a         (21) taking the natural logarithm of both sides:     1 2 2 1 2 1 1 1n 1n a h a                (22) the term k is evaluated by substituting the value of h in equation (19)  h ha k e     (23) and  can be computed from equations (14 and 15) as:     1 tan e o            (24) spectral analysis of magnetic anomalies 6; therefore, based on equations (22) – (24), we can easily estimate the depth h of the polarization angle  and the magnetization intensity related parameter k of the buried cylinder. 5. synthetic example the hartley transform approach is illustrated by a synthetic model assuming a depth to the center of the horizontal circular cylinder 10h  units, a polarization angle 60  and 1k  unit (figure 2). the even component, the odd component, the hartley transform and the amplitude spectrum are computed and shown in figures 3a, b, c and d, respectively. using the method that has been developed throughout the text, the parameters ( k , h and  ) of the horizontal circular cylinder are estimated and the results are shown in table 1. it can be noticed that the interpreted results, using the proposed technique, agree well with the assumed values. figure 2. response of vertical magnetic effect of a 2-d horizontal circular cylinder. 6. noise analysis to investigate the noise effect on our estimation method, we added a synthetic anomaly with 5% and 10% of white gaussian noise (wgn) as shown in figures 4 and 5. the even components, the odd components, the hartley transforms and the amplitude spectra of the contaminated anomalies are shown in figures 6 and 7, respectively. the interpreted results are shown in table 2. it is clear that the present technique produces satisfactory results even though the anomaly was contaminated with up to 10% of wgn. table 1. synthetic example in arbitrary units theoretical model k h  assumed values 1 10 60 o interpreted values 1.071 9.94 57.16 o percentage of error 7.1 6 4.73 mansour a. al-garni 75 table 2. synthetic example in arbitrary units, contaminated with 5% and 10% of wgn. theoretical model k h  assumed values 1 10 60 o interpreted values with 5% of wgn 0.957 9.686 56.433 o interpreted values with 10% of wgn 0.912 9.082 57.028 o figure 3. the even component (a), the odd component (b), the hartley transform (c) and the amplitude spectrum (d) of the horizontal circular cylinder. spectral analysis of magnetic anomalies 75 figure 4. response of the vertical magnetic effect of a horizontal circular cylinder with 5% of wgn. figure 5. response of the vertical magnetic effect of a horizontal circular cylinder with 10% of wgn. 7. field example the proposed technique is tested with an example of vertical magnetic anomaly over a narrow band of quartz-magnetite in mangampalli near karimnagar town, india (murthy et al. 1980), as shown in figure 8. the anomaly is digitized at 15 ft intervals over 540 ft. the even component, odd component, hartley transform, and the amplitude spectrum are computed and shown in figure 9. the interpretation parameters, using the procedures mentioned in the text, are tabulated and shown in table 3. it shows that the results of the proposed technique inversion are in good agreement with the other published ones. mansour a. al-garni 75 figure 6. the even component (a), the odd component (b), the hartley transform (c) and the amplitude spectrum (d) of the horizontal circular cylinder anomaly, contaminated with 5% of wgn. spectral analysis of magnetic anomalies 75 figure 7. the even component (a), the odd component (b), the hartley transform (c) and the amplitude spectrum (d) of the horizontal circular cylinder anomaly, contaminated with 10% of wgn. mansour a. al-garni 76 table 3. field example over a narrow band of quartz-magnetite in mangampalli near karimnagar town, india method depth in feet murthy et al. (1980) 78 sudhakar et al. (2004) 87 al-garni (2009) 82.93 present technique 83.26 figure 8. vertical magnetic anomaly over a narrow band of quartz-magnetite in mangampalli near karimnagar town, india (murthy et al. 1980). 8. conclusion spectral analysis, using the hartley transform, of the magnetic anomalies due to a horizontal circular cylinder has been carried out. this approach was applied first to a synthetic data and then to a real data of the vertical magnetic anomaly over a narrow band of quartz-magnetite in mangampalli near karimnagar town. the noises effect on the present technique is tested. this technique shows a level of confidence in the quantitative interpretation of the parameters of the vertical magnetic effect of horizontal cylinder anomalies. due to the fact that the hartley transform is purely real, it in general has advantages over the conventional spectral analysis (fourier transform) in terms of its efficient and economical calculations particularly for more sophisticated problems. it is very interesting to notice that the interpreted results of the real data agree well with those obtained by other techniques, published in the literature. 9. acknowledgment the author thanks prof. n. sundararajan, department of earth sciences, sultan qaboos university, sultanate of oman, for his suggestions to improve the manuscript. spectral analysis of magnetic anomalies 77 figure 9. the even component (a), the odd component (b), the hartley transform (c) and the amplitude spectrum (d) of the vertical magnetic anomaly over a narrow band of quartz-magnetite in mangampalli near karimnagar town. mansour a. al-garni 78 6. references al-garni, m.a., 2009. interpretation of some magnetic bodies using neural networks inversion. arabian journal of geosciences 2: 175-184. bracewell, r.n. 1983. the discrete hartley transform. journal of the optical society of america 73: 18321835. mohan, n.l., seshagiri rao, s.v., 1982. spectral interpretation of gravity anomalies due to horizontal slab like bodies with lateral variation of density. proc. ind. acad. sci. earth planet sci. 91: 43-54. mohan, n.l., sundararajan, n. and seshagiri rao, s.v., 1982. interpretation of some twodimensional magnetic bodies using hilbert transforms. geophysics 47: 376-387. murthy, r.i.v., rao, v.c., krishna, g.g., 1980. a gradient method for interpreting magnetic anomalies due to horizontal circular cylinders, infinite dykes and vertical steps: journal of earth system science 89: 31-42. rajan, n.s. 1993. discussion on the use of hartley transform in geophysical applications. geophysics 56: 1058-1059. hartley, r.v.l., 1942. a more symmetrical fourier analysis applied to transmission problems. proc. ire 30 2: 144-150. saatcilar, r., ergintav, s., canitez, n., 1990. the use of the hartley transform in geophysical applications. geophysics 55: 1488-1495. saatcilar, s., ergintav, s., 1991. solving elastic wave equations with the hartley method. geophysics 56: 274-278 sudhakar, k.s., rao, r.p.r., murthy, r.i.v., 2004. modified werner deconvolution for inversion of magnetic anomalies of horizontal circular cylinders. j. ind. geophys. union 8: 179-183. sundararajan, n., 1995. 2-d hartley transforms. geophysics 60: 262-267. sundararajan, n., 1997. fourier and hartley transforms-a mathematical twin. indian journal of pure applied mathematics 28: 1361-1365. sundararajan, n., al-garni, m.a., ramabrahmam, g., srinivas, y., 2007. a real spectral analysis of the deformation of a homogeneous electric field over a thin bed a hartley transform approach. geophysical prospecting 55: 901-910. sundararajan, n., brahmam, g., 1998. spectral analysis of gravity anomalies caused by slab-like structures: a hartley transform technique. journal of applied geophysics 39: 53-61. villasenor, j.d., bracewell, r.n., 1987. optical phase obtained by analog hartley transformation. nature 330: 735-737. received: 21 september 2010 accepted: 12 february 2011 photovoltaic cells and systems: 43-54 squ journal for science, 13 (2008) © 2008 sultan qaboos university simulation of decadal precipitation over nairobi in kenya muthama nzioka john*, manene m.moses** and ndetei cornelius joseph* *department of meteorology, university of nairobi, kenya; **school of mathematics, university of nairobi, kenya, p.o.box 30197-00100 nairobi, kenya, email: jmuthama @uonbi.ac.ke. محاكاة معدل سقوط األمطار فوق مدينة نيروبي بكينيا موزس مانينى و كورنيليوس جوزيف نديتى . جون نزيوكا موثاما، م عند دراسة تغير معدل سقوط األمطار فوق كينيا وعالقة ذلك بالعوامل المناخية األخرى، وجد انه من الضروري :خالصة من أجل ذلك تم استخدام طريقة االنحدار خطوة بخطوة فـي هـذه . لسقوط األمطار تحليل المعدالت غير المنتظمة زمنيا مة بيانات سقوط األمطار مـع ءوقد تمت موا . الدراسة التي تستهدف تحسين مراقبة سقوط األمطار في نيروبي والتنبؤ به مـن أكتـوبر حتـى و mam)(عدة دوال رياضية وتم اختيار أفضل نموذج رياضي في الفترات من مارس حتى مايو . من موسم سقوط األمطار لثالثة محطات رصد بطريقة االنحدار خطوة بخطوة) ond(ديسمبر ومن خالل النتائج المتحصل عليها، فقد انتقت طريقة االنحدار خطوة بخطوة كثيرة الحدود من الدرجة الرابعـة كأفضـل . الموضحة أعالهond و mamمة لتحليل بيانات ءموا استنتجنا . للحصول على متغيرات كثيرة الحدود من الدرجة الرابعة ) سنوات 10(مت دورة شمسية عشر سنوية كما استُخد من هذه الدراسة انه يمكن استخدام دالة كثيرة حدود من الدرجة الرابعة للتنبؤ بأعلى معدل لألمطار وكذلك بالتصور العام ذه المعلومات للتخطيط وإلدارة الموارد هن الخطأ، ويمكن استخدام لسقوط األمطار الموسمية فوق نيروبي، بنسبة مقبولة م . ى لمناطق أخراستعمال هذه الطريقةالمائية في نيروبي كما يمكن abstract: in investigating kenya rainfall variability and its relationship to other climatic elements it has become imperative to analyze the irregularly distributed rainfall events in time. to meet this requirement, this study used a stepwise regression technique. the study seeks to improve existing rainfall monitoring and prediction in nairobi. monthly rainfall data was fitted to several mathematical functions. the best mathematical model which best simulated the march-may (mam) and october -december (ond) seasonal rainfall over the three stations of analysis was chosen using a stepwise regression technique. the value of r-squared for the best fit was computed to show the percentage of rainfall information that is explained by the variation in the independent (time) variable. from the results obtained, the stepwise regression technique selected the fourth degree polynomial as the best fit for analyzing the march-may (mam) and october -december (ond) seasonal rainfall data set. solar cycle period of ten (10) years was employed to get the fourth degree polynomial variables. hence from the study, it can be deducted that the 4th degree polynomial function can be used to predict the peak and the general pattern of seasonal rainfall over nairobi, with acceptable error values. this information 43 muthama nzioka john, et al. can be used in the planning and management of water resources over nairobi. the same information can be extended to other areas. keywords: stepwise regression; rainfall variability; polynomial function; solar cycle period; nairobi. 1. introduction t here is an ongoing effort to better understand the coherent multidecadal fluctuations in the global climate system that result from interactions between the various components of the climate system itself, such as the oceans, land, and atmosphere. it is generally assumed that the slowly varying sea surface temperatures (ssts) are the dominant source of this variability (e.g., kawamura et al. 1995a,b; livezey and smith 1999; mo et al. 2001; hoerling et al. 2001), which has prompted several extended climate simulations using general circulation models (gcms) forced by the observed near-global ssts (graham 1994; lau and nath 1994). chelliah and bell, 2004 studied the coherent decadal fluctuations in tropical convection and surface temperatures over the central pacific, the west african monsoon region, the amazon basin, and the indian ocean, which are shown to constitute the dominant decadal-scale mode of variability in the global tropics. the east african region is characterized by a complex topography. this topographical inhomogeneity includes large lakes, rift valleys, flat plains and snow-capped mountains on the equator. almost all facets of societal and economic activities in the region are critically dependent on the variability of seasonal rainfall, which occurs during boreal spring (long rains, march-may) and autumn (short rains, october-december). however, the societies are often unprepared to adjust quickly to dramatic deviations from normal rainfall regimes. extremes in weather and climate may result in loss of lives and damage to property including massive disruptions of existing infrastructures. these negative impacts have been detrimental to the economy. the forecasting of severe weather and extreme climate events is one of the major challenges facing meteorological services worldwide and more so in the tropics. however, researchers have made enormous efforts in addressing the issue of accurate rainfall predictability. amongst some of the techniques that have been employed to predict rainfall in east africa include the use of numerical and statistical methods. mathematical functions especially polynomial regressions have also been used to characterize weather elements including rainfall in different parts of the world. for instance, christine et al (1998) used polynomial regression to derive a simple model for each monthly climate variable to relate climate to position and elevation on digital elevation model (dem) in ireland. accuracy assessments with subsets of each climate data set showed that polynomial regression can predict average monthly climate in ireland with mean absolute errors of 5 to 15 mm for monthly precipitation, 0.2 to 0.5°c for monthly averaged maximum and minimum temperature, and 6 to 15 min for monthly averaged sunshine hours. camberlin and philippon (2001) presented a forecast of the march-may 2001 rain season in east africa, using complementary statistical techniques: the multiple linear regression (mlr) and the linear discriminant analysis (lda) as in folland et al. (1991). their prediction scheme involved the use of sea surface temperatures (sst) indexes and atmospheric predictors. the march to may period corresponds to the main rain season in equatorial eastern africa (so-called "long rains"). although this rain season exhibits lesser interannual variability than that of october-december ("short rains"), it is the main agricultural period in east africa, and droughts severely affect the entire economy (e.g., in 2000 in kenya). yet, these interannual variations are much less known than those of the "short rains". in particular, the teleconnections with sea surface temperature anomalies (both regional and global) are much weaker (ogallo et al., 1988; rowell et al., 1994 ; mutai and ward, 2000), and this precludes the definition of acute seasonal rainfall prediction models based on that sole variable. the rainfall over east africa is of oscillatory character in time, and as shown by ogallo (1977), the result of the spectral analysis indicated that there were some oscillations in the annual rainfall series. potts (1971), and rodhe and virji (1996) showed that oscillatory peaks of 2-2.5, 3.5 and 5.6 years in addition to other peaks 44 simulation of decadal precipitation over nairobi in kenya associated with el nino (e.g., ropelewski and halpert 1987) exist in east africa rainfall. however, it has never been clear as to when these oscillations occurred in the rainfall. in investigating kenya rainfall variability and its relationship to other climatic elements, it has become imperative to analyze the irregularly distributed rainfall events in time. to meet this requirement, this study used stepwise regression technique. the study seeks to improve existing rainfall monitoring and prediction in nairobi. 2. data and methods monthly totals rainfall data obtained from the kenya meteorological department (kmd) was used in the study. the data was for three stations in nairobi city, namely dagoretti (10 18's, 360 45'e), jkia (10 19's, 360 55'e) and wilson (10 19's, 360 49'e) which are on the same homogeneous climatic zone. the data covers more than 30 years which was considered as sufficient climatic period. 2.1 data quality control and estimation of missing records data quality control is important in order to detect any discontinuities in the data that may have occurred from non-natural influences like changes in observational schedules and methods, instrumental and other human processes (wmo, 1966). heterogeneity makes records not strictly comparable over long time periods and between different stations. it is therefore important to ascertain the homogeneity of any meteorological data before using it in any study. the single mass curve was used to check on homogeneity of the rainfall data. the mass curve was obtained by plotting cumulative records of rainfall against time. basically, from plot of single mass curve, a straight line indicates a homogenous record whereas heterogeneity can be indicated by significant deviations, of some of the plots from the straight line. the missing rainfall records were less than 10% of the total data. the different methods of estimating missing data (wmo, 1962) include; the arithmetic mean method, the isopleths method, thiessen polygon method, isohyetal method, finite differencing method, correlation and regression method. in this study the correlation method was used to estimate the missing records. the correlation method of estimating the missing data is computed as; missing period periodx x y y = ⋅ (1) where yperiod refers to the period of the station with complete data set, x is the mean of the available data set for the station with missing records, y is the long term mean of the station with complete data set and rxy is the correlation coefficient, and is given by; ( )( ) ( ) ( ) 2 1 1 1 22 1 1 . 1 1 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ −− −− = ∑ ∑ ∑ = = = n i n i ii i n i i xy yy n xx n yyxx nr (2) 2.2 choosing the best fit model monthly rainfall data for the three stations (i.e dagoretti, jkia and wilson) was fitted to several mathematical functions. these mathematical functions were grouped into five families based on their characteristic behaviour as given by muthama (2002). these families include exponential models which have the exponential or logarithmic functions involved, growth models characterized by a monotonic growth from some fixed value to an asymptote, the yield density models which have the ‘asymptotic’ and ‘parabolic’ yield density relations, processes producing sigmoidal or ‘s’ –shaped growth curves, and a miscellaneous family 45 muthama nzioka john, et al. described to include the sinusoidal fit, gaussian model, hyperbolic fit, heat capacity model, rational function, etc. the best mathematical model which best simulated the march-may (mam) and october -december (ond) seasonal rainfall over the three stations of analysis was chosen. single mass curve for dagoretti (1955-2002) y = 85.127x 55629.449 r2 = 0.999 0 10000 20000 30000 40000 50000 60000 ja n55 ja n58 ja n61 ja n64 ja n67 ja n70 ja n73 ja n76 ja n79 ja n82 ja n85 ja n88 ja n91 ja n94 ja n97 ja n00 period c um m ul at iv e r ai nf al l ( m m ) cum rf linear (cum rf) figure 1. single mass curve for dagoretti. single mass curve for wilson (1957-2002) y = 75.198x 50235.120 r2 = 0.999 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 ja n57 ja n62 ja n67 ja n72 ja n77 ja n82 ja n87 ja n92 ja n97 ja n02 period c um m ul at iv e r ai nf al l ( m m ) cum rf linear (cum rf) figure 2. single mass curve for wilson. through the use of stepwise regression technique, the fourth degree polynomial was selected as the best fit for analyzing the data set. this technique involves choosing the variables, i.e., terms, to include in a multiple regression model. forward stepwise regression starts with no model terms. at each step it adds the most statistically significant term (the one with the highest f statistic or lowest p-value) until there are none left. backward stepwise regression starts with all the terms in the model and removes the least significant terms until 46 simulation of decadal precipitation over nairobi in kenya all the remaining terms are statistically significant. it is also possible to start with a subset of all the terms and then add significant terms or remove insignificant terms. single mass curve for jkia (1958-2002) y = 61.473x 42336.819 r2 = 0.999 0 5000 10000 15000 20000 25000 30000 35000 40000 ja n58 ja n61 ja n64 ja n67 ja n70 ja n73 ja n76 ja n79 ja n82 ja n85 ja n88 ja n91 ja n94 ja n97 ja n00 period c um m ul at iv e r ai nf al l ( m m ) cum rf linear (cum rf) figure 3. single mass curve for jkia. the oscillations of the mam and ond rainfalls followed a unique repetitive pattern which may be associated with solar cycle. recent observation shows a strengthening of tropical circulation associated with the decadal variability in the tropical mean radiative energy budget (chen et al., 2002; wielicki et al., 2002). hence, solar cycle period of ten (10) years was employed to get the fourth degree polynomial variables. the fourth degree polynomial function is of the form; 2 3y a bx cx dx ex= + + + + 4 (3) where a,b,c, d and e are constants and x refers to the independent variable (also called the predictor) and y is the dependent variable (also called the predictand). the error sum of squares (sse) was computed for 5, 10 and 11 years periods. the sum of squared prediction errors (sspe) is given by; 2 1 )ˆ( t n t t yysspe −= ∑ = (4) where is the one-step predicted value and is the observed/recorded value. tŷ ty 3. results and discussion the results for data quality control tests and 4th degree polynomial fit of the mam and ond rainfalls is as depicted below. 3.1 data quality control results the single mass curve was used to ascertain the quality of the data. cumulative rainfall was plotted against time and the plot showed that data for the three stations used in the study were homogeneous. the rainfall records were therefore declared of good quality and hence suitable for climatological analysis. the single mass 47 muthama nzioka john, et al. curves are shown in figures 1, 2 and 3. r-squared values (also called the coefficient of determination) have also been calculated by assuming a linear trendline. r-squared value is a number from 0 to 1 that reveals how closely the estimated values for the trendline correspond to the actual data. a trendline is most reliable when its rsquared value is at or near 1. figure 1 shows the single mass curve for dagoretti, and it is clear from the plot that the data record over this station was of good quality as depicted in the almost straight line. the r2 value for the mass curve fit was very close to 1 and the linear trendline equation was of the form y mx b ;= + ‘m’ being the slope and ‘b’ the intercept. from the single mass curve for wilson, it is also evident that the data record used was of good quality as shown in figure 2 above. the r2 value was also very close to 1, a clear indication that the trendline was most reliable. figure 3 shows the single mass curve for jkia. similarly, the data record over this station was homogeneous as illustrated by the near straight line. the computed r2 value was also very close to 1 and the linear trendline equation was of the form where ‘m’ was the slope and ‘b’was the intercept. hence the data records used in this study were homogeneous for the three stations of interest, and hence the data was declared fit for use in the analysis. the linear trendlines for the various mass curve fits were reliable since they were very close to 1. y mx b ,= + 3.2 the error sum of squares (sse) the error sum of squares (sse) was used to assess the deviation of predicted rainfall values from the observed values. the computed sse values for 10 years were lower in comparison to the sse values for 5 or 11 years. hence, the sum of squared prediction errors (sspe) was lower for 10 years as compared to 5 and 11 years. table 1 below summarizes the sspe value results obtained for 10 and 11 years respectively. it is evident from table 1 that the sspe values for 10 years cycle were lower as compared to the sspe values for 11 years cycle. table 1. sspe values for 10 and 11 years cycles. 10 years cycle station data period sspe for mam sspe for ond dagoretti 1957-2003 1139570.1 1371506 jkia 1958-2002 703804.56 1111207 wilson 1957-2002 1047649.8 1034849 11 years cycle station data period sspe for mam sspe for ond dagoretti 1957-2003 1199634.3 1426785 jkia 1958-2002 764238.11 1164118 wilson 1957-2002 1158147.2 1091048 3.3 inter-seasonal rainfall variability table 2 illustrates the rainfall variability during the march-may (mam) and october-december (ond) seasons over nairobi. 48 simulation of decadal precipitation over nairobi in kenya table 2. mam and ond seasonal rainfall variability. range here refers to the difference between maximum and minimum rainfall whereas std dev is the standard deviation. march-may season dagoretti jkia wilson range std dev range std dev range std dev sum of 5 years 625.9 204.1 692.2 248.0 1485.5 528.6 sum of 10 years 312.4 142.7 188.6 78.4 458.2 210.7 sum of 11 years 362.8 161.1 714.1 354.5 805.0 371.3 october-december season dagoretti jkia wilson range std dev range std dev range std dev sum of 5 years 1320.7 380.8 947.0 344.6 834.8 315.9 sum of 10 years 1327.1 553.8 1156.6 560.6 1468.9 664.4 sum of 11 years 1539.2 638.9 1303.8 600.2 1237.1 518.2 as observed from table 2, the sum of mam rainfall had minimal variability over a decade (10 years) as compared to 5 and 11 years where the variability was more pronounced, as depicted in the range and standard deviation values. information on the minimal variability in mam seasonal rainfall over a ten year period can be used in water planning and management over nairobi. the sum of october-december rainfall had minimal variability over nairobi for 5 years period as compared to 10 and 11 years periods. hence it is recommended that water planning and management over nairobi for the ond season should be for a period of 5 years. observed and modelled mam rainfall in dagoretti 50 150 250 350 450 550 650 750 850 950 1050 1150 19 57 19 62 19 67 19 72 19 77 19 82 19 87 19 92 19 97 20 02 period to ta l m a m r ai nf al l ( m m ) obs modelled figure 4. recorded and simulated mam rainfall at dagoretti. 49 muthama nzioka john, et al. observed and modelled ond rainfall in dagoretti 50 150 250 350 450 550 650 750 850 950 1050 1150 19 55 19 60 19 65 19 70 19 75 19 80 19 85 19 90 19 95 20 00 20 05 period o n d t ot al r ai n fa ll (m m ) obs modelled figure 5. recorded and simulated ond rainfall at dagoretti. observed and modelled mam rainfall in jkia 0 100 200 300 400 500 600 700 800 900 1000 19 58 19 63 19 68 19 73 19 78 19 83 19 88 19 93 19 98 20 03 period t ot al m a m r ai n fa ll (m m ) obs modelled figure 6. recorded and simulated mam rainfall at jkia. 50 simulation of decadal precipitation over nairobi in kenya observed and modelled ond rainfall in jkia 0 100 200 300 400 500 600 700 800 900 1000 19 58 19 63 19 68 19 73 19 78 19 83 19 88 19 93 19 98 20 03 period to ta l o n d r ai nf al l ( m m ) obs modelled figure 7. recorded and simulated ond rainfall at jkia. observed and modelled mam rainfall in wilson 0 100 200 300 400 500 600 700 800 900 1000 19 57 19 62 19 67 19 72 19 77 19 82 19 87 19 92 19 97 20 02 period t ot al m a m r ai n fa ll (m m ) obs modelled figure 8. recorded and simulated mam rainfall at wilson. 51 muthama nzioka john, et al. 3.4 fourth degree polynomial fit results through various curve fitting analyses carried out, it was evident that the 4th degree polynomial function was the best fit for the three stations of analysis selected (i.e dagoretti, jkia and wilson). the simulated marchmay (mam) and october-december (ond) rainfalls using the 4th degree polynomial fit for the three stations of analysis is as depicted in figures 4-9. observed and modelled ond rainfall in wilson 0 100 200 300 400 500 600 700 800 900 1000 19 57 19 62 19 67 19 72 19 77 19 82 19 87 19 92 19 97 20 02 period to ta l m a m r ai nf al l ( m m ) obs modelled 4 4 figure 9. recorded and simulated ond rainfall at wilson. the 4th degree polynomial function used to get the simulated mam rainfall over dagoretti was of the form 2 3y a bx cx dx ex= + + + + , where a = 812.6, b = -223.5, c = 65.5, d = -8.6 , e = 0.385. from figure 4, the march-may rainfall over dagoretti seems to have a significant decadal cycle. this 10 years cycle is analogous to the solar cycle. though some of the peaks are not well captured, but the overall rainfall trend is clearly illustrated. the polynomial equation for the simulated ond rainfall over dagoretti was of the form 2 3y a bx cx dx ex= + + + + , where a = 673.8, b = 433.1, c = 151.1, d = 19.6, e = 0.836. from figure 5, the 4th degree polynomial fit depicts the mean rainfall over dagoretti. the predicted rainfall seems also to have a unique oscillation pattern of 10 years. a comparison of figures 4 and 5 shows that there is minimum variability in the march-may seasonal rainfall over dagoretti as compared to the october-december seasonal rainfall. this variability may be associated with the systems that influence the short (ond) and the long (mam) rainfalls over kenya such as the inter-tropical convergence zone (itcz), easterly and westerly winds, monsoons and orographic features among others. 52 simulation of decadal precipitation over nairobi in kenya the polynomial equation for the simulated mam rainfall over jkia was of the form 2 3y a bx cx dx ex= + + + + 4 4 4 4 , where a = 654.4, b = 287.3, c = 89.1, d = 11.6, e = 0.523. from figure 6, similar decadal cycle pattern as observed over dagoretti for the same season was repeated. the rainfall peaks slowly decayed over a period of 10 years. the polynomial equation for the simulated ond rainfall over jkia was of the form 2 3y a bx cx dx ex= + + + + , where a = 482.3, b = -238.6, c = 82.2, d = -10.5, e = 0.432. figure 7 depicts the mean rainfall over jkia, and has the same decadal cycle pattern as figure 5. the polynomial equation for the simulated mam rainfall at wilson was 2 3y a bx cx dx ex= + + + + , where a = 843.3, b = 272.3, c = 69.8, d = 8.6, e = 0.392. figure 8 above has the same decadal cycle pattern as figures 6 and 4. by the use of the 4th degree polynomial fit, the prediction of the peak and general rainfall for the march-may season seems to be well simulated over wilson as compared to dagoretti and jkia. the polynomial equation for ond rainfall over wilson was 2 3y a bx cx dx ex= + + + + , where a = 686.7, b = 520.7, c = 186.9, d = 24.5, e = 1.051. figure 9 has the same decadal cycle pattern as figures 7 and 5 above. even though figure 9 does not predict the peaks well, but the general pattern of the mean seasonal rainfall has been captured. 4. conclusions amongst the numerous mathematical functions considered, the fourth degree polynomial was found to be the best fit for rainfall prediction purposes in nairobi, for both the short rains (october-december) and the long rains (march-may). the ten years period cycle of rainfall which was used to generate the 4th degree polynomial function, corresponded to the sunspots cycle of approximately 11.3 years. the ten years period cycle had the least sum of squared prediction errors (sspe), as compared to five and eleven years period cycles for both the long and the short rains. the sum of the march-may rainfall had minimal variability over a ten-year period as compared to 5 and 11 years periods. unlike the march-may rainfall, the sum of october-december rainfall had minimal variability over a 5-year period. the 4th degree polynomial function was found to predict the peaks and the general pattern of march-may seasonal rainfall over nairobi with minimal/acceptable error values. for the october-december season, the 4th degree polynomial function simulated the general pattern of the mean values. from this study, it can be concluded that planning for water use and management over nairobi for the march-may season should be for a ten year period, since we have minimal variability during this period. for october-december season, it is recommended that planning and management of water over nairobi should be for a period of 5 years. 5. references camberlin, p. and philippon n. 2001. the east african march-may rainy season associated atmosphere dynamics and predictability over the 1968-97 period. am. meterol. soc. 15: 1002-1019. 53 muthama nzioka john, et al. chelliah, m. and bell, g.d. 2004. tropical multidecadal and interannual climate variability in the ncep– ncar reanalysis. j. climate, 17: 1777-1803. chen, h.l., and rao, a.r. 2002. testing hydrologic time series for stationarity. j. hydrol. eng. 7: 129–136. christine, l.g., john, d.a and scott, v.o. 1998. mapping monthly precipitation, temperature, and solar radiation for ireland with polynomial regression and a 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analysis and prognosis in meteorology. technical note no. 71. wmo no.178. tp.88. w.m.o. 1966. climate change. technical notes no., 79. wmo no.195 tp.100. received 9 march 2007 accepted 22 september 2008 54 4. conclusions amongst the numerous mathematical functions considered, the microsoft word proofreading-comp040616-1.doc 51-62 squ journal for science, 10 (2005) © 2005 sultan qaboos university 51 conditional fault-diameter of torus networks abderezak touzene and khaled day department of computer science, college of science, sultan qaboos university, p.o. box 36, al-khod 123, sultanate of oman, email: touzene@squ.edu.om, kday@squ.edu.om. torusالقطر المختل المشروط لشبكات عبدالرزاق توزان و خالد داي المربعة المختلة مع افتراض توزيعات مشروطة لنقاط torusنحصل في هذا البحث على قطر شبكات :خالصة نبـرهن أن . الخلل حيث أننا نفترض أن لكل نقطة سليمة في الشبكة ما ال يقل عن نقطة مجاورة سليمة من الخلل المربعة والتي يساوي مقدار الربط فيها أربعة، وتحت الشرط المذكور لتوزيع نقاط الخلل، يمكن أن torusشبكة torusنستنتج من هذا أن القطر المختل المشروط لشبكات . تتحمل إلى خمس نقاط خلل بدون قطع االتصال بينها المربعة يساوي القطـر فـي torusوط لشبكات كما نستنتج أن القطر المختل المشر .المربعة قيمته ستة وحدات التي تحتوي علـى ( المربعة إلى مجموعة الشبكات torusبهذه النتيجة تنضم شبكة . غياب أي خلل زائد وحدتان والتي يساوي القطر المختل المشروط فيها القطـر السـليم زائـد ) star-graph وشبكات hypercubeشبكات راسة نظامين خوارزميين لتوجيه االتصاالت ذات قدرة على تحمل نقاط خلل في نقترح أيضا في هذه الد . وحدتان .باستخدام المسالك غير المتقاطعة التي تم تصميمها في هذا البحثالشبكة وذلك abstract: we obtain the conditional fault-diameter of the square torus interconnection network under the condition of forbidden faulty sets (i.e. assuming that each non-faulty processor has at least one non-faulty neighbor). we show that under this condition, the square torus, whose connectivity is 4, can tolerate up to 5 faulty nodes without becoming disconnected. the conditional node connectivity is, therefore, 6. we also show that the conditional fault-diameter of the square torus is equal to the fault-free diameter plus two. with this result the torus joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault-diameter has been shown to be only two units over the fault-free diameter. two fault-tolerant routing algorithms are discussed based on the proposed vertex disjoint paths construction. keywords: fault-tolerance, forbidden faulty sets, torus, node connectivity, conditional node connectivity, conditional fault-diameter, fault-tolerant routing. abderezak touzene and khaled day 52 1. introduction he node connectivity and the fault diameter have been used as measures of the fault-tolerance of interconnection networks. these measures however do not reflect the real resilience of these networks. it is true that when the number of faulty nodes is equal to the connectivity, the network may become disconnected. however this is very unlikely to happen since only very special fault distributions of these faults cause disconnection. for instance, in the torus, the node-connectivity is 4 and therefore 4 faulty nodes may cause disconnection. however, the network becomes disconnected only when all the 4 faulty nodes are neighbors of the same node which is very improbable. in an attempt to better quantify the fault resilience of a network, the concept of forbidden faulty sets has been introduced esfahanian (1989). the idea is to assume that each node has at least one nonfaulty neighbor. under this forbidden faulty set condition the number of tolerable faulty nodes is significantly larger with a slight increase in the fault diameter. esfahanian (1989) proved that for the binary n-cube, whose connectivity is n, 2n-3 nodes can fail (under the forbidden faulty set condition) without disconnecting the network. latifi (1993) then showed that the corresponding conditional fault diameter increases only by 2. in rouskov et al. (1996) similar results for the star graph network have been established. (latifi and naraghi-pour, 1994) has generalized this idea by assuming that each node has at least k non-faulty neighbors. similar results for the m-ary generalized n-cube network have also been obtained (wu, 1998). in this paper we contribute to the study of the properties of the torus by establishing its conditional node connectivity and its conditional fault-diameter. we show that under the condition of forbidden faulty sets, the torus (whose connectivity is 4) can tolerate up to 5 faulty nodes without becoming disconnected. the corresponding conditional fault-diameter is shown to be equal to the fault-free diameter plus two (i.e. 2+k ). a fault tolerant routing algorithm is discussed based on the construction of node-disjoint paths in the presence of faults under the forbidden faulty sets condition. the rest of the paper is organized as follows. in section 2 we introduce the notations and include some preliminaries. section 3 establishes the conditional faulty diameter of the torus. in section 4 we discuss how a fault tolerant routing can be derived and section 5 concludes the paper. 2. notations and preliminaries definition 1: the node-connectivity c(g) (or point-connectivity) of a graph g is the minimum number of nodes of g whose removal results in a disconnected or trivial graph. for any two nodes in the torus there are four node-disjoint paths connecting them (day and alayyoub, 1997), therefore c(torus) = 4. we now define the conditional node connectivity. definition 2: the conditional node connectivity cc(g) of a graph g is the minimum number of nodes of g whose removal results in a disconnected or trivial graph, provided that each of the remaining nodes has at least one adjacent node in g that is not removed. we will obtain the conditional node connectivity of the torus as a consequence of obtaining its conditional fault-diameter. definition 3: the square torus (k-torus) is a wrap-around mesh which consists of k rows and k columns. each row and each column consists of a cycle of k nodes. any two nodes are connected by two paths one is called the shortest path on the cycle and the other is called the longest path on the cycle. in what follows we will adopt the following notations: if we consider two nodes x and y in the same column cm ( xm, and y m), m=0..k-1, we denote by xs m, ys m the respective neighbors of x and y located on the shortest path between x and y in cm. we denote by xl m, yl m the respective neighbors of x and y located on the longest path between x and y in cm. we use similar notation for the second t conditional fault-diameter of torus networks 53 node in the shortest path xss m, yss m . and xll m, yll m are the second nodes in the longest path between x and y in cm. any node xm in cm has 4 neighbors: xs m, xl m, xm+1, xm-1. see figure 1. 1−mc mc 1+mc x ll xl x x s x ss y ss y s y y l y ll figure 1. x and y in the same cycle mc . 3. conditional fault-diameter of the k-torus the fault-diameter of an interconnection network is the maximum distance between any two nodes in the presence of a number of faults equal to the connectivity of the network minus one. definition 4: the fault-diameter fd(g) of a graph g is the maximum distance between any two nodes of g in the presence of at most c(g)-1 faulty nodes. definition 5: the conditional node diameter cfd(g) of a graph g is the maximum distance between any two nodes of g in the presence of at most c(g)-1 faulty nodes, provided that each of the nonfaulty nodes has at least one non-faulty adjacent node in g. we now obtain the conditional fault-diameter of the k-torus. theorem 1. the conditional fault diameter of the k-torus under the forbidden sets assumption is k+2. proof: consider two nodes x and y at distance d(x, y)=l in a k-torus with at most 5 faulty nodes. in the first case, we consider that x and y belong to the same column c0. the case where x and y belong to a same row is symmetric and can be treated similarly. in the second case we consider that x and y are located in different columns and different rows of the torus. case 1. if x and y are on the same columns (say c0 ) and similarly for x and y on the same row. case 1.1. if all faults are either outside the target cycle c0 or are located along the longest path between x and y, then the shortest path between x and y is fault-free of length l ≤ k+2 case 1.2. if there is only one fault in the target cycle and this fault is located on the shortest path between x and y, then the longest path between x and y is fault-free of length k-l ≤ k+2. 1.3. if the number of faults in the target cycle is 4 or 5, then there are two node-disjoint paths between x and y: • b1: x, x1, shortest path in c1 to reach y1, y. abderezak touzene and khaled day 54 • b2: x, xk-1, shortest path in ck-1 to reach yk-1, y. at least one of these two paths is fault-free. the length of these paths is l+2 ≤ k+2. see figure 2 (a). case 1.4. the number of faults in c0 is 2 or 3: we discuss several cases based on the number of faults which are neighbors of x and y. case 1.4.1. if these faults are located on the shortest path between x and y, then we have the same conclusion as in case 1.2. case 1.4.2. all faults are not neighbors of x or y. the following four paths have no common nodes other than x, y and their neighbors: • p1: x, xs0, xs1, shortest path in c1 to reach ys1, ys, y. • p2: x, xs0, xsk-1, shortest path in ck-1 to reach ysk-1, ys, y. • p3: x, xl0, xl1, longest path in c1 to reach yl1, yl, y. • p4: x, xl0, xlk-1, longest path in ck-1 to reach ylk-1, yl, y. if the number of faults in c0 is 3, then at least two of these paths are fault-free. if the number of faults in c0 is 2, then at least one of these paths is fault-free. the length of the above paths is less than k+1 < k+2. see figure 2 (b). case 1.4.3. one fault is neighbor of y, the second and the third (if 3 faults) are not a neighbor of x: this case can be solved using slight modification of the paths in case 1.4.2 as follows: if the faulty neighbor of y is ys 0: we use p3, p4 and • m1: x, xs0, xs1, shortest path in c1 to reach y1, y (path length l+2 ≤ k+2). • m2: x, xs0, xsk-1, shortest path in ck-1 to reach yk-1, y (path length l+2 ≤ k+2). if the faulty neighbor of y is yl 0 , we use p1, p2 and • m3: x, xl0, xl1, longest path in c1 to reach yl1, y1, y (path length k-l+2 ≤ k+2) • m4: x, xl0, xlk-1, longest path in ck-1 to reach ylk-1, y k-1, y (path length k-l+2 k+2). see figure 2 (c). the symmetric case where the fault is neighbor of x is similar. case 1.4.4. two faults are neighbors of y (ys 0 and yl 0), the third fault, if any, is not neighbor of x. there are four paths: m1, m2, and • s1: x, x1, x2, shortest path in c2 to reach y2, y1, y (path length l+4 ≤ k+2). • s2: x, xk-1, xk-2, shortest path in ck-2 to reach yk-2, yk-1, y (path length l+4 ≤ k+2). note that y1 and yk-1 cannot be both faulty at the same time (forbidden sets assumption). if both are not faulty, then one of these four paths will be fault-free. assume now that one of them is faulty (say yk-1). we end up only with m1, s1 (a minimum of three faults already consumed). an additional path is m3. in the presence of a maximum of 2 other faults, one among the three paths is fault-free of length less than or equal to k-l+2 < k+2. see figure 2 and 3. now we consider a third fault in c0, which is a neighbor of x. if the third faulty node is xl 0 , then we make use of the same paths even without the need to m3. if the third faulty node is xs 0, then we use the four paths: b1, b2, m3 and m4. since y1 and yk-1 are common nodes to the four paths, the same distribution of faults on y1 and yk-1 leads to the same conclusions. the case where both faults are neighbors of x only is a symmetric case and can be solved similarly. case 1.4.5. one fault is neighbor of y and the second is neighbor of x: if the faulty neighbor of x is xl 0 we will use the two paths p1, p2 (if ys 0 is fault-free), or m1 and m2 (if ys 0 is faulty). the two other paths are: • m5: x, x1, longest path in c1 to reach yl1, y1, y (path length k-l+2 ≤ k+2), • m6: x, xk-1, longest path in ck-1 to reach ylk-1, y k-1, y (path length k-l+2 ≤ k+2), if yl0 is faulty (ys 0 is fault-free), or • m7: x, x1, longest path in c1 to reach yl1, yl, y (path length l+2 ≤ k+2), conditional fault-diameter of torus networks 55 1−kc 0c 1c 1−kc 0c 1c 1−kc 0c 1c p4 p3 xl 0 m4 m3 xl 0 xl 0 x x k-1 x x 1 x xs 0 xs 0 xs 0 p2 p1 b2 b1 m2 m1 y s0 ys 0 ys 0 y y k-1 y y 1 y yl 0 yl 0 yl 0 (b) (a) (c) figure 2. paths for cases 1.3, 1.4.2 and 1.4.3. 1−kc 0c 1c 1−kc 0c 1c 2−kc 1−kc 0c 1c 2c m6 m5 m8 m7 x x x s2 s1 y y y figure 3. paths for cases 1.4.3, 1.4.4 and 1.4.5. • m8: x, xk-1, longest path in ck-1 to reach ylk-1, yl, y (path length l+2 ≤ k+2), if yl0 is fault free (ys 0 is faulty). now if the neighbor of x, xs 0 is faulty: a similar technique is used to construct four node-disjoint paths (the common nodes are fault-free) between x and y. these paths will depend on which neighbor of y will be faulty (ys 0 or yl 0 ). abderezak touzene and khaled day 56 2−kc 1−kc 0c 1c 2c 1−kc 0c 1c x x l2 l1 b2 b1 l4 l3 y y l6 l5 l6 l5 (a) (b) figure 4. paths for case 1.4.6. case 1.4.6. the number of faults in c0 is two and both faults are neighbors of x and y at the same time: in this case y0s , y 0 l are faulty and x 0 l = y 0 l , (l=2). the case x 0 s = y 0 s is symmetric and can be solved similarly. we can construct 6 paths as follows: • l1: x, x0s, shortest path in c0 to reach y0ss, yss1, ys1, y1, y (path length l+2 ≤ k+2). • l2: x, x0s, shortest path in c0 to reach y0ss, yssk-1, ysk-1, yk-1, y (path length l+2 ≤ k+2). • l3: x, x0s, xs1, xs2, shortest path in c2 to reach y2,y1, y (path length l+4 ≤ k+2). • l4: x, x0s, xsk-1, xsk-2, shortest path in ck-2 to reach yk-2,yk-1, y (path length l+4 ≤ k+2). • l5: x, x1, yl1, y1, y (path length 4). • l6: x, xk-1, ylk-1, yk-1, y (path length 4). note that the nodes y1 and yk-1 are common nodes to the six paths, but fortunately they cannot be faulty at the same time (forbidden sets assumption). see figure 4 (a). if both are not faulty, then in presence of 3 faults outside c0, three among the six above paths will be fault-free. if we assume that yk-1 is faulty and y1 is fault-free, then at least one of the three paths l1, l3, l5 will be fault-free. if the node yk-1 is not faulty and y1 is faulty, then at least one of the three paths l2, l4, l6 will be fault-free. the length of the above paths is less than or equal to k+2. now if we consider that there is a third faulty node in c0, which is xs 0. we make use of the following paths: b1, b2 and l5, l6. see figure 4(b). note that these paths have some common nodes: l5 and b1 have two nodes in common, which are x1 and y1. l6 and b2 have two nodes in common, which are xk-1 and yk-1. in presence of two faults outside c0, if all these four nodes are not faulty, then there are at least two fault-free paths between x and y. under the forbidden sets assumption, nodes x1 and xk-1 cannot be both faulty in the same time. and nodes y1 and yk-1 cannot be both faulty in the same time. if both nodes x1 and y1 are faulty, then b2 and l6 will be fault-free. if both nodes xk-1 and yk-1 are faulty, then b1 and l5 will be fault-free. if yk-1 and x1 are faulty, then an alternative path will be x, xk-1 in b2, xs k-1 in b2, xss k-1 in b2 , xss 0 in c 0, xss 1 in b1, continue on b1 to reach y. and similarly for the symmetric case (y1 and xk-1 are faulty), jump from b1 to b2 from the node xss 1 in b1 to the node xss 0 , xss k-1 in b2, then continue on b2. the length of these paths is less than or equal to k+2. case 2. nodes x and y do not belong to the same column or the same row. without loss of generality, we assume that x =x0 belongs to c0, and y=ym belongs to cm. let us consider the six-node disjoint paths connecting the columns c0 to cm. these paths can be divided into two groups: conditional fault-diameter of torus networks 57 1−kc 0c cm-2 cm-1 cm cm+1 1−kc 0c cm-3 cm-2 cm-1 cm cm+1 p* p* x x b1 a5 a4 a3 a2 a1 short_rc y y figure 5. paths for cases 2.3 and 2.4.1. group 1 • xl0 ,xl1, xl2 , shortest path in this row to reach xlm-1 , xlm . • x, x1 , x2 , shortest path in this row to reach xm-1 , xm . group 2 • xs0, xs1 , xs2 , shortest path in this row to reach xsm-1 , xsm . • yl0, yl1 , yl2 , shortest path in this row to reach ylm-1 , ylm . • y0, y1 , y2 , shortest path in this row to reach ym-1 , ym . • ys0, ys1 , ys2 , shortest path in this row to reach ysm-1 , ysm . in presence of five faults, at least one of the above six paths is fault-free. if the fault-free path is in group 1, then we will construct paths starting from x going to y. otherwise, we construct paths starting from y going to x. in what follows, to simplify the analysis, we will always consider that the fault-free path is from group 1, and we denote this path p* . the other case is similar (symmetric). case 2.1. the column cm is fault-free: there is at least one fault-free path from x to y, which starts at x, p* to reach x* m , shortest path in c m to reach y (x* m represents xs m, x m or xl m depending on which of the three paths of group 1 corresponds to p* ). the length of the constructed fault-free path between x and y is at most l+2 ≤ k+2. case 2.2. the column cm contains 5 faults: the following path named short_rc (rc stands for rows then columns): x, xs 0 , shortest path in c 0 to reach y0, shortest path in this row to reach ym-1 , y. this path is fault-free of length l ≤ k+2. case 2.3. the number of faults in cm is 4. we use the path short_rc, if it is fault-free. otherwise short_rc contains the fifth fault and there are no more faults outside c m. an alternative way is to start from x, p* to reach x* m , x* m+1 , shortest path on cm+1 to reach ym+1 , y. the length of the constructed fault-free path using b1 is l+4. see figure 5. remark 1. if l ≤ k-2, then the length of the constructed path is less than or equal to k+2. otherwise, (l= k-1, or k), we construct another path as follows: x, xk-1, xk-2, longest path on this row to reach xm+1 , shortest path in cm+1 to reach y m+1, y. it is simple to see that the length of this fault-free path in all cases (l > k-2) is less than or equal to k+2. abderezak touzene and khaled day 58 case 2.4. the number of faults in cm is 1 (4 faults outside). case 2.4.1. the nodes ys m , yl m are both not faulty: we consider the 5 following paths: • a1: x, p* to reach x* m, x* m+1, shortest path in cm+1 to reach ym+1, y (path length l+4). • a2: x, p* to reach x* m-1, shortest path in cm-1 to reach ysm-1, ysm, y (path length l+2). • a3: x, p* to reach x* m-2, shortest path in cm-2 to reach ym-2, ym-1 , y (path length l+2). • a4: x, p* to reach x* m-3, shortest path in cm-3 to reach ylm-3, ylm-2,ylm-1, ylm, y (path length l+4). • a5: x, xs 0 , shortest path in c0 to reach yll0, shortest path in this row to reach yllm,ylm , y (path length l+4 ). these five paths are node-disjoint or the common nodes are fault-free. at least one among the five path will be fault-free. if the fault-free path is of length l+4, then if l ≤ k-2, the considered path will have a length ≤ k+2. otherwise, we construct an alternative path using a similar technique as described in remark 1. see figure 5. remark 2. the existence of the paths a4, a3, a2 is subject to the condition: the column distance c between c0 and cm is greater or equal to 4. otherwise, we consider the extreme case where no one of these paths exists (c=1). since there is only one fault in cm , if the fault belongs to the longest path between xm and y in cm, then the path x, xm , shortest path in cm to reach y, will be fault-free. otherwise, the longest path between xm and y in cm will be fault-free and we construct five paths as follows: • 1: x, x0l, pl to reach xl m, xl m+1, shortest path in cm+1 to reach ysm+1, ysm, y. • 2: x, x0l, pl to reach xl m, longest path in cm to reach y. • 3: x, x 0l, pl to reach xl m, xll m, xll m+1, longest path in cm+1 to reach ym+1, y. • 4: x, x0s, shortest path in c0 to reach y0, shortest path in this row to reach y. • 5: x, x0l, longest path in c0 to reach yl0, shortest path in this row to reach y. these five paths are node disjoint or the common nodes are fault-free. if we denote by r the row distance between x and y , the longest path will be of length k-r+1 ≤ k+2. see figure 6. case 2.4.2. node ys m is faulty. the case where yl m is faulty is trivial, because the shortest path between x* m and y will be fault-free and of maximum length of k+2. we construct the following four paths: • c1: x, p* to reach x* m, x* m+1, shortest path in cm+1 to reach ym+1, y (path length l+4). • c2: x, p* to reach x* m-1, shortest path in cm-1 to reach ym-1, y (path length l+2 ). • c3: x, p* to reach x* m-2, shortest path in cm-2 to reach ylm-2, ylm-1, ylm, y (path length l+4). • c4: x, xs0, shortest path in c0 to reach yll0 , shortest path in this row to reach yllm, ylm, y (path length l+4). if any one of the above paths is fault-free, the problem is solved. otherwise, all the faults are consumed. we focus on the fault of path c4: if the fault belongs to the shortest path within c0 , an alternative path (disjoint with c1, c2, c3) will be x, x1, shortest path in c 1 to reach yll 1 , shortest path in this row to reach yll m, yl m, y (path length ≤ l+4 ). if the faulty node is not in c0 , an alternative path will be : c4’: x, xs, shortest path in c 0 to reach yll 0 , ylll 0 (successor of yll 0 ), shortest path in this row to reach ylll m, yll m, yl m, y (path length l+6). if l ≤ k-4, this path is fault-free of length ≤ k+2. see figure 7 (a). remark 3. if l > k-4, we need to construct another path using longest path which are not much longer than the shortest paths (see remark 1 for l= k or k-s). let us decompose l= r+c, where r (respectively c) is the row distance (respectively the column distance) between x and y. if we focus on the case l= k-3, there are two cases: • r= / 2k⎢ ⎥⎣ ⎦ and c= / 2 3k⎢ ⎥ −⎣ ⎦ , the alternative path will be pr: x, x l 0 , longest path in c0 to reach ylll 0, shortest path in this row to reach ylll m, yll m, yl m, y. (path length=k-2 < k+2). if conditional fault-diameter of torus networks 59 c= / 2k⎢ ⎥⎣ ⎦ and r= / 2 3k −⎢ ⎥⎣ ⎦ , the alternative path will be pc: x, x k-1, longest path that row to reach xm+2, shortest path in cm+2 to reach yl m+2, yl m+1, yl m, y. (path length=k-2 < k+2) 1−kc 0c cm cm+1 x 1 4 y 5 2 3 figure 6. distance between c0 and cm is 1 . • r= / 2 1k⎢ ⎥ −⎣ ⎦ and c= / 2 2k⎢ ⎥ −⎣ ⎦ , the alternative path is pr (path length= k-1 < k+2). pc will be used for the reversed case. a similar technique leads to the construction of a fault-free path between x and y, of length ≤ k+2, when l= k-2. case 2.5. the number of faults in cm is 2 or 3: case 2.5.1. the nodes ys m , yl m are both not faulty or only one of them is faulty: similar to 2.4. case 2.5.2. the nodes ys m , yl m are both faulty: the nodes ym-1 , ym+1 could not be both faulty at the same time (forbidden sets assumption). case 2.5.2.1. if the node ym-1 is not faulty. we consider the paths c1, c2, a3 and • d1 : x, xs , shortest path in c0 to reach yl0 , shortest path in this row to reach ylm-1, ym-1, y (path length l+2 ). note that the three paths a3, c2 , d1 have only one common node (ym-1). if there are 3 faults in cm, then two among the four above paths will be fault-free. if there are only two faults in cm, then only one among the four above paths will be fault-free. case 2.5.2.2. if the node ym+1 is fault-free (ym-1 is faulty), we consider the paths c1 and • d2: x, xs, shortest path in c0 to reach yll0 , shortest path in this row to reach yllm+1, ylm+1, ym+1, y. (path length l+6 ) if c1 is fault-free, the problem is solved. otherwise, we use the following path: • d3: is a modification of the path c1, bridging the faulty node, using the nodes of cm+2, then back to c1 (path length l+6 ). in the presence of three faults in cm, d2 and d3 will be fault-free. if there are only two faults in cm, then only d2 or d3 will be fault-free. the longest path (l+6) will be acceptable when l ≤ k-4. otherwise, an alternative path of length less than k+2 will be derived using the same technique as in remark 3. see figure 7 (b). abderezak touzene and khaled day 60 1−kc 0c cm-2 cm-1 cm cm+1 1−kc 0c cm-2 cm-1 cm cm+1 p* p* x x c4 c3 c2 c1 d3 y y d1 d2 c4’ (a) (b) figure 7. paths for cases 2.4.2 and 2.5. 4. fault-tolerant routing we now illustrate the usefulness of the fault-free paths constructions of the previous section by describing two fault-tolerant routing algorithms that make use of these paths. fault-tolerant routing has drawn a lot of attention in the literature (suh et al. 2000; chen et al. 2001; ho et al. 2002; wu 2003). different ways of achieving fault-tolerant routing have been proposed. some methods require extra hardware resources to route packets around faulty components while others simply bypass faulty components, as well as some healthy components, to maintain network regularity such as in (ibm 2002). another technique is based on reconfiguring the routing tables in the case of failure, adapting them to the new topology after the failure such as in casado et al. (2001), pinkston et al. (2003) and lysne et al. (2003). a more recently proposed methodology uses intermediate nodes (gomez et al. 2004). the methodology is valid for any network topology. in nordbotten et al. (2004), the idea of using intermediate nodes is extended to using multiple intermediate nodes for some paths. in what follows, we describe two fault-tolerant routing algorithms for the square torus. it has been shown in the previous section that for any two nodes x and y at distance l, we are able to construct between these two nodes a fault-free path of length at most l+6 ≤ k+2 (assuming at most five faulty nodes satisfying the forbidden faulty set condition). we propose the following two faulttolerant routing algorithms: 4.1 parallel routing algorithm parallel routing algorithm has been used to design fault tolerant routing for the star graph in rouskov et al. (1996). in our case, the basic idea is first to identify the case (see section 3) according to the location of x and y in the torus and then apply the described construction of the parallel paths between x and y. the routing process can send a message in parallel on the constructed vertexdisjoint paths to guarantee delivery because at least one of these paths is not faulty. this routing process is known as parallel routing algorithm. it consists of generating all the possible paths of interesting length between the source and the destination nodes. the generation of the routes results conditional fault-diameter of torus networks 61 from the union of all the paths generated for each case described in the previous section. as an example, if the source node x and the destination node y do not belong to the same row and not to the same column, all the paths of case two will be generated. the generation of all paths of the case is necessary because the distribution of the faults is not known. each fault distribution may correspond to a sub-case of the given case and thus to a set of paths to cover the corresponding fault distribution. the disadvantage of this routing algorithm is the communication overhead due to the presence of multiple copies of the same message in the network. if a wormhole routing model is used, this algorithm may increase link contention problem and thus the communication delay. 4.2 single path fault-tolerant routing algorithm it is possible to achieve lower cost fault-tolerant routing using a single routing path but at the expense of additional failure detection and routing path reconfiguration mechanisms. a similar approach has been used in day and al-ayyoub (2001) for the star graph. we can associate with each source node x and destination node y, at any time, only one path among all the possible paths generated in the cases of the previous section. this path is called the active routing path. in our routing algorithm the choice of the active routing path starts by simply selecting the shortest path among the generated ones (cases) to ensure high communication efficiency. in fact, this routing approach requires link failure detection mechanisms and a mechanism for switching to a new active routing path for a given source node when a link failure is detected on its current active routing path. first we make the following failure assumptions: 1. lower level fault detection and diagnosis mechanisms exist. each node knows exactly the failure status of all its adjacent links. each node's information about the status of its adjacent links is updated dynamically via these fault detection and diagnosis mechanisms. 2. link failure and repairs may happen at any time, but the total number of faulty links does not exceed 5 under forbidden faulty set condition at any time. 3. we also assume that the delay for detecting an adjacent link failure is negligible. a routing initiated at a source node x continues to follow the edges of its current active routing path (arp), until a link failure is detected. the node that has detected the failure will report it to the source node x using the arp backward. the source node will switch to another arp chosen from the remaining possible paths (the shortest among them) and then resends the message using the new arp. this approach guarantees message delivery; in the worst case it may use all the possible arps (at least one among them is fault-free). this approach is efficient because it uses shortest paths as much as possible and it reduces considerable link contentions under heavy load network condition. 5. conclusion we have contributed in this paper to the study of the fault-tolerance of the square torus interconnection network by establishing its conditional fault-diameter under the condition of forbidden faulty sets (i.e., assuming that each non-faulty processor has at least one non-faulty neighbor). we have shown that under this condition the k-torus, whose connectivity is 4, can tolerate up to 5 faulty nodes without becoming disconnected. the conditional node connectivity in this case is therefore 6. we have also shown that the conditional fault-diameter of the k-torus is 2k + . with this result the torus joins a group of interconnection networks (including the hypercube and the star-graph) whose conditional fault-diameter has been shown to be only two units over the fault-free diameter. we have also illustrated the usefulness of our results by describing two possible fault tolerant routing algorithms for the torus under the forbidden faulty set condition. abderezak touzene and khaled day 62 6. references casado, r., bermudez, a., duato, j., quiles, f.j., and sanchez, j.l. 2001. a protocol for deadlock-free dynamic reconfiguration in high speed local area networks, ieee transactions on parallel and distributed systems, 12(2): 115-132. chen, c.l., and chiu, g.m. 2001. a fault-tolerant routing scheme for meshes with non convex faults," ieee transactions on parallel and distributed systems, 12(5): 467-475. day, k., and al-ayyoub, a.e. 1997. fault diameter of k-ary n-cube networks, ieee trans. on parallel and distributed systems, 8(9): 903-907. day, k., and al-ayyoub, a.e. 2001. adaptive fault-tolerant routing in star networks, journal of interconnection networks, 2(2): 213-231. esfahanian, a.h. 1989. generalized measures of fault tolerance with application to n-cube networks, ieee transactions on computers, 38(11): 1586-1591. gomez, m., duato, j., flich, j., lopez, p., robles, a., nordbotten, n., lysne, o., and skeie, t. 2004. an efficient fault-tolerant routing methodology for meshes and tori, computer architecture letters, 3, may. ho, c.t., and stockmeyer, l. 2002. a new approach to fault-tolerant wormhole routing for mesh-connected parallel computers, proceedings of 16th international parallel and distributed processing symposium, april. ibm bg/l team, an overview of bluegene/l supercomputer, acm supercomputing conference, 2002. latifi, s. 1993. combinatorial analysis of fault-diameter of the n-cube, ieee transactions on computers, 42(1): 27-33. latifi, s., hegde, m., and naraghi-pour, m. 1994. conditional connectivity measures for large multiprocessor systems, ieee trans. on computers, 43(2): 218-222. lysne, o., pinkston, t., and duato, j. 2003. a methodology for developing dynamic network reconfiguration processes, proceedings of the international conference on parallel processing, pp. 77-86. nordbotten, n., gomez, m., flich, j., lopez, p., robles, a., skeie, t., lysne, o., and dusto, j. 2004. a fully adaptive fault-tolerant routing methodology based on intermediate nodes, proceedings of the ifip international conference on network and parallel computing, pp. 341-356. pinkston, t., pang, r., and duato, j. 2003. deadlock-free dynamic reconfiguration schemes for increased network dependability, ieee transactions on parallel and distributed systems, vol. 14(8): 780-794. rouskov, y., latifi, s., and srimani, p.k. 1996. conditional fault diameter of star graph networks, journal of parallel and distributed computing, 33: 91-97. suh, y., dao, b., duato, j., and yalamanchili, s. 2000. software-based rerouting for fault-tolerant pipelined communication, ieee transactions on parallel and distributed systems, 11(3): 193-211. wu, j. 1998. fault tolerance measures for m-ary n-dimensional hypercube based on forbidden faulty sets, ieee transactions on computers, 47(8): 888-983. wu, j. 2003. fault-tolerant and deadlock-free routing in 2d meshes based on odd-even turn model, ieee transactions on computers, 52, no. 9, september. received 16 june 2004 accepted 10 july 2005 squ journal for science, 2020, 25(1), 61-77 doi:10.24200/squjs.vol25iss1pp61-77 sultan qaboos university 61 behavior of small variable mass particle in electromagnetic copenhagen problem abdullah a. ansari international center for advanced interdisciplinary research (icair), sangam vihar, new delhi, india. email: icairndin@gmail.com. abstract: the paper presents the behavior of the motion properties of the variable mass test particle (third body), moving under the influence of the two equal primaries having electromagnetic dipoles. these primaries move on the same circular path around their common center of mass in the same plane. we have determined the equations of motion of the test particle whose mass varies according to jean's law. using the system of equations of motion we have evaluated the locations of equilibrium points, their movements and basins of the attracting domain. finally, we examine the stability of these equilibrium points, all of which are unstable. keywords: variable mass; electromagnetic dipoles; copenhagen problem; attracting domain. سلوك جسيم ذو كتلة خاضعة لتغيرات صغيرة في مشكلة كوبنهاجن الكهرومغناطيسية عبدالجبار أنصاريعبدهللا تأثير جسمان اوليان متساويان لهما قطبان مغنتسيان. )الجسم الثالث( تحت حركة جسيم ذو كتلة متغيرة الورقة العلمية سلوك خصائص هذه تقدم ملخص:ال ة الجسيم حيث الجسمان األوليان يتحركان على نفس المصار الدائري مركزه مركزهما الكتلي المشترك المتواجد في نفس المصتح. قمنا بإتقييم معادالت حرك ا بحساب أماكن نقاط التوازن ، حركتهما و أحواض مجاالت الجذابة. في نفرض ان كتلته تتغير حسب قانون جان . باستعمال نضام معادالت الحركة، قمن آخر العمل قمنا بالتترق لمسألة إستقرار نقاط التوازن و وجدنا أن كلها غير مستقرة. كهرومغناطيسي، مسألة كوبنهاق، مجال ذو جاذبية. كتلة متغيرة، ثنائي الألقطابتاحية: مفالكلمات ال 1. introduction elestial mechanics is a part of applied mathematics; basically it is the study of the motion properties of satellites under the influence of celestial bodies. the motion of these satellites or spacecraft is affected by the celestial bodies in many ways, such as by the different shapes of the bodies (i.e. heterogeneous body, homogeneous body, irregular triaxial bodies, oblate body, finite straight segments, cylindrical shape, etc.), radiation pressure, resonances, magnetic dipoles, charged bodies, yarkovskii effects, the albedo effect, variable mass effects, etc. for more details, see [1] and [2]. an artificial body (satellite or spacecraft) is also perturbed by the electromagnetic dipoles which are studied by [3-5]. [3] presented the motion properties of charged particles as equilibrium points and their stability in the field of two magnetic dipoles. [4] has investigated the three-dimensional equilibrium points in a magnetic-binary system and then, by using the method of characteristic exponent, examined their stability. in continuation of the work of [4], [5] studied the basins of attraction in the electromagnetic copenhagen problem. the copenhagen problem where two primary bodies of equal mass are moving on the same circular path in the same plane is also commonly studied in celestial mechanics. [6] used the methods of chaotic scattering to investigate this problem. [7] used studied the asymptotic orbits and terminations of families in the copenhagen restricted threebody problem. [8] studied the copenhagen problem with quasi-homogeneous potential or manev-type potential and illustrated the equilibrium locations and the regions of permitted motion. [9] derived the translational-rotational equations of motion and investigated the stability of its equilibrium points. [10] have investigated equilibrium positions as well as the basins of attraction in the copenhagen restricted three-body problem numerically. c mailto:icairndin@gmail.com ansari, a.a. 62 after careful study of the literature presented, we became interested in studying and extending this topic with variable mass. variable mass is an interesting topic in celestial mechanics and dynamical astronomy, which is widely studied in the restricted problem (two-body, three-body, four-body and five-body) [11-21]. however, no article yet exists in the literature addressing the combination of electromagnetic dipole and variable mass. this paper is organized as follows. the literature review is presented in section 1. the equations of motion are presented in section 2 while section 3 contains the investigation of equilibrium points and basins of attracting domain. the stability of these equilibrium points are examined in section 4. finally the manuscript completes with a conclusion in section 5. figure 1. geometric configuration of the electromagnetic copenhagen problem 2. equations of motion the well-known copenhagen problem where two bodies of equal masses m1 and m2 both are taken as point masses which are moving in circular orbits on the same circular path around their common center of mass. in this paper two bodies are also taken as electromagnetic dipoles with magnetic moments mi (i = 1, 2). now we are interested to determine the equations of motion of the third variable mass (m) body of charge q (figure 1) with dimensionless variables in the synodic coordinate system where the variation of mass of the test particle originates from one point and has zero momenta ([17] and [3]) which reveals as: �̇� 𝑚 (�̇� −𝜔 𝑦)+( �̈� −𝑓1�̇� + 𝑔1�̇�) = 𝜔 2𝑥 + 𝑞 𝜔 𝑚 𝑐 (𝑥 𝜕𝐴2 𝜕𝑥 −𝑦 𝜕𝐴1 𝜕𝑥 +𝐴2), �̇� 𝑚 (�̇� +𝜔 𝑥)+( �̈� −ℎ1�̇� + 𝑓1�̇�) = 𝜔 2𝑦 + 𝑞 𝜔 𝑚 𝑐 (𝑥 𝜕𝐴2 𝜕𝑦 −𝑦 𝜕𝐴1 𝜕𝑦 −𝐴1), �̇� 𝑚 �̇� +( �̈� −𝑔1�̇� + ℎ1�̇�) = 𝑞 𝜔 𝑚 𝑐 (𝑥𝜕𝐴2 𝜕𝑧 −𝑦𝜕𝐴1 𝜕𝑧 ). (1) where 𝑓1 = (2 𝜔 +�̂� 𝐶𝑢𝑟𝑙 𝐴) 𝑞 𝑚 𝑐 , 𝑔1 = (𝑗̂ 𝐶𝑢𝑟𝑙 𝐴) 𝑞 𝑚 𝑐 , ℎ1 = (𝑖̂ 𝐶𝑢𝑟𝑙 𝐴) 𝑞 𝑚 𝑐 , (2) variable mass in electromagnetic copenhagen problem 63 with 𝐴 = (𝐴1,𝐴2,𝐴3) = ( �̅�1 ×�̅�1 𝑟1 3 + �̅�2 ×�̅�2 𝑟2 3 ) , �̅�1 = (𝑥 −0.5,𝑦,𝑧), �̅�2 = (𝑥 +0.5,𝑦,𝑧), �̅�1 = (0,0,1), �̅�2 = (0,0,𝜆), 𝐴1 = (− 𝑦 𝑟1 3 − 𝜆 𝑦 𝑟2 3 ), 𝐴2 = ( 𝑥 −0.5 𝑟1 3 + 𝜆(𝑥 +0.5) 𝑟2 3 ), 𝐴3 = 0, and also ω is the mean motion of the system, λ and c are constants. we choose the unit of time and charge of dipoles such that ω = 1 and (q/mc) = 1, hence equations (1, 2) become as �̇� 𝑚 (�̇� −𝑦)+( �̈� −𝑓2�̇� + 𝑔2�̇�) = ω𝑥, �̇� 𝑚 (�̇� + 𝑥)+( �̈� −ℎ2�̇� + 𝑓2�̇�) = ω𝑦, �̇� 𝑚 �̇� +( �̈� −𝑔2�̇� + ℎ2�̇�) = ω𝑧, (3) with ω = 1 2 (𝑥2 +𝑦2)+(𝑥𝐴2 −𝑦𝐴1) (4) 𝑓2 = (2 + �̂� 𝐶𝑢𝑟𝑙 𝐴) , 𝑔2 = (𝑗̂ 𝐶𝑢𝑟𝑙 𝐴), ℎ2 = (𝑖̂ 𝐶𝑢𝑟𝑙 𝐴), (5) due to variation of the mass of the infinitesimal body, we cannot study the properties of this body directly. therefore we will use jean's law, 𝑑𝑚 𝑑𝑡 = −𝜆1𝑚 𝜆2, (6) where λ1 is constant coefficient and λ2 is within the limits 0.4 ≤ λ2 ≤ 4.4, for the stars of the main sequence. while for the rocket λ2 = 1, therefore the mass of the rocket m = m0 e -λ 1 t varies exponentially where m0 is the mass of the test particle at time t = 0. we will use the meshcherskii space time transformations to preserve the dimension of the space and time 𝑥 = 𝜆3 −1/2 𝛼, 𝑦 = 𝜆3 −1/2 𝛽, 𝑧 = 𝜆3 −1/2 𝛾, 𝑑𝑡 = 𝑑𝜏 (7) where λ3 = m/m0, now we can express the components of velocity and acceleration as �̇� = 𝜆3 −1/2 (�̇� + 1 2 𝜆1𝛼), �̇� = 𝜆3 −1/2 (�̇� + 1 2 𝜆1𝛽), �̇� = 𝜆3 −1/2 (�̇� + 1 2 𝜆1𝛾), (8) �̈� = 𝜆3 −1/2 (�̈� + 𝜆1�̇� + 1 4 𝜆1 2𝛼), �̈� = 𝜆3 −1/2 (�̈� +𝜆1�̇� + 1 4 𝜆1 2𝛽), �̈� = 𝜆3 −1/2 (�̈� + 𝜆1�̇� + 1 4 𝜆1 2𝛾), (9) ansari, a.a. 64 after using equations (6, 7, 8 and 9) in equation (3), we get ( �̈� − 𝑓3�̇� + 𝑔3�̇�) = v𝛼 +𝑉1, ( �̈� − ℎ3�̇� + 𝑓3�̇�) = v𝛽 + 𝑉2, ( �̈� − 𝑔3�̇� + ℎ3�̇�) = v𝛾 + 𝑉3, (10) where, v = 1 2 (𝛼2 + 𝛽2)+ 𝜆1 2 8 (𝛼2 + 𝛽2 + 𝛾2)+ 𝜆3 −1/2 (𝛼𝐵2 − 𝛽𝐵1) (11) 𝑉1 = 𝜆3 3/2 𝜆1 2 (𝛽 𝜕𝐵2 𝜕𝛼 − 𝛽 𝜕𝐵1 𝜕𝛽 − 𝛾 𝜕𝐵1 𝜕𝛾 ), 𝑉2 = 𝜆3 3/2 𝜆1 2 (−𝛼 𝜕𝐵2 𝜕𝛼 +𝛼 𝜕𝐵1 𝜕𝛽 − 𝛾 𝜕𝐵2 𝜕𝛾 ), 𝑉3 = 𝜆3 3/2 𝜆1 2 (𝛼 𝜕𝐵1 𝜕𝛾 + 𝛽 𝜕𝐵2 𝜕𝛾 ), 𝑓3 = 𝜆3 3/2 (2 𝜆3 −3/2 + �̂�.𝐶𝑢𝑟𝑙 𝐵) , 𝑔3 = 𝜆3 3/2 (𝑗̂.𝐶𝑢𝑟𝑙 𝐵), ℎ3 = 𝜆3 3/2 (𝑖̂ .𝐶𝑢𝑟𝑙 𝐵), (12) 𝐵 = (𝐵1,𝐵2,𝐵3) , 𝐵1 = (− 𝛽 ℓ1 3 − 𝜆 𝛽 ℓ2 3 ), 𝐵2 = ( 𝛼 − 𝜆3 1/2 0.5 ℓ1 3 + 𝜆(𝛼 + 𝜆3 1/2 0.5) ℓ2 3 ), 𝐵3 = 0, ℓ1 = √(𝛼 − 𝜆3 1/2 0.5) 2 + 𝛽2 + 𝛾2, ℓ2 = √(𝛼 + 𝜆3 1/2 0.5) 2 + 𝛽2 + 𝛾2 (13) 3. analysis of equilibrium points and basins of attracting domain 3.1 equilibrium points we will put all the derivatives with respect to time on the left hand side of the system (10) to zero, hence v𝛼 + 𝑉1 = 0, (14) v𝛽 + 𝑉2 = 0, (15) v𝛾 + 𝑉3 = 0. (16) after solving equations (14), (15) and (16), we can find the locations of equilibrium points. we have plotted the locations of equilibrium points numerically in α-β-plane as shown in figures 2, 3 and 4. variable mass in electromagnetic copenhagen problem 65 (a) λ1 = 0 and λ3 = 1 (b) λ1 = 0.2 and λ3 = 0.4 (c) λ1 = 0.2 and λ3 = 0.8 (d) λ1 = 0.2 and λ3 = 1.4 figure 2. locations of equilibrium points at λ = 1 in α β-plane ansari, a.a. 66 (a) λ1 = 0 and λ3 = 1 (b) λ1 = 0.2 and λ3 = 0.4 (c) λ1 = 0.2 and λ3 = 0.8 (d) λ1 = 0.2 and λ3 = 1.4 figure 3. locations of equilibrium points at λ = 7 in α β-plane. variable mass in electromagnetic copenhagen problem 67 (a) λ1 = 0 and λ3 = 1 (b) λ1 = 0.2 and λ3 = 0.4 (c) λ1 = 0.2 and λ3 = 0.8 (d) λ1 = 0.2 and λ3 = 1.4 figure 4. locations of equilibrium points at λ = 15 in α β-plane. ansari, a.a. 68 (a) λ = 1 (b) λ = 7 (c) λ = 15 figure 5. movement of equilibrium points at λ1 = 0, λ3 = 1 (blue) and λ1 = 0.2, λ3 = 0.4 (green), 0.8 (red), 1.4 (cyan) in α β-plane. figure 2 presents the locations of equilibrium points at λ = 1 where figure 2(a) presents the classical case (λ 1 = 0 and λ3 = 1) which coincides with [5], where three equilibrium points (l1, 2, 3) were also obtained i.e. only collinear equilibrium points. out of these equilibrium points l2 is situated at the origin, which is also the center of mass of the primaries, while l1 and l3 lie left and right of the origin. further, figures 2(b), 2(c) and 2(d) present the locations of equilibrium points when λ1 = 0.2, λ3 = 0.4, 0.8 and 1.4, respectively i.e. the variation of mass cases. in these three cases we observe that at λ1 = 0.2 and λ3 = 0.4, the two equilibrium points (l1 and l3) move toward the origin as well as moving anti-clockwise from the α-axis. as we increase the value of λ3, we find that these two equilibrium points move away from the origin keeping l2 at the origin. we can see the movement of the equilibrium points (l1 and l3) in figure 5(a). again, figure 3 presents the locations of equilibrium points at λ = 7, where figure 3(a) presents the classical case which also coincides with [5], where seven equilibrium points were obtained. but as we increase the value of λ3 by variable mass in electromagnetic copenhagen problem 69 keeping the value of λ1 the same at 0.2, we find only five equilibrium points, which mean that due to variation of mass, the number of equilibrium points reduces to five. the movement of all equilibrium points due to change of λ3 can be seen in figure 5(b). in the same way, figure 4 represents the case when λ = 15, where figure 4(a) represents the classical case and shows five equilibrium points, out of which three (l1, l2 and l3) are collinear and two (l4 and l5) are non-collinear. but when we consider the variation of mass case, i.e. λ1 = 0.2, λ3 = 0.4, 0.8 and 1.4, we observe that l1 and l3 move downward from the α--axis. we can see the complete movement of these equilibrium points in figure 5(c). in this way, the variation parameters are working as catalytic agents. 3.2 basins of the attracting domain to solve the multivariate functions, we will use a simple, fast and accurate n-r iterative method. therefore we illustrate the basins of the attracting domain for our present model. this method is activated when an initial condition is given to the configuration plane, while it stops when the positions of the equilibrium points are reached with some predefined accuracy. the regions of convergence are composed of all the initial values that tend to a specific equilibrium point. this is one of the most important qualitative properties of the dynamical systems. it is illustrated in the following way: after classifying a dense uniform grid of 1024×1024 initial conditions, a multiple scan of the configuration plane was done. by setting the maximum number of iterations to be 500, we set the predefined accuracy as 10 -15 . using the above iterative method, we plotted the basins of attracting domain for three cases. the mathematical formulae for our model in α-β-plane when γ = 0, is presented by: 𝛼𝑛+1 = α𝑛 −( (v𝛼+𝑉1)(v𝛽𝛽+𝑉2𝛽)−(v𝛽+𝑉2)(v𝛼𝛽+𝑉1𝛽) (v𝛼𝛼+𝑉1𝛼)(v𝛽𝛽+𝑉2𝛽)−(v𝛼𝛽+𝑉1𝛽)(v𝛽𝛼+𝑉2𝛼) ) (𝛼𝑛,𝛽𝑛) , (17) 𝛽𝑛+1 = β𝑛 −( (v𝛽+𝑉2)(v𝛼𝛼+𝑉1𝛼)−(v𝛼+𝑉1)(v𝛽𝛼+𝑉2𝛼) (v𝛼𝛼+𝑉1𝛼)(v𝛽𝛽+𝑉2𝛽)−(v𝛼𝛽+𝑉1𝛽)(v𝛽𝛼+𝑉2𝛼) ) (𝛼𝑛,𝛽𝑛) . (18) where αn, βn are the values of α and β coordinates of the n th step of the newton-raphson iterative process in equations (17) and (18). the first and second derivatives are obtained from the right hand sides of the equations of motion (10). if the initial point converges rapidly to one of the equilibrium points then this point (α, β) will be a member of the basin of attracting domain. this process stops when the successive approximation converges to an attractor (in the dynamical system attractor means equilibrium point). for the classification of different equilibrium points on the plane, we used a color code. here we have represented the basins of attracting domain at λ = 1, 7, and 15 (taken from [5]) and these are shown in figures 6(a), 7(a) and 8(a). figures 6(b), 7(b) and 8(b) are the zoomed parts of figures 6(a), 7(a ) and 8(a) respectively. from figure 6(b), we observe that all the equilibrium points belong to cyan colored regions which extend to infinity. from figure 7(b), we observe that there are seven attracting points (equilibrium points) out of which l 1, l4, l5 and l7 belong to the cyan, blue, light green and green colored regions which are extended to infinity respectively while l2 belongs to the light blue colored region which covers a finite region. again from figure 8(b), we observe that l1 belongs to the cyan colored region, l2, l4 and l5 belong to the light blue colored region, while l3 belongs to the light green region, all of these regions extending to infinity. ansari, a.a. 70 (a) λ = 1 (b) zoomed part of figure (a) near primaries figure 6. basins of attracting domain at λ1 = 0.2, λ3 = 1.4 in α β-plane. (a) λ = 7 (b) zoomed part of figure (a) near primaries figure 7. basins of attracting domain at λ1 = 0.2, λ3 = 1.4 in α β-plane. variable mass in electromagnetic copenhagen problem 71 (a) λ = 15 (b) zoomed part of figure (a) near primaries figure 8. basins of attracting domain at λ1 = 0.2, λ3 = 1.4 in α β-plane. 4. stability of equilibrium points to reveal the stability properties of the small body's motion in its vicinity (α0+ α1, β0+ β1, γ0 + γ1), where α1, β1, γ1 are small movements from the equilibrium points (α0, β0, γ0). the variational equations for the system (10) can be written as: 𝛼1̈ −𝑓3𝛽1̇ + 𝑔3𝛾1̇ = (𝑉𝛼1𝛼1 0 +𝑉1𝛼1 0 )α1 +(𝑉𝛼1β1 0 +𝑉1β1 0 )β1 +(𝑉𝛼1γ1 0 +𝑉1𝛾1 0 )γ1, 𝛽1̈ −ℎ3𝛾1̇ + 𝑓3𝛼1̇ = (𝑉β1𝛼1 0 +𝑉2𝛼1 0 )α1 +(𝑉β1β1 0 +𝑉2β1 0 )β1 +(𝑉β1γ1 0 +𝑉2𝛾1 0 )γ1, 𝛾1̈ −𝑔3𝛼1̇ + ℎ3𝛽1̇ = (𝑉γ1𝛼1 0 +𝑉3𝛼1 0 )α1 +(𝑉γ1β1 0 +𝑉3β1 0 )β1 +(𝑉γ1γ1 0 +𝑉3𝛾1 0 )γ1. (19) where the superscript 0 denotes the value at the corresponding equilibrium point. in the phase space, the above system (19) can be rewritten as: α̇1 = 𝛼2, β̇1 = 𝛽2, γ̇1 = 𝛾2, ansari, a.a. 72 α2̇ = (𝑉𝛼1𝛼1 0 +𝑉1𝛼1 0 )α1 +(𝑉𝛼1β1 0 +𝑉1β1 0 )β1 +(𝑉𝛼1γ1 0 +𝑉1𝛾1 0 )γ1 +𝑓3𝛽2 −𝑔3𝛾2, β2̇ = (𝑉β1𝛼1 0 +𝑉2𝛼1 0 )α1 +(𝑉β1β1 0 +𝑉2β1 0 )β1 +(𝑉β1γ1 0 +𝑉2𝛾1 0 )γ1 +ℎ3𝛾2 −𝑓3𝛼2, γ2̇ = (𝑉γ1𝛼1 0 +𝑉3𝛼1 0 )α1 +(𝑉γ1β1 0 +𝑉3β1 0 )β1 +(𝑉γ1γ1 0 +𝑉3𝛾1 0 )γ1 +𝑔3𝛼2 −ℎ3𝛽2. (20) we use meshcherskii space-time inverse transformations to examine the stability of the equilibrium points because the mass and distance of the small particle change with time. 𝛼3 = 𝜆3 −1/2 𝛼1, 𝛽3 = 𝜆3 −1/2 𝛽1, 𝛾3 = 𝜆3 −1/2 𝛾1, 𝛼4 = 𝜆3 −1/2 𝛼2, 𝛽4 = 𝜆3 −1/2 𝛽2, 𝛾4 = 𝜆3 −1/2 𝛾2. (21) with the help of equation (21), the system (20) can be written as follows: �̇� = 𝑀 𝑋, where �̇� = ( α3̇ β3̇ γ3̇ α4̇ β4̇ γ4̇ ) , 𝑋 = ( 𝛼3 𝛽3 𝛾3 𝛼4 𝛽4 𝛾4 ) and 𝑀 = ( 1 2 𝜆1 0 0 𝑉𝛼1𝛼1 0 +𝑉1𝛼1 0 𝑉β1𝛼1 0 +𝑉2𝛼1 0 𝑉γ1𝛼1 0 +𝑉3𝛼1 0 0 1 2 𝜆1 0 𝑉𝛼1β1 0 +𝑉1β1 0 𝑉β1β1 0 +𝑉2β1 0 𝑉γ1β1 0 +𝑉3β1 0 0 0 1 2 𝜆1 𝑉𝛼1γ1 0 +𝑉1𝛾1 0 𝑉β1γ1 0 +𝑉2𝛾1 0 𝑉γ1γ1 0 +𝑉3𝛾1 0 1 0 0 1 2 𝜆1 −𝑓3 𝑔3 0 1 0 𝑓3 1 2 𝜆1 −ℎ3 0 0 1 −𝑔3 ℎ3 1 2 𝜆1 ) . the characteristic equation for the matrix m is 𝜆4 6 +𝛼5𝜆4 5 +𝛼4𝜆4 4 +𝛼3𝜆4 3 +𝛼2𝜆4 2 +𝛼1𝜆4 +𝛼0 = 0, (22) where 𝛼0 = 1 64 (−8(2(−4(𝑉1𝛾1 0 +𝑉𝛼1𝛾1 0 )(𝑉2𝛽1 0 +𝑉𝛽1𝛽1 0 )+4(𝑉1𝛽1 0 +𝑉𝛼1𝛽1 0 )(𝑉2𝛾1 0 +𝑉𝛽1𝛾1 0 )) variable mass in electromagnetic copenhagen problem 73 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )−2(−4( (𝑉1𝛾1 0 +𝑉𝛼1𝛾1 0 )(𝑉2𝛼1 0 +𝑉𝛽1𝛼1 0 ) +4(𝑉1𝛼1 0 +𝑉𝛼1𝛼1 0 )(𝑉2𝛾1 0 +𝑉𝛽1𝛾1 0 ) ) (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 ) +2(−4(𝑉1𝛽1 0 +𝑉𝛼1𝛽1 0 )(𝑉2𝛼1 0 +𝑉𝛽1𝛼1 0 )+4(𝑉1𝛼1 0 +𝑉𝛼1𝛼1 0 )(𝑉2𝛽1 0 +𝑉𝛽1𝛽1 0 ))(𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )) +8ℎ3 (−4(𝑉1𝛾1 0 +𝑉𝛼1𝛾1 0 )(𝑉2𝛼1 0 +𝑉𝛽1𝛼1 0 )+4(𝑉1𝛼1 0 +𝑉𝛼1𝛼1 0 )(𝑉2𝛾1 0 +𝑉𝛽1𝛾1 0 ))𝜆1) +8𝑔3 (−4(𝑉1𝛾1 0 +𝑉𝛼1𝛾1 0 )(𝑉2𝛽1 0 +𝑉𝛽1𝛽1 0 )+4(𝑉1𝛽1 0 +𝑉𝛼1𝛽1 0 )(𝑉2𝛾1 0 +𝑉𝛽1𝛾1 0 ))𝜆1) +32𝑓3𝑉2𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 −32𝑓3𝑉𝛽1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 +8(4ℎ3𝑉1𝛽1 0 +4𝑔3𝑉1𝛽1 0 +4ℎ3𝑉𝛼1𝛽1 0 +4𝑔3𝑉𝛽1𝛽1 0 )(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 +32𝑓3𝑉𝛽1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 −32𝑓3𝑉1𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 −32𝑓3𝑉𝛼1𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 +32𝑓3𝑉1𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 −8(4ℎ3𝑉1𝛼1 0 +4𝑔3𝑉2𝛼1 0 +4ℎ3𝑉𝛼1𝛼1 0 +4𝑔3𝑉𝛽1𝛼1 0 )(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 −32𝑓3𝑉2𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 +32𝑓3𝑉𝛼1𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 −16𝑓3ℎ3𝑉1𝛾1 0 𝜆1 2 −16𝑓3𝑔3𝑉2𝛾1 0 𝜆1 2 −16𝑓3 2𝑉3𝛾1 0 𝜆1 2 −16𝑓3ℎ3𝑉𝛼1𝛾1 0 𝜆1 2 −4ℎ3(4ℎ3𝑉1𝛼1 0 +4𝑔3𝑉2𝛼1 0 +4ℎ3𝑉𝛼1𝛼1 0 +4𝑔3𝑉𝛽1𝛼1 0 )𝜆1 2 −4𝑔3(4ℎ3𝑉1𝛽1 0 +4𝑔3𝑉2𝛽1 0 +4ℎ3𝑉𝛼1𝛽1 0 +4𝑔3𝑉𝛽1𝛽1 0 )𝜆1 2 +4(−4(𝑉1𝛽1 0 +𝑉𝛼1𝛽1 0 )(𝑉2𝛼1 0 +𝑉𝛽1𝛼1 0 )+4(𝑉1𝛼1 0 +𝑉𝛼1𝛼1 0 )(𝑉2𝛽1 0 +𝑉𝛽1𝛽1 0 ))𝜆1 2 −16𝑓3𝑔3𝑉𝛽1𝛾1 0 𝜆1 2 −16𝑓3ℎ3(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 2 −16𝑉1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 2 −16𝑉𝛼1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 2 −16𝑓3𝑔3(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 2 −16𝑉2𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 2 −16𝑉𝛽1𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 2 −16𝑓3 2𝑉𝛾1𝛾1 0 𝜆1 2 +16𝑉1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 2 +16𝑉2𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 2 +16𝑉𝛼1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 2 +16𝑉𝛽1𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 2 −8𝑓3𝑉1𝛽1 0 𝜆1 3 +8𝑔3𝑉1𝛾1 0 𝜆1 3 +8𝑓3𝑉2𝛼1 0 𝜆1 3 −8ℎ3𝑉2𝛾1 0 𝜆1 3 −8ℎ3𝑉𝛽1𝛾1 0 𝜆1 3 −8𝑓3𝑉𝛼1𝛽1 0 𝜆1 3 +8𝑔3𝑉𝛼1𝛾1 0 𝜆1 3 +8𝑓3𝑉𝛽1𝛼1 0 𝜆1 3 −8𝑔3(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 3 +8ℎ3(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 3 +4𝑓3 2𝜆1 4 +4𝑔3 2𝜆1 4 +4ℎ3 2𝜆1 4 −4𝑉1𝛼1 0 𝜆1 4 −4𝑉2𝛽1 0 𝜆1 4 −4𝑉3𝛾1 0 𝜆1 4 −4𝑉𝛼1𝛼1 0 𝜆1 4 −4𝑉𝛽1𝛽1 0 𝜆1 4 −4𝑉𝛾1𝛾1 0 𝜆1 4 +𝜆1 6) ansari, a.a. 74 𝛼1 = 1 64 (−16ℎ3(−4(𝑉1𝛾1 0 +𝑉𝛼1𝛾1 0 )(𝑉2𝛼1 0 +𝑉𝛽1𝛼1 0 )+4(𝑉1𝛼1 0 +𝑉𝛼1𝛼1 0 )(𝑉2𝛾1 0 +𝑉𝛽1𝛾1 0 )) −16𝑔3(−4(𝑉1𝛾1 0 +𝑉𝛼1𝛾1 0 )(𝑉2𝛽1 0 +𝑉𝛽1𝛽1 0 )−64𝑓3𝑉2𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 ) +4(𝑉1𝛽1 0 +𝑉𝛼1𝛽1 0 )(𝑉2𝛾1 0 +𝑉𝛽1𝛾1 0 ))+64𝑓3𝑔3𝑉2𝛾1 0 𝜆1 −16(4ℎ3𝑉1𝛽1 0 +4𝑔3𝑉2𝛽1 0 +4ℎ3𝑉𝛼1𝛽1 0 +4𝑔3𝑉𝛽1𝛽1 0 )(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 ) −64𝑓3𝑉𝛽1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )+64𝑓3𝑉1𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 ) +64𝑓3𝑉𝛼1𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )+64𝑓3𝑓3𝑉3𝛾1 0 𝜆1 +64𝑓3ℎ3𝑉𝛼1𝛾1 0 𝜆1 +16(4ℎ3𝑉1𝛼1 0 +4𝑔3𝑉2𝛼1 0 +4ℎ3𝑉𝛼1𝛼1 0 +4𝑔3𝑉𝛽1𝛼1 0 ))(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 ) −64𝑓3𝑉1𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )+64𝑓3𝑉2𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 ) −64𝑓3𝑉𝛼1𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )+64𝑓3𝑉𝛽1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )+64𝑓3ℎ3𝑉1𝛾1 0 𝜆1 +16ℎ3(4ℎ3𝑉1𝛼1 0 +4𝑔3𝑉2𝛼1 0 +4ℎ3𝑉𝛼1𝛼1 0 +4𝑔3𝑉𝛽1𝛼1 0 )𝜆1 +16𝑔3(4ℎ3𝑉1𝛽1 0 +4𝑔3𝑉2𝛽1 0 +4ℎ3𝑉𝛼1𝛽1 0 +4𝑔3𝑉𝛽1𝛽1 0 )𝜆1 −16(−4(𝑉1𝛽1 0 +𝑉𝛼1𝛽1 0 )(𝑉2𝛼1 0 +𝑉𝛽1𝛼1 0 )+4(𝑉1𝛼1 0 +𝑉𝛼1𝛼1 0 )(𝑉2𝛽1 0 +𝑉𝛽1𝛽1 0 ))𝜆1 +64𝑓3ℎ3(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 +64𝑓3𝑔3𝑉𝛽1𝛾1 0 𝜆1 +64𝑉1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 +64𝑉2𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 +64𝑉𝛼1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 +64𝑓3𝑔3(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 +64𝑉𝛽1𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 +64𝑓3𝑓3𝑉𝛾1𝛾1 0 𝜆1 −64𝑉1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 −64𝑉2𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 −64𝑉𝛼1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1 +64𝑉𝛽1𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )𝜆1)+48𝑓3𝑉1𝛽1 0 𝜆1 2 −48𝑔3𝑉1𝛾1 0 𝜆1 2 −48𝑓3𝑉2𝛼1 0 𝜆1 2 +48ℎ3𝑉2𝛾1 0 𝜆1 2 +48𝑓3𝑉𝛼1𝛽1 0 𝜆1 2 −48𝑔3𝑉𝛼1𝛾1 0 𝜆1 2 −48𝑓3𝑉𝛽1𝛼1 0 𝜆1 2 +48ℎ3𝑉𝛽1𝛾1 0 𝜆1 2 +48𝑔3(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 2 −48ℎ3(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 2 −32𝑓3 2𝜆1 3 −32𝑔3 2𝜆1 3 −32ℎ3 2𝜆1 3 +32𝑉1𝛼1 0 𝜆1 3 +32𝑉2𝛽1 0 𝜆1 3 +32𝑉3𝛾1 0 𝜆1 3 +32𝑉𝛼1𝛼1 0 𝜆1 3 +32𝑉𝛽1𝛽1 0 𝜆1 3 +32𝑉𝛾1𝛾1 0 𝜆1 3 −12𝜆1 5) 𝛼2 = 1 64 (−64𝑓3ℎ3𝑉1𝛾1 0 −64𝑓3𝑔3𝑉2𝛾1 0 −64𝑓3ℎ3𝑉1𝛾1 0 −64𝑓3𝑓3𝑉3𝛾1 0 −64𝑓3ℎ3𝑉𝛼1𝛾1 0 −16ℎ3(4ℎ3𝑉1𝛼1 0 +4𝑔3𝑉2𝛼1 0 +4ℎ3𝑉𝛼1𝛼1 0 +4𝑔3𝑉𝛽1𝛼1 0 ) −16𝑔3(4ℎ3𝑉1𝛽1 0 +4𝑔3𝑉2𝛽1 0 +4ℎ3𝑉𝛼1𝛽1 0 +4𝑔3𝑉𝛽1𝛽1 0 )−64𝑓3𝑔3𝑉𝛽1𝛾1 0 variable mass in electromagnetic copenhagen problem 75 +16(−4(𝑉1𝛽1 0 +𝑉𝛼1𝛽1 0 )(𝑉2𝛼1 0 +𝑉𝛽1𝛼1 0 )+4(𝑉1𝛼1 0 +𝑉𝛼1𝛼1 0 )(𝑉2𝛽1 0 +𝑉𝛽1𝛽1 0 )) −64𝑓3𝑓3𝑉𝛾1𝛾1 0 −64𝑓3ℎ3(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )−64𝑉1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 ) −64𝑉𝛼1𝛾1 0 (𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )−64𝑓3𝑔3(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )−64𝑉2𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 ) −64𝑉𝛽1𝛾1 0 (𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )+64𝑉1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )+64𝑉2𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 ) +64𝑉𝛼1𝛼1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )+64𝑉𝛽1𝛽1 0 (𝑉3𝛾1 0 +𝑉𝛾1𝛾1 0 )−96𝑓3𝑉1𝛽1 0 𝜆1 +96𝑔3𝑉1𝛾1 0 𝜆1 +96𝑓3𝑉2𝛼1 0 𝜆1 −96𝑓3𝑉𝛼1𝛽1 0 𝜆1 +96𝑔3𝑉𝛼1𝛾1 0 𝜆1 +96𝑓3𝑉𝛽1𝛼1 0 𝜆1 −96ℎ3𝑉𝛽1𝛾1 0 𝜆1 −96ℎ3𝑉2𝛾1 0 𝜆1 −96𝑔3(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )𝜆1 +96ℎ3(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )𝜆1 +96𝑓3 2𝜆1 2 +96𝑔3 2𝜆1 2 +96ℎ3 2𝜆1 2 −96𝑉1𝛼1 0 𝜆1 2 −96𝑉2𝛽1 0 𝜆1 2 −96𝑉3𝛾1 0 𝜆1 2 −96𝑉𝛼1𝛼1 0 𝜆1 2 −96𝑉𝛽1𝛽1 0 𝜆1 2 −96𝑉𝛾1𝛾1 0 𝜆1 2 +60𝜆1 4), 𝛼3 = 𝑓3𝑉1𝛽1 0 −𝑔3𝑉1𝛾1 0 −𝑓3𝑉2𝛼1 0 +ℎ3𝑉2𝛾1 0 +𝑓3𝑉𝛼1𝛽1 0 −𝑔3𝑉𝛼1𝛾1 0 −𝑓3𝑉𝛽1𝛼1 0 +ℎ3𝑉𝛽1𝛾1 0 +2𝑉2𝛽1 0 𝜆1 +𝑔3(𝑉3𝛼1 0 +𝑉𝛾1𝛼1 0 )−ℎ3(𝑉3𝛽1 0 +𝑉𝛾1𝛽1 0 )−2𝑓3 2𝜆1 −2𝑔3 2 −2ℎ3 2𝜆1 +2𝑉1𝛼1 0 𝜆1 +2𝑉𝛽1𝛽1 0 𝜆1 +2𝑉𝛼1𝛼1 0 𝜆1 +2𝑉𝛾1𝛾1 0 𝜆1 − 5 2 𝜆1 3, 𝛼4 = 𝑓3 2 +𝑔3 2 +ℎ3 2 −𝑉1𝛼1 0 −𝑉2𝛽1 0 −𝑉3𝛾1 0 −𝑉𝛼1𝛼1 0 −𝑉𝛽1𝛽1 0 −𝑉𝛾1𝛾1 0 + 15 4 𝜆1 2, 𝛼5 = −3𝜆1. we have solved equation (22) numerically for three different values of parameter λ (1, 7, 15) and evaluated characteristic roots which are given in tables (1-3). we observed from these roots given in these three tables 1, 2, 3 that all the equilibrium points are unstable because at-least one characteristic root is either a positive real number or positive real part of the complex characteristic root, while [5] found in his investigation that some equilibrium points are stable in some interval values for the parameter λ. in this way we can say that these variation parameters convert to all the equilibrium points as unstable. therefore it is easy to say that these variation parameters have great impact on this dynamical system. table 1. corresponding characteristic roots of equilibrium points in α-β-plane at λ = 1, λ1 = 0.2, λ3 = 1.4. s.n. equilibrium point (α, β) roots nature 1 1.8922290573, 0.2249047710 + 0.1238455712 ± 0.9648772652 i + 1.8829013676, 1.7305925101 + 0.1000000000, + 0.1000000000 unstable 2 0.0000000000, 0.0000000000 + 0.1919166735 ± 15.3247492922 i + 2.9831536654, + 0.0999999999 2.9669870125, + 0.1000000000 unstable 3 1.8922290573, 0.2249047710 + 0.1238455712 ± 0.9648772652 i + 1.8829013676, + 0.1000000000 + 0.0999999999, 1.7305925101 unstable ansari, a.a. 76 table 2. corresponding characteristic roots of equilibrium points in α-β-plane at λ = 7, λ1 = 0.2, λ3 = 1.4. s.n. equilibrium point (α, β) roots nature 1 2.9288319681, 0.5956468434 + 0.1244710980 ± 0.7705292447 i + 1.7304695528, 1.5794117488 + 0.1000000000, + 0.1000000000 unstable 2 0.1420900714, 0.0070146815 + 0.1993522521 ± 46.6873463284 i + 2.8958790218, + 0.1000000000 2.8945835262, + 0.0999999999 unstable 3 0.4622777422, 0.7320519601 + 0.0897598108 ± 7.5033419383 i + 1.8018965165, + 0.0999999999 + 0.1000000000, 1.5814161383 unstable 4 0.3598259379, 0.8004678161 + 0.0957408351 ± 6.8651530569 i + 0.1000000000, + 1.6062369651 1.3977186353, + 0.1000000000 unstable 5 1.0704385208, 1.5676578978 + 1.2156733907 ± 0.0888414341 i + 0.1000000000, 0.8781507268 1.1531960546, + 0.1000000000 unstable table 3. corresponding characteristic roots of equilibrium points in α-β-plane at λ = 15, λ1 = 0.2, λ3 = 1.4. s.n. equilibrium point (α, β) roots nature 1 3.5192043182, 0.9124002233 + 0.1245222506 ± 0.6945789131 i + 1.6854000078, + 0.0999999999 1.5344445091, + 0.1000000000 unstable 2 + 0.1939056387, 0.0096053140 + 0.1999647710 ± 76.6270430841 i + 2.8730485051, 2.8729780473 + 0.1000000000, + 0.1000000000 unstable 3 1.9795166567, 1.3700857646 + 0.1000000000, 1.2570087540 0.5578040967, + 0.8068614037 + 1.4079514469, + 0.1000000000 unstable 4 0.5347180082, 0.6049358108 + 0.0922083409 ± 17.2608437186 i + 1.8078564632, + 0.1000000000 1.5922731451, + 0.1000000000 unstable 5 0.6759400828, + 0.4504694723 + 0.1005874123 ± 15.9957018321 i + 1.5269661797, 1.3281410043 + 0.1000000000, + 0.1000000000 unstable conclusion in this paper we have investigated the effect of variation of mass of the infinitesimal body (test particle) under the influence of the electromagnetic copenhagen problem. we have found that these variation parameters have great impact on the behavior of this dynamical system. in our investigation, firstly we have determined the equations of motion where both variation parameters λ1 and λ3 are clearly visible. using this system of equations of motion we numerically illustrated the equilibrium points for three values of magnetic moment ( λ = 1, 7, 15) (taken from [5]) and respectively we found three, seven and five equilibrium points for the four different values of variation parameters λ 1 = 0, 0.2 and λ3 = 1, 0.4, 0.8, 1.4. the complete movements of these equilibrium points are presented in figure (5). we have also performed the newton-raphson basins of attracting domain in the above said three cases of λ and for fixed values of λ1 = 0.2 and λ3 = 1.4. the variations of attracting domain are presented in the figures 6, 7 and 8. for a clearer view, we have shown the figures in the zoomed parts of figures 6(a), 7(a) and 8(a) in figures 6(b), 7(b) and 8(b), respectively. in the following investigation we have explored numerically the stability of corresponding equilibrium points, for which we have evaluated the characteristic roots corresponding to the equilibrium points, and these are given in tables 1, 2 and 3. we observed from the tables that all the equilibrium points are unstable, which finding is clearly different from that of the investigation done by [5]. conflict of interest the author declares no conflict of interest. variable mass in electromagnetic copenhagen problem 77 acknowledgment the author is thankful to prof. rabah kellil for his valuable suggestions to bring this manuscript up to 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three-body problem when both the primaries are heterogeneous spheroid of three layers and infinitesimal body varies its mass. journal of astrophysics and astronomy, 2018, 39, 57. 21. ansari, a.a., et. al. effect of charge in the circular restricted three-body problem with variable masses. journal of taibah university for science, 2019, 13(1), 670-677. received 11 october 2019 accepted 17 december 2019 https://doi.org/10.1016/j.newast.2019.101282 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 8 (2003) 97-106 © 2003 sultan qaboos university some aspects of the anatomy and histology of digestive tracts in two sympatric species of freshwater fishes taher ba-omar, reginald victor and daniel tobias department of biology, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, email: taher@squ.edu.om. بعض الجوانب التشريحية والنسيجية للجهاز الهضمي لنوعين من أسماك المياه العذبة دانيال توباز طاهر بن عبدالرحمن باعمر، ريجنالد فيكتور و من aphanius dispar and garra barreimiaeدراسة مقارنة للجهاز الهضمي لنوعين من أسماك المياه العذبة : خالصة كما تم تقييم العالقة . والقناة الهضمية وعدد عكنات المعدة وارتفاعها األسماكتم قياس كل من طول . منظور تشريحي ونسيجي سوف . كذلك تم توصيف ومقارنة أنسجة الجهاز الهضمي لكال السمكتين . أعاله إليها المشار واألجزاءبين طول هاتين السمكتين . تملك معدة حقيقيةاألسماكه كانت هذإذا نتائج هذه الدراسة لمناقشة ما تستخدم abstract: comparative anatomy and histology of the digestive tracts of two sympatric species of freshwater fish, aphanius dispar (cyprinodontidae) and garra barreimiae (cyprinidae) are studied. morphometric measurements of alimentary canal such as length and the number and height of rugae in sections have been made for both species. relationships between these morphometric characters and the total length of fish have been evaluated. the ratio between the length of alimentary canal and total length of fish in both species reflects their feeding habits. histology of the ‘stomach’ and ‘intestine’ of these two species as shown by light microscopy has been described and compared. results of this study are used to discuss the query whether these species have true stomachs. keywords: aphanius; garra; fish; anatomy; histology; stomach; intestine 1. introduction several studies have been carried out on the digestive tracts of teleost fishes (grau et al. 1992; osman and caceci 1991; gargiulo et al. 1997;1998). recently, we have studied the structure and ultrastructure of the stomach of aphanius dispar (rüppell 1828), a cyprinodont fish with special reference to stress from starvation (ba-omar et al. 1998; ba-omar and victor, 2000). what is referred to as ‘stomach’ in these studies is the morphologically distinct, enlarged sac-like portion of the gut separated from intestine by a constriction (ba-omar and victor, 2000). however, it is well known that many fish including cyprinids and cyprinodonts lack a ‘true’ stomach, that is a portion of the digestive tube with a typically acid secretion and a distinctive epithelial lining different from that of the intestine (lagler et al. 1977). from our work so far on a. dispar, the 'stomach' we describe could well be a ‘stomach-like’ pouch, a hollow organ covered by an intestinal mucosa. despite being different in gross anatomy, this portion of the alimentary canal could well be the same as that of 'true' intestine both histologically and functionally. therefore, it is necessary to describe and compare sections of alimentary canal above and below the constriction that seemingly separates 'stomach' from that of 'intestine' in a. dispar. in this study, we also compare the anatomy and histology of the alimentary canal of another cyprinid, garra barreimiae that is sympatric with a. dispar in the freshwaters of oman. these two species occupy different feeding niches. the cyprinid, is a benthic herbivore, while a. dispar 97 taher ba-omar, reginald victor and daniel tobias is an ubiquitous omnivore. both species have ‘stomachs’ and ‘intestines’ sensu ba-omar and victor (2000). the descriptions of alimentary canals provided here are of value in their own right because very little is known about the biology of these species. however, we also use the results to address the existence of ‘stomachs’ in these species. 2. materials and methods specimens of aphanius dispar and garra barreimiae were collected from wadi al-khod near sultan qaboos university, sultanate of oman (lat. 23ο 30' n; long. 58ο 40' e). both species are sympatric in the temporary and permanent pools of the same wadi (i.e. seasonal river) system. most often they are mutually exclusive in the same pools. g. barreimiae, however, regularly shares its habitat with another cyprinid cyprinion microphthalmum. all fishes for this study were collected in freshwater, although a. dispar also lives in brackish waters of the coastal lagoons and estuaries. the fishes were kept in an aerated holding tank in the laboratory and were fed with the commercial tetramin flakes ad libitum daily. for each species 11 specimens irrespective of sex were killed and the entire alimentary canal was removed from each fish. the total length of the fish and the entire gut length were measured in mm. the size ranges of a. dispar and g. barreimiae were 30 – 48 and 29 – 69 mm, respectively. ten percent buffered formalin (ph 7.3) at room temperature was used to fix the gut. the entire gut was processed, embedded in paraffin with an anterior-posterior orientation and serially sectioned at 5 µm. serially numbered paraffin sections were stained using mayer’s hematoxylin – eosin for examination under routine light microhoscopy. the histological topography was studied separately for the ‘stomach’ and ‘intestine’ regions under low and high magnifications (100 – 400 x). all measurements of rugae ( i.e. internal folds) were made on 25 randomly chosen representative sections. in each section five randomly chosen rugae were measured making up a total of 125 measurements for each region. measurements in µm were made using an ocular meter calibrated with a stage micrometer. data transformations were made wherever necessary. all statistical analyses were performed using systat (version 7.0) and all graphs were generated using sygraph (version 7.0). 3. results 3.1 aphanius dispar in the alimentary canal of aphanius dispar two distinct parts, an anterior dilated segment, presumably the ‘stomach’, and a posterior tubular segment, presumably the ‘intestine’, are recognized (figure 1a). the anterior segment is shorter than the posterior segment, which is approximately five times longer. the mean alimentary canal length of a. dispar is approximately twice the total length (tl) of the fish (table 1). figure 2 shows the positive relationship between the total length (tl) and the length of alimentary canal in a. dispar irrespective of sex. the regression equation describing this relationship, length of alimentary canal = 58.483 (tl) is significant (n = 11; anova , f = 10.609; r = 0.736; p < 0.01). figure 3 shows the histological organization of the ‘stomach’. it is composed of four different layers, mucosa, submucosa, muscularis and serosa. the four layers differ in their thickness and the mucosa is thrown into rugae. these rugae vary in length and width. they are made of columnar epithelial cells with the nuclei located at the basal side. figure 4 presents the histology of the ‘intestine’. it is not different from that of the 'stomach'. part of the mucosa is thrown into rugae while the rest is flat. the heights of the rugae are shorter than those found in the ‘stomach’. table 1 shows the number and the mean heights of rugae in the ‘stomach’ and in the ‘intestine’. the number of rugae in the ‘stomach’ was significantly higher than those in the intestine (t-test, t = 4.912; p < 0.001). there is no correlation between the number 98 anatomy and histology of digestive tracts of rugae in the ‘stomach’ and in the ‘intestine’(n = 11; r = 0.148; p > 0.05). similarly, the height of rugae in the ‘stomach’ (figure 5) is significantly greater than that in the intestine (paired t-test, t = 19.162; p < 0.001). there is no correlation between rugae heights of the ‘stomach’ and those of the ‘intestine’( n = 125; r = -0.157; p > 0.05). figure 1a. aphanius dispar and its alimentary canal; stomach (large arrow) and intestine (small arrow). figure 1b. garra barriemiae and its alimentary canal; stomach (large arrow) and intestine (small arrow). 99 taher ba-omar, reginald victor and daniel tobias figure 2. relationship between total length and alimentary canal length in aphanius dispar. table 1: morphometric measurements comparing alimentary canals of aphanius dispar and garra barreimiae; n = number of measurements; values given or mean ± standard deviation; * indicates significant differences within species at p<0.001. character n a. dispar g. barriemiae total length (mm) 11 39.1 ± 3.4 49.6 ± 10.7 canal length (mm) 11 77.3 ± 16.6 371.1 ± 134.3 stomach – no. of rugae 62 32 ± 6* 15 ± 4* intestine – no. of rugae 62 25 ± 6* 12 ± 2* stomach – rugae height (µm) 125 21.1 ± 9.3* 10.3 ± 3.0* intestine – rugae height (µm) 125 4.3 ± 2.0* 1.4 ± 0.7* 3.2 garra barreimiae the external morphology of the alimentary canal is characterized by a ‘stomach’ and an ‘intestine’. the ‘stomach’ is short and poorly dilated. (figure 1b). the alimentary canal of garra barreimiae is a long tube with a narrow lumen. its length is nearly 7.5 times the total length (tl) of the fish (table 1). the positive relationship between the total length (tl) and the length of the alimentary canal (figure 6) described by the equation, length of alimentary canal = -210.46 (tl) is significant (n = 11; anova, f =83.492; r = 0.950; p < 0.001). 100 anatomy and histology of digestive tracts figure 3. light micrograph of a transverse section showing histological organization of the ‘stomach’ of aphanius dispar fish; folds (rugae) (large open arrowheads), mucosa (m), submucosa (sm), muscularis (small arrow). bar = 25 mµ . figure 4. light micrograph of a transverse section showing histological organization of the intestine of aphanius dispar fish; mucosa (m) and muscularis (small arrows). bar = 25 µm. 101 taher ba-omar, reginald victor and daniel tobias figure 5. box plots showing the fold length in aphanius dispar and garra barriemiae (ad = aphanius dispar intestine, ad-s = aphanius dispar stomach, ga = garra barriemiae intestine and ga-s = garra barriemiae stomach). figure 6. relationship between total length and alimentary canal length in garra barriemiae. 102 anatomy and histology of digestive tracts igure 7. light micrograph of a transverse section showing the histological organization of the he histology of the ‘stomach’ is shown in figure 7. it is composed of four different layers, muc the histology of the ‘intestine’. its basic structure is the same as that of the ‘stom s well as their heights in these two regio ach other in the gross anatomy of the alimentary cana f ‘stomach’ of garra barriemiae fish; rugae (folds) (large open arrowheads), mucosa (m), submucosa (sm), muscularis (small arrows). bar = 25 µm. t osa, submucosa, muscularis and serosa all characterised by varying thickness. the mucosa is thrown into rugae with variable heights and widths. these are made of columnar epithelial cells with basal nuclei. figure 8 shows ach’. the rugae heights are variable and shorter than those of the ‘stomach’. the structure of the columnar epithelium is the same as that in the ‘stomach’. numbers of rugae in the ‘stomach’ and the ‘intestine’ a ns are given in table 1 and figure 5. both the numbers (t-test, t = 3.950; p < 0.001) and rugae heights (paired t-test, t = 32.726; p < 0.001) are significantly different. there are no correlations between the numbers of rugae (n = 25; r = 0.320; p > 0.05) or between the heights of rugae (n = 125; r = 0.055; p > 0.05) in the ‘stomach’ and in the ‘intestine’. 3.3 comparison of a. dispar and g. barreimiae a. dispar and g. barreimiae do not resemble e l. the histological organization of the ‘stomach’ and ‘intestine’ show very close resemblances. table 1 shows the morphometric measurements of the ‘stomach’ and ‘intestine’ of both species. the ratio of the total length of fish to the length of alimentary canal in adult fish ( total length / alimentary canal length) is different in both species. in a. dispar this ratio ranged from 0.40 to 0.66, while in g. barreimiae it ranged from 0.12 to 0.17. these ratios were significantly different (t-test on arcsin transformed data, t = 17.346; df = 20; p < 0. 001). the mean numbers of rugae in both the ‘stomach’ and ‘intestine’ of a. dispar were significantly higher than those of g. barreimiae (table 1). 103 taher ba-omar, reginald victor and daniel tobias igure 8. light micrograph of a transverse section showing the histological organization of the 4. discussion the anatomical structure of the intestine, its relative length in particular, depends on the nature of fo remarkably similar desp ussion on the histology of the ‘stomach’ of a.dispar has been provided elsew f intestine of the garra barriemiae fish; mucosa (m) and muscularis (small arrows). bar = 25 µm. od eaten by fishes (kapoor et al. 1975; anderson, 1986; kuperman and kuz'mina 1994). the length of the disgestive tracts in general not only increases from carnivorous to herbivorous diet, but their looping is more complex in herbivores than in carnivores and omnivores (alhussainy 1949; lagler et al. 1977). the gross anatomy of alimentary canals in aphanius dispar and garra barreimiae further confirms these findings. a. dispar, with a relatively short alimentary canal and a simpler loop is an omnivore which includes live animal food, while g. barreimiae with its extremely long alimentary canal and a complex loop is a herbivorous benthophage feeding on epilithic and epipsammic algae. the ratio of the total length of the fish to the total length of the alimentary canal in adult fish seems to be a good indicator of the feeding habits. the omnivorous a. dispar had a significantly higher ratio than the herbivorous g. barreimiae. the histologies of the ‘stomach’ and ‘intestine’ of these two species are ite morphometric differences. it has been reported earlier that the height of microvilli decreased from the anterior to the posterior part of the fish intestine (yamamoto 1966; kayanja et al. 1975; stroband 1977; noaillac-depeyre and gas 1979; anderson 1986). the number of rugae and the height of rugae significantly decreased from the anterior 'stomach' to the posterior 'intestine' in both species (table 1). it appears that the columnar epithelial cells forming the brushborder along the margins of rugae are larger in the anterior 'stomach' region than in the posterior 'intestine' region. adequate disc here (ba-omar et al. 1998; ba-omar and victor, 2000). the histology of the alimentary canal of g. barreimiae has been provided for the first time in this study. comparisons of the number and the height of rugae in both species are significantly different both in the 'stomach' and in the 'intestine' (table 1). the total length (tl) ranges of a. dispar and g. barreimiae studied 104 anatomy and histology of digestive tracts overlapped (table 1). therefore, the differences in histological measurements can not be explained by the differences in size range alone. the internal epithelia of the 'stomach' and the 'intestine' in both species have goblet cells and columnar cells with microvilli that appear as a brush border. these characters are similar to those reported for other cyprinids, but special cellular nests reported in the intestinal epithelia of some cyprinids were absent in these species (al-hussainy 1949). whether the columnar cells with microvilli are equally absorptive in both 'stomach' and 'intestine' regions of both species requires histochemical verification. the histological organization of the ‘stomachs’ described for both species here raises the ques light and electron microscopy did not show the pres references al-hussaini, a.h. 1949. on the functional morphology of the alimentary tract of some fish in anderson, t.a. 1986. histological and cytological structure of the gastrointestinal tract of the ba-omar, t.a., victor, r. and tobias, d.b. 1998. histology of the stomach of aphanius ba00. ultrastructural changes in the epithelium of the stomach gargiulo, a.m., ceccarelli, p., dall’ agelio, c. and pedini, v. 1997. gargiulo, a.m., ceccarelli, p., dall’ agelio, c. and pedini, v. 1998. histology and grau, a., crespo, s., sarasquete, m.c., gonzalez, d.e. and canales, m.l. 1992. tion whether these are true ‘stomachs’. several cyprinids have earlier been described as stomachless (al-hussainy 1949; lagler et al. 1997). the 'stomach' in both species studied here is not as distinct as those described for freshwater fishes like pike, burbot and sunfish (williams and nickol 1989; kuperman and kuz'mina 1994), but nevertheless it is a morphological entity separated from the 'intestine' by a constriction. histological studies in a. dispar using ence of gastric glands ((ba-omar et al. 1998; ba-omar and victor, 2000). also gastric glands were not seen in the ‘stomach’ of g. barreimiae. it is often argued that the presence of gastric glands and their function are essential for defining a ‘true’ stomach. stomachs store ingested food and by contraction facilitate the movement of food down the alimentary canal. therefore, the absence of gastric glands alone need not qualify the absence of a ‘stomach’. both a. dispar and g. barreimiae have ‘stomachs’ in the morphological sense and terms like ‘stomach-like pouch’ and ‘intestinal bulb’ are not necessary for their description. the histological organization of ‘stomach’ in both a. dispar and g. barreimiae indicates a greater surface area than that of ‘intestine’. it is quite likely that the ‘stomachs’ of these species play an important role in the absorption of food. again the conventional thinking that the‘intestine’ is the only place where absorption of digested food takes place has to be readdressed. based on the available evidence, this paper prefers to maintain that the cyprinodont a. dispar and the cyprinid g. barreimiae have demarcated ‘stomach’ and ‘intestine’. relation to differences in their feeding habits: cytology and physiology. quart. j. micros. sci. 90: 323-354. luderick, gerilla tricuspidata (pisces, kuphosidae), in relation to diet. j. morph. 190: 109119. dispar (ruppell 1828), a cyprinodont fish, with emphasis on changes caused by stress from starvation. trop. zool. 11:11-17. omar, t.a. and victor, r. 20 of aphanius dispar (cyprinodontidae), due to stress from starvation. squ j. scientific. res. science and tech., 5:1-9. ultrastructural study on the stomach of tilapia spp. (teleostei). anat. histol. and embryol. 26: 331-336. ultrastructure of the gut of the tilapia (tilapia spp), hybrid teloest. anat. histol. and embryol. 27: 89-94. the tract of the amberjack seriola dumerili, risso: a light and scanning electron microscope study. j. fish biol. 41: 287-303. 105 taher ba-omar, reginald victor and daniel tobias kapoor, b.g., smith, h. and verighina, i.a. 1975. the alimentary canal and digestion in teleosts, pp109-239. in: russell f.s & young m., edits. advances in marine biology. vol iii, london: academic press. kayanja, f.j.b., maloiy, g.m.o. and reite, o.b. 1975. the fine structure of the intestinal epithelium of the tilapia grahami. anat. anz. 138: 451-462. kuperman, b.i. and kuz’mina, v.v. 1994. the ultrastructure of the intestinal epithelium in fishes with different types of feeding. j. fish biol. 44: 181-193. lagler, k.f., bardach, j.e., miller, r.r., and passino, d.r.m. 1977. icthyology (2nd edition). new york: john wiley. noaillac-depeyre, j. and gas, n. 1979. structure and function of the intestinal epithelial cells in the perch (perca fluviatilis l.). anat. rec. 195: 621-640. osman, a.h.k. and caceci, t. 1991. histology of the stomach of tilapia nilotica (linnaeus, 1758) from the river nile. j. fish biol. 38: 211-223. stroband, h.w.j. 1977. growth and diet dependent structural adaptations of the digestive tract in juvenile grass carp (ctenopharingodon idelle val.). j. fish. biol. 11: 167-174. williams, j.a. and nickol, b.b. 1989. histological structure of the intestine and pyloric caeca of the green sunfish, lepomis cyanellus rafinesque. j. fish biol. 35: 359-372. yamamoto, t. 1966. an electron microscope study of the columnar epithelial cell in the intestine of fresh water teleosts: gold fish (carassius auratus) and rainbow trout (salmo irideus). zeit. fur zellf. 72: 66-87. received 11 february 2003 accepted 4 september 2003 106 some aspects of the anatomy and histology of digestive tracts in two sympatric species of freshwater fishes taher ba-omar, reginald victor and daniel tobias department of biology, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, email: taher@squ.edu.om. øçåñ èä úèïçáñíãä èçúãñ¡ ñíìäçáï� keywords: aphanius; garra; fish; anatomy; histology; stomach; intestine s everal studies have been carried out on the diges in this study, we also compare the anatomy and histology of the alimentary canal of another cyprinid, garra barreimiae that is sympatric with a. dispar in the freshwaters of oman. these two species occupy different feeding niches. the cyprinid, is a be materials and methods 3. results 3.1 aphanius dispar character a. dispar g. barriemiae 3.2 garra barreimiae 4. discussion the anatomical structure of the intestine, its relative length in particular, depends on the nature of food eaten by fishes (kapoor et al. 1975; anderson, 1986; kuperman and kuz'mina 1994). the length of the disgestive tracts in general not only incre references kapoor, b.g., smith, h. and verighina, i.a. 1975. the alimentary canal and digestion in teleosts, pp109-239. in: russell f.s & young m., edits. advances in marine biology. vol iii, london: academic press. kayanja, f.j.b., maloiy, g.m.o. and reite, o.b. 1975. the fine structure of the intestinal epithelium of the tilapia grahami. anat. anz. 138: 451-462. noaillac-depeyre, j. and gas, n. 1979. structure and function of the intestinal epithelial cells in the perch (perca fluviatilis l.). anat. rec. 195: 621-640. osman, a.h.k. and caceci, t. 1991. histology of the stomach of tilapia nilotica (linnaeus, 1758) from the river nile. j. fish biol. 38: 211-223. stroband, h.w.j. 1977. growth and diet dependent structural adaptations of the digestive tract in juvenile grass carp (ctenopharingodon idelle val.). j. fish. biol. 11: 167-174. microsoft word math041130-corrected.doc 69-77 squ journal for science, 11 (2006) © 2006 sultan qaboos university 69 two new measures of fuzzy divergence and their properties om parkash*, p.k. sharma** and subhash kumar*** department of mathematics,guru nanak dev university,amritsar 143005,email:omparkash777@yahoo.com*,hindu college, amritsar143001,email: pk_sharma7@rediffmail.com**, s.s.m. college, dinanagar***. قياسان جديدان للتباعد المشوش وخواصهما شارما و سبهاش كومار. ك.باركاش ، ب. أوم في هذا البحث يتم . في األبحاث ايجاد كثيراً من قياسات التباعد الموجه وقياسات التباعد المشوش المقابل لهملقد تم :خالصة . المطلوبةتطوير قياسين جديدين للتباعد المشوش ، كما يتم مناقشة خواصهما abstract: several measures of directed divergence and their corresponding measures of fuzzy divergence are available in the exiting literature. two new measures of fuzzy divergence have been developed and their desirable properties have been discussed. keywords: fuzzy set, fuzzy divergence, symmetric divergence, convex function. 1. introduction he concept of distance has been proved to be very important for its applications to science and engineering. naturally, attempts were made to extend the concept of distance for applications to problems in economics, sociology, psychology, linguistics, genetics, biology, etc. it was however soon realized that the concept of distance would need a modification for such applications. to explain the necessity for a new concept of distance for social, economics, statistical, business and management sciences, we consider the following typical problems in these sciences: 1. find the distance between the intellectual attainment of two students whose proportions of grades a,b,c,d,e are ( )1 2 3 4 5, , , ,p p p p p and ( )1 2 3 4 5, , , ,p p p p p , respectively. 2. find a measure for the variation in the intellectual attainments of a class of m students when the proportions of grades of the ith student are given by ( ) ( )1 2, ,...., ; 1, 2,...,i i nip p p i m= . 3. find the distance between income distributions in two countries whose proportions of persons in n groups are ( )1 2, ,...., np p p and ( )1 2, ,...., nq q q . t om parkash, p.k. sharma and subhash kumar 70 4. find the distance between balance sheets of two companies or between the balance sheets of the same company in two different years. . 5. find a measure for the improvement in income distribution when income distribution ( )1 2, ,...., nq q q is changed to ( )1 2, ,...., nr r r by some government measures when the ideal distribution is assumed to be ( )1 2, ,...., np p p . 6. find a measure for comparing the distribution of industry or poverty in different regions of a country. 7. find the measure of genetic distance between two breeds of animals or between two species of plants. a measure d(p: q) of divergence or distance or cross entropy or directed divergence which has found deep applications in many disciplines can be defined as the discrepancy of the probabilities distribution p from another probabilities distribution q. in some sense, it measures the distance of p from q. the most useful measure of directed divergence is due to kullback and leibler (1951). it is given by ( ) 1 : in n i i i i p d p q p q= = ∑ (1.1) distance measure is a term that describes the difference between fuzzy sets. liu (1992) gave the axiom definition of distance measure and discussed the relationships between distance measure and fuzzy entropy. distance measure can be considered as a dual concept of similarity measure. many researchers, such as yager (1979), kosko (1992) and kaufmann (1975) have used distance measures to define fuzzy entropy. liu (1992) extended yager’s formula to give a general relationship between distance (or similarity measure) and fuzzy entropy and obtained some important conclusions. zadeh (1968) introduced the concept of fuzzy sets in which imprecise knowledge can be used to define an event. using the concept of fuzzy message conditioning, a fuzzy distance measure between two fuzzy sets has been suggested by bhandari and pal (1993). bhandari and pal (1993) introduced a measure corresponding to kullback and leibler’s (1951) probabilistic directed divergence given by ( ) ( ) ( ) ( ) ( )( ) ( ) ( )1 1 i a:b log 1 log 1 n a i a i a i a i i b i b i x x x x x x µ µ µ µ µ µ= ⎡ ⎤− = + −⎢ ⎥ −⎣ ⎦ ∑ (1.2) where ( )a ixµ gives the degree of belongingness of the element ix to the set a. the symmetric fuzzy divergence between two fuzzy sets a and b is given by ( ) ( ) ( )j a:b =i a:b +i b:a (1.3) since there are non-exponential models, innovation diffusion models, epidemic models, a variety of models in economics, social sciences, biology or even in physical sciences, we need a variety of information measures for each field to extend the scope of their applications. hence the development of new generalized parametric and non-parametric measures of divergence is important for the fuzzy distributions. in this paper, we have developed such important measures of fuzzy directed divergence. in section 2, we propose two new measures of fuzzy directed divergence and prove their validity. some desirable properties of these measures have also been studied. in section 3, the proposed measures are generalized. 2. two new measures of fuzzy divergence we now propose a new measure of fuzzy divergence which corresponds to ferreri’s (1980) measure of directed divergence for a probability distribution. this measure is given by two new measures of fuzzy divergence and their properties 71 ( ) ( )( ) ( ) ( ) ( )( ){ } ( )( )( )( ) 1 1 1 log 11 : ; 0 1 1 1 1 log 1 1 a i a i n b i a i a i a i b i a x a x a x i a b a a a x a x a x µ µ µ µ µ µ = +⎡ ⎤ +⎢ ⎥+⎢ ⎥= >⎢ ⎥+ − ⎢ ⎥+ + − + −⎢ ⎥⎣ ⎦ ∑ (2.1) we know that ( ) ( )( ) ( ) ( )( ) ( ) 0 1 0 0 1 /1 log 0 1 / n a ia i i b i a x n aa x n a a x n a µ αµ α µ β= ⎡ ⎤+ ++ ≥⎢ ⎥ + + +⎢ ⎥⎣ ⎦ ∑ where ( ) ( )0 0 0 0 1 1 ; ; , n n a i b i i i x xµ α µ β α β = = = =∑ ∑ may be different from unity, or ( )( ) ( ) ( ) ( ) 00 1 0 1 1 log log 1 n a i a i i b i a x n a a x n a a x n a µ α µ α µ β= + + + ≥ + + + ∑ (2.2) similarly, ( )( ){ } ( )( )( )( ) ( )( ) ( ) ( ) 1 0 0 0 1 1 1 1 log 1 1 1 1 log 1 n a i a i i b i a x a x a x n a a n a a n a a µ µ µ α α β = + − + − + − + − ≥ + − + − ∑ (2.3) adding (2.2) and (2.3) and dividing by a , we get ( ) ( )0 0: ,ai a b f α β≥ where ( ) ( ) ( )( ) ( ) ( ) 00 0 0 0 0 0 0 11 , log 1 log 1 n a an a f n a n a a a n a n a a αα α β α α β β ⎧ ⎫+ −+⎪ ⎪ = + + + −⎨ ⎬ + + −⎪ ⎪⎩ ⎭ (2.4) differentiating (2.4) w.r.t. 0a , we have ( ) ( ) ( ) 00 0 0 0 0 1 , log log 1 n a an a f n a n a a αα α β β β + −+ ′ = − + + − also ( ) ( ) ( ) ( )( )0 0 0 0 2 , 0 1 an a f n a n a a α β α α + ′′ = > + + − om parkash, p.k. sharma and subhash kumar 72 thus ( )0 0,f α β is a convex function of 0α which has its minimum value when 0 0 0 0 2 1 2 n a n na a n na n a n na a n na α α β β + + − + = = = + + − + that is , when 0 0n a n aα β+ = + or when 0 0α β= and the minimum value is 0 so that ( )0 0, 0f α β > and vanishes when 0 0α β= . consequently, ( ):ai a b is a convex function of ( ) ia ixµ ∀ . again, differentiating (2.4) w.r.t. 0β , we have ( ) ( ) ( ) 00 0 0 0 0 1 , 1 n a an a f n a n a a αα α β β β + −+ ′ = + + + − also, ( ) ( ) ( ) ( )( ) ( )( ) 00 0 0 2 2 0 0 1 , 0 1 a n a aa n a f n a n a a αα α β β β + −+ ′′ = + > + + − thus ( )0 0,f α β is a convex function of 0β and consequently, ( ):ai a b is a convex function. thus for all values of 0α and 0β , we have (i) ( )a:b 0ai ≥ (ii) ( )a:b 0 when a=bai = (iii) ( ):ai a b is a convex. hence ( )a:bai is a valid measure of fuzzy directed divergence and ( ) ( ) ( )a:b a:b b:aa a aj i i= + (2.5) is a valid measure of fuzzy symmetric divergence . now ( ) ( ) ( ) 0 a:b 0 and a:b i a:ba aa a lt i lt i → →∞ = = thus ( ) ( ) ( ) min max : 0 and : i a:bi a b i a b⎡ ⎤ ⎡ ⎤= =⎣ ⎦ ⎣ ⎦ monotonicity of ( ):ai a b differentiating (2.1) both sides w.r.t. ,a we get two new measures of fuzzy divergence and their properties 73 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 2 1 1 11 : log 1 1 1 1 11 log 1 1 1 n a i a i i b i b i n a i a i i i b i a x a xd i a b da a a x a x a a x a a x a a a x a a xβ µ µ µ µ µ µ µ µ = = ⎡ ⎤+ + = − − +⎢ ⎥ + +⎣ ⎦ ⎡ ⎤+ − + + − − +⎢ ⎥ + − + +⎢ ⎥⎣ ⎦ ∑ ∑ (2.6) we know that log 1 0x x− + ≤ . thus ( ) ( )ψ log 1 0x x x= − − + ≥ so that ( ) 1 1ψ 1 1x x x ⎛ ⎞′ = − − = −⎜ ⎟ ⎝ ⎠ . if ( )0 1, ψ 0x x′< < < and if ( )1, ψ 0x x′> > and if ( )1, ψ 1 0x = = so that the graph of ( )ψ x is as shown in figure 1. thus ( ): 0a d i a b da ≥ so that ( )a:bai is an increasing function of a . hence as a increases from 0 to ∞ , ( )a:bai increases from 0 to ( )i a:b . om parkash, p.k. sharma and subhash kumar 74 now we propose another measure of fuzzy directed divergence which include fuzzy directed divergence corresponding to kullback and leibler’s (1951) probabilistic measure and fuzzy directed divergence corresponding to kapur’s (1985) measure of probabilistic directed divergence in particular or in limiting cases. this measure is given by ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )( ) ( )( ) 1 1 1 : log 1 log 1 1 111 1 log 1 1 log 1 1 1 n a i a i a a i a i i b i b i n a ia i a i a i i b i b i x x i a b x x x x a xa x a x a x a a x a x µ µ µ µ µ µ µµ µ µ µ µ = = ⎡ ⎤− = + −⎢ ⎥ −⎣ ⎦ ⎡ ⎤⎧ + −+ ⎪ − + + + −⎢ ⎥⎨ + + −⎢ ⎥⎪⎩⎣ ⎦ ∑ ∑ (2.7) we know that ( ) ( ) ( ) 0 1 0 0 / log 0 / n a i a i i b i x x x µ µ α α µ β= ≥∑ or ( ) ( ) ( ) 0 0 1 0 log log β n a i a i i b i x x x µ α µ α µ= ≥∑ (2.8) similarly, ( )( ) ( ) ( ) ( ) 00 1 0 1 1 log log 1 n a i a i i b i x n x n x n µ α µ α µ β= − − − ≥ − − −∑ (2.9) adding (2.8) and (2.9), we get ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 0 0 0 0 0 0 1 log 1 log 1 log log n a i a i a i a i i b i b i x x x x x x n n n µ µ µ µ µ µ α α α α β β = ⎡ ⎤⎛ − + −⎢ ⎥⎜ −⎢ ⎥⎝⎣ ⎦ − ≥ + − − ∑ (2.10) adding (2.4) from (2.10), we get ( ) ( )0 0: ,ai a b g α β≥ where ( ) ( ) ( ) ( )( ) ( ) ( ) 0 0 0 0 0 0 0 0 00 0 0 0 0 , log log 11 log 1 log 1 n g n n n a an a n a n a a a n a n a a α α α β α α β β αα α α β β − = + − − ⎫⎧ + −+ ⎪ + + + + −⎨ ⎬ + + − ⎪⎩ ⎭ (2.11) two new measures of fuzzy divergence and their properties 75 differentiating (2.11) w.r.t. 0α , we have ( ) ( ) ( ) 00 0 0 0 0 0 0 0 0 1 , log log log log 1 n a an n a g n n a n a a αα α α α β β β β β + −− + ′ = − + − − + + − and ( ) ( ) ( )( )( )0 0 0 0 0 0 2 , 0 na a g n n a n na a α β α α α α + ′′ = > − + + − so that ( )0 0,g α β is a convex function of 0α which has its minimum value when 0 0α β= , that is when ( ) ( )a i b ix xµ µ= , and the minimum value is 0 so that ( )0 0, 0g α β ≥ and vanishes when 0 0α β= . consequently, ( )a:bai is a convex function of ( )a ixµ and similarly we can prove that ( ):ai a b is a convex function of ( )b ixµ . thus for all real values of 0α and 0β , we have (i) ( )a:b 0ai ≥ (ii) ( )a:b 0ai = when a = b (iii) ( )a:bai is convex so that ( )a:bai is a valid measure of fuzzy directed divergence and ( ) ( ) ( )a:b a:b b:aa a aj i i= + is a valid measure of symmetric divergence. the following relations are obvious : ( ) ( ) ( ) ( ) ( ) a:b (a:b) a:b a:b a:b a:b a a a a i i i j j j = − = + also ( ) ( ) 0 a:b i a:baa lt i → = 3. generalized measure of fuzzy divergence a generalization of kullback leibler’s (1951) measure is given by ( ) ( ) ( ) ( ) ( )( ) ( ) ( )1 1 : 1 1 n i i b i b i i b i b i x x i a b x x x x µ µ µ µ µ µ α α = ⎡ ⎤⎛ ⎞ ⎛ ⎞− ′ = φ + − φ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟−⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ∑ (3.1) where ( )φ ⋅ is a twice differentiable convex function with ( )1 0φ = . the measure (1.1) can be obtained by taking ( ) logx x xφ = in (3.1) om parkash, p.k. sharma and subhash kumar 76 similar generalizations of ( )a:bai and ( )a:bai are given by ( ) ( )( ) ( ) ( ) ( )( ){ } ( )( )( )( ) 1 1 1 : ; 0 1 1 1 a i b i n b i a i a i b i b x a x x i a b a a x a x x αµ µ αµ α αµ µ α µ = ⎡ ⎤⎛ ⎞1+ + φ⎢ ⎥⎜ ⎟ 1+⎢ ⎥⎝ ⎠ ′ = >⎢ ⎥⎛ ⎞1+ 1−⎢ ⎥+ + − φ⎜ ⎟⎢ ⎥⎜ ⎟1+ −⎝ ⎠⎣ ⎦ ∑ (3.2) and ( ) ( ) ( ) ( ) ( )( ) ( )( ) ( )( )1 : 1 1 n ii a b i b i i i b i xx i a b x x x x αα β µµ µ µ µ µ= ⎡ ⎤⎛ ⎞1−⎛ ⎞ ′ = φ + − φ⎢ ⎥⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟−⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ∑ ( )( ) ( ) ( ) ( )( ){ } ( )( ) ( )( ) 1 1 1 1 1 ; 0 1 1 a i b i b i n b i i a i b i x a x a x x a a x x αµ µ µ αµ α µ α µ = ⎡ ⎤⎛ ⎞1+ + φ + + −⎢ ⎥⎜ ⎟⎜ ⎟1+⎢ ⎥⎝ ⎠ − >⎢ ⎥ ⎡ ⎤1+ −⎢ ⎥+φ⎢ ⎥⎢ ⎥1+ −⎢ ⎥⎣ ⎦⎣ ⎦ ∑ (3.3) now differentiating (3.2) w.r.t. a , we get, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 2 1 1 1 1 1 1 1 1 1 1: 1 1 1 1 1 1 1 1 1 1 1 1 a i a i a i b i b i b i n a ia i b i a i a i b i b i a x a x a x a x a x a x a xd i a b da a a x a x a x a x a x µ µ µ µ µ µ µ µ µ µ µ µ = ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ + + ′⎢ ⎥−φ + − φ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ + + +⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎢ ⎥ ⎛ ⎞+ −′ ⎢ ⎥ = +φ⎜ ⎟⎢ ⎥⎜ ⎟+ −⎝ ⎠⎢ ⎥ ⎢ ⎥⎛ ⎞ ⎛ ⎞+ − + −⎢ ⎥′+ − φ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥+ − + −⎝ ⎠ ⎝ ⎠⎣ ⎦ ∑ (3.4) if we take ( ) ( ) ( ) ( ) ( ) ( )1 1 ,h x x x x x x′ ′= −φ + − φ + − φ then ( ) ( ) ( )1h x x x′ ′′= − φ since ( ) 0x′′φ > ( ) if 0 1h x x′ < < < and ( ) 0 if 1h x x′ > > two new measures of fuzzy divergence and their properties 77 also since ( ) 0,φ 1 = we have ( )1 0h = . thus equation (3.4) gives that ( )( ): 0a d i a b da ′ > thus ( )a:bi′ is an increasing function of a . also, ( ) 0 : 0 a lt i a a b → ′ = and ( ) ( ): :aalt i a b i a b→∞ ′ ′= 4. conclusion it has been observed that there are redundancies and overlapping in similar situations which if removed can increase the efficiency of the process. the development of new parametric and non-parametric measures of information will definitely reduce uncertainty and consequently the process can be more efficient. thus development of new generalized probabilistic and fuzzy measures of divergence is necessary to get as much insight as possible into the various physical situations. many such fuzzy divergence measures can be generated for different situations. 5. acknowledgement one of the authors, p.k. sharma expresses his warm thanks to the university grants commission for providing financial assistance for the preparation of this paper. 6. references bhandari, d. and pal, n.r. 1993. some new information measures for fuzzy sets. infor. sci., 67: 209-228. ferreri, c. 1980. hyperentropy and related heterogeneity, divergence and information measures. statistica, 40(2): 155-168. kapur, j.n. 1985. some new measures of entropy and divergence. jour math. phy. sci., 19(6): 489-501. kaufmann, a. 1975. introduction to the theory of fuzzy subsets. academic press, new york. kosko, b. 1992. neural networks and fuzzy systems. prentice hall, englewood cliffs, n j. received 30 november 2004 accepted 22 august 2006 microsoft word phys081124-f edited_checked.doc 71-83 squ journal for science, 14 (2009) © 2009 sultan qaboos university 71 anisotropy in rfe2 intermetallics: an nmr study c. carboni department of physics, college of science, sultan qaboos university, p.o. box 36, postal code 123, alkhod, muscat, sultanate of oman, email: carlo@squ.edu.om. nmr دراسة : rfe2تباين خواص المركبات المعدنية كاربوني. ك باسـتخدام اعتمـاد طيـف الـرنين . 3oh tb3++3mt+. النادرةاألرضلقد إستقصينا تباين خواص أيونات :خالصـة 2tmfe 2tbf 2hofe الموجودة في المركبات mt169 , bt159, ho165المغناطيسي النووي على شدة المجال لنوى تفاعل الدقيق لهذه األيونات على طيف الرنين المغناطيسي النووي و الذي يعطى شـدة يطغى ال . و المركبات ذات الصلة .كما قمنا بمقارنة القياسات بالحسابات النظرية. جيجاهيرتز7 الى 2االستقطاب في حيز التردد من abstract: the anisotropy of the ho3+, tb3+ and tm3+ rare-earth ions in rfe2 compounds is investigated using the field dependence of the nmr spectra of 169tm, 159tb and 165ho in polycrystalline tmfe2, tbfe2, hofe2 and related pseudo-binary compounds. the very large hyperfine interaction in these ions dominates the nmr spectrum; the nmr frequencies in the 2 to 7 ghz range provide therefore a measure of the localized 4 f moment and its orientation in the crystal field. we compare the nmr measurements to single ion computations that include magnetostriction. keywords: cubic laves phases, rare-earth intermetallic, hyperfine splitting, magnetic anisotropy, nmr. 1. introduction he cubic laves phases series rfe2 where r is a rare-earth element is the simplest of the several intermetallic compounds in which rare-earth and iron magnetism coexist. for more than 30 years the rfe2 compounds and their pseudo-binary (rr') fe2 and r(fem)2 alloys where m is a transition metal have been the subject of intense investigations. these compounds have provided and continue to provide (sawickki et al, 2000) a fertile ground to test theoretical models. more recently epitaxially grown films (lee et al, 2000, de la fuente et al, 2001, gordeev et al, 2001, oster et al, 2005), x-ray magnetic circular dichroism investigations (fujiwara et al, 2005, dumesnil et al, 2002, parlebas et al, 2006) and the hydrated rfe2 materials (paul-boncour, 2004) have attracted the attention of several researchers. however, there are some basic questions in the rfe2 that are not yet completely resolved. there is still uncertainty about the anisotropy of the iron sub-lattice, about the t c. carboni 72 contribution of magneto-elastic effects to the measured anisotropy (mougin et al, 2000), about the crystal-field interaction at the lanthanide site and about the role of the ordered super-lattice of vacancies in the c15 laves phases (gratz et al, 1996). also, the distribution of the total magnetization between the iron and lanthanide sublattices and the relative contribution of localized and itinerant moments is still an open question (fujiwara et al 2005). in the present paper the anisotropy of the rare-earth ion is investigated using the field dependence of the nmr spectra of 169tm(i = 1/2), 159tb(i = 3/2) and 165ho(i = 7/2) in polycrystalline tmfe2, tbfe2, hofe2 and some pseudo-binary compounds. in the ho3+, tb3+ and tm3+ ions the very large hyperfine interaction dominates the nmr spectrum; the nmr frequencies in the 2 to 7 ghz range provide therefore a measure of the localized 4 f moment and its orientation in the crystal field. we compare our nmr measurements to single-ion computations that include the distortion of the cubic environment of the lanthanide ion due to the magnetostriction. the results from the computation suggest that the magnetostriction does not have a significant effect on the nmr spectrum. 2. theory in this section we describe the model used for the computation of the magnitude and the orientation of the moments in rfe2 compounds subjected to a magnetic field applied in any arbitrary direction but before doing so, we need to clarify a possible confusion between two senses of the term “anisotropy”. there are two distinct aspects to the anisotropy of a magnetic material, the energy anisotropy and the magnetization anisotropy. the former, conventionally specified by classical “anisotropy constants” denotes the angular variation of the free energy, whereas the latter denotes the angular variation of the magnitude of the ionic moment. for the rfe2 compounds in which the exchange interaction exh may, at least to a first approximation, be considered isotropic both types of anisotropy are manifestations of the crystal-field interaction cfh at the lanthanide site. the relationship between energy and magnetization anisotropy is not straightforward. for example, it is not necessarily the case that the hardest direction of magnetization (i.e. the direction for which the free energy is greatest) is the direction in which the ionic moment is most quenched. the crystal-field interaction cfh in the 2rfe is a small perturbation on the exchange interaction exh the energy anisotropy may thus be regarded as a quasi-classical effect of first order in cfh . the magnetization anisotropy, on the other hand, is an essentially quantum mechanical effect associated with those terms in cfh that do not commute with exh . the quenching of the ionic moment is a second order effect varying as the ratio of square of the strength of cfh to that of exh . a fuller discussion of these points can be found in section 4.4 of mccausland and makenzie (1979). 2.1 the effective electronic hamiltonian the orientation of the lanthanide and the iron moments in a crystal of rfe2 subjected to a magnetic field applied at an arbitrary angle is a compromise between several competing interactions. there is the ferrimagnetic coupling between the lanthanide and the iron, the crystal-field interaction, the interaction with the applied field and indirectly the magnetostriction which affects the crystal field. if one assumes that the iron sub-lattice is isotropic in both senses, the magnitude of the iron moment is constant and its direction always collinear to the total field fetotb at the iron site, the equilibrium orientation of the two moments in the presence of a field applied at an arbitrary direction is as shown on figure 1. the total field at the lanthanide site is mbb λ−= a ln tot where m is the iron moment and λ the lanthanide-iron exchange constant. anisotropy in rfe2 intermetallics 73 the lanthanide ion is described by the effective electronic hamiltonian figure 1. the orientation with respect to the direction of the applied field ba of the iron moment m, the lanthanide moment µ, the total field lntotb at the lanhanide site and the total field fe totb at the iron site. fe exb and fe exb are respectively the exchange field seen by the iron and the exchange field seen by the lanthanide ion. µbvobob lntot26644el ⋅−++=h (1) where the n nb o denote the cubic crystal-field terms in the notation of lea, leask and wolf (1962). the operators 4o and 6o are respectively combinations of fourth order and sixth order stevens operators equivalent (stevens 1952); the explicit form of these operators is given in the appendix. the term 2v is the second order crystal-field term arising from the distortion of the cubic environment of the ion caused by magnetostriction (buschow 1977). ba ba m µ ln exb ln totb fe exb fe totb d ir ec ti on o f t he ap pl ie d fi el d c. carboni 74 [ ])(kk)(kk)(kk )1j2(j k2 311313233232122121 me 2 jjjjjjjjjjjjv +++++− = (2) where k is a unit vector parallel to the total angular momentum j of the 4 f electrons of the ion and mek is the magneto elastic constant. the indices 1, 2 and 3 denote respectively the directions of the three four-fold axis of the cubic unit cell. the crystal-field parameters are phenomenological parameters determined experimentally. in transparent compounds these parameters can be accurately obtained from the optical absorption spectrum. in metals the determination of the crystal field parameters is not straightforward; they are obtained by combinations of different experimental techniques which can produce conflicting results (mcmorrow et al, 1989). for the rfe2 series there is to our knowledge no detailed comprehensive analysis for the crystal field parameters. to date the most widely accepted sets of crystal field parameters for the rfe2 are the ones obtained by germano and butera (1981). the parameters for the tb, ho and tm compounds are given in table 1 together with the exchange and the magnetoelastic constant. germano and butera obtained the crystal field parameters from specific heat measurements. in their analysis the magenostriction is not taken into account, the site symmetry is considered exactly cubic; this plus the fact that the contribution from the crystal field to the specific heat is relatively small may raise questions concerning the accuracy of the parameters. nevertheless most of the predictions based on these parameters are in fairly good agreement with experiments; these parameters are used faute de mieu for the present work. the computed direction of spontaneous magnetization in hofe2, tmfe2 and tbfe2 at zero temperatures is respectively the <100>, <110> and <111> direction. table 1. the exchange fields, the crystal-field parameters and the magnetoelestic constants obtained by germano and butera (1981) for hofe2, tbfe2 and tmfe2. λm (t) 104 b4 (k) 10 6b6 (k) kme (k/ion) tbfe2 162 101 20 -13 hofe2 108 -9.26 5.1 -1.7 tmfe2 70 55 35 -9.0 in tmfe2 the computation reveals a low-lying first excited state that strongly prefers the <111> direction. the existence of this excited state is responsible for the reorientation of the magnetization at about 55 k reported by germano and butera. above 55 k the <111> direction is the preferred orientation for the magnetization. the experiments reported in the present work were carried out at liquid-helium temperatures where only the ground state is significantly populated therefore the <110> direction is strongly preferred in tmfe2. 2.2 computation in zero applied field and in the absence of magnetostriction the ground state and ground state energy of the lanthanide ion can be readily obtained form the hamiltonian 1. the expectation value of zj for the ground state is then obtained to calculate the intra-ionic contribution to the hyperfine splitting and the rare-earth’s moment. in the presence of an applied field at an arbitrary orientation one must first determine the orientation of ln totb . to determine the equilibrium orientation of lntotb in an applied field we have minimized with respect to the polar angles of the iron moment, feθ and feφ the free energy per formula unit at absolute zero including the magnetostriction. at zero temperature the free energy is simply anisotropy in rfe2 intermetallics 75 , (3)el fef u ts u h h= − = = + where ( )fe ah 2 λ= −b m.µ is the contribution from the iron sub-lattice and the expectation values are calculated using the ground state of the lanthanide ion. in writing equation (3) it is implicitly assumed that the iron sub-lattice is isotropic in both senses. the minimization of the free energy (3) is not straightforward. the term 2v depends on the orientation of the lanthanide moment that is itself the object of the computation. the computation was done by iterations. an educated guess of the orientation of the lanthanide moment was used for the first iteration. the computation was repeated until self-consistency and minimum energy was achieved. it was observed that the term 2v does not affect significantly the outcome of the computation. in order to investigate the behavior of polycrystalline samples in applied fields we have computed the magnitude and orientation of the lanthanide moment in hofe2 , tbfe2 and tmfe2 at various fields applied in 30 different orientations equally spaced over the portion of the unit sphere defined by the <100>, <111> and <110> directions. the results for the 8 t field are summarized in table 2 and figure 2. figure 2 is a planar projection of the portion of the unit sphere under consideration. the orientation of the moment is represented on the figure by a point corresponding to the intersection of the direction of the moment and the surface of the unit sphere. the shaded areas around the <100>, <110> and <111> axis represent the loci of the direction of the holmium, the thulium and the terbium moments respectively, when the direction of the applied field is scanned across the entire area of the unit sphere under consideration. one can see that an 8 t field applied in any direction hardly moves the thulium moment away from its <110> preferred orientation, 5 degrees at most when the field is along the <111> direction. holmium, on the other hand, can be more readily moved away from the <100> preferred orientation, 25 degrees when the field is along the <110> axis. table 2. the computed orientation of the iron’s magnetic moment m, the lanthanide magnetic moment µ and the total field lntotb at the lanthanide site for an 8 tesla field applied along each of the principal crystallographic directions. the column before last gives the computed intra-ionic contribution to the dipolar hyperfine splitting and the last column gives the total field-dependent contribution (intra-ionic plus the contribution from applied field). ψ is the angle between the applied field and the lanthanide moment. ba m lntotb µ ion θ φ θ φ θ φ θ φ a’ = a<j>z (mhz) a’+ γβcosψ (mhz) 0 0 54.0 45 52 45 52 45 3171 3219 45 0 54.2 44 53 43 54 43 3171 3236 tb3+ 54.7 45 54.7 45 54.7 45 54.7 45 3171 3250 0 0 0 0 0 0 0 0 6488 6559 45 0 25 0 27 0 26 0 6479 6546 ho3+ 54.7 45 13 45 15 45 13.5 45 6484 6537 0 0 48 0 44 0 44 0 2308 2328 45 0 45 0 45 0 45 0 2309 2337 tm3+ 54.7 45 45 0 45 5 45 4 2308 2331 c. carboni 76 30 10 20 30 40 40 2010 <110> <111> <100> tbfe2 hofe2 tmfe2 figure 2. the planar projection of the portion of the unit sphere under consideration. the angles along both axes are in degrees. the shaded areas around the <100>, <110> and <111> axis represent the loci of the direction of the holmium, the thulium and the terbium moments respectively, when the direction of an applied 8 t field is scanned across the entire area of the unit sphere under consideration. table 2 gives the computed polar angles of the iron moment m , the lanthanide moment µ and the total field at the lanthanide site lntotb when the 8 tesla field ab is applied along each of the principal crystallographic orientations. the last two columns give computed field dependent contributions to the dipolar hyperfine splitting which will be discussed in the next section. 2.3 the hyperfine splitting the theory of the hyperfine splitting in rare-earth compounds is described in detail in mccausland and makenzie (1979), bunbury et al (1989) and li et al (1996) whose notation we shall follow. the hyperfine splitting of the electronic states is described to first order by the effective nuclear spin hamiltonian { })ii(ih 22zz 31tt pah −+= (4) where i is the nuclear spin, ta at and tp are respectively the dipolar and the quadrupolar hyperfine parameters. the z-axis is chosen to be parallel to j . preliminary computations have shown that in the exchange dominated rfe2 compounds second order contributions to the hyperfine parameters are at most 0.05%. therefore, the second order terms (bunbury et al 1989) have been neglected in the present work. because of the strong hyperfine coupling in ho3+, tb3+ and tm3+ the total dipolar hyperfine constant is dominated by the dipolar intraionic term (5) ' za a j= anisotropy in rfe2 intermetallics 77 where a, the dipolar hyperfine coupling constant, is 6497 mhz for ho3+, 3180 mhz for tb3+ and 2333 mhz for tm3+, the intra-ionic contribution a' is therefore very sensitive to small variations of the 4 f moment and provides an accurate measure of the moment. the extra-ionic contribution to the dipolar splitting is zb n nga h µ⎛ ⎞′′ ′′= ⎜ ⎟ ⎝ ⎠ (6) where zb′′ is the component along j of b′′ the extra-ionic field at the lanthanide nucleus. ′′b is the vector sum of various terms a dip p n′′ = + + +b b b b b (7) where ab is the applied field, dipb is the dipolar field, pb is the field due to conduction electrons polarized by the spin of the parent ion and nb is the transferred hyperfine field from neighboring rare-earth and iron ions. to a good approximation ( )dip p n+ +b b b can be regarded as independent of the applied field. since we are interested in the field dependence of the hyperfine splitting, we will consider the field independent part of the extra-ionic contribution to the dipolar hyperfine splitting ( ) ( )thf n n dip p na g / h b b b= µ + + (8) as a free parameter to be determined from the zero-field nmr spectrum; thfa is equal to the difference between the computed intraionic contribution and the measured total dipolar hyperfine parameter in zero fields. the total dipolar hyperfine splitting is therefore t thfa a a b cosγ′= + + ψ (9) where ψ is the angle between the applied field and the lanthanide moment and γ is the gyromagnetic factor. the field dependent contribution ( )a b cosγ′ + ψ computed in a field of 8 t applied along each of the three principal crystallographic axis is given in table 2. 3. experiment. the compounds were prepared by melting the constituents in an arc furnace under an atmosphere of purified argon. for the thulium compounds, the starting materials contained a 3% excess of tm to compensate for the anticipated loss by evaporation. the resulting ingots were re-melted three times, annealed for two weeks at 900 0c and finally crushed to form a fine powder sample. x-ray examination revealed less than 5% of nonlaves phases. approximately 5 mg of the powder, embedded in epoxy resin, was located close to the current antinode of the central conductor of a tunable coaxial resonator of the type described by mccausland and makenzie (1979). the nmr measurements were carried out at 1.3 k and 4.2 k in magnetic fields up to 8 t using the microwave spin-echo spectrometer described by carboni et al (1989). the spectra were obtained by varying the frequency at fixed values of the applied field. c. carboni 78 figure 3. the 169tm nmr line of thulium in tmfe2 in zero fields and in an applied field of 7.5 t. for tmfe2 and tbfe2 the measured relaxation times are of the order of several micro seconds which is an order of magnitude larger than the pulse separation (200 ns) used to take the spectra so the nmr lines are negligibly distorted by relaxation. in pure ho fe2 the transverse relaxation time is of the order of 200 ns, too short to obtain a reliable spectrum. the seven lines of the 165ho (i = 7/2) spectrum could not be unequivocally identified. the 165ho nmr data presented here were obtained mainly from specimens with a few percent of holmium substituted in tmfe2, lufe2 and yfe2 where the relaxation times are less prohibitive and the spectra in low fields are resolved. the spectrum of 159tb(i = 3/2) consists of three lines; because of the strong quadrupolar hyperfine coupling the lines are very well resolved; the separation between the lines is of the order of 350 mhz. the spectrum of 169tm(i = 1/2) consists of a single line. a summary of the hyperfine parameters measured in the various compounds investigated at liquid helium temperatures and in zero fields is given in table 3. for comparison previously published data from other r': rfe2 materials have also been included in the table. 4. discussion. the nmr line of 169tm:tmfe2, in zero fields and in an applied field of 7.5 tesla are shown in figure 3. the field dependence of the measured total hyperfine parameter ta of 169tm:tmfe2, is shown in figure 4-a; the variation is linear with a slope of (3.42 + 0.05) mhz/t. the slope is less than the value of 3.52 mhz/t expected for the nuclear spin parallel to the applied field. we also observe that the applied field causes only a small broadening of the nmr line (see figure 5). anisotropy in rfe2 intermetallics 79 a b tbfe2 t = 4.2 k figure 4. the measured total dipolar hyperfine parameter of 169tm:tmfe2 and 159tb:tbfe2 as a function of the applied field. these two observations confirm the prediction from our computations that the moment of the tm3+ ion in all the crystallites of the specimen has remained close to the <110> orientation even at high fields. the computation c. carboni 80 shows that there is a significant quenching of <jz> if the moment is rotated away from the <110> orientation with a concomitant reduction of the hyperfine splitting. the reduction is 28% if the thulium moment is forced along the <100> direction corresponding to a shift of more than 350 mhz in the nmr frequency. therefore, if the rare-earth moments rotate to become close to the direction of the applied field one expects a line broadening of the order of 200 to 300 mhz. this is not observed. when the thulium ion is placed in a non magnetic and isotropic host like 1% 169tm (tm:lufe2) we observe that at decreases with applied field with a slope of (–13 + 2) mhz/t, much larger than the -3.52 mhz/t expected for the nuclear spin anti-parallel to the applied field. the line broadens rapidly with the applied field; the line width is 10 mhz in a field of 0.7 t and the line is too broad for reliable measurements in a field of 1 t. assuming that the lutetium sub-lattice does not contribute significantly to the anisotropy these observations can be interpreted as follows: the applied fields causes a significant rotation of the iron moments towards a direction parallel to the applied field. because of the strong ferimagnetic coupling between the thulium ion and the iron sublattice, the thulium moments are gradually rotated away from the strongly preferred <110> orientation hence the sharp reduction in the intraionic contribution to at and the line broadening. finally we note from table 3 that when the thulium ion is placed in the hofe2 host there is an increase of about 10 mhz in the dipolar hyperfine parameter and not the expected reduction of about 350 mhz if the thulium moment was forced along the <100> orientation preferred by the hofe2 host. one can conclude that thulium moment has remained close to the <110> direction and that therefore the iron together with the holmium sublattice are not along the <100> direction. the increase in the dipolar hyperfine parameter is due to the larger transferred hyperfine field in the holmium host due the fact that ho3+ has a larger projected spin (σho = 2.0) than tm 3+ (σtm = 1.0) (mccausland and makenzie, 1979). a refined analysis of the data presented in this section is still in progress and will be presented in a separate publication (carboni et al 2009, to be published). table 3. the measured hyperfine parameters of tm3+, ho3+ and ho3+ in various rfe2 hosts. (a) li et al (1996), (b) de azevedo (1986). (c) al assadi et al (1984). nucleus and host at (mhz) pt (mhz) 169tm:tmfe2 2 +2456 1% 169tm (tm:ho fe2) 2 +2467 1% 169tm (tm:lu fe2) 2 +2445 169tm (tm:y fe2) (a) 2 +2422 169tm (tm:gd fe2) (a) 2 +2466 1% 165ho (ho:tmfe2) 5 +6920 1 +60 3% 165ho (ho:lufe2) 10 +6850 2 +57 165ho (ho:yfe2) (c) 10 +6860 2 +59 165ho (ho:gdfe2) (c) 10 +6986 159tb:tbfe2 3 +3798 2 +5 34 159tb(tb:lufe2) (b) 3 +3693 2 +349 159tb(tb:gdfe2) (b) 3 +3822 2 +356 the field dependence of the measured total dipolar hyperfine parameter at of 159tb:tbfe2, is shown on figure 4b; the variation is linear with a slope of (9.5 + 0.1) mhz/t. the field dependence of the line-width is given in figure 5. the data shows that like for tmfe2 the anisotropy is, as predicted by the computation, very large and the terbium ion remains close to the <111> direction even at high fields. a detailed investigation of the zero field hyperfine splitting of tb3+ in various rfe2 hosts has been done by w m de azevedo (de azevedo, 1986 and de azevedo et al 1985). except in the tmfe2 host, the nmr spectra from 165ho in the rfe2 hosts are poorly resolved because the transverse relaxation time is comparable to the minimum pulse separation available on the spectrometer. anisotropy in rfe2 intermetallics 81 moreover, the nmr lines broaden rapidly with the applied field hence the large uncertainty on the hyperfine parameters for the holmium given in table 3. in the hofe2 compound it was not possible to obtain the complete 7-lines spectrum therefore it was not possible to obtain a value for the dipolar hyperfine parameter. the quadrupolar parameter pt obtained from the spacing between adjacent lines for this compound is (55 + 5) mhz. figure 5. the behavior of the line width of the central line of the nmr spectra of 169tm:tmfe2, 159tb:tbfe2 and 165ho: ho(tmfe2). for holmium in the tmfe2 host the spectrum is well resolved in fields up to 5 t. however, as can be seen in figure 5, the line-width increases sharply with the applied field. if one assumes that the line broadening is mainly due to a spread of the orientations of the ho3+ moments with respect to the crystallites axis then, since it has been established that the tm3+ moment remains along the <110> direction, one can conclude that the applied field does, as predicted by the computation, achieve some rotation of holmium moment away from the <100> direction. the slope of at versus field is (8.3 + 0.2) mhz/t, significantly less than the expected 8.9 mhz/t; this is almost certainly due to a gradual quenching of the holmium moment as it is rotated away from its preferred direction. 5. acknowledgements the experimental part of this work was done during the time the author was at the university of manchester (uk) supported by grants from the uk engineering and physical science research council (epsrc). the author is also grateful to prof mah mccausland and dr d stp bunbury for comments, discussions and support. c. carboni 82 appendix the steven operator equivalent pertaining to a site of cubic symmetry. [ ] 222404 )1(3)1(625)1(3035 +++−−+−= jjjjjjjjo zz ( )44 2 14 4 jjo −+ += [ ] [ ] )1((60)1(40)1(5 294)1(525)1(1057)1(3105231 222 222460 6 +−+++− ++−++−+−= jjjjjj jjjjjjjjjo zzzz [ ]( ) ( ) [ ]38)1(1138)1(11 444414424146 −+−+++−+−= −+−+ jjjjjjjjjjo zz in the notation of lea leak and wolf: 4 6 0 66 4 4 0 44 o21oo o5oo −= += 6. references al assadi, k.f., mackenzie, i.s. and mccausland, m.a.h. 1984. domain and domain-wall nuclear magnetic resonance of 265ho in (gd,y)fe2, j phys f: met. phys 14: 525. bunbury, d.st.p., carboni, c. and mccausland, m.a.h. 1989. field dependence of the hyperfine splittings in holmium hydroxide j. phys. condens. mat. 1: 1307. bushow, k.h.j. 1977. intermetallic compounds of rare earth and 3-d transition metals, rep prog phys 40: 1179-1256. carboni, c., mackenzie, i.s. and mccausland, m.a.h. 1989. nuclear magnetic resonance at microwave frequencies, hyperfine interactions 51: 1139. carboni, c., bunbury, d.st.p. and mccausland, m.a.h. 2009. crystal-field anisotropy of tmfe2. to be published. de azevedo, w.m., mackenzie, i.s. and berthier, y.j. 1985. nmr of 159tbfe2 and tbfe3. j phys f. met. phys. 15: l243. de azevedo, w.m. 1986. the hyperfine interaction of terbium in magnetically ordered compounds, phd thesis, university of manchester, uk. dumesnil, k., dufour, c., mangin, ph. and rogalev, a. 2002. magnetic springs in exchange coupled dyfe2-yfe2 superlattices: an element selective x-ray magnetic circular dichroism study, phys. rev. b, 65: 094401-094406. de la fuente., c., arnaudas, j.i., ciria, m., del moral, a., dufour, c., mougin, a. and dumesnil, k. 2001. magnetic and magnetoelestic behavior of epitaxial tbfe2-yfe2 bilayers, phys. rev. b 63: 054417-054427. fujiwara, a., asakura, k., harada, i., ogasawara, h. and kotani, a. 2005. xmcd study on electronic and magnetic states of rare earth 5d electrons in laves compounds rfe2, phys. scr. t115: 113114. germano, d.j. and butera, r.a. 1981. heat capacity of, and crystal-field effect in, the rfe2 intermetallic compounds, phys. rev. b, 24(7): 3912-3927 gordeev, s.n., beaujour, j-m l., bowden, g.j., rainford, b.d., de groot, p.a.j., ward, r.c.c., wells, m.r. and jansen, a.g.m. 2001. giant magnetoresistence by exchange springs in dyfe2-yfe2 superlattices, phys. rev. lett. 87: 186808-186812. anisotropy in rfe2 intermetallics 83 gratz, e., kottar, a., lindbaum, a., mantler, m., latroche, m., paul-boncour, v., acet, m., barner, c., holzapfel, w.b., pacheco, v. and yvon, k. 1996. temperature and pressure-induced structural transitions in rare-earth deficient rni2 laves phases, j. phys.: condens. matter 8: 8351-8361. lea, k.r., leask, j.m. and wolf, w.p. 1962. the raising of angular momentum degeneracy of f-electron terms by cubic crystal field, journal of the physics and chemistry of solids, 23: 1381-1405. lee, s.j., lange, r.j., canfield, p.c., harmon, b.n. and lynch, d.w. 2000. optical and magnetooptical properties of rfe2 and rco2, phys. rev. b, 61: 9669-9679. li y, carboni, c., ross, j.w., mccausland, m.a.h. and bunbury, d.st.p, 1996. hyperfine fields at lanthanides nuclei in the intermetallic compounds rfe2, j phys condens. matter 8: 865. mcmorrow, d.f., mccausland, m.a.h. and han, z.p. 1989. exchange and crystal field interaction of ho3+ in gdal2 : a single crystal nmr study, j phys condens. matter 1: 10439-10458. mccausland, m.a.h. and mackenzie, i.s. 1979. nuclear magnetic resonance in rare earth metals, adv. phys. 28: 305. mougin, a., dufour, c., dumesnil, k. and mangin, p. 2000. strain induced magnetic anisotropy in single crystal rfe2 (110) thin films, phys. rev. b, 62: 9517-9531. oster, j., wiehl, l., adrian, h. and huth, m. 2005. magnetic and magnetoelastic properties of epitaxial (211)-oriented rfe2 thin films j. mag. mag. mater., 292: 164-177. parlebas, j.c., asakura, k., fujiwara, a., harad, i. and kotani, a. 2006. x-ray magnetic circular dichroism at rare-earth l23 absorption edges in various compounds and alloys, physics reports, 431-1: 1-38. paul-boncour, v. 2004. comparison of the influence of hydrogen on the magnetic properties of rmn2 and rfe2 laves phase compounds, journal of alloys and compounds, 367: 185-190. sawickki, m., bowden, g.j., de groot, p.a.j., rainford, b.d., beaujour, j-m l., ward, r.c.c. and wells, m.r. 2000. exchange springs in antiferromagnetically coupled dyfe3-yfe2 superlattices, phys rev b 62: 5817-5820. stevens, k.w.h. 1952. matrix elements and operator equivalents connected with the magnetic properties of rare-earth ions, proc. phys. soc. a 65: 209-215. received 24 november 2008 accepted 23 august 2009 microsoft word chem100409-f edited_tobefinalised.doc 19-29 squ journal for science, 15 (2010) © 2010 sultan qaboos university 19 screening and purification of a chymotrypsin inhibitor from entrolobium saman seeds maher ali. maqtari* and a.b. mohamed. saad department of chemistry, sanaá university faculty of sciences, sultanate of oman, *email: proteinase_613@hotmail.com.. سامان انترولوبيوم بذور من وتنقيه مثبط الكا يموتربسين البروتينيفحص محمد سعدالباسط وعبد ألمقطري أحمد علي ماهر سامان آايموتربسين انهيبيتورقد تم فصله وتنقيته بالطرق التقليدية لتنقيه البروتينات مثل الترسيب انترولوبيوم :خالصة ٍ (وجل فلتريشن ) (deae-celluloseالتبادل أاليوني الكروماتوجرافي م،بالحامضيه ،الحرارة، آبريتات االمونيو sephadex g75 .( ألفصل الكهربائي النتائج النهائية وجدت بأنه متجانس من خالل استخدام) sds-page و( page gel, filtration و isoelectric focusing . ون بواسطة دالت17978الوزن الجزئي لمثبط الكايموتربسين آان sds-page و gel filtration .سامان آايموتربسين انترولوبيوم. . أالمينو اسيد لهذا المثبط وجدت بأنها سيرين ويظهر طيف امتصاصي في منطقه االشعه فوق البنفسجية مع قيمه امتصاص ,)shٍ( انهيبيتور يفتقر إلى مجموعه الثايول يشير إلى عدم circular dichroic (cd) .هر عدم وجود التربتوفانظمثبط يالطيف القاعدي لهذا ال. 2,99منخفضة هي درجه مئوية آما اظهر هذا المثبط ثبات 97وجود أي ترآيب ثنائي للبروتين مع ثبات عالي في مختلف درجات الحرارة حتى ) samanea saman( مان التخصص لهذا المثبط من انترولوبيوم سا .12,0 إلى 2,0عالي عند المدى الهيدروجيني من آايموتربسين يثبط بقوه بواسطة آايموتربسين انهيبيتور، . التظهر أي نشاط ضد السيستين، الكاربوآسيل وأيضا ميتالوبروتينيز آايموتربسين انهبيتور يظهر معقد مترابط بثباته مع الكايموتربسين وهذا المعقد قد تم فصله ودراسته ونتائج هذه الدراسة دلت ثابت التفكك لمعقد . إلنزيم الكايموتربسين ) single headed inhibitor( جود موقع واحد نشط على هذا المثبط على و دراسة التحوير الكيميائي للمثبط آان نوع . مولر 8ـ9,05x 10الكايموتربسين والكايموتربسين انهبيتور قد تم تعينها وهي الكايموتربسين ،فان هذا المثبط يظهر نشاطيه ضد بعض أنواع البكتيريا والفطريات إلى جانب نشاط هذا المثبط تجاه . تايروسين .الممرضة ولكن لم يتم آتابتها في هذا البحث abstract: a chymotrypsin inhibitor was isolated and purified from the seeds of enterolobium saman (leguminaceae family) by extraction with 100 mm phosphate buffer, heat treatment, ammonium sulphate precipitation, ion-exchange chromatography on deaecellulose and filtration through sephadex g-75. the final preparation appeared to be homogeneous by both chromatographic and electrophoretic analyses. esci had a molecular weight of about 17,890 and an isoelectric point of 5.8. esci inhibited bovine chymotrypsin at an inhibitor-enzyme molar ratio of 1:2. the inhibition mode of chymotrypsin inhibitor was competitive on bovine chymotrypsin. investigation has been carried out on the complex formed between chymotrypsin and chymotrypsin inhibitor by physico-chemical methods. an apparent dissociation constant (ki) of 9.05 x 10-8 m has been calculated for the complex. this enzymemaher ali al maqtari and a.b. mohmed saad 20 inhibitor complex was isolated by gel filtration on sephadex g-75 and a molecular weight of 43.000 was estimated for the complex. the inhibitor did not have any effect on other proteinases, such as papain, bromelin, elastase, α-amylase, trypsin and pepsin. the chemical modification of lysine residues indicated that –nh2 groups are not essential for the activity of esci toward chymotrypsin. the inhibitor was an acidic protein and was stable over a wide ph range of 2-12 and temperature range of 10oc-97oc. keywords: samanea saman; serine proteinase inhibitor; chymotrypsin inhibitor; singleheaded inhibitor. abbreviations: esci, enterolobium saman chymotrypsin inhibitor; cia, chymotrypsin inhibitory activity; atee, n-acetyl-l-tyrosine ethyl ester; nb, nutrient broth; sds-page, sodium dodecyl sulphste-polyacrylamide gel electrophoresis; cd, circular dichroism; tpck, l-1-chloro-3-(4-tosylamide)-4-phenyl-2-butanone hc; apne, n-acetyl-d,l phenylalanyl-βnaphthyl ester; tnbs, trinitrobenzene sulfonic acid; chd, 1, 2 cyclohexane dion, pda, potato dextrose agar; mic, minimal inhibitory concentration; ciu, chymotrypsin inhibitory unit; pvdf, (polyvinylidenedifluoride membrane); caps, [3-(cyclohexylamino) propane-1sulphonic acid; pi, proteinase inhibitor; bsa, bovine serum albumin; tca, trichloroacetic acid 1. introduction he protease inhibitor (pi) protein, the natural antagonists of protease, is a small protein which is quite common in nature and present in all life forms (fritz, 2000). plant protein inhibitors of proteases have been known for many years and their function is presently the subject of much interest. serine proteinase inhibitors are universal throughout the plant kingdom and have been described in many plant species. therefore, the number of known and partially characterized inhibitors of serine proteinases is enormous (haq et al., 2004). serine proteinase inhibitors have been reported from a variety of plant sources and are the most studied class of proteinase inhibitors (mello et al., 2002; haq and khan, 2003). although the biological role of protein proteinase inhibitors is not still sufficiently clear, it has been suggested that they may perform three main functions-serving as storage proteins, being regulators of activity of endogenous proteinases and acting as agents protecting plants against insects and pathogenic microflora. these inhibitors are probably important physiologically and even in molecular evolution. furthermore, they serve as excellent models for research on protein-protein interaction. the pis are important tools to achieve a better understanding of fundamental principles and can be used to design new substances for the control of diseases and pathologic processes. plant protein inhibitors of proteases have been known for many years and their function is presently the subject of much interest. enterolobium saman (rain tree) is a member of the leguminaceae family. the seeds and the pulp are edible and nutritious for livestock and make an excellent feed supplement (george and craig, 2005). the present paper describes the extraction, purification and biochemical characterization of chymotrypsin inhibitor from enterolobium saman seeds. 2. material and method enterolobium saman (samanea saman) seeds were procured from bangalore (india), the local area. all biochemical's and enzymes used in this investigation were purchased from sigma chemical co. (st. louis, usa). all other chemicals used were of analytical grade. t screening and purification of a chymotrypsin 21 2.1 extraction of chymotrypsin inhibitor the whole seeds were ground to fine powder and defatted with chilled acetone at 4oc. the defatted flour was extracted with 100 mm phosphate buffer (ph 7.6) for 3 h. at 4oc (1:10 w: v ratio). the supernatant was separated by centrifugation (30 min at 10.000 rpm) and the clear supernatant was used as a crude extract for estimation of chymotrypsin inhibitory activity and protein. protein was estimated by the method of lowry et al. (1951). 2.2 assay of chymotrypsin and chymotrypsin inhibitory activity the inhibition spectrum of esci was established by assay proteolytic or esterolytic activity of the enzyme on appropriate substrates. in principle, a fixed amount of the enzyme was incubated with various amounts of the inhibitor and the residual enzyme activity was assayed. the activity of chymotrypsin or its inhibition was routinely assayed by the method of kakade et al., (1969) and the method suggested by schwert and takenaka (1955) using casein and atee as substrate, respectively. 2.3 purification of chymotrypsin inhibitor enterolobium saman chymotrypsin inhibitor was isolated in an apparently homogeneous form by the following procedure. acetone defatted enterolobium saman flour was stirred with 100 mm phosphste buffer (ph 7.6) for 3 hr at 4oc. the extract was centrifuged at 10.000 rpm for 30 min. the ph of the supernatant was adjusted to 5.0 with 0.2 m acetic acid and the suspension was heated to 70oc with stirring. after 10 min at 70oc the supernatant was rapidly chilled in an ice-bath and centrifuged at 10.000 rpm for 10 min to remove the precipitate. the ph of the supernatant from the previous step was adjusted to 7.0 with diluted ammonium hydroxide. solid ammonium sulphate was added to 80% saturation with constant stirring at 0oc. the suspension was centrifuged at 10.000 rpm for 15 min .the precipitate was dissolved in 10 mm tris-hcl buffer (ph 8.0) and dialyzed. the ammonium sulphate fraction (80 mg protein) was applied to the deae-cellulose column and eluted with a starting buffer. thereafter, a gradient elution with increasing strength (0.2m nacl) was performed. the fraction containing cia was pooled, dialyzed and lyophilized. protein (20 mg) from deae-preparation in 1.0 ml phosphate buffer (ph 7.0) was applied to a sephadex g-75 column and chromatographed using 100 mm phosphate buffer (ph 7.0) as the effluent. the active fractions were pooled, dialyzed and lyopholilized. the final preparation showed a single protein band in page and this band was shown to possess cia by a specific staining method. 2.4 page analysis of inhibitors polyacrylamide gel electrophoresis was performed according to the method of davis (1964). for visualization of the inhibitor in acrylamide gels, after electrophoresis the gels were first incubated with trypsin solution (100 µg /ml) and then with the substrate (n-acetyl-d,l phenylalanyl-β-naphthyl ester)-dye (diazoblueb mixture by the method of filho and moreira, (1978). the cia appeared as a clear zone against a pink background. 2.5 determination of molecular weight for estimation of m.w. the sample and the marker proteins were incubated at 50oc for 1 hr in 0.1 ml phosphate buffer, with 10 µl 20% sds and 10 µl β-mercaptoethanol by the method of weber and osborn (1969). the mw marker proteins used were bsa (66 kda), ovalbumin (43kda), carbonicanhydrase (29 kda), soybeanti (20.1 kda) and lysozyme (14.3 kda) for sds-page. 2.6 isoelectric point isoelectro focusing was done by the method of wringley (1969) in 7.5 % page tube gels with 2% ampholyte gradient between ph 3 and ph 10. the upper and lower reservoirs were 0.2 % sulphuric acid and 0.4 % maher ali al maqtari and a.b. mohmed saad 22 ethanolamine, respectively. the run was performed in room temperature. after the run, the gels were stained for cia and protein. 2.7 n-terminal sequencing the purified (esci) was separated by sds-page in 12% gel and stained with coomassie brilliant blue , then electro blotted on to a pvdf in 10 mm caps as described by matsudaira, ( 1987) . the protein band was cut out and loaded on to the sequencer. 2.8 stability of the inhibitor the stability of inhibitors at different ph (2-12) values was assayed by incubating chymotrypsin inhibitor solution at different ph values at 5oc overnight. then the ph of the mixture was brought to 7.0 and its inhibitor activity towards chymotrypsin was assayed as described above. to study the thermostability, the inhibitor prepared was incubated at different temperatures (10-1210 c) by 10oc interval in a water bath for 10 min. 2.9 circular dichroism spectra (cd-spectra) the cd spectra were recorded on a jasco-810 cd spectropolarimeter with a cell length of 0.1 cm at 10oc. the inhibitor (2 mg/ml) in distilled water was placed in a 2 mm quartz cuvette and spectra were recorded from 200-300 nm at intervals of 1 nm and a well time of 2 seconds. 2.10 chemical modification 2.10. 1 modification of the amino groups the free amino groups were modified according to the method of haynes et al., (1967). 500 µg of esci was incubated in different test tubes with 0.1 % tnbs in 2 ml of 4 % na2 co3, (ph 8.5) at 40 oc for different time intervals. the reaction was stopped by the addition of 1 ml of 10 % sds followed by 0.5 ml of 1 n hcl. the extent of modification of each sample was determined by measuring the absorbance of the solution at 344 nm. the residual cia was determined during the course of modification by removing aliquots from each reaction mixture at pre determined time intervals. the control inhibitory activity was estimated from an inhibitor solution incubated in the same manner without tnbs. 2.10.2 modification of arginine group arginine groups were modified by the method of liu et al., (1968). 10 mg chd was allowed to react with 5.0 mg esci in 5.0 ml 200 mm triethanolamine buffer, (ph 7.8) in the dark for 12 h. the residual cia was determined in relation to an inhibitor control without chd after dialysis in cold condition for 36 hours. 2.11 isolation of the chymotrypsin-esci complex the enzyme-inhibitor complex was isolated by gel filtration on sephadex g-75. a mixture of inhibitor (2mg) and chymotrypsin (1mg) in 2 ml, 100 mm phosphate buffer (ph 7.6) was allowed to stand at room temperature for 15 min. this solution was then chromatographed on a sephadex g-75 column equilibrated with 100 mm phosphate buffer (ph 7.0) and the column was then developed with the same buffer solution. the a280 nm of the fractions was measured. cia and chymotrypsin activity in the fraction was determined. estimation of the apparent dissociation constant (ki) of the esci-chymotrypsin complex was performed according to the method of grob (1950). fixed concentrations were calculated assuming of a m.w of 17890 for esci and 25000 for bovine chymotrypsin. 2.12 kinetic measurement the nature of inhibition of chymotrypsin by esci was studied by incubating chymotrypsin with varying concentrations of substrate (casein) in the presence and absence of the inhibitor. the substrate (1-5 mg) was screening and purification of a chymotrypsin 23 incubated with 40 µg chymotrypsin for 10 min at 37 oc .after the incubation period, the reaction was stopped by adding 6 ml 5% tca. a 280 nm of the solution was read against a blank incubation sample, but without enzyme. the assay was repeated in the presence of 10 and 20 µg of the inhibitor in the reaction mixture. 2.13 specificity of esci the inhibitory activity of esci towards α-chymotrypsin was determined using casein (kakade and liener, 1970) or atee (schwert and takenaka, 1955) as substrate. the casein digestion method (murachi, 1970) was used to determine the activity or inhibition of papain and bromelin. elastolyatic activity of elastase was determined by the method of (naughton and sanger, 1961) using elastin-congo red as substrate. the activity of pepsin was assayed by the method of (anson, 1938). the esterolytic activity of subtilisin-bpn' was assayed using atee as substrate in a manner similar to the α-chymotrypsin assay; α-amylase (pancreatic) activity or its inhibition was measured by the method of (saunders and lang, 1973). 3. result and discussion esci was purified from mature seeds based on chymotrypsin inhibitory activity. a procedure has now been evolved for the purification of chymotrypsin inhibitor from enterolobium saman seeds as summarized in table 1. the cia was eluted by a linear gradient of increasing ionic strength. the chymotrypsin inhibitor was desorbed from the deae-cellulose column at an ionic strength of 0.063 m nacl (figure 1), and then was finally separated by sephadex g-75 column (figure 2). table 1. summary of purification of enterolobium saman chymotrypsin inhibitors (esci) (from 100gm of defatted flour) *yield and fold purification are calculated on the basis of ciu using casein as substrate. purification steps total protein (mg) total activity units ciu x104 specific activity ciu/mg fold purification* ciu yield %* ciu crude extract 50400 215.88 42.83 1.0 100 ph&heated treated extract 28820 197.31 68.47 1.59 91.4 80% (nh4)2so4 5320 138.26 259.90 6.06 64.0 deae-cellulose 1220 103.32 846.80 19.77 47.86 sephadex g-75 760 64.86 853.49 20.0 25.6 maher ali al maqtari and a.b. mohmed saad 24 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1 8 15 22 29 36 43 50 57 64 71 78 85 fraction number a 2 80 n m 0 50 100 150 200 250 300 350 400 (c iu ) x 10 figure 1. ion-exchange chromatography on deae-cellulose column of the esci. □□ absorbance at 280 nm;●●chymotrypsin inhibitory activity. 0 0.2 0.4 0.6 0.8 1 1 9 17 25 33 41 49 57 65 73 81 fraction numbe r a 2 80 n m 0 100 200 300 400 500 c iu /f ra ct io n figure 2. gel filtration on sephadex g-75 of esci. □□ absorbance at 28n nm, ●●chymotrypsin inhibitory activity 0 0.1 0.2 0.3 1 6 11 16 21 26 31 36 41 46 51 56 61 fraction number a 2 80 n m figure 4. gel filtration on sephadex g-75 of a mixture of bovine chymoptrypsin and esci. protein was monitored at 280 nm ● ● screening and purification of a chymotrypsin 25 table 2. effect of ph and temperature on esci. * inhibitory activity at 10oc was taken as 100%. † boiling water. ‡ autoclaving at 1.04 kg/cm2 pressure a b c d figure 3. electrophoretic analysis of esci. (a) page of purified esci in 10% gel stained with coomassie brilliant blue (b) visualization of the chymotrypsin inhibitory band on the gel. (c) isoelectric point in a 7.5% tube gel. (d) molecular weight determination of purified esci by sdspage in 12% gel the chymotrypsin inhibitor isolated from enterolobium saman by the procedures described above appeared to be homogeneous by the criteria of page (figure 3a), sds-page (figure 3d), gel filtration on sephadex g75 (figure 4) and isoelectric-focussing (figure 3c). the final preparation showed one protein band in page and this band was shown to possess cia by a specific staining method (figure 3b). the studies with pure preparation have shown that the cia has a broad ph stability and thermo stability (table 2). temp.oc ciu% ph ciu/mg 10* 100 2.6 1673.3 25 100 3.2 1666.6 30 100 5.0 1670.0 40 99.3 6.0 1753.0 50 98.2 7.0 1703.5 60 97.9 7.6 1780.0 70 95.5 8.6 1640.0 80 95.31 9.6 1620.0 97† 92.62 10.6 1680.0 > 121‡ 0.0 12.6 1576.6 kda 66 43 29 20.1 14.3 maher ali al maqtari and a.b. mohmed saad 26 the mr of esci was determined as 17890 ± 100 sds-page and gel filtration on sephadex g-75. many legume inhibitors have their molecular weight in the range of 15,000-20,000 da. single headed inhibitors have been isolated from barley bean (prakash et al., 1996), crotalaria paulina seeds ((luiza et al., 1999), and caesalpinia echinata (pau-brasil) seeds (cruz-silva .et al., 2004)????. the kunitz-type inhibitor found in e.saman supports the notion that there is a relationship between the types of inhibitors found in leguminous seeds and the evolution of the leguminous plants, since only kunitz-type inhibitors are present in the relatively primitive plants of caesalpinoideae. this conclusion was reached by norioka et al. (1988) who investigated the presence of both kunitz and bowman-birk inhibitors in seeds of 34 legumes by gel filtration. the results were compared to the morphological classification of leguminosae: the seeds of the more primitive leguminosae (caesalpinoideae and mimosoideae) contain mainly kunitz-type inhibitors, whereas those of a more advanced family (papilinoideae) contain only bowman-birk-type inhibitors. 0 10 20 30 40 50 60 70 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 figure 5. lineweaver-burk plot of the inhibition of caseinolytic activity of chymotrypsin by esci. ▲▲ without inhibitor, ■ ■ with 10 µg of esci, ●● with 20 µg of esci. 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 esci] ([m] x 10-7) figure 6. inhibition of bovine chymotrypsin by esci. c on ce nt ra tio n of c hy m ot ry ps in in hi bi te d ([ m ] x 1 07 ) screening and purification of a chymotrypsin 27 figure 7. cd-spectra of the purified chymotrypsin inhibitor (esci) (2.0 mg/ml) in distilled water. 0 20 40 60 80 100 0 20 40 60 80 100 120 incubation time (min) (% ) f re e am in o gr ou ps & (% ) r es id ua l c hy m ot ry ps in in hi bi to ry ac tiv ity i nh ib ito ry figure 8. time course of modification of free amino groups with tnbs % free amino groups ■■% residual cia ▲▲. figure 9. n-terminal sequences of es. inhibitor n-terminal sequences esci s-n-l-l-l maher ali al maqtari and a.b. mohmed saad 28 chymotrypsin activity in the presence (10 and 20 µg) and absence of esci was measured at different substrate concentrations. the double-reciprocal plot of the kinetic data is shown in (figure 5). it can be seen that esci inhibited trypsin by a competitive mechanism involving competition of the substrate and inhibitor for the site on the enzymes. most naturally occurring proteinase inhibitions inhibit the respective enzymes competitively. the dissociation constants (ki) of the esci-chymotrypsin was calculated to be 9.05 x 10-8 m. the low ki indicates a high affinity between the inhibitor and chymotrypsin. the extreme stability of the esci in acidic ph and higher temperatures suggests that the esci has little or no ordered structure. the cd-spectra of the esci (figure 7) in distilled water shows the complete absence of αhelical content. the changes in the conformation of the esci in different ph and temperatures could not be carried as the proteins exhibited random coil secondary structures in cd-spectra. the modification of arginine residues by a group specific reagent does not have any significant effect on the trypsin inhibitory activity of esci. the modification of lysine residues showed the participation of fast acting nh2 groups in the reactive site of esci (figure 8). this suggests that lysine is perhaps at the active site of the esci. esci most probably belong to the class of tyrosine type inhibitor. specificity of the inhibition of different classes of proteinases by esci was tested against the enzymes from various sources (table 3). esci inhibited only bovine chymotrypsin and showed no activity against other proteolytic enzymes tested. this establishes that the inhibitory activity of esci against bovine chymotrypsin with atee as substrate (figure 6) is stoichiometric. n-terminal groups of the enterolobium saman inhibitors have been detected by precise protein sequencing system iisc, bangalor (figure 9). the n-terminal sequence up to 5-residues was s-n-l-l-l. 4. conclusions in this work we describe the purification and characterization of a new chymotrypsin inhibitor from enterolobium saman (samanea saman) which belongs to the class of tyrosine inhibitor. the inhibitor existed as a monomer with molecular weight of 17,890 da. judging from its molecular mass and the inhibitory activity against chymotrypsin, chymotrypsin can be considered as a kunitz type inhibitor. this inhibitor highly inhibited bovine chymotrypsin, but did not show any activity against other proteolytic enzymes tested. 5. acknowledgments we gratefully thank the department of chemistry, faculty of sciences, sana'a university and bangalore university, india, for a research assistantship and the college of agricultural sciences, sana'a, for technical assistance. 6. references anson, m.l. 1938. the extinction of pepsin, trypsin, papain and cathepsin with hemoglobin. j.gen. physiol. 22: 79. cruz-silva, andrezza. j, viviane. a, adriar. a, maria luiza. v, misako. u and claudi mariana. s. 2004. a proteinase inhibitor from caesalpinia echinata seeds for plasma kallikrein, plasmin and factor xii. biol. chem. 385: 1083-1086. davis, b.j. 1964. disc lectrophoresis. ii. method and application to human serum proteins. ann. ny acad.sci.,121: 404 -427. filho.j.x. and moreira. r.a. 1978. visualization of proteinase inhibitors in sds-polyacrylamide gels. anal. biochem. 84: 296-303. fritz, h. 2000. foreword. in k. von der helm, b.d. korant, and j.c. cheronis (eds.), proteases as targets for therapy. berlin: springer-verlag, pp. v-vi. screening and purification of a chymotrypsin 29 george. w.s and craig. r.e. 2005. samanea saman (rain tree) fabaceae (legume family). specific profiles for pacific island agroforestry. grob, d. 1950. proteolytic enzymes.iii. further studies on protein, polypeptide and other inhibitors of serum proteinase, leucoproteinase, trypsin and papain.` j.gen. physiol. 33, 103. haq, s.k. and r.h. khan. 2003. characterization of a proteinase inhibitor from cajanus cajan (l.) j. protein. chem. 22: 543-554. haq, s.k., s.m. atif, and rh. khan. 2004. protein proteinase inhibitor genes in combat against insects, pests, and pathogens: natural and engineered phytoprotection. arch biochem biophys. 431: 145-159. haynes, r., osuga, d.t. and feeney, r.e. 1967. modification of amino groups in inhibitors of proteolytic enzymes. biochemistry, 6: 541. kakade, m.l., simons, n. and liener, i.e. 1970. note on the determination. of trypsin and chymotrypsin inhibitor activity using casein. analyt. biochem. 33: 225-258. liu, w.h. feinstein, g.osuga, d.t., haynes, r. and feeney, r.e. 1968. modification of arginines in trypsin inhibitors by 1, 2-cyclohexanedione. biochemistry, 7: 2886-2892. lowry, o.h., rosebrough, n.j., farr, a.l. and randall, r.j. 1951. protein measurement with folin phenol reagent. j. biol. chem. 193: 265–275. luiza, a., luciana, c., jose, c., benedito, o., jurgen, k. and sergin, m.life. 1999. isolation and characterization of a new trypsin inhibitor from crotalaria paulina seeds. , 48: 519-523. matsudaira, 1987. sequence from picomole quantities of proteins electroblotted onto polyvinylidene difluoride membranes. journal of biological chemistry 262: 10035 10038. mello, g.c., m.l.v. oliva, j.t. sumikawa, o.l.t. machado, s. marangoni, j.c. novello, and m.l.r. macedo. 2002. purification and characterization of a new trypsin murachi, t. 1970. bromelian enzymes. methods enzymol. 19: 273-275. naughton and sanger .1961. purification and specificity of pancreatic elastase. biochem. j.78: 156-161 norioka, s. hara, s., ikenaka, t. and abe, j. 1988. distribution of the kunitz and the bowman-birk family proteinase inhibitors in leguminous seeds. agric. biol. chem. 52: 1245-1252. prakash, b., selvaraj, s., murthy, mr., sreerama, yn., rao, dr. & gowda, lr. 1996. analysis of the amino acid sequences of plant bowman .birk inhibitors. j mol evol 42: 560–569. saunders, r.m., and lang, j.a. 1973. alpha-amylase inhibitors in triticum aestivum: purification and physical-chemical properties. phytochemistry. 1973, 12: 1237-1241. schwert, g.w. and takenaka, y. 1955.a spectrophotometric determination of trypsin and chymotrypsin. biochem biophys acta 16: 570-575. wringley, c.w. 1969. shandon instrument applications, 29:1. received 9 april 2010 accepted 12 october 2010 microsoft word chem070127.doc 1-6 squ journal for science, 12 (1) (2007) © 2007 sultan qaboos university 1 screening of antioxidant and radical scavenging activities of some omani medicinal plants saleh al-busafi*, mubarak al-riyami, khadija al-ouwaisi and abdulkhader hisham department of chemistry, college of science, sultan qaboos university, p.o. box 36, postal code 123, muscat, sultanate of oman, *email: saleh1@squ.edu.om. في عمانالكشف عن أنشطة مضادات التأكسد وكبح الشوارد لبعض النباتات الطبية عبدالقادر هشام و صالح البوصافي، مبارك الريامي، خديجة العويسي تمفي هذه الدراسه . وأنشطة كبح الشوارد لعشرة نباتات طبيه عمانيه األنشطه ألمضاده لألكسدهتقييملقد تم :خالصة لقد وجدنا أن نبات أكاسيا تورتيليس ونبات . نبات الريحان كمرجع لما عرف عنه من نشاط قوي لوقف التأكسداستخدام . تفروسيا هوسكنشتي لها أنشطة مرتفعة لمضادات التأكسد وكبح الشوارد abstract: n-butanol extracts of nine medicinal plants, cressa cretica, ziziphus spinachrist, acacia tortilis, tephrosia haussknechti, aristolochiae bracteolata, citrullus colocynthis, teucrium mascatense, rhazya stricta and nerium oleander, found in oman were screened for their antioxidant activity using phosphomolybdenum complex assays and their radical scavenging activity using dpph assays. ocimumi basilicum, a plant with well documented antioxidant activity, was used as a reference. a. tortilis, and t. haussknechti extracts possessed very high antioxidant activity (aoa) and high radical scavenging activity (rsa). keywords: antioxidant activities, radical scavenging, dpph, phosphomolybdenum complex. 1. introduction pices have been used since ancient times to improve taste and aroma of different types of food and some of them are well known for their antioxidant properties (madsen and bertelsen, 1995). antioxidants are widely used as additives in food, pharmaceutical, and cosmetic industries to provide protection against oxidative degradation. numerous degenerative diseases such as brain dysfunction, cancer, heart diseases and immune system decline could be the result of cellular damage caused by reactive oxygen species and free radicals present in human diet and antioxidants may play an important role in the prevention such diseases (aruoma, 1998). a great number of aromatic, spicy, medicinal and non-medicinal plants contain chemical compounds exhibiting antioxidant properties. several studies were carried out on plants, such as rosemary and sage have led to the development of natural antioxidant formulations for food, cosmetic, and other applications (cuvelier et al., 1996). however, scientific studies on the antioxidant properties of several plants used in omani traditional s saleh al-busafi, et al. 2 medicine are still rather scarce. therefore, the evaluation of such properties seems to be a useful task with a view to find new sources of natural antioxidants. the present work deals with preliminary studies on the antioxidant and radical scavenging activities of the n-butanol extracts prepared from the following plants: cressa cretica (convolvulaceae), ziziphus spina-christi (rhamnaceae), acacia tortilis (leguminosae), tephrosia haussknechtii (leguminosae), aristolochiae bracteolata (aristolochiacae), citrullus colocynthis (cucurbitaceae), teucrium mascatense (labiatae), rhazya stricta (apocynaceae) and nerium oleander (apocynaceae) which are readily available plants growing in northern oman. to the best of our knowledge, only little information on the antioxidant and radical scavenging properties of these plants is available in the literature. c. cretica is an annual plant that grows in saline soils and is used to treat minor wounds. the aerial parts of c. cretica are source of flavonoids (shahat et al., 2004), and terpenoids (ramachandran and ali, 2003). antioxidant properties of the plant have not been reported. z. spinachristi is one of the five popular trees in oman. the fruits are edible. the crushed leaves are used as a natural cleaning as well as a conditioner for the hair. hair washed with ziziphus leaves becomes particularly lustrous and soft (miller and morris, 1988). it has been reported that the volatile fraction of flowers and leaves of z. spina-christi possesses antimicrobial activity (el-hamouly and mohamed, 2001) and the plant is rich in flavoniod glycosides and triterpenoid saponins. a. tortilis is the most commonly seen tree in oman (miller and morris, 1988). the plentiful flowers of a. tortilis attract honey bees and these flowers are known to produce the best honey in oman. even though the reports on flavonoid isolation from a. tortilis (muhaisen et al., 2002) are available in the literature, the information on antioxidant properties of this plant are not found. t. haussknechti is a bright-flowered shrub of rocky, lower altitude hill-sides which is the most common tephrosia species in northern oman (mandaville, 1978). the leaves of t. haussknechti are used to treat earache, swollen joints (ghazanfar, 1994) but no antioxidant properties are reported . a. bracteolata is a source of aristolochic acids (el tahir, 1991), which is used to treat wounds, snakebites but no antioxidant properties are reported in the literature. the seeds of c. colocynthis are used to treat tumors and the green flesh of the immature fruit is taken in small quantities as a purgative (miller and morris, 1988). the fruits of c. colocynthis contain flavones (maatooq, et al., 1997), triterpenes glycosides (hatam, 1989) but antioxidant properties of the plant have not been reported. t. mascatense is an aromatic perennial, a native of oman which is used in traditional medicine for fever, diabetes and stomach pain (mandaville, 1978; ghazanfar, 1994). the composition and antimicrobial activity of this plant was recently reported (hisham et al, 2006) no studies on the antioxidant properties of this plant is available. r. stricta, known as ‘harmal’ in arabic is used in arabian folk medicine as a remedy for respiratory ailments and fevers (mandaville, 1978). alkaloids have been isolated from the leaves of r. stricta (atta-urrahman and habib-ur-rahman, 1996) and antioxidant action of the leaves extract has been reported (ali et al., 2000) in traditional medicine, various parts of n. oleander are used for treatment of cough, swellings, eyes and skin diseases. methanolic extract of the fresh leaves of n. oleander showed central nervous system (cns) depressant effect in mice (begum et al., 1999). flavonoids were present in all organs of the plant (duret and paris, 1977), but roots and the leaves of n. oleander contain triterpenoids (begum et al., 1997) with no antioxidant properties reported in the literature. it was noticed that the antioxidant activity of the above selected plants were either not investigated or poorly investigated and therefore testing of their antioxidant and antiradical properties is of interest, primarily to find new promising sources of natural antioxidants. screening of antioxidant and radical scavenging activities 3 0 20 40 60 80 100 r ed u ct io n o f d p p h (% ) 1 2 3 4 5 6 7 8 9 10 figure-1: dpph radical scavenging activities of n-buoh extracts. 1. oscimum basilicum; 2. cressa cretica; 3. ziziphus spina-christi; 4. acasia tortilis; 5. tephrosia hausknechti; 6 aristolochia bracteolate;7 citrullus colocynthis; 8.teucrium mascatense; 9 rhazya stricta ;10. nerium oleander 2. results and discussion 2.1 dpph radical-scavenging activities the n-buoh extracts of the plants were prepared as described in section 3 and their free radical scavenging activity was determined by dpph free radical method (brand-williams et al., 1995). the n-buoh extract of ocimumi basilicum (labiatae), a plant well known for its antioxidant and radical scavenging properties, was used as a reference. the 1,1-diphenyl-2-picrylhydrazyl (dpph) radical is a stable radical with a maximum absorption at 517 nm. when dpph• reacts with an antioxidant compound, which can donate hydrogen, it is reduced and the color changes from deep-violet to light-yellow. the results of dpph radical-scavenging activity of n-butanol extracts are shown in figure 1. six out of nine n-buoh extracts used in the present study showed high level of dpph scavenging activities ie., c.cretica-87.7%, z. spina-christi-83.5%, a. tortilis-89.8 %, t. hausknechti-88.4% and t. mascatense-89.1%. in fact the extracts of a. tortilis and t. mascatense are having remarkably higher level of radical scavenging activity compared to o. basilicum. on the other hand, the extracts of a. bracteolate-57.8%, c. colocynthis-39.6%, r. stricta-31.3%, and n. oleander-37.2% showed only moderate or weaker activities. 2.2 antioxidant activity evaluation by the phosphomolybdenum method the antioxidant activity of the extracts was evaluated by phosphomolybdenum method, which is based on the reduction of mo(vi) to mo(v) by the antioxidant compound(s) and the formation of a green plant saleh al-busafi, et al. 4 phosphate/mo(v) complex with a maximal absorption at 695 nm. the results of antioxidant activity exhibited by different plant extracts are summarized in table 1. table 1. antioxidant activities of n-buoh extracts plant aw a oscimum basilicum 1.0 cressa cretica 0.78 ziziphus spina-christi 1.0 acasia tortilis 1.4 tephrosia hausknechti 1.0 aristolochia bracteolata 0.88 citrullus colocynthis 0.82 teucrium mascatense 0.97 rhazya stricta 0.75 nerium oleander 0.99 a aw, activity relative to oscimum basilicum on a weight basis the extract of a. tortilis exhibited higher antioxidant activity than o. basilicum, while extracts of z. spinachristi, t. hausknechti and n. oleander showed antioxidant activities, similar to the reference extract. the extracts of a. bracteolate, t. mascatense and c. colocynthis showed moderate antioxidant activities, whereas c. cretica and r. stricta exhibited only weak activities compared to the reference plant extract. 3. experimental 3.1 reagents 1,1-diphenyl-2-picrylhydrazyl (dpph), sodium phosphate and ammonium molybdate were purchased from sigma-aldrich and all solvents were of analytical grade. 3.2 plant material ocimum basilicum (leaves and stems), cressa cretica (leaves and stems), ziziphus spina-christ (leaves), acacia tortilis (leaves), tephrosia haussknechti (leaves and stems), aristolochiae bracteolata (leaves and stems), citrullus colocynthis (fruits), teucrium mascatense (leaves and stems), rhazya stricta (leaves and stems) and nerium oleander (leaves) were collected from northern oman during 2003 and were authenticated by department of biology, sultan qaboos university. the freshly cut plants were dried in the drying room with ventilation at ambient temperature prior to use for investigation. 3.3 extraction the dried, powdered plant materials were extracted with methanol (500 ml)at room temperature and the methanol extracts were concentrated under reduced pressure to get greenish viscous materials which were first partitioned with hexane/h2o, then with etoac/h2o and finally with n-butanol/h2o to give hexane extracts, screening of antioxidant and radical scavenging activities 5 ethyl acetate extracts and n-butanol extracts. the concentrated n-butanol extracts were used for the evaluation of the antioxidant activities. 3.4 dpph radical-scavenging activity the free radical scavenging activity of the plant extracts was determined by dpph free radical method (brand-williams et al., 1995). a 2.0 ml methanolic solution of dpph (0.1 mm) was mixed with 0.1 ml of extract solution (0.1 mg/ml) in methanol and, after 60 min standing; the absorbance of the mixture was measured at 517 nm against methanol as the blank on a uv/visible light spectrophotometer (shimadzu uv 1650 pc, japan). triplicate measurements were made and the radical scavenging activity was calculated by the percentage of dpph that was scavenged using the following formula: % reduction = [(ab – aa)/ab] x 100 where: ab-absorption of blank sample; aaabsorption of tested extract solution. 3.5 evaluation of antioxidant activity the antioxidant activity of plant extracts was evaluated by the phosphomolybdenum method according to the procedure of prieto et al., (1999). an aliquot of 0.3 ml of sample solution (1 mm in methanol) was combined in a 4-ml vial with 3 ml of reagent solution (0.6 m sulfuric acid, 28 mm sodium phosphate and 4 mm ammonium molybdate). the vials were capped and incubated in a water bath at 95 °c for 90 min. after the samples had cooled to room temperature, the absorbance of the mixture was measured at 695 nm against a blank. the antioxidant activity was expressed relative to that of ocimumi basilicum (labiatae). 4. conclusions the n-buoh extracts a. tortilis, t. mascatense and t. hausknechti were found to be the strongest radical scavengers in dpph radical assay and the strongest antioxidants in phosphomolybdenum assay among the plants screened. they are promising plants for further investigation of antioxidant properties particularly a. tortilis of which antiradical and antioxidant activities were higher than that of o. basilicum. in a previous work, we showed that aristolochic acid and aristolochic acid-d isolated from a. bracteolata, is as effective as vitamin c in antioxidant activity on a molar basis (al-busafi et al., 2004). the results in table-1 suggests that the plants a. tortilis, t. hausknechtii and z. spina-christi may have better antioxidants than vitamin c. 5. acknowledgements we acknowledge, with thanks, financial support from the sultan qaboos university. 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(lisse, netherlands), 42(4-5): 349-352. received 27 january 2007 accepted 31 october 2007 photovoltaic cells and systems: 13-25 squ journal for science, 13 (2008) © 2008 sultan qaboos university studies of surface area and pore structure on portland cement produced in bajil and amran, yemen a.m. saad*, abdul-basit a. saleh**, fatima a. al-kadri*, abdulla s. babaqi*, abdulla a. basissa* and s.a. abo el-enein*** *department of chemistry, faculty of science, sana'a university, p.o. box 11923, sana'a, yemen, email: bassetsaad@yahoo.com;**department of physics, faculty of science, sana'a university, p.o.box 8211, sana'a, yemen; ***department of chemistry, faculty of science, ain-shams university, egypt. دراسة المساحة السطحية و التركيب المسامي إلسمنت بورتالندي أنتج في باجل وعمران باليمن صالح أبـو وعبدالباسط محمد سعد، عبدالباسط علي صالح، فاطمة القادري، عبداهللا بابقي، عبداهللا باعيسى العينين ، 0.30إسمنت /تالندية مختلفة المسامية وبنسبة ماءتم تحضير مجموعة من عجائن اإلسمنت ذو المواصفات البور :خالصة الترآيب المسامي وآذا . يوم28 يومًا إلى 0.021 مستخدمين أزمنة تميؤ مختلفة بدًءا من 0.55 و 0.50، 0.45، 0.40، 0.35 وقد وجد . الممتز لعجائن اإلسمنت المجففة تم قياسها باستخدام غاز النتروجين(vl–t) سمك الطبقة الممتزة –منحنيات الحجم أنه يمكن ربط النتائج التي تم الحصول عليها مع ميكانيكية التميؤ وذلك من خالل مالحظة النظام المسامي للعينات المجففة، آما أما منحنيات االمتزاز وتحرير . لوحظ أن آافة أنواع منحنيات االمتزاز األيزوثرمية للعينات الجافة تتبع الصنف الثاني .األيزوثرمية فقد دّلت على عدم إمكانية عودة المادة الممتزة بشكل انعكاسي إال في بعض الحاالت النادرةاالمتزاز abstract: portland cement pastes of various porosities were prepared using water/cement ratios of 0.30, 0.35, 0.40, 0.45, 0.50 and 0.55; and were hydrated for various time intervals ranging from 0.021 to 28 days. pore structure and vl–t plots (plots of volume vs. thickness) of the hardened cement pastes were measured using nitrogen gas as the adsorbate. the results were found to be related to the mechanism of hydration as controlled by the pore system of the hardened pastes. type іі adsorption isotherms of nitrogen were obtained for all hardened cement pastes. the adsorption-desorption isotherms indicated the existence of closed hysteresis loops for most of the investigated samples and in some other cases, these isotherms were fully reversible. keywords: surface area; pore size; portland cement; cement paste; adsorption. 13 a.m. saad et al. 1. introduction s tudies of surface area and pore structure of portland cement pastes have significant values in understanding the nature of this compound material. in the present investigation, we study the surface area and pore structure of two types of portland cement produced in yemen by two main factories, bajil and amran. this work constitutes a second part of a previous investigation, in which the kinetics of hydration was studied (babaqi et al., 2001). the hardened cement pastes were prepared at various initial water/cement (w/c) ratios and hydrated for various time intervals ranging from 0.021 to 28 days. as reported by abo-el-enein et al. (1982), nitrogen was used as adsorbate to measure the surface area and porosity of the cement pastes. the results of adsorption of nitrogen gas for the hydrated cement pastes are represented graphically. each graph represents a number of adsorption isotherms obtained after various hydration time intervals of a certain paste made with a definite w/c ratio (initial porosity). all adsorption isotherms graphs were found to be similar in shape to type ii of brunauer classification (brunauer and emmett, 1935, brunauer et al., 1940), which is characterized by a low pressure region concave to the pressure axis, a high pressure region convex to the pressure axis, and an intermediate almost linear portion. 2. materials and experimental in the present investigation, we used two types of ordinary portland cement produced by amran and bajil cement factories in yemen. their surface area was 3100 cm2/g. table 1 lists the chemical oxide compositions of these two types. henceforth, we will refer to amran and bajil cement as "sample a" and "sample b", respectively. table 1. chemical oxides compositions and ignition loss (%) of the two samples of ordinary portland cement oxides sio2 al2o3 fe2o3 mgo cao so3 ignition loss sample a 21.35 5.20 3.05 2.11 61.98 1.96 1.48 sample b 21.31 5.58 4.16 1.93 64.25 2.11 1.85 2.1 hydration treatment various cement pastes were prepared for the two types of the ordinary portland cement by mixing dry weighed cement with distilled water continuously for 3 minutes. the w/c ratios were by weight; and each fresh paste was moulded into polyethylene plastic bottles and cured at 100% relative humidity for 24 hours. the specimens were remoulded and cured under water for the desired times of hydration. all pastes were hydrated for various time intervals of 0.021, 0.083, 0.25, 1, 3, 7 and 28 days. at each time interval, the hydration reaction was stopped by immersing about 10 g of the ground specimen in about 100 ml of methanol/acetone mixture (1:1 by volume) and magnetically stirring for about one hour. the solid sample was then filtered with g4-sintered glass washed with about 30 ml of methanol and then dried at 80 to 90 ºc for 3 hours. the dried samples were kept in a desiccator until the time of testing. 2.2 adsorption measurements the surface characteristics of the hardened cements pastes were studied from the adsorption of nitrogen gas at liquid nitrogen temperature (–195.8 ºc). the apparatus used was a volumetric apparatus of conventional type. it was made from a pyrex glass that could be divided into two parts, a vacuum line and an adsorption system. 14 studies of surface area and pore structure on portland cement before carrying out a run, it was necessary to calibrate the dead space of the bulb and its connecting tubes. calibration was made by use of pure helium (99.9% pure, supplied from british oxygen company, london). the dead space was divided into two parts: a small dead space enclosed by stopcocks, which constitutes the volume of the tube connecting the manometer to the burette; and a big dead space, which includes the total volume. for calibration, the adsorbent was thoroughly vacuumed in situ to a pressure of approximately 10–5 mmhg at the required temperature. after purging, the adsorption bulb was immersed and a suitable amount of pure helium was introduced to the dead space. after attaining thermal equilibrium, the pressure of the helium in the burette was measured. successive higher pressures were obtained by further raising the mercury in the gas burette to known volumes. for each pressure and known volume of the gas burette, the corresponding volume of the big dead space was calculated. the same procedure was repeated for determining the volume of the small dead space. in the latter case, the sample bulb was isolated by closing the connecting stopcock. the adsorption isotherm was determined by introducing measured volumes of the adsorbent (nitrogen gas) to the sample bulb and measuring the equilibrium pressure. the adsorbed amount could then be calculated. successive higher pressures were obtained by raising the level of mercury in the gas burette. the saturated vapor pressure of the adsorbate was determined periodically during the adsorption run by measuring the pressure directly, which was in equilibrium with liquid adsorbate in the liquid nitrogen thermometer. the adsorption data were plotted for volume of nitrogen adsorbed, v (cm3/g), as a function of equilibrium relative vapor pressure, p/p0, where p is the equilibrium pressure and p0 is the saturated vapor pressure of adsorbate. the pressure was read with the aid of a cathetometer to 0.01 mm. all readings were corrected for mercury depression and temperature. 3. results and discussion 3.1 surface area and pore structure a great deal of information concerning the properties of an adsorbent is known when its surface area is determined. a well developed method is to estimate the specific area of a solid from measurements of the adsorption of gases or vapors. the method depends on the fact that it is possible, from the adsorption isotherms, to find and evaluate the volume of gas or vapor adsorbed when the entire surface of the absorbent is covered with a complete unimolecular layer known as the monolayer capacity. many theories have been put forward to estimate the monolayer capacity of an active solid. great variations, however, were encountered as adsorbents are not alike in their external or internal surface and differ in their molecular structure, capillary, and pores size. langmuir equation was the first successful theoretical trial to estimate the monolayer capacity, vm, from adsorption isotherms. however, the equation failed to yield reliable vm values for isotherms other than type i isotherm of brunauer’s classification (brunauer et al., 1938). the most familiar method of determining the monolayer capacity and hence the specific surface area is the one that is based on the brunauer, emmett, and teller (bet) equation (brunauer et al., 1938), which can be written in a linear form as: , 11 )( 0mm0 p p cv c cvppv p ⋅ − += − (1) where v is the volume of the gas adsorbed at a relative vapor pressure (p/p0) and c is a constant characteristic of the heat of adsorption in the first adsorbed layer, which is a measure of the energy of interaction between the gas and the solid surface. the plot of )( 0 ppv p − vs. 0p p is linear within a limited range of relative vapor pressure, generally between 0.05 and 0.3. values of vm can be calculated from the slope cv c m 1− and the intercept cvm 1 at a zero relative 15 a.m. saad et al. pressure. using equation (1), it was possible to describe type ii and type iii isotherms depending on the values of the constant c. reliable values of vm were obtained with type ii isotherms having well-defined knee bends (i.e., those of high values of c). the surface area, ∑, was evaluated from: , 22400 m σn v =∑ (2) where vm is the monolayer capacity in ml (n.t.p.) per g , n is avogadro’s number, and σ is the area occupied by a single molecule adsorbed on the surface. if the monolayer capacity (sm) is expressed in g/g., then equation (2) will take the form: ,m σn m s =∑ (3) where m is the molecular weight of the used vapor. 3.2 adsorption-desorption isotherms adsorption-desorption isotherms of nitrogen gas were measured volumetrically at liquid nitrogen temperature on the hardened pastes made from sample a and sample b cements with low (w/c = 0.30) and high (w/c = 0.50) initial porosities. pastes made from sample a cement were designated as ia and va and those made from sample b cement were designated as ib and vb. the results of adsorption of nitrogen gas for the hydrated pastes made from sample a and sample b cements are given in terms of the adsorbed amount s (expressed in cm3/g), the adsorbent, and the equilibrium relative vapor pressure of the adsorbate. these results are represented graphically in figures 1–4. each of these figures represents a number of adsorption isotherms obtained after various hydration time intervals of a certain paste made with a definite w/c ratio (initial porosity). all isotherms show common characteristics, and the adsorption isotherms of nitrogen gas on the various hardened cement pastes seem to belong to type ii of brunauer’s classification (brunauer and emmett, 1935, brunauer et al., 1940), which consists of a low pressure region that is concave to the pressure axis, a high pressure region convex to the pressure axis, and an intermediate almost linear portion. this linear portion converses a long range of intermediate relative vapor pressures. the behavior of adsorption-desorption isotherms indicates the existence of closed hysteresis loops for a number of the investigated hydrated samples while for other samples, the adsorption-desorption isotherms are fully reversible (i.e., the desorption branches are consided on the adsorption branches of the isotherms). this behavior has been noticed in other investigations made by using nitrogen gas as an adsorbate or by using other vapors (mikhail and.abo-el-enein, 1972, abo-el-enein et al., 1974, mikhail et al., 1975, mikhail et al., 1978, abo-el-enein et al., 1978, abo-el-enein et al., 1985, hekal et al., 1987, abo-el-enein et al., 1990). the results of figures 1–4 also indicate that the sigmoid shape of the isotherms depends primarily on the initial porosity of the hardened cement pastes, as controlled by the initial w/c ratio of the paste, as well as the age of hydration of the paste. 3.3 surface areas and pore volumes from the adsorption isotherms, the specific surface areas were evaluated by applying bet equation (brunauer et al., 1938). the total pore volumes, vp, were taken as the saturation values of the isotherms. the mean hydraulic radii, гn (å), were also calculated from: 4 bet p n 10)å( ⋅=γ s v (4) where sbet is the bet specific surface area. 16 studies of surface area and pore structure on portland cement figure1. adsorption-desorption isotherms of nitrogen on the hardened cement pastes ia made with w/c ration at various ages of hydration (0.021, 0.25, 3, and 28 days). table 2. some surface characteristics of the hardened cement pastes ib and vb made with low and high initial porosities from nitrogen adsorption. sample sbet (m 2/g) bet c-constant vp (ml/g) mean γn (å) pastes ib (w/c = 0.30) ib 0.021 days 118.58 5 0.1248 10.52 ib 0.083 days 84.91 4 0.1685 19.84 ib 0.25 days 108.74 4 0.1014 9.32 ib 1 day 104.22 4 0.1326 12.72 pastes vb (w/c = 0.50) vb 0.021 days 50.00 5 0.1248 24.96 vb 0.083 days 45.61 4 0.0655 14.36 vb 0.25 days 46.17 4 0.0624 13.52 vb 1 day 51.60 5 0.0936 18.14 the calculated values of sbet (m 2/g), the bet c-constants, vp (ml/g), and гn (å) of the total pore system, are all summarized in tables 2 and 3 for pastes made from sample b (pastes ib and vb) and sample a (pastes ia and va) cement, respectively. the values of sbet and vp listed in table 2 for pastes made from sample b cement indicate that pastes with low porosity (pastes ib) possess higher surface areas and pore volumes than those of high porosity (pastes vb). these behaviors are mainly related to the crystalline characteristic and physical state of hydration products formed within the pore system of the hardened pastes. evidently, hydrates 17 a.m. saad et al. formed with low porosity pastes (ib) are almost more amorphous with ill-crystallized character as compared with those of crystalline hydrates formed with high porosity pastes (vb). figure 2. adsorption-desorption isotherms of nitrogen on the hardened cement pastes va made with w/c ration at various ages of hydration (0.021, 0.25, 3, and 28 days). since гn represents the average width of the total pore system accessible to nitrogen molecules, the relatively low values of гn obtained for the lower porosity pastes (ib) are mainly a consequence of the increased accessibility of nitrogen molecules used to measure larger fractions of the total pore system of the hardened pastes for the higher porosity pastes (vb). however, гn values are relatively high, which indicate a decreased accessibility of the nitrogen molecules towards the pore system of these hardened pastes (vb). in addition, the total pore volumes measured by nitrogen are higher for pastes made with a low initial w/c ratio (pastes ib) than those made with a high initial porosity (pastes vb). table 3 lists the main surface characteristics of the hardened pastes made from sample a cement (pastes ia and va) at different ages of hydration, namely, 0.021, 0.25, 3 and 28 days. evidently, the bet surface areas as well as the total pore volumes are higher for pastes made from low initial w/c ratio (pates ia) as compared with those made with high initial w/c ratio (pastes va). these results are easily explained in terms of the different degrees of crystallinity of hydrates formed in the lower porosity pastes (ia) when compared with those formed in the higher porosity pastes (va). the values of the c-constants of bet equation reported in tables 2 and 3 are very low for all of the hardened cement pastes investigated in this study (pastes ib, vb, ia and va). since the bet c-constant can be taken as a rough indication for the degree of interaction between the solid surface and the adsorbate molecules, hence, it is an adequate measure for the heat of adsorption in the first adsorbed layer. therefore, the heat of adsorption of nitrogen gas on the various hardened cement pastes (ib, vb, ia and va) is very low, indicating non-specific adsorbent-adsorbate interactions. 18 studies of surface area and pore structure on portland cement figure 3. adsorption-desorption isotherms of nitrogen on the hardened cement pastes ib made with w/c ration at various ages of hydration (0.021, 0.083, 0.25, and 1 day). table 3. some surface characteristics of the hardened cement pastes ia and va made with low and high initial porosities from nitrogen adsorption. sample sbet (m 2/g) bet c-constant vp (ml/g) mean γn (å) pastes іa (w/c = 0.30) іa 0.021 days 66.12 4 0.2469 37.75 іa 0.25 days 82.58 5 0.1919 23.23 іa 3 days 80.32 7 0.1704 22.34 іa 28 days 87.00 9 0.1638 18.83 pastes va (w/c = 0.50) va 0.021 days 36.60 5 0.1365 37.30 va 0.25 days 42.20 4 0.1310 31.04 va 3 days 70.00 7 0.1606 22.94 va 28 days 94.00 26 0.1599 16.97 3.4 pore structure and vl–t plots several investigators have offered t-curves for nitrogen. cranston and inkley (1957) derived a composite curve from nitrogen isotherms on 15 nonporous materials. another t-curve, based on a variety of other nonporous adsorbents was derived by de boer and coworkers (lippens et al., 1964, de boer et al., 1965). 19 a.m. saad et al. figure 4. adsorption-desorption isotherms of nitrogen on the hardened cement pastes vb made with w/c ration at various ages of hydration (0.021, 0.083, 0.25, and 1 day). if we restrict ourselves to nitrogen and to only one temperature (liquid nitrogen temperature), it is a fortunate fact that for a wide variety of adsorbents, the multi-molecular adsorption curve (the t-curve) proved to be identical. this fact has led de boer to the claim of a “universal” multi-molecular adsorption curve for nitrogen. other investigators (mikhail et al., 1968), however, have shown that even for nitrogen, the existence of the so-called universal multi-molecular adsorption curve can be considered as an oversimplified statement for the actual situation. to obtain a “correct” t-curve suitable for a particular application, mikhail et al., (1968) considered another factor besides the absence of porosity, namely, the c-constant of bet equation. they emphasized the importance of using the “correct” t-curve in a particular pore structure analysis. by “correct” t-curve, they meant a t-curve on which the heat of adsorption of nitrogen is of the same order of magnitude as the heat of adsorption of the sample under study. the statistical thickness t(å) of the adsorbate can be obtained from : ,10 414,22 4 bet asp ⋅⋅= s vmv t (5) where m is the molecular weight of nitrogen, vsp is the specific volume of nitrogen in ml/g, va is the amount adsorbed in cm3/g at stp, and sbet is the specific area in m 2/g. in calculating the value of t, the density of the adsorbate is considered to be equal to the density of liquid nitrogen at the temperature of the isotherms (–195.8 °c). a practical way to use the t-curve for nitrogen is to plot experimental adsorption curves as a function of t-values; hence, f(t)v = is taken instead of ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = 0p p fv . 20 studies of surface area and pore structure on portland cement figure 5. vl–t plots of nitrogen adsorption on the low-porosity cement pastes ia at various ages of hydration (0.021, 0.25, 3, and 28 days). in any normal case of multi-molecular adsorption, the experimental points should fall on a straight line passing through the origin. the slope of this line gives the specific surface area st in m 2/g according to the following equation: ,10 4lt ⋅= t v s (6) where vl is the volume in ml/g of nitrogen adsorbed and t is the statistical thickness in å. concerning the shape of the vl–t plots, lippens and de boer (1965) have pointed out three possibilities with regard to the slope of the vl–t plot (straight line, deviates upwards, or deviates downwards from the straight line). in the present investigation, the vl–t plots were constructed on the basis of the adsorption branches of isotherms by using the t-values published for solids, having low values of the c-constant of the bet equation (i.e., low heat of adsorption) as obtained from the adsorption of nitrogen on a number of nonporous oxides. figures 5–8 show the vl–t plots for the hardened cement pastes ia, va, іb, and vb, respectively. a definite criterion for the correctness of the vl–t plot is the close agreement between the surface areas obtained from these plots (known as s) and the bet surface areas (sbet). this agreement is shown in tables 4 and 5 for the hardened pastes made from sample a and sample b cements, respectively, which support the use of the suggested t-curve for the adsorption of nitrogen on the hardened cement pastes. the vl–t plots shown in figures 5–8 indicate, in most of the investigated cases, downward deviations from the initial straight lines, which pass through the origin. in some other cases, a slight upward deviation is noticed, indicating the presence of mesopores with limited sizes. the downward deviations, however, demonstrate the existence of narrow pores in the pore system of the hardened cement pastes. 21 a.m. saad et al. figure 6. vl–t plots of nitrogen adsorption on the low-porosity cement pastes va at various ages of hydration (0.021, 0.25, 3, and 28 days). table 4. the bet surface area sbet as compared with the surface area st obtained from the vl–t plots for the hardened cement pastes іb and vb made with low and high initial porosities. sample sbet (m 2/g) st (m 2/g) pastes іb (w/c = 0.30) іb 0.021 days 118.59 1106.50 іb 0.083 days 84.91 85.50 іb 0.025 days 108.74 100.10 іb 1 day 104.22 100.30 pastes vb (w/c = 0.50) vb 0.021 days 50.00 52.10 vb 0.083 days 45.61 47.20 vb 0.25 days 46.17 45.20 vb 1 day 51.60 51.10 22 studies of surface area and pore structure on portland cement figure 7. vl–t plots of nitrogen adsorption on the low-porosity cement pastes ib at various ages of hydration (0.021, 0.083, 0.25, and 1 day). figure 8. vl–t plots of nitrogen adsorption on the low-porosity cement pastes vb at various ages of hydration (0.021, 0.083, 0.25, and 1 day). 23 a.m. saad et al. table 5. the bet surface areas sbet as compared with the surface areas st obtained from the vl–t plots for the hardened cement pastes іa and va made with low and high initial porosities. sample sbet (m 2/g) st (m 2/g) pastes іa (w/c = 0.30) іa 0.021 days 66.12 62.10 іa 0.025 days 82.58 80.00 іa 3 days 80.32 80.70 іa-28 days 87.00 85.00 pastes va (w/c = 0.50) va 0.021 days 36.60 38.10 va 0.25 days 42.20 39.20 va 3 days 70.00 72.00 va 28 days 94.20 98.80 evidently, the vl–t plots shown in figures 5 and 6 for sample a low and high porosity cement pastes indicate the existence of only upward deviations from the initial straight line passing through the origin. this fact leads to a conclusion that the entire pore system of the hardened cement pastes ia and va consist mainly of meso-pores. the results of figure 7 obtained for sample b low porosity cement pastes (ib), however, show only downward deviations from the initial straight line passing through the origin. therefore, the pore system of these pastes consists mainly of micro-pores. for sample b high porosity cement pastes (vb), the pore system is found to be consisting mainly of micro-pores at the early ages of hydration (0.021–1 days) whereas at the later ages of hydration (3–28 days), only meso-pores are detected. 4. conclusion type іі adsorption isotherms of nitrogen were obtained for all of the investigated hardened cement pastes. in addition, the adsorption-desorption isotherms indicated the existence of closed hysteresis loops for most of the investigated samples. in some other cases, the adsorption-desorpion isotherms were fully reversible. the bet surface areas as well as the total pore volumes were found to be higher for the lower porosity cement pastes (іa and іb) than those made with higher initial porosities (pastes va and vb). this is mainly due to the different crystalline habit of the hydrates formed within the pore system of the various investigated cement pastes. on the other hand, the mean hydraulic radii of the total pore system accessible to nitrogen molecules were found to have lower values for the lower porosity pastes (іb) compared with the higher porosity pastes (vb). the c-constant values of the bet equation are very low, which indicate a very low heat of adsorption of nitrogen gas on the various hardened cement pastes. this indicates non-specific interactions between the adsorbate (nitrogen) and the adsorbent (cements pastes). the constructed vl–t plots indicate the existence of both microand/or mesopores of limited sizes. 5. references abo-el-enein, s.a., abd-el-khalik, m., hanafi, s. and el-hosiny, f.i. 1985. surface area and pore structure of polymer-impregnated hardened cement pastes. zement-kalk-gips, 38(11): 675-678. abo-el-enein, s.a., ata, a.a., hassanein a. and mikhail r.s. 1982. kinetics and mechanism of slag cement hydration. j. chem. tech. biotech., 32: 939-945. abo-el-enein, s.a., daimon, m., ohsawa, s. and kondo, r. 1974. hydration of low porosity slaglime pastes. cem. concr. res., 4(2): 299-312. 24 studies of surface area and pore structure on portland cement abo-el-enein, s.a., hekal, e.e., el-hosiny, f.i. and abd-el-khalik, m. 1990. autoclaved calcium silicate hydrates. 1-rate of formation and molar composition, il cemento, 87: 147-160. abo-el-enein, s.a., mikhail, r.sh., daimon, m. and kondo, r. 1978. surface area and pore structure of hydrothermal reaction products of granulated blast furnace slag. cem. concr. res., 8(2): 151-160. babaqi, a.s., baissa a.a., saad a.m., al-kadri f.a., abo-el-enein, s.a. 2001. hydration studies and pore structure on the portland cement produced in bajil and amran, yemen, yemeni j. sci, 2 (2): 2135. brunauer, s. and emmett, p.h. 1935. the use of van der waals adsorption isotherms in determining the surface area of iron synthetic ammonia catalysts. j. amer. chem. soc., 57: 1754-1755. brunauer, s., deming, l.s., deming, w.e. and teller, e. 1940. on a theory of the van der waals adsorption of gases. j. am. chem. soc., 62: 1723-1732. brunauer, s., emmett, p.h. and teller, e. 1938. adsorption of gases in multimolecular layers. j. am. chem. soc., 60: 309-319. cranston, r.w. and inkley, f.a, 1957. the determination of pore structures from nitrogen adsorption isotherms. adv. catalysis, 9: 143-154. de boer, j.h., linsen, b.g. and osinga, th.j. 1965. studies on pore systems in catalysts: vi. the universal t curve. j. catalysis, 4(6): 643-648. hekal, e.e., hanafi, s., abo-el-enein, s.a. and ghorab, h.y. 1987. nitrogen adsorption on low and high porosities alite pastes. tiz-tonindustrie-zeitung (tiz-fachberichte), 111(9): 607-611. lippens, b.c. and de boer, j.h. 1965. studies on pore systems in catalysts: v. the t method. j. catalysis, 4(3): 319-323. lippens, b.c., linsen, b.g. and de boer, j.h. 1964. studies on pore systems in catalysts i. the adsorption of nitrogen; apparatus and calculation. j. catalysis, 3(1): 32-37. mikhail, r.sh. and abo-el-enein, s.a. 1972. studies on water and nitrogen adsorption on hardened cement pastes i development of surface in low porosity pastes. cem. concr. res., 2(4): 401-414. mikhail, r.sh., abo-el-enein, s.a. and abd-el-khalik, m. 1975. hardened slag-cement pastes of various porosities. iii. surface area in relation to pore structure. j. appl. chem. biotech., 25(11): 849-857. mikhail, r.sh., abo-el-enein, s.a., abd-el-khalik, m. and gabr, n.a. 1978. autoclaved slagclinker-sand pastes surface area, pore structure and compressive strength. cem. concr. res., 8(1): 77-85. mikhail, r.sh., brunauer, s. and bodor, e.e. 1968. investigations of a complete pore structure analysis: i. analysis of micropores. j. colloid and inter. sci., 26(1): 45-53. received 1 march 2008 accepted 26 october 2008 25 microsoft word math070227-f.doc 41-52 squ journal for science, 12 (1) (2007) © 2007 sultan qaboos university 41 synchronization and persistence in diffusively coupled lattice oscillators adu a.m. wasike* and k.t. rotich school of mathematics,university of nairobi,p.o. box 3019700100, nairobi, kenya, *email: aduwasike@yahoo.com. المزدوجة للمذبذبات التوافق والثبات في انتشار الشبكة روتيش. ت. و ككسوا. م.أدو أ كل . دراسة التوافق والثبات في نظام من شبكات المذبذبات المتطابقة والتي تنتشر زوجياً في جوارها األقربتم :خالصة طبيق ثبوتية كما تم ت. و قد تم عمل هذا ضمن إطار نظرية المتنوعات الالمتغيرة . نظام جزئي له جاذب كلي متراص . الزائدية الطبيعية للحصول على شروط عامة لثبات وقوة التوافق المتنوع abstract: we consider the synchronization and persistence of a system of identical lattice oscillators that are diffusively coupled to their nearest neighbours. each subsystem has a compact global attractor. this is done in the framework of invariant manifold theory. normal hyperbolicity and its persistence are applied to obtain general conditions for the stability and robustness of the synchronization manifold. ams(mos) subject classifications: 37c80, 37d10. keywords: lattice oscillators, bravais lattice, synchronization manifold, robustness. 1. introduction here has been great interest in the synchronization of coupled oscillators on a one dimensional integer lattice. aside from the mathematical interest in the problem, coupled oscillators occur in physics, engineering, communications, signal processing and many other areas see for instance (see for instance afraimovich et al.(1992), cuomo (1993) and oppenheim (1993), and references therein. in electrical circuit theory, much work is due to chua and roska (1993), in particular in the studies of cellular neural networks (cnn). metallurgy is another area where lattice systems are found ( see for instance cahn (1960)). basic to the study of synchronization, two fundamental questions are of interest. the first is to do with the stability of the synchronization state of the system and the second is its robustness. robustness of the synchronization state is its ability to be insensitive to small perturbations in the system that generates it. for coupled identical systems, the diagonal of the system is invariant. synchronization is equivalent to the attracting property of the diagonal, which in turn is determined by the lyapunov exponents normal to the diagonal. more specifically, if all the lyapunov exponents normal to the diagonal are negative, then the coupled oscillators are synchronized. in t adu a.m. wasike and k.t. rotich 42 practice, for instance in the implementation of some model, various perturbations are unavoidable. moreover, numerical computations of model equations deal with solving “perturbed models”. for this reason, it is natural to address the question of not only the stability of the synchronization manifold but also its persistence or rather robustness under perturbations. much of the work on synchronization is on one dimensional lattice and deals mainly with its stability (see for instance the classical paper of fujisaki and yamada (1983)). normal hyperbolicity and the generalized lyapunov exponents have been used to establish conditions for the stability and persistence of synchronization manifold for two dissipative systems each with a compact global attractor (see for instance chow and liu (1997), josića (1977)). there is less repertoire on this subject in the twoand threedimensional lattices. the problem we consider in this paper therefore, is concerned with the synchronization, stability, and persistence of oscillations of a system of ordinary differential equations (ode's) indexed by points in an m-dimensional integer lattice { }, 1, 2 .m m+ ∈z this system is what we shall refer to as lattice differential equations (lde's). by a lattice oscillator, we mean a system of lde's with every lattice point having an attracting periodic orbit ( see for instance chow and liu (1997), wasike (2003)). we look at these two phenomena for oscillators that are linearly and symmetrically coupled via a diffusion-like coupling to their nearest neighbours on m-dimensional lattices. this is how we approach this problem. we set the problem in the framework of dynamical systems and then consider the two aspects of synchronization based on invariant manifold theory. in particular, we shall apply the ideas of generalized lyapunov exponents and normal hyperbolicity as defined in fenichel (1971), and hirsch et al. (1977) respectively. this approach will enable us to compare the rate of growth in the transversal direction to the synchronization manifold and that along the manifold. we first look at the one-dimensional lattice, then proceed to the two-dimensional case. most of the definitions basic terminology and some results will be given in § 2 while §3 deals with a two dimensional lattice. in every case, we give conditions that guarantee synchronization of oscillators and the stability of synchronization manifold under perturbation. we also give conditions under which the synchronization manifold is robust. §4 is the conclusion. let us suppose that the dynamics at every lattice site i is governed by the system of odes ( ),i iz g z= (1) where the dot “.” denotes differentiation with respect to time ( ), , 2,di it z z t d= ∈ ≥r 1,....., ,i n= the number of oscillators, ( ), , 1.r d dg c r∈ ≥r r suppose that, for each i, there is a compact global attractor for equation (1); that is, there exist a compact set which is invariant under the flow defined by equation (1) and the ω -limit set for each orbit of equation (1) belongs to this set. we shall now couple these systems to obtain oneand two-dimensional lattices. 2. one dimensional lattice now let us couple the 2n ≥ identical subsystems in equation (1) to yield ( ) ( ) ( ): , ,z b k z f z x z k= + = (2) where ( )1 2, ,......., t nz z z z= with t denoting transpose, iz denotes the coordinates of a point on the lattice, b(k) a real symmetric matrix depending on the coupling strength 0,k ≥ describes the coupling configuration. if we consider symmetric nearest neighbour diffusive coupling on a linear lattice (m = 1) with neumann diffusively coupled lattice oscillators 43 boundary conditions and assume that oscillators influence each other equally (k=constant), then ( ) 1 db k k i= ∆ ⊗ with ,1 1 1 0 0 0 0 0 1 2 1 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 1 1 n x n −⎛ ⎞ ⎜ ⎟−⎜ ⎟ ⎜ ⎟− ∆ = ∈⎜ ⎟ ⎜ ⎟ ⎜ ⎟− ⎜ ⎟⎜ ⎟−⎝ ⎠ r (3) di a xd d identity matrix, ( ) ( ) ( ) ( )( ) ( )1 2, ,......., , t r nd nd nf z g z g z g z c= ∈ r r ; and ⊗ is a kronecker product. definition 1. equation (2) is symmetrically synchronized if there exists a compact diagonal-like, smooth dmanifold mk that belongs to the manifold { }1 1 2 2: .... 0 .ndm z r z z z= ∈ = = = ≠ 1m has a boundary and is inflowing invariant and locally attracting. we refer to this set as the “diagonal” or the synchronization manifold in ndr , (see for instance hale (1997)). for the system to be synchronized, the diagonal 1m must be invariant and attracting under the flow defined by equation (2). in many applications, we are usually interested in local synchronization; that is, instead of requiring global attraction of 1m , we seek for local attraction. in this case we will say that the system in question is locally symmetrically synchronized. let us suppose that system (2) has a compact global attractor km for each k. we say that equation (2) is symmetrically synchronized if its solution z is in the set 1m for all 0;t ≥ that is, .1km m⊂ km needs to persist under perturbation for synchronization to be of physical interest. definition 2. let ( ),x z k be the vector field defined in equation (2) and ( ),x t k be its perturbation, then; synchronization manifold km is 1c stable or persistent if for any 0,∈> there exist 0δ > such that for any ( ) ( ) 1, , cx z k x z k δ− < and the system ( ) ( ),z t x z k= is locally synchronized with the synchronization manifold km such that 1 .k k c m m− < ∈ adu a.m. wasike and k.t. rotich 44 we say that the synchronization manifold is robust if 1.∈≪ very often in the study of synchronization, systems have a natural invariant submanifold. a necessary and sufficient condition for such synchronization and persistence is normal hyperbolicity mané (1977). the manifold km is normally hyperbolic if, under the dynamics linearized about the invariant manifold, the growth (decay) rate of vectors transverse to the manifold dominates the growth (decay) rate of the vectors tangent to the manifold, that is; the expansion (contraction) of the flows in the direction normal to the manifold is exponentially greater than the expansion (contraction) of the flows tangent to the manifold (see for instance hirsch et al. (1977), mané (1977)). the growth/decay rates of vectors can be characterized in terms of generalised lyapunov exponents determined from the linearized equations of motion around the synchronization manifold (see for instance fenichel (1971), wiggins (1994)). let us make this more precise. consider the linearization of equation (2) along the manifold km ( )( )0; ,z a z t z z= (4) where ( )0;z t z is the solution of equation (2) with ( )0 00 ; kz z z m= ∈ ( ) ( )a z jf z= is the jacobian matrix of f at z. assume there is an invariant splitting of the fundamental matrix solution of equation (4), ( )0; ;t zφ that is, ndz z zkt r t m n= ⊕ for ,kz m∈ ( ) ( ) ,, 000; t zz k kzt z t m t mφ = and ( ) ( )00 , 0 ; z z t zt z n nφ = for all and . 1t r∈ let ( )0;c t zφ and ( )0;s t zφ denote the restrictions of ( )0;t zφ on 0z kt m and 0zn respectively, where 0z kt m and 0zn are the tangent and normal vectors to km at 0z respectively and ⊕ indicates the direct sum of the two vector spaces. definition 3. the generalized lyapunov exponents for 0z km∈ are defined as ( ) ( )00 1 l im sup ln ; ,s t z t z t α →∞ = φ (5) ( ) ( ) ( )( ) 0 0 0 ln ; l im sup , ln ; s t c t z z m t z β →∞ φ = φ (6) where, for a linear operator ( ) ( )}{ ( ), min : 1, ,l m l l x x x d l d l= = ∈ is the domain of the operator l. the generalized lyapunov exponents have been used in the study of normally hyperbolic invariant manifolds (see hirsch et al. (1977), fenichel (1971), chow and liu(1997)). the uniformity lemma in fenichel (1971) states that α and β achieve their maximums on km . for this reason we need to show that there exists an invariant manifold km in the solution space of equation (2). we describe this manifold in appropriate coordinates that display vectors transverse and tangent to it. since we are considering coupled identical oscillators, the diagonal is invariant. we therefore show that the matrix 1∆ has zero as an eigenvalue with the diffusively coupled lattice oscillators 45 corresponding generalized eigenspace that belongs to the diagonal in ndr and the other eigenvalues are bounded to the left-hand side of the complex plane. as a consequence of the preceding statement, the following hypotheses about ( )b k are made: h1 for each ( ),k b k is self adjoint, 0 0λ = is an eigenvalue of ( )b k with the corresponding generalized eigenvectors ( )1, 1, ..........1 nde vec r∈, whose span is the diagonal in ndr . h2 for 2,n > there exist a 0k and a bounded set ndu r∈ such that for each 0k k> , equation (2) has a global attractor .ka u∈ let us now show that equation (2) satisfies the two hypotheses. clearly the eigenvalues of ( )b k are 0 0λ = and 2 2 1, 2, ..... 1cos ,s n s k s n π λ −⎛ ⎞= − + =⎜ ⎟ ⎝ ⎠ (see for instance lancaster and tismenetsky (1995)). hence h1 is satisfied. for h2 we have to make a coordinate transformation that we now describe. from h1 we can introduce a new coordinate system ( )1 2 1, , ,..... , , , t nd d d nz ye ew w w w w w y nd − −= + = ∈ ∈ −r r ,1 1 1 1, 1 , j j j n j j w z z j n y z n + = = − ≤ ≤ − = ∑ (7) where je is the usual unit vector in nr with zeros except for 1 at the jth position and 1 ,i j j i j e e e n= = −∑ with ( ),1 2 1,......, .ne e e e −= the set , , 1 1je e j n≤ ≤ − is an orthogonal basis for nr . using transformation in (7) in equation (2), we obtain ( ) ( ) ( ) 1 , , 1 , d n j j w k i w f w y y g z n = = ∆⊗ + = ∑ (8) where the function ( ) ( ) ( ) ( )( )1 2 1, , , , , ......., , t nf w y f w y f w y f w y−= with ( ) ( ) ( )( )1, , 1 1,j j jf w y g z g z j n+= − ≤ ≤ − and the matrix ∆ is given by adu a.m. wasike and k.t. rotich 46 ( ) ( )1 x 1 . 2 1 0 0 0 0 0 1 2 1 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 1 2 n n− − −⎛ ⎞ ⎜ ⎟−⎜ ⎟ ⎜ ⎟− ∆ = ∈⎜ ⎟ ⎜ ⎟ ⎜ ⎟− ⎜ ⎟⎜ ⎟−⎝ ⎠ r the eigenvalues of ∆ are 2 2 co s , 1, 2, 3, ....., 1,s s s n n π λ = − − = − (see for instance lancaster and tismenetsky (1995)). since the matrix 1∆ has zero as an eigenvalue and other eigenvalues are bounded to the left-hand side of the complex plane, equation (8) satisfies h1 and h2 hence there exists an invariant manifold km of equation (8) containing the attractor ka and attracting bounded sets of ndr (see hale (1997)). as the coordinate transformation in equation (7) is linear, it follows that equation (2) satisfies h2. the first equation in (8) describes the motion transverse to the synchronization manifold ;km that is, it describes the deviations .1j jz z +− synchronization means that the deviations dampen out as .t → ∞ from the first equation in (8), this is equivalent to saying that { }0w = is exponentially stable. since we are interested in local synchronization, the criteria of local attractivity of the synchronization manifold and its persistence is determined by the ratio of the growth rates of vectors transverse and tangential to it. the following theorem relates robustness and lyapunov exponents. 2.1 main results in this section, we state and proof a theorem that relates robustness and lyapunov exponents. for this purpose, we shall need some results due to chow and liu (1997). these results make use of the well-known theorems in invariant manifold theory regarding persistence of invariant manifolds, (see for example, fenichel (1971), hirsch et al. (1977), and mané (1977)) and they are stated thus: lemma 1 (chow and liu (1997)). consider equation (2) and suppose that the synchronization manifold km is invariant, then if ( )0 0,zα < for all ,0 kz m∈ then the manifold km is attracting and hence (2) is synchronized. lemma 2 (chow and liu (1997)). suppose that km is locally synchronized, then the synchronization is 1c table if and only if ( )0 0zα < and ( )0 1zβ < for all .0 kz m∈ theorem 3. if equation (2) satisfies h1 and h2, then there exist a 0k such that for all ,0k k> there is a positively invariant synchronization manifold km that is attracting and 1c stable or persistent. proof. characterizing growth rates in the fashion described above requires knowledge of the linearized dynamics near orbits on the invariant manifold as .t → ∞ diffusively coupled lattice oscillators 47 linearization of (8) along the solution ( )( )00, y t which corresponds to ( ) ( )( ), kw t y t m∈ yields ( )( ) ( )( ) 1 0 0 0 , 0 zn d z i d g y t k iw w y yd g y t − ⎛ ⎞⊗ + ∆ ⊗⎛ ⎞ ⎛ ⎞⎜ ⎟=⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ (9) where ( )( ) ( )( )0 0zd g y t j g y t= is the jacobian matrix of g at ( )0y t the solution of equation (1). notice that there is a continuous invariant splitting of ; ,n d n dk k kt m t m tm n= ⊕r r where ⊕ refers to the whitney sum of the tangent and normal bundles. since system (9) is uncoupled and ( )( )1 0zni d g y t− ⊗ and dk i∆ ⊗ commute, the fundamental matrix solution of equation (9) is of the form ( ) ( ) ( ) ( )0 0 : : , 0 t k ts l l w t e t z y t e λ λ λ +⎛ ⎞⎛ ⎞ ⎜ ⎟≈ = φ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ (10) where ,1s s nd dλ ≤ ≤ − are the eigenvalues of the coupling matrix di∆ ⊗ and ,1 ,l l dλ ≤ ≤ are the lyapunov exponents of the trajectories defined by ( )( )0 .zy d g y t y= the invariant manifold{ }0w = is generated by the second equation in (9). therefore ( )0,c t zφ corresponds to tle λ while ( )0,s t zφ corresponds to ( ) .l tk se λλ + the maximum eigenvalue of ∆ is 21 4 sin 2n π λ =− and hence ( ) ( )0 1: ,mz kα ζ λ= − + where 1 1:ζ λ= − is the maximum eigenvalue of the coupling configuration and mλ is the maximum lyapunov exponent defined by ( )( )0zy d g y t y= in .km thus by lemma 1, { }0w = is attracting and the coupled system is locally synchronized if ( )0 0;zα < that is, k satisfies 1 1 mk λξ > . to insure robustness of the synchronization manifold, the condition for normal hyperbolicity must be satisfied. km is robust if and only if for all ,0 kz m∈ ( ) ( )( ) 0 0 0 0sup , inf ,s cz z t t m t tφ < φ (see for instance hirsch et al. (1977) page 10). this is equivalent to saying that ( ) ( ) ( ( )) : 0 0 0 ln , lim sup 1. ln , s t c t z z m t z β →∞ φ = < φ adu a.m. wasike and k.t. rotich 48 by lemma 2, we require that ( )0 0zα < and ( )0 1;zβ < that is, 1 1,m m kλ ζ λ − < where mλ is the minimum lyapunov exponent defined by ( )0zy d g y y= in .km this is satisfied if ( ) 1 1 .mmk λ λζ −> thus we conclude that for synchronization, stability and robustness of the synchronization manifold ,km k must satisfy the inequality ( ), 1 1 max .mm mk λ λ λζ ⎧ ⎫⎪ ⎪ > −⎨ ⎬ ⎪ ⎪⎩ ⎭ taking ( ),0 1 1 max mm mk λ λ λζ ⎧ ⎫⎪ ⎪ = −⎨ ⎬ ⎪ ⎪⎩ ⎭ completes the proof. 3. two dimensional lattice oscillators in this section we study the existence and stability of the synchronization manifold and its persistence. results similar to those of one dimensional case can be shown to hold. all that one needs is to show that a synchronization manifold exists and make appropriate coordinate transformation which decomposes the flow along the invariant manifold into transversal and tangential flows and study the condition of normal hyperbolicity using generalized lyapunov exponents. let us consider an xn n simple (or bravais) square lattice. let , 1 , ,dijz i j n∈ ≤ ≤r be the coordinate of the (i,j)th site oscillator and the matrix x , 1 : . n nd nd ij i j z = ⎡ ⎤= ∈⎣ ⎦ rζ also let ( ), , ..........,1 2 nz z z=ζ with ,1ndrz r n∈ ≤ ≤r be its r th column. we therefore define the vector valued function of z as ( ) . 1 2 , , ,2 1 2 t n d z z zr nrr r n z z vec z ζ = ⎛ ⎞ ⎜ ⎟ ⎜ ⎟= ∈⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ rζ (11) we also define the kronecker sum of 1∆ with itself as: 1 1 1 1 ,n ni i∆ ⊕ ∆ = ∆ ⊗ + ⊗ ∆ (see, for example lancaster and tismenetsky(1985) for details on matrix tensor algebra). let us couple the subsystems ( )ij ijz g z= thus: ( ) ( )1 1 ,dk i g⎡ ⎤= ∆ ⊗ + ∆ +⎣ ⎦ζ ζ ζ ζ (12) diffusively coupled lattice oscillators 49 where ( ) ( ) ( ) ( ) ( )( )1 21: , ,........ . n nij ij g z f z f z f z = ⎡ ⎤= = ⎣ ⎦ g ζ this type of coupling corresponds to symmetric nearest neighbour diffusive coupling on a simple square lattice with neumann boundary conditions. writing equation (12) in vector notation we obtain: ( ) ( )vec k vec vec g= +ζ β ζ ζ , (13) where the matrix ( ) ( )1 1: .dk k i= ∆ ⊕ ∆ ⊗β for system (13) to be synchronized, the diagonal must be an invariant set which will be the case if all the ( )ijg z are the same, and ( )kβ has zero as an eigenvalue with the diagonal as the corresponding generalized eigenspace. in this situation, we must also have all other eigenvalues of ( )kβ less than zero. we therefore make the following assumptions on ( )kβ . h3 for each ( )k, kβ is self adjoint, 0 = 0λ is an eigenvalue of ( )kβ with the corresponding generalized eigenvectors ( ) 2 1,1,........,1 n de vec ∈r whose span is the diagonal in . 2n dr h4 for 2,n > there exists a 0k and a bounded set 2n du ∈ r such that for each ,0k k> equation (13) has a global attractor 2 .ka u∈ it is trivial to show that equation (13) satisfies h3. symmetric synchronization occurs when ( ) vec = 0, 0.k vec λ= ≠β ζ ζ ζ thus we require that 0λ = be an eigenvalue of ( )kβ . indeed the eigenvalues of ( )kβ are ( )( ) ( ){ }: , 0 , 1 ,sp sp s pk k s p nσ µ µ λ λ= = + ≤ ≤ −β with 0 0, 2 2 cos , , , 1 12 s p n nξ ξ π λ λ ξ ξ= = − − = ≤ ≤ − each occurring d times, the order of .di the corresponding eigenvector to 0λ = is given by ( ) 2 .: col 1,1,.........,1 n dv = ∈r the synchronization manifold corresponds to the span{ }v that we define as follows: { },21 1 1: , 1 1j jjm z z z m j n+= = ∈ ≤ ≤ −z thus h3 is satisfied. to proof that h4 is satisfied, we need to make a coordinate transformation. the transformation used in one dimensional case can be rewritten to suit the two dimensional case as follows. , 1 1 , 1 1, 1 nd j j jj n nd jj w z z j n z y z y n + = = − ≤ ≤ − ∈ = ∈∑ r r (14) adu a.m. wasike and k.t. rotich 50 where ( ), , .........., ,1 2 t ny y y y= with ,1 . n i i jj y z = = ∑ let e be as defined in § 2 , and je be the usual unit vector in . nr the set , , 1 1je e j n≤ ≤ − is an orthogonal basis for nr , and in this basis we can write z as ( ) ,, 2n d -nd nvec = e y e i vec⊗ + ⊗ ∈z w w r (15) where ( ), , ..........,1 2 1: nw w w −=w with , 1 1ndjw j n∈ ≤ ≤ −r as its rth column. using equations (14) and (15), equation (13) satisfies ( ) ( ) ( ) 1 1 1 , 1 , d n jd j vec = k i vec vec f y y k i y f z n = ⎡ ⎤∆ ⊕ ∆ ⊗ +⎣ ⎦ = ∆ ⊗ + ∑ w w w, (16) where ( ) ( ) ( )1 1, ( , ,......, , ),nf y f y f y−=w w w with ( ) ( ) ( )1, .j j jf y f z f z += −w since the matrix ( )kβ has zero as an eigenvalue and other eigenvalues bounded to the left hand side of the complex plane, equation (13) satisfies h3 and h4 hence there exists an invariant manifold 2 km of equation (13) containing the attractor 2ka and attracting sets bounded sets of 2n dr ( see hale (1997)). the first equation in (16) describes the transverse motion to the synchronization manifold, ,2km and the second equation describes the motion tangent to the manifold .2km symmetric synchronization is equivalent to , , 0p q r sz z− → as ,t → ∞ for all , , , .p q r s this means that 0→w as t → ∞ . this implies that the synchronization manifold is attracting. 3.1 synchronization and persistence of 2km since our interest is local synchronization of the invariant manifold, we shall seek to show that the manifold is locally attracting. the manifold 2km is attracting if the lyapunov exponents of the flow defined by the first equation in equation (16) are less than zero. theorem 4. if system (13) satisfies h3 and h4, then there exists a 0k such that for all ,0k k> there is a positively invariant synchronization manifold 2km that is attracting and 1c stable or persistent. proof. linearization of (16) along 2km ; that is, ( ) ( )( ) ( )( )0, 0, ,t y t y t=w where ( ) ( )( ) ( ) ( ))0 01 02 0n: , ,......,y t y t y t y t= , a solution to equation (12), gives diffusively coupled lattice oscillators 51 ( ) ( )( ) ( )( ) 1 1 0 0 0 0 ndk i i dg y tvec vec yy dg y t − ⎛ ⎞∆ ⊕ ∆ ⊗ + ⊗⎛ ⎞ ⎛ ⎞⎜ ⎟=⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠ w w (17) where ( )( ) ( )( )0 0: ,n zdg y t i diag d g y t= ⊕ is the is the jacobian matrix of f at ( )0y t . notice that there is a continuous invariant splitting of 2 2 2 2, ,n d n d k kt t m tm n= ⊕r r where 22 n d nd ktm −∈ r and ndn ∈ r . from lemma 1, =w 0 is locally synchronized if the maximum lyapunov exponent of the trajectories defined by the first equation in equation (17) are negative. since equation (17) is uncoupled, and the matrices ( )1 dk i∆ ⊕ ∆ ⊗ and ( )( )1 0ni dg y t− ⊗ commute, the fundamental matrix solution of equation (17) is of the form ( ) ( ) ( ) ˆ 0 0 ˆ: ; , 0 k ti ti vec t e t z y t e λ λζ λ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ +⎛ ⎞⎛ ⎞ ⎜ ⎟≈ = φ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ w where , 2ˆ 1k n d ndζλ ζ≤ ≤ − are the eigenvalues of ( ) , 21 , 1ik i n d ndλ∆ ⊕ ∆ ≤ ≤ − and , 1i j ndλ ≤ ≤ are the lyapunov exponents over 2 km . the maximum eigenvalue ˆ ζλ of 1∆ ⊕ ∆ is the maximum eigenvalue of 1 : 0∆ = plus the maximum eigenvalue of ;1: ξ∆ = that is, . 2 2 1: 4 sin 2 s n π ξ ξ− = − = − let mλ and mλ be the maximal and the minimal lyapunov exponents over . 2 2 1km m⊂ then from the definition of lyapunov type numbers in §2, we see that ( )0 1 mz kα ξ λ= − + and ( ) 10 .m m k z λ ξ β λ − = thus by lemma 2, the synchronization manifold 2km is robust if k satisfies the inequality ( ) 1 1 max , .mm mk λ λ λξ ⎧ ⎫⎪ ⎪ > −⎨ ⎬ ⎪ ⎪⎩ ⎭ taking ( )0 1 1 max , mm mk λ λ λξ ⎧ ⎫⎪ ⎪ = −⎨ ⎬ ⎪ ⎪⎩ ⎭ completes the proof. 4. conclusion we have observed that persistence of the synchronization manifold crucially depends on the relationship between the dissipativeness of the individual oscillators and the coupling strength. there is a critical value of the coupling strength, 0k , above which the robustness of the synchronization manifold is guaranteed. the synchronization manifold needs to be normally hyperbolic and invariant in order for it to be robust. the proof adu a.m. wasike and k.t. rotich 52 for the condition of robustness depends on the coupling configuration and persistence of normal hyperbolicity. this work can easily be extended to three dimensional cases. 5. references afraimovich, v.s., bykov, v. and shilnkov, l. 1983. on structurally unstable attracting limit sets of lorenz attractor type, {\it tran. of moscow math. soc. 44:153-216. cahn, j.w. 1960. theory of growth and interface motion in crystalline material, acta metallurgica 8: 554-562. chow, s.n., liu, w. 1997. synchronization, stability and normal hyperbolicity. resenhas ime-usp. 3: 139158. cuomo, k.m. and oppenheim, a.v. 1992. synchronized chaotic circuits and systems for communications, mit research laboratory of electronics technical report 575 (unpublished). cuomo, k.m., oppenheim, a.v., 1993. circuit implementation of synchronized chaos with applications to communications, it phys. rev. lett. 71(1): 65-68. cuomo, k.m., oppenheim, a.v. 1993. chaotic signals and systems for communication, icassp 3: 137140. chua, l.o. and roska, t. 1993. the cnn paradigm. ieee trans. circuits syst., 40: 147-156. fenichel, n. 1971. persistence and smoothness of invariant manifolds for flows. ind., univ. math. j., vol. 21 3: 193-225. fujisaka, h., yamada, t. 1983. stability theory of synchronized motion in coupled-oscillators systems. prog. theor. phys. 69: 32-47. hale, j. 1997. diffusive coupling, dissipation and synchronization j. dyn. differ. equ. 9: 1-52. hirsch, m.w., pugh, c.c., shub, m. 1977. invariant manifolds, lecture notes in mathematics vol 583. springer-verlag: berlin, heidelberg, new york. josića, k. 2000. synchronization of chaotic systems and invariant manifolds, nonlinearity 13:1321-1336. lancaster, p. 1985. tismenetsky, m.; the theory of matrices, academic press. mané, r. 1977. persistent manifolds are normally hyperbolic, trans. amer. math. soc. 246: 261-283. wasike, a.a.m. 2003. synchronization and oscillator death in diffusively coupled lattice oscillators international journal of mathematical science, 2(1): 67-82. wiggins, s. 1994. normally hyperbolic invariant manifolds in dynamical systems; springer-verlag: berlin, heidelberg, new york. received 27 february 2007 accepted 11 october 2007 microsoft word phys040516-final.doc 93-100 squ journal for science, 10 (2005) © 2005 sultan qaboos university 93 employment of some parameters to enhance laser-drilling of aluminum oday a. hamadi p.o. box 55159, baghdad 12001, iraq, email:odayata2001@yahoo.com. تحسين عملية تثقيب األلمنيوم بالليزر من خالل توظيف بعض العوامل عدي عطا حمادي ظيف ودراسة بعض العوامل المؤثرة على عملية تثقيب عينات من األلمنيوم في هذا البحث، جرى تو :خالصة هذه العوامل هي طريقة النبضات المتعددة والسيطرة على درجة حرارة . ياك النبضي-باستخدام ليزر النيدميوم البحث أن هذه بينت النتائج المقدمة في هذا. العينة والضغط الواطيء للمحيط وتسليط المجال الكهربائي على العينة العوامل يمكن أن تعمل على تحسين عملية التثقيب من خالل زيادة عمق التثقيب في عينات األلمنيوم عند نفس .قيمة طاقة الليزر المستخدمة للتشعيع abstract: in this work, some parameters affecting drilling of aluminum samples by a pulsed nd:yag laser were studied. these parameters are multi-pulses irradiation, controlling sample temperature, low-pressure ambient and application of electric field on the sample. results presented in this work explained that these parameters can enhance drilling process throughout increasing hole depth in aluminum samples at the same laser energy used for irradiation. keywords: laser, aluminum and aplication 1. introduction aser-material interaction is determined mainly by reflection, absorption and transmission of the material to the wavelength of laser beam. laser beam is partially reflected at the surface of material and this reflection represents a loss in the incident energy and hence energy contributing the interaction. another part of incident energy is absorbed since transmission is supposed to be neglected in metals. the absorbed energy may be dissipated due to thermal conduction of the material as well as absorption and scattering of laser beam by removed or evaporated material during the process (ready 1978a). laser heating of opaque metals is a surface effect. this leads to a rise in temperature of the metal surface since the energy absorption is higher at the surface and decreasing with depth inside the material due to the effect of thermal diffusivity of the material (wagner 1974). the following relation determines the rise in surface temperature caused by laser irradiation as (wilson and hawkes 1987): l oday a. hamadi 94 1 2 o o 1 2 ( )s r n t t i k τ π − = + (1) where ts and to are the final measured and initial temperatures of the surface, respectively, io is the incident power density, r is the surface reflectivity, k is thermal conductivity, n is thermal diffusivity and τ is the laser pulse duration. laser irradiation is an important source to heat the material during a very short time to high temperatures that cannot be achieved by conventional sources. metal temperature varies with time at a rate of 106 ºc/s during laser-material interaction in drilling (von allmen 1978). regarding equation (1), the surface temperature is related to the square root of the laser pulse duration τ as well as thermal diffusivity n, and related inversely to the thermal conductivity k. the latter has a negative effect on surface temperature since the higher thermal conductivity admits more thermal energy to dissipate inside the material. in turn, the surface temperature in laser-material interaction relates to its reflectivity r. practically, surface reflectivity decreases during irradiation time and is not constant as seen in equation (1) (ready 1978b, chun and rose 1970). vaporization and material removal are the principles of cutting and drilling processes by laser. when the laser power density is as high as 106 w/cm2, surface temperature rises fast to the vaporization point. accordingly, there will be no more melting as vaporization is reached and a hole is formed. interaction between a laser beam and a metal surface is dependent on several parameters, such as incident power density, pulse duration and surface absorption. consequently laser drilling and material removal are dependent on these parameters. laser drilling is one of the earliest applications that accompanied laser invention. hence, it attracted a wide interest by researchers and its fundamentals are now well established. about 90% of the material removed in laser drilling is in the form of liquid drops condensed on the walls of the hole as the rest being material vapor (ready 1978a, charchan 1972). the velocity of material removal and the hole formation are related by (steen 1991): 0[ ( ) ] s v v i v c t t lρ = − + (2) where i is the absorbed power density, ρ is the material density, c is the specific heat capacity, tv and lv are temperature and latent heat of vaporization, respectively. the depth of the hole formed by a laser pulse is given by (luxon and parker 1985): 0 0([ ) ]v v e d a c t t lρ = − + (3) where e0 is the incident laser energy and a is the area affected by laser beam. when the absorption of the incident laser power and the rise in surface temperature to vaporization point occurr, three consequent processes result in hole formation and material removal; they are (chun and rose 1970): a) surface vaporization during the stage of laser pulse b) rise in pressure inside the crater formed due to the removal of the surface layer as a result of vapor expansion c) removal of the melt outside the hole. there are many advantages of the laser drilling compared to the conventional methods. contamination of the processed region is already avoided since the process is carried out by a light (laser) beam, i.e., contactless processing. high accuracy drilling, small size holes and hence small and limited heat affected zone (haz) and invariant properties of material are satisfied by laser. brittle employment of some paramaters 95 materials such as glass and ceramics can be drilled by laser more easily than by conventional methods. also, some solid materials that cannot be drilled or processed conventionally, are drilled easily by high power lasers of high power densities and short pulses. thus, laser drilling is the fastest since processing time is as short as laser pulse duration. laser drilling has some disadvantages, due to the limited transmission of laser beam inside material and the limited penetration. internal surface of hole is rather non-uniform and rough due to condensation of the material vapor. somehow, laser drilling is so expensive compared to the conventional methods. 2. experiment samples of high-pure aluminum were cut with 1x1cm2 area and 3mm thickness, polished, grinded, distilled in water and alcohol and then dried with hot air. samples were irradiated by a pulsed jk2000 nd:yag laser of 1.06 µm wavelength, 7j maximum output energy and 300 µs pulse duration. the maximum laser power density obtained was 4.8 mw/cm2. dimensions of the holes in the samples were introduced and measured by a leitz-metallux 3 optical microscope. samples were moved in front of laser beam by an x-y micrometer stage. in order to introduce the effect of sample preheating on laser drilling, a tungsten lamp of 650w power and 0.5-3.5 µm emission spectrum to heat the sample and a k-type thermocouple to measure temperature were used. a voltage supply was used to apply an electric field on the sample mounted between two parallel 1cm-spaced copper plates. to study the effect of ambient pressure on the drilling process, a vacuum chamber as down as 10-2 mbar with a rotary vacuum pump was used. the data were fitted by a 2-order polynomial function to explain the best behavior. 3. results and discussion in figure 1, the hole depth is measured with laser energy and it was observed that the hole depth increased as irradiation laser energy was increased. this increase in the laser energy caused the material to absorb more energy and raise the surface temperature of the sample. the amount of material melted and removed from the hole increased too due to the vapor pressure generated (ready 1978a; chun and rose 1970). at higher energies, the variation of the hole depth is not linear with the variation of laser energy because the energy absorbed by the material – that should increase with increasing incident laser energy is affected by vapor and plasma formed and may absorb some energy (ready 1978b; duley 1987; nonhof 1988). the results in figure 1 are obtained by a single pulse irradiation. samples were then irradiated by multi-pulses of laser with a 100% overlap. the whole thickness of the aluminum sample was penetrated by 6 pulses as shown in figure 2. the effect of multi-pulses irradiation is interpreted as being due to two reasons. first, the variation of the laser beam focus just after the first laser pulse is due to vaporization of a layer of material and formation of the hole. now, the laser beam is not focused at the bottom of hole and this increases the spot size and decreases the laser power density, hence causing the vaporization and the material removal by the next pulse and so on (rykalin, et al. 1978). the second reason is that the phase transformation at the bottom of the hole due to the vaporization and the material removal by the first laser pulse causes heat accumulation. resolidification of some melted material on the walls of the hole may distort the hole section and decrease material removal by the next pulse. this decreases the effect of the next pulse (banas and webb 1982). in general, despite the fact that material removal decreases after the first pulse, the hole depth increases with increasing number of pulses on the hole as each pulse removes a layer of material (ready 1978a, ready 1978b). oday a. hamadi 96 0 100 200 300 400 500 600 700 800 900 0 1 2 3 4 5 6 7 laser energy (j) figure 1. variation of the hole depth measured with varying incident laser energy. 0 500 1000 1500 2000 2500 3000 3500 0 1 2 3 4 5 6 7 no. of pulses figure 2. effect of multi-pulses irradiation on the variation of the hole depth measured with varying incident laser energy (e=6j). h ol e d ep th ( µm ) h ol e d ep th ( µm ) employment of some paramaters 97 0 100 200 300 400 500 600 700 800 900 0 1 2 3 4 5 6 7 laser energy (j) 300k 396k 452k 495k 525k 550k figure 3. the effect of sample preheating on the variation of the hole depth measured with varying incident laser energy. 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 300 350 400 450 500 550 600 sample temperature (k) figure 4. the behavior of thermal diffusivity of the aluminum sample with temperature. h ol e d ep th ( µm ) n (c m 2 / s) oday a. hamadi 98 0 200 400 600 800 1000 1200 1400 0 1 2 3 4 5 6 7 laser energy (j) h ol e d ep th ( µ m ) in vacuum in air p=10-2mbar figure 5. the effect of environment vacuum on the variation of the hole depth measured with varying incident laser energy. 0 200 400 600 800 1000 1200 0 1 2 3 4 5 6 7 laser energy (j) h ol e d ep th ( µ m ) with e-field without e-field v=2kv figure 6. the effect of applied electric field on the variation of the hole depth measured with varying incident laser energy. employment of some paramaters 99 figure 3 indicates the effect of the sample preheating on the hole depth, as can be seen, all curves of different preheating temperatures are similar to the case of non-heating (300k) but with a decrease in the hole depth. this is attributed to the effect of thermal diffusivity which drops with temperature contrary to the case in most metals. figure 4 shows the behavior of thermal diffusivity of an aluminum sample with temperature. this effect shows that it is better to carry out drilling of aluminum at room temperature. samples were mounted and irradiated inside the vacuum chamber at a 10-2 mbar pressure and the hole depth was measured as a function of incident laser energy, then compared to results obtained in air. figure 5 explains the effect of vacuum environment on laser drilling; the hole depth increases by about 40% in vacuum than in air. low pressure ambient contributes effectively to the vapor expansion and the material removal (rykalin, et al. 1978) and hence increases the laser beam transmission inside the hole leading to more penetration inside the sample (von allmen 1976). the effect of the electric field on laser drilling of the aluminum sample is also studied. figure 6 shows the hole depth measured as a function of laser energy. the hole depth increases by 23% due to application of the electric field compared to the case without applied field. this effect may be caused by the force resulting from the applied electric field. since material vapor contains charged particles (electrons and ions), this force removes these particles from the hole decreasing the absorption of the laser beam energy by the vapor and hence increasing the penetration depth inside the sample (chen et al. 1996, voisey et al. 1999, lehane and kwok 2001). 4. conclusions according to the results obtained and presented in this work, drilling of an aluminum samples by pulsed nd:yag laser can be controlled and enhanced employing several parameters. multi-pulses irradiation, control of sample temperature, low-pressure environment and application of electric field can enhance the process and increase the hole depth. employing all four parameters, the hole depth can be increased to twice its expected size. with any doubt, the results obtained in this work could not have been achieved without employing these parameters for the same laser energy used for the irradiation, thus the improvement advantages to laser drilling processes. 5. references banas, c. and webb, r. 1982. laser macro-material processing. proc. ieee. 70(6): 556. charchan, s. 1972. lasers in industry. van nostrand reinhold co., ch.3, ch.4, pp.247-256. chen, x., lotshaw, w.t., ortiz, a.l., staver, p.r., erikson, c.e., mclaughlin, m.h. and rockstroh, t.j. 1996. laser drilling of advanced aterials: effects of peak power, pulse format and wavelength. j. laser appl. 8(5): 233-239. duley, w. 1976. co2 lasers effects and applications, ch. 4,5 academic press , new york. lehane, c. 1976 and kwok, h.s. 2001. enhanced drilling using a dual-pulse nd:yag laser. appl. phys. a 73: 45-48. luxon, j. and parker, d. 1985. industrial lasers and their applications. ch. 11, prentice-hall. nonhof, c. 1988. material processing with nd-lasers, ch. 1,5,6, electro-chemical publications ltd. ready, j. 1978. industrial applications of lasers. academic press, ch. 13-15. ready, j. 1978. lasers in modern industry. dearbon (michigan), p.73, 203. rykalin, n, uglov, a. and kokora, a. 1978. laser machining and welding. pergamon press, ch. 1, 2, 4. steen, w. 1991. laser material processing. p.74, 75, 99, 101. voisey, k.t., westley, j., byrd, p. and clyne, t.w. 1999. effects of assist gas in the laser drilling of thermal barrier coated superalloys, online information. oday a. hamadi 100 von allmen, m., blasé, p., affolter, k. and strumer, e. 1978. absorption phenomena in metal drilling with nd-lasers. ieee j. quantum electron. 14(2): 85-88. von allmen, 1976. laser drilling velocity in metals. j. appl. phys. 47(12): 5460-5463. wilson, j. and a. hawkes, j. 1987. lasers principles and applications. ch. 5, prentice-hall. received 16 may 2004 accepted 13 february 2005 squ journal for science, 2019, 24(2), 78-87 doi: http://dx.doi.org/10.24200/squjs.vol24iss2pp78-87 sultan qaboos university 78 molecular characterization of fumonisin mycotoxin genes of fusarium sp isolated from corn and rice grains latifa a. al-husnan 1 , muneera d.f. al-kahtani 1 and randa m.a. farag 2 * 1 biology department, faculty of science, princess noruah bint abdulrahman university (pnu), riyadh, kingdom of saudi arabia; 2 virology-molecular biology, health sciences research center (hscr), princess noruah bint abdulrahman university (pnu), riyadh, kingdom of saudi arabia; *email: rmfaraj@pnu.edu.sa. abstract: fungi mycotoxins can be a serious risk to health and lead to substantial economic loss. the environmental conditions of saudi arabia, with its mostly warm temperatures, are conducive to the growth of toxigenic fungi resulting in mycotoxin production in different food items. the current study elucidates the natural occurrence of toxigenic fungi and mycotoxin production in grains in saudi arabia. samples of white rice and corn (yellow, red) grains were collected from different local markets and houses. three fungal isolates were obtained from the corn and rice grains and examined using potato dextrose agar (pda) and carnation leaf agar (cla) media. fusarium spp. were the most prominent fungi in yellow corn, red corn and white rice grains. three isolated f. moniliforme strains were identified using molecular characterization of the trichothecene 3-o acetyltransferase (tri101) toxin gene. the dna genome of the three fusarium moniliforme isolates (namely, f. moniliforme_1, f. moniliforme_2 and f. moniliforme_3, which correspond to isolates from yellow corn, red corn and white rice, respectively) were used as a template for pcr to amplify trichothecene 3-o acetyltransferase (tri101). partially sequenced fragments amplified using a specific primer set were used to confirm the identification of, and to evaluate the phylogenetic relationships among the three isolates as well as to identify the corresponding antigenic determinants. the epitope prediction analysis demonstrated that there were four epitopes with scores equal to 1 in f. moniliforme_1, f. moniliforme_2 and f. moniliforme_3, respectively. interestingly, there were great dissimilarities in the epitope sequences among the three isolates except in nstpracaseqevs, stssradssslstd and ctlcprslmassvr. this indicates that the unique antigenic determinants predicted in the trichothecene 3-o acetyltransferase (tri101) toxin gene could be used for designing a broad spectrum antibody for rapid detection of fusarium spp. in foods. keywords: fumonisin; pcr; sequences; phylogenetic tree; antigenic determinants. الذرة و االرز حبوب من المعزول لفطرالفيوزاريوم فيومونيسين سموم لجينات الجزيئى الوصف فرج أحمد رانده محمد و القحطانى منيرة ،لطيفة الحسينان ظروف مما الشك فيه أن االصابات الفطرية للمواد الغذائية تمثل عواقب وخيمة بسبب المخاطر على الصحة العامة والخسائر االقتصادية.كما ان ال :صلخمال في المواد الغذائية البيئية و ارتفاع درجات الحرارة بالمملكة العربية السعودية توفر البيئة المناسبة لنمو الفطريات مما يؤدي إلى إنتاج السموم الفطرية عينات من األرز المختلفة. توضح الدراسة الحالية التواجد الطبيعي للفطريات السمية والسموم الفطرية في الحبوب في المملكة العربية السعودية. تم جمع ن الحبوب المطحونة وحبوب األرز األبيض والذرة )الصفراء والحمراء( من مختلف األسواق المحلية والمنازل ,حيث تم عزل ثالث عزالت فطرية م الفيوزاريوم كان األكثرانتشار في الذرة الصفراء .,pda dextro ) ) carnation leaf agar (cla)باستخدام اوساط غذائية مناسبه لنمو الفطريات o-3م توصيف جزيئي لجين باستخدا m. moniliforme والذرة الحمراء وحبوب األرز األبيض. تم تحديد ثالث سالالت معزولة من الفطر acetyltransferase (tri101). تم استخدام جينوم الحمض النووي لعزالت الفيوزاريوم الثالثة وهي moniliforme (f. moniliforme_1 و f. moniliforme_2 و f. moniliforme_3 تم استخدام أجزاء متسلسلة جزئياً ، والتي تقابل العزالت من الذرة الصفراء والذرة الحمراء واألرز األبيض ، لتحليل الجزيئى تم تضخيمها باستخدام مجموعة برايمر محددة لتأكيد التحديد ، لتقييم العالقات البينيه لالحماض االمينيه بين العزالت الثالثة. أظهر ا على f. moniliforme_3 و f. moniliforme_2 و f. moniliforme_1 في 1لألحماض االمينية أن هناك أربع بروتينات ذات درجات تساوي molecular characterization of fumonisin mycotoxin genes 79 ، nstpracaseqevs التوالي. من المثير لالهتمام ، كان هناك اختالف كبير في تسلسل االحماض االمينية من بين ثالث عزالت إال في stssradssslstd و ctlcprslmassvr. 3المتنبأ بها في جينة هذا يشير إلى أن المحددات الفريدة لمولدات االحماض االمينية-o acetyltransferase (tri101) يمكن استخدامها لتصميم جسم مضاد واسع النطاق للكشف السريع عن fusarium ،sp. األطعمة ألغراض في .مراقبة الجودة .تعين التغيرات الجينية لالحماض االمينيةو شجرة العالقات الجينية ،تتابع القواعد النيتروجينيه ،تفاعل البلمرة المتسلسل ،الفيوموسين :مفتاحيةال كلماتال 1. introduction ungi cause major crop diseases during harvest and storage under higher temperature and humidity conditions [1]. while more than 25 different fungi species are known to invade stored grains and legumes [2], certain species such as aspergillus, fusarium and penicillum are responsible for most spoilage and germ damage during storage [3,4]. they cause a reduction in baking quality and nutritive value, produce undesirable odors, color and change the appearance of stored food grade seeds [5]. mycotoxins are secondary metabolites produced by fungi, which cause health hazards to animals and human beings [6, 7]. moreover, fungal infestation of the seed coat may not only decrease seed viability, but also cause abnormal seedling development [1,7]. a large number of mycotoxin producing fungi which are associated with groundnuts, peanuts, cereals such as maize, rice, sorghum, wheat, barley and oats, and spices such as black pepper, ginger, nutmeg, chilly, etc. are of great significance worldwide [8], but knowledge regarding fungal seed decay and its importance for plant demographic and community processes is quite limited [9,10]. fungal genera, such as aspergillus sp; fusarium sp; penicillium sp; alternaria sp; and epicoccum sp. have been isolated from seeds of beans, cowpea, peas, and cocoa [3, 11, 12]. regarding legumes in saudi arabia, very little information exists with respect to natural contamination with toxigenic fungi and mycotoxins. aflatoxin(s) have been detected in some aspergillus isolates while fumonisin has been found in some fusarium isolates [13]. among food contaminants, mycotoxins may cause substantial economic loss due to reducing availability of commodities with acceptable levels of mycotoxins present, and their possibly greater cost [14]. mycotoxins continue to pose various health risks to consumers depending on the specific mycotoxin consumed and the level of exposure, and the health status of individuals in the population [15]. the majority of mycotoxins of greatest concern for human and animal health are produced by the genera aspergillus, penicillium, and fusarium, the so-called field fungi, which frequently infect various food commodities [10, 15], and outbreaks of mycotoxicoses in humans and animals, caused by ingestion of products containing mycotoxins have been reported [4, 16]. however, further studies confirm that the toxic effects depend on intake dose, toxin type, duration of exposure, metabolism, mode of action, and defense mechanism [17,18]. humans are exposed to mycotoxins throughout their lives due to consumption of fungus-contaminated food products, but sufficient quantities of mycotoxins in food and feedstuff can adversely affect human and animal health [14, 18]. many human diseases, especially carcinogenic, teratogenic, hepatic, and gastrointestinal ones, have been found to be linked to the ingestion of mycotoxin-contaminated products [4, 19, 20]. this study was conducted to determine the bioinformatics characterization of fumonisins isolated from corn and rice grain in saudi arabia. fumonisins are produced by species of fusarium genera, principally f. proliferatum, f. verticillioides, and f. nygamai [21]. fumonisin b1 (fb1) is the most abundantly occurring and toxicologically most significant derivative [22]. fumonisins are widely found as contaminants in corn, rice, figs, beer, and other commodities. temperatures of 15 to 30 °c and 0.9 to 0.995 water activity have been reported as optimum for fumonisin production [23]. fb1, due to its cancer-promoting activity, is designated as a possible human carcinogen [24], and fumonisins are probably linked to human esophageal cancer [4, 25]. it is also known that they are nephrotoxic and hepatotoxic [26] and cause neural tube defects in experimental animal species, and may also affect humans [27]. several studies have revealed mycotoxin contamination worldwide in rice, for example, aflatoxins have been found in the united arab emirates [28], fumonisins in iran and argentina [25, 29], ota in morocco [30], zea in nigeria [31], don in italy [32], nivalenol in korea [33] and citrinin in egypt [34]. in this study, we have hypothesized that mycotoxins affect human populations because the storage conditions in local markets and houses are conducive to mycotoxin production. as most of the corn and rice are grown during the wet season, they are susceptible to mycotoxin contamination. rice is shown to be a good substrate for toxigenic fungi like a. flavus, a. ochraceus, penicillium citrinum, and f. proliferatum [35, 36]. humidity, temperature, storage conditions, and transport time are the factors that influence mycotoxin production in rice. in the early 20th century, many human diseases occurring in japan and other asian countries were attributed to mycotoxins consumed in mold-damaged rice [4, 37]. unfortunately, enactment of stringent rules for mycotoxin control in food is not always the best solution [4, 38]. a beneficial effect in saudi arabian mycotoxin-contaminated food is left for domestic population and developing grain producing countries [39]. the impact of mycotoxin standards is more drastic for the population of developing countries [1, 39]. therefore, whilst in terms of quantity, availability of food for consumption might not be a problem, the availability of high-quality food which is free from mycotoxins, or at least, having toxin levels in permissible limits, is a matter of great concern in saudi arabia and other highly populated areas of the world [1, 39]. thus, the regulatory authorities should aim to facilitate trade without compromising the protection of consumers’ health [4, 39]. therefore, the aim of this study was to determine the fusarium species that are naturally occurring in contaminating corn and rice seeds (as the main crops imported in saudi arabia) by the molecular identification of toxigenic mycotoxin profiles of those species and protein structural analysis depicted from the gene(s) responsible for toxin biosynthesis. we have hypothesized that by studying f al-husnan, l.a. et al 80 the molecular properties of fumonisins, we could in future be able to produce vaccines for those species of fusarium genera which have a higher prevalence in developing countries [4, 10, 39]. 2. materials and methods 2.1 grain samples: 150 samples of corn (yellow and red grains) and rice were collected from markets and houses from different areas of saudi arabia (riyadh, hail, qasim, asir,tabuk, jizan, jouf, jeddah and dammam). about 0.5 1 kg of samples was taken randomly and collected in clean dry packaging. 2.2 isolation of mycotoxigenic fusarium species agar plate and blotter tests were used to isolate fusarium spp. as described by neergaard [40]. the grains were divided into two groups; the first group was disinfected with sodium hypochlorite 1% for 2 min and the second group was non-disinfected. all grains were washed several times by sterilized water, and then dried between sterilized filter papers. half of each group was plated on potato dextrose agar (pda). all dishes were incubated for 5 to 7 days at 25 °c. 2.3 purification and identification of fusarium species fusarium isolates were identified as species based on the morphological characteristics of the macroconidia, microconidia and general mycelium presentation from a single spore isolate grown for 7-10 days on sna with an olympus bh-2 light microscope [41]. when macroconidia, microconidia and mycelial characteristics from sna were insufficient for identifying the species, further examination of the samples were done on different agar media. potato dextrose agar (pda) was used to identify colony pigment characteristics of aerial mycelium on the agar [40, 41] carnation leaf agar (cla) was used to identify macroconidia, chlamydospores and the presentation of aerial mycelium. a single colony was transferred and purified by the hypha tip technique onto a da medium in the presence of streptomycin (50 mg /ml). cultured fungi were processed for molecular identification using specific primers for the trichothecene 3-o acetyltransferase (tri101) toxin gene. all conditions of isolation and purification of mycotoxins were performed under sterilization to prevent any external agent from polluting the seeds. 2.4 molecular identification of trichothecene 3-o acetyltransferase (tri101) toxin gene 2.4.1 isolation of genomic dna the mycelium mass of fusarium species isolates grown on a pda broth medium was harvested by centrifugation at 6000 rpm for 10 min. the pellets were washed twice by pbs buffer and stored at 20 °c. total dna of three isolates was isolated using the lysozyme-dodecyl sulfate lysis method as described by leach et al. [41]. 2.4.2 amplification and purification of trichothecene 3-o acetyltransferase (tri101) gene specific pcr reactions were conducted to assess the presence of tri101 gene. the primers used were: fad-u1 (5′-gatctcgacatggcctttgtcccc-3′); fad-d1 (5′-gaacaggtggtgaatgacgtgcttc-3′) [40]. the pcr amplification conditions included initial denaturation at 94 ° c for 5 min, then 35 cycles at 94 °c for 30 s, 55 °c for 60 s followed by extension step at 72 °c for 90 s and a final extension at 72 °c for 7 min. the amplification reaction was performed by thermal cycler (cot thermocycler model 1105). purification of pcr product was detected by electrophoresis using agarose 1.5% in 1x tae buffer and stained with ethidium bromide [21, 41]. the trichothecene 3-o acetyltransferase (tri101) gene fragment was excised from the gel and purified using a qia quick gel extraction kit (qiagen, berlin, germany). dna sequencing by purified pcr products were prepared for sanger sequencing technology using the dna sequencer technique (sigma, central lab, pnu, ksa). dna sequences of fusarium isolates were aligned using bio edit software version 7 (www. mbio-ncus. edu/bio. edit) and were compared to the reference sequences accessions of fusarium spp. available in the nucleotide database at ncbi using biastn-algorithm to identify closely related sequences (http/www.ncbi.nih.gov). dendrograms were constructed using un-weighted pair group method with arithmetic (upgma) on genbank. 2.5 epitope prediction and antigenicity the primary amino acid sequence of the trichothecene 3-o acetyltransferase (tri101) protein was evaluated from the corresponding nucleotide sequence using mega 6.0 software. the linear b-cell epitopes in the primary amino acid sequence of the coat protein was performed using the bcpreds server with default parameters (http://ailab.cs.iastate.edu/bcpreds/), which implements a support vector machine (svm) and the subsequence kernel method [42]. flexible length linear b-cell epitopes were predicted using the fbcp red [43] method with a specificity cut-off, 75%. the antigenicity of each amino acid residue in the primary protein sequence was determined using a semi-empirical method, which makes use of the physicochemical properties of each amino acid and its frequency of occurrence in experimentally known segmental epitopes. molecular characterization of fumonisin mycotoxin genes 81 3. results the fusarium isolates were selected for molecular identification using trichothecene 3-o acetyltransferase (tri101) gene sequencing. three fusarium isolates represented grains from yellow corn, red corn and white rice and were designated as f. moniliforme_1, f. moniliforme_2 and f. moniliforme_3, respectively. 3.1 molecular characters of toxin gene: total dna was extracted from fusarium isolates [f. moniliforme_1 (yellow corn isolate), f. moniliforme_2 (red corn isolate) and f. moniliforme_3 (white rice isolate)] from infected grains. the trichothecene 3-o acetyltransferase (tri101) gene of three f. moniliforme isolates was amplified from isolated dna of mycelium. the nucleotide partial sequence of the trichothecene 3-o acetyltransferase (tri101) gene in the three isolates was compared with published isolates in the genbank. the sequence homology revealed that the gene of interest was the trichothecene 3-o acetyltransferase (tri101) gene and the test fungal isolates were fusarium moniliforme isolates. a multiple sequence alignment (msa) was constructed using clustal w software between the three studied isolates (figure 1a). the alignment showed many conserved regions in all sequences and also distinguished the heterogeneity positions among the aligned sequences. phylogenetic analysis was performed by construction of a phylogenetic tree using a neighbor-joining method to unravel the relationships among all fusarium moniliforme isolates (figure 1b). the phylogenetic tree resulted in two clades in which fusarium moniliforme_1 (yellow corn isolate) and fusarium moniliforme_2 (red corn isolate) were in the same cluster whilst fusarium moniliforme_3 (white rice isolate) was separate in a different cluster (figure 2a, b). thus, the molecular identification based on sequence homology of the trichothecene 3-o acetyltransferase (tri101) gene confirmed the identity and phylogeny of the studied three fusarium moniliforme isolates. figure 1. a and b are msa for phylogeny of the three studied fusarium sp. isolates (f. moniliforme_1 (red corn isolate) and f. moniliforme_2 (white rice) were in the same cluster whilst fusarium f. moniliforme_3 (yellow corn isolate) was separate in a different cluster. al-husnan, l.a. et al 82 a 1 11 21 31 41 51 60 | | | | | | | kwlsrysstpsasyqasfrstpksvystpsliplnipllsvpsskvlsaspnpshgsqar 60 ......eeeeeeeeeeeeee...........................eeeeeeeeeeeee skpralaretqelplsslsrtflvlktsamilqrprsraerrhtlwrcltrtssrqgrry 120 e...............................eeeeeeeeeeeeee.............. lldlvlvpttqslfycsstssradssslstditvlwiwakmrsvysprravtthspkrkr 180 ..eeeeeeeeeeeeee.eeeeeeeeeeeeee.....eeeeeeeeeeeeee.......... ptsiarrfltlkttrlapriirlsnlmlvvtlfsrrsvqagrsshsalrpcqssrmllpr 240 ............................................................ llthqqsscrltmlfrrssgsrplacvskesmalhlpssavllmldrqwvsrtttqaffk 300 ....................eeeeeeeeeeeeee.........................e tptttrpsaksptshsaqqhhafvqnstpracaseqevsrrictttptsptyprlmrthl 360 eeeeeeeeeeeee............eeeeeeeeeeeeee.eeeeeeeeeeeeee...... pascvlgprwdsgittldsdwlsprldgqslsllractlcprslmassvrrllgtriwtd 420 .....eeeeeeeeeeeeee.................eeeeeeeeeeeeee.......... rrirsgp 427 ....... b 1 11 21 31 41 51 60 | | | | | | | kwlsrysstpsasyqasfrstpksvsstpsliplnipllsvpsskvlsaspkpshgsqar 60 .eeeeeeeeeeeeee.eeeeeeeeeeeeee.................eeeeeeeeeeeee skprslaretqelpssllrtflvlktsamilqrprsraerrdtlwrcltrtssrqgrryl 120 e.eeeeeeeeeeeeee...............eeeeeeeeeeeeee............... ldlvlvpttqslfycsstssradssslstditvlwiwakmrsvysprravtthspkrrpt 180 .eeeeeeeeeeeeee.eeeeeeeeeeeeee.....eeeeeeeeeeeeee........... siarrfltlkttrlapriirlsnlmlvvtlfsrrsvqagrsshsaarpcqssrmllprll 240 ............................................................ thqqsscrltmlfrrssgnrplacvskesmalhlpssavllmldrqwvsrtttqaffksp 300 ..................eeeeeeeeeeeeee.........................eee tttrpsakspkshsaqqhhafvqnstpracaseqevsrrictttptsptyprlmrthlpa 360 eeeeeeeeeee............eeeeeeeeeeeeee.eeeeeeeeeeeeee........ scvlgprwdsgiktlgsdwvsprldgqslsllractlcprslmassvrrflgtriwtdrr 420 ...eeeeeeeeeeeeee.................eeeeeeeeeeeeee............ irsgp 425 ..... c 1 11 21 31 41 51 60 | | | | | | | kwlsrysstpsasyqasfrstpksvsstpsliplnipllsvpsskvlsaspkpshgsqar 60 .eeeeeeeeeeeeee.eeeeeeeeeeeeee.................eeeeeeeeeeeee srpralaketqelplssllrtflvlktsamilqrprsraerrdtlwrcltrtssrqgrry 120 e.eeeeeeeeeeeeee................eeeeeeeeeeeeee.............. lldlllvpttqclfycsstssradssslstditvlwiwakmrpvysprravtthspkrkr 180 ..eeeeeeeeeeeeee.eeeeeeeeeeeeee.....eeeeeeeeeeeeee.......... ptsiarrfltlkttrlapriirlsnlmlvvtlfsrrsvqagrsshsaprpcqssrmllpr 240 ............................................................ llthqqsscrltmlfrrssgirplacvskesmalhlpssavllmldrqwvsrtttqaffk 300 ................eeeeeeeeeeeeee.............................e tptttrpsaksptshsaqqhhafvqnstpracaseqevsrrictttrtsptyprlmrthl 360 eeeeeeeeeeeee............eeeeeeeeeeeeee..eeeeeeeeeeeeee..... pascvlgprwhsgittlgsdwvsprldgqslsllractlcprslmassvrrflgtriwtd 420 .....eeeeeeeeeeeeee.................eeeeeeeeeeeeee...rrirsgp 427 figure 2. amino acid residues of trichothecene 3-o acetyltransferase (tri101) protein in a: fusarium spp._1 (yellow corn), b: fusarium spp._2 (red corn) and c: fusarium spp._3 (white rice) showing predicted epitopes (red) that are highlighted. molecular characterization of fumonisin mycotoxin genes 83 table 1. flexible length predictions of epitopes in the amino acids sequence of trichothecene 3-o acetyltransferase (tri101) protein of the three studied fusarium isolates no. epitope/fusarium sp._1 (yellow corn) score/ epitope/ fusarium sp._2 (red corn) score/ epitope/ fusarium sp._3(white rice) score/ 1 rictttptsptypr 1 rictttptsptypr 1 ictttrtsptyprl 1 2 ktptttrpsakspt 1 ksptttrpsakspk 1 ktptttrpsakspt 1 3 nstpracaseqevs 1 nstpracaseqevs 1 nstpracaseqevs 1 4 sstpsasyqasfrs 0.998 sfrstpksvsstps 1 sfrstpksvsstps 1 5 saspnpshgsqars 0.996 saspkpshgsqars 0.998 saspkpshgsqars 0.998 6 stssradssslstd 0.993 stssradssslstd 0.993 lgprwhsgittlgs 0.997 7 srplacvskesmal 0.974 qrprsraerrdtlw 0.984 stssradssslstd 0.993 8 lgprwdsgittlds 0.967 wlsrysstpsasyq 0.974 qrprsraerrdtlw 0.984 9 qrprsraerrhtlw 0.94 nrplacvskesmal 0.949 wlsrysstpsasyq 0.974 10 ctlcprslmassvr 0.892 lgprwdsgiktlgs 0.896 rssgirplacvske 0.967 11 iwakmrsvysprra 0.871 ctlcprslmassvr 0.892 pralaketqelpls 0.953 12 dlvlvpttqslfyc 0.794 iwakmrsvysprra 0.871 ctlcprslmassvr 0.892 13 dlvlvpttqslfyc 0.794 iwakmrpvysprra 0.883 14 prslaretqelpss 0.704 dlllvpttqclfyc 0.708 the epitope prediction analysis demonstrated that there were 1, 2, 3 and 4 epitopes with a score equal to 1 in f. moniliforme _1, f. moniliforme _2 and f. moniliforme_3, respectively. also there were great variations in the epitope sequences among the three isolates except for nstpracaseqevs, stssradssslstd and ctlcprslmassvr, which where common among all isolates. these residues with high frequencies of occurrence in antigenic determinants are highlighted (yellow) in the antigenicity profile (figure 3). figure 3 also shows the variability in the positions and types of amino acid residues with high antigenic frequency. 4. discussion fungal infections not only cause considerable economic loss, there is no doubt that contamination of grains and foodstuffs with mycotoxins has become a danger that can’t be ignored [40, 43]. many species are well known mycotoxin producers with various toxicological properties which pose high risk to human and animal health [44, 45]. environmental factors and host species have a strong impact on the occurrence of a specific chemotype and the incidence of fusarium species [46]. the distribution of fusarium species in maize is influenced by climatic conditions, pathogenicity and competition between other fungi [47]. the type of environmental factor identified in the incidence of fusarium species was demonstrated in recent eu maize surveys [48]. in these studies, the prevalence of species varied year-to-year and is believed to be associated with the differences in climatic conditions between years [49, 50]. as was reported by [51], the presence of toxigenic fungi on small grains has a negative impact on the safety and quality of animal feed and human food [51]. the genus fusarium includes cosmopolitan and ubiquitous mold fungi in which saprobes and plant pathogens are many. fusarium species causes yield losses in processing and production [51, 52]. being able to grow at low temperature, fusarium spp. are responsible for spoilage of food through contamination during transport and storage [9, 17, 52]. in addition, reduction in nutritive value, insipidness and discoloration are other problems resulting from contamination of grains by fusarium [53]. the advance of rapid and accurate identification of fusarium and/or their metabolites are mandatory for the implementation of preventive measures in the whole food production system, as was reported by [54]. the molecular characterization of three fusarium spp. isolated from small grains (yellow corn, white rice and red corn) using the mycotoxin gene, trichothecene 3-o acetyltransferase (tri101), allowed for coupled identification and mycotoxin screening in the three fusarium isolates [54, 55]. following the molecular identification of fusarium spp., b-cell epitopes in the trichothecene 3-o acetyltransferase (tri101) gene were predicted. the characterization of b-cell epitopes using computational tools is highly advantageous for the synthesis of specific antibodies for rapid detection of microbial pathogens in their environments [56]. epitope prediction saves labor and time for validation experiments. the identification of epitopes plays a crucial role in vaccine design, immunodiagnostic testing and antibody production [56]. in other study bcpreds serves were used to predict epitopes found in the primary amino acids sequence of trichothecene 3-o acetyltransferase (tri101) protein, where bcpreds has proved highly efficient for predicting linear b-cell epitopes in sars-cov s protein [56, 57]. there was variability in the sequence and numbers of epitopes among the three toxin proteins analyzed [57]. in the present study, a fixed length of epitopes (14 residues) was observed. the epitope prediction analysis demonstrated that there were 1, 2, 3 and 4 epitopes with scores equal to 1 in f. moniliforme_1, f. moniliforme_2 and f. moniliforme_3, respectively. interestingly, there were great dissimilarities in the epitope sequences among the three isolates except for nstpracaseqevs, stssradssslstd and ctlcprslmassvr, which were common al-husnan, l.a. et al 84 among all isolates. this result suggests its exploitation for the design of a specific antibody to be used for rapid detection of different fusarium species in small grains. epitope prediction has many implications in pathogen detection and differentiation applications. consideration of the occurrence of fusarium spp. on small grains is important in the risk assessment of mycotoxins and in proactively setting up preventive measures [57]. a b c figure 3. kolaskar and tongaonkar antigenicity scale for prediction of antigenic determinants in trichothecene 3-o acetyltransferase (tri101) in a: fusarium spp._1 (yellow corn), b: fusarium spp._2 (red corn) and c: fusarium spp._3 (white rice) amino acid residues of high frequencies in epitopes are distinguished (yellow). molecular characterization of fumonisin mycotoxin genes 85 conclusion the identification of immunodiagnostic testing and antibody production of a 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markers for two fusarium graminearum clade species. molecular ecology notes, 2004, 4, 468-470. received 9 october 2018 accepted 7 february 2019 squ journal for science, 2019, 24(1), 57-70 doi: 10.24200/squjs.vol24iss1pp57-70 sultan qaboos university 57 two groups 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) and 𝟐 𝟑: 𝑷𝑺𝑳𝟐(𝟕) of order 1344 mehmet koca 1 , ramazan koc 2 and nazife o. koca 3 * 1 retired professor; 2 department of physics, faculty of engineering, gaziantep university, 27310 gaziantep, turkey; 3 department of physics, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *e-mail: nazife@squ.edu.om. abstract: we analyze the group structures of two groups of order 1344 which are respectively non-split and split extensions of the elementary abelian group of order 8 by its automorphism group 𝑃𝑆𝐿2 (7). two groups have the same number of conjugacy classes and the set of dimensions of irreducible representations is equal. the group 23.𝑃𝑆𝐿2(7) is a finite subgroup of the lie group 𝐺2 preserving the set of octonions ±𝑒𝑖 , (𝑖 = 1,2, … ,7) representing a 7dimensional octahedron. its three maximal subgroups 23: 7: 3, 23. 𝑆4 and 4. 𝑆4: 2 correspond to the finite subgroups of the lie groups 𝐺2, 𝑆𝑂(4) and 𝑆𝑈(3) respectively. the group 2 3: 𝑃𝑆𝐿2(7) representing the split extension possesses five maximal subgroups 23: 7: 3, 23: 𝑆4, 4: 𝑆4: 2 and two non-conjugate klein’s group 𝑃𝑆𝐿2(7). the character tables of the groups and their maximal subgroups, tensor products and decompositions of their irreducible representations under the relevant maximal subgroups are identified. possible implications in physics are discussed. keywords: finite groups; discrete octonions; group extensions; character table; tensor products. 𝟐و 𝑷𝑺𝑳𝟐(𝟕).𝟐𝟑مجموعتين 𝟑: 𝑷𝑺𝑳𝟐(𝟕) 4411عدد عناصرها محمد كوجا 4 ، رمضان كوك 2 نزيفة أوزيدس كوجا و 4 وهن على الترتيب االمتداد المقسوم وغير المقسوم لمجموعة األبيليان االبتدائية ذات 4411قمنا بتحليل الشكل لمجموعتين عدد عناصرهن :صلخمال . .المجموعتين يمتلكن نفس العدد من كوجنسي كالسس وأيضا أبعادهن متساوية في تمثيل الريديوسبل𝑃𝑆𝐿2(7)العناصر الثمانية في جروب األوتومورفيسم 𝑃𝑆𝐿2(7) 2.المجموعة 𝑒𝑖±وتحافظ على مجموعة الكوتنيونس 𝐺2هي مجموعة جزئية منتهية من ليا جروب 3 , (𝑖 = 1,2, … وتمثل أوكتاهدرون (7, :23 في سبعة أبعاد. لها ثالثة مجموعة جزئية 7: .23 و 3 𝑆4 4و. 𝑆4: و 𝐺2وهذه المجموعات الجزئية تمثل مجموعات جزئية منتهية من ليا جروب 2 𝑆𝑂(4) و𝑆𝑈(3) 23بالترتيب. المجموعة: 𝑃𝑆𝐿2 2 تمثل االمتداد المقسوم تمتلك خمس مجموعات جزئية وهي (7) 3: 7: :23 و 3 𝑆4 4و: 𝑆4: 2 ول الخصائص لهذه المجموعات ومجموعاتهن الجزئية ومنتجات التنسر وتقسيماتهن . جدا𝑃𝑆𝐿2(7)واثنتين من المجموعات الغير المرافقة للكلين جروب إلى تمثيالتهن الريديوسبل تحت مجموعاتهن الجزئية كلها تم تحديدها. كما تمت مناقشة بعض التطبيقات في الفيزياء. .الخصائص، منتجات التنسر المجموعات المنتهية، كواتنينس المنفصلة، إمتداد المجوعة، جدول: مفتاحيةالكلمات ال 1. introduction e have introduced some part of this work in an earlier publication [1]. since then we have observed that the simple group like 𝑃𝑆𝐿2(7) [2] and the subgroups thereof 7: 3 [3], 𝑆4 and 𝐴4 [4, 5, 6, 7, 8, 9] have been proposed to explain the properties of the tri-bimaximal neutrino mixing [10]. when the charged leptons and quark masses are incorporated into the scheme we may think of much larger discrete symmetries broken down to the aforementioned finite subgroups of 𝑆𝑈(3). along with these lines we would like to introduce two groups of order 1344 which are non-split and split extensions of the elementary abelian group 23 of order 8 by its automorphism group 𝑃𝑆𝐿2(7). before we proceed further a glossary may be introduced for the group theoretical concepts and notations used throughout the paper. we follow the notations of the atlas of finite groups [11]. a cyclic group of order p is denoted by p. an elementary abelian group of order 𝑝𝑛 (denoted also by 𝑝𝑛 ) is the direct product of n cyclic groups of each having order p. thus, the elementary abelian group 23 is the direct product of three cyclic groups of order 2. w mehmet koca et al 58 the group a.b denotes any group possessing a normal subgroup a, for which the corresponding quotient group is b. this is used for the non-split extension. the group a:b indicates the split extension, or the semi-direct product 𝐴 ⋊ 𝐵. here a copy of the quotient group b is a subgroup of the group a:b. this shows that the intersection of a and b is just the unit element. the quotient group of interest here is the special projective group 𝑃𝑆𝐿2(7) and this has been discussed in the physics literature extensively [2,12,13]. the paper is organized as follows. for the group 23.𝑃𝑆𝐿2(7) which is the automorphism group of the octonionic set ±𝑒𝑖, (𝑖 = 1,2, … ,7) we review in section 2 the basic structure of the octonion algebra and introduce the group 7: 3 as the automorphism of the 7 imaginary units 𝑒𝑖, (𝑖 = 1,2, … ,7). in section 3 we extend the automorphism to the full group of automorphism including the change of sign of the imaginary units of octonions and point out that the diagonal matrices form the elementary abelian subgroup of the automorphism group. the quotient group 𝑃𝑆𝐿2(7) is explicitly constructed and the maximal subgroups of the group 23.𝑃𝑆𝐿2 (7) are identified. in section 4 we discuss the construction of the group by using a finite subgroup of 𝑆𝑂(4) based on the preservation of the quaternion subalgebra of the octonion algebra. section 5 deals with the construction of the 7-dimensional irreducible representation of the group 23: 𝑃𝑆𝐿2(7) and its five maximal subgroups, two of which, are the non-conjugate klein’s group 𝑃𝑆𝐿2(7). in the concluding section 6, we point out as to how these groups can be used in physics. in appendix a we study the tensor products of the irreducible representations. appendix b lists the decompositions of the irreducible representations under the maximal subgroups. 2. octonions and the group 𝟕: 𝟑 the octonions (cayley numbers) are sets of real numbers 𝑞 = (𝑞0, 𝑞1, 𝑞2, 𝑞3, 𝑞4, 𝑞5, 𝑞6, 𝑞7) = 𝑞0. 1 + 𝑞1𝑒1 + 𝑞2𝑒2 + 𝑞3𝑒3 + 𝑞4𝑒4 + 𝑞5𝑒5 + 𝑞6𝑒6 + 𝑞7𝑒7 (1) where 𝑒𝑖 , (𝑖 = 1,2, … . ,7) are 7 imaginary octonionic units. octonions are added like vectors and multiplied as follows 1. 𝑒𝑖 = 𝑒𝑖 . 1 = 𝑒𝑖 , 𝑒𝑖 𝑒𝑗 = −𝛿𝑖𝑗 + ∑ 𝜙𝑖𝑗𝑘 7 𝑘=1 𝑒𝑘 (𝑖, 𝑗, 𝑘 = 1,2, … ,7) (2) where 𝜙𝑖𝑗𝑘 are completely antisymmetric in 𝑖, 𝑗, 𝑘 with the values ±1. we choose the basis as shown in figure 1 such that [14] 𝜙123 = 𝜙246 = 𝜙435 = 𝜙367 = 𝜙651 = 𝜙572 = 𝜙714 = 1, (3) which follows from the cyclic rotation of the triangle in figure 1. figure 1. octonionic multiplication based on quaternionic multiplication. the 7-imaginary units form 35 triads, 7 of which are associative and follow the ordering such that 𝑒𝑖 𝑒𝑗 𝑒𝑘 = −1 when 𝑖, 𝑗, 𝑘 take one of the values in (3). the 28 anti-associative triads can be obtained from the following four anti-associative triads 𝑒1(𝑒2𝑒4) = 𝑒5 = −(𝑒1𝑒2)𝑒4 −𝑒1(𝑒2𝑒6) = 𝑒7 = (𝑒1𝑒2)𝑒6 −𝑒1(𝑒2𝑒5) = 𝑒4 = (𝑒1𝑒2)𝑒5 𝑒1(𝑒2𝑒7) = 𝑒6 = −(𝑒1𝑒2)𝑒7 (4) 𝑒5 𝑒1 𝑒2 𝑒4 𝑒3 𝑒6 𝑒7 two groups 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) and 𝟐 𝟑: 𝑷𝑺𝑳𝟐(𝟕) of order 1344 59 by using the cyclic permutation (1243657). the seven associative triads correspond to the lines of the finite projective geometry of seven lines and seven points of the fano plane. without changing the signs of the octonionic imaginary units in figure 1, we can obtain two operations preserving the octonion algebra. let 𝛼 transform the octonionic units 𝑒𝑖 in the cyclic order (𝑒1𝑒2𝑒4𝑒3𝑒6𝑒5𝑒7) so that 𝛼 7 = 1. let 𝛽 fix 𝑒1 and permute the associative triad (𝑒2𝑒4𝑒6) and the anti-associative triad (𝑒3𝑒7𝑒5) in the indicated orders. it is clear that 𝛽3 = 1 and preserves the octonion algebra. indeed, the transformation (𝑒3𝑒7𝑒5) is sufficient to determine the rest of the transformations of the quaternionic imaginary units. it is easy to prove that two generators generate a finite group of order 21 satisfying the generation relations: 𝛼 7 = 𝛽3 = 𝛽−1 𝛼𝛽𝛼 3 = 1. (5) it is clear from (5) that 𝛼 generates a normal subgroup of order 7 and hence the structure of the group 7: 3. the conjugacy classes are given by the set of group elements 𝐶1 = (1), 𝐶2 = ( 𝛼, 𝛼 2, 𝛼 4), 𝐶3 = ( 𝛼 3, 𝛼 5, 𝛼 6), 𝐶4 = (𝛼 𝑎 𝛽), 𝐶5 = (𝛼 𝑎𝛽2), (𝑎 = 0, 1, … , 6). (6) the character table of the group is depicted in table 1. 𝐶𝑖 [𝑗] denotes the i th conjugacy class and [j] represents the order of the elements in the conjugacy class. 𝜒[𝑎] is the character of the irreducible representation 𝑎. table 1. the characteristics table of the frobenius group 7: 3. 7: 3 𝐶1 7𝐶2 [3] 7𝐶3 [3] 3𝐶4 [7] 3𝐶5 [7] 𝜒[1] 1 1 1 1 1 𝜒[11] 1 𝜇 𝜇 1 1 𝜒[12] 1 𝜇 𝜇 1 1 𝜒[31] 3 0 0 𝜂 𝜂 𝜒[32] 3 0 0 𝜂 𝜂 here, 𝜒[12] = 𝜒[ 11 ], 𝜒[32] = 𝜒[ 31], 𝜇 = 1 2 (−1 + 𝑖√3), 𝜂 = 1 2 (−1 + 𝑖√7). one can easily check that the 7-dimensional representation obtained by the generators 𝛼 and 𝛽 is reducible and can be decomposed as 7 = 1 + 31 + 31. 3. the group 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) as the automorphism group of the octonionic set ±𝒆𝒊 now we allow the octonionic units 𝑒𝑖 to also take negative values, or, in other words, we also include the octonionic conjugates in the transformations. any linear transformation on a non-associative triad determines the transformations of 7 imaginary units. let us take the non-associative triad (𝑒1𝑒2𝑒7) and impose the transformation 𝑒1 → 𝑒1, 𝑒2 → 𝑒2, 𝑒7 → −𝑒7. this transformation leads to the transformations 𝑒3 → 𝑒3, 𝑒4 → −𝑒4, 𝑒5 → −𝑒5 and 𝑒6 → −𝑒6. let us call it 𝑁1 = (𝑒1 → 𝑒1, 𝑒2 → 𝑒2, 𝑒3 → 𝑒3, 𝑒4 → −𝑒4, 𝑒5 → −𝑒5, 𝑒6 → −𝑒6, 𝑒7 → −𝑒7) and denote it as a diagonal matrix with non-zero entities 𝑁1 = (1, 1, 1, −1, −1, −1, −1). (7) this diagonal transformation leaves the associative triad (123) intact and changes the signs of the other 4 octonionic units. when we take 𝛼, 𝛽 and 𝑁1 as generators we obtain a group of order 168, but not isomorphic to 𝑃𝑆𝐿2(7). it has, by construction, a normal subgroup of order 8 generated by three diagonal transformations 𝑁1, 𝑁2 and 𝑁7 where 𝑁2 = (1, −1, −1, 1, −1, −1, 1) and 𝑁7 = (−1, 1, −1, 1, −1,1, −1). they generate the elementary abelian group 2 3 where the other elements are defined as 𝑁3 = 𝑁1𝑁2 = 𝑁2𝑁1, 𝑁4 = 𝑁7𝑁1 = 𝑁1𝑁7, 𝑁5 = 𝑁7𝑁2 = 𝑁2𝑁7, 𝑁6 = 𝑁7𝑁3 = 𝑁3𝑁7. (8) mehmet koca et al 60 more compactly, they can be written as 𝑁𝑖 𝑁𝑗 = 𝑁𝑗 𝑁𝑖 = 𝑁𝑘 , (𝑖𝑗𝑘 = 123, 147, 165, 246, 257, 345, 367). (9) the 7-diagonal matrices can be used to define the fano plane. one can show that the set of group elements 𝑁𝑖 , (𝑖 = 1,2, … ,7) is invariant under the conjugations of the generators so that the group can be designated as 23: 7: 3 the order of which is 168 but since it has a normal subgroup it is not isomorphic to the simple group 𝑃𝑆𝐿2 (7). the 7dimensional representation of the group 23: 7: 3 obtained from the generators 𝛼, 𝛽 and 𝑁1is irreducible and denoted by 71 in the character table of the group 2 3: 7: 3 given in table 2. table 2. the characteristics table of the group 23: 7: 3. 23: 7: 3 𝐶1 7𝐶2 [2] 28𝐶3 [3] 28𝐶4 [3] 28𝐶5 [6] 28𝐶6 [6] 24𝐶7 [7] 24𝐶8 [7] 𝜒[1] 1 1 1 1 1 1 1 1 𝜒[11] 1 1 𝜇 𝜇 𝜇 𝜇 1 1 𝜒[12] 1 1 𝜇 𝜇 𝜇 𝜇 1 1 𝜒[31] 3 3 0 0 0 0 𝜂 𝜂 𝜒[32] 3 3 0 0 0 0 𝜂 𝜂 𝜒[71] 7 -1 1 1 -1 -1 0 0 𝜒[72] 7 -1 𝜇 𝜇 −𝜇 −𝜇 0 0 𝜒[73] 7 -1 𝜇 𝜇 −𝜇 −𝜇 0 0 note that in table 2 the characters satisfy the relations𝜒[12] = 𝜒[ 11 ], 𝜒[32] = 𝜒[ 31 ], 𝜒[73] = 𝜒[ 71 ] and the other irreducible representations are real. the group 23: 7: 3 is not the full automorphism group of the set of octonions ±𝑒𝑖 . in fact, a transformation of the form 𝛾: ( 𝑒1 ↔ −𝑒4, 𝑒2 ↔ −𝑒5, 𝑒3 → −𝑒3, 𝑒6 → 𝑒6, 𝑒7 → −𝑒7) preserves the octonion algebra and does not belong to the group of elements of the group 2 3: 7: 3. adjoining 𝛾 as a new generator then 𝛼, 𝛽, 𝛾 and 𝑁1 together generate the group of order 1344. we will prove that it has the structure 23.𝑃𝑆𝐿2(7) which can also be generated by two generators 𝛼 and 𝛾 only. here the group 𝑃𝑆𝐿2(7) is the quotient group whose generators are defined by the conjugations over the elements of the elementary abelian group 23: 𝛼 ̃: 𝑁𝑖 → 𝛼 −1𝑁𝑖 𝛼, 𝛽 ̃: 𝑁𝑖 → 𝛽 −1𝑁𝑖 𝛽, 𝛾 ̃: 𝑁𝑖 → 𝛾 −1𝑁𝑖 𝛾. (10) they permute the diagonal matrices as 𝛼 ̃ = (𝑁1𝑁2𝑁4𝑁3𝑁6𝑁5𝑁7), 𝛽 ̃ = (𝑁3𝑁2𝑁1)(𝑁4𝑁6𝑁5)(𝑁7) 𝛾 ̃ = (𝑁1𝑁5)(𝑁2)(𝑁3𝑁7)(𝑁4)(𝑁6). (11) the group generated by the generators in (11) is isomorphic to the klein’s group 𝑃𝑆𝐿2 (7) of order 168 and the 7dimensional representation obtained from (11) is reducible 7 = 1 + 6. this is expected because 7 diagonal matrices 𝑁𝑖 form the fano plane whose automorphism group is the klein’s group. the character table of the group 𝑃𝑆𝐿2(7) is shown in table 3. (note the difference between table 2 and table 3). table 3. the characteristics table of the group 𝑃𝑆𝐿2(7). 𝑃𝑆𝐿2(7) 𝐶1 21𝐶2 [2] 56𝐶3 [3] 42𝐶4 [4] 42𝐶5 [7] 42𝐶6 [7] 𝜒[1] 1 1 1 1 1 1 𝜒[31] 3 -1 0 1 𝜂 𝜂 𝜒[32] 3 -1 0 1 𝜂 𝜂 𝜒[6] 6 2 0 0 -1 -1 𝜒[7] 7 -1 1 -1 0 0 𝜒[8] 8 0 -1 0 1 1 here again the characters satisfy 𝜒[32] = 𝜒[31]. a copy of the 𝑃𝑆𝐿2(7) does not exist in the group 2 3.𝑃𝑆𝐿2 (7), therefore it is not a subgroup and hence the latter group is the non-split extension of the group 23 by the group 𝑃𝑆𝐿2(7). the character table of the groups 2 3.𝑃𝑆𝐿2(7) and 2 3: 𝑃𝑆𝐿2(7) is given in table 4. two groups 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) and 𝟐 𝟑: 𝑷𝑺𝑳𝟐(𝟕) of order 1344 61 table 4. the characteristics table of the groups 23.𝑃𝑆𝐿2(7) and 2 3: 𝑃𝑆𝐿2(7). 23. 𝑃𝑆𝐿2(7) 𝐶1 𝐶2 [2] 𝐶3 [2] 𝐶4 [3] 𝐶5 [4] 𝐶6 [4] 𝐶7 [6] 𝐶8 [7] 𝐶9 [7] 𝐶10 [8] 𝐶11 [8] 23: 𝑃𝑆𝐿2(7) 𝐶1 𝐶2 [2] 𝐶3 [4] 𝐶4 [3] 𝐶5 [2] 𝐶6 [2] 𝐶7 [6] 𝐶8 [7] 𝐶9 [7] 𝐶10 [4] 𝐶11 [4] elements 1 7 84 224 42 42 224 192 192 168 168 𝜒[1] 1 1 1 1 1 1 1 1 1 1 1 𝜒[31] 3 3 -1 0 -1 -1 0 𝜂 𝜂 1 1 𝜒[32] 3 3 -1 0 -1 -1 0 𝜂 𝜂 1 1 𝜒[6] 6 6 2 0 2 2 0 -1 -1 0 0 𝜒[71] 7 -1 -1 1 -1 3 -1 0 0 1 -1 𝜒[72] 7 7 -1 1 -1 -1 1 0 0 -1 -1 𝜒[73] 7 -1 -1 1 3 -1 -1 0 0 -1 1 𝜒[8] 8 8 0 -1 0 0 -1 1 1 0 0 𝜒[14] 14 -2 -2 -1 2 2 1 0 0 0 0 𝜒[211] 21 -3 1 0 -3 1 0 0 0 -1 1 𝜒[212] 21 -3 1 0 1 -3 0 0 0 1 -1 the character table shows that all the representations are real except the 3-dimensional representations which satisfy 𝜒[32] = 𝜒 [31 ]. the group 23.𝑃𝑆𝐿2(7) has three maximal subgroups having the structures 2 3: 7: 3, 4. 𝑆4: 2 and 2 3. 𝑆4 of respective orders 168, 192 and 192. the group 2 3: 7: 3 preserves the octonion multiplication and the 7-dimensional representation denoted by 71 is irreducible. it is a subgroup of the lie group 𝐺2 and the groups 4. 𝑆4: 2 and 2 3. 𝑆4 are finite subgroups of the groups 𝑆𝑈(3) and 𝑆𝑂(4) respectively, as we will study in the next section. the lie groups 𝑆𝑈(3) and 𝑆𝑂(4) are the maximal subgroups of the lie group 𝐺2. 3.1 maximal subgroups 𝟒. 𝑺𝟒: 𝟐 𝐚𝐧𝐝 𝟐 𝟑. 𝑺𝟒 of the group 𝟐 𝟑.𝑷𝑺𝑳𝟐(𝟕) the group 23.𝑃𝑆𝐿2 (7) has two maximal subgroups of order 192. now we discuss some properties of the first subgroup 4. 𝑆4: 2. let 𝑒𝑖 = −𝑒𝑖 denote the octonionic conjugate. define the transformation 𝜃 = (𝑒1𝑒5)(𝑒2𝑒3𝑒4𝑒7𝑒2𝑒3𝑒4𝑒7)(𝑒6𝑒6), with 𝜃 8=1. (12) the generators 𝛾 and 𝜃 generate the group 4. 𝑆4: 2 which represents a finite subgroup of 𝑆𝑈(3) as the generators fix the octonion ±𝑒6. the character table of the group 4. 𝑆4: 2 is shown in table 5. table 5. the characteristics table of the groups 4. 𝑆4: 2 and 4: 𝑆4: 2 4. 𝑆4: 2 𝐶1 𝐶2 [2] 𝐶3 [2] 𝐶4 [2] 𝐶5 [2] 𝐶6 [2] 𝐶7 [3] 𝐶8 [4] 𝐶9 [4] 𝐶10 [4] 𝐶11 [4] 𝐶12 [6] 𝐶13 [8] 𝐶14 [8] 4: 𝑆4: 2 𝐶1 𝐶2 [2] 𝐶3 [2] 𝐶4 [4] 𝐶5 [4] 𝐶6 [4] 𝐶7 [3] 𝐶8 [2] 𝐶9 [2] 𝐶10 [2] 𝐶11 [2] 𝐶12 [6] 𝐶13 [4] 𝐶14 [4] elements 1 3 4 12 12 12 32 12 6 6 12 32 24 24 𝜒[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 𝜒[11] 1 1 -1 1 -1 -1 1 1 1 1 -1 -1 1 -1 𝜒[12] 1 1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 1 𝜒[13] 1 1 1 -1 -1 1 1 -1 1 1 -1 1 -1 -1 𝜒[21] 2 2 -2 0 0 -2 -1 0 2 2 0 1 0 0 𝜒[22] 2 2 2 0 0 2 -1 0 2 2 0 -1 0 0 𝜒[31] 3 3 3 -1 -1 -1 0 -1 -1 -1 -1 0 1 1 𝜒[32] 3 3 3 1 1 -1 0 1 -1 -1 1 0 -1 -1 𝜒[33] 3 3 -3 1 -1 1 0 1 -1 -1 -1 0 -1 1 𝜒[34] 3 3 -3 -1 1 1 0 -1 -1 -1 1 0 1 -1 𝜒[61] 6 -2 0 0 -2 0 0 0 -2 2 2 0 0 0 𝜒[62] 6 -2 0 0 2 0 0 0 -2 2 -2 0 0 0 𝜒[63] 6 -2 0 -2 0 0 0 2 2 -2 0 0 0 0 𝜒[64] 6 -2 0 2 0 0 0 -2 2 -2 0 0 0 0 mehmet koca et al 62 this is also one of the maximal subgroups of the chevalley’s group 𝐺2(2) [15] preserving the octonionic root system of 𝐸7. the 7-dimensional representation can be written as 7 = 1 + 6, or more properly, 71 = 11 + 63. by adjoining the generator 𝛼 which permutes the 7 imaginary octonionic units one can generate the group 23.𝑃𝑆𝐿2(7). it is easy to prove that 𝛾 ̃and �̃� = (𝑁1𝑁4𝑁2𝑁5)(𝑁3)(𝑁6𝑁7) with 𝛾 ̃ 2 = �̃�4 = 1 generate the subgroup 𝑆4 as the quotient group. let 𝑎 and 𝑏 be the generators of a group, then the standard generation relation of 𝑆4 is 𝑎 4 = 𝑏3 = (𝑎𝑏)2 = 1 [16]. this relation can be satisfied if we define 𝑎 = 𝛾 ̃�̃�𝛾 ̃ and 𝑏 = 𝛾 ̃ �̃�−1. the group 23. 𝑆4 can be generated by the generators 𝐴 = (𝑒1𝑒7 𝑒3𝑒1𝑒7𝑒3)(𝑒2𝑒4𝑒6𝑒2𝑒4𝑒6)( 𝑒5𝑒5), 𝐵 = (𝑒1) (𝑒2𝑒6𝑒2𝑒6)( 𝑒3𝑒5𝑒3𝑒5)(𝑒4)(𝑒7), (13) 𝐴6 = 𝐵4 = 1. the elements 𝐴 ̃and 𝐵 ̃can be obtained as follows 𝐴 ̃ = (𝑁1𝑁6𝑁2)(𝑁3𝑁5𝑁4)(𝑁7), 𝐵 ̃ = (𝑁1𝑁3)(𝑁2)(𝑁4𝑁6)(𝑁5)(𝑁7). (14) now define 𝑎 = 𝐵 ̃𝐴 ̃ = (𝑁1𝑁4)(𝑁2𝑁3𝑁5𝑁6)(𝑁7) and 𝑏 = �̃� −1. it is straightforward to show that they satisfy the 𝑆4 generation relation 𝑎 4 = 𝑏3 = (𝑎𝑏)2 = 1. hence, the quotient group is 𝑆4 as claimed. the matrix representations of 𝐴 ̃and 𝐵 ̃do not preserve the octonion algebra, and therefore a copy of 𝑆4 does not exist in the group 2 3. 𝑆4. hence it is the non-split extension of the group 23 by 𝑆4. it is clear from the generators 𝐴 and 𝐵 that they preserve the sets of octonionic units (±𝑒2 ± 𝑒4 ± 𝑒6) and (±𝑒1 ± 𝑒3 ± 𝑒5 ± 𝑒7) separately, so that the 7 × 7 matrix representation can be written in the block diagonal form of 3 × 3 and 4 × 4 matrices. this proves that the 7-dimensional representation of the group 23.𝑃𝑆𝐿2(7) can be decomposed as 71 = 31 + 41 under the group 2 3. 𝑆4. a rigorous proof can also be given by noting that the group 23. 𝑆4 is a finite subgroup of 𝑆𝑂(4) which preserves the quaternion substructure of the octonion algebra. let h represent a quaternion. then an octonion can be written as ℎ + 𝑒7ℎ where the quaternionic imaginary units are taken as 𝑒1, 𝑒2 and 𝑒3. it can be proved that the quaternion preserving transformation on the octonion ℎ + 𝑒7ℎ [17] can be written as ℎ + 𝑒7ℎ → 𝑝ℎ𝑝 + 𝑝ℎ𝑞 (15) where p and q are unit quaternions. the first term 𝑝ℎ𝑝 preserves the scalar part of the octonion. therefore, without loss of generality, we can also write it as 𝑝 𝐼𝑚(ℎ)𝑝. since we are interested in the transformations of the set ±𝑒𝑖 , (𝑖 = 1,2, … ,7) we can write it as 𝐼𝑚 (𝑉0) + 𝑒7𝑉0 → 𝑝𝐼𝑚( 𝑉0)𝑝 + 𝑒7𝑝𝑉0𝑞 (16) where the set 𝑉0 = {±1, ±𝑒1, ±𝑒2, ±𝑒3} represents the elements of the quaternion group of order 8. so, the question now turns out to be for which unit quaternions p and q the set of quaternions 𝑉0 is preserved. the answer lies in the finite quaternion subgroups involving 𝑉0 as a subgroup. they are the binary tetrahedral group 𝒯, binary octahedral group 𝒪 and the binary icosahedral group ℐ[16]. it turns out that we need to invoke the binary octahedral group whose sets of elements can be written as the union of 6 quaternionic sets [18] 𝒪 = 𝑉0 + 𝑉+ + 𝑉− + 𝑉1 + 𝑉2 + 𝑉3. (17) here the sets of quaternions are defined as 𝑉0 = {±1, ±𝑒1, ±𝑒2, ±𝑒3} 𝑉+ = 1 2 (±1 ± 𝑒1 ±𝑒2 ± 𝑒3), even number of (+sign) 𝑉− = 1 2 (±1 ± 𝑒1 ±𝑒2 ± 𝑒3), odd number of (+sign) 𝑉1 = { 1 √2 (±1 ± 𝑒1 ), 1 √2 ( ±𝑒2 ± 𝑒3)}, (18) 𝑉2 = { 1 √2 (±1 ± 𝑒2 ), 1 √2 ( ±𝑒3 ± 𝑒1)}, 𝑉3 = { 1 √2 (±1 ± 𝑒3 ), 1 √2 ( ±𝑒1 ± 𝑒2)}. they satisfy the multiplication table as shown in table 6. two groups 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) and 𝟐 𝟑: 𝑷𝑺𝑳𝟐(𝟕) of order 1344 63 table 6. multiplication table for the binary octahedral group. 𝑉0 𝑉+ 𝑉− 𝑉1 𝑉2 𝑉3 𝑉0 𝑉0 𝑉+ 𝑉− 𝑉1 𝑉2 𝑉3 𝑉+ 𝑉+ 𝑉− 𝑉0 𝑉3 𝑉1 𝑉2 𝑉− 𝑉− 𝑉0 𝑉+ 𝑉2 𝑉3 𝑉1 𝑉1 𝑉1 𝑉2 𝑉3 𝑉0 𝑉+ 𝑉− 𝑉2 𝑉2 𝑉3 𝑉1 𝑉− 𝑉0 𝑉+ 𝑉3 𝑉3 𝑉1 𝑉2 𝑉+ 𝑉− 𝑉0 to determine the pair of quaternions p and q we use the notation 𝑝ℎ𝑞 ≔ [𝑝, 𝑞]ℎ. later, we simply drop the quaternion h and write the 𝑆𝑂(4) group elements as the pair [𝑝, 𝑞]. since we have 𝑉0 = 𝑝𝑉0𝑞 → 𝑞 = 𝑉0𝑝𝑉0 = 𝑉0𝑝𝑉0 (19) and p can take values from the sets 𝑉0, 𝑉+, 𝑉−, 𝑉1, 𝑉2, 𝑉3, then the corresponding sets of quaternions 𝑞 can be determined from the table 6 as 𝑉0, 𝑉−, 𝑉+, 𝑉1, 𝑉2, 𝑉3. therefore the 𝑆𝑂(4) group elements preserving the set 𝑉0 can be written as the union of pairs of sets [𝑉0, 𝑉0] + [𝑉+, 𝑉−] + [𝑉−, 𝑉+] + [𝑉1, 𝑉1] + [𝑉2, 𝑉2] + [𝑉3, 𝑉3]. (20) this is a group of order 192 with 13 conjugacy classes which can be converted to a 4 dimensional irreducible representation if the basis is chosen as the unit quaternions 1, 𝑒1, 𝑒2, 𝑒3 . when the term [𝑝, 𝑝] is incorporated into the group 23. 𝑆4, it can be converted into a 7 × 7 matrix representation in the block diagonal form of 3 × 3 and 4 × 4 matrices. this proves that the 7-dimensional irreducible representation of the group 23.𝑃𝑆𝐿2 (7) can be decomposed as 71 = 31 + 41 under the irreducible representations of the group 2 3. 𝑆4 . the character table of the group 2 3. 𝑆4 is given in table 7. its elementary abelian subgroup 23 can be generated by the group elements, say [1, −1], [𝑒1, −𝑒1] and [𝑒2, −𝑒2,], and it can be proven that the group 2 3 is a normal subgroup. it is also easy to identify its maximal subgroups. for example, the set [𝑉0, 𝑉0] + [𝑉+, 𝑉−] + [𝑉−, 𝑉+] forms a group of order 96 and [𝑉0, 𝑉0] + [𝑉1, 𝑉1] forms a group of order 64. table 7. the characteristics table of the groups 23. 𝑆4 and 2 3: 𝑆4 23. 𝑆4 𝐶1 𝐶2 [2] 𝐶3 [2] 𝐶4 [2] 𝐶5 [2] 𝐶6 [3] 𝐶7 [4] 𝐶8 [4] 𝐶9 [4] 𝐶10 [4] 𝐶11 [6] 𝐶12 [8] 𝐶13 [8] 23: 𝑆4 𝐶1 𝐶2 [2] 𝐶3 [2] 𝐶4 [4] 𝐶5 [4] 𝐶6 [3] 𝐶7 [2] 𝐶8 [2] 𝐶9 [2] 𝐶10 [2] 𝐶11 [6] 𝐶12 [4] 𝐶13 [4] elements 1 1 6 12 24 32 6 6 12 12 32 24 24 𝜒[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 𝜒[11] 1 1 1 1 -1 1 1 1 -1 -1 1 -1 -1 𝜒[2] 2 2 2 2 0 -1 2 2 0 0 -1 0 0 𝜒[31] 3 3 -1 -1 -1 0 -1 3 1 1 0 -1 1 𝜒[32] 3 3 -1 -1 1 0 -1 3 -1 -1 0 1 -1 𝜒[33] 3 3 3 -1 1 0 -1 -1 1 1 0 -1 -1 𝜒[34] 3 3 -1 -1 -1 0 3 -1 1 1 0 1 -1 𝜒[35] 3 3 -1 -1 1 0 3 -1 -1 -1 0 -1 1 𝜒[36] 3 3 3 -1 -1 0 -1 -1 -1 -1 0 1 1 𝜒[41] 4 -4 0 0 0 1 0 0 -2 2 -1 0 0 𝜒[42] 4 -4 0 0 0 1 0 0 2 -2 -1 0 0 𝜒[6] 6 6 -2 2 0 0 -2 -2 0 0 0 0 0 𝜒[8] 8 -8 0 0 0 -1 0 0 0 0 1 0 0 since the group 23. 𝑆4 leaves the subsets (±𝑒1, ±𝑒2, ±𝑒3) and 𝑒7(±1, ±𝑒1, ±𝑒2, ±𝑒3) invariant it is easy to construct its 7 conjugate groups by permuting the quaternionic subsets (123), (246), (435), ( 367), (652), ( 572), (714) by the mehmet koca et al 64 group generator 𝛼 so that the group is extended by the inclusion of the generator 𝛼 to the full automorphism group 23.𝑃𝑆𝐿2(7) of the octonionic set ±𝑒𝑖 . 4. construction of the 7-dimensional irreducible representation of the group 𝟐𝟑:𝑷𝑺𝑳𝟐(𝟕) although the groups are not isomorphic to each other, the split extension 23:𝑃𝑆𝐿2(7) has the same character table with the non-split extension 23. 𝑃𝑆𝐿2(7). a close inspection shows that the class structures are the same although the powers of the group elements are not always the same. to give an example from the lower rank groups possessing the same character table, we may quote the dihedral group of order 8 and the quaternion group denoted by 𝑉0 in our notation. the group 23:𝑃𝑆𝐿2(7) does not preserve the octonion algebra. then let us assume that the group 23:𝑃𝑆𝐿2(7) acts on a 7-dimensional real vector space with the vector components 𝑥𝑖 (𝑖 = 1,2, … ,7) . let us assume the notation 𝑥𝑖 = − 𝑥𝑖 . the construction of this group is easy by using its maximal subgroups. we have already discussed that the automorphism group 𝑃𝑆𝐿2(7) of the elementary abelian group 2 3can be generated by 𝛼 ̃, 𝛽 ̃and 𝛾 ̃ in (11) and there exists a copy of the 𝑃𝑆𝐿2(7) in the group 2 3:𝑃𝑆𝐿2(7). for the representation of 𝛼 ̃, 𝛽 ̃and 𝛾 ̃ defined over 𝑁𝑖, we can simply replace 𝑁𝑖 by 𝑥𝑖 and define the diagonal matrices 𝑁𝑖 as if they are acting on the vector components 𝑥𝑖 . we can then simply adjoin an element from the elementary abelian group 23 to generate the whole group. therefore, it would suffice to take 𝛼 ̃, 𝛽 ̃, 𝛾 ̃ of 𝑃𝑆𝐿2 (7) and 𝑁1 as the generators of the group 2 3:𝑃𝑆𝐿2(7). although this group does not preserve the octonion algebra there exists yet a maximal subgroup 23: 7: 3 generated by 𝛼 ̃, 𝛽 ̃and 𝑁1 preserving the octonion algebra, as we discussed in section 3. it is quite natural to expect that the groups 23: 𝑆4 and 4: 𝑆4: 2 are maximal subgroups of order 192 in the group 23:𝑃𝑆𝐿2(7). the group 2 3: 𝑆4 can be generated by 𝐴 ̃, 𝐵 ̃and 𝑁1 and its character table is depicted in table 7. similarly, the subgroup 4: 𝑆4: 2 can be generated by the generators 𝛾 ̃, �̃� and 𝑁1. its character table is displayed in table 5. the group 23:𝑃𝑆𝐿2(7) is a maximal subgroup of the simple group 𝐴8, the even permutations of the 8 letters [11] isomorphic to the maximal rotation subgroup of the coxeter-weyl group 𝑊(𝑆𝑈(8)) ≅ 𝑆8. we have already listed the maximal subgroups of the group 23:𝑃𝑆𝐿2(7) as the groups 𝑃𝑆𝐿2(7), 2 3: 7: 3, 23: 𝑆4 and 4: 𝑆4: 2 . there exists yet another 𝑃𝑆𝐿2(7) not conjugate to the one generated by 𝛼 ̃, 𝛽 ̃and 𝛾 ̃ , as conway proved [19]. to see this, let us replace the generator 𝛾 ̃ by an another generator 𝛿 = (𝑥1𝑥5)(𝑥2)(𝑥3𝑥7)(𝑥4)(𝑥6), with 𝛿 ∈ 23:𝑃𝑆𝐿2(7) and 𝛿 2 = 1 instead of 𝛾 ̃. one can show that 𝛼 ̃, 𝛽,̃ 𝛿 and 𝑁1 generate the same irreducible representation of the group 23:𝑃𝑆𝐿2(7) in which the 𝛼 ̃, 𝛽,̃ 𝛿 represent the generators of another group 𝑃𝑆𝐿2 (7). this is a miraculous structure, in that the 𝑃𝑆𝐿2 (7) =< 𝛼 ̃, 𝛽,̃ 𝛿 > is not conjugate to the group 𝑃𝑆𝐿2(7) =< 𝛼 ̃, 𝛽,̃ 𝛾 ̃ > . it is straightforward to show that �̃�𝛿 = 𝛿𝛾 ̃ = 𝑁7 . it is also true that 7-dimensional representation of the group 𝑃𝑆𝐿2(7) = < 𝛼 ̃, 𝛽,̃ 𝛿 > is irreducible while the 7dimensional representation of the group 𝑃𝑆𝐿2 (7) =< 𝛼 ̃, 𝛽,̃ 𝛾 ̃ > is reducible with 7 = 1 + 6. conway attributes this exceptional behavior to the holomorph of an elementary abelian group to exhibit this miraculous feature. therefore, the group 23:𝑃𝑆𝐿2(7) has five maximal subgroups 2 3: 7: 3 , 23: 𝑆4, 4: 𝑆4: 2 and two nonconjugate 𝑃𝑆𝐿2(7). 5. conclusion the main motivation was that the groups 23. 𝑃𝑆𝐿2(7) and 2 3: 𝑃𝑆𝐿2(7) could be used as the broken symmetry of the mass matrices of quarks, charged leptons and neutrinos when they are considered as a single mass matrix. the particle physics literature is full of examples of models demonstrating that the groups 𝑃𝑆𝐿2(7) and its maximal subgroups 7: 3 and 𝑆4 can describe the symmetries of the neutrino mass matrix. here we have studied the constructions of two groups 23. 𝑃𝑆𝐿2(7) and 2 3: 𝑃𝑆𝐿2(7) of order 1344 and given their character tables, including those of their maximal subgroups. the simple finite subgroup 𝑃𝑆𝐿2(7) of 𝑆𝑈(3) occurs either as a factor group or factor and maximal subgroup in these groups. we have also seen that the extension of the frobenious group 7: 3 by the elementary abelian group 23 leading to the group 23: 7: 3 of order 168 is a subgroup in both groups of order 1344. we have also listed the tensor products of the irreducible representations of the groups 23. 𝑃𝑆𝐿2(7) and 2 3: 𝑃𝑆𝐿2(7) including those of their maximal subgroups in appendix a and given the decompositions of the irreducible representations with respect to the irreducible representations of the relevant maximal subgroups in appendix b. another possible use of these groups in particle physics may arise as follows. the operators, charge conjugation 𝐶, parity 𝑃 and time-reversal 𝑇 generate the elementary abelian group 23 =< 𝐶, 𝑃, 𝑇 > of order 8 when they act on the bilinear dirac fields 𝜓γ𝜓 constructed by 16 γ matrices. the dirac bilinear forms constitute 7 eigenvectors of the 7 operators generated by the charge conjugation, parity and the timereversal operators with the eigenvalues ±1 besides the scalar bilinear dirac field which represents the eigenvector of the unit operator. the representation of the generators can be taken as the matrices 𝑁𝑖 (𝑖 = 1,2, … ,7). the elementary abelian group can be extended by its automorphism group 𝑃𝑆𝐿2(7) to either of the groups 2 3. 𝑃𝑆𝐿2(7) or 2 3: 𝑃𝑆𝐿2(7). one can construct an effective hamiltonian as the products of dirac bilinear fields 𝜓γ𝜓. formal properties of parity violation, 𝐶𝑃 violation two groups 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) and 𝟐 𝟑: 𝑷𝑺𝑳𝟐(𝟕) of order 1344 65 and even 𝐶𝑃𝑇 violation can be explained as invariances under the subgroups of the quotient group 𝑃𝑆𝐿2(7). if we simply impose the 𝛾 ̃ invariance we can prove that the parity violating weak interaction should take the form of either 𝑉 − 𝐴 or 𝑉 + 𝐴. if we impose only 𝛽 ̃invariance we obtain cpt preserving but cp violating interaction. invariance under the generator 𝛼 ̃only leads to the cpt violating terms along with a necessary violation of the lorentz invariance. appendix a. tensor products first of all, we note that the groups 7: 3, 23: 7: 3, 𝑃𝑆𝐿2(7), 2 3. 𝑃𝑆𝐿2(7) and 2 3: 𝑃𝑆𝐿2(7) all have 3-dimensional complex representations. moreover, the group 23: 7: 3 has three 7-dimensional irreducible representations; one real, and two complex representations. the real representation preserves the octonion algebra. tensor products of the irreducible representations of the group 𝑃𝑆𝐿2(7) and its maximal subgroups are listed in the reference [2]; therefore we will not reproduce them. the other tensor products are given as follows. tensor products of the irreducible representations of the group 23: 7: 3 11 × 11 = 12 12 × 12 = 11 11 × 12 = 1 12 × 31 = 31 11 × 31 = 31 12 × 32 = 32 11 × 32 = 32 12 × 71 = 72 11 × 71 = 73 12 × 72 = 73 11 × 72 = 71 12 × 73 = 71 11 × 73 = 72 31 × 31 = 32 + 32 + 31 32 × 32 = 31 + 31 + 32 31 × 32 = 1 + 11 + 12 + 31 + 32 32 × 71 = 71 + 72 + 73 31 × 71 = 71 + 72 + 73 32 × 72 = 71 + 72 + 73 31 × 72 = 71 + 72 + 73 32 × 73 = 71 + 72 + 73 31 × 73 = 71 + 72 + 73 71 × 71 = 1 + 31 + 32 + 2(71) + 2(72) + 2(73) 71 × 72 = 12 + 31 + 32 + 2(71) + 2(72) + 2(73) 71 × 73 = 11 + 31 + 32 + 2(71) + 2(72) + 2(73) 72 × 72 = 11 + 31 + 32 + 2(71) + 2(72) + 2(73) 72 × 73 = 1 + 31 + 32 + 2(71) + 2(72) + 2(73) 73 × 73 = 12 + 31 + 32 + 2(71) + 2(72) + 2(73) tensor products of the irreducible representations of the groups 23. 𝑃𝑆𝐿2(7) and 2 3: 𝑃𝑆𝐿2(7) 31 × 31 = 32 + 6 32 × 32 = 31 + 6 31 × 32 = 1 + 8 32 × 6 = 31 + 72 + 8 31 × 6 = 32 + 72 + 8 32 × 71 = 212 31 × 71 = 212 32 × 72 = 6 + 72 + 8 31 × 72 = 6 + 72 + 8 32 × 73 = 211 31 × 72 = 211 32 × 8 = 32 + 6 + 72 + 8 31 × 8 = 31 + 6 + 72 + 8 32 × 14 = 211 + 212 31 × 14 = 211 + 212 32 × 211 = 73 + 14 + 211 + 212 31 × 211 = 73 + 14 + 211+212 32 × 212 = 71 + 14 + 211 + 212 31 × 212 = 71 + 14 + 211+212 6 × 6 = 1 + 2(6) + 72 + 2(8) 6 × 71 = 71 + 14 + 211 6 × 72 = 31 + 32 + 6 + 2(72) + 2(8) 6 × 73 = 73 + 14 + 212 6 × 8 = 31 + 32 + 2(6) + 2(72) + 2(8) 6 × 14 = 71 + 73 + 2(14) + 211+212 6 × 211 = 71 + 14 + 3(211 ) + 2(212) mehmet koca et al 66 6 × 212 = 73 + 14 + 2(211) + 3(212) 71 × 71 = 1 + 6 + 71 + 14 + 211 71 × 72 = 73 + 211 + 212 71 × 73 = 72 + 211 + 212 71 × 8 = 14 + 211 + 212 71 × 14 = 6 + 71 + 8 + 14 + 2(211) + 212 71 × 211 = 6 + 71 + 72 + 73 + 8 + 2(14) + 2(211) + 2(212) 71 × 212 = 31 + 32 + 72 + 73 + 8 + 14 + 2(211) + 3(212) 72 × 72 = 1 + 31 + 32 + 2(6) + 2(72) + 2(8) 72 × 73 = 71 + 211 + 212 72 × 8 = 31 + 32 + 2(6) + 2(72) + 2(8) 72 × 14 = 14 + 2(211) + 2(212 ) 72 × 211 = 71 + 73 + 2(14) + 2(211) + 3(212) 72 × 212 = 71 + 73 + 2(14) + 3(211) + 2(212) 73 × 73 = 1 + 6 + 73 + 14 + 212 73 × 8 = 14 + 211 + 212 73 × 14 = 6 + 73 + 8 + 14 + 211 + 2(212) 73 × 211 = 31 + 32 + 71 + 72 + 8 + 14 + 3(211) + 2(212) 73 × 212 = 6 + 71 + 72 + 73 + 8 + 2(14) + 2(211) + 2(212) 8 × 8 = 1 + 31 + 32 + 2(6) + 2(72) + 3(8) 8 × 14 = 71 + 73 + 14 + 2(211) + 2(212) 8 × 211 = 71 + 73 + 2(14) + 3(211) + 3(212) 8 × 212 = 71 + 73 + 2(14) + 3(211) + 3(212) 14 × 14 = 1 + 2(6) + 71 + 72 + 73 + 8 + 2(14) + 3(211) + 3(212) 14 × 211 = 31 + 32 + 6 + 2(71) + 2(72) + 73 + 2(8) + 3(14) + 5(211) + 4(212) 14 × 212 = 31 + 32 + 6 + 71 + 2(72) + 2(73) + 2(8) + 3(14) + 4(211) + 5(212) 211 × 211 = 1 + 31 + 32 + 3(6) + 2(71) + 2(72) + 3(73) + 3(8) + 5(14) + 6(211) + 7(212) 211 × 212 = 31 + 32 + 2(6) + 2(71) + 3(72) + 2(73) + 3(8) + 4(14) + 7(211) + 7(212 ) 212 × 212 = 1 + 31 + 32 + 3 (6) + 3(71) + 2(72) + 2(73) + 3(8) + 5(14) + 7(211) + 6(212). tensor products of the irreducible representations of the groups 4. 𝑆4: 2 and 4: 𝑆4: 2 11 × 11 = 1 12 × 12 = 1 13 × 13 = 1 11 × 12 = 13 12 × 13 = 11 13 × 21 = 21 11 × 13 = 12 12 × 21 = 22 13 × 22 = 22 11 × 21 = 22 12 × 22 = 21 13 × 31 = 32 11 × 22 = 21 12 × 31 = 33 13 × 32 = 31 11 × 31 = 34 12 × 32 = 34 13 × 33 = 34 11 × 32 = 33 12 × 33 = 31 13 × 34 = 33 11 × 33 = 32 12 × 34 = 32 13 × 61 = 62 11 × 34 = 31 12 × 61 = 61 13 × 62 = 61 11 × 61 = 62 12 × 62 = 62 13 × 63 = 64 11 × 62 = 61 12 × 63 = 64 13 × 64 = 63 11 × 63 = 63 12 × 64 = 63 11 × 64 = 64 21 × 21 = 1 + 13 + 22 22 × 22 = 1 + 13 + 22 21 × 22 = 11 + 12 + 21 22 × 31 = 31 + 32 21 × 31 = 33 + 34 22 × 32 = 31 + 32 21 × 32 = 33 + 34 22 × 33 = 33 + 34 21 × 33 = 31 + 32 22 × 34 = 33 + 34 21 × 34 = 31 + 32 22 × 61 = 61 + 62 two groups 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) and 𝟐 𝟑: 𝑷𝑺𝑳𝟐(𝟕) of order 1344 67 21 × 61 = 61 + 62 22 × 62 = 61 + 62 21 × 62 = 61 + 62 22 × 63 = 63 + 64 21 × 63 = 63 + 64 22 × 64 = 63 + 64 21 × 64 = 63 + 64 31 × 31 = 1 + 22 + 31 + 32 32 × 32 = 1 + 22 + 31 + 32 31 × 32 = 13 + 22 + 31 + 32 32 × 33 = 11 + 21 + 33 + 34 31 × 33 = 12 + 21 + 33 + 34 32 × 34 = 12 + 21 + 33 + 34 31 × 34 = 11 + 21 + 33 + 34 32 × 61 = 61 + 63 + 64 31 × 61 = 62 + 63 + 64 32 × 62 = 62 + 63 + 64 31 × 62 = 61 + 63 + 64 32 × 63 = 61 + 62 + 63 31 × 63 = 61 + 62 + 64 32 × 64 = 61 + 62 + 64 31 × 64 = 61 + 62 + 63 33 × 33 = 1 + 22 + 31 + 32 34 × 34 = 1 + 22 + 31 + 32 33 × 34 = 13 + 22 + 31 + 32 34 × 61 = 61 + 63 + 64 33 × 61 = 62 + 63 + 64 34 × 62 = 62 + 63 + 64 33 × 62 = 61 + 63 + 64 34 × 63 = 61 + 62 + 64 33 × 63 = 61 + 62 + 63 34 × 64 = 61 + 62 + 63 33 × 64 = 61 + 62 + 64 61 × 61 = 1 + 12 + 21 + 22 + 32 + 34 + 61 + 62 + 63 + 64 61 × 62 = 11+13 + 21 + 22 + 31 + 33 + 61 + 62 + 63 + 64 61 × 63 = 31 + 32 + 33 + 34 + 61 + 62 + 63 + 64 61 × 64 = 31 + 32 + 33 + 34 + 61 + 62 + 63 + 64 62 × 62 = 1 + 12++21 + 22 + 32 + 34 + 61 + 62 + 63 + 64 62 × 63 = 31 + 32 + 33 + 34+61 + 62 + 63 + 64 62 × 64 = 31 + 32 + 33 + 34+61 + 62 + 63 + 64 63 × 63 = 1 + 11 + 21 + 22 + 32 + 33 + 61 + 62 + 63 + 64 63 × 64 = 12+13 + 21 + 22 + 31 + 34 + 61 + 62 + 63 + 64 64 × 64 = 1 + 11+21 + 22 + 32 + 33 + 61 + 62 + 63 + 64 tensor products of the irreducible representations of the groups 23. 𝑆4 and 2 3: 𝑆4 11 × 11 = 1 2 × 2 = 1 + 11 + 2 11 × 2 = 2 2 × 31 = 31 + 33 11 × 31 = 33 2 × 32 = 32 + 34 11 × 32 = 34 2 × 33 = 31 + 33 11 × 33 = 31 2 × 34 = 32 + 34 11 × 34 = 32 2 × 35 = 35 + 36 11 × 35 = 36 2 × 36 = 35 + 36 11 × 36 = 35 2 × 41 = 8 11 × 41 = 42 2 × 42 = 8 11 × 42 = 41 2 × 6 = 6 + 6 11 × 6 = 6 2 × 8 = 41 + 42 + 8 11 × 8 = 8 31 × 31 = 1 + 2 + 31 + 33 32 × 32 = 1 + 2 + 32 + 34 31 × 32 = 36 + 6 32 × 33 = 35 + 6 31 × 33 = 11 + 2 + 31 + 33 32 × 34 = 11 + 2 + 32 + 34 31 × 34 = 35 + 6 32 × 35 = 33 + 6 31 × 35 = 34 + 6 32 × 36 = 31 + 6 31 × 36 = 32 + 6 32 × 41 = 42 + 8 31 × 41 = 41 + 8 32 × 42 = 41 + 8 31 × 42 = 42 + 8 32 × 6 = 31 + 33 + 35 + 36 + 6 mehmet koca et al 68 31 × 6 = 32 + 34 + 35 + 36 + 6 32 × 8 = 41 + 42 + 2(8) 31 × 8 = 41 + 42 + 2(8) 33 × 33 = 1 + 2 + 31 + 33 34 × 34 = 1 + 2 + 32 + 34 33 × 34 = 36 + 6 34 × 35 = 31 + 6 33 × 35 = 32 + 6 34 × 36 = 33 + 6 33 × 36 = 34 + 6 34 × 41 = 41 + 8 33 × 41 = 42 + 8 34 × 42 = 42 + 8 33 × 42 = 41 + 8 34 × 6 = 31 + 33 + 35 + 36 + 6 33 × 6 = 32 + 34 + 35 + 36 + 6 34 × 8 = 41 + 42 + 2(8) 33 × 8 = 41 + 42 + 2(8) 35 × 35 = 1 + 2 + 35 + 36 36 × 36 = 1 + 2 + 35 + 36 35 × 36 = 11 + 2 + 35 + 36 36 × 41 = 42 + 8 35 × 41 = 41 + 8 36 × 42 = 41 + 8 35 × 42 = 42 + 8 36 × 6 = 31 + 32 + 33 + 34 + 6 35 × 6 = 31 + 32 + 33 + 34 + 6 36 × 8 = 41 + 42 + 2(8) 35 × 8 = 41 + 42 + 2(8) 41 × 41 = 1 + 31 + 34 + 35 + 6 41 × 42 = 11 + 32 + 33 + 36 + 6 41 × 6 = 41 + 42 + 2(8) 41 × 8 = 2 + 31 + 32 + 33 + 34 + 35 + 36 + 2(6) 42 × 42 = 1 + 31 + 34 + 35 + 6 42 × 6 = 41 + 42 + 2(8) 42 × 8 = 2 + 31 + 32 + 33 + 34 + 35 + 36 + 2(6) 6 × 6 = 1 + 11 + 2(2) + 31 + 32 + 33 + 34 + 35 + 36 + 2(6) 6 × 8 = 2(41) + 2(42) + 4(8) 8× 8 = 1 + 11 + 2 + 2(31) + 2(32) + 2(33) + 2(34) + 2(35) + 2(36) + 4(6) appendix b. decomposition of the irreducible representations in terms of the irreducible representations of the maximal subgroups decompositions of the irreducible representations of the groups 23. 𝑃𝑆𝐿2 (7) and 2 3: 𝑃𝑆𝐿2(7) under the maximal subgroup 23: 7: 3 irreducible representations of 23. 𝑃𝑆𝐿2(7) and 23: 𝑃𝑆𝐿2(7) irreducible representations of 23: 7: 3 1 1 31 31 32 32 6 31 + 32 71 71 72 1+31 + 32 73 71 8 11 + 12 + 31 + 32 14 72 + 73 211 71 + 72 + 73 212 71 + 72 + 73 two groups 𝟐𝟑.𝑷𝑺𝑳𝟐(𝟕) and 𝟐 𝟑: 𝑷𝑺𝑳𝟐(𝟕) of order 1344 69 decompositions of the irreducible representations of the group 23: 𝑃𝑆𝐿2(7) under the maximal subgroup 𝑃𝑆𝐿2(7) irreducible representations of 23: 𝑃𝑆𝐿2(7) irreducible representations of 𝑃𝑆𝐿2(7) 1 1 31 31 32 = 31 32 = 31 6 6 71 7 72 7 73 1 + 6 8 8 14 6 + 8 211 31 + 32 + 7 + 8 212 6 + 7 + 8 decompositions of the irreducible representations of the group 23: 7: 3 under the maximal subgroup 7: 3 irreducible representations of 23: 7: 3 irreducible representations of 7: 3 1 1 11 11 12 = 11 12 = 11 31 31 32 = 31 32 = 31 71 1 + 31 + 32 72 12 + 31 + 32 73 11 + 31 + 32 decompositions of the irreducible representations of the group 𝑃𝑆𝐿2(7) under the maximal subgroup 7: 3 irreducible representations of 𝑃𝑆𝐿2 (7) irreducible representations of 7: 3 1 1 31 31 32 = 31 32 = 31 6 31 + 32 7 1 + 31 + 32 8 11 + 12 + 31 + 32 references 1. koca, m. and koc, r. octonions and the group of order 1344. turkish journal of physics, 1995, 19, 304-319. 2. luhn, c., nasri, s. and ramond, p. simple finite non-abelian flavor groups. journal of mathematicalphysics, 2007, 48(12), 123519. 3. luhn, c., nasri, s. and ramond, p. tri-bimaximal neutrino mixing and the family symmetry z_7 xz_3. physics letters b, 2007, 652(1), 27-33. 4. pakvasa s., and sugawara, h. discrete symmetry and cabibbo angle. physics letters b, 1978, 73, 61-64;grimus, w. and lavoura, l. s3 x z2 model for neutrino mass matrices. journal of high energy physics(jhep), 2005, 08:013; grimus, w. and lavoura, l. a model realizing the harrison-perkins-scott lepton mixing matrix. journal of high energy physics, 2006, 01:018; mohapatra, r.n., nasri, s. and yu, h.b. s3 symmetry and tri-bimaximal mixing. physics letters b, 2006, 639(3-4), 318-321. 5. babu, k.s., ma, e. and valle, j.w.f. underlying a4 symmetry for the neutrino mass matrix and the quark mixing matrix. physics letters b, 2003, 552, 207-213. 6. hagedorn, c., lindner, m. and mohapatra, r.n. s4 flavor symmetry of quarks and leptons in su(5) grand unified theory. journal of high energy physics, 2006, 06:042. mehmet koca et al 70 7. varzielas, i. de medeiros and ross, g.g. su(3) family symmetry and neutrino bi-tri-maximal mixing. nuclear physics b, 2006, 733(1), 31-47. 8. kaplan, d.b. and schmaltz, m. flavor unification and discrete non-abelian symmetries. physics review d, 1994, 49 (7), 3741-3750. 9. ma, e. near tribimaximal neutrino mixing with delta (27) symmetry. physics letters b, 2008, 660, 505-507. 10. harrison, p.f., perkins, d.h. and scott, w.g. tri-bimaximal mixing and the neutrino oscillation data. physics letters b, 2002, 530, 167-173. 11. conway, j.h, curtis, r.t., norton, s.p , parker, r.a. and wilson, r.a., atlas of finite groups. oxford university presss, 1985. 12. bauer, m. and itzykson, c. modular transformations of su(n) 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and symmetry. a.k. peters, ltd, natick, ma, 2003. 18. koca, m., koc, r. and al-barwani, m. quaternionic roots of so(8), so(9), f4 and the related weyl groups. journal of mathematical physics, 2003, 44, 3123-3140; koca, m., koc, r. and al-barwani, m. quaternionic root systems and subgroups of the aut (f4). journal of mathematical physics, 2006, 47, 043507043521. 19. conway, j.h. three lectures on exceptional groups, chap 10 in conway, j.h. and sloane, n.j.a. sphere packings, lattices and groups, springer verlag, 1998. received 1 may 2018 accepted 15 october 2018 microsoft word math071023-f edited_checked.doc 45-51 squ journal for science, 14 (2009) © 2009 sultan qaboos university 45 stability of the synchronization manifold in an all-to-all time lag diffusively coupled oscillators adu a.m. wasike department of mathematics, masinde muliro university of science and technology, p.o.box 190 kakamega, kenya. email: aduwasike@yahoo.com. بات متنوعات التوافق في المذبب الشبكي المزدوج ذو اإلعاقة الزمنية من الكل إلى الكل ث كسوا. م.أدو أ في هذه الورقة درسنا أنظمة شبكات المذبذبات المتطابقة والمترابطة كل واحد مع األخر بشبكة ترابط ذات اعاقة :خالصة االنقسام الطبيعي للنظام إلى متنوع توافق ومتنوع توافق النظام استعملنا ولتقدير زمن اإلعاقة الذي تتبعه ثبوتية. زمنية . كما الحظنا ان كل مذبذب يتبع حل دوري وحيد. ومتنوع مستعرض abstract: we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. we use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. each oscillator has a unique periodic solution that is attracting. keywords: exponential stability, time lag, gronwall's inequality. 1. introduction n the past few years, there have been many papers concerned with the synchronization and stability of systems with diffusive coupling (see for instance afraimovich et. al., 1983, 1986, chow and liu 1977, hale 1977, wasike 2003, 2007, and references therein). other than numerical estimates have been studied by rossoni et al., 2005). there are few results that deal with the problem of stability of the synchronization manifold in a system with a time lag in the coupling in a mathematically rigorous manner (see for instance wasike 2003, 2007). let us suppose that we have n subsystems , 1, 2,..., ,djz j n∈ =r with the dynamics of each jz given by the solutions of the system of d first order equations ( ) ( ), , ,dj jz g z g c u= ∈ r (1) i adu a.m. wasike 46 where the dot denotes differentiation with respect to time t and u is some open set in dr . suppose that, for each j , there is a compact global attractor for equation (1); that is, there is a compact set which is invariant under the flow defined by equation (1) and that the w − limit set of each orbit of equation (1) belongs to this set. now suppose that these systems are coupled linearly with terms that involve some constant time lag, 0r > , to obtain ( ) ( ) ( )( ) ( )( ), ,z t kb z t z t r f z t= − + (2) where 0k > , is a positive constant representing the coupling strength, ( ) ( ) ( )( )1 ,..., ,nz t z t z t= ( )( ) ( )( ) ( )( )( )1 ,... nf z t g z t g z t= and ( ) ( )( ),b z t z t r− is a linear function in ( )z t and ( )z t r− indicating the coupling configuration. as a specific example, we shall be interested in the coupling configuration given by ( ) ( )( ) ( ) ( ) ( ), 1 ,n d n db z t z t r n i i z t i i z t r− = − − ⊗ + ⊗ − (3) where ,n di i are identity matrices of order n and d respectively, ni is an n n× matrix whose entries are all 1's except the principal diagonal that is all zeroes, ⊗ is the kronecker product (see for instance graham 1981). indeed equation (2) can be written ( ) ( ) ( ) ( ) ( )( ) 1, 1 n j j i j i i j z t k n z t z t r g z t = ≠ ⎛ ⎞ = − − + − +⎜ ⎟ ⎝ ⎠ ∑ (4) this type of coupling corresponds to an all-to-all nearest neighbour diffusive coupling. 2. preliminaries let [ ]( ), 0 , ndx c r r= − be the space of continuous functions from [ ], 0r− to ndr endowed with the usual supremum topology. for any ,xϕ ∈ equation (2) has a unique solution ( ),z t ϕ with ( )( ) ( )0,z ϕ θ ϕ θ= for θ on the interval [ ], 0r− . if we let ( )( )( ) ( ) [ ], , , 0t t z t rϕ θ θ ϕ θ= + ∈ − and assume that all solutions are uniquely defined for 0,t ≥ then ( )t t is 0c − semigroup on x . assume that system (4) defines a semiflow ( )kt t and has a global attractor ;ka that is, ka is a compact set which is invariant ( )( ), 0k k kt t a a t= ≥ and, for any bounded set ( )( ), , 0 ask kb x dist x t t b a t⊂ → → ∞ . the global attractor ka is uniformly bounded with respect to k . let a ∞ be the global attractor for the equation ( ) ( )( )z t f z t= (5) with this notation, we say that system (4) is synchronized if the global attractor ka belongs to the diagonal set ( ) ( ) ( )( ) ( ) ( ){ }1 1, , ,... , | , ... , ,n nm z t z t z t z t z tϕ ϕ ϕ ϕ ϕ= = = = stability of the synchronization manifold 47 that is invariant under ( )t t . m will be an inertial manifold, see for instance hale (1997). from the definition of the attractor, this implies that ( )( ), , 0,dist x z t mϕ → as t → ∞ for all ;kaϕ ∈ that is, the difference ( ) ( ) 0 asj iz t z t t− → → ∞ for all ,i j . of course, for the system to be synchronized we have to show that ka a∞= for k sufficiently large. this is the case if we consider identical subsystems. in this case the linear operator ( ) ( )( ),kb z t z t r− has zero as an eigenvalues lie to left-half of the complex plane. this is why we make the following hypotheses on ( ) ( )( ),kb z t z t r− . h1 for each , 0k is an eigenvalue ( ) ( )( ),kb z t z t r− and ( )1,1,...,1 nde vec= ∈ r is its corresponding generalized eigenvector. moreover, all other eigenvalues of ( ) ( )( ),kb z t z t r− lie to left-half of the complex plane for 0 r< < ∞ . h2 ( )kt t is dissipative and has a compact global attractor ka which is invariant under ( )kt t . furthermore ( )( ), 0k kdist t t a m → as t → ∞ and 0k > for all 0 r< < ∞ . h3 assume the semigroup can be represented in a natural way as a linear part ( )kdt t plus a nonlinear part and ( )kdt t m m⊂ for all 0t ≥ . the verification of the stability of the manifold m proceeds by going through the following steps: (1) we introduce a new coordinate x m m ⊥= ⊕ , where m ⊥ is also invariant under the linear flow ( )kdt t , (2) show that there exists 1, 0kl c≤ > such that ( ) | , 0 tck kdt t m le t −⊥ ≤ ≥ this is the scheme that is typically followed in many applications (see for instance hale, (1996). let us check that the matrix of the coupling configuration ( ) ( )( ),kb z t z t r− satisfies h1. the eigenvalues λ , of the linear operator ( ) ( )( ),kb z t z t r− are given by the zeroes of ( ) ( )( ) ( )( )1 , dn s c − ∆ = ∆ ∆λ λ λ (6) where ( ) ( )( )1 1 ,rc k n e−∆ = + − − λλ λ (7) and ( ) ( )1 rs n k ke−∆ = + − + λλ λ (8) adu a.m. wasike 48 clearly 0=λ is an eigenvalue of ( ) 0c∆ =λ and the corresponding generalized eigenvector is ( )1,1,...,1 nde vec= ∈ r . as long as 0, 2,k n> ≥ other than 0 , all roots of ( )∆ λ have negative real parts for all 0,r ≥ (see bose (1989), theorem 3.1 page 143). from h1 we can introduce a new coordinate system ( )1 2 1, , ,..., , t nz ye ew w w w w −= + = , nd dw −∈ r ,dy ∈ r 1 1 , 1 1, 1 , j j j n jj w z z j n y z n + = = − ≤ ≤ − = ∑ (9) where je is the usual unit vector in nr with zeros except for 1 at the thj position and 1 , j j ii j e e e n= = −∑ with ( )1 2 1, ,..., ne e e e −= . the set , ,1 1je e j n≤ ≤ − is an orthogonal basis for nr . with this transformation equation (4) becomes ( ) ( ) ( ) ( )( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) 1 1 1 , 1 1 , , 1, 2,..., 1, 2 n j j j j j j y t k n y t r y t g z t n w t k n w t w t r g w y j n = = − − − + = − − + − + = − ∑ (10) where ( ) ( )( ) ( )( )1,j j jg w y g z t g z t+= − . 3. main results in order to prove the theorem on the stability of a synchronization manifold with a small delay, we need to state a lemma that will be useful in the estimate of the delay r for which stability synchronized manifold can be deduced from that of a system without a delay ( )0r = . the proof of this lemma can be found in halanay (1996). lemma 1. (halanay (1996) ) if ( ) ( ) ( ) 0sup t r t f t f t f for t t σ α β σ − ≤ ≤ ≤ − + ≥ and if 0 ,α β> > then there exist 0γ > and 0k > such that ( ) ( )0t tf t ke γ− −≤ for all 0t t≥ (halanay (1996) pg 378). theorem 2. consider equation (2) and assume it satisfies the hypotheses h1, h2, h3 . then there is an 0r such that for any 2,n ≥ and 0,k > equation (2) has a stable synchronized solution for all 00 r r< < . proof. for the synchronized manifold to be stable, all transverses to it must asymptotically dampen out. this is equivalent to saying the zero solution of the second equation in (10) must be exponentially stable. linearization of (10) about ( ) ( )( ) ( )( )0, , 0y t w t y t= gives ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) 0 0 1 1 , 1 1 , y t j y t k n y t k n y t r w t j y t k n y t k n y t r ⎡ ⎤= − − + − −⎣ ⎦ ⎡ ⎤= − − + − −⎣ ⎦ (11) stability of the synchronization manifold 49 where ( )( )0j y t is the jacobian of ( )( )g z t at ( )( )0 , 0y t and ( ) ( ): , 1,..., 1.djw t w t j n= ∈ = − notice that (11) has a natural splitting c sx x x= ⊕ each of which is invariant under the linearized flow ( );kdt t that is, ( ) { }, 0, 0, , .p pkdt t x x t p c s= ∀ ≥ ∈ consider the second equation in equation (11). if the large r is small, it is quite natural to suppose that it can be neglected and we consider the system of ordinary differential equations (odes). ( ) ( ) ( ) ( ),w t a t w t hw t= + (12) where ( ) ( )( ) ( )0 1a t j y t k n i= − − and ( )1h k n i= − − with i a d d× identity matrix. let us suppose that the trivial solution of equation (12) is uniformly asymptotically stable. we could expect that for r sufficiently small the trivial solution of ( ) ( ) ( ) ( )w t a t w t hw t r= + − (13) would be likewise asymptotically stable. this is indeed true for some values of r . this result indicates that the synchronized manifold will also be stable for sufficiently small values of r . suppose that the trivial solution ( ) ( ) ( )1 0, 1 1,j j jw t w z t z t j n+= = − = ∀ ≤ ≤ − of equation (12), is uniformly asymptotically stable. if ( ),w t s is the fundamental matrix solution of equation (12), we then have ( ) ( ), ,t sw t s le α− −≤ where 0, 0l α> > are constants. let ( )w t be any solution of equation (13) then ( ) ( ) ( ) ( ) ( ) ( ) 0 , 0 0 , t w t w t w w t s h w s r w s ds= + − −⎡ ⎤⎣ ⎦∫ . (14) when t r> we can write equation (14) as ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 , 0 0 , , r t r w t w t w w t s h w s r w s ds w t s h w s r w s ds= + − − + − −⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦∫ ∫ we know from equation (12) and gronwall's lemma that for 0 s r≤ ≤ the estimate : ( ) ( )0 1exp ,w s r k k ϕ≤ +⎡ ⎤⎣ ⎦ where ϕ is the initial function of the solution w given on [ ], 0r− , that ( )0 1 0 0 sup , sup t r t r k a t k h ≤ ≤ ≤ ≤ = = . it follows that for 0 s r≤ ≤ we have, in any case, ( ) ( ) ( )0 12 expw s r w s r k k ϕ− − ≤ +⎡ ⎤⎣ ⎦ . for s r≥ we may write ( ) ( ) ( ) ( ) ( ) ( ) s r s r s s w s r w s w d a w hw r dσ σ σ σ σ σ − − − − = = + −⎡ ⎤⎣ ⎦∫ ∫ . adu a.m. wasike 50 hence ( ) ( ) ( ) ( )0 1 sup s r s w s r w s r k k w σ σ − ≤ ≤ − − ≤ + , and thus obtain ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 0 10 1 0 1 1 0 1 1 0 1 1 0 1 2 exp sup 1 2 exp 1 sup 2 1 exp 1 r t st t t s r s r s t t r tt s r s r s t r w t le le k r k k ds le k r k k w ds le lk r k k e e lk r k k e e w ds le k r k k e αα α σ α α α α α σ α α ϕ ϕ σ ϕ ϕ α σ ϕ α − −− − − − ≤ ≤ − − − − ≤ ≤ − ≤ + +⎡ ⎤⎣ ⎦ + + = + + −⎡ ⎤⎣ ⎦ + + ⎛ ⎞= + + −⎡ ⎤⎜ ⎟⎣ ⎦ ⎝ ⎠ ∫ ∫ ∫ (15) let ( ) ( )0 1 0 1 2 1 1 exprl l e k r k kαϕ α ⎛ ⎞ = + − +⎡ ⎤⎜ ⎟ ⎣ ⎦ ⎝ ⎠ , and ( )1 0 1m lk r k k= + . then equation (15) gives the estimate ( ) ( ) ( )0 sup t t st r s r s w t l e m e w dsαα σ σ− − − ≤ ≤ ≤ + ∫ . let ( ) ( )0 sup tt s r s r s v t e l m e w dsα α σ σ− − ≤ ≤ ⎡ ⎤= +⎢ ⎥⎣ ⎦∫ . then, we have ( ) ( ) ( ) ( ) ( ) 0 sup sup sup tt s t t r s r s t r t t r t v t e l m e w ds e me w v t m w α α α α σ σ σ α σ σ α σ − − ≤ ≤ − ≤ ≤ − ≤ ≤ ⎡ ⎤= − + +⎢ ⎥⎣ ⎦ = − + ∫ (16) however, ( ) ( )w t v t≤ . hence by equation (16) ( ) ( )sup sup t r t t r t w v σ σ σ σ − ≤ ≤ − ≤ ≤ ≤ . thus . ( ) ( ) ( )sup s r s v t v t m v σ α σ − ≤ ≤ ≤ − + if ,m α< it follows by lemma 1 that there exist constants n and γ such that ( ) ( )0t tv t ne γ− −≤ stability of the synchronization manifold 51 consequently, the trivial solution of equation (13) is exponentially stable provided that m α< . this condition leads to ( )1 0 1 r lk k k α < + . taking ( )0 1 0 1 r kk k k α = + , completes the proof of our proposition. 4. conclusion we have shown that if a system of equations without delay has a stable synchronization manifold, the introduction of small delays does not affect the stability of the manifold. 5. references afraimovich, v.s. bykov, v. and shilnkov, l. 1983. on structurally unstable attracting limit sets of lorenz attractor type, tran. of moscow math. soc. 44: 153-216. afraimovich, v.s, verchev, n.n. and riabonvich, m.i. 1986. stochastic synchronization of oscillations in dissipative systems. radio phy. quantum electron. 29: 37-49 bose, f.g. 1989. stability conditions for the general limear difference – differential equation with constant coefficients and one constant delay. j. math. anal. appl. 140: 136-176. chow, s.n., lin, w. 1997. synchronization, stability and normal hyperbolicity. resenhas ime-usp. 3: 139158. halanay a. 1996. differential equation, stability of oscillators time-lags. academic press. hale, j. 1997. diffusive coupling, dissipation and synchronization. j. dyn. differ. equ. 9: 1-52. hale, j. 1996. attracting, manifolds for evolutionary equations cdsns 96-257. rossoni, e., chen, y., ding, m., feng, j. 2005. stability of synchronous oscillations in systems of hh neurons with delayed diffusive and pulsed coupling, phys. rev. e 71: 061904. graham, a. 1981. kronecker products and matrix calculus with applications. ellis horwood limited. wasike, a.a.m., ogana, w. 2002. periodic solutions of a system of delay differential equations for a small delay science and technology, 7: 295-302. wasike, a.a.m. 2002. periodic solutions of systems of delay differential equations indian journal of mathematics, 44 no. 1: 95-117. wasike, a.a.m. 2003. synchronization and oscillator death in diffusively coupled lattice oscillators international journal of mathematical science, 2(1): 67-82. wasike, a.a.m., rotich, p.t. 2007. synchronization, persistence in diffusively coupled lattice oscillators squ journal for science, 12(1): 41-52. received 23 october 2007 accepted 8 april 2009 the squared slacks transformation in squ journal for science, 17 (1) (2012) 22-29 © 2012 sultan qaboos university 22 the squared slacks transformation in nonlinear programming paul armand* and dominique orban** *institut de recherche xlim, cnrs et universite de limoges, limoges, france, email: paul.armand@unilim.fr. **gerad and departement de mathematiques et de genie industriel, ecole polytechnique de montreal, cp 6079, montreal, quebec, canada, email: dominique.orban@gerad.ca. abstract: in this short paper, we recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in many algorithmic frameworks routinely used in nonlinear programming. numerical examples performed with the sequential quadratic programming method illustrate those reasons. our results are reproducible with state-of-the-art implementations of the methods concerned and mostly serve a pedagogical purpose, which we believe will be useful not only to practitioners and students, but also to researchers. keywords: squared slacks transformation, nonlinear programming. تحويل المربعاث الزائذة في البرمجت غير الخطيت بول أرمانذ و دومينيك أوربان م انمتشاجحاخ انمقيذج إنى معادالخ ووقذو ينتحى انضائذج اخوثيه في هزي انىسقح انقصيشج طشيقح استخذاو انمشتع :خصمل أسثاب عذج نمضاس هزا انتحىيم في انعذيذ مه انخىاسصمياخ انمتذاونح في انثشمجح غيش انخطيح. نتىضيح تهك األسثاب، ذاو أدسجىا في هزي انىسقح أمثهح عذديح تاستخذاو طشيقح انثشمجح انتشتيعيح انمتسهسهح. مه انممكه انحصىل عهى وتائجىا تاستخ ، إر وعتقذ أن تهك انىتائج مفيذج نيس نهتطثيقيه تعهيميحانطشق انحذيثح انمتعهقح تهزا انمىضىع وانتي تخذو تشكم أساسي أسثاب وانطالب فحسة، واوما نهثاحثيه أيضا. 1. introduction c onsider the nonlinear inequality constrained optimization problem    minimize subject to 0 , n x r f x c x   (1) where f and c are 2c functions from n r into r. to simplify, we assume that there is a single inequality constraint, but our arguments still hold in the general case. a simple technique to convert the inequality the squared slacks transformation 23 constraint into an equality constraint is to add a new variable y r that appears squared in the reformulation     2 , minimize subject to 0 , n x r y r f x c x y     (2) hence the name, squared slack. the two problems are equivalent in the sense that * x solves (1) if and only if * * ( , ( ))x c x  solves (2). this transformation can be used to derive optimality conditions of an inequality constrained problem, (see for example (bertsekas, 1999, §3.3.2) and an interesting discussion on this subject in (nash, 1998)). the use of squared slacks has also been advocated for algorithmic purposes (see for example (tapia, 1980)). in (gill et al., 1981, §7.4), the authors give theoretical reasons why converting (1) into (2) may be a bad idea, but the literature does not appear to state the numerical drawbacks of the approach clearly. the purpose of this note is to demonstrate why many algorithmic frameworks of nonlinear programming will fail on problems of the form (2), arising from a squared slack transformation or in their own right. among other reasons, we wish to communicate this fact to potential practitioners, who are not necessarily aware of the arcane corners of optimization methods. we wish to show that such simple, innocuous-looking transformations can be disastrous. this note is mainly motivated by the fact that some users, and some researchers, know that the usage of squared slacks is discouraged in practice, but the reason why remains unclear. the frameworks that are concerned are the sequential quadratic programming (sqp) method, the augmented lagrangian method, and conjugate-gradient-based methods, among others. it is important to realize that (2) satisfies the same regularity conditions as (1) and does not defeat the convergence theory of those methods, but illustrates cases where things can, and do, go wrong. we show that the main difficulty comes from the linearization of the first order conditions and a bad choice of the starting point. the rest of the paper is organized as follows. section 2 presents a parameterized two-dimensional problem that illustrates the major shortcomings of sqp-type methods. section 3 presents numerical experiments with a standard implementation of the sqp method to illustrate our point. however, the results are reproducible with state-of-the-art implementations. we elected to not choose a particular existing solver for two main reasons. the first is to ensure that we are running the plain sqp method, with no bells and whistles often found in state-ofthe-art software. the second is that the central point of this paper concerns algorithms, not particular implementations. we leave to the interested reader the possibility to make his or her own opinion by reproducing the numerical tests performed in this paper with his or her favorite implementation of the sqp method. finally, section 4 describes other well-known families of algorithms subject to similar shortcomings. conclusions are discussed in section 5. we believe that the examples given in this note can serve as pedagogical tools to expose the somewhat surprising behavior of some minimization methods for the solution of nonlinear problems. hopefully, they will also be useful to design better methods that do not suffer the same shortcomings. 2. shortcomings of some current methods in this section, we present a few example problems on which several of the most widely used nonlinear optimization algorithms are bound to fail. the reason for this failure is that the problems, without being complex or artificial, cause a certain behaviour of the algorithm which corresponds precisely to a case that is usually 'ruled out' of the theory by means of assumptions. by way of example, we cite boggs and tolle (1995), where the authors mention various types of solution that an sqp algorithm can produce and that do not correspond to a local constrained minimizer of (1). those cases are when the iterates 1. are unbounded (in violation of assumption c1 in (boggs and tolle, 1995)), 2. have a limit point that is a critical point of (1) but not a local minimizer, or 3. have a limit point that is a critical point of the measure of infeasibility 2 ( , ) | ( ) | .x y c x y we will use the following simple parametrized example to expose those problematic cases. it is based on the addition of squared slacks to convert an inequality constraint into an equality. paul armand and dominique orban 24 example 1 consider the problem 2 2 , 1 minimize subject to 0 , 2 x x y r x ax e y     (3) where a r is a parameter. various values of a will illustrate each of the three shortcomings listed above. figure 1. illustration of problem (3) with = 0a . the two solutions, (0, 1) are indicated by black circles, and correspond to global minimizers. starting from 0( , 0),x we observe kx  and 0ky  for all k. a typical sqp method will stop and claim to have found an optimal solution, with the help of a (very) large multiplier. figure 2. illustration of problem (3) with 0a  . the (global) minimizers are (0, 1), indicated by black circles. the point indicated by a red square is a local maximizer. starting from 0( , 0),x an sqp method will converge to the local maximizer. figures 1, 2 and 3 show the various situations graphically. note that for all ,a r example 1 satisfies the linear independence constraint qualification at all feasible points. one of its features is that the inequality constraint is not active at the minimum of each inequality constrained problem. the squared slacks transformation 25 figure 3. illustration of problem (3) with 0a  . the (global) minimizers are (0, 1), indicated by black circles. the point indicated by a red square is a critical point of the infeasibility measure. using a starting point of the form 0( , 0),x an sqp method will converge towards the red square. for the purpose of reference, note that the first-order optimality conditions of (1) are given by         0 and , 0 . f x z c x z c x z c x           (4) the main reason for the failure on example 1 is the following. assume that problem (1) is regular in the sense that * ( ) 0c x  at any critical point *.x problem (2) is then regular as well and the karush-kuhn-tucker conditions are necessary for first-order optimality. the lagrangian for problem (2) is       2, , ,l x y f x c x y    where  is the lagrange multiplier associated to the equality constraint, and at a first-order critical point, we must have       2 = 0 . f x c x y c x y                (5) note that in (5), the complementarity condition of (4) is only apparent as the equality = 0,y so that the sign restrictions on the multiplier and on the constraints in the second part of (4) do not appear. as it turns out, the sign of the multiplier can be recovered from the second-order optimality conditions (see (bertsekas, 1999, §3.3.2)). this pseudo-complementarity condition and the loss of sign restriction creates a difficulty in linearization-based methods. indeed, any method that linearizes conditions (5) at a point ( , , )x y  will compute a step = ( , , )x yd d d d satisfying 0 .yd yd y    (6) assume at some stage in the process we have = 0y and 0.  the linearization (6) then necessarily implies that = 0.yd thus, if ever = 0y it will always remain equal to zero at subsequent iterations. of course, if (1) is such that the constraint is inactive at * ,x any method based on a linearization of (5) is bound to fail. such is the paul armand and dominique orban 26 case with the examples of this section. a typical class of methods computing the step according to (6) is the class of sqp methods. 3. numerical experiments in order to eliminate side effects sometimes found in sophisticated implementations, we implemented a basic sqp method for equality-constrained problems, as given in (nocedal and wright, 1999, algorithm 18.3), for example. the method is globalized with a backtracking linesearch on the 1l -penalty merit function 2 ( , ) ( ) | ( ) | ,x y f x c x y  where > 0 is a penalty parameter, and the lagrange multipliers are updated using the least-squares estimates. in all cases, the starting point is chosen as (0,0) with the initial multiplier set to 1 2. in the following tables, k is the iteration number, ( , )k kx y is the current iterate, k is the current lagrange multiplier estimate, kl is the gradient of the lagrangian evaluated at ( , , )k k kx y  and k is the steplength computed from the backtracking linesearch. table 1. iterations of the sqp method on problem (2) with = 0a k kl | ( , ) |k kc x y 1k  kx ky k 0 5.00e 01 1.00e  00 0.00e  00 0.00e  00 5.00e  01 1 0.00e  00 6.92e  01 3.68e  01  3.68e  01 0.00e  00  5.32e  01 2 0.00e  00 2.55e  01 1.00e  00  1.37e  00 0.00e  00  5.37e  00 3 0.00e  00 9.36e  02 1.00e  00  2.37e  00 0.00e  00  2.53e  01 4 0.00e  00 3.45e  02 1.00e  00  3.37e  00 0.00e  00  9.78e  01 5 0.00e  00 1.27e  02 1.00e  00  4.37e  00 0.00e  00  3.45e  02 6 0.00e  00 4.66e  03 1.00e  00  5.37e  00 0.00e  00  1.15e  03 7 0.00e  00 1.72e  03 1.00e  00  6.37e  00 0.00e  00  3.71e  03 8 8.88e 16 6.31e  04 1.00e  00  7.37e  00 0.00e  00  1.17e  04 9 0.00e  00 2.32e  04 1.00e  00  8.37e  00 0.00e  00  3.60e  04 10 0.00e  00 8.54e  05 1.00e  00  9.37e  00 0.00e  00  1.10e  05 11 0.00e  00 3.14e  05 1.00e  00  1.04e  01 0.00e  00  3.30e  05 12 0.00e  00 1.16e  05 1.00e  00  1.14e  01 0.00e  00  9.84e  05 13 1.78e 15 4.25e  06 1.00e  00  1.24e  01 0.00e  00  2.91e  06 14 1.78e 15 1.56e  06 1.00e  00  1.34e  01 0.00e  00  8.55e  06 15 1.78e 15 5.75e  07 1.00e  00  1.44e  01 0.00e  00  2.50e  07 16 0.00e  00 2.12e  07 1.00e  00  1.54e  01 0.00e  00  7.26e  07 17 0.00e  00 7.79e  08 1.00e  00  1.64e  01 0.00e  00  2.10e  08 18 0.00e  00 2.86e  08 1.00e  00  1.74e  01 0.00e  00  6.06e  08 19 0.00e  00 1.05e  08 1.00e  00  1.84e  01 0.00e  00  1.74e  09 20 0.00e  00 3.88e  09 1.00e  00  1.94e  01 0.00e  00  5.00e  09 table 1 gives the detail of the iterations in the case where = 0.a as expected, we see that = 0ky for all k. because the least-squares estimates happen to yield the exact multipliers in the present case, the gradient of the lagrangian always vanishes. in order to satisfy the first-order optimality conditions, there thus only remains attaining feasibility, which is achieved by having kx converge to . note also that | |k converges to . this behaviour is that of the first shortcoming of section 2. some backtracking linesearch iterations were only the squared slacks transformation 27 necessary at the first iteration, the unit step was always accepted at the other iterations. note that the fact that kx 'escapes' to  can be observed in practice by tightening the stopping tolerance. table 2 gives the detail of the iterations in the case where = 1.a  the results are representative of any value < 0.a here, kx converges to a value which is a local maximizer. this illustrates the second shortcoming of section 2. again, no backtracking was necessary on this problem, except at the first iteration. table 2. iterations of the sqp method on problem (2) with = 1a  k kl | ( , ) |k kc x y 1k  kx ky k 0 1.00e  00 1.00e  00 0.00e  00 0.00e  00 5.00e  01 1 2.78e  17 5.68e  01 4.56e  01  2.28e  01 0.00e  00  1.27e  01 2 0.00e  00 3.59e  02 1.00e  00  5.44e  01 0.00e  00  3.44e  01 3 0.00e  00 1.49e  04 1.00e  00  5.67e  01 0.00e  00  3.62e  01 4 0.00e  00 2.56e  09 1.00e  00  5.67e  01 0.00e  00  3.62e  01 table 3. iterations of the sqp method on problem (2) with = 2a k kl | ( , ) |k kc x y 1k  kx ky k 0 5.00e 01 1.00e  00 0.00e  00 0.00e  00 5.00e  01 1 0.00e  00 7.55e  01 2.93e  01 2.93e  01 0.00e  00  4.43e  01 2 0.00e  00 6.39e  01 2.06e  01 5.29e  01 0.00e  00  1.74e  00 3 0.00e  00 6.16e  01 1.00e  01 7.39e  01 0.00e  00 7.82e  00 4 0.00e  00 6.15e  01 1.26e  02 6.57e  01 0.00e  00  9.23e  00 5 1.11e 16 6.14e  01 4.12e  03 6.92e  01 0.00e  00  5.18e  02 6 0.00e  00 6.14e  01 1.46e  06 6.93e  01 0.00e  00  4.33e  05 7 0.00e  00 6.14e  01 2.09e  12 6.93e  01 0.00e  00 7.55e  10 8 0.00e  00 6.14e  01 1.00e  19 6.93e  01 0.00e  00  5.19e  07 finally, table 3 gives the detail of the iterations in the case where = 2,a but again, the results are representative of any value (0, ).a e this situation is that given in the third shortcoming of section 2. backtracking was used in this case and the algorithm stopped claiming that the steplength was too small. as a side note, we remark that when = ,a e there is a unique feasible point for (2) that has = 0.y the sqp algorithm converges towards that point, which is in fact a saddle point. for > ,a e the feasible set is made of two disconnected curves. each one intersects the axis = 0.y one of those intersection points is a local maximizer while the other one is a local minimizer, but neither of them has = 0.x depending on the value of the starting point, the sqp algorithm converges to one or the other. we decided to not report those results here since they do not add new elements to the present analysis. finally, the above numerical results hold not only for an initial 0 = 0y but of course, also for 0y sufficiently close to 0. this is an effect of finite precision however, and not a shortcoming of the sqp method. 4. other algorithmic frameworks as we showed in (6), any traditional sqp-type method will necessarily generate iterates of the form ( , 0)kx when started from 0( , 0)x with a nonzero lagrange multiplier. in this section, we show that similar conclusions hold for a variety of families of algorithms for nonlinear programming. paul armand and dominique orban 28 augmented-lagrangian-based methods fail for a reason similar to that given in section 2. note that the squared slacks transformation can again be used to derive the proper form of the augmented lagrangian for inequality-constrained problems (bertsekas, 1996, §3.1-3.2; bertsekas, 1999, §4.2). minimization of the augmented lagrangian with squared slacks with respect to the slacks only yields the usual form for inequalityconstrained problems. as we illustrate below, the direct application of the augmented lagrangian algorithm to the formulation involving the slacks suffers the same pitfalls as the sqp method. consider the augmented lagrangian for (2)           2 2 21 , , ; , 2 l x y f x c x y c x y        (7) where > 0 is a penalty parameter and where  is the current estimate of the lagrange multiplier. the step is computed from the newton equations for (7), where           , , , ; 2 , f x x y c x l x y y x y               (8) and                   2 2 2 2 , 2 , , ; , 2 2 , 4 t t f x x y c x c x c x y c x l x y y c x x y y                        where 2 ( , ) = ( ( ) )x y c x y    . in particular, the newton equations yield 2 ( ) ( ( , ) 2 ) = ( , )x yy c x d x y y d y x y         where xd and yd are the search directions in x and y respectively. whenever = 0y , the latter equation becomes  ( ) = 0 ,yc x d  so that = 0yd provided that ( ) 0,c x   or equivalently, provided that ( ,0) 0.x  note, in the second component of (8), a 'complementarity' expression similar to that in the second component of (5). the iterative minimization of (7) using the truncated conjugate gradient also preserves = 0.y indeed, when started from 0( , 0),x the first search direction 0p is the steepest descent direction and has the form 0( , 0) for some 0 .r  the initial residual 0 0=r p thus will have the same form and so will the next iterate 1 1 0 0 0( , ) = ( , 0)x y x   and the residual 1.r a property of the conjugate gradient method is that at the k-th iteration, the search direction 1span{ , }k k kp p r (golub and loan, 1996, corollary 10.2.4). therefore 1p necessarily shares the same form 1( , 0). a recursion argument thus shows that the k-th conjugate-gradient iterate has the form ( , 0).k this method will therefore also be unable to depart from the hyperplane = 0.y 5. discussion when the constraint of (1) is inactive, the optimal multiplier is = 0. however, in (2) we will frequently observe | |   when starting with 0 = 0y to reach dual feasibility. looking for instance at the results of table 1, the final iterate ( 19.4, 0) is feasible to within the prescribed tolerance. to compensate in dual feasibility, we need to have a large multiplier. in this sense, the addition of squared slacks has created a critical point at infinity. for lack of a better initial value, implementations often set their variables to zero prior to starting the optimization, provided the objective and constraints are well defined at the origin. modeling languages also often the squared slacks transformation 29 set the variables to zero unless the user specifies otherwise. the difficulties exposed in this paper thus certainly occur in practice and illustrate another reason why starting points should not be chosen to be zero. unfortunately, the problem is difficult to avoid. of course, it seems that we should not add squared slacks to convert inequality constraints into equality constraints. however problems having the form (2) where the variable y does not appear in the objective may arise in their own right. if at all feasible, it is recommended that equality constraints involving squared slack variables be converted to inequality constraints. it is worth noting that any problem of the form       , minimize subject to 0 , x y f x c x g y  where (0) = 0,g (0) = 0g  and (0) 0g   will exhibit a similar behavior. for instance, the functions ( ) = cosh( ),g y y and ( ) = arctan( )g y y dy have the desired properties. the objective may also have the form ( , )f x y and the same conclusions hold if ( ,0) / = 0.f x y  6. acknowledgments we are grateful to an anonymous referee for comments that improved the presentation of this paper. 7. references bertsekas, d. 1996. constrained optimization and lagrange multiplier methods. athena scientific, belmont ma, usa. bertsekas, d. 1999. nonlinear programming (2nd edition). athena scientific, belmont ma, usa. boggs, p.t. and tolle, j.w. 1995. sequential quadratic programming. acta numerica, 4: 1–51. gill, p.e., murray, w. and wright, m. 1981. practical optimization. academic press, london. golub, g.h. and van loan, c.f. 1996. matrix computations (3rd edition). johns hopkins university press, baltimore, md, usa. nash, s.g. 1998. sumt (revisited). operations research, 46: 763–775. nocedal, j. and wright, s.j. 1999. numerical optimization. springer series in operations research. springer-verlag, new york, usa. tapia, r.a. 1980. on the role of slack variables in quasi-newton methods for constrained optimization. in l.c.w. dixon and g.p. szegö (eds.) numerical optimization of dynamic systems, pp. 235–246. north holland publishing company. received 13 april 2011 accepted 25 september 2011 squ journal for science, 2019, 24(2), 109-121 doi:10.24200/squjs.vol24iss2pp109-121 sultan qaboos university 109 finite element convergence analysis of a schwarz alternating method for nonlinear elliptic pdes messaoud boulbrachene department of mathematics, sultan qaboos university, p.o. box 36, pc 123, alkhoud, muscat sultanate of oman. email: boulbrac@squ.edu.om. abstract: in this paper, we prove uniform convergence of the standard finite element method for a schwarz alternating procedure for nonlinear elliptic partial differential equations in the context of linear subdomain problems and nonmatching grids. the method stands on the combination of the convergence of linear schwarz sequences with standard finite element l  -error estimate for linear problems. keywords: schwarz method; finite elements; convergence. تحليل تقارب العناصر المحدودة لطريقة شوارز المتناوبة ألجهزة للمعادالت التفاضلية اإلخطية الجزئية بولبراشنمسعود لطريقة العناصر المحددة القياسية إلجراء تناوب شوارتز للمعادالت التفاضلية اإلخطية الجزئية في سياق في هذه الورقة ، نثبت التقارب الموحد :صلخمال وتقدير العناصر المحدودة لإلرهاب في تكمن الطريقة في الجمع بين التقارب بين تسلسل شوارز .مشاكل النطاق الفرعي الخطي والشبكات غير المتطابقة المشكالت الخطية. .، التقاربطريقة شوارز، العناصر المحدودة: مفتاحيةالكلمات ال 1. introduction he schwarz alternating method can be used to solve elliptic boundary value problems on domains that consist of two or more overlapping subdomains. the solution is approximated by an infinite sequence of functions that results from solving a sequence of elliptic boundary value problems in each of the subdomains. there has been extensive analysis of the schwarz alternating method for nonlinear elliptic boundary value problems [1-4] and the references therein). also, the effectiveness of schwarz methods for these problems (especially those in fluid mechanics) has been demonstrated by many authors. in this paper, we are concerned with the finite element convergence analysis of overlapping schwarz alternating methods in the context of nonmatching grids for nonlinear pdes, where the schwarz sub problems are linear. this study constitutes, to some extent, an improvement of the one achieved in [5], on a schwarz method with nonlinear sub problems. for that, we develop an approach which combines the convergence result of lui [6], with standard finite element error estimate for linear elliptic equations. for other works on finite element convergence analysis in the maximum norm of overlapping nonmatching schwarz method, we refer to [7-12]. the rest of the paper is organized as follows. in section 2, we state the continuous alternating schwarz sub problems and define their respective finite element counterparts in the context of nonmatching overlapping grids. in section 3, we give  l   convergence analysis of the method. t boulbrachene, m. 110 2. preliminaries we begin by laying down some definitions and classical results related to linear elliptic equations. 2.1 linear elliptic equations let ω be a bounded polyhedral domain of r²or r³ with sufficiently smooth boundary ∂ω. we consider the bilinear form ω ( , ) u vdxa u v    (1) the linear form  , = ( ) ( )f v f x v x dx   (2) the right hand side: f is a regular function, (3) the space     g 1= v such that = on ωv h v g  (4) where g is a regular function defined on  . we consider the linear elliptic equation: find ( )g v  such that      1 0 a( , )+c , , v v f v v h      (5) where such that , 0 0c r c c     (6) let h v be the space of finite elements consisting of continuous piece-wise linear functions, , 1, 2,..., ( ) s s m h  be the basis functions of h v , and ( )m h denote the number of vertices of the triangulation in ω. let also 0 hv be the subspace of hv defined by   0 such that 0 on h h v v v v    (7) the discrete counterpart of (.,.) consists of finding g h h v  } such that     0 a( , )+c , , hh hv v f v v v     (8) where g h v is the space of     g such that= v = on ω h h h v v v g  (9) and h  is the lagrange interpolation operator on ∂ω. theorem 1. [13] under suitable regularity of the solution of problem (5), there exists a constant c independent of h such that 2 ( ) ln h l ch h      lemma 1. [5] let    1w h c    satisfy ( , ) ( , ) 0a w c w   ∀ non-negative φ∈  10h  , and 0w  on ∂ω. then 0w  on  . the proposition below establishes a lipschitz continuous dependency of the solution with respect to the data. notation 1. let    , , , f g f g be a pair of data, and  ,f g  and  ,f g  be the corresponding solutions to (5). proposition 1. under the conditions of lemma 1, we have: ( )( ) ( ) 1 max , ll l f f g g                (10) proof. first, set ( )( ) 1 max , ll f f g g            finite element convergence analysis of a schwarz alternating method 111 then ( )l f f f f      ( )l c f f f       ( )( ) 1 max , ll f c f f g g             f c  so      10a( , )+ , a( , ) , ( , ) 0, c c h                      a( + , )+c + , ,f c          on the other hand, we have 0 on       so ( , ) ( , ) 0 0 on a c                       thus, making use of lemma 1, we get 0      on  similarly, interchanging the roles of the couples    , , ,f g f g , we obtain 0 on       which completes the proof. remark 1. lemma 1 holds true in the discrete case. indeed, assume that the discrete maximum principle (d.m.p) holds, i.e. the matrix resulting from the finite element discretization is an m-matrix. then we have: lemma 2. let h w v satisfy  , ,( 0 1, 2,..., () ) s s s ma c w hw       and 0w  on ω . then 0w  on  . proof. the proof is a direct consequence of the discrete maximum principle. let  ,f g and  ,f g be a pair of data and  ,h h f g  and  ,h h f g  be the corresponding solutions to problem (8). proposition 2. let the d.m.p hold. then, under conditions of lemma 2, we have ( )( ) ( ) 1 max , h h ll l f f g g                proof. the proof is similar to that of the continuous case. indeed, as the basis functions s  > 0 of the space h v are positive, it suffices to make use of the discrete maximum principle. let  ,f g and  ,f g be a pair of data and  ,h h f g  and  ,h h f g  be the corresponding solutions to problem (8). 3. schwarz alternating methods for nonlinear pdes 3.1 the nonlinear pde consider the nonlinear pde: find  2u c  such that ( ) in 0 on u cu f u u        (11) boulbrachene, m. 112 or in its weak form: find  10 u h  such that        10, , ( ), a u v c u v f u v v h     (12) where (.)f is a non-decreasing nonlinearity we assume that (.)f is lipschitz continuous, that is ( ) ( ) ,f x f y k x y x y    r such that k  where  is defined in (6). theorem 2. [14] under the above assumptions, problem (11) has a unique solution. 3.2 the linear schwarz sub problems we decompose ω into two overlapping smooth subdomains 1  and 2  such that: 1 2     (13) we denote by i  the boundary of i  , i i j     , and i i    . we assume that the intersection of i and j ; i j is empty. let 0 2 u be an initial guess. we define the alternating schwarz sequences ( 1 1 n u  ) on 1  such that  1 21 1 n u c    solves 1 1 1 1 1 1 1 1 1 1 1 1 2 2 ( ) in 0 on on n n n n n n u cu f u u u u                (14) and the sequence  12 n u  such that  1 22 2 n u c    solves 1 1 2 2 2 2 1 2 2 1 1 2 1 2 ( ) in 0 on on n n n n n n u cu f u u u u                (15) note that schwarz subdomain problems (14) and (15) are linear. theorem 3. [6] the sequences (14) and (15) converge uniformly in  2 1c  and   2 2 c  , respectively, to / , 1, 2 i i u u i   , where u is the solution of (11). 3.3 the variational linear schwarz sub problems the corresponding variational problems read as follows: 1 1 1 n u v   solves      0 1 11 1 1 1 1 1 2 1 , , / / n n n n b u v f u v v v u u           (16) finite element convergence analysis of a schwarz alternating method 113 and 1 2 2 n u v   solves      0 1 22 2 2 1 2 2 2 2 , , / / n n n n b u v f u v v v u u           (17) where  1i iv h  ;   0 1 0i i v h  (18)    , i i b u v u v cuv dx      (19)  , ( ) ( ) i i u v u x v x dx    (20) 3.4 the discretization for 1, 2i  , let be i h  be a standard regular and quasi-uniform finite element triangulation in i  ; i h , being the mesh size. the two meshes being mutually independent on 1 2   , a triangle belonging to one triangulation does not necessarily belong to the other. let us define the discrete analog of spaces i v and 0 iv , respectively, that is  1( )such that / ii i h h k v v c v p k        0 such that 0 on i i i h h v vv v    and let ih  denote the lagrange interpolation operator on i  the discrete maximum principle (see [15,16]). we assume that the respective matrices resulting from the discretization of problems (16) and (17) are m-matrices. 3.5 the finite element linear schwarz sub problems let 2 0 h u be the discrete analog of 0 2 u that is,   2 2 0 0 2h h u r u where 2h r denotes the finite element interpolation operator in ω. we define the sequence   1 1n h u  such that 1 1 1n hh u v   solves        1 1 1 1 1 2 0 1 1 1 1 , , / n n hh h n n h h h b u v f u v v v u u            (21) and the sequence ( 2 1n h u  ) such that 2 2 1n hh u v   solves        2 2 2 2 2 1 0 1 2 1 1 2 2 , , / / n n hh h n n h h h b u v f u v v v u u              (22) 4. l  convergence analysis this section is devoted to the proof of the main result of the present paper. to that end, we begin by introducing two discrete auxiliary schwarz sequences and prove a fundamental lemma. boulbrachene, m. 114 4.1 auxiliary discrete schwarz sub problems we construct a sequence   1 1n h   such that 11 1n hh v   solves        1 1 1 2 1 1 1 0 1 1 1 1 , , / / n h n n h h h n b v f u v v v u u               (23) and the sequence   2 1n h   such that 22 1n hh v   solves        2 2 2 1 2 2 1 0 2 1 1 2 2 , , / / h n h h n n n h b v f u v v v u u               (24) then, it is clear that 1 1n h   and 2 1n h   are the finite element approximation of 1 1n u  and 1 2 n u  defined in (16) and (17), respectively. notation 2. from now on, we shall adopt the following notations:    1 21 2. , .l l      (25)      1 21 2. , . , .l l l          (26) 1 2h h h     (27) 4.2 the main result the following lemma will play a key role in proving the main result of this paper. lemma 3. 1 1 1 1 1 2 2 1 1 2 0 0 n n n n i i i i h h h i i u u u u           2 2 1 1 2 2 2 1 2 0 0 n n n n i i i i h h h i i u u u u          proof. the proof will be carried out by induction. for n=1, we have in 1  . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 h h h h u u u u      and, making use of proposition 2, we obtain 1 1 1 1 0 0 0 0 1 1 1 1 1 1 2 2 1 1 1 1 1 max ( ) ( ) , h h h h h h u u u f u f u u u               1 1 0 0 0 0 1 1 1 1 2 2 1 1 2 max , h h h k u u u u u            we then have to distinguish between two cases 0 0 0 0 0 0 1 1 2 2 1 1 1 2 1 1 : max , h h h k k u u u u u u            finite element convergence analysis of a schwarz alternating method 115 and 0 0 0 0 0 0 1 1 2 2 2 2 1 2 2 2 : max , h h h k u u u u u u           case 1. implies that 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 h h h k u u u u u       and hence 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 h h h u u u u u     case 2. implies that 1 1 1 1 0 0 1 1 1 1 2 2 1 1 2 h h h u u u u u     and, in both cases, we have 1 1 1 1 0 0 0 0 1 1 1 1 1 1 2 2 1 1 1 2 h h h h u u u u u u u       (28) similarly, we have in 2  1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 h h h h u u u u      1 1 0 0 1 1 2 2 2 2 1 1 2 2 2 max , h h h h h k u u u u u              1 1 0 0 1 1 2 2 2 2 1 1 2 2 1 max , h h h k u u u u u            here also we need to consider the following two cases: 1: 0 0 1 1 0 0 2 2 1 1 2 2 2 1 2 max , h h h k k u u u u u u            2: 0 0 1 1 1 1 2 2 1 1 1 1 2 1 1 max , h h h k u u u u u u           case 3. implies that 1 1 1 1 0 0 2 2 2 2 2 2 2 2 2 h h h k u u u u u       so 1 1 1 1 0 0 2 2 2 2 2 2 2 2 2 h h h u u u u u     boulbrachene, m. 116 case 4. implies that 1 1 1 1 1 1 2 2 2 2 1 1 2 2 1 h h h u u u u u     1 1 1 1 0 0 0 0 2 2 1 1 1 1 2 2 2 1 1 2 h h h h u u u u u u         thus, in both cases, we have 1 1 1 1 1 1 0 0 0 0 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 h h h h h u u u u u u u u          (29) for n = 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 h h h h u u u u      2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 max ( ) ( ) , h h h h h u f u f u u u              2 2 1 1 1 1 1 1 1 1 2 2 1 1 2 max , h h h k u u u u u            case 1. 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 max , h h h k u u u u u u            2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 h h h k u u u u u       2 2 1 1 1 1 1 1 1 1 h h u u u    2 2 1 1 0 0 0 0 1 1 1 1 1 1 2 2 1 1 1 2 h h h h u u u u u u         case 2. 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 max , h h h u u u u u u           2 2 2 2 1 1 1 1 0 0 0 0 1 1 1 1 2 2 1 1 1 1 2 2 1 1 2 1 1 2 h h h h h h u u u u u u u u u             so in both cases 2 2 2 2 1 1 1 1 0 0 0 0 1 1 1 1 2 2 1 1 1 1 2 2 1 1 2 1 1 2 h h h h h h u u u u u u u u u             (30) or finite element convergence analysis of a schwarz alternating method 117 2 1 2 2 1 1 1 1 2 2 1 1 2 0 0 i i i i h h h i i u u u u          (31) on the other hand 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 h h h h u u u u      2 2 1 1 2 2 2 2 2 2 1 1 2 2 2 max , h h h k u u u u u            case 1. 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 h h h k u u u u u       2 2 1 1 2 2 2 2 2 2 h h u u u    2 2 1 1 1 1 0 0 0 0 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 h h h h h u u u u u u u            case 2. 2 2 2 2 2 2 2 2 2 2 1 1 2 2 1 h h h u u u u u     2 2 2 2 1 1 1 1 0 0 0 0 2 2 1 1 2 2 1 1 1 1 2 2 2 1 2 1 1 2 h h h h h h u u u u u u u u               so in both cases 2 2 2 2 2 2 1 1 1 1 0 0 0 0 2 2 2 2 1 1 2 2 1 1 1 1 2 2 2 2 1 2 1 1 2 h h h h h h h u u u u u u u u u u                or 2 2 2 2 2 2 1 1 2 2 2 1 2 0 0 i i i i h h h i i u u u u          (32) now assume that 1 1 1 1 1 2 2 2 1 2 0 0 n n n n i i i i h h h i i u u u u           and 2 2 1 1 2 2 2 1 2 0 0 n n n n i i i i h h h i i u u u u          and let us prove that 1 1 1 1 1 1 1 2 2 1 1 2 0 0 n n n n i i i i h h h i i u u u u             and 1 1 1 1 2 2 1 1 2 2 2 1 2 0 0 n n n n i i i i h h h i i u u u u              boulbrachene, m. 118 indeed, we have 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 n n n n n n h h h h u u u u             1 1 1 1 1 1 2 2 1 1 1 max , n n n n n n h h h h h k u u u u u                1 1 1 1 1 1 2 2 1 1 2 max , n n n n n n h h h k u u u u u              and, as above, we need to distinguish between two cases: 1: 1 1 2 2 1 1 1 2 1 max , n n n n n n h h h k k u u u u u u            and 2: 1 1 2 2 2 2 1 2 2 max , n n n n n n h h h k u u u u u u           case 1. implies that 1 1 1 1 1 1 1 1 1 1 1 1 1 n n n n n n h h h k u u u u u           1 1 1 1 1 1 1 1 n n n n h h u u u       1 1 1 1 1 1 1 2 2 1 1 2 0 0 n n n n i i i i h h h i i u u u               while case 2. implies that 1 1 1 1 1 1 1 1 2 2 1 1 2 n n n n n n h h h u u u u u          1 1 1 1 1 1 2 2 1 1 2 0 0 n n n n i i i i h h h i i u u u              so in both cases 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 0 0 n n n n n n i i i i h h h h i i u u u u u                 1 1 1 2 2 1 2 0 0 n n i i i i h h i i u u          likewise 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 n n n n n n h h h u u u u u            1 1 1 1 2 2 2 2 1 2 2 2 2 max , n n n n h h h h h k u u u u u                1 1 1 1 2 2 2 2 1 1 2 2 1 max , n n n n n n h h h k u u u u u               finite element convergence analysis of a schwarz alternating method 119 here also we need to discuss two cases: case 1: 1 1 2 2 1 1 2 2 2 1 2 max , n n n n n n h h h k k u u u u u u             implies 1 1 1 1 2 2 2 2 2 2 2 2 2 n n n n n n h h h u u u u u          1 1 2 2 1 1 2 2 2 1 2 0 0 n n n n i i i i h h h i i u u u              case 2: 1 1 1 1 2 2 1 1 1 1 2 1 1 max , n n n n n n h h h k u u u u u u              implies 1 1 1 1 1 1 2 2 2 2 1 1 2 2 1 n n n n n n h h h u u u u u            1 1 1 1 2 2 1 1 1 1 2 2 2 1 1 2 0 0 n n n n n n i i i i h h h h i i u u u u                   then, in both cases, we have 1 1 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 0 0 n n n n n n n n i i i i h h h h h i i u u u u u u                      1 1 1 1 2 2 1 2 0 0 n n i i i i h h i i u u           which completes the proof. theorem 4. there exists n h > 0 with lim 0 n n h   , such that  1 1 lim 0, 1, 2 i i i h ln u u i      proof. let us give the proof for i=1, the case i=2 being similar. indeed, as 1 1 1 1 1 2 2 1 1 2 0 0 n n n n i i i i h h h i i u u u u           and 2 1 1 1 ln n n h u ch h  2 2 2 2 ln n n h u ch h  then,   2 1 1 1 2 1 ln n n h u u n ch h   (33) boulbrachene, m. 120 also 1 1 1 1 1 1 1 1 1 n n n n n h h u u u u u u     let ε>0. theorem 3 implies that there exists 0 n n such that, ∀ 0 n n 1 1 1 2 n u u    taking account of (33), the theorem follows by choosing n h > 0 such that   2 0 ln , 2 1 n n h h n n n c      conclusion we have proved convergence of the standard finite element approximation for alternating schwarz procedure in the context of nonmatching grids. other type of discretizations may also be considered like mixing finite elements and finite differences. also, the knowledge of a rate of convergence of the schwarz procedure will enable derivation of error estimate, in each subdomain, between the discrete schwarz sequence and the exact solution of the nonlinear pde. conflict of interest the author declares no conflict of interest. acknowlegement the author would like to thank sultan qaboos university for providing financial support to attend and present the paper at international conference on mathematics (icomath2018), istanbul, 3-6 july, 2018, turkey. references 1. proceedings of the 1st international symposium on domain decomposition for partial differential equations, editors, glowinski, r., meurant, g., golub, g.h., s.i.a.m, phildelphia, usa, 1998. 2. lions, p.l. on the schwarz alternating method i, proceedings of the1st, international symposium on domain decomposition methods for partial differential equations. siam philadelphia, usa, 1988, 1-41. 3. lions, p.l. on the schwarz alternating method ii, proceedings of the 2nd international symposium on on domain decomposition methods for partial differential equations. siam, philadelphia, usa, 1989, 47-70. 4. lui, s-h. on monotone and schwarz alternating methods for nonlinear elliptic pdes. mathematical modelling and numerical analysis, (esaim:m2an), 2001, 35, 1, 1-15. 5. harbi, a. and boulbrachene, m. maximum norm analysis of a nonmatching grids method for nonlinear elliptic pdes. journal of applied mathematics, article id 605140, 2011, 1-18. 6. lui, s-h. on linear monotone iteration and schwarz methods for nonlinear elliptic pdes. numerishe mathematik, 2002, 109-129. 7. boulbrachene, m., cortey-dumont, p. and miellou, j.c. mixing finite elements and finite differences on a subdomain decomposition method, proceedings of the 2nd international symposium on domain decomposition methods for partial differential equations, siam, philadelphia, usa, 1988, 198-216. 8. boulbrachene, m. and saadi, s. maximum norm analysis of an overlapping nonmatching grids method for the obstacle problem, advances in difference equations, 2006, 1-10. 9. harbi, a. maximum norm analysis of an arbitrary number of nonmatching grids method for nonlinear elliptic pdes, journal of applied mathematics. article id 895182, 2013, 1-21. 10. boulbrachene, m. and al-farei, q. maximum norm error analysis of a grids method nonmatching grids finite element method for linear pdes. applied mathematics and computation, 2014, 238, 21-29. 11. harbi, a. maximum norm analysis of a nonmatching method for a class of variational inequalities with nonlinear source terms. journal of inequalities and applications, 2016, 181, 1-27. 12. bahi, m., boulaares, s. and haiour, m. the maximum norm analysis of a nonmatching grids method for a class of parabolic equations with nonlinear source terms, applied sciences, 2018, 20, 1-17. finite element convergence analysis of a schwarz alternating method 121 13. nitsche, j. l  convergence of finite element approximations, mathematical aspects of finite element methods, lecture notes in mathematics, 1977, 606, 261-274. 14. pao, c.v. nonlinear parabolic and elliptic equations, plenium press, new york, 1992.. 15. ciarlet, p.g. and raviart, p.a. maximum principle and uniform convergence for the finite element method, computer methods in applied mechanics and engineering, 1973, 2, 17-31. 16. karatson, j. and korotov, s. discrete maximum principle for finite element solutions of nonlinear elliptic problems with mixed boundary conditions, numerische mathematik, 2005, 99, 669-698. received 6 december 2018 accepted 13 may 2019 microsoft word biol090315-f edited_checked_final _2_.doc squ journal for science, 15(2010) 1-8 © 2010 sultan qaboos university 1 an approach to analyze the ambiguity in rna structure shailendra singh and *amardeep singh *department of computer science and engineering, pec university of technology, chandigarh160012, india, email: shailendra_sing@yahoo.com, department of computer engineering, university college of engineering (ucoe), punjabi university, patiala, india, email: amardeep-dhiman@yahoo.com. rnaطريقة لتحليل عدم الوضوح في شكل ال سيالندرا سنج و أمارديب سنج المرتبة الثانية من حيث rna هما من أهم الجزيئات في الخلية اإلنسانية حيث تحتل ال rna وال dnaان :خالصة العديد من هنالك . وتكوين البروتينdnaاهمية الحامض النووي في خلية األنسان وهي تمثل عامل الوصل مابين ال ثم استعمال المعلومات الجينيةتخزين ومن إن . المتواجدة في مختلف الخاليا ولكل منها مهمة محددةrnaأنواع ال تلعب دوراً أساسياً في الخاليا لذ فإن rnaإن ال . rnaبواسطة الخلية يعتمد أساساً على المظهر الخارجي وشكل ال هنالك عدة طرق . نوع سلسلة النيوكلوتايداتلها لمعرفة العالقة السائدة لكل أو لبعض غالتيمكن اس rnaفهم تركيبة ال والمهام التي rna والتي يمكن أن تؤدي لمعلومات قد تساعد لمعرفة عمل ال rnaوأنواع من التحاليل لشكل ال ع متعددة من األشكال الثانوية ل في هذه الورقة تمت دراسة ومناقشة أنوا. تؤديها وذلك بدرجات متفاوتة من التفاصيل rna وقد تم إختيار أشكال محددة لدراسة االحتماالت المختلفة والتي تبين وضوح الرؤية لشكل ال .rna abstract: dna and rna are two very important bio-molecules of the human cell. rna is the second major form of nucleic acid in human cells that plays an intermediary role between dna and functional protein. several classes of rna’s are found in cells, each with a / its distinct function. understanding of storage and utilization of a cell’s genetic information is based on the structure of rna. however, many experimental results have shown that rna plays another greater role in the cells. rna sequences which contain signals at the structure level can be exploited to detect functional motifs common to all, or a portion of, those sequences. different types of analysis of a structure can provide functional information in different degrees of detail. this paper discusses various types of rna secondary structure representation and which structure can be adopted as appropriate for a probabilistic approach that avoids ambiguity. keywords: secondary structure, stochastic context-free grammar (scfg), derivation tree. shailendra singh and amardeep singh 2 1. introduction na is a biological polymer consisting of monomers called nucleotides. each nucleotide consists of a (ribose) sugar, a phosphate group and a base. there are four main types of bases: adenine (a), cytosine (c), guanine (g), and uracile (u). the base-paired structure formed by the watson-crick base-pairs a-u and cg and the wobbling base-pair g-u can be divided into loops, also known as ‘structure elements’. a loop is a formation of a base-pair that encloses a chain of nucleotides or other base-pairs. rna primary structure is commonly represented by a string, s, over the alphabet ∑ = {a, g, c, u}. rna is mostly involved in the biological machinery that expresses the genetic information from dna to rna. information is encoded in rna by the linear arrangement of the four different constituent nucleotides. rna molecules perform a number of critical functions. many of these functions are related to protein synthesis. some rna molecules bring genetic information from a cell’s chromosomes to its ribosome's, where proteins are assembled. the rna plays a very important role in bio cells. determining rna shapes has gained considerable importance in the last decade because it is essential for researchers to know the shape of a molecule, in order to understand its role within a cell. a lot of work has been done in the structural analysis of rna in the bioinformatics field, but there exist a large number of challenging problems like the analysis of ambiguities in rna structure, prediction of structure, and predictions of functions performed (hiroshi, et al. 2005 and, jizhen, et al. 2006). the structure of an rna molecule is closely related to its function (yinglei, s. et al. 2004). for this reason, predicting the secondary structure of an rna molecule based on its primary sequence has been of interest to many researchers. since rna structure is essentially governed by base pairing of nucleotides, many computational methods and algorithms have been proposed for finding the “optimal base pairing” of rna in an efficient manner (keum, y. s. 2006, mount, d. w. 2004, and rafael, g. 2006). for the computer science community, the primary structure of bio-molecules is just a very long string of commands forming long programs written in any computer programming language. this long program in the form of a long string is to be processed by compilers, translators etc. using regular expressions, grammars, and similar other techniques. according to noam chomsky, the context free grammar (cfg) has great importance in the linguistic field, computer science, engineering and bioinformatics. it is a more powerful class of formal grammars than the regular grammar. cfgs are often used to define the syntax of programming languages (byung-jun, y. and vaidyanathan, p.p. 2007). a cfg, also called a type 2 grammar, is similar to a regular grammar, but it permits a greater variety of production rules. the other methods used for the analysis of rna structure are the free energy based model and conditional log-linear models (cllms). cllms are a generalization of grammar based models (dowell, r.d. and eddy s. r. 2004). according to the evaluation done by its authors, it has accuracies that are better than those of the current probabilistic and physics based models. one purpose of this paper is to present an effective method for analyzing the ambiguity in rna structure and estimating a stochastic context-free grammar to model a family of rna sequences (yuki, k., hiroyuki, s. and tadao, k. 2003). 2. analysis of rna structure the importance of grammars in compliers is well-known. the grammars are useful tools to model character sequences and, in a certain way, these tools are useful to model molecular biological sequences (yan, d. and yulei, z. 2005). many bioinformatics problems can be reformulated in terms of formal languages, producing the corresponding grammar from the available data. among several utilities contributed by grammars, the main contribution is the ability to test by derivations if a sequence is syntactically correct, i.e. if it belongs to a determined language. a derivation can be represented as a tree-like structure known as a ‘derivation tree’. this tree reflects the syntactical structure of a sequence. it is possible that for a given sequence there may be more than one derivation tree. in this case, we say that the grammar is ambiguous. in ambiguous grammar, complexity of the derivation rises given that the number of possible trees grows exponentially with the length of the r an approach to analyze the ambiguity in rna structure 3 sequence to be derived. stochastic syntactic analysis algorithms for the class of stochastic context free grammars (scfg) have been proposed and their application has been demonstrated in pattern classification problems. 3. context free grammar for rna type-2 grammars, or cfgs, are used to identify the secondary structure of rna molecules from the given nucleotide sequence when we consider an rna sequence as a string (or a valid sentence) of a programming language. the grammar is a major tool for a parser to build a parse tree to check if the given string is a valid sentence. the whole leaves of a parse tree constitute a sentence of the language defined by the grammar. as the name ‘context-free grammar’ implies, the non-terminals on the left-hand side of a production rule do not consider the context in which it is situated. for example, one of the applications of productions as shown in figure 1 can generate the rna sequence “agcgucagugacuugaugcu” by the following derivation, and the equivalent derivation tree is shown in figure 7. 3.1 productions p = { s0→ s1, s7 → as8u s1→ as2u, s8 →gs9u s2 → gs3c, s9 → us10 s3→ cs4g, s10 → gs11 s4 →gs5u, s11 → as12 s5→ us6a s12 → c } s6 → cs7g figure 1. set of production rules ‘p’ figure 1 shows a set of production rules p that generates an rna sequence for a certain restricted structure, in which s0,s1……s12 are non-terminals. a, g, c and u are terminals. beginning with the start symbol s0, any production with s0 left of the arrow can be chosen to replace s0. if the production s0 → s1 is selected, then the symbol s1 replaces s0. this derivation step is written as s0 → s1, where the arrow signifies application of a production. next, if the production s1→ a s2 u is selected, the derivation step is s1→a s2 u. continuing with the same procedure of replacing left-hand side with the right-hand side of an appropriate production, we obtain the following derivation terminating with the desired sequence: 3.2 derivation s0→s1 →as2u (s1→ as2u) →ags3cu (s2 → gs3c) →agcs4gcu (s3→ cs4g) →agcgs5ugcu (s4 →gs5u) →agcgus6augcu (s5→ us6a) → agcgucs7gaugcu (s6 → cs7g) shailendra singh and amardeep singh 4 →agcgucas8ugaugcu (s7 → as8u) →agcgucags9uugaugcu (s8 →gs9u) → agcgucagus10uugaugcu (s9 → us10) → agcgucagugs11uugaugcu (s10 → gs11) → agcgucagugas12uugaugcu (s11 → as12) → agcgucagugacuugaugc (s12 → c) 4. different secondary structure for rna rna secondary structures can be displayed in different kinds of representations. depending on the use of the rna molecules, specific representations are more or less useful. the bracket notation as shown in figure 2 is a text-based representation. the structure has been reflected in a string of dots and brackets. dots denote nonbonding bases and a pair of brackets indicates a base-pair. a more convenient representation, which expands in all directions in a plane and thus is closer to a spatial representation, is the squiggle plot as shown in figure 3. it is the most appropriate plot to easily describe the approximate spatial structure of rna. base-pairs are given as two bases connected through either a straight line (watson-crick base-pairs) or a circle indicating the so-called wobbling base-pair, g-u. considering rna in a more theoretical way, the representations as trees or as arc-annotated sequences are well-accepted. in recent years, tree-representations of rna secondary structures have occurred in the literature, and algorithmic applications on trees are performed successfully. arc-annotated sequences focus on representing sequences as straight lines. arcs indicate base-pairings. this kind of representation is used in this paper mainly due to its beneficial representation of single base and base-pair operations. a similar representation to the arcannotated sequence is the drawing of this sequence on a circle as shown in figure 5. arcs are plotted as curved lines inside this circle. the mountain plot as shown in figure 6 is useful for large rnas. plateaus represent unpaired regions, and the heights of these mountains are determined by the number of base-pairs in which the partial sequences are embedded. figure 7 shows a derivation tree for a given sequence and figure 8 shows the appropriate way representation of a sequence. 4.1 dot-bracket representation figure 2. dot-bracket representation an approach to analyze the ambiguity in rna structure 5 4.2 squiggle plot figure 3. squiggle plot 4.3 arc-annotated sequence figure 4. arc-annotated sequence 4.4 circle representation figure 5. circle representation 4.5 mountain plot representation figure 6. mountain plot representation shailendra singh and amardeep singh 6 4.6 derivation tree representation figure 7. derivation tree representation 4.6 most appropriate way representation figure 8. most appropriate way representation an approach to analyze the ambiguity in rna structure 7 5. assignment of probability on productions a scfg extends the definition of context free grammars by associating a probability to every production in the grammar. consequently every string that the grammar can generate is assigned a probability which is equal to the product of the probabilities of the productions used in the string’s derivation. the probability of a parse tree can be calculated as a product of the probabilities of the production instances in the tree. there are various methods used to determine such probabilities, and using one such method, the assignment of probabilities is as shown in table 1. to derive the trained grammar, the initial grammar was designed by using some prior knowledge about the rna family. table 1. probabilities for the type 2 grammar, with uniform distribution placed over each set of the same type of production. category of productions productions probabilities c#1 s0→s1 0.3000 c#2 s1→as2u 0.0250 c#2 s2 →gs3c 0.0250 c#2 s3→cs4g 0.0250 c#2 s4 →g s5u 0.0250 c#2 s5 →us6a 0.0250 c#2 s6 → cs7g 0.0250 c#2 s7 →as8 u 0.0250 c#2 s8 →gs9u 0.0250 c#3 s9 → us10 0.0666 c#3 s10 →gs11 0.0666 c#3 s11 → as12 0.0666 c#4 s12 → c 0.3000 6. conclusion a detailed understanding of the functions and interactions of rna requires knowledge of their structures. for many rna molecules, the secondary structure is highly important to the correct function of the rna, often more so than the actual sequence. one of the problems with cfgs is that they generally have an ambiguity in the grammar that results in more than one parse tree for a sequence, and alternative parse trees reflect alternative secondary structures. thus a grammar often gives several possible secondary structures for one rna sequence. the scfg is used to overcome the problem of ambiguity. one of the advantages of a scfg is that it can provide the most likely parse tree. if the grammar and their probabilities are carefully designed, the correct secondary structure will appear as the most likely parse tree among the alternatives. the grammar itself may be a valuable tool for representing a rna family or domain. for (long-chain) rna there are exponentially many possible structures which may be assigned to rna, but assigning the correct one can only be done on the basis of a probability distribution. however, the most challenging future problem is to model a family of longer rna sequences, and also the variations of rnas like mrna, trna, and sirna. shailendra singh and amardeep singh 8 6. references byung-jun, y. and vaidyanathan, p.p. 2007. computational identification and analysis of noncoding rnas. ieee signal processing magazine, 24(1): 64-74. dowell, r.d. and eddy s.r. 2004. evaluation of several lightweight stochastic context free grammars for rna secondary structure prediction. bmc bioinformatics, 5: 71-78. hiroshi, m., kengo, s. and 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k. 2003. a comparative study on formal grammars for pseudoknots, proceedings of genome informatics, 14: 470-471. received 15 march 2009 accepted 17 may 2010 a galerkin method for a gaseous squ journal for science, 17(2) (2012) 224-231 © 2012 sultan qaboos university 224 a galerkin method for a gaseous ignition model m. salman* and j. kim** *department of mathematics, statistics and physics, university of qatar, doha, qatar, email: msalman@qu.edu.qa. **department of mathematics, tuskegee university, tuskegee, alabama, usa, email: jtkim@tuskegee.edu. abstract: we consider a galerkin procedure to solve a parabolic integrodifferential equation that arises in a gas combustion model. this model has been proposed by kassoy and poland, and subsequently analyzed by bebernes, eberly and bressan. the problem is formulated in the variational form. in order to estimate the error, some intermediate projection has been employed. under certain conditions on the given data, the 2 l error estimate has been obtained. a fully descretized version by using an extrapolated crank-nicolson method has been applied and the order of convergence derived. keywords: crank-nicolson, error estimate, galerkin method, gaseous ignition model. ركين لنموذج إشعال غازياالطريقة ج كيم ياجنت محمد سلمان و نموذج احتراق الغاز. لقد تم اقتراح هذا عنلحل المعادلة التفاضلية المكافئة التي تنشأ ركيناالج طريقةنفترض :خصمل المشكلة في شكل طرحت وقد .تم تحليله بواسطة بيبيرنيس وابيرلي و ريسانفيما بعد ند والالنموذج من قبل كاسي وبو متنوع. وبغية تقدير الخطأ، فقد استخدم إسقاط متوسط. تم الحصول على تقدير الخطأ 2 l تحت شروط مناسبة على بيانات نيكلسون وإيجاد درجة التقارب.-تم تطبيق أدلة األبعاد التامة باستخدام طريقة كرانكومعطية. 1. introduction assoy and poland (1983) developed an ignition model for a reactive gas in a bounded container to describe the induction period. during this period, the spacially uniform pressure increases and causes heating effects in the system. the pressure of the gas can be expressed in terms of a space integral term in the induction model that governs the temperature perturbation ( , ).u x t this model is described by the set of equations (bebernes and bressan, 1988) 1 1 = ( , ) , ( , ) (0, ) , | | u t tu u e u x t dx x t           (1) k a galerkin method for a gaseous ignition model 225 ( , 0) = ( ), ,u x g x x  (2) ( , ) = 0, ( , ) (0, ) ,u x t x t   (3) where  is a bounded domain in n with a smooth boundary , and volume | |, > 1. the model has been subsequently studied by bebernes and bressan (1982), bebernes and bressan (1988), and bebernes et al. (1989). bebernes and bressan (1982) analyzed this model and proved that for any positive value of the frak-kamenetski parameter  and any value of the gas constant 1,  equations (1) have a unique classical solution ( , )u x t on [0, ),t where  is a bounded domain and t can be infinite. when t is finite, the solution blows up as .t t for a critical value crit (see (kassoy and poland, 1983)), and crit> ,  the solution blows up in a finite time. bebernes and eberly (1989) used the semigroup analysis to show the existence and uniqueness of a nonextended solution. additional comparison results have been provided in the case of a spherically symmetric domain. blowup occurs at a time < t where t is the blowup time of the solid fuel ignition model. the location of the blowup has been also discussed. depending on the nonlinearity of f, blowup can take place everywhere or at a single point (bebernes and eberly, 1989). in this paper, we study a finite element approximation to the solution of the gas combustion model that is described by the partial differential equation (bebernes and eberly, 1989) 1 1 = ( ) ( , ) , ( , ) (0, ) , | | t tu u f u u x t dx x t          (4) ( , 0) = ( ), ,u x g x x  (5) ( , ) = 0, ( , ) (0, ) .u x t x t   (6) we assume f is a lipschitz function such that ( ) > 0, ( ) 0,f u f u  and ( ) 0.f u  in this work we develop estimates for error when a galerkin method is applied. the error is optimal in the sense of the 2 l norm. this work is motivated by that of cannon and lin (1990a, 1990b). an extensive study of the finite element method for parabolic equations can be found in a book by thomée (2006). 2. formulation of the variational problem and galerkin approximation let hs be a finite dimensional subspace of the sobolev space 1 0 ( )h  such that 1 0( ( ) ) , ( ) ( ) ,inf s s s w s h w v h w v ch v v h h           (7) where 1,s   is the 2 l norm, and s  is the sobolev norm defined on ( ). s h  problem (4) is equivalent to finding a 1 0( ) ( ) s u h h    such that 1 0 1 1 ( , ) ( , ) = ( ( ), ) , for all ( ) , | | t tu v u v f u v u dx v dx v h              (8) where ( , )  is the inner product on 2 ( )l  defined as ( , ) = .u v uv dx  the continuous galerkin approximation : [0, ] hu t s is defined as a solution to 1 1 ( , ) ( , ) = ( ( ), ) , | | t t hu u f u u dx dx s                  ( , 0) = ( ) ,u x g x (9) where ( )g x is the 2 l projection of ( )g x into ,hs i.e., m. salman and j. kim 226 ( , ) = 0 for .hg g s   given a basis =1{ } m i i for ,hs u can be written as =1 ( , ) = ( ) ( ) . m i i i u x t t x  then the variational equation can be written as the nonlinear initial value problem ( ) ( ) = ( ( )) , (0) = ,b t a t f t c a a a a g (10) where a, b, and c are the matrices = ( , ) , 1 1 = ( ) = ( , ) , | | = ( , ) , i j ij i j i i i j a b b dx dx c                    for , = 1, 2, ,i j m , and the vectors a, f, and g are defined by =1 ( ) = ( ( )) , ( ) = ( ( ), ) , = ( , ) . i m i i j i i t t f g       a f a g the matrix b is positive definite, since =1 = m t ij i j i b b  a a 2 2 =1 =1 1 1 = ( ) | | m m i i i i i i dx            2 21 1 = ( ) | | u u dx        21 > 0 for 0 ,u u    where we used the schwarz inequality 22 2 2 ( ) 1 =| | .u dx u dx dx u        with the assumption that ( )f u is uniformly lipschitz, then it follows from the theory of ordinary differential equations that the initial-value problem (10) has a unique solution for > 0.t 3. projection of the solution let : [0, ] hw t s such that ( ( ), ) = 0 for all .hu w s     (11) then w is the elliptic projection of 1 0( ) ( ) s u h h    into hs that satisfies the following properties (thomée, 2006) , s s u w ch u  (12) 1 , s s u w ch u     (13) . s t t s u w ch u  (14) a galerkin method for a gaseous ignition model 227 4. error estimates let = = ,u u u w w u       where = u w  and = .w u  from (8), (9) and (11), we get ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) 1 1 ( , ) ( , ) ( ( ), ) | | 1 1 ( , ) ( ( ) ( ), ) ( ) , | | t t t t t t t t t t t w u w u w w u u w u f u u dx dx w u f u f u u u dx dx                                                              i.e., 1 1 1 1 ( , ) ( , ) = ( , ) ( ( ) ( ), ) . | | | | t t t tf u f u dx dx dx dx                                  (15) we choose =  and rewrite the equation 2 221 1 1 1 1 1 ( ) = ( , ) ( ( ) ( ), ) . 2 2 | | | | t t d d dx f u f u dx dx dt dt                            (16) assuming that f is uniformly lipschitz with 1 2 1 2( ) ( ) .f u f u l u u   (17) then, using schwarz and young's inequalities implies 22 2 2 221 1 1 1 ( ) . 2 2 | | t d d c dx c l l dt dt                       (18) with the use of poincaré-friedrichs' inequality (gilbarg and trudinger, 1983) 1/ | | , n n u u         we obtain 22 2 2 22 2/1 1 1 1 | | ( ) ( ) ( ) . 2 2 | | n t n d d c c dx l c dt dt                      (19) if the lipschitz constant of f is small enough such that 2/| | < ( ) , n n l   (20) then we can also choose  small enough so that 2/| | ( ) . n n l c      thus, we have 22 2 221 1 1 1 ( ) . 2 2 | | t d d dx c c c dt dt               (21) integrating both sides from 0 to t after dropping 2 c  to get 22 2 22 0 1 1 ( ) ( , 0) ( ) . | | t tdx c d                  then, using schwarz inequality to obtain 22 2 2 0 1 ( , 0) ( ) . | | t tc d           m. salman and j. kim 228 here 2 ( , 0) = ( , 0) ( , 0) ( , 0) ( , 0) ( , 0) ( , 0) , s s s s w u w u u u ch g g g ch g                  and 22 t  can be replaced by their upper bound in (12) and (14). this implies 0 ( ) . s s t ts s s u u ch g ch u u d    (22) this establishes the following theorem. theorem 1. suppose that problem (4) possesses a solution u in 1 0( ) ( ), s h h   tu in ( ), s h  and f is uniformly lipschitz that satisfies (17) and (20). then, the continuous galerkin solution u of (9) satisfies (22). proof. the next step is to get an estimate for ( ).u w  for that purpose we put = t  in (15). this yields   22 21 1 1 1 1 = ( , ) ( ( ) ( ), ) . 2 | | | | t t t t t t t d f u f u dx dx dx dt                             (23) this implies 2 2 2 22 21 1 ( ) ( ) . 2 t t t t d c c c f u f u dt                   (24) estimating the righthand side we get 2 2 2 22 21 1 . 2 t t t d c cl c u u dt               (25) selecting  small so that 1 > ,c   we can drop the t terms to get 22 2 .t d c c u u dt      (26) upon integrating from 0 to t, we get 22 2 2 0 0 ( , 0) ) , t t tc c u u d           (27) where 1 1 ( , 0) ( , 0) ( , 0) ( , 0) ( , 0) , s s u u w u g g ch g                    (28) and  1 110 0 01 ( ( , ) ( , ) ) . t t s s s tss s u u d ch g g g ch u u d d                     (29) the double integration can be interchanged, a process to suppress one of the integrals, then the right hand side simplifies to 1 0 0 1 1 1 ( ) . t t s ts s s u u d c g g h g u u d                (30) in view of (28) and (30), estimate (27) may become 2 1 1 01 1 1 1 ( ) . s t s ts s s s g g ch g c g g h g u u d                     (31) this proves the theorem. a galerkin method for a gaseous ignition model 229 theorem 2. under all the assumptions mentioned in theorem 1, we have   1 01 1 1 1 . s t ts s s s u u ch g u u u d            (32) note that as g being the 2 l projection of g onto ,hs , it legitimizes the estimates , s s g g ch g  1 1 . s s g g ch g      5. a priori estimate on extrapolated crank-nicolson-galerkin method in order to get a fully discretized version of the galerkin method, we introduce the time mesh =mt mk for = 0, 1, , ,m m where k is a uniform time step. for the rest of this section, we denote 1 1 = ( ) , 2 m m mf f f  as an averaged value of f on the nodes mt and 1.mt  in the crank-nicolson method, we replace the time derivative in (9) by 1= ( ) /m m mu u u k  and u by 1= ( ) / 2.m m mu u u  this defines 1mu  as a solution to the nonlinear system 1 1 ( , ) ( , ) = ( ( ), ) , . | | m mm m hu u f u u dx dx s                    the nonlinearity due to ( )mf u can be overcome by replacing the argument of ( )mf u by an extrapolated u over the time steps m and 1,m  i.e. 1 3 1 ( ) ( ) . 2 2 m m mf u f u u   we denote these extrapolated values by 1 3 1ˆ = . 2 2 m m mf f f  (33) this produces the new linearized equation in 1mu  as 1 1ˆ( , ) ( , ) = ( ( ), ) , . | | mm m m hu u f u u dx dx s                    (34) note that this extrapolation process will result in a second order accuracy 2 1 1/2 3 1 ˆ = = ( ) , 2 2 m m m mu u u u o k   with 1/2 1/2= (., ).m mu u t  we shall estimate the error ( , )m mu u t  ( , ) = ( , ) ( , ) ( , )m m m m m mu u t u w t w t u t        = ,m m  where the estimate of m is shown in (12). we now consider m by writing ( , ) ( , ) = ( , ) ( , ) ( , ) ( , )m m mm m mu u w w                    1 1ˆ= ( ( ) ( ), ) , , | | m m m m m m u u f u f u u dx dx w t t                              (35) where m. salman and j. kim 230 1 1 ( ) = ( ( ) ( )) . 2 m m mf u f u f u  this implies 1 1 ( , ) ( , ) | | mm m dx dx                    1 1ˆ= ( ( ) ( ), ) , . | | m m m m m m m m u u f u f u u dx dx u t t                                   (36) setting = ,m  we can get   2221 1 1 ˆ( ) ( ) , 2 2 | | m m mm m m m m m u dx c f u f u u t                              (37) where we have used the poincaré-friedrichs' inequality .m m   this implies   2 222 21 1 1 ˆ( ) ( ) . 2 2 | | m m m m m m m u dx c f u f u u t                           (38) the last two norms on the right hand side are of orders 2s h and 4 ,k respectively. moreover 1/2 1/2 ˆ ˆ( ) ( ) ( ) ( ) ( ) ( )m m m m m mf u f u f u f u f u f u      2 1/2 ˆ( )m mc u u k   (39) 2 1/2 ˆ ˆ ˆ( )m m m mc u u k       2 1( ) , s m mc h k      where ˆ ,m ˆm and ˆmu are the extrapolated representations for ,m m and ,mu respectively. on the other hand, the left hand side of (38) is bounded below by   22 21 1 1 1 . 2 2 | | 2 m m mdx              (40) now, in view of (39) and (40), estimate (38) can be written as 2 2 2 2 2 1 1(1 ) ( ) , s m m mck ck ck h k        or 2 2 2 2 2 2 1 1(1 2 )( ) ( ) . s m m m mck ck ck ck h k          (41) a repeated application of (41), with a small k, implies 22 2 2 2 1 0( ) ( ) . s m c k c h k      if 0 and 1 are both calculated with an accuracy 2 ( ) ( ), s o h o k we get the following result 2 ( ) , s m c h k   which proves the following theorem. theorem 3. the extrapolated crank-nicolson solution mu of (34) satisfies 2 ( ) ,max s m m m u u c h k   where c depends on u. a galerkin method for a gaseous ignition model 231 6. references bebernes, j. and bressan, a. 1982. thermal behaviour for a confined reactive gas. j. diff. equations, 44: 118-133. bebernes, j. and bressan, a. 1988. total blowup versus single point blowup. j. diff. equations, 73(1): 30-44. bebernes, j. and eberly, d. 1989. mathematical problems from combustion theory. applied mathematics series, vol. 83, springer-verlag, new york. bebernes, j., bressan, a., kassoy, d. and riley, n. 1989. the confined non-diffusive thermal explosion with spatially homogeneous pressure variation. comb. sci. tech., 63: 45-62. cannon, j. and lin, y-p. 1990a. a galerkin procedure for diffusion equations with integral boundary conditions. int. j. engng. sci., 28(7): 579-587. cannon, j. and lin, y-p. 1990b. a priori 2 l error estimates for finite element methods for nonlinear diffusion equations with memory. siam j. numer. anal., 27(3): 595-607. gilbarg, d. and trudinger, n.s. 1983. elliptic partial differential equations of second order. springerverlag. kassoy, d. and poland, j. 1983. the induction period of a thermal explosion in a gas between infinite parallel plates. combustion and flame, 50: 259-274. thomée, v. 2006. galerkin finite element methods for parabolic problems. springer series in computational mathematics, springer-verlag new york, usa. received 21 february 2011 accepted 15 november 2011 photovoltaic cells and systems: 1-10 squ journal for science, 18 (2013) © 2013 sultan qaboos university 1 optimised methods for quantitative analysis of solasodine and its glycoside solamargine by high performance liquid chromatography sana s. al-sinani and elsadig a. eltayeb* department of biology, college of science, sultan qaboos university, p.o. box 36, al-khoud, 123 muscat, sultanate of oman,*email: eatayeb@squ.edu.om. abstract: improved and simplified hplc conditions for the determination and quantification of both the steroidal glycoalkaloid (solamargine) and its aglycone (solasodine) are described. the best isocratic conditions were developed using a c18 column and methanol in combination with an ammonium dihydrogen phosphate buffer. the isocratic conditions were shown to be more reproducible, less time consuming and to give sharper peaks (better separation). the effects of adjusting solvent: buffer ratio, buffer ph and buffer molarity were evaluated. keywords: hplc; solamargine; solasodine; steroidal glycoalkaloids; aglycone. للتحلٌل الكمً لمركب السوالسودٌن والكالوٌده السكري السوالمارجٌن باستخدام جهاز المثلىالطرق (hplcكروماتوغرافٌا السوائل عالً الكفاءة ) سناء سالم السنانً و الصادق عبدهللا الطٌب من األلكلوٌدات السكرٌه وهو لتحدٌد وتقدٌر كمٌات مركبٌن أحدهما مبسطةهذه المقالة العلمٌة تصف طرٌقة مطورة و :ملخص solamargine واآلخر ألكالوٌد وهوsolasodine ستخدام جهاز ابhplcستخدام اطوٌر أفضل الظروف لهذه الطرٌقة ب. تم ت والمٌثانول باإلضافة إلى فوسفات األمونٌوم ثنائً الهٌدروجٌن كمحلول منظم، حٌث تبٌن أن الظروف المستخدمة c18عمود ستهالكاً للوقت وتعطً أفضل عملٌة فصل للمواد. أٌضا تم تقٌٌم تأثٌر ضبط كل من العوامل ان تكرارها وهً أقل والمطورة ٌمك التالٌة: نسبة المذٌب إلى المحلول المنظم، مقٌاس الحموضة للمحلول المنظم، والتركٌز الموالري للمحلول المنظم. ن االكلوٌدات السكرٌة واالجلٌكون. و سوالمارقٌن ، سوالسودٌ hplc جهاز :مفتاح الكلمات 1. introduction teroidal glycolakaloids (sgas) are naturally occurring nitrogen containing toxins found in the solanaceae family (carman et al., 1986; friedman and dao, 1992). sgas contain three structural portions: a polar, water soluble sugar moiety with three or four monosaccarides, a non-polar steroid unit and a basic portion with either indolizidine or oxa-azaspirodecane structure (cherkaoui et al., 2001; kuronen et al., 1999). uv absorption spectra of sgas and steroidal glycoalkaloid aglycones (sgaas) are very simple and similar (kuronen et al., 1999). they lack chromatographic groups in the common operating range of uv spectrophotometry and absorb only at the low wavelength end of the uv spectrum. this means that they have low uv sensitivity and can be detected and identified by diode array detection (dad) uv only when present in relatively high amounts (5-10 ng/injection) (cherkaoui et al., 2001; crabbe and fryer, 1980; kuronen et al., 1999). steroidal glycoalkaloids are of great interest from both ecological and human health aspects. they may also play important roles in the plant's efforts to protect itself against herbivores and microbial pathogens. they have been described as being antibiotic, antifungal, antimicrobial, and antiviral (lee et al., 2007). in probably the majority of plants which elaborate glycoalkaloids, the main aglycone is solasodine (cherkaoui et al., 2001). solasodine (figure 1) is a water insoluble steroidal alkaloid considered as potential raw material for steroid drug manufacture (eltayeb et al., 1997; jacob and malpathak, 2005). it occurs in species of solanum plants in the form of the water soluble s sana s. al-sinani and elsadig a. eltayeb 2 triglycosides, solsonine and solamargine (weissenberg, 2001) (figure 1). because of the great importance of solasodine in the pharmaceutical industry, there are many publications concerned with the search for solasodine glycosides in various plants (kreft et al., 2000). for our study concerning the extraction and quantification of solasodine from the leaves of solanum incanum, we required rapid and accurate analytical techniques for the determination of solasodine and related compounds. it has been reported that only small structural differences in the steroid, or basic portion as well as the nature, number and order of attachments of sugar units in the carbohydrate moiety, influence the biological activity of the sgas. separation and determination of these structurally closely related compounds represent an enormous analytical challenge (kuronen et al., 1999). a number of analytical methods have been reported for the determination of individual and total glycoalkaloids in solanum plants (carman et al., 1986; eanes et al., 2008). figure 1. chemical structure of steroidal glycoalkaloids: a) solasodine b) sugar side chains. a useful analysis method consists of three major steps: extraction of the alkaloids with aqueous or non-aqueous solvents, removal of interfering substances (impurities), and analysis. the methods in current use for the analysis of sgas include: thin layer chromatography (tlc), gas chromatography (gc), high performance liquid chromatography (hplc), mass spectrometry (ms), combined gc-ms, lc-ms, immunoassays, colorimetry, titrimetry or gravimetry (carman et al., 1986; eanes et al., 2008; eltayeb et al., 1997; friedman and dao, 1992; kreft et al., 2000; trivedi and pundarikakshudu, 2007). it must be pointed out that each method has its relative advantages and disadvantages, and no method is able to analyze the whole set of complex compounds in different types of samples. the methods of colorimetry, titrimetry or gravimetry are best suited to the determination of the total steroid base (crabbe and fryer, 1980). if further separation into aglycone and the various glycosides is required, then a chromatographic separation, either by paper or thin layer chromatography, is needed before the chemical analysis. this leads to a considerable increase in the errors involved and in the analysis time (kuronen et al., 1999). gas chromatography has also been used for the analysis of steroidal alkaloids. however, these compounds have low volatility and are thermally unstable. operation must be in all-glass systems at temperatures near the limit for packing materials. only the aglycone forms can be analyzed directly; glycosides and sugars require permethylation or silylation (crabbe and fryer, 1980). high performance liquid chromatography (hplc) should overcome the volatility and stability problems of gas chromatography. although glycoalkaloids show limited absorption of ultraviolet (uv) light, hplc separation followed by uv detection can still be considered a viable method, due to the relatively widespread availability of such instrumentation, its sensitivity, its suitability for separating non-volatile species or thermally fragile ones, and its adaptability to accurate quantitative determination (dinan et al., 2001; eanes et al., 2008). since wavelengths less than 210 nm are required for solasodine and its glycosides, the range of solvents which can be used is limited and the use of solvent gradient programming is unlikely to be appropriate (crabbe and fryer, 1980; kuronen et al., 1999). the main aim of this study solamargine(sm): h= chacotriose solasonine(sn): h= solatriose (a) (b) quantitative analysis of solasodine and its glycoside solamargine 3 was to investigate the effect of chromatographic conditions on the hplc behavior of sgas and sgaas and to develop a simple method for quantification of sgas and sgaas, using commercial model compounds of solasodine and solamargine. 2. experiments 2.1 chemicals and reagents solasodine obtained from sigma (st. louis, mo, usa) and solamargine obtained from glycomix ltd (uk) were used as reference compounds. distilled water was deionized before use. hplc-grade acetonitrile and methanol were obtained from sigma aldrich (germany). ammonium dihydrogen phosphate from bdh ltd (poole, england) was prepared in water at different concentrations and phs as buffers and these solutions were filtered through a 0.45 µm membrane filter before use (whatman, germany). orthophosphoric acid (85%) was from bdh ltd (poole, england). 2.2 preparation of standards the glycoalkaloid standard solutions were prepared by dissolving solasodine and solamargine (400 µg/ml) in methanol. the stock solutions were stored at 4 ˚c. hplc working standards were prepared by diluting the stock solutions in methanol. 2.3 hplc procedure a waters associates (milford, ma) hplc system comprised of a 626 pump, a 996 photodiode array (pda) detector and a 717 plus autosampler was used. the column was a symmetry c18 5µm (4.6×150 mm) from waters. the solvent flow rate was 1 ml/min and the absorption was measured at 200-205 nm. under isocratic conditions, the mobile phase consisted of a methanol: ammonium dihydrogen phosphate buffer at different ratios and different ph values. all solvent ratios are given on a volume basis. the mobile phase was filtered through a 0.45 µm filter and degassed before use. the injector loop was 5µl. hplc conditions were according to those reported by crabbe and fryer (1980), with some modifications. 3. results the aim of this work was to find chromatographic conditions suitable for the detection and quantification of solasodine and solamargine. the degree of separation for solasodine and solamargine was very strongly dependent on chromatographic conditions. 3.1 effect of solvent/buffer ratio methanol (meoh) was the organic portion of the mobile phase, whereas the buffer was ammonium dihydrogen phosphate (ah2p) 100 mm, acidified to ph 2.5 and ph 3.5 with 85% orthophosphoric acid as, according to eanes et al. (2008), it produced better separations of the sgas and sgaas under isocratic conditions. figures 2a-d and 3a-d show the chromatograms that were obtained when using a meoh/ah2p (100 mm/ph 2.5 for solasodine and 100 mm/ph 3.5 for solamargine) mobile phase system at different ratios. it can be seen that the solasodine (aglycone) eluted much faster (retention time (rt) 2.9 minutes) when the percentage of the methanol in the mobile phase was increased to 80% (figure 2d). under these conditions, the solamargine (sgas) eluted too quickly to be detected (results are not shown), requiring that the methanol percentage be decreased. however, decreasing the percentage of the methanol to 60% and 55 % resulted in an increase of the run times (7.9 minutes for solasodine and 7.7 minutes for solamargine respectively), and in a broadening of solasodine and solamargine bands (figures 2a and 3a). when different ratios of acetonitrile (acn)/ammonium dihydrogen phosphate (ah2p) (ph 2.5/ 100 mm) were used, solasodine and solamargine were either not detected at all, eluted as very broad peaks or could not be reproduced after several injections (results are not shown). these results show that the optimal isocratic solvent conditions were 70% methanol:30 % ah2p (ph 2.5/100 mm) buffer for the separation of solasodine, but 65% methanol:35% ah2p buffer (ph 3.5/100 mm) for the separation of solamargine. 3.2 effect of ph of the buffer a change in ph is an effective way to vary separation selectively for ionic samples. figures 4a-d and 5a-d illustrate the separation of solasodine and solamargine at different ph values when using an ammonium dihydrogen phosphate buffer. as the ph of the buffer was decreased, solasodine was eluted earlier, peaks were sharper and the peak shapes improved compared to those at higher ph. figure 4d shows that at ph 5.5 separation of solasodine worsened and was delayed (rt 10 minutes). the chromatograms in figure 5a-d show that varying ph from 2.5 (a) to 3.5 (b), 4.5(c), and 5.5(d) did little to improve the separation of solamargine. overall, lowering the ph of the mobile phase decreased the retention time of solamargine. the peaks were narrower with buffer ph 2.5 for solasodine and ph 3.5 for solamargine. sana s. al-sinani and elsadig a. eltayeb 4 3.3 effect of molarity of the buffer solasodine was eluted as broad and tailing peaks when no buffer was used (figure 6a, b) as compared to the case when a 100 mm ah2p buffer (ph 2.5) was used. when the mobile phase was buffered, tailing of the recorded peaks was greatly reduced and peaks were eluted earlier (figure 2b-d). increasing the molarity of the ah2p (ph 3.5) from 20 mm to 100 mm increased retention time of solamargine but improved the resolution (figure 7a, b). the use of a buffer helped to reduce the tailing in both solasodine and solamargine. hence an ammonium dihydrogen phosphate buffer (100 mm) was chosen as it produced better separation of both solasodine and solamargine. figure 2. effect of the percentage of the organic solvent on the separation of solasodine at temperature 25 ˚c and flow rate 1 ml/min. meoh:ah2p (ph 2.5100 mm) 70%:30% (b) meoh:ah2p (ph 2.5/100 mm) 80%:20% meoh:ah2p (ph 2.5/100 mm) 75%:25% (c) (d) (a) meoh:ah2p (ph 2.5/100 mm) 60%:40% quantitative analysis of solasodine and its glycoside solamargine 5 figure 3. effect of the percentage of the organic solvent on the separation of solamargine at temperature 25 ˚c and flow rate 1 ml/min. (a) meoh:ah2p (ph 2.5/100 mm) 70%:30% meoh:ah2p (ph 3.5/100 mm) 55%:45% (a) meoh:ah2p (ph 3.5/100 mm) 60%:40% meoh:ah2p (ph 3.5/100 mm) 65%:35% meoh:ah2p (ph 3.5/100 mm) 58%:42% (b) (c) (d) sana s. al-sinani and elsadig a. eltayeb 6 figure 4. effect of the ph of the buffer on the separation of solasodine at temperature 25 ˚c and flow rate 1 ml/min. meoh:ah2p (ph 2.5/100 mm) 65%:35% meoh:ah2p (ph 3.5/100 mm) 65%:35% (a) (b) meoh:ah2p (ph 4.5/100 mm) 70%:30% meoh:ah2p (ph 5.5/100 mm) 70%:30% (c) (d) (b) meoh:ah2p (ph 3.5/100 mm) 70%:30% quantitative analysis of solasodine and its glycoside solamargine 7 figure 5. effect of the ph of the buffer on the separation of solamargine at temperature 25 ˚c and flow rate 1 ml/min. figure 6. effect of using water instead of buffer on separation of solasodine at temperature 25 ˚c and flow rate 1 ml/min. meoh:ah2p (ph 4.5/100 mm) 65%:35% (c) meoh:h2o 65%:35% meoh:h2o 55%:45% (a) (b) meoh:ah2p (ph 5.5/100 mm) 65%:35% (d) sana s. al-sinani and elsadig a. eltayeb 8 figure 7: effect of buffer concentration on the separation of solamargine at different percentages at temperature 25 ˚c and flow rate 1 ml/min. 4. calibration results calibration was performed by injecting solasodine and solamargine standards at levels ranging from 6-800 µg/ml for solasodine and from 25-200 µg/ml for solamargine. the calibration plots for solasodine and solamargine are shown in figures 8 and 9. good linearity of response was found for both solasodine and solamargine, with correlation coefficients greater than 0.9950. meoh:ah2p (ph 3.5/20 mm) 65%:35% meoh:ah2p (ph 3.5/20 mm) 60%:40% meoh:ah2p (ph 3.5/100 mm) 60%:40% (a) (c) (d) meoh:ah2p (ph 3.5/100 mm) 65%:35% (b) quantitative analysis of solasodine and its glycoside solamargine 9 y = 7549.2x + 46888 r² = 0.9969 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 50 100 150 200 250 p e a k a re a i n m il li o n s concentration of solamargine (µg/ml) figure 8. calibration plot for solasodine in the concentration range of 6-800 µg/ml. figure 9. calibration plot for solamargine in the concentration range of 25-200 µg/ml. 5. discussion the chromatographic properties of sgas (solamargine) and their aglycones (solasodine) were evaluated by monitoring their elution characteristics in high performance liquid chromatography (hplc). the results show the importance of a careful choice of the chromatographic conditions for successful lc separation of these compounds. the hplc procedure for quantification of solasodine and solamargine was developed using methanol for the mobile phase. commercial solasodine and solamargine were used as external standards. solasodine is relatively non polar, and virtually insoluble in water but soluble in alcohols and nonpolar solvents such as chloroform and benzene. solamargine is less polar, but, because of the presence of sugars in the glycosides, these compounds have a much greater polarity, which increases as more sugars are attached (crabbe and fryer, 1980). because of the low polarity of the molecules to be separated, reversed phase chromatography was chosen by using a waters association (milford, usa) system with c18 packing (with methanol-buffer, methanol-water, or acetonirilebuffer, acetonitrile-water). in an attempt to detect and quantify solasodine and solamargine in two separate chromatographic runs with isocratic elution, a methanol/ammonium dihydrogen phosphate buffer (ph 2.5/100 mm) solvent system was evaluated initially, since this was found to be the best mobile phase system eluting reproducibly both the sgas and sgaas (crabbe and fryer, 1980; eanes et al., 2008). this study shows that the most appropriate isocratic solvent conditions for the separation of solasodine were 70% methanol: 30% ah2p (ph 2.5/100 mm) buffer, but that 65% methanol: 35% ah2p buffer (ph 3.5/100 mm) was necessary for the elution of solamargine. furthermore, solasodine and solamargine could not be detected at all when different ratios of acn: ah2p buffer (100 mm/ ph 2.5) were used: under these conditions it eluted as broad peaks or could not be reproduced after several injections. the latter results are not consistent with the results of eanes et al., sana s. al-sinani and elsadig a. eltayeb 01 (2008), which used acn as the organic portion of the mobile phase and a c18 nucleosil column. they showed that the best set of isocratic conditions for the separation of solasodine was 60% acn:40% ah2p buffer (100 mm/ ph 2.5), and for solamargine it was 30% acn:70% ah2p buffer (100 mm /ph 2.5). most of the previous studies developed a hplc procedure for quantification of solamargine using acn. kuronen et al.’s (1999) experiments revealed that an acn:25 mm teap buffer (ph 3.0) was the best solvent system eluting reproducibly both sgas and sgaas under both isocratic and gradient elution conditions from silica-based c18 columns. the optimal isocratic solvent conditions were 25-30% acn in a triethylammonium phosphate (teap) buffer (ph 3.0) for the separation of sgas, but for the separation of sgaas 40-60% acn in a teap buffer (ph 3.0) was necessary (kuronen et al., 1999). these results are in agreement with results previously reported by lee et al. (2007) who obtained separation of solanine and solasodine with a reverse-phase column (cosmosil 5c18-ar-ii, 250 mm× 4.6 mm) eluting at a flow rate of 1 ml/min also using acn: teap buffer but with a linear solvent gradient elution from 20 to 70% acn in 20 mins. it must be pointed out that some reported studies on the analysis of sgaas and sgas (eanes et al., 2008; kuronen et al., 1999) assumed that because the weak solvent of the mobile phase was water, acidified to ph 3.0 with 85% orthophosphoric acid, both sgas and sgaas eluted as broad and tailing peaks at varying retention times or even not at all. however, they found that the use of a buffer helped to reduce tailing of peaks in both solasodine and solamargine and the retention times decreased with decreasing the ph of the buffer. these results are consistent with the results of this study. by using a low ph mobile phase, both basic functional groups of glycoalkaloids and acidic silanol groups on the silica support are fully protonated minimizing ionic interactions between them and providing more reproducible separations (kuronen et al., 1999). 6. references carman, a.s., kuan, s.s., ware, g.m., francis, o.j. and kirschenhenheuter, g.p. 1986. rapid high-performance liquid chromatographic determination of the potato glycoalkaloids alpha.-solanine and alpha.-chaconine. j. agricultural and food chemistry, 34(2): 279-282. cherkaoui, s., bekkouche, k., christen, p. and veuthey, j.l. 2001. non-aqueous capillary electrophoresis with diode array and electrospray mass spectrometric detection for the analysis of selected steroidal alkaloids in plant extracts. j. chromatography a, 922(1-2): 321-328. crabbe, p.g. and fryer, c. 1980. rapid quantitative analysis of solasodine, solasodine glycosides and solasodiene by high-pressure liquid chromatography. j. chromatography a, 187(1): 87-100. dinan, l., harmatha, j. and lafont, r. 2001. chromatographic procedures for the isolation of plant steroids. j. of chromatography a. 935(1-2): 105-123. eanes, r.c., tek, n., kirsory, o., frary, a., doganlar, s. and almeida, a.e. 2008. development of practical hplc methods for the separation and determination of eggplant steroidal glycoalkaloids and their aglycones. j. liquid chromatography & related technologies. 31(7): 984-1000. eltayeb, e.a., al-ansari, a.s. and roddick, j.g. 1997. changes in the steroidal alkaloid solasodine during development of solanum nigrum and solanum incanum. phytochemistry, 46(3): 489-494. friedman, m. and dao, l. 1992. distribution of glycoalkaloids in potato plants and commercial potato products. j. agricultural and food chemistry, 40(3): 419-423. jacob, a. and malpathak, n. 2005. plantlet regeneration enhances solasodine productivity in hairy root cultures of &lt;i&gt; solanum khasianum &lt;/i&gt; clarke. in vitro cellular & developmental biology plant, 41(3): 291-295. kreft, s., zel, j., pukl, m., umek, a. and strukelj, b. 2000. non-aqueous capillary electrophoresis for the simultaneous analysis of solasodine and solasonine. phytochemical analysis, 11(1): 37-40. kuronen, p., väänänen, t. and pehu, e. 1999. reversed-phase liquid chromatographic separation and simultaneous profiling of steroidal glycoalkaloids and their aglycones. j. of chromatography a, 863(1): p. 2535. lee, m.-h., cheng, j.-j., lin, c.-y., chen, y.-j. and lu, m.-k. 2007. precursor-feeding strategy for the production of solanine, solanidine and solasodine by a cell culture of solanum lyratum. process biochemistry, 42(5): 899-903. trivedi, p. and pundarikakshudu, k. 2007. novel tlc densitometric method for quantification of solasodine in various &lt;i&gt; solanum &lt;/i&gt; species, market samples and formulations. chromatographia, 65(3): 239-243. weissenberg, m. 2001. isolation of solasodine and other steroidal alkaloids and sapogenins by direct hydrolysis-extraction of solanum plants or glycosides therefrom. phytochemistry, 58(3): 501-508. received 9 april 2013 accepted 21 july 2013 photovoltaic cells and systems: squ journal for science, 16 (2011) 1-12 © 2011 sultan qaboos university 1 environmental aspects of the accelerated urbanization in sana’a, yemen ahmed m. alderwish* and fayad a. alderwish** *department of earth and environmetal science, sana’a university, p.o.box 11903, sana’a, yemen, email: alderwish@y.net.ye,**department of architecture, faculty of engineering, sana’a university, yemen. في صنعاء ، اليمن جوانب بيئية للتمدن المتسارع أحمد الدرويش وفياض الدرويش .الرئٌسٌةِ كل مشروعات التنمٌة فً السائدِة ذات أولوٌة ٌةمشاكل الصحالٌَِجُب أَْن َتُكوَن ِمْن وجهِة نظر بٌئٌِة :ملخص % من السكان 36. الجنوبًه الموزعة من حقل المٌاه المٌاتعقٌم % فقط من السكان. ال بد من 63المؤسسة العامة للمٌاه تزود المستشفٌات، مشارٌع فًمٌاه ذات جودة مثٌرة للتساؤل. التوسع بالالشرب من محطات تنقٌة خاصة تقدم ٌشترون مٌاه وتجنت تدهور تنمٌة حضرٌة مستدامة إلٌجادالخطرة المنتجة. النفاٌاتكمٌات فًٌؤثر والصٌدلٌات والصناعاِت الَبْدء ببرامج إدارة لَتخفٌض أَو َمْنع إنتاج إن مراقبة وتحسٌن إدارة النفاٌات الخطرة.بالبٌئة، ٌجب البدء فورا در/المصا للتعامل مع حةصحٌ ة/بٌئٌةاقتصادٌ ةطرٌقالخطوَة األولى إلى تكونأَو عملٌات أخرى ساالنتاج عملٌاتالنفاٌات أثناء دراك التجنب الكامل إلنتاج نفاٌات ٌجب البحث عن طرق لتدوٌر هذه النفاٌات. ملوثات نه ال ٌمكن إأالنفاٌات الخطرة. وبما كاسٌد تحمٌض الصور، كبرٌت أالهواء الرئٌسٌة بصنعاء تشمل الغبار والمعلقات الجزئٌة الصلبة، أول أكسٌد الكربون، حركة هً الرئٌسة فً صنعاء. انبعاث مصادر التلوث المتإن و الهٌدروكربونات. أكسٌد الكبرٌتالهٌدروجٌن، آمونٌا، المسموح، مما ٌستوجب المراقبة، على األقل فً مناطق االختناقات تتجاوز ن بعض الغازات أالغازات من حرق الوقود ٌبٌن مع تبنى المرورٌة )المزدحمة(. تكامل االهتمام البٌئً مع النمو االقتصادي فً الٌمن ٌجب أن ٌحدث فً مرحلة التخطٌط على تحسٌن الصحة العامة ورفاهٌة السكان لمنطقة المشروع. اإلجراءات المخفّفة التً َتتعلُّق بحماٌِة تكزجابٌة وترطرق اٌ وتحسٌن الصحة العامة ٌجب أن تكون من األهداف األساسٌة عند إجراء تقٌٌم بٌئً للمشارٌع التً تقع ضمن البٌئة الحضرٌةِ مناطق الحضر أو تؤثر على بٌئتها. abstract: from an environmental viewpoint, the prevailing health problems must be a “first priority” in all major development projects. public water supply provides only 36% of domestic water. disinfection of public water supply from the south well field is essential to avoid health problems. about 60% of the drinking water sold by „hygienic‟ stations is of questionable quality. expansion and upgrading in hospitals, pharmacies and industries (waste producers) will have an immediate impact on the amount of hazardous waste that will have to be disposed of. to achieve a sustainable urban development and to avoid environment/resources degradation, care should be taken now to monitor and improve handling and management of hazardous waste. initiating management programs for reducing or preventing the generation of waste during production processes or other operations would mailto:alderwish@y.net.ye ahmed m. alderwish and fayad a. alderwish 2 be the first step to an economically and environmentally sound way of dealing with hazardous wastes. as complete elimination cannot be realized, ways to recycle the wastes should be sought. major air pollutants in sana‟a include dust and spm, carbon monoxide, photochemical oxidants, hydrogen sulfide and ammonia, sulfur oxides and hydrocarbons. the main sources of pollution in the cities are the mobile sources. the emissions of gases from oil consumption are exceeding the permissible level and it is essential that the gases be monitored, at least in the congested areas of the cities. integration of environmental concerns with economic growth in yemen should occur at the planning stage, adopting a positive approach and focusing on improvement in the health and welfare of the residents of the program area. mitigating measures relating to the protection of the urban environment and improving public health must be primary objectives of eia investigation for any upgrading project within urban areas and any other projects impacting on an urban environment. keywords: urban; development; sana‟a; environment; health; water supply. 1. introduction or many observers t he greatest concern is surely the massive increase in the numbers of the urban poor. available data suggest that in a large number of the world‟s poorest countries, the proportion of urban poor is increasing faster than the overall rate of urban population growth, ( un-habitat, 2004). an estimated 72 percent of the urban populations of africa now live in slums, ( un-habitat, 2003). the proportion is 43 percent for asia and the pacific, 32 percent for latin america, and 30 percent for the middle east and northern africa ( un-habitat, 1998). a long-standing urban bias in social infrastructure investments has contributed to the widely held belief in the development literature that living conditions must be far better in large cities than in smaller cities or towns. but with the locus of poverty moving to cities, the longassumed advantages enjoyed by residents of large cities have been called into question, (brockerhoff and brennan, 1998). in addition, the international debt crisis has hit many countries hard, and the implementation of structural adjustment programs in many developing countries has led to a retrenchment of government subsidies and social expenditures that has affected urban residents disproportionately (nrc, 2003). cities throughout the world exhibit an incredible diversity of characteristics, economic structures, levels of infrastructure, historic origins, patterns of growth, and degrees of formal planning. yet, many of the problems that they face are strikingly familiar. the urban population explosion in yemen has created major problems for government agencies responsible for providing adequate facilities to its citizens. a s in other developing countries, urbanization in yemen is so rapid that planners have little time to make provision for this phenomenal growth. sana‟a is one of the fastest growing cities in yemen. rapid industrialization, and consequent demographic changes, have created stress on civic amenities and outstripped the resources of the authorities to provide basic needs such as clean water, as well as posing major challenges for sustainable development. to begin to deal with these challenges will, at a minimum, require accurate assessment of the present situation. this study assesses the current environmental aspects of basic service delivery in the city of sana‟a, assesses the environmental aspects and disease transmission associated with urban development, and discusses urban expansion, including industrial and hazardous waste, and air pollution. natural environmental constraints together with degradation of land and ecosystems are outlined. 2. study area and methods the study is based on the available literature, discussions with concerned officials and observations. for f environmental aspects of the accelerated urbanization 3 the purpose of assessing the current environmental aspects of the sana‟a city, each component has been investigated using an appropriate approach based on the available data and information. for domestic water supply in sana‟a, the public water supply system could not cover all of the urban population. consequently, a private water supply sector developed to fill the gap between the quantity of water supplied by national water and sanitation authority (nwsa) and the city demand. it has developed from a complementary activity into an important economic activity. previous studies conducted in yemen (ace, burns & mcdonnell international, 1993; haskoning, 1991), provide useful background information on the hazardous waste management. several hazardous waste producers and the nature of their waste have been described, without, however, detailed quantitative information on many of the potential hazardous pollutants or the mitigation measures. hazardous wastes being produced within sana‟a area include: waste oil produced by commerce and vehicle servicing, halogenated solvents produced from dry cleaning services, cyanides, f r o m t h e production of polyurethane sponge, acids and alkalis from small laboratories within factories, batteries which are disposed of indiscriminately after use, and sludge from factories which is not dumped locally “near to factories” but probably goes to landfill sites, etc. there is no information on the composition or their quantities of any of these and hence it is difficult to assess how serious their environmental threat is. nevertheless, pollution by hazardous chemicals is very harmful to humans and the environment, even at very low concentration. moreover, these chemicals are very long-lived and very hard to clean up from the environment. for example, if a hazardous contaminant reaches groundwater it will move in the direction of groundwater flow in the shallow aquifer and probably be intercepted in some year‟s time in an area where groundwater is used. to date, there are no monitoring stations for air quality in all o f yemen, consequently air pollutants and their sources have been identified indirectly. emissions of gases were estimated analytically from oil consumption. table 1 shows the consumption of petrol in sana‟a during 2010 and the corresponding emitted gases as well as the permissible level based on world bank guidelines. although these figures are only estimates from the sold oil, they indicate that for some gases the emission is exceeding the permissible level. there is no study in yemen concerning health impacts of these gases. however, studies from other countries indicated that the presence of these gases at high concentration in air might cause several respiratory diseases and lung cancers. table 1. quantities of petrol consumption and emitted gases in the air of sana‟a in 2010 pollutant petrol consumption (liter) nox hydrocarbon spm co sox emission (tones/year) 935,832 17,138 19,993 5,090 171,561 2,214 approx. emission microgram/m3/day 146 171 43 1,468 19 p.l. microgram/m3/day 150 160 50 30 150 source: modified epa‟s reports. the main constraint of the natural environment in sana‟a city is that it is surrounded by a mountainous area. despite being very attractive scenically, the steep bare mountainsides coupled with intensive rainfall of short duration, causes occasional serious damage due to sediment-laden flooding. these special geographic features impose certain difficulties on the design, operation and maintenance of road, storm, and sewage drainage, and hence pose special environmental problems. on the base of a sana‟a urban ecology study conducted in 1993, (norra, 1995), the following areas have been identified as protection and/or ecological improvement areas: wadi al salya, hadda, area east of dar salm, wadi shamlan, wadi dhar, wadi assir, old city gardens, irrigation system water pools out of earth and ahmed m. alderwish and fayad a. alderwish 4 natural stones, and samnah village. all these areas are of relative high biological richness except large areas of wadi al syla. nevertheless, wadi al syla, as an abandoned area, has a high potential to improve the ecological situation in sana‟a. trees are necessary in this area to improve the air quality. nonetheless, forestation should not block the fresh wind lane of wadi al syla by densely planted trees, as it provides fresh air to the entire city. 3. results and discussion 3.1 aspects of water supply the large increases in the numbers of urban residents in the developing world imply that municipal authorities responsible for these sectors face very serious challenges. in many cities, the scarcity of public water supplies forces many low-income urban residents to use other water sources such as private water vendors who charge many times more than the local public rate. consequently, people in slums often must pay much more for lower quality water than other urban residents (satterthwaite, 1997). the supply of water in sana‟a relies fully on the local groundwater resources and all the water comes from three well fields called western, eastern and southern well fields. for the southern well fields most of the water is pumped directly into the distribution network, i.e. without chlorination. an important health implication for pumping water without disinfection has been realized from the incorrect conclusion drawn by (dar al handasah (1999), when they attempted to relate the source of families‟ water supply or their method of sewage disposal to the incidence of diarrhea, intestinal infections, and skin diseases over some areas in sana‟a. it has been found that much better and clearer relationships do exist between the incidence of diarrhea, intestinal infections, and skin diseases, and those areas receiving a public water supply that has not been chlorinated. although the distribution system is equipped with three reservoirs constructed as balancing reservoirs, due to the present imbalance between demand and supply the reservoirs cannot be filled (figure 1). consequently, this has led people to install tanks (below ground surface) to receive and store water. these tanks are not clean and usually have iron sedimentation at the bottom. further, in some of these tanks there are cockroaches, dead mice, algae, etc. private water is provided via numerous small local distribution networks and a large fleet of water tankers (small trucks that can carry about 4m 3 ). it is estimated that the private sector provides about 64% of the water used for domestic purposes in sana‟a, (jica, 2007). so far, no comprehensive study of the private water supply sector had been done. the quality of the water provided by nwsa complies with who standards for safe drinking water. it is doubtful, though, that the quality at the tap can be considered safe. the reason is that the distribution network is operated on a rotational basis and consequently a deterioration of the water quality in the system is most probable. al-hamdi (1994) identifies direct microbiological contamination of the distribution network caused by the temporary depressurization of, and subsequent infiltration of domestic sewage into, the transport pipelines for drinking water. no coliform bacteria were detected in any of the drinking water samples. this was attributed to the retaining of bacteria by soil particles. using data from nwsa files provides a picture that is far from complete because monitoring is not done regularly or comprehensively. there are no nwsa standard requirements for the monitoring of public supply water. it would be a valuable step forward if some moves in this direction could be made as new public supplies as well as the numbers of people served are increasing in number. more investment in laboratory facilities is probably required. the ideal water quality assessment would be based upon a comprehensive set of samples simultaneously and correctly taken across the city, and analyzed by the same laboratory by the same analyst to avoid discrepancies. water samples analyzed from private wells (alderwish and dottridge, 1999; ruseman,1996), indicate that deteriorating water quality exists over a large part of sana‟a city (old city, al-qa‟a, and al-hasaba) as reflected by the high values of ec (2,000 to 4,000 ms/cm). cesspits that drain domestic wastewater to the shallow groundwater aquifer microbiologically pollute groundwater sampled from the quaternary loose deposits. depending on the subsoil conditions, the safe distance between the bottom of a cesspit and the intake level of a well should, for bacteria elimination, be between 75m and 285m. investigations carried out by environmental aspects of the accelerated urbanization 5 sawas technical team on 1995 revealed that distances as short as 7 m frequently occur, (foppen et al. 1996). as a consequence about 85% of the private wells used for domestic water supplies provide “un-safe” (from a microbiological point of view) water for drinking purposes according to who standards. figure 1. public water supply coverage, (dar al-handasah 1999). several private vendors are providing “hygienic” drinking water for about 60% of the urban population. it is being provided through plastic containers of 10 and 20 liters capacity. stations are equipped with various ahmed m. alderwish and fayad a. alderwish 6 water treatment systems, which can include sand filter, chlorinated vessel, reverse osmosis, etc. the quality of the water produced by these stations is very questionable. in 1997, a team from nwsa visited 14 of these stations and concluded that most of the stations are simply cheating the public, and the following was observed: chlorination is not done or it is done improperly, most of purification systems‟ components are not working (left as decoration), ground and pipes to fill containers are not clean, some stations have more than one raw water source, there is no expert technician in any of these stations to follow up the efficiency of the station and the quality of water produced; and finally, to date there is no comprehensive investigation nor regular and proper monitoring for these stations by any public authority. as is the case in the water supply distribution network, sewerage systems are more available to upperand middle-class neighborhoods than they are in poorer neighborhoods, particularly unregulated neighborhoods on the urban periphery. 3.2 industrial and hazardous waste improving public sanitation is another major urban environmental challenge that needs to be immediately addressed in virtually all cities in the developing world, cohen (2006). failure to collect garbage as well as inadequate waste management and recycling policies and practices mean that cities are being inundated by their own waste. similar to the situation of african cities, waste management has been described as „a monster that has aborted most efforts made by city authorities, state and federal governments and professionals alike‟, (onibokun, 1999). industrial and hazardous waste can impact the environment in three principle forms, air pollution, water pollution and solid wastes. although in sana‟a there is some kind of zoning, it seems that it either came too late or it is not strictly enforced as reflected in the presence of industrial sites in the middle of the residential areas and vice-versa. an old large industry, yemen textile corporation factory was established at the boundary of what was then the city. now however it is in the middle of the city. other more recent smaller and medium-scale industries (e.g., small food and soft drink manufacturers) exist within the city. it is understood that there is a plan to move out these small-medium industries fro m the city center. in the following, major hazardous waste producers in sana‟a together with the major media with which the contaminants are associated are briefly described. hospital waste (hazardous and non-hazardous) is generally stored in drums, collected by the municipalities and dumped somewhere on landfills. although public hospitals have their own furnaces to incinerate the waste, only the tb clinic in sana‟a is using its facilities. the number of hospital beds in sana‟a city in 2010 is estimated as 3,146. assuming a similar average solid waste production of 635 kg/year for every hospital bed, ( haskoning, 1991), 2,000 tons/year of hospital waste is generated in sana‟a. these figures are excluding wastes produced by private clinics and private hospitals. it should be noted that, if separation of hazardous waste (pathological chemicals and radioactive waste) from the non-hazardous waste (domestic waste) is carried out at hospitals, the generated hazardous waste quantities from hospitals can be reduced by 90%. the chemical waste from laboratories connected to hospitals, e.g., x-ray departments, blood banks etc. are disposed of into the sewerage system, (about 10 tons/year in sana‟a). among these chemicals, there is cyanide, chromate, phenol and mercury. all are very toxic chemicals. chemicals disposed of in larger quantities are acids, alkalis and methyl blue. major pollution control problems associated with hospitals waste handling are: the potential spread of infections via contamination of workers using poor procedures to handle hospital wastes, and potential contamination of soils, surface waters, and groundwater due to inadequate storage and most probably inadequate disposal of hospital wastes. the amount of pharmaceutical waste is difficult to assess due to the existence of illegally (uncounted) imported medicines. in sana‟a there are 385 pharmacy shops. some of the illegal operators indicate an average annual generation of 20 kg/year of expired medications. an estimate of the amount of pharmaceutical waste in sana‟a indicates that about 53 tons/year is generated including that from suppliers of medicines and the pharmaceutical industry (yedco). major pollution control problems associated with pharmaceutical industries environmental aspects of the accelerated urbanization 7 are potential soil and groundwater contamination brought on by disposal of expired medicines or pharmaceutical process residuals; human health problems may result from ingestion of expired medicines. textile factory waste is one of the worst possible, with hazardous pollutants released to the urban air, water and soil environments. the factory produces 15 million yards of finished textiles annually and produces several thousand cubic meters of wastewater believed to be contaminated with a range of hazardous polyarmotic hydrocarbons, cyanide, heavy metals and paint solvents, together with mineral oil. this mixture is collected in three open drains and, after cursory settlement in four lagoons, is discharged at a point 400 meters north of the factory into a dry stream channel (wadi al syla). some farmers use this water for irrigation, (al eryani et al. 1991). major pollution control problems associated with textile factories besides their hazardous chemicals is the improper waste water management, and the possibility of emitting volatile organic compounds (vocs) as air emissions. the yemen textile corporation factory and its environs need urgent attention with respect to its environmental acceptability and immediate action could be taken by installing properly designed and managed treatment plant to remove the hazardous chemicals before release from the factory. photographic waste includes photo laboratories‟ chemicals that are used to develop films and print photos ( mainly solvents, silver and acids). the total number of photo laboratories is still limited, but is growing. in sana‟a there are 18 labs. the average use of chemicals in labs is 4,000 liter/year, (haskoning, 1991). the total use of chemicals in sana‟a is thus estimated as 81,000 liter/year. the chemicals are, without exception disposed into the sewerage system. the major pollution control problems associated with the photographic, printing and publishing industries are: potential contamination from discharge of untreated wastewater containing printing inks, solvents, silver, and acids, and air emissions of volatile organic compounds, dependent on the types and quantity of ink used by the industry. there are numerous petrol and diesel filling stations existing in sana‟a. although the possibility of leakage of new tanks is small, they may cause environmental risk in the urban areas where slow, longterm leakage of fuel from buried tanks, sufficient to contaminate groundwater to the extent of only 0.1 mg/l, can render the resource unusable for a long time after the leak has been stopped, ( edworthy, 1991). p e o p l e working in these gas stations are unaware of the risk of smoking while filling gas into cars, which indicate improper management. there are no extinguishers in many of these stations. major oil storage tanks, especially where they are located over an aquifer, or adjacent to public water supply facilities should be surrounded by a fuel-tight retaining wall or bund, impounding sufficient capacity to hold the contents of the tank in the event of spillage. the floor of the areas should also be sealed to prevent infiltration of oil. 3.3 air pollution congestion in many large cities can also be extremely severe and air pollution is now a serious environmental concern in many cities (cohen, 2006). concentrations of carbon monoxide, lead, and suspended particulate matter in many large cities greatly exceed world health organization guidelines. major air pollutants in sana‟a include dust and suspended particles, (solid particulate matters (spm)), carbon monoxide, photochemical oxidant, hydrogen sulfide and ammonia, sulfur oxides, and hydrocarbons. several have concentrations exceeding world health organization guidelines. among the greatest environmental health concerns are exposure to fine particulate matter and to lead which contributes to learning disability in young children. emissions from power plants electricity is supplied by three major thermal power plants located in coastal areas. these plants supply a total of 435 mw electricity distributed mainly through a national grid network. in sana‟a there is a standby station that produces 50 mw of electricity. only for dahaban electrical station, located 10 km northwest of sana‟a city center, has an eia been undertaken recently, (carl bro international, 1998). the study showed that the emission concentration contribution of no2, so2 and particles from the station are within the permissible levels, 136, 84, and 20 microgram per cubic meter, respectively. ahmed m. alderwish and fayad a. alderwish 8 sources of solid particulate matter naturally, the central highland of yemen (sana‟a) receives in average 10 dust storms per year, and 100 days of the year are classified as dusty to hazy. the landscape surrounding the cities under consideration are almost devoid of plant cover and consequently rain and wind erosion facilitates the local suspension of solid particulate matters (spm) in the city‟s atmosphere. in sana‟a, the concentration of spm in the air, is increased due to the presence of numerous stone quarries and brick kilns at the city limits. the concentration of spm is further aggravated by vehicle traffic using the unpaved roads within the city. t h e main constituents of spm emitted from vehicles a r e soot, lead, and heavy metals such as v, cr, and ni that are present in the fuel. the estimated production of particulate emission from the use of fuel (benzene and diesel) sold in 2010 in sana‟a corresponds to 5,090.5 tons/yr. it is expected that the concentration of lead in congested parts of the city would be in the range that requires monitoring. the concentration of spm can be noticed visually through the building up of dust and haze during the day wh i c h reaches high concentrations during the afternoon when not washed out by afternoon rains during the rainy seasons. carbon monoxide emissions in general, as heavy vehicle traffic is concentrated in the center of the city, the estimated amount of carbon monoxide emission from fuel is 171,561 tons/year. this estimate, as with the case of spm is believed to be quite conservative since the majority of motor vehicles are old models and badly in need of maintenance. hence, concentration of carbon monoxide in the congested parts of the cities would be in a range that requires monitoring. photochemical oxidants the emission of hydrocarbons and nitrogen oxides, together combined with long periods of sunshine and relatively calm winds, will facilitate the local formation of photochemical oxidants as a secondary pollutant, i.e., ozone, and hence the concentrations of these oxidants warrant observation (table 1). hydrogen sulfide and ammonia the concentration of hydrogen sulfide and ammonia should be monitored in the northern section of the sana‟a city. the source of these gases is the over loaded waste treatment plant located in the north of the city. the noxious odor of these gases is intensified during calm nights in the vicinity of the plant, or spread over a large part of the northern part of sana‟a city as the prevalent wind in sana‟a (civil aviation meteorological authority, cama) is the northnortheastern wind. sulfur oxides the main sources of the sulfur oxides in yemen result from combustion of fuels that contain sulfur, and production and use of sulfuric acid. the estimated amount of sulfur oxides from the combustion of fuel does not exceed 2,214 tons/year. heavy fuel oil does contain higher concentrations of sulfur. nevertheless, it is not expected that sulfur oxide concentration will exceed international limits in the near future. hydrocarbons hydrocarbons play an important role in the formation of photochemical oxidants. the major sources of these pollutants at the present time arise from motor vehicle exhaust and evaporation. the estimated amount of this pollutant in sana‟a from fuel driven motor vehicles is 19,993 tons/year. again this estimation is believed to be conservative due to the abnormal smoke and fumes emitted from car exhaust throughout these cities. using the us epa air pollution emission factor, it is estimated that the amount evaporated from transporting and dispensing this fuel will add about 44,700 tons annually to the air environment of sana‟a. volatile organic compounds (vocs) vocs generators are mainly the textile industries, the printing and publishing industry (dependent on the types and quantity of ink used by the industry), and the petrochemical industry which also emits air toxins. environmental aspects of the accelerated urbanization 9 a popular response to urban transportation congestion problems has been government investment in large-scale public transportation systems such as underground or overland metro systems. less attention has been devoted to expanding and improving public bus networks, which tend to be overcrowded and poorly maintained. in many cities, private mini-bus locals have filled a hole in the market by providing low-cost urban transportation where standard bus routes have proved insufficient. 3.4 natural constraints a nd degradation o f ecosystems sana‟a basin (3,200 km 2 ) is an inter-montane plain located in the central yemen highlands. sana‟a city stands on southern part of the sana‟a plain with elevation of about 2,200 m.a.s.l. and surrounded to the west, south and east by mountains rising to about 3,000 m.a.s.l (figure 2). the vegetation in the urban area was cut by man to build, or as firewood and as rangeland for livestock. virtually no places remain where man has not influenced the vegetation; the vegetation that is found currently is not “natural.” with respect to the fauna in sana‟a cities only a fragmented and incomplete picture can be presented, because very little information on the subject is available for these areas. in conclusion it can be stated that very little is known on flora and fauna of sana‟a. figure 2. elevation map for sana'a basin indicating the basin digital elevation model. ahmed m. alderwish and fayad a. alderwish 10 urbanization trends before 1980, the built-up area of sana‟a city was virtually confined within the inner ring road. at present, the urban area covers about 132 km 2 , almost the total area with the outer ring road (alstaeen street), and two important new urbanizations towards the south (the hadda area). the city must extend to the south because in the north, the international airport, the wastewater treatment plant and important agricultural land all block the city‟s development (figure 3). there are several ongoing urban development problems that may cause ecological problems now or in the future: the extension of free areas (future built-up areas)/planning of neighborhoods, the uncontrolled housing around sana‟a and along wadi al syla, t h e road construction in wadi al syla between marib road and airport road, the 60 m road between the medical faculty and the libyan housing project, the endangering of the tree covered areas around hadda by housing, and the increase of squatter areas. figure 3. analysis of city growth of sana‟a city/ yemen during the last 30 years (zeug et al. 2008). the urban population and the larger merchants form a group of resource users. they look upon the exploitation of groundwater resources and agro industry as investment opportunities. they are no longer closely attached to the land nor do they bear a responsibility towards the other urban people. they have greatly stimulated the introduction of new technologies in yemen, but they have not succeeded in providing a framework for a sustainable profit on their investments. implementing decentralization would probably diminish part of this negative attitude. also it is expected that decentralization of basic services would improve the environmental aspects of these services. for example, if revenue is kept at the branch, instead of sent to the central office, the branch would be able to improve its service by using the surplus of this revenue. preservation of natural areas in sana’a the area near dar salm, in the southeast of sana‟a is covered by many trees, mainly acacia nilotica and schinus molle as well as opuntia ficus indica. a lot of old stone walls can be found in this area. these stone environmental aspects of the accelerated urbanization 11 walls subdivide the whole area into small garden-like sites. the whole area shows no recent maintenance or use except signs of grazing and recreation. this spot is part of the area between the taiz road and the kohlan roads, which might be surfaced in future. therefore the high development pressure of sana‟a will endanger this site. it has to be worked out together with the owners and the residents of dar salm how this area can be preserved asa natural and probably, cultural, monument. 4. conclusion like other large cities in developing countries, impact congestion is very real and is greatly diminishing the quality of life in sana‟a city. the prevalence of private water vendors highlights the high and growing demand for water that is not currently being met by the municipalities, and the trend for the immediate future appears unchanged. questions about water quality, both public and private, and the adverse health effects are cause for serious concern. the immediate introduction of standards for monitoring the quality of public supply of water is a priority. given the adverse economic effect on the poor due to the reliance on private distributors, it is suggested that a comprehensive study of the private water supply sector in the city be undertaken. priority should be given to remedial action programs focusing on community health education, directed at women and children, regarding safe water-handling practices as well as sanitation and hygiene. investigations provide evidence that the present hazardous solid and liquid waste disposal techniques jeopardize the urban environment, public health and quality of groundwater below cities. consequently, to achieve a sustainable urban development, care should be taken now to monitor and improve handling and management of hazardous waste. eias should be conducted for the establishment of all new industry regardless of its scale. initiating management programs for reducing or preventing the generation of waste during production processes or other operations would be the first step to an economically and environmentally sound way of dealing with hazardous wastes. as complete elimination cannot be realized, ways to recycle the wastes should be sought. when reduction or recycling of hazardous wastes prove unsuccessful, treatment of waste will be required and may be done either through incineration or proper storage. given that the main sources of air pollution in the cities are the mobile sources, „the heavy vehicle traffic‟ hopefully will decrease with improved transportation measures. monitoring of air quality, including monitoring of the concentrations of lead and carbon monoxide in congested parts of the cities should take place for health and environmental reasons. more and enforced regulation of vehicles and fuel would help reducing these pollutants. public education regarding solid waste disposal should take place. t o face the problems of possible overdevelopment and the ecological degradation of the sana‟a basin it will be necessary to mark a city border and to restrict housing beyond this line, stop neighborhood planning until the studies on sana‟a future urban development are completed, control unauthorized housing, intensify the development of existing free areas instead of new neighborhoods, and intensify the protection of tree covered areas, wadis, fresh wind lanes and potential recreation areas. solutions to urban problems are increasingly being sought at the local rather than the state or national level. these trends underscore the urgent need to build and support the capacity of local governments to manage the environmental and social service problems that accompany rapid urban growth. 5. acknowledgments the authors acknowledge the contribution of many anonymous persons in this work. 6. references al eryani, m., ba-issa a., alshwibi, y., and ba-bagi, a (editors). 1991. groundwater pollution in the sana‟a basin a preliminary appraisal, environmental protection council, sana‟a. yemen. ahmed m. alderwish and fayad a. alderwish 12 alderwish, a.m. and dottridge, j., 1999. urban recharge and its influence on groundwater quality in sana‟a, yemen. in: groundwater in the urban environment: selected city profiles, volume 21 of the international contribution to hydrogeology, eds. chilton j., a.a. balkem, rotterdam, the netherlands: 85-90. al-hamdi, m., 1994. groundwater pollution due to domestic waste water in the sana‟a city area. msc. thesis no. ee 138, ihe, delft, the netherlands. associated consulting engineers, burns & mcdonnell international 1993. fourth urban development project, municipal environmental component. phase i, final r eport. overview of existing waste management systems. mhup. yemen. brockerhoff, m., and brennan, e., 1998. the poverty of cities in developing regions. popul dev rev; 24: 75-114. carl bro international als., 1998. environmental assessment. second review draft. sana‟a emergency power project. public electricity corporation. roy. cohen, b. 2006. urbanization in developing countries: current trends, future projections, and key challenges for sustainability. technology in society, 28: 63-80 dar al-handasah., 1999. sana‟a 1 e nvironmental impact assessment. sana‟a w ater supply and sanitation project. nwsa, roy. edworthy, k.j., 1991. environmental aspects of water management in northern yemen. technical report. technical secretariat of the high council for water. undp/dtcd project yem/88/001. foppen, j.w., hoogeveen, r., wiesenekker, h., alhaimy, i and ali k.z. 1996. hydrochemistry of the sana‟a basin and microbiology of the groundwater below sana‟a. sawas technical report no. 13. tno/nwsa. haskoning royal dutch engineers and architects., 1991. hazardous waste in the republic of yemen. technical final report. support to the secretariat of the environmental protection council. yemen. jica (japan international cooperation agency). 2007. study for water resources management and rural water supply improvement. water resources management action plan for sana‟a basin. draft final main report. national water resources authority, ministry of water and environment. yemen. kruseman, g.p., 1996. sources for sana‟a water supply (sawas). final technical report and executive summary. nwsa/tno. netherlands/yemen. national research council., 2003. cities transformed: demographic change and its implications in the developing world. washington, dc: national academies press. onibokun, a.g., 1999. managing the monster: urban waste and governance in africa. ottawa: international development research center. satterthwaite, d., 1997. urban poverty: reconsidering its scale and nature. ids bull; 28: 9-23. norra, 1995, 2 nd e d . intermediate work report, sana‟a urban ecology, followup study. mchup/gtz planning assistance for urban development. united nations human settlements programme (un-habitat). 2003. the challenge of slums: global report on human settlements. london: earthscan. united nations human settlements programme (un-habitat) 2004/2005. the state o f the world‟s cities. zeug, g., eckert, s., steiner, u., kukuk, t., and ehrlich, d., 2008. monitoring urban growth and its impact on the environment: the case of sana‟a, yemen. isde conference, 12-14 november, potsdam. received: 25 september 2011 accepted: 31 december 2011 photovoltaic cells and systems: 102-117 squ journal for science, 16 (2011) © 2011 sultan qaboos university 102 dynamical properties of omani crude oils for flow through a vertical annulus and a cylindrical pipe sayyadul arafin* and s.m. mujibur rahman department of physics, college of science, sultan qaboos university, p.o.box 36, al-khoud, 123 muscat, sultanate of oman, *email: sayfin@squ.edu.om. الخواص الديناميكية للنفط العماني الخام عند سريانه عبر أنبوب حلقي أو أسطواني سيد العارفين و الشيخ مجيب الرحمن عتماد الكثافة واللزوجة على درجة الحرارة لعينات من النفط الخام ابالتحقيق في مدى دراسة اية هذه القمنا في بد :خصمل تم استخدام بيانات القياسات في دراسة الخواص الديناميكية لهذه ثم تلفة في سلطنة عمان. مخ هيدروكربونيةجمعت من حقول تحت تأثير الجاذبية والضغوط المختلفة عند درجات حرارة مختلفة. لقد قمنا بنمذجة سريان العينات الهيدروكربونيةالمواقع التقريب النيوتوني لسريان المائع الطبقي وذلك خدامباستالمختلفة لخام النفط عبر أنبوب رأسي )أ( حلقي )ب( أسطواني إليجاد خواص سريان هذه العينات . تم تطوير برنامج حاسوبي بحيث يمكن إعتماد سريان المائع على درجة الحرارة من . 0222وأعلى من 0222أقل من الفصل بين وضع السريان الطبقي ووضع السريان المضطرب بالنسبة ألعداد رينولد ومعدل سريان الكتلة وقوة اللزوجة على السطح الجامد ليست بالجديدة اعتمدت للتشكيل الجانبي للسرعة ماذج التيالن مختلفة؛ aipعينات نفط خام عمانية مع قيم الستخدام)المستحدثة( لكن الحسابات المقدمة في هذا البحث تهدف بالتحديد يناميكية لهذه العينات المحددة في إطار التقريب النيوتوني . يمكن أن تكون قى النتائج المحسوبة الضوء على الخواص الدتونل ذاث فائدة في أغراض مختلفت مثل استخراج النفط الخام ونقله عبر للخواصالخواص الفيزيائية المقاسة والحسابات الالحقة األنابيب. abstract: we have initially investigated the temperature dependence of density and viscosity of a number of crude oils, collected from various hydrocarbon reservoirs in oman. the measured data are then utilized to investigate the flow dynamics of these hydrocarbon fluids under gravity and applied pressures at various temperatures. we have modeled the flow of the various crude oil samples through a vertical (a) annulus and (b) cylindrical pipe all treated within the newtonian fluid flow approximation of a laminar flow to investigate the flow properties of these samples. a computer program is developed so that the temperature dependence of the fluid flow distinctly separates the laminar mode from a turbulent mode with respect to reynolds numbers within the ranges re<2000 and re>2000. the adopted models of the velocity profiles, mass rate of flow and viscous force on the solid surface are not novel, but the present calculations aim to specifically use the various omani crude oil samples with various aip values; the calculated results shed some light on the dynamics of these specific samples within newtonian approximation. the measured physical properties and the subsequent calculations of the relevant dynamical properties might be useful for various purposes e.g. extraction and transportation of crude oils through pipes. keywords: dynamics; flow properties; hydrocarbon fluids; cylinder and annulus. dynamical properties of omani crude oils 301 1. introduction emperature dependence of thermo-physical properties, e.g., densities and viscosities of hydrocarbon fluids plays an important role in many fields of petroleum industries including enhanced oil recovery, oil purification, and transportation of produced fluids (ahmed, 2000). when producing heavy oils, the high viscosity manifests as one of the impediments to recovering these oils from the oil rigs. the temperature dependence of the transport properties influences the relevant flow dynamics, which in turn affect the flow mechanism (li et al. 2004). we present here a model study of the temperature dependence of certain dynamic properties such as velocity distribution, mass rate of flow and viscous force on the solid surface through a vertical annulus and a cylinder. the present investigation primarily aims at understanding the profile of a number of dynamic properties of omani crude oils through a vertical annulus at various temperatures and applied pressures. we may mention that fluid flow through an annulus has wide applications in various branches of science and technology including nuclear reactor engineering, oil and gas production, aero-engines, turbo-machinery, chemical engineering, steam generators and heat exchangers. knowledge of the dynamics of energy flows either in the form of heat transfer or fluid flows through a vertical annulus or normal cylinder under atmospheric and pressurized conditions, can help us understand the re-flooding phenomenon during the emergency cooling in a water-cooled reactor (shiotsu and hama, 2000). it is particularly important in the petroleum industry because annular flow of liquid and gas in a pipeline segregates the material of lighter molecular weight by restricting its flow down the center of the pipe while allowing the material of heavier molecular weight to form a thin film and flow along the pipe wall. the lighter mass fluid or gas can also be in the form of a mist or colloidal suspension known as an emulsion. the interface between the flowing materials may not be entirely precise, and can involve gas and liquid mixtures. it has been suggested (prada and bannwart, 2001) that the use of a core-annular flow pattern may be made attractive as an artificial lift method in heavy oil wells by inducing the flow pattern by the lateral injection of relatively small quantities of water in order to get a lubricated oil core along the pipe. concurrently we have also investigated the flow properties of a number of omani crude oil samples through a vertical cylinder. the research work on vertical upward core flow is nonetheless scanty; particularly, the theme of research on flow dynamics with omani crudes is novel and in its infancy (arafin et al. 2011). however, the works of shertok (1975), bai et al. (1996) and, ho and li (1994) on various samples are worth mentioning here. the prime interest in annular flow is to study the parameters relevant to the transport of fluids through straight pipes whether horizontal or vertical. however, presently, interest in annular flow goes beyond straight pipes to include intersections in pipe line networks, such as t-junctions, where phase segregation is likely to exist (adechy and issa, 2004). we have used here the newtonian fluid approximation relevant only to laminar and linear fluids flows. certainly crude oils are far from newtonian fluids. it is relevant to mention here that the newtonian approximation is highly limited to homogeneous, isotropic and non-compressible systems where stress-velocity gradient relations are non-linear. above all, any non-newtonian fluid has a non-zero term on the right hand side of the momentum-balance equation. consideration of non-newtonian approximation will certainly necessitate the non-linear form of the navier-stokes equation. thus it is apparent that the present approximation yields qualitative results only. thus for a non-laminar and nonlinear case, the situation will be certainly complex, and that will be considered in a future endeavor. in the present investigation, initially, the densities of the samples were measured by using the anton paar density meter (dma 5000) within temperatures from 20°c to 70°c, at steps of 5°c. subsequently, the kinematic and dynamic viscosities for all the samples were measured within this range of temperatures using a state-of-the-art cannon-fenske viscometer. finally, the density and viscosity data were utilized to calculate the velocity distribution, maximum and average velocities of the bulk samples, and their mass flow rate under various thermal conditions. the calculations were constrained by prefixing the reynolds number, re, at 2000, ensuring a laminar flow as suggested by bird et al. (2002). t http://www.springerlink.com/content/7581u35430540303/fulltext.html#cr1 http://www.springerlink.com/content/7581u35430540303/fulltext.html#cr6 http://www.springerlink.com/content/7581u35430540303/fulltext.html#cr3 sayyadul arafin and s.m. mujibur rahman. 301 the layout of the paper is as follows: in section 2 we describe the experimental details for measuring the densities and viscosities of the samples followed by a display of graphical results for temperature dependence of density and viscosity, and we end with fitting formulas. basic model-based formulation for the dynamical quantities is presented in section 3. details of calculated results are presented and discussed in section 4 followed by some concluding remarks in section 5. 2. experimental measurements in this section, we describe the experimental details of measuring the densities and viscosities at various temperatures for all the five samples. 2.1 density measurements at various temperatures we briefly introduce here the classification of the crude oil samples that were procured from different oil fields in oman. the two samples (oman export and receive line) comprising mixtures of crude oils were collected from the petroleum development of oman (pdo). the other three samples were collected from erad field, mabruk field, and zal-41 field located in different regions in oman. we have used the american petroleum institute (api) oil gravity number to classify our oil samples: 0 141.5 131.54 api    (1) here, 0  is the density (g cm−3) measured at temperature 15.6°c and at atmospheric pressure. the api numbers usually vary from 5 for very heavy oils to nearly 100 for light condensates (batzle and wang, 1992). clearly, our samples may be classified into three types. the heavy type is represented by the erad (api = 19.19) sample; to the intermediate type belong the oman export (api = 33.41) and receive line samples (api = 34.13), while the light type consists of mabruk (api = 39.47) and zal-41 (api = 40.89) samples. the densities of the samples were measured by using the anton paar density meter (dma5000) as shown in figure 1. the unit consists of a u-shaped oscillating tube, a system for electronic excitation, frequency counting, and a display. the injected sample volume is kept constant and vibrated. the density is calculated based on a measurement of the sample oscillation period and temperature. the temperature was controlled to ± 0.01°c during the measurement using a built-in thermostat. by measuring the damping of the u-tube’s oscillation caused by the viscosity of the filled-in sample, the instrument automatically corrects the viscosityrelated errors. the anton paar density meter is calibrated to measure density to an accuracy of ± 5 × 10 −3 kg m −3 . this device was used to measure the density in the range of temperature varying from 20°c to 70°c, through temperature increments of 5°c. from the practical point of view, density data of crude oil as a function of temperature provide important information, which is useful for various industrial applications ranging from exploration to refining and transportation. the density data of crude oil were plotted in figure 2. these data can be adequately represented by the equation:  ( ) r r t m t t    (2) where ρr is the density at 20°c, m is the slope of the density versus temperature curve (dρ/dt), t is the temperature (°c), and tr is the room temperature (20°c). http://www.springerlink.com/content/7581u35430540303/fulltext.html#cr2 http://www.springerlink.com/content/7581u35430540303/fulltext.html#fig1 http://www.springerlink.com/content/7581u35430540303/fulltext.html#fig2 dynamical properties of omani crude oils 301 figure 1. anton paar density meter (dma 5000). 20 30 40 50 60 70 780 800 820 840 860 880 900 920 940 r 2 =0.99988 erad r 2 =1 oman r 2 =1 receive r 2 =0.9999 mabruk d e n s it y ,  ( k g m -3 ) temperature, t( o c) erad oman receive mabruk zal-41 r 2 =1 zal 41 figure 2. density versus temperature for various collected crude oils. the error in density, δρ, is 0.005 kg m -3 .the equations for density as a function of temperature obtained by a fitting procedure are written in the form of eq. 2 as follows: erad sample: ( ) 933 . 008 0.638 ( ) r t t t    (3a) oman export sample: ( ) 868 . 980 0.699 ( ) r t t t    (3b) receive line sample: ( ) 851 . 426 0.701( ) r t t t    (3c) mabruk sample: ( ) 824 .645 0.683( ) r t t t    (3d) zal_41 sample: ( ) 817 .772 0.686( ) r t t t    (3e) sayyadul arafin and s.m. mujibur rahman. 301 2.2 viscosity measurements at various temperatures two types of cannon-fenske viscometers, type 350 and 300 with calibration constant 5 × 10 −6 m 2  s −1 and 2.5 × 10 −6 m 2  s −1 respectively, were used to measure the viscosity. a cannon-fenske viscometer type 350, was used to measure viscosity of the erad sample, the heaviest crude among the five samples. for the rest of the crude oil samples, a cannon-fenske viscometer type 300 was used. the working principle of the viscometer is based on the fact that the average velocity of steady flow in a round tube depends inversely on viscosity. the viscometer determines the kinematic viscosity by timing the fluid flow through a capillary tube as it passes between two etched lines on the glass wall. in our experiment, the viscometer was inserted into a constant temperature bath whose temperature was controlled to ± 0.1°c using a haake d8 circulation thermostat. to establish the efflux time, the thermostat was set at a desired temperature and the sample liquid was allowed to fall freely down past an upper mark and the time taken for the meniscus to pass the lower mark was measured. the kinematic viscosity (ν k) was determined by multiplying the measured transit time of the fluid column in seconds with the calibration constant. the error of the viscosity measurement is < 0.35%. the error in the measurement of viscosity is too small to be shown in the plot (figure 3a b). from the figures 3a and 3b, it is clear that the kinematic viscosity decreases exponentially (arrhenius type) as the temperature increases; this correctly reflects the effect of temperature on the crude oil viscosity. from the plot, it is also evident that crude oil samples with lower api values have higher kinematic viscosity. an identical behavior of the viscosities of various omani crude oils has been reported previously (george et al. 2006). the equations of kinematic viscosity as a function of temperature were obtained by exponential fit of the data of various crude oil samples. these are listed as follows: erad: ( /11.98) ( ) 106.12 21384.40 t k t e    (4a) oman export: ( / 23.72) ( ) 3.21 47.46 t k t e    (4b) receive line: ( / 23.88) ( ) 4.66 36.44 t k t e    (4c) mabruk: ( /17.95) ( ) 3.27 26.70 t k t e    (4d) zal-41: ( / 28.6) ( ) 2.05 16.19 t k t e    (4e) the dynamic viscosity, μ(pa s), is determined from the product of kinematic viscosity, ν, and density, ρ (μ = νρ). it is noted that the viscosity of a fluid is highly temperature-dependent. the viscosity of the crude oil decreases exponentially as the temperature increases from 20°c to 70°c. the present results are consistent with the correlation approach (naseri et al. 2005) for prediction of crude oil viscosity. 3. formulation the present study applies only to steady-state flow relevant to newtonian fluids. by steady state flow it is understood that the flow conditions at each point in the stream do not change with time. for this approximation, the momentum balance equation is (bird et al. 2002): 0 in out j j dp dp f dt dt    (5) where pin and pout are the momentum entering into and going out of the system respectively. σfj is the sum of the forces acting on the system. as shown in figure 4, we focus our attention on a region of length l, http://www.springerlink.com/content/7581u35430540303/fulltext.html#fig3 http://www.springerlink.com/content/7581u35430540303/fulltext.html#cr5 http://www.springerlink.com/content/7581u35430540303/fulltext.html#cr7 dynamical properties of omani crude oils 301 sufficiently far from the ends of the wall so that the entrance and exit disturbances are not included in l. this ensures that in this region the velocity component vz does not depend on z. figure 3. kinematic viscosity versus temperature for the: (3a) erad sample and (3b) oman export, receive line, mabruk, and zal-41 samples. zal -41 sample erad sample (low api) sayyadul arafin and s.m. mujibur rahman. 301 3.1 flow through a vertical annulus the flow of fluids in an annulus (figure 4) is encountered frequently in physics, chemistry, biology, and engineering. the laminar flow of fluid in an annulus may be analyzed by means of momentum balance described in the previous section. by considering an incompressible fluid flowing in steady state in the annular region between two coaxial circular cylinders of radii κr and r (figure 4), the equation for velocity profile of bird et al. (2002) can be written with slight rearrangement in the form: figure 4. flow through an annulus. the various forces acting on the top and bottom surface of the annulus.   2 2 2 0 1 1 ln 4 ln l out z out out p p r r r v l r r                            (6) where κ is the ratio of the inner to the outer radius (κ = rin/rout), po is the atmospheric pressure, and r is the distance measured from the outer surface of the inner cylinder to the inner surface of the outer cylinder. the quantity pl represents the combined effect of pressure, pl and the gravitational term (ρgl). μ and ρ are viscosity and density of the fluid respectively. with the help of figure 4 it can be shown that the term (p0 pl ) is the net pressure, δp which can be replaced by δp = δp = paρgl. pa is the applied pressure as shown in figure 4. since ρ is a function of temperature, the net pressure, δp, is a function of temperature as well. the fluid will remain static if the net pressure is equal to zero, which means that the applied pressure, pa at the bottom of the annulus will exactly balance ρgl. since our prime objective is to determine the temperature dependence of flow dynamical properties of omani crude oils 301 properties we express all the relevant equations as a function of temperature through the temperature dependence of μ and ρ. therefore eq. 6 can be written in terms of net pressure as:   2 2 2 1 , 1 ln 4 ln out z out out p r r r v r t l r r                            (7) the second term in the square bracket may be termed as the pipe characteristic function, which at any point along r depends solely on the pipe dimension. eq. 7 works only under the conditions that (i) the fluid is of constant density ρ (incompressible), (ii) the flow is laminar, (iii) the annulus length (l) is very large and (iv) there are no end effects. in fact, at the tube entrance and exit, the flow will not necessarily be parallel everywhere, so the tube surface effect will be ignored (bird et al. 2002). since, we need to know the maximum velocity, the average velocity and the shear stress at a surface we have to know the range of the applied pressure for the flow to be in laminar at a given radius, length, viscosit y and density. in this study we have assumed the flow to be laminar by restricting the reynolds number, re to 2000 and constraining re by the equation (bird et al. 2002):  re 2 1out zr v        (8) where, z v  is the average velocity of the velocity profile, z v given by:       2 8 out z p t r v t b t l     (9) b may be termed the annular constant. it is obtained from the expression:    2 2 1 1 ln b               (10) combining equations (8) and (9) it can be shown that:         2 3 4 re 1 out tl p t r b t       (11) because μ 2 (t) decreases more rapidly with increasing temperature than ρ does, δp will therefore decrease with increasing temperature. substituting eq. 11 in eq. 7 and eq. 9, the expressions for z v and  z v in terms of reynolds number, re, reduce respectively to:          2 2 1re , 1 ln 1 ln z out out out t r r v r t r t b r r                          (12) sayyadul arafin and s.m. mujibur rahman. 330 with         re 2 1 z out t v t t r        (13) both z v and z v  will decrease with increasing temperature because the viscosity decreases more rapidly with increasing temperature than density. although re depends on temperature through ρ and μ, as suggested by eq. 8, we have kept it fixed at 2000 for all temperatures. this will force the average velocity to adjust according to eq. 8. by doing so no generality is lost with regard to the condition for laminar flow. this strategy makes the computation simple and less cumbersome. the mass rate of flow, w is given by (bird et al. 2002):        2 21out zw t r t v t      (14) substituting eq. 13 in eq. 14 one can get:      1 re 2 out r t w t     (15) again, the mass rate of flow, w will decrease with increasing temperature because of the presence of μ in the numerator of eq. 14. by keeping re fixed at 2000, the net pressure, δp, z v , z v  and w have been calculated from eq. 10, eq. 11, eq. 12 and eq. 14 respectively as a function of temperature, t. the viscous force exerted by the fluid on the walls of the annulus, fz, is given by (bird et al. 2002):    2 2( ) 1z outf t r p t    (16) since δp decreases sharply with temperature (eq. 11) at a fixed re, fz is expected to decrease with increasing temperature sharply as well. 3.2 flow through a vertical cylinder the equation of the velocity profile, z v obtained for a laminar flow through a cylindrical tube (bird et al. 2002) is expressed as:   22 ( ) 1 4 o l z p p r r v r l r             (17) where r is the radius of the cylinder. the variable r is the distance measured from the center to the inner wall of the cylinder. the temperature dependence of z v for a cylinder is:   22 ( , ) 1 ( ) 4 z p t r r v r t t l r                        (18) where     0 l ap p p p t gl     . the reynolds number, re for the flow in a cylinder is given (bird et al. 2002) by the equation:       re( ) 2 z t t r v t t      (19) dynamical properties of omani crude oils 333 with,       2 8 z p t r v t t l     (20) figure 5. flow in a vertical cylinder of length l and radius r. the various forces acting on the top and bottom faces of the cylinder are shown by arrows. as in the case of annular flow, we have kept the reynolds number, re, fixed at 2000 for the study of laminar flow in a cylinder as well. following the same derivation procedure as in an annulus, one can show, in terms of re, that the net pressure, δp, average velocity, z v  and velocity profile, z v , for a cylinder can be written as:       2 3 4 re tl p t r t     (21) ( ) re ( ) ( ) 2 z t v t t r      (22) and 2 re ( ) ( ) 1 ( ) z t r v t r t r              (23) and, finally the mass rate of flow,      4 ( ) 8 ( ) a p t gl r t w t t l       can be expressed as sayyadul arafin and s.m. mujibur rahman. 331 re ( ) ( ) 2 r w t t   (24) the viscous force exerted by the fluid on the wall of the cylinder, fz, is given by (bird et al. 2002):     2 z f t r p t  (25) as in the case of an annulus, fz will decrease with increasing temperature in a similar fashion. 4. results and discussions 4.1 vertical annulus the calculated results on dynamical properties of the two extreme samples, namely zal-41 [lightest] and erad [heaviest] samples through an annulus are presented and discussed in this section. the outer radius (rout) and inner radius (rin) of the annulus are 0.5 m and 0.1 m respectively (rin/ rout = κ = 0.2 ) and length, l=50 m. -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 70 o c 70 o c 70 o c 70 o c 20 o c 20 o c 20 o c v e lo c it y p ro fi le , v z ( m s -1 ) distance, r(m) 20 o c zal-41 sample re=2000 (a) -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 40 o c 40 o c 40 o c40 o c 30 o c30 o c 30 o c 30 o c 20 o c20 o c 20 o c v e lo c it y p r o fi le , v z ( m s 1 ) distance r(m) 20 o c erad sample re=2000 (b) figure 6. the velocity profiles for the (6a) flow of light (zal-41 sample) and (6b) heavy (erad sample) crude oils through an annulus at various temperatures. since the velocities [eqs.7 and 9] within the bulk of the fluid depend on the viscosity ( )t , which decreases as the temperature increases, it seems that the profile of ( ) z v t as shown in figure 6 is in contradiction with these equations. but the infused constraint owing to using a fixed reynolds number re = 2000 in eq. 12 and eq. 13, turns back the velocity profile; this is now reflected by the joint effect of )(/)( tt  which essentially decreases with temperature. dynamical properties of omani crude oils 331 20 30 40 50 60 70 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 re=100 re=500 re=1000 n e t p r e s s u r e ,  p ( p a ) temperature, t( o c) zal-41 annulus re=2000 (a) 20 30 40 50 60 70 0 200 400 600 800 1000 re=100 re=500 re=1000 n e t p r e s s u r e ,  p ( p a ) temperature, t o c) re=2000 erad sample annulus (b) figure 7. the net pressure as function of temperature at various reynolds numbers, re for (7a) zal-41 sample and (7b) erad sample. 20 30 40 50 60 70 0 2 4 6 8 10 12 14 16 18 20 re=100 re=500 re=1000 m a s s r a te o f fl o w , w ( k g m s 1 ) temperature, t( o c) zal-41 annulus re=2000 (a) 20 30 40 50 60 70 0 100 200 300 400 500 600 700 800 re=100 re=500 re=1000 m a s s r a te o f fl o w , w ( k g m s 1 ) temperature, t( o c) erad annulus re=2000 (b) figure 8. the mass rate of flow w through an annulus as a function of temperature at various reynolds number, re, values for (8a) light (zal-41) and (8b) heavy (erad) crude oils. the profile of the curves in figure7 can be explained in terms of eq. 11 which clearly demonstrates that for a fixed reynolds number re, the net pressure ( )p t will decay because of the presence of the factor 2 ( ) / ( )t t  which decreases as t increases keeping also in mind that ( )t decreases more rapidly than ).(t the rapid increase of viscosity values at the limit of the low temperature range is also truly reflected zal-41sample annulus erad sample cylinder zal-41 annulus erad annulus sayyadul arafin and s.m. mujibur rahman. 331 accordingly in the ( )p t curves in the figure. concurrently it is also relevant to mention that the results ideally reflect the varying viscous nature of the lightest (zal-41) and heaviest (erad) samples through a rapid variation of the profile of ( )p t at this limit. the profiles of )(tp and w(t) display some similar features; this is primarily because of the presence of the viscosity at the numerators in eq. 11 and eq. 15. 20 30 40 50 60 70 0.0 0.1 0.2 0.3 0.4 0.5 0.6 v is c o u s f o rc e o n t h e s o li d s u rf a c e , f z ( n ) temperature, t( o c) zal-41 sample (light) api=40.89 (a) re=2000 20 30 40 50 60 70 0 100 200 300 400 500 600 700 800 v is c o u s f o rc e o n t h e s o li d s u rf a c e , f z ( n ) temperature, t( o c) erad sample (heavy) api=19.19 re=2000 (b) figure 9. the viscous force, fz, on the walls of the annulus as a function of temperature at reynolds number 2000 for: (9a) light (zal-41) and (9b) heavy (erad) crude oils. owing to the presence of the net pressure ( )p t in the viscous force fz, figure 9 follows the profile of ( )p t as shown in figure 7. -0.10 -0.05 0.00 0.05 0.10 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 70 o c 70 o c 20 o c v e lo c it y p r o fi le , v z ( m s 1 ) distance, r(m) 20 o c zal-41 sample re=2000 (a) -0.10 -0.05 0.00 0.05 0.10 -8 -6 -4 -2 0 2 4 6 8 70 o c 70 o c 40 o c 40 o c 30 o c 30 o c 20 o c v e lo c it y p r o fi le , v z ( m s 1 ) distance r(m) erad sample 20 o c re=2000 (b) figure 10. the velocity profile at various temperatures as a function of the distance, r from the center of the cylinder towards its surface for (10a) zal-41 sample and (10b) erad sample. zal-41sample (light) api = 40.89 re = 2000 erad sample (heavy) api = 19.19 re = 2000 dynamical properties of omani crude oils 331 4.2 vertical cylinder the calculated results on dynamical properties of two extreme samples, namely zal-41 [lightest] and erad [heaviest] samples through cylindrical tubes are presented and discussed in this section. the length and radius of the cylinder are 30 m and 0.1m respectively. 20 30 40 50 60 70 0 5 10 15 20 25 30 re=100 re=500 re=1000 n e t p r e s s u r e ,  p ( p a ) temperature, t o c zal-41 cylinder re=2000 (a) 20 30 40 50 60 70 0 5000 10000 15000 20000 25000 30000 35000 40000 re=100 re=500 re=1000 n e t p r e s s u r e ,  p ( p a ) temperature, t( o c) re=2000 erad sample cylinder (b) figure 11. the net pressure on the fluid samples in a cylinder as function of temperature at various reynolds number re values for: (11a) a zal-41 sample and (11b) an erad sample. figures 10 (a-b) show plots of the net pressure values as a function of temperature for upward laminar flow (re=2000) of zal-41 and erad crude oil samples through a cylindrical pipe. the pipe is 30 m long and has a radius of 10 cm. the net pressure is quite high at low temperatures and decreases sharply up to about 40 o c after which it slowly reduces to zero at higher temperatures. the heavy crude oil (erad sample) which has low api value (19.19) shows a sharp decrease in net pressure in comparison with the light crude oil (zal-41 sample) having a high api value of 40.89. the shape of the curves can be predicted from equation (11) which involves the viscosity term, μ 2 in its numerator indicating that this term decreases more rapidly than the density, ρ in the denominator. the zero net pressure means that the applied pressure, pa should equal the pressure (ρgl) due to the column of liquid in the cylinder. since ρ decreases with increasing temperature, the applied pressure should decrease as well in order to balance the liquid column pressure for no flow through the pipe. pa in general will decrease with increasing temperature for a fixed reynolds number. owing to the presence of the net pressure ( )p t in the viscous force fz, figure 13 follows the profile of ( )p t as shown in figure 11. 5. conclusions we have investigated a few dynamical properties of some omani crude oils through an annulus and a cylindrical pipe of fixed dimensions, in terms of the measured density and viscosity of these samples at various temperatures. the underlying methodology involves a simple model of fluid dynamics based on newtonian approximation applied to laminar flow. zal -41 sample cylinder erad sample cylinder sayyadul arafin and s.m. mujibur rahman. 331 the measured density and viscosity respectively follow the equations:  ( ) o r t m t t    and ( ) t e o t        within the selected range of temperatures. subsequently we have studied the dynamical properties of these samples through an annulus and a finite-dimension cylindrical tube. 20 30 40 50 60 70 0.0 0.5 1.0 1.5 2.0 2.5 3.0 re=100 re=500 re=1000 m a s s r a te o f fl o w , w ( k g s 1 ) temperature, t( o c) re=2000 zal-41 cylinder (a) 20 30 40 50 60 70 0 20 40 60 80 100 120 re=100 re=500 re=1000 m a s s r a te o f fl o w ,w ( k g m s 1 ) temperature, t( o c) erad sample cylinder re=2000 (b) figure 12. the mass rate of flow w through a cylindrical pipe as a function of temperature at various reynolds number re values for: (12a) a light zal-41 sample and (12b) a heavy erad sample. 20 30 40 50 60 70 0 5 10 15 20 25 v is c o u s f o r c e , f z ( n ) temperature, t( o c) zal-41 sample (light) api = 40.89 re = 2000 (a) 20 30 40 50 60 70 0 5000 10000 15000 20000 25000 30000 v is c o u s f o r c e , f z ( n ) temperature, t( o c) erad sample(heavy) api=19.19 -500 (b) figure 13. the viscous force fz on the walls of the cylinder as a function of temperature at reynolds number 2000 for: (13a) light (zal-41) and (13b) heavy (erad) crude oils. zal -41 sample cylinder erad sample cylinder erad sample (heavy) api = 19.19 zal-41 sample (light) api = 40.89 re = 2000 dynamical properties of omani crude oils 331 the investigation of the dynamical properties using simplified models in conjunction with the measured viscosity data sheds some light on the omani crude oil properties. however, we would like to make the following critical remarks in light of the presented findings: (a) the concept of momentum balance used in the formalism is merely an approximation applicable for ideal newtonian liquid. any non-newtonian fluid has indeed a non-zero term on the right hand side of the momentum-balance equation. consideration of non-newtonian approximation will certainly necessitate the usage of the non-linear form of the navier-stokes equation. thus it is apparent that the present approximation yields qualitative results only. (b) the dynamic properties reported in the article have been studied by using simplified models and geometry that have neglected wall and end effects, coarseness and non-linearity. these effects should be looked at using more realistic models and geometry within the realm of a non-newtonian fluid model. (c) the omani crude oils investigated have been treated as isotropic fluids without any inherent phase separation or segregation among components. these effects might be relevant to any investigation of dynamic properties. presently we are working on a project considering the above points. 6. references adechy, d. and issa, r.i., 2004. modeling of annular flow through pipes and t-junctions. computers and fluids, 33: 289-313. ahmed, t. 2000. reservoir engineering handbook. gulf publishing, houston,tx. arafin, s., al-habsi, n. and rahman, s.m.m., 2011. transport properties and model-based dynamical properties of omani crude oils. arab j. geosci. [springer], doi 10.1007/s/12517-011-0301-z. bai, r., kelkar, k., and joseph, d.d., 1996. direct simulation of interfacial waves in a high-viscosityratio and axisymmetric core-annular flow, j. fluid mech, 327: 1-34. batzle, m. and wang, z. 1992. seismic properties of pore fluids. geophysics 57: 1396-1408. bird, r.b., stewart, w.e. and lightfoot, e.n., 2002. transport phenomena. john wiley & sons, new york. george, a.k., arafin, s., singh, r.n. and carboni, c., 2006. a correlation between surface, transport and thermo-elastic properties of liquid hydrocarbon: an experimental investigation. j. phys: condens. matter 18: 3691-3701. ho, w.s. and li, n.n. 1994. core-annular flow of liquid membrane emulsion. aiche j., 40: 1961-1968. li h.-b., wu c. and zheng. y-g., 2004. plane flow model of non-newtonian turbulent stratified flow in wells and pipes. j. pet. sci. & eng. 44: 223-229. naseri, a., nikazar, m., mousavi, s.a. and deghani, a.a.m., 2005. a correlation approach for prediction of crude oil viscosities. j. pet. sci. & eng. 47: 163-174. prada, j.w.v. and bannwart, a.c., 2001. modeling of vertical core-annular flows and application to heavy oil production. transaction of the asme, 123: 194-199. shertok, j.t. 1975. velocity profiles in core-annular flow using a laser-doppler velocimeter. ph.d. thesis, princeton university, department of chemical engineering, princeton, nj. shiotsu, m. and hama, k., 2000. film boiling heat transfer from a vertical cylinder in forced flow of liquids under saturated and sub-cooled conditions at pressures. nucl. engg. design, 200: 23-38. received: 30 october 2011 accepted: 20 november 2011 photovoltaic cells and systems: 34-44 squ journal for science, 16 (2011) © 2011 sultan qaboos university 34 synthesis of highly ordered crystalline wurtzite (zno) membrane for seleniumchromium separation sh. labib and n.a. tadros nuclear chemistry department, hot laboratories center, atomic energy authority, p.o.box 13759, cairo, egypt, email: dr_sh_labib@yahoo.com. تكوين غشاء رقيق من بلورات أكسيد الزنك عالية التنظيم لفصل السيلينيوم والكروميوم تادروس نادية ولبيب شيراز سييٌا احسييٌ ٌكر تثرييصة ٌريي أ سييٌا احرص نييٌ أ سييٌا احرص نييٌ ك يي أهيي ا احث يي حيير ح مييٌ يي فييً :ملخصص ظ كف ح ميٌ ي ك حيف ح ني فً اح لك احهال ً ت ٌر سٌا اححٌحصنٌكر ثصسحراارأ تالة على اعص صة ننع ٌيكا ا اسيصة ثثحيةأ يص نيحظر احك احش (wurtzite)غشٌ اة احتك احثصثة أحر ح مٌ اح كر ك احسٌلٌنٌكر. عنن ي سيٌا أة نسيث جير جسيٌ صة اشغشيٌ اح مي ة ثاٌيصا فيًحيك ظ كجيكا اٌيصاة ك ا . أشع سٌنٌ كاح جه اإلح ح كنً اح صسح احثليك ياٌيصاة ح سيٌ احسيلكف فيً يص ٌكميح احياك اح عيص حهي ا اش سيٌا ) ٌ ك ي 3إحيى 1..5( ي احسٌ ٌكر اح مصف ي . كاح ي كر كاحسيٌلٌنٌكر عنني يحألغشٌ اح م ة. حر ع ا اس نل على رنصئص اح ن حألغشٌ اح رحص ة على اح عيص ح ي ي ك ي ثير نسيحنحل احياك اح ثٌي كثنسيث عصحٌي رص ني ثعنني اح ي كر. ه ه احا اس حر فن عنن احسيٌلٌنٌكر ي ك عنني فيًاحريكاص اح سيص ٌ حألغشيٌ اح مي ة فني عنني احسيٌلٌنٌكر ك فيًش سيٌا احرص نيٌ احرتثيًاحسلكف اح كر رالحهص. abstract: pure zno and composite zno-ceo2 coated thin films on titania substrates were prepared using a chelating sol-gel method under controlled conditions to be used in the separation and/or rejection of se(iv) and cr(vi). xrd and sem studies confirmed the formation of highly ordered arrays of crystalline wurtzite microstructure with mixed orientation. an increase in average particle size of the prepared membranes from 1.25 to 3 µm with increasing ceo2 percent was observed indicating the vital role of ceo2 as secondary phase in improving the crystallinity of the coated films formed. detailed study of the separation performance of the selected membranes toward se(iv)-cr(vi) was studied. a high separation performance for the different membranes prepared was observed toward se(iv) with respect to cr(vi). the polar characteristic of zno thin films played an essential role in se(iv) separation. however, a high permeation flow of cr(vi) through the membranes was governed by the capillary pressure induced within the porous structure of the membranes. keywords: rutile substrate; pure and composite zno membranes; polymeric sol-gel; seiv separation; crvi permeation. synthesis of highly ordered crystalline wurtzite (zno) membrane 57 1. introduction eavy metals discharged into the environment from various industries constitute one of the major causes of water and soil pollution (oboh and aluor, 2008) and in turn, their presence and accumulation have a toxic effect on human, animal and plant life. (oboh and aluyor, 2008). selenium and chromium, as examples of heavy metals, contain undesired properties that affect humans and environments. selenium, when it is present in the form of seleno-proteins, is an essential element to human nutrition. moreover, as inorganic, se(iv), se(vi) and secn are very toxic to wildlife (cafferky et al. 2006). chromium naturally occurring as trivalent cr(iii) is an essential nutrient, necessary to life, while hexavalent chromium cr(vi) is known to be highly toxic; its compounds are highly soluble in water, and carcinogenic in mammals. commercially, cr(vi) is available in the form of potassium chromate and potassium dichromate (jeyasingh and philip, 2005). membrane processes are one of the most efficient methods used to remove toxic elements due to the simplicity in treatment (saffag et al. 2004), higher selectivity and permeability, excellent chemical, thermal and mechanical stability under operating conditions, low maintenance and defect free production (chen, 2002). owing to its specific chemical, surface and microstructural properties, zno has many industrial applications such as the production of adhesive tapes, automotive tires, ceramics, glasses, varistors, gas sensors, saw devices, and catalyst and transparent electrodes (roy and basu, 2002). so, zno is considered to be a promising material to be studied as a ceramic membrane. this paper deals with the preparation of pure zno and composite zno-ceo2 ceramic membranes to remove or separate se(iv) and cr(vi) elements from their aqueous solutions using a chelating sol-gel process (guizard et al.1999). in general the sol-gel process provides a simple method used for the preparation of inorganic membranes with high thermal and chemical stability, controlled microstructure and uniform pore size (srinivasan and kumar 2006; xomeritakis et al.2003). highly crystalline and crack free films of pure zno and composite zno-ceo2 ceramic membranes deposited over porous ceramic substrates were prepared under controlled parameters of processing. separation performance of the optimized pure and composite zno membranes was determined by their higher flux, separation and or rejection toward the toxic elements se(iv) and cr(vi). 2. experimental 2.1 substrate preparation disk rutile substrates of thickness (0.1cm), diameter (10 cm), pore size distribution (0.1-1μm) and porosity (55.8 vol.%) were used for pure zno and composite (zno-ceo2) deposition. these substrates were home made from titania powder [acros rutile powder, 99.5% ,usa]. the starting powder was thermally treated in an air oven at 500 °c for 30 min before any treatments, ground in an agate mortar for 30 min, pressed uniaxially at 12 k.n using p.v.a as binders and sintered at 1200 ° c/1h (labib, 2006). 2.2 membrane preparation pure and composite zno sols were prepared using zinc nitrate hexahydrate [99% merck, germany], cerium (iii) nitrate hexahydrate [99.5% alpha aesar, germany], isopropyl alcohol [99.8% scharlau, spain], acetylacetone [≥ 99% merck, germany] and distilled water. all the reagents used were a.r. grade. the molar ratio of the precursors used and the composition of the samples prepared are shown in table 1. polymeric zinc oxide sol was prepared by drop-wise addition of an alcoholic mixture of isopropyl alcohol (5 mol) and distilled water (0.5 mol) to the stirred alcoholic solution of zinc nitrate and acetyl acetone having molar ratio (isoprop.alc./zinc nitrate /acetyl acetone) 10:0.5:2 respectively. otherwise, the different composite zinc oxidecerium oxide sols were prepared by adding 10, 30 and 50% cerium nitrate to each of the alcoholic solutions of 90, 70 and 50% zinc nitrate, followed by adding acetyl acetone. (isoprop.alc./zinc nitrate-cerium nitrate/acetyl h sh. labib and n.a.tadros 58 acetone: 10:0.5:2). the mixed polymeric sols were prepared by drop-wise hydrolysis with the alcoholic mixture of isopropyl alcohol and distilled water. table 1. optimized precursor's molar ratios and the composition of the different samples. metal salt [m] isopropyl alcohol [m] acetyl acetone [m] distilled water [m] 0.5 15 2 0.5 sample zno % ceo2 % 100z 100 0 90z 90 10 70z 70 30 50z 50 50 the different prepared polymeric sols were stirred vigorously for 20 min. the dip coat process was performed at room temperature by immersing rutile substrates into the different prepared polymeric sols for 24h (immersion and withdrawal rate: 0.5mm/s). after dip coating, the different ceramic membranes were left overnight to dry at room temperature. the prepared membranes as well as the different prepared polymeric sols were then dried at 200 °c/1h with a heating and cooling rate of 4°c/min. the process of dipping, withdrawing and drying was repeated 4 times to obtain a suitable coating thicknesses and to repair any defects in the first coating layer (sekulic et al. 2006). finally, both the supported and unsupported membranes were sintered at 500 ° c/1h with a heating and cooling rate of 4 ° c/min. 2.3 membrane characterization the crystal structures of the different prepared membranes were identified using x-ray diffraction xrd (philips x’pert multi-purpose diffractometer). a copper-tube x-ray tube operating at 40 kv and 30ma was used, and the wavelength kα1used was 1.54056 a°. the scan was performed over the range 2(5-80). the identification of the crystalline phases present was done using the jcpds database cards. the microstructures and coating thicknesses of the prepared membranes were studied using a scanning electron microscope sem (jeol jem-1200 ex ii, made in japan). prior to sem analysis the samples were sputtered with a thin layer of gold using jeol fine coat model jfc-1100e ion sputter. 2.4 membrane performance studies the most suitable membranes were selected for the separation of the mixed and individual selected heavy metals (sei(v) and cr(vi) from their solutions. synthetic solutions of 100, 50 and 10 ppm of both se(iv) and cr(vi) were prepared from selenium oxide (99.9% sigma-aldrich, germany) and potassium dichromate (99.5% adwic, egypt) respectively. the separation experiments were conducted at room temperature under atmospheric pressure, and the selected membranes of an area 0.0314 m 2 were placed inside a home-made cross flow tubular filtration apparatus made from glass. the cross flow tubular filtration apparatus was adjusted in the vertical position such that the ceramic membranes could be held inside its inner diameter as marked by the grey arrow in figure 1. this position allowed a uni-directional flow of the feed solution from the ceramic support toward the external ceramic membrane surface. after each run, the membranes were washed several times with distilled water and isopropyl alcohol. the separation permeability of the ceramic membranes was determined in terms of rejection coefficient r or separation coefficient s that was calculated as a percentage according to eq, (1) (yang et al.1998): s = (1-cp/cf) x 100 (1) synthesis of highly ordered crystalline wurtzite (zno) membrane 59 where, cp is the heavy metal concentration in the permeate solution and cf is the heavy metal concentration in the feed solution (yang et al.1998). the concentration of the heavy metal in the permeate solution was measured using an atomic absorption spectrophotometer (ms spect. soolar aa, england). also, the fluxes j of the membranes were determined using eq. (2) (idris and zain, 2006): j = v/a.δt (2) where, v is the permeate volume (l), a is the membrane area (m 2 ) and δt is the permeation time (hour) (idris and zain, 2006). figure 1. cross flow tubular filtration apparatus used in the separation experiments. the selectivity coefficient s was defined as the ratio of initial fluxes for heavy metal 1 and heavy metal 2 respectively, as given in eq. (3) (kozlowski et al. 2002): s = jm1/jm2 (3) 3. results and discussion 3.1 structural properties figure 2 shows the xrd patterns of pure zno and composite zno-ceo2 membranes thermally treated at 500 °c/1h. the intensities of the given wurtzite peaks were very low because the films obtained were very thin as shown in the sem investigations given in figure 5. minor diffraction peaks of the wurtzite structure were identified at scattering angles 2(56.83, 62.75, 72.5, 76.79) corresponding to the basal planes (110, 103, 201, 004) respectively. x-ray patterns matched the patterns of polycrystalline wurtzite (jcpds card no. 03-0888) with unit cell parameters, a = b = 3.2489å and c=5.2å (kenanakis et al. 2007). the crystalline rutile phase was identified (jcpds card no. 84-1283) with unit cell parameters, a = b = 4.593å and c = 2.958å respectively. the strongest diffraction patterns of the rutile phase existed at 2(27.5, 36.11, 41.27 and 54.5) corresponding to the basal planes (110, 101, 111, 211) respectively. the sharpness of the diffraction peaks was a reflection of the high ordered domains and this in turn was clarified by the uniform microstructure of the membranes obtained (guizard et al.1999; panda et al. 2008). sh. labib and n.a.tadros 5: as shown in figure 2, there was no peak difference between the different membranes prepared. this was due to the lower coating thickness values of the obtained films as outlined previously. no diffraction peaks of ceo2 phase were observed. ceo2 phase fluorite structure (jcpds card no. 75-0076) was clearly observed in the diffraction pattern of the non-supported membrane (50z) as shown in figure 3. the broadness of the ceria peak is indicative of the presence of smaller size ceria crystallites in the zno matrix, (i.e. nano crystallite ceria particles in the zno matrix) (mishra et al. 2003). figure 2. xrd patterns of pure zno and composite zno-ceo2 membranes thermally treated at 500 0 c/1h. (a) 100z, (b) 90 z, (c)70z and (d) 50 z. figure 3. xrd patterns of non supported-membrane 50z thermally treated at 500 0 c/1h. the jcpds card number of the prepared powder 50z was 36-1451, corresponding to pure zincite, which indicated no impurities in the unsupported membranes. synthesis of highly ordered crystalline wurtzite (zno) membrane 5; 3.2 microstructural studies figures 4 (a-d) show the sem at a magnification power of 1500x of pure zno and composite zno-ceo2 thin films coated over rutile substrates. no variation in particle microstructure was observed in these figures. a continuous hexagonal array of wurtzite particles was shown in the different figures separated by uniform pores. it was observed that no aggregated particles were present. the particle size increased from 1.25μm to 1.56μm with the addition of 10% ceo2, see figures 4 (a-b). a further increase in ceo2% was accompanied by an increase in particle size to 2.3 μm and 3 μm, as shown in figures 4 (c-d) respectively. the increase of grain size can be attributed to the increased ability of ceo2 atoms to move toward stable sites in the lattice of zno leading to the crystallinity improvement (öztaş, 2008). an inhomogeneous grain size distribution was observed in sample 70z, figure 4(c), making it non homogeneous thin film. the average pore diameter values for 100z, 90z and 50z were 0.94, 0.63 and 1.25μm respectively as shown in figures 4 (a, b, d). figures 5 (a-d) show the cross sem of zno membranes thermally treated at 500 0c/1h. the fractured coating thicknesses of the different films were very thin and uniform confirming that the bonding strength between the film and the substrate was strong (hwang et al.2005). the coating thicknesses of the different zno films deposited were found to be 375 nm for 100z, 1071 nm for 90z, 1428 nm for 70z and 1785 nm for 50z. the increase of the different films coating thickness with increasing ceo2% means that a fundamental factor impacting the grain size is the increase of coating thickness leading to the decrease of micro-strain and energy band gap in the coated films (öztaş, 2008). figure 4. sem of zno membranes thermally treated at 500 0 c/1h (a) 100z, (b) 90 z, (c) 70 z and (d) 50 z. 3.3 seiv-crvi separation characteristics the separation studies of se(iv) and cr(vi) were performed on the three different membranes 100z, 90z and 50z. high separation rate of se(iv) values of 80-90% were obtained through the different membranes as sh. labib and n.a.tadros 64 outlined in table 2. however very low percentages of cr(vi) separation were observed through the different membranes. slight differences in the separation percentage from one membrane to another were due to the characteristic atomic configuration of wurtzite crystal structure, which possesses crystal polarity (jang at al, 2005; ban et al. 2007). this polarity played an important role in selenium separation, leading to strong interaction between se particles and zno surface charge (saffag et al. 2004). as concluded, the membrane surface charge was significant to the membrane performance, because it affected the electrostatic repulsion between the ions or charged molecules and the membrane surface (childress and elimelech, 2000). on the other hand, the high rejection rate of cr(vi) through the different membranes was governed by the capillary pressure induced within the porous structure of the membranes (guizard et al. 2002). figure 5. cross sem of zno membranes thermally treated at 500 0 c/1h, magnification 2500 x, (a) 100z, (b) 90 z, (c) 70 z and (d) 50 z. with a mixture of 100 seiv-50 cr(vi), a 100% separation rate of se(iv) and a 100% flow rate of cr(vi) were observed through the different membranes, as shown in figure 6. this was due to the increase in the membrane separation performance with the decrease in the effluent concentrations. figure 7 shows a decrease in se(iv) and cr(vi) flux through the different membranes as a function of se(iv) and cr(vi) concentrations. this decrease is explained as follow: the higher the concentration, the higher the osmotic pressure and the lower the permeation flux (saffag et al. 2004). permeation flux must be proportional to the reciprocal of the membrane thickness, but for a very thin layer, the flux doesn't vary with the thickness of the layer (byun, 2009). in this case, the flux is controlled by the kinetics of transport through the porous structure and / or the surface exchange reaction (byun, 2009). thus the lowest values of se(iv) flux through the different membranes with respect to cr(vi) flux were related to the higher separation coefficient of se(iv) in comparison to cr(vi) as given previously. cr(vi) flux increased with increasing membrane pore diameter as shown in figure 7b, where the flux order was 50z > 90z > 100z, meaning that wider pore diameter had lesser resistance to cr transport and so higher flux synthesis of highly ordered crystalline wurtzite (zno) membrane 64 value. this result confirmed that the transport of cr(vi) through the different membranes was by the capillary pressure induced within the porous structure of the membranes as outlined before (guizard et al. 2002). the selectivity coefficients for the competitive transport of cr(vi) and se(iv) from the prepared aqueous solutions through the membranes used are given in table 3. the decrease of the selectivity coefficient values for the competitive ions with increasing their concentrations is due to the lower permeation flux at higher concentration (saffag et al. 2004). table 2. se(iv) and cr(vi) separation coefficient results obtained with the selected membranes. membrane type average pore diameter (µm) average particle size (µm) heavy metal concentration separation coefficient for se(iv) separation coefficient for cr(vi) 100z 90z 50z 0.94 0.63 1.25 1.25 1.56 3.0 100 ppm 90-92% 2-10 % 100z 90z 50z 50 ppm ≥ 86% 0.12 % 100z 90z 50z 10 ppm 82-86% 0.1-2 % figure 6. performance of zinc oxide membranes toward 100se(iv)-50cr(vi). the highest selectivity was obtained through the synthesized membrane 90z. this result is mainly due to its having the narrowest pore size of 90z with respect to the other membranes as shown in table 2. sh. labib and n.a.tadros 64 figure 7. variation of flux of a se(iv) and b cr(vi) through different membranes as a function of se(iv) and cr(vi) concentrations respectively. 4. conclusion the objective of this study was to prepare pure zno and composite zno-ceo2 membranes with high permeability to be used in the separation and or rejection of se(iv) and cr(vi). highly ordered hexagonal arrays and crack free thin films of zno and zno-ceo2 deposited over titania substrates were prepared using a chelating sol-gel process. the addition of ceo2 to a zno matrix had a great effect on grain size and pore size as well as to the coating thickness of the different films. this result affected the separation performance as well as the selectivity and the flux. a high separation performance for the different membranes prepared was observed toward se(iv) with respect to cr(vi). the higher separation rate of se(iv) was mainly due to the polar characteristic of wurtzite structure. on the other hand, the higher rejection rate of cr(vi) was governed by the capillary pressure induced by the porous structure of the different membranes selected; the membrane 90z, having the narrowest pore diameter, was characterized by the highest selectivity in comparison to 100z and 50z membranes. so, it is concluded that the zno membranes described in this paper show high separation synthesis of highly ordered crystalline wurtzite (zno) membrane 65 performance and can be used with high accuracy in the separation of se(iv) from its aqueous solutions. also, a high separation percentage of se(iv) from cr(vi) can be obtained, leading to the decrease of toxicity of any industrial waste containing se(iv) and cr(iv) heavy metals. table 3. the selectivity coefficient values for the competitive transport of cr(vi) and se(iv) through the selected membranes. membrane type metal ions concentrations (ppm) selectivity coefficient cr(vi) se(iv) 100z 100 100 1.24 50 50 1.10 10 10 1.16 90z 100 100 1.50 50 50 2.60 10 10 4.00 50z 100 100 1.20 50 50 1.40 10 10 1.50 5. references ban, t., sakai, t. and ohya, y., 2007. synthesis of zinc oxide crystals with different shapes from zincate aqueous solutions stabilized with triethanolamine. cryst. res. technol., 42: 849-855. byun, y.ch., 2009. oxygen transport in ba(fe, co, zr)o3-δ. m.sc. thesis, der rheinisch-westfälischen technischen hochschule aachen, germany. cafferky, k.d., richardson, d.d. and caruso, j.a., 2006. icp-ms speciation analysis: three roles of selenium spectroscopy, 21: 18-24. chen, j.ch., 2002. evaluation of polymeric membranes for gas separation processes: poly (ether-b-amide) pepax block copolymer” m.sc. thesis, waterloo university, ontario, canada. childress, a.e. and elimelech, m., 2000. relating nanofiltration membrane performance to membrane charge (electrokinetic) characteristics. environ. sci. technol., 34: 3710-3716. guizard, c.g., julbe, a.c. and ayral, a., 1999. design of nanosized structures in sol-gel derived porous solid. j. mater. chem., 9: 55-65. guizard, c., ayral, a. and julbe, a., 2002. potentiality of organic solvents filtration with ceramic membranes. a comparison with polymer membranes, desalination, 147: 275-280. hwang, k.s., jeon, y.s., kang, b.a., nishio, k., tsuchiya, t. and kor, j., 2005. crystallinity, surface morphology and optical properties of nanocrystalline zno films prepared with a metal naphthenate. phys. soc., 46: 521-526. idris, a. and zain, n.m.j., 2006. effect of heat treatment on the performance and structural details of polyethersulfone ultrafiltration membranes. teknologi, 44: 27-40. jang, k.w., minegishi, t., suzuki t., hong, s.k., oh, d.c., hanada, t., cho, m.w. and yao, t., 2005. control of crystal polarity of zno and gan epitaxial layers by interfacial engineering. ceram. proc. res., 6:167-183. jeyasingh, j. and philip, l., 2005. bioremediation of chromium contaminated soil: optimization of operating parameters under laboratory conditions. j. hazard. mater, b118: 113-120. sh. labib and n.a.tadros 66 kenanakis, g., androulidaki, m., koudoumas, e., savvakis, c. and katsarakis, n., 2007. photoluminescence of zno nanostructures grown by the aqueous chemical growth technique. superlattices and microstructures, 42: 473-478. kozlowski, c., apostoluk, w., walkowiak, w. and kita, a., 2002. removal of cr (vi), zn, and cd ions by transport across polymer inclusion membranes with basic ion carriers physicochemical. problems of mineral processing, 36: 115-122. mishra, b.g., rao, g.r. and poongodi, b., 2003. hydrogen transfer reaction of cyclohexanone with 2propanol catalyzed by ceo2-zno material: promoting effect of ceria. proc. indian acad. sci. 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cyprinodontidae): a microscopic study squ journal for science, 2014, 19(1), 1-7 © 2014 sultan qaboos university 1 the effect of starvation on the liver of aphanius dispar (pisces; cyprinodontidae): a microscopic study taher a. ba-omar*, mariam al-amri, jameela al-belushi and reginald victor department of biology, college of science, sultan qaboos university, p.o.box: 36, pc 123, al-khod, muscat,sultanate of oman.*email: taher@squ.edu.om. abstract: stress due to starvation is not an uncommon phenomenon in freshand brackish water fish living in arid environments. this study, a part of a larger investigation on the effects of stress due to starvation on the organ systems of aphanius dispar, a cyprinodont fish in oman, reports on the histopathological changes in the liver, using light and transmission electron microscopy. the hepatocytes showed structural and ultrastructural changes in response to 24, 48, 72 and 96 hours of starvation. the hepatocytes of the starved fish groups were characterized by a reduction in the size of their cells and their nuclei, chromatin condensation, loss of stored glycogen, large lipid droplets, wide intercellular spaces and the variable sizes of their mitochondria. swirls of smooth endoplasmic reticulum (ser) were seen in some of the starved fishes, which may indicate their involvement in lipid metabolism and the breakdown of glycogen. this paper makes a further contribution to the understanding of the physiology of fish in arid zones. keywords: aphanius dispar fish; liver; hepatocytes; ultrastructure; starvation; arid zones. مجهرٌةثٍر التجىٌع على كبذ سمك الصذ: دراسة أت طاهر باعمر، مرٌم العامري، جمٍلة البلىشً و رٌجنالذ فٍكتىر ىحح فٍ اىَناطق اىجافح. اسَاك اىتٍ تؼُش فٍ اىَُاه اىؼذتح واىَجهاد اىناتج ػن اىتجىَغ ظاهزج طثُؼُح ػنذ األَؼتثز اإل ملخص: ستخذاً اىَُنزوسنىب اىضىٍئ إػضاء سَل اىصذ تأوهذه اىذراسح جشء ٍن دراسح ىتىضُح تأثُز اىتجىَغ ػيً تؼض ، 24، 42واىتٍ تذأخ تاىظهىر تؼذ ٍزور ، ىتجىَغ ػيً خالَا مثذ سَل اىصذتىضح هذه اىذراسح تأثُز اىٍ ، وواىَُنزوسنىب اِ ىتجىَغ ، وَتضح هذا اىتغُز ٍن خاله حجٌ اىخالَا واىذٌ تذأ َتقيص وتنثف اىنزوٍاتُن فٍ اىنىي وفقذ تؼضا ساػح ٍن ا 69و 24 تغُز فٍ اَض أتساع اىَسافح تُن خالَا اىنثذ، وتثُن اىذراسح إٍن اىجيُنىجُن وظهىر قطزاخ دهنُح مثُزج داخو اىخالَا اىنثذَح و َض نذوتالسٍا فٍ ػَيُح األألسَاك واىذٌ َذه ػيً ٍشارمح اذوتالسٍا اىناػَح فٍ تؼض األن، مَا تثُن تنذص األ حجٌ اىَاَتىمنذرَا سَاك اىتٍ تؼُش فٍ اىَناطق اىجافح.ػضاء األأوتؼتثز هذه اىىرقح جشء ٍهٌ ىفهٌ وظائف ىيقطزاخ اىذهنُح وتنسُز اىجيُنىجُن. .اىَناطق اىجافحو اىتزمُة اىذقُق اىتجىَغ، سَل اىصذ، اىنثذ، خالَا اىنثذ، مفتاح الكلمات: 1. introduction ish living in the shallow freshand brackish water pools of arid regions have to endure extremely hard environmental conditions. apart from the physical and chemical conditions of the water, biological factors such as food availability exacerbated by intraand inter-specific competition, could cause a level of stress requiring physiological adaptations to survive through periods of starvation of varying duration. these pools are potential breeding grounds for mosquitoes and other disease causing insects and their control primarily depends on the presence of their natural predators. predators that are not capable of adapting to the physical and biological stress will become excluded competitively, and this is undesirable from the perspective of biological control. aphanius dispar (rüppell 1828), a cyprinodont fish, is widely distributed in the fresh and brackish waters of the middle east. it is an important, native bio-control agent of mosquito larvae [1]. it is a robust species that can adapt to a variety of habitats with differing water temperatures and stream flow, and to salinity ranges from that of freshwater to seawater and to other chemical parameters [2,3,1,4]. reductions in food availability in a. dispar habitats can be due to a variety of factors including the physical and chemical conditions of the environment as well as the biological conditions such as primary and secondary production, population size and competition for resources [5]. f the effect of starvation on the liver of aphanius dispar 2 although some hardy fish like a. dispar may physiologically tolerate and adapt to short periods of starvation, detectable histopathological changes in organ systems are likely to occur. during starvation, there is a rapid depletion of energy forcing the animal to use its stored reserves in tissues and cells in order to stay alive [6]. vertebrate liver is a storehouse of glycogen and lipids; it is one of the organs that is primarily affected by starvation. teleost liver cells are sensitive to environmental changes such as those in water temperature, chemical quality and feeding conditions [5]. histological studies describing the structural and ultrastructural changes of the liver in fish stressed by starvation are few. of these, several studies have investigated the biochemical changes in liver tissue during starvation [7,8,9,10,11]. ba-omar et al. [12] studied the anatomy and histology of a. dispar, and investigated the ultrastructural changes in the epithelium of the stomach of a. dispar (cyprinodontidae) due to stress from starvation. here, we present a study of the liver of a. dispar when impacted by starvation using light and transmission electron microscopy. 2. materials and methods adult a. dispar specimens were collected from small fresh-water ponds near sultan qaboos university campus, al khod, in the sultanate of oman. fish were acclimatized in an aerated holding tank for two weeks and were fed with commercial tetramin flakes ad libitum twice daily. an experimental tank with an inner glass visijar was prepared with dechlorinated tap water. after a stabilization period of seven days, 40 fish, measuring from 3.5 6.5 cm, irrespective of sex, were randomly transferred from the holding tank to the outer area of the experimental tank. the feeding regimen for these fish was the same as that for those in the holding tank. the experiment was conducted after another acclimatization period of seven days. at the start of the experiment, 32 fish were randomly transferred to the inner visijar and were deprived of food. the six remaining control fish in the outer area of the experimental tank were fed with commercial tetramin flakes ad libitum twice daily as usual. the water in the inner visijar was replaced with dechlorinated, pre-stabilized water at short intervals to prevent coprophagy. six starving fish were randomly sacrificed at intervals of 24, 48, 72 and 96 hours for histological studies. at the end of the experiment, the six control fish, fed throughout the experimental duration were also sacrificed for histological investigations. the fish were placed in an ice bath and were immediately decapitated. livers were dissected out, cut into small pieces and immediately fixed in karnovsky fixative buffered with sodium cacodylate to ph of 7.4 for four hours at 4 °c. the tissues were washed twice with sodium cacodylate and then kept in this buffer at 4 °c. the tissues were then postfixed in a 1% aqueous solution of osmium tetroxide for 1 hour, dehydrated in a series of graduated concentrations of alcohol and embedded in agar 100 resin. semi-thin and ultrathin sections were cut using an ultramicrotome using glass knives. the semi-thin sections were stained with 1% toluidine blue and the ultrathin sections were stained with super saturated uranyl acetate and lead citrate, and both were examined using a jeol jem-1230 tem. 3. results a. dispar were able to survive food deprivation for over 96 hrs. however, after this time, some experimental fish became lethargic and others became moribund. therefore, the experiments were terminated after the maximum set duration of 96 hours. a. light microscopy semi-thin sections of the normally fed a. dispar showed the general structure of the liver. the liver is composed of a continuous compact layer of hepatocytes which are arranged in rays of cords surrounding the sinusoids and the central veins. the hepatocytes are polyhedral in shape and have round central nuclei (figure 1). figure 1. light micrograph of normally fed a. dispar showing: normal structure of the liver; hepatocytes (arrows); sinusoid (s) and central vein (cv) x400. taher a. ba-omar et al 3 some alterations to the liver structure were seen in the groups of fish starved for 24, 48, 72 and 96 hours (figure 2). these alterations were in the form of vacuolation and degeneration of the liver tissue. the vacuolation and degeneration characteristics started to appear at 24 hours and became progressively more pronounced with the increase in the duration of starvation (figure 2). these characteristics represent necrosis of the hepatocytes. 3.2 transmission electron microscopy the hepatocytes of the normally fed a. dispar showed polyhedral cells with centrally located round or ovoid nuclei. some hepatocytes possessed nucleoli. the rough endoplasmic reticulum (rer) were arranged in parallel stacks of cisternae (figure 3). the rer were seen around the nuclei in some cells and in others they were seen within the boundary of the cell membrane (figure 3). the shape and size of mitochondria varied; some were elongated and others were rounded with well-developed cristae. the mitochondria were usually seen in association with rer (figure 3). in the starved groups, the hepatocytes showed ultrastructural alterations dependent on the duration of starvation. the prominent features in the liver of starved fish (starved for 24, 48,72 and 96 hours) were the condensation of rers around the nuclei and the increase in the quantity of glycogen (figures 4-7). the mitochondria were seen in association with rer and some of these were large and condensed. lysosomes were also present (figures 5b, 7b). figure 3. electron micrograph of the normally fed a. dispar showing: normal nuclei (n), nucleolus (ns), mitochondria (arrows), rough endoplasmic reticulum (rer). figure 2. light micrographs of saved a. dispar fish showing: (a) 24 hr, (b) 48 hr, (c) 72 hr, (d) 96 hr with alterations of the liver structures, vacuolization (arrows) x400. a n n ns b rer rer the effect of starvation on the liver of aphanius dispar 4 n a rer c ser g n g b g rer figure 5. electron micrographs of 48 hr starved a. dispar (a & b) showing: nuclei (n), mitochondria (arrows), rough endoplasmic reticulum (rer), glycogen (g) and lysosomes (ls). figure 4. electron micrographs of 24 hr starved a. dispar (a c) showing: nuclei (n), mitochondria (arrows) rough endoplasmic reticulum (rer), glycogen (g) and swirls of smooth endoplasmic reticulum (ser). b ِ l ِ s g g a n fig. 3: electron micrograph of the normally fed a. dispar showing normal nuclei (n), nucleolus (ns), mitochondria (arrows), rough endoplasmic reticulum (rer). n ls rer g g taher a. ba-omar et al 5 in the starved groups, the hepatocytes showed ultrastructural alterations dependent on the duration of starvation. the prominent features in the liver of starved fish (starved for 24, 48, 72 and 96 hours) were the condensation of rers around the nuclei and the increase in the quantity of glycogen (figures 4-7). the mitochondria were seen in association with rer and some of these were large and condensed. lysosomes were also present (figures 5b, 7b). some hepatocytes were characterized by chromatin condensation and shrinkage of their nuclei, and the presence of vacuoles (figures 4b, 7a). they also had irregular-shaped nuclei with some being shrunken and folded (figures 4b, 7a). some cytoplasmic organelles, such as the mitochondria and ser had a bizarre appearance (figures 4b,7a). some cells had lost contact with their neighbors (figure 7). 4. discussion this histological study looked at the effect of starvation on the liver of a. dispar and showed changes in its structure, both under light and transmission electron microscopy. many empty spaces were observed in light micrographs and this could be correlated to the decrease in the size of hepatocytes or the breakdown of tissue by apoptosis caused by starvation. many fish go through natural periods of starvation and consequently have to overcome starvation using biochemical, physiological, and behavioral strategies [6]. the effects of nutrient depletion during starvation are quite different in each fish organ [8]. segner and moller [14] showed a decrease in the size of the nucleus in the hepatocytes of the olive flounder as a result of starvation. however, these authors also showed that the re-feeding of this fish resulted in the enlargement of hepatocytes and the narrowing of intercellular spaces. figure 6. electron micrographs of 72 hr starved a. dispar (a & b) showing: nucleus (n), mitochondria (arrows), rough endoplasmic reticulum (rer), glycogen (g) and lipid droplets (ld). n rer g ld ld n n b figure 7. electron micrographs of 96 hr starved a. dispar fish (a & b) showing: disintegration of the cytoplasmic organelles and shrinkage of nucleus (n) and intercellular space (arrows), lysosomes (ls) and mitochondria (m). b n ls a a g g m m n the effect of starvation on the liver of aphanius dispar 6 the hepatocytes of a. dispar underwent those ultrastructural changes that have previously been described for other species [14]. widened intercellular spaces are indicative of the decreasing size of some cells, where the diameter of the cell nucleus is reduced. there was also depletion of glycogen and lipid in the cell, condensation of chromatin material and depletion of ribosome-studded er [15,6]. as seen in flounders, the starved a. dispar rapidly lost vitality after 96 hours of starvation. there were stark differences between the starved and fed groups. in the starved groups, cell junctions often were dissolved, except in those complexes surrounding bile canaliculi. this finding indicates metabolic dysfunction and disturbed communication at the tissue level [6]. the effects of starvation on the liver of juvenile flounders showed a decrease in stored products, reduction of endoplasmic reticulum, increased numbers of lysosomes and macrophages, proliferation of collagenous fibers and dissolution of cell junctions [14,6]. the results obtained in our study were similar to findings on the olive flounder in that the size of mitochondria increased due to starvation. additionally, we observed the bizarre appearance of mitochondria and the ser. some hepatocytes showed cell death in the form of necrosis. from these results we can conclude that starvation has an effect on the structure of hepatocytes. it is not uncommon to find large numbers of dead a. dispar in shallow wadi pools in any season. post-mortem examination of the livers from these fish using histology may help to determine if there are other factors which produce similar effects to those of starvation. therefore, future studies should look at the effect of other physical factors like temperature and chemical environment, including salinity, on the hepatocytes of a .dispar. the effect of hazardous substances like pesticides could also mimic the effect of starvation. ba-omar and victor [13] discussed the changes in the intestinal epithelium of a. dispar subjected to starvation and this study adds hepatocytes to the list of cells investigated. studies [16,13,12,17,18] have been steadily adding information on the biology of this small, but ecologically important fish which can serve as a biocontrol agent of mosquito larvae, as a candidate for bioassay in toxicological studies and also as an indicator of environmental impacts in aquatic ecosystems. unfortunately, the introduction of exotic tilapia to natural water bodies in oman is at present posing a serious threat to a. dispar (and also to two other species of freshwater fish) and a premature local extinction of this species is a serious possibility; this may put an end to the accumulation of knowledge on this ecologically versatile eurytopic fish. references 1. haas, r. notes on the ecology of aphanius dispar in the sultanate of oman. freshwater biol., 1982, 12, 8995. 2. lotan, r. sodium chloride and water balance in the euryhaline teleost aphanius dispar (cyprinodontidae). zeits. vergleisch. physiol., 1969, 65, 455-462. 3. lotan, r. osmotic adjustment in the euryhaline teleost aphanius dispar (cyprinodontidae). zeitsr. vergleisch. physiol., 1971, 75, 383-387. 4. plaut, i. resting metabolic rate, critical swimming speed, and routine activity of the euryhaline cyprinodontid, aphanius dispar, acclimated to a wide range of salinities. physiol. biochem. zool., 2000, 73(5), 590-596. 5. storch, v. and juario, j.v. the effect of starvation and subsequent re-feeding on the hepatocytes of chanos chanos. fish biol., 1983, 23, 95-103. 6. hur, j., jo, j.h. and park, i.s. effects of long term starvation on hepatocyte ultrastructure of olive flounder paralichthys olivaceus. ichthyol res.,2006, 53, 306-310. 7. cunnane, s.c. differential utilization of long chain fatty acids during triacylglycerol depletion. ii. rat liver after starvation. lipids,1988, 23(4), 372-374. 8. hung, s.o., liu, w., li, h. and storebaken, t. effect of starvation on some morphological and biochemical parameters in white sturgeon, acipenser transmontanus. aquaculture, 1997, 151, 357-363. 9. kristen, l., wall, k.l. and crivello, j. effects of starvation on liver microsomal p450 activity in juvenile pleuronectes americanus. comp. biochem. physiol., part c: pharm. toxicol. endocr., 1999, 123, 273-277. 10. deng, l., zhang, m., lin, r, christopher, h.k. and cheng, c.h.k. effects of food deprivation on expression of growth hormone receptor and proximate composition in liver of black sea bream acanthopagrus schlegeli. comp. biochem. physiol. part b: biochem. mol. biol., 4224, 137, 21-432. 11. morales, e.a., jiménez, a.b., hidalgo, m.c., abellán, e. and cardenete, g. oxidative stress and antioxidant defenses after prolonged starvation in dentex dentex liver. comp. biochem. physiol., 2004, 139, 153-161. 12. ba-omar, t.a., victor, r. and tobias, d.b. some aspects of the anatomy of and histology of the digestive tracts in two sympatric species of freshwater fishes. squ j. scientific res.sci. & tech., 2003, 8, 97-106. 13. ba-omar, t.a. and victor, r. ultrastructural changes in the epithelium of the stomach of aphanius dispar (cyprinodontidae), due to stress from starvation. squ j. scientific res.sci. & tech., 2000, 5, 1-9. 14. segner, h. and moller, h. electron microscopical investigations on starvation induced liver pathology in flounders platichthys flesus. mar. ecol. prog. ser.,1984, 19, 193-196. taher a. ba-omar et al 7 15. moon, t.w. and johnston, j.a. amino acid transport and inter-conversions in tissues of freshly caught and food-deprived plaice, pleuronectes platessa l. j. fish biol., 1981, 19, 653-663. 16. ba-omar, t.a., victor, r. and tobias, d.b. histology of the stomach of aphanius dispar (ruppell 1828), a cyprinidont fish, with emphasis on change caused by stress from starvation. trop. zoo., 1998, 11, 11-17. 17. ba-omar, t.a., al-jardani, s. and victor, r. effects of pesticide temephos on the gills of aphanius dispar (pisces: cyprinodontidae). tissue and cell, 2011, 43, 29-38. 18. al-ghanbousi, r., ba-omar, t.a. and victor, r. effect of deltamethrin on the gills of aphanius dispar: a microscopic study. tissue and cell, 2012, 44, 7-14. received 1 may 2013 accepted 3 november 2013 squ journal for science, 2020, 25(1), 10-16 doi:10.24200/squjs.vol25iss1pp10-16 sultan qaboos university 10 nutrient content, in vitro ruminal fermentation characteristics and antimethanogenic potential of three algerian asteraceae species serine amokrane 1 *, rabah arhab 2 , serina calabro 3 , raffaella tudisco 3 , and federico infascelli 3 , moufida aggoun 4 1 biotechnology research center (c.r.bt), biotechnology and environment division, ali mendjli, nouvelle ville, uv 03 bp e73 constantine, algeria; 2 natural and life sciences department, exact sciences and natural and life sciences faculty, larbi ben m’hidi university, oum el bouaghi, algeria; 3 department of veterinary medicine and animal production (dmvpa), university of napoli federico ii, via f delpino 1, 80137 napoli, italy; 4 nutrition, food and agri-food technologies institute (inataa), mentouri brothers university, constantine, algeria.*email: s.amokrane @crbt.dz-am. abstract: the in vitro rumen fermentation parameters and the antimethanogenic potential of three asteraceae species: chamaemelum nobile, centaurea pulata and chrysanthemum segetum were determined. serum bottles containing 200 mg of each plant and 30 ml of the culture medium (artificial saliva plus rumen juice) were incubated for 24 h. after incubation, ph, volatile fatty acid (vfa), ammonia (nh3) and methane (ch4) productions were recorded. methanogens and protozoa were quantified using a real time pcr technique (qpcr). cumulative gas productions, in vitro organic matter digestibility and vfa were not significantly affected by the added species when compared to the control (p > 0.05). the effects of chamaemelum nobile and chrysanthemum segetum on methane production, nh3 and acetate to propionate ratio (c2:c3) were similar. the two species were able to modulate rumen fermentation to produce significantly lower ch4 concentrations (-24.3% and -27.1%, respectively) compared to the control. c.pulata produced the highest cumulative gas and stimulated the microbial metabolism with an increase in c2:c3 ratio, nh3 and methane production (p < 0.05). no significant effect of the three species on methanogenic archaea and protozoa was registered (p > 0.05). the three species studied herein show a good potential for mitigating ruminal methane production without any undesirable effects on the main fermentation parameters. keywords: asteraceae; achaea bacteria; gas production; methane; protozoa and ruminal fermentation. المحتوى الغذائي، خصائص تخمر الكرش المخبري و اإلمكانات المضادة إلنبعاث الميثان لثالثة أنواع أستراسيا جزائرية يليانفيس، سيرينا كالبروا، رافييال توديسكو و فيديريكو ونقع أرحاب، موفيدا ابحر، أمقران سيرن تم اختيارها عموما لوفرتها في chrysanthemum segetumو chamaemelum nobile ،centaurea pulata : اأسترا سي نواعأ ثالثة :صلخمال تم حضن زجاجات المصل الحاوية .ستخدام تقنية إنتاج الغاز المخبريإنبعاث الميثان بالمراعي الطبيعية شرق الجزائر لتقييم إمكاناتها الغدائية و المضادة إل تم قياس معدل الحموضة ،ساعة. بعد ذالك 02 لمدةصطناعي و عصير الكرش( مل من الوسط الغذائي )اللعاب اإل 02مغ من كل نبتة مع 022ل وقت ال pcr تقنيةباالعتماد على بكتيريا الكرش المنتجة للميثان و البر وتوزواالميثان. تم تحديد كمية ، إنتاج الغاز ومونيااأل ،االحماض الدهنية المتطايرة، .الحقيقي p)حماض الدهنية المتطايرة بشكل ملموس في األنواع المضافة مقارنة بالمرجعنتاج األ، وإالهضم المخبري للمادة العضوية ،لم يتأثر إنتاج الغاز التراكمي كان . البروبيونات نفسه/مونيا وعلى نسبة الخالتاأل ،على إنتاج الميثان chrysanthemum segetumو chamaemelum nobile.كان تأثير (0.05 < أنتجت (.٪ على التوالي02,1-و 02,0-)القدرة على تعديل التخمر في الكرش إلنتاج تراكيز من الميثان أقل بكثير مقارنة بالمرجعلنفس النوعين c.pulata االمونيا والميثان و البروبيونا/الخالتيض الميكروبي مع زيادة في نسبة الغاز التراكمي و حفزت األ كمية أكثر من(p < 0.05). لم يتم تسجيل تظهر إمكانية جيدة لتخفيف إنتاج نأ هنا المدروسة الثالثة األنواع نأش من(. p> 0.05البر وتوزوا )على البكتيريا المنتجة للميثان وأي تأثير لألنواع الثالثة .مرغوب فيه على معظم العوامل التخمريةيثان في الكرش بدون أي تأثير غيرالم http://crbt.dz/ nutrient content, in vitro ruminal fermentation characteristics 11 الكرش.،البر وتوزوا، الميثان ،إنتاج الغاز ،البكتيريا المنتجة للميثان، ةالعائلة المركب: الكلمات المفتاحية 1. introduction ivestock farming is one of the largest sources of methane emission within the agriculture sector, which accounted for 39% of the sector’s total greenhouse gas (ghg) output in 2011, with an increase from 5.0 gt co2 eq yr -1 in 2000 to 5.3 gt co2 eq yr -1 in 2011. in respect of this fact, and with global demands for milk and meat predicted to double by 2050, global agricultural emissions are expected to increase by 18% and 30% in 2030 and 2050 respectively respectively [1]. methane (ch4) emission from enteric fermentation is not only an important ghg associated with environmental problems, but it is also an energetically (2-15% of ingested gross energy) wasteful process. therefore, reduction in methane emission from ruminants enhances the efficiency of nutrient utilization and the animals’ performance, and reduces the impact of ch4 on global warming and atmospheric pressure. the asteraceae family is one of the largest families of flowering plants, consisting of approximately 1,600 to 1700 genera and over 24,000 species. despite the global distribution of asteraceae plants and their potential use as sources of antimicrobial agents [2], their effect as ruminal antimethanogenic agents is very little investigated. in this context, the present study was conducted to determine the in vitro fermentation characteristics and to test the antimethanogenic action of three plants belonging to the asteraceae family: chamaemelum nobile, chrysanthemum segetum and centaurea pulata. these species were selected for their wide variety of medicinal properties (including antibacterial and anti-inflammatory applications), for their prevalent consumption by grazing small ruminants and for their abundance in wild and cultivated habitats in eastern algeria. their antimethanogenic activity was evaluated by the survey of in vitro methane production, and by methane-forming archaea and protozoa enumeration by qrt-pcr. 2. materials and methods 2.1 sample collection and preparation the aerial parts of chamaemelum nobile (cn), chrysanthemum segetum (cs) and centaurea pulata (cp) (commonly named, roman chamomile, golden daisy and black knapweed, respectively) were harvested between march and june 2012 from a wild population in ibn ziad, located in the north-west of constantine, algeria (36°22'45'' latitude, 6°28'19'' longitude). the samples were washed, air dried in an open area and ground to pass through a 1-mm sieve in a wiley mill (brabender ohg duisburg, germany). the powder was stored in closed jars for chemical analysis and in vitro incubation. 2.2 chemical analysis dry matter (dm; method 934.01), ash (id 942.05) and ether extract (ee; method 920.39c) were determined using aoac procedures [3]. nitrogen (n) was determined according to the kjeldahl method (crude protein cp was calculated as n × 6.25). ndf, adf and adl were determined according to the methods of van soest et al., [4] (ankom 200 technology, fairport, new york, usa). hemicelluloses (hc) and cellulose (c) were calculated as ndf – adf, and adf – adl, respectively. proximate analysis of the control (50% alfalfa hay, 20% ryegrass hay and 30% corn) was also done under the same conditions. all measurements were carried out in triplicate and were presented as the average of three analyses ± standard deviation. 2.3 in vitro rumen fermentation the nutritive value and antimethanogenic potential of the three plants were examined in short term batch incubations using the in vitro gas production technique (ivgpt). the trials were conducted in serum bottles (120 ml capacity). rumen liquor was collected manually from three cows (mw= ± 680 kg) maintained on a standard diet (grass hay: concentrate mixture; 50:50) prior to the morning feeding. the collected inocula were immediately transported to the laboratory in pre-warmed and pre-co2-n2 flushed thermos flasks, where it was strained through muslin cloth and mixed with a buffer medium in the ratio of 1:2 (v/v) as described by menke and steingass [5]. 30 ml of the incubation medium was distributed into each serum bottles containing approximately 200 mg of each plant under a continuous flow of co2 to avoid oxygen contamination and maintain anaerobic conditions. the sealed serum bottles were incubated at 39 ± 0.5 °c for 24h in an orbital incubator (stuart, s1500, uk). under the same conditions, three bottles containing only a buffer-inoculum mixture served as a blank and three flasks containing buffer-inoculum mixture and control diet served as a control. 2.4 fermentation parameters gas pressure accumulated in the headspace of each bottle was recorded, following the reading pressure technique (rpt) as described by theodorou et al., [6], using a manual pressure transducer (cole and parmer instrument co, illinois, usa). total volume of gas (related to incubated organic matter, ml/g) was corrected by subtracting total gas produced in the blank from total gas produced by the tested flasks. methane concentration was estimated using a gas chromatograph (gc-17 a, shimadzu, japan) equipped with a porapack q column (80/100mesh), tcd (thermal l amokrane serine et al 12 conductivity detector) and fid (flame ionization detector) using a certified gas standard mixture of 50% ch4 and 50% co2. gas and methane production were recorded at 3, 6, 9, 12 and 24h post-inoculation. after 24h of incubation, the ph of each media culture was recorded (hanna instruments, inc., woonsocket, rt, usa). individual volatile fatty acids were determined by gas chromatography equipped with packed 15% sp-1220/1% h3po4 on a 100/120 column. 1ml from each bottle was mixed with 1ml oxalic acid (0.06 m), mixed uniformly then centrifuged (at 12,000 g and 4 °c for 10 min). supernatant was collected into appropriate gc vials for vfa analysis. the ammonia was determined by the kjeldahl procedure. for determination of digestibility, the incubation content of each flask was filtered through pre-weighed sintered glass crucibles (schott duran, mainz, germany, porosity # 2) under vacuum. the residues were dried (105 °c for 24h), ashed (550 °c over night) and reweighed. the weight difference between incubated om and the undegraded residue represents the true organic matter digestibility (ivomd, %). the partitioning factor (pf) and microbial biomass yield (mby) were calculated according to makkar [7] and blûmmel et al., [8] equations. the relative (r) antimethanogenic effect was evaluated as mentionned by lópez et al., [9]. 2.5 quantitative real time pcr for methanogens and protozoa quantification total rumen genomic dna was extracted from fermentation liquor using the fast dna spin kit for soil (mp biomedicals, heidelberg, germany) according to the manufacturer’s instructions. for each sample, 1.5 ml aliquot taken from each serum bottle was centrifuged at 12,000 g for 5 min and the supernatant was removed before dna extraction. total microbial dna isolated in duplicate was purified using the silica-based spin tm filter method, and stored at -20 °c until the analysis. nucleic acid concentration was measured by spectrophotometer (nanodrop 2000c, thermo scientific, german) and evaluated by separating 2 μl of each sample on agarose gel in 1x tris-borate-edta buffer (0.8%, w/v). the primer sets for total bacteria were the following: forward: 5′gtgstgcayggytgtcgtca-3′ and r: 5′-acgtcrtccmcaccttcctc-3′ [10]. the primer sets for quantification of methanogenic archaea were targeted against the methyl coenzyme-m reductase (mcra) gene: forward: 5’-ttcggtggatcdcaragrgc-3’ was designed to target the conserved amino acid sequence fggsqr, while the reverse primer 5’-gbargtcgwawccgtagaatcc-3’ targeted the gfygydl conserved amino acid sequence [11]. assays were set up using the sybr ® green pcr master mix (applied biosystems), 300 nm forward and reverse primers, dna template (100 ng), and water to 25 µl, under the following conditions: one cycle of 50 °c for 2 min and 95 °c for 2 min for initial denaturation, 40 cycles at 95 °c for 15 seconds and 60 °c for 1 min for primer annealing and product elongation. the relative quantification of methanogenic archaea was expressed as a proportion of total rumen bacterial 16s rdna according to the equation of denman and mcsweeney [12]: relative quantification = 2 -(ct target ct total bacteria) . for ciliate protozoa enumeration, the primers were targeted against 18s rdna gene: f: 5’gagctaatacatgctaaggc-3’and r: 5’cctcactacaatcgagatttaagg-3’ [13]. 1.2 μl of dna template was used in 30μl, which included 15 μl of sybr® green pcr master mix (applied biosystems),) and 400 nm of each primer. cycling conditions were: 50 °c for 2 min and 95 °c for 8 min, followed by 40 cycles of 95 °c for 15 secondes, 55 °c for 30 s, and 72 °c for 30s, with a final step of 72 °c for 5 min [14]. the qpcr assays were performed on a 7300 real-time pcr system (applied biosystems). each qpcr was done in triplicate. a negative control without the template dna was used in every qpcr assay. 3. statistical analysis the data were analyzed using one way anova in statistical package for the social sciences (ibm spss statistics, version 17.0.0.3, 2009). the minimum significant difference was generated from tukey’s test as the basis of the multiple comparisons among means. the magnitude of correlation between variables was done using pearson’s multiple comparison tests. 4. results and discussion 4.1 chemical composition of the asteraceae species and control the proximate analysis of the three species and the control are reported in table 1. the main constituents of the three tested plants are structural carbohydrates (between 234 and 470 g/kg dm) and nonfibrous carbohydrates (ranging from 282 to 500.9 g/kg dm). the three species are also characterised by their high ash content (between 108 and 139 g/kg dm). according to guimaràtes et al., [15], carbohydrates were the most abundant macronutrients followed by crude protein in c. nobile, and fructose was the most abundant sugar, followed by glucose and sucrose. the crude protein (cp) content varied between the species samples, being particularly high for c. pulata (101 g/kg dm) and c. nobile (94.8 g/kg dm) comparatively to c. segetum (50.5 g/kg dm), which could give them wide nutritional benefits to supplement poor quality nitrogen deficient feedstuffs nitrogen-poor feedstuffs. regarding lipid content, c. pulata and c. segetum showed half the oil content (47.9 and 49.3 g/kg dm, respectively) compared to c. nobile (84.1 g/kg dm). furthermore, the analysis of insoluble dietary fibre content (cellulose, hemicelluloses and lignin) showed that cellulose was the most abundant fraction (373, 239 and 192 g/kg dm for c. segetum, c. nobile and c.pulata, respectively), whereas lignin was less abundant fraction, being two times superior for c. nobile (80 g/kg dm) than for nutrient content, in vitro ruminal fermentation characteristics 13 c. segetum and c. pulata (49 and 36.7 g/kg dm, respectively). chang et al., [16] reported similar data for lignin content but a much lower content of cellulose (101 g/kg dm) in chrysanthemum coronarim (42 g/kg dm). however, our results were not far from those reported for similar species, other asteraceae species and other mediterranean shrubs [15, 17, 18]. the differences observed between authors were probably due to the geographical location, season, and maturity stage of plants sampled. table 1. chemical composition (g kg -1 dm) of the asteraceae species and control diet (means ± sd). substrates control diet c. pulata c. nobile c. segetum dm 908 ± 0.57 936 ± 0.14 939 ± 5.23 932 ± 0.71 ash 60.9 ± 0.28 115 ± 1.56 139 ± 3.82 108 ± 2.55 cp 90.5 ± 0.14 101 ± 0.21 94.8 ±0.21 50.5 ± 3.54 ee 17.9 ± 0.22 47.9 ± 1.20 84.1 ± 1.70 49.3 ± 0.92 ndf 426 ± 0.71 234 ± 0.07 399 ± 5.59 470 ± 5.09 adf 329 ± 0.35 229 ± 5.59 319 ± 7.28 422 ± 0.64 adl 61.6 ± 0.21 36.7 ± 2.69 80 ± 1.20 49 ± 2.69 cellulose (c) 267 ± 0.71 192 ± 2.90 239 ± 6.08 373 ± 2.05 hemicelluloses (hc) 97.5 ± 0.49 5.3 ± 5.66 79.8 ± 12.8 47.2 ± 5.73 nfc 404 ± 0.57 500.9 ± 0.07 282 ± 3.68 321 ± 10.2 dm= dry matter, cp= crude protein, ee= ether extract, ndf=neutral detergent fiber, adf= acid detergent fiber, adl=acid detergent lignin, nfc= non fibrous carbohydrates: [100 – (% ndf + % cp + % ee + % ash)]. 4.2 in vitro gas and methane productions, and true digestibility of the asteraceae species in addition to the broader potential of using plants as feed additives in rumen nutrition illustrated by the accomplishment of the fc framework 5 project “rumen up”, several screening assays have been reported in literature, where a large number of plant species (more than 500 species) have been examined in in vitro batch cultures to study their potential to enhance the fermentation pathway and decrease methanogenesis. for instance, garcía-gonzález et al., [19] have examined more than 150 herbs and species for their potential to enhance ruminal fermentation and decrease ch4 production; these authors identified rheum officinale (rhizomes and roots), frangula alnus (bark) and allium sativum (bulb) as the most efficient in decreasing methanogenesis (more than 20%). in another experiment, the same authors examined frangula alnus and rheum officinale in a rumen-simulating fermenter (rusitec). they concluded that the milled rhizomes of rheum spp. were the most effective in methane abatement without any notable effect on rumen fermentation pattern. similarly, durmic et al., [20] assessed 128 australian woody perennial plants for their potential to enhance fermentation pathways in the rumen, and reported that ch4 production was reduced with the plant species cullen australasicum, enchy-laena tomentosa, eremophila longifolia, maireana astrotricha and templetonia retusa. this favourable effect has been attributed as most likely due to the presence of plant secondary metabolites. in our experiment, the three plants species were chosen because chrysanthemum segetum and centaurea pulata have not been yet investigated regarding their effect on ruminal fermentation pattern and methanogenesis, while a few reports have examined chamaemelum nobile as an additive to reduce methane production in vitro. cumulative gas production (cgp), recorded for the three species after 24h of incubation, was not significantly affected, compared to the control (p > 0.05, tab.2). a low gas production was recorded for c. segetum (108 ml/g iom) and a high one was noted for c. pulata (118.1 ml/g iom). this latter species stimulates methane production. however, c. segetum and c. nobile produced less methane than the control (p < 1% ; 30.1 and 31.1 ml/g iom, respectively). methane concentration in the gas was decreased by greater than 20% when incubating c. nobile and c. segetum in vitro in a ruminal fluid buffer mixture. this reduction was -24.3% and -27.1% for c. nobile and c. segetum, respectively. in the case of these two species, methane represented approximately 27% of the gas pool. furthermore, its production for c. pulata was 8 units higher than c. nobile and c. segetum. the same results were reported by kulivand and kafilzadeh [17]. these authors have studied eight different grasses collected from kermanshah (iran) for their chemical composition, kinetic parameters and antimethanogenic effect and have remarked that chamaemelum nobile is the best grass in terms of nutritive value and antimethanogenic effect (more than 20%). however, our results are inconsistent with those obtained by garcia-gonzalez et al., [19], who did not observe any noticeable effect of chamaemelum nobile flowers on in vitro methane production and other fermentation parameters. the reasons for such inconsistencies are not clear, but we hypothesize that the effect of the phenolic compounds contained in plants prevails over that of the fibre content. therefore, ch4 production was affected due to the effect of these active plant compounds on the metabolic process involved in methanogenesis, either by reducing available metabolic h2 and redirecting it to other sinks and thus limiting the substrate supply for methanogenesis, or by directly inhibiting the enzymes of microbes associated with methanogenesis. amokrane serine et al 14 table 2. in vitro gas and methane productions and true organic matter digestibility of the three species and control. substrates control c. pulata c. nobile c. segetum s.e.m prob. omcv ( mmol/g iom) 5.17 a ± 0.08 5.27 a ± 0.19 5.04 a ± 0.22 4.85 a ± 0.51 0.06 0.13 omcv (ml/g iom) 116 a ±1.99 118.1 a ±4.35 113.1 a ±5.09 108 a ±11.5 1.47 0.13 ch4 (mmol/g iom) 1.85 b ± 0.10 1.87 b ± 0.05 1.38 a ± 0.17 1.34 a ± 0.11 0.05 ˂ 0.0001 ch4 (ml/g iom) 41.4 b ± 2.28 42 b ± 1.20 31.1 a ± 3.83 30.1 a ± 2.55 1.26 ˂ 0.0001 ch4 (mmol/mmol gas) 35.7 b ± 2.40 35.6 b ± 1.87 27.6 a ± 3.94 27. 8 a ± 2.75 0.99 ˂ 0.0001 rˊ (%) 1.74 b ± 6.38 -24.3 b ± 12.3 -27.1 a ±6.91 3.74 ˂ 0.0001 ivomd (%) 44.3 ab ± 0.80 48.1 b ± 1.64 42.8 a ± 5.43 41.7 a ± 3.89 0.02 ˂ 0.0001 pf (mg/ml) 4.89 c ± 0.13 4.42 b ± 0.11 4.07 a ± 0.19 4.48 b ± 0.11 0.07 ˂ 0.0001 mby (mg) 244.5 ab ± 6.94 257 c ± 11.64 206.5 a ± 8.72 226 b ± 6.90 0.01 omcv = cumulative gas production related to incubated organic matter, ch4= methane related to incubated om, ivomd = in vitro true organic matter digestibility, r’= effect of plant on methane production, pf = partitioning factor, mby = microbial biomass yield, s.e.m.= standard errors of means, prob.= probability. means with different superscripts within the same line being significantly different (p < 0.05). the nature, activity and concentration of these secondary moieties have been reported to influence the antimethanogenic activity of various plants additives differently [7, 21, 22]. thus, the reduction in methane production for c. nobile and c. segetum is probably due to the use of the accumulated hydrogen by another metabolic pathway. in this case, it is probably the propionate production pathway because the concentration of this fatty acid is high for both species compared to the control (25.7 and 31.7%, respectively). very limited data are available on the effect of c. segetum, c. nobile and c. pulata phytochemical compounds on rumen fermentation and methanogenesis, amokrane et al., [23] reported the presence of substantial amounts of polyphenols in c. segetum and c. nobile extracts (207.3 and 99.4 g/kg dm, respectively), represented mainly by flavonoids, followed by condensed tannins. hence, this information could indicate that flavonoids contained in the two species may be responsible for the decrease of methane production observed in vitro in our study. the sesquiterpenelactones and flavonoids are the major constituents of centaurea species [24]. the compound or combination of compounds responsible for these effects should be identified using advanced chemical tools to confirm this hypothesis. c. pulata produced the highest cumulative gas and was also characterized by its high ivomd (48.1%) compared to the control (44.3%) and the two other species (p <1%, tab. 2). this indicates that this species is highly fermentable. in addition, this species stimulates ruminal microbiota growth because the microbial biomass yield (mby) was also significantly increased compared to the control (5.1%) and to the other species (19.7% and 12% for c. nobile and c. segetum, respectively). despite the pf at 24h of the tested plant significantly decreased as compared to the control, it remained in the theoretical range (2.75 and 4.41) reported by blümmel et al., [8] for a good microbial synthesis. it is widely recognized that feedstuffs with higher gas production and ivdmd tend to have higher ch4 production per gram dm incubated [25]. in our study, the higher ch4 production with c.pulata was not expected as its high soluble carbohydrate content (500.9 g/kg dm) suggests the promotion of propionate production. our results were inconsistent with those of chaves et al., [26] who indicated in their study that diet quality affected ch4 production in an in vitro study where low concentrations of non-fibrous carbohydrates in both legumes and grasses contributed to a low ivdmd and consequently high ch4 production per gram digested dm. hence, a positive correlation between nfc concentrations and ch4 production was observed (0.796, p ˂ 0.05, results not presented). however, no correlation was registered between ndf content and ch4 production (-0.513, p ˂ 0.05). as speculated above, the presence of secondary metabolites would likely be responsible for these discrepancies. due to its nutritional particularity (especially high cp and ash content) and its high digestibility, c. pulata could have a complementary role for animal feeding and grazing. 4.3 in vitro fermentation parameters and archaea bacteria and protozoa quantification of the three species and the control ammonia production and acetate to propionate ratio were similar for c. nobile and c. segetum (p > 0.05). for both parameters, the highest values were recorded for c. pulata (p <1%, tab.3). the same table shows that c. pulata has the highest concentration of total vfa (5.15 mmol./g om) compared to the control (5.04 mmol./g om), c. nobile (4.85 mmol./g om) and c. segetum (4.76 mmol./g om) although a significant slight decrease in ph was registered for c. pulata. the values are in the optimum range for methane production (7.0-7.2), gas production (6.6-7.6) and all rumen microbiota development [27]. although there was no significant effect of the three species on methanogenic archaea bacteria and protozoa (tab. 3, p > 0.05), the methanogenesis (methane production) declined for c. nobile and c. segetum. in our study no correlation was observed between methane production and methanogens count. however, methane production and the number of protozoa were strongly correlated (0.566, p ˂ 0.01). kamra et al., [21] have confirmed that in the presence of 5 mm of bromoethanesulphonic acid (bes), methanogenesis was completely nutrient content, in vitro ruminal fermentation characteristics 15 inhibited while the number of methanogens assessed by real time pcr was not affected. in addition, zhou et al., [28] have reported using pcr-dgge analysis that the activity of individual species rather than the total number of methanogens has the greatest effect on ch4 production. table 3. in vitro fermentation parameters recorded after 24h of incubation (ph, volatile fatty acids and ammonia productions) of the asteraceae species and control. substrates control c. pulata c. nobile c. segetum s.e.m prob. in vitro fermentation parameters ph 7.08 b ± 0.01 6.98 a ± 0.06 7.07 b ± 0.07 7.06 ab ± 0.02 0.02 0.01 n-nh3 (mg/l) 14.6 b ± 0.40 14.8 b ± 0.73 13 a ± 0.88 12.9 a ± 0.87 0.23 ˂ 0.0001 vfat (mmol/g om) 5.04 ab ± 0.05 5.15 b ± 0.09 4.85 ab ± 0.32 4.76 a ± 0.24 0.05 0.01 acetate (mmol.) 3.09 ab ± 0.10 3.34 c ± 0.12 2.51 a ± 0.69 2.59 a ± 0.37 0.10 0.005 propionate (mmol.) 1.01 a ±0.06 1.04 a ± 0.03 1.33 b ± 0.21 1.27 b ± 0.08 0.03 ˂ 0.0001 butyrate (mmol.) 0.53 a ± 0.09 0.61 a ± 0.06 0.61 a ± 0.05 0.64 a ± 0.08 0.16 0.14 a : p ratio 3.05 b ± 0.26 3.20 b ± 0.21 2.04 a ± 0.23 1.91 a ± 0.19 0.14 ˂ 0.0001 archaea bacteria and protozoa quantification archaea bacteria (× 10 5 cell/ml) 8.47 a 7.51 a 7.59 a 9.03 a 0.247 ciliate protozoa (× 10 3 cell/ml) 3.85 a 4.10 a 3.11 a 3.32 a 0.054 vfa = total volatile fatty acids, nh3 = ammonia production, a: p = acetate and propionate ratio, s.e.m. = standard error of the mean, prob. = probability, means with different superscripts within the same line being significantly different (p < 0.05). 5. conclusion this is the first report on the effect of c. pulata and c.segetum species on ruminal fermentation pattern and ch4 production in vitro. in addition to its nutritional diversity, c.pulata behaved similarly to the control; thus, it could have a supplementary role for animal feeding and grazing. c.nobile and c.segetum were able to successfully modulate rumen fermentation characteristics, and offer potential as antimethanogenic agents without compromising forage digestibility. consequently pasturing of these two species may be a potent strategy to decrease ch4 emissions in algeria. the discrepancy encountered between chemical composition and methane production from in vitro trials suggests further assessment of these species regarding their secondary metabolites contents, although, in most studies, the 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journal for science, 17(2) (2012) 187-199 © 2012 sultan qaboos university 781 local projection stabilization method for incompressible flow problems a.m. essefi* and k. nafa** department of mathematics and statistics, sultan qaboos university, college of science, p.o. box 36, al-khoudh 123, muscat, sultanate of oman, *email:essefi@squ.edu.om and **email:nkamel@squ.edu.om. abstract: this paper analyzes local projection stabilization (lps) methods for the solution of stokes problem using equal order finite elements. their convergence, stability and accuracy properties are investigated. the resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations. two classes of lps methods are distinguished: one-level and two-level methods. numerical examples using bilinear interpolations are presented to validate the analysis and assess the accuracy of both approaches. keywords: finite elements, local projection stabilization, rates of convergence, stability. غير قابلة لالنضغاط الاستقرار طريقة االسقاط المحلي لحل مسائل السوائل اللزجة كمال نافع و ي افعفيفة الس .لعناصر محدودة متساوٌة درجة خدامستباستوكس مسألةلحل وضعًاإلسقاط الم طرقً هذا البحث ف نحلل :ملخص إلى أفضل مستقرة وتؤدي وضعًٌقة اإلسقاط المنبرهن ان طرتها. وخصائص دقتلك الطرق استقرارونتحرى تقارب مستوى واحد واثنٌن. نصف ذات اسقاطاتفٌن من الطرق: نصنمٌز بٌن نسب للتقارب سواء بالنسبة للسرعة أو للضغط. للتحقق من صحة التحلٌل وتقٌٌم مدى دقة كال النهجٌن.استقراءات شبه خطٌة أمثلة عددٌة باستخدام 1. introduction umerical approximations of incompressible flows require a compatibility condition between the discrete velocity and pressure spaces (girault and raviart, 1986; brezzi and fortin (1991)). this condition prevents, in particular, the use of equal order interpolation spaces for the two variables, which is the most attractive choice from a computational point of view. the two-level local projection technique has been introduced by becker and braack (2001) and nafa (2008) to circumvent the inf-sup condition and to allow the use of simple equal order interpolations such as 1 1 p p and 1 1 q q velocity-pressure approximations. this method consists in introducing the 2 l -projection of the pressure gradient as a new unknown of the problem. hence, a third equation to enforce the projection property is added to the original discrete equations, n a.m. essefi and k. nafa 788 and a weighted difference of the pressure gradient and its local projection is introduced into the continuity equation. in this paper we analyze the lps and distinguish two classes of lps methods: the one-level enriched method and the two-level method. the stability and error estimate results presented here are more general than those given in becker and braack (2001). in fact, the proofs extend the stability and error estimate results of becker and braack (2001) and nafa (2008) to the one-level enriched approximation case. numerical results are presented to justify the order of convergence and assess the performance accuracy of both lps methods using bilinear finite element interpolation. 2. discrete stokes problem let  denote an open, bounded, connected subset of 2 , where  denotes its lipschitz continuous boundary. let   2 1 h      f ,   2 1 0h      v , and  20q l  . we consider the usual stokes problem with homogeneous dirichlet boundary conditions. find  , p q u v satisfying in . 0 in on p          u f u u 0 (1) where  20l  is the set of square integrable functions with null average. the weak formulation of the above problem reads        , , . , . ,p q       u v v u f v (2) for all test functions  ,q q v v where  .,. denotes the 2l -inner product on the region  . the compact form of the weak formulation of (1) is given by      , ; , ,b p q f q q q   u v v v v, , (3) where        , ; . .b p q p q     u v u v v u, , , , and    f q v f v, , 3. local projection stabilization let ht be a shape regular partition of the region  into quadrilateral elements k, and assume hv and hq are finite dimensional subspaces of v and q respectively, consisting of continuous functions. we denote by kh the local mesh size, the mesh size is then defined by max .k k th h h   then, the galerkin discrete problem reads      , ; , .h h h h h h h h h hb p q f q q q   u v v v v, , , (4) let hm be a coarser mesh partition of the domain into quadrilateral elements m which are defined as the union of one or more neighboring elements k of the partition .ht we assume that the partition of  into macro-elements hm m is non-overlapping, shape regular and such that local projection stabilization method 781 , , m k hh h k m m m     where kh and mh denote the maximum diameter of k and m, respectively. let  1hy h  be a scalar finite element space of continuous, piecewise polynomial functions over .ht since we are interested in the case of equal order interpolation, we define the approximation spaces as follows 2 , .h h h hy q y q v v let  hd m be a discontinuous finite dimensional space defined on the macro-element .hm m we introduce the associated discontinuous global space  d d .h h m m h m    figure 1. reference macro-element (right) and macro-element (left). then, we define the equal order approximation finite element spaces of velocity and pressure respectively by:              2 21 0 |k 1 2 0 |k / , h / , h r h h r h h q k k t q q l q q k k t                   v vv (5) where, for each integer  0, rr q k denotes standard quadrilateral finite elements by means of a reference element (as illustrated in figure 1) as polynomials of degree less or equal to r with respect to each variable. further, we define the space of discontinuous functions       2 22 |k 1 / , .h h h r hl q m m μ            d λ λ (6) we define the local 2 l -projection    2: dm hl m m  which generates the global projection  2: dh hl   by      2|| , , .h m m hm m m l          to which, we associate the fluctuation operator    2 2:h l l    defined as ,h hid   where id stands for the identity operator in  2 .l  for simplicity we use the same notations id, ,m h and h for vector valued functions. now, the stabilizing term is defined by     0, , .h h h m h h h h m m m h s b p q q       p , (7) thus, the lps discrete problem reads: find  h h h hp q u v, such that a.m. essefi and k. nafa 711      , ; , h h h h h h h h h h h hb p q f q q q   u v v v v, , , (8) where      , ; , ; ,h h h h h h h h h h h hb p q b p q s b p q u v u v, , , (9a) and     .h h h h hf q f qv v, , (9b) the stabilized formulation given in (8) is written component-wise as      , , . , h h h h h h hp       u v v f v v v, (10a)      h0,, . , 0, h h m h h h h hm m m h q p p q q q            u (10b)    h0, , 0, .m h h h h hm m m h p p          ξ ξ d (10c) in order to prove the stability and convergence of the solution of the stabilized method given in (8) we introduce the following assumptions. assumption a1. the fluctuation operator satisfies the approximation property   ,0, , , , 0 . l l h m hl mm q ch q q h m m m l r        (11) assumption a2. there exists an interpolation operator  1:h hi h y  such that    1 10 0v :h hi h y h   with the error estimates  0, 1, , v v v v v s h k h kk k s k i h i ch      (12) for all   v ,sh k and all , 1 1,hk t s r    where  k denotes a certain neighborhood of k. assumption a3. further, assume that the local inf-sup condition       1 v 0, 0, v , inf sup v h h m q d mh h y m h hm mh h q q     (13) holds for all hm m with a positive constant 1 independent of the mesh size h. the following theorem defines hj and hj interpolation operators that are important for deriving error estimates for the lps method (matthies et al. 2007). theorem 1. assume that assumptions a2 and a3 are satisfied. then, there are interpolation operators  1:h hj h y  and :h hj v v satisfying the following orthogonality and approximation properties    1, 0, , h h h hj d h          (14a)  0, 1, , s h m h mm m s m j h j ch          (14b) and  , 0, , h h h h     ω j ω φ φ d ω v (15a) local projection stabilization method 717  0, 1, , . s h m h mm m s m h ch     ω j ω ω j ω ω (15b) for all       2 , , , s s hh m h m m m   ω v and 1 1,s r   where  m denotes again a certain neighborhood of m. next, we introduce the following mesh-dependent norm on the product space h hqv     2 2 2 2 0, 0, .h h h h m h h m m m h q q q         v v 1, , (16) 3.1 stability theorem 2. assume that assumptions a2 and a3 hold and the parameters m are such that 2 /m mh c  for all elements .hm m then, there is a positive constant independent of h such that             2 ,0 , , , ; , inf sup . , . , h h h h h q qh h h h r qh h h h h h h h b q r q r        0 v v ω v v ω v ω (17) the proof is found in (nafa and wathen, 2009). 3.2 error estimates first, we introduce the following consistency error (ganesan et al., 2008). lemma 3. assume that the fluctuation operator h  satisfies assumption a1. let       2 1r r p h q h        u v, be the solution of stokes problem and  h h h hp q u v, be the solution of the lps stabilized problem. then, the consistency error can be estimated by     1/2 22 2 , , ; r h h h h m m h hr m m m h b p p q c h p q              u-u v v, , (18) for all   .h h h hq q v v, then, the error estimate of the lps method is given by the following theorem. theorem 4. assume that the solution  pu, of (3) belongs to     2 1 , r r h q h       v  h h h hp q u v, is the solution of the local projection method (8), and m are such that 2 /m mh c  for all elements .hm m then, the following error estimates hold  1, 1, ,0, r h h r r p p ch p         u u u (19) for some positive constant c independent of h. proof. let h hj uu and hp i p be the interpolants of the velocity and pressure respectively. by virtue of theorem 2, there exist  h h h hq q v v, satisfying   .h hq cv , (20) we have a.m. essefi and k. nafa 711       2 22 1, 0, , , .h h h h h h h h h h h hp p p p s p p p p         u -u u -u (21) hence,   22 1/2 1, 0, 1 / , .h h h h h h h hp p p p     u -u u -u (22) thus, by equivalence of norms on finite dimensional spaces in 2  , it yields   22 1/2 1, 0, 2 / , .h h h h h h h hp p p p     u -u u -u (23) in addition, we have       2 , ; , 1 / h h h h h h h h h h h h h b p p q p p q     u -u v u -u v , , (24) i.e.           2 2 , ; , ; , 1 / 1 / . h h h h h h h h h h h h h h h h h h b p p q b p p q p p q q        u -u v u-u v u -u v v , , , , (25) using the result of the consistency estimate with 2 ,m mch  we obtain     , , ; rh h h h h r h h b p p q ch p q    u-u v v , , (26) where,      , ; , ; .h h h h h h h h h h h hb p p q b p p q s b p p q    u -u v u -u v, , , the terms of  , ;h h h hb p p qu -u v , will be estimated using the approximation properties of the interpolations hj and ,hi      1, 1, 1, , r h h h h h hr ch q           u u v u u v u v , (27) and     1, ,0, , . . r h h h h h hr p p c p p ch p q       v v v , (28) to estimate the last term we shall use the integration by part and the orthogonality property of ,hj       . , , .h h h h h h hq q , q       u u u u u u (29) thus,    1/2 1/2 221 0, 0, . , .h h m h m h hm m m m m mh h q q                            u u u u (30) hence,      1/2 1/2 2 22 1 2 2 1, 0, . , r h h m m m h hr m m m m m mh h q c h q                               u u u     1/2 21 2 2 1, , r m m h hr m m m h c h q                 u v , (31) i.e. local projection stabilization method 711      1, . , , r h h h hr q c h q      u u u v (32) for some positive constant .c  now, to estimate the stabilizing term  h h hs b p p q , we use the 2 l -stability of the fluctuation operator h and the approximation property of .hi we obtain the following:     , ,h h h m h h h h m m h s b p p q k p p k p         1/2 1/2 2 2 0,0, .m h h m h h mm m m m mh h p p q                           (33) thus by (11) we get       1/2 22 2 1, , r h h h m m h h hr m m m h s b p p q c h p p q                v,     1/2 22 2 , , r h h h m m h h hr m m m h s b p p q c h p p q              v, using 2 ,m mch  we have     1/2 22 1 , , . r h h h m h hr m m m h s b p p q c h p q             v, (34) hence     , , . r h h h h hr s b p p q ch p q    v, (35) using (26) and (35), we get  0,1, 1, , r h h h r r p p ch p         u u u . □ the required error estimate then follows using the triangular inequality together with the interpolant estimates. as already observed, the existence of the interpolation operators hj and hj is fundamental, in lps methods, for deriving the error estimates. since, assumption a3 may not be fulfilled, the existence of these operators is not always guaranteed. 3.3 two-level local projection stabilization this class of stabilized schemes uses discontinuous pressure gradient projection approximations of degree 1r  which are defined on the coarser mesh 2 .h hm t let 2 , 1h r  be the 2 l -projection onto hd then 2 , 1h h rk id   here, for rectangular elements, the spaces hy and hd are chosen as , 1,2/ / . disc h h r h r hy d q q  (36) it has been proved in (matthies et al., 2007) that the pairs given by (36) satisfy assumptions a3. 3.4 one-level enriched equal order stabilization from the implementation point of view, a drawback of the two-level approach is the fact that the added stabilizing term produces a larger stencil which may not fit in the data structure of an available programming a.m. essefi and k. nafa 711 code. a general theory which allows the derivation of a novel class of local projection stabilization by enrichment of the approximation spaces has been established in (matthies et al., 2007). this class of stabilized schemes uses approximation and projection spaces defined on the same mesh and leads to much more compact stencils than in the two-level approach. let , 1, h h h rμ t   be the 2 l -projection onto ,hd and , 1.h h rid    for rectangular elements, the spaces hy and hd are chosen as ,1 1,, / / b disc h h r hr h y d q q  (37) or ,2 1,, / / b disc h h r hr h y d q p  (38) where      ,1 1ˆ,, ˆ ˆ ˆspan , 1, , b r r h ir h k q k q k b x i d     (39)      ,2 ˆ, 1,, ˆ ˆ ˆ b r h r hr h k q k q k b q k  (40) and k̂ b is a biquadratic bubble function on the reference element ˆ .k here also the pairs given by (37) and (38) satisfy assumptions a3. note that, the local projection method described above does not add an extra cost to the solution of stokes algebraic system. this is due to the elimination of pressure gradient unknowns at element level (nafa and wathen, 2009). 4. numerical results numerical results for two stokes problems are presented. the performance of the first order two -level method 1, 0,2/h hq q and the one-level method 1, 0, / b h hq q approximations are obtained for 2 0m mh  where 0 is a constant. 4.1 problem 1 the first problem consists of solving stokes problem in the unit square with exact solution   1 2, ,tu u p given by 2 2 2 2 1 2( , ) 2 (1 ) (1 ) (1 2 ), ( , ) 2 (1 )(1 2 ) (1 )u x y x x y y y y u x y x x x y y         and 2 ( , ) .p x y x x  numerical results are obtained, using the lps method, for 1.  calculations were performed for 0 0.1  and 0 1  using the two-level and one-level methods. the results given in figures 2-5 indicate that the error norms 0,h  u u and 1,h  u u converge at the predicted rates, while 0,h p p   seems to converge at a rate of about 3/2 as observed by becker and braack (2001) and by nafa and wathen (2009). local projection stabilization method 711 figure 2. velocity error norm using 1, 0,2/h hq q interpolation with 0 0.1  (left) and 0 1  (right). figure 3. pressure error norm using 1, 0,2/h hq q interpolation with 0 0.1  (left) and 0 1  (right). figure 4. velocity error norm using 1, 0,/ b h hq q interpolation with 0 0.1  (left) and 0 1  (right). a.m. essefi and k. nafa 711 4.2 problem 2 to test the accuracy of the method, we consider the standard poisseuille flow in the channel    0, 4 0,1 .   we prescribe a parabolic inflow profile and use natural outlet conditions. the dirichlet boundary conditions are not imposed on the whole boundary and natural boundary conditions 0p     u n n are employed. the solution of the problem is given by         2 1 2, 1 4 1 2 , , 0 and , 8 2 .u x y y u x y p x y x      figure 5. pressure error norm using 1, 0,/ b h hq q interpolation with 0 0.1  (left) and 0 1  (right). figure 6. velocity profile using 1, 0,2/h hq q interpolation with 0 0.1  . local projection stabilization method 711 figure 7. pressure contours using 1, 0,2/h hq q interpolation with 0 0.1  . first, the problem is solved using 1, 0,2/h hq q approximation on a 32x16 grid. the obtained results are illustrated in figures 6 and 7 respectively, for the velocity and pressure solutions. we observe that the approximated pressure solution is exact even near the boundaries. in addition, figure 8 shows that the velocity profile at the outlet boundary is in perfect agreement with the exact solution there. the numerical solution of the poiseuille problem is also performed on a 32x16 grid using the one -level enriched approximation 1, 0,/ . b h hq q we obtain similar results to the two-level method for the velocity profiles as shown in figure 9. the pressure solutions obtained for 0 10,  10 2 , 10 3 , and 10 4 , respectively, are illustrated in figure 9. we note that while varying the coefficient 2 0m mh  over the wide range from 0.1 to 10 4 , the obtained results change considerably. these results show that the pressure solution for the enriched one -level method is more sensitive to the choice of the parameter α0 as compared to the two-level method. figure 8. velocity profile at the outlet of the channel using 1, 0,/ b h hq q interpolation with 0 0.1  (left) and 0 1  (right). a.m. essefi and k. nafa 718 5. conclusion the convergence, stability and accuracy of lps for the stokes problem has been investigated using the one-level and two-level bilinear finite element interpolation. the numerical results show that the order of convergence for both approaches is as predicted theoretically for the velocity. but, the l 2 rate of convergence for the pressure is approximately 3/2 as noted by other researchers (becker and braack, 2001; nafa and wathen, 2009). also, we observe that the computation of the poisseuille solution produces the exact velocity independently of the parameter 0 for both methods. however, it is shown that the pressure is exact even near the boundaries for the two-level method and depends on the parameter 0 for the one-level enriched method. in fact, to obtain results similar to those obtained by the two-level method, we have to take large values for 0 . figure 9. pressure contours using 1, 0,/ b h hq q interpolation with different values of 0 . 6. references becker, r. and braack, m. 2001. a finite element pressure gradient stabilization for the stokes equations based on local projections, calcolo 38(4): 173-199. brezzi, f. and fortin, m. 1991. mixed and hybrid finite element methods, springer verlag, new york, usa. ganesan, s., matthies, g. and tobiska, l. 2008. local projection stabilization of equal order interpolation applied to the stokes problem, math. comp., 77: 2039-2060. girault, v. and raviart, p.a. 1986. finite element methods for navier-stokes equations, springer verlag, berlin, germany. 0 (a) 10  2 0(b) 10  3 0( ) 10c   4 0(d) 10  local projection stabilization method 711 matthies, g. skrypacz, p., tobiska, l. 2007. a unified convergence analysis for local projection stabilisations applied to the oseen problem, m2an math, model. numer. anal., 41(4): 713-742. nafa, k. 2008. two-level pressure stabilization method for the generalized stokes problem, international journal of computer, mathematics 3-4: 579-585. nafa, k. and wathen, a. 2009. local projection stabilized galerkin approximations for the generalized stokes problem, comput. methods appl. mech. engrg., 198: 877-883. received 13 january 2011 accepted 21 december 2011 full page photo 211-220 squ journal for science, 12 (2) (2007) © 2007 sultan qaboos university 211 experimental design for nonlinear problems abdelbasit k.m department of mathematics and statistics, college of science, sultan qaboos university,p.o.box 36, pc 123, al-khodh, muscat, sultanate of oman, email: khidir@squ,edu.om.. الخطیة تصمیم التجارب للمسائل غیر عبدالباسطمحمد خضر إعتمدت تصمیمات التجارب للمسائل غیر الخطیة إلى حد كبیر على معاییر المثالیة المستخدمھ للنماذج الخطیة. :خالصة ع غیر المعروفة. علیھ ال یمكن التجمالتصمیمات الناتجة من إستخدام ھذه المعاییر للمسائل غیر الخطیة تعتمد على معالم عمال ھذه التصمیمات مباشرة ألن تحدیدھا یتطلب معرفة المعالم التى ستجرى التجربة لتقدیرھا. یمكن التغلب على ھذه إست العقبة بإستخدام عدة تجارب متتا بعة أو إستخدام اسلوب بییز أو إستخدام التقدیرات المتوفرة لھذه المعالم أو تخمین قیمھا. ثم نستعرض معاییر المثالیة المستخدمة عادة التصمیمات اإلحصائیة للتجارب یة موجزه عننبدأ فى ھذه الورقة بنبذه تاریخ للمسائل غیر الخطیة و نناقش عوائق إستخدامھا و وسائل التغلب على ھذه العوائق. بعدھا ننتقل لمناقشة موضوع حساسیة ً نبذه موجزه عن التصمیمات المتتا بعة و تصمیمات بییز و نضع بین یدى القارئ التصمیمات محلیة المثالیة. نعرض أیضا بعض المسائل العالقة للبحوث المستقبلیة. abstract: experimental designs for nonlinear problems have to a large extent relied on optimality criteria originally proposed for linear models. optimal designs obtained for nonlinear models are functions of the unknown model parameters. they cannot, therefore, be directly implemented without some knowledge of the very parameters whose estimation is sought. the natural way is to adopt a sequential or bayesian approach. another is to utilize available estimates or guesses. in this article we provide a brief historical account of the subject, discuss optimality criteria commonly used for nonlinear models, the associated problems and ways of overcoming them. we also discuss issues of robustness of locally optimal designs. a brief review of sequential and bayesian procedures is given. finally we discuss alternative design criteria of constant information and minimum bias and pose some problems for future work. keywords: optimal designs, sequential designs, bayesian designs, constant information, minimum bias. abdelbasit k.m 212 1. introduction experiments are investigations where the investigator has some control over the system under study. such investigations are very common in many fields, where the effect of some factors on a specified response variable is to be investigated. design objectives include: 1. reduction of systematic errors, due to controllable factors that are of no interest to the experimenter, but may influence the response. such factors are commonly known as nuisance factors. 2. minimization of experimental error, due to random variability and/or uncontrollable and unknown factors that may influence response. 3. the appropriate number of experimental units to be used. it is generally desirable to have an experiment large enough for effects of practical significance to be detected, but not too large to waste experimental material detecting small effects of no practical significance. most of the early developments of the subject were closely associated with agricultural field experiments, and with the names of fisher (1935) and yates (1935, 1936, 1937). this remains an active research area today. most of the designs developed then were informal emphasizing the key concepts of blocking and randomization to meet the first two of the objectives stated above. the models used are linear with a continuous response variable and categorical explanatory variables. these models can generally be written as: e(y) = θ tx (1) where y is the observed response, θ is a p×1 vector of unknown parameters and x is a p×1 indicator vector whose elements are zeros and ones. the variance of y is assumed constant and denoted by σ2. when n observations are made, the observation y is an n×1 vector whose ith element is yi, where e (yi) = θ txi . equations (1) can now be written as: e(y) = xθ t (2) where x is an n×p matrix whose ith row is xit .the matrix x is called the design matrix. the normal equations for estimating θ are given by: xtxθ̂ = xty (3) the matrix xtx is usually singular and some conditions-known as estimability conditions are imposed to make it nonsingular. the estimator θ̂ of θ is then (xtx)-1 xty with cov (θ̂ ) = σ2 (xtx)-1. the experimental design model in (1) is a special case of the polynomial regression model, usually written in the form: e(y/x) = θ t f(x) (4) where f(x) is a function of x only. all the equations above apply with x replaced by f(x). the polynomial regression models do not usually suffer from the non-singularity problem of the experimental design model and no estimability conditions are needed. models are said to be non-linear if they are not linear in the parameters and, therefore, can not be written in the form of equation (4). such models are written as: experimental design for nonlinear problems 213 e(y/x) = f(x,θ ) (5) where f(x,θ ) is nonlinear in θ . consideration of design issues for polynomial regression models, lead to the development of the notion of optimality activated by elfving (1952, 1959) and kiefer (1959). for models of the form (5) the fisher information matrix is i (θ ) = f(x,θ ) [f(x,θ )]t (6) for linear models as in equations (2) and (4), i (θ ) is independent of ө and the variance of the maximum likelihood estimator θ̂ is σ2 i-1(θ ). optimality criteria call for the maximization of some real valued function of fisher's information matrix. this is equivalent to the minimization of a function of i⁻¹(θ ) which is proportional to the asymptotic covariance matrix of the maximum likelihood estimator. thus optimality criteria are variance based. when the model is nonlinear, i (θ ) is a function of the unknown parameters θ and, so are the optimal designs. an account of the history of the development of experimental designs can be found in atkinson and bailey (2001) for instance. we introduce below commonly used optimality criteria. 2. optimality criteria the optimality criterion adopted for a given problem naturally depends on the main objective of the experiment. that leads to several optimality criteria being proposed and studied, such as i. d-optimality: this is by far the most commonly adopted optimality criterion. a design is called doptimum if it minimizes det i⁻¹(θ ). the criterion treats all the p parameters as of equal interest, which makes it the most appealing when estimation of the parameter is the main objective. it guarantees confidence ellipses of the smallest volume. when interest is in a subset of the parameters or some specific linear combination at θ of the parameters, modifications known as dsand daoptimality are used (see atkinson and donev; 1992, chapters 10 and 11). ii. g-optimality: a design is called g-optimum if it minimizes the maximum standardized variances of predicted response. an equivalence theorem (kiefer and wolfowitz, 1960) proves the asymptotic equivalence of dand goptimality. iii. a-optimality: a design is called a-optimum if it minimizes the average variance of the maximum likelihood estimators of the parameters. this is equivalent to the minimization of the trace of i⁻¹(θ ). iv. e-optimality: a design is called e-optimum if it minimizes the variance of the least well estimated contrast at θ (ata=1). this is equivalent to the minimization of the largest eigen value of i⁻¹( θ ). this means that d-, aand e-optimality can be defined in terms of the eigenvalues p λλλ ,,, 21 k of the information matrix i (θ ). they correspond to the minimization of ∏ ∑ = = p i p i i max 1 1 1 1 )(, 1 , 1 λ λλ respectively. an appealing property of dand goptimality that is not shared by aand e-optimality is the invariance of optimal designs under reparametrization. in addition to the above most commonly used criteria, there are several others (see atkinson and donev, 1992). these include: abdelbasit k.m 214 v. c-optimality: minimize the variance of the estimate of ct θ , where ct θ is the linear combination of parameters of main interest. vi. q-optimality: minimize average prediction variance over a specified design region (see myers et al, 1994). vii. f-optimality: minimize the width of fieller's fiducial interval (finney, 1971). owing to the use of the alphabet in the naming of these criteria, we now see reference to alphabetic optimal designs (e.g. myers et al, 1994). the theory of optimal designs and methods of construction of optimal designs are the subjects of several books including silvey (1980), atkinson and donev (1992), pukelsheim (1993) and cox and reid (2000). for reviews and sample applications of optimal designs to applied problems in education, business, marketing, epidemiology, microbiology, environmental science, pharmaceutical and medical research and manufacturing industry, see berger and wong (editors, 2005). 3. non-linear models when optimality criteria are used for linear models the optimal designs have attractive properties and can be constructed and used (see silvey, 1980). most of the literature on nonlinear problems, adopted the same criteria. since the information matrix depends on the unknown model parameters for nonlinear models, so do the resulting optimal designs. this presents a serious hurdle to the implementation of these designs in practice. the first non-linear design problem was the dilution series introduced by fisher (1922) well before his later foundation work on linear problems the problem he considered then involved a single parameter exponential model. fisher argued that the magnitude of the variance relative to the parameter should be minimized rather than the variance in isolation. he thus considered minimizing the coefficient of variation i⁻¹(logθ ). he noticed that i (logθ ) is almost independent of θ and utilized this property to construct a design that provides a specified proportion of the total information. this strategy was generalized by abdelbasit and plackett (1981, 1983) and studied in greater details by abdelbasit (1998). stallard and gravenor (2006) discuss further design issues on the dilution series. later work on designs for non-linear problems did not, however, follow fisher's approach. instead it focused on optimality criteria originally proposed for linear models, resulting in parameter dependent optimal designs. despite their litle practical value, these designs provided useful reference points for designs that can be implemented (ford..et al, 1992). this probably is the main justification for the extensive literature on such designs. dette et al (2004) investigate eand c-optimal designs for a broad class of non-linear regression models. dette and sahm (1998) consider maximum variance optimality criterion of elfving (1959) in the context of non-linear response models and constructed mini-max optimal designs. dette and haines (1994) develop a procedure for constructing e-optimal designs for a broad class of two parameter models. examples illustrate the main features of the procedure. hedayat et al (2004) identify classes of 2-parameter non-linear models, for which d-optimal designs are precisely supported on two points. they also obtain some efficient designs that allow for model checking. dependence of optimal designs on unknown parameters is the major problem limiting implementation. a number of methods are used in the literature to overcome this problem. among these are : a. proceeding sequentially b. adopting a bayesian approach c. using the best available estimates or guesses, leading to what are called locally optimal designs. in all the three approaches either preliminary estimates for the parameters or prior distributions have to be used. an immediate question is how robust (or sensitive) the resulting designs are to poor initial estimates and priors ? experimental design for nonlinear problems 215 4. sequential designs this is the natural approach when optimal designs depend on the unknown model parameters. the experimenter runs the first experiment using the best available estimate or guess and similarly use estimates obtained from an experiment to run the next. abdelbasit and plackett (1983) obtained sequential designs for one parameter exponential and two parameter logistic models. they concluded that: a. the better the initial estimate, the more experimental subjects should be used in the first stage. b. with good initial estimates and relatively small number of subjects, it may not be worthwhile to go beyond one experiment. c. underestimating the variance is more serious than overestimating it. d. the smaller the variance, the more sensitive the design becomes to poor initial estimates. one of the earliest problems considered in this area are the dose-response problems, where interest lies in the estimation of the parameters of the response curve or its percentiles. most of the interest was initially in the median of the response curve, commonly known as the median effective dose ed50. later extreme percentiles ed100p where p is close to 1 or 0 were considered. dixon and mood (1948) proposed the up and down method for estimating the ed50. subjects are tested one at a time at equally spaced doses and the experimenter performs the experiment at the next higher dose in case of no response and the next lower dose in case of a response. bortot and giovagnoli (2005) proposed a second order up and down method, where the next step is based on the outcome of the last two. robbins and monro (1951) extended the up and down method to a variable step size, where the doses get closer to each other as they approach the ed50. a discussion of these methods is given in wetherill and glazebrook (1986). a modification to improve the performance of the robbins-monro procedure at extreme percentiles is given by joseph (2004). a summary of developments in sequential designs for estimating ed50 is given by wu (1985) where he proposes new designs and compare via simulation small sample size performances. more generally sitter and forbes (1997) consider a class of symmetric binary response models and showed that for many of the optimality criteria (e.g. a-, d-, e-, fand goptimality); the optimal second stage design consists of two points symmetrically placed about the ed50, with possibly different weights at each point. sinha and wiens (2002) investigate sequential design methodologies when the fitted model is possibly of an incorrect parametric form. their small sample simulation results indicate that their designs reduce mean squared error due to model misspecification and heteroscedastic variation. hu (1998) studied the consistency of parameter estimators in sequential non-linear cases and established consistency of baye's estimators in stochastic regression models. sequential procedures are not practical except in situations where possible response is immediate, and their properties are hard to explore analytically. hence their use in practice remained limited. 5. bayesian designs since optimum designs for nonlinear models depend on the values of the unknown parameters θ , a bayesian approach to the design seems natural. assuming an initial estimate or guess is effectively an assumption of prior knowledge about θ . if such knowledge can be expressed in the form of a prior probability distribution, the posterior expected information can be obtained. the optimality criteria above can then be applied to the posterior expected information. chaloner and lantz (1989) derived general bayesian theory for non-linear models, applied it to the abdelbasit k.m 216 logistic regression and numerically obtained optimal designs for one and two parameter cases. chaloner (1993) also considered bayesian designs for one parameter, single explanatory variable models. consistency issues are addressed by hu (1998). dette and neugebauer (1997) obtained bayesian d-optimal designs for exponential growth models with up to three explanatory variables. 6. locally optimal designs these are probably the most commonly used and most extensively studied in the literature. issues associated with such designs are robustness to poor initial estimates and efficiency relative to an optimal or another design. in the context of dose-response problems, and when interest is in a single parameter, typically the ed50, finney (1971) obtained symmetrical two and three points f-optimal designs. abdelbasit and plackett (1983) used simulation to compare the use of fiducial intervals and asymptotic intervals. they concluded that asymptotic intervals are not inferior to fiducial intervals. their results were re-examined by sitter and wu (1993a) who supported finney's proposal and concluded that abdelbasit and placket's conclusion resulted from their large sample size. sitter and wu (1993b) also considered f-optimality together with other alphabetic ones. for further comparisons of the fiducial and asymptotic methods see faraggi et al (2003) and yangxin (2005). for the standard two parameter logistic model, abdelbasit and plackett (1983) derived d-optimal designs. their work was generalized by minkin (1987) and khan and yazidi (1988). myers et al (1994) developed optimal designs for the logistic model using several alphabetic criteria. sitter and fainaru (1997) obtained alphabetic optimal designs for a class of symmetric models that include the probit and logistic models. dette and sahm (1997) obtained standardized aand eoptimal designs for the probit and logit models. the reason for standardization of the information matrix is the scale dependency of the aand eoptimality criteria. ford et al (1992) used canonical forms in the construction of locally dand c-optimal designs for various non-linear problems. dette and sahm (1998) considered minimax designs and fandom and seidel (2000) gave a minimax algorithm that works efficiently for constructing optimal symmetric balanced designs. the question of robustness remains a key question for all locally optimal designs. sitter (1992) used minimax procedures to obtain designs that are robust to poor initial estimates. the procedure yield designs with more design points and larger spread. the more the uncertainty about the parameter, the more spread out is the design and supported on more points. the issue of robustness is also addressed by many authors including abdelbasit and plackett (1983), myers et al (1994), kalish (1990), hedayat et al (1997), moerbeek (2005) and melas (2005). cox (1998) suggests that problems caused by non-linearity of the model may not be that serious. he considered the case of estimating small treatment differences, and showed that the problem caused by nonlinearity of exponential family distributions is not severe, and the usual normal theory applies well if the data are not very heterogeneous. situations with more than one explanatory variable are studied by abdelbasit and plackett (1982) in relation to joint action of stimuli (see also antonello and raghavaroo, 2000). atkinson et al (1995) introduced gender as a second explanatory variable and sitter and torsney (1995) extend dand coptimal designs for binary response data to the case of two design variables. design problems for bivariate response cases are investigated by heisi and myers (1996) who consider the bivariate response (efficacy, toxicity) modeled by a bivariate logistic and developed dand q-optimal designs. they also discuss robustness of the designs obtained. dragalin and fedorov (2005) developed an adaptive design for efficacy-toxicity response with bivariate correlated binary response.the main problems of all optimal designs are that they : a. heavily depend on the precise specification of the model. b. usually offer no possibility of checking the assumed model, since they invariably have as many points as the number of parameters to be estimated c. can not be implemented, when the model is non-linear, because they are functions of the unknown model parameters. in the remainder of this article we introduce alternative design strategies that try to avoid the above problems. experimental design for nonlinear problems 217 7. fisher's constant information somehow, the first design criterion proposed for non-linear models (fisher; 1922) was hardly pursued further in the literature. abdelbasit and plackett (1981, 983) showed that fisher's results for a single scale parameter hold for any model and not just the exponential. they also showed that uniform designs are constant information designs for a single location parameter. they used the word reliable to describe designs that make the information function independent of the parameter. they also showed that uniform designs are d-reliable for two parameter models when the probability of response at dose x can be written as: p(x) = f{β(x – μ)} (7) for any specified distribution function f (.). a design is called d-reliable if it makes the determinant of the information matrix independent of the parameters. a numerical investigation by abdelbasit (1998) examined the use of the criterion for one and two parameter logistic models. his results indicate that the resulting designs have far more points than the number of parameters. 8. bias-based designs minimum bias (all bias) criterion was introduced by box and draper (1959) to rival design criteria based solely on variance. they noted that unless the variance contribution to the mean squared error is many times greater than bias contribution, the designs that minimize mean squared error are very similar to minimum bias designs. abdelbasit and butler (2006) extended box and draper criteria to generalized linear models of the form fy(y, θ ,φ) = exp{(yθ -b(θ ))/a(φ) + c(y,φ)} (8) this family includes most of the standard probability distributions. the parameter θ is called the canonical parameter. abdelbasit and butler (2006) derived minimum bias designs for the canonical and non-canonical cases, and presented as examples; the binary, the poisson and exponential cases. their results suggest that equally spaced designs minimize the bias-standard error ratio and the mean square error-variance ratio. 9. concluding remarks the main hurdle of dependence of designs on unknown model parameters is yet to be resolved. variancebased optimal design criteria seem to have matured, but offer no practical solution. alternative design criteria other than optimality need to be sought. the abovementioned constant information and minimum bias are examples of such alternatives. at present the scarce results available indicate that these criteria yield designs with too many design points as opposed to the too few of optimal designs. a search for a compromise that combines the merits of the various approaches is worth perusing. very little is known, however, about the statistical properties of the designs based on either of the two alternatives suggested above. further work in this area is needed, and the efficiency of these designs relative to optimal or other designs needs to be investigated. a comparative analysis of alternative approaches (variance based, bias based and constant information) is also needed for providing useful guidance to the practitioner. 10. references abdelbasit k.m 218 abdelbasit, k.m. 1998. constant information design for binary data. journal of science and technology; sultan qaboos university, 3: 57-66. abdelbasit, k.m. and butler, n.a 2006. minimum bias designs for generalized linear models. sankhya; 68(4): 587-599. abdelbasit, k.m and plackett. 1983. experimental design for binary data. journal of the american statistical association; 78: 90-98. abdelbasit, k.m and plackett, r.l. 1982. experimental design for joint action. biometrics; 38: 171179. abdelbasit, k.m and plackett, r.l 1981. experimental design for categorial data. international statistical reviews; 49: 111-126. antonello, j.m. and raghavarao. 2000. optimal designs for the individual and joint exposure general logistic regression models. journal of biopharmaceutical statistic; 10: 351-367. atkinson, a.c. and 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a large number of varieties. j. agric. sci.; 26: 424-455. yates, f. 1937. the design and analysis of factorial experiments. technical communications; 35, harpenden : imperial bureau for soil science. received 7 december 2006 accepted 6 november 2007 full page photo 75-85 squ journal for science, 12 (2) (2007) © 2007 sultan qaboos university 75 action plan for monitoring, mitigation and management of harmful algal blooms in the coastal waters of oman alkindi, a.y.a*, al-ghelani, h.m.h.**, amer, s.***, al-akhzami, y.k**. department of biology, college of science, sultan qaboos university, p.o. box 36, pc123, alkhodh, sultanate of oman, *email: aakindy@squ.edu.om.. ** ministry of agriculture and fisheries, p.o. box 467, pc. 113 muscat, sultanate of oman. ***department of biological sciences and chemistry, college of arts and science, p.o.box 33, pc 616, university of nizwa, sultanate of oman. خطة عمل لمراقبة وإدارة ظاھرة المد األحمر في میاه الشواطئ العمانیة والتقلیل من أضرارھا ، حمد الغیالني، شھلھ عامر و یونس األخزميعبدالعزیز الكندي ونمو الطحالب الضارة، وأظھرت ة المد األحمرخلیج عمان نظام بیئي واقتصادي ثري یتأثر باستمرار بحدوث ظاھر :خالصة الدراسات التي أجریت أخیرا زیادة في عدد أنواع الطحالب التي تتسبب في اآلثار الضارة، وفي ھذا البحث یتم تقصي أنواع األحمر مراقبة لألبحاث العلمیة عن ظاھرة المدثالثة من الطحالب التي تسبب تكوین ھذه اآلثار الضارة، ویقدم الباحثون خطة عمل تحوي نظام مراقبة بیئي فاعل لنمو الطحالب الضارة واحتواء آثارھا.متضمنة abstract : the gulf of oman, an ecologically and economically rich ecosystem, is frequently impacted by occurrences of harmful algal blooms. recent studies indicate an increase in the number of causative species and harmful impacts. many red tide incidents in oman have been found leading to hypoxia. the frequent bloom forming species here are karenia selliformis, nitzschia pungens, prorocentrum arabianum and trichodesmium erythraeum. we review work carried out in this area, and we propose here a management action plan for not only an effective monitoring system for harmful algal blooms (habs), but also mitigation of their adverse impacts and rapid response system. keywords: harmful algae, hab management, mariculture. 1. introduction he oman coast has been witnessing occurrences of harmful blooms (hab) since 1978 (mathews et al., 2001; morton et al., 2002; al-busaidi et al., 2007). the coastal waters are since then regularly monitored. in general, the deleterious effects associated with habs are on human health, marine resources and tourism industry. t alkindi, a.y.a., al-ghelani, h.m.h., amer, s., al-akhzami, y.k 76 physiological mechanisms, singly or in combination, leading to fish mortality, include physical damage or irritation of gill tissue leading to mucus production, blood hypoxia and possibly bacterial infection (speare et al., 1989), toxigenic reactions to ichthyotoxic agents (tanaka et al., 1994, mallet et al., 1985), blood hypoxia from environmental oxygen depletion (rensel, 1993), and gas bubble trauma from oxygen super saturation (kills 1979). although much is known about the mechanisms responsible for fish death from habs, there is still lack of information on several important species and groups of fish killing habs. the problems arising from habs are very diverse and the causes are many, therefore effective management is required to mitigate the threat posed by habs to the economic development of coastal areas and human health. strategies are needed to efficiently manage marine resources, protect public and ecosystem health, encourage and support aquaculture development, and contribute to policy decision about coastal zone issues. 1.1 policies for management and mitigation of habs these can be broadly classified into prevention, restoration, amelioration and no action at all (turner et al., 2000). 1.1.1 prevention policies these can cover strategies that aim at minimization of the probability of formation of habs in the marine ecosystem. such strategies may be directed for example, at preventing the accidental introduction of exotic harmful algae (resulting from shipping activities). sophisticated monitoring and surveillance of a wide and complex variety of factors, conditions, and mechanisms present in the marine waters are needed to identify the presence of harmful aquatic organisms in time. 1.1.2 restoration policy program restoration is implemented once habs has occurred and can be achieved by use of trained crews and special equipment to keep the bloom formation from spreading. 1.1.3 amelioration policies this strategy is characterized by individual programs. amelioration policies comprise of various mitigation measures that can be adopted to reduce impact on marine living resources, human health and recreation. these programs do not focus on attaining the environmental conditions preceding the bloom formation. amelioration programs can for instance focus on (partial) cleaning activities often translated in actions such as the removing of algal foams from the beach for example by using naturally occurring clay (chim, 1998; choi et al., 1998). 2. objectives of designing a monitoring program a well-defined objective is essential in designing a hab environmental monitoring program. a design that is too superficial may produce data inadequate for the intended use; a design that is too complicated may be labour intensive and costly. we should consider the procedure that must match our own specific objectives and sitespecific conditions. monitoring is to: • prevent algal toxins from reaching human consumers • prevent algal toxins from reaching consumers of drinking water (from desalination plants) • minimize damage to living resources such as fish • minimize economic loss to fishermen, aquaculturists, tourists, industry etc. • establish basic knowledge about form and function of the ecosystem investigated and the extent to which it is influenced by anthropogenic factors. action plan for harmful algae management 77 • establish detailed knowledge about selected ecosystem processes to make it possible to understand and predict ecosystem response to eutrophication or exceptional physical and biological events • establish patterns and trends for algal populations the ultimate goal is to determine the principal causes of red tide, in order to achieve better skill for forecasting their occurrence and predicting the consequences of phytoplankton on environmental changes in coastal waters. 3. action plans and mitigation measures hab monitoring programs must be dynamic and operable in difficult conditions. the following monitoring modes have been suggested (andersen et al., 2003): • normal / routine mode: to operate in non hab situation. • watch mode: to operate when a hab is observed, in rather low concentrations or when low levels of algal toxin are detected in fish / shellfish. • alert mode: to operate when a hab is observed in critical concentrations, when algal toxins are observed in concentrations close to or exceeding regulatory limits or where hab effects on fish are observed. the change of a hab monitoring program from one mode to another must be triggered by specific observations or combinations of observations such as the changes in water temperature, chlorophyll content and fish behavior. 3.1 common design elements of amount program according to andersen et al. (2003) the basic elements of a hab monitoring program include: 1. sampling of plankton, fish and water. 2. analysis of the samples (identification of harmful algae, quantification of harmful algae measuring toxicity in water, fish). 3. environmental observation such as discolouration of the water, fish kills and other animal behavior. 4. evaluation of results. 5. dissemination of information and implementation of regulatory action. 6. action plans / mitigation measures. it is essential to make reliable measurements of the monitored variables. site and organism specific features influence the monitoring design. where upwelling is a factor, oceanography must be assessed. at sites where flushing is important to hab events, this physical feature must be evaluated; where nutrient loading increases, nutrient chemistry should be measured. the monitoring program, therefore, must be designed in accordance with the major ecological and behavioral features represented by the hab taxa, their planktonic life mode and the habitat factors regulating their occurrence and growth. 3.2 sampling design considerations it is important that all routines for sampling, sample analysis, data analysis and storage be clearly defined. pre-printed forms should be available to be filled in with the monitoring data. raw data from the monitoring program should be kept in files, paper or electronic form for later reference and investigation. data should be stored in a computer database to facilitate data handling, quality assurance and analysis. 3.3 frequency and distribution of sampling hab events are often fast moving, and subject to meteorologically induced disruptions or accumulations. the basic monitoring strategy therefore should be one of high sampling frequency, particularly when the objective is to determine environmental control mechanisms. ideally, samples should be collected daily but certainly not less than twice a week during longer lasting blooms. the logistics of the sampling requirement alkindi, a.y.a., al-ghelani, h.m.h., amer, s., al-akhzami, y.k 78 obviously are more easily met in coastal regions from which land based monitoring operations can be launched. diel sampling may sometimes be needed to unravel the basic features and phytotactic migratory behavior of hab flagellates as a factor in the bloom episode. some species exhibit a night rise/day descent, others the opposite diel pattern (kamykowski, 1976; kamykowski, 1981). therefore diel abundance at a given depth in the water column and among species can vary significantly because of different motility speeds and diel response patterns. 3.4 physical habitat measurements among physical factors, temperature and salinity should be measured at multiple depths along a spatial gradient. vertical density profile, if not directly measured, can be calculated from vertical temperature and salinity profiles to evaluate the degree of water column mixing. this is particularly important in upwelling hab outbreaks that often develop after intense sunlight (smayda, 2003). 3.5 chemical habitat measurements the chemical environment is a complex mixture of macronutrients including nitrogen and phosphorous, micronutrients, iron and other trace metals, organic nutrients, water quality factors and secretions by plankton. it is essential to measure macronutrients in a qualitative and predictive monitoring program. long-term measurements of nh4, no3, po4 will reveal trends of nutrient enrichment of water. increasing evidence suggests that hab events in near shore and more open habitats tend to occur with greater frequency and magnitude when nutrient enriched and may increase progressively with nutrification (smayda, 1989; hickel et al., 1989; honjo, 1993). inorganic nitrogen, phosphorous and oxygen are the minimal chemical measurements that should be made particularly where anthropogenic nutrients modification is occurring. growing evidence suggests that dissolved inorganic nitrogen (don) may be of greater nutritional value to some hab organisms than expected (berg et al., 1997). micronutrients also influence hab taxa, with evidence strongest for iron regulation and cupric ion selectivity (takahashi and fukazawa, 1982; anderson and morel, 1978). 3.6 oxygen monitoring routine monitoring of seasonal water column oxygen levels with emphasis on bottom water concentrations, is essential in shallower, poorly flushed coastal waters, at aquacultural sites and in regions exhibiting environmental degradation. a progressive decrease in bottom water oxygen levels can induce die offs in poorly flushed regions subjected to increased nutrient loading and phytoplankton abundance. increased phytoplankton biomass during poorly grazed bloom events such as ceratium blooms (hickel et al., 1989) become nutrient limited, link to the bottom waters and decomposed leading to hypoxia or anoxia. 3.7 remote sensing monitoring large-scale physically driven events is considerably more difficult than standard monitoring programs. it requires a large interdisciplinary research team, access to a wide variety of physical oceanographic instrumentation of ships and is costly. satellites and other remote sensing detectors to establish the local incursions, frontal structure and regional movements of water masses based on temperature and chlorophyll signatures have been successfully used in open coastal waters (kahru et al., 1994; keafer and anderson, 1993). flow-through systems which are deployed on ferries have also been used to monitor hab populations and accompanying physical and chemical condition (harashima et al., 1997). from a practical viewpoint, the taxonomic diversity of hab species complicates monitoring operation, which requires a high degree of specialized expertise. the automated detection of harmful species e.g., with specific molecular probes (scholin and anderson, 1998), seems an attractive approach that would increase monitoring efficiency. targeted studies and technological innovations are also essential to improve our understanding of habs. the behavior variability of bloom species and regulation challenge the design of hab monitoring programs. hab bloom events often appear to be stochastic–the result of the bloom species being at the right action plan for harmful algae management 79 place at the right time (smayda and reynolds, 2001), i.e., being seeded at a time and place when their ecophysiological requirements are accommodated by the bloom habitat. this unpredictability challenges the design of monitoring programs. within a given hab event, several species may exhibit concurrent blooms, with their bloom stages in or out of phase with each other. termination of one hab event may be followed by another, resulting in a series of hab outbreaks during a given year (wong and wu, 1987). effective monitoring programs must deal with such situations. 4. hab management in mariculture economic looses from hab impacts on mariculture can be devastating to local or regional economies but truly large scale fish killing blooms do not occur frequently in mariculture in oman. mariculture fish may be less affected by blooms for a variety of reasons, such as remote geographical location, lower density of bloom organisms, smaller extent of bloom and success of management or mitigation efforts. beside the economic losses, fish mariculture functions as a valuable indicator of the health of our coastal seas. fish reared in mariculture cages may be affected more than wild fish that have the freedom to move and escape from the harmful blooms. improperly located mariculture has the capability of actually stimulating algal blooms, but there are effective strategies for dealing with nutrient and other wastes from net pens that have been or are being adopted in different parts of the world (rensel, 2001). the occurrence of habs sometimes are unpredictable, but the effects may be successfully avoided or managed by a variety of means. in practice, fish farmers in areas not subject to recurring hab events are often ill prepared to deal with fish kills subsequent to major fish losses. therefore, while preparing plans to manage habs the local conditions, resources and abilities should be taken into consideration. conceptual / mathematical models can be developed through hindcasting of empirical data and other means that may give indication of periods of increased hab risk (anderson et al., 2001). remote sensing from buoys, aircrafts, satellites and biosensors that provide sea surface temperature, current data, salinity, chlorophyll and characterization of the species, can help track bloom advection into or through coastal areas with aquaculture facilities. fish losses may occur very rapidly, so advance preparation of a management plan is recommended and systems must be ready for immediate action. 4.1 environmental factors related to site selection site selection is one of the most important criteria for successful mariculture, both in terms of success of a project and for environmental protection. 4.1.1 basic hydrographic monitoring this should be conducted in the general vicinity of proposed fish mariculture in order to evaluate site suitability for the fish species to be reared, minimize benthic and water column impacts, and establish hab risks. vertical monitoring of water temperature, salinity, dissolved oxygen, water transparency and chlorophyll during high risk periods can be strong indicators of the potential for certain types of bloom. in temperate waters, large scale mariculture should be located in moderate to deep water areas where currents disperse solids and wastes adequately. highest consideration should be given to areas already replete with dissolved macronutrients where other factors such as light and vertical mixing limit primary productivity. adverse effects of habs may be reduced or avoided by selecting marine aquaculture sites with moderate or greater vertical mixing and tidal current velocity. microflagellates and dinoflagellates blooms tend to dissipate in turbulent areas and cell growth is reduced (whyte, 1997). 4.1.2 nutrient enrichment nutrient enrichment from fish farm waste has been associated with increased phytoplankton growth and occurrence of the algal blooms, mainly for farms located in shallow, poorly flushed sites that are sensitive to alkindi, a.y.a., al-ghelani, h.m.h., amer, s., al-akhzami, y.k 80 nutrient addition. increasingly this type of mariculture location is rarely sanctioned for new sites in both developing and developed economies (folke et al., 1994). 5. monitoring practices at mariculture the occurrence of habs is sometimes unpredictable, but the effects on fish farms may be successfully avoided or managed by a variety of means. in practice fish farmers in areas not subject to recurring habs are often ill prepared to deal with fish kills. plans should be prepared to manage habs, while considering local conditions, resources and abilities. monitoring can vary from occasional, simple, qualitative, microscopic examination of plankton net tow contents to detailed, daily species count from water bottles or composite depth samples and remote sensing of chlorophyll by automatic profiling probes and aerial surveys. it may also be possible to detect the onset of a hab by monitoring fish behavior. in some cases fish will reduce or stop feeding, seem lethargic, fall back in water currents, or may orient themselves unusually in the water, often swimming close to the surface and losing their self righting ability. different sized fish or species of fish may react with different behavior patterns and physiological responses and some related fish species are found to be more susceptible to habs than others. atlantic salmon, salmo salar, are generally more susceptible to the effects of heterosigma akashiwo than the pacific salmon oncorhynchus kisuthch, or o. tshawytscha, with lethal effects more prevalent in the larger size classes (black et al., 1991). 6. mitigation strategies at mariculture action plans for aquaculture operations include a range of mitigation measures such as: • stop feeding the fish (wong and wu, 1987) • preparing for and/or conducting pre-emptive harvest (wong and wu, 1987) • moving culture pens into waters with less risk of hab (rensel and whyte, 2003) • applying perimeter skirts to culture pens (rensel, 2001) • aeration (colt et al., 1991, boyd and watten, 1989) • potentially suppressing the hab by adding materials to disperse or suppress the algal bloom (e.g. clays etc., sengco et al., 2001, maruyama et al., 1987). 6.1 oxygenation and aeration several aeration technologies are available to prevent fish mortality from environmental hypoxia including aeration from coarse bubble air stones, venturi, aspiration nozzles etc. however, coarse bubble does little to flush microalgal cells from skirted pens (kills, 1979). the method has not been used on a commercial scale but can be used in net pens equipped with perimeter skirts to retain the oxygenated water. moderate levels of oxygen supersaturation (< 300% of air concentration with oxygen; boyd and watten, 1989) may be beneficial to salmonid and yellow tail subjected to compromised water quality (boyd and watten, 1989; okaichi, 1989). supersaturated oxygen in fish culture has been used with some success in freshwater fish hatcheries and is often referred to as “oxygen supplementation”. although oxygen supersaturation has proved effective in the laboratory in reducing fish losses due to at least one harmful alga (c. concavicornis), the economics of supplying the entire net pen with large volumes of oxygen are not favorable (rensel, 1992). oxygenation of fish culture water by aeration is not recommended to sustain marine fish exposed to habs because it is marginally effective in increasing the ambient concentration of dissolved oxygen during the blooms. this is because the transfer rate of dissolved oxygen to water is proportional to the difference between ambient and desired concentrations (rensel and whyte, 2003). the exception would be during the senescent phase of very high density blooms that in some cases may result in environmental hypoxia at night due to algal respiration and cell decay (rensel and whyte, 2003). action plan for harmful algae management 81 6.2 moving net pens towing net pens from an area affected by the habs to a known refuge area is one of the most effective mitigation measures and is a preferred method in some regions. it does however present considerable risk and expense, particularly for larger systems. towing of net pens has been used for preventing salmon losses due to h. akashiwo in puget, sound, washington state and british columbia (horner et al., 1997; whyte 1997). 6.3 alternative culture systems a number of alternative fish mariculture technologies have been proposed or tested in the past. most do not appear to be economically or technically feasible at present due in part to the globalization of the fish markets that cause intense competition among producers. some new cage designs are practical and economical, but offer no inherent advantages for dealing with habs. 6.4 feeding and handling practices during minor habs episodes, a useful management practice is to immediately withhold feed at the onset and during the event. this reduces fish digestive demand for oxygen, which is required for other essential metabolic functions. increasing the amount of oxygen rich carbohydrate in the diet and reducing the oxygen poor fat content could reduce the metabolic demand for oxygen by the fish (rensel and whyte, 2003). 6.5 water treatment there has been growing interest in recent years in various means of elimination of harmful algal bloom by different types of water treatment. one of the most promising methods appears to be the use of clay to flocculate cells from the water column. certain types of naturally occurring blooms destroy or precipitate habs in and near fish rearing farms in the republics of korea and japan. several hab genera have been treated like cochlodinium, chatonella and heterosigma (maruyama et al., 1987; shirota, 1989; kim 1998, choi et al., 1998). excessive use of clay treatment at fish farms has the potential to adversely affect benthic and epibenthic fauna, primarily by sedimentation (maruyama et al., 1987). additional research is needed to understand aspects of clay flocculation. many chemicals are capable of killing hab organisms but most lack specificity toward target organisms. for example, copper sulphate has been widely used in the past for limiting freshwater blooms of algae, but it is not currently considered a viable option for freshwater habs or near mariculture because of negative impacts on non-target organisms, contamination of sediments, temporary effects and high costs (cooke et al., 1993). one large scale treatment is the proposed use of a submerged electrode set at a potential to neutralize harmful oxygen radical produced by chatonella antiqua (tanaka et al., 1994). also treatment with sodium per (oxo) carbonate in a concentration of 50 mgl-1 eliminated 90% of the chatonella cells, after only 2 hours both in the inshore tanks and in the shallow surface layer of shido bay, japan, in 1987 (okaichi et al., 1990). the concentration of sodium per (oxo) carbonate did not significantly alter the ambient ph. 6.6 therapeutics at present there are no readily available internationally approved therapeutic drugs designed specifically to treat fish that have been affected by habs. one of the major killers of farmed fish is considered to be the formation of superoxide anion radical (o-2) by chatonella antiqua and heterosigma akashiwo (tanaka et al., 1994; oda et al., 1997), and cochlodinium polykrikoides (kim et al., 1999). the mechanism of death is considered by some to be mucus stripping from the gills of the fish, which leads to osmoregulatory dysfunction and ultimately to death. reduction of the oxygen radical to the more harmful hydroxy radical is effected in the seawater. treating the radicals with enzymes superoxide dismutase, catalase, and glutathione peroxidase has been demonstrated to protect fish in laboratory studies (yang et al., 1995) and could also alleviate the problem in affected water (colt et al., 1991). consequences of physical damage include hypersecretion of mucus and blood hypoxia. chemicals that can reduce mucus production could potentially provide mitigative action. mucolytic agents fed to fish as l cysteine alkindi, a.y.a., al-ghelani, h.m.h., amer, s., al-akhzami, y.k 82 ethyl ester, have reportedly reduced gill mucus production and sustained fish during exposure to harmful chaetoceros in the laboratory (yang and albright, 1994). this appears to be a useful approach to dealing with acute exposures, but extended exposures over months, may not be effective. other drugs such as adrenaline and acetylcholine that are vasoactive agents, regulating the distribution of blood to the gill secondary lamellae (part et al., 1982) could possibly be of some use in treating hab affected fish. the need to administer these drugs orally and the potentially high cost, however, limits their usefulness. other possible mitigation practices for hab causing fish kill include acclimation of fish to decreased oxygen conditions (shepard, 1995) which elevates the number of erythrocytes in blood. 7. sampling procedures fish kills in aquaculture may have a wide variety of causes, including toxic chemical discharges, disease, environmental hypoxia or anoxia, due to algal bloom decay, discharge of oxygen demanding wastes by other industries, etc. in some cases it may be difficult to ascertain the cause of a specific fish kill, as a number of hab species may be present in water-column samples. 7.1 hydrographic and phytoplankton sampling immediate phytoplankton sampling is perhaps the most important diagnostic tool if a hab is suspected. it is typically more important than normal techniques of fish-tissue analysis. many lesions and abnormalities including those of gill may represent more than one cause (anderson et al., 2003). if sampling is delayed too long and major weather changes occur, the causative hab species may not be detected. dissolved oxygen sampling should be conducted through out the day especially just before sunrise if microalgal bloom respiration or upwelling of low-oxygen water is suspected as a cause of fish mortality (andersen et al., 2003). 7.2 gross morphology of affected fish external appearance of the fish should be carefully noted, including the presence of excessive mucus on the gills or flowing from the opercular cavity, the colour and shape of gills, condition of scales and fins, presence of lesions and other abnormalities. scraping of the gill surface to prepare a microscope slide as a wet mount can be simple and effective method to see if certain hab species are present (rensel and whyte, 2003) 7.3 tissue for histopathology and bacteriology sampling of moribund fish and apparently unaffected fish, rather than dead fish, is highly recommended. fish that have been dead for more than a few minutes may be useless to determine the cause of death using histopathology because tissues are rapidly affected by post-mortem changes (speare and ferguson, 1989). 8. conclusion the challenge is to understand the critical features and mechanisms underlying the population dynamics of hab species. this understanding will serve as a basis for improved monitoring and to build models that predict the occurrence, movement, toxicity and environmental effects of habs. in summary, the sultanate of oman has the largest coastline in the arab world. at present, the fishing industry is prosperous, but there are many environmental hazards such as industry and biological factors that can kill a large population of fish. it is significant to point out there is a need for more experts to monitor the marine environment, 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community assembly application of recent models to harmful dinoflagellate blooms. j. plankton. res., 23: 447-461. speare, d.j. and ferguson, h.w. 1989. fixation artifacts in rainbow trout (salmo gairdneri) gills: a morphometric evaluation. can. j. fish. aq. sc., 46: 780-785. speare, d.j., brackett, j. and ferguson, h.w. 1989. sequential pathology of the gills of coho salmon with a combined diatom and microsporidian gill infection. can. vet. j., 30: 571-575. tanaka, k., muto, t. and shimida, m. 1994. generation of superoxide radicals by the marine phytoplankton organism, chatonella antiqua. j. plankton res., 16: 161-169. takahashi, m. and fukazawa, n. 1982. a mechanism of “red tide” formation ii. effect of selective nutrient stimulation on the growth of different phytoplankton species in natural water. mar. biol., 70: 267273. turner, r.k., van den bergh, j.c.j.m., soderqvist, t., barendregt, a., van den straaten, j., maltby, e. and van ierland,e.c. 2000. ecological-economic analysis of 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accepted i july 2007 preconditioning large indefinite linear squ journal for science, 17 (1) (2012) 63-79 © 2012 sultan qaboos university 63 preconditioning large indefinite linear systems giovanni fasano * and massimo roma ** *department of management, university ca’foscari venezia, venice, italy, e-mail: fasano@unive.it. *the italian ship model basin insean, rome, italy. **dipartimento di ingegneria informatica automatica e gestionale a. ruberti, sapienza università di roma, roma, italy, e-mail: roma@dis.uniroma1.it. abstract: after briefly recalling some relevant approaches for preconditioning large symmetric linear systems, we describe a novel class of preconditioners. our proposal is tailored for large indefinite linear systems, which arise very frequently in many different contexts of numerical analysis and nonlinear optimization. our preconditioners are built as a byproduct of the krylov subspace method used to solve the system. we describe theoretical properties of the proposed class of preconditioners, namely their capability of both shifting some eigenvalues of the system’s matrix to controlled values, and reducing the modulus of the other ones. the results of a numerical experimentation give evidence of the good performance of our proposal. keywords: krylov subspace methods, large indefinite linear systems, large scale optimization, preconditioners, quasi-newton updates. لجملة كبيرة من المعادالت الخطية غير المحددة يةشرطتهيئة جوڤاني فاسانو و ماسيمو روما لجملة كبٌرة من المعادالت الخطٌة المتناظرة، نصف نوع ٌةشرطالتهٌئة الالمتعلقة ب طرقبعد سرد سرٌع لبعض ال :ملخص هر فً التحلٌل العددي دة التً كثٌرا ما تظقٌمٌالئم الجمل الخطٌة الكبٌرة غٌر الهذا المقترح . رقالطهذه جدٌد من ٌلوف الجزئً المستعملة فً حل تلك اكرفضاء نتٌجة جانبٌة لطرٌقة كالمقترحة رٌقةطنبنً ال مثلٌات غٌر الخطٌة.واأل المسبقة وخاصة قدرتها على تغٌٌر تهٌئة بوصف الخواص النظرٌة لهذا الصنف من أدوات ال تقوم هذه الدراسةالجمل. باقً القٌم الذاتٌة. تظهر نتائج التجارب لإلى قٌم متحكم فٌها وتقلٌص القٌم المطلقة الخطٌة جملللالقٌم الذاتٌة لمصفوفة بعض ٌة مدى فاعلٌة الطرٌقة المقترحة.العدد 1. introduction he efficient solution of large linear systems (or a sequence of slowly varying linear systems) is of fundamental importance in many contexts of numerical analysis and nonlinear optimization. in this paper we first recall a few relevant approaches for preconditioning large indefinite linear systems. observe that in many contexts of numerical analysis (see e.g. http://math.nist.gov/matrixmarket) and nonlinear optimization, the t mailto:fasano@unive.it giovanni fasano and massimo roma 64 iterative efficient solution of linear systems and sequences of linear systems is sought. truncated newton methods in unconstrained optimization, kkt systems arising in constrained optimization, interior point methods, and pde constrained optimization are just some examples from optimization. we first show that using information from quasi-newton updates may often provide effective preconditioners. the latter are sometimes endowed with theoretical properties related to the spectrum and the condition number of the preconditioned matrix. then, we describe a novel class of preconditioners for the solution of large indefinite linear systems, without assuming any sparsity pattern of the system matrix. in particular, the class of preconditioners we propose uses information collected from krylov subspace methods, in order to assess the structural properties of the system matrix. we iteratively construct our preconditioners either indirectly using (but not performing) a factorization of the system matrix (see, e.g. (fasano and roma, 2007; golub and van loan, 1996; stoer, 1983)), obtained as by product of krylov subspace methods, or performing a jordan canonical form on a very small size matrix. we address our preconditioners using a general krylov subspace method; then, we prove theoretical properties for such preconditioners, and describe results which indicate how to possibly select the parameters which characterize the definition of the preconditioners. the basic idea of our approach is to apply a krylov subspace method to generate a positive definite approximation of the inverse of the system matrix. the latter is then used to build our preconditioners, needing to store just a few vectors, without requiring any product of matrices. we assume that the entries of the system matrix are not known and the information necessary to build the preconditioner is gained by using a routine, which computes the product of the system matrix times a vector. in the paper (fasano and roma, 2011b) we experiment our preconditioners both in numerical analysis and nonconvex optimization frameworks. in particular, we test our proposal on significant linear systems from the literature. then, we focus on the so called newton-krylov methods, also known as truncated newton methods (see (nash, 2000) for a survey). in these contexts, both positive definite and indefinite linear systems are considered. we recall that in case the optimization problem in hand is nonconvex, i.e. the hessian matrix of the objective function is possibly indefinite and at least one eigenvalue is negative, the solution of newton's equations within truncated newton schemes may require some care. indeed, the krylov subspace method used to solve newton's equation, should be suitably applied considering that optimization frameworks require the computation of descent directions, which have to satisfy additional properties (dennis and schnabel,1983; nocedal and wright, 2000). in this regard our proposal provides a tool, in order to preserve the latter properties. the paper is organized as follows. in section 2 we briefly recall relevant approaches from the literature. then, in section 3 we describe our class of preconditioners for large indefinite linear systems, by using a general krylov subspace method. we detail some theoretical properties of our proposal, along with some hints on its calculation. finally, a section of conclusions and future work completes the paper. regarding the notations, for a n n real matrix m we denote with [ ]m the spectrum of m; ki is the identity matrix of order k and we use the capital letter t to indicate a tridiagonal matrix. finally, with 0c we indicate that the matrix c is positive definite, and  denotes the euclidean norm. 2. some approaches for preconditioning large symmetric systems let us consider the following linear system = , , , n n n ax b a r b r    (1) where a is symmetric and nonsingular, and n is large. we assume that the structure of the matrix a is unknown as is its sparsity pattern. we recall that in case of special structures of matrix a, suitable preconditioners may be built for solving (1) (see (higham, 2002)). as is well-known, the main rationale behind the idea of using a preconditioner to solve the linear system preconditioning large indefinite linear systems 65 (1), consists in introducing the nonsingular matrix m, such that solving =max mb (2) is possibly simpler in some sense than solving (1). of course, to the latter purpose the extreme choices for m are =m i and 1 =m a  (the latter being the ideal choice). in most cases (always when n is large) there is no chance to compute 1 a  (or computing 1 a  is no cheaper than solving (1)). notwithstanding this difficulty, the preconditioner m can be chosen according to the following alternative guidelines:  the linear system (2) should be of easy solution thanks to the structure of matrix m (e.g. preconditioners for linear systems from pdes discretization often have a suitable block-structure which is suggested by the problem in hand);  the condition number ( )ma should be relatively small. the latter fact may be helpful when attempting to solve the preconditioned system (2), with a technique sensitive to ( )ma (e.g. the krylov subspace methods);  the eigenvalues in the spectrum [ ]ma should be as clustered as possible (see e.g. (nocedal and wright, 2000)). the latter fact may again be helpful whenever krylov subspace methods are adopted to solve (2). since we want to deal with the large scale case, without any assumption on the sparsity pattern of a, the main approaches in the literature for building and applying a preconditioner to (1) often gain information on the system matrix by computing the matrix-vector product ,a v with , n v r or rely on numerical differentiation. in particular, among the approaches proposed we have the following:  approximate inverse preconditioners based on using the bfgs update method (see also (nash, 1985; benzi et al., 2000), and references therein). here, the main adopted idea is that a bfgs update may be suitably used to compute the approximate inverse # a of matrix a. then, the matrix # a is applied as a preconditioner.  preconditioners based on the l-bfgs method (see also (morales and nocedal, 2000; 2001), and the class of preconditioners limited memory preconditioners (lmps) by giraud and gratton (2006)), which pursue an idea similar to approximate inverse preconditioners in the previous item.  approximate inverse preconditioners based on the use of krylov subspace methods (see also (simoncini and szyld, 2007; fasano and roma, 2009)), where a krylov subspace method is used to determine the solution of (1) and to provide information in order to build a preconditioner for (1).  band preconditioners based on matrix scaling/balancing (see also (roma, 2005)).  preconditioners based on numerical differentiation (see e.g. (higham, 2002)).  band preconditioners based on the bfgs method (see e.g. (luksan et al., 2010)), where a bfgs update is partially modified, so that suitable band preconditioners are defined for linear systems. this approach was mainly tested within truncated-newton frameworks. for each of the preconditioning strategies mentioned above we have both a theoretical analysis and a numerical experience, for validation. in this paper we want to follow and generalize the approach proposed in fasano and roma (2009), where at any step, an iterative krylov subspace method is used to compute the approximate inverse # ,a over an increasing dimensional subspace. note that as detailed in section 3, our approach also encompasses diagonal and block-diagonal preconditioners. 3. our class of preconditioners in this section we first introduce some preliminaries, then we propose our class of preconditioners. consider the indefinite linear system giovanni fasano and massimo roma 66 = ,ax b (3) where n n a r   is symmetric, n is large and . n b r suppose any krylov subspace method is used for the solution of (3), e.g. the lanczos process or the cg method (golub and van loan, 1996) (but minres (saad, 2003) or planar-cg methods (hestenes, 1980; fasano, 2005) may be also alternative choices). they are equivalent as long as 0,a whereas the cg, though cheaper, in principle may not cope with the indefinite case. in the next assumption 3.1 we suppose that a finite number of steps, say ,h n of the adopted krylov subspace method are performed. assumption 3.1 let us consider any krylov subspace method to solve the symmetric linear system (3). suppose at step h of the krylov subspace method, with 1,h n  the matrices , n h hr r   h h ht r   and the vector 1 n hu r  are generated, such that 1 1 1= , , and t h h h h h h har r t u e r     (4) , if is indefinite = , if is positive definite t h h h h h t h h h h v b v t t l d l t      (5) where • 1= ( ),h hr u u = 0, t i ju u = 1,iu 1 ,i j h   • 1 = 0, t h iu u 1 = 1,hu  1 ,i h  • ht is irreducible and nonsingular, with eigenvalues 1, , h  not all coincident, • 1= diag { }h i h ib   , 1= ( ) h h h hv v v r   orthogonal, ( , )i iv is an eigenpair of ,ht • 0hd is diagonal, hl is unit lower bidiagonal. remark 3.1 note that most of the common krylov subspace methods for the solution of symmetric linear systems at iteration h may easily satisfy assumption 3.1 (saad, 2003; stoer, 1983). in particular, also observe that from (4) we have = , t h h ht r ar so that whenever 0a , then 0.ht since the jordan form of ht in (5) is required only when ht is indefinite, it is important to check whenever 0.ht without computing the eigenpairs of ht if unnecessary. for this purpose, note that the krylov subspace method adopted always provides relation = , t h h h ht l d l with hl nonsingular and hd block diagonal (blocks can be 1 1 or 2 2 at most), even when ht is indefinite (saad, 2003; stoer, 1983; fasano and roma, 2007). thus, checking the entries of hd will suggest if the jordan form = t h h h ht v b v is really needed for ,ht i.e. if ht is indefinite. furthermore, the matrix ht captures much information on the eigenvalues of a, corresponding to eigenvectors in 1span{ , , }.hu u indeed, let , n v r then hr v belongs to the krylov subspace 1span{ , , }.hu u now, considering that = t h h hr ar t from (4), and recalling that = , t h h hr r i relation 2 2t hm v v t v m v  implies 2 2 2 2 = ( ) ( ) = . t h h h hm r v m v r v a r v m v m r v  preconditioning large indefinite linear systems 67 thus, m and m are respectively a lower bound and an upper bound of eigenvalues of a, corresponding to eigenvectors in 1span{ , , }.hu u observe also that from assumption 3.1 the parameter 1h  may be possibly nonzero, i.e. the subspace 1span{ , , }hu u is possibly not an invariant subspace under the transformation performed by matrix a (thus, in this paper we consider a more general case with respect to (baglama et al., 1998)). remark 3.2 the adopted krylov subspace method may in general perform m h iterations, generating the orthonormal vectors 1, , .mu u then, we can set 1 = ( , , ),h h r u u with 1{ , , } {1, , },h m and change relations (4-5) accordingly; i.e. assumption 3.1 may hold selecting any h out of the m vectors (among 1, , mu u ) computed by the krylov subspace method. remark 3.3 for relatively small values of the parameter h in assumption 3.1 (say 20,h  as it often suffices in the applications), the computation of the eigenpairs ( , ),i iv = 1, , ,i h of ht when ht is indefinite may be extremely fast, with standard codes. for example, if the cg is the krylov subspace method used in assumption 3.1 to solve (3), then the matlab (2011) (general) function eigs() requires as low as 4 10   seconds to fully compute all the eigenpairs of ,ht for = 20,h on a commercial laptop. in the case where the cg is the krylovsubspace method of choice, the matrix ht is tridiagonal. nonetheless, in a separate paper (fasano and roma, 2009) we consider a special case where the request (5) on ht may be considerably weakened under mild assumptions. moreover, in the paper (fasano and roma, 2011b) we also prove that for a special choice of the parameter 'a' used in our class of preconditioners (see below), strong theoretical properties may be stated. on the basis of the latter assumption, we can now define our preconditioners and show their properties. to this aim, considering for the matrix ht the expression (5), we define (see also (gill et al., 1992)) 1d | | , | |= diag {| |}, if is indefinite , | | = , if is positive definite . t h h h h i h i hef h h h v b v b t t t t        as a consequence, when ht is indefinite we have 1 1 ˆ| | =| | = , t h h h h h h ht t t t v i v   where the h nonzero diagonal entries of the matrix ˆhi are in the set { 1, 1}.  furthermore, it can be easily seen that | |ht is positive definite, for any h, and the matrix 1 2 1 | | | | =h h h ht t t i   is the identity matrix. now let us introduce the following n n matrix, which depends on the real parameter 'a':   d 1 1= ( ) | | , 1 , ef t t t t h h h h h h h h h hm i r r r t r a u u u u h n       1 , 1 1 ( 1) , 1 | | 0 = | | 1 0 t hh h tt h h n h hh t n h n h rt ae r u r uae i r                                 (6) d = ( ) | | = | | , ef t t t n n n n n n n n nm i r r r t r r t r  (7) where hr and ht satisfy relations (4-5), ,a r the matrix [ ( 1)] , 1 n n h n hr r      is such that giovanni fasano and massimo roma 68 , 1 , 1 ( 1)= t n h n h n hr r i    and 1 , 1| |h h n hr u r    is orthogonal. observe that of course the matrix , 1n hr  in (6) always exists, with , 1 , 1 1 1= ( | )( | ) . t t n h n h n h h h hr r i r u r u    using the parameter dependent matrix hm in (6-7) we are now ready to introduce our class of preconditioners   # 1 1( , , ) = | | t t h n h h h hm a d d i r u r u d            1 2 1 1 | | | | 1 th h h h h h t h t ae r du r du ae             (8) # 1 ( , , ) = | | . t n n n nm a d r t r  (9) theorem 3.1 consider any krylov subspace method to solve the symmetric linear system (3). suppose that assumption 3.1 holds and the krylov method performs h n iterations. let ,a r = 0, and let the matrix n n d r   be such that 1 , 1| |h h n hr u dr    is nonsingular, where   , 1 , 1 1 1= | | tt n h n h n h h h hr r i r u r u    . then, we have the following properties: a) the matrix # ( , , )hm a d is symmetric. furthermore when 1,h n  for any 1 1/2 { ( | | ) }, t h h ha r e t e      # ( , , )hm a d is nonsingular; when =h n the matrix # ( , , )hm a d is nonsingular; b) the matrix # ( , , )hm a d coincides with 1 hm  as long as either = nd i and = 1, or = ;h n c) for 1 1/2 | |<| | ( | | ) t h h ha e t e   the matrix # ( , , )hm a d is positive definite. moreover, if = nd i the spectrum # [ ( , , )]h nm a i is given by 1 2 # ( 1) | | [ ( , , )] = ; 1 h h h n n h t h t ae m a i i ae                        d) when 1:h n  if d is nonsingular then # ( , , )hm a d a has at least  3h  singular values equal to 2 1 / ; if d is nonsingular and = 0a then the matrix # ( , , )hm a d a has at least  2h  singular values equal to 2 1 / ; e) when = ,h n then # 1 ( , , ) = ,n nm a d m  [ ] = [| |]n nm t  and 1 1 [ ] = [ ] { 1, 1},n nm a am        i.e. the n eigenvalues of the preconditioned matrix # ( , , )hm a d a are either +1 or -1. proof. see (fasano and roma, 2011b) for the proof. □ the corollary which follows considers the important particular case obtained by setting = 0,a = 1 and preconditioning large indefinite linear systems 69 = ,nd i in the definition of the preconditioner # ( , , ).hm a d corollary 3.2 consider any krylov subspace method to solve the symmetric linear system (3). suppose that assumption 3.1 holds and the krylov subspace method performs h n iterations. then, the preconditioner   # 1 1(0,1, ) = | | t h n n h h h hm i i r u r u           1 1 1 | | 0 | | 0 1 th h h h h t r u r u           (10) # 1 (0,1, ) = | | , t n n n n nm i r t r  (11) is such that a) the matrix # (0,1, )h nm i is symmetric and nonsingular for any ;h n b) the matrix # (0,1, )h nm i coincides with 1 ,hm  for any ;h n c) the matrix # (0,1, )h nm i is positive definite. moreover, its spectrum # [ (0,1, )]h nm i is given by  # 1[ (0,1, )] = | | ;h n h n hm i t i         d) when 1,h n  then the matrix # (0,1, )h nm i a has at least  2h  singular values equal to +1; e) when = ,h n then [ ] = [| |]n nm t  and # 1 1 [ (0,1, ) ] = [ ] = [ ] { 1, 1},n n n nm i a m a am         i.e. the n eigenvalues of # (0,1, )h nm i a are either +1 or -1. proof. the result is directly obtained from (6-7) and theorem 3.1, with = 0,a = 1 and = .nd i □ remark 3.4 as stated in the comments to relation (6), the matrix , 1n hr  in the statement of theorem 3.1 always exists, such that 1 , 1| |h h n hr u r    is orthogonal. however, , 1n hr  is neither built nor used in (8-9), and it is introduced only for theoretical purposes. furthermore, it is easy to see that since 1 , 1| |h h n hr u r    is orthogonal, any nonsingular diagonal matrix d may be used in order to satisfy the hypotheses of theorem 3.1. remark 3.5 observe that the case h n in theorem 3.1 is of scarce interest for large scale problems. indeed, in the literature of preconditioners the values of 'h' typically do not exceed 10-20 (morales and nocedal, 2001; gratton et al., 2011). moreover, for small values of h in (8), the computation of the inverse matrix 1 2 | | 1 h h t h t ae ae           (12) in order to provide # ( , , )h nm a i or # ( , , ),hm a d may be cheaply performed when ht is either indefinite or positive definite. indeed, after a brief computation we have 1 1 1 1 1 2 2 4 2 1 2 1 | | | | | | | | | | = , 1 | | t h h h h h h h h h t t h h h a t t e e t t e t ae ae e t a                                (13) with giovanni fasano and massimo roma 70 2 1 2 = . 1 | | t h h h a a e t e      (14) thus, when ht is indefinite, remark 3.3 and relation (13) will provide the result. on the other hand, in case 0,ht it suffices to use (13). finally, the proper setting of the parameter 'a' allows to easily control the condition number of matrix (12). figure 1. the condition number of matrix a (i.e. ( )cond a ) along with the condition number of matrix # (0,1, )h nm i a (i.e. 1 ( )cond m a  ), when {10, 20, 30, 40, 50, 60, 70, 80, 90},h  and a is randomly chosen with entries in the uniform distribution [ 10,10].u  4. preliminary numerical results in order to preliminarily test our proposal on a general framework, without any assumption on the sparsity pattern of the matrix a, we used our parameter dependent class of preconditioners # ( , , ),hm a d setting = 1 and = .nd i we anticipate that in our numerical experience we obtain very interesting results concerning the correspondence between theoretical and numerical results. indeed, all the results stated in theorem 3.1 for the singular values of the (possibly) unsymmetric matrix # ( , , ) ,hm a d a seem to hold in practice also for the eigenvalues of # ( , , )hm a d a (it is worth recalling that since # ( , , ) 0hm a d , then # # 1/2 # 1/2 [ ( , , ) ] [ ( , , ) ( , , )h h hm a d a m a d am a d     ]), so that # ( , , )hm a d a has only real eigenvalues. regarding the numerical investigation, we used 3 different sets of test problems. first, we considered a set of symmetric linear systems as in (3), where the number of unknowns n is set as = 1000,n and the matrix a has also a moderate condition number. we simply wanted to experience how our class of preconditioners affects the condition number of a. in particular (see also (geman, 1980)), a possible choice for the latter class of matrices is given by ,= { }, [ 10,10], , = 1, , ,i j ija a a u i j n  (15) where , ,=i j j ia a are random entries in the uniform distribution [ 10,10],u  between -10 and +10. then, also the vector b in (3) is computed randomly with entries in the set [ 10,10].u  we computed the preconditioners preconditioning large indefinite linear systems 71 (8-9) by using the conjugate gradient (cg) method (higham, 2002), which is one of the most popular krylov subspace iterative methods to solve (3) (golub and van loan, 1996). we remark that the cg is also often used in case the matrix a is indefinite, though it can prematurely stop. as an alternative choice, in order to satisfy assumption 3.1 with a indefinite, we can use the lanczos (1950) process, minres methods (paige and saunders, 1975) or planar-cg methods (fasano, 2005). in (8) we set the parameter h in the range { 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 },h  and we preliminarily chose = 0a (though other choices of the parameter 'a' yield similar results), which satisfied items a) and c) of theorem 3.1. we have generated several matrices like (15), obtaining very similar results. in particular, given one instance of a as in (15), we plotted in figure 1 the condition number ( )a of a ( ( )cond a ), along with the condition number # ( (0,1, ) )h nm i a of # (0,1, )h nm i a ( 1 ( )cond m a  ): in both cases the condition number  was calculated by preliminarily computing the eigenvalues 1, , n  (using matlab (2011) routine eigs()) of a and # (0,1, )h nm i a respectively, then obtaining the ratio | |max = . | |min i i i i    evidently, numerical results confirm that the order of the condition number of a is pretty similar to that of the condition number of # (0,1, ) .h nm i a this indicates that if the preconditioners (8) are used as a tool to solve (3), then most preconditioned iterative methods which are sensitive to the condition number (e.g. the krylov subspace methods) are, on average, not expected to perform worse with respect to the unpreconditioned case. however, it is important to remark that the spectrum # [ (0,1, ) ]h nm i a tends to be shifted with respect to [ ],a inasmuch as the eigenvalues in [ ]a whose absolute value is larger than +1 tend to be scaled in # [ (0,1, ) ]h nm i a (see figure 2). the latter property is an appealing result as described in section 1, since the eigenvalues of # (0,1, )h nm i a will be 'more clustered'. the latter phenomenon was better investigated by introducing other sets of test problems, described hereafter. table 1. the adopted linesearch-based truncated newton method giovanni fasano and massimo roma 72 figure 2. comparison between the full/detailed spectra (left/right figures) [ ]a (unprecond) and # [ (0,1, ) ]h nm i a (precond), with a randomly chosen (eigenvalues are sorted for simplicity); without loss of generality we show the results for the values 5= = 20h h and 6= = 30.h h the intermediate eigenvalues in the spectrum # [ (0,1, ) ],h nm i a whose absolute value is larger than 1, are in general smaller than the corresponding eigenvalues in [ ].a the eigenvalues in # [ (0,1, ) ]h nm i a are more clustered near +1 or -1 than those in [ ].a in a second experiment we generated the set of matrices a such that = ,a hdh (16) where , n n h r   = 500n , is a householder transformation given by = 2 , t h i vv with n v r a randomly chosen unit vector. the matrix n n d r   is diagonal (so that its non-zero entries are also eigenvalues of a, while each column of h is also an eigenvector of a). the matrix d is such that its perc n eigenvalues are larger (about one order of magnitude) than the remaining (1 )perc n  eigenvalues (we set = 0.3perc ). finally, again we computed the preconditioners (8-9) by using the cg, setting the starting point 0x so that the initial residual 0b ax was a linear combination (with randomly chosen coefficients -1 and +1) of all the n eigenvectors of a. we strongly highlight that the latter choice of 0x is expected to be not favorable when applying the cg, in order to build our preconditioners. in the latter case the cg method is indeed expected to perform exactly n iterations before stopping (see also (nocedal and wright, 2000; saad, 2003)), so that the matrices (4.2) may be significant to test the effectiveness of our preconditioners, in case of small values of h (broadly speaking, h small implies that the preconditioner contains correspondingly little information on the inverse matrix 1 a  ). we compared the spectra [ ]a and # [ (0,1, ) ],h nm i a in order to verify again how the preconditioners (8) are able to cluster the eigenvalues of a. following the guidelines in (morales and nocedal, 2001), in order to test our proposal also on a different range of values for the parameter h, we set preconditioning large indefinite linear systems 73 { 4 , 8 , 12 , 16 , 20 }.h  the results are given in figure 3 (full comparisons) which includes all the 500 eigenvalues, and figure 4 (details) which includes only the eigenvalues from the 410-th eigenvalue to the 450-th eigenvalue. observe that our preconditioners are able to shift the largest absolute eigenvalues of a towards -1 or +1, so that the clustering of the eigenvalues is enhanced when the parameter h increases. for each value of h the matrix a is (randomly) recomputed from scratch, according to relation (16). this explains why in the five plots of figures 3-4 the spectrum of a changes. again, a behavior very similar to figures 3-4 is obtained also using different values for the parameter 'a'. figure 3. comparison between the full spectra [ ]a (unprecond) and # [ (0,1, ) ]h nm i a (precond), with a nonsingular and given by (16) (eigenvalues are sorted for simplicity); we used different values of h ( 1 = 4,h 2 = 8,h 3 = 12,h 4 = 16,h 5 = 20h ), setting = 500.n the large eigenvalues in the spectrum # [ (0,1, ) ]h nm i a are in general smaller (in modulus) than the corresponding large eigenvalues in [ ].a a 'flatter' piecewise-line of the eigenvalues in # [ (0,1, ) ]h nm i a indicates that the eigenvalues tend to cluster around -1 and +1, according with the theory. giovanni fasano and massimo roma 74 figure 4. comparison between a detail of the spectra [ ]a (unprecond) and # [ (0,1, ) ]h nm i a (precond), with a nonsingular and given by (16) (eigenvalues are sorted for simplicity); we used different values of h ( 1 = 4,h 2 = 8,h 3 = 12,h 4 = 16,h 5 = 20h ), setting = 500.n the large eigenvalues in the spectrum # [ (0,1, ) ]h nm i a are in general smaller (in modulus) than the corresponding large eigenvalues in [ ].a a 'flatter' piecewise-line of the eigenvalues in # [ (0,1, ) ]h nm i a indicates that the eigenvalues tend to cluster around -1 and +1, according with the theory. to complete our preliminary experience we tested our class of preconditioners in optimization frameworks. in particular, we considered a standard linesearch-based truncated newton method in table 1, where for any 0k  the solution of the symmetric linear system (newton's equation) 2 ( ) = ( )k kf x d f x  is required. we considered several unconstrained optimization problems from cuter collection (gould et al., 2003), and for each problem we applied the truncated newton method in table 1. at the outer iteration k we computed the preconditioner # (0,1, ),h nm i with {4, 8, 12, 16, 20},h  by using the cg to solve the equation 2 ( ) = ( ).k kf x d f x  then, we adopted # (0,1, )h nm i as a preconditioner for the solution of newton's equation at the subsequent iteration preconditioning large indefinite linear systems 75 2 1 1( ) = ( ) .k kf x d f x   the iteration index 'k' was the first index such that both relations 31 10 and 0.95k k k k k x x x       (17) hold (the first relation implies that 1 ,k kx x  while the second holds when the search direction 1( ) /k k kx x   approaches newton's step). thus, the index k was chosen in order to have 1k kx x  small, i.e. the entries of the hessian matrices 2 ( )kf x and 2 1( )kf x  are not expected to differ significantly. for simplicity we just report the results on two test problems, using = 1000,n in the set of all the optimization problems experienced. very similar results were obtained for almost all the test problems. figure 5. the condition number of matrix 2 1( )kf x  ( ( )cond a ) along with the condition number of matrix # 2 1(0,1, ) ( )h n km i f x  ( 1 ( )cond m a  ), for the optimization problem noncvxun, when 1 17.h  the condition number of 2 1( )kf x  is close to the condition number of # 2 1(0,1, ) ( ),h n km i f x  for any value of the parameter h. the value = 175k was chosen as in (17) and it was 176 175 0.083.x x  in figures 5-6 we consider the problem noncvxun. for the sake of brevity we only show the numerical results using = 16h in (8). observe that since 1kx  is close to kx (i.e. we are eventually converging to a local minimum) the hessian matrix 2 1( )kf x  is positive semidefinite. furthermore, again the eigenvalues larger than +1 in 2 1[ ( )]kf x   are scaled in # 2 1[ (0,1, ) ( )].h n km i f x   similarly we show in figures 7-8 the results for the test function nondquar in cuter collection. the test problems in this optimization framework, where the preconditioner # (0,1, )h nm i is computed at the outer iteration k and used at the outer iteration 1,k  confirm that the properties of theorem 3.1 may hold also when # (0,1, )h nm i is used on a sequence of linear systems = ,k ka x b when ka changes slightly with k. giovanni fasano and massimo roma 76 figure 6. comparison between the full spectra/detailed spectra (left figure/right figure) of 2 1( )kf x  (unprecond) and # 2 1(0,1, ) ( )h n km i f x  (precond), for the optimization problem noncvxun, with 4= = 16.h h the eigenvalues in # 2 1[ (0,1, ) ( )]h n km i f x   larger than +1 are evidently scaled, so that # 2 1[ (0,1, ) ( )]h n km i f x   is more clustered. figure 7. the condition number of matrix 2 1( )kf x  ( ( )cond a ) along with the condition number of matrix # 2 1(0,1, ) ( )h n km i f x  ( 1 ( )cond m a  ), for the optimization problem nondquar, when 1 17.h  the condition number of 2 1( )kf x  is now slightly larger than the condition number of # 2 1(0,1, ) ( )h n km i f x  (though they are both 10 10 ). the value = 40k was chosen as in (17) and it was 41 40 0.203.x x  5. conclusions we have given theoretical and numerical results for a class of preconditioners, which are parameter dependent. the preconditioners in our proposal can be built by using any krylov method for the symmetric preconditioning large indefinite linear systems 77 linear system (3), provided that it is able to satisfy the general conditions (4-5) in assumption 3.1. the latter property may be appealing in several real problems, where a few iterations of the adopted krylov subspace method may suffice to compute an effective preconditioner. figure 8. comparison between the full spectra/detailed spectra (upper figure/lower figures) 2 1[ ( )]kf x   (unprecond) and # 2 1[ (0,1, ) ( )]h n km i f x   (precond), for the optimization problem nondquar, with 4= = 16.h h some nearly-zero eigenvalues in the spectrum 2 1[ ( )]kf x   are shifted to non-zero values in # 2 1[ (0,1, ) ( )].h n km i f x   since many eigenvalues in 2 1[ ( )]kf x   are zero or nearly-zero, the preconditioner # (0,1, )h nm i may be of slight effect, unless large values of the parameter h are considered. giovanni fasano and massimo roma 78 our proposal seems tailored also for those cases where a sequence of linear systems of the form = , = 1, 2,k ka x b k requires a solution (e.g., see (morales and nocedal, 2001) for details), where ka slightly changes with the index k. in the latter case, the preconditioner # ( , , )hm a d in (8-9) can be computed applying the krylov subspace method to the first linear system 1 1= .a x b then, # ( , , )hm a d can be used to efficiently solve = ,k ka x b with = 2, 3,k . on this guideline, in a future work we are going to experience our proposal with other preconditioners described in section 2. in particular, we think that a comparison with the proposals in (gratton et al., 2011; morales and nocedal, 2000) could be noteworthy. finally, the class of preconditioners in this paper seems to be an interesting tool also for the solution of linear systems in financial frameworks. in particular, in future works we want to focus on symmetric linear systems arising when we impose kkt conditions in portfolio selection problems, with a large number of titles in the portfolio, along with linear equality constraints (see also (al-jeiroudi et al., 2008)). 6. acknowledgment the first author wishes to thank the italian ship model basin insean, cnr institute, for their support. 7. references al-jeiroudi, g., gondzio, j. and hall, j. 2008. preconditioning indefinite systems in interior point methods for large scale linear optimization. optimization methods and software, 23: 345–363. baglama, j., calvetti, d., golub, g. and reichel, l. 1998. adaptively preconditioned gmres algorithms. siam journal on scientific computing, 20: 243–269. benzi, m., cullum, j. and tuma, m. 2000. robust approximate inverse preconditioner for the conjugate gradient method. siam journal on scientific computing, 22: 1318–1332. dennis, 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appl., 14: 1–59. stoer, j. 1983. solution of large linear systems of equations by conjugate gradient type methods. in mathematical programming. the state of the art, a. bachem, m. grötschel, and b. korte, eds., berlin heidelberg, springer-verlag, pp. 540–565. received 15 july 2011 accepted 13 september 2011 photovoltaic cells and systems: 57-67 squ journal for science, 16 (2011) © 2011 sultan qaboos university 57 ground radiometric method as a tool for determining the surface boundary of a buried bauxitic karst kamal kareem ali*, salih muhammad awadh and jassim muhammad hemad department of earth science, college of science, university of baghdad, baghdad, iraq, *email : kkak1962@yahoo.com. المدفونة لحدود السطحية لخسفات البوكسايتفي تعيين ا األرضية شعاعيةاستخدام القياسات اإل و جاسم محمد حمد ضكمال كريم علي ، صالح محمد عو مسمماتاضخنمممكخيممتطشخمسممت يلشخاخيممط ختفمم خمتايممت خ مم خذ مم خخ9قياسممالخخل لةيممشخاعيممعاىيشخىلمم خ مم خخ42تممأخذ مم خ :خصص مل تمأخاسمت اأخم يماشخذيمعشخنمكختط يكخاخعتي خ)خاخج تاسيخاعسة (خ يخاخص تاءخاخغتتيمشخممكخاخعمتا خاخ سةاضخاخت طسايتيشخ تممأخ فليممالخخفيممانخاخ يمما خا يممعاىيخاخطلمميخ مميخاختتتممشخاخسمم يش خ اخمممد ختتلمم ت خي يمم خاخصمم ي أخ،غاممماخ أخذعتتمم خق مم اض خىي ماضخختاتيمشختمأخجمعمماخممكختتمتخا تتماتأخي تمت خاخمختا نما شخ،خجمعضخىي اضخممكخاختتتمشخاخسم يشخى م خطم خ ف مشخقيمان ت يمم خاخ مم خخ،تاخت طسممايضخاخ سممةيخطيممشغاممماخاخ يةيممش خاخممم شخاخممتتينخمممكخةمم خاخ تاسممشخةمم خختأيممعش للممضخخ،خاخ سممةش تي مماختتا مضخاخ لةيمشخخ،ىم خ قيفمشخ06-06خاخس يشخخل سةش ختتا حخاخ يا خا يعاىيخىل خسم خاخ سمةشخاخت طسمايتيشخممك ىم خ قيفمش خىمليماضخاختج يمشخاخطيميا يمشخ اصمشخا اتمشخخ150خ–خ100 يعاىيشخختط يكخاخعتيم خاخم أخي تنمكخاخ سمةشخممكخا سمة ختتعمالخخم خاخ ماكخةم خاخع اصمتخامتمدضخمكخصم تخاخغ ماءختاتجما خاعخ232اخث تي أخ238خاخي شخ فلضخاخي تا ي أخ يممعاىي خسممتاخاغ مماءخةمم اخاخ مما ختاخ يمما خا أختفتيتمماخمممماخ5ىلمم خىممم خىلمم خاسمم خاخمعمما كخاخ ي يممشخ اخت طسممايضخاخممم كخ خمم خاخطمماكخ يمما ماخا يممعاىيخذقمم خمممكخمسممت خاخ لةيممشخخ،خمممكخاخع اصممتخاخميممعشخذصممت ضخصمم تخاخغ مماءخاخميمم شخ انممتش صم تخاخغ ماءخخ ميخ232اخث تيم أخ238خ-يعاىيخخلي تا يم أكخقيأخاخ يا خا ذا يعاىيش ختيكخاخت لي خاخ يةيخعيعشخغاماخ ختيطممت خ خطغممأخ مميخاخت طسممايضخ تفممشخاخ مميكخاخةل تمميخىلمم خاختمم اخيخ260خ–خ240تيطممت خ خطغممأ خ مميخ مميكختلغممضخخ3خ–خ0.5 م ممماختممأخت يمم خق ممتخاخ سممةشخخ،خيممعا تسمممضخ تي ممشختسمما أخا خ،خيممعاىيخىلمم خاخسمم تاالىتممما خىلمم ختتممايكخاخيمم خا كخ تيفمشخقيمانخذأ ختتمتةكخاخ تاسمشخاخ اخيمشخخ200خ–خ150 اخ أختتا حخمكخخ،ق اعيعاىيخشخاخ أخيمث خاخي خا اخت طسايتي خخخ ج خاخ سةاضخاخت طسايتيشخ ت ي خ ةاخاخس يش طيشخىكخمةي خج الخخلخاعتنيشخيعاىيشاخ لةيشخا abstract: forty two ground radiometric measurements along nine traverses within a rectangular network area were taken across a bauxitic karst within the ubaid formation (lower jurassic) in the western desert of iraq. a 4-channel gamma ray spectrometer (gad-6) with sodium iodide nai (tl) crystal (gsp-4s) was used in the field to measure the total radioactivity of the surface soil. soil samples collected from the surface at each measurement point and core samples collected from a test well penetrating the karst were analyzed by gamma ray spectrometer. the main objective of this study was to detect the hidden bauxitic karst and determine its surface boundary. the radioactivity on the surface of the karst was ranging between 60 and 80 count per second (c/s), while the background radioactivity of the ubaid formation, which hosts the karst, was ranging between 100 and150 c/s. chemical weathering, kamal kareem ali et al. 85 especially dissolution and leaching moved uranium ( 238 u) and thorium ( 232 th) from the overburden downward. accordingly, these elements have been adsorbed on the surface of clay minerals and bauxite buried at a depth of about 5m causing enrichment with radioactivity. the leached overburden lack radioelements, so its radioactivity was less than background radioactivity level. the gamma ray spectroanalysis showed that the radioactivity of 238 u and 232 th in the overburden was 0.5 and 3 bq/kg, whereas, in the bauxite and flint clay bed, it was 240 and 160 bq/kg respectively. based on the radioactivity anomaly contrast on the surface, an isorad map was plotted and the karst diameter which represents low anomaly was determined to be ranging from 150 to 200m. the current study demonstrates that the ground radiometric method is quite useful for detecting the bauxitic karst and inferring its surface boundaries. keywords: radiation; karst; bauxite; gamma ray; ubaid formation; isorad. 1. introduction auxite comprising 55% alumina is the principal source of aluminum. from a geological point of view, bauxite is a residual rock that formed intermittently throughout much of the earth’s history during periods of intense continental subaerial weathering. bauxite deposits are usually classified according to their mineralogy, chemistry, and host-rock lithology (b’ardossy and aleva, 1990). of all known bauxite deposits, about 88% is of laterite type, 11.5% is of karst type, and the remaining 0.5% is of tikhvin type (b’ardossy, 1995; b’ardossy and aleva, 1990; meyer, 2004). in 2001, bauxite was mined in 22 countries. the 12 largest producing countries account for about 97% of the world production (plunkert, 2001); australia is currently the largest producer, with about 53.3 million metric dry tons (mt) of bauxite, followed by guinea (15.7 mt), brazil (13.9 mt), jamaica (12.4 mt), china (9.5 mt), and india (8.39 mt). the bauxite ore is red colored because of iron content (10–25%). it also contains various amounts of water and silica (abbady and el-arabi, 2006). in iraq, karst bauxite was discovered in 1989 within the ubaid formation in the western desert between wadi hauran and wadi al-hussainiyat (figure 1). sediments formed essentially from bauxite with minor karst-filling sediments were named later as the nuwaifa formation. radiometric methods are used in the investigation of mineral deposits and ores in many parts of the world. initially, radioactivity measurements in boreholes and airborne gamma spectrometry were used in petroleum exploration (howell and frosch, 1939; lundberg et al. 1952; kellogg, 1975). darnley and ford (1987) concluded that in many cases, the airborne gamma-ray spectrometry technique is probably more useful than any other single airborne geophysical or remote sensing technique for providing information directly interpretable in term of surface geology (darnley and ford, 1987). it is one of the most important methods that has been used as aid to geologic mapping (darnley and grasty, 1971; kotel'nikov and grigor'ev, 1972 ; darnley, 1991; shives, 1996; rabie et al. 2000; buccianti et al. 2009). also, gamma ray measurements have been applied in investigation of mineral deposits (constello and norquay, 1967; tixer and alger, 1970; iaea,2003)). in northern canada, polymetallic mineralization was discovered using gamma-ray surveys (charbonneau,1987; gandhi et al. 1996). these surveys have resulted in exploration and production of significant canadian deposit types that contain gold, cobalt, copper, bismuth and tungsten. airborne gamma ray measurements were used for identifying serpentinized ultramafic rocks and associated soils in northern california which are characterized by high concentrations of cr and ni. because ultramafic rocks and their soils are naturally lacking in radioelements, gamma-ray surveys can be used to produce quasi-geochemical maps that identify radiometrically deficient areas (mc-caffety and van gosen, 2009). some other applications include underwater investigations. (van wijngaarden et al. 2002). airborne gamma spectrometry surveys helped in exploring some bauxite deposits in saudi arabia (al-bassam and mustafa, 1989). also, there is some information about the radioactivity associated with bauxite deposits in gant in hungary, and unterlaussa in austria (valeton, 1972). there is the chance of the b http://gsc.nrcan.gc.ca/gamma/ref_e.php#regional http://www.springerlink.com/content/?author=g.+n.+kotel'nikov http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=a.%20buccianti&field=au http://gsc.nrcan.gc.ca/gamma/ref_e.php#mazlake http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=b.s.%20van%20gosen&field=au ground radiometric method 85 association of uranium and thorium with bauxite and clay deposits (samama, 1984), depending on the similarity of the geochemical environment during the deposition, and on the behavior of these elements (al-atia, 1993). figure 1. location map showing the distribution of karsts and the study area in the western desert of iraq. airborne radiometric measurements carried out in iraq with a traverse interval of 2 km did not yield any radioactive anomalies as the surface area of the karst ranges between 0.2 and 0.4 km on average, and 34 m to 105 m depth (al-rubaii, 1997). however, the present work aims to discuss the capability of the ground radiometric method in detecting the surface boundaries of buried karst containing bauxite and clay minerals in the western desert of iraq. 2. the study area the study area is located in the middle of the western desert of iraq near the crossing of wadi hauran and wadi hussainiyat. it is accurately determined with longitudes (41˚ 04′ 32″ 41˚ 05′ 11″) and latitudes (33˚ 32′ 2″ 33˚ 32′ 21″) (figure 1). in the northwest of wadi hussainiyat, some sporadic karsts containing bauxite deposits (mustafa et al. 1991) are scattered within dolomite of the ubaid formation (lower jurassic). the studied karst (figure 2) has identification number 47 in the classification list that has been prepared by the geological survey and mineral investigation company in iraq (al-rubaii, 1997). kamal kareem ali et al. 06 figure 2. simplified geological map showing mesozoic and tertiary formations exposed in the study area. 3. geological setting 3.1 geomorphology valleys, hills, plateaus, pediments and karstification are the common features that can be seen in the study area. wadi huaran and wadi hussainiyat, which are seasonal valleys, are important valleys in the region surrounded by hills formed from dolomite and dolomitic limestone and are mostly covered with black quartzite because of the desert varnish (buday and hack, 1980). two main plateaus exist; the first is the ubaid plateau, which appears to be a rugged plateau characterized by exposures of yellow dolomite of the ubaid formation (l. jurassic) and hosts most of the bauxitic karsts; and the second one is the ghar plateau, which is a low rugged plateau formed essentially from conglomerates of the ghar formation (miocene) covered with calcrete. some of the bauxitic karsts are covered partially with the sediments of the ghar formation. 3.2 lithostratigraphy paleozoic, triassic, jurassic and tertiary rocks are exposed in the western desert of iraq. in the study area, the paleozoic rocks are not exposed and are mainly covered with sedimentary rocks belonging to the triassic, jurassic and tertiary ages (figure 2). these formations are nearly horizontal, consisting mainly of carbonate and/or clastic rocks (jassim and goff, 2006). several wadies have been filled with quaternary deposits. a lithostratigraphic sequence could be described from oldest to youngest as in the zor hauran formation (u. triassic), which has a tidal to sub-tidal depositional environment composed of marl, marly dolomite, limestone, dolomitic limestone and with dolomite at the top (buday and hack, 1980). the ubaid formation (l. jurassic) consists of chert interbededed with dolostone at the bottom; with light gray dolostone and greenish yellow shale containing secondary gypsum at the top of the formation. it conformably emplaces on ground radiometric method 06 zor hauran formation representing the first sedimentary cycle of the jurassic with an average thickness of 65m (al-mubarak, 1983). karstification is the most important feature in the ubaid formation (al-rubaii, 1997). the hussainiyat formation (m. jurassic) deposited unconformably on the ubaid formation when the tidal environment changed to the continental environment. it is composed of a clastic unit at the bottom of the formation, whereas the top is composed of limestone. the clastic unit is comprised of sand, silt, kaolinite and iron oxide, which indicates a fluviatile environment (jassim and goff, 2006). figure 3. sketch diagram of karst showing the stratigraphic column, vertical and horizontal dimensions without scale. 4. the nature of karst according to sweeting (1972) two features of karst are observed in the western desert of iraq; the first is sink holes, which belong to the active karstification system, whereas the second feature is fossil karsts, which belong to the buried karstification system. the current study was conducted on buried karst. chemical weathering of run-off water and ground water is considered an important factor forming karst in a humid climate. karsts appear to be contemporaneously filled with sediments during karstification. the stratigraphic column in the studied karst could be described lithologicaly from the bottom to the top as sand, bauxitic clay and flint clay, sandy clay, red clay and soil (al-rubaii,1997) (figure 3). sand appears to be unconsolidated white sand fining upward with an average thickness of 3 m. flint clay has a white to gray color with an average thickness of 8 m characterized by concoidal fractures containing kaolinite mixed with organic matters and pyrite surrounded by bauxitic clay. bauxite existes as hard lenses within flint clay characterized by pisolitic texture. sandy clay, red clay with soil representes the overburden of bauxite ore. sand soil red clay sandy clay ubaid formation bauxite and flint kamal kareem ali et al. 06 5. materials and methods total radioactivity measurements were recorded at the surface of the probable buried karst in the region. nine traverses, including forty two measurement points (figure 4) were achieved with a portable gad-6 nai(tl) scintillation counter (sintrex, canada). readings were recorded in counts per second (c/s) after 300 second at each location. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 0 50 100 150 200 250 300 350 400 450 distance (m) 0 50 100 150 200 250 300 350 400 450 500 550 d is ta n c e ( m ) figure 4. network measurements on the surface of the probable karst. soil samples were collected from the surface soil at each measurement point, as well as the core samples that were collected from the test well (sm77, karst 47). the nature and mineralogy of the core samples were identified according to the field observations (al-rubaii, 1997). samples were overnight dried at 100˚c, crushed, sieved through a 1 mm mesh sieve and analyzed for uranium ( 238 u), thorium ( 232 th) and potassium ( 40 k) using a gamma spectrometric system based on a pure germanium detector with an efficiency of 40% (tennelec, usa) attached to an 8192-channel personal computer analyzer. the activity concentrations of 238 u, 232 th and 40 k were determined with the computer code gdr-4 (nucleus, usa). merinelli beaker geometry was used for the measurements. the energy and efficiency of measurement was calibrated by europium-152 ( 152 eu, iaea, vienna) standard source. positional data were recorded using a portable gps receiver. ground radiometric method 06 6. results and discussion the total radioactivity count rates in the study area range from 57 to 147 cps (table 1). it was recorded as 60 to 90 cps in the central part of the study area (probable karst), while the background radiation was 100 -150 cps (ali, 2004; ali and alsheikh, 2009) in the surrounding area and the ubaid formation, which hosts the bauxite karsts. an isorad map of the total radioactivity measurements at the surface of the studied area was plotted (figure 5). since the surface radiometric measurements reflect the radioactivity of the top few meters of the soil (not more than three meters), the map in figure 5 obviously exhibits the radioactivity on the surface of karst as depleted level in comparison with the background radiation of the areas surrounding the karst (ubaid formation). the continuous chemical washing of the sediments at the surface of the karst caused leaching alkalis and some elements downward (millot, 1970). the humid climate that was prevalent during jurassic time participated in activation of chemical weathering; dissolution and washing of overburden moved uranium, thorium, potassium and rubidium with alkalis downward producing an overburden depleted with radioelements, especially uranium and thorium, whereas the buried sediments filled the karst enriched with radioelements due to adsorption of those radionuclides (u and th) by clay minerals and bauxite deposits. 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 450 500 50 60 70 80 90 100 110 120 130 140 150 r a d io a c ti v it y ( c p s ) surface distance (m) s u rf a c e d is ta n c e ( m ) figure 5. isorad map plotted from data in table 1, displaying the depletion of radioactivity at the overburden of karst (the blue color), and illustrates the estimated boundary of the karst by contour line of 90 cps. kamal kareem ali et al. 06 this mechanism led to accumulating the radioactive materials within clay beds, flint and bauxite at a depth of more than 5m which can’t be detected by the portable gamma ray spectrometer (eisenbud and gesell, 1997), while the washed overburden remained with radioactivity less than the background radiation in comparison with the surrounded area. table 1. total radioactivity in the studied area. radioactivity total count (cps) measurement point no. radioactivity total count (cps) measurement point no. 110 22 147 1 115 23 135 2 140 24 141 3 88 25 143 4 94 26 138 5 98 27 139 6 110 28 65 7 146 29 97 8 100 30 125 9 96 31 140 10 105 32 60 11 130 33 60 12 118 34 102 13 100 35 118 14 100 36 145 15 110 37 57 16 123 38 96 17 117 39 115 18 120 40 138 19 118 41 68 20 119 42 68 21 57 147 range according to the scale of figure 5 the surface diameter of the karst is estimated to be about 150 to 200 m. these results were supported by results of the gamma spectral analysis which have been done on the surface soil samples and the core samples collected from well penetrating the karst (table 2). the results showed, that the radioactivity of 238 u and 232 th in the surface soil is as low as 0.5 bq/kg and 3 bq/kg respectively at the surface of the karst, while the average radioactivity of 238 u, 232 th and 40 k in soil surface and rock samples of the ubaid formation outside the karst were 33 bq/kg, 26 bq/kg and 359 bq/kg respectively. on the other hand, the radioactivity of 238 u and 232 th in bauxite and flint clay at depth more than 5 m of the karst center is higher, and reaches up to 240 bq/kg and 160 bq/kg respectively. this case is interpreted as that the source rock including radioelements were washed and leached from the high lands of the older formations such as the gaara fotmation (permocarboniferous) which have a relatively high concentration of radioelements (ali, 2004; ali and alsheikh, 2009). then, these were accumulated in the low lands at the first stage and filled the karsts. the continuous washing and leaching of the surface soil introduced karsts with overburden depleting in radioelements. the leached elements were accumulated within ground radiometric method 08 the clay and bauxitic beds at depth of more than 5 m. it is believed that the ga'ara formation outcroping to the west of the study area is the main source rocks that has supplied radioactive elements to younger formations (ali, 2004; ali and alsheikh, 2009). the regional background radiation of the area, represented by the ubaid formation and other lower jurassic formations, is between 100 and 150 cps. the radioactivity concentration of the different lithologies within the karst are illustrated in figure 6. soil has a finite capacity to adsorb potassium (chrestopher et al. 2007). concentration of 40 k in the surface soil was higher than of its concentration in the others beds of the test well, but it was lower than its concentration in the soil and rock samples collected from the ubaid formation which was found to be 359bq/kg in average (table 2). on the other hand, 238 u and 232 th have low radioactivity in the surface soil, while they have higher radioactivity in the deeper beds (red clay, sandy clay, flint and sand) within the karst (figure 3). 0 50 100 150 200 250 r a d io a c ti v it y ( b q /k g ) 40k 238u 232th radioactive elements soil red clay sandy clay flint sand figure 6. radioactivity concentration of selected core samples from the test well within the studied karst. table 2. total radioactivity (cps) and radioactivity of 238 u, 232 th and 40 k in selected samples of the test well penetrating the karst and the average(av.) radioactivity in samples selected from the ubaid formation(host rock). sample type depth (m) total radioactivity (cps) radioactivity (bq/kg) 40 k 238 u 232 th soil 0 5.0 80 194 0.5 3 red clay 5.0 20.0 130 150 90 11 sandy clay 20.0 23.5 130 89 85 50 flint 23.5 25.0 115 0.5 240 160 sand 25.0 26.6 90 41 61 14 ubaid formation surface 116 (av.) 359 (av.) 33(av.) 26(av.) the radioelements u-238 and th-232 were leached from the overburden (soil) leaving it poor with radioactivity. thereafter these elements are accumulated in the clay beds and flint so they have relatively high concentrations as shown in the histogram (table 2) and (figure 6). kamal kareem ali et al. 00 7. conclusion from the results obtained from this study, it can be concluded that the ground radiometric survey coupled with gamma ray spectroanalysis technique can be considered as an effective technique in preliminary studies to detect mineral deposits especially those deposits containing radioelements. this study confirms that the detailed ground radioactivity measurements technique is one of the important methods and a successful technique for providing useful information in the investigation of clay and bauxite deposits. accordingly, also this technique has enough capability in determining the surface boundary of the bauxites karst and its dimensions. 8. references abbady, a.g.e and el-arabi, a.m., 2006. naturally occurring radioactive material from the aluminium industry, a case study: the egyptian aluminium company, nag hammady, egypt, j. radiol. prot., 26 (1): 415-422. al-atia, m.j., 1993. study of possibility of using the radiometric methods for bauxite deposits exploration in western desert of iraq. inter. rep. no. 2211 a, geosurv. baghdad, iraq. al-bassam, k. and mustafa. m., 1989. report about bauxite ore site in al-zubayra saudi arabia. internal report no. 1795, g, geosurv., baghdad, iraq. ali, k.k. and alsheikh, z., 2009. natural radioactivity of the southeast limb of gaara depression – west of iraq. "proceeding of the 3 rd scientific conference of college of science", university of baghdad, 24-26 march 2009, baghdad, iraq. ali, k.k., 2004. radiogeological study of western desert-iraq with special emphasis on radioecology. ph.d. thesis, baghdad university. al-mubarak, m., 1983. regional mapping of the southern and western desert of iraq. unpublished report. geoserv., baghdad. iraq. al-rubaii, d.a.h., 1997. geochemistry and mineralogy of the karst bauxite rocks in the western desert of iraq. m.sc. unbuplished thesis. university of baghdad, college of science. 117p. b’ardossy, g., 1995. carboniferous to jurassic bauxite deposits as paleoclimatic and paleogeographic indicators. can. soc. petroleum geologists, mem. 17: 283-93. b’ardossy, g. and aleva, g.j.j., 1990. lateritic bauxites developments in economic geology. elsevier, amsterdam. buccianti, a., apollaro, c., bloise, a., de rosa, r., falcone, g., scarciglia, f., tallarico, a., and vecchio, g., 2009. natural radioactivity levels (k, th, u and rn) in the cecita lake area (sila massif, calabria, southern italy): an attempt to discover correlations with soil features on a statistical base. geoderma. 152 (1-2): 145-156. buday, t. and hack, j. 1980. on the geological survey of the western part of the western desert of iraq. geol. survey iraq. internal report. baghdad, iraq. charbonneau, b.w., 1987. gamma spectrometric and magnetic anomalies associated with cu-u mineralization, faber lake volcanic belt, district of mackenzie, nwt, in current research, part c, geological survey of canada. paper 88-1c :255-258. chrestopher, a.b. claude, e.b. and rouse, d.b., 2007. potassium adsorption by bottom soils in ponds for inland culture of marin shrimp in alabama. journal of the world aquaculture society. 38 (1): 85-91. constello, j.t. and norqauy, i.p., 1967. logging the prairie evaporates formation in saskatchewan, in miming and underground geophysics/1967, economic. geology. 26: 492-496. darnley, a.g., 1991. the development of airborne gamma-ray spectrometry: case study in technological innovation and acceptance, nuclear geophysics. 5 (4): 377-402. darnley, a.g. and ford, k.l., 1987. regional airborne gamma-ray surveys: a review. in: exploration ’87 (ed. g.d.garland), 229-240. third decennial international conference on geophysical and geochemical http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=a.%20buccianti&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=c.%20apollaro&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=a.%20bloise&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=r.%20de%20rosa&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=g.%20falcone&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=f.%20scarciglia&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=a.%20tallarico&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=g.%20vecchio&field=au ground radiometric method 06 exploration for minerals and groundwater. special volume 3. geological survey of canada, ontario, canada.. darnley, a.g., and grasty, r.l., 1971. mapping from the air by gamma-ray spectrometry, geochemical exploration, special volume. 11: 485-500. eisenbud, m. and gesell, t., 1997. environmental radioactivity, 4th edition, academic press, usa. gandhi, s.s., prasad, n. and charbonneau, b.w., 1996. geological and geophysical signatures of a large polymetallic exploration target at lou lake, southern great bear magmatic zone, nwt; in current research, 96-1e, geological survey of canada, 147-158. howell, l.g., and frosch, a., 1939. gamma-ray well logging: geophysics, 4:106-114. iaea , 2003, guidelines for radioelement mapping using gamma ray spectrometry data, iaea-tecdoc-1363. jassim, s.z. and goff g.c., 2006. geology of iraq. dloin, prague and moravian museum, brno. czech republic. kellogg, w.c., 1975. observations and interpretation of radioactive patterns over some california oil fields, mining magazine, 47: 26-28. kotel'nikov, g.n. and grigor'ev, v.v., 1972. the application of radiometric methods in the mapping of discontinuous structures (faults) and in searching for rare-metal deposits. translated from atomnaya énergiya. 33 (6): 989-990. lundberg, h., roulston, k.i., pringle, r.w. and brownell, g.w., 1952. oil exploration with scintillation counters: oil in canada, 4: 40-46. mccafferty, a.e. and van gosen, b.s., 2009. airborne gamma-ray and magnetic anomaly signatures of serpentinite in relation to soil geochemistry, northern california. applied geochemistry. 24 (8):1524-1537. meyer, f.m. 2004. availability of bauxite reserves. natural resources researches.13 (3): 161-172. millot, g. 1970. geology of clay. chapman and hall, london. mustafa, m. hussain, d.a., and jibraail, a.s., 1991. exploration results about bauxite in north of hussayniat, western desert, part 1, inter. rep., 45p., geosurv., baghdad, iraq. plunkert, p, a, 2001. bauxite and alumina. u.s. geol. survey, minerals year book, metals and minerals, usa. http://minerals.er.usgs.gov/minerals/pubs/commodity/bauxite/bauxmyb01.pdf rabie, s.i., ammar, a.a. and goud, m.a., 2000. application of factor analysis as an aid to geological mapping, using aerospectrometric data, wadi atalla area, central eastern desert, egypt: proceedings of the fourth arab conference on the peaceful uses of atomic energy, tunis, 3:19-45. samama, j., 1984. uranium in lateritic terrain in surficial uranium deposits. iaea, tecdoc. 322, 53-59. shives, r.b.k., 1996. application of airborne multiparameter geophysical data (gamma-ray, magnetometer, vlf-em) to mapping and exploration in the rusty lake and snow lake areas; in extech 1: a multidisciplinary approach to massive sulphide research in the rusty lake-snow lake greenstone belts, manitoba, ed. by g.f. bonham-carter, a.g. galley and g.e.m. hall, geological survey of canada bulletin, 426: 277-279. sweeting, m.n., 1972. karst land forms. macmillon, london. tixer, m.j. and alger, r.p., 1970. log evaluation of nonmetallic mineral deposits: geophysics, 35: 124142. valeton, i., 1972. bauxites, vol. 1: developments in soil science, elsevier, new york. van wijngaarden, m., venema, l.b., de meijer, r.j., zwolsman, j.j.g., van, o.b. and gieske, b., 2002. radiometric sand-mud characterization in the rhine–meuse estuary part a. geomorphology. 43: 87-101. received: 29 january 2011 accepted: 12 october 2011 http://www.springerlink.com/content/?author=g.+n.+kotel'nikov http://www.springerlink.com/content/?author=v.+v.+grigor'ev http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=a.e.%20mccafferty&field=au http://journals2.scholarsportal.info.proxy.lib.uwaterloo.ca/search-advanced.xqy?q=b.s.%20van%20gosen&field=au photovoltaic cells and systems: 33-40 squ journal for science, 18 (2013) © 2013 sultan qaboos university 33 volatile compounds of the leaves and flowers of lavandula dhofarensis a.g. miller john r. williams, majekodunmi o. fatope*, salma m.z. al-kindy, fakhr eldin o. suliman and salim h. al-saidi department of chemistry, college of science, sultan qaboos university, p.o. box 36, al-khoud, 123 muscat, sultanate of oman, *email: majek@squ.edu.om. abstract: the leaves and flowers of lavandula dhofarensis were collected from the dhofar region of oman and hydro-distilled to give low boiling volatiles, which did not condense at 10 o c. the dichloromethane extract of the hydrosol was analyzed by gc/fid and gc/ms. sixty four compounds were identified in the volatiles of the leaves, accounting for 78.7% of the total. the major components were caryophyllene oxide (8.0%), germacrene (7.9%), spathulenol (7.8%), and caryophyllene (6.6%). eighty six compounds were also identified in the volatiles of the leaves plus flowers, comprising 94.5% of the total. the major compounds were camphor (12.9%), viridiflorol (10.5%), -terpinyl acetate (7.5%), valerenal (7.2%), -gurjunene (5.6%), and spathulenol (5.5%). compounds such as linalool, linalyl acetate, 1,8-cineole, and -ocimene, which are usually found as the major components of lavender oils, were either absent or detected at low levels (<0.1%) in the hydrosol of l. dhofarensis. this investigation showed that the fragrance essence of l. dhofarensis is different from the other lavandula species. l. dhofarensisis is regionally endemic to wetter areas of oman. keywords: lavandula dhofarensis; lamiaceae; volatile composition; valerenal; caryophyllene oxide; viridiflorol; -terpinyl acetate; spathulenol; leaves and flowers. lavandula dhofarensis نبات وزهور من أوراق المتطايرةالمواد ، فخر الدين سليمان و سالم السعيدي وليم، ماجيك فاتوب، سلمى الكندي جون سلطنة من منطقة ظفار فً lavandula dhofarensisمن أوراق وزهوراستخالص المواد المتطاٌرة بواسطة التقطٌر تم :ملخص كما تم تحلٌل مستخلص ثانً كلورٌد المٌثان من هذه المواد المتطاٌرة منخفضة الغلٌان باستخدام الكروماتوغرافٌا وطٌف .عمان وراق. المركبات فً األ رةمتطاٌالمن اجمالً المركبات 7.87%مركبا فً هذه المواد وهذه تمثل اربعة وستونالكتلة. تم تحدٌد caryophyllene oxide ،(7.9%) germacrene ،(7.8%) spathulenol ،(6.6%) (%8.0)فً االوراق هً: الرئٌسة β-caryophyllene من اجمالً (5.89%). كما تم تحدٌد ستة وثمانون من المركبات المتطاٌرة فً االوراق والزهور وهذه تمثل viridiflorol (10.5%) ،α-terpinyl acetate (7.5%)، (7.2%)، (12.9%) (camphor)الكافور على المركبات وتحتوي valerenal ،(5.6%) α-gurjunene (%5.5)و spathulenolوهً: . المركبات التً غالباً ما تتواجد فً زٌوت الالفندر linalool ، linalyl acetate ،1,8-cineole و-ocimene أقل من نبات أو تواجدت بكمٌات ضئٌلةغابت عن زٌوت هذا ال تتواجد l. dhofarensisisكما وان . هذه الدراسة أظهرت أن عطرٌة هذا النبات تختلف عن أنواع االفندر األخرى. (%180( فقط فً المناطق الرطبة من سلطنة عمان. ;lavandula dhofarensis; lamiaceae; volatile composition; valerenal; caryophyllene oxide: مفتاح الكلمات ; viridiflorol; -terpinyl acetate; spathulenol; ر8وأوراق وزه 1. introduction avandula dhofarensis a.g. miller (lamiaceae) (figure) is a leafy wild-growing perennial herb, producing an aromatic smell of lavender or faintly of lemons (miller and morris, 1988). it grows in clumps; the stems are hairy l john r. williams et al. 4. and much-branched and the leaves are ovate with up to 5 pairs of segments. the leaves are 7.5 to 50 mm long and 3 to 20 mm wide. the flowers are lilac in color and 15 to 70 mm long. it is endemic to the dhofar region of oman where it is commonly known as ‘heryen ekúlún’ and ‘hilbēn’ in jabbali vernacular (miller and morris, 1988). l. dhofarensis is not found in drier areas of oman. the genus lavandula comprises about 30 species which are found in mediterranean countries (miller and morris, 1988). lavender oils have a delightful smell, and neurological, antimicrobial and insect repellant properties (miller and morris, 1988; cavanaugh and wilkinson, 2002; lis-balchin and hart, 1999). the pleasant smell of the flowers of lavenders are used in linen chests to perfume clothes or deter clothes moth (miller and morris, 1988). it is believed that the smell of lavenders clears the head and lifts the spirits (rich, 1997). the lavenders are useful medicinal plants (cavanaugh and wilkinson, 2002; harborne and williams, 2002; chamberlain and bollen, 2011) which accumulate volatile compounds in the leaves and flowers and their oils have several applications in animal health management, flavoring, and the cosmetic and perfume industries (pirali-kheirabadi and teixeira da silva, 2010; guillen et al., 1996). figure. lavandula dhofarensis a.g. milller. the chemical composition of the essential oil of the lavandula species (l. augustifolia miller (= l. officinalis chaix = l vera de candolle), l. viridis l’her, l. pubescens dec, l. dentate l., l. lanata l., l. canariensis miller, l. latifolia m., l. stoechas l. and l. mutifida l.) have been extensively investigated by different extraction methods and gc/ms analyses (guillen et al., 1996; kim and lee, 2002; paul et al., 2004; chorgrani et al., 2010; porto et al., 2009; pallado et al., 1997; an et al., 2001; cong et al., 2008; shellie et al., 2002; da porto and decorti, 2010). guillen et al. (1996) analyzed the components of the oil of the aerial parts of l. latifolia cultivated in north eastern spain and found 57 compounds of which linalool (36.9%), 1,8-cineole (31.3%), and camphor (13.6%) were major components. pallado et al. (1997) identified up to 38 compounds in the oil of l. officinalis. the group also observed that the chemical composition of oil varied with extraction methods. with supercritical fluid extraction, the major constituents were linalyl acetate (21.2%), camphor (14.2%), and linalool (13.9%). in contrast, soxhlet extraction yielded camphor (19.7%), eucalyptol (17.2%), and eugenol (8.4%) as the major components; and steam distillation produced oil containing camphor (26.6%), linalool (20.1%), and eucalyptol (18.7%). an and hatfield (2001) analyzed the fragrance of living l. angustifolia flowers by solid-phase micro-extraction coupled to gc and ion-trap ms. they identified 42 compounds, the major components being linalool, linalyl acetate, terpin-4-ol, (e)-caryophyllene, (z)-and (e)-ocimene. cong et al. (2008) identified 17 compounds in the hydro-distilled oil of l. angustifolia growing in china and found linalool (44.5%), geraniol (11.0%), lavandul acetate (10.8%), 3,7-dimethyl-2,6-octadien-1-ol (10.4%) and isoterpineol (6.8%) as major components. based on botanical features, the lavenders fall into four categories: l. latifolia, l. angustifolia, l. stoechas, sometimes known as french lavender, and lavandula x intermedia, a sterile breed between l. latifolia and l. angustifolia. from a literature review, the most frequently identified volatile components of the aerial parts of the lavenders irrespective of group or analysis method are linalool, linalyl acetate 1,8-cineole, camphor, terpinen-4-ol, and -ocimene (porto et al., 2009). broadly, the lavenders may be grouped as linalool or camphor chemotypes, based on the most abundant component of the floral oil. the percentage composition of each of the major components varies from one species to the other and the relative levels of each component determine the market value, smell and medicinal application of their oils. however, no references to the components of the oil or volatiles produced by l. dhofarensis were found in the literature. volatile compounds of lavandula dhofarensis 49 as part of our investigation of the composition and bioactivity of the essential oil from fragrant endemic plants in oman, we report here, for the first time, the chemical composition of steam-distilled volatiles of l. dhofarensis subspecies dhofarensis. 2. experimental 2.1 chemicals pure standards of linalool, -terpineol, 1,4-cineol, terpinolene, camphor, cedrol, fenchol, anethole, and c8-c20 alkane standard solutions were purchased from fluka; eugenol, borneol,-caryophyllene, caryophyllene oxide from aldrich; p-cymene,  -terpiene, -terpineol, and veratrole from acros organics; phellandrene from cica reagent, and p-menth-1-en-4-ol from merck. 2.2. plant material the fresh leaves and flowers of l. dhofarensis subspecies dhofarensis were collected from the dhofar region of oman, 4.4 km from the ma’amura roundabout on the salalah-marbat road at an altitude of 40 m in september 2002 and identified by dr. shahina ghazanfar. a voucher specimen was deposited in the herbarium of the botanical garden at sultan qaboos university under the code name np020. approximately 600 g of fresh plant material (either leaves only or combined leaves and flowers) were subjected to hydro-distillation using a 10-liter stove still apparatus (essential oil university, new albany, in, usa) for 3 h. no condensed oil was visible in the arm of the modified clevenger-type apparatus used but the condensed steam had a distinct and pleasant odor. the hydrosol was extracted twice with 2.0 ml of dichloromethane and dried over anhydrous sodium sulfate. the organic solution was transferred to gc-ms auto-sampler vials, ready for analysis. 2.3 analysis of the volatile extract gc/fid analyses were performed on a focus gc gas chromatograph (thermo electron corporation, italy) equipped with fid detector, and a db-1 column, 30 m x 0.25 mm, 0.25 µm film thickness (j and w scientific, folsom, ca, usa). analyses were conducted under the following conditions: the carrier gas was he; flow rate 2.7 ml/min; injection port temperature, 250 o c; oven temperature, programmed from 35 250 c at 5 c /min up to 200 c and 20 c/min and then held at the upper limit of 250 c. split/split less injection: solutions of oil in dichloromethane were injected in split mode at a ratio of 1:20. gc/ms analyses were performed on a shimadzu (kyoto, japan) gcms-qp5050a using a 30 m × 0.250 mm × 0.25 µm db-1 column from j and w scientific (folsom, ca, usa). the carrier gas was helium at a flow rate of 2.7 ml/min and the split mode had a ratio 1:20. the injector and detector temperatures were 275 c. after injection, the oven temperature was kept at 35 c for 2 minutes, and then programmed at a rate of 2 c/min to a temperature of 200 c for 5 minutes followed by an increase to the final temperature of 240 c at 5 c/min. for the mass spectra, the electron impact ionization was at 70 ev, and the acquisition scan was from m/z 40 to 500 (1000 amu/sec at 0.5 sec intervals). qualitative data were obtained electronically from area percent data. some compounds were identified by comparison of gc retention times with those of standards on a gc-fid instrument, by computer matching of mass spectral fragmentation patterns using digital library (wiley spectral library of 229,000 spectra) of the gc-ms instrument or by comparison of their calculated retention indices relative to c8-c20 standard n-alkane with literature values (shellie et al., 2002; da porto and decorti 2010; migel et al., 2004; baratta et al., 1998; gancel et al., 2003). table 1. composition of l. dhofarensis subspecies dhofarensis volatiles for leaves only and combined leaves and flowers. no. compound a,e ri b (calc) ri (lit) 16-20 area (%) c leaves leaves + flowers leaves leaves + flowers 1 -pinene 921 939, 930, 927 1.5 2 verbenene 936 0.1 3 sabinene 956 976, 958, 963 0.1 4 1-octen-3-ol 961 0.2 5 3-octanol 978 0.2 6 m-cymene 1003 1003 1026 1006 0.1 0.3 7 thujol 1005 0.1 8 octyl formate 1055 0.6 9 terpinolene d 1071 1088,1064, 1075 0.7 john r. williams et al. 43 no. compound a,e ri b (calc) ri (lit) 16-20 area (%) c leaves leaves + flowers leaves leaves + flowers 10 nonanal 1080 1102, 1083 0.2 11 linalool d 1081 1082 1098, 1074 1098 0.1 0.6 12 fenchyl alcohol d 1088 1088 1.1 13 -campholene aldehyde 1094 1094 0.2 0.2 14 camphor d 1095 1095 12.9 15 octenyl acetate 1097 1.2 16 trans-pinocarveol 1110 1106 0.2 17 3-octanyl acetate 1111 0.7 18 trans-verbenol 1118 1118 1114 1.2 0.7 19 pinocarvone 1124 1124 0.2 0.2 20 nonenal 1130 0.1 21 p-mentha-1,5-dien-8ol 1136 1136 1167 0.3 0.3 22 terpine-4-ol 1149 1149 1177 0.1 0.3 23 p-cymen-8-ol 1151 1151 1183 0.3 0.4 24 myrtenal 1153 1154 0.2 0.1 25 -terpineol d 1161 1161 1189 1148 0.1 0.9 26 verbenone 1164 0.3 27 berbenone 1164 0.2 28 decanal 1180 0.1 29 trans-carveol 1188 0.3 30 octyl acetate 1194 1137 1.4 31 cumin aldehyde 1197 1200 1.5 32 carvone 1200 1201 1242 0.4 0.2 33 neral 1205 0.1 34 nerol 1232 1206 0.2 35 citral 1236 1245 0.2 36 linalyl acetate 1238 0.1 37 2-caren-10-al 1241 0.3 38 trans-anethole 1250 0.2 39 2-undecanone 1271 1291 2.3 0.1 40 carvacrol 1278 1298 0.3 41 cis-octahydro-8amethyl-2(1h)naphthalenone 1306 2.1 42 cis-octahydro-4amethyl-2(1h)naphthalenone 1308 1.2 43 eugenol d 1319 1319 1356 1327 0.1 0.1 44 bicycloelemene 1321 0.6 45 -terpinyl acetate 1324 1326 0.1 7.5 46 -cubebene 1336 1345,1332 0.3 47 2-heptadecanone 1343 0.5 48 e-damascenone 1351 1380 0.1 49 -copaene 1360 1360 1380, 1375,1374 0.3 0.5 50 -bourbonene 1366 1366 1384, 1362,1379 2.3 2.2 51 methyleugenol 1368 1384, 1362,1379 2.3 1.3 52 -elemene 1375 1375 1391 2.9 0.2 53 dehydroaromadendrene 1379 0.2 54 2,4dihydroxyeicosane 1385 0.1 volatile compounds of lavandula dhofarensis 47 no. compound a,e ri b (calc) ri (lit) 16-20 area (%) c leaves leaves + flowers leaves leaves + flowers 55 -caryophyllene d 1398 1397 1418 1391 6.6 0.3 56 aristole 1399 0.3 57 calarene 1410 1432 0.3 58 gurjunene 1419 1432, 1400 2.1 59 -bergamotene 1421 1414 2.2 60 dehydroaromadendrene 1425 1.8 61 -humulene 1428 1454, 1447 2.0 62 aromadendrene 1435 1435 1461, 1419 2.2 0.5 63 -gurjunene 1439 5.6 64 -ionone 1449 0.3 65 1,1,3,6,8pentamethyl-1,2dihydronaphthalene 1449 0.2 66 -amorphene 1452 0.2 67 germacrene 1455 1457, 1474 7.9 1.9 68 widdrene 1457 1429 0.3 69 -selinene 1458 1485, 1476 0.4 70 2,3,5,8-tetramethyl decane 1461 0.3 71 -cubebene 1462 1408 1.0 0.1 72 -cedrenoxide 1466 0.1 73 bicyclogermacrene 1468 1480, 1500 1.5 74 -muurolene 1475 0.6 75 retro-ionone 1480 0.1 76 -bisabolene 1487 1509 0.5 77 calamenene 1488 0.8 78 isogeraniol 1492 0.1 79 -cadinene 1496 1495 1524 3.3 0.6 80 -sesquiphellandrene 1498 0.1 81 bisabolol oxide 1499 0.1 82 -calacorene 1504 0.4 83 1,3,5,5,6,6hexamethyl-1,3cyclohexadiene 1508 1.8 84 trans, trans-2,4dodecadienal 1508 0.6 85 elemol 1514 0.4 86 farnesyl acetone 1530 2.1 87 viridiflorol 1531 1590 10.5 88 spathulenol 1541 1540 1560, 1569 8.0 2.0 89 caryophyllene oxide d 1544 1543 1581 8.0 2.0 90 globulol 1548 1583 0.6 91 salvial-4(14)-en-1one 1552 1552 0.5 0.2 92 dihydro-neoclovene 1556 1556 0.8 0.3 93 -ionone 1559 0.2 94 2,4-dimethyl-1decene 1563 0.2 95 humulene oxide 1568 2.6 0.5 96 1,2-methylenedioxy5,6-dimethoxy-4allylbenzene 1576 1.1 97 carotol 1581 0.1 98 dihydro-cis-carveol 1589 0.4 99 diepi--cedrene 1595 1.4 100 widdrol 1600 1.2 john r. williams et al. 4. no. compound a,e ri b (calc) ri (lit) 16-20 area (%) c leaves leaves + flowers leaves leaves + flowers 101 isospathulenol 1600 0.5 102 -cadinol 1603 0.8 103 -eudesmol 1605 1649 0.3 104 -cadinol 1609 1653 0.3 105 torreyol 1610 1645 3.0 0.7 106 valerenal 1615 0.5 7.2 107 1,4-cis-1,7-transacorenone 1617 0.3 108 9-aristolen-1.-ol 1618 0.7 109 -damascone 1620 0.9 110 -tetrahydrocostunoli 1623 2.7 111 nerolidol epoxyacetate 1625 1.1 112 thujyl alcohol 1625 0.5 113 3-butyl-3-octen-2-one 1630 0.3 114 (z)-valerenyl acetate 1632 0.5 115 4e,6e-diisopropenyl1e,2-cyclohexane 1636 0.1 116 p-nonylphenol 1646 0.2 117 tridecanal 1646 0.1 118 campherenone 1651 0.3 119 -cedrol 1661 0.4 120 -1-cadinene aldehyde 1663 0.2 121 citronellal 1671 0.6 a list of compounds in elution order from db-1 column. b ri relative to c8-c20 n alkanes on db-1 column. c gc peak area % d identification by standard e identification by ms/ri 3. results and discussion a total of 64 and 86 components were identified in the volatiles of the leaves and leaves plus flowers respectively of l. dhofarensis subspecies dhofarensis (table 1). these compounds accounted for 78.7% of the leaf volatiles and 94.5% of the leaf plus flower volatiles. for the leaves, 37.3% were sesquiterpene hydrocarbons and 30.1% were oxysesquiterpene derivatives (table 2). for the combined leaves and flowers, 18.2% were sesquiterpene hydrocarbons and 34.0% were oxysesquiterpenes (table 2). from table 3, the major components in the leaf volatiles were caryophyllene oxide (8.0%), germacrene (7.9%), spathulenol (7.8%), and -caryophyllene (6.6%). table 2. compound distribution in the analyzed volatiles of l. dhofarensis subspecies dhofarensis. compound class amount present in volatiles (%) leaves leaves and flowers monoterpene hydrocarbons 1.8 1.0 oxymonoterpenes 6.5 30.0 sesquiterpene hydrocarbons 37.3 18.2 oxysesquiterpenes 30.1 34.0 others 3.0 11.3 the major components in the leaf and flower volatiles were camphor (12.9%), viridiflorol (10.5%), -terpinyl acetate (7.5%), valerenal (7.2%), -gurjunene (5.6%), and spathulenol (5.5%). compared to other lavandula species (paul et al., 2004; chorgrani et al., 2010; porto et al., 2009; pallado et al., 1997; an et al., 2001; cong et al., 2008; shellie et al., 2002; da porto and decorti, 2010) the percentages for these compounds are high with the exception of camphor. qualitative studies of lavender have also shown variable composition of the major components: linalool (35-37%), linalyl acetate (21-34%), 1,8-cineole (4-11%) and camphor (5-12%) (da porto and decorti, 2010). surprisingly, linalool, linalyl acetate, the two major components of several lavender flower oils, and 1,8-cineole, a major component of lavender herb oil, were found only at low levels (≤ 0.6%) in the volatiles of l. dhofarensis (table 1). one possible volatile compounds of lavandula dhofarensis 45 reason for the difference observed is that other workers used mostly flower heads whereas in this study, the flowers were steam-distilled with the leaves and the amount of flowers compared to leaves was low. the flowers were not collected, extracted and analyzed separately because l. dhofarensis grows naturally as a small crop in oman; the ecosystem could be harmed if, for example, 600 g of flower heads were taken from the wild. from table 3, camphor, viridiflorol, -terpinyl acetate, valerenal, and -gurjunene were the major components of the flowers. surprisingly, germacrene, torreyol, humulene oxide, 2-undecanone, and -elemene were present in the leaf volatiles at higher levels (table 3) suggesting their absence or presence at trace levels in the flower essence. l. stoechas and l. lanata have high camphor levels in flowers while l. augustifolia, l. dentate and l. pinnata are low in camphor (< 2%). l. dhofarensis flowers have low levels of linalool and linalyl acetate (< 1%), and high levels of camphor (12.9%) and valerenal (7.2%). there is thus some similarity between l. dhofarensis, l. lanata and l. stoechas. the low levels of linalool and linalyl acetate, (table 1) and the high level of camphor (12.9%) in the floral oil volatiles of l. dhofarensis (table 1 and table 3) distinctly support the grouping l. dhofarensis as a camphor chemotype. table 3. major components of the volatiles of l. dhofarensis subspecies dhofarensis. constituent amount present in volatiles (%) leaves leaves and flowers camphor 12.9 viridiflorol 10.5 caryophyllene oxide 8.0 2.0 germacrene 7.9 1.9 spathulenol 7.8 5.5 -caryophyllene 6.6 0.3 -terpinyl acetate 0.1 7.5 -gurjunene 5.6 -cadinene 3.3 0.6 torreyol 3.0 0.7 valerenal 0.5 7.2 -tetrahydrocostunolide 2.7 humulene oxide 2.6 0.5 2-undecanone 2.3 0.1 -bourbonene 2.3 2.2 -elemene 2.9 0.2 -gurjunene 2.1 1,3,5,5,6,6-hexamethyl-1,3-cyclohexadiene 1.8 dehydroaromadendrene 1.8 octyl acetate 1.4 4. conclusion the results taken together, this investigation showed that caryophyllene oxide, germacrene, spathulenol, viridiflorol, valerenal, camphor, and -terpinyl acetate are the major components of the hydrosol of l. dhofarensis. l. dhofarensis is thus different from other lavenders and the presence of camphor could lower the market value and applications of the fragrance essence of l. dhofarensis in aromatherapy. 5. acknowledgements this work was supported by his majesty’s research trust fund at sultan qaboos university through grant sr/sci/chem/01/01. the authors are grateful to dr. s.a. ghazanfar of the royal botanical gardens, kew, richmond, uk for the identification of the plant samples. 6. references an, m., haig, t. and hatfield, p. 2001. on-site sampling and analysis of fragrance from living lavender (lavendula angustifolia l.) flowers by solid-phase micro extraction coupled to gas chromatography and iontrap mass spectrometry. j. chromatography a, 917: 245-250. baratta, m.t., dorman, h.j.d., deans, s.g., figuieiredo, a.c., barroso, j.g. and ruberto, g. 1998. antimicrobial and antioxidant properties of some commercial essential oils. flavour and fragrance j., 13: 235-244. john r. williams et al. .1 cavanaugh, h.m.a. and wilkinson, j.m. 2002. biological activities of lavender essential oil. phytotherapy research, 16: 301-308. chamberlain, g. and bollen, p. 2011. compositions comprising extracts of boswella, tea tree, aloe and lavender oil and methods of treating wounds, burns and skin 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these in turn were studied in connection with the problem of the arc length of an ellipse, whence the name derives. in this paper, we extend floquet theorem and another theorem (which is mentioned in [1]) related to it, which are dependent on elliptic functions. keywords: meromorphic function; periodic function; elliptic function; floquet theorem; fundamental matrix. و مبرهنة فلوكت مضاعفة الدورانالدوال نفيا حميد محمد و نازنين قادر محمد سعيد ، مجالحقيقي بقيمها على حولمثلما يتم تعريف الدالة الدورية لمت. ان باتجاهيندور ذاتدالة مرومورفية يفي التحليل العقدالدالة الناقصة عتبر ت :صلخمال أن تكون تحليلية، انالدورمضاعفة هذه الدالة لال يمكن .األساسي، الذي يتكرر بعد ذلك في الشبكةضالع أللة الناقصة بقيمها على متوازي ايتم تعريف الدا ال الناقصة ألول مرة بواسطة تاريخيا، تم اكتشاف الدو .ثابتة تكونيجب أن دالة كلن فإليوفيل، مبرهنة ، وحسب اكليقيدة م ألنها ستكون عندئذ دالة مع الدوال لعالقتهاهذه ة دراسومن ناحية أخرى تم وستاف جاكوبي؛ جا بواسطة كارل نظري هاللتكامالت الناقصة، وتم تحسينهنريك أبيل كدوال عكسية نيلز بها، ذات صلة[( 1]المذكورة في )ت و مبرهنة أخرى يفلوك عمم في هذا البحث، مبرهنة ن .سمإلا ذا تم إعطائهاناقص، ومن هقطع لقوس السألة طول م .لى الدوال الناقصةتمد عوالتي تع .المصفوفة األساسيةالدالة المرومورفية، الدالة الدورية، الدالة الناقصة، مبرهنة فلوكت، :مفتاحيةالكلمات ال 1. introduction n our opinion, complex analysis is one of the most beautiful areas of mathematics. it has one of the highest ratios of theorems to definitions (i.e., a very low “entropy”), and many applications to things that seem unrelated to complex numbers. also, it is a comprehensive subject, which provides every mathematician with helpful data. in this respect and due to the usefulness of this subject, we have chosen elliptic functions to be the focus of our work. we need to give a definition of what an elliptic function is, so we will restrict ourselves to meromorphic functions which are functions having only poles as singularities. a doubly periodic function is a function that has two primitive periods, namely 2𝑤1 and 2𝑤3 with 𝑓(𝑧 + 2𝑚𝑤1 + 2𝑛𝑤3) = 𝑓(𝑧); 𝑚, 𝑛 ∈ ℤ. the set of all points of the form 2𝑚𝑤1 + 2𝑛𝑤3, with 𝑚 and 𝑛 being integers is called the period lattice. an elliptic function is a meromorphic function that admits two independent primitive periods. at least one of the two primitive periods of an elliptic function should be complex since the ratio of these two periods should be non-real. i mailto:nafya.mohammad@uor.edu.krd https://en.wikipedia.org/wiki/complex_analysis https://en.wikipedia.org/wiki/meromorphic_function https://en.wikipedia.org/wiki/periodic_function https://en.wikipedia.org/wiki/fundamental_parallelogram_(complex_analysis) https://en.wikipedia.org/wiki/lattice_(group) https://en.wikipedia.org/wiki/doubly_periodic_function https://en.wikipedia.org/wiki/holomorphic_function https://en.wikipedia.org/wiki/bounded_function https://en.wikipedia.org/wiki/entire_function https://en.wikipedia.org/wiki/liouville%27s_theorem_(complex_analysis) https://en.wikipedia.org/wiki/niels_henrik_abel https://en.wikipedia.org/wiki/inverse_function https://en.wikipedia.org/wiki/elliptic_integral https://en.wikipedia.org/wiki/elliptic_integral https://en.wikipedia.org/wiki/carl_gustav_jacobi https://en.wikipedia.org/wiki/arc_length https://en.wikipedia.org/wiki/ellipse doubly periodic functions and floquet theorem 101 in 1998, gesztesy and weikard [2] provided an overview of elliptic algebro-geometric solutions of the kdv and akns hierarchies, in which they concentrated on floquet theorem. also, weikard in 2000 [3] dealt with differential equations with meromorphic solutions, which is related to floquet theorem, while chouikha [4] paid more attention to properties and developments of elliptic functions, and in particular jacobi elliptic functions. the main work in this paper is the extension of the floquet theorem based on elliptic functions. 2. preliminaries definition 2.1. a function 𝑓: ℂ ⟶ ℂ∞ with two periods 2𝑤1 and 2𝑤3, the ratio of which is not real, is called ‘doubly periodic’. definition 2.2. a function that is analytic in the region 𝐷 except for poles in 𝐷, is called ‘meromorphic’ in 𝐷. definition 2.3. a doubly periodic meromorphic function is called ‘elliptic’. table (1) contains 12 jacobi elliptic functions (as examples of elliptic functions) with their periods, zeros, poles, and residues of the functions at the poles. table 1. some information on jacobi elliptic functions. functions periods zeros poles residues 𝑐𝑑 (𝑧, 𝑘) 4𝑚𝐾 + 2𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + 2𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + (2𝑛 + 1)𝐾′𝑖 (−1)𝑚−1/𝑘 𝑐𝑛 (𝑧, 𝑘) 4𝑚𝐾 + 4𝑛𝐾′𝑖 (2𝑚 + 2𝑛 + 1)𝐾 + 2𝑛𝐾′𝑖 2𝑚𝐾 + (2𝑛 + 1)𝐾′𝑖 (−1)𝑚+𝑛−1𝑖/𝑘 𝑐𝑠 (𝑧, 𝑘) 2𝑚𝐾 + 4𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + 2𝑛𝐾′𝑖 2𝑚𝐾 + 2𝑛𝐾′𝑖 (−1)𝑛 𝑑𝑐 (𝑧, 𝑘) 4𝑚𝐾 + 2𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + (2𝑛 + 1)𝐾′𝑖 (2𝑚 + 1)𝐾 + 2𝑛𝐾′𝑖 (−1)𝑚−1 𝑑𝑛 (𝑧, 𝑘) 2𝑚𝐾 + 4𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + (2𝑛 + 1)𝐾′𝑖 2𝑚𝐾 + (2𝑛 + 1)𝐾′𝑖 (−1)𝑛−1𝑖 𝑑𝑠 (𝑧, 𝑘) 4𝑚𝐾 + 4𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + (2𝑛 + 1)𝐾′𝑖 2𝑚𝐾 + 2𝑛𝐾′𝑖 (−1)𝑚+𝑛 𝑛𝑐 (𝑧, 𝑘) 4𝑚𝐾 + 4𝑛𝐾′𝑖 2𝑚𝐾 + (2𝑛 + 1)𝐾′𝑖 (2𝑚 + 1)𝐾 + 2𝑛𝐾′𝑖 (−1)𝑚+𝑛−1/𝑘′ 𝑛𝑑 (𝑧, 𝑘) 2𝑚𝐾 + 4𝑛𝐾′𝑖 2𝑚𝐾 + (2𝑛 + 1)𝐾′𝑖 (2𝑚 + 1)𝐾 + (2𝑛 + 1)𝐾′𝑖 (−1)𝑛−1𝑖/𝑘′ 𝑛𝑠 (𝑧, 𝑘) 4𝑚𝐾 + 2𝑛𝐾′𝑖 2𝑚𝐾 + (2𝑛 + 1)𝐾′𝑖 2𝑚𝐾 + 2𝑛𝐾′𝑖 (−1)𝑚 𝑠𝑐 (𝑧, 𝑘) 2𝑚𝐾 + 4𝑛𝐾′𝑖 2𝑚𝐾 + 2𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + 2𝑛𝐾′𝑖 (−1)𝑛−1/𝑘′ 𝑠𝑑 (𝑧, 𝑘) 4𝑚𝐾 + 4𝑛𝐾′𝑖 2𝑚𝐾 + 2𝑛𝐾′𝑖 (2𝑚 + 1)𝐾 + (2𝑛 + 1)𝐾′𝑖 (−1)𝑚+𝑛−1𝑖/(𝑘. 𝑘′) 𝑠𝑛 (𝑧, 𝑘) 4𝑚𝐾 + 2𝑛𝐾′𝑖 2𝑚𝐾 + 2𝑛𝐾′𝑖 2𝑚𝐾 + (2𝑛 + 1)𝐾′𝑖 (−1)𝑚/𝑘 where 0 < 𝑘 < 1, 𝑘′ = √1 − 𝑘2 , 𝐹 ( 𝜋 2 , 𝑎) = ∫ 1 √(1 − 𝑣2)(1 − 𝑎2𝑣2) 𝑑𝑣 1 0 , 𝐾 = 𝐹 ( 𝜋 2 , 𝑘) and 𝐾′ = 𝐹 ( 𝜋 2 , 𝑘′). more information about elliptic functions is provided in [5]. definition 2.4 [3, p3]. two matrices 𝐴, 𝐵 ∈ 𝐸𝑛×𝑛 (where 𝐸 denotes the field of elliptic functions of the same periods) are said to be of the same kind (with respect to 𝐸) if there exists an invertible matrix 𝑇 ∈ 𝐸 𝑛×𝑛 such that 𝐵 = 𝑇−1(𝐴𝑇 − 𝑇′) and 𝑇′ is the derivative of matrix 𝑇. example 2.5. two matrices 𝐴 = [ 1 𝑠𝑛 𝑡 0 1 ] and 𝐵 = [ 1 + 2 𝑠𝑛 𝑡 2 𝑠𝑛 𝑡 −2 𝑠𝑛 𝑡 1 − 2 𝑠𝑛 𝑡 ] are of the same kind since there exists an invertible matrix 𝑇 = [ 1 0 2 2 ] such that 𝐵 = 𝑇−1(𝐴𝑇 − 𝑇′). it is obvious that the set 𝐸 is closed under the operations of addition, subtraction, multiplication, division by nonzero divisor, and differentiation [2, p278]. now, we consider the set 𝑆 of all invertible matrices whose entries are elliptic functions of the same periods (or the entries of the matrices are elements of 𝐸). nafya h. mohammed and nazaneen q.m. saeed 102 note 2.6. since the all the operations of addition, subtraction, multiplication and differentiation on 𝑆 depend directly on the operations on 𝐸, and 𝐸 is closed under these operations, we can say that 𝑆 is closed under the all these operations. theorem 2.7. any pair of matrices in 𝑆 is of the same kind. proof. since the relation “of the same kind” is an equivalence relation [3, p3], then every element of 𝑆 is of the same kind as itself. thus we prove the theorem for any distinct pair of matrices in 𝑆, and for this purpose we show the elements of 𝑆 by the set {𝑇𝑖 ; 𝑖 ∈ ℕ}. at the first step, we fix 𝐴 = 𝑇1 and choose 𝑇𝑚1 ∈ {𝑇𝑖 ; 𝑖 ∈ ℕ, 𝑖 ≠ 1} arbitrarily. by note 2.6 and the closedness property of 𝑆, 𝑇𝑚1 −1, 𝑇𝑚1 ′ and 𝐴𝑇𝑚1 are in 𝑆 , and then 𝑇𝑚1 −1(𝐴𝑇𝑚1 − 𝑇𝑚1 ′ ) ∈ 𝑆. we name this element 𝐵𝑚1 (so, 𝐵𝑚1 ∈ 𝑆). thus for two elements 𝐴 and 𝐵𝑚1 in 𝑆 there exists 𝑇𝑚1 ∈ 𝑆 such that 𝐵𝑚1 = 𝑇𝑚1 −1(𝐴𝑇𝑚1 − 𝑇𝑚1 ′ ). thus 𝐴 and 𝐵𝑚1 are of the same kind. again, we choose 𝑇𝑚2 ∈ {𝑇𝑖 ; 𝑖 ∈ ℕ, 𝑖 ≠ 1 𝑎𝑛𝑑 𝑖 ≠ 𝑚1} and, in the same way as above, we can say that 𝑇𝑚2 −1(𝐴𝑇𝑚2 − 𝑇𝑚2 ′ ) ∈ 𝑆. we name this element 𝐵𝑚2 (so, 𝐵𝑚2 ∈ 𝑆). thus for two elements 𝐴 and 𝐵𝑚2 in 𝑆 there exists 𝑇𝑚2 ∈ 𝑆 such that 𝐵𝑚2 = 𝑇𝑚2 −1(𝐴𝑇𝑚2 − 𝑇𝑚2 ′ ). thus 𝐴 and 𝐵𝑚2 are of the same kind, and so on. in the second step, we let 𝐴 = 𝑇2 and repeat the previous step. we continue by choosing the elements 𝐴 and 𝑇𝑚𝑖, (𝑚𝑖 ∈ ℕ), such that 𝐴 is fixed and 𝑇𝑚𝑖 is arbitrary, to complete the proof. 3. extension of floquet theorem remark 3.1. in [3] it has been mentioned that, in the basic work of floquet, the independent variable is complex, and the entries of the matrix of the coefficients are analytic functions, and that if these coefficients are not so, then the only possible singularities are isolated singularities. thus, if we want to extend the floquet theorem the poles of the entries of the matrix of the coefficients do not affect the extension, because when establishing the theorem, floquet took it into consideration that some of the functions might have isolated singularities and we extend this theorem depending on the periods of the matrix of the coefficients, and assume that the matrix of the coefficients belongs to 𝑆. in other words, in this paper the entries of the matrix of the coefficients are meromorphic and doubly periodic functions. now, let 𝑋1(𝑡), ⋯ , 𝑋𝑛(𝑡) be 𝑛 solutions of the linear homogenous system 𝑋′ = 𝐴(𝑡) 𝑋 (1) and 𝑋(𝑡) = [[𝑋1(𝑡)] ⋯ [𝑋𝑛(𝑡)]], so 𝑋(𝑡) is an 𝑛 × 𝑛 matrix solution of (1). if 𝑋1(𝑡), ⋯ , 𝑋𝑛(𝑡) are linearly independent, then 𝑋(𝑡) is non-singular and is called a fundamental matrix. theorem 3.2. consider the linear homogenous system (1), where 𝐴(𝑡) ∈ 𝑆. if 𝑊(𝑡) is a fundamental matrix of system (1) such that 𝑊(𝑡0) = 𝐼 (where 𝐼 represents the identity matrix), then: i. 𝑊(𝑡 + 2𝑚𝑤1 + 2𝑛𝑤3) are also fundamental matrices of (1), ∀ 𝑚, 𝑛 ∈ ℤ. ii. corresponding to every such 𝑊(𝑡) there exist an invertible periodic matrix 𝑃(𝑡) of period 2𝑚𝑤1 + 2𝑛𝑤3 and a constant matrix 𝑅 such that 𝑊(𝑡) = 𝑃(𝑡)𝑒𝑡𝑅. proof. at the beginning, we mention that our proof will be based on using mathematical double induction. we divide the proof of the theorem into two parts: i. first we prove the theorem for fundamental periods of 𝐴(𝑡). case 1: if 𝑚 = 1, 𝑛 = 0, then similar to the proof of the floquet theorem in [6], 𝑊(𝑡 + 2𝑤1) is a fundamental matrix of (1) and there exist an invertible matrix 𝐶0 and a constant matrix 𝑅0 such that 𝐶0 = 𝑊(2𝑤1) = 𝑒 2𝑤1𝑅0 , and we define the matrix 𝑃0(𝑡) by 𝑃0(𝑡) = 𝑊(𝑡)𝑒 −𝑡𝑅0 then it is clear that 𝑃0(𝑡) is periodic of period 2𝑤1 and invertible. so 𝑊(𝑡) = 𝑃0(𝑡)𝑒 𝑡𝑅0 is a fundamental matrix of (1). case 2: if 𝑚 = 0, 𝑛 = 1, in the same way 𝑊(𝑡 + 2𝑤3) is a fundamental matrix of (1) and there exist 𝐶0 ∗ and 𝑅0 ∗ such that 𝐶0 ∗ = 𝑊(2𝑤3) = 𝑒 2𝑤3𝑅0 ∗ and we define the matrix 𝑃0 ∗(𝑡) = 𝑊(𝑡)𝑒−𝑡𝑅0 ∗ . clearly 𝑃0 ∗(𝑡) is periodic of period 2𝑤3 and invertible. so 𝑊(𝑡) = 𝑃0 ∗(𝑡)𝑒𝑡𝑅0 ∗ . doubly periodic functions and floquet theorem 103 ii. in this part we prove the theorem for any period of 𝐴(𝑡). case 1. if 𝑚 = 𝑛, suppose 𝑚 = 𝑛 ≠ 0. now, for 𝑚 = 𝑛 = 1, 𝑊(𝑡 + 2𝑚𝑤1 + 2𝑛𝑤3) = 𝑊(𝑡 + 2𝑤1 + 2𝑤3) and since 𝐴(𝑡) ∈ 𝑆, 𝑊′(𝑡 + 2𝑤1 + 2𝑤3) = 𝐴(𝑡) 𝑊(𝑡 + 2𝑤1 + 2𝑤3). then 𝑊(𝑡 + 2𝑤1 + 2𝑤3) is a matrix solution of (1) and, since it is invertible, 𝑊(𝑡 + 2𝑤1 + 2𝑤3) is the fundamental matrix of (1). therefore, there exists an invertible matrix 𝐶1 such that 𝑊(𝑡 + 2𝑤1 + 2𝑤3) = 𝑊(𝑡) 𝐶1; by taking 𝑡 = 𝑡0 = 0, 𝐶1 = 𝑊(2𝑤1 + 2𝑤3). so, there exists a matrix 𝑅1 such that 𝐶1 = 𝑒 (2𝑤1+2𝑤3)𝑅1, see [6, p.139]. we define the matrix 𝑃1(𝑡) = 𝑊(𝑡)𝑒 −𝑡𝑅1. in this way we easily show that 𝑃1(𝑡) is periodic of period 2𝑤1 + 2𝑤3 and invertible. so 𝑊(𝑡) = 𝑃1(𝑡)𝑒 𝑡𝑅1 . suppose that the theorem is true for = 𝑛 = 𝑘 . this means 𝑊(𝑡 + 2𝑘𝑤1 + 2𝑘𝑤3) is a fundamental matrix of (1) and there exists an invertible matrix 𝐶𝑘 = 𝑊(2𝑘𝑤1 + 2𝑘𝑤3) and a constant matrix 𝑅𝑘 such that 𝐶𝑘 = 𝑒 (2𝑘𝑤1+2𝑘𝑤3)𝑅𝑘 and 𝑊(𝑡) = 𝑃𝑘(𝑡)𝑒 𝑡𝑅𝑘 where 𝑃𝑘(𝑡)is invertible and periodic of period 2𝑘𝑤1 + 2𝑘𝑤3. we want to prove that it is true for 𝑚 = 𝑛 = 𝑘 + 1. now, 𝑊′(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) = 𝐴(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) . 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) = 𝐴((𝑡 + 2𝑘𝑤1 + 2𝑘𝑤3) + (2𝑤1 + 2𝑤3)) . 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) = 𝐴(𝑡 + 2𝑘𝑤1 + 2𝑘𝑤3) . 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) = 𝐴(𝑡) . 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) so, 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) is a matrix solution of (1) and also an invertible matrix, then it is the fundamental matrix of (1). since 𝑊(𝑡) and 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) are both fundamental matrices of (1) we must find 𝐶𝑘+1, in which 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) = 𝑊(𝑡). 𝐶𝑘+1. for 𝑡 = 𝑡0 = 0, 𝐶𝑘+1 = 𝑊(2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) = 𝑊(2𝑘𝑤1 + (2𝑤1 + 2𝑘𝑤3 + 2𝑤3)) = 𝑊(2𝑘𝑤1)𝑊(2𝑘𝑤3 + (2𝑤1 + 2𝑤3)) ⋮ = 𝑊(2𝑘𝑤1)𝑊(2𝑘𝑤3)𝑊(2𝑤1)𝑊(2𝑤3) = 𝐶𝑘 ∙ 𝐶1. hence we have found an invertible matrix 𝐶𝑘+1, and for this invertible matrix there exists a matrix 𝑅𝑘+1 such that 𝐶𝑘+1 = 𝑒 (2(𝑘+1)𝑤1+2(𝑘+1)𝑤3)𝑅𝑘+1. we define a matrix 𝑃𝑘+1(𝑡) by 𝑃𝑘+1(𝑡) = 𝑊(𝑡)𝑒 −𝑡𝑅𝑘+1 . 𝑃𝑘+1(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3) = 𝑊(𝑡 + 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3). 𝑒 −(𝑡+2(𝑘+1)𝑤1+2(𝑘+1)𝑤3)𝑅𝑘+1 = 𝑊(𝑡). 𝑊(2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3). 𝑒 −𝑡 𝑅𝑘+1 . 𝑒−(2(𝑘+1)𝑤1+2(𝑘+1)𝑤3)𝑅𝑘+1 = 𝑊(𝑡). 𝑒−𝑡 𝑅𝑘+1 . so, 𝑃𝑘+1(𝑡) is periodic of period 2(𝑘 + 1)𝑤1 + 2(𝑘 + 1)𝑤3 and it is invertible. hence 𝑊(𝑡) = 𝑃𝑘+1(𝑡). 𝑒 𝑡 𝑅𝑘+1 ; and the theorem is true for all 𝑚, 𝑛 ∈ ℕ; 𝑚 = 𝑛. case 2: if 𝑚 ≠ 𝑛. a. we fix 𝑚 = 𝑎; 𝑎 ∈ ℕ; and prove the theorem for 𝑛 = 1, 2, 3, ⋯ by mathematical induction. for 𝑛 = 1, similar to case 1, we can easily show that 𝑊(𝑡 + 2𝑎𝑤1 + 2𝑤3) is a fundamental matrix of (1), and we can find the invertible matrix 𝐶1 ∗ = 𝑊(2𝑎𝑤1 + 2𝑤3), and for this matrix there exists a matrix 𝑅1 ∗ such that 𝐶1 ∗ = 𝑒(2𝑎𝑤1+2𝑤3)𝑅1 ∗ . we define a matrix 𝑃1 ∗(𝑡) by 𝑃1 ∗(𝑡) = 𝑊(𝑡)𝑒−𝑡𝑅1 ∗ . we can also show that it is periodic of period 2𝑎𝑤1 + 2𝑤3, and is an invertible matrix. then 𝑊(𝑡) = 𝑃1 ∗(𝑡)𝑒𝑡𝑅1 ∗ . suppose the theorem is true when 𝑛 = 𝑘. that means 𝑊(𝑡 + 2𝑎𝑤1 + 2𝑘𝑤3) is the fundamental matrix of (1) and there exist 𝐶𝑘 ∗ = 𝑊(2𝑎𝑤1 + 2𝑘𝑤3) and 𝑅𝑘 ∗ such that 𝐶𝑘 ∗ = 𝑒(2𝑎𝑤1+2𝑘𝑤3)𝑅𝑘 ∗ and 𝑃𝑘 ∗(𝑡) = 𝑊(𝑡)𝑒−𝑡 𝑅𝑘 ∗ which is invertible and periodic of period 2𝑎𝑤1 + 2𝑘𝑤3. nafya h. mohammed and nazaneen q.m. saeed 104 for 𝑛 = 𝑘 + 1 we can easily show that 𝑊(𝑡 + 2𝑎𝑤1 + 2(𝑘 + 1)𝑤3) is a fundamental matrix of (1) and find the invertible matrix 𝐶𝑘+1 ∗ = 𝐶𝑘 ∗ . 𝐶0 ∗ = 𝑊(2𝑎𝑤1 + 2𝑘𝑤3). 𝑊(2𝑤3) and for this invertible matrix there exists a matrix 𝑅𝑘+1 ∗ such that 𝐶𝑘+1 ∗ = 𝑒(2𝑎𝑤1+2(𝑘+1)𝑤3)𝑅𝑘+1 ∗ . we define the matrix 𝑃𝑘+1 ∗ (𝑡) by 𝑃𝑘+1 ∗ (𝑡) = 𝑊(𝑡)𝑒−𝑡𝑅𝑘+1 ∗ and show that it is periodic of period 2𝑎𝑤1 + 2(𝑘 + 1)𝑤3 and is an invertible matrix. then 𝑊(𝑡) = 𝑃𝑘+1 ∗ (𝑡)𝑒𝑡𝑅𝑘+1 ∗ . again, we fix 𝑚 = 𝑎 + 1 and repeat the previous steps b. we fix 𝑛 = 𝑏; 𝑏 ∈ ℕ and prove the theorem for 𝑚 = 1, 2, 3, ⋯ by mathematical induction. hence the theorem is true for all 𝑚, 𝑛 ∈ ℕ. example 3.3. consider the linear homogenous system { 𝑥1 ′ = 𝑥1 + 𝑠𝑛 𝑡 𝑥2 𝑥2 ′ = 𝑥2 ; the fundamental matrix of this system is 𝑊(𝑡) = [ 𝑒𝑡 1 𝑘 𝑒𝑡(−𝑙𝑛(𝑑𝑛 𝑡 + 𝑘 𝑐𝑛 𝑡) + ln (1 + 𝑘)) 0 𝑒𝑡 ]. note that 𝑊(0) = 𝐼 , and then, by the above theorem, 𝑊(𝑡 + 4𝐾 + 8𝐾′𝑖) is also the fundamental matrix of the system where 𝐾 = ∫ 𝑑𝜃 √1−𝑘2 𝑠𝑖𝑛2𝜃 ; 𝜋 2 0 |𝑘| < 1 , 𝐾′ = ∫ 𝑑𝜃 √1−𝑘′ 2 𝑠𝑖𝑛2𝜃 𝜋 2 0 ; 𝑘′ = √1 − 𝑘2. also for 𝑊(𝑡) we can find a constant invertible matrix 𝑅 = [ 1 0 0 1 ] and a doubly periodic matrix 𝑃(𝑡) of periods 4𝐾 + 8𝐾′𝑖 such that 𝑃(𝑡) = [1 −1 𝑘 ln (√1 − 𝑘2𝑠𝑛2𝑡 + 𝑘√1 − 𝑠𝑛2𝑡 + 1 𝑘 ln(1 + 𝑘)) 0 1 ] and 𝑊(𝑡) = 𝑃(𝑡)𝑒𝑡𝑅. note 3.4. we have only explained the case for the extension of the floquet theorem when 𝑚, 𝑛 ∈ ℕ. however it is clear that this extension is true for all 𝑚, 𝑛 ∈ ℤ, and we can show this by considering −2𝑤1 and −2𝑤3 as the fundamental periods of 𝐴(𝑡). thus the proof of the extended theorem by depending on this note is completed. 4. another relative to floquet theorem the halphen theorem is another relative of the floquet theorem and expresses the fact that, if in a homogeneous linear system of differential equations the matrix of the coefficients are rational functions that are bounded at infinity and if also the general solution is meromorphic, then a fundamental matrix of solutions exists such that its elements are in the form 𝑅(𝑥) exp (𝜆𝑥), in which 𝑅 is a rational function and 𝜆 is a special complex number. due to the closeness of the halphen theorem to the floquet theorem, the rest of the article presents a version of the halphen theorem as a relative of floquet theorem. in this version, the entries of the matrix of the coefficients of system (1) are bounded at a bounded region which is suitably large but contains a finite number of parallelograms. definition 4.1. for any elliptic function 𝑓 on ℂ with two fundamental periods 2𝑤1 and 2𝑤3, we define the function 𝑓 ∘ by 𝑓∘(𝑡) = 𝑓 ( 𝑤 (4𝑚𝐾 + 2𝑛𝐾′𝑖)𝑖 log 𝑡) ; 𝑤 = 2𝑚𝑤1 + 2𝑛𝑤3 , which is a meromorphic function on ℂ − {0}. remark 4.2. since the entries of 𝐴(𝑡) are elliptic functions of two periods 2𝑤1 and 2𝑤3, then the 𝑧 −plane will be divided into an infinite number of parallelograms and period strips by these two periods, in such a way that each two non-parallel period strips will intersect each other in one parallelogram. let 𝐿1 and 𝐿2 be two period strips which intersect each other in the period parallelogram denoted by ∆. figure 1. period parallelogram generated by the intersection of two non-parallel period strips. doubly periodic functions and floquet theorem 105 definition 4.3. we define a bounded region 𝐿 by taking the period strip 𝐿2 which is suitably large but contains a finite number of parallelograms. theorem 4.4. suppose that all entries of the matrix of the coefficients 𝐴(𝑡), of system (1) are bounded at 𝐿. if system (1) has only meromorphic solutions, then there exists a constant (𝑛 × 𝑛) matrix 𝐽 in jordan normal form and an (𝑛 × 𝑛) matrix 𝑅∘ whose entries are rational functions over ℂ, such that the following statements hold: i. suppose that there are non-negative integers 𝑣1, ⋯ , 𝑣𝑟−1 such that 𝜆, 𝜆 + 𝑖𝑣1, ⋯ , 𝜆 + 𝑖𝑣𝑟−1 are all the eigenvalues of 𝐴∘(0) which are equal to 𝜆 modulo . then 𝜆 is an eigenvalue of 𝐽 with algebraic multiplicity 𝑟. ii. system (1) has a fundamental matrix given by 𝑋(𝑡) = [𝑅∘(exp(𝑖(4𝑚𝐾 + 2𝑛𝐾′𝑖)𝑡/𝑤)) ∙ 𝑒𝑥𝑝((4𝑚𝑘 + 2𝑛𝑘′𝑖)𝐽𝑡/𝑤)]. (2) conversely, suppose that 𝑅∘ is an invertible (𝑛 × 𝑛) matrix whose entries are meromorphic functions and 𝐽 is a constant (𝑛 × 𝑛) matrix. then 𝑋(𝑡) as in the equation (2) is a fundamental matrix of system (1) where 𝐴(𝑡) ∈ 𝑆 and is of the same kind as a matrix whose entries are bounded at 𝐿. proof. we define the function 𝑓∘ as in definition 4.1. on the other hand, in [1] it was mentioned that if 𝑓 is a doubly periodic function, then 𝑓 does not have finitely many poles in the period strip, and hence does not have definite limits at the ends of the period strip, and consequently we cannot say 𝑓∘ is a rational function. so, to deal with this, we define the bounded region 𝐿 as in definition 4.3. now, the theorem can be proved by taking = 4𝑚𝐾 + 2𝑛𝐾′𝑖 , and the rest of the proof is similar to the proof of the theorem 1 in [3]. to avoid our repeating the technical steps of the proof and for better understanding, it is necessary that the reader to refer to [3]. example 4.5. this example explains the converse of the above theorem. consider the linear homogenous system 𝑥1 ′ = 𝑥1 + √1 − 𝑠𝑛 2(𝑓(𝑡)) ∙ √1 − 𝑘2𝑠𝑛2(𝑓(𝑡)) ∙ 𝑥2, 𝑥2 ′ = 𝑥2 (3) and let 𝑅0 = [ 1 𝑠𝑛 (𝑓(𝑡)) 0 1 ] (where 𝑓(𝑡) = 1 𝑖 log 𝑒𝑖𝑡) be an invertible matrix whose entries are meromorphic functions and 𝐽 = [ 1 0 0 1 ] be a constant matrix, then by the above theorem 𝑅0 × 𝑒𝑡𝐽 = [ 1 𝑠𝑛 (𝑓(𝑡)) 0 1 ] × [ 𝑒𝑡 0 0 𝑒𝑡 ] = [ 𝑒𝑡 𝑒𝑡𝑠𝑛 (𝑓(𝑡)) 0 𝑒𝑡 ] is the fundamental matrix of system (3) and it is clear that the matrix of the coefficients of the system 𝐴(𝑡) = [1 √1 − 𝑠𝑛 2(𝑓(𝑡)) ∙ √1 − 𝑘2𝑠𝑛2(𝑓(𝑡)) 0 1 ] is of the same kind as matrix 𝐵 that is bounded at 𝐿 and 𝐵 = [ 3 . √1 − 𝑠𝑛2(𝑓(𝑡)) √1 − 𝑘2𝑠𝑛2(𝑓(𝑡)) + 1 − 3 2 + 9 2 √1 − 𝑠𝑛2(𝑓(𝑡)) √1 − 𝑘2𝑠𝑛2(𝑓(𝑡)) + 1 + 3 2 −2 ∙ √1 − 𝑠𝑛2(𝑓(𝑡)) √1 − 𝑘2𝑠𝑛2(𝑓(𝑡)) 1 − 3 ∙ √1 − 𝑠𝑛2(𝑓(𝑡)) √1 − 𝑘2𝑠𝑛2(𝑓(𝑡)) ] . 5. conclusion in this work, doubly periodic functions are introduced generally and some jacobi elliptic functions are specifically illustrated. the concepts of matrices of the same kind and additionally doubly periodic functions were applied for the extension of floquet theorem. furthermore, there is a detailed description of any pair of matrices, the entries of which are elliptic functions of the same periods, which are of the same kind. in addition it has been proved that if 𝑊(𝑡) is a fundamental matrix of system (1), then there exists an invertible doubly periodic matrix 𝑃(𝑡) and a constant matrix 𝑅 such that 𝑊(𝑡) = 𝑃(𝑡)𝑒𝑡𝑅. finally, another theorem that is related to the theorem of floquet is presented, with an example to explain it. conflict of interest the authors declare no conflict of interest. acknowledgment the authors thank the anonymous reviewers for their valuable suggestions, helpful comments, and constructive criticisms for improving the manuscript during the process of preparing this article for publication. nafya h. mohammed and nazaneen q.m. saeed 106 references 1. mohammad, n.h. extension of floquet theorem based on elliptic functions. m.sc. thesis, salahaddin university, hawler, kurdistan region-iraq, 2003. 2. gesztesy, f. and weikard, r. elliptic algebro-geometric solutions of the kdv and akns hierarchies-an analytic approach. bulletin of the american mathematical society, 1998, 35(4), 271-317. 3. weikard, r. floquet theory for linear differential equations with meromorphic solutions. electronic journal of qualitative theory of differential equations., 2000, 8, 1-6. 4. chouikha, a.r. on properties of jacobi elliptic functions and applications. journal of nonlinear mathnetical physics, 2005, 12(2), 162-169. 5. freitag, e. and busam, r. complex analysis (2nd edition), springer-verlag, berlin, 2005. 6. myint-u, t. ordinary differential equations. elsevier north holland, new york, 1978. received 1 st january 2020 accepted 26 july 2020 squ journal for science, 2014, 19(2), 1-7 © 2014 sultan qaboos university 1 the effect of salinity on solamargine and solasonine contents of solanum incanum plants grown in oman sana s. al sinani and elsadig a. eltayeb* department of biology, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: eatayeb@squ.edu.om. abstract: in addition to its traditional medicinal importance, solanum incanum (thorn apple) is also a rich source of important cytotoxic glycoalkaloids such as solamargine and solasonine. the effect of salinity stress on solamargine and solasonine production by solanum incanum plants grown in soil has been investigated. salinity stress has been applied by adding nacl to the soil, in concentrations: 0.0 (control), 75, 150, and 225 mm for 8 weeks. hptlc method was used for analysis of solamargine and solasonine in leaves, stem and roots. a positive correlation was observed between 150 mm nacl salinity and production of solamargine and solasonine in leaves. in roots, solamargine content was not affected by nacl treatment, whereas solasonine content increased with a short-term salinity treatment. however, salinity seems to reduce the production of solamargine and solasonine in the roots of solanum incanum. the possibility of using nacl as an efficient and economical elicitor of glycoalkaloid production in solanum incanum plants is rejected on the basis of the results obtained. keywords: salinity; glycoalkaloids; solamargine;solasonine; hptlc. والسوالسوًيي بواسطة ًبات السوالًام إًكاًام في سلطٌة عواىجأثير درجة الولوحة على إًحاج السوالهارجيي والصادق عبذهللا الطيب يةسالن السٌاًبٌث سٌاء في إسخخذايٓانى إْاياً إلَخاج األنكانٕيذاث انسكزيت يثم انسٕاليارجيٍ ٔانسٕالسَٕيٍ باإلضافت ذراً حعخبز َباحاث انسٕالَاو إَكاَاو يص هلخص: انسٕاليارجيٍ ٔانسٕالسَٕيٍ ححج حأثيز انًهٕحت باسخخذاو يحهٕل كهٕريذ انصٕديٕو عُذ درجاث حزكيز حخزأح َخاج إانطب انشعبي. حًج دراست نفصم انًزكباث ٔححذيذ كًياحٓا في hptlcطزيقت سخخذيج اأسابيع. 8ييهي يٕل نًذة 227ٔ 071، 57بيٍ صفز )انًجًٕعت انضابطت(، األنكانٕيذاث في ييهي يٕل ٔإَخاج 071يٕجب بيٍ حزكيز انًهٕحت عُذ رحباط اجذٔر ٔأٔراق ٔسيقاٌ انُباحاث. ٔقذ حٕصهج انذراست إنى أٌ ُْاك في حيٍ أٌ إَخاج انسٕالسَٕيٍ ارحفع عُذ اسخخذاو انًهٕحت نفخزة يذكز إلَخاج انسٕاليارجيٍ اً أٔراق انُباحاث. أيا في انجذٔر فهى حجذ انذراست حأثيز هت فعانت قصيزة. عًٕيا فإَّ يبذٔ أٌ انًهٕحت حقهم إَخاج األنكانٕيذاث في جذٔر انُباحاث. ٔحثبج ْذِ انذراست أٌ إسخخذاو انًهٕحت ال يعخبز ٔسي نزيادة إَخاج األنكانٕيذاث. hptlc، األنكانٕيذاث انسكزيت، انسٕالسَٕيٍ، انسٕاليارجيٍ، انًهٕحت: الكلوات هفحاح 1. introduction alinity is the major environmental factor limiting plant growth and productivity [1,2]. it has been estimated that about 940 million hectares of land around the world are already salinized [3]. an excess of ions in the root medium often causes osmotic strain, ion specificity/ toxicity, nutritional imbalances, changes in cell metabolite levels and diminished growth and yield [4]. salinity is one of the major factors that can reduce substrate water potential, thereby restricting the water-nutrient uptake by plants [5]. plants have evolved a variety of physiological and biochemical processes as responses to stress conditions, e.g. solute accumulation and the development of enzymatic antioxidant systems [6]. short-term effects include reduction in plant growth due to the osmotic effects of the accumulation of salts near the root zone, which reduces cell expansion. long-term effects include excessive salt absorption, which causes plants to suffer ionic stress, leading to premature leaf aging following a reduction in the available photosynthetic area [1,3,7]. accumulation of na + in the tissues of plants growing in saline media restricts the uptake of essential nutrients (mainly n, p, k + and ca 2+ ), thereby reducing the plant biomass production [8]. thus, salinity affects growth and can alter leaf water potential, stomatal conductance, and transpiration [9]. s sana s. al sinani and elsadig a. eltayeb 2 in addition to osmotic stress and ion toxicity, plants subjected to salinity experience oxidative stress and lipid peroxidation, which can cause a loss of membrane integrity [7]. salinity has been reported to disturb the integrity of cell membranes by inducing structural changes and replacing ca with na on the plasma membrane, thus altering k/na ratio [10]. on the other hand, proline accumulation in plant cells exposed to nacl-stress is a widespread phenomenon. proline accumulation is correlated to growth inhibition induced by nacl [11]. the negative effect of soil salinity depends on plant tolerance aptitude and salinity level [8]. many plants develop mechanisms either to exclude salt from their cells or to tolerate its presence within the cells [9]. salt tolerance in plants is a complex phenomenon that may involve developmental changes as well as physiological and biochemical processes [3]. the genus solanum (family: solanaceae), with more than 1700 species, is widespread in the temperate and tropical regions of the world [12,13] and is characterized by the presence of steroidal glycoalkaloids (sgas) of great interest from the ecological view point and human health aspects [14-17]. about 20 solanum species have been reported from arabia. in oman, seven species of solanum, viz. s. cordatum, s. incanum, s. melongena, s. nigrum, s. surattense, s. tuberosum, and s. villosum are found [18]. solanum incanum, commonly known as thorn apple, is an important medicinal plant. in oman its leaves, fruits (berries) and roots are used as a traditional medicine [19]. in most of the plants containing glycoalkaloids, the main aglycone is solasodine [20]. it occurs in about 200 species of solanum in the form of the water soluble triglycosides, solasonine (sn) and solamargine (sm) [21]. these two compounds bear the same aglycone, solasodine, and differ from each other only in the nature of the trioses involved, namely, solatriose for solasonine and chacotriose for solamargine (figure 1) [15,22]. solamargine and solasonine stand out economically because their chemical structures are very similar to steroidal hormones, and are therefore used as an important source of medicines, such as contraceptives and steroidal anti-inflammatory drugs [23]. these glycoalkaloids have been studied for their antidiabetic, antifungal, antiparasitic, antibiotic, antimicrobial, antiviral and most extensively, for anticancer properties [13,23,24]. various biotic and abiotic factors, used as elicitors, have been reported to increase secondary-metabolite yield; application of nacl enhances alkaloid production [25]. in a study on the effect of salinity on growth, tuberization and chemical composition with special reference to the total glycoalkaloid (tga) content of seven potato varieties, salinity reduced the tga levels of tubers mostly during the exponential phase of growth with further reduction at maturity [26]. although much of the recent research focuses on physiological and metabolic processes under salt-stress, few data are available on glycoalkaloid accumulation. most of the previous studies have attempted to enhance the production of solasodine by s. nigrum using nacl-stress in the culture medium. the present study was undertaken with the objective of exploring the possibility of enhancing glycoalkaloid production in s. incanum plants under field conditions by using nacl as an efficient and economical elicitor. 2. experimental 2.1 plant material solanum incanum l. seeds obtained from plants grown in al jabal al akhdar, were grown in the green house at sultan qaboos university. germination (on damp filter paper in petri dishes at 21-25 ˚c, 14 hr light, 70% rh) occurred within 3 weeks, and at one month, seedlings were transplanted to 15 cm diameter pots containing acid washed sand soil: clay soil: compost (1:1:1) and kept in university's green house at 21-25 °c, 14 hr light, 70% rh. the plants were irrigated with irrigation water 2 times a week until germination had completed. 2.2 nacl treatment twelve-week old plants were divided into four groups and subjected to different nacl treatments in order to study the effect of salinity-stress on ga production in s. incanum plants. control plants were irrigated two times a week. the other three groups were treated separately with 75 mm, 150 mm, and 225 mm nacl. the plants were irrigated with saline water two times a week. sampling was done after 2, 4, and 6 weeks for each treatment, where five plants were randomly selected for analysis of the gas. each plant was divided into leaves, stem, and roots, weighed fresh, and dried in an oven at 60 °c to constant wt. (ca 3 days) and then reweighed. 2.3 chemicals and reference compounds solamargine and solasonine obtained from glycomix (whiteknights road, united kingdom) were used as reference compounds. distilled water was deionized before use. hplc grade methanol and chloroform were obtained from sigma aldrich (germany) and ammonia solution from merck (darmstadt, germany). effect of salinity on solamargine and solasonine 3 figure 1. chemical structure of solasodine and its respective glycoalkaloids. 2.4 hptlc instrumentation and conditions the samples were spotted in the form of bands (4 mm width), with a camag microlitre syringe on precoated hptlc silica gel glass plates 60f-254 ( 20 cm x 10 cm, merck kgaa, germany) using a camag linomat v (muttenz, switzerland) and were controlled by wincats software (camag). a constant application rate of 120 nl/s was employed and space between two bands was 6.2 mm. the slit dimension was kept at 5.00 mm×0.30 mm, and a 20 mm/s scanning speed was employed. the mobile phase of the ga consisted of chloroform: methanol: 5% ammonia, (7:3:0.50, v/v/v). linear ascending development was carried out in a 20×10 cm twin trough glass chamber, saturated with the mobile phase. the optimized chamber saturation time for the mobile phase was 15 min at room temperature. the length of the chromatogram run was 90 mm. subsequent to development, the hptlc plates were dried in an oven at 60 °c for 5 min. densitometric scanning was performed on a camag tlc scanner iv (absorbance mode 530 nm) with wincats software after spraying the developed plate with anisaldehyde sulphuric acid reagent and heating on a hot plate at 110 °c for 5 minutes. 2.5 sample preparation in a simple method of extraction, 0.5 g of dried and powdered s. incanum organs (leaves, stems, and roots) were extracted using 30 ml methanol: chloroform (2:1) by sonication at 40 °c for 45 minutes. the mixture was filtered using whatman no. 1 filter paper and washed with methanol. the filtrate was evaporated to dryness in a water bath at 40 °c. dried extracts were dissolved in methanol and filtered using a 0.2 µm syringe filter. the final volume was made to 5 ml with methanol and stored at 4 °c for application onto hptlc plate for quantification. 2.6 standard solamargine and solasonine one mg/ml (1000 µg/ml) solutions of the standard solamargine and solasonine were prepared in methanol. a mixture of the glycoalkaloids solamargine and solasonine was prepared by mixing 0.5 ml of each so that the concentration of each compound in the mixture was 0.5 mg/ml (500 µg/ ml). these solutions were used for application on hptlc plate for preparation of a standard plot. 2.7 calibration curve of solamargine and solasonine different volumes of standard solution of the mixture of gas 0.1, 0.2, 0.4, 0.5, 1.0, 2.0, 4.0, 5.0, 10.0 µl of 500 µg/ml were spotted in triplicate on the hptlc plate to obtain 50, 100, 200, 250, 500, 1000, 2000, 2500, 5000 ng/spot of each ga, respectively. the data in peak area vs. solamargine and solasonine concentration were treated with the linear least square regression and the regression equation thus obtained from the standard curve was used to estimate both the gas in different samples. sana s. al sinani and elsadig a. eltayeb 4 2.8 quantification of solamargine and solasonine the same method was applied for the analysis of solamargine and solasonine contents in leaves, stem and root of s. incanum plants grown at different salinity concentrations (at intervals of 2, 4, and 6 weeks). samples of 10 µl each were applied in quadruplicate on the hptlc plate. the ga yield was quantified using the regression equation of the calibration curve. 3. results and discussion 3.1 gas in s. incanum after salinity treatment solamargine and solasonine produced well separated compact bands on silica gel hptlc plate with chloroform: methanol: 5% ammonia (7: 3: 0.5) after visualization using anisaldehyde sulphuric acid reagent (figures not shown). the rf values for solamargine and solasonine were 0.26±0.02 and 0.14±0.02 respectively. chromatograms were scanned at 530 nm in absorbance mode (figures 2 and 3). the identity of the ga band from the sample solution was confirmed by comparison of its rf and spectra with those from the standard gas. figure 2. hptlc chromatogram of solasonine (rf 0.13) and solamargine (rf 0.27) 1000 ng/spot each at 530 nm. figure 3. hptlc chromatogram of sample at 530 nm, using solvent system chloroform: methanol: 5% ammonia (7: 3: 0.5) showing the presence of solasonine and solamargine. linear regression calibration curves were plotted using peak area against concentration, and found to be linear in the range of 50 to 2000 ng/ml for both solamargine and solasonine, with good linear relationships of 0.9987 and 0.9962, respectively. 0.90 solasonine solamargine 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 rf 0 50 400 350 300 250 200 150 100 500 450 au 0.00 au 0 50 400 350 300 250 200 150 100 500 450 3 solamargine 1 2 4 5 6 7 8 9 10 11 12 13 14 15 solasonine 0.00 0.20 0.40 0.60 0.80 1.00 rf effect of salinity on solamargine and solasonine 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 c o n tr o l 7 5 m m 1 5 0 m m 2 2 5 m m c o n tr o l 7 5 m m 1 5 0 m m 2 2 5 m m c o n tr o l 7 5 m m 1 5 0 m m 2 2 5 m m 2 wks 4 wks 6 wks c o n c e n tr a ti o n i n m g /g concentration and duration of nacl treatment leaves stems roots the accuracy of the method was tested by the standard addition method at 3 concentrations (0, 50, 100, 150), which showed recovery within the range of 99.1%-101.7%. the method’s precision was analysed for repeatability and reproducibility by analysing 3 concentrations of standard solution six times a day and on six different days, which showed a %rsd < 2%. the method was applied for the analysis of solasonine and solamargine content in leaf, stem and root samples of solanum incanum, which had been subjected to the salinity treatment. solamargine and solasonine concentrations in different samples were analysed from the regression equation using values of area obtained from wincats software. the mean values of gas in samples are shown in figures 4 & 5. figure 4. effect of different concentrations of nacl (untreated (control), 75 mm, 150 mm, 225 mm ) on content of solamargine in leaves, stems and roots of s. incanum after 2, 4, and 6 weeks analyzed by hptlc. the study revealed that no significant difference or regular change occurred in solamargine content after salinity-stress among same samples of leaves collected at different time intervals or among treatments of up to 6 weeks. the control leaves as well as those treated with salt concentration of 75 mm nacl showed a similar pattern of solamargine content whereas medium treatment (150 mm nacl) increased the solamargine content in the 2 and 6 week old leaf samples. there was no regular pattern of change in solamargine concentration in the stem and root samples. among leaf samples, solamargine content was highest in samples at salinity-stress (75 mm nacl) at the 4th week. the salinity stressed samples showed a good and constant amount of solamargine irrespective of treatment at different dose levels. among stem samples, solamargine content was not affected by salinity stress, whereas it was reduced in roots. with regard to solasonine content, again no regular pattern of change was observed among samples stressed with salinity. on the whole, root samples showed solasonine levels that are significantly greater quantity than stem and leaf samples. salinity-stress did not produce any regular pattern in solasonine content of plant organs, but an increase in salinity above the minimal level increased the solasonine content after the second week of salinity treatment. in the stem also, an increase in the salinity significantly increased solasonine content as compared to the control. equivalent levels of solasonine could be achieved in leaves and stems of untreated plants after 12 weeks of plant growth. after four weeks of salt-stress, solasonine content decreased in leaves and stem, but increased in roots at all the three nacl concentrations, with the highest production being at 125 mm. analysis of root samples showed that salinity-stress significantly increased solasonine content in the 4th week and caused no effect later on. these increased contents of solasonine in roots could be achieved in untreated plants at the 14th week of plant growth. salinity treatments of eight weeks reduced the solasonine production in roots (at 75 and 125 mm nacl concentrations), but had no significant effect in leaves and stems. this could be due to heavy disruption in physiological processes under high salinity levels. some of our results corroborate the earlier reports in certain respects, showing stimulated alkaloid production by salinity-stress [11,12,25]. jasmin [11] investigated the effect of 8 weeks of salinity-stress on sana s. al sinani and elsadig a. eltayeb 6 0 1 2 3 4 5 6 7 8 9 10 11 12 c o n tr o l 7 5 m m 1 5 0 m m 2 2 5 m m c o n tr o l 7 5 m m 1 5 0 m m 2 2 5 m m c o n tr o l 7 5 m m 1 5 0 m m 2 2 5 m m 2 wks 4 wks 6 wks c o n c e n tr a ti o n i n m g /g concentration and duration of nacl treatment leaves stems roots in vitro solasodine production by solanum nigrum, and reported that nacl-stress stimulated solasodine accumulation. the response to nacl-stress was more prominent after 4 and 6 weeks. however, differences were non-insignificant between 150 mm and 200 mm of nacl [11]. bhat et. al. [12] also noted enhanced solasodine production with increased nacl level in s. nigrum. ahmad and abdullah [26] observed a decrease in total glycoalkaloid (tga) level in potato tubers due to salinity but the differences between different concentrations of salt and the control were small. biosynthesis of solasodine starts from acetyl coenzyme a, which later converts to mevalonic acid, via the mevalonic acid pathway, in which cholesterol, a key intermediate of solasodine, is synthesized. high salinity seems to enhance in vitro cholesterol production, which in turn increases solasodine in tissues, or alternatively, the enhanced yield could be due to the over expression of the genes concerned. this can explain the short-term effect of salinity. long-term effects include excessive salt absorption, which causes plants to suffer ionic stress, leading to premature leaf aging, following a reduction in the available photosynthetic area to maintain growth [1,3,7]. this may lead to a reduction in the production of sugars needed for the glycosylation of solasodine to produce glycoalkaloids. figure 5. effect of different concentrations of nacl (untreated (control), 75 mm, 150 mm, 225 mm ) on content of solasonine in leaves, stems and roots of s. incanum after 2, 4, and 6 weeks analyzed by hptlc. although salinity seems to enhance solamargine production in leaves of solanum incanum, using 150 mm nacl, has no effect on solamargine production in stem and reduces the production of glycoalkaloid in roots. however, the enhanced contents of solamargine in leaves can be achieved without any salt treatment at 12 weeks of growth. the salt concentrations that can give higher production in solasonine are 150 mm and 225 mm for leaves and stems but for a short term of two weeks of salinity. on the other hand, salinity decreased the solasonine contents in roots, which seem to be the higher source of the compound in s. incanum plants, for short and long terms of salinity. as for solamargine, the untreated leaves, stems and roots can produce contents equal to those formed after salinity at 12 weeks of plant growth for leaves and stems and after 14 weeks of plant growth for roots. however, it should be mentioned that the plants were negatively affected by the salinity treatments (data are not shown). our results do not support the claim that it is possible to enhance production of the glycoalkaloids solamargine and solasonine in field grown solanum incanum plants using nacl as an efficient and economical elicitor. references 1. lópez-climent, m.f., arbona, v., pérez-clemente, r.m. and gómez-cadenas, a. relationship between salt tolerance and photosynthetic machinery performance in citrus. environ. and exptal. bot., 2008, 62, 176-184. 2. zribi, l., fatma, g., fatma, r., salwa, r., hassan, n. and néjib, r.m. application of chlorophyll fluorescence for the diagnosis of salt stress in tomato “solanum lycopersicum (variety rio grande)”. scientia horti., 2009, 120, 367-372. 3. da 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al-safeen2 1 department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman; 2 department of mathematics and statistics, jordan university of science and technology, irbid 22110, jordan. *email: kamel@squ.edu.om. abstract: in this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. the fractional derivatives are described in the caputo sense. we apply both the homotopy perturbation method and the homotopy analysis method, to solve certain shallow water equations with time-fractional derivatives, and explicitly construct convergent power series solutions. the results obtained reveal that these methods are both very effective and simple for finding approximate solutions. some numerical examples and plots are presented to illustrate the efficiency and reliability of these methods. keywords: homotopy perturbation; fractional differential equation; shallow water equations; approximate solutions. لحل معادالت المياه الضحلة الكسرية طريقة هوموتوبي للتشتت محمد السعافينكامل الخالد و تمثلكسرٌة التً التفاضلٌة الجزئٌة ال المعادالتمن ألنظمةٌجاد الحلول العددٌة للتشتت إل هوموتوبًطرٌقة فً هذا البحث تم استخدامملخص : التحلٌلٌة وطرٌقة هوموتوبً للتشتت هوموتوبًقمنا بتطبٌق كال الطرٌقتٌن, طرٌقة حلة. المشتقات الكسرٌة معرفة بطرٌقة كابوتا. المٌاه الض النتائج بٌنت ، متقاربةالت هندسٌة الحلول على شكل متسلس بإٌجادقمنا ، حلة ذات المشتقات الكسرٌة الزمنٌةالض لمٌاهانظام الذي ٌمثل لحل ال حٌث تم توضٌح ذلك من خالل بعض االمثلة والرسومات. ،ان الطرٌقتٌن تتسمان بالسهولة والدقة اضطراب هوموتوبً، المعادالت التفاضلٌة الكسرٌة، معادالت المٌاه الضحلة و الحلول التقرٌبٌة.مفتاح الكلمات: 1. introduction he flow of water in a wide channel, with rectangular cross-section, and a smoothly varying bottom surface, is governed by the one-dimensional shallow water equations (swes). the assumptions of hydrostatic pressure distribution and small bottom slope are used in deriving these equations [1]. in the onedimensional case, the flow of a fluid in an infinitely wide channel with time-fractional derivative can be presented by using shallow water equations )(' 0)( xgvvuvd uvud xxt xt     (1.1) t mailto:kamel@squ.edu.om homotopy perturbation method 75 subject to the conditions that the initial velocity and the initial height of the water be ),()0,( 1 xgxu  ),()0,( 2 xgxv  x .r the fractional differential operator  t d describes the fractional time-derivatives of order of the system (1.1), where 10  . the fractional derivatives are considered in the caputa sense [2]. in the case 1 , the fractional differential equation reduces to the classical shallow water equations. in equation (1.1) the functions ),( txu and ),( txv represent the total height above the bottom and the flux velocity respectively, and 0)(' xg is the depth of a point from a fixed reference level of the water. bermudez and vazquez [3] failed to find an exact analytical solution for the shallow water equations when the bottom is not flat for 1 in a literature search. in last few years many papers have been devoted to the numerical solution of these equations using finite difference and finite element methods [3]. in [1], the authors consider the same problem with 1 , and they implement adomian's decomposition method. in recent years, there has been a growing interest in the field of fractional calculus. oldham and spanier [4], miller and ross [5], momani [6] and podlubny [7,8] provide the history and a comprehensive treatment of this subject. several fields of application of fractional differentiation and fractional integration are already well established, and some others are just starting. many applications of fractional calculus can be found in the literature [9,10]. for this reason, it is important to solve time fractional partial differential equations. it was found that fractional time derivatives arise generally as infinitesimal generators of the time evolution when taking a long time scaling limit. hence, the importance of investigating fractional equations arises from the necessity to sharpen the concepts of equilibrium, stability states, and time evolution in the long time limit. there has been some attempt to solve linear problems with multiple fractional derivatives. in this paper, we consider 10  , with 0)(' xg ,and with the same analysis as in [11,3], we implement the homotopy perturbation method (hpm), and homotopy analysis method (ham) for obtaining explicit and numerical solutions of those fractional shallow water equations with source terms. we will also illustrate that how the homotopy methods help to achieve accurate solutions. 2. basic principles of fractional calculus this section is devoted to a description of the operational properties for the purpose of acquainting the reader with sufficient fractional calculus theory. many definitions and studies of fractional calculus have been proposed in the last two centuries. these definitions include those of, riemman liouville, weyl, reize, campos, caputa, and nishimoto fractional operator. the riemann liouville definition of fractional derivative operator  a j is defined as follows: definition 2.1 let   r . the operator  a j defined on the usual lebesque space ],[ 1 bal by         a a dttftxxfj ,)()( )( 1 )( 1 and )()( 0 xfxfj a  , for ,bxa  is called the riemannliouville-fractional integral operator of order  . properties of the operator  a j can be found in [4, 7], here we mention the following: for 0,],,[ 1  balf and 1 1. )(xfj a  exists for almost every ],[ bax  2. )()( xfjxfjj aaa    3. )()( xfjjxfjj aaaa   4.         )( )1( )1( axxj a kamel al-khaled and mohamed k. al-safeen 76 as mentioned in [6,8], the riemann-liouville derivative has certain disadvantages when trying to model realworld phenomena with fractional differential equations. therefore, we shall now introduce a modified fractional differentiation operator  d proposed by caputo in his work on the theory of viscoelasticity [2]. definition 2.2the fractional derivative of )(xf in the caputo sense is defined as ,)()( )( 1 )()( )( 0 1 dttftx m xfdjxfd m x mm           where 0,,1  xnmmm  lemma 2.1 if ,1 mm   and ],,[ 1 balf  then )()( xfxfjd aa   , and       1 0 )( ! )( )0()()( m k k k aa k ax fxfxfdj  the caputo fractional derivative is considered in the caputo sense. for more details on the geometric and physical interpretations of fractional derivatives of both riemann-liouville and caputo types see [2, 6]. definition 2.3 for m to be the smallest integer that exceeds  , the caputo fractional derivatives of order 0 are defined as 1 0 ( , ) 1 ( , ) ( , ) ( ) , ( ) m t m m m u x t u x d u x t t d t m                   if mm  1 , and for nm , we have ( , ) ( , ) ( , ) m m u x t u x t d u x t t t          for mathematical properties of fractional derivatives and integrals one can consult the above mentioned references. 3. homotopy methods liao [12] and he [13] employed the basic ideas of homotopy in topology to propose general analysis methods for nonlinear problems, namely the homotopy analysis method (ham), and homotopy perturbation method (hpm). these methods have been successfully applied to solve many types of nonlinear problems. to illustrate the basic ideas of these methods, we consider the general form of the partial differential equation 0)(][][  rfuaud (3.1) with boundary conditions of the form    r n u ub ,0),( (3.2) where d is a nonlinear operator, a is a general differential operator, b is the boundary operator, )(rf a known analytical function, and  is the boundary of the domain  . generally speaking, the operator a can be divided into two parts, namely l and n , where l is the linear operator, and n is the nonlinear operator. therefore, equation (3.1) can be rewritten as 0)()()(  rfunul (3.3) by means of generalizing the traditional homotopy method, liao [14] constructs a homotopy rpr  ]1,0[:),( which satisfies the zero-order deformation equation 0 ( , ) (1 ) [ ( ) ( )] ( ) [ ] 0h p p l l u p h r d        (3.4) homotopy perturbation method 77 where ]1,0[p is the embedding parameter, 0 is a nonzero auxiliary parameter, 0)( rh is the an auxiliary function, 0 u is an initial guess of u , and  is an unknown function. it is important, that one has great freedom to choose auxiliary things in (ham) (i.e., the initial guess, the auxiliary linear operator, the auxiliary parameter  , and the auxiliary function )(rh ). obviously, from equation (3.4), we have 0 ( , 0) ( ) ( ) 0, ( ,1) [ ] [ ] ( ) 0h l l h d a f r            (3.5) the changing process of p from zero to unity is just that of ),( pr varies (or deforms) from the initial guess )( 0 ru to the solution u . in topology, this is called deformation, and ),()( 0 ull  )()( rfa  are termed ‘homotopic’. expanding );( pr in a taylor series with respect to the embedding parameter p , we have m m m pruupr )(),( 1 0     (3.6) where 0 | ),( ! 1 )(     pm m m p pr m ru  . (3.7) as proved by liao [14], if the auxiliary linear operator, the initial guess, the auxiliary parameter  , and the auxiliary function are properly chosen, the series (3.6) converges at 1p , and one has     1 0 )()( m m xuuru (3.8) which must be one of the solutions of the original nonlinear equations. for the sake of simplicity, the governing equation can be deduced from the zero-order deformation equation (3.4). define the vector },...,{ 0 nm uuu   , and differentiating equation (3.4) m times with respect to the embedding parameter p , and then setting 0p and finally dividing them by !m , we have the so-called mth -order deformation equation 1 1 [ ( ) ( )] ( ) ( ( )) m m m m m l u r u r h r r u r     (3.9) where 1 1 01 1 [ ( , )] ( ( )) | (1 ) ( ) ( 1)! m m m p mm d r p r u r f r m p            and       1,1 1,0 m m m  . (3.10) it should be emphasized that )(ru m for 1m is governed by the linear equation (3.9) with the linear boundary conditions that come from the original problem, which can be easily solved by symbolic computation software such as maple or mathematica. by directly substituting the series (3.6) into the zerothorder deformation equation (3.4), and then equating the coefficients of the like powers of p , one can obtain exactly the same high-order deformation equation as (3.9), as proved by sajid et al.[15]. as 1 and 1)( rh , equation (3.4) becomes 0 ( , ) (1 )[ ( ) ( )] [ ( )]h p p l l u p d      (3.11) kamel al-khaled and mohamed k. al-safeen 78 which is used mostly in the homotopy perturbation method [13], whereas the solution obtained directly, without using taylor series [16]. for equation (3.11) the perturbation procedure is applied by assuming the p as a perturbation parameter, i.e. the solution can be written as a power series in p : ...)()()(),( 2 210  pruprurupr this method does not require an additional small parameter, this being its main advantage in comparison with the usual perturbation procedure. the approximate solution of equation (3.1), therefore, can be readily obtained: ...)()()()1;( 210  rururuh  (3.12) the convergence of the series (3.12) has been proved in [17]. in [18], the homotopy analysis method was used to derive the adomian decomposition method, i.e., if the auxiliary parameter 1 , the auxiliary function 1)( rh , the auxiliary linear operator, and the initial guess are properly chosen, the adomian decomposition is a special case of the homotopy analysis method, as allan [18] shows. 4. solutions of fractional shallow water equations we solve the fractional system (1.1), subject to the initial conditions 1 2 sec ( ) ( , 0) ( ) ( ); ( , 0) 0 ( ), 4 h x u x g x g x v x g x x r      (4.1) we take the reference point to be 1, and )exp(1 )exp( )( 2 2 x x xg    . according to [19], we choose the linear operators as: ),;,()];,([ ptxdptxl itii    with property 0][ cl i , for ,2,1i where c is a constant. also, we choose the system of nonlinear operators as 1 1 2 1 2 [ ( , ; ), ( , ; ) [ ( , ; ) ( , ; )]n x t p x t p x t p x t p x        (4.2) and, 2 1 2 2 2 1 ( ( , ; ), ( , ; )] '( ) ( , , ) ( , , ) ( , , )n x t p x t p g x x t p x t p x t p x x              4.1 the hpm solution we implement the homotopy perturbation method (hpm) to solve the system (1.1). the homotopy equations are: for 2,1i , we have ,0 2 (1 ) [ ( , ; ) ( , )] [ [ ( , ; ) [ ( , , ), ( , , ) ( )] 0 i i i i i i i i p l x t p z x t p l x t p n x t p x t p f x         (4.3) where [0,1]p  is an embedding parameter, and ,0 ( , ), 1, 2 i z x t i  , are the initial approximations satisfying the given conditions, while );,( ptx i  , for 1, 2i  are approximate solutions. in view of the homotopy perturbation method, expanding the solutions of equations (4.3) as a power series in p as: for 1, 2i  , we have ...),(),();,( 1,0,  ptxztxzptx iii  (4.4) where the initial approximations are given by homotopy perturbation method 79 1 1,0 2 2,0 ( , ; ) ( , ) ( , 0), ( , ; ) ( , ) ( , 0)x t p z x t u x x t p z x t v x     substituting the above, and arranging coefficients of the same power of p , we get powers of p : 1,1 2,0 1,0 2,1 1,0 2,0 2,0 ( , ) [ ( , ) ( , )] 0 ( , ) [ ( , )] '( ) ( , ) [ ( , )] 0 t t d z x t z x t z x t x d z x t z x t g x z x t z x t x x               powers of 2 p : 1,2 2,1 1,0 2,0 1,1 ( , ) [ ( , ) ( , ) ( , ) ( , )] 0 a d z x t z x t z x t z x t z x t x       and 0)],([),()],([ ),()],([),( 0,21,21,2 0,21,12,2           txz x txztxz x txztxz x txzd t  (4.5) and so on for the rest of the coefficients of the same powers of p . the method of finding the solution is based on applying the operator  j on both sides of equations (4.5) with initial approximations 0)0,( , xz mi , for 1, 2m  and 1, 2i  to obtain 2 1,0 1,12 0 1 3 2 1,2 1,2 1,2 1,2 1,2 sec ( ) exp( ) ( , ) , ( , ) 0 4 1 exp( ) 1 ( , ) [ ( , ) ( , )] [[ ( , ) ( , )] 4 (1 2 ) h x x z x t z x t x z x t s x t s x t s x t s x t              (4.6) and 2,0 2,2 2,1 sec ( ) tanh( ) ( , ) 0 , ( , ) 0 , ( , ) 4 (1 ) t h x x z x t z x t z x t        (4.7) where 2 3 0 1,2 1,0 2 2 1 1,2 1,0 2 2 2 1,2 2 2 2 3 2 1,2 sec ( ) ( , ) [ ( , )] 4 (1 2 ) sec ( ) tanh ( ) ( , ) [ ( , )] 4 (1 2 ) 2 exp( 2 ) 2 exp( ) sec ( ) tanh( ) ( , ) (1 exp( )) 1 exp( ) 4 ( , ) sec ( ) tanh( ) t h x s x t z x t t h x x s x t z x t x x x x h x x s x t x x s x t t h x x                        and so on. in the same manner, the rest of the components of the homotopy perturbation solutions can be obtained using maple package. the third-order term approximate solutions for equation (1.1) are given by kamel al-khaled and mohamed k. al-safeen 80 1,0 1,1 1,2 2,0 2,1 2,2 ( , ) ( , ) ( , ) ( , ), ( , ) ( , ) ( , ) ( , )u x t z x t z x t z x t v x t z x t z x t z x t      (4.8) 4.2 the ham solution we implement the homotopy analysis method to solve the system (1.1). thus we construct the zerothorder deformation equations ,0 1 2 (1 ) [ ( , ; ) ( , )] ( , )[ [ ( , ; )] [ ( , ; ), ( , ; )] ( )] i i i i i i i i i p l x t p z x t p h x t l x t p n x t p x t p f x          (4.9) for .2,1i when ,0p we get 1 ,0 2 ,0 ( , ; 0) ( , ) ( , 0), ( , ; 0) ( , ) ( , 0) i i x t z x t u x x t z x t v x     while for 1p , we have ).,()1;,(),,()1;,( 21 txvtxtxutx   expanding );,( ptx i  in a taylor series with respect to p , then for 1, 2i  one has m m miii ptxztxzptx ),(),();,( 1 ,0,     where 0, | );,( ! 1 ),(     pm i m mi x ptx m txz  . assuming that the above series is convergent when 1p  , due to (4.9) for 1, 2, 3i  we have     1 ,0, ),(),()1;,( m miii txztxztx . for the sake of simplicity, we can deduce that governing equations (4.9) from the zeroth-order deformation equations to the mth -order deformation equations are as follows: for 1, 2i  , , 1 , 1, 1 2, 1 [ ( , ) ( , )] ( , ) [ , ] i i m m i m i i m m m l z x t z x t h x t r z z      (4.10) where         1 0 1,2,1 1,11,21,1,1 ),(),([ ),(],[ m n nmn mtmmm txztxz x txzdzzr  1 2, 1, 1 2, 1 2, 1 1, 1 2, 2, 1 0 [ , ] ( , ) ( , ) ( , ) ( , ) (1 ) '( ) m m m m t m m n m n m n r z z d z x t z x t z x t z x t g x x x                    now, applying the operator  t j on both sides of , , 1 , 1, 1 2, 1 [ ( , ) ( , )] ( , ) [ , ] t i m m t i m i i i m m m d z x t d z x t h x t r z z         yields that for 1, 2i  , , , 1 , 1 , 1, 1 2, 1 ( , ) ( , 0) [ ( , ) ( , 0)] [ ( , ) [ , ]] i m i m m i m i m i t i i m m m z x t z x z x t z x j h x t r z z           (4.11) for simplicity, we assume , 21   and 1),(),( 21  txhtxh , and ,0)0,( , xz mi for 1, 2i  and 1, 2,...m  . according to equation (4.11), we now successively obtain homotopy perturbation method 81 2 1,0 1,12 0 1 3 2 1,2 1,2 1,2 1,2 1,2 exp( ) sec ( , ) , ( , ) 0, 1 exp( ) 4 ( , ) [ ( , ) ( , )] [ ( , ) ( , )] 4 (1 2 ) x hx z x t z x t x z x t s x t s x t s x t s x t             (4.12) and )1(4 tanhsec)1( ),( )1(4 tanhsec ),( 0),( 2,2 1,2 0,2            xhxth txz xhxt txz txz   (4.13) where 2 3 2 0 1,2 2 sec exp( ) sec ( , ) [ ] 4 (1 2 ) 1 exp( ) 4 t h x x hx s x t x           2 2 2 1 1,2 2 sec tanh exp( ) sec ( , ) [ ] 4 (1 2 ) 1 exp( ) 4 t hx x x hx s x t x          2 2 2 1,2 2 2 2 2 exp( 2 ) 2 exp( ) sec tanh ( , ) (1 exp( ) 1 exp( ) 4 x x x x hx x s x t x x          xhxttxs tanhsec),( 23 2,1  and so on. in the same manner, the rest of the components of the homotopy analysis solutions can be obtained using maple package. the third-order term approximate solutions for equation (1.1) are given by 1,0 1,1 1,2 2,0 2,1 2,2 ( , ) ( , ) ( , ) ( , ); ( , ) ( , ) ( , ) ( , )u x t z x t z x t z x t v x t z x t z x t z x t      5. numerical results in this section we shall illustrate the two techniques by different values of  for the fractional shallow water equations. all the results are calculated by using the symbolic calculus software mathematica, using the (hpm). the result shown in figure 1 represents the height of the water, when 1 , which agrees with the results in [1] in which the adomian decomposition method was used. figure 2 represents the velocity of the water when 1 , which begins with zero and, at any later instant of time, changes from positive to negative as x changes from positive to negative. figure 3 shows the height of water when 25.0 , while figure 4 shows the velocity of water for 25.0 . figures 75  show two profiles of the height of the wave for different values of  when the time changes from 1 to 2 . figures 108  show again profiles for the velocity. from the figures 5-10, it is observed that the physical behavior of the approximate solutions at different values of  has the same behavior as that obtained when  =1. this shows the approximate solution is efficient. comparison of figures 5-10 shows that the solution continuously depends on the fractional derivatives. a clear conclusion can be drawn from figures 5-10 that the solution tends to zero as |x| approaches infinity. it is also observed that as time changes from 1 to 2, the wave starts to bifurcate into two waves. we conclude that as the time-fractional derivative increases, the wave solution also changes continuously. tables 1 and 2 show some numerical values for different values of  using (hpm) and (ham), where only the third-order term of the approximate solutions were used. from the tables, we can read that results presented by (ham) when 1 can be considered as results of (hpm). kamel al-khaled and mohamed k. al-safeen 82 6. conclusions the fundamental goal of this paper is to propose an efficient algorithm for the solution of fractional shallow water equations. this goal has been achieved by generalized mth -order deformation of ham for approximate solutions of non-homogeneous systems. it should be emphasized that, within the frame of the homotopy perturbation method, we have great freedom to choose the initial guess, and the auxiliary linear operator l . the convergence of the series solution by ham is dependent upon four factors [15,20], i.e., the initial guess, the auxiliary linear operator, the auxiliary function ),( txh , and the auxiliary parameter  , while the convergence of series solution that is obtained by hpm is only depend upon two factors: the auxiliary linear operator, and the initial guess. using the hpm we overcome the difficulties arising in the calculation of ham; moreover the calculations in the hpm are simple and straightforward. the reliability of the method and the reduction in the size of the computational domain give this method a wide applicability. table 1. numerical values of ),( txu using hpm. t x  =0.5  =0.75  =1 0.2 0.5 0.8 0.2 0.4 0.7 0.2 0.4 0.7 0.2 0.4 0.7 0.703295 0.673630 0.583692 0.655611 0.647070 0.590625 0.607928 0.620510 0.597558 0.724389 0.685380 0.580625 0.692810 0.667791 0.585216 0.649529 0.643682 0.591509 0.731904 0.689566 0.579532 0.715215 0.680270 0.581959 0.684221 0.663006 0.586465 table 2. numerical values of ),( txv using hpm. t x  =0.5  =0.75  =1 0.2 0.5 0.8 0.2 0.4 0.7 0.2 0.4 0.7 0.2 0.4 0.7 0.024410 0.044338 0.060744 0.038596 0.070105 0.096046 0.048820 0.088676 0.121490 0.015741 0.028591 0.039171 0.031295 0.056845 0.077879 0.044522 0.080860 0.110793 0.009674 0.017572 0.024075 0.024186 0.043932 0.060187 0.038698 0.070291 0.096300 homotopy perturbation method 83 figure 1. approximate numerical solution ),( txu with 1 figure 2. approximate numerical solution ),( txv with 1  figure 3. approximate numerical solution ),( txu with 0.25  kamel al-khaled and mohamed k. al-safeen 84 figure 4. approximate numerical solution ),( txv with 0.25  figure 5. approximate numerical solution ),( txu with 0.25  for 1t  to 2t  figure 6. approximate numerical solution ),( txu with 1  for 1t  to 2t  homotopy perturbation method 85 figure 7. approximate numerical solution ),( txu with 0.5  for 1t  to 2t  figure 8. approximate numerical solution ),( txv with 1  for 1t  to 2t  figure 9. approximate numerical solution ),( txv with 0.5  for 1t  to 2t  figure 10. approximate numerical solution ),( txv with 0.25  for 1t  to 2t  kamel al-khaled and mohamed k. al-safeen 86 references 1. al-khaled, k. and allan, f. construction of solutions for the shallow water equations by the decomposition method. comput. simul., 2004, 66, 479-486. 2. caputo, m. linear models of dissipation whose q is almost frequency independent ii, geophysics. j. r. astron. soc., 1967, 13, 529-539. 3. bermudez, a. and vazquez, m. upwind methods for hyperbolic conservation laws with source terms. comput. fluids, 1994, 23,1049-1071. 4. oldham, k.b. and spanier, j. the fractional calculus, academic press, new york, 1974. 5. miller, k.s. and ross, b. an introduction to the fractional calculus and fractional differential equations, john wiley and sons inc. new york, 1993. 6. momani, s. non-perturbative analytical solutions of the space and time fractional burgers' equations. chaos soliton fractals., 2006, 28, 930-937. 7. podlubny, i. fractional differential equations, academic press, new york, 1999. 8. podlubny, i. gemmetric and physical interpretation of fractional integration and fractional differentiation. frac. calc. appl. anal. 2002, 5, 367-386. 9. kisela, t. power functions and essentials of fractional calculus on isolated time scales. adv. diff. equ., 2013, 2013, 259. 10. podlubny, i. what euler could further write, or the unnoticed "big bang" of the fractional calculus. frac. calc. appl. anal. 2013, 16, 501-506. 11. liao, s.j. comparison between the homotopy analysis method and homotopy perturbation method. appl. math. comput., 2005, 169, 1186-1194. 12. liao, s.j. the proposed homotopy analysis technique for the solution of nonlinear problems, ph.d. thesis, shanghai jiao tong university, 1992. 13. he, j.h. homotopy-perturbation method: a new nonlinear analytical technique. appl. math. comput., 2003, 135, 73-79. 14. liao, s.j. beyond perturbation: introduction to the homotopy analysis method, chapman and hall/crc press, boca raton, 2003. 15. sahid, m., hayat, t. and asghar, s. comparison between the ham and hpm solutions of thin film flows of non-newtonian fluids on a moving belt. nonlin. dynam., 2007, 50, 27-35. 16. abbasbandy, s. the application of homotopyanalysis method to solve a genaralized hiroto-satsuma coupled kdv equations. phys. lett. a , 2007, 361, 478-483. 17. he, j.h. homotopy-perturbation technique. comput. math. appl. mech. eng., 1999, 178, 257-262. 18. allan, f. derivation of the adomian decomposition method using the homotopy analysis method. appl. math. comput., 2007, 190, 6-14. 19. al-saafeen, m.k. homotopy perturbation method for fractional hirota-satsuma coupled kdv equations, master thesis, jordan university of science and technology, 2008. 20. song, l.n. application of homotopy analysis method to fractional kdv-burgers-kuramoto equation. phys. lett. a, 2007, 367(1-2), 88-94. received 10 february 2014 accepted 14 april 2014 squ journal for science, 2014, 19(2), 21-28 © 2014 sultan qaboos university 21 dioxygen binding by cobalt(ii) complexes of 8,8'-bis(aminomethyl)-2,2'-biquinoline muhammad s. khan 1*, nawal k. al-rasbi1 and edwin c.constable2 1 department of chemistry, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman, 2 department of chemistry, university of basel, spitalstrasse 51, ch-4056 basel, switzerland. *email: msk@squ.edu.om. abstract: a new series of co(ii) complexes of the type colx2 , where l is a tetra-dentate ligand 8,8'bis(aminomethyl)-2,2'-biquinoline and x= scn – , bf4 – , i – or no3 – , have been synthesized and characterized. the complexes have magnetic moments in the range typical of a low-spin d 7 co(ii) center. the interaction of these co(ii) complexes with dioxygen was studied by e.s.r. spectroscopy. a dicobalt(iii) peroxo-bridged complex was formed in dmf solution, associated with the formation of an e.s.r.-silent solution compatible with the formation of low-spin d 6 co(iii) species. similar behavior was also observed for the interaction of these co(ii) complexes with dioxygen in the presence of ancillary ligands such as pyridine and 2methylimidazole. the dioxygen complexes proved successful as oxygen carrier oxidation catalysts for tripehnylphosphine and 2,6-bis( t -butyl)phenol. keywords: biquinoline; cobalt(ii); dioxygen interaction; e.s.r. ثىائي كويىونيه-'2,2-ثىائي أميىوميثيم-'8,8مع مركبات انكوبانث مه ارجباط األكسجيه ادويه س. كوويسحابمو ةانراسبيخ. ووال محمذ س. خان، x و ثُائي كىيُىنيٍ -'2,2-ثُائي أييُىييثيم-'8,8 انًخشابطهى n4حيث con4x2 بانصيغت كىبانجانسهسهت جذيذة نًشكباث حى حكىيٍ مهخص: d (ii)سَيٍ يغُاطيسي يطابق نكىبانج. هزِ انًشكباث نذيها (l). يع bf4, i, no3 أو scn حساوي 7 حفاعم هزِ حى دساست وقذ يُخفض انغضل. انًشكباث يع غاص األكسجيٍ باسخخذاو حقُيت انشَيٍ اإلنيكخشوَي. حيث يخكىٌ يشكب بزسحيٍ يٍ انكىبانج يخصهخيٍ بجسش يٍ رسحي أكسجيٍ في d (iii)وانخي يطابق َخائج انشَيٍ اإلنيكخشوَي نذيها نزسة كىبانج dmfيحهىل 6 يُخفض انغضل. وقذ نىحظج َخائج يشابهت نخفاعم هزِ انًشكباث ييثيم ايذيضول. نقذ أثبخج انًشكباث جذاسحها بُقم األكسجيٍ في أكسذة حشايفُيم فىسفيٍ و -2يع األكسجيٍ عُذ حىاجذ يخشابطاث يٍ انبشيذيٍ و ثُائي ث بيىحيم فيُىل. -2,2 .انشَيٍ اإلنيكخشوَي، حفاعم يع األكسجيٍ ، كىبانجكىيُىنيٍ ، : مفحاح انكهمات 1. introduction he transport of dioxygen by reversible binding to transition metal complexes plays an essential role in the life processes of multicellular organisms. in recent years our understanding of the molecular basis of in vivo oxygen binding and transport has been aided by a wide range of in vitro studies. numerous simple chemical systems have been developed, which exhibit dioxygen binding that is reversible to variable degrees [1-4]. although the common biological transport systems contain iron at the dioxygen binding site, coordination compounds of cobalt have proved to be valuable models for understanding and controlling the types of metaldioxygen interaction that may occur [5,6]. the nature of dioxygen binding by cobalt(ii) complexes has been shown to depend crucially upon the nature of the ligands coordinated to the metal [7]. limiting behavior is observed in the formation of 1:1 complexes containing cobalt(iii) superoxides and 1:2 complexes with peroxidebridged dicobalt(iii) species. this behaviour is typified by complexes such as [co(salen)] (h2salen = h2l 1 ) and [co(acacen)] (h2acen = h2l 2 ) or [co(bzacen)] (h2bzacen = h2l 3 ). in the solid state [co(salen)] reversibly absorbs dioxygen at a ratio of 2:1 to give a compound in which the dioxygen bridges the cobalt atoms of two coplanar complex molecules; i.e. approaching the peroxide-bridged dicobalt(iii) structure [8,9]. in n,ndimethylformamide (dmf) solution, the complex also reacts reversibly with dioxygen to form a peroxo-bridged dicobalt(iii) complex [10]. in this case, the cobalt(iii) centers are six-coordinate and the remaining axial site is occupied by a dmf ligand. in contrast to this, the complexes [co(acacen)] or [co(bzacen)] react with dioxygen t mailto:msk@squ.edu.om muhammad s. khan et al 22 only in the presence of a strong axial donor such as pyridine, to yield six-coordinate cobalt(iii) superoxide complexes [co(acacen)(py)(o2)] or (co(bzacen)(py)(o2)] [11-14]. complexes of neutral macrocyclic ligands are also known to react reversibly with dioxygen. we wish to report in this paper the synthesis and characterization of some cobalt complexes of the tetra-dentate ligand 8,8'-bis(aminomethyl)-2,2'-biquinoline (l), and also to describe the interactions of these complexes with dioxygen in a variety of solvents. n n nh2nh2 l n oh n ho h2l 1 oh n n ho me r me r h2l 2 r = me h2l 3 r = ph chart 1. ligands l used in this work and some related ligands h2l 1-3 . 2. experimental infra-red spectra were recorded in compressed kbr pellet on perkin elmer ft 910 or perkin elmer 983 spectrophotometers. mass spectra were recorded on a kratos ms 30 mass spectrometer. electronic spectra were recorded on a pye-unicam pu 8800 spectrophotometer. e.s.r. spectra were recorded using a varian e 109 spectrometer; g values were determined by reference to a 2,2-diphenyl-l-picrylhydrazyl hydrate standard (g = 2.0036). magnetic susceptibilities were measured using a johnson matthey susceptibility balance calibrated using copper sulphate pentahydrate and mercury cobalt thiocyanate. the ligand 8,8'-bis(aminomethyl)-2,2'biquinoline (l) was prepared as reported in the literature [15]. all chemicals, reagents, cobalt salts and solvents were purchased from sigma aldrich and used without further purification. synthesis of {col(scn)2} a degassed solution of l (0.05 g, 0.16 mmol) in methanol (5 ml) was added to a boiling solution of co(scn)2 (0.03 g, 0.17 mmol) in methanol (25 ml) maintained under an atmosphere of dinitrogen. the resultant solution was heated to reflux for 2 h, and allowed to cool. the fine green solid which precipitated was collected by filtration and dried to yield {col(scn)2} (0.055 g, 70%). the nitrate and the iodide derivatives were prepared in an analogous manner from the appropriate cobalt salts. synthesis of {col(bf4)2.h2o} to a degassed solution of l (0.40 g, 1.27 mmol) in methanol (200 ml) maintained under an atmosphere of dinitrogen was added a degassed solution of co(bf4)2.6h2o (0.33 g, 1.3 mmol) in methanol (5 ml). the resultant deep purple solution was heated to reflux under a dinitrogen atmosphere for 2 h, and allowed to cool. the solution was then concentrated under reduced pressure and allowed to cool, when a purple-red complex was obtained (0.48 g, 70%). the solid was reasonably stable in air, but was routinely stored under dinitrogen. recrystallization by the diffusion of diethyl ether vapor into an acetonitrile solution of the complex yielded fine red needles, which crumbled to a red powder upon removal of the solvent mixture of recrystallization. synthesis of {lco(-o2)coli4} dioxygen was bubbled through a solution of (coli2.h2o) (0.20 g, 0.32 mmol) in boiling methanol (700 ml) for 15 min. the resultant red-brown solution was filtered, and the filtrate concentrated by boiling in air to about 50 ml volume. upon cooling, a red-brown microcrystalline solid precipitated, which was collected by filtration and dried in air to yield {lco(-o2)coli4).6h2o (0.107 g, 55%). dioxygen binding by cobalt(ii) complexes 23 typical conditions for the oxidation of triphenylphosphine a suspension of {coli2.h2o} (0.05 g, 0.08 mmol) in methanol (70 ml) was treated with dioxygen to yield a redbrown solution. a similar flask was prepared containing only methanol (70 ml). each of these flasks had triphenylphosphine (0.1 g, 0.38 mmol, oxide free) added. these solutions were maintained at 25 c and dioxygen was bubbled through each for 4 h. after this period tlc analysis indicated that in the solution containing the metal complex, the triphenylphosphine had been completely converted to triphenylphosphine oxide, whereas there were no detectable amounts of triphenylphosphine oxide in the control reaction. the solution containing the cobalt complex was evaporated to dryness and the residue extracted with diethyl ether (2 x 50 ml). the ether extract was then evaporated to dryness to yield triphenylphosphine oxide (0.10 g, 95%) as a white crystalline solid which was shown to be pure by infrared, 1 h and 31 p nmr spectroscopy. typical conditions for the oxidation of 2,6-bis( t -butyl)phenol 2,6-bis( t -butyl)phenol (0.3 g, 1.45 mmol) was added to a solution of {col(bf4)2.h2o) (0.05 g, 0.09 mmol) in dmf (25 ml). dioxygen was then bubbled through the solution for 12 h, after which period the red crystalline product was collected by filtration. these red needles were characterized as pure tetra( t -butyl)diphenoquinone by infrared and 1 h nmr spectroscopy (0.10 g, 30%). the filtrate was poured into water (10 ml) and the dark coloured solution extracted with diethyl ether (3 x 50 ml). the ether extract was dried (mgso4) and evaporated to dryness in vacuum. the residue was dissolved in the minimum volume of chloroform and chromatographed on a silica column (chcl 3 eluant) to yield pure 2,6-bis( t -butyl)quinone (0.185 g, 60%). a control experiment in which no cobalt complex was present showed very small quantities of oxidation product. 3. results and discussion we have previously described the preparation of the tetradentate ligand 8,8'bis(aminomethyl)-2,2'-biquinoline (l) which was intended as a precursor to macrocyclic ligands containing a 2,2'-biquinolyl moiety [15]. in the course of our investigations into the coordination chemistry of this ligand we noticed that the cobalt(ii) complexes underwent partially reversible changes upon interaction with dioxygen. the reaction of cobalt(ii) salts with l in methanol in the absence of dixoygen resulted in the formation of colored solutions containing complexes with a 1:1 metal:ligand stoichiometry. these complexes are either green (i – , scn – or no3 – ) or red-purple (bf4 – ), depending upon the presence and nature of coordinating anions. in general, the complexes were obtained as monohydrated species. the compounds obtained from cobalt(ii) iodide or cobalt(ii) nitrate both exhibited room temperature magnetic moment close to 2.2 b.m in the solid state, while the thiocyanate showed a moment of 2.51 b.m. and the tetrafluoroborate exhibited a room temperature solid state moment of 3.12 b.m. in each case the magnetic moments were considerably below the spin-only value expected for a high-spin d 7 ion (3.87 b.m.) and significantly below the usual values observed for high-spin cobalt(ii) complexes (4.5 5.3 b.m. in various geometries), which exhibit large orbital contributions at room temperature. table 1. elemental analysis and magnetic moments for co(ii) complexes. compound calc c h n found c h n eff (b.m.) {col(bf4)2.h2o} 42.6 3.5 9.6 42.9 3.2 9.8 3.12 {col(no3)2.h2o} 46.6 3.9 16.3 46.6 3.6 15.5 2.25 {coli2.h2o} 37.2 3.1 8.4 37.0 3.0 8.1 2.23 {col(scn)2} 54.0 3.7 17.2 53.9 3.7 17.0 2.51 {co2l2(o2)i4.6h2o} 34.4 3.4 8.0 34.1 3.2 7.8 0 low-spin complexes of cobalt(ii) commonly exhibit square planar four coordinate or square pyramidal five coordinate geometries, and the magnetic moments for these compounds are typically in the range 2.0 3.0 b.m. at room temperature, although a very wide range of values have been reported [8,14,15]. we have previously demonstrated that the ligand l may form six-coordinate ([mnlc12]) and five-coordinate ([culci]ci) complexes [13]. the magnetic data for the cobalt(ii) complexes is consistent with the presence of a low-spin metal center. low-spin d 7 is expected to exhibit a large jahn-teller effect in six-coordinate complexes and such compounds are relatively rare. we propose that the green complexes we have isolated are five-coordinate in the solid state with the axial site occupied by the coordinating anion. the red-purple tetrafluoroborate salt probably contains a square planar cation. we believe that common solution species are formed in which other ancilliary ligands or solvent molecules may occupy the axial site. the compounds have limited solubility, and we have not been able to obtain consistent solution conductivity measurements. solid state e.s.r. spectra of the complexes were not well-resolved. the e.s.r. spectrum at 77 k of a green frozen methanolic solution of {col(no3)2.h2o} prepared and maintained under a dinitrogen atmosphere is shown in figure 1a. this spectrum exhibits two anisotropic g values and is typical of a d 7 low-spin cobalt(ii) complex. the parallel (g// = 2.028) and perpendicular (g = 2.307) components are both well-resolved, and the perpendicular component clearly exhibits hyperfine coupling to the 59 co nucleus (i = 7/2, muhammad s. khan et al 24 a = 100 g). the e.s.r. spectrum of a green frozen solution of the same complex in dmf is shown in figure lb, and very closely resembles that of the methanolic solution (g// = 2.034, g = 2.307, a = 100 g). this suggests that the solution species is grossly similar in each case. these spectra are similar to those previously reported for [co(acacen)(py)] (py pyridine) in general shape and hyperfine coupling (a = 80-100 g) [18]. treatment of the methanolic and dmf solutions of {col(no3)2.h2o} with dioxygen resulted in slightly different qualitative behaviour. upon bubbling dioxygen through a methanolic solution, a slight brownish tint developed. the e.s.r. spectrum of a frozen methanolic solution at 77 k which had been pretreated with dioxygen very closely resembles that of a methanolic solution of the starting complex, as seen in figure la. quantitative studies revealed that the development of the brown tint was associated with decreases in signal intensity, but no new features were observed in the e.s.r. spectrum. in contrast, bubbling dioxygen through a green solution of {col(no3)2.h2o) in dmf resulted in a rapid change in colour of the solution to red-brown. the e.s.r spectrum of this red-brown solution (frozen glass, 77 k) is shown in figure 1c. the change from green to red-brown upon passing dioxygen through the dmf solution is associated with the formation of an e.s.r-silent solution species. this is compatible with the conversion of the lowspin d 7 cobalt(ii) complex to a low-spin d 6 cobalt(iii) species. the cobalt(iii) center could be directly coordinated to a diamagnetic oxygen reduction product (oxo or peroxo) or there might be no direct co-o interactions in the diamagnetic species. these observations are indicative of a process in which the interaction with dioxygen is facilitated by the presence of a strongly ligating solvent such as dmf, with the reaction in methanol being slow and incomplete. these observations parallel those previously reported for the interaction of [co(salen)] with dioxygen [8,9]. (a) (c) figure 1. (a) e.s.r. spectrum of a green frozen methanol solution of {col(no3)2.h2o} at 77 k (b) e.s.r. spectrum of a green frozen dmf solution of {col(no3)2.h2o} at 77 k and (c) e.s.r. spectrum of a red-brown frozen dmf solution of {col(no3)2.h2o} at 77 k after exposure to dioxygen. when dinitrogen was bubbled through the red-brown dmf solution which had been obtained after oxygenation, these colour changes were reversed and a green solution was obtained. methanolic solutions showed a similar behavior. the e.s.r. spectra of the frozen green solutions in methanol or dmf obtained after flushing with dinitrogen were identical in all respects to those of the original solutions before oxygenation. this is strongly indicative of a reversible interaction with dioxygen. behaviour of this type is associated with species in which the e.s.r. -silent product retains co-o interactions. this is a strong supporting evidence for the formation of a cobalt(iii) peroxo complex upon reaction with dioxygen (figure 2). the overall similarity of behaviour to that reported for [co(salen)] and related species suggests that the likely product is a binuclear peroxo-bridged dicobalt(iii) complex. the oxygenation-deoxygenation cycle may be repeated a number of times, although some gross decomposition eventually occurs. the deoxygenation may also be effected by evacuating the dmf or methanolic solutions. solutions of {coli2.h2o} in methanol or dmf exhibited similar colour changes upon reaction with dioxygen, and e.s.r. spectroscopy indicated that the presence of the coordinating iodide ion facilitated dioxygen binding in methanolic solution. the passage of dioxygen through boiling methanolic solutions of {coli2.h2o} resulted in a color change from green to red, and upon concentration of this solution a red crystalline product formulated as {lco(o2)coli4.6h2o} was obtained. this complex was diamagnetic and dmf solutions were e.s.r.-silent. oxygen uptake experiments upon dmf solutions of {col(no3)2.h2o} confirmed a stoichiometry for the reaction of 0.5 o2:1 co. the data is consistent with the formation of a dicobalt(iii) peroxo-bridged complex as shown in figure 2. (b) dioxygen binding by cobalt(ii) complexes 25 co nn n n o o co nn n n figure 2. proposed structure for the dicobalt(iii) peroxo complex. it is known that the binding of dioxygen to iron and cobalt complexes may be modified by or dependent upon the presence of other ligands in the solution, and we have investigated the behavior of {col(no3)2.h2o} solutions in the presence of ancillary ligands. the addition of a few drops of pyridine (py) to a dmf solution of {col(no3)2.h2o} yields a green solution; the e.s.r. spectrum at 77 k of a frozen dmf solution of {col(no3)2.h2o} containing pyridine is shown in figure 3a. the spectrum is well-resolved and it is apparent that there are differences from the e.s.r. spectrum in the absence of pyridine. the parallel (g11 = 2.087) and perpendicular (g = 2.379) components are slightly shifted with respect to the spectrum in the absence of pyridine. furthermore, some of the lines in the parallel part of the spectrum exhibit additional hyperfine coupling to 14 n (i = 1, a = 11 g) and the coupling to 59 co is reduced (a = 80 g). these observations are compatible with the formation of a pyridine adduct in which one pyridine is coordinated to an axial site lying above the square plane described by the four nitrogen donors of the ligand l. this compound could be a five-coordinate square-based pyramidal species (figure 4a, a = py) or an octahedral ion with solvent occupying the remaining octahedral site (figure 4b, a = py). both of these structures are compatible with the reduction of the hyperfine coupling to the cobalt, as observed for complexes with h2l 2 or h2l 3 [18]. figure 3. (a) e.s.r. spectrum of a green frozen dmf solution of {col(no3)2.h2o} containing pyridine at 77 k. (b) e.s.r. spectrum of a green frozen dmf solution of {col(no3)2.h2o} containing 2-methylimidazole at 77 k. upon exposure of dmf solution of {col(no3)2.h2o} containing pyridine to dioxygen, a red-brown solution was obtained. once again, this frozen red-brown solution was e.s.r-silent at 77 k, suggesting that a similar peroxobridged dicobalt(iii) complex was formed. the red-brown compound was reconvened to the green e.s.r-active species upon bubbling dinitrogen through the solution. this process of oxygenation-deoxygenation could be repeated five times with no noticeable decomposition and no changes in the intensity or the character of the e.s.r. spectrum of the green species. very similar behavior was observed upon the addition of 2-methylimidazole (meim) to a dmf solution of {col(no3)2.h2o}. the e.s.r. spectrum at 77 k of a frozen solution containing 2-methylimidazole is shown in figure 3b. the changes in the spectrum are similar to those seen upon the addition of pyridine (g11 = 2.034, g= 2.313, aco= 70 g, an = 16 g), suggesting the formation of an axially substituted complex (figure 4a or 4b, a = meim). this green solution also reacted reversibly with dioxygen to yield an e.s.r.-silent red solution. the resemblances between the behavior of the cobalt(ii) complexes with l and those with h2salen and related ligands are remarkable. in the presence of ancillary ligands such as pyridine, the [co(salen)] system also changes its dioxygen binding behaviour to yield 1:1 superoxo adducts. we have investigated the effect of solvent upon the reactions of 1:1 cobalt(ii) complexes of l with dioxygen. the compounds {col(no3)2.h2o}, {coli2.h2o} or {col(scn)2.h2o} are not significantly soluble in solvents other than water, methanol or dmf. the reaction of l with methanolic solutions of cobalt(ii) tetrafluoroborate in the absence of dioxygen results in the formation of deep red-purple solutions. concentration of these solutions in anaerobic conditions (b) (a) muhammad s. khan et al 26 allows the isolation of a deep red-purple coloured crystalline complex formulated as {col(bf4)2.h2o}. this material is very air-sensitive in solution, but is moderately stable in the solid state. we have repeatedly attempted to obtain xray quality crystals of this product; the recrystallization of the complex by the diffusion of diethyl ether vapour into an acetonitrile solution of {col(bf4)2.h2o} results in the formation of beautiful red-purple needles. these needles lose solvent immediately when they are removed from the mother liquor, and we have been unable to mount x-ray quality crystals. the e.s.r. spectrum at 77 k of a frozen solution of {col(bf4)2.h2o} in dmf is identical to that of a dmf solution of {col(no3)2.h2o} (g11 = 2.034, g = 2.310). the e.s.r. spectrum at 77 k of a frozen solution of {col(no3)2.h2o} in acetonitrile is shown in figure 5; the spectrum qualitatively resembles that of the dmf solution, although the hyperfine coupling to 59 co is not so well-resolved. these observations are indicative of similar solution species in dmf for {col(bf4)2.h2o} and {col(no3)2.h2o} and of similar solution species in dmf and acetonitrile for {col(bf4)2.h2o}. both dmf and acetonitrile solutions of {col(bf4)2.h2o} react reversibly with dioxygen to generate e.s.r.-silent oxidation products. (a) co nn n n a (b) co nn n n a y figure 4. (a) proposed structures for the complexes with ancillary ligand: a = py or meim (b) proposed structures for the complexes with ancillary ligand a and a coordinating solvent y. figure 5. e.s.r. spectrum of a frozen acetonitrile solution of {col(no3)2.h2o} at 77 k. in contrast to the behavior of {col(bf4)2.h2o} solutions discussed above, very different behavior was observed for acetonitrile solutions in the presence of ancillary ligands. acetonitrile solutions of {col(bf4)2.h2o} containing pyridine react with dioxygen to produce orange solutions, which are e.s.r-active. the e.s.r. spectrum at 77 k of such a frozen solution is shown in figure 6. once again an anisotropic spectrum is observed (g  = 2.009, g11 = 2.067), and a much reduced hyperfine coupling constant to cobalt is seen (a = 10 g). this is compatible with a structure in which the unpaired spin density is significantly localized upon some other nucleus, and is suggestive of a cobalt(iii) superoxide complex in which the spin density is essentially on oxygen (figure 7). very similar results were obtained with solutions of {col(bf4)2.h2o} in neat pyridine. once again, the reaction with dioxygen was to some extent reversible, and at least four oxygenation-deoxygenation cycles were possible without any detectable decomposition of the complex. gas uptake experiments confirmed a stoichiometry for the reaction of 1o2:1co. dioxygen binding by cobalt(ii) complexes 27 figure 6. e.s.r. spectrum of an orange frozen dmf solution of {col(bf4)2.h2o} containing pyridine at 77 k after exposure to dioxygen. co nn n n a o o figure 7. proposed structure for the cobalt(iii) superoxo complex with ancillary ligand a = py or meim. we have made a preliminary assessment of the use of these dioxygen complexes as oxygen carrier oxidation catalysts. the addition of an excess of triphenylphosphine to a red-brown solution obtained by the passage of dixoygen through a methanolic solution of {coli2.h2o} resulted in the formation of a brown-green solution. thin layer chromatography (tlc) of the solution indicated the formation of some triphenylphosphine oxide. the solution was stirred at room temperature under an atmosphere of dioxgen for 2 hours, after which period tlc analysis indicated the complete conversion of triphenylphosphine to triphenylphosphine oxide. the product triphenylphosphine oxide could be isolated from the solution in 95% yield. amounts of phosphine up to ten times the weight of cobalt complex could be oxidized with no detectable loss of activity. the passage of dioxygen through dmf solutions of the red compound {lco(-o2) coli4.6h2o} containing triphenylphosphine also resulted in the formation of triphenylphosphine oxide. in both cases, the rate of oxidation of triphenylphosphine was considerably faster than that observed in the absence of the cobalt complex. we have not further investigated the mechanism of this reaction, which could proceed by direct reaction of the phosphine with the peroxo-bridged compound. these cobalt complexes are also active in the oxidation of 2,6-bis( t -butyl)phenol. when dmf solutions of any of the complexes were stirred with 2,6-bis( t -butyl) phenol under dioxygen, tlc analysis indicated the disappearance of 2,6-bis( t -butyl)phenol and the formation of two new products. upon standing, dark red crystals of tetra( t -butyl) diphenoquinone separated, which were characterized by mass, infrared and 1 h n.m.r. spectroscopy. the other product of the reaction was similarly identified as 2,6-bis( t -butyl)quinone. once again, only catalytic quantities of the cobalt complexes were required for the oxidation of the phenol, and total yields of the two oxidation products were in excess of 90%. in general it was found that the product distribution was 6:4 2,6-bis( t -butyl)quinone:tetra( t butyl)diphenoquinone. 4. conclusion the co(ii) complexes colx2 based on l= 8,8'-bis(aminomethyl)-2,2'-biquinoline and x= scn – , bf4 – , i – or no3 – , have confirmed their oxygen-binding tendency in dmf solution. a dicobalt(iii) peroxo-bridged complex is formed, associated with the formation of an e.s.r.-silent solution compatible with the formation of a low-spin d 6 co(iii) species. the introduction of ancillary ligands such as pyridine and 2-methylimidazole into the co(ii) complex has enhanced their oxygen-binding tendency in solution. an axially substituted mononuclear complex has formed to yield an e.s.r.-silent solution typical for low-spin d 6 co(iii) species. muhammad s. khan et al 28 5. acknowledgement one of the authors (m.s.k.) acknowledges sultan qaboos university for a research grant (ig/sci/chem/13/01) and for a research leave. references 1. murray, l.j., dinca, m., yano, j., chavan, s., bordiga, s., brown, c.m. and long, j.r. highly-selective and reversible o2 binding in cr3(1,3,5-benzenetricarboxylate)2. j. am. chem. soc., 2010, 132(23), 7856-7857. 2. sun, y., chen, k., jia, l. and li, h. toward understanding macrocycle specificity of iron on the dioxygen binding ability: a theoretical study. phys. chem. chem. phys., 2011, 13(30), 13800-13808. 3. henrici‐olivé, g. and olive, s. activation of molecular oxygen. angew. chem. int. ed., 1974, 13(1), 29-38. 4. sheldon, r.a. and kochi, j.k., chapter 4, activation of molecular oxygen by metal complexes, in metalcatalyzed oxidations of organic compounds, p 71-119, isbn 9780126393804, academic press, new york,1981. 5. sheldon, r.a., metal-catalyzed oxidations of organic compounds: mechanistic principles and synthetic methodology including biochemical processes. elsevier, 2012. 6. buckingham, d.a., and clark, c.r. in comprehensive coordination chemistry, (eds.) wilkinson, g., gillard, r.d. and mccleverty, j.a. pergamon press, oxford, p 749-750, 1987. 7. tiné, m.r. cobalt complexes in aqueous solutions as dioxygen carriers. coord. chem. rev., 2012, 256(1), 316327. 8. shahabadi, n., kashanian, s. and darabi, f. dna binding and dna cleavage studies of a water 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soc., 1970, 92(1), 61-65. received 19 august 2014 accepted 10 november 2014 squ journal for science, 2015, 20(2), 1-11 © 2015 sultan qaboos university 1 energy management through heat integration: a simple algorithmic approach for introducing pinch analysis nasser a. al-azri department of mechanical and industrial engineering, college of engineering, sultan qaboos university, p.o. box: 33, pc 123, al-khod, muscat, sultanate of oman. email: nalazri@squ.edu.om. abstract: pinch analysis is a methodology used for minimizing energy and material consumption in engineering processes. it features the identification of the pinch point and minimum external resources. two common established approaches are used to identify these features: the graphical approach and the algebraic method, which are time-consuming and susceptible to human and calculation errors when used for a large number of process streams. this paper presents an algorithmic procedure to heat integration based on the algebraic approach. the algorithmic procedure is explained in a didactical manner to introduce pinch analysis for students and novice researchers in the field. matlab code is presented, which is also intended for developing a matlab toolbox for process integration. keywords: algorithmic approach; heat integration; pinch analysis; process integration. إدارة انطاقت من خالل انتكامم انحراري: مذخم خوارزمي مبسط نتقذيم مبذأ انتحهيم اننقطي ناصر بن أحمذ انعسري انحذ األدَٗ نهًٕاد ٔانطاقة انًستٓهكة فٙ انعًهٛات انُٓذسٛة. ٔيٍ خٕاصّ أَّ ٚتعزف عهٗ إٌ يبذأ انتحهٛم انُقطٙ ْٕ طزٚقة تستخذو إلٚجاد مهخص: تستٓهكاٌ َقطة انفصم ٔانحذ األدَٗ يٍ انًٕارد انخارجٛة. ٔيٍ انًعتاد استخذاو طزٚقتٍٛ نهتعزف عهٗ تهك انخٕاص: احذاًْا بٛاَٛة ٔاألخزٖ جبزٚة، ٔحسابٛة عُذ استخذايًٓا نعذد كبٛز يٍ انعًهٛات االَسٛابٛة. تقذو ْذِ انٕرقة إجزاء خٕارسيٙ ٚستخذو فٙ بشزٚة ءٔقتا طٕٚال يع احتًال ٔقٕع أخطا ٙ نهطالب انتكايم انحزار٘ يبُٙ عهٗ أساس انطزٚقة انجبزٚة نهتحهٛم انُقطٙ. ٔقذ تى شزح ْذا اإلجزاء بطزٚقة تعهًٛٛة كًذخم نًبذأ انتحهٛم انُقط ا انًجال. ٔقذ تى عزض بزَايج ياتالب انذ٘ ٚذْف أٚضا إنٗ تطٕٚز أدٔاتّ فٙ يجال تكايم انعًهٛات. ٔانباحثٍٛ انًبتذئٍٛ فٙ ْذ َٓج خٕارسيٙ، تكايم حزار٘، تحهٛم َقطٙ، تكايم عًهٛات. :كهماث مفتاحيت 1. introduction ith the rapidly soaring prices of energy, energy management and alternative energy are increasingly becoming more relevant than ever. moreover, alternatives that were once perceived to be uneconomical have become worth revisiting and investigating. heat integration is an energy management strategy that employs pinch analysis to decrease the consumption of energy. it can be implemented either at grass-roots, when the process plant is being designed, or by retrofitting an existing process. retrofitting, however, has to be economically justifiable as, in many cases, the additional capital is more than the anticipated savings. heat integration was introduced by linnhoff et al. [1], this being the first application of pinch analysis, which is extensively explained and researched in the literature [1-4]. in heat integration, energy from external resources is minimized by using the thermal pinch diagram which targets the optimal matching of hot and cold streams while maintaining thermodynamic feasibility. the use of the thermal pinch is not merely limited to identifying the maximum potential for heat integration, it can also be used in determining the level of steam mains from the grand composite curve when cogeneration is also considered, along with the production of steam [5-10]. the paper presented here discusses a simple algorithmic approach to the application of pinch analysis. this approach is explained in a step-by-step format to extend the benefit to students and novice researchers. w nasser a. al-azri 2 2. thermal pinch diagram before designing the utility system of a processing plant, minimum utility targets need to be determined using the pinch diagram [11,12]. for given heat exchange streams, the heat exchanged is calculated from: ( ) ( ) where q is the heat exchanged (in kw), m is the mass flow rate (in kg/s), cp is the specific heat capacity (in kj/kg.k), t is the temperature (in o c or k), while subscripts h and c denote hot and cold respectively, and superscripts s and t denote supply and target respectively. in a heat-versus-temperature diagram (figure 1), a hot stream is represented by an arrow whose tail is located at supply temperature ( ) and head at target temperature ( ) and which is drawn with a slope equal to the product of the stream flow rate and the specific heat (mcp). these arrows are then arranged in ascending order of their target temperature i.e. by sliding the arrows vertically while maintaining their horizontal projection on the t-axis. figure 1. constructing a hot stream curve using superposition. figure 2. thermal pinch diagram. energy management through heat integration 3 figure 3. suboptimal integration when streams match beyond pinch point. figure 4. overlapping implies thermodynamically unfeasible integration. cold streams are represented on the diagram using a similar procedure, but they are arranged in ascending order of supply temperature ( ). for both types of streams, if one stream overlaps with another of its kind (cold or hot) in their horizontal projections, the overlapping segments will be represented by a single segment extending from the upper point in the top segment to the lowest point in the lower segment, as shown in figure 1. after the two (hot and cold) stream curves have been constructed, the cold stream will then be slid until it touches the hot stream without overlapping, at a point, known as the pinch point, as shown in figure 2. nasser a. al-azri 4 the minimum heating utility, in figure 2, is the minimum possible heat required from an external source and so is the minimum cooling utility. the pinch point has a very significant meaning, as it represents the temperature value above which any purchase of external cooling indicates a loss of integration opportunity and below which any purchase of external heating indicates a loss of integration opportunity. the loss of integration opportunity results in an increase of external heating and cooling resources, each equivalent to the gap above the pinch point, as shown in figure 3. on the other hand, overlapping (figure 4) implies an exchange of heat from lower temperature to higher temperature, which is thermodynamically unfeasible. in many cases, the maximum saving obtained from pinch analysis is impractical to achieve because of economic constraints [13]. in such cases, it is used as a benchmark for assessing the level of feasible integration. 3. the algorithmic approach in addition to the pinch diagram, the algebraic method is commonly used in heat integration. in this method, hot and cold streams are split into the smallest possible temperature intervals [11,12]. the heat requirement for a cold interval is supplied from a hot interval at the same temperature range or higher. the matching starts at the highest interval, and if heat needed by the cold interval at a given range exceeds that offered by the hot one, the excess is to be supplied from an external source. on the other hand, if the heat offered by the hot interval exceeds the requirement of the cold one, the excess is passed to the next pair of intervals. the process continues until the last interval at which, if there is still some excess heat offered by hot streams, it will be discharged to an external cooling source. this procedure is explained here in more detail in an algorithmic format. the algorithmic approach is not only important for dealing with a large number of streams and hence avoiding the cumbersome graphical method, but is equally important when the matching is to be optimized based on additional practical constraints, such as economic feasibility and distance constraints within the processing plant [14,15,16]. 3.1 input 1. h hot streams with source temperature , target temperature and thermal capacity ( ) for all i = 1, 2, 3, … , h. 2. c cold streams with source temperature , target temperature and thermal capacity ( ) for all j = 1, 2, 3, … , c. notice that for hot streams, and for cold streams. 3. minimum temperature gradient tmin to assure a sufficient temperature difference for heat transfer. 3.2 algorithm 1. for all and , j = 1, 2, 3, … c (for cold streams) 2. establish the set t of all supply and target temperatures in the problem: * + for i = 1, 2, 3, … , h and j = 1, 2, 3, … , c. 3. sort t in a descending order such that: { } * + where n is the total number elements representing the unique set of all supply and target temperatures. in the set t, each interval between two consecutive elements can be thought of as a heat exchanger that will integrate hot and cold streams in that interval. hence, we will have n-1 intervals representing n-1 heat exchangers. 4. for each hot stream with temperature interval , -, split the interval into segments such that: [ ] [ ] , , , where and * + . then, calculate the total heat to be supplied by each interval (n) by all hot streams whose temperature range coincide with that interval: ( ) ( ) for all i = 1, 2, 3, ... , h and n = 1, 2, 3, … , n-1 where tu and tl are the upper and lower limits of interval n, respectively. 5. perform the same segmentation for each cold stream [ ] by splitting the interval into segments such that: [ ] [ ] , , [ ] and calculate the heat to be supplied at each interval (n) to all cold streams whose temperature range coincide with that interval: ( ) ( ) for all j = 1, 2, 3, ... , c and n = 1, 2, 3, … , n-1. 6. for each interval in t, starting in a descending order, integrate heat requirements with cooling requirements. set qexternal heating = 0. energy management through heat integration 5 set tp=-9999 (for initiation purposes, if retained then integration is not possible). for n = 1, 2, 3, … , n-2 (all intervals except the last) if qhot,n – qcold,n> 0, pass the surplus heat (qhot,n – qcold,n) to the next interval: qhot,n+1 = qhot,n+1 + (qhot,n – qcold,n). else (i.e.qhot,n – qcold,n 0), add the deficit (qcold,n–qhot,n) to the load to be supplied from an external source: qexternal heating = qexternal heating + (qcold,n–qhot,n). update the pinch temperature tp: tp = tn+1. 7. for the last interval (n-1) if qhot,n-1 – qcold,n-1  0, the surplus heat (qhot,n-1 – qcold,n-1) will constitute the external cooling utility: qexternal cooling = (qhot,n-1 – qcold,n-1). else add the deficit (qcold,n-1–qhot,n-1) to the load to be supplied from an external source: qexternal heating = qexternal heating + (qcold,n-1 – qhot,n-1) let qexternal cooling = 0. 4. illustrative example as an example for showing the application of the algorithm, the process shown in figure 5 has two coolers and two heaters, with their details shown in table 1. in the absence of any heat integration, the total cooling utility is qexternal cooling= 83 mw and the total heating utility is qexternal heating= 56 mw. the minimum temperature difference is tmin = 10 k. this information is used as input to the algorithmic procedure. figure 5. a process with two heaters and two coolers. table 1. the total process utility requirement. stream m cp (kw/k) t s (k) t t (k) q (mw) h1 300 460 350 33 h2 500 400 300 50 total 83 c1 600 420 490 42 c2 200 320 390 14 total 56 nasser a. al-azri 6 1. the cold stream supplies and target temperatures are altered as given in table 2 after considering the minimum temperature difference: table 2. modified cold stream temperatures. stream m cp (kw/k) t s (k) t t (k) q (mw) c1 600 430 500 42 c2 200 330 400 14 2. establish the set t of all supply and target temperatures: * +. 3. sort elements in t in a descending order: * +. there are seven elements (n = 7) and six intervals from [500, 460] to [330, 300]. 4. split the hot streams as given in table 3 to evaluate utility requirements at each interval: table 3. hot stream temperatures. stream (i,n) m cp (kw/k) t s (k) t t (k) q (mw) h1 300 460 350 33 h1,2 h1,3 h1,4 460 430 400 430 400 350 9 9 15 h2 500 400 300 50 h2,4 h2,5 h2,6 400 350 330 350 330 300 25 10 15 the second subscript is the interval number in the set of the six intervals. the total heat to be discharged at each interval (see table 4): table 4. heat discharged. interval (n) [500,460] 1 [460,430] 2 [430,400] 3 [400,350] 4 [350,330] 5 [330,350] 6 qhot,n (mw) 0 9 9 40 10 15 5. repeat step 4 for the cold streams (see table 5): table 5. cold stream temperatures. stream (i,n) m cp (kw/k) t s (k) t t (k) q (mw) c1 600 430 500 42 c1,2 c1,1 430 460 460 500 18 24 c2 200 330 400 14 c2,5 c2,4 330 350 350 400 4 10 the total heat needed at each interval (see table 6): table 6. heat requirement. interval (n) [500,460] 1 [460,430] 2 [430,400] 3 [400,350] 4 [350,330] 5 [330,350] 6 qcold,n (mw) 24 18 0 10 4 0 energy management through heat integration 7 6. start the integration step from interval 1. if the heat needed by the cold interval (qcold,n) exceeds that offered by the hot one (qhot,n), the excess is added to the load supplied externally (qexternal heating). on the other hand, if the heat offered by the hot interval (qhot,n) exceeds the requirement of the cold one (qcold,n), the excess is passed to the next hot interval which is updated, (qhot,n=qhot,n+ qhot,n-1). table 7. heat requirement. interval (n) [500,460] 1 [460,430] 2 [430,400] 3 [400,350] 4 [350,330] 5 [330,350] 6 qhot,n (mw) 0 9 9 40 10 15 qhot,n (updated) 9 9 49 49 60 qcold,n (mw) 24 18 0 10 4 0 qhot,n – qcold,n -24 -9 9 39 45 60 qexternal heating 24 33 33 33 33 33 tp (k) 500 430 430 430 430 430 7. in the last interval as given in table 7, one can see that qexternal cooling= (qhot,6 – qcold,6) = 60 mw and qexternal heating= 33 mw and the pinch point is the lower bound of the second interval, tp= 430 k. the main principle of the algorithm is the fact that heat at the highest temperature is of the best quality, as it can always cover heat requirements at all intervals below it. hence, heat requirements are sorted by temperature so that heat requirements at higher temperatures are given priority for supply over those at lower temperatures. the surplus from high intervals can then be moved to the next lower, but not vice versa. from step 6, at the highest interval, one can see that there is a deficiency (heat requirement, qcold> 0) but no heat supply (qhot= 0). this requirement must be covered by an external source since no heat is available at that temperature or higher. at the next temperature interval, heat supply is less than heat required (qhot<qcold), so the available supply will only cover part of the requirement and the remaining part must be covered from an external supply since all other supplies are at lower intervals. at the third interval, there is a heat supply but no heat required (qhot> 0, qcold= 0). this supply can be passed on to the next lower interval. at intervals 4, 5 and 6, the heat supply is more than required and so heat will be passed on to the lower interval until 60 mw accumulates at the lowest interval, which then needs to be covered by an external cooling source. the pinch point is the temperature above which no cooling utilities should be supplied externally and below which no heating utilities should be purchased. so as long as heat is supplied from an external source at a given interval, pinch point cannot be higher than the lower bound of that interval. in this procedure, pinch point is maintained as the lower bound of the last interval at which heat was supplied externally, which is the lower bound of the second interval in the example. the output of this example can be verified using the graphical approach described in the introduction. figure 6 shows the pinch diagram using the graphical method, where the hot stream composite is matched against the cold one while maintaining the thermodynamic constraints of heat flow. the horizontal projection of both streams on one another represents the maximum integration i.e. heat flow from hot streams to the cold ones. 5. practical example a practical example for which the graphical method is quite cumbersome is the two sets of 20 hot streams and 15 cold streams in a process, as presented in table 8. this process as is, without integration, requires 1628.5 mw of cooling utility and 1451.1 mw of heating utility. upon the implementation of the above algorithm using matlab (see appendix), and with tmin = 10 k, the cooling utility can be minimized to 204.6 mw and the heating utility can potentially be minimized to 27.2 mw with the pinch point at 899 k. nasser a. al-azri 8 figure 6. thermal pinch diagram for the illustrative example. the same results are shown in the graphical pinch diagram (figure 7), where the horizontal projection of hot and cold streams represents the maximum integration, of 1423.9 mw exchanged from the hot streams to the cold ones. table 8. hot and cold streams from a large process. hot m cp t s t t cold m cp t s t t stream (kw/k) (k) (k) stream (kw/k) (k) (k) h1 346 501 359 c1 502 314 401 h2 169 590 405 c2 549 263 577 h3 794 714 565 c3 396 244 370 h4 240 600 463 c4 666 192 356 h5 414 626 272 c5 738 378 540 h6 445 899 846 c6 493 260 527 h7 401 679 382 c7 518 342 685 h8 394 785 743 c8 319 502 846 h9 496 634 351 c9 282 491 553 h10 244 663 398 c10 380 499 681 h11 770 455 304 c11 484 127 207 h12 383 737 694 c12 717 277 378 h13 551 513 507 c13 412 192 357 h14 722 619 559 c14 512 608 737 h15 803 863 741 c15 601 597 939 h16 473 905 625 h17 543 817 640 h18 606 744 548 h19 674 568 298 h20 216 891 523 energy management through heat integration 9 figure 7. thermal pinch diagram for the practical example. 6. conclusion an algorithmic approach to pinch analysis has been presented in an algorithmic setting which is helpful for introducing pinch analysis as well as handling large problems and hence eliminating human errors encountered with the graphical method. two examples have been solved and compared to the graphical method to show the applicability of the algorithm. the presented algorithm is based on segmenting heat supply and requirement by temperature. integration then starts from the highest interval and moves downwards by covering deficiencies from external sources, and then passing the surplus down to the next interval until the surplus at the last interval sums up the external cooling needs. the pinch point is maintained as the lower bound of the last interval at which heat was supplied externally. the results obtained from this procedure conform to those obtained using the graphical method. a further development of the algorithm could be through the introduction of additional constraints such as minimum allowable distance and amount of heat between heat exchangers. references 1. linnhoff, b., townsend, d.w., boland, d., hewitt, g.f., thomas, b.e.a., guy, a.r. and marsland, r.h. user guide on process integration for the efficient use of energy. institute of chemical engineers (icheme), warwickshire, uk, 1982. 2. hohman, e.c. optimum networks for heat exchanger. university of southern california, los angeles, 1971. 3. linnhoff, b. and hindmarsh, e. the pinch design method for heat exchanger networks. chemical engineering science, 1983, 38(5), 745-763. 4. umeda, t., itoh, j. and shiroko, k. a thermodynamic approach to the synthesis of heat integration systems in chemical processes. computers and chemical engineering, 1979, 3, 273-282. 5. raissi, k. total site integration, phd thesis, department of process integration, university of manchester institute of science and technology, manchester, uk, 1994. 6. mavromatis, s.p. and kokossis, a.c. conceptual optimization of utility networks for operational variations. i. targets and level optimization. chemical engineering science, 1998, 53(8), 1585-1608. 7. varbanov, p.s., doyle, s. and smith, r. modeling and optimization of utility systems. transactions of icheme, 2004, 82(a5), 561-578. 8. beangstrom, s.g. and majozi, t. a process integration technique for steam system synthesis involving multiple levels. the 11 th international symposium on process systems engineering, singapore, 2012. 9. chen, c., lin, c. and lee, j. retrofit of steam power plants in a petroleum refinery. applied thermal engineering, 2013, 61,7-16. 10. sun, l., doyle, s. and smith, r. process utility systems conceptual design by graphical methods. computer aided chemical engineering, 2014, 33, 1813-1818. nasser a. al-azri 10 11. el-halwagi, m.m. pollution prevention through process integration. academic press, san diego, california, usa, 2003. 12. el-halwagi, m.m. process integration. academic press, san diego, california, usa, 2006. 13. al-azri, n. process integration and utility system optimization, phd thesis, department of chemical engineering, texas a&m university, texas, usa, 2008. 14. al-azri, n., al-thubaiti, m. and el-halwagi, m. an algorithmic approach to the optimization of process cogeneration, clean technologies and environmental polices, 2008, 11(3), 329-338. 15. navarro-amorós, m., caballero, j., ruiz-femenia, r. and grossmann, i. an alternative disjunctive optimization model for heat integration with variable temperatures. computers and chemical engineering, 2013, 56, 12-26. 16. onishi, v., ravagnani, m. and caballero, j. simultaneous synthesis of work exchange networks with heat integration. chemical engineering science, 2014, 112, 87-107. appendix: matlab code %the purpose of this function is to find pinch point, %minimum heating and cooling utilities for two sets of %cold and hot streams. %input: %set of hot streams hs=[m.cp ts tt]; %set of cold streams cs=[m.cp ts tt]; %minimum allowable temperature tmin %input example: %hs=[ 300 460 350 % 500 400 300]; %cs=[ 600 420 490 % 200 320 390]; %tmin=10; function[]=algomassex_heat(hs,cs,tmin) %1. adjust the temperature of cold streams ys=zeros(size(cs,1),2); for i=1:size(cs,1) ys(i,:)=[cs(i,2)+tmin cs(i,3)+tmin]; end %2.-3. all unique supply and target temperatures sorted concenr=sortrows(unique([hs(:,2);hs(:,3);ys(:,1);ys(:,2)]),-1) %matrix exchanged is used to store heat requirements at each interval exchanged=zeros(size(concenr,1)-1,5); for i=1:size(concenr,1)-1 %for all possible unique segments exchanged(i,1:2)=transpose(concenr(i:i+1)); %4. find the heat available in hot streams for all intervals for j=1:size(hs,1) %for all hot streams if exchanged(i,1)<=hs(j,2)&&exchanged(i,2)>=hs(j,3) %if this hot stream overlap with segment, add its heat to the %interval exchanged(i,3)=exchanged(i,3)+hs(j,1)*(exchanged(i,1)exchanged(i,2)); end end %5. find the heat needed by cold streams for all intervals for j=1:size(cs,1) %for all process cold streams if exchanged(i,2)>=ys(j,1)&&exchanged(i,1)<=ys(j,2) %if this cold stream overlap with segment, add its required %heat to the interval exchanged(i,4)=exchanged(i,4)+cs(j,1)*(exchanged(i,1)exchanged(i,2)); end end end pinch=nan;%dummy initiation for the pinch point (nan=undefined) which will be %produced in the case where integration is not possible at all. %6. integrate heating and cooling requirements for intervals 1 to n-1 energy management through heat integration 11 for i=1:size(exchanged)-1 %for each segment if exchanged(i,3)>=exchanged(i,4) %pass surplus heat to the next interval exchanged(i+1,3)=exchanged(i+1,3)+(exchanged(i,3)-exchanged(i,4)); else exchanged(i,5)=exchanged(i,4)-exchanged(i,3); %add the deficit to the load supplied by external heating pinch=exchanged(i+1,1) %update the pinch point end end %7. for the last interval if exchanged(size(exchanged,1),3)>=exchanged(size(exchanged,1),4) %surplus will constitute external cooling external_cooling=(exchanged(size(exchanged,1),3)exchanged(size(exchanged,1),4)); else exchanged(size(exchanged,1),5)=exchanged(size(exchanged,1),4)exchanged(size(exchanged,1),3); %add the deficit to the load supplied by external heating external_cooling=0; end excess_heating=sum(exchanged(:,5))%external heating is the sum of all %external heating load at all segments external_cooling y_at_pinch=pinch %pinch point received 3 june 2014 accepted 27 february 2015 photovoltaic cells and systems: squ journal for science, 2014, 19(1), 43-53 © 2014 sultan qaboos university 43 fabrication and surface characterization of poly(4-aminodiphenylamine) film modified electrode and its application for lead and cadmium determination mohammed m. al-hinaai 1 , salim h. al-harthi 2 and emad a. khudaish 1* 1 department of chemistry, college of science, sultan qaboos university, po box: 36, pc 123, alkhod, muscat, sultanate of oman; 2 department of physics, college of science, sultan qaboos university, po box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: ejoudi@squ.edu.om. abstract: poly(4-aminodiphenylamine), padpa, film was synthesized electrochemically on a glassy carbon electrode by potentiodynamic repetitive cycling of 4-aminodiphenylamine (4-adpa) in 1.0 m hcl. the mechanistic steps involved the oxidation of the protonated monomer to diimine species followed by its dimerization to form the mono-charged radical intermediate, which was considered as the initiation step for the progress of polymerization. the electrochemical properties and surface morphology of the film modified electrode were characterized using electrochemical and various surface scanning techniques. the xps data demonstrated the existence of =n bonding responsible for polymer formation, while the afm image revealed a uniform and symmetrical fiber structure with low energy dissipation. the modified electrode was primarily applied as an environmental sensor for the simultaneous and selective determination of cd 2+ and pb 2+ ions in water samples. the detection limit for cd 2+ and pb 2+ ions was 25 and 14 g l 1 , respectively. keywords: electropolymerization; 4-aminodiphenylamine; sensors; cadmium; lead. أيينىا داي فنيم أيين( نقطب كهربائي يعذل واستخذاياته في تقذير أيىنات انرطاص – 4تشييذ وتقييى نغالف رقيق ين بىنيًر ) وانكادييىو عًاد خذيشو يحًذ انهنائي، سانى انحارثي أيٍُٕ داي فٍُم أيٍٍ(عهى سطخ قطت انكشثٌٕ انزجبجً ٔرنك ثإيشاس جٓذ كٓشثبئً – 4رصٍُع طجقخ سقٍقخ يٍ ثٕنًٍش ) رى :يهخض . رزضًٍ يٍكبٍَكٍخ انزفبعم أكسذح يٕالسي 1أيٍُٕ داي فٍُم أيٍٍ( انًزاثخ فً يذهٕل دبيض انٍٓذسٔكهٕسٌك– 4يزغٍش ٔيزسهسم نًبدح ) ٌٌٕ انًٕجت انجزسي األثعًهٍخ ركبرف نجزيء ثُبئً ٌذعى ى يبدح داي اًٌٍٍ ٔانزً ثذٔسْب رًشدبدي انذبيم نجشٔرٌٕ انانجزيء األ انزي ًٌثم انخطٕح االسبسٍخ نعًهٍخ انجهًشح نهٕصٕل انى رذضٍش انجٕنًٍش انُٓبئً. نقذ رى دساسخ انصفبد انكٓشثبئٍخ ٔانزشكٍت انسطذً َزبئج انٕصف انفٍزٌبئً ٔانضٕئً ٍخ ٔانطشق انفٍزٌبئٍخ نزٕصٍف انسطٕح.نطجقخ انجٕنًٍش انشقٍقخ ثٕاسطخ انطشق انكٓشٔكًٍٍبئ . يُخفضخ( انًسؤٔنخ عٍ ركٌٍٕ انجٕنًٍش انزي ٔصف ثأَّ يٍ أَسجخ يُزظًخ ٔيزًبثهخ راد طبقخ رشزذ -n=أٔضذذ ٔجٕد انشاثطخ ) خزٍبسي نكم يٍ إٌَٔبد انشصبص ٔانكبديٍٕو زايٍ ٔاإلأٌ انقطت انكٓشثبئً انًعذل رى اسزخذايّ نهزطجٍقبد انجٍئٍخ انًزصهخ ثبنزقٍٍى انًز جزء يٍ انجهٌٍٕ نكم يٍ انشصبص ٔانكبديٍٕو عهى انزٕانً. 52ٔ 14فً عٍُبد انًٍبِ دٍث ٔصهذ دذٔد انزقٍٍى انى .أيٍُٕا داي فٍُم أيٍٍ، أقطبة دسبسخ، كبديٍٕو، سصبص – 4انجهًشح انكٓشٔكًٍٍبئٍخ، : يفتاح انكهًات 1. introduction n recent years, electrochemical polymerization has received a great deal of attention as a unique method to construct and modify various electrode surfaces with certain polymeric films. the fabrication, characterization and application of polymer modified electrodes (pmes) are important themes and a core area of research in chemistry. electrochemical methods can effectively tailor the chemical and physical properties of the resulting polymer, including mechanical i emad khudaish et al 44 resistance, electrical conductivity, stability and high electron affinity [1]. they can also exert control over the parameters of the film thickness and homogeneity [2]. these novel pmes may potentially find application in a wide range of technologies including, energy storage systems [3], membrane gas separation [4], electrocatalysis [5], and sensors [6]. the polymeric films can be further incorporated by some modifiers such as enzymes [7], nanoparticles [8] and polymer composite structures [9] to facilitate certain applications. since the pioneering work of diaz and coworkers in the late 70s [10,11], the fabrication of modified electrodes with highly stable and conductive polymeric films (polypyrrol, polyaniline, and polythiophene) has been a further developmental step towards their effective application in corrosion inhibition [12], light emitting diodes [13], electro-photosensitization [14] and biosensors [15]. the electrochemical polymerization of aromatic amines such as aniline (ani) has been studied widely [16], exploring the reaction mechanism and the kinetics of polyaniline (pani) growth on conducting substrates. the initial step is the formation of the ani cationic radical followed by dimerization reactions, and then chain growth via the linkage of radical ions or the connection of the radical with the neutral monomer. the major intermediate product was characterized as the dimer-aniline like constituent called 4-aminodiphenylamine (4-adpa) [17]. recently, planes et al. [18] have identified 4-adpa as the ani-dimer intermediate produced via head-to-tail coupling of ani cation radicals using a spectroscopic method. the conductivity and molecular mass of poly(4-aminodiphenylamine) prepared in aqueous hcl solution [19] were found to be significantly less than those of pani due to the for mation of oligomeric products composed of four monomeric units. in another study, using in situ ftir and uv-vis methods, zimmermann et al. [20] concluded that the main structure formed during the electrochemical polymerization of 4-adpa was the anitetramer. a composite conducting film was also constructed by electrochemical polymerization of 4-adpa at ph = 5.0 in the presence of ani [21]. the incorporation of ani was featured for two reasons: (i) due to the lack of homopolymerization reaction of 4-adpa where its electrochemical oxidation is believed to be slow and inefficient, and (ii) to enhance the propagation reactions of the oxidized 4-adpa species. the resulting film showed a good catalytic reactivity towards a number of redox couples in a weakly acidic buffer solution. another novel work of cotarelo et al. [22] was devoted to characterizing the polymeric film produced by electrochemical oxidation of 4-adpa in a strongly acidic medium using a number of microscopic and spectroscopic techniques. it was concluded that the resulting polymer displayed electrochemical, morphological and spectroscopic characters similar to those shown by pani. considerable attention has been given to environmental contamination with heavy metal ions for health and safety reasons. therefore, a trace monitoring of these metal ions in the environment is an important but analytically challenging task. the maximum admissible limit for pb 2+ and cd 2+ ions for drinking water quality are 15 and 5 g l -1 , respectively, as reported by the united states environmental protection agency (usepa) in 2008. electrochemical stripping analysis was recognized as an efficient tool for simultaneous monitoring of heavy metals [23]. the scope of sensing tools has been developed significantly for simultaneous and selective trace quantification of heavy metals via appropriate surface modifications, for example by the incorporation of bismuth film [24], boron-doped diamond [25], polypyrrole [26], poly(3,4-diaminoterthiophene) [27] and polyaniline [28]. the present work is devoted to studying the nature of resulting padpa film deposited at glassy carbon electrode (padpa/gce) and its application for trace determination of cadmium (cd 2+ ) and lead (pb 2+ ) ions. surface modification with padpa was selected due to the structural limitations and involvement of different intermediates in producing pani, while the formation of padpa is known to proceed via a single specific intermediate, as illustrated in scheme 1 given below. therefore, producing a thin and smooth polymeric film at lower oxidative applied potential and avoiding the polymer over-oxidation is another important major theme of the present work. moreover, the presence of a surface modifier, such as a conducting polymer, is likely to increase the electrode surface area and its adsorption capacity. 2. experimental 2.1 reagents electrochemical measurements for metal analysis were carried out in an equimolar 0.1 m mixture of (kcl + hcl) solution (ph = 2.12) prepared in millipore water. the electrolyte was degassed by purging oxygen-free nitrogen gas for 10 min, and blanketed throughout the experiment. a stock solution of the 4-adpa monomer (aldrich) was prepared by dissolving a certain amount in 1.0 m hcl and sonicated for 5 min at 35 o c using (jac ultra sonic, korea). standard solutions (1000 ppm, atomic absorption standard solutions) of cd(ii) and pb(ii) purchased from bdh chemicals, uk, were diluted as required and used for simultaneous and selective determination. also, cu(ii) and hg(ii) (bdh chemicals, uk) were used for interference studies. all other chemicals were of analytical-reagent grade and used as received. 2.2 electrochemical measurements the electrochemical measurements including cyclic voltammetry (cv) and differential pulse anodic stripping voltammetry (dpasv) experiments were conducted using a bas 50w work station. the measurements were performed in a 20 ml electrochemical cell using a glassy carbon electrode (gce) with a geometric area of 0.071 cm 2 as the working electrode, a platinum coil with a geometric area of 1.90 cm 2 as the counter electrode, and an ag/ agcl/ polymeric film modified electrode 42 kcl(sat.) as the reference electrode. the potentiostat and electrodes were from bioanalytical system, west lafayette, in, usa. prior to each experiment, the working electrode was polished using a polishing cloth and alumina slurry (5.0 and 1.0m), washed with acetone, ultrasonicated for 5 min and finally rinsed thoroughly with distilled water. the electrode was then pre-treated electrochemically by scanning the potential repeatedly between -400 mv to +1000 mv for 25 cycles at a scan rate (v) of 100 mv s 1 and terminating at the anodic potential limit in the supporting electrolyte, in order to establish a reproducible electrode surface and avoid any previous fouling effect. such a reversible potentiodynamic scan produces a surface composed of carbon-oxygen functional groups of phenol and quinol forms that increase the electrode reactivity and the grafting efficiency. the cv experiments were utilized mainly to study the progress of the electrochemical polymerization, and the stability and the sensitivity of the resulting polymeric film modified electrode. the typical parameters controlling the dpasv experiment were (i) deposition time = 120 s, (ii) deposition potential = 00 mv (with stirring mode), (iii) final potential = +200 mv at scan rate of 40 mv s 1 , (iv) pulse amplitude = 50 mv, (v) sample width = 25 ms, (vi) pulse width = 50 ms, (vii) pulse period = 100 ms and (viii) quiet time = 10 s. 2.3 characterization techniques the structure and surface morphology of the polymer deposited at glassy carbon disks (5 mm  100 m) (from hochtemperature-werkstoffe, gmbh, germany) by repetitive potentiodynamic cycles were investigated by x-ray photoelectron spectroscopy (xps) using an omicron nanotechnology xps system, and by atomic force microscopy (afm) using a nanoscope v multimode microscope (veeco instrument, usa). the xps spectra obtained were deconvoluted using casaxps program (casa software ltd, uk), in which the background was simulated using shirley function and the peaks were fitted using a gaussian lorentzian function. the afm images were recorded ex situ using a tapping mode at a scan rate and imaging resolution of 0.5 hz and 512 pixels, respectively. electrochemical impedance spectro scopy (eis) was employed to further investigate the interfacial structure due to surface modification and extract important information about the rate of electron transfer, the double-layer capacitance and the diffusion limited process. the eis was carried out on eis 300 (gamry, usa) connected to a three-electrode cell composed of ag/agcl, kcl(satd) and platinum coil as reference and counter electrodes, respectively. the working electrode was either the bare gce or padpa/gce modified electrode. the eis measurements were conducted at an open circuit potential of 5.0 mm [fe(cn)6] 3/4 redox probe in the frequency range from 0.1 hz to 100 khz. 2.4 treatment and preparation of the water sample a treated waste water sample used for agricultural irrigation was collected from the botanical garden located inside the sultan qaboos university. the sample was collected in 100 ml polyvinyl bottles, filtered and acidified with 1.0 ml of 1.0 m hcl. prior to analysis, 5.0 ml of the sample was pipetted in a small vial and mixed with the required amounts of metal standard solutions. the standard addition method was applied to determine the concentration of both metal ions with reference to the metal-free water sample. 3. results and discussion 3.1 electrochemical polymerization of 4-adpa using cv method figure 1 shows typical cyclic voltammograms (cvs) corresponding to the electrochemical polymerization of padpa at gce using 5.0 mm 4-adpa in 1.0 m hcl solution. the polymeric film was obtained by repetitive potential scans (25 cycles) between -200 mv and +800 mv vs. ag/ agcl at 50 mv s 1 . a pair of redox peak currents was developed (anodic) at +425 mv and (cathodic) +197 mv which increased constantly upon subsequent cycling. the reversible voltammetric waves describe the formation of reduced and oxidized oligomers called the leucoemeraldine and pernigraniline, respectively, which involves the transfer of two electrons and two protons [29]. the initiation step for the propagation of the polymer is the formation of a cationic intermediate called n-phenylquinonediimine (pqdi) [30] as shown in the mechanistic reaction presented in scheme 1. this step is followed by a dimerization step of pqdi with the monomer to form the mono-charged radical intermediate responsible for the growth of the polymer. petr et al. have confirmed the formation of pqdi as the only product formed during the oxidation of 4adpa by in situ uv-vis electrochemical measurements [31]. hence, in the reverse scan, the remaining surface amount of pqdi (not dimerized) may undergo a reduction reaction which gives rise to a smaller current response at 340 mv. it should be noted that the relative amount of both constituents (oxidized and reduced forms) depends on the acid concentration, the oxidative applied potential and the degree of polymerization (number of cycles). the experimental data presented in figure 1 can be expressed in consecutive steps initiated by the formation of radical intermediates, dimerization, oligo-merization and the deposition of less soluble oligomers (tetramers and/or octamers) at the electrode surface [19,20]. the formation of an adhering polymeric film at the electrode surface was confirmed by petr et al. [33] using electrochemical and electron spin resonance (esr) methods. the electrochemical emad khudaish et al 44 behavior of the modified electrode was examined by stepping the electrode potential between 400 mv to +900 mv vs. ag/agcl in a monomer-free aqueous solution of 0.10 m hcl. figure 1. typical cvs (25 cycles) depicting the electrochemical polymerization of padpa onto gce using 5.0 mm 4-adpa monomer in 1.0 m hcl (the first segment is indicated by the dotted line). h n nh3 n nh2 + 2h+ + 2e4-aminodiphenylamine (4-adpa) n-phenylquinonediimine (pqdi) (4-adpa) + (pqdi) 2 mono-charged radical intermediate h n nh2 scheme 1: the initiation steps for the electrochemical polymerization of padpa. figure 2 depicts the electrode behavior as a function of scan rates in a monomer-free 0.10 m hcl solution. a redox surface type is developed that increased with increasing the scan rate from 25 to 300 mv s 1 . in the anodic scan, three peak currents arose at potentials +300, +350 and +440 mv, respectively (shown at the slowest potential scan rate). apparently, a consecutive electron transfer process occurred due to a successive transition states of the surface material. in the reverse scan, the electron transfer also produces three cathodic peaks obtained at +435, +365 and +310 mv, respectively. figure 2. the development of redox surface-type behavior as a function of scan rates in mv s 1 ; (a) 25, (b) 50, (c) 75, (d) 100, (e) 125, (f) 150, (g) 175, (h) 200, (i) 250 and (j) 300. polymeric film modified electrode 44 the first two peaks are shifted to more positive potential and increased with subsequent increase in the scan rate consistent with increasing the rate of electron transfer process. furthermore, these anodic peaks are found to merge at scan rates higher than 200 mv s -1 . a similar trend was apparent for the cathodic peaks that merged and shifted to a more negative potential. the peak separation (e) at the highest scan rate approached 216 mv suggesting the attachment of surface materials. the experimental data of the peak current as a function of scan rates (not shown) were further studied to calculate the surface coverage   of the deposited polymeric film in (mol cm2) applying eq. (1) [34]. v rt afn i 4 22 p         (1) the calculated surface concentration was 2.71  10 10 mol cm 2 , taking into consideration that n = 2 and a is the geometric area while other terms have their usual thermodynamic descriptions. 3.2 surface morphological studies xps and afm methods were used to characterize the elemental structure of the electrode surface and confirm the deposition of the polymer. figure 3 demonstrates the xps short scan of c 1s which is deconvoluted into three peaks at 283.9, 285.1 and 287.3 ev corresponding to c-c, c-n and c=o bonds, as anticipated from the original structure of the monomer [22]. similarly, the n 1s short scan gave rise to three peaks at 398.8, 400.1 and 402.3 ev corresponding to the tertiary amine (=n) bonding, neutral and protonated primary amines (nh2) and (nh3 + ) respectively. the presence of =n group is indicative of the fact that successive oxidation and deprotonation processes took place in the polymerization of the padpa. afm images reveal a uniform and symmetrical fiber structure with a lower energy dissipation factor. this could be attributed to reduction in the roughness factor of the film, having an average height of 35 nm and a cumulative surface area of 65 nm 2 . it also shows a low and uniform young’s modulus (~15 gpa) pertinent to the deposition of a pristine padpa substance. the surface roughness of the polymer is expected to become much coarser by increasing the number of potentiodynamic cycles in which a new route of polymerization process may control the progress of film formation. 3.3 electrochemical impedance studies the ac impedance spectra presented by nyquist plot in the presence of 0.5 m kno3 solution containing 5.0 mm [fe(cn)6] 3/4 are shown in figure 4. two characteristic parts are identified in the plot as a linear curve and a semicircular shape, which occurred at low and high frequencies, respectively. the linear trend corresponds to the diffusion limited process while the arc shape represents the rate of electron transfer process. to understand the electrical properties of the electrode/solution interfaces, a modified randle’s equivalent circuit (inset of figure 4) was selected for fitting the impedance data [35]. the eis data recorded at the bare gce (inset) showed a charge transfer resistance (rct) with a given diameter of 147 , compared to the padpa/gce modified electrode that revealed a larger value of 2670 . this trend evidently demonstrates that padpa was successfully assembled at the gce. 3.4 applications 3.4.1 simultaneous determination of cadmium and lead ions figure 5 depicts the application of the modified electrode for simultaneous determination of cd 2+ and pb 2+ employing the dpasv method in which the anodic peak currents were recorded as a function of metal ion concentrations. the (i–e) curve illustrates the rising up of a couple of well-defined peaks at –825 mv and –535 mv, corresponding to the stripping of cd 2+ and pb 2+ , respectively. the peak separation (e = 290 mv) is significantly large, indicating an excellent selectivity and catalytic activity of the present system. moreover, the anodic peak currents of both ions are increasing linearly with the concentration as illustrated by the calibration curve given in the inset of figure 5. the sensitivity of the present system is evaluated by means of the slope difference of both ions obtained from the experimental data presented in figure 5. the slope ratio of lead to cadmium ions   22 cdpb /ss is close to 2.75 indicating a higher sensitivity in determination of lead ions. the surface affinity of both ions was expected to be the same unless possible interaction forces occurred between them due to differences in their electronegativity values. therefore, pb 2+ ions of higher electronegativity were reduced and formed a micro-structure of particles or coated film at cathodic potential lower than that of cd 2+ ions, which may have caused the formation of an intermetallic (pb-cd) structure [35]. the expected events occurred during deposition potential period when the preferential deposition of pb was followed by a direct deposition of cd at both the polymeric film and the pb matrix already existing on the electrode surface. during the anodic stripping mode, cd deposited at the polymeric film will first dissolute at – 825 mv and the remaining cd deposited on to pb will be stripped with pb at more positive potential. it should be noted that the positive emad khudaish et al 44 potential shift in the stripping of both ions shown in figure 5 with increasing the concentration is an indication of such energetic interaction. figure 3. surface topographic analysis represented by xps short scans of c 1s and n 1s with afm images of dissipation and dmt modulus of the padpa/gce surface film. figure 4. eis data for padpa/gce and bare gce (insert) with the modified randle’s equivalent circuit. figure 5. dpasv curves recorded at padpa/gce in acidified 0.1 m kcl solution (ph = 2.12) for the simultaneous determination of cd 2+ and pb 2+ ions. the range of [cd 2+ ] and [pb 2+ ] are indicated by the calibration curve (ip vs [m 2+ ]) given in the inset. polymeric film modified electrode 44 moreover, the limit of detection (lod) was calculated using (3/s) where  is the standard deviation obtained from 5 replicates of the blank. the lods were 25 and 14 g l 1 for cd 2+ and pb 2+ , respectively. the sensitivity of the present system given by the slope of the linear relationship of ip vs [m 2+ ] was compared with other electrochemical systems [36-42] and presented in table 1. the present work showed a good sensitivity for both metal ions suggesting the construction of a robust solid state sensor for environmental applications. it should be noted that the stripping analysis of each ion in the concentration range of 50 to 500 g l 1 was conducted separately to evaluate the surface catalytic efficiency and the rational scenario of binary concentrations. such primary analysis along with controlling the method parameters, in particular the deposition potential and accumulation period, enhance the separation facility and minimize possible suppression of the cadmium peak [43]. therefore, the linear concentration range of cd 2+ ions presented in figure 5 must have been relatively high to produce a significant change in the stripping peak current. apparently, the binary solution of the above selected recipe allows a regular and steady deposition of both ions at the electrode surface, where only two symmetrical and well defined peaks arose regardless of the relative extent of surface capacitance due to the presence of the polymeric film. table 1. the sensitivity of various electrochemical systems in (a/ g l 1 ) evaluated from the simultaneous determination data of both metal ions in their binary mixture. surface cadmium lead ref. bi/pani 0.73 0.074 [36] pedot 0.004 0.008 [37] pani 0.021 0.059 [38] bi/nafion 0.027 0.019 [39] ppma 0.007 0.098 [40] bdd 0.015 0.013 [41] bi/poly(p-absa) 0.031 0.019 [42] padpa 0.038 0.104 this work however, the estimated base peaks for the stripping of cd and pb at their highest concentrations shown above were found to be 175 and 100 mv, respectively. the above important observations pertaining to analytical peak separation and low detection limits, suggest an excellent stability, sensitivity and adsorption capacity of the present electrocatalytic system. it is worthy to note that the above data were collected without intervening electrode conditioning between successive concentrations. the stability and the reproducibility of the modified electrode were examined by repeating the dpasv experiment 10 consecutive times in the presence of 250 g l 1 (pb) and 500 g l 1 (cd). the peak separation was successfully maintained, indicating a good stability of the modified electrode, while the current variation was 4.7% for pb and 6.6% for cd, suggesting that the electrode reactivity is not affected critically by the adsorption of analytes and can be used multiple times. 3.4.2 selective determination of cadmium and lead ions the electrode selectivity and hence the interference trend was tested for each metal ion by sequentially changing the concentration of one metal ion in the presence of a high and constant concentration of the second one. figure 6 depicts the effect of 1000 g l 1 of pb 2+ in the determination of cd 2+ ions using the dpasv method. the stripping peak of cd is well separated and occurred at –820 mv vs (ag/ agcl) and increased linearly with increasing [cd 2+ ] despite a possible interfering tendency that may be initiated by the presence of large [pb 2+ ]. the calibration curve for the linear plot of ip vs. [cd 2+ ] is shown in the inset of figure 6, and the calculated lod (3σ/s) was 23 g l 1 . nevertheless, the stripping peak of pb (present in a large scale) obtained at –0 mv does not hinder or manipulate the stripping peak of cd, indicating that padpa active sites are capable of accommodating both metals during the accumulation period. in a similar fashion, the data presented in figure 7 illustrates that the presence of 2000 g l 1 cd does not alter the stripping peak position of pb, which maintained its symmetrical shape and sharpness, and increased subsequently with increasing [pb 2+ ]. the calibration curve for the linear plot of ip vs. [pb 2+ ] is shown in the inset of figure 7, and the calculated lod (3σ/s) was 13 g l 1 . accordingly, it can be concluded that the surface based material did not deteriorate due to deposition of both metals and sustained its structure during the stripping mode in the positive scan. 3.4.3 interference studies the presence of foreign metal ions in the water sample may change the nature and the morphology of the electrode surface and hence affect the electrochemical measurements of analytes under investigation. for this task, the simultaneous determination of 250 g l 1 (pb) and 500 g l 1 (cd) was investigated in the presence of 5000 g l 1 of emad khudaish et al 25 the foreign ion. foreign ions such as na + , mg 2+ , ni 2+ , co 2+ , al 3+ , fe 3+ , vo4 3 , mno4  , cl  , and no3  had no interference on the present system. the effect of cu 2+ and hg 2+ on the stripping voltammetry of pb and cd ions is presented in figures 8(a) and (b), respectively. the presence of 2500 g l 1 cu 2+ (solid line) distorted the development of the cd peak which appears very broad and unsymmetrical, while the peak potential of pb was only shifted by +100 mv from its usual position (dotted line). the presence of 1000 g l 1 hg 2+ (solid line) had a direct effect on the symmetry of the cd peak current, which became much sharper and increased three fold the original value (dotted line), while it had no effect on the peak current of pb. the above trend could be interpreted as due to the formation of a thin hg layer that played a major r ole in the enhancement of the cd voltammetric signal. 0 10 20 30 40 50 60 70 80 -1200 -1000 -800 -600 -400 -200 0 i/  a e / mv vs (ag/agcl) cd pb i a y = 47.401x r² = 0.9972 0 5 10 15 20 25 30 35 40 45 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 i p /  a [cd2+]/ mg l1 figure 6. dpasv curves recorded at padpa/gce in acidified 0.1 m kcl solution (ph = 2.12) for the selective determination of cd 2+ in the presence of 1.0 mg l 1 pb 2+ . the range of [cd 2+ ] is (a) 0 increased by 0.1 mg l 1 each time to a final (i) 0.8 mg l 1 (inset is the calibration curve represented by ip vs [cd 2+ ]. figure 7. dpasv curves recorded at padpa/gce in acidified 0.1 m kcl solution (ph = 2.12) for the selective determination of pb 2+ in the presence of 2.0 mg l 1 cd 2+ . the range of [pb 2+ ] is (a) 0 increased by 0.05 mg l 1 each time to a final (i) 0.4 mg l 1 (inset is the calibration curve represented by ip vs [pb 2+ ]. 3.4.4 analytical test to water sample the proposed system was tested for the determination of both metal ions in a water sample treated and prepared as described above in section 2.4. polymeric film modified electrode 21 figure 8. interference study on the stripping peaks of 0.5 mg l 1 cd 2+ and 0.25 mg l 1 pb 2+ in the presence of (a) 2.5 mg l 1 of [cu 2+ ] and (b) 1.0 mg l 1 of [hg 2+ ] using acidified 0.1 m kcl solution (ph = 2.12). the analytical results including the recovery percentage are given in table 2. the recoveries were more than 97% (the calculated relative standard deviation values were less than 10%), and demonstrate that the present system can offer a sensitive and accurate method for the monitoring of trace metal ions. table 2. analytical parameters and recovery percentage (n = 3) for cd 2+ and pb 2+ ions in water samples using standard addition method. the regression data obtained from figure 5 were used to calculate their concentrations. metal ions (i) (a) [actual] (g l 1 ) [found] (g l 1 ) recovery (%) ) 2+ (cd (1) 1.84 50 48.4 96.8 (2) 3.76 100 98.9 98.9 (3) 5.69 150 149.7 99.8 ) 2+ (pb (1) 2.45 25 24.4 97.7 (2) 5.21 50 50.1 100.2 (3) 7.88 75 75.8 101.0 4. conclusions a chemically modified electrode was fabricated via the electrochemical polymerization of padpa at gce in 1.0 m hcl solution. the surface coverage of the coated film was influenced by the applied anodic potential that initiated the progression of polymerization and defined the nature of the resulting polymer. the polymeric film modified electrode exhibited a reversible electrochemical behavior, demonstrated by the development of redox active sites. the estimated surface roughness and cumulative surface area of the modified electrode under the present working conditions is an index for possible doping process on the film matrix to improve its catalytic properties for certain analytical applications. the constructed modified electrode showed a potential capacity to be a reliable environmental sensor for the simultaneous determination of cd 2+ and pb 2+ ions. the incorporation of certain 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19(2) 77-90 © 2014 sultan qaboos university 77 projection of polyhedra onto coxeter planes described with quaternions mudhahir al-ajmi*, mehmet koca and hashima bait bu salasel department of physics, sultan qaboos university, p.o. box: 36, al-khoudh 123, muscat, sultanate of oman. *email: mudhahir@squ.edu.om. abstract: 3-dimensional convex uniform polyhedra have been projected onto their corresponding coxeter planes defined by the simple roots of the coxeter diagram . the projected vertices of a polyhedron onto its corresponding coxeter plane constitute an orbit of the dihedral group . in this paper, we use the quaternionic representations of the coxeter group elements and the vertices of the polyhedra. keywords: coxeter group; group theory; quaternions; projection. كىزجر باسحخذام الرباعيات إسقاط محعذدات السطىح على سطخ بىسالسل بيث مظاهر العجمي و مهمث كىجا ودشيمة ٌتى باستخذاو ( coxeter plane) عهى سطح كىكزتز ثالثٍة األبعاداإلسقاط انعًىدي نهًجسًات األفالطىنٍة واألرخًٍذٌة وانكاتاالنٍة ملخص: (coxeter). انًتجهات انساقطة نهذه انًجسًات عهى سطح كىكزتز (coxeter diagram i2(h)) انجذور انبسٍطة ألشكال كىكزتز نهتعبٍز عن عناصز (quaternions). استخذينا انزباعٍات (dihedral group)ًجًىعات ثنائٍة األسطح هتحتىي عهى انتًاثم اننقطً ن فً هذه انىرقة انبحثٍة.وعن رؤوس انًجسًات (coxeter) تزيجًىعة كىكز انزباعٍات، االسقاط. نظزٌة انًجًىعات ، يجًىعة كىكزتز، :مفحاح الكلمات 1. introduction ymmetries of objects play a vital role in the analysis of structure, bonding and spectroscopy of molecules in several scientific disciplines. group theory provides a great tool for understanding symmetry phenomena in physics. using group theory to study the symmetry of polyhedra is helpful for physicists to develop an understanding of crystallography and quasi-crystallography. in this paper we use the rank-3 coxeter-dynkin diagrams, a special technique in lie algebra, to construct the symmetries of polyhedra. a symmetry group may contain transformations such as reflections, rotations, rotary reflections and inversions which leave the object unchanged. coxeter groups are abstractions of the symmetry groups only generated by reflections group elements. they are useful in describing the symmetry of regular and semi-regular polytopes in arbitrary dimensions [1]. the list of convex uniform polyhedra contains platonic solid, archimedean solids and their duals, the catalan solids. these special polyhedra have been successfully used to describe the crystals in physics, molecular symmetry in chemistry and some viral structures in biology [2]. to describe the symmetry of all convex uniform polyhedra we use three main finite coxeter groups 3, 3, and 3. invoking quaternions is an efficient tool for representing elements of the coxeter groups of rank-3 and rank-4. quaternions have been used to represent rotations and reflections since their discovery in 1843 [3] and have now become used to represent the coxeter groups [4]. they are also used to symbolize the simple roots and weights of coxeter-dynkin diagrams. furthermore the vertices of polyhedra are written in terms of pure imaginary quaternions. quaternions are used because of their compactness, stability and simplicity, which make this method easy to use when compared to other methods that are based on orthogonal matrices or euler angles. the objective of this paper is to project the vertices of several 3d polyhedra onto their corresponding 2d coxeter planes. we define a coxeter plane by the simple roots of the coxeter diagram where is the coxeter number. when projected onto the coxeter plane, the vertices of any polyhedron form orbits of the dihedral group . s mailto:mudhahir@squ.edu.om mudhahir al-ajmi et al 78 orthogonal projection of higher dimensional lattices onto 2 or 3 dimensional subspaces can be related to quasi-crystal structures. we organize the paper as follows. in section 2, definitions of finite reflection groups, quaternions, and coxeter groups are given. we then describe the platonic solids, the archimedean solids and their duals with respectively their symmetry groups in section 3. in section 4, we study the projections of the convex uniform polyhedra. finally, section 5 contains our conclusive remarks. 2. finite reflection groups the dihedral group is the group which involves the rotation through an angle , which is expressible as the product of two reflections and whose mirrors have an angle of between them. here, plane symmetries preserve a regular -sided polygon where . the reflections and generate a dihedral group , which is a subgroup of the symmetric group of order . a hypercomplex number is defined as quaternion, which can be written in general as ∑ (1) with , being the set of real numbers, and the quaternionic units which satisfy (i,j,k=1,2,3) (2) where ij and ijk are the kronecker and levi-civita symbols, and where summation over the repeated indices is implicit. any quaternion can be split into two parts, a scalar part: , and a vector part: . the following definitions will be useful in our discussions. the conjugate of a quaternion is defined by ̅ (3)  we define the inverse quaternion as ( ⌈ ⌉ ) ̅ (4)  the scalar product of two quaternions and is given by , (5) or as ̅ ̅ . (6)  the product of and ̅ gives a real non-negative number called the norm of . ̅ ∑ | | ̅ (7) the norm of does not equal zero and is the length of the quaternion. the unit quaternion is a normalized quaternion when | | . the binary tetrahedral (bt) group is represented by the following set of 24 quaternions [5]. , (8) this set represents the vertices of the 24-cell. the binary octahedral ( ) group consists of the union of set and [3] where projection of polyhedra onto coxeter planes described with quaternions 79 { √ √ √ √ √ √ } . (9) the order of the group (10) is 48. the binary icosahedral ( ) group is of order 60×2=120. the union of two sets and represents the set of quaternions of the binary icosahedral group as . (11) the set in the quaterionic form is [6]: (12) where √ √ the golden ratio and its algebraic conjugate respectively. the vertices of the 600-cell [7] consists of the set of quaternions . however, the set represents the vertices of the snub 24-cell [8]. a coxeter group is defined as an abstract group that is generated by elements subject to the relations ( ) (13) where and for all , so that . the pair is called a coxeter system; it consists of a group and a set of generators . the cartan matrix is defined by ( ) ( ) (14) the matrix elements are scalar products of two simple roots and satisfy the following criteria: 1. every cartan matrix has an inverse defined by ( ) (15) where is the fundamental weight defined as the basis vectors of the dual space. the real and the dual space are in the same space. 2. the relation between and satisfies: ( ) (16) (17) (18) the summation over repeated indices is implicit. mudhahir al-ajmi et al 80 finite coxeter groups are generated by simple reflections as finite euclidean reflection groups. a reflection of a vector in a finite dimensional euclidean space is a linear transformation by a reflection generator r of the finite coxeter group with respect to a hyperplane perpendicular to the root vector . this can be defined by the formula [5] (19) here, is a vector which is usually called the root vector or simply root. this root vector is called a simple root in lie algebra. the norm of the simple root is fixed as √ . if is an arbitrary simple root written in terms of quaternions, then the reflection of an arbitrary vector with respect to the plane orthogonal to the simple root can be written as the product of quaternions √ ̅ √ (20) we then define this reflection operation by a different notation as * √ √ + (21) here, the asterisk signifies that we take the conjugate of λ. however, a rotation can be written in our notation as ̅ (22) 3. polyhedra platonic and archimedean solids platonic solids are made of regular polygons (triangle, square or pentagon) meeting in identical vertices. on the other hand, the archimedean solids are convex polyhedra whose faces are regular polygons. one can obtain 5 of them by truncation of the platonic solids and the others by expansion and snubification. the archimedean solids are vertextransitive (vertices move to each other in any symmetry operation). the method explained in [4] gives only the vertices of 11 archimedean solids. the other two chiral solid vertices are taken from [9]. the first platonic solid is the tetrahedron and its polyhedral group is the tetrahedral group where its group elements can be written as 3 ( ) {[ , ] [ , ] }w a p p t t    ; , p t t t . (23) the coxeter-weyl group is represented by the coxeter-dynkin diagram shown in figure 1 [6] figure 1. coxeter-dynkin diagram of w(a3). to obtain the orbit of the group, corresponding to the vertices of the tetrahedron, we use the method described in [6]. we apply the group elements on the highest weight written in a general form: which can be written in terms of quaternionic imaginary units as . in [6], the values of and are found from eq (18). replacing these values in λ, we obtain: the seven special cases of are indicated by ones or zeros and called the dynkin indices. the cube and the octahedron are dual of each other, and they also have the same polyhedral symmetry group, which is the octahedral group with 48 elements given by 3 3 4 2 ( ) ( ) {[ , ] [ , ] [ , ] [ , ] }; w b aut a s c p p p p t t t t          ,p t t t . (24) projection of polyhedra onto coxeter planes described with quaternions 81 the coxeter group of this polyhedral symmetry group is represented by the coxeter-dynkin diagram shown in figure 2. figure 2. coxeter-dynkin diagram of w(b3). the other platonic solids that are dual of each other are the icosahedron and the dodecahedron. their polyhedral symmetry group is the icosahedral group of order 120 given by 3 5 2 ( ) {[ , ] [ , ] };w h a c p p p p p i      (25) the coxeter-dynkin diagram of the icosahedral group is shown in figure 3. figure 3. coxeter-dynkin diagram of w(h3). the five different platonic solids are displayed in table 1. catalan solids to construct the dual of a solid we connect vertices which go through the centers of the faces of each solid. the set of new polyhedra is called the catalan solids. they are not semi-regular since they have more than one set of vertices and their faces are not regular polygons in general. they are made of scalene triangles, isosceles triangles, rhombuses, kites or irregular pentagons. obviously they are still convex. the symmetry groups of catalan solids are the same as their archimedean duals. some of the archimedean and catalan solids do not have the full symmetry group of a platonic solid but only the rotational symmetry group of the octahedron or the icosahedron. the catalan solids are face-transitive (faces move onto each other in any symmetry operation). in this paper, we take vertices of the catalan solid from [7]. the archimedean and their dual catalan solids are displayed in tables 1-4. 4. projecting polyhedra onto their coxeter planes coxeter plane the product of all reflections in a coxeter group is called the coxeter element: and its order is called coxeter number . there is a unique plane on which the coxeter element acts as a rotation by an angle . this plane is called the coxeter plane [1]. every coxeter group has a maximal subgroup isomorphic to the dihedral group of order 2h. we use the following technique to determine the coxeter planes of the three main polyhedaral symmetry groups. the coxeter group elements are given in eq. (8) and the group is represented by the coxeter-dynkin diagram shown in figure 1. the coxeter element of this group is where its order (coxeter number) since . let us define a dihedral group as a coxeter plane with generators and of we define as the product of generators and which are orthogonal to each other (26) and the generator as . (27) the dihedral group 〈 〉 is a subgroup of where . the dihedral group is and has 8 elements. the dihedral group represented by the coxeter-dynkin diagram is shown in figure 4, mudhahir al-ajmi et al 82 figure 4. coxeter-dynkin diagram of where are the simple roots and the norm and the scalar products are given as ‖ ‖ ‖ ‖ √ , ( ) √ (28) using eq. (14) the cartan matrix of is ( √ √ ). using eq. (19), the generators and of correspond to a reflection at a hyperplane perpendicular to the root vectors given as (29) (30) √ (31) √ . (32) in eqs (31 & 32) we use eq. (19), replacing α with γ. in eq. (29) we define as a linear combination of and : (33) where equals zero, and in eq (30), is defined as (34) where and equal zero. combining the equations above we can get the values of coefficients , and : √ , . then, eqs (33 & 34) become √ these simple roots and define the coxeter plane. however and are not orthogonal to each other. so, we define an orthogonal set of vertices given by ̂ √ (35) ̂ (36) where ̂in x-axis , ̂in y-axis and ̂ ̂ ̂ ̂ . using the same argument as above, we define the coxeter plane as 〈 〉 of with generators and where the coxeter number of equals 6. the dihedral group represented by the coxeter-dynkin diagram is shown in figure 5. projection of polyhedra onto coxeter planes described with quaternions 83 figure 5. coxeter-dynkin diagram of . are the simple roots and . using eq. (14) the cartan matrix of d6 is ( √ √ ) using the method explained above for the i2 (4), and for the i2 (6) can be written in terms of quaternions as √ (37) (38) where , , and √ [6]. the two components of and in the x-axis and y-axis are orthogonal to each other: ̂ √ √ (39) ̂ √ (40) where ̂ ̂ ̂ ̂ . using the argument introduced above, we define the coxeter plane as 〈 〉 of with generators and respectively. the cartan matrix of is ( √ √ ) the coefficients and are √ √ and the coefficient then and can be written in terms of quaternions as √ , √ (41) √ (42) from [4], , , and . the two orthogonal components of and are ̂in x -axis and ̂in y -axis ̂ √ (43) ̂ (44) projection in our work we use the orthogonal projection of polyhedra in three-dimensions onto their corresponding coxeter planes. by taking the scalar product of an arbitrary vector of a polyhedron with ̂and ̂ of the coxeter plane for , and we can determine the horizontal and vertical components of the projected vectors and of the orbit onto the coxeter plane. mudhahir al-ajmi et al 84 projection of polyhedra having tetrahedral symmetry. we can take the scalar product of the vertices of a polyhedron with ̂ ̂ in eqs (31  32) to get and of vertices of the polyhedra having tetrahedral symmetry. let us now consider the tetrahedron which has tetrahedral symmetry. here, . when the vertex is multiplied (as a scalar product) with ̂ ̂ the horizontal and vertical projections become respectively . / . / when this projection is applied to all vertices of , we obtain the full projection of the tetrahedron in figure 6. the solid line shows the projection of the front faces and the dashed line represents the projection of the back faces, and this applies to all following figures. figure 6. projection of the tetrahedron. the radius in this projection equals √ . the angle between all vertices of this polyhedron and the x-axis is 45  . the lines between the vertices indicate the nearest neighbor pairs. we find the same result for the vector . in the figure above it is clear that there are 4 vertices at the corners with but no central vertex with 6 edges, and that the faces of the tetrahedron are triangular. the angle between the edges is 90. therefore this polygon has 4-fold rotational symmetry. in the case of truncated tetrahedron the projected vectors result in two circles. the first one has a radius of √ with 4 projected vertices each having an angle of 45 with the x-axis. the second one has a radius of √ with 8 projected vertices of and . the projected vertices of and have angles equal to 71.56 and 18.4 with the x-axis respectively as shown in figure 7. figure 7. projection of the truncated tetrahedron. the projection shows us 18 edges of the truncated tetrahedron with 8 faces (4 triangles and 4 hexagons) and 12 vertices. this projection an “edge first” projection with 8-fold symmetry. we can apply a similar projection to the dual of the truncated tetrahedron which has a symmetry group. the projected vertices are shown figure 8. projection of polyhedra onto coxeter planes described with quaternions 85 figure 8. “edge first” projection of the dual of the truncated tetrahedron. applying the same projection to the other vertices of tetrahedral solids we can get their projections. table 1 lists the results of projecting the platonic solids onto their coxeter planes. table 2 lists the results of projecting solids having symmetry onto their coxeter planes. we take the scalar product of the vertices of polyhedra that have the octahedral symmetry with ̂ ̂ of as defined in eqs. (39  40) to get their and components in the coxeter plane. table 3 lists the results of the projections of the archimedean solids onto their coxeter plane. taking the scalar product of the vertices of each polyhedron having an icosahedral symmetry with ̂ ̂ in eqs. (43  44) we get their and onto the (x,y)-plane of . the set of invariant points of the polyhedra having icosahedral symmetry projected onto the coxeter plane of is listed in table 3. 5. conclusion in this paper we projected the platonic, regular archimedean and catalan polyhedra in 3 onto the coxeter plane. we defined the coxeter plane by the root system of the dihedral group generated by coxeter-dynkin diagram . our projection preserves the h-fold symmetry of the root system which is a subgroup of its complete symmetry. obviously, after projection, the regular polygons become irregular. however, it can be seen how the polygons still meet at the same vertices. the dynkin indices chosen were 0’s and 1’s for a general vector. this work can be extended for those polyhedra whose vertices can be constructed by choosing arbitrary integer values of dynkin indices. table 1. list of the platonic solids and their projection onto coxeter plane. platonic solids dynkin indices of symmetry group 3d polyhedra projection  vertices/ radius radius tetrahedron (0,4) √ octahedron (0,6) 0 √ cube (2,6) 0 √ dodecahedron (0,10,10) 0 √ ⁄ √ √ mudhahir al-ajmi et al 86 platonic solids dynkin indices of symmetry group 3d polyhedra projection  vertices/ radius radius icosahedrons (2,10) 0 √ ⁄ table 2. an archimedean polyhedron having w(a3) symmetry and its projection onto its coxeter plane. polyhedron 3d polyhedron projection  vertices/ radius radius dual projection  vertices/ radius radius truncated tetrahedron (0,4,8) 0, √ , √ (0,4,4) 0, √ , √ table 3. list of the polyhedra (archimedean & catalan) having w(b3) symmetry and their projection onto coxeter plane. polyhedra (w(b3)) 3d polyhedra projection  vertices / radius radius dual projection  vertices / radius radius cub-octahedron (0,6,6) 0 √ √ (2,12) 0 √ truncated cube (0,6,6,12) 0 √ √ √ √ √ (2,6,6) 0 √ √ √ truncated octahedron (0,12, 12) 0 √ √ (2,6,6) √ projection of polyhedra onto coxeter planes described with quaternions 87 polyhedra (w(b3)) 3d polyhedra projection  vertices / radius radius dual projection  vertices / radius radius small rhombicubocta hedron (0,6, 12,6) 0 √ √ ( √ ) √ √ (2,6,6,6,6) √ √ √ √ 1 great rhombicub-octa hedron (0,12, 12,12, 12) 0 √ √ √ √ √ √ √ (2,6,6,12) 0 √ √ √ √ √ snub cube (0,6,6, 6, 6) 0 √ √ √ √ √ where √ ⁄ (2,6,6,6 6,6) √ √ √ √ √ √ √ ( √ ) where √ ⁄ mudhahir al-ajmi et al 88 table 4. list of the polyhedra (archimedean & catalan) having w(h3) symmetry and their projection onto coxeter plane. polyhedra (w(h3)) 3d polyhedra projection # vertices/ radius radius dual projecti on # vertices/ radius radius icosidodeca hedron (0,10, 10, 10) 0 √ ⁄ √ √ (2,12, 10) √ ( √ ) √ √ truncated icosahedron (0,10, 10, 20,20) 0 √ ⁄ √ √ √ √ √ √ (2,10, 10,10) √ ( √ ) √ √ √ √ truncated dodecahedron (0,20, 10, 10,20) 0 √ √ √ √ √ √ (2,10, 10) √ √ √ √ √ ( √ ) √ small rhombicosi dodecahedron (0,10, 20, 20,10) 0 √ ⁄ √ √ (2,10, 10, 10,10, 10,10) 0 √ ( √ ) √ √ √ √ projection of polyhedra onto coxeter planes described with quaternions 89 polyhedra (w(h3)) 3d polyhedra projection # vertices/ radius radius dual projecti on # vertices/ radius radius √ √ √ √ √ √ 1 great rhombicosi dodecahedron (0,20, 20, 20,20, 20,20) 0 √ √ √ √ √ ( √ ) √ ( √ ) √ ( √ ) (2,10, 10, 10,10, 20) √ ( √ ) √ √ √ √ √ √ √ √ 1 mudhahir al-ajmi et al 90 polyhedra (w(h3)) 3d polyhedra projection # vertices/ radius radius dual projecti on # vertices/ radius radius snub dodoca hedron (10,10, 10,10, 10,10) √ √ √ √ √ ( ) √ √ √ √ √ ( ) √ (2,10, 10, 10,10, 20,10, 10,10) 0 √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ √ references 1. coxeter, h.s.m. regular polytopes ( 3 rd edition). new york: dover publications., 1973, 33-57. 2. zuber, j.b. quantum symmetries in theoretical physics and mathematics (bariloche, 2000) contmp. math. 294, amer. math. soc., providence , ri. 3. hamilton, w.r. 1853. lectures on quaternions. london: whittaker. 4. koca, m., koc, r. and al-ajmi, m. polyhedra obtained from coxeter groups and quaternions. j. math. phys., 2007, 48, 113514-113527. 5. koca, m., koc, r. and al-barwani, m. quaternionic root systems and subgroups of the aut(f4). j. math. phys., 2006, 47, 043507. 6. koca, m., koca, n.o. and al-ajmi, m. branching of the w(h4) polytopes and their dual polytopes under the coxeter groups w(a4) and w(h3) represented by quaternions. turk. j. phys., 2012, 36, 309-333. 7. koca, m., koc, r. and al-ajmi, m. group theoretical analysis of 4d polytopes 600-cell and 120-cell with quaternions. j. phys. a: math. and theor., 2007, 40, 7633. 8. koca, m., koc, r. and al-ajmi, m. quaternionic representation of the coxeter group h4 and the polyhedra. j. phys. a: math. gen., 2006, 39, 14047-14054. 9. koca, m., koca, n.o. and al-shu'eili, m. chiral polyhedra derived from coxeter diagrams and quaternions. squ j. sci., 2011, 16, 63-82. 10. koca, m., koca, n.o. and koc, r. catalan solids derived from 3d-root systems. j. math. phys., 2010, 51, 043501. received 24 october 2013 accepted 22 june 2014 microsoft word ersc090525-f edited_corrected.doc 31-40 squ journal for science, 15 (2010) © 2010 sultan qaboos university 31 study of groundwater potentiality and sea water intrusion along the coastal plain, wadi thuwal, ksaa case study based on dc resistivity mansour a. al-garni* and hamdy i.e. hassanein geophysics department, faculty of earth sciences, king abdulaziz university, saudi arabia, *email: maalgarni@kau.edu.sa. دراسة احتمالية وجود المياه الجوفية وأثر اختراق مياه البحر إلى منطقة وادي ثول خالل السهل الساحلي، المملكة العربية دراسة بالمقاومة الكهربية –السعودية حسانين . القرني وحمدي ا. منصور ع ه صالحة وتلك التي قد تكون تأثرت باختراق أن غرض الدراسة هو تحديد المناطق التي يمكن أن توجد فيها ميا :خالصة على السهل الساحلي بوادي ثول الذي 2 كلم170فقد تم قياس المقاومة الكهربية على مساحة تقرب من . مياه البحر اليها ئيأن القياسات المقاومية التي اجريت على اساس النموج الطبقي الكهربا. يحده البحر األحمر غربا وتالل بركانية شرقا لذلك فان التحليل االحصائي . طبقات جيولوجيةتعبر عن تعطي قيما واسعة النطاق التي اليمكن ان تكون حقيقية المتعدد وقد قمنا . كان ضروريا للتغلب على هذه الظاهرة وللحصول على الصورة الحقيقية الطبقية الجيولوجية لتفسير البيانات التي تشمل على عدد من ) slm(كورة الى اخرى احصائية للكهربية االرضية المذ اكهربيةبتحوير النماذج الطبقية فالنموذج المحور حدد لنا عمق . الطبقات المساوية للطبقات الجيولوجية تحت كل موقع تم فيه قراءة المقاومية الكهربية .حر في المنطقةطبقة الصخور االساسية، والطبقات الحاملة للماء والمستوى المائي واثر اختراق ماء الب abstract: the present study mainly aims to outline zones that have groundwater potentiality with good quality and those which are affected by sea water intrusion. the electrical resistivity data were acquired over an area of about 170 km2 of a coastal plain, wadi thuwal, which is bounded by the red sea in the west and the volcanic hills in the east. in such an area, resistivity measurements, using n-layering model, generally reveal a wide range of resistivity values which do not reflect the reality. hence, the statistical analysis has to be involved to overcome this problem and to make the final interpretation reliable. in our case, the n-layer models were modified to other statistical geoelectric models (slm), consisting of a number of layers equivalent to the stratigraphic layering beneath each ves site. the modified models were used to outline the depth to the bed rock, groundwater accumulation zones and water table as well as to define the effect of sea water intrusion through the study area. keywords: wadi thuwal; coastal plain; dc resistivity; n-layering model; statistical model. mansour a. al-garni and hamdy i.e. hassanein 32 1. introduction he dcresistivity in general has been successfully used to delineate the fresh water/saline water interface (el-waheidi, 1992; choudhury et al 2001) as well as water content (kessels et al 1985). the studied area is about 170 km2 along the red sea coastal plain where it lies at the downstream of wadi khulase (figure 1). it is mainly covered by holocene wadi deposits, quaternary basalts (harrat thuwal) and miocene sediments. it is shown that the structural pattern beneath the study area is affected by more than one phase of faulting. the surface of miocene deposits is considered as a bed rock (m. abdulwahid unpublished data). the lithology and configuration of the surface of miocene deposits play the main significant role in building up the drainage pattern beneath the eolian and alluvian cover of the study area. this work represents an attempt to study the subsurface structural setting and to delineate the ground water distribution in wadi thuwal area, as well as the seawater intrusion effect through it. 2. data acquisition a vertical electrical sounding (ves) survey was conducted at 88 selected sites using schlumberger array to measure the surface and subsurface variation in resistivity. the well-known elrec-t system (ires) was used as an electrical resistivity meter, utilizing 1200 kw. 2.1 vertical electrical sounding data analysis 2.2.1 n-layering technique a ves survey provides a series of apparent resistivity values as a function of depths. these values are obtained at each ves location, using different electrode spacings. the half current electrode spacing (ab/2) reached up to 140 m where the spacing between the potential electrodes (mn) varied from 2m to 20m according to the rule of thumb of schlumberger array (ab≥5mn). these measurements were made along 8 e-w profiles, covering the study area. the resistivity curves fall into the following types: qh, kq, hk, q and h. sampling of the continuous smoothed curve at the rate of 6 logarithmically equally spaced points per logarithmic cycle was done to obtain a digitized sounding curve. in general, sampling the apparent resistivity is done from right to left, starting from the largest current electrode spacing, where the effect of near surface inhomogeneity is disregarded (al-garni, 1996). we used zohdy’s method (zohdy, 1989) to invert the ves field resistivity measurements to a number of horizontal geoelectric layers. the study area has a large aerial extension with significant variable surface and subsurface structural and environmental depositional regimes built up over a long period of time, where these two factors have led to a wide range of resistivity values (0.9-2568.5 ohm.m). therefore, statistical analysis was suggested to define and classify the obtained resistivity data as normal distribution groups with known statistical parameters related to certain lithological and/or structural environment units and constrained by reliable depth limits. 2.2.2 statistical analysis the process of statistical analysis involves all the data as one population to check their normality. the standard deviation of the measured resistivity values all over the area is 227. the kolmogorov-smirnov test of normality (clark and evans, 1954; montgomery and runger, 1994; cressie, n.a.c, 1991; and king, ronald s. and bryant julstrom 1982) shows that this population of resistivity measurements do not have a normal distribution, where the kolomgrov-smirnov statistical index >> the critical value (table 1). this indicates that the population of data assemblage could be classified into different populations; hence, the statistical analysis was used to implement the classification. t study of ground water potentiality and sea water intrusion 33 table 1. results of statistical analysis of the resistivity data of the study area. # of data min max mean s.d. k-s c.k-s at α=.05 761 0.86 2568.5 127.8 227 0.288 0.049 legend sand and drainage lines aeolian sand dip direction normal inferred alluvial asphaltic roads harrat flood desert roads miocene ves locations study area a b figure 1. location (a) and geology and the ves sites distribution of wadi thuwal area, ksa (al-garni et al 2009) (b). accordingly, the calculated resistivity values, using n-layering modeling technique, are classified into six different normal distribution classes each of which corresponds to certain lithological ensembles of distinguishable resistivity character. table 2 shows the statistical parameters and the results of normality distribution analysis. to define the depth limitations of each one of the classes, the data involved in each class was plotted individually and compiled as a depth resistivity graph (figure 2), which shows that the resistivity values decrease with increasing depth. the upper 10 m, which is related to the surface and near surface lithological variations, has a wide resistivity range (1-2570 ohm.m). the resistivity of the section between 10 and 20 m ranges between 0.8 -200 ohm.m. it is underlain by the third section (20-30 m), with resistivity values, ranging between 1.8-40.0 ohm.m. the last section, which is deeper than 30 m, has a resistivity range between 2.5-20 ohm.m. the geoelectric n-layering model (nlm), which was obtained from the n-layer modeling technique (zohdy, 1989), can be modified to another equivalent geoelectric statistical layering model (slm). in this case, the number of geoelectric layers will be reduced and it will lead to more realistic lithological units. for example, at ves 1001, ten layers are interpreted using n-layer technique (nlm) whereas this number is reduced to six geoelectric layers using statistical analysis (slm). mansour a. al-garni and hamdy i.e. hassanein 34 table 2. results of normality test and the 6 unit statistical parameters. code number statistical parameters 1 2 3 4 5 6 number of values 194 151 134 168 104 10 range 0.98.1-24.7 25.2-78.6 80.8-255.3 260.2-933.3 960.3-2568.5 mean 4.1 14.2 45.7 149.6 478.9 1322.4 standard deviation 1.9 4.8 16.1 52.3 186.3 482.4 kolmogorov-smirnov stat. index 0.096 0.105 0.107 0.102 0.129 0.253 critical k-s stat, pha =.05 0.097 0.109 0.116 0.104 0.132 0.409 -5 4 -5 2 -5 0 -4 8 -4 6 -4 4 -4 2 -4 0 -3 8 -3 6 -3 4 -3 2 -3 0 -2 8 -2 6 -2 4 -2 2 -2 0 -1 8 -1 6 -1 4 -1 2 -1 0 -8 -6 -4 -2 0 depth in m 0.1 1 10 100 1000 10000 r es is tiv ity in o hm .m the relation between resistivity variations with depth 260-960 ohm.m 80-260 ohm.m 25-80 ohm.m 8-25 ohm.m 0-8 ohm.m >960 ohm.m figure 2. resistivity clusters versus depths. the developed classification, resistivity contours, and the geology are superimposed all together to implement the correlation (figure 3). this shows certain distinctive zones of low resistivity values, taking an elongated extension, which is mostly attributed to the surface courses of the floods during the successive rainy seasons. the interpreted low resistivity values, using statistical geoelectric layers (sgl) (1, 2 and 3), are present on the surface of such zones. the interpreted higher resistivity values, using sgl (4, 5 and 6), occur mainly in areas that are covered by alluvial terraces. the interpreted depth beneath each model was reduced to sea level in order to reveal the relation between the resistivity distributions and the geomorphologic and environmental variations. the obtained resistivity values and their corresponding depths were used to construct eight w-e cross-sections along profiles, coded as 1000, study of ground water potentiality and sea water intrusion 35 2000, 3000, 4000, 5000, 6000, 7000 and 8000, respectively (figure 4). the interpreted resistivity classes (table 2) were considered as contour intervals. figure 3. distribution of sgl, surface resistivity contours, and geology of wadi thuwal area. 3. interpretation of the resistivity data the lateral and vertical resistivity variations along each profile show that the basement rocks and the overlain sedimentary miocene deposits were affected by different structural events, changing their structural setting at the surface of the bedrock. hence, the depositional and hydrological regimes of the recent quaternary deposits are controlled by these changes. (figure 4) shows that the main water table level of the study area is the sea level, ranging between 10 and 20 m from the surface. the bedrock is characterized by low resistivity values (1 to 8 ohm.m), extending beneath the entire study area. this indicates that the lithological composition of the bedrock is mainly clay, which may be attributed to the salinity content near the shoreline (at the north western part of the study area, figure 6). the bedrock is overlain by two geoelectric layers. the first, coded no.2, ranging between 8 and 25 ohm.m in resistivity, represents sediments of sand and gravel saturated with water regardless of the quality. the second, coded no.3, which ranges in resistivity between 25 and 80 ohm.m, represents sediments of sand and gravel partially saturated with water (figure 4). these two units are considered to be the most significant units for conducting groundwater exploration, where the thickness of water saturation of these zones varies according to the level of precipitation. the resistivity behavior of unit no.3 is almost the same as that of no.2, yet the thickness of the water saturation zone is greater. these two zones can be observed along profiles 2000 (v2007 and 2014), 3000 (v3006, 3008, 3014 and 3015), 4000 (bewteenv4008 and 4011), 5000 (v5008 and 5009), 6000 (v6005 and 6006), 7000 (v7003) and 8000(v8002) (figure 4). mansour a. al-garni and hamdy i.e. hassanein 36 the three geo-electric units no. 4, 5 and 6 are present frequently, occupying the upper part of the geoelectric sections, and they are characterized by high resistivity values. these units have no significant impact on the water exploration. however, their lithological characters may control the flow of the floods and water percolation through them. figures (5a and b) show the topographic contour maps (depth to sea level) of the upper surface of both geo-electric units no.1 and 2, respectively, which reveal the effect of the structural events. there are five zones (sz1, sz2, sz3, sz4, and sz5) of low resistivity values, which can be delineated based on the correlation between the resistivity and bedrock topography (figure 5a). three zones (sz1, sz2 and sz3), which are located below sea level, are invaded by the sea water intrusion where high salinity of groundwater is expected. the other two zones (sz4 and sz5), which are located above sea level, prevalently contain an abundance of clay accumulations. figure (5b) shows five significant catchment zones (z1, z2, z3, z4 and z5) within the second geo-electric layer. the resistivity values of this layer and its relative topography (above the sea level) indicate the presence of water of good quality. figure (5c) shows the thickness variations of this layer all over the studied area, where the average thickness of the groundwater bearing layer at these zones is about 10 m. figure (6) shows the interpreted faults and outlines the sea water intrusion zones (swi) and fresh water occurrences (fwo-1, fwo-2, fwo-3 and fwo-4). it shows also that the sea water intrusion and fresh water flow are controlled by the subsurface structures. the area at the east of the fault f4 is affected by sea water intrusion, whereas the most expected fresh water occurrences are located at the west of f7. 0 2000 4000 6000 8000 10000 12000 14000 16000 easting in m from 511911e -1 00 0 0 10 00 e le va tio n (m ) *4 0 v80 01 v80 02 v80 03 v80 04 geoelectric section along ves profile 8000-to-sea level sea level 0 2000 4000 6000 8000 10000 12000 14000 16000 easting in m from 511911e -1 00 0 0 10 00 e le va ti o n (m ) *4 0 v70 01 v70 02 v70 03 v70 04 v70 05 v70 06v70 07 geoelectric section along ves profile 7000-to-sea level sea level 0 2000 4000 6000 8000 10000 12000 14000 16000 easting in m from 511911e -1 00 0 0 10 00 e le va tio n (m ) *4 0 v60 01 v60 02 v60 03 v60 04 v60 05 v60 06 v60 07 v60 08 geoelectric section along ves profile 6000-to-sea level sea level easting in m from 511911e 00 50 0 15 00 e le va tio n (m ) *4 0 v50 01 v50 02 v50 03 v50 04 v50 05 v50 06 v50 07 v50 08 v50 09 geoelectric section along ves profile 5000-to-sea level sea level 400 600 800 960 1000 1400 2000 3000 l5 l6 figures to be completed on the next page. study of ground water potentiality and sea water intrusion 37 0 2000 4000 6000 8000 10000 12000 14000 16000 easting in m from 511911e -1 00 0 0 10 00 20 00 e le va tio n (m ) *4 0 v40 01 v4 002 v40 03 v40 04 v40 05 v40 06 v4 007v40 08 v40 09 v40 10 v4 011 v40 12 sea level geoelectric section along ves profile 4000-to-sea level 0 2000 4000 6000 8000 10000 12000 14000 16000 easting in m from 511911e -1 00 0 0 10 00 20 00 e le va tio n (m ) *4 0 v300 1 v3002 v300 3 v300 4 v300 5 v300 6 v300 7 v300 8 v300 9 v101 0 v3011 v0 12 v301 3 v3014 v 3015 v3 016 sea level geoelectric section along ves profile 3000-to-sea level 0 2000 4000 6000 8000 10000 12000 14000 16000 easting in m from 511911e -1 00 0 0 10 00 20 00 e le va tio n (m ) *4 0 v200 1 v200 2 v200 3 v200 4 v200 5 v200 6 v200 7 v200 8 v200 9 v201 0 v201 1 v201 2 v201 3 v201 4 v201 5 sea level geoelectric section along ves profile2000-to-sea level 0 2000 4000 6000 8000 10000 12000 14000 16000 easting in m from 511911e -1 00 0 0 10 00 20 00 e le va tio n (m ) *4 0 v100 1 v100 2 v100 3 v100 4 v100 5 v10 07 v100 8 v100 9 v101 0 v101 1 v101 2 v101 3 v101 4v101 5v101 6 sea level geoelectric section along ves profile1000-to-sea level figure 4. geoelectric resistivity sections relative to sea level. 4. conclusion and recommendation the present study shows that the water-table level generally ranges between depths of about 10 m to 20 m under the ground surface. the bedrock is characterized by low resistivity, ranging between 1 and 8 ohm.m. this range of resistivity values indicates that the lithological composition of the bedrock is mainly of clay. the interpreted structural regime helped to delineate the sea water intrusion as well as the fresh water catchment zones. the bedrock is overlain by two water bearing geo-electric layers with different degrees of water saturation. the first layer’s resistivity ranges between 8 and 25 ohm.m, representing sands and gravels saturated with water. the significant water accumulations are observed as thicker zones along the extension of this layer. the conducted study defined four main fresh water occurrence zones with average thickness up to 10 m (fwo1, fwo2, fwo3, fwo5) for abundant groundwater supply. more detailed study is recommended to be conducted at these zones before drilling. the statistical approach shows that it was an appropriate method for interpreting the resistivity data in this study. hence, the methodology can be generalized and it is advised that it be applied in such coastal plain environment studies. mansour a. al-garni and hamdy i.e. hassanein 38 0 2000 4000 6000 8000 10000 12000 14000 16000 eastern in m from 511911e utm 0 20 00 40 00 60 00 80 00 10 00 0 n or th in g in m fr om 2 33 99 33 n u t m depth relative to sea level 2 4 6 8 10 re si st iv ity in o hm .m 20 ves sites sz4 sz2 sz3 sz5 sz4 sz1 relatively high salinity zone sz1 a 0 2000 4000 6000 8000 10000 12000 14000 eastern in m from 511911e utm 0 20 00 40 00 60 00 80 00 10 00 0 n or th in g in m fr om 2 33 99 33 n u t m layer 2 depth contoures from sea level in m 2 4 6 8 10 12 14 16 18 20 30 60 100 200 300 600 900 1000 2000 re si st iv ity in o hm .m z2 z1 z3 z1 z5 z4 20 subsurface water channels ground water occurencesz2 legend b 0 2000 4000 6000 8000 10000 12000 14000 eastern in m from 511911e utm 0 20 00 40 00 60 00 80 00 10 00 0 n or th in g in m fr om 2 33 99 33 n u t m calculated thickness of layer no.2 2 4 6 8 10 12 14 16 18 20 30 60 100 200 300 600 900 1000 2000 re si st iv ity in o hm .m z2 z3 z1 z5z4 20 z2 ground water occurences legend c figure 5. the depth contour map of the upper surface of the interpreted sgl no.1 (a), the depth contour map of the interpreted sgl no. 2 (b), and thickness contour map of layer no. 2, showing zones of water of relatively good quality (c). study of ground water potentiality and sea water intrusion 39 0 2000 4000 6000 8000 10000 12000 14000 16000 easting from ref.point 511951m e 0 20 00 40 00 60 00 80 00 10 00 0 12 00 0 14 00 0 n or th in g fro m re f. po in t 2 44 99 33 m e 1 1 1 1 1 1 111 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11111111 1 11 1 1 1 11111111 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 f1 f2 f3 f4 f5f6 f7 sea water intrusion(saline water) s w i sca fwo-4 fwo-2 salty clay acumulations fresh water occurrences 1 2 layer 1 distribution under the study area resistivity < 8 ohm.m layer 2 distribution under the study area resistivity range=(8-25) swi fwo sca fwo-3 fwo-1 fwo-5 inferred fault faultf1f1 figure 6. interpretation results of wadi thuwal area. 5. acknowledgment the authors are greatly thankful to the king abdulaziz city for science and technology (kacst) for supporting this study at-26-82. the authors would like to express their sincere thanks to the editors and the anonymous reviewers, for the thorough review that highly improved the original manuscript. 6. references abdulwahid, m. (unpublished data), geology and structural framework of harrat thuwal, north of jeddah, saudi arabia. al-garni, m.a. 1996. direct current resistivity investigation of groundwater in the lower mesilla valley, new mexico and texas: ms thesis, colorado school of mines, 120 p. al-garni, m.a., el-behiry, m.g, gobashy, m.m, hassanein, h.i., and el-kaliouby, h.m. 2009. geophysical studies to assess groundwater potentiality and quality at wadi thuwal area, north of jedda, ksa. king abdulaziz city for science and technology, project no. at-26-82, p. 394. choudhury, k., saha, d.k., and chakraborty, p. 2001. geophysical study for saline water intrusion in a coastal alluvial terrain. j. apllied geophy., 46: 189-200. clark, p. and evans f. 1954. distance to nearest neighbor as a measure of spatial relationships in populations. ecology, 35: 445-453. cressie, n. a. c. 1991. statistics for spatial data. john wiley & sons inc., new york. mansour a. al-garni and hamdy i.e. hassanein 40 el-waheidi, m.m., merlanti, f., and pavan, m. 1992. geoelectrical resistivity survey of the central part of azraq plain (jordan) for indentifying saltwater/freshwater interface. j. applied geophy., 29: 125133. kessels, w., flentgeh, i., kolditz, h. 1985. dc geoelectric sounding to determine water content in the salt mine asse (frg). geophysical prospecting, 33: 456-446. king, ronald s. and bryant julstrom. 1982. applied statistics using the computer. alfred publishing company, sherman oaks, california. montgomery, d.c. and runger g.c. 1994. applied statistics and probability for engineers. john wiley & sons inc., new york. zohdy. a.a.r. 1989. a new method for the automatic interpretation of schlumberger and wenner sounding curves. geophysics, 54: 245-253. received 25 may 2009 accepted 21 april 2010 squ journal for science, 2015, 20(1), 1-10 © 2015 sultan qaboos university 1 histopathological and ultrastructural changes in the liver and gills of the killifish aphanius dispar (cyprinodontidae) exposed to aflatoxin b1 horiya h. al-azri, taher ba-omar*, abdulkadir elshafie and michael j. barry department of biology, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: taher@squ.edu.om. abstract: aflatoxin b1 (afb1) is a mycotoxin which can cause serious toxicity to animals and humans. the aim of this study was to investigate the effects of afb1 in aphanius dispar fish and measure residues in tissues after in vivo exposure. aphanius dispar were fed diets containing 50, 100, 150 and 200 µg afb1/kg for 10, 20 and 30 days. at the end of the experiment, the liver and gills were dissected out and processed for light and electron microscopy. during the experiment, no external changes or unusual behavior were observed in the fish. histopathological and ultrastructural changes in liver appeared under all four treatments: 50, 100, 150 and 200 µg afb1/kg. gill tissues were affected at high doses of 100,150 and 200 µg afb1/kg. accumulation of afb1 residues in liver and gill tissues was found to be related to a dose and duration of exposure. keywords: afb1; aphanius dispar; liver; gills; fish; ultrastructure. afb1االفالتىكسن انتغيرات انمرضية وانتركيبية نكبذ وخياشيم سمك انصذ بعذ تعرضها نسميات باري مايكمو انعزرية ، طاهر باعمر ، عبذانقادر انشفيع هالل حىرية خطٍشة ىيحٍىاّاث واىبشش. حهذف هزٓ اىذساست ىيخحقق ٍِ اَثاس ىًسَحذ اىسَىً اىفطشٌت اىخً ٌَنِ أُ حسبب أ( هىafb1فالحىمسٍِ )أ :مهخص عيى سَل اىصذ وقٍاس اىسَىً فً األّسدت ورىل بعذ حعشض اىسَنت ىهزٓ اىسٍَاث . حٌ حغزٌت سَل اىصذ بىخباث غزائٍت ٍخفاوة afb1اىسٍَت ىـ ٌىٍا. وفً ّهاٌت اىخدشبت، حٌ قخو اىسَل وحٌ 30، 20، 10/ مغ ىَذة afb1ٍٍنشوغشاً 200و 100، 100، 00واىخً ححخىي عيى اىخشامٍز ّسدت اىنبذ واىخٍاشٌٍ باسخخذاً اىَدهش اىضىئً واىَدهش اإلىنخشوًّ. وأثْاء اىقٍاً أذ واىخٍاشٌٍ ىحفظها فً ٍىاد حافظت ورىل ىذساست اسخخشاج اىنب ز خشامٍباىخدشبت ىٌ ٌالحظ أي حغٍٍشاث خاسخٍت أو سيىك غٍش عادي عيى األسَاك. وحظهش اىْخائح حغٍشاث حششٌحٍت ٍشضٍت وحشمٍبٍت فً اىنبذ فً اى / مدٌ. مَا afb1ٍٍنشوغشاً 200، 100، 100مبش اىخأثٍشاث عْذ حْاوه خشعاث أ/ مغ. وماّج afb1ٍٍنشوغشاً 200، 100، 100، 00 فً أّسدت اىنبذ واىخٍاشٌٍ واىخً حعخَذ عيى حدٌ اىدشعت وٍذة اىخعشض ىيسٍَاث. afb1حٌ اىعثىس عيى حشامٌ سَىً اىخشمٍب اىذقٍق،سَل اىصذ، اىنبذ، اىخٍاشٌٍ، اىسَل ،afb1 سٍَاث :كهمات مفتاحية 1. introduction flatoxins are naturally occurring mycotoxins that are produced as secondary metabolites by several fungi, mainly aspergillus flavus and aspergillus parasiticus. aflatoxin b1 is the most prevalent and biologically active aflatoxin and is strongly carcinogenic, mutagenic and teratogenic in humans and animals [1, 2]. although aflatoxins have been detected in food products worldwide, they are much more prevalent in regions with hot and humid climates that favor the growth of the two aspergillus species. commercial aquaculture is a relatively recent development in the middle-east, but may eventually form an important source of economic activity in the region. the climate of northern oman is hot and humid and provides an ideal environment for production of aflatoxins. previous studies have detected significant levels of aflatoxins or aspergillus species in local black tea, spices and herbal medicine [3-5]. the toxicity of aflatoxins has been measured in rainbow trout [6], sea bass [7], coho salmon [8], nile tilapia [9] and channel catfish [10]; however, most studies have focused on its effects on growth or tumour formation. susceptibility to the toxic effects of aflatoxins varies widely between species. the effects are influenced by species, sex, age, dose level, period of exposure to the toxin, nutritional status and effect of other chemicals [11]. a http://en.wikipedia.org/wiki/mycotoxin http://en.wikipedia.org/wiki/aspergillus_flavus http://en.wikipedia.org/wiki/aspergillus_parasiticus horiya h. al-azri et al. 2 the killifish, aphanius dispar (rüppell, 1828) (teleostei, cyprinodontidae) is a common fish in oman and has been used as a model organism for toxicity testing [12,13]. the first signs of toxicological damage often appear at the level of the cell, and structural changes can act as bioindicators of harm. afb1 is bioactivated by the cytochrome p450 system form [ 3 h]afb1-dna adduct(s) [14]. the highest concentrations of cytochrome p450 occur in the liver and this is commonly reported as a major site of aflatoxin toxicity. the gills are in close contact with both the external environment and the blood system, and are important organs for respiration, osmoregulation, acid-base balance and nitrogenous waste excretion in aquatic animals. however, little is known about the impact of aflatoxins on gill structures. the aims of this study were to investigate the histopathological and ultrastructural changes in liver and gills of aphanius dispar and quantify afb1 residues in these tissues. 2. materials and methods aphanius dispar (0.6-3.9 g; 2-6 cm) were collected from a spring-fed channel and acclimatized to laboratory conditions for at least ten days before the start of the experiments. the fish were maintained in aerated glass aquaria (50 x 30 x 25 cm) filled with 17 liters of de-chlorinated tap water, with a photoperiod of 12 hours light to 12 hours dark. every 48 hours 50-70% of the aquarium water was changed while the ph and ammonia of the water were measured weekly. fish were fed once a day with a commercial fish feed, tetra min ® (tetra gmbh. d49304, germany). a stock solution of afb1 was prepared by dissolving 2 mg of 99.9% pure afb1 (sigma, usa) in 10 ml of 30% analytical grade ethanol. test solutions were prepared using a dilution of the stock in 30% ethanol. four different concentrations of afb1 were prepared (50, 100, 150 and 200 µg afb1/kg). one hundred fish, divided into five groups of 20 fish and placed into separate aquaria under a fume hood, were fed once a day with the aflatoxin contaminated food (50, 100, 150 and 200 µg afb1/kg). the control was fed once a day with feed mixed with ethanol free of afb1. on days 10, 20 and 30 after the start of the experiment, five fish were randomly collected from each tank. the fish were anaesthetized by placing them in chilled water and their weight and length were measured. the liver and gills were then dissected out. portions of liver and gills were immediately fixed in 10% buffered formalin and processed for light microscopy. sections were stained with hematoxylin and eosin (h & e). small portions of the liver and gills were also fixed in 2.5% karnovsky fixative at 4 0 c for 4 h and then washed twice with sodium cacodylate buffer at a ph of 7.4 and finally double fixed with osmium tetroxide. to process the tissues for transmission electron microscopy, semi-thin and ultra-thin sections were cut using an ultra-microtome. the semithin sections were stained with toluidine blue and the ultra-thin sections were stained with uranyl acetate and lead citrate and were observed under a jeol jem-1230 transmission electron microscope operating at 80 kv. afb1 residues in the liver and gills were also measured on days 10, 20 and 30. fish from each treatment were removed and anaesthetized, and the liver and gill tissue were removed and weighed. residues were measured using a commercial test kit (vicam™ aflatest, usa). 3. results during the experiment, water parameters remained within acceptable limits (temp: 27± 1 0 c; ammonia: 0.009±0.02 mg/l; ph: 6-8). there was no mortality and fish behaved normally. light microscopy (lm) liver the livers of control fish had polyhedral hepatocytes, with homogenous cytoplasm and large spherical centrally located nuclei (figure 1a). the hepatocytes contained glycogen granules and few lipid droplets of various sizes. on day 10, the livers of fish treated with 50 and 100 µg afb1/kg were normal. on days 20 and 30 fish treated with 50 µg afb1/kg showed hepatocellular vacuolation, where the vacuoles appear as sharply rounded spaces with distinct outlines and displace the nucleus to the periphery (figure 1b). these vacuoles were assumed to be fat droplets (figure 1c). on days 10, 20 and 30 fish treated with 100, 150 and 200 µg afb1/kg displayed hepatocellular degeneration especially at a concentration of 200 µg afb1/kg, fish treated with which exhibited diffuse advanced fatty change where most hepatocytes had a signet-ring appearance with formation of fat cysts on the 30 th day of exposure (figure 1d-f). gills the gills of control fish had distinct primary and secondary lamellae (figure 2a). the region between the secondary lamellae and the primary lamellae was lined with stratified squamous epithelium. this region contained the mucous cells and chloride cells. on day 10, the gills of fish treated with 100, 150 and 200 µg afb1/kg showed mild epithelial hyperplasia with lamellar fusion, and mild desquamation of secondary lamellae (figure 2b). on day 20, fish treated with 100, 150 and 200 µg afb1/kg showed mucous degeneration characterized by goblet cell histopathological and ultrastructural changes in the liver gills 3 hyperplasia of the basal epithelial cells (figure 2c). on day 30, fish treated with 100, 150 and 200 µg afb1/kg showed multifocal lamellar necrosis (figure 2d). figure 1. light micrographs of h&e stain of a. dispar liver showing: a) control liver; b) liver of fish treated with 50 µg afb1/kg for 20 days; c) liver of fish treated with 50 µg afb1/kg for 30 days. sinusoid (s); lipid (l); glycogen (g); d) liver of fish treated with 200 µg afb1/kg for 10 days ; e) liver of fish treated with 200 µg afb1/kg for 20 days; f) liver of fish treated with 200 µg afb1/kg for 30 days x400. figure 2. light micrographs of gills showing: a) gills of control fish; b) gills of fish treated with 100 µg afb1/kg for 10 days. a c s l g a c b d e f b cc cc cc pi sl sl 20 µm p a horiya h. al-azri et al. 4 cm l l l rer g n figure 2. light micrographs of gills showing: c) gills of fish treated with 150 µg afb1/kg for 20 days; d) gills of fish treated with 200 µg afb1/kg for 30 days. primary lamella (pl); secondary lamella (sl) chloride cell (cc); pillar cell (p); lamellar fusion (brackets); desquamation (white arrow); hyperplasia (black arrows); hypertrophy of chloride cells (stars); necrosis (thick black arrows ); a (toluidine blue stain), b-d (h&e stain), x400. transmission electron microscopy (tem) liver hepatocytes of the control fish showed normal cytoplasmic organelles such as rough endoplasmic reticulum (rer) and mitochondria, and were enriched with glycogen (figure 3). rer was arranged near the nucleus in 7-10 parallel arrays next to the plasmatic membrane. mitochondria appeared as spherical or elongated profiles with numerous cristae and were often surrounded by rer (figure 3). figure 3. electron micrographs of the control fish liver showing: cell membrane (cm); lipid droplet (l); nucleus (n); nucleolus (nu); rough endoplasmic reticulum (rer); mitochondria (m) and glycogen (g). on day 10, fish treated with concentrations ≥ 50 µg abf1/kg showed an increase in the number of lipid droplets and lysosomes, irregular shaped nuclei, vacuolation in the cytoplasm and swelling of the mitochondria (figures 4, 5). more damage was seen on days 20 and 30, including an increase and accumulation of lipid droplets, condensation of chromatin, an increase of vacuolation in the cytoplasm, reduced amounts of glycogen, loss of the cellular membrane, loss of mitochondrial cristae, and disarrangement and destruction of rough endoplasmic reticulum (rer) (figure 6). c d histopathological and ultrastructural changes in the liver gills 5 l l l figure 4. electron micrographs of fish liver: a) liver of fish treated with 50 µg afb1/kg for 20 days; b) liver of fish treated with 70 µg afb1/kg for 20 days: b) mitochondria (m); lysosome (ly); lipid droplet (l). figure 5. electron micrographs of fish liver: a) liver of fish treated with 70 µg afb1/kg for 30 days; b) liver of fish treated with 150 µg afb1/kg for 10 days, mitochondria (m); lysosome (ly); lipid droplet (l); cytoplasmic vacuoles (arrows) and nucleus (n). gills four different cell types could be differentiated in the primary lamellae; basal cells, chloride cells, accessory cells, and pavement cells (pvc) (figure 7). the chloride cells were often distributed in the interlamellar region and were characterized by abundant mitochondria (figure 7a). accessory cells (filament-rich cells) are flat, found between neighboring chloride cells, and had denser cytoplasm than chloride cells with few mitochondria. secondary lamellae consisted of two epithelial cell layers separated from the pillar cells by a basement membrane. in addition, the pvc of the secondary lamellae were polygonal in shape, and displayed smooth surfaces with only long micro-ridges running parallel to the cells (figure 7b ). after ten days, fish treated at 100, 150 and 200 µg afb1/kg, showed changes including irregular shaped nuclei of the chloride cells, chromatin condensation of nuclei and increased size of goblet cells (figure 8a). by day 20, there were signs of damage to the cellular membrane and cytoplasmic vacuoles in many chloride cells (figure 8b). on day 30, severe cellular damage, dilation of primary lamellae, degeneration (cell death) of epithelial cells in primary and secondary lamellae, hypertrophy of chloride cells, and the appearance of some chloride cells with degenerative nucleus and large cytoplasmic vacuolation were apparent (figure 9). n n rer l b a horiya h. al-azri et al. 6 figure 6. electron micrographs of fish liver treated with 200 µg afb1/kg for 30 days (a&b) showing: mitochondria (m); rough endoplasmic reticulum (rer); lipid droplet (l). figure 7. electron micrographs of the gill of the control (a&b) showing: a) inter lamellar space; b) secondary lamellae; chloride cell (cc); pavement cell (pvc); pillar cell (p); nucleus (n); mitochondria (black arrows); microridges (white arrows). figure 8. electron micrographs of the gill. a) gill of fish treated with 100 µg afb1/kg for 10 days; b) gill of fish treated with 100 µg afb1/kg for 20 days; chloride cell (cc); nucleus (n); microridges (arrows); vacuoles (stars). l l l rer m l b a a b 2 µm n b a n n cc a histopathological and ultrastructural changes in the liver gills 7 figure 9. electron micrographs of the gill of fish treated with 200 µg afb1/kg for 30 days (a&b); primary lamellae (pl); secondary lamellae (sl); chloride cell (cc); cell death (arrows). aflatoxin b1 residues accumulation of afb1 following dietary exposure in a. dispar liver and gills is summarized in figure 10. no afb1 was detected in the liver and gills of the control fish. in the fish treated with 50 µg afb1/kg, afb1 residues were not detected on days 10 and 20. however, afb1 residues were detected on day 30 at this dosage. in fish treated with 100, 150 and 200 µg afb1/kg, afb1 residues in liver and gill tissues increased as the exposure was prolonged and the concentration of afb1 in the feed increased, with higher concentrations being detected on day 30 than on day 20. figure 10. afb1 residues in a. dispar in day 10, 20 and 30 of the exposure; a) afb1 residues in liver tissues; b) afb1 residues in gill tissues. (control = 0 ppb). 4. discussion exposure to aflatoxin is often associated with acute mortality in fish. cagauan et al. [15] reported that tilapia (oreochromis mossambicus) exposed to dosages of 53.02 115.34 afb1 µg/kg of feed had 67% mortality in 90 days. anh et al. [9] found that tilapia fed with 10,000 afb1µg/kg for 8 weeks had increased mortality. this notwithstanding, in the present study no mortality was reported, even though we used concentrations similar to cagauan et al. [15]. however, presumably mortality could occur, if the exposure time lasted for a longer period. the liver is the primary site of aflatoxin bioactivation and is normally the main site of toxicity [8]. we found no effect of aflatoxin after 30 days on liver histopathology at 50 g afb1/kg. anh et al. [9] showed no effect on nile tilapia (oreochromis niloticus) at concentrations up to 250 µg/kg, and [16] showed no effect on black tiger shrimp (penaeus monodon) fed with aflatoxin dosages up to 100 g/kg. there is some evidence that damage will cc cc pl sl a b 0 0.5 1 1.5 2 2.5 3 3.5 0 30 50 70 100 150 200 a f b 1 r e si d u e s p p b afb1 conc. in feed ppb afb1 residues in gills 10 20 30 days 0 0.5 1 1.5 2 2.5 3 3.5 0 30 50 70 100 150 200 a f b 1 r e si d u e s p p b afb1 conc. in feed ppb afb1 residues in liver 10 20 30 days b a horiya h. al-azri et al. 8 occur following long-term chronic exposure, as [17] found liver tumors in rainbow trout fed with 0.5 µg afb1/kg for 6 months. stored glycogen was the most prominent feature in the hepatocytes of control fish. the concentration of glycogen decreased with both increasing time and increasing concentration dosages. decreasing glycogen storage was also reported by [18] for labeo calbasu and also [19] for rainbow trout (oncorhynchus mykiss). fatmi and ruby [18] proposed that aflatoxin increased the energy demands on the fish, thus requiring the utilization of stored glycogen. the reduction of hepatic glycogen stores may also arise from either an inhibition of glycogenic enzymes, an inhibition of glyconeogenesis, a decrease in glucose transport into hepatocytes, or an increase in the activity of enzymes metabolizing glycogen precursors [20, 21]. in the present study, the number and size of lipid droplets in the hepatocytes of treated fish liver increased as afb1 concentration increased. hussein and brasel, [22] indicated that the increase in lipids is due to the reduction of enzyme synthesis and activity. chou and marth [23] suggested that the increase observed in the hepatic lipid production might be due to reduced oxidation of fats or increased lipid synthesis. moreover, the present study showed damage to mitochondria which was also observed by [24]. damage to mitochondria and the disappearance of cristae may result in decreased oxidation, which can cause accumulation of lipids in the liver [25]. breakage of cell membranes, which would affect the normal cell functions and structure, was also seen in the present study. rough endoplasmic reticulum (rer) showed some damage and loss of its arrangement in some areas. sahoo et al. [26] reported that afb1 disrupts rer, reduces rna synthesis, the attachment of polyribosomes to rer, and damages ribosomes, thus severely affecting protein synthesis. nuclear damage, including nuclear shrinkage, irregularity and condensation, was obvious. afb1 interacts with the complex structure of chromatins, by forming dna-afb1 adducts [2]. these changes may damage the normal functioning of the nuclei, and affect dna and rna metabolism. the gills are among the most vulnerable structures of the teleost fish because of their external location and intimate contact with water. they are liable to damage by any irritant materials whether dissolved or suspended in the water [27]. they are directly exposed to toxins occurring in the external environment which often cause pathological changes in fish [28]. at aflatoxin concentrations ≥100 g, we observed hyperplasia of the epithelial layer of primary lamellae and fusion of secondary lamellae, desquamation of epithelial cells, and cellular degeneration which resulted in necrosis of the gill epithelial tissues by day 30 of the experiment. changes in the present study were in agreement with the observation of [26] on labeo rohita fish exposed to afb1. histopathological changes of the gills may result in hypoxia, respiratory failure, and problems with ionic and acidbase balance [29]. ferguson [30] reported that the fusion and hyperplasia of gill lamellae may be induced by the effect of the toxin which alters glycoprotein in the mucus covering of the cells, thus affecting the negative charges of the epithelium and causing adhesion to the adjacent lamellae. changes in the epithelial cells, such as hyperplasia and the fusion of some secondary lamellae, are examples of defense mechanisms which increase the distance between the external environment and the blood and thus serve as a barrier to the entrance of contaminants [31]. as a consequence of the increased distance between water and blood, the oxygen uptake is impaired [32]. another finding in this study was chloride cell proliferation in the gills of fish treated with 100, 150 and 200 µg afb1/kg. pawert el al. [33] explained that the increased number of chloride cells may be due to increased secretion, or to adaptive processes to a different ionic environment. in the present study, the histopathological changes in the chloride cells may indicate osmoregulatory dysfunctioning. exposure to aflatoxin also increased mucus secretion by the gills, possibly leading to impaired gas exchange [33]. microridges are known to have a mucus anchoring function that protects the epithelium against microbial or solid agents in suspension and are a mucus retention structure in gill epithelium [13]. they increase the surface area of the epithelial cells that are in contact with the external environment [34]. a number of studies have reported the detection of afb1 residues in the liver and muscles of fish, but there is no information on the accumulation of aflatoxin in gills. rajeev et al. [35] reported that afb1 accumulation in the liver and muscle tissues of hybrid sturgeon fish increased with increasing dietary levels of the toxin in experimental diets. in the present study, the amount of afb1 residues detected in liver tissues was lower than that detected in gills. one explanation is that the liver has the greatest concentrations of detoxifying enzymes, and that concentrations may therefore be lower in this organ. randall et al. [36] demonstrated that the gills can be a major route of uptake even for chemicals with low water solubility. 5. conclusion afb1 induced significant changes to the cellular organelles and architectures of major cell components. the histopathological changes and accumulation of afb1 in a. dispar tissues were dose and time dependent. the structural changes of the cell organelles of the liver and gills due to dietary afb1 exposure indicated a reduction in cell and tissue functionality, which could disrupt their metabolic and detoxification roles. the prolonged feeding of fish on low levels of dietary afb1 (50 µg afb1/kg) induced not only serious health problems in exposed fish that could result in economic losses for the fish industry, but also may represent a high risk to fish consumers through their residues in liver and gill tissues. histopathological and ultrastructural changes in the liver gills 9 references 1. iarc. some naturally occurring substances, food items and constituents, heterocyclic aromatic amines, and mycotoxins. iarc monographs evaluation of carcinogenic risks in humans. international agency for research on cancer world health organization, lyon, france. 1993, 56, 489-521. 2. santacroce, m.p., conversano, m.c., casalino, e., lia, o., zizzadoro, c. centoducati, g. and crescenzo, g. aflatoxins in aquatic species: metabolism, toxicity and perspectives. revs. in fish biol. and fisheries, 2007, 18(1), 99-130. 3. elshafie, a.e., al-lawatia, t., and al-bahry, s.n. fungi associated with black tea and tea quality in the sultanate of oman. mycopathologia, 1999, 145(2), 89-93. 4. elshafie, a.e., al-rashdi, t.a., al-bahry, s.n and bakheit, c.s. fungi and aflatoxins associated with spices in the sulatanate of oman. mycopathologia, 2002, 155, 155-160. 5. elshafie, a.e, al siyabi, f.m., salih, f.m., ba omar, t., al bahry, s.n. and al kindi, s. the mycobiota of herbal drug plants in oman and possible decontamination by gamma radiation. phytopathologia mediterranea, 2003, 42(2), 149-154. 6. williams, d.e., orner, g., willard, k.d., tilton, s., hendricks., j.d., pereira, c., benninghoff, a.d. and bailey, g.s. rainbow trout (oncorhynchus mykiss) and ultra-low dose cancer studies. comparative biochem. physiol. part c: toxicol. & pharmacol., 2009, 149(2), 175-181. 7. el-sayed, y.s and khalil, r.h. toxicity, niochemical effects and residue of aflatoxin b1 in marine waterreared sea bass (dicentrarchus labrax l.). food and chemical toxicol., 2009, 47(7), 1606-1609. 8. hendricks, j.d. carcinogenicity of aflatoxins in nonmammalian organisms. in: eaton, d.l., groopman, j.d. 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carboni*, e. al-abry and s. arafin department of physics, college of science, sultan qaboos university, p.o.box 36, al khod 123, muscat, sultanate of oman, *email: carlo@squ.edu.om. اتجاه مغناطيسية مواد األنثنايدس كارلو كاربوني ، إيمان العبري و سيد العارفين االنثنايدس عند درجة حرارة صفر وإعتماده على التفاعالت الكهربائية و أيوناتتم فحص إتجاه مغناطيسة :خالصة تغير نسبة التفاعالتللمغناطيسية واعتمادها على وجدت االشكال التي توضح اإلتجاه8 الى 3 من jلكل قيم . المغناطيسية تم كما.لشدة المجال البلوري والتي تمثل النسبة بين الحد الرابع والحد السادس x و النسبية r المغناطيسية للكهربية االلتفاء و فقد وجد أن تغير االتجاه يتم تدريجيا عند بعض خطوط . للمغناطيسيةطوط تالقي اإلتجهاهات المتعدده فحص خ تم مشاهدة نوعين من السلوك عند القيم الحرجة . x و r حرجة للمتغيراتيكون التغير فجائيا عند قيم االخر عند البعض وهناك حدود عند القيم الحرجة يكون فيها اتجاه المغناطيسية في مستوى وفي جميع االتجاهات والنوع x و rللمتغيرات وفي الحالة . ن اتجاه المغناطيسية ممثل في اتجاهين حسب االتجاهين للتركيب البلورياالخر يكون لبعض الحدود ويكو . األخيرة تكون منطقة قريبة من الحد يكون فيها اتجاه المغناطيسية غير مستقر abstract: the zero temperature direction of spontaneous magnetisation of lanthanide ions at a site of cubic symmetry is investigated as a function of the electrostatic and magnetic interactions. for all the values of j between j = 3 and j = 8, two-dimensional diagrams giving the orientation of spontaneous magnetisation are obtained as a function of the parameters r representing the relative strength of the magnetic to electrostatic interaction and the parameter x representing the relative strength of the fourth to the sixth order terms in the crystal field. the boundaries between regions of the parameter space with different directions of spontaneous magnetisation are investigated. it is found that at some boundaries there is a gradual rotation of the direction of spontaneous magnetisation and that at other boundaries there is a sudden change of orientation of spontaneous magnetisation at a critical value of the (r,x) parameters. two types of behaviour are observed when there is a critical value of (r,x). there are boundaries where there is at the critical value a degenerate plane in which all the orientations can be direction of spontaneous magnetisation and some boundaries where two different principal crystallographic axes can be direction of spontaneous magnetisation at the critical value. in the latter case there is a region near the boundary where an unstable equilibrium orientation for the magnetisation can be found. c. carboni, e. al-abry and s. arafin 54 keywords: spin reorientation, crystal field, yxho1-xco2, gdxho1-xco2, gdxyyho1-xyco2hoco2 . 1. introduction he direction of spontaneous magnetisation in magnetic rare-earth compounds is the result of a delicate balance between the electrostatic and magnetic interactions experienced by the lanthanide ion. the electrostatic interaction is due to the interaction of the localised 4f electrons of the lanthanide ion with the electric field gradients set up by the lattice at the ion’s site. the magnetic interactions can arise from dipoledipole or exchange interactions. these interactions between the ion and its surrounding in the solid are small compared to the intra-ionic interactions and can be regarded a perturbation on the free ion states (morrisson and leavitt, 1982). the free ion states are almost pure russell-saunders states; l, s and j are good quantum numbers and remain good quantum numbers in the solid. the effect of the interactions in the solid is to split the (2j+ 1)fold degenerate free-ion states without causing significant admixture of the sates. because of the large spin-orbit interaction (1000k or more) only the ground manifold is significantly populated at room temperature or below therefore all the populated states have the same l, s and j and the states of the ion in the solid are expressed as linear combinations of the | mj> states. ∑ += −= = ji ji ii mae (1) the omitted l, s and j labels have the values given by hund’s rule for the ground manifold. the magnetic properties of a compound and in particular its direction of spontaneous magnetisation are determined by the composition of the low-lying states in the ground manifold. for each state the direction of spontaneous magnetisation is the orientation of < j> for which the state has the lowest energy. different states may have different directions of spontaneous magnetisation. at any given temperature the direction of spontaneous magnetisation of a compound is the thermal average over the populated states. when the temperature is changed, the concomitant change in the population of the states may give rise to the “spin reorientations” observed in several rare-earth compounds. in the present paper we consider a lanthanide ion at a site of cubic symmetry in a compound at sufficiently low temperature so that only the ground state of the ground manifold the ion is significantly populated. this zero temperature assumption is justified because it is valid for most rare earth compounds at liquid helium temperatures. the evolution of the direction of spontaneous magnetisation at zero temperature will be investigated as a function of the relative strengths of the interactions in the solid. following mccausland and mackenzie (1980) the magnetic interactions will be treated in a rather cavalier manner and will be described by a single isotropic vector parameter. with this simplification it is possible to construct, following the work of lea et al. (1962), a dimensionless two-parameters hamiltonian to obtain the orientation of spontaneous magnetisation of the lanthanide ion. the direction of spontaneous magnetisation can then be presented on a simple twodimension diagram as a function of the two parameters. 2. theory the theoretical approach to write the perturbation hamiltonian for the ion follows lea, leask and wolf (1962), mccausland and mackenzie (1980) and bunbury et al. (1995). the ground manifold is assumed to be a pure russell-saunders state and the interactions with the solid are treated as a perturbation in first order. the small amount of intermediate coupling and j-mixing is ignored [4, 5] 2.1 the electronic hamiltonian the strengths of the crystal-field and the magnetic interactions of the ion in the solid are of the same order and the operators describing these two interactions do not commute. the ion in the solid is described by the combined effective electronic hamiltonian: t the direction of spontaneous magnetisation of lanthanide ions 55 h el = h cf + h z (2) where hcf, the crystal-field hamiltonian, stands for the electrostatic interaction and hz stands for all the magnetic interactions. following lea et al. (1962), the crystal field hamiltonian at the site of cubic symmetry is written: )21)(1()5(),( 46 0 6 6 4 4 0 4 4 cf oooo −−++= xf w f wx xwh (3) where the mno are stevens operator equivalents [6]. w and x are the phenomenological crystal field parameters; the parameter w gives the strength of the crystal field and the dimensionless parameter x gives the relative strength of the fourth-order to the sixth-order term. f4 and f6 are numerical constants tabulated by lea et al. (1962) . for completeness the operator equivalents and the values of the coefficients f4 and f6 for the relevant values of j are given in appendix 1. as already mentioned all the magnetic interactions are considered to be isotropic and therefore, following mccausland and mackenzie (1980) can be represented by a vector α. the magnetic interactions are thus described by the hamiltonian. j⋅= αzh (4) it is enphasised that the assumptions made when writing equation 4 are not necessarily valid for all real compounds. in particular in the presence of anisotropy in the exchange interaction or in magneto-electric materials one will have to introduce extra terms in the magnetic interaction to describe the anisotropy or the coupling to the electrostatic terms. such refinements will inevitably introduce extra parameters in the hamiltonian and therefore make the outcome of this investigation rather complex and difficult to represent on simple two-dimension diagrams. however, one can reasonably expect that apart from some possible extreme exceptions the very much simplified expression of the magnetic interactions used here will give a description that is not too far from the reality. therefore, for the general case of well-behaved materials the interactions of the 4-f shell are described by the hamiltonian joooo ⋅+−−++= α)21)(1()5(),( 4606 6 4 4 0 4 4 el xf w f wx xwh (5) since we are concerned with the direction of spontaneous magnetisation as a function of the relative strengths of the crystal-field and magnetic interactions it is preferable to consider the dimensionless hamiltonian ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ −−+++⋅= )21)(1( 1 )5( 46 0 6 6 4 4 0 4 4 oooojr x ff x elh (6) where the parameter r is a vector with the same direction as α and magnitude )w/( α . | r| is the relative strength of the magnetic to the electrostatic interaction. there are only two parameters, | r| and x, in the hamiltonian. the direction of spontaneous magnetisation can therefore be readily mapped on a two-dimensional diagram as a function of | r| and x. 2.2 the direction of spontaneous magnetisation to determine the direction of spontaneous magnetisation for a given value of | r| and x, one has to find the orientation of r that yields the lowest energy for the ground state of the electronic hamiltonian subjected to the condition that the computed orientation of j is parallel to the input orientation of r. the later condition is stating that the spontaneous magnetisation is parallel to the local field at the ion’s site. we note in passing that j will be parallel to r in the case of pure compounds. in the case of an impurity ion in a host with competing magnetic anisotropy j is not necessarily parallel to r; such cases are not considered in the present work. in the remainder of this paper, the orientations of r where j is found to be parallel to r will be referred to as self-consistent orientations. by symmetry, the principal crystallographic orientations, < 110>, < 100> and < 111> are selfconsistent orientations. however, these orientations are not necessarily the only ones or do any of them correspond necessarily to the lowest energy. c. carboni, e. al-abry and s. arafin 56 figure 1. the convention and notation used for the computation. a: the x, y and z axis are taken along the edges of the cubic unit cell. by symmetry only the directions within the hashed tetrahedron need to be considered. b: the polar angles of the input vector r are called θ and φ and the computed polar angles of j are labelled θ’ and φ’. 3. computation strategy a pedestrian approach to mapping the magnetic orientation phase diagram as a function of | r| and x would be to input systematically values of x and | r| and to let the software find which one of the self-consistent orientations has the lowest energy for each (r,x). however, a rough estimate of the computer time required for this approach is prohibitively too long. a more computer-time efficient approach had to be used for the present work. in this paragraph we give a description of the approach taken for the computation and define the notation used. the reference frame to write the hamiltonian is defined as shown in figure 1-a. the x, y and z axis are taken along the edges of the cubic unit cell. the quantisation axis is the z axis. because of symmetry only the direction within the tetrahedron delimited by the four-fold (< 100> ) the two-fold (< 110> ) and the three-fold (< 111> ) directions as shown in figure 1-a is considered. the polar angles of the input vector r are called θ and φ and the computed polar angles of j are labelled θ’ and φ’ as illustrated in figure 1-b the self-consistent condition is obtained when (θ = θ’) and (φ = φ’). the large amount of experimental data available in the literature shows that apart from few exceptions the direction of spontaneous magnetisation at low temperature is along one of the symmetry axis. it is therefore reasonable to assume that the direction of spontaneous magnetisation is along one of the symmetry axis except in the regions of the {r,x} parameter space near the boundaries between regions with different orientations of spontaneous magnetisation. the computation was performed in two steps. in the first step a diagram indicating, for each value of (r,x), the crystallographic orientation along which the magnetisation has the lowest energy was obtained. in the second step a refined investigation of the regions of the {r,x} parameter space in the vicinity of the boundaries between the regions in the diagrams obtained in the first step was carried out. x z <100> y <110> <111> a x z y θ φ r θ’ φ’ j b the direction of spontaneous magnetisation of lanthanide ions 57 3.1 the magnetic orientation diagram in the first step, the value of x was scanned from –1 to + 1 in steps of 0.01 at fixed values of | r|. for each value of (x, | r| ) the energy of the ground state corresponding to r parallel to each of the three principal directions was computed. the software returned the orientation giving the lowest energy for the ground state. this orientation was taken as the direction of spontaneous magnetisation. the diagrams shown in figure a-1 to a-11 in appendix 2 for the different values of j were thus obtained. the range and increment steps for | r | were decided on a case-by-case basis for each value of j. in all cases for the upper bound we used realistic values observed experimentally which do not exceed 80 in ferromagnetic compounds such as the rfe2 compounds [7]. in most cases we present our computations with values of | r | less than 30. above this value nothing interesting has been observed. except in cases where the ground state in the absence of magnetic interactions is degenerate and contains a conjugate magnetic doublet in the limit very small | r| the value of < j> goes to zero and therefore the magnetic anisotropy becomes negligible; rounding errors occurring in the computation can lead to erroneous results. therefore, we do not report any computations with values of | r| less than 0.1. all the computations were done in double precision. 3.2 the boundaries in the second step we have investigated the boundaries between the regions of the {r,x} parameter space with different orientations of spontaneous magnetisation. there are two fundamentally different reasons why a change of direction of spontaneous magnetisation can occur. the first one is trivial and is observed if there is an energy level cross-over. in this case there is a change of ground state at the cross-over; if the two states involved have different orientations of spontaneous magnetisation there is an abrupt change of direction of spontaneous magnetisation at the cross-over. the second and more interesting situation is where the evolution of the components of the ground state as function of (r,x) yields a different stable orientation for j. for all the boundaries shown in figures a-1 to a-11 the evolution of the energy of the ground and first exited states across the boundary has been investigated at selected points. it has been found that there are no energy level cross-over at the transitions. the change in direction of spontaneous magnetization is in all cases due to a continuous evolution of the components of the ground state. in this case two types of behaviour can be expected at the boundaries. there could be a region where there is a continuous rotation of the direction of spontaneous magnetisation from one axis to the other or there could be a sudden jump from one orientation to the other at a critical value of (r,x). our work has shown that both types of behaviour are observed and that there are two possible ways in which the sudden reorientation can occur. the three types of reorientation will be discussed in more details in the next section. in order to minimize the amount of computer time required we have made the assumption that any interesting behaviour will be observed in the plane defined by the orientations on each side of the boundary under investigation. the computations were therefore restricted to those planes with only a few spot calculations outside the plane to ascertain the validity of the assumption. a systematic scans approach to the computation rather than a minimisation routine was used. for any given value of (r, x) near the boundary the polar angles θ and φ of r were scanned in steps of 0.1 degrees in the plane defined by the two orientations of interest. at each step the energy of the ground state and the polar angles θ’ and φ’ of the direction of j were calculated. the data was then analysed manually to find the self-consistent orientation with the lowest energy. 4. results and discussion the orientation diagram for the direction of spontaneous magnetisation was mapped for the values of j between 3 and 8 in steps of ½. the diagrams are presented in figures a-1 to a-11 in appendix 2. the label in each region of the diagrams gives the direction of spontaneous magnetisation in that region of the {r,x} parameter space. typical behaviours at the boundaries between regions of different orientations of spontaneous c. carboni, e. al-abry and s. arafin 58 magnetisation are given in figures 2 to 4. the types of reorientation at each boundary are summarized in table 1. 4.1 the orientation diagrams for all the values of j investigated, it is found that each one of the three principal crystallographic axis, < 100 >, < 110 > and < 111> can be the orientation of spontaneous magnetisation for some values of the (r,x) parameters. for a dominant positive fourth-order term in the crystal field (x ~ + 1) the spontaneous magnetisation is always along a three-fold axis (< 111> ). for a dominant negative fourth-order term in the crystal field (x ~ -1) the spontaneous magnetisation is always along a four-fold axis (< 100> ). regions with respectively the four-fold axis and the three-fold axis as the direction of spontaneous magnetisation are never found adjacent to each other except in the limit r = 0. this observation implies that a direct reorientation between the < 111> and the < 100> cannot be observed as a function of x or r. for j = 3 and j = 3.5 there are only three regions in the diagram, one at the top (x ~ + 1) and one at the bottom (x ~ -1) where three-fold axis and the four-fold axis are respectively the directions of spontaneous magnetisation and the region between these two where the direction of spontaneous magnetisation is the two-fold axis. this arrangement of the three main open regions is found for all values of j and is observed even at unrealistic large values of r (r > 1000). note that for j = 3 and j = 3.5 the boundaries converge to the same point at r = 0 therefore, in materials where the exchange interaction is weak, the two fold axis is rarely found to be the direction of spontaneous magnetisation for ions with j = 3 or 3.5. for j ≥ 4 there are, within the region where direction of spontaneous magnetisation is the two-fold axis some closed areas with different directions of spontaneous magnetisation. these closed areas are always bound on one side by the r = 0 axis. there are no common boundaries between two closed areas except at the limit of r = 0. finally we note in passing that nothing particular is observed around the value of r = 1 where there is a change in the relative strengths of the electrostatic and magnetic interactions. 4.2 the boundaries as already mentioned three types of reorientation transitions have been observed; the continuous transition with a gradual reorientation of the direction of spontaneous magnetization and two types of discontinuous reorientations with a sudden change of the direction of spontaneous magnetization at a critical value of (r,x). we discuss first the continuous reorientation. in this case there is near the boundary a band where a self consistent orientation of r is found in a direction other than the principal crystallographic directions. that intermediate self consistent orientation also corresponds to a minimum in the energy of the ground state. as an example for this type of transition the results of the computation for the point | r | = 15 and x = -0.25 at the < 100> / < 110> boundary for j = 4.5 are given in figure 2. for the value of θ = 25.4o it is found that θ’ is equal to θ (figure 2a). this value of θ also corresponds to a minimum in the energy of the ground state (figure 2b). therefore that intermediate orientation is the orientation of spontaneous magnetization. the direction of spontaneous magnetization thus obtained for different values of x varying from x = -0.24 to x = -0.26 at r = 15 is given in figure 2c. there is a continuous rotation of the direction of spontaneous magnetization. the curve of the self-consistent orientation as function of the parameter x has infinite slope at the two critical values of x. one could see an analogy between figure 2c and the behavior observed in the case of a temperature driven spin reorientation however, in the present case the reorientation is not driven by temperature, it is driven by the evolution of the ground state of the ion as the relative strengths of the electrostatic and magnetic interaction is altered. this type of reorientation is called type c in table 1. the direction of spontaneous magnetisation of lanthanide ions 59 a b c figure 2. the type c continuous reorientation for j = 4.5 at r = 15. a: at x = -0.25 the value of (θ-θ’) is zero when θ = 25.4 degrees. b: the minimum energy for the ground state is also found for θ = 25.4 degrees. c: the evolution of the direction of spontaneous magnetisation across the boundary. there is a well defined band from x = 0.2563 to x = -0.2456 in which the direction of spontaneous magnetisation is at an intermediate angle. an intermediate self consistent orientation of r is also found near the boundary in the first type of discontinuous reorientation however this self-consistent orientation does not correspond to a minimum in the energy of the ground state; it corresponds to a maximum. in this type of reorientation there is a band near the boundary in which there exists an intermediate unstable equilibrium orientation for the magnetization but the change-over from of the direction of spontaneous magnetization from one axis to the other occurs at a critical value of (r,x). an example of this type of transition for j = 5.5 at r = 20 and x ~ 0.1 near the < 110> / < 111> boundary is shown in figure 3. for easy comparison, the energy curves presented in figure 3b have been shifted so that so that the value at φ = 0 is zero for all the curves. for x = 0.110 the < 110> direction (φ = 0) corresponds c. carboni, e. al-abry and s. arafin 60 to the lowest energy, it is the direction of spontaneous magnetization and for x = 0.100 the < 111> direction (φ = 45) is the direction of spontaneous magnetization. there is a value of x between 0.100 and 0.110 for which the energy with r along the < 110> direction is the same as that with r along the < 111> direction; both directions can therefore be direction of spontaneous magnetization. at that value of x there is a sudden change of the direction of spontaneous magnetization. this type of reorientation with a critical value of (r,x) at which the two axis are direction of spontaneous magnetization is called type da in table 1. figure 3. the type da discontinuous reorientation for j = 5.5 at r = 20. a: there is a well defined band in which an intermediate self consistent orientation of r can be found however, this orientation corresponds to a maximum in the energy of the ground state. b: there is a value of x for which the magnetisation along the < 100> direction has the same energy as it has when along the < 111> direction. both directions can be direction of spontaneous magnetization. the third type of reorientation is illustrated in figure 4. as in figure 3b the energy curves in figure 4a have been shifted so that the value at θ = 0 is zero for all the curves. for all the values of x near the boundary it is found that the energy varies monotonously (figure 4a) and that the value of (θ – θ’) does not change sign (figure 4b) when the polar angle of r is scanned from one axis to the other. there are no intermediate selfb a the direction of spontaneous magnetisation of lanthanide ions 61 consistent orientations in the plane defined by the < 100> and the < 110> axis. however, there is a critical value of x for which all the orientations in the plane have the same energy and θ’ is equal to θ for all values of θ. at that critical value of (r,x) all the orientations in the plane can be direction of spontaneous magnetization. this type of reorientation is called type dp in table 1. the type of all the boundaries in figures a-1 to a-11 are summarised in table 1. all the reorientations between the < 110> and the < 111> directions are of type da. the reorientation between the < 100> and the < 110> directions are continuous except for j less or equal to 4 where they are of type dp. figure 4. the type dp of discontinuous reorientation for j = 4 at r = 16. a: there is no self consistent orientation of r. b: at a critical value of x all the directions in the plane defined by the < 100> and the < 110> axis can be direction of spontaneous magnetisation. the width ∆x at constant r of the reorientation band in the type c boundary can vary from 0.04 where it is easily identified to about 10-6 where it may be mistakenly seen as a type dp. for example, the width ∆x of the boundary of the closed domain in the diagram for j = 7 is 5x10-6 at r = 0.8. the energy difference between the three self consistent orientations in the plane is 1x10-6 that is almost the limit of confidence of our computations. an illustration of the limits of our computation for the type dp boundaries is given in table 2 for j = 3. for both values of x given in the table the energy of the ground state varies monotonously as the angle θ is varied from zero to forty five degrees; the energy difference between the magnetisation being along the < 100> and being b a c. carboni, e. al-abry and s. arafin 62 along the < 110> axis is about 5x10-6. a change of a change of 5x10-10 in the value of x causes the change of the direction of spontaneous magnetisation from one axis to the other. table 1. the types of reorientation. in the type c there is a continuous rotation of the direction of spontaneous magnetization from one axis to the other. in the type da there is a critical value of the parameters where both axes can be direction of spontaneous magnetization. in the type dp there is a critical value of the parameters where all the directions in the plane defined by the two axis involved are directions of spontaneous magnetization. j boundary type j boundary type 3 < 100> / < 110> dp 6 < 100> / < 110> c < 110> / < 111> da < 110> / < 111> closed da 3.5 < 100> / < 110> dp < 110> / < 100> closed c < 110> / < 111> da < 110> / < 111> da 4 < 100> / < 110> dp 6.5 < 100> / < 110> c < 110> / < 111> closed da < 110> / < 111> closed da < 110> / < 111> da < 110> / < 100> closed c 4.5 < 100> / < 110> c < 110> / < 111> da < 110> / < 111> closed da 7 < 100> / < 110> c < 110> / < 100> closed c < 110> / < 111> closed da < 110> / < 111> da < 110> / < 100> closed c 5 < 100> / < 110> c < 110> / < 111> da < 110> / < 111> closed da 7.5 < 100> / < 110> c < 110> / < 100> closed c < 110> / < 111> closed da < 110> / < 111> da < 110> / < 100> closed c 5.5 < 100> / < 110> c < 110> / < 111> da < 110> / < 111> closed da 8 < 100> / < 110> c < 110> / < 100> closed c < 110> / < 111> closed da < 110> / < 111> da < 110> / < 100> closed c < 110> / < 111> da table 2. the limit of the computation for the type dp boundary. a change of a change of 5x10-10 causes the change of the direction of spontaneous magnetisation from one axis to the other. x e (<100>) e(<110>) -0.169 413 660 5 -67.565 397 765 -67.565 397 771 -0.169 413 661 0 -67.565 397 768 -67.565 397 762 should any of the boundaries labelled dp in table 1 be continuous, the reorientations would occur over a range of values of x smaller than 5x10-10. finally we note that a situation where there is a minimum in the energy that does not correspond to a self consistent orientation has not been observed. 5. conclusion since the parameters r and x are not easily accessible to the experimentalist one might ask if the work presented can have any use for the interpretation of experimental data. the parameter r can in principle be the direction of spontaneous magnetisation of lanthanide ions 63 varied by the application of an external magnetic field; however, the applied field must be along the selfconsistent orientation otherwise it will introduce anisotropy and invalidate the tenet of our analysis. however, many experimentalists make use of the fact that because the lanthanide ions have identical outer electrons-shells the ion under investigation can be placed in a homologue compound with a different rare earth. in particular the magnetic interactions can be reduced by substituting a magnetic ion by yttrium, lanthanum or lutetium (although yttrium is not strictly part of the lanthanide series) or increased by introducing gadolinium. it is usually assumed that yttrium, lanthanum and lutetium have no magnetic moment and that the substitution does not affect significantly the crystal field at the site of the ion of interest; it is also assumed that gadolinium does not interact with the crystal field. these assumptions have been shown not to be tenable in many compounds, too numerous to be reviewed here; however, dilution and substitution has enable researchers to clarify so many problems that the assumptions can be justified as a first approximation. an interesting compound is hoco2. the ho 3+ (j = 8) ion is at a site of cubic symmetry. according to gignoux et al. (1975) the direction of spontaneous magnetisation at low temperature is the < 110> direction; the parameters r = 45.8 and x = -0.4665 derived from the data of gignoux et al. (1975) place the compound in the area corresponding to the < 110> orientation in our diagram close to the boundary with a continuous reorientation. a small increase in r will causes the compound to magnetise along the < 100> axis. how ever, the parameters given by aubert et al. (1978) place the compound just inside the reorientation area and those published by castet et al. (1982) place the compound on the other (< 100> ) side of the boundary. the author and co-workers at the university of manchester (uk) [11 and 12] have investigated by 165ho nmr the series of compounds yxho1-xco2, gdxho1-xco2 and gdxyyho1-x-yco2 at 1.3 k in zero applied field. the direction of spontaneous magnetisation can be inferred from the behaviour of the hyperfine parameters [13 and 14]. it was found that hoco2 is just inside the reorientation region, it magnetises at a small angle to the < 110> axis. yxho1-xco2 for x = 0.05 (smaller r) magnetises along the < 110> direction. the compounds gdxho1-xco2 for x < 0.40 are inside the reorientation region, the angle between the direction of spontaneous magnetisation and the < 100> axis decreases with increasing concentration of gadolinium (increasing r). for x > = 0.40 the spontaneous magnetisation is along the < 100> direction. finally the compound gdxyyho1-x-yco2 with an average value of r corresponding to the reorientation region was observed to magnetise at a small angle to the < 100> direction. details of this experiment and the analysis will be published elsewhere. the knowledge of the position of the compound hoco2 on the diagram is therefore of some help in ascertaining or controlling the direction of spontaneous magnetisation in this series of compounds. 6. acknowledgements the author c c is indebted to dr m a h mccausland d, st p bunbury and o. prakash for discussions during his time at the university of manchester. e al-abry is grateful to the ministry of higher education of the sultanate of oman for providing a scholarship. appendix 1: stevens operators equivalent and the coefficients f4 and f6 the stevens equivalent operators for the non vanishing terms in the crystal field hamiltonian for a site of cubic symmetry. [ ] 222404 )1(3)1(625)1(3035 +++−−+−= jjjjjjjjo zz ( )44 2 14 4 jjo −+ += [ ] [ ] )1((60)1(40)1(5 294)1(525)1(1057)1(3105231 222 222460 6 +−+++− ++−++−+−= jjjjjj jjjjjjjjjo zzzz [ ]( ) ( ) [ ]38)1(1138)1(11 444414424146 −+−+++−+−= −+−+ jjjjjjjjjjo zz c. carboni, e. al-abry and s. arafin 64 the value of the coefficients f4 and f6 given by lea. leask and wolf. j f4 f6 j f4 f6 3 15 180 6 60 7560 3.5 60 1260 6.5 60 7560 4 60 1260 7 60 3780 4.5 60 2520 7.5 60 13860 5 14 1260 8 60 13860 5.5 60 3780 table a 1. the values of the coefficients f4 and f6 corresponding to different values of j. appendix 2: the orientation diagrams the direction of spontaneous magnetisation of lanthanide ions 65 c. carboni, e. al-abry and s. arafin 66 7. references aubert, g., gignoux, d., givord, f., lemaire, r. and michelutti, b. 1978. magnetization reorientation in hoco2 . solid state com., 25: 85. bunbury, d.st.p., carboni, c., mccausland, m.a.h., cone, r., mroczkowsky, s. and ross, j.w. 1995. the hyperfine splitting of the ground state and first excited state of holmium in yttrium hydroxide. j phys. condens. matte, 7, 6125-36. bunbury, d.st.p., carboni, c., mccausland, m.a.h. and prakash, o.1986. spin reorientation in hoco2, an nmr study, proc. xxiii congress ampere on magnetic resonance (istituto superiore di sanita, roma) p. 296. carboni, c. 1984. diploma report, design of a microwave resonator to measure the nmr of 3+ho in metallic single crystals. university of manchester, unpublished. carboni, c., gignoux, d. and ross, j.w. 1996. the field dependence of the hyperfine splitting of terbium in tbni5, j. phys condens. matter, 8: 1763-74. carboni, c., mccausland, m.a.h., bunbury, d.s.p., reid, b.l., lataifeh, m. and abell, j.s. 1992. crystal-field anisotropy of tb3+, ho3+, and tm3+ in gadolinium. j. magn. magn. matter. 104107: 1513. castet, a., gignoux, d. and hennion, b. 1982. new aspects of the magnetic excitations in hoco2. phys. rev. b25: 337. germano, d.j. and butera, r.a. 1981. heat capacity of, and crystal-field effects in, the rfe2 intermetallic compounds (r=gd, tb, dy, ho, er, tm, and lu) phys. rev. b, 24(1): 3912. gignoux, d., givord, f., lemaire, r. 1975. magnetic properties of single crystals of gdco2, honi2, and hoco2; phys. rev. b12: 3878. lea, k.r., leask, j.m. and wolf, w.p. 1962. the raising of angular momentum degeneracy of f-electrons by cubic crystal field, journal of the physics and chemistry of solids, 23: 1381-1405. mccausland, m.a.h, and makenzie, i.s. 1980. nuclear magnetic resonance in rare earth metals, taylor and francis ltd., london. morrisson, c.a. and leavitt, r.p. 1982. handbook of physics and chemistry of rare earths, vol 5, gschneider, k.a and eyring, l eds. north holland publishing company. prakash, o., bunbury, d.st.p., mccausland, m.a.h. 1984. on the ground state of ho3+ in ferromagnetic hoal2, z phys b58, 39. stevens, k.w.h. 1952. matrix elements and operator equivalents connected with the magnetic properties of rare-earth ions, proceedings of the physical scociety, a, 65: 209-215. received 11 october 2006 accepted 29 january 2007 squ journal for science, 2020, 25(2), 112-123 doi:10.24200/squjs.vol25iss2pp112-123 sultan qaboos university 112 effects of thermal stratification and anisotropic porous material in a symmetrically heated vertical channel basant k. jha, muhammad k. musa* and abiodun o. ajibade department of mathematics, ahmadu bello university, zaria, nigeria, *email: mmkabirxy@yahoo.com. abstract: the coexistence in nature of thermally stratified fluids and directionally inclined porous structures abound in geophysical fluid flow. despite their important applications especially in underground flow, their combined effects on natural convection have not been intensively investigated. this article aims to investigate a fully developed time dependent natural convection of viscous incompressible stably stratified fluid in the presence of anisotropic porous material. the semi analytical solutions of the governing equations for the temperature and velocity fields are obtained using the laplace transform technique, riemann sum approximation and d’alembert methods. the choice of the d’alembert method is to provide a systematic decoupling procedure for the coupled governing equations while still retaining their original orders. this research establishes that the fluid maximum or minimum velocity can be attained by properly manipulating the anisotropic parameters. keywords: transient free convection; anisotropic porous materials; stably stratified fluid; riemann sum approximation; d'alembert method; symmetric heating. بالتساوي ن سخ ت قناة عمودية تأثيرات الطبقات الحرارية والمواد المسامية متباينة الخواص على موسى وأبيدون و. أجيباد محمد ك.اه، وبسنت ك. ج الجيوفيزيائية. على الرغم من تطبيقاتها المهمة خاصة في تدفق السوائلميل إلى الطبقية حرارياً والهياكل المسامية ت السوائلالتعايش في طبيعة إن :صلخمال حراري الطبيعي الحمل ال دراسةالبحث إلى اهدف هذيآثارها المشتركة بشكل مكثف على الحمل الحراري الطبيعي. دراسة لم يتم فإنه التدفق الجوفي، وجود مادة مسامية متباينة الخواص. يتم الحصول على الحلول شبه بلسائل اللزج غير القابل للضغط الطبقي المستقر ا زمنالمطّور بالكامل والمعتمد على المبرت ،اختيار طريقة د إن لمبرت.ا،د ةقيريمان وطرتقريب مجموع البالس و تالحرارة والسرعة باستخدام تحويال لتحكم في مجاليالتحليلية لمعادالت ا أنه يمكن تحقيق السرعة القصوى أو الدنيا للسائل من خالل الدراسة تاألصلية. أثبتدرجاتها المقترنة مع االحتفاظ ب لتحكمفصل منظم لمعادالت ا ؤدي إلىي متباينة الخواص. ؤثراتلمل تغيير مقبول بالتساوي. تسخينال ؛المبرت،طريقة د ؛ريمان مجموع تقريب ؛سائل طبقي مستقر ؛مواد مسامية متباينة الخواص ؛الحمل الحراري العابر :مفتاحيةالكلمات ال 1. introduction nalytical and numerical study of free convective fluid flow through porous materials continues to receive considerable attention in the literature. this is as a result of their wide industrial and technological applications such as in noise reduction in aerodynamics [1], combustion devices [2], biological systems and biotechnology [3], waste water treatment plants [4] and in nuclear reactors [5]. as a result of these endless important applications, investigations involving the impact of a porous matrix in fluid flow formation is still on-going. thus, by taking the hall effect into account, [6] have examined the peristaltic transport of williamson fluid through a porous medium. the results of the investigation on peristaltic flow of a compressible maxwell fluid resulting from the surface acoustic wave in a parallel-plane micro-channel through a porous medium in the presence of a constant magnetic field have been presented by [7]. [8] investigated the peristaltic motion in a gall bladder induced by the sinusoidal traveling wave and noted that the hall parameter enhances the mean velocity distribution, the reversal flow and the perturbation function. a effects of thermal stratification and anisotropic porous material 113 according to khaled and vafai [9], in an attempt to investigate the role of porous media in the transport processes, the classical (darcy) model, which simply presents a linear relationship between the superficial average velocity (𝑈) and the pressure difference (𝑃) applied across the porous medium, was developed. as a result of its limitations, the darcy model was later extended to account for cases where large fluid flow (forchheirmen’s model) and boundary effects (brinkman’s model) are required. it is important to state here that most of the earlier investigations of natural convection through porous media (such as vafai [10] and pop and ingham [11]) were conducted on the basis of the following assumptions: (a) that the ambient flow media outside the flow regions were taken to be of uniform density as well as at constant temperature (isothermal) and (b) the preferential direction of some physical quantities such as the permeability of the beads or fibers of the porous media were generally neglected (isotropic). these assumptions failed to capture the true forms in which geophysical fluids, especially, are encountered in nature, as well as how naturally existing or artificially developed porous media behave. several types of research where the fluid density in the ambient medium is non-uniform and varies with height are currently being investigated. this phenomenon, which has an over bearing effect on natural convection due to density variation, is termed in the existing literature as ‘stratification of the media’. several applications ranging from cooling circuit boards in electronic devices to the triggering of heat circulation in the atmosphere which influences weather conditions abound in industry and in nature. stratification generally consists of fluid layers of different densities such that, under gravitational influence, they are arranged so that fluids of higher densities are found beneath those of lower densities. publications on the role played by thermal stratification on the heat convection processes include the demonstration of the effect of thermally stratified ambient fluid on mhd by gurminder et al. [12]. deka and paul [13, 14] have shown that thermal stratification suppresses the fluid momentum in the boundary layer and also observe that stratification transforms the transient state to a steady state as time progresses. shapiro and fedorovich [15] presented an analytical description of the steady shallow convective flow of a viscous and diffusive stably stratified fluid over a differentially heated lower boundary. in a controlled laboratory experiment, falasca et al. [16] took a stratified atmospheric boundary layer into account, and analyzed the simulations of an urban heat island. another excellent research work worth mentioning here is the impact of stably stratified fluid in the presence of magneto-hydrodynamic (mhd) conducted by deka and bhattacharya [17]. in studying transport problems, especially when a porous medium is incorporated into the transport equation, consideration of the orientation of the fibers or beads of the porous matrix becomes very interesting. anisotropy results from the preferential orientation of the grains or fibers that constitute the porous structure. thus, while investigating heat transfer in the presence of anisotropic porous medium with oblique principal axes, vajravelu and prasad [18] observed that anisotropy is characterized by the ratio of permeability (𝑘∗ = 𝑘1 𝑘2 ) and the angle of orientation (𝜑) between the horizontal direction and principal axis 𝑘2 with the permeability. bera and khalili [19] suggest that the permeability of the porous media act as a conductivity of the fluid flow and that for large values of anisotropic permeability ratio, (𝑘∗ > 1), a decrease in the anisotropic angle of orientation (𝜃), within the closed interval [0𝑜 , 90𝑜 ], enhances the total permeability along the main flow direction, which consequently aids in strengthening the fluid convection current. expressing the penetration length of the convective flow and heat transfer rate in terms of the anisotropic properties of the porous medium, karmakar and sekhar [20] demonstrated that the directional permeability of the anisotropic porous structure greatly influences the fluid flow through a composite porous channel. in another investigation, yovogan and degan [21] established that anisotropic parameters can be used to predict environmental aquatic behaviour. other reports on the various roles played by anisotropy parameters can also be found in degan et al. [22], filip et al. [23], and filip et al. [24]. in all the above cases examined, the influence of anisotropy and thermal stratification on temperature and fluid velocity are studied separately. the purpose of the present article is to simultaneously examine the combined effects of thermal stratification and anisotropic porous material on the transient free convective mode of fluid flow in a symmetrically heated vertical channel. the semi-analytical solution presented in this article expands the data base of known analytical/semi-analytical solutions for transient natural convection flow in a channel filled with anisotropic porous material in a stably stratified medium. 2. mathematical analysis consider the problem of time dependent natural convection in a symmetrically heated vertical channel as depicted in figure 1.0. the coordinate systems of the problem are selected in such a way that the 𝑦 − 𝑎𝑥𝑖𝑠 is the direction of the fluid flow and perpendicular to the gravitational pull and the channel walls while the 𝑥 − 𝑎𝑥𝑖𝑠 is parallel to them. the fluid occupying the region −ℎ ≤ 𝑦′ ≤ ℎ is assumed to be thermally stratified. according to deka and paul [13], thermal stratification is as a result of the combined effects of 𝑑𝑇∞(𝑥 ′) 𝑑𝑥′ ; the ambient fluid temperature (or vertical advection) which depends on the height 𝑥 ′ of the transport medium, and 𝑔 𝐶𝑝 , the rate of reversible work done on the fluid particles by compression. here, 𝑇∞(𝑥 ′) is the varying environmental temperature, 𝑔 is the gravitational constant and 𝐶𝑝 is the specific heat capacity of the fluid at a constant pressure. in the present investigation, the working basant k. jha et al 114 fluid is air (𝑃𝑟 = 0.71) so that 𝐶𝑝 = 1012𝐽𝐾𝑔 −1𝐾 −1. as a result, the work of compression on the air particle 𝑔 𝐶𝑝 is negligible since 𝑔 = 9.8 𝑚𝑠−2 . hence the thermal stratification can therefore be seen as being dominated by the vertical advection temperature term. accordingly, three possible situations exist: (i) the adiabatic or neutral (𝑆 ′ = 0) case which, according to deka and paul [14], represents the largest rate at which temperature can decrease with height without resulting in instability (ii) unstable stratification (𝑆 ′ < 0), in which less dense fluid exists at the bottom of a denser fluid and (iii) stable stratification (𝑆 ′ > 0), which characterizes the scenario where the less dense fluid is found at the top of the denser fluid. this last characterization is the focus of this research. figure 1. schematic diagram of the problem. further, it is assumed that the channel is saturated with anisotropic porous materials. anisotropic porous structure is characterized by the ratio of permeability of the porous material; 𝑘∗ = 𝑘1 𝑘2 and the angle of orientation 𝜑 which is the angle between the horizontal direction and principal axis 𝑘2 with the permeability. at 𝑡 ′ ≤ 0, both the stratified fluid and the channel walls are maintained at a temperature 𝑇0. at time 𝑡 ′ > 0, the natural convective process is triggered by the symmetric heating of the bounding walls from the initial thermodynamically equilibrium (𝑇′ = 𝑇0 ) state to 𝑇 ′ = 𝑇1 . under these assumptions, and following degan et al. [22] and deka and bhattacharya [17] the governing equations for fluid velocity and temperature distributions are given as follows: 𝜕𝑈′ 𝜕𝑡 ′ = 𝜐𝑒𝑓𝑓 𝜕2𝑈′ 𝜕𝑦′2 − 𝑈′ υ 𝐾 + 𝑔𝛽(𝑇′ − 𝑇0) (1) 𝜕𝑇′ 𝜕𝑡 ′ = 𝑘 𝜌𝐶𝑝 𝜕2𝑇′ 𝜕𝑦′2 − 𝑆 ′𝑈′ (2) due to the symmetric heating of the channel walls, the initial and boundary conditions consistent with the physical situation are: 𝑡 ′ ≤ 0, 𝑇′ = 𝑇0 , 𝑈 ′ = 0 𝑎𝑡 − h ≤ 𝑦’ ≤ +ℎ 𝑡 ′ > 0 𝜕𝑈′ 𝜕𝑦′ = 0, 𝜕𝑇′ 𝜕𝑦′ = 0 at 𝑦′ = 0 (3) 𝑈′ = 0, 𝑇′ = 𝑇1 𝑎𝑡 𝑦 ′ = +ℎ where the second order symmetric tensor 𝐾 is defined as: 𝐾 = [ 𝑘1 𝑐𝑜𝑠 2(𝜑) + 𝑘2𝑠𝑖𝑛 2(𝜑) (𝑘1 − 𝑘2)𝑠𝑖𝑛(𝜑)𝑐𝑜𝑠(𝜑) (𝑘1 − 𝑘2)𝑠𝑖𝑛(𝜑)𝑐𝑜𝑠(𝜑) 𝑘2𝑐𝑜𝑠 2(𝜑) + 𝑘1𝑠𝑖𝑛 2(𝜑) ] . (4) introducing the following non-dimensional quantities 𝑈= 𝑈′h 𝜐 , 𝑇 = 𝑇ʹ−𝑇0 𝑇1−𝑇0 , 𝑦 = 𝑦′ ℎ , 𝛾 = 𝜐𝑒𝑓𝑓 𝜐 , 𝑡 = 𝑡′𝜐 h2 , 𝑆 = 𝑆ˊℎ 𝑇1−𝑇0 , pr = 𝜐𝜌𝐶𝑝 𝑘 , 𝐷𝑎 = 𝑘1 ℎ2 and 𝐺𝑟 = 𝑔𝛽(𝑇1−𝑇0)h 3 𝜐2 equations (1)-(3) can then be expressed in dimensionless form as: 𝜕𝑈 𝜕𝑡 = 𝛾 𝜕2𝑈 𝜕𝑦2 − 𝑎 𝑈 𝐷𝑎 + 𝐺𝑟𝑇 (5) 𝑘2 𝑘1 𝜑 𝑦 𝑥′ 𝑦′ = −ℎ 𝑦′ = 0 𝑇1 𝑇1 𝑦′ = +ℎ effects of thermal stratification and anisotropic porous material 115 𝜕𝑇 𝜕𝑡 = 1 𝑃𝑟 𝜕2𝑇 𝜕𝑦2 – 𝑆𝑈 (6) where 𝑎 = 𝑐𝑜𝑠2(𝜑) + 𝑘 ∗ 𝑠𝑖𝑛2(𝜑) is obtained from equation (4) and the initial and boundary conditions now assume the following form: 𝑡 ≤ 0; 𝑈 = 0, 𝑇 = 0 at 0 ≤ 𝑦 ≤ 1 𝑡 > 0; 𝜕𝑈 𝜕𝑦 = 0, 𝜕𝑇 𝜕𝑦 = 0 at 𝑦 = 0 (7) 𝑈 = 0, 𝑇 = 1 at 𝑦 = 1 2.1 solutions since equations (5) and (6) are second order coupled partial differential equations, laplace transform techniques defined for any arbitrary function as 𝑓(̅𝑦, 𝑡) = ∫ 𝐹𝑒 −𝑝𝑡 𝑑𝑡 ∞ 0 , are employed to produce coupled second order ordinary differential equations: 𝑑2𝑈 𝑑𝑦2 − 𝑈 𝛾 ̅ (𝑝 + 𝑎 𝐷𝑎 ) = − gr 𝛾 �̅� (8) 𝑑2�̅� 𝑑𝑦2 − 𝑆𝑃𝑟𝑈 − 𝑝𝑃r�̅� = 0 (9) where in order to ensure convergence, the laplace parameter 𝑝 > 0. it is observed that equations (8) and (9) are coupled second order ordinary differential equations in the laplace domain. attempting to solve these equations by directly eliminating the velocity (or temperature) will simply lead to solving a set of complex couple equations of a higher order. thus, in this research, the d’alembert method (ziyaddin and huseyin [25]) is used. this method allows for the systematic decoupling of the governing equations while still retaining their initial orders. multiplying through equation (8) by 𝐷 and adding the resulting equation to equation (9) produces: 𝑑2 𝑑𝑦2 (𝐷𝑈 + �̅�) − 𝛿 2(𝐷�̅� + �̅�) = 0 (10) where the quadratic function in terms of 𝐷 is chosen and defined as: 𝐷2 + 𝐷 𝐺𝑟 (𝑃 + 𝑎 𝐷𝑎 − 𝛾𝑝𝑃𝑟) + 𝛾𝑆𝑃𝑟 𝐺𝑟 = 0 . (11) similarly 𝛿 2 = 𝛾𝑝𝑃𝑟−𝐷𝐺𝑟 𝛾 . (12) the general solution of equation (10) is obtained and is given as: 𝐷𝑈 + �̅� = 𝐴1 cosh(𝛿𝑦) + 𝐴2 sinh(𝛿𝑦) (13) by applying the boundary conditions (7) on equation (13), the expressions for 𝐴1 and 𝐴2 are obtained (see appendix b) so that the equation (13) becomes: 𝐷𝑈 + �̅� = 1 𝑝 ( cosh(𝛿𝑦) cosh( 𝛿) ) (14) replacing 𝐷 and 𝛿 in equations (14) with their corresponding roots: 𝐷1, 𝐷2 , and 𝛿1, 𝛿2 respectively (see appendix b) obtained by solving equations (11) and (12) one after the other, yields: 𝐷1𝑈 + �̅� = 1 𝑝 ( cosh(𝛿1𝑦) cosh( 𝛿1) ) (15) 𝐷2𝑈 + �̅� = 1 𝑝 ( cosh(𝛿2𝑦) cosh( 𝛿2) ) (16) solving these equations simultaneously, the expressions for the velocity and temperature profiles in the laplace domain are obtained and presented as: 𝑈 = 1 𝑝(𝐷1−𝐷2) [ cosh(𝛿1𝑦) cosh(𝛿1) − cosh(𝛿2𝑦) cosh(𝛿2) ] (17) �̅� = 1 𝑝(𝐷1−𝐷2) [ 𝐷1cosh(𝛿2𝑦) cosh(𝛿2) − 𝐷2cosh(𝛿1𝑦) cosh(𝛿1) ] (18) 3. nusselt number, skin friction, and volumetric mass flow rate in order to understand the behaviour of the heat being transferred from the wall surface into the channel, the frictional force developed at the wall-fluid interface, which tends to hinder the fluid flow and the amount of fluid flowing per unit area, the rate of heat transfer (𝑁𝑢1 = 𝑑�̅�(𝑦,𝑝) 𝑑𝑦 │𝑦=1), skin friction(𝜏1̅ = 𝑑�̅�(𝑦,𝑝) 𝑑𝑦 │𝑦=1), and volumetric mass flow (�̅� = ∫ 𝑈(𝑦, 𝑝)𝑑𝑦 1 0 ) are respectively investigated. the expressions for these physical quantities are derived and presented as follows: basant k. jha et al 116 𝑁𝑢1 = 1 𝑝(𝐷1−𝐷2) [ 𝐷1𝛿2sinh(𝛿2) cosh(𝛿2) − 𝐷2𝛿1sinh(𝛿1) cosh(𝛿1) ] (19) 𝜏1̅ = 1 𝑝(𝐷1−𝐷2) [ 𝛿1sinh(𝛿1) cosh(𝛿1) − 𝛿2sinh(𝛿2) cosh(𝛿2) ] (20) �̅� = 1 𝑝(𝐷1−𝐷2) [ sinh(𝛿1) 𝛿1cosh(𝛿1) − sinh(𝛿2) 𝛿2cosh(𝛿2) ] (21) to convert equations (17)-(21) to their corresponding time domain, their respective laplace inverses are obtained. this, however, would be complicated to achieve, hence a numerical approach based on the riemann-sum approximation method is employed. according to jha and apere [26] and jha and isa [27] the laplace inverse of any function �̅�(𝑦, 𝑝) can be approximated by: 𝑈(𝑦, 𝑡) = 𝑒𝜀𝑡 𝑡 [ 1 2 𝑈(𝑦, ) + 𝑅𝑒 ∑ 𝑈 (𝑦, + 𝑖𝑘𝜋 𝑡 ) (−1)𝑘𝑛𝑘=1 ] . (22) in this representation, 𝑅𝑒 and 𝑖 = √−1 are real and imaginary numbers respectively, and 𝑛 is the number of iterations used in the method. if the number of iterations must be minimized and faster convergence is to be achieved, it was suggested (tzou [28]) that the product of the time (𝑡) and the real part of bromwich contour ( ) used for inverting a function from the laplace domain to its corresponding time domain should be 4.7. by appropriately replacing 𝑈(𝑦, 𝑝), the laplace inverses of equations (18)-(21) can similarly be obtained. 4. validation of the semi-analytical method used: steady state model in order to establish the accuracy of the semi-analytical approach employed in computing the transient state solutions, the corresponding steady state solutions for the velocity and temperature equations have been derived analytically. the transient states results obtained are compared with the results from steady states (see paul et al. [29]). thus, by setting 𝜕𝑈 𝜕𝑡 = 0 and 𝜕𝑇 𝜕𝑡 = 0 in equations (5) and (6) respectively, the steady state mathematical model is obtained: 𝑑2𝑈 𝑑𝑦2 − 𝑎 𝑈 𝛾𝐷𝑎 = − 𝑇𝐺𝑟 𝛾 (23) 𝑑2𝑇 𝑑𝑦2 − 𝑝𝑟𝑆𝑈 = 0 (24) and the corresponding boundary conditions become: 𝑑𝑈 𝑑𝑦 = 𝑑𝑇 𝑑𝑦 = 0, at 𝑦 = 0 (25) 𝑈 = 0, 𝑇 = 1 at 𝑦 = 1 the exact solutions of equations (23) and (24) satisfying the boundary conditions (25) are obtained by using the d’alembert method and are given as: 𝑈 = 1 (𝐵1−𝐵2) [ cosh(𝛼2𝑦) cosh(𝛼2) − cosh(𝛼1𝑦) cosh(𝛼1) ] (26) 𝑇 = 1 (𝐵1−𝐵2) [ 𝐵1cosh(𝛼2𝑦) cosh(𝛼2) − 𝐵2cosh(𝛼1𝑦) cosh(𝛼1) ] (27) the expressions for 𝐵1, 𝐵2, 𝛼1 and 𝛼2 are presented in appendix b table 1. comparison between transient state (riemann-sum approximation method) and steady state (exact solution) velocity and temperature distributions. t y transient velocity temperature 0.5 0.2 0.5484 0.7367 0.4 0.5230 0.5091 0.6 0.3619 0.3180 0.8 0.1801 0.1526 1.0 0.2 0.5485 0.7368 0.4 0.5231 0.5092 0.6 0.3621 0.3182 0.8 0.1802 0.1527 t y transient velocity temperature 1.5 0.2 0.5484 0.7367 0.4 0.5231 0.5092 0.6 0.3621 0.3182 0.8 0.1802 0.1527 steady state 0.2 0.5485 0.7367 0.4 0.5231 0.5092 0.6 0.3621 0.3182 0.8 0.1802 0.1527 effects of thermal stratification and anisotropic porous material 117 it is observed from table 1.0 that the numerical results for the transient state velocity and temperature distributions obtained with the riemann sum approximation method agree excellently with the numerical values for the exact solutions for the steady state velocity and temperature as 𝑡 → 𝑃𝑟. thus, this result further confirms the accuracy of the riemann sum approximation method employed. 5. results and discussion in order to have an insight into the present problem, numerical computations for velocity, temperature, skin friction, rate of heat transfer and volumetric mass flow rate are performed for different values of the controlling parameters. line graphs and contour maps (figures. 2-19) are depicted for transient state temperature and velocity profiles along with those of nusselt number, skin friction, and volumetric mass flow rate to clearly show the influence of these parameters. first, the accuracy of the results obtained needs to be confirmed. to achieve this, tables 2.0 and 3.0 have been constructed. it is clear that for 𝑃𝑟 = 0.71 (air) and 𝑃𝑟 = 7.0 (water), by neglecting the anisotropic parameter as well as allowing the vertical advection to coincide with the rate of reversible work done on the fluid particles by compression, the numerical data generated for the present research favourably compare with the numerical results provided by jha [30] with respect to skin friction, and by jha and singh [31] with respect to skin friction and volumetric mass flow rate, as seen in table 2.0 and table 3.0 respectively. table 2. comparing the numerical values of skin friction (𝜏) for water ( 𝑃𝑟 = 7.0) in the work of jha [30] and the present work in the absence of anisotropic and thermal stratification parameters. table 3. comparing skin friction (𝜏) and mass flow rate (𝑄): jha and singh [31] and the present work in the absence of anisotropic and thermal stratification parameters jha [30] present work 𝑡/𝐷𝑎 0.5000 0.2500 0.1667 0.5000 0.2500 0.1667 0.2 0.13371 0.12945 0.12546 0.1338 0.1295 0.1259 0.4 0.18466 0.17383 0.16503 0.1847 0.1739 0.1656 0.6 0.22307 0.20454 0.19071 0.2231 0.2046 0.1915 2.0 0.38786 0.32025 0.28029 0.3880 0.3204 0.2804 4.0 0.50951 0.40216 0.34203 0.5097 0.4023 0.3422 6.0 0.56955 0.44255 0.37248 0.5697 0.4427 0.3727 present work jha and singh [31] 𝑃𝑟 𝑡 𝜏 𝑄 𝜏 𝑄 0.4 0.4526 0.1115 0.4523 0.1114 0.71 0.6 0.6108 0.1756 0.6105 0.1754 1.0 0.8246 0.2622 0.8242 0.2620 0.4 0.1984 0.0195 0.1983 0.0195 7.0 0.6 0.2496 0.0349 ------- 0.0348 1.0 0.3424 0.0684 0.3422 0.0683 basant k. jha et al 118 figures 2-5 exhibit the effect of thermal stratification (𝑆) on temperature, fluid velocity, rate of heat transfer and skin friction. as seen in the figures, an increase in the stratification parameter suppresses the temperature within the vertical channel (figure 2) and as a result, a weak velocity current is created (figure 3). this is because stratification creates fluid layers which increase with height. these layers create resistance (layering effects) to temperature penetration hence a decrease in both the temperature and velocity distributions are observed. the numerical simulation conducted also revealed that increasing the stratification parameter enhances the rate of heat transfer (figure 4) but decreases the frictional force at the surface-fluid interface (figure 5). figure 4. rate of heat transfer for different 𝑆 with 𝑃𝑟 = 0.71 , 𝑘∗ = 0.2 , 𝜑 = 450, gr=70.0, 𝐷𝑎 = 0.01 and 𝛾 = 1.5 figure 3. velocity distribution for different 𝑆 with 𝑃𝑟 = 0.71 , 𝜑 = 450, 𝐷𝑎 = 0,01, 𝑡 = 0.4, gr=70.0, 𝛾 = 1.5 and 𝑘∗ = 0.2 figure 2. temperature distribution for different 𝑆 with 𝑃𝑟 = 0.71 , 𝜑 = 450, 𝑡 = 0.4, 𝐷𝑎 = 0.01, gr=70.0, 𝛾 = 1.5 and 𝑘∗ = 0.2 figure 5. skin friction for different 𝑆 with 𝑃𝑟 = 0.71 , 𝑘∗ = 0.2 , 𝜑 = 450, gr=70.0, 𝐷𝑎 = 0.01 and 𝛾 = 1.5 figure 7. velocity distribution for different 𝜑 and 𝑘∗ with 𝑃𝑟 = 0.71 , 𝑡 = 0.4, 𝑆 = 2.5, 𝐷𝑎 = 0.01, gr=70.0, 𝛾 = 1.5 and 𝑦 = 0.4 figure 6. temperature distribution for different 𝜑 and 𝑘∗ with 𝑃𝑟 = 0.71, 𝑡 = 0.4, 𝑆 = 2.5, 𝐷𝑎 = 0.01, gr=70.0, 𝛾 = 1.5 and 𝑦 = 0.4 effects of thermal stratification and anisotropic porous material 119 the second order permeability tensor defined in equation (4) physically characterizes the direction along which fluid in an anisotropic porous system flows under imposed transport constraints. thus from figure 1 and the expression 𝑎 = 𝑐𝑜𝑠2(𝜑) + 𝑘∗𝑠𝑖𝑛2(𝜑) obtained from equation (4), if 𝜑 = 900 the preferential orientation of the bead or fibers of the anisotropic porous matrix becomes entirely a function of the anisotropic ratio of permeability (as 𝑎 = 𝑘∗). in addition, it is also seen that if the angle of orientation 𝜑 = 00, the principal permeability axis 𝑘2 coincides with the horizontal transverse distance (𝑦) so that 𝑎 = 1. this situation is identical to the case when 𝑘∗ = 1; ( 𝑘1 = 𝑘2) , as seen in figures 6 and 7, which represents the state where the porous medium transforms to purely isotropic so that the preferential orientation of the grains of the porous structure is neglected. in particular, figure 6 shows that if 𝑘∗ > 1 an increase in the permeability 𝑘1is observed. consequently, an increase in temperature penetration is noticed as the anisotropic angle of orientation increases form 𝜑 = 00 to 𝜑 = 900. on the other hand, if 𝑘∗ < 1 an increase along the permeability 𝑘2 is observed resulting in the attenuation of fluid temperature as the angle of orientation is increased. this behavior is transmitted into the fluid velocity distribution as depicted in figure 7. for 𝑘∗ < 1, the fluid velocity increases as 𝜑 increases and for 𝑘∗ > 1, the graph shows a decrease in the fluid velocity as the angle of orientation increases form 𝜑 = 00 to 𝜑 = 900. these flow trends have been observed and reported by bera and khalili [19]. in addition, the numerical simulation conducted indicates that both the rate of heat transfer (figure 8) and the skin friction (figure 9) at the walls are enhanced if the anisotropic angle of orientation (𝜑) is increased, and for small values of the anisotropic ratio of permeability(𝑘∗ < 1). if the anisotropic ratio of permeability is large (𝑘∗ > 1), a converse trend is observed. it is also interesting to note that, from the experiment conducted by liakopoulos [32] on the permeability of soil (acting as porous material), the pores of the soil were observed to be larger when the permeability of the porous media is increased horizontally. this allows more water to flow when 𝑘1 < 𝑘2. this result explains, as seen in figure 7, why the fluid attains its maximum velocity when 𝜑 = 𝜋 2 and minimum velocity when 𝜑 = 00 as 𝑘 ∗ < 1. for 𝑘∗ > 1 however, the fluid velocity is least when 𝜑 = 𝜋 2 and maximum when 𝜑 = 00. figure 8. rate of heat transfer for different 𝜑 and 𝑘∗ with 𝑃𝑟 = 0.71 , 𝑡 = 0.4 , 𝑆 = 2.5, gr =70.0, 𝐷𝑎 = 0.01 and 𝛾 = 1.5 figure 9. skin friction for different values of 𝜑 and 𝑘∗ with 𝑃𝑟 = 0.71 , 𝑡 = 0.4 , 𝑆 = 2.5, gr =70.0, 𝐷𝑎 = 0.01 and 𝛾 = 1.5 figure 10. velocity distribution for different 𝐷𝑎 with 𝑃𝑟 = 0.71 , 𝜑 = 450, 𝑆 = 2.5, 𝑡 = 0.4, gr =70.0, 𝛾 = 1.5 and 𝑘∗ = 0.2 figure 11. temperature distribution for different 𝑡 with 𝑃𝑟 = 0.71 , 𝜑 = 450, 𝑆 = 2.5, 𝐷𝑎 = 0.01, gr =70.0, 𝛾 = 1.5 and 𝑘∗ = 0.2 basant k. jha et al 120 as a result of the linear relationship that exists between the measure of permeability (𝐷𝑎) of the anisotropic porous medium and the principal axis 𝑘1 with the permeability of the porous matrix, increasing the darcy number (𝐷𝑎) results in an increase in the pores of the anisotropic porous medium along with permeability 𝑘1 of the anisotropic porous structure, so that 𝑘1 > 𝑘2. this variation leads to an increase in the void of the porous passages of the anisotropic porous matrix thereby resulting in a decrease in the relative friction between the flowing fluid and porous material, and hence an increase in the fluid velocity is observed, as seen in figure 10. figures 11 and 12 depict the influence of time (𝑡) on both the temperature and velocity profiles. as expected, the temperature distribution in the channel saturated with an anisotropic porous matrix is observed to increase with an increase in time (𝑡). this trend as seen in the temperature profile is replicated in the fluid velocity, as the fluid flow progresses with time. the combined roles of the anisotropic parameters (𝑘∗ and 𝜑) and that of the thermal stratification (𝑆) on the volumetric mass flow rate are respectively presented in figures 13 and 14. it is observed (figure 13) that when 𝑘∗ < 1, increasing 𝜑 results in the increase in the volumetric mass flow rate while a converse trend is achieved when 𝑘∗ > 1. on the other hand, the volumetric mass flow rate is observed to be suppressed with an increase in thermal stratification (𝑆) as displayed in figure 14. 6. conclusion in this paper, the mathematical model which takes into account the anisotropic porous material and fluid associated with vertical thermal advection and compression works on the fluid particles is investigated. laplace transform, d’alembert and riemann sum approximation methods are employed to obtain the solutions for the transient state governing equations. solutions for the corresponding steady state problem were also obtained for the purpose of method validation. it was found that at 𝑡 ≫ 𝑃𝑟, numerical values for the transient and steady states velocity and temperature distributions coincide. moreover, the validity of the results obtained have been established. in investigating the influence of some of the controlling parameters present in the solutions obtained, special interest is placed on the role played by anisotropy and stratification parameters. the study has established that: i. the inclusion of the thermal stratification and anisotropic factors in the temperature and velocity equations have an overbearing influence on the physical quantities studied. figure 12. velocity distribution for different 𝑡 with 𝑃𝑟 = 0.71 , 𝜑 = 450, 𝑆 = 2.5, 𝐷𝑎 = 0.01, gr=70.0, 𝛾 = 1.5 and 𝑘∗ = 0.2 figure 13. mass flow rate for different values of𝜑 and 𝑘∗ with 𝑃𝑟 = 0.71 , 𝑡 = 0.4 , 𝑆 = 2.5, gr=70.0, 𝐷𝑎 = 0.01 and 𝛾 = 1.5 figure 14. mass flow rate for different values of 𝑆 with 𝑃𝑟 = 0.71 , 𝜑 = 450, 𝑘∗ = 0.2, gr=70.0, 𝛾 = 1.5 and 𝐷𝑎 = 0.01 effects of thermal stratification and anisotropic porous material 121 ii. in addition, due to the layering effect induced by the thermal stratification, thermal and hydrodynamic distributions in a channel have be found to be suppressed with an increase in stratification. iii. the conditions for the attainment of maximum (or minimum) velocity with respect to the variation of anisotropic parameters have been demonstrated. 7. future investigation and recommendations: researchers have constructed, and worked on another form of porous media, the bidisperse porous media. the model suggested for the porous media is for isotropy and the fluid is non-stratified. it will be interesting if anisotropy and stratification terms are included into the extended brinkman model for bidisperse porous media. since the resulting model is a set of coupled equations coupling the fluid in frictional and porous phases of the porous media, the methods used in the present investigation could be very helpful. conflict of interest the authors declare no conflict of interest. appendix a nomenclature symbol definitions units β coefficient of thermal expansion [𝐾 −1] 𝜐𝑒𝑓𝑓 effective viscosity of the saturated porous media ⌈𝑚 2𝑠−1⌉ 𝜐 kinematic viscosity of the fluid ⌈𝑚2𝑠−1⌉ 𝑔 acceleration due to gravity ⌈𝑚𝑠 −2⌉ 𝑘 thermal conductivity of the fluid ⌈𝑤𝑚−1𝑘−1⌉ 𝛾 ratio of viscosities 𝐶𝑝 specific heat of the fluid at constant pressure ⌈𝐽𝑘𝑔 −1𝑘−1⌉ 𝑘1 and 𝑘2 permeabilities along the principal axes of the anisotropic porous medium [𝑚 2] 𝑘∗ ratio of anisotropy permeability 𝜑 anisotropic angle of inclination [deg or rad] 𝑆 dimensionless stratification parameter 𝑆′ dimensional stratification parameter [𝑚𝐾 −1] 𝐷𝑎 darcy number 𝐺𝑟 grashoff number 𝑃𝑟 prandtl number �̅� temperature of the fluid in laplace domain ⌈𝐾⌉ �̅� dimensionless temperature of the fluid 𝑇′ dimensional temperature of the fluid ⌈𝐾⌉ 𝑇0 temperature of the plate at 𝑦 = 0 ⌈𝐾⌉ 𝑇1 temperature of the plate at 𝑦 = 1 ⌈𝐾⌉ 𝑡′ dimensional time ⌈𝑠⌉ t dimensionless time 𝑈′ dimensional velocity of the fluid ⌈𝑚𝑠 −1⌉ 𝑈 dimensionless fluid velocity in laplace domain 𝑈 dimensionless fluid velocity 𝜏1̅ transient state skin friction on the plate at 𝑦 = 1 𝑁𝑢1 transient state rate of heat transfer on the plate at 𝑦 = 1 ⌈𝑊𝑠 −1⌉ �̅� volumetric mass flux rate ⌈𝑐𝑚3𝑠−1⌉ appendix b 𝐴1 = 1 𝑝 cosh(𝛿) , 𝐴2 = 0 𝐵1 = 𝑎 2𝐷𝑎𝐺𝑟 + 1 2 √( 𝑎 𝐷𝑎𝐺𝑟 ) 2 − 4𝛾𝑆𝑃𝑟 𝐺𝑟 , 𝐵2 = 𝑎 2𝐷𝑎𝐺𝑟 − 1 2 √( 𝑎 𝐷𝑎𝐺𝑟 ) 2 − 4𝛾𝑆𝑃𝑟 𝐺𝑟 𝐷1 = − 1 2 ( 𝑝 𝐺𝑟 + 𝑎 𝐺𝑟𝐷𝑎 − 𝛾𝑝𝑃𝑟 𝐺𝑟 ) + 1 2 (√( 𝑝 𝐺𝑟 + 𝑎 𝐺𝑟𝐷𝑎 − 𝛾𝑝𝑃𝑟 𝐺𝑟 ) 2 − 4𝛾𝑆𝑃𝑟 𝐺𝑟 ) 𝐷2 = − 1 2 ( 𝑝 𝐺𝑟 + 𝑎 𝐺𝑟𝐷𝑎 − 𝛾𝑝𝑃𝑟 𝐺𝑟 ) − 1 2 (√( 𝑝 𝐺𝑟 + 𝑎 𝐺𝑟𝐷𝑎 − 𝛾𝑝𝑃𝑟 𝐺𝑟 ) 2 − 4𝛾𝑆𝑃𝑟 𝐺𝑟 ) basant k. jha et al 122 𝛿1 = √(𝑝𝑃𝑟 − 𝐷1𝐺𝑟 𝛾 ), 𝛿2 = √(𝑝𝑃𝑟 − 𝐷2𝐺𝑟 𝛾 ), 𝛼1 = √ 𝐵1𝐺𝑟 𝛾 and 𝛼2 = √ 𝐵2𝐺𝑟 𝛾 references 1. yuan, y., xu, k. and zhao, k. numerical analysis of transport in porous media to reduce aerodynamic noise past a circular cylinder by application of porous foam. journal of thermal analysis and calorimetry-springer. https://doi.org/10.1007/s10973-019-08619-5. 2019. 2. ismail, a.k., ibrahim, n.h., shamsuddin, k.a., abdullah, m.z. and zubair, m. a practical approach in porous medium combustion for domestic application: a review iop conference. series: material science and engineering. https://doi.org/10.1088/1757-899x/370/1/012004. 2018. 3. vafai, k. porous media applications in biology in systems and biotechnology, crc press isbn 9780367383671. 2019. 4. andreas, s.k., joaquin, j.m. and denise, m.m. transport of nanoand micro plastic through 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transient natural convection between two vertical walls filled with a porous material having variable porosity. mathematical engineering in industry., 2001, 8(3), 177-185 30. jha, b.k. transient natural convection through vertical porous stratum. heat and mass transfer, 1997, 33, 261263. 31. jha, b.k. and singh, a.k. transient free-convection in a vertical porous due to symmetric heating. international journal of applied mechanics and engineering, 2003, 8(3), 497-502. 32. liakopoulos a.c. darcy's coefficient of permeability as symmetric tensor of second rank. hydrological sciences journal, 1965, 10(3), 41-48. received 20 may 2020 accepted 16 august 2020 squ journal for science, 2020, 25(1), 25-44 doi:10.24200/squjs.vol25iss1pp25-44 squ journal for science, 2020, 25(1), 26-47 doi:10.24200/squjs.vol25iss1pp26-47 sultan qaboos university 26 dimension reduction and relaxation of johnson’s method for two machines flow shop scheduling problem mekonnen redi* and mohammad ikram department of mathematics, arba minch university, arba minch, ethiopia. *email: mekonnen.redi@ambou.edu.et. abstract: the traditional dimensionality reduction methods can be generally classified into feature extraction (fe) and feature selection (fs) approaches. the classical fe algorithms are generally classified into linear and nonlinear algorithms. linear algorithms such as principal component analysis (pca) aim to project high dimensional data to a lower-dimensional space by linear transformations according to certain criteria. the central idea of pca is to reduce the dimensionality of the data set consisting of a large number of variables. in this paper, pca was used to reduce the dimension of flow shop scheduling problems. this mathematical procedure transforms a number of (possibly) correlated jobs into a smaller number of uncorrelated jobs called principal components, which are the linear combinations of the original jobs. these jobs are carefully determined so that from the solution of the reduced problem multiple solutions of the original high dimensional problem can readily be obtained, or completely characterized, without actually listing the optimal solution(s). the results show that by fixing only some critical jobs at the beginnings and ends of the sequence using johnson's method, the remaining jobs could be arranged in an arbitrary order in the remaining gap without violating the optimality condition that also guarantees minimum completion time. in this regard, johnson's method was relaxed by terminating the listing of jobs at the first/last available positions when the job with minimum processing time on either machine attains the highest processing time on the other machine for the first time. by terminating johnson's algorithm at an early stage, the method minimizes the time needed for sequencing those jobs that could be left arbitrarily. by allowing these jobs to be arranged in arbitrary order it gives job sequencing freedom for job operators without affecting minimum completion time. the results of the study were originally obtained for deterministic scheduling problems but they are more relevant on test problems randomly generated from uniform distribution 𝑈[𝑎,𝑏] with lower bound 𝑎 and upper bound 𝑏 and normal distribution 𝑁[𝜇,𝜎2] with mean 𝜇 and standard deviation 𝜎2. keywords: dimension reduction; flow shop scheduling problems; principal component analysis; relaxation of johnson’s algorithm. جهازين متجر التدفق في جدولةلمسألة جونسون تخفيض وإسترخاء البعد لطريقة ميكونين ريدي و محمد إكرام fe يتم تصنيف خوارزميات. (fs)واختيارها (fe) يمكن تصنيف طرق تخفيض األبعاد التقليدية عموًما باالقتراب من استخراج الصفات :لخصمال إلى عرض البيانات عالية األبعاد (pca) الكالسيكية عموًما في خوارزميات خطية وغير خطية. تهدف الخوارزميات الخطية مثل تحليل المكونات الرئيسية ألبعاد لمجموعة البيانات التي تتكون من عدد كبير المركزية هي تخفيض ا pca على فضاء أقل بعدًا باستخدام التحويالت الخطية وفقًا لمعايير معينة. إن فكرة في هذه الورقة لتخفيض البعد لمسائل جدولة متجر التدفق. يحول هذا اإلجراء الرياضي عدد )ممكن( من الوظائف pca من المتحوالت. لقد تم استخدام موعات خطية من الوظائف األصلية. يتم تحديد هذه الوظائف بعناية المرتبطة إلى عدد أصغر من الوظائف غير المرتبطة تسمى المكونات الرئيسية، وهي مج مثلى. تظهر النتائج حيث أن حل مسألة التخفيض يؤدي إلى حلول متعددة للمسألة األصلية عالية األبعاد، أو تمييزها بشكل كامل، بدون جدولة فعالية للحلول ال ت ونهايات المتسلسلة باستخدام طريقة جونسون، أنه يمكن ترتيب الوظائف المتبقية بشكل عشوائي أنه من خالل تثبيت عدد من الوظائف الحرجة فقط في بدايا في هذا الصدد، تم استرخاء طريقة جونسون بإنهاء قائمة الوظائف في الفجوة المتبقية دون انتهاك شرط األمثلية الذي يضمن الحد األدنى أيضا الكتمال الزمن. و ى/األخيرة عندما تكون الوظيفة مع زمن المعالجة األدنى على أحد األجهزة التي تصل ألعلى زمن للمعالجة على جهاز آخر ألول في المواضع المتاحة األول .مرة mailto:mekonnen.redi@ambou.edu.et dimension reduction and relaxation 27 ن خالل السماح من خالل إنهاء خوارزمية جونسون في مرحلة مبكرة، فإن الطريقة تقلل الزمن الالزم لتسلسل تلك الوظائف التي يمكن تركها بشكل عشوائي. م األصل تم الحصول على بترتيب هذه الوظائف عشوائيا يتم الحصول على حرية التسلسل لمؤثرات الوظيفة بدون التأثيرعلى الحد األدنى الكتمال الزمن. ففي والحد a مع الحد األدنى u[a,b]نتائج الدراسة لمسائل الجدولة الحتمية، لكنها كانت أكثر صلة بمسائل االختبار التي تم إنشاؤها عشوائيًا من التوزيع المنتظم .σ^2واالنحراف المعياري μمتوسط مع الn[μ,σ^2] والتوزيع الطبيعي bاألعلى .نسترخاء خوارزمية جونسوإجر التدفق ، تحليل المكون الرئيسي ، جدولة مت مسائل، تخفيض البعد: المفتاحيةالكلمات 1. introduction wo machines flow shop scheduling problem has been considered as a major problem in machine sequencing because it appears independently and as a sub-problem in the '𝑛-jobs, m-machines problem'. the criterion of optimality in a flow shop scheduling problem is usually specified as minimization of makespan, which is defined as the time gap between the beginning of the first job on the first machine and finishing of the last job on the last machine to ensure that all jobs are completed on all machines. the objective of minimizing makespan in the two machines flow shop scheduling model is also known as johnson's problem. the johnson's algorithm is an exact solution method of the two machines, one-way, no-passing scheduling tasks problem, which serves as a basis for many heuristic algorithms. this rule is a complete list of ordering the jobs by filling the first or the last available space based on minimum operation times in the two machines from the waiting list into the optimal list until finally only one free space in the optimal list and one last job to be assigned remain in the waiting list. in this procedure, 𝑛! comparisons are needed to obtain the optimal sequence. this needs large computation time for large size problems. to overcome this limitation, the current study identified a relaxation of johnson's algorithm by developing an early stopover criteria, due to the fact that, after listing only some important jobs at the beginning and end of the optimal sequence using johnson's method, it does not matter in whichever order the remaining jobs are operated as far as makespan is concerned. these criteria minimize the time needed for further computations of ordering the remaining jobs in either direction (first/last available positions) and it reduces the dimension of the problem. by allowing the remaining jobs to be arranged in an arbitrary order irrespective of johnson's method without violating the optimality condition, the study creates job sequencing freedom for job operators to give priority without affecting minimum completion time. 2. literature review johnson [1] produced a pioneering work on machine sequencing literature and great advancements have been made in the field after other researchers also started to investigate solutions to many related problems. the studies discussed in this literature review are mainly concerned with relaxations that were oriented to produce alternate optimal solutions of the problem different from the strict johnson's rule. in this regard, an early work on the relaxation of johnson's method for the two machines flow shop scheduling problem was that of ikram [2]. the study produced alternate ways of performing jobs in a way different from the one specified by johnson's method without affecting minimum completion time by interchanging two jobs at a time from the optimal johnson's sequence subject to the existence of certain conditions. in [3] also, the concept of [2] was used to find alternate optimal solutions for ‘𝑛-jobs, 2machines flow shop scheduling problem with transportation time and equivalent job-block’. in [4] the idea was extended to ‘𝑛-jobs, 3-machines’ flow shop scheduling problem' based on the work of [2]. these studies are indicators of increasing pressures on alternate ways of performing the same set of jobs in different ways without affecting minimum completion time. alternate ways enable the assigning of priorities between jobs, and give freedom for job operators. for those groups of studies that generate alternate optimal sequences by interchanging two jobs at a time from the optimal johnson's sequence, the total number of such alternate sequences is 2𝑘 where 𝑘 is the number of all interchangeable pairs. in the original paper [1], johnson also solved the 'n-jobs, 3-machines flow shop scheduling problem' in which the processing order for all the jobs in three machines a,b and c is a → b → c for two particular cases for which all jobs ji; i = 1,2,3,…,n;; satisfy max{b} ≤ min{a} or max{b} ≤ min{c}. few relaxations were made to this condition. the same assumption was made in [4] to the formulation of their alternate solution for the three machine problem. conway, maxwell and miller [5] have shown that the same rule works if b is a non-bottleneck machine, i.e., is a machine that can process any number of jobs at the same time. maggu, alam and ikram [6] also developed an algorithm for a special type of 'n -jobs, m-machines scheduling problem' which is an extension of johnson's ‘𝑛-jobs, m-machines’ sequencing rule. the general '𝑛-jobs, m-machines problem' becomes np-complete [7] for all 𝑚 ≥ 3 (cannot be solved optimally in polynomial time) and the johnson's algorithm can be applied only for some few particular cases that obey some primary conditions. the general '𝑛-jobs, m-machines' flow shop scheduling problems are np-hard, so exact optimization techniques are impractical for large size problems. in other words, classical optimization methods such as the branch and bound method, dynamic programming, etc. can be used only for small size problems. problem size has been the main challenge for the development of solution methods for these problems because the solution space in its original form is of combinatorial order of number of jobs, which makes it more difficult to solve the problems in polynomial time for large 𝑛. therefore, large size problems are solved by heuristic methods. t mekonnen redi et al 28 many heuristic methods reduce the 𝑚 machines into two virtual machines and apply johnson's algorithm based on some specific rules or decisions. important and earlier heuristic algorithms are due to palmer [8], gupta [9] and campbell, dudek, and smith’s (cds) heuristic [10]. the other heuristic is due to nawaz, enscore, and ham [11], and is known as the neh heuristic. both cds and neh are constructive heuristics. this means that they produce a sequence of at most 𝑚 − 1 solutions from which the best sequence is chosen. in these methods, all 𝑚 machines are first divided into two groups which are considered as two virtual machines, and the problem is solved by applying johnson's algorithm. the other heuristic, the hfc heuristic of koulamas [12] on the other hand, is an improvement heuristic. in contrast, an improvement heuristic starts with a given sequence and searches for improvement, but the computational effort is unpredictable. improvement heuristics are usually based on generic methods such as neighborhood search. they also use the algorithm of johnson in the first phase, and then by specific rules, make better solutions, starting from an existing feasible solution in a sequence of steps. in another heuristic, rapid access (ra) heuristic [13], two virtual machines are defined, and as in the cds heuristic, method and weights are assigned, one for each virtual machine. finally, the flow shop scheduling problem is solved by applying johnson's algorithm. in [7] also, two variants of heuristic algorithms were developed to solve the classic flow shop scheduling problem. the first algorithm was a constructive heuristic, in which each job was placed in the optimal schedule based on a greedy-type selection. the second algorithm changes the construction of an optimal schedule in a stochastic manner. in [14] also, genetic algorithms were used to solve the two machines flow shop problem with the objective of minimizing makespan. the multi-objective flow shop scheduling problems have been the subject of extensive studies. the majority of bicriteria flow shop investigations consider the combination of makespan with other performance measures [15-19]. in multi-objective problems, creating alternate solutions for the makespan objective by applying the results of this study will relax the other objectives and open more space for the applicability of multi-criteria decision making. all the above works emphasize the importance of the two machines flow shop scheduling problem and the high reliance of solution methods on johnson's algorithm. according to [7], even though the various studies have suggested many approaches, it is difficult to find the simplest approach to find an optimal sequence for solving the 𝑛jobs, 𝑚-machines flow shop scheduling problems. problem size has been the major challenge for all these heuristic methods. researchers point out the need for scheduling algorithms to minimize makespan for the ‘𝑛-jobs 𝑚-machines’ flow shop scheduling problems with the simplest steps as an alternative. however, little attempt has been made in the previous studies to decrease problem size for the applicability of the exact (heuristic) methods developed so far. dimension reduction would create enough room for the application of these methods. once the optimal sequence for the reduced problem is identified, it enables the complete characterization of all alternative optimal solutions of the original high dimensional problem. this research therefore considers dimension reduction for the two machine flow shop scheduling problem to be an important first step to decrease problem size, while at the same time creating alternative ways of sequencing jobs that guarantee the non-increase of total elapsed time on the fictitious machines formed by reducing the 𝑚 machines into two virtual machines. 3. problem statement and basic assumptions in this problem two machines (𝐴 and 𝐵) of high automation and unlimited buffer size are working together in such a way that machine 𝐴 is always available to start the next job as soon as it finishes the current job. the finished jobs in machine 𝐴 are then immediately transferred to the queue in machine 𝐵, and machine 𝐵 operates the jobs in the same order as they have been executed in machine 𝐴. if there is no job in the queue, machine 𝐵 has to wait until machine 𝐴 finishes the current job. in this case an idle time occurs for machine 𝐵 between its finishing of previous job and until machine a finishes its current one. the objective of the problem is therefore to minimize the sum of all these idle times in machine 𝐵 for all the jobs from start to end. the criterion of optimality in a flow shop scheduling problem is usually specified as minimization of makespan, which is defined as the time gap between the beginning of the first job on the first machine and finishing of the last job on the last machine to ensure that all jobs are completed on both machines. many variants of the problem have evolved since its formulation. as an objective function, mean flowtime, completion time variance and total tardiness can also be used. the results originally obtained in [1] are among the very first formal results in the theory of scheduling. the objective of minimizing makespan in the two machines flow shop scheduling model is also known as johnson's problem. the johnson's algorithm is an exact solution method of the two machines, one-way, no-passing scheduling tasks problem which serves as a basis for many heuristic algorithms [20]. the values of the processing times of a job 𝑗 𝑖 on machines 𝐴 and 𝐵 are denoted by 𝑎𝑗 𝑖 and 𝑏𝑗 𝑖 respectively for 𝑖 = 1,2,…,𝑛 are deterministically known, constant and positive. they include also all the necessary auxiliary times involved in the technological process. the following important assumptions are made in the problem. assumption 1: a set of 𝑛 unrelated, multiple-operation jobs are available for processing at time zero. (each job requires 2 operations, and each operation requires a different machine.) assumption 2: both machines are continuously available. assumption 3: only one operation is carried out on a machine at a time. assumption 4: once an operation begins in a machine, it proceeds without interruption. dimension reduction and relaxation 29 assumption 5: processing times are known in advance and are deterministic, constant and positive. assumption 6: setup times for the operations are sequence independent and are included in processing times. assumption 7: the time required in moving jobs from one machine to another is negligibly small. assumption 8: the same job-sequence is maintained over each machine, in other words no passing is allowed. 3.1. algorithm: johnson's rule johnson's rule: job 𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) precedes job 𝑗 𝑙 = (𝑎𝑗 𝑙 , 𝑏𝑗 𝑙 ) in an optimal sequence {𝑗∗ 𝑖 , 𝑖 = 1,2,3,… ,𝑛} if 𝑚𝑖𝑛{𝑎𝑗 𝑖 , 𝑏𝑗 𝑙 }≤ 𝑚𝑖𝑛{𝑎𝑗 𝑙 , 𝑏𝑗 𝑖 }. in practice, an optimal sequence is directly constructed with an adaptation of johnson's rule. the positions in sequence are filled by a one-pass mechanism that, at each stage, identifies a job that should fill either the first [last] available position.  step 1 examine the columns of 𝐴 and 𝐵 for processing times on machines 𝐴 and 𝐵 and find the smallest processing time among unscheduled jobs (waiting list).  step 2a if the smallest processing time occurs for the first machine, then place the corresponding job in the first available position in the sequence (optimal list). (ties may be broken arbitrarily.) go to step 3.  step 2b if the smallest processing time occurs for the second machine, then place the corresponding job in the last available position in the sequence (optimal list). (ties may be broken arbitrarily.) go to step 3.  step 3 remove the assigned job from consideration (waiting list) and return to step 1 until all sequence positions are filled. 3.2. algorithm: alternate formulation of johnson's rule an alternative way to describe johnson's rule [21] that provides a different perspective on the structure of optimal schedules is used for this study. in this formulation, the problem is considered as a sequencing problem put mathematically as 𝑃 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖); 𝑖 = 1,2,3,…,𝑛} where 𝑎𝑗𝑖 and 𝑏𝑗 𝑖 are processing times of job 𝑗 𝑖 on machines 𝐴 and 𝐵, respectively with no passing of jobs on the two machines in the order 𝐴 → 𝐵. the jobs in 𝑃 are then partitioned into two disjoint clusters 𝐽 1 and 𝐽 2 where 𝐽 1 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 ≤ 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} and 𝐽 2 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 > 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛}. we call jobs in 𝐽 1 jobs of the first kind and jobs in 𝐽 2 jobs of the second kind. it is important to note that jobs in 𝐽 1 have longer processing time (at least equal) on the second machine while jobs in 𝐽 2 have strictly longer processing time on the first machine. then in the optimal johnson's sequence, jobs in 𝐽 1 are first arranged in a non-decreasing order of their processing times on the first machine and then jobs in 𝐽 2 are arranged in a non-increasing order of their processing times on the second machine. the present approach is often helpful and easy to apply and implement. therefore, we follow this procedure to describe the optimal johnson's sequence for the two machines flow shop scheduling problem.  step 1: let 𝐽 1 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 ≤ 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} and 𝐽 2 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 > 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛}  step 2: arrange the members of set 𝐽 1 in non-decreasing order of 𝑎𝑗 𝑖 to get an ordered set 𝐽∗ 1 , and arrange the members of set 𝐽 2 in non-increasing order of 𝑏𝑗 𝑖 to get an ordered set 𝐽∗ 2 .  step 3: an optimal sequence is the ordered set 𝐽∗ 1 followed by the ordered set 𝐽∗ 2 . notation the optimal johnson's sequence for 𝑃 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖); 𝑖 = 1,2,3,…,𝑛} is denoted by {𝑗 ∗ 𝑖 = (𝑎𝑗∗ 𝑖 , 𝑏𝑗∗ 𝑖 ); 𝑖 = 1,2,3,… ,𝑛} = 𝑗∗ 1 → 𝑗∗ 2 → ⋯ → 𝑗∗ 𝑛 with an asterisk (*) on 𝑗. we represent by 𝑗∗ 𝑖 = (𝑎𝑗∗ 𝑖 , 𝑏𝑗∗ 𝑖 ) a job at the 𝑖𝑡ℎ position in an optimal johnson's sequence with corresponding processing times on machines 𝐴 and 𝐵, equal to 𝑎𝑗∗ 𝑖 units and 𝑏𝑗∗ 𝑖 units, respectively, and we denote its completion times on machines 𝐴 and 𝐵 by 𝐶1(𝑗 ∗ 𝑖 ) and 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑖 ) , respectively. we represent by 𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) a job at the 𝑖𝑡ℎ position in a sub-optimal sequence with corresponding mekonnen redi et al 30 processing times on machines 𝐴 and 𝐵, equal to 𝑎𝑗 𝑖 units and 𝑏𝑗 𝑖 , respectively, and its completion times on machines 𝐴 and 𝐵 by 𝐶1(𝑗𝑖) and 𝐶𝑚𝑎𝑥(𝑗𝑖) , respectively. 4. data mining and dimension reduction real-world data are typically noisy, enormous in volume, and may originate from a jumble of heterogenous sources [22]. powerful and versatile tools are very much needed to automatically uncover valuable information from the tremendous amounts of data and to transform such data into organized knowledge. this necessity has led to the birth of data mining. data mining is the process of discovering interesting patterns and knowledge from large amounts of data, having made a closer investigation of attributes and data values. as a general technology, data mining can be applied to any kind of data as long as the data are meaningful for a target application. the state-of-art data mining tools could be employed for flow shop scheduling problems to overcome the limitations of the solution methods for large size problems. due to the limited number of studies so far which have applied the state-of-the-art dimension reduction methods for flow shop scheduling problems, this paper examines the two machines flow shop scheduling problem more closely because of its significant contribution to other flow shop problems. in the absence of real-world data for a typical study, generated data play an important role. for this study, generated data from a uniform distribution 𝑈[𝑎,𝑏] with lower bound 𝑎 and upper bound 𝑏 and a normal distribution 𝑁[𝜇,𝜎2] with mean 𝜇 and standard deviation 𝜎2 were used for different parameter values, and alternatives were analysed to describe a large size problem in terms of a small number of parameters. the effort was to discover important features of flow shop scheduling problems. this knowledge discovery process involves a sequence of logical understanding of the basic features of the high dimensional problem to extract a low dimensional representation of its key features. as was suggested in [22], data mining involves a sequence of procedures that require the planners' understanding of the problem at hand. we further elaborate these steps in the context in which they have been applied to this study. some of these procedures were applied in earlier studies of flow shop scheduling problems with a different context. for example, the first step, data integration (where multiple data items may be combined), was studied by equivalent job blocks. the concept of equivalent job blocking was introduced in [23] in the theory of scheduling. in the context of this study, however, multiple jobs were, for simplicity, represented by a single representative job, which may be different from the context of equivalent job blocks. in the second step of data mining, data selection, data relevant to the analysis task are retrieved from the database. the other, following, steps of data mining were contextually used for flow shop scheduling problems to use them for the proposed study to fill the research gap in applying these techniques for dimension reduction. in the third step, data transformation, data are transformed and consolidated into forms appropriate for mining. this step was used for this study to group jobs with identical processing times that hold equal priority in the optimal sequence. thus it is enough to represent jobs with equal priority by a single representative job to reduce the dimension of the problem. this step was used in the principal component analysis (see section 4. 1). the fourth step, the data mining step, is an essential process where intelligent methods are applied to extract data patterns and to understand how only important patterns are exhibited. this step was used to develop mini-max criteria (see section 4.2) to reduce the dimension of jobs of the first kind (see section 4.2.1) and jobs of the second kind (see section 4.2.2). the fifth step, the pattern evaluation step, consists of identifying the truly interesting patterns representing knowledge based on interestingness measures, and checking whether further conclusions could be reached about the high dimensional problem from its low dimensional representation. this step was carried out in this research by formulating the results in the form of theorems and giving analytic mathematical proofs (see section 4.2). in the sixth step, the knowledge presentation step, illustrations are made to confirm the findings on a theory of knowledge; it aims to present mined knowledge convincingly to other users. this involves the organization of this study in a form of publication with all the necessary background information to acceptable competency levels. in particular, the illustration example in section 5 also plays this role. in the next sub-sections the main findings of the study are organized as theorems and algorithms. in section 4.1 principal component analysis (pca) is discussed in the sense of its application for dimension reduction of flow shop scheduling problems. in section 4.2 further dimension reduction is carried out using mini-max criteria. here, two investigations are made independently for the two kinds of jobs discussed earlier. for jobs with more processing time on the second machine, an early stopover criteria was achieved when the job assigned to the first available position with minimum processing time criteria, for the first time, attains the highest processing time on the second machine for all jobs of the first kind (see section 4.2.1). similarly, for jobs with more processing time on the first machine, an early stopover criteria was achieved when the job assigned to the last available position with minimum processing time criteria, for the first time, attains the highest processing time on the first machine for all jobs of the second kind (see section 4.2.2). finally, these results are formulated in the form of algorithms. the first algorithm is a dimension reduction algorithm and it combines the dimension reductions carried out dimension reduction and relaxation 31 in section 4.1 and section 4.2 together. the second algorithm is a relaxation of johnson's algorithm and it combines the early stopover criteria achieved in section 4.1 and section 4.2 as termination criteria for johnson's algorithm. 4.1. dimension reduction by principal component analysis the state-of-the-art dimensional reduction (dr) methods are divided into projective methods and methods that model the manifold on which the data lies. perhaps the simplest approach is to attempt to find low dimensional projections that extract useful information from the data, by maximizing a suitable objective function [25]. cluster analysis is one of the major data analysis methods which are widely used for many practical applications. the purpose of clustering is to group together data points, which are close to one another [26]. let problem 𝑃 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖); 𝑖 = 1,2,3,…,𝑛} be the original high dimensional problem where the notation 𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ); 𝑖 = 1,2,3,… , 𝑛 means job 𝑗 𝑖 has processing time equal to 𝑎𝑗 𝑖 units on machines a and processing time of 𝑏𝑗 𝑖 units on machine 𝐵 , and the aim is to find the optimal sequence s = {𝑗∗ 𝑖 ; 𝑖 = 1,2,3,…,𝑛} that minimizes total elapsed time of operating all jobs in the same order in the two machines uninterrupted with no passing of jobs on the two machines in the order a → 𝐵. now we partition all jobs in 𝑃 into two clusters, by defining a function 𝐽: 𝑃 → {0,1} given by the formula (1). 𝐽(𝑗𝑖) = 𝐽((𝑎𝑗𝑖,𝑏𝑗𝑖)) = { 0 𝑖𝑓 𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝑃: 𝑎𝑗𝑖 ≤ 𝑏𝑗𝑖 1 𝑖𝑓 𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝑃: 𝑎𝑗𝑖 > 𝑏𝑗𝑖 (1) let 𝐽 1 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝐽(𝑗 𝑖 ) = 𝐽((𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 )) = 0} and 𝐽 2 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝐽(𝑗 𝑖 ) = 𝐽((𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 )) = 1}. define the projection mapping :𝑓:𝑃 → {0,1} × ℜ given by the formula (2). 𝑓(𝑗𝑖) = 𝑓((𝑎𝑗𝑖,𝑏𝑗𝑖)) = { (0,𝑎𝑗𝑖) 𝑖𝑓 𝐽((𝑎𝑗𝑖,𝑏𝑗𝑖)) = 0 (1,𝑏𝑗𝑖) 𝑖𝑓 𝐽((𝑎𝑗𝑖,𝑏𝑗𝑖)) = 1 (2) this map specifies the kind of job and the corresponding processing time of the job that is relevant for assigning it to the optimal johnson’s sequence. let the image of 𝑃 under 𝑓 be given by 𝐼𝑚(𝑃) = 𝑓(𝑃) = {𝑥:𝑥 = 𝑓(𝑗𝑖) 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒 𝑗𝑖 ∈ 𝑃}. we call the elements of 𝑓(𝑃) principal components of 𝑃. then the inverse image of 𝑓 is given by 𝑓−1(𝑃): 𝑓(𝑃) → 𝑃 given by the formula (3). 𝑓−1(𝑥) = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑓(𝑗 𝑖 ) = 𝑓((𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 )) = 𝑥} (3) equation (3) clusters all jobs into disjoint equivalence classes consisting of exactly those jobs in 𝐽 1 that have equal processing times on the first machine or those jobs in 𝐽 2 that have equal processing times on the second machine. in the optimal johnson's sequence the jobs in each cluster are arranged successively. let there be 𝐾 principal components 𝑥1, 𝑥2,… ,𝑥𝐾 with 𝜂1, 𝜂2,… ,𝜂𝐾 number of jobs in 𝑓 −1(𝑥1), 𝑓 −1 (𝑥2),… ,𝑓 −1(𝑥𝐾) , respectively, such that 𝜂1 + 𝜂2 + ⋯+ 𝜂 𝐾 = 𝑛. thus all jobs in the same cluster could be represented by a single job from the group and number of reserved positions for these jobs by 𝜂 1 , 𝜂 2 ,… ,𝜂 𝐾 . in particular if we determine to represent each cluster with the job that has the longest total processing time on the two machines, then a unique identifier is assigned to each job. define 𝑓∗:{𝑥1, 𝑥2,… ,𝑥𝐾} → 𝑃 given by the formula (4). 𝑓∗(𝑥𝑘) = 𝑗𝑘 = (𝑎𝑗𝑘, 𝑏𝑗𝑘) where 𝑎𝑗𝑘 + 𝑏𝑗𝑘 = 𝑚𝑎𝑥(𝑎𝑗𝑖,𝑏𝑗𝑖)∈𝑓 −1(𝑥𝑘) {𝑎𝑗 𝑖 + 𝑏𝑗 𝑖 } (4) this is a choice function selecting the job with highest total processing time on the two machines from each cluster. the collection 𝑃∗ = {(𝑓∗(𝑥𝑘), 𝜂𝑘, 𝑓 −1(𝑥𝑘)) , 𝑘 = 1,2,… ,𝐾} characterizes all jobs in 𝑃 that occupy equal priority in the optimal johnson's sequence by 𝑓−1(𝑥𝑘), the total number of jobs in the group by 𝜂𝑘 and a representative job 𝑓∗(𝑥𝑘) for 𝑘 = 1,2,…,𝐾. this way the original high dimensional problem is represented by a lower dimensional sub-problem 𝑃∗. for each job 𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃, there is a unique identifier (𝑓∗(𝑥𝑘), 𝜂𝑘, 𝑓 −1(𝑥𝑘)) ∈ 𝑃 ∗ such that 𝑓((𝑎𝑗𝑖,𝑏𝑗𝑖)) = 𝑓((𝑎𝑗𝑘,𝑏𝑗𝑘)) and 𝑓 ∗(𝑥𝑘) = (𝑎𝑗 𝑘 , 𝑏𝑗 𝑘 ). mekonnen redi et al 32 thus, the original high dimensional flow shop scheduling problem was defined in terms of the low dimensional sub-problem from which the solution of the original two machines flow shop scheduling problem could be obtained more readily by replacing the representative job by the block of jobs it corresponds to. more specifically, the original '𝑛 -job 2-machine problem' is reduced into 𝐾 clusters with 𝜂 1 , 𝜂 2 ,… ,𝜂 𝐾 number of jobs respectively where 𝜂 1 + 𝜂 2 + ⋯+ 𝜂 𝐾 = 𝑛. at this stage of dimension reduction there are at least 𝜂 1 ! ∗ 𝜂 2 ! ∗ …∗ 𝜂 𝐾 ! alternative optimal sequences to this problem. 4.2. dimension reduction of jobs by means of mini-max criteria the traditional and the state-of-the-art dimension reduction methods can be generally classified into feature extraction (fe) and feature selection (fs) approaches. fe algorithms aim to extract features by projecting the original high-dimensional data to a lower-dimensional space through algebraic transformations [26]. the classical fe algorithms are generally classified into linear and nonlinear approaches. in contrast to the fe algorithms, fs algorithms have been widely used on large-scale data and aim at finding out a subset of the most representative features according to some objective function. it is optional that we assume dimensional reduction by pca method discussed in the previous section has already been carried out for the problem before we apply mini-max criteria in this section. principle of mathematical induction (pmi) we use the principle of mathematical induction (pmi) to prove the results of the next section. it states as follows: let 𝑃(𝑛) be a property that depends on natural numbers 𝑛 satisfies the following two conditions: i. 𝑃(𝑘0) holds true and ii. 𝑃(𝑘 + 1) holds true whenever 𝑃(𝑘) holds true. then 𝑃(𝑛) holds true for all natural numbers 𝑛 ≥ 𝑘0. 4.2.1. dimension reduction of jobs with more processing time on the second machine theorem 1 let the '𝑛jobs, 2machines' sequencing problem 𝑃 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖); 𝑖 = 1,2,3,…,𝑛} be in the reduced form after dimension reduction using pca has been performed where the notation 𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) means 𝑎𝑗 𝑖 and 𝑏𝑗 𝑖 are processing times of job 𝑗 𝑖 on machines 𝐴 and 𝐵 respectively for all 𝑖 = 1,2,3,…,𝑛 and the machine order is 𝐴 → 𝐵 with no passing rule. suppose we partition all jobs in 𝑃 into two disjoint classes 𝐽 1 and 𝐽 2 where 𝐽 1 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 ≤ 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} and 𝐽 2 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 > 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛}. let there be 𝑛1 jobs in 𝐽1 and 𝑛2 jobs in 𝐽2 with 𝑛1 + 𝑛2 = 𝑛. let the sequence {𝑗 ∗ 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} = 𝑗∗ 1 → 𝑗∗ 2 → 𝑗∗ 3 → ⋯ → 𝑗∗ 𝑛 be an optimal johnson's sequence obtained by the second alternative rule. consider the jobs in 𝐽 1 only. let 𝑏𝑗∗ 𝑘 = 𝑚𝑎𝑥𝑎𝑗𝑖≤𝑏𝑗𝑖 {𝑏𝑗 𝑖 : (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃} = 𝑚𝑎𝑥(𝑎𝑗𝑖,𝑏𝑗𝑖) ∈𝐽1 {𝑏𝑗 𝑖 } occur in the optimal sequence for some job 𝑗∗ 𝑘 = (𝑎𝑗∗ 𝑘 , 𝑏𝑗∗ 𝑘 ) where 1 ≤ 𝑘 ≤ 𝑛1. if this job is not unique, choose the first occurrence of all such jobs. that is, choose the job 𝑗 ∗ 𝑘 = (𝑎𝑗∗ 𝑘 , 𝑏𝑗∗ 𝑘 ) such that 𝑏𝑗∗ 𝑘 =𝑚𝑎𝑥(𝑎𝑗𝑖,𝑏𝑗𝑖) ∈𝐽1 {𝑏𝑗 𝑖 } and 𝑎𝑗∗ 𝑘 =𝑚𝑖𝑛𝑏𝑗𝑖=𝑏𝑗∗𝑘 {𝑎𝑗 𝑖 : (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝐽 1 }. then the block of jobs 𝑗∗ 𝑘+1 → 𝑗∗ 𝑘+2 → 𝑗∗ 𝑘+3 → ⋯ → 𝑗∗ 𝑛1 could be arranged in an arbitrary order within the block while keeping all the remaining jobs fixed in their position in the optimal johnson's sequence without violating the optimality condition. moreover, these jobs do not create any idle time for machine , and the completion time of job 𝑗∗ 𝑘+𝑚 on machine 𝐵 is given by the formula (5) for 𝑘 ≤ 𝑘 + 𝑚 ≤ 𝑛1. 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘+𝑚 ) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗∗ 𝑘+𝑖 𝑚 𝑖=1 (5) consequently, the completion time of all jobs of the first kind on machine 𝐵 is given by the formula (6) irrespective of the order of operation of the jobs 𝑗∗ 𝑘+1 → 𝑗∗ 𝑘+2 → 𝑗∗ 𝑘+3 → ⋯ → 𝑗∗ 𝑛1 . 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗∗ 𝑖 𝑛1 𝑖=𝑘+1 (6) proof let {𝑗∗ 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} = 𝑗∗ 1 → 𝑗∗ 2 → 𝑗∗ 3 → ⋯ → 𝑗∗ 𝑛 be an optimal johnson’s sequence, and 𝑗∗ 𝑘 be the job described in the theorem. let machine 𝐴 finish job 𝑗∗ 𝑘 at 𝐶1(𝑗 ∗ 𝑘 ) and machine 𝐵 finish job 𝑗∗ 𝑘 at 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) and let the sequence of jobs 𝑗 k+1 → 𝑗 k+2 → 𝑗 k+3 → ⋯ → 𝑗 n1 be any permutation of the sequence 𝑗∗ k+1 → 𝑗∗ k+2 → 𝑗∗ k+3 → ⋯ → 𝑗∗ n1 . dimension reduction and relaxation 33 for any job 𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛 the following relation (7) holds. 𝐶1(𝑗𝑖) + 𝑏𝑗𝑖 ≤ 𝐶𝑚𝑎𝑥(𝑗𝑖) (7) from which we get also 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘 ≤ 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ). for any job 𝑗 𝑘+𝑖 ; 𝑖 = 1,2,… ,𝑛1 − 𝑘 the following relations (8)-(9) hold. 𝑎𝑗 𝑘+𝑖 ≤ 𝑏𝑗 𝑘+𝑖 ≤ 𝑏𝑗∗ 𝑘 (8) 𝑎𝑗∗ 𝑘 ≤ 𝑎𝑗 𝑘+𝑖 ≤ 𝑏𝑗 𝑘+𝑖 (9) let us consider the starting and finishing times of the jobs in {𝑗 𝑘+𝑖 ; 𝑖 = 1,2,… ,𝑛1 − 𝑘} on the two machines 𝐴 and 𝐵. it is important to note that at any stage of machine sequencing, if machine 𝐵 finishes job 𝑗 𝑖 at 𝑡 = 𝐶𝑚𝑎𝑥(𝑗𝑖) and machine 𝐴 finishes the next job 𝑗 𝑖+1 at 𝑡 = 𝐶1(𝑗𝑖+1), then machine 𝐵 starts job 𝑗𝑖+1 at 𝑚𝑎𝑥{𝐶1(𝑗𝑖+1), 𝐶𝑚𝑎𝑥(𝑗𝑖)}. 1. machine 𝐴 starts job 𝑗 𝑘+1 at 𝑡 = 𝐶1(𝑗 ∗ 𝑘 ) and completes it at 𝑡 = 𝐶1(𝑗𝑘+1) = 𝐶1(𝑗 ∗ 𝑘 ) + 𝑎𝑗 𝑘+1 . using equations (7)-(9), the finishing time of job 𝑗 𝑘+1 on machine 𝐴 satisfies the relations (10)-(13) below. 𝐶1(𝑗𝑘+1) = 𝐶1(𝑗 ∗ 𝑘 ) + 𝑎𝑗 𝑘+1 (10) 𝐶1(𝑗𝑘+1) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 (11) 𝐶1(𝑗𝑘+1) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘 (12) 𝐶1(𝑗𝑘+1).≤ 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) (13) the right side of (13) is the finishing time of job 𝑗∗ 𝑘 on machine b. hence machine b starts job 𝑗 𝑘+1 at 𝑚𝑎𝑥{𝐶1(𝑗𝑘+1),𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 )} = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ). thus, this job does not create any idle time for machine 𝐵. the finishing time of this job on machine 𝐵 is given by equation (14). 𝐶𝑚𝑎𝑥(𝑗𝑘+1) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗 𝑘+𝑖 1 𝑖=1 (14) thus, the theorem holds true for 𝑚 = 1. 2. machine 𝐴 starts job 𝑗 𝑘+2 at 𝑡 = 𝐶1(𝑗𝑘+1) and completes it at 𝑡 = 𝐶1(𝑗𝑘+2) = 𝐶1(𝑗𝑘+1) + 𝑎𝑗𝑘+2. using equations (7)-(9), the finishing time of job 𝑗 𝑘+2 on machine 𝐴 satisfies the relations (15)-(18) below. 𝐶1(𝑗𝑘+2) = 𝐶1(𝑗 ∗ 𝑘 ) + 𝑎𝑗 𝑘+1 + 𝑎𝑗 𝑘+2 (15) 𝐶1(𝑗𝑘+2) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 (16) 𝐶1(𝑗𝑘+2) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗∗ 𝑘 (17) 𝐶1(𝑗𝑘+2) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘 + 𝑏𝑗 𝑘+1 (18) 𝐶1(𝑗𝑘+2) ≤ 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 = 𝐶𝑚𝑎𝑥(𝑗𝑘+1) (19) the right side of (19) is the finishing time of job 𝑗 𝑘+1 on machine 𝐵. hence machine 𝐵 starts job 𝑗 𝑘+2 at 𝑚𝑎𝑥{𝐶1(𝑗𝑘+2),𝐶𝑚𝑎𝑥(𝑗𝑘+1)} = 𝐶𝑚𝑎𝑥(𝑗𝑘+1). thus, this job does not create any idle time for machine 𝐵. using (14) the finishing time of this job on machine 𝐵 is given by equations (20)-(21). 𝐶𝑚𝑎𝑥(𝑗𝑘+2) = 𝐶𝑚𝑎𝑥(𝑗𝑘+1) + 𝑏𝑗𝑘+2 = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 (20) 𝐶𝑚𝑎𝑥(𝑗𝑘+2) = 𝐶𝑚𝑎𝑥(𝑗𝑘+1) + 𝑏𝑗𝑘+2 = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗 𝑘+𝑖 2 𝑖=1 (21) thus, the theorem holds true for 𝑚 = 2. mekonnen redi et al 34 induction assumption 3. suppose the formula works for 𝑚 such that 𝑘 + 1 ≤ 𝑘 + 𝑚 ≤ 𝑛1 i. e. machine 𝐵 finishes job 𝑗𝑘+m at formula (22). 𝐶𝑚𝑎𝑥(𝑗𝑘+𝑚) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 + ⋯+ 𝑏𝑗 𝑘+𝑚 (22) 𝐶𝑚𝑎𝑥(𝑗𝑘+𝑚) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗 𝑘+𝑖 𝑚 𝑖=1 (23) then machine 𝐴 finishes job 𝑗 𝑘+m+1 at time 𝑡 = 𝐶1(𝑗𝑘+𝑚+1) given by equation (24) 𝐶1(𝑗𝑘+𝑚+1) = 𝐶1(𝑗 ∗ 𝑘 ) + 𝑎𝑗 𝑘+1 + 𝑎𝑗 𝑘+2 + ⋯+ 𝑎𝑗 𝑘+𝑚+1 (24) using equations (7)-(9), the finishing time of job 𝑗 𝑘+m+1 on machine 𝐴 satisfies the relations (25)-(29) below. 𝐶1(𝑗𝑘+m+1) = 𝐶1(𝑗 ∗ 𝑘 ) + 𝑎𝑗 𝑘+1 + 𝑎𝑗 𝑘+2 + ⋯+ 𝑎𝑗 𝑘+m+1 (25) 𝐶1(𝑗𝑘+m+1) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 + ⋯+ 𝑏𝑗 𝑘+m+1 (26) 𝐶1(𝑗𝑘+m+1) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 + ⋯+ 𝑏𝑗 𝑘+m + 𝑏𝑗∗ 𝑘 (27) 𝐶1(𝑗𝑘+m+1) ≤ 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘 + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 + ⋯+ 𝑏𝑗 𝑘+m (28) 𝐶1(𝑗𝑘+m+1) ≤ 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 + ⋯+ 𝑏𝑗 𝑘+m = 𝐶max(𝑗𝑘+m) (29) the right side of (29) is the finishing time of job 𝑗 𝑘+m on machine 𝐵. hence machine 𝐵 starts job 𝑗 𝑘+m+1 at 𝑚𝑎𝑥{𝐶1(𝑗𝑘+𝑚+1), 𝐶𝑚𝑎𝑥(𝑗𝑘+𝑚)} = 𝐶𝑚𝑎𝑥(𝑗𝑘+𝑚). thus, this job does not create any idle time for machine 𝐵. the finishing time of this job on machine 𝐵 is given by equations (30)-(31). 𝐶𝑚𝑎𝑥(𝑗𝑘+𝑚+1) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 + ⋯+ 𝑏𝑗 𝑘+𝑚+1 (30) 𝐶𝑚𝑎𝑥(𝑗𝑘+𝑚+1) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗 𝑘+𝑖 𝑚+1 𝑖=1 (31) hence the formula also works for 𝑚 + 1. thus, by the principle of mathematical induction, formula (5) holds for all m such that 𝑘 + 1 ≤ 𝑘 + 𝑚 ≤ 𝑛1. thus, the finishing time of job 𝑗∗ 𝑛1 is given by: 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘+1 + 𝑏𝑗∗ 𝑘+2 + ⋯+ 𝑏𝑗∗ 𝑛1 (32) 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗∗ 𝑖 𝑛1 𝑖=𝑘+1 (33) equation (33) is identical to (6). the total elapsed time to finish 𝑛1 jobs of the first kind on machine 𝐵 is 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘+1 + 𝑏𝑗∗ 𝑘+2 + ⋯+ 𝑏𝑗∗ 𝑛1 and it is independent of the order of the jobs 𝑗 𝑘+1 , 𝑗 𝑘+2 , 𝑗 𝑘+3 ,… , 𝑗 𝑛1 and it creates no additional idle time for machine 𝐵 after job 𝑗∗ 𝑘 . since the jobs 𝑗 𝑘+1 , 𝑗 𝑘+2 , 𝑗 𝑘+3 ,… , 𝑗 𝑛1 are permutations of the jobs 𝑗∗ 𝑘+1 , 𝑗∗ 𝑘+2 , 𝑗∗ 𝑘+3 ,… , 𝑗∗ 𝑛1 , we get 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗 𝑘+1 + 𝑏𝑗 𝑘+2 + ⋯+ 𝑏𝑗 𝑛1 = 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘+1 + 𝑏𝑗∗ 𝑘+2 + ⋯+ 𝑏𝑗∗ 𝑛1 . the optimal sequence is also obtained by one of these permutations and the total elapsed time in the optimal sequence to finish 𝑛1 jobs of the first kind is 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑘+1 + 𝑏𝑗∗ 𝑘+2 + ⋯+ 𝑏𝑗∗ 𝑛1 . if, further, we keep all jobs in 𝐽 2 fixed in the optimal sequence, the total elapsed time to finish all jobs with the above freedom will be equal to the optimal value. hence any sequence obtained by the above sequencing freedom is optimal. since we are free to arrange the jobs 𝑗∗ 𝑘+1 , 𝑗∗ 𝑘+2 , 𝑗∗ 𝑘+3 ,… , 𝑗∗ 𝑛1 in an arbitrary order, the above machine sequencing freedom creates (𝑛1 − 𝑘)! sequences all of which are optimal. for references, we call the job 𝑗∗ 𝑘 in the above theorem formulation the minimal job of {𝑗∗ 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} = 𝑗∗ 1 → 𝑗∗ 2 → 𝑗∗ 3 → ⋯ → 𝑗∗ 𝑛 and we call the block of jobs 𝑗∗ 𝑘+1 → 𝑗∗ 𝑘+2 → 𝑗∗ 𝑘+3 → … → 𝑗∗ 𝑛1 the free jobs of first kind. dimension reduction and relaxation 35 4.2.2. dimension reduction of jobs with more processing time on the first machine theorem 2 let the '𝑛jobs, 2machines' sequencing problem 𝑃 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖); 𝑖 = 1,2,3,…,𝑛} be in the reduced form after dimension reduction using pca has been performed where the notation 𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) means 𝑎𝑗 𝑖 and 𝑏𝑗 𝑖 are processing times of job 𝑗 𝑖 on machines 𝐴 and 𝐵 respectively for all 𝑖 = 1,2,3,…,𝑛 and the machine order is 𝐴 → 𝐵 with no passing rule. suppose we partition all jobs in 𝑃 into two disjoint classes 𝐽1 and 𝐽2 where 𝐽1 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝑃: 𝑎𝑗𝑖 ≤ 𝑏𝑗𝑖; 𝑖 = 1,2,3,…,𝑛} and 𝐽2 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝑃: 𝑎𝑗𝑖 > 𝑏𝑗𝑖; 𝑖 = 1,2,3,…,𝑛}. let there be 𝑛1 jobs in 𝐽1 and 𝑛2 jobs in 𝐽2 with 𝑛1 + 𝑛2 = 𝑛. let the sequence {𝑗 ∗ 𝑖 ; 𝑖 = 1,2,3,…,𝑛} = 𝑗∗ 1 → 𝑗∗ 2 → 𝑗∗ 3 → ⋯ → 𝑗∗ 𝑛 be an optimal johnson's sequence obtained by the second alternative rule. consider the jobs in 𝐽2 only. let 𝑎𝑗∗𝑞 = 𝑚𝑎𝑥𝑎𝑗𝑖>𝑏𝑗𝑖 {𝑎𝑗𝑖: (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝑃} = 𝑚𝑎𝑥(𝑎𝑗𝑖,𝑏𝑗𝑖) ∈𝐽2 {𝑎𝑗𝑖} occur in the optimal sequence for some job 𝑗 ∗ 𝑞 = (𝑎𝑗∗𝑘,𝑏𝑗 ∗ 𝑘 ) where 𝑛1 + 1 ≤ 𝑞 ≤ 𝑛. if this job is not unique, choose the last occurrence of all such jobs. that is, choose the job 𝑗∗ 𝑞 = (𝑎𝑗∗𝑞,𝑏𝑗 ∗ 𝑞 ) such that 𝑎𝑗∗𝑞 =𝑚𝑎𝑥(𝑎𝑗𝑖,𝑏𝑗𝑖) ∈𝐽2 {𝑎𝑗𝑖} and 𝑏𝑗∗𝑞 =𝑚𝑖𝑛𝑎𝑗𝑖=𝑎𝑗∗𝑞 {𝑏𝑗𝑖, (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝐽2}. let the sequence {𝑗𝑖; 𝑖 = 𝑛1 + 1, …,𝑞 − 2,𝑞 − 1} = 𝑗𝑛1+1 → ⋯ → 𝑗𝑞−2 → 𝑗𝑞−1 be any permutation of the sequence {𝑗 ∗ 𝑖 ; 𝑖 = 𝑛1 + 1, …,𝑞 − 2,𝑞 − 1} = 𝑗∗ 𝑛1+1 → ⋯ → 𝑗∗ 𝑞−2 → 𝑗∗ 𝑞−1 . then individual jobs in the block of jobs 𝑗∗ 𝑛1+1 → ⋯ → 𝑗∗ 𝑞−2 → 𝑗∗ 𝑞−1 could be arranged in an arbitrary order among themselves while keeping all the remaining jobs fixed in their position in the optimal sequence without violating the optimality condition. in other words, the sequence 𝑗∗ 1 → 𝑗∗ 2 → 𝑗∗ 3 → ⋯ → 𝑗∗ 𝑛1 → 𝑗𝑛1+1 → ⋯ → 𝑗𝑞−2 → 𝑗𝑞−1 → 𝑗 ∗ 𝑞 → 𝑗∗ 𝑞+1 → 𝑗∗ 𝑞+2 → 𝑗∗ 𝑞+3 → ⋯ → 𝑗∗ 𝑛 is also optimal. more specifically, the completion time of the job 𝑗∗ 𝑞 on machine 𝐵 is independent of the order of jobs 𝑗 𝑛1+1 ,… , 𝑗 𝑞−2 , 𝑗 𝑞−1 and is given by equation (34). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 }. (34) proof let the sequence 𝑗 𝑛1+1 → ⋯ → 𝑗 𝑞−2 → 𝑗 𝑞−1 be any permutation of the sequence 𝑗∗ 𝑛1+1 → ⋯ → 𝑗∗ 𝑞−2 → 𝑗∗ 𝑞−1 . let us consider the finishing times of the job 𝑗∗ 𝑞 starting from any job 𝑗 𝑛1+1 ,… , 𝑗 𝑞−2 , 𝑗 𝑞−1 downward. first, observe that for all jobs 𝑗 𝑛1+1 ,… , 𝑗 𝑞−2 , 𝑗 𝑞−1 we see that the following relations (35) (36) hold. 𝑏𝑗 𝑞−𝑖 < 𝑎𝑗 𝑞−𝑖 ≤ 𝑎𝑗∗ 𝑞 (35) 𝑏𝑗∗ 𝑞 ≤ 𝑏𝑗 𝑞−𝑖 ≤ 𝑎𝑗 𝑞−𝑖 (36) we use induction on the number of jobs in between 𝑛1 and 𝑞. 1. we first show the theorem holds for the case when there is no job in between 𝑛1 and 𝑞 i. e. 𝑞 − 1 = 𝑛1. in this case, machine 𝐴 starts job 𝑗∗ 𝑞 at 𝐶1 (𝑗 ∗ 𝑛1 ) and completes it at 𝐶1 (𝑗 ∗ 𝑞 ) given by equation (37). 𝐶1 (𝑗 ∗ 𝑞 ) = 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 (37) thus machine 𝐵 starts job 𝑗∗ 𝑞 at 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 )}, and completes it at 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞 ) given by equation (38) 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 } (38) if we replace 𝑚 = 0 in the formula in equation (34), we get equations (39)-(41). 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−0−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 0 𝑖=1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−0−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 0 𝑖=1 } (39) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−1 ) + 𝑎𝑗∗𝑞 + 𝑏𝑗 ∗ 𝑞 ,𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−1 ) + 𝑏𝑗∗𝑞} (40) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗𝑞 + 𝑏𝑗 ∗ 𝑞 ,𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗𝑞} (41) equation (41) is identical to equation (38). mekonnen redi et al 36 thus, the theorem holds true for the case when 𝑞 − 1 = 𝑛1. 2. we next show the theorem holds for the case when there is only one job in between 𝑛1 and 𝑞 i. e. 𝑞 − 2 = 𝑛1. in this case, machine 𝐴 starts job 𝑗 𝑛1+1 at 𝐶1 (𝑗 ∗ 𝑛1 ) and completes it at 𝐶1 (𝑗𝑛1+1 ) = 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 and machine 𝐵 starts job 𝑗 𝑛1+1 at 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 )}, and completes it at 𝐶𝑚𝑎𝑥 (𝑗𝑛1+1 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 + 𝑏𝑗 𝑛1+1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗 𝑛1+1 }. then, machine 𝐵 starts job 𝑗∗ 𝑞 at 𝐶1 (𝑗𝑛1+1 ) and completes it at 𝐶1 (𝑗 ∗ 𝑞 ) = 𝐶1 (𝑗𝑛1+1 ) + 𝑎𝑗∗ 𝑞 and machine 𝐵 starts job 𝑗∗ 𝑞 at 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞 ) , 𝐶𝑚𝑎𝑥 (𝑗𝑛1+1 )}. 𝑚𝑎𝑥 {𝐶1 (𝑗𝑛1+1 ) + 𝑎𝑗∗ 𝑞 ,𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 + 𝑏𝑗 𝑛1+1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗 𝑛1+1 }} (42) 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 + 𝑎𝑗∗ 𝑞 ,𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 + 𝑏𝑗 𝑛1+1 ,𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗 𝑛1+1 } (43) but since 𝑏𝑗 𝑛1+1 ≤ 𝑎𝑗 𝑛1+1 ≤ 𝑎𝑗∗ 𝑞 , we get 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 + 𝑏𝑗 𝑛1+1 ≤ 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 + 𝑎𝑗∗ 𝑞 . thus, the maximum of the three numbers in equation (43) reduces to a maximum of two numbers in equation (44). 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗 𝑛1+1 + 𝑎𝑗∗ 𝑞 ,𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗 𝑛1+1 } (44) thus, the finishing time of job 𝑗∗ 𝑞 on machine 𝐵 is given by the equation (45) 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + 𝑎𝑗 𝑛1+1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + 𝑏𝑗 𝑛1+1 } (45) (11) if we put 𝑚 = 1, in the formula (34) we get (46)-(49) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−1−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 1 𝑖=1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−1−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 1 𝑖=1 } (46) 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−2 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + 𝑎𝑗 𝑞−1 ,𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−2 ) + 𝑏𝑗∗ 𝑞 + 𝑏𝑗 𝑞−1 } (47) 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + 𝑎𝑗 𝑞−1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + 𝑏𝑗 𝑞−1 } (48) 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + 𝑎𝑗 𝑛1+1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + 𝑏𝑗 𝑛1+1 } (49) equation (49) is identical to equation (45). thus, the formula works for 𝑚 = 1. thus, the theorem holds for the case when 𝑞 − 2 = 𝑛1. induction assumption 3. suppose for any 𝑚 such that 𝑛1 + 1 ≤ 𝑞 − 𝑚 ≤ 𝑞, the finishing time of the job 𝑗 ∗ 𝑞 on machine 𝐵 is independent of the order of jobs 𝑗 𝑞−𝑚 ,… , 𝑗 𝑞−2 , 𝑗 𝑞−1 and is given by equation (50). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (50) we want to show that the formula works for 𝑚 + 1. it is sufficient that we show the finishing time of the job 𝑗∗ 𝑞 on machine 𝐵 is independent of the order of jobs 𝑗 𝑞−𝑚−1 , 𝑗 𝑞−𝑚 ,… , 𝑗 𝑞−2 , 𝑗 𝑞−1 and is given by equation (51). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚+1 𝑖=1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚+1 𝑖=1 } (51) machine 𝐴 starts job 𝑗 𝑞−𝑚−1 at 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) and completes it at 𝐶1 (𝑗𝑞−𝑚−1) = 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 and machine 𝐵 starts job 𝑗 𝑞−𝑚−1 at 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 )} and the finishing time is given by equation (52). 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗𝑞−𝑚−1 + 𝑏𝑗𝑞−𝑚−1,𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗𝑞−𝑚−1} (52) dimension reduction and relaxation 37 since there are 𝑚 jobs 𝑗 𝑞−𝑚 ,… , 𝑗 𝑞−3 , 𝑗 𝑞−2 , 𝑗 𝑞−1 , by induction assumption, the finishing time of the job 𝑗∗ 𝑞 on machine 𝐵 is independent of the order of jobs 𝑗 𝑞−𝑚 ,… , 𝑗 𝑞−3 , 𝑗 𝑞−2 , 𝑗 𝑞−1 and is given by equation (53). 𝑚𝑎𝑥 {𝐶1 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 , 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (53) equation (53) is rewritten as equation (54) to save space, and substituting equation (52) in equation (54), we get equation (55). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (54) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗𝑞−𝑚−1) + 𝑎𝑗∗𝑞 + 𝑏𝑗 ∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 + 𝑏𝑗 𝑞−𝑚−1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗 𝑞−𝑚−1 } + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (55) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗𝑞−𝑚−1) + 𝑎𝑗∗𝑞 + 𝑏𝑗 ∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 + 𝑏𝑗 𝑞−𝑚−1 + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗 𝑞−𝑚−1 + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (56) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 + 𝑏𝑗 𝑞−𝑚−1 + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗 𝑞−𝑚−1 + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (57) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚+1 𝑖=1 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚+1 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚+1 𝑖=1 } (58) but since 𝑏𝑗 𝑞−𝑖 < 𝑎𝑗 𝑞−𝑖 ≤ 𝑎𝑗∗ 𝑞 , the second number in (58) is less than the first number. 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗 𝑞−𝑚−1 + 𝑏𝑗∗ 𝑞 + ∑ 𝑏j 𝑞−𝑖 𝑚+1 𝑖=1 (59) < 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗∗𝑞 + 𝑏𝑗 ∗ 𝑞 + ∑ 𝑎j𝑞−𝑖 𝑚+1 𝑖=1 (60) the maximum of the three numbers in equation (58) reduces to a maximum of two numbers given in equation (61). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚+1 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚+1 𝑖=1 } (61) if we substitute 𝑚 + 1 in place of 𝑚 in the formula in equation (34) also, we get 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (62) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−1−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚+1 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−1−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚+1 𝑖=1 } (63) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚+1 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−2 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚+1 𝑖=1 } (64) mekonnen redi et al 38 equation (64) is identical to equation (61). hence we have shown that the theorem also holds for 𝑚 + 1. thus, by the principle of mathematical induction the theorem holds for all 𝑚 such that 𝑛1 + 1 ≤ 𝑞 − 𝑚 ≤ 𝑞 − 1. if 𝑞 − 𝑚 = 𝑛1 + 1 i. e. 𝑚 = 𝑞 − 𝑛1 − 1 the formula (64) yields equations (65)-(66). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑚 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−𝑚−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑚 𝑖=1 } (65) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑞−(𝑞−𝑛1−1)−1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑞−𝑛1−1 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑞−(𝑞−𝑛1−1)−1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑞−𝑛1−1 𝑖=1 } (66) by simplification, the formula (66) for 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) reduces to the formula (67) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑞−𝑖 𝑞−𝑛1−1 𝑖=1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑞−𝑖 𝑞−𝑛1−1 𝑖=1 } (67) changing the index 𝑞 − 𝑖 by the index 𝑛1 + 𝑖, the formula (67) for 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) reduces to the formula (68) and (69). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑎𝑗∗ 𝑞 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑖 𝑞−1 𝑖=𝑛1+1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑏𝑗 𝑖 𝑞−1 𝑖=𝑛1+1 } (68) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗 𝑖 𝑞 𝑖=𝑛1+1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + ∑ 𝑏𝑗 𝑖 𝑞 𝑖=𝑛1+1 } (69) formula (69) gives the completion time of the job 𝑗∗ 𝑞 explicitly as maximum of the sum of processing times of the jobs in the two machines and that of job 𝑗∗ 𝑞 . in this formula the maximum of the two numbers 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑎j 𝑖 𝑞 𝑖=𝑛1+1 and 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + ∑ 𝑏j 𝑖 𝑞 𝑖=𝑛1+1 is symmetric with respect to jobs and so it is independent of the order of operations. thus, the theorem was proved. since the jobs 𝑗 𝑛1+1 ,… , 𝑗 𝑞−2 , 𝑗 𝑞−1 are permutations of the jobs 𝑗∗ 𝑛1+1 ,… , 𝑗∗ 𝑞−2 , 𝑗∗ 𝑞−1 , and the optimal sequence is also obtained by one of these permutations and the total elapsed time in the optimal sequence to finish 𝑞 jobs 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 )given by formula (69) reduces to formula (70). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1 (𝑗 ∗ 𝑛1 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗∗ 𝑖 𝑞 𝑖=𝑛1+1 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) + ∑ 𝑏𝑗∗ 𝑖 𝑞 𝑖=𝑛1+1 } (70) if further we keep all jobs in 𝐽 1 fixed in the optimal sequence, the total elapsed time to finish all jobs with the above freedom will be equal to the optimal value. hence any sequence obtained by the above sequencing freedom is optimal. since we are free to arrange the jobs 𝑗∗ 𝑛1+1 → ⋯ → 𝑗∗ 𝑞−2 → 𝑗∗ 𝑞−1 in an arbitrary order, the above machine sequencing freedom creates (𝑞 − 𝑛1 − 1)! sequences, all of which are optimal. for reference, we call the job 𝑗 ∗ 𝑞 in the above formulation the maximal job of {𝑗∗ 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} = 𝑗∗ 1 → 𝑗∗ 2 → 𝑗∗ 3 → ⋯ → 𝑗∗ 𝑛 and we call the block of jobs 𝑗∗ 𝑛1+1 → … → 𝑗∗ 𝑞−3 → 𝑗∗ 𝑞−2 → 𝑗∗ 𝑞−1 the free jobs of second kind. dimension reduction and relaxation 39 concluding remark combining the results of section 4.2.1 and section 4.2.2, by substituting 𝐶𝑚𝑎𝑥 (𝑗 ∗ 𝑛1 ) in formula (70) by the right hand side in formula (33), 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) reduces to the formula (71) and (72). 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1(𝑗 ∗ 𝑘 ) + ∑ 𝑎𝑗∗ 𝑖 𝑛1 𝑖=𝑘+1 + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗∗ 𝑖 𝑞 𝑖=𝑛1+1 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗∗ 𝑖 𝑛1 𝑖=𝑘+1 + ∑ 𝑏𝑗∗ 𝑖 𝑞 𝑖=𝑛1+1 } (71) 𝐶𝑚𝑎𝑥 ( 𝑗 ∗ 𝑞 ) = 𝑚𝑎𝑥 { 𝐶1(𝑗 ∗ 𝑘 ) + 𝑏𝑗∗ 𝑞 + ∑ 𝑎𝑗∗ 𝑖 𝑞 𝑖=𝑘+1 𝐶𝑚𝑎𝑥(𝑗 ∗ 𝑘 ) + ∑ 𝑏𝑗∗ 𝑖 𝑞 𝑖=𝑘+1 } (72) at this point by looking at the formula in (72) only, we suggest not to conclude that the union of the free jobs of first and second kind could also be arranged in an arbitrary order because there are just a few particular cases for which this conclusion does not hold true. thus, we need to compute the sequence dependent starting and completion times of the remaining jobs 𝑗∗ 𝑞+1 → 𝑗∗ 𝑞+2 → 𝑗∗ 𝑞+3 → ⋯ → 𝑗∗ 𝑛 on the two machines to find total elapsed time. 4.3. algorithm: dimension reduction thus we have proved the following algorithm. let problem 𝑃 = {𝑗𝑖 = (𝑎𝑗𝑖,𝑏𝑗𝑖); 𝑖 = 1,2,3,…,𝑛} with no passing of jobs on the two machines in the order 𝐴 → 𝐵 be given where 𝑎𝑗 𝑖 and 𝑏𝑗 𝑖 are processing times of job 𝑗 𝑖 on machines 𝐴 and 𝐵, respectively for 𝑖 = 1,2,3,…,𝑛.  step 1: partition all jobs in 𝑃 into two clusters, 𝐽 1 and 𝐽 2 where 𝐽 1 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 ≤ 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛} and 𝐽 2 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑎𝑗 𝑖 > 𝑏𝑗 𝑖 ; 𝑖 = 1,2,3,… ,𝑛}. identify all jobs in 𝐽 1 and 𝐽 2 . let there be 𝑛1 jobs in 𝐽1 and 𝑛2 jobs in 𝐽2.  step 2: let �̅� = {𝑎𝑗 𝑖 : (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝐽 1 } be the set of distinct operation times on machine 𝐴 for all jobs of the first kind and let �̅� = {𝑏𝑗 𝑖 : (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝐽 2 } be the set of distinct operation times on machine 𝐵 for all jobs of the second kind.  step 3: define 𝑓 1 : �̅� → ℜ by the map given by 𝑓 1 (𝑎𝑗 𝑙 ) = 𝑚𝑎𝑥 {𝑎𝑗𝑖 =𝑎𝑗𝑙 } {𝑏𝑗 𝑖 : (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝐽 1 } 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑎𝑗𝑙 ∈ �̅�. this definition assigns the highest processing time on machine 𝐵 for each distinct processing time on machine 𝐴.  step 4: define 𝑓 2 : �̅� → ℜ by the map given by 𝑓 2 (𝑏𝑗 𝑙 ) = 𝑚𝑎𝑥 {𝑏𝑗𝑖 =𝑏𝑗𝑙 } {𝑎𝑗 𝑖 : (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝐽 2 } ,𝑓𝑜𝑟 𝑎𝑙𝑙 𝑏𝑗𝑙 ∈ �̅�. this definition assigns the highest processing time on machine 𝐴 for each distinct processing time on machine 𝐵. 𝐽 1̅ = {(𝑎𝑗 𝑖 , 𝑓 1 (𝑎𝑗 𝑖 ))}𝑓𝑜𝑟 𝑎𝑙𝑙 𝑎𝑗 𝑖 ∈ �̅� and 𝐽 2̅ = {(𝑓 2 (𝑏𝑗 𝑙 ), 𝑏𝑗 𝑖 )}𝑓𝑜𝑟 𝑎𝑙𝑙 𝑏𝑗 𝑖 ∈ �̅� give distinct equivalence classes.  step 5: therefore, the reduced problem at the end of the first phase of dimension reduction becomes sequencing jobs in �̅� = j 1̅ ∪ j 2̅ .  step 6: let 𝑏1 = 𝑚𝑎𝑥{𝑎𝑗𝑖∈�̅�} {𝑓 1 (𝑎𝑗 𝑖 )} and 𝑎1 = 𝑚𝑎𝑥{𝑏𝑗𝑖∈�̅�} {𝑓 2 (𝑏𝑗 𝑖 )} let 𝑎∗ = 𝑚𝑖𝑛 {𝑓 1 (𝑎𝑗𝑖 )=𝑏1} {𝑎𝑗 𝑖 } and 𝑏∗ = 𝑚𝑖𝑛 {𝑓 2 (𝑏𝑗𝑖 )=𝑎1} {𝑏𝑗 𝑖 }  step 7a: identify the job 𝑗𝑙1 = (𝑎𝑗𝑙1 ,𝑏𝑗𝑙1 ) ∈ 𝐽1 such that 𝑎𝑗𝑙1 + 𝑏𝑗𝑙1 = 𝑚𝑎𝑥𝑎𝑗𝑖>𝑎 ∗{𝑎𝑗𝑖 + 𝑏𝑗𝑖, (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝐽1}.identify the job 𝑗𝑙2 = (𝑎𝑗𝑙2 ,𝑏𝑗𝑙2 ) ∈ 𝐽2 such that 𝑎𝑗𝑙2 + 𝑏𝑗𝑙2 = 𝑚𝑎𝑥𝑏𝑗𝑖>𝑏 ∗{𝑎𝑗𝑖 + 𝑏𝑗𝑖, (𝑎𝑗𝑖,𝑏𝑗𝑖) ∈ 𝐽2}  step 7b: 𝐽 1̅ ̅ = {(𝑎𝑗 𝑖 , 𝑓 1 (𝑎𝑗 𝑙 )): 𝑎𝑗 𝑖 ≤ 𝑎∗𝑓𝑜𝑟 𝑎𝑙𝑙 𝑎𝑗 𝑖 ∈ �̅�} ∪ {𝑗 𝑙1 } and 𝐽 2̅ ̅ = {(𝑓 2 (𝑏𝑗 𝑙 ), 𝑏𝑗 𝑖 )𝑓𝑜𝑟 𝑎𝑙𝑙 𝑏𝑗 𝑖 ∈ �̅�} ∪ {𝑗 𝑙2 }.  step 8 therefore, the reduced problem at the end of the second phase of dimension reduction becomes sequencing jobs in �̅̅� = 𝐽 1̅ ̅ ∪ 𝐽 2̅ ̅. mekonnen redi et al 40 4.4. algorithm: relaxation of johnson's algorithm the johnson's algorithm is an exact solution method of the two machines, one-way, no-passing scheduling tasks problem, which serves as a basis for many heuristic algorithms. this rule is a complete list of ordering the jobs by filling the first or the last available space based on minimum operation times in the two machines from the waiting list until, finally, only one free space and one last job to be assigned remain in the waiting list. we make 𝑛! comparisons to obtain the optimal sequence. to overcome the problem of computation time, the current study identified a relaxation of johnson's algorithm by developing an early stopover criteria due to the fact that after listing only some critical jobs at the beginning and end of the optimal sequence using johnson's procedure, it does not matter in whichever order the remaining jobs are operated as far as makespan is concerned.  step 0: compute 𝑑 = 𝑏𝑗𝑖 − 𝑎𝑗𝑖; 𝑖 = 1,2,3,…,𝑛. waiting list 1 is 𝐽1 = {𝑗𝑖 = (𝑎𝑗𝑖, 𝑏𝑗𝑖) ∈ 𝑃: 𝑏𝑗𝑖 − 𝑎𝑗𝑖 ≥ 0; 𝑖 = 1,2,3,… ,𝑛}. waiting list 2 is 𝐽 2 = {𝑗 𝑖 = (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝑃: 𝑏𝑗 𝑖 − 𝑎𝑗 𝑖 < 0; 𝑖 = 1,2,3,… ,𝑛}.  step 1a identify the job 𝑗∗ 𝑘 = (𝑎𝑗∗ 𝑘 , 𝑏𝑗∗ 𝑘 ) such that 𝑏𝑗∗ 𝑘 =𝑚𝑎𝑥(𝑎𝑗𝑖,𝑏𝑗𝑖) ∈𝐽1 {𝑏𝑗 𝑖 } and 𝑎𝑗∗ 𝑘 =𝑚𝑖𝑛𝑏𝑗𝑖=𝑏𝑗∗𝑘 {𝑎𝑗 𝑖 , (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝐽 1 }  step 1b identify the job 𝑗∗ 𝑞 = (𝑎𝑗∗ 𝑞 , 𝑏𝑗∗ 𝑞 ) such that 𝑎𝑗∗ 𝑞 =𝑚𝑎𝑥(𝑎𝑗𝑖 ,𝑏𝑗𝑖) ∈𝐽2 {𝑎𝑗 𝑖 } and 𝑏𝑗∗ 𝑞 =𝑚𝑖𝑛𝑎𝑗𝑖=𝑎𝑗∗𝑞 {𝑏𝑗 𝑖 , (𝑎𝑗 𝑖 , 𝑏𝑗 𝑖 ) ∈ 𝐽 2 }  step 2 (johnson’s algorithm main) examine the columns of 𝐴 and 𝐵 for processing times on machines 𝐴 and 𝐵 and find the smallest processing time among unscheduled jobs (waiting list). apply johnson’s algorithm on 𝑃 and remove the scheduled job from 𝑃, waiting list 1 and waiting list 2 until jobs 𝑗∗ 𝑘 or 𝑗∗ 𝑞 are assigned. go to step 3.  step 3a (mini-max criteria 1) if 𝑗∗ 𝑘 is scheduled, then remove all unscheduled jobs in waiting list 1 from 𝑃 and terminate this step. go to step 2.  step 3b (mini-max criteria 2) if 𝑗∗ 𝑞 is scheduled, then remove all unscheduled jobs in waiting list 2 from 𝑃 and terminate this step. go to step 2.  step 4 (relaxation of johnson’s algorithm) if both 𝑗∗ 𝑘 and 𝑗∗ 𝑞 are assigned, then terminate johnson's algorithm main. go to step 5.  step 5a if waiting list 1 is non-empty, then choose at random a job in waiting list 1 and assign the corresponding job in the first available position in sequence and remove the assigned job from the waiting list 1. repeat this step until waiting list 1 is empty.  step 5b if waiting list 2 is non-empty then choose at random a job in waiting list 2 and assign the corresponding job in the last available position in sequence and remove the assigned job from the waiting list 2. repeat this step until waiting list 2 is empty.  step 6 repeat steps 5a and 5b until all 𝑃, waiting list 1 and waiting list 2 are empty. in the relaxation algorithm above, we did not violate johnson's algorithm except termination criteria. thus, ties for jobs with equal processing time on the two machines may be broken arbitrarily. 5. illustrative example in the following example, the two machines flow shop sequencing problem of 100 jobs indexed 𝑗 1 , 𝑗 2 , 𝑗 3 … ,𝑗 100 was generated from a normal distribution 𝑁[𝜇,𝜎2] with mean 𝜇 and standard deviation 𝜎2 in microsoft excel spreadsheet user interface for different values of the parameters. the processing time on machine 𝐴 was assumed to follow a normal distribution with mean 𝜇 = 58 and standard deviation 𝜎2 = 2 and the processing time on machine 𝐵 was assumed to follow a normal distribution with mean 𝜇 = 51 and standard deviation 𝜎2 = 8. the procedure was as follows: in columns 2 and 3 random numbers were generated from [0,1] representing the probabilities of processing times on machines 𝐴 and 𝐵 respectively. in column 4 we computed the inverse of the cumulative normal distribution function for probability values defined in column 2, with distribution mean 𝜇 = 58 and standard deviation 𝜎2 = 2. similarly, in column 5 we computed the inverse of the cumulative normal distribution function for probability values defined in column 3, with distribution mean 𝜇 = 51 and standard deviation 𝜎2 = 8. thus, the numbers in columns 4 and 5 represent the corresponding processing times on machines 𝐴 and 𝐵. in column 6, jobs were assigned the value 0 if the value in column 4 was less than or equal to the value in column 5, and 1 otherwise to partition all jobs into two clusters 𝐽 1 and 𝐽 2 as explained before. then the jobs were sorted in ascending value on column 6 to arrange all jobs of dimension reduction and relaxation 41 the first kind before jobs of the second kind. next all jobs of the first kind only were selected and sorted by ascending value on column 4 to arrange all jobs of the first kind in a non-decreasing order of processing time on the first machine. similarly, all jobs of the second kind only were selected and sorted in ascending value on column 5 to arrange all jobs of the second kind in a non-increasing order of processing time on the second machine. the resulting sequence was, therefore, an optimal johnson's sequence and the corresponding sequence positions for all jobs were assigned in column 1, starting from beginning to end. table 1 below gives the results. the formulas for starting and completion of jobs on the first machine a were entered in columns 7 and 8. similarly, the formulas for starting and completion of jobs on second machine b were entered in columns 9 and 10. the formula to calculate the idle time (slack time) due to each job was entered in column 11 so that the formulas automatically run for any other permutations of the jobs. after identifying the optimal johnson’s sequence, applying the mini-max criteria discussed earlier, the maximum processing time on the second machine for all jobs of the first kind was identified to be 65 , and its first occurrence was in the 𝑗∗ 8 in the optimal johnson’s sequence. similarly applying the mini-max criteria discussed earlier, the maximum processing time on the first machine for all jobs of the second kind was identified to be 63 and its last occurrence was in the 𝑗∗ 82 in the optimal johnson’s sequence. in the next step the concept of random numbers was used to generate multiple alternate optimal sequences and to verify the findings of this study. in column 12, a new sequence in terms of random numbers was defined for all jobs as follows. for the jobs up to and including the minimal job, the same sequence order as the optimal johnson's sequence was maintained. also, for jobs starting from the maximal job onward, the same sequence order as the optimal johnson's sequence was maintained. but for free jobs of the first kind, a random number between 0 and 1 was added to the minimal job position number, and for free jobs of the second kind a random number between 0 and 1 was subtracted from the maximal job position and all jobs are sorted in increasing order of the values in column 12. then a new sequence was defined in column 13 to get an alternate optimal sequence. then comparisons were made between the johnson's sequence in table 1 and the alternate sequence in table 2. table 1. optimal johnson's sequence for the generated problem in the illustration example. joh seq rand a rand b a b j1/ j2 in a out a in b out b idle relax alt seq 1 0.071 0.782 55 57 0 0 55 55 112 55 1.000 1 2 0.060 0.837 55 59 0 55 110 112 171 0 2.000 2 3 0.070 0.718 55 56 0 110 165 171 227 0 3.000 3 4 0.163 0.786 56 57 0 165 221 227 284 0 4.000 4 5 0.106 0.743 56 56 0 221 277 284 340 0 5.000 5 6 0.157 0.951 56 64 0 277 333 340 404 0 6.000 6 7 0.211 0.951 56 64 0 333 389 404 468 0 7.000 7 8 0.327 0.954 57 65 0 389 446 468 533 0 8.000 8 9 0.676 0.972 57 62 0 446 503 533 595 0 9.173 12 10 0.694 0.852 57 60 0 503 560 595 655 0 9.398 15 11 0.630 0.834 58 59 0 560 618 655 714 0 9.931 22 12 0.323 0.915 58 64 0 618 676 714 778 0 9.401 16 13 0.693 0.864 58 62 0 676 734 778 840 0 9.480 18 14 0.805 0.870 59 60 0 734 793 840 900 0 9.306 13 15 0.379 0.862 59 61 0 793 852 900 961 0 9.505 19 16 0.572 0.947 59 63 0 852 911 961 1024 0 9.995 23 17 0.852 0.995 59 61 0 911 970 1024 1085 0 9.016 9 18 0.503 0.909 59 59 0 970 1029 1085 1144 0 9.046 10 19 0.718 0.897 59 59 0 1029 1088 1144 1203 0 9.108 11 20 0.964 0.990 60 62 0 1088 1148 1203 1265 0 9.475 17 21 0.922 0.920 60 60 0 1148 1208 1265 1325 0 9.322 14 22 0.543 0.833 61 62 0 1208 1269 1325 1387 0 9.843 21 23 0.683 0.934 62 64 0 1269 1331 1387 1451 0 9.626 20 24 0.770 0.675 58 57 1 1331 1389 1451 1508 0 24.300 43 25 0.785 0.715 61 57 1 1389 1450 1508 1565 0 24.570 58 26 0.376 0.415 60 56 1 1450 1510 1565 1621 0 24.046 25 27 0.029 0.555 57 56 1 1510 1567 1621 1677 0 24.870 72 28 0.274 0.310 57 56 1 1567 1624 1677 1733 0 24.199 37 mekonnen redi et al 42 29 0.578 0.497 60 56 1 1624 1684 1733 1789 0 24.434 53 30 0.755 0.500 57 55 1 1684 1741 1789 1844 0 24.443 54 31 0.943 0.323 59 55 1 1741 1800 1844 1899 0 24.013 24 32 0.855 0.396 56 55 1 1800 1856 1899 1954 0 24.924 77 33 0.970 0.458 55 54 1 1856 1911 1954 2008 0 24.987 80 34 0.143 0.582 55 54 1 1911 1966 2008 2062 0 24.663 66 35 0.320 0.269 57 54 1 1966 2023 2062 2116 0 24.654 64 36 0.909 0.432 61 54 1 2023 2084 2116 2170 0 24.384 51 37 0.270 0.731 56 53 1 2084 2140 2170 2223 0 24.185 34 38 0.727 0.561 60 53 1 2140 2200 2223 2276 0 24.583 61 39 0.456 0.534 56 53 1 2200 2256 2276 2329 0 24.357 47 40 0.766 0.567 59 53 1 2256 2315 2329 2382 0 24.848 71 41 0.316 0.277 58 53 1 2315 2373 2382 2435 0 24.489 55 42 0.855 0.225 59 52 1 2373 2432 2435 2487 0 24.200 38 43 0.461 0.768 54 52 1 2432 2486 2487 2539 0 24.050 27 44 0.785 0.254 58 52 1 2486 2544 2544 2596 5 24.202 39 45 0.946 0.380 59 52 1 2544 2603 2603 2655 7 24.240 40 46 0.104 0.389 58 51 1 2603 2661 2661 2712 6 24.372 48 47 0.178 0.608 60 51 1 2661 2721 2721 2772 9 24.616 62 48 0.493 0.477 57 51 1 2721 2778 2778 2829 6 24.891 74 49 0.235 0.217 58 51 1 2778 2836 2836 2887 7 24.084 29 50 0.617 0.354 60 51 1 2836 2896 2896 2947 9 24.535 57 51 0.951 0.645 58 51 1 2896 2954 2954 3005 7 24.907 75 52 0.370 0.230 59 51 1 2954 3013 3013 3064 8 24.087 30 53 0.806 0.734 61 50 1 3013 3074 3074 3124 10 24.196 36 54 0.229 0.705 61 50 1 3074 3135 3135 3185 11 24.935 79 55 0.463 0.591 62 50 1 3135 3197 3197 3247 12 24.158 33 56 0.663 0.397 58 50 1 3197 3255 3255 3305 8 24.919 76 57 0.839 0.498 57 50 1 3255 3312 3312 3362 7 24.742 67 58 0.938 0.768 58 50 1 3312 3370 3370 3420 8 24.837 70 59 0.464 0.279 61 49 1 3370 3431 3431 3480 11 24.316 45 60 0.395 0.404 55 49 1 3431 3486 3486 3535 6 24.347 46 61 0.827 0.591 57 49 1 3486 3543 3543 3592 8 24.047 26 62 0.806 0.499 59 49 1 3543 3602 3602 3651 10 24.526 56 63 0.394 0.359 57 49 1 3602 3659 3659 3708 8 24.581 60 64 0.280 0.637 60 49 1 3659 3719 3719 3768 11 24.137 32 65 0.436 0.178 57 48 1 3719 3776 3776 3824 8 24.781 68 66 0.096 0.643 59 48 1 3776 3835 3835 3883 11 24.383 50 67 0.268 0.459 57 48 1 3835 3892 3892 3940 9 24.647 63 68 0.382 0.376 57 47 1 3892 3949 3949 3996 9 24.056 28 69 0.484 0.250 61 47 1 3949 4010 4010 4057 14 24.122 31 70 0.423 0.437 63 47 1 4010 4073 4073 4120 16 24.926 78 71 0.599 0.595 58 46 1 4073 4131 4131 4177 11 24.798 69 72 0.305 0.735 58 46 1 4131 4189 4189 4235 12 24.572 59 73 0.023 0.265 57 46 1 4189 4246 4246 4292 11 24.267 41 74 0.377 0.505 54 46 1 4246 4300 4300 4346 8 24.881 73 75 0.454 0.512 60 46 1 4300 4360 4360 4406 14 24.306 44 76 0.549 0.446 57 46 1 4360 4417 4417 4463 11 24.188 35 77 0.164 0.711 57 45 1 4417 4474 4474 4519 11 24.376 49 78 0.996 0.297 57 45 1 4474 4531 4531 4576 12 24.999 81 79 0.951 0.460 57 45 1 4531 4588 4588 4633 12 24.397 52 80 0.067 0.652 60 45 1 4588 4648 4648 4693 15 24.284 42 81 0.235 0.226 58 44 1 4648 4706 4706 4750 13 24.662 65 82 0.990 0.189 63 44 1 4706 4769 4769 4813 19 82.000 82 83 0.220 0.172 56 43 1 4769 4825 4825 4868 12 83.000 83 84 0.475 0.147 58 43 1 4825 4883 4883 4926 15 84.000 84 85 0.465 0.154 58 43 1 4883 4941 4941 4984 15 85.000 85 86 0.757 0.152 59 43 1 4941 5000 5000 5043 16 86.000 86 dimension reduction and relaxation 43 87 0.855 0.157 60 43 1 5000 5060 5060 5103 17 87.000 87 88 0.411 0.126 58 42 1 5060 5118 5118 5160 15 88.000 88 89 0.482 0.108 58 41 1 5118 5176 5176 5217 16 89.000 89 90 0.548 0.101 58 41 1 5176 5234 5234 5275 17 90.000 90 91 0.623 0.086 59 40 1 5234 5293 5293 5333 18 91.000 91 92 0.626 0.083 59 40 1 5293 5352 5352 5392 19 92.000 92 93 0.758 0.070 59 39 1 5352 5411 5411 5450 19 93.000 93 94 0.812 0.074 60 39 1 5411 5471 5471 5510 21 94.000 94 95 0.575 0.059 58 38 1 5471 5529 5529 5567 19 95.000 95 96 0.279 0.051 57 38 1 5529 5586 5586 5624 19 96.000 96 97 0.159 0.040 56 37 1 5586 5642 5642 5679 18 97.000 97 98 0.266 0.038 57 37 1 5642 5699 5699 5736 20 98.000 98 99 0.853 0.030 60 36 1 5699 5759 5759 5795 23 99.000 99 100 0.744 0.017 59 34 1 5759 5818 5818 5852 23 100.000 100 767 observe first from table 1 the following values: machine 𝐴 completes the minimal job at time 𝐶1(𝑗 ∗ 8 ) = 𝟒𝟒𝟔 and machine 𝐵 completes it at time 𝐶𝑚𝑎𝑥(𝑗 ∗ 8 ) = 𝟓𝟑𝟑. machine 𝐴 completes all jobs of the first kind at time 𝐶1(𝑗 ∗ 23 ) = 𝟏𝟑𝟑𝟏 and machine 𝐵 completes the same jobs at time 𝐶𝑚𝑎𝑥(𝑗 ∗ 23 ) = 𝟏𝟒𝟓𝟏. machine 𝐴 completes the maximal job at time 𝐶1(𝑗 ∗ 82 ) = 𝟒𝟕𝟔𝟗 and machine 𝐵 completes it at time 𝐶𝑚𝑎𝑥(𝑗 ∗ 82 ) = 𝟒𝟖𝟏𝟑. machine 𝐴 completes the last job at time 𝐶1(𝑗 ∗ 100 ) = 𝟓𝟖𝟏𝟖 and machine 𝐵 completes it at 𝐶𝑚𝑎𝑥(𝑗 ∗ 100 ) = 𝟓𝟖𝟓𝟐. all the values described here are outlined in table 1 by dark line in the corresponding rows containing the values. also observe the following values: the sum of the processing times of free jobs of the first kind on machine 𝐵 is ∑ 𝑏𝑗∗ 𝑖 23 𝑖=9 = 𝟗𝟏𝟖. thus, 𝐶𝑚𝑎𝑥(𝑗 ∗ 8 ) + ∑ 𝑏𝑗∗ 𝑖 23 𝑖=9 = 533 + 918 = 𝟏𝟒𝟓𝟏 = 𝐶𝑚𝑎𝑥(𝑗 ∗ 23 ). thus equation (6) is verified. the sum of the processing times of free jobs of the second kind on machine 𝐴 is ∑ 𝑎𝑗∗ 𝑖 (81) 𝑖=24 = 𝟑𝟑𝟕𝟓 and the sum of the processing times of free jobs of the second kind on machine 𝐵 is ∑ 𝑎𝑗∗ 𝑖 (81) 𝑖=24 = 𝟐𝟗𝟐𝟖. therefore, 𝐶1(𝑗 ∗ 23 ) + 𝑎𝑗∗ 82 + 𝑏𝑗∗ 82 + ∑ 𝑎𝑗∗ 𝑖 (81) 𝑖=24 = 1331 + 63 + 44 + 3375 = 𝟒𝟖𝟏𝟑 and 𝐶𝑚𝑎𝑥(𝑗 ∗ 23 ) + 𝑏𝑗∗ 82 + ∑ 𝑏𝑗∗ 𝑖 81 𝑖=24 = 1451 + 44 + 2928 = 𝟒𝟒𝟐𝟑. thus, 𝑚𝑎𝑥{𝐶1(𝑗 ∗ 23 ) + 𝑎𝑗∗ 82 + 𝑏𝑗∗ 82 + ∑ 𝑎𝑗∗ 𝑖 (81) 𝑖=24 , 𝐶𝑚𝑎𝑥(𝑗 ∗ 23 ) + 𝑏𝑗∗ 82 + ∑ 𝑏𝑗∗ 𝑖 81 𝑖=24 } = 𝑚𝑎𝑥{4813,4423} = 𝟒𝟖𝟏𝟑 = 𝐶𝑚𝑎𝑥(𝑗 ∗ 82 ). thus equation (71) is verified. the total elapsed time is 𝐶𝑚𝑎𝑥(𝑗 ∗ 100 ) = 𝟓𝟖𝟓𝟐 the total idle time for machine 𝐵 was i = 767 (see the value at the end of column 11 in tables 1 and 2). it remains to verify theorems 1 and 2. we show this by sorting the jobs in optimal johnson's sequence in ascending order of the values assigned to the jobs in column 12, and compare the finishing times of jobs of the first kind as well as the maximal job. to do this, we copy all the values in the bold cells for johnson's sequence (table 1) and sort the jobs in ascending value in column 12. this gives a different sequence of jobs. table 2. alternate optimal sequence for the generated problem in the illustration example. joh seq rand a rand b a b j1/ j2 in a out a in b out b idle relax alt seq 1 0.071 0.782 55 57 0 0 55 55 112 55 1.000 1 2 0.060 0.837 55 59 0 55 110 112 171 0 2.000 2 3 0.070 0.718 55 56 0 110 165 171 227 0 3.000 3 4 0.163 0.786 56 57 0 165 221 227 284 0 4.000 4 5 0.106 0.743 56 56 0 221 277 284 340 0 5.000 5 6 0.157 0.951 56 64 0 277 333 340 404 0 6.000 6 7 0.211 0.951 56 64 0 333 389 404 468 0 7.000 7 8 0.327 0.954 57 65 0 389 446 468 533 0 8.000 8 17 0.852 0.995 59 61 0 446 505 533 594 0 9.173 9 mekonnen redi et al 44 18 0.503 0.909 59 59 0 505 564 594 653 0 9.398 10 19 0.718 0.897 59 59 0 564 623 653 712 0 9.931 11 9 0.676 0.972 57 62 0 623 680 712 774 0 9.401 12 14 0.805 0.870 59 60 0 680 739 774 834 0 9.480 13 21 0.922 0.920 60 60 0 739 799 834 894 0 9.306 14 10 0.694 0.852 57 60 0 799 856 894 954 0 9.505 15 12 0.323 0.915 58 64 0 856 914 954 1018 0 9.995 16 20 0.964 0.990 60 62 0 914 974 1018 1080 0 9.016 17 13 0.693 0.864 58 62 0 974 1032 1080 1142 0 9.046 18 15 0.379 0.862 59 61 0 1032 1091 1142 1203 0 9.108 19 23 0.683 0.934 62 64 0 1091 1153 1203 1267 0 9.475 20 22 0.543 0.833 61 62 0 1153 1214 1267 1329 0 9.322 21 11 0.630 0.834 58 59 0 1214 1272 1329 1388 0 9.843 22 16 0.572 0.947 59 63 0 1272 1331 1388 1451 0 9.626 23 31 0.943 0.323 59 55 1 1331 1390 1451 1506 0 24.300 24 26 0.376 0.415 60 56 1 1390 1450 1506 1562 0 24.570 25 61 0.827 0.591 57 49 1 1450 1507 1562 1611 0 24.046 26 43 0.461 0.768 54 52 1 1507 1561 1611 1663 0 24.870 27 68 0.382 0.376 57 47 1 1561 1618 1663 1710 0 24.199 28 49 0.235 0.217 58 51 1 1618 1676 1710 1761 0 24.434 29 52 0.370 0.230 59 51 1 1676 1735 1761 1812 0 24.443 30 69 0.484 0.250 61 47 1 1735 1796 1812 1859 0 24.013 31 64 0.280 0.637 60 49 1 1796 1856 1859 1908 0 24.924 32 55 0.463 0.591 62 50 1 1856 1918 1918 1968 10 24.987 33 37 0.270 0.731 56 53 1 1918 1974 1974 2027 6 24.663 34 76 0.549 0.446 57 46 1 1974 2031 2031 2077 4 24.654 35 53 0.806 0.734 61 50 1 2031 2092 2092 2142 15 24.384 36 28 0.274 0.310 57 56 1 2092 2149 2149 2205 7 24.185 37 42 0.855 0.225 59 52 1 2149 2208 2208 2260 3 24.583 38 44 0.785 0.254 58 52 1 2208 2266 2266 2318 6 24.357 39 45 0.946 0.380 59 52 1 2266 2325 2325 2377 7 24.848 40 73 0.023 0.265 57 46 1 2325 2382 2382 2428 5 24.489 41 80 0.067 0.652 60 45 1 2382 2442 2442 2487 14 24.200 42 24 0.770 0.675 58 57 1 2442 2500 2500 2557 13 24.050 43 75 0.454 0.512 60 46 1 2500 2560 2560 2606 3 24.202 44 59 0.464 0.279 61 49 1 2560 2621 2621 2670 15 24.240 45 60 0.395 0.404 55 49 1 2621 2676 2676 2725 6 24.372 46 39 0.456 0.534 56 53 1 2676 2732 2732 2785 7 24.616 47 46 0.104 0.389 58 51 1 2732 2790 2790 2841 5 24.891 48 77 0.164 0.711 57 45 1 2790 2847 2847 2892 6 24.084 49 66 0.096 0.643 59 48 1 2847 2906 2906 2954 14 24.535 50 36 0.909 0.432 61 54 1 2906 2967 2967 3021 13 24.907 51 79 0.951 0.460 57 45 1 2967 3024 3024 3069 3 24.087 52 29 0.578 0.497 60 56 1 3024 3084 3084 3140 15 24.196 53 30 0.755 0.500 57 55 1 3084 3141 3141 3196 1 24.935 54 41 0.316 0.277 58 53 1 3141 3199 3199 3252 3 24.158 55 62 0.806 0.499 59 49 1 3199 3258 3258 3307 6 24.919 56 50 0.617 0.354 60 51 1 3258 3318 3318 3369 11 24.742 57 25 0.785 0.715 61 57 1 3318 3379 3379 3436 10 24.837 58 72 0.305 0.735 58 46 1 3379 3437 3437 3483 1 24.316 59 63 0.394 0.359 57 49 1 3437 3494 3494 3543 11 24.347 60 38 0.727 0.561 60 53 1 3494 3554 3554 3607 11 24.047 61 47 0.178 0.608 60 51 1 3554 3614 3614 3665 7 24.526 62 67 0.268 0.459 57 48 1 3614 3671 3671 3719 6 24.581 63 35 0.320 0.269 57 54 1 3671 3728 3728 3782 9 24.137 64 81 0.235 0.226 58 44 1 3728 3786 3786 3830 4 24.781 65 dimension reduction and relaxation 45 34 0.143 0.582 55 54 1 3786 3841 3841 3895 11 24.383 66 57 0.839 0.498 57 50 1 3841 3898 3898 3948 3 24.647 67 65 0.436 0.178 57 48 1 3898 3955 3955 4003 7 24.056 68 71 0.599 0.595 58 46 1 3955 4013 4013 4059 10 24.122 69 58 0.938 0.768 58 50 1 4013 4071 4071 4121 12 24.926 70 40 0.766 0.567 59 53 1 4071 4130 4130 4183 9 24.798 71 27 0.029 0.555 57 56 1 4130 4187 4187 4243 4 24.572 72 74 0.377 0.505 54 46 1 4187 4241 4243 4289 0 24.267 73 48 0.493 0.477 57 51 1 4241 4298 4298 4349 9 24.881 74 51 0.951 0.645 58 51 1 4298 4356 4356 4407 7 24.306 75 56 0.663 0.397 58 50 1 4356 4414 4414 4464 7 24.188 76 32 0.855 0.396 56 55 1 4414 4470 4470 4525 6 24.376 77 70 0.423 0.437 63 47 1 4470 4533 4533 4580 8 24.999 78 54 0.229 0.705 61 50 1 4533 4594 4594 4644 14 24.397 79 33 0.970 0.458 55 54 1 4594 4649 4649 4703 5 24.284 80 78 0.996 0.297 57 45 1 4649 4706 4706 4751 3 24.662 81 82 0.990 0.189 63 44 1 4706 4769 4769 4813 18 82.000 82 83 0.220 0.172 56 43 1 4769 4825 4825 4868 12 83.000 83 84 0.475 0.147 58 43 1 4825 4883 4883 4926 15 84.000 84 85 0.465 0.154 58 43 1 4883 4941 4941 4984 15 85.000 85 86 0.757 0.152 59 43 1 4941 5000 5000 5043 16 86.000 86 87 0.855 0.157 60 43 1 5000 5060 5060 5103 17 87.000 87 88 0.411 0.126 58 42 1 5060 5118 5118 5160 15 88.000 88 89 0.482 0.108 58 41 1 5118 5176 5176 5217 16 89.000 89 90 0.548 0.101 58 41 1 5176 5234 5234 5275 17 90.000 90 91 0.623 0.086 59 40 1 5234 5293 5293 5333 18 91.000 91 92 0.626 0.083 59 40 1 5293 5352 5352 5392 19 92.000 92 93 0.758 0.070 59 39 1 5352 5411 5411 5450 19 93.000 93 94 0.812 0.074 60 39 1 5411 5471 5471 5510 21 94.000 94 95 0.575 0.059 58 38 1 5471 5529 5529 5567 19 95.000 95 96 0.279 0.051 57 38 1 5529 5586 5586 5624 19 96.000 96 97 0.159 0.040 56 37 1 5586 5642 5642 5679 18 97.000 97 98 0.266 0.038 57 37 1 5642 5699 5699 5736 20 98.000 98 99 0.853 0.030 60 36 1 5699 5759 5759 5795 23 99.000 99 100 0.744 0.017 59 34 1 5759 5818 5818 5852 23 100.00 100 767 table 2 was obtained from table 1 by sorting in ascending values on column 12. to check that it is also the optimal sequence, we checked the values in the bold cells with those recorded for johnson's sequence (table 1); in particular we checked the total elapsed time 𝐶𝑚𝑎𝑥(𝑗 ∗ 100 ) = 𝟓𝟖𝟓𝟐 for each "sort ascending values on column 12" instruction. it can easily be verified that table 2 also gives an optimal sequence irrespective of the order of free jobs of the first kind and free jobs of the second kind if the y are scheduled together. thus, the results of the two theorems were verified with this example. our final conclusion about dimension reduction was made in reference to the above example. at termination of johnson's algorithm, the problem size was reduced to those jobs that hold fixed position in all the alternate optimal sequences. in the above example, the problem size was reduced from 100 to only 29 jobs (8 jobs at the beginning, 19 jobs at the end and a representative job each for free jobs of the two kinds. this is a significant dimension reduction at very low cost of computation. this may be expressed as a 71% decrease in problem size. there are at least 15! ∗ 57! alternate optimal sequences for the illustrative example above obtained by this procedure only. 6. summary, conclusion and recommendation the purpose of this study was to apply dimension reduction methods for flow shop scheduling problems to decrease problem size. the development of solution methods for the ‘n -jobs m –machines’ flow shop scheduling problems was limited by the number of jobs n and number of machines m. due to these difficulties solutions have been developed either for a small number of jobs or a small number of machines. to enable solution methods to be applicable for a large number of jobs, it was important to cluster jobs into principal components by defining a projective mapping. mekonnen redi et al 46 this removes the redundant information in the original problem. then solution methods are needed for only targeted jobs and once the sequence positions of the targeted jobs in the optimal sequence are identified, a number of alternate optimal solutions could be obtained by simple enumeration techniques. alternate solutions give sequencing freedom for job operators to decide on the relative priority of different jobs. in the optimal sequence it is not necessary to list all the jobs in an order, but rather a few targeted jobs at the beginnings and ends of the sequences completely determine the completion time. more specifically, the first occurrences of the two jobs at the beginnings and ends of the optimal sequence for which the processing time on one machine attains its highest processing time on the other machine are very important because they completely determine the extent to which further computation of jobs to be assigned in the remaining sequence positions is no longer important as far as makespan is concerned. therefore, johnson's method was relaxed by terminating listing jobs at the first available positions when the job selected with the minimum processing time criteria on the first machine attains the highest processing time on the second machine for the first time and also by terminating listing jobs at the last available positions when the job with the minimum processing time criteria on the second machine attains the highest processing time on the first machine for the first time. the remaining jobs could be arranged in any convenient way in the remaining gaps without affecting minimum completion time. conflict of interest the authors declare no conflict of interest. references 1. johnson, s.m. optimal two and three-stages production schedules with set up time included, naval resh. logistic quarterly, 1954, 1(1), 61-68. 2. ikram, m. on certain new terms in sequencing theory and on alternative optimal sequences. pure and applied mathematic sciences, 1975, 2, 1, 45-50. 3. prabha. 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"on 2xn sequencing problem with transportation times of jobs", pure and' applied mathematika sciences, 1980, 12(1-2), 1-6. 24. burges, c.j.c. dimension reduction: a guided tour, foundations and trends in machine learning, 2009, 2(4), 275-365. 25. indhumathi, r., sathiyabama, s. reducing and clustering high dimensional data through principal component analysis, international journal of computer applications, 2010, 11(8), 1-4. 26. yan, j., zhang, b., liu, n., yan, s., cheng, q., fan, w., yang, q., xi, w., chen, z. effective and efficient dimensionality reduction for large-scale and streaming data preprocessing. ieee transactions on knowledge and data engineering, 2006, 18(3), 320-332. received 5 february 2019 accepted 30 october 2019 full page photo squ journal for science, 12 (2) (2007)121-141 © 2007 sultan qaboos university 121 application of neural networks to data mining zlatinka svetoslavova kovacheva higher college of technology, al khuwair, muscat, oman,e-mail: zkovacheva@hotmail.com البیانات نتطبیقات الشبكات العصبیة في التنقیب ع ذالتینكا سفیتوسالفوفا كوفاتشیفا یانات واألرقام التي في األغلب ال تكون مفھومة لمعظم الناس بحیث یتم بیب في البیانات ھو علم مھم الستخالص المعلومات من الالتنقخالصة : تستخدم لعمل استخالص المعلومات وتقدیمھا بلغة سھلة ومفھومة,كما یقوم تنقیب البیانات باستخدام البیانات الحالیة المتوفرة إلستنباط بیانات جدیدة الشبكات العصبیة أیضا تستخدم كأداة تحلیل تكون مصممة لبناء النماذج التفسیریة وفي الوقت الحالي توجد شبكات لتوقعات حول حقل معین.ا عصبیة تقوم باستخدام عملیات حسابیة معقدة بشكل مباشر لتساھم في عملیة بناء النماذج التفسیریة حیث أن اخر تطورات البحث في الشبكات ة تجعلھا قریبة جدا من تعریف التنقیب في البیانات فھي أیضا تقوم باستخالص المعلومات من البیانات الغامضة لتقدمھا بمصطحات العصبی الھدف األساسي من ھذه المراجعة ھو مقارنة الشبكات العصبیة بغیرھا من أسالیب تنقیب البیانات ولعرض بعض واضحة ومفھومة للجمیع. لدورالشبكات العصبیة في تنقیب البیانات على الواقع.األمثلة والتطبیقات abstract: data mining accomplishes nontrivial extraction of implicit, previously unknown, and potentially useful information of data. the aim of data mining is to discover knowledge out of data and present it in a form that is easily comprehensible to humans. neural networks are analytic techniques capable of predicting new observations from other observations after executing a process of so-called learning from existing data. neural network techniques can also be used as a component of analyses designed to build explanatory models. now there is neural network software that uses sophisticated algorithms directly contributing to the model building process. the latest developments in research on neural networks bring them much closer to the ideal of data mining: knowledge out of data in understandable terms. the main goal of the review is to compare neural networks with other techniques for data mining and to overview some examples of application of neural networks to data mining processes in practice. keywords: data mining, neural network, artificial neuron, perceptron, hopfield model, neural network software and application. 1. introduction 1. 1 data mining s a result of the rapid development of information technologies in the recent decades, the amount of amassed information increases at such a high rate that the most important emphasis in data processing is laid on the methods for data extraction, analysis and understanding. data mining is an analytic process designed a zlatinka svetoslavova kovacheva 122 to explore data (usually large amounts of data typically business or market related) in search of consistent patterns and/or systematic relationships between variables, and then to validate the findings by applying the detected patterns to new subsets of data. the ultimate goal of data mining is prediction and predictive data mining is the most common type of data mining and one that has the most direct business applications. (witten, and frank 2000). the term predictive data mining is usually applied to identify data mining projects with the goal to design a statistical or neural network model or set of models that can be used to predict some response of interest. for example, a credit card company may want to engage in predictive data mining, to derive a model or set of models (e.g., neural networks) that can quickly identify transactions which have a high probability of being fraudulent. other types of data mining projects (e.g., to identify cluster or segments of customers) use drill-down descriptive and exploratory methods. for more details see (weiss et al., 1997). in the business environment, complex data mining projects may require the coordinate efforts of various experts, stakeholders, or departments throughout an entire organization. in the data mining literature, various "general frameworks" have been proposed to organize the process of gathering data, analyzing data, disseminating results, implementing results, and monitoring improvements. in general, the process of data mining consists of three stages: § the initial exploration, § model building or pattern identification with validation/verification, and § deployment (i.e., the application of the model to new data in order to generate predictions). stage 1: exploration this stage usually starts with data preparation which may involve cleaning data, data transformations, selecting subsets of records and in case of data sets with large numbers of variables ("fields") performing some preliminary feature selection operations to bring the number of variables to a manageable range (depending on the statistical methods which are being considered). data preparation and cleaning is an often neglected but extremely important step in the data mining process. it is particularly applicable to the typical data mining projects where large data sets collected via some automatic methods (e.g., via the web) serve as the input into the analyses. often, the method by which the data was gathered was not tightly controlled, and so the data may contain out-of-range values (e.g., income: -100), impossible data combinations (e.g., gender: male, pregnant: yes), and the like. analyzing data that has not been carefully screened for such problems can produce highly misleading results, in particular in predictive data mining. then, depending on the nature of the analytic problem, this first stage of the process of data mining may involve anywhere between a simple choice of straightforward predictors for a regression model, to elaborate exploratory analyses using a wide variety of graphical and statistical methods. data reduction in the context of data mining is usually applied to projects where the goal is to aggregate or amalgamate the information contained in large datasets into manageable (smaller) information nuggets. data reduction methods can include simple tabulation, aggregation (computing descriptive statistics) or more sophisticated techniques like clustering, principal components analysis, etc. the concept of drill-down analysis applies to the area of data mining, to denote the interactive exploration of data, in particular of large databases. the process of drill-down analyses begins by considering some simple break-downs of the data by a few variables of interest (e.g., gender, geographic region, etc.). various statistics, tables, histograms, and other graphical summaries can be computed for each group. next one may want to "drilldown" to expose and further analyze the data "underneath" one of the categorizations, for example, one might want to further review the data for males from one region. again, various statistical and graphical summaries can be computed for those cases only, which might suggest further break-downs by other variables (e.g., income, age, etc.). at the lowest ("bottom") level are the raw data: for example, you may want to review the addresses of male customers from one region, for a certain income group, etc., and to offer to those customers some particular services of particular utility to that group. application of neural networks to data mining 123 stage 2: model building and validation this stage involves considering various models and choosing the best one based on their predictive performance (i.e., explaining the variability in question and producing stable results across samples). this may sound like a simple operation, but in fact, it sometimes involves a very elaborate process. there are a variety of techniques developed to achieve that goal many of which are based on so-called "competitive evaluation of models", that is, applying different models to the same data set and then comparing their performance to choose the best. these techniques, which are often considered the core of predictive data mining, include: bagging (voting, averaging), boosting, stacking (stacked generalizations), and meta-learning. the concept of bagging (voting for classification, averaging for regression-type problems with continuous dependent variables of interest) applies to the area of predictive data mining, to combine the predicted classifications (prediction) from multiple models, or from the same type of model for different learning data. it is also used to address the inherent instability of results when applying complex models to relatively small data sets. suppose your data mining task is to build a model for predictive classification, and the dataset from which to train the model (learning data set, which contains observed classifications) is relatively small. you could repeatedly sub-sample (with replacement) from the dataset, and apply, for example, a tree classifier to the successive samples. in practice, very different trees will often be grown for the different samples, illustrating the instability of models often evident with small datasets. one method of deriving a single prediction (for new observations) is to use all trees found in the different samples, and to apply some simple voting: the final classification is the one most often predicted by the different trees. note that some weighted combination of predictions (weighted vote, weighted average) is also possible, and commonly used. a sophisticated (machine learning) algorithm for generating weights for weighted prediction or voting is the boosting procedure. the concept of boosting applies to the area of predictive data mining, to generate multiple models or classifiers (for prediction or classification), and to derive weights to combine the predictions from those models into a single prediction or predicted classification. a simple algorithm for boosting works like this: assign greater weight to those observations that were difficult to classify (where the misclassification rate was high), and lower weights to those that were easy to classify (where the misclassification rate was low). then apply the classifier again to the weighted data and continue with the next iteration (application of the analysis method for classification to the re-weighted data). boosting will generate a sequence of classifiers, where each consecutive classifier in the sequence is an "expert" in classifying observations that were not well classified by those preceding it. during deployment (for prediction or classification of new cases), the predictions from the different classifiers can then be combined (e.g., via voting, or some weighted voting procedure) to derive a single best prediction or classification. boosting can also be applied to learning methods that do not explicitly support weights or misclassification costs. in that case, random sub-sampling can be applied to the learning data in the successive steps of the iterative boosting procedure, where the probability for selection of an observation into the subsample is inversely proportional to the accuracy of the prediction for that observation in the previous iteration (in the sequence of iterations of the boosting procedure). stage 3: deployment that final stage involves using the model selected as best in the previous stage and applying it to new data in order to generate predictions or estimates of the expected outcome. the concept of deployment in predictive data mining refers to the application of a model for prediction or classification to new data. after a satisfactory model or set of models has been identified (trained) for a particular application, one usually wants to deploy those models so that predictions or predicted classifications can quickly be obtained for new data. for example, a credit card company may want to deploy a trained model or set of models (e.g., neural networks) to quickly identify transactions which have a high probability of being fraudulent. the concept of data mining is becoming increasingly popular as a business information management tool where it is expected to reveal knowledge structures that can guide decisions in conditions of limited certainty. zlatinka svetoslavova kovacheva 124 recently, there has been increased interest in developing new analytic techniques specifically designed to address the issues relevant to business data mining (e.g., classification trees), but data mining is still based on the conceptual principles of statistics including the traditional exploratory data analysis and modelling and it shares with them both some components of its general approaches and specific techniques. (pregibon 1997 and hastie et al. 2001). however, an important general difference in the focus and purpose between data mining and the traditional exploratory data analysis (eda) is that data mining is more oriented towards applications than the basic nature of the underlying phenomena. in other words, data mining is relatively less concerned with identifying the specific relations between the involved variables. for example, uncovering the nature of the underlying functions or the specific types of interactive, multivariate dependencies between variables are not the main goal of data mining. instead, the focus is on producing a solution that can generate useful predictions. therefore, data mining accepts among others a "black box" approach to data exploration or knowledge discovery and uses not only the traditional exploratory data analysis (eda) techniques, but also such techniques as neural networks which can generate valid predictions but are not capable of identifying the specific nature of the interrelations due to its applied importance, data mining emerges as a rapidly growing and major area (also in statistics) where important theoretical advances are being made. for more details see (edelstein, 1999, berry and linoff, 2000, han and kamber 2000). 2. neural networks neural networks is one of the data mining techniques.they are analytic techniques modelled after the (hypothesized) processes of learning in the cognitive system and the neurological functions of the brain and capable of predicting new observations (on specific variables) from other observations (on the same or other variables) after executing a process of so-called learning from existing data. as the prediction is usually an activity of the human brain, to automate this process, it is necessary to understand “how the human brain learns?” 2.1 biological neurons the brain is a collection of about 10 billion interconnected neurons. each neuron is a cell that uses biochemical reactions to receive, process and transmit information. a neuron's dendritic tree is connected to a thousand neighbouring neurons. when one of those neurons fire, a positive or negative charge is received by one of the dendrites. the strengths of all the received charges are added together through the processes of spatial and temporal summation. spatial summation occurs when several weak signals are converted into a single large one, while temporal summation converts a rapid series of weak pulses from one source into one large signal. the aggregate input is then passed to the soma (cell body). the soma and the enclosed nucleus don't play a significant role in the processing of incoming and outgoing data. their primary function is to perform the continuous maintenance required to keep the neuron functional. the part of the soma that does concern itself with the signal is the axon hillock. if the aggregate input is greater than the axon hillock's threshold value, then the neuron fires, and an output signal is transmitted down the axon. the strength of the output is constant, regardless of whether the input was just above the threshold, or a hundred times as great. the output strength is unaffected by the many divisions in the axon; it reaches each terminal button with the same intensity it had at the axon hillock. this uniformity is critical in an analogue device such as a brain where small errors can snowball, and where error correction is more difficult than in a digital system. (see figure 1). application of neural networks to data mining 125 each terminal button is connected to other neurons across a small gap called a synapse. the physical and neurochemical characteristics of each synapse determines the strength and polarity of the new input signal. this is where the brain is the most flexible, and the most vulnerable. changing the constitution of various neuro transmitter chemicals can increase or decrease the amount of stimulation that the firing axon imparts on the neighbouring dendrite. altering the neurotransmitters can also change whether the stimulation is excitatory or inhibitory. many drugs such as alcohol and lsd have dramatic effects on the production or destruction of these critical chemicals. the infamous nerve gas sarin can kill because it neutralizes a chemical (acetylcholinesterase) that is normally responsible for the destruction of a neurotransmitter (acetylcholine). this means that once a neuron fires, it keeps on triggering all the neurons in the vicinity. one no longer has control over muscles, and suffocation ensues. for more details see (abdi, 1994, 1999, anderson, 1995, reilly et al., 1982). learning occurs by changing the effectiveness of the synapses so that the influence of one neuron on another changes. biological neurons are believed to be the structural constituents of the brain. a neural network can: • learn by adapting its synaptic weights to changes in the surrounding environments; • handle imprecise, fuzzy, noisy, and probabilistic information; and • generalize from known tasks or examples to unknown ones. zlatinka svetoslavova kovacheva 126 in more practical terms neural networks are non-linear statistical data modeling tools. they can be used to model complex relationships between inputs and outputs or to find patterns in data. a neural network can learn. one of the neural net paradigms is supervised learning. in supervised learning, a neural net directly compares the network output with a known correct or desired answer in the training process. a neural network is characterized by: • network topology, • connection strength between neurons, • node properties, • internal controls, and • the updating rules. 2.2 artificial neural networks artificial neural networks (ann) are an attempt to mimic some, or all, of these characteristics. an artificial neural network (ann) is either software or hardware that can simulate biological neural networks. artificial neural networks can perform computations and have learning abilities. these features distinguish neural network software from other software. see (patterson, d.,1996; carling, a.,1992). an artificial neural network (ann), also called a simulated neural network (snn) or commonly just neural network (nn) is an interconnected group of artificial neurons that uses a mathematical or computational model for information processing based on a connectionist approach to computation. in most cases an ann is an adaptive system that changes its structure based on external or internal information that flows through the network. 2.2.1 a simple model of an artificial neuron as complicated as the biological neuron is, it may be simulated by a very simple model. an artificial neuron (see figure 2) is a device with many inputs and one output. the neuron has two modes of operation; the training mode and the using mode. in the training mode, the neuron can be trained to fire (or not), for particular input patterns. in the using mode, when a taught input pattern is detected at the input, its associated output becomes the current output. if the input pattern does not belong in the taught list of input patterns, the firing rule is used to determine whether to fire or not. figure 2. a simple artificial neuron application of neural networks to data mining 127 the inputs each have a weight that they contribute to the neuron, if the input is active. the neuron can have any number of inputs; neurons in the brain can have as many as a thousand inputs. the firing rule is an important concept in neural networks and accounts for their high flexibility. a firing rule determines how one calculates whether a neuron should fire for any input pattern. it relates to all the input patterns, not only the ones on which the node was trained. a simple firing rule can be implemented by using hamming distance technique. the rule goes as follows: take a collection of training patterns for a node, some of which cause it to fire (the 1-taught set of patterns) and others which prevent it from doing so (the 0-taught set). then the patterns not in the collection cause the node to fire if, on comparison, they have more input elements in common with the 'nearest' pattern in the 1-taught set than with the 'nearest' pattern in the 0-taught set. if there is a tie, then the pattern remains in the undefined state. for example, a 3-input neuron is taught to output 1 when the input (x1,x2 and x3) is 111 or 101 and to output 0 when the input is 000 or 001. then, before applying the firing rule, the truth table is; x1: 0 0 0 0 1 1 1 1 x2: 0 0 1 1 0 0 1 1 x3: 0 1 0 1 0 1 0 1 out: 0 0 0/1 0/1 0/1 1 0/1 1 as an example of the way the firing rule is applied, take the pattern 010. it differs from 000 in 1 element, from 001 in 2 elements, from 101 in 3 elements and from 111 in 2 elements. therefore, the 'nearest' pattern is 000 which belongs in the 0-taught set. thus the firing rule requires that the neuron should not fire when the input is 001. on the other hand, 011 is equally distant from two taught patterns that have different outputs and thus the output stays undefined (0/1). by applying the firing in every column the following truth table is obtained; x1: 0 0 0 0 1 1 1 1 x2: 0 0 1 1 0 0 1 1 x3: 0 1 0 1 0 1 0 1 out: 0 0 0 0/1 0/1 1 1 1 the difference between the two truth tables is called the generalisation of the neuron. therefore the firing rule gives the neuron a sense of similarity and enables it to respond 'sensibly' to patterns not seen during training. 2.2.2 a more complicated neuron the previous neuron doesn't do anything that conventional computers don't do already. a more sophisticated neuron is the mcculloch and pitts model (mcp). the difference from the previous model is that the inputs are 'weighted', the effect that each input has at decision making is dependent on the weight of the particular input. the weight of an input is a number which when multiplied with the input gives the weighted input. these weighted inputs are then added together and if they exceed a pre-set threshold value, the neuron fires. in any other case the neuron does not fire. (see figure 3). zlatinka svetoslavova kovacheva 128 figure 3. an mcp neuron in mathematical terms, the neuron fires if and only if; x1w1 + x2w2 + x3w3 + ... +xnwn > t the addition of input weights and of the threshold makes this neuron a very flexible and powerful one. the mcp neuron has the ability to adapt to a particular situation by changing its weights and/or threshold. various algorithms exist that cause the neuron to 'adapt'; the most used ones are the delta rule and the back error propagation. the former is used in feed-forward networks and the latter in feedback networks. 2.3 architecture of neural networks 2.3.1 feed-forward networks feed-forward anns allow signals to travel one way only; from input to output. there is no feedback (loops) i.e. the output of any layer does not affect that same layer. feed-forward anns tend to be straight forward networks that associate inputs with outputs. they are extensively used in pattern recognition. this type of organisation is also referred to as bottom-up or top-down. (see figure 4). 2.31.2 feedback networks feedback networks can have signals travelling in both directions by introducing loops in the network. feedback networks are very powerful and can get extremely complicated. feedback networks are dynamic; their 'state' is changing continuously until they reach an equilibrium point. they remain at the equilibrium point until the input changes and a new equilibrium needs to be found. feedback architectures are also referred to as interactive or recurrent, although the latter term is often used to denote feedback connections in single-layer organisations. the commonest type of artificial neural network consists of three groups, or layers, of units: a layer of "input" units is connected to a layer of "hidden" units, which is connected to a layer of "output" units. the activity of the input units represents the raw information that is fed into the network. the activity of each hidden unit is determined by the activities of the input units and the weights on the connections between the input and the hidden units. the behaviour of the output units depends on the activity of the hidden units and the weights between the hidden and output units. application of neural networks to data mining 129 figure 4. an example of a simple feedforward network figure 5. perceptron this simple type of network is interesting because the hidden units are free to construct their own representations of the input. the weights between the input and hidden units determine when each hidden unit is active, and so by modifying these weights, a hidden unit can choose what it represents. (mandic, 2001). we also distinguish single-layer and multi-layer architectures. the single-layer organisation, in which all units are connected to one another, constitutes the most general case and is of more potential computational power than hierarchically structured multi-layer organisations. in multi-layer networks, units are often numbered by layer, instead of following a global numbering. (fukushima, 1975). 2.4 perceptrons the most influential work on neural nets in the 60's went under the heading of 'perceptrons' a term coined by frank rosenblatt. the perceptron turns out to be an mcp model ( neuron with weighted inputs ) with some additional, fixed, pre-processing. units labelled a1, a2, aj , ap are called association units and their task is to extract specific, localised featured from the input images. perceptrons mimic the basic idea behind the zlatinka svetoslavova kovacheva 130 mammalian visual system. they were mainly used in pattern recognition even though their capabilities extended a lot more. see figure 5 (minsky and papert, 1969). 2.5 hopfield model and boltzmann machine one of the most popular networks is the hopfield network. this recurrent net is completely connected. the boltzmann machine is closely related to the hopfield model. the boltzmann machine is a special type of neural network, in which each neuron configuration has a certain probability to appear. (the name comes from the following fact: the boltzmann machine is a probabilistic neural network which forms a markov chain; the invariant distribution of the markov chain is similar to the "boltzmann distribution" in statistical physics). most software is "programmed" to perform certain tasks. these tasks are fixed. for example, chess game software will not play solitary. neural network software is not programmed; it is trained. neural networks do what they are trained to do. what you train is what you get. the neural network attempts to simulate the human brain. the human brain has front-end subsystems and can only handle preprocessed information. the front-end subsystems for humans are eyes, ears, ... the same is also true for neural networks. there are two types of data used by neural network systems: user data (or application data), and neural data. neural networks use neural data. user data depends on the applications. put it in another way: neural nets speak neural language, users speak user language. the information processed by a neural network has to be prepared by a front-end subsystem. this is called data encoding. a neural network can not usually handle the user-application data directly. similarly, after neural computation, the result usually does not make sense to humans directly; the front-end system is responsible for converting the neural output data back into user-application data. this is called data decoding. front-end systems are basically a language translator. a neural network system consists of the front-end subsystem and a neural network subsystem: 2.6 training neural networks neural networks can be explicitly programmed to perform a task by manually creating the topology and then setting the weights of each link and threshold. however, this by-passes one of the unique strengths of neural nets: the ability to program themselves. the most basic method of training a neural network is trial and error. if the network isn't behaving the way it should, change the weighting of a random link by a random amount. if the accuracy of the network declines, undo the change and make a different one. it takes time, but the trial and error method does produce results. the neural network to the left is a simple one that could be constructed using such a trial and error method. the task is to mirror the status of the input row onto the output row. to do this it would have to invent a binary to decimal encoding and decoding scheme with which it could pass the information through the bottle-neck of the two neurons in the centre. unfortunately, the number of possible weightings rises exponentially as one adds new neurons, making large general-purpose neural nets impossible to construct using trial and error methods. in the early 1980s two researchers, david rumelhart and david parker, independently rediscovered an old calculus-based learning algorithm. the back-propagation algorithm compares the result that was obtained with the result that was expected. it then uses this information to systematically modify the weights throughout the neural network. this training takes only a fraction of the time that trial and error method take. it can also be reliably used to train networks on only a portion of the data, since it makes inferences. the resulting networks are often correctly configured to answer problems that they have never been specifically trained on. as useful as back-propagation is, there are often easier ways to train a network. for specific-purpose networks, such as pattern recognition, the operation of the network and the training method are relatively easy to observe even though the networks might have hundreds of neurons. also referred to as connectionist architectures, parallel distributed processing, and neuromorphic systems, an artificial neural network (ann) is an information-processing paradigm inspired by the way the densely interconnected, parallel structure of the mammalian brain processes information. artificial neural networks are application of neural networks to data mining 131 collections of mathematical models that emulate some of the observed properties of biological nervous systems and draw on the analogies of adaptive biological learning. the key element of the ann paradigm is the novel structure of the information processing system. it is composed of a large number of highly interconnected processing elements that are analogous to neurons and are tied together with weighted connections that are analogous to synapses. learning in biological systems involves adjustments to the synaptic connections that exist between the neurons. this is true of anns as well. learning typically occurs by example through training, or exposure to a truthed set of input/output data where the training algorithm iteratively adjusts the connection weights (synapses). these connection weights store the knowledge necessary to solve specific problems. although anns have been around since the late 1950's, it wasn't until the mid-1980's that algorithms became sophisticated enough for general applications. today anns are being applied to an increasing number of realworld problems of considerable complexity. they are good pattern recognition engines and robust classifiers, with the ability to generalize in making decisions about imprecise input data. they offer ideal solutions to a variety of classification problems such as speech, character and signal recognition, as well as functional prediction and system modeling where the physical processes are not understood or are highly complex. anns may also be applied to control problems, where the input variables are measurements used to drive an output actuator, and the network learns the control function. the advantage of anns lies in their resilience against distortions in the input data and their capability of learning. they are often good at solving problems that are too complex for conventional technologies (e.g., problems that do not have an algorithmic solution or for which an algorithmic solution is too complex to be found) and are often well suited to problems that people are good at solving, but for which traditional methods are not. one of the major advantages of neural networks is that, theoretically, they are capable of approximating any continuous function, and thus the researcher does not need to have any hypotheses about the underlying model, or even to some extent, which variables matter. 3. comparison of neural networks with other data mining techniques 3.1 neural networks versus conventional computing techniques neural networks take a different approach to problem solving than that of conventional computers. conventional computers use an algorithmic approach i.e. the computer follows a set of instructions in order to solve a problem. unless the specific steps that the computer needs to follow are known the computer cannot solve the problem. that restricts the problem solving capability of conventional computers to problems that we already understand and know how to solve. but computers would be so much more useful if they could do things that we don't exactly know how to do. neural networks process information in a similar way the human brain does. the network is composed of a large number of highly interconnected processing elements (neurones) working in parallel to solve a specific problem. neural networks learn by example. they cannot be programmed to perform a specific task. the examples must be selected carefully otherwise useful time is wasted or even worse the network might be functioning incorrectly. the disadvantage is that because the network finds out how to solve the problem by itself, its operation can be unpredictable. on the other hand, conventional computers use a cognitive approach to problem solving; the way the problem is to solved must be known and stated in small unambiguous instructions. these instructions are then converted to a high level language program and then into machine code that the computer can understand. these machines are totally predictable; if anything goes wrong is due to a software or hardware fault. neural networks and conventional algorithmic computers are not in competition but complement each other. there are tasks are more suited to an algorithmic approach like arithmetic operations and tasks that are more suited to neural networks. even more, a large number of tasks, require systems that use a combination of the two approaches (normally a conventional computer is used to supervise the neural network) in order to perform at maximum efficiency. zlatinka svetoslavova kovacheva 132 3.2 main drawbacks of classical statistical techniques classical statistical techniques have the following main drawbacks : § they impose restrictions on the number of input data: one is limited to a few inputs among dozens or hundreds available, imposing a priori variable selection, with all the inherent pitfalls ; § regressions are performed using simple dependency functions (linear, logarithmic) that are not very realistic ; § the hypothesis is made that there only one dependency function over the whole data set, instead of many distinct niches ; § other hypotheses imposed by their underlying theories (normal distributions, equiprobabilities, uncorrelated variables) known to be violated, but that are necessary for their good operation ; § the need to use hare-brained methods to transform data. in all cases one has to call on an expert of the method and perform many weeks, even a few months' worth of work. more fundamentally, to quote professor peter d.m. macdonald, of mcmaster university, ontario, canada, about the saarenvirta data set, ‘traditional approaches to statistical inference fail with large databases, however, because with thousands or millions of cases and hundreds or thousands of variables there will be a high level of redundancy among the variables, there will be spurious relationships, and even the weakest relationships will be highly significant by any statistical test. the objective is to build a model with significant predictive power. it is not enough just to find which relationships are statistically significant’. 3.3 neural nets and linear statistics comparing neural networks with linear statistics, the following conclusions are drawn: § neural nets need less constraining hypotheses (the dependency must be a function, nothing more); § qualitative (enumerative) data are straightforwardly handled ; § no preprocessing, «binning», simplification or reduction of quantitative variables is necessary ; § it has been demonstrated that linear regression and logistic regression are particular cases of neural nets (with one layer and a linear threshold function). the same thing happens with principal component analysis (pca) whose values are contained in the weights of the neurodes of a one-layer, linearthreshold function network performing self-association (i.e. with outputs being the same as the inputs, and fewer neurodes than in/outputs in the intermediate layer: see at the end of the document for a picture). neural networks do what every good «new» theory does: they encompass and generalise the previous statistical techniques. for more details see (ripley, 1996). 3.4 neural networks and scorecards neural models are «nonlinear», that is, they are better able to account for the complexity of human behaviour than linear, more simplistic ones. for instance, if a loan's risk decreases with age for renters and increases with age for owners, a neural network will do what a scorecard cannot do and «understand» the relation between both variables with respect to the outcome, thus performing better reclassifyings. taking into account the relation between age and lodging situation, rather than striking a weighting on account of each variable separately, is known as nonlinearity, and is the main advantage of neural networks. 3.5 neural networks and expert systems when we compare the neural networks with expert systems, the following conclusions are drawn: application of neural networks to data mining 133 § the «knowledge» has to be specially formatted by a «knowledge engineer» starting from the expert's knowledge. using expert systems, the time required for analysis and formatting are increased and not decreased; § experts systems are slow to develop, and slow and expensive to update; § material problems are not the only ones: there are fundamental, epistemological problems like: it is not appropriate to represent knowledge in the form of decision rules or decision trees . no tolerance to missing or erroneous values; § the need to manually update (at a cost) expert systems each time expertise changes, while with a neural net, it is enough to launch a new learning process. the immense advantage of neural nets is that one goes directly from factual data to the model without any human work, without tainting the result with oversimplification or preconceived ideas. 3.6 neural networks and typical profiles § the typical profile reflect the centre (centroid) of the cloud, not its shape ; § one does not know how many niches there are; the centroid might lie in the middle of two niches and outside both. 3.7 neural networks and «by hand» modeling § this calls on experts, and is costly and slow (3-4 models per year) ; § one has to wait until the «expert» has developed his own «mental model» neural networks build the model directly without waiting for anyone to build their own «expertise». 3.8 main advantages of neural networks we can outline the following advantages of neural networks comparing with other data mining techniques : § ability to account for any functional dependency. the network discovers (learns, models) the nature of the dependency without needing to be prompted. no need to postulate a model, to amend it, etc.; § one goes straight from the data to the model without intermediary, without recoding, without binning, without simplification or questionable interpretation; § insensitivity to « moderate » noise or unreliability in the data. § no conditions on the predicted variable: it can be a yes/no output, a continuous value, one or more classes among n, etc.; § ease of handling, much less human work than traditional statistical analysis. no competence in math, statistics or informatics is required; § no need to manually detect collinearities; § in segmentation, the net determines by itself how many clusters there are in each class; § for the novice user, the idea of learning is easier to understand than the complexities of multivariate statistics; § speed of use: 10 microseconds when hardwired, a few milliseconds on a 1 ghz computer; § spatial relations (geomarketing etc.) are easily analysed and modelled; § the final model is continuous and derivable and lends itself easily to further work: detection of centroids (typical profiles) by «gradient ascent», sensitivity computation (by partial derivation), display with any desired precision, etc.; § explanation and prediction the consumers' decision-making processes are badly understood and so far badly modelled by causal models. in other words, bringing out behaviour rules as such seems inherently difficult. this reminds us of the bitter failures of expert systems. the neural net works better exactly because it models associations and not causes; § the «black box» problem validating the model. the neural model is validated using a number of examples that were excluded from the learning set, called the «test set». expected and predicted values zlatinka svetoslavova kovacheva 134 are compared. performance is evaluated using the reclassifying rate (when classifying) or the average deviation between expected and predicted values when predicting a numerical value. this validation method is as objective as can be, is common in data analysis and can be applied to any kind of predictor, even to an expert person. 3.9 main drawbacks of neural nets of course, neural networks do not dispense one from knowing their problem, defining the classes in a meaningful way, not omitting important variables, etc. the main problem is that the neural net is a «black box»: it does not explain its decision. let us notice,though, that the same can be said about more traditional techniques, regression analysis for instance. an important disadvantage, however, is that the final solution depends on the initial conditions of the network, and, it is virtually impossible to "interpret" the solution in traditional, analytic terms, such as those used to build theories that explain phenomena. 3.10 why use neural networks? neural networks have two fundamental advantages : § the ability to represent any function, linear or not, simple or complicated. neural nets are what mathematicians call «universal approximators» (kolmogorov, 1957); § the ability to learn from representative examples, by «error backpropagation» (le cun, mcclelland, 1986, werbos, 1974). model building, or «learning», is automatic. neural networks, with their remarkable ability to derive meaning from complicated or imprecise data, can be used to extract patterns and detect trends that are too complex to be noticed by either humans or other computer techniques. a trained neural network can be thought of as an "expert" in the category of information it has been given to analyse. this expert can then be used to provide projections given new situations of interest and answer "what if" questions. other reasons for their application include: • adaptive learning: an ability to learn how to do tasks based on the data given for training or initial experience; • self-organisation: an ann can create its own organisation or representation of the information it receives during learning time; • real time operation: ann computations may be carried out in parallel, and special hardware devices are being designed and manufactured which take advantage of this capability; • fault tolerance via redundant information coding: partial destruction of a network leads to the corresponding degradation of performance. however, some network capabilities may be retained even with major network damage. however, building neural model belongs to data analysis and not to magic (even though, to quote arthur c. clarke, sufficiently advanced technology is indistinguishable from magic). the data must be explicative and in a large enough amount. neural networks do not perform miracles. but if used sensibly they can produce some amazing results. 4. applications of neural networks to data mining processes in practice neural networks have broad applicability to real world business problems. in fact, they have already been successfully applied in many industries. the tasks to which artificial neural networks are applied tend to fall within the following broad categories: • function approximation, or regression analysis, including time series prediction and modeling. application of neural networks to data mining 135 • classification, including pattern and sequence recognition, novelty detection and sequential decision making. • data processing, including filtering, clustering, blind source separation and compression. application areas include system identification and control (vehicle control, process control), game-playing and decision making (backgammon, chess, racing), pattern recognition (radar systems, face identification, object recognition and more), sequence recognition (gesture, speech, handwritten text recognition), medical diagnosis, financial applications, knowledge discovery in databases, visualization and e-mail spam filtering. since neural networks are best at identifying patterns or trends in data (for the purposes of data mining), they are well suited for prediction or forecasting needs including: § sales forecasting ; § industrial process control ; § customer research ; § data validation ; § risk management; § target marketing . ann are also used in the following specific paradigms: recognition of speakers in communications; diagnosis in medicine; recovery of telecommunications from faulty software; interpretation of multimeaning words; undersea mine detection; texture analysis; three-dimensional object recognition; hand-written word recognition; facial recognition, etc. 4.1 neural networks in medicine artificial neural networks (ann) are currently a 'hot' research area in medicine and it is believed that they will receive extensive application to biomedical systems in the next few years. at the moment, the research is mostly on modelling parts of the human body and recognising diseases from various scans (e.g. cardiograms, cat scans, ultrasonic scans, etc.). neural networks also contribute to other areas of research such as neurology and psychology. they are regularly used to model parts of living organisms and to investigate the internal mechanisms of the brain. neural networks are ideal in recognising diseases using scans since there is no need to provide a specific algorithm on how to identify the disease. neural networks learn by example so the details of how to recognise the disease are not needed. what is needed is a set of examples that are representative of all the variations of the disease. the quantity of examples is not as important as the 'quantity'. the examples need to be selected very carefully if the system is to perform reliably and efficiently. neural networks are used experimentally to model the human cardiovascular system. diagnosis can be achieved by building a model of the cardiovascular system of an individual and comparing it with the real time physiological measurements taken from the patient. if this routine is carried out regularly, potential harmful medical conditions can be detected at an early stage and thus make the process of combating the disease much easier. a model of an individual's cardiovascular system must mimic the relationship among physiological variables (i.e., heart rate, systolic and diastolic blood pressures, and breathing rate) at different physical activity levels. if a model is adapted to an individual, then it becomes a model of the physical condition of that individual. the simulator will have to be able to adapt to the features of any individual without the supervision of an expert. this calls for a neural network. another reason that justifies the use of ann technology, is the ability of anns to provide sensor fusion which is the combining of values from several different sensors. sensor fusion enables the anns to learn complex relationships among the individual sensor values, which would otherwise be lost if the values were individually analysed. in medical modelling and diagnosis, this implies that even though each sensor in a set may be sensitive only to a specific physiological variable, anns are capable of detecting complex medical conditions by fusing the data from the individual biomedical sensors. zlatinka svetoslavova kovacheva 136 anns are used experimentally to implement electronic noses. electronic noses have several potential applications in telemedicine. telemedicine is the practice of medicine over long distances via a communication link. the electronic nose would identify odours in the remote surgical environment. these identified odours would then be electronically transmitted to another site where an door generation system would recreate them. because the sense of smell can be an important sense to the surgeon, telesmell would enhance telepresent surgery. an application developed in the mid-1980s called the "instant physician" trained an autoassociative memory neural network to store a large number of medical records, each of which includes information on symptoms, diagnosis, and treatment for a particular case. after training, the net can be presented with input consisting of a set of symptoms; it will then find the full stored pattern that represents the "best" diagnosis and treatment. 4.2 neural networks in business business is a diverted field with several general areas of specialisation such as accounting or financial analysis. almost any neural network application would fit into one business area or financial analysis. there is some potential for using neural networks for business purposes, including resource allocation and scheduling. there is also a strong potential for using neural networks for database mining, that is, searching for patterns implicit within the explicitly stored information in databases. most of the funded work in this area is classified as proprietary. thus, it is not possible to report on the full extent of the work going on. most work is applying neural networks, such as the hopfield-tank network for optimization and scheduling. 4.2.1 banking ann are useful for predicting the issue of loans (credit scoring) and predicting the recovery of bad loans (recovery scoring). they are applied for forecasting the behaviour of new customers, identifying «good risks» and offering them loans. 4.2.2 finance ann are used for redicting share prices, volatilities. they help for position-taking, portfolio and asset management. 4.2.3 industry ann predicting demand for a product or service for better production planning. servo-control for machines or chemical reactors (through «model inversion») is applied. 4.2.4 marketing there is a marketing application which has been integrated with a neural network system. the airline marketing tactician (a trademark abbreviated as amt) is a computer system made of various intelligent technologies including expert systems. a feedforward neural network is integrated with the amt and was trained using back-propagation to assist the marketing control of airline seat allocations. the adaptive neural approach was amenable to rule expression. additionaly, the application's environment changed rapidly and constantly, which required a continuously adaptive solution. the system is used to monitor and recommend booking advice for each departure. such information has a direct impact on the profitability of an airline and can provide a technological advantage for users of the system. while it is significant that neural networks have been applied to this problem, it is also important to see that this intelligent technology can be integrated with expert systems and other approaches to make a functional system. neural networks were used to discover the influence of undefined interactions by the various variables. while these interactions were not defined, they were used by the neural system to develop useful conclusions. it is also noteworthy to see that neural networks can influence the bottom line. application of neural networks to data mining 137 predicting function of neural networks facilitates the process of marketing targeting and turnover prediction; analysis and prediction of crime, tax return analysis for fraud detection; risk analysis for renters; economic forecasting; etc. (bigus, 1996). equipped with accurate forecasts, the customers are able to save on resources or improve their return on investment. neural nets do not replace staff, but they improve an organisation's operation by letting them build models they would not have had the time to make using older techniques. 4.2.5 credit evaluation the hnc company, founded by robert hecht-nielsen, has developed several neural network applications. one of them is the credit scoring system which increase the profitability of the existing model up to 27%. the hnc neural systems were also applied to mortgage screening. a neural network automated mortgage insurance underwritting system was developed by the nestor company. this system was trained with 5048 applications of which 2597 were certified. the data related to property and borrower qualifications. in a conservative mode the system agreed on the underwritters on 97% of the cases. in the liberal model the system agreed 84% of the cases. this is system run on an apollo dn3000 and used 250k memory while processing a case file in approximately 1 sec. 5. neural network software neural network software is used to simulate, research, develop and apply artificial neural networks, biological neural networks and in some cases a wider array of adaptive systems. 5.1 simulators neural network simulators are software applications that are used to simulate the behavior of artificial or biological neural networks. they focus on one or a limited number of specific types of neural networks. they are typically stand-alone and not intended to produce general neural networks that can be integrated in other software. simulators usually have some form of built-in visualization to monitor the training process. some simulators also visualize the physical structure of the neural network. 5.1.1 research simulators historically, the most common type of neural network software was intended for researching neural network structures and algorithms. the primary purpose of this type of software is to, through simulation, gain a better understanding of the behavior and properties of neural networks. today in the study of artificial neural networks, simulators have largely been replaced by more general component based development environments as research platforms. commonly used artificial neural network simulators include the stuttgart neural network simulator (snns), pdp++ and java nns. snns (stuttgart neural network simulator) is a neural network simulator originally developed at the university of stuttgart. while it was originally built for x11 under unix, there are windows ports. its successor javanns never reached the same popularity. pdp++ (parallel distributed processing++) is neural simulation software written in c++ for the creation of connectionist models. development initially began in 1995 at carnegie mellon university, and is currently in version 3.2, with version 4.0 well underway at the university of colorado at boulder. the software is featured in the textbook computational explorations in cognitive neuroscience. pdp++ features a modular design, based on the principles of object-oriented programming. it has been known to work in microsoft windows, various unices, solaris, darwin and several other operating systems. csuper-script (variously, css and c^c), a built-in c++-like interpreted scripting language, allows access to virtually all simulator objects and can initiate all the same actions as the gui, and more. zlatinka svetoslavova kovacheva 138 in the study of biological neural networks however, simulation software is still the only available approach. in such simulators the physical biological and chemical properties of neural tissue, as well as the electromagnetic impulses between the neurons are studied. commonly used biological network simulators include xnbc and the bnn toolbox for matlab. 5.1.2 data analysis simulators unlike the research simulators, the data analysis simulators are intended for practical applications of artificial neural networks. their primary focus is on data mining and forecasting. data analysis simulators usually have some form of preprocessing capabilities. unlike the more general development environments data analysis simulators use a relatively simple static neural network that can be configured. a majority of the data analysis simulators on the market use backpropagation networks or self-organizing maps as their core. the advantage of this type of software is that it is relatively easy to use. this however comes at the cost of limited capability. some data analysis simulators work in conjunction with other computational environments, such as microsoft excel or matlab. data analysis simulators include: ward systems neuroshell, palisade, neuraltools, alyuda neurointelligence, netlab, easynn-plus, neuralworks predict and dozens of others. alyuda neurointelligence is an neural network software for experts designed for intelligent support in applying neural networks to solve real-world forecasting, classification and function approximation problems; to use intelligent features to preprocess datasets; to find efficient architecture and to analyze performance and apply the neural network to new data. experts can create and test their solutions much faster, increase their productivity and improve results. neuralworks predict is an integrated, state-of-the-art tool for rapidly creating and deploying prediction and classification applications. predict combines neural network technology with genetic algorithms, statistics, and fuzzy logic to automatically find optimal or near-optimal solutions for a wide range of problems. predict incorporates years of modeling and analysis experience gained from working with customers faced with a wide variety of analysis and interpretation problems. in microsoft windows environments neuralworks predict can be run either as an add-in for microsoft excel to take advantage of excel's rich data handling and graphing capabilities, or as a command line program that offers powerful batch mode processing. in unix and linux environments, neuralworks predict runs as a command line program. 5.2 development environments development environments for neural networks differ from the software described above primarily on two accounts – they can be used to develop custom types of neural networks and they support deployment of the neural network outside the environment. in some cases they have advanced preprocessing, analysis and visualization capabilities. popular development environments are: • the mathworks nn toolbox which is based on the matlab computing environment; • the gblearn2 library of the lush programming language. the neural network toolbox extends matlab with tools for designing, implementing, visualizing, and simulating neural networks. neural networks are invaluable for applications where formal analysis would be difficult or impossible, such as pattern recognition and nonlinear system identification and control. the neural network toolbox provides comprehensive support for many proven network paradigms, as well as graphical user interfaces (guis) that enable you to design and manage your networks. the modular, open, and extensible design of the toolbox simplifies the creation of customized functions and networks. 5.2.1 component based environments a more modern type of development environments that are currently favored in both industrial and scientific use are based on a component based paradigm. the neural network is constructed by connecting adaptive filter components in a pipe filter flow. this allows for greater flexibility as custom networks can be built as well as custom components used by the network. in many cases this allows a combination of adaptive application of neural networks to data mining 139 and non-adaptive components to work together. the data flow is controlled by a control system which is exchangeable as well as the adaptation algorithms. the other important feature is deployment capabilities. with the advent of component-based frameworks such as .net and java, component based development environments are capable of deploying the developed neural network to these frameworks as inheritable components. in addition some software can also deploy these components to several platforms, such as embedded systems. component based development environments include: joone, peltarion synapse and neurodimension neurosolutions. joone (java object oriented neural engine) is a component based neural network framework built in java. joone consists of a component-based architecture based on linkable components that can be extended to build new learning algorithms and neural networks architectures. components are plug-in code modules that are linked to produce an information flow. new components can be added and reused. beyond simulation, joone also has to some extent multi-platform deployment capabilities. joone has an gui editor to graphically create and test any neural network, and a distributed training environment that allows for neural networks to be trained on multiple remote machines. as of 2006, joone is the only free component based neural network development environment available. unlike the two other (commercial) systems that are in existence, synapse and neurosolutions, it is written in java and has direct cross-platform support. a limited number of components exist and the graphical development environment is rudimentary so it has significantly fewer features than its commercial counterparts. joone can be considered to be more of a neural network framework than a full integrated development environment. unlike its commercial counterparts, it has a strong focus on code-based development of neural networks rather than visual construction. while in theory joone can be used to construct a wider array of adaptive systems (including those with non-adaptive elements), its focus is on backpropagation based neural networks. neurosolutions is a neural network development environment developed by neurodimension. it combines a modular, icon-based (component based) network design interface with an implementation of advanced learning procedures, such as conjugate gradients, levenberg-marquardt and backpropagation through time. the software is used to design, train and deploy neural network (supervised learning and unsupervised learning) models to perform a wide variety of tasks such as data mining, classification, function approximation, multivariate regression and time-series prediction. synapse is a component based development environment for neural networks and adaptive systems. created by peltarion, synapse allows data mining, statistical analysis, visualization, preprocessing, design and training of neural networks and adaptive systems and the deployment of them. it utilizes a plug-in based architecture making it a general platform for signal processing. the first version of the product was released in may 2006. the disadvantage of component-based development environments is that they are more complex than simulators. they require more learning to fully operate and are far more complicated to develop. the latter leads to a reduction in software diversity. simple simulators and custom neural nets have traditionally had a large amateur development scene. there are hundreds of different neural network simulators, but only a few component-based development environments. 5.3 custom neural networks the majority implementations of neural networks available are however custom implementations in various programming languages and on various platforms. basic types of neural networks are simple to implement directly. there are also many programming libraries that contain neural network functionality and that can be used in custom implementations. zlatinka svetoslavova kovacheva 140 6. conclusion data mining has a lot to gain from neural networks. their ability to learn makes them very flexible and powerful. furthermore there is no need to devise an algorithm in order to perform a specific task; i.e. there is no need to understand the internal mechanisms of that task. they are also very well suited for real time systems because of their fast response and computational times which are due to their parallel architecture. the neural net supplies answers, but not explanations. indeed, the neural model embodies correlations (like intuitive associations), not causal relations (explanations). examining the neural network itself only shows us meaningless numeric values. the neural model is a ‘black box’. on the other hand, this model being continuous and derivable, one can, beyond simple interrogation, ‘explore’ it to determine typical profiles, the degree of explicative power of each variable, reclassify collections of examples to determine their associated probabilities, visualize data and predictions, very 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heat transfer; convection; slip flow; variable properties. mohammad m. rahman 56 1. introduction n recent years, the flow dynamics due to a rotating disk, originating from the early formulation of von karman (1921), has been a popular area of research. since then many researchers (cochran, 1934; roger and lance, 1960; benton, 1965; kuiken, 1971; owen and rogers, 1989; herrero et al 1994; kelson and desseaux, 2000; andrsson and korte, 2002; takhar et al 2002) have studied and reported results on disk-shaped bodies with or without heat transfer. flow due to a rotating disk is encountered in many industrial, geothermal, geophysical, technological and engineering applications. a few of them are rotating heat exchangers, rotating disk reactors for bio-fuels production, computer disk drives, and gas or marine turbines. nomenclature a constant b constant b magnetic field vector 0b applied magnetic field cf skin friction coefficient pc specific heat at constant pressure d constant e electric field ec eckert number e− charge of electron f dimensionless radial velocity g dimensionless tangential velocity h dimensionless axial velocity ha hartman number j electric current density kn knudsen number m hall current parameter nu nusselt number en electron concentration per unit volume p pressure within the boundary layer p∞ pressure of the ambient fluid ep electronic pressure pr variable prandtl number pr∞ ambient prandtl number q velocity vector wq surface heat flux re rotational reynolds number r cylindrical radial coordinate t temperature within boundary layer tu target velocity u velocity along radial direction v velocity along tangential direction w velocity along axial direction sw non-dimensional suction velocity ww suction velocity x , y , z cartesian coordinates greek symbols β hall factor γ relative temperature difference parameter ρ density of the fluid ∞ρ density of the ambient fluid µ coefficient of dynamic viscosity µ∞ dynamic viscosity of the ambient fluid υ∞ kinematic viscosity of the ambient fluid σ electric conductivity κ thermal conductivity κ∞ thermal conductivity of the ambient fluid η similarity parameter ξ target momentum accommodation coefficient λ mean free path θ dimensionless temperature φ tangential coordinate ω angular velocity ε slip factor i convective hydromagnetic slip flow 57 wt temperature at the surface of the disk ∞t temperature of the ambient fluid φ viscous dissipation function τ shear stress the effects of an applied magnetic field on the steady flow due to the rotation of a disk of infinite or finite extent were studied by el-mistikawy et al. (1991) and el-mistikawy and atia (1990). atia and aboul-hassan (1997) studied steady hydromagnetic flow due to an infinite disk rotating with uniform angular velocity in the presence of an axial magnetic field. in their analysis they neglected the induced magnetic field but considered hall current. attia (1998) studied the effects of suction as well as injection in the presence of a magnetic field on the unsteady flow past a rotating porous disk. it was found that the combined effect of a magnetic field with strong injection may stabilize the growth of the boundary layer. sparrow et al. (1971) studied the flow of newtonian fluid due to the rotation of a porous-surfaced disk with a set of linear slip-flow conditions. a substantial reduction in torque then occurred as a result of surface slip. miklavcic and wang (2004) further revisited the problem of sparrow et al. and pointed out that the slipflow boundary conditions could also be used for slightly rarefied gases or for flow over grooved surfaces. arikoglu and ozkol (2006) studied mhd slip flow over a rotating disk with heat transfer. it is observed that both the slip factor and the magnetic flux decrease the velocity in all directions and thicken the thermal boundary layer. recently, osalusi et al. (2008) studied thermal-diffusion and diffusion-thermo effects on mhd slip flow due to a rotating disk. in classical treatment of thermal boundary layers, fluid properties (such as density, viscosity, thermal conductivity) are assumed to be constant; however, experiments indicate that this assumption only makes sense if temperature does not change rapidly for the application of interest. to predict the flow behavior accurately, it may be necessary to take into account these variable properties. zakerullah and ackroyd (1979) investigated free convection flow above a horizontal circular disk considering variable fluid properties. in the case of fully developed laminar flow in concentric annuli, the effect of the variable property has been investigated by herwig and klemp (1988). atia (2006) studied unsteady hydromagnetic flow due to an infinite rotating disk, considering temperature dependent viscosity in a porous medium with hall and ion-slip currents. maleque and sattar (2005a) studied the effect of variable properties on the steady laminar convective flow due to a rotating disk while maleque and sattar (2005b) further investigated the same problem in the presence of hall current. osalusi and sibanda (2006) revisited the problem of maleque and sattar (2005a), considering magnetic effect. when fluid properties such as viscosity and thermal conductivity vary with temperature, prandtl number (see section 2) varies too. all of these afore-mentioned works considered prandtl number as constant within the boundary layer, although viscosity and thermal conductivity depends on temperature. hence one of the motivations behind this study is also to investigate how variable prandtl number affects the flow and heat transfer characteristics. in the present study we extend the work of maleque and sattar (2005b) and analyze the flow and heat transfer characteristics in the presence of viscous dissipation and joule heating, considering slip flow boundary condition at the surface of a uniformly heated rotating disk. the resulting governing equations are solved numerically applying nachtsheim-swigert (1965) iteration technique. graphical results for non-dimensional velocity and temperature profiles including skin-friction coefficient and the nusselt number in tabular form are presented for a range of values of the parameters characterizing the flow. the accompanying discussion provides physical interpretations of the results. 2. mathematical model let us consider a steady hydromagnetic laminar flow of an electrically conducting fluid due to a porous rotating disk of infinite extent in the presence of an external uniform magnetic field directed perpendicular to the disk. the fluid properties are taken as strong functions of temperature. a uniform suction or injection through the disk is considered for the whole range of suction or injection velocities. mohammad m. rahman 58 2.1 basic equations the equations governing the steady hydromagnetic laminar convective flow are: equation of continuity: .( ) 0ρ∇ =q , (1) navier–stokes equation: [ ]( . ) .( ) ( )pρ µ∇ = −∇ + ∇ ∇ + ×q q q j b , (2) ohm’s law for a moving conductor with hall currents: [ ]( ) epσ β β= + × − × + ∇j e q b j b , (3) maxwell electromagnetic equations: . 0, , . 0∇ = ∇× = ∇ =j e 0 b , (4) energy equation: 2 ( . ) .( )p j c t tρ κ µ σ ∇ = ∇ ∇ + + φq , (5) 2 2 22 2 2 u v w u v v w x y z y x z y ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞ φ = + + + + + +⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦ ( ) 2 22 . 3 w u x z ∂ ∂⎛ ⎞ + + − ∇⎜ ⎟∂ ∂⎝ ⎠ q . (6) here q is the velocity vector, b is the magnetic field vector, e denotes the electrical field vector which results from charge separation and is in the z -direction, j is the current density vector, p is the pressure, ρ is the density of the fluid, µ is the viscosity of the fluid, σ is the electrical conductivity of the fluid, κ is the thermal conductivity of the fluid, pc is the specific heat of the fluid, t is the temperature of the fluid, and φ is the viscous dissipation function. in equation (3) the term ( )σβ ×j b denotes the hall effects where 1 een β = designates the hall factor, e− is the charge of electron, en is the electron concentration per unit volume and ep is the electronic pressure. in equation (5) the term 2j σ represents joule heating whereas µφ is the viscous dissipation or frictional heating effects. 2.2 governing equations in non-rotating cylindrical polar coordinates ( , , )r zφ , let us consider a disk which rotates with constant angular velocity ω about the z -axis. the disk is placed at 0z = , and the fluid occupies the region 0z > , convective hydromagnetic slip flow 59 where z is the vertical axis in the cylindrical coordinates system with r and φ as the radial and tangential axes respectively. the components of the flow velocity q are ( , , )u v w in the directions of increasing ( , , )r zφ respectively. the surface of the rotating disk is maintained at a uniform temperature wt and far away from the wall, the free stream is kept at a constant temperature t∞ and at a constant pressure p∞ . the fluid is assumed to be newtonian, viscous and electrically conducting. an external uniform magnetic field is applied in the z direction. the electron–atom collision frequency is assumed to be relatively high so that the hall effect cannot be neglected. ion-slip effects are however ignored in the present analysis. from equation (4), using the relation 0∇⋅ =b for the magnetic field ( , , )x y zb b b=b , we obtain that 0 (constant)zb b= everywhere in the fluid. this assumption is valid only when the magnetic reynolds number is very small so that magnetic induction effects can be ignored. for the current density ( , , )x y zj j j=j we obtain from the relation 0∇⋅ =j that constantzj = . hence we consider that the disk is non-conducting and therefore 0zj = at the disk and hence zero everywhere. finally we consider the case of a short circuit problem in which the applied electric field =e 0 and also assume that the induced magnetic field is negligible in comparison with the applied magnetic field. in the absence of electric field e and electron pressure ep equation (3) becomes 0 0 2 2 ( ) ( ) , , 0 1 1 b v mu b mv u m m σ σ+ −⎡ ⎤ = ⎢ ⎥+ +⎣ ⎦ j , (7) where 0m bσβ= is called hall current parameter. it can be further shown that 2 2 0 0 2 2 ( ) ( ) , , 0 1 1 b mv u b v mu m m σ σ⎡ ⎤− + × = −⎢ ⎥+ +⎣ ⎦ j b . (8) we also assume that the fluid properties, viscosity ( µ ), thermal conductivity (κ ) and density ( ρ ) are functions of temperature alone and obey the following laws (see jayaraj, 1995; later used by malek and sattar, 1995b; osalusi and sibanda, 2006) [ ]/ at tµ µ∞ ∞= , [ ]/ b t tκ κ∞ ∞= , [ ]/ d t tρ ρ∞ ∞= , (9) where a , b and d are arbitrary exponents while µ∞ , κ∞ and ρ∞ are the viscosity, thermal conductivity and density of the ambient fluid respectively. the flow configurations and geometrical coordinates are shown in figure 1. due to steady axially symmetric, compressible hydromagnetic laminar flow of a homogeneous fluid the governing equations take the following form (see malek and sattar, 1995b): ( ) ( ) 0ru rw r z ρ ρ ∂ ∂ + = ∂ ∂ , (10) mohammad m. rahman 60 22 0 ( ),2(1 ) bu v u p u u u u w mv u r r z r r r r r z z m σ ρ µ µ µ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ − + = − + + + + − ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠ (11) 2 0 ( ),2(1 ) bv uv v v v v u w v mu r r z r r r r z z m σ ρ µ µ µ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + = + + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ + ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + −⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (12) figure 1. flow configurations and coordinate system ( )1 ,w w p w wu w w r z z r r r r z z ρ µ µ µ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + = − + + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (13) 2 2 p t t t t t u v c u w r z r r r z z z zr ρ κ κ κ µ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ = + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + + + +⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦ 2 2 20 2 ( )(1 ) b u v m σ + + (14) if the mean free path of the fluid particles is comparable to the characteristic dimensions of the flow field domain, the assumption of continuum media is no longer valid, and as a consequence navier–stokes equation breaks down. in the range 0.1 10kn< < of knudsen number, the high order continuum equations (burnett equations) should be used. for the range of 0.001 0.1kn< < , no-slip boundary conditions cannot be used and should be replaced with the following expression (gad-el-hak, 1999): 2 t u u z ξ λ ξ − ∂ = ∂ , (15) φ rω z wt t∞ 0b w uv p∞ x y convective hydromagnetic slip flow 61 where tu is the target velocity, ξ is the target momentum accommodation coefficient and λ is the mean free path. for 0.001kn < , the no-slip boundary condition is valid; therefore, the velocity at the surface is equal to zero. in this study the slip and the no-slip regimes of the knudsen number that lies in the range 0 0.1kn< < are considered. 2.3 boundary conditions by using equation (15), the appropriate boundary conditions for our model are (i) on the surface of the disk ( 0z = ): tu u= , tv r u= ω + , ww w= (slip flow and permeable surface conditions), (16a) wt t= (uniform surface temperature). (16b) (ii) matching with the quiescent free stream ( z → ∞ ): 0u = , 0v = , t t∞= , p p∞= . (16c) 3. transformation of the model to obtain the solutions of the governing equations (10)-(14) together with the boundary conditions (16) we introduce a dimensionless normal distance from the disk, ( )1/ 2zη υ∞= ω along with the von-karman transformation ( )1/ 2( ), ( ), ( ), 2 ( ), ( ), u rf v rg w h p p p t t t η η υ η ρ υ η θ η ∞ ∞ ∞ ∞ ∞ ⎫= ω = ω = ω ⎪ ⎬ − = ω − = ∆ ⎪⎭ (17) where υ∞ is the kinematic viscosity of the ambient fluid and wt t t∞∆ = − . now substituting (17) into (10)-(14) we obtain the following nonlinear ordinary differential equations 12 (1 ) 0h f dhγ θ γθ −′ ′+ + + = , (18) 2 1 2 2 2(1 ) [ ](1 ) ( )(1 ) 01 d a ahaf a f f g hf mg f m γ γθ θ γθ γθ− − −′′ ′ ′ ′+ + − − + + + − + = + , (19) 2 1 2(1 ) [2 ](1 ) ( )(1 ) 01 d a ahag a g fg hg g mf m γ γθ θ γθ γθ− − −′′ ′ ′ ′+ + − + + − + + = + , (20) 2 1 2 2 2 2(1 ) pr (1 ) pr (1 ) ( )1 d b bhab h ec f g m θ γ γθ θ θ γθ γθ− − −∞ ∞′′ ′ ′+ + − + + + + ++ 2 2pr (1 ) ( ) 0a bec f gγθ −∞ ′ ′+ + = , (21) where ( )1/ 20ha b σ ρ∞= ω is the hartmann number, pr pcµ κ∞ ∞ ∞= is the ambient prandtl number, 2( ) pec r c t= ω ∆ is the eckert number and t tγ ∞= ∆ is the relative temperature difference parameter, which is positive for a heated surface, negative for a cooled surface and zero for uniform properties. thus by using (17) boundary conditions (16) become , 1 , , 1 at 0,sf f g g h wε ε θ η′ ′= = + = = = (22a) mohammad m. rahman 62 0, 0, 0, 0 as ,f g p θ η= = = = → ∞ (22b) where 1/ 2 2 ( ) ξ ε λ υ ξ ∞ − = ω is the slip factor and 1/ 2( )sw w υ − ∞= ω represents a uniform suction when 0sw < and uniform injection when 0sw > at the surface of the disk. 3.1 particular cases a number of special cases can be derived from the full transformed momentum and energy equations (18)-(21) with the boundary conditions (22) which are as follows: i 0swγ = = without heat transfer no-slip condition hassan and attia (1997) ii 2 0ha m ecγ = = = = heat transfer without joule heating no-slip condition kelson and desseaux (2000) iii 2 0ha mγ = = = without heat transfer slip condition miklavcic and wang (2004) iv 0sw m ecγ = = = = heat transfer without joule heating slip condition arikoglu and ozkol (2006) v 2 0ha m ec= = = heat transfer without joule heating no-slip condition maleque and sattar (2005a) vi 0m ec= = heat transfer without joule heating no-slip condition osalusi and sibanda (2006) vii 0ec = heat transfer without joule heating no-slip condition maleque and sattar (2005b) 4. variable prandtl number the prandtl number is a function of viscosity and as viscosity varies across the boundary layer, the prandtl number varies, too. the assumption of constant prandtl number inside the boundary layer may produce unrealistic results. therefore, prandtl number related to the variable viscosity is defined by (1 ) pr (1 ) pr (1 ) (1 ) a p p p a b a b b c c cµ µ γθ µ γθ γθ κ κ γθ κ ∞ ∞ − − ∞ ∞ ∞ + = = = + = + + (23) at the surface ( 0η = ) of the disk, this can be written as pr pr (1 )a bw γ − ∞= + . (24) from equation (23) it can be seen that for 0γ → , the variable prandtl number pr equals the ambient prandtl number pr∞ . for η → ∞ that is outside the boundary layer, ( )θ η becomes zero. therefore pr equals pr∞ regardless of the values of γ . table 1 shows the variation of the prandtl number at the surface of the disk for several values of γ for a fixed value of the ambient prandtl number pr 0.64∞ = and the exponents 0.7a = , 0.83b = . from this table we see that for a positive value of γ , prandtl number at the surface of the disk prw decreases as γ increases. the opposite effect is observed when γ is negative. it must be noted that for 1γ ≤ − no physically viable solutions exist. convective hydromagnetic slip flow 63 table 1. values of pr versus γ for pr 0.64∞ = , 0.7a = , 0.83b = at 0η = . γ -0.8 -0.5 -0.2 0.0 0.2 0.5 1.0 3.0 5.0 pr 0.789 0.700 0.659 0.640 0.625 0.607 0.585 0.534 0.507 in light of the above discussions, using (23) the non-dimensional temperature equation (21) can be rewritten as 1 2(1 ) pr(1 )d ab hθ γ γθ θ γθ θ− −′′ ′ ′+ + − + + 2 2 2 2 2 2(1 ) pr (1 ) ( ) pr ( ) 0aha m ec f g ec f gγθ − ′ ′+ + + + + = . (25) equation (25) is the corrected non-dimensional form of the energy equation in which prandtl number is treated as variable. it is mentionable that this correction does not appear in the literature. 5. parameters of engineering interest the parameters of engineering interest for the present problem are the skin-friction coefficient (cf ) and the nusselt number ( nu ) which indicate physically wall shear stress and rate of heat transfer respectively. the action of the variable properties in the fluid adjacent to the disk sets up a tangential shear stress, which opposes the rotation of the disk. as a consequence, it is necessary to provide a torque at the shaft to maintain a steady rotation. the radial shear stress rτ and tangential shear stress tτ are defined by: 1/ 2 0 (1 ) re (0)ar z u w f z r τ µ µ γ∞ = ⎡ ⎤∂ ∂⎛ ⎞ ′= + = + ω⎜ ⎟⎢ ⎥∂ ∂⎝ ⎠⎣ ⎦ , (26) 1/ 2 0 1 (1 ) re (0)at z v w g z r τ µ µ γ φ ∞ = ⎡ ⎤⎛ ⎞∂ ∂ ′= + = + ω⎢ ⎥⎜ ⎟∂ ∂⎝ ⎠⎣ ⎦ . (27) hence the skin-frictions ( 2 2cf rτ ρ∞= ω ) along radial and tangential directions are obtained as 1/ 2(1 ) re (0)arcf fγ − ′= + , (28) 1/ 2(1 ) re (0)atcf gγ − ′= + . (29) the rate of heat transfer from the disk surface to the fluid is computed by the application of fourier’s law as given below 1/ 2 0 (1 ) (0).bw z t q t z κ κ γ θ υ∞= ∞ ⎛ ⎞∂ ω⎛ ⎞ ′= − = − ∆ + ⎜ ⎟⎜ ⎟∂⎝ ⎠ ⎝ ⎠ (30) hence the nusselt number ( w rq nu tκ∞ = ∆ ) is obtained as 1/ 2(1 ) re (0),bnu γ θ′= − + (31) where 2re r υ∞= ω is the rotational reynolds number. thus from equations (28), (29) and (31) we see that skin-friction coefficient and nusselt number are proportional to the numerical values of (0)f′ , (0)g′ and (0)θ′− which are calculated in the process of integration when solving the corresponding differential equations. mohammad m. rahman 64 6. method of solutions the set of equations (18)-(20) and (25) are highly nonlinear and coupled and therefore the system cannot be solved analytically. the system of transformed governing equations (18)-(20) and (25) with boundary conditions (12) is solved numerically using shooting method similar to that described by nachtsheim-swigert (1965). in equation (22) there are three asymptotic boundary conditions and hence three unknown surface conditions ( )0f′ , ( )0g′ and ( )0θ′ . nachtsheim-swigert developed an iteration technique to overcome the difficulties of determining the guess values of the unknown surface boundary conditions required for the shooting method. within the context of the initial value method and the nachtsheim-swigert shooting iteration technique the outer boundary conditions may be functionally represented by ( )max( ) (0), (0), (0) , 1, 2 6,j j jf g jη θ δ′ ′ ′ψ = ψ = = (26) where 1 fψ = , 2 gψ = , 3 θψ = , 4 f′ψ = , 5 g′ψ = , 6 θ′ψ = . the last three of these represents asymptotic convergence criteria. choosing ( ) 10f g′ = , ( ) 20g g′ = and ( ) 30 gθ′ = and expanding in a first-order taylor’s series after using equations (26) yields 3 max , max 1 ( ) ( ) ,jj j c i j i i g g η η δ = ∂ψ ψ = ψ + ∆ = ∂∑ 62,1=j (27) where subscript ‘c’ indicates the value of the function at maxη determined from the trial integration. solution of these equations in a least-square sense requires determining the minimum value of 6 2 1 j j δ = ∏ = ∑ (28) with respect to ig ( 3,2,1=i ). now differentiating ∏ with respect to ig we obtain ∑ = = ∂ ∂6 1 0 j i j j g δ δ . (29) substituting equation (27) into (29) after some algebra we obtain 3 1 , 1, 2, 3,ik k i k a g b i = ∆ = =∑ (30) where 6 6 , 1 1 . , ; , 1, 2, 3. j j jik i j c j ji k i a b i k g g g= = ∂ψ ∂ψ ∂ψ = = − ψ = ∂ ∂ ∂∑ ∑ (31) now solving the system of linear equations (30) we obtain the missing (unspecified) values of ig as i i ig g g≅ + ∆ . (32) thus adopting this numerical technique aforementioned, a computer program was set up for the solutions of the governing non-linear ordinary differential equations (18)-(20) and (25) of our problem where the integration technique was adopted as a sixth-order runge-kutta method of integration. the velocity and temperature are determined as a function of the coordinate η and displayed graphically. convective hydromagnetic slip flow 65 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 η f ws = 0.5, 0, -0.5, -1.0, -2.0 (a) 0 2 4 6 0 0.2 0.4 0.6 0.8 η g ws = 0.5, 0, -0.5, -1.0, -2.0 (b) 0 2 4 6 -0.5 0 0.5 1 1.5 2 η -h w s = 0 w s = -0.5 w s = -1.0 w s = -2.0 w s = 0.5 (c) 0 2 4 6 8 10 12 14 0 0.2 0.4 0.6 0.8 1 η θ w s = 0.5, 0, -0.5, -1.0, -2.0 (d) 0 3 6 9 12 15 0.625 0.63 0.635 0.64 η pr ws = 0.5, 0, -0.5, -1.0, -2.0 (e) figure 2. variation of (a) radial velocity, (b) tangential velocity, (c) axial velocity, (d) temperature profile, and (e) variable prandtl number for several values of sw . mohammad m. rahman 66 6.1 numerical experiment in this paper, the effects of hall current, viscous dissipation and joule heating on a steady hydromagnetic convective slip flow of a viscous, newtonian, electrically conducting fluid with variable properties over a rotating porous disk have been investigated numerically by using nachtsheim-swigert shooting iteration technique. it can be seen that the solutions are affected by the seven parameters, namely suction (or injection) parameter sw , magnetic field parameter (or hartmann number) ha , hall current parameter m , relative temperature difference parameter γ , prandtl number pr , eckert number ec and slip parameter ε . since experimental data of the physical parameters are not available, in the numerical simulations the choice of the values of the parameters was dictated by the values chosen by the previous investigators. for the present investigation we considered our working fluid as flue gas. for flue gases (ambient prandtl number, pr 0.64∞ = ) the values of the exponents a , b and d are taken as 0.7a = , 0.83b = and 1.0d = − (see jayaraj, 1995). the default values of the other parameters which we considered are 1.0sw = − , 2 0.5ha = , 0.5m = , 0.2γ = , pr 0.625= , 0.2ec = , and 0.2ε = unless otherwise specified. 6.2 code verification to assess the accuracy of the present code, we reproduced the values of (0)f′ , (0)g′ , ( )h ∞ and (0)θ′ for constant property models of kelson and desseaux (2000) (herein and after referred as kd2000) (see case-ii in section 3.1) and arikoglu and ozkol (2006) (herein and after referred as ao2006) (see case-iv in section 3.1). tables 2-4 show the comparisons of the data produced by the present code and those of kd2000 and ao2006. in fact the results show a close agreement, and hence justify the use of the present code for the current model. table 2. numerical values of (0)f′ , (0)g′− and (0)θ′− for various values of sw with 2 0ha m ec γ= = = = and pr 0.71= . (0)f′ (0)g′− (0)θ′− sw present kd2000 present kd2000 present kd2000 4 0.24304404 0.243044 0.02892121 0.0289211 0.00001075 0.0000107 3 0.30914768 0.309147 0.06028945 0.0602893 0.00057793 0.000576 2 0.39893387 0.398934 0.13595275 0.135952 0.01103604 0.011013 1 0.48948057 0.489481 0.30217432 0.302173 0.08504687 0.084884 0 0.51022378 0.510233 0.61592380 0.615922 0.32637889 0.325856 -1 0.38954065 0.389569 1.17526180 1.175222 0.79393633 0.793048 -2 0.24241310 0.242421 2.03859590 2.038527 1.43876482 1.437782 -3 0.16558828 0.165582 3.0122231 3.012142 2.13677058 2.135585 -4 0.12475268 0.124742 4.00526266 4.005180 2.84369011 2.842381 convective hydromagnetic slip flow 67 table 3. numerical values of (0)f′ and (0)g′− for various values of ε with 2 0sw ha m ec γ= = = = = and pr 0.71= . (0)f′ (0)g′− ε present ao2006 present ao2006 0.0 0.51022378 0.51023261 0.61592380 0.61592201 0.1 0.42144560 0.42145363 0.60583699 0.60583524 0.2 0.35257377 0.35258100 0.58367858 0.58367676 0.5 0.22384294 0.22384820 0.50281179 0.50280970 1.0 0.12792035 0.12792364 0.39492982 0.39492759 2.0 0.06100834 0.06101009 0.27337241 0.27337013 5.0 0.01858796 0.01858852 0.14339025 0.14338820 10 0.00681240 0.00681255 0.08103175 0.08103008 20 0.00236161 0.00236159 0.04378973 0.04378846 table 4. numerical values of ( )h− ∞ and (0)θ′− for various values of ε with 2 0sw ha m ec γ= = = = = and pr 0.71= . ( )h− ∞ (0)θ′− ε present ao2006 present ao2006 0.0 0.88344324 0.8844741 0.32637889 0.32586063 0.1 0.88055012 0.8813642 0.33402796 0.33349695 0.2 0.87334256 0.8739572 0.33732324 0.33678090 0.5 0.84230103 0.8423926 0.33521597 0.33465287 1.0 0.79003973 0.7894772 0.32099888 0.32043299 2.0 0.71185974 0.7103133 0.29357940 0.29299798 5.0 0.58730981 0.5837646 0.24466400 0.24440461 10 0.49317208 0.4875846 0.20570012 0.20504924 20 0.40816322 0.3999758 0.16953552 0.16882963 6.3 effect of step size to see the effects of the integration step size η∆ , we ran the code for our model with three different step sizes namely ,01.0=∆η ,005.0=∆η and 001.0=∆η . in each case, we found excellent agreement among the results. it was also found that 001.0=∆η provided sufficiently accurate (error less than 610− ) results and further refinement of the grid size was therefore not warranted. 7. results and discussion for the purpose of discussing the results, the numerical calculations are presented in the form of nondimensional velocity (radial, tangential and axial) and temperature profiles. in the calculations the values of the parameters namely suction (or injection) parameter sw , magnetic field parameter (or hartmann number) ha , hall current parameter m , relative temperature difference parameter γ , prandtl number pr , eckert number ec and slip parameter ε are varied. mohammad m. rahman 68 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 η f ha 2 =0, 0.5, 0.8, 1.0 (a) 0 2 4 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 η g ha 2 =0, 0.5, 0.8, 1.0 (b) 0 2 4 6 1 1.04 1.08 1.12 1.16 1.2 η -h ha 2 =0, 0.5, 0.8, 1.0 (c) 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 η θ ha 2 =0, 0.5, 0.8, 1.0 (d) 0 2 4 6 8 10 0.625 0.63 0.635 0.64 η pr ha 2 =0, 0.5, 0.8, 1.0 (e) figure 3. variation of (a) radial velocity, (b) tangential velocity, (c) axial velocity, (d) temperature profile, and (e) variable prandtl number for several values of ha . convective hydromagnetic slip flow 69 the effects of the suction (or injection) parameter ( sw ) on the radial, tangential and axial velocity profiles are shown in figures 2 (a)-(c) respectively. from figures 2(a)-(b) we see that radial and tangential velocity profiles decrease very rapidly as the suction velocity ( 0sw < ) intensifies. the maximum of the radial velocity profiles moves towards the surface of the disk. it is also apparent that the thickness of the boundary layer decreases as suction velocity increases. therefore, suction stabilizes the boundary layer growth. from figure 2(c) we found that for strong suction, inward axial velocity is nearly constant. figure 2(d) depicts the variation of the temperature profiles for various values of the suction parameter. the effect of the suction parameter on the thermal boundary layer is found to be similar to those of the radial and tangential velocity boundary layers. applying suction, one can control the flow and heat transfer characteristics. in figure 2(e) we have plotted variable prandtl number as a function of η to show the variation of the prandtl number throughout the boundary for several values of the suction parameter. from this figure we see that within the boundary layer for a fixed value of η variable prandtl number increases as the suction parameter increases while far away from the surface of the disk pr equals its ambient value pr∞ . an opposite effect is found for the case of fluid injection ( 0sw > ). the influence of the magnetic field parameter (hartmann number) ha on f , g , and h− distributions is depicted in figures 3(a)-(c). an increase in ha induces a significant decrease in radial and tangential velocity profiles throughout the boundary layer; this is due to fact that imposition of a magnetic field to an electrically conducting fluid creates a drag force called the lorentz force that has a tendency to slow down the flow around the disk at the expense of increasing its temperature. from figure 3(c) it is also apparent that inward axial velocity decreases substantially with the increase of the hartmann number. an increase in hartmann number increases temperature profiles and hence increases the thermal boundary layer as can be seen from figure 3(d). the variation of the prandtl number within the boundary layer for different values of the hartmann number is depicted in figure 3(e). this figure reveals that variable prandtl number decreases with the increase of the hartmann number. in figures 4(a)-(d), the influence of hall current parameter ( m ) on f , g , h− and θ distributions across the boundary layer are given. the parameter m has remarkable effect on the velocity profiles. it is observed that radial as well as inward axial velocity profiles increase as the hall current parameter increases up to a certain value of 1m < . beyond this value of m , profiles of f and h− decrease with the further increase of m . it can be explained as follows: from equation (19) we see that the radial velocity term with hall current is 2 2 (1 )1 aha f m γθ −− + + . an increase in m ( 1< ) will induce very minor alterations in the expression 2 1 1 m+ . however in equation (20), the term 2 2 ( )(1 )1 aha mf g m γθ −− + + + gives an effective contribution to the radial velocity through 2 2 (1 )1 aha mf m γθ −− + + indicating that an increase in m ( 1< ) causes a direct increase in the radial velocity. but for 1m > an opposite scenario is observed. conversely we observe that the tangential velocity ( g ) increases with an increase in hall current parameter. from equation (20) we see that the tangential velocity is affected via the term 2 2 (1 )1 aha g m γθ −− + + , thus a change in m produces very little effect, due to the inverse relationship of m and the tangential velocity g . this effect will impede the tangential mohammad m. rahman 70 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 0.12 η f m = 0.5 m = 0 m = 50 m = 10 m = 1.0 (a) 0 2 4 6 0 0.2 0.4 0.6 0.8 η g m = 0, 1.0, 10, 50 (b) 0 2 4 6 0.95 1 1.05 1.1 1.15 1.2 η -h m = 0 m = 0.5 m = 1.0 m = 10 m = 50 (c) 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 η θ m = 0, 0.5, 1.0, 10 (d) 0 2 4 6 8 10 0.625 0.63 0.635 0.64 η θ m = 0, 0.5, 1.0, 10 (e) figure 4. variation of (a) radial velocity, (b) tangential velocity, (c) axial velocity, (d) temperature profile, and (e) variable prandtl number for several values of m . convective hydromagnetic slip flow 71 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 η f γ = 0, 0.2, 0.5, 1 (a) 0 2 4 6 0 0.2 0.4 0.6 0.8 η g γ = 0, 0.2, 0.5, 1 (b) 0 2 4 6 8 10 0.9 1 1.1 1.2 1.3 η -h γ = 0 γ = 0.2 γ = 0.5 (c) 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 η θ γ = 0, 0.2, 0.5, 1 (d) 0 2 4 6 8 10 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 η pr γ = 0, 0.2, 0.5, 1 pr =0.64∞ (e) figure 5. variation of (a) radial velocity, (b) tangential velocity, (c) axial velocity, (d) temperature profile, and (e) variable prandtl number for several values of γ . mohammad m. rahman 72 flow. however it will be swamped out by 2 2 (1 )1 aha mg m γθ −+ + , the much greater direct proportionality in the factor affecting the tangential velocity in given equation (19). this positive term accelerates the flow for increase in m , explaining the rise in tangential velocity with increase in m . the mechanism by which hall currents influence hydromagnetic disk flow is therefore via secondary effects and coupling in the momentum equations. figure 4 (d) reveals that the thickness of the thermal boundary layer decreases as m increases. the variation of the variable prandtl number for different values of m within the boundary layer is shown in figure 4(e). it is clearly observed that an increase in m increases pr within the boundary layer. for very large values of m , increasing the effect of m on pr is less pronounced due to the fact that 2 1 1 m+ approaches to its limiting value 0 when m → ∞ , and as a consequence resistive effect of the magnetic field on the flow and temperature field is diminished. figures 5(a)-(d) explain the variation of the nondimensional radial, tangential, axial velocity and temperature profiles for various values of the relative temperature difference parameter γ . from figure 5(a), we see that due to the existence of the centrifugal force the radial velocity increases and attains its maximum value for all values of γ . it is also observed that the maximum values of the radial velocity are 0.07276499, 0.08221263, 0.09128975 and 0.09893225 for 0γ = , 0.2, 0.5 and 1.0, respectively, and occur at 0.390η = , 0.494, 0.643 and 0.871, respectively. it is seen that the maximum velocity increases by 36% when γ increases from 0 to 1.0. the case 0γ = corresponds to constant property of the working fluid. it is also seen that the smallest maximum value of the radial velocity is found for the case of constant property ( 0γ = ), which contradicts directly the findings of maleque and sattar (2005b). from figure 5(b), it is found that the tangential velocity increases with the increasing values of γ . it can be seen from figure 5(c) that inward axial velocity decreases with the increase of γ . it is also observed that close to the surface of the disk the effect of γ gives rise to the familiar inflection point profile, which indicates that fluid with variable property on a highly heated surface, may lead to the destabilization of the laminar flow resulting in the development of the viscous sub-layer. figure 5(d) depicts that temperature profile increases significantly with the increase of γ . quantitatively, at 8.0η = the value of θ increases by 6026.8% when the value of γ increases from 0 to 1.0. thus the thickness of the thermal boundary layer increases markedly with the increase of γ which is a direct contradiction to the findings of maleque and sattar (2005b), and osalusi and sibanda (2006). studying a limited set of parameter values such as 0γ = , 0.5 (maleque and sattar, 2005b) and 0γ = , 0.01 (osalusi and sibanda, 2006) and considering prandtl number as constant within the boundary layer, they concluded that an increase in γ does not change the thickness of the thermal boundary layer. figure 5(e) shows that variable prandtl number pr decreases very rapidly within the boundary layer for the increase of γ . for 0γ = variable prandtl number pr equals the ambient prandtl number pr∞ . for a fixed value of γ ( 0)> , pr increases as η increases and for η → ∞ , i.e. outside the boundary layer, it converges to its ambient value pr∞ . from this figure it is also clear that at the surface of the disk (at 0η = ), 0γ = , 0.2, 0.5, and 1 corresponds to pr 0.64= , 0.625, 0.607, 0.585 when other parameter values are fixed. thus the effects of pr on the velocity and temperature functions give the reverse effect of γ on them. convective hydromagnetic slip flow 73 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 η f ε = 0, 0.2, 1.0, 4.0, 8.0 (a) 0 2 4 6 0 0.2 0.4 0.6 0.8 1 η g ε = 0, 0.2, 1.0, 4.0, 8.0 (b) 0 2 4 6 0.8 0.9 1 1.1 1.2 η -h ε = 0 ε = 0.2 ε = 1.0 ε = 4 ε = 8 (c) 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 η θ ε = 0, 1.0, 4.0, 8.0 (d) 0 2 4 6 8 10 0.625 0.63 0.635 0.64 η pr ε = 0, 1.0, 4.0, 8.0 (e) figure 6. variation of (a) radial velocity, (b) tangential velocity, (c) axial velocity, (d) temperature profile, and (e) variable prandtl number for several values of ε . mohammad m. rahman 74 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 η f ε = 0, 0.2, 1.0, 4.0, 8.0 (a) 0 2 4 6 0 0.2 0.4 0.6 0.8 1 η g ε = 0, 0.2, 1.0, 4.0, 8.0 (b) 0 2 4 6 0.8 0.9 1 1.1 1.2 η -h ε = 0 ε = 0.2 ε = 1.0 ε = 4 ε = 8 (c) 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 η θ ε = 0, 1.0, 4.0, 8.0 (d) 0 2 4 6 8 10 0.625 0.63 0.635 0.64 η pr ε = 0, 1.0, 4.0, 8.0 (e) figure 7. variation of (a) radial velocity, (b) tangential velocity, (c) axial velocity, (d) temperature profile, and (e) variable prandtl number for several values of ε . convective hydromagnetic slip flow 75 in figures 6(a)-(d) we displayed velocity and temperature profiles for various values of the slip factor (ε ). here 0ε = represents no-slip condition at the surface of the disk. from figure 6(a) we see that the radial boundary layer decreases very rapidly with the increase of the slip factor. the thickness of the radial boundary layer is higher for no-slip flow compared to the slip flow. fig. 6(a) further indicates that for large values of ε i.e. ε → ∞ , the rotating disk does not cause rotation of the fluid particles. because in this range of ε the flow becomes entirely potential, there will be no motion in the fluid. this can be further explained as follows: the centrifugal force acting on the rotating disk (as like a centrifugal fan) will throw out the fluid that sticks to it. on the other hand, the flow in the axial direction will come forward to compensate for this thrown fluid. but increasing the slip on the surface of the disk reduces the amount of fluid that can stick on it; as a consequence the efficiency of the rotating disk is reduced substantially and is unable to transfer its circumferential momentum to the fluid particles. a reduction in the circumferential velocity results in a reduction in the centrifugal force which in turn decreases the inward axial velocity substantially as can be seen from figure 6(c). from figure 6(d) we see that the thermal boundary layer increases as slip factor ε increases. figure 6(e) shows a decreasing effect of ε on the variable prandtl number throughout the boundary layer. in table 5 we present skin-friction in radial and tangential directions and rate of heat transfer for various values of the pertinent parameters for a fixed value of pr . it can be seen that skin-friction in the radial direction decreases while skin-friction in the tangential direction increases with the increase of the suction parameter ( 0)sw < . on the other hand, the rate of heat transfer increases with the increase of the suction parameter. an opposite effect is observed for the case of injection ( 0)sw > . table 5 also shows that skin-friction in the radial direction increases for all increasing values of the hartmann number except in the range of 0 0.707ha≤ < (not precisely determined). in this range of ha , radial skin-friction decreases as ha increases. tangential skin-friction increases while the rate of heat transfer decreases for all increasing values of the hartmann number. the effects of the hall current parameter on the radial and tangential skin-frictions and the rate of heat transfer can be seen from table 5. skin-friction in the radial direction increases within the range of 0 1m≤ ≤ . outside of this range of m an opposite behavior is observed. tangential skin-friction decreases when m increases within the range of 0 1m≤ ≤ , and outside this range of m tangential skin-friction increases with the further increase of m . the rate of heat transfer increases with the increase of m for some cm m< . but for the existence of strong hall current i.e. cm m> the rate of heat transfer decreases with the further increase of m . the effect of increasing eckert number ec has a decreasing effect on the radial skin-friction and on the rate of heat transfer whereas it has a very minor increasing effect on the tangential skin-friction as can be seen from table 5. the variation of the radial and tangential skin-frictions and the rate of heat transfer for some selected values of the slip factor ε are shown in table 5. from here we see that skin-friction in both directions decreases with the increase of the slip factor. the largest skin-friction is found for the case of no-slip at the surface. on the other hand the rate of heat transfer increases with the increase of slip factor within the range of 0 1ε≤ ≤ . but outside of this range of ε , the rate of heat transfer decreases with the further increase of the slip factor. thus the rate of heat transfer can be strongly controlled by controlling the slip on the disk. mohammad m. rahman 76 table 5. numerical values of (0)f′ , (0)g′− and (0)θ′− for various values of sw , 2ha , m , ec , and ε with 0.2γ = , pr 0.625= , 0.7a = , 0.83b = , 1.0d = − . sw 2ha m ec ε (0)f′ (0)g′− (0)θ′− 0.5 0.5 0.5 0.2 0.2 0.30626574 0.57918115 0.05772346 0.0 0.5 0.5 0.2 0.2 0.28341282 0.69042730 0.16076663 -0.5 0.5 0.5 0.2 0.2 0.24952322 0.81807709 0.30083407 -1.0 0.5 0.5 0.2 0.2 0.20853272 0.96222468 0.47057060 -2.0 0.5 0.5 0.2 0.2 0.12995186 1.28487051 0.86659713 -1.0 0.0 0.5 0.2 0.2 0.21477746 0.78866948 0.49905518 -1.0 0.5 0.5 0.2 0.2 0.20853272 0.96222468 0.47057060 -1.0 0.8 0.5 0.2 0.2 0.20907598 1.04165765 0.45885733 -1.0 1.0 0.5 0.2 0.2 0.21011307 1.08825472 0.45234655 -1.0 0.5 0.0 0.2 0.2 0.13956413 0.95761163 0.43868718 -1.0 0.5 0.5 0.2 0.2 0.20853272 0.96222468 0.47057060 -1.0 0.5 1.0 0.2 0.2 0.24406352 0.93179389 0.49107437 -1.0 0.5 10 0.2 0.2 0.23051412 0.80677029 0.50468008 -1.0 0.5 50 0.2 0.2 0.21822032 0.79212583 0.50044457 -1.0 0.5 0.5 0.0 0.2 0.20858805 0.96208379 0.53127404 -1.0 0.5 0.5 0.2 0.2 0.20853272 0.96222468 0.47057060 -1.0 0.5 0.5 0.4 0.2 0.20847731 0.96236597 0.40974692 -1.0 0.5 0.5 0.8 0.2 0.20836700 0.96264871 0.28795509 -1.0 0.5 0.5 1.0 0.2 0.20831208 0.96279014 0.22698731 -1.0 0.5 0.5 0.2 0.0 0.36777423 1.17657272 0.43706560 -1.0 0.5 0.5 0.2 0.2 0.20853272 0.96222468 0.47057060 -1.0 0.5 0.5 0.2 1.0 0.05117315 0.53881089 0.48991829 -1.0 0.5 0.5 0.2 4.0 0.00578668 0.20435375 0.47419596 -1.0 0.5 0.5 0.2 8.0 0.00158190 0.11227042 0.46583227 finally, the significance of the relative temperature difference (γ ) on the rate of heat transfer for both variable prandtl number ( prv ) and constant prandtl number ( prc ) is tabulated in table 6. from this table we see that in both cases the rate of heat transfer from the surface of the disk to the fluid decreases for all increasing values of γ . we also see that rate of heat transfer for the variable property case is lower than the constant property case and the relative error between them increases significantly with the increase of γ . therefore, consideration of prandtl number as constant within the boundary layer for variable property is unrealistic. it is also mentionable that for our studied parameter values the relationship between the relative temperature difference parameter and the variable prandtl number is an inverse relationship. so, the effect of pr on the radial and tangential skin-frictions and on the rate of heat transfer is just the reverse of the effect of γ on them. convective hydromagnetic slip flow 77 table 6. numerical values of (0)θ′− for various values of γ for 1.0sw = − , 2 0.5ha = , 0.5m = , 0.2ec = , and 0.2ε = with 0.7a = , 0.83b = , 1.0d = − . (0)θ′− γ prv prc pr pr error = 100 pr v c v − × 0.0 0.64904702 0.64904702 0.0% 0.2 0.47057060 0.47627008 1.2% 0.5 0.31906666 0.32769165 2.7% 1.0 0.19338897 0.20237407 4.6% 3.0 0.05065792 0.05674936 12.0% 5.0 0.01661496 0.02066049 24.3% 8. conclusions in this study we experiment numerically on the effects of hall current, viscous dissipation and joule heating on hydromagnetic slip flow over a porous rotating disk taking into account the variable properties of the fluid. we illustrate the flow and heat transfer characteristics in terms of non-dimensional velocity and temperature profiles and tabulate skin-friction and rate of heat transfer, and show how the flow fields are influenced by the material parameters entering into the problem. as a result of computations the following conclusions can be drawn: 1. suction stabilizes the boundary layer’s growth. 2. slip factor significantly controls the flow and heat transfer characteristics. 3. increasing slip factor forces decrease of the prandtl number within the boundary layer. 4. hall parameter markedly controls the radial and axial flows. for strong hall current (large 1)m > flow along these directions decreases. 5. hall current strongly controls the rate of heat transfer from the disk to the fluid. very strong hall current may reduce the heat transfer rate. 6. hall current increases variable prandtl number within the boundary layer. 7. the resistive effect of an applied magnetic field (lorentz force) on the velocity and temperature profiles is apparent. 8. increasing viscous dissipation parameter (or eckert number) decreases the rate of heat transfer from the disk to the fluid. 9. the rate of heat transfer in a fluid of constant property is higher than in a fluid of variable property. 10. the thickness of the thermal boundary layer is lower for a fluid of constant property than for a corresponding fluid of variable property. 11. for modeling thermal boundary layers with temperature dependent viscosity, prandtl number must be treated as variable inside the boundary layer. mohammad m. rahman 78 9. references aboul-hassan, a.l. and attia, h.a. 1997. flow due to a rotating disk with hall effect. phys. lett. a., 228: 286-290. andersson, h.i. and de korte, e. (2002). mhd flow of a power law fluid over a rotating disk. european j. mech. b./fluids, 21: 317-324. arikoglu, a. and ozkol, i. 2006. on the mhd and slip flow over a rotating disk with heat transfer. int. j. numer methods heat fluid flow, 28: 172-184. attia, h.a. 1998. unsteady mhd flow near a rotating porous disk with uniform suction or injection. fluid dyn. res., 23: 283-290. attia, h.a. 2006. unsteady flow and heat transfer of viscous incompressible fluid with temperature-dependent viscosity due to a rotating disc in a porous medium. j. phys. a, math. gen., 39: 979-991. benton, e.r. 1965. on the flow due to a rotating disc. j. fluid mech., 24: 781-800. cochran, w.g. 1934. the flow due to a rotating disc. proc. cambridge phil. soc. 30: 365-375. el-mistikawy, t.m.a., attia, h.a. and megahed, a.a. 1991. the rotating disk flow in the presence of weak magnetic field. proc. fourth conf. theoret. appl. mech., cairo, egypt, 5–7 november 1991, pp. 6982. el-mistikawy, t.m.a. and attia, h.a. 1990. the rotating disk flow in the presence of strong magnetic field. proc. third int. cong. fluid mech., cairo, egypt, 2-4 january 1990, 3: 1211-1222. gad-el-hak, m. 1999. the fluid mechanics of micro devices-the free scholar lecture. j. fluid eng-t. asme., 121: 5-33. herrero, j., humphrey, j.a.c. and giralt, f. 1994. comparative analysis of coupled flow and heat transfer between co-rotating discs in rotating and fixed cylindrical enclosures, am. soc. mech. eng., heat transfer div. 300: 111-121. herwig, h. and klemp, k. 1988. variable property effects of fully developed laminar flow in concentric annuli. asme j. heat trans., 110: 314-320. jayaraj, s. 1995. thermophoresis in laminar flow over cold inclined plates with variable properties. heat mass trans., 40: 167-174. kelson, n. and desseaux, a. 2000. note on porous rotating disk flow. anziam j. 42(e): c837-c855. kuiken, h.k. 1971. the effect of normal blowing on the flow near a rotating disk of infinite extent. j. fluid mech., 47: 789-798. maleque, a.k. and sattar, a.m. 2005a. steady laminar convective flow with variable properties due to a porous rotating disk. j. heat trans., 127: 1406-1409. maleque, a.k. and sattar, a.m. 2005b. the effects of variable properties and hall current on steady mhd laminar convective fluid flow due to a porous rotating disk. int. j. heat mass trans., 48: 4963-4972. miklavcic, m. and wang, c.y. 2004. the flow due to a rough rotating disk. z. angew. math. phys., 55: 235-246. nachtsheim, p.r. and swigert, p. 1965. satisfaction of asymptotic boundary conditions in numerical solution of system of nonlinear of boundary layer type. nasa tn-d3004. osalusi, e., side, j. and harris, r. 2008. thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady mhd convective and slip flow due to a rotating disk with viscous dissipation and ohmic heating. int. commu. heat mass trans., 35: 908-915. osalusi, e. and sibanda, p. 2006. on v ariable laminar convective flow properties due to a porous rotating disk in a magnetic field. rom. j. phys., 51: 933-944. owen, j.m. and rogers, r.h. 1989. flow and heat transfer in rotating disc system, rotor–stator systems, vol. 1, research studies press, taunton, uk and john wiley, ny. roger, m.g. and lance, g.n. 1960. the rotationally symmetric flow of a viscous fluid in presence of infinite rotating disc. j. fluid mech., 7: 617-631. convective hydromagnetic slip flow 79 sparrow, e.m., beavers, g.s. and hung, l.y. 1971. flow about a porous-surface rotating disk. int. j. heat mas tranfer., 14: 993-996. takhar, h.s., singh, a.k. and nath, g. (2002). unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid. int. j. therm. sci., 41: 147-155. von karman, t. 1921. uber laminare und turbulente reibung. zamm, 1: 233-255. zakerullah, m. and ackroyd, j.a.d. 1979. laminar natural convection boundary layers on horizontal circular discs. j. appl. math. phys., 30: 427435. received 22 june 2009 accepted 14 february 2010 photovoltaic cells and systems: squ journal for science, 17 (1) (2012) 80-83 © 2012 sultan qaboos university 08 a new criterion for optimality in nonlinear programming l.m. graña drummond* and a.n. iusem** *faculdade de administracao e ciencias contabeis, universidade federal de rio de janeiro, brazil, email: bolsigeno@gmail.com. **instituto de matematica pura e aplicada (impa), rio de janeiro, brazil, email: iusp@impa.br. abstract: we establish a sufficient condition for the existence of minimizers of real-valued convex functions on closed subsets of finite dimensional spaces. we compare this condition with other related results. keywords: nonlinear programming, convexity, recession cone. في البرمجة غير الخطية يةمثللألمعيار جديد ألفريدو أيوزمموند و ادر راناجويس ل مغلقة من جزئيةفي إطار مجموعات محدبة لدالة حقيقية ىصغرشرطاُ كافياُ لوجود قيم تقترح هذه الورقة :خصمل . به مرتبطةنتائج أخرى عدودة األبعاد. نقارن هذا الشرط ممح فضاءات 1. introduction ecessary and/or sufficient conditions for determining whether an optimization problem has an optimum have been studied for centuries. for instance, a very well-known classical result is the bolzano-weierstrass theorem, which states that any continuous function attains its minimum value on a compact subset of its domain. many other conditions have been proposed and, in general, these criteria are useful not just for theoretical purposes, but also from an algorithmic point of view. here, for a real-valued convex objective and a closed constraint set, we propose a new condition for establishing the existence of optima. first, let us introduce some notation which will be used in the sequel. if c ⊂ r n , then the recession cone of c, which is denoted by 0 + c, is the set of directions contained in c, i.e., 0 + c = {v ∈ r n │c + tv ⊂ c ∀ t ≥ 0}. we denote by conv(c) the convex hull of c, i.e., the 'smallest' convex set that contains c, that is to say, the set of all convex combinations of elements of c. the set cl(c) will stand for the closure of c. for a function f : r n → r and α ∈ r, the α-level set of f is given by γα = {x ∈ r n │f(x) ≤ α}. finally, argminx∈c f (x) is the set of minimizers of f on c. n mailto:bolsigeno@gmail.com mailto:iusp@impa.br a new criterion for optimality 08 2. the optimality criterion in this section we propose our optimality criterion: a set of conditions which ensures the existence of an optimum for a constrained nonlinear problem with convex objective function. theorem 2.1 let f : r n → r be a convex function and ω a closed subset of r n . assume that i. f is bounded from below on ω , ii. 0 + cl(conv(ω)) ∩ γf(0) = {0} . then, argminx∈ω f(x) ≠ ø. proof. by virtue of bolzano-weierstrass theorem, we can assume that ω is unbounded. let infx∈ω f(x) = ν ∈ r and {x k } ⊂ ω be a minimizing sequence, i.e., such that limk→∞ f(x k ) = ν. if {x k } has a bounded subsequence, since ω is closed and f is continuous (because it is a real-valued convex function), there exists ∈ ω such that f( ) = ν and, therefore, x ∈ argminx∈ω f(x) and the proof is complete. so let us assume that {x k } has no bounded subsequences. refining the sequence if necessary, we can assume that, for some x̂ ∈ r n with ˆ 1,x  lim k k x    and ˆlim k k x x k x   . we claim that x̂ ∈ 0 + cl(conv(ω)). take x ∈ cl(conv(ω)) and t ≥ 0. we have ˆ lim (1 ) k k k k t t x tx x x x x      . since {x k }⊂ ω, we have that xtx ˆ is the limit of convex combinations of elements of cl(conv(ω)). hence, xtx ˆ ∈ cl(conv(ω)) and our claim is true. let us now see that x̂ ∈ γf(0). indeed,   1 1 ˆ( ) lim (1 ) 0 k 1 1 lim (1 ) (0) k (0) , k f x f x k k x x k f x f k k x x f                   using the continuity of f in the first equality, its convexity in the inequality, and the facts that f(x k ) → ν ∈ r and 1 0 k x  in the last equality. thus, x̂ ∈ γf(0) and, therefore, x̂ ∈ cl(conv(ω)) ∩ γf(0) = {0}, in contradiction with the fact that ˆ 1.x  so we conclude that argminx∈ω f (x) ≠ ø. □ 3. final remarks clearly, the novelty of theorem 2.1 lies in hypothesis (ii), and thus it is worthwhile to discuss it further. we observe first that it implies that ω ∩ γf(0) is bounded. indeed, since this set is contained in u = [cl(conv(ω))] ∩ γf(0) , it suffices to establish the boundedness of u. since u is convex by the convexity of f , if it were unbounded, then l.m. graña drummond and a.n. iusem 08 a well known property of the recession cone (see rockafellar, 1970) entails that there exists a nonzero u ∈ o + (u) ⊂ o + (cl(conv(ω)) ∩ o + (γf(0)) , using another well known property of the recession cone in the inclusion. since 0 belongs to γf(0), it follows that u = 0+u belongs to γf(0), and hence to o + (cl(conv(ω)) ∩ γf(0), contradicting (ii), and thus establishing the boundedness of ω ∩ γf(0). now, since ω ∩ γf(0) is clearly closed, if it were not only bounded but also nonempty, it would be compact, in which case, by bolzano-weierstrass result, f would attain its minimum on ω ∩ γf(0), but a minimizer of f on this set obviously also minimizes f on ω, establishing the result of theorem 2.1 in a direct way. in other words, under (ii), the result of theorem 2.1 is rather immediate when γf(0) intersects the feasible set ω. the point here is that we do not assume that γf(0) intersects ω. in cases where ω ∩ γf(0) is empty, the above mentioned boundedness conclusion becomes void, and in principle it says nothing about the existence of solutions of the optimization problem. for instance, taking n = 1, f(x) = max{0, x + 1} and ω = [1, +∞), we have γf(0) = (−∞, 0], so that ω ∩ γf(0) = ø , but on the other hand, o + (cl(conv(ω)) = [0, +∞) and (ii) holds, as well as the conclusion of theorem 2.1. secondly, we mention that theorem 2.1 has a certain resemblance to the following result, which appears as theorem 1 in graña drummond et al. (2008): theorem 3.1 take f : r n → r m , ø ≠ ω ⊂ r n . fix w ∈ r m , w ≠ 0, and define hw = {y ∈ r m │<w, y> = 0}. assume that i) f is bounded from below in ω (i.e., there exists z ∈ r m such that zi ≤ f(x)i for all x ∈ ω and all i ∈{1, ... , m}), ii) 0 + cl(conv(ω)) ∩ hw = {0} , iii) f(ω) is closed . then argminx∈ω < w, f(x) > ≠ ø . in fact, the prooflines of both theorems 2.1 and 3.1 are rather similar, but it is important to point out that despite this resemblance (resulting basically from the similarity of assumption (ii) in both theorems), there is an essential difference, which makes them quite independent of each other. indeed, in theorem 2.1 the set which is equal to {0} according to assumption (ii) is a subset of the domain of f, namely r n , while in assumption (ii) of theorem 3.1 such a set is a subset of the codomain of f, namely r m . this is made clear also in the closedness assumptions of both theorems: in theorem 2.1 we assume that ω is closed, while in theorem 3.1, f(ω) is assumed to be closed. we mention that if we look at theorem 3.1 in the scalar case, namely m = 1, it becomes trivial. taking, without loss of generality, w = 1, we get hw = {0}, so that (ii) holds automatically, and the remaining assumptions just indicate that f(ω) ⊂ r is closed and bounded below, so that it has a minimum, and hence f has a minimizer in ω. on the other hand, in the case of theorem 2.1 (for which we have always m = 1), assumption (ii) is not automatically satisfied, and we need indeed an additional property of f, namely its convexity, in order to establish that it attains its minimum on ω (note that theorem 3.1 does not require any convexity properties of f, and in fact not even its continuity; closedness of its image, in conjunction with assumption (ii), does the job). finally, we mention the following related existence result, which appears as theorem 4.3 in (iusem and sosa, 2003): theorem 3.2 let ω ⊂ r be closed and convex, and f : r n → r ∪ {+∞} a proper, convex and lower semicontinuous function. if the following auxiliary problem (ap) : find x ∈ r n such that ||x|| = 1 and f (x + y) ≤ f (y) for all y ∈ ω, does not have solutions, then argminx∈ω f(x) ≠ ø . we remark that the result of theorem 3.2 might be rephrased also in terms of a recession cone, making it look more like theorems 2.1 and 3.1, but it has an essential difference with regard to them: its validity is a new criterion for optimality 08 restricted to the case of convex optimization, meaning that both the objective f and the feasible set ω must be convex, while theorem 2.1 demands only closedness, but not convexity of ω. 4. acknowledgment the work of the second author (a.n. iusem) was partially supported by cnpq grant no. 301280/86. 5. references graña drummond, l.m., maculan, n. and svaiter, b.f. 2008. on the choice of parameters for the weighting method in vector optimization. mathematical programming, 111: 201-216. iusem, a.n. and sosa, w. 2003. new existence results for equilibrium problems. nonlinear analysis, 52: 621-635. rockafellar, r.t. 1970. convex analysis. princeton university press, new jersey. received 11 may 2011 accepted 19 august 2011 squ journal for science, 2021, 26(1), 22-30 doi:10.24200/squjs.vol26iss1pp22-30 sultan qaboos university 22 travelling wave solutions for fisher’s equation using the extended homogeneous balance method mohammad m. fares 1 , usama m. abdelsalam 1,2 * and faiza m. allehiany 3 1 department of mathematics, university of technology and applied sciences al rustaq, oman; 2 department of mathematics, faculty of science, fayoum university, egypt; 3 department of mathematics, faculty of applied sciences, umm al-qura university, mecca, saudi arabia. *email: usamaahmad.rus@cas.edu.om. abstract: in this work, the extended homogeneous balance method is used to derive exact solutions of nonlinear evolution equations. with the aid of symbolic computation, many new exact travelling wave solutions have been obtained for fisher’s equation and burgers-fisher equation. fisher’s equation has been widely used in studying the population for various systems, especially in biology, while burgers-fisher equation has many physical applications such as in gas dynamics and fluid mechanics. the method used can be applied to obtain multiple travelling wave solutions for nonlinear partial differential equations. keywords: traveling wave solutions; partial differential equations; extended homogeneous balance method and fisher’s equation. وسعةلمعادلة فيشر باستخدام طريقة التوازن المتجانس الم الحلول الموجية محمد فارس، أسامة محمد عبدالسالم و فايزة محمد اللحياني محمد . بمساعدةالتفاضلية الجزئيةلمعادالت ا )التحليلية( لبعض ي هذا العمل ، تم استخدام طريقة التوازن المتجانس الموسعة الشتقاق الحلول الدقيقةف :صلخمال الدقيقة الجديدة لمعادلة فيشر ومعادلة برجر فيشر. تم استخدام معادلة فيشر على نطاق الموجية حلول ال، تم الحصول على العديد من بعض البرامج الحسابية أن معادلة برجر فيشر لها العديد من التطبيقات الفيزيائية مثل ديناميكيات الغاز كمافي علم األحياء ، كذلكواسع في دراسة السكان ألنظمة مختلفة ، و للمعادالت التفاضلية الجزئية غير الخطية الموجيةحلول التطبيق الطريقة المستخدمة للحصول على العديد من وميكانيكا الموائع. يمكن ، معادلة فيشر. طريقة التوازن المتجانس الموسعةالحلول الموجية ، المعادالت التفاضلية الجزئية ، :مفتاحيةالكلمات ال travelling wave solutions for fisher’s equation 23 1. introduction he exact travelling wave solutions of nonlinear evolution equations play an important role in the study of nonlinear physical phenomena, for example, the wave phenomena observed in fluid mechanics, plasma physics, optical fibers, solid state physics, chemical kinematics, chemical physics and geochemistry. explicit solutions to the mathematical modelling of physical problems are of fundamental importance. many methods have been developed for finding the exact solutions of nonlinear evolution equations, such as the inverse scattering method [1, 2], bilinear transformation [1, 3, 4], the tanh-function method [5, 6], extended tanh method [7-10], sine-cosine method [11, 12], fexpansion method [13], general expansion method [14, 15], and (𝐺′/𝐺) method [16-18]. the homogeneous balance (hb) method, which is a direct and effective algebraic method for the computation of exact traveling wave solutions, was first proposed by wang [19, 20]. later [21,22], the hb method was extended to search for other kinds of exact solutions. fan [23] used the hb method to search for backlund transformation and similarity reduction of nonlinear pdes. he also showed that there is a close connection among the hb method, weiss, tabor, carnevale (wtc) method and clarkson, kruskal (ck) method. the extended homogeneous balance method is used to solve many nonlinear evolution equations [24-28]. the fisher’s equation [29,30] is a nonlinear partial differential equation of second order. 𝑢𝑡 = 𝑢𝑥𝑥 + 𝑢(1 − 𝑢). fisher proposed this equation as a model for the propagation of a mutant gene with 𝑢(𝑥, 𝑡) denoting the density of advantages. this equation is encountered in chemical kinetics, population dynamics, flame propagation, autocatalytic chemical reactions and branching brownian motion processes. the aim of this work is to propose an extension of the homogeneous balance method to construct more other kinds of exact solutions to nonlinear pdes. in order to illustrate the effectiveness and convenience of the method, the method is applied to fisher’s equation and burgers-fisher equation. in the following section, let us simply describe the extended homogeneous balance method. 2. proposed analytical method in general, consider a given pde, say in two variables 𝐻(𝑢, 𝑢𝑡 , 𝑢𝑥 , 𝑢𝑥𝑥 , . . . . ) = 0. (1) we seek for the special solution of eq. (1), the travelling wave solution, in the form 𝑢(𝑥, 𝑡) = 𝑢(𝜁), 𝜁 = 𝑥 − 𝜆 𝑡, (2) where 𝜗 and 𝐿 are constants to be determined later. using the transformation (2), eq. (1) reduces to a nonlinear ordinary differential equation (ode). the next crucial step is that the solution we are looking for is expressed in the form 𝑢(𝜁) = ∑ 𝑛 𝑖=0 𝑎𝑖 𝜔 𝑖 + ∑ 𝑛 𝑖=1 𝑏𝑖 [1 + 𝜔] −𝑖 , (3) and 𝜔 ′ = 𝑘 + 𝑀𝜔 + 𝑃𝜔2, (4) where 𝑎𝑖 and 𝑏𝑖 are constants, while 𝑘, 𝑀 and 𝑃 are parameters to be determined later, 𝜔 = 𝜔(𝜁), and 𝜔 ′ = 𝑑𝜔/𝑑𝜁. the mechanism for solitary wave solutions to occur is the fact that different effects (such as, the dispersion and nonlinearity) that act to change the wave forms in many nonlinear physical equations have to balance each other. therefore, one may use the above fact to determine the parameter 𝑛, which must be a positive integer, and can be found by balancing the highest-order linear term with the nonlinear terms [26]. substituting (3) and (4) in the relevant ode will yield a system of odes with respect to 𝑎0, 𝑎𝑖 , 𝑏𝑖 , 𝑘, 𝑀, 𝑃 and 𝜆 (where 𝑖 = 1, . . . , 𝑚), because all the coefficients of 𝜔 𝑗 (where 𝑗 = 0,1, . ..) have to vanish. with the aid of mathematica, one can determine 𝑎0, 𝑎𝑖 , 𝑏𝑖 , 𝑘, 𝑀, 𝑃 and 𝜆. it is to be noted that the riccati equation (4) can be solved using the homogeneous balance method as follows: case i: when p = 1, m = 0, the riccati eq. (4) has the following solutions 𝜔 = {[𝑐]𝑙𝑙 − √−𝑘 tanh[√−𝑘𝜁], 𝑤𝑖𝑡ℎ𝑘 < 0, −√−𝑘 coth[√−𝑘𝜁], 𝑤𝑖𝑡ℎ < 0, (5) 𝜔 = − 1 𝜁 , with 𝑘 = 0, (6) t mohammad m. fares et al. 24 and 𝜔 = {[𝑐]𝑙𝑙√𝑘 tan[√𝑘𝜁], 𝑤𝑖𝑡ℎ 𝑘 > 0, −√𝑘 cot[√𝑘𝜁], 𝑤𝑖𝑡ℎ 𝑘 > 0. (7) since cothand cot-type solutions appear in pairs with tanhand tan-type solutions, respectively, they are omitted in this paper. case ii:, let 𝜔 = ∑ 𝑚𝑖=0 𝐴𝑖 tanh 𝑖 (𝑝1𝜁). balancing 𝜔 ′ with 𝜔2 leads to 𝜔 = 𝐴0 + 𝐴1tanh(𝑝1𝜁). (8) substituting equation (8) into (4), we have the following solution of eq. (4) 𝜔 = − 𝑝1 2𝑃 tanh( 𝑝1 2 𝜁) − 𝑀 2𝑃 , with 𝑃𝑘 = 𝑀2−𝑝1 2 4 . (9) similarly, let 𝜔 = ∑ 𝑚𝑖=0 𝐴𝑖 coth 𝑖 (𝑝1𝜁), then we obtain the following solution: 𝜔 = − 𝑝1 2𝑃 coth( 𝑝1 2 𝜁) − 𝑀 2𝑃 with 𝑃𝑘 = 𝑀2−𝑝1 2 4 . case iii:, we suppose that the riccati eq. (4) has the following solutions of the form 𝜔 = 𝐴0 + ∑ 𝑚 𝑖=0 (𝐴𝑖 𝑓 𝑖 + 𝐵𝑖 𝑓 𝑖−1𝑔), (10) with 𝑓 = 1 cosh𝜁+𝑟 , 𝑔 = sinh𝜁 cosh𝜁+𝑟 , (11) substituting equations (10) and (11) into (4), we have the following solution of eq. (4) 𝜔 = − 1 2𝑃 (𝑀 + sinh(𝜁)+√𝑟2−1 cosh(𝜁)+𝑟 ) , with 𝑃𝑘 = 𝑀2−1 4 (12) where 𝑟 is an arbitrary constant. it should be noticed that solution (12), as 𝑟 = 1, degenerates to 𝜔 = − 1 2𝑃 [𝑀 + tanh ( 𝜁 2 )] (13) case iv:, we suppose that the riccati eq. (4) has the following solutions of the form 𝜔 = 𝐴0 + ∑ 𝑚 𝑖=0 sinh 𝑖−1(𝐴𝑖sinh𝜂 + 𝐵𝑖 cosh𝜂), (14) where 𝑑𝜂/𝑑𝜁 = sinh𝜂 or 𝑑𝜂/𝑑𝜁 = cosh𝜂 balancing 𝜔′ with 𝜔2 leads to 𝑚 = 1 𝜔 = 𝐴0 + 𝐴1sinh𝜂 + 𝐵1 cosh𝜂. (15) when 𝑑𝜂/𝑑𝜁 = sinh𝜂, we substitute (15) and 𝑑𝜂/𝑑𝜁 = sinh𝜂 into (4) and set the coefficient of sinh𝑖 𝜂cosh𝑗 𝜂, 𝑖 = 0,1,2, 𝑗 = 0,1 to zero and solve the obtained set of algebraic equations to get 𝐴0 = −𝑀 2𝑃 , 𝐴1 = 0, 𝐵1 = 1 𝑃 , (16) where 𝑘 = 𝑀2−4 4𝑃 , while 𝐴0 = −𝑀 2𝑃 , 𝐴1 = ±√ 1 2𝑃 , 𝐵1 = 1 𝑃 , (17) where 𝑘 = 𝑀2−1 4𝑃 . to 𝑑𝜂/𝑑𝜁 = sinh𝜂 we have sinh𝜂 = −𝑐𝑠𝑒𝑠ℎ𝜁, cosh𝜂 = −coth𝜁. (18) from (16)-(18) we obtain 𝜔 = − 𝑀+2coth𝜁 2𝑃 . (19) travelling wave solutions for fisher’s equation 25 where 𝑘 = 𝑀2−4 4𝑃 , and 𝜔 = − 𝑀±𝑐𝑠𝑒𝑠ℎ𝜁 +coth𝜁 2𝑃 . (20) where 𝑘 = 𝑀2−1 4𝑃 3. applications of the proposed method in this section, we will illustrate the above approach for a class of nonlinear evolution equations namely, fisher’s equation. 3.1 example 1. fisher’s equation we apply the extended homogeneous balance method to construct the traveling wave solutions for fisher’s equation [24,25]. the fisher’s equation is a nonlinear partial differential equation of second order, of the form 𝑢𝑡 = 𝑢𝑥𝑥 + 𝑢(1 − 𝑢). (21) applying the transformation 𝑢(𝑥, 𝑡) = 𝑈(𝜁), 𝜁 = 𝑥 − 𝜆𝑡 to eq. (21) we find 𝑉 satisfies the following ordinary differential equation −𝑈 + 𝑈2 − 𝜆𝑈′ − 𝑈′′ = 0. (22) balancing 𝑈′′ with 𝑈2 yields |𝑚| = 2.therefore, we are looking for the solution in the form 𝑈 = 𝑎0 + 𝑏0 + 𝑎1𝜔 + 𝑏1(1 + 𝜔) −1 + 𝑎2𝜔 2 + 𝑏2(1 + 𝜔) −2, (23) substituting eqs. (23) and (4) in eq. (22), we get a polynomial equation 𝜔. hence, equating the coefficient of 𝜔 𝑗 (i.e., 𝑗 = 0,1,2, . ..) to zero and solving the obtained system of overdetermined algebraic equation using symbolic manipulation package mathematica, results in: the first set: 𝑎1 = 0, 𝑃 ≠ 0, 𝑎0 = 1 2 (−12𝑃2 + 12𝑘𝑃 + 1), 𝑏1 = 1 2 √3√−384𝑃4 + 576𝑘𝑃3 − 192𝑘3𝑃 + 1, 𝑎2 = 0, 𝑏2 = 6(𝑘 2 − 2𝑃𝑘 + 𝑃2), 𝜆 = −480(𝑘𝑃2𝑏1 − 𝑃 3𝑏1). (24) the second set: 𝑏2 = 0, 𝑃 ≠ 0, 𝑘 = 𝑀2−1 4𝑃 , 𝑎0 = 1 2 (𝑀2 + 8𝑘𝑃 + 1), 𝑏1 = 0, 𝑎2 = 6𝑃 2 , 𝑀 ≠ 0, = −36𝑃𝑀6 + 432𝑘𝑃2𝑀4 − 1728𝑘2𝑃3𝑀2 + 211𝑃𝑀2 + 2304𝑘3𝑃4 − 424𝑘𝑃2 − 35𝑃 + 70𝑃𝑎0 35𝑀 , 𝜆 = 6 7 (36𝑀9 − 432𝑘𝑃𝑀7 + 1728𝑘2𝑃2𝑀5 − 73𝑀5 − 2304𝑘3𝑃3𝑀3 + 160𝑘𝑃𝑀3 + 70𝑎0𝑀 3 − 35𝑀3 −1152𝑘2𝑃2𝑀 + 280𝑘𝑃𝑀 − 560𝑘𝑃𝑎0𝑀 + 2𝑀 + 560𝑘 2𝑃𝑎1). (25) for the first set (24), if 𝑀 = 0, 𝑃 = 1 we get the solutions satisfying case i for 𝑘 > 0. therefore, the solutions of fisher’s equation of the type (21), will be 𝑢1(𝑥, 𝑡) = 𝑎0 + 𝑏2+𝑏1(√𝑘tan(√𝑘𝜁)+1) (√𝑘tan(√𝑘𝜁)+1) 2 , (26) 𝑢2(𝑥, 𝑡) = 𝑎0 + (√𝑘cot(√𝑘𝜁)+1)𝑏1+𝑏2 (√𝑘cot(√𝑘𝜁)+1) 2 . (27) for 𝑘 < 0, 𝑢3(𝑥, 𝑡) = 𝑎0 + 𝑏2 +𝑏1(1−√−𝑘tanh(√−𝑘𝜁)) (√−𝑘tanh(√−𝑘𝜁)−1) 2 , (28) mohammad m. fares et al. 26 𝑢4(𝑥, 𝑡) = 𝑎0 + (1−√𝑘coth(√𝑘𝜁))𝑏1+𝑏2 (√𝑘coth(√𝑘𝜁)−1) 2 , (29) now for the solutions satisfying cases ii & iii & iv, we have the compatibility condition, 𝑃𝑘 = 𝑀2−𝑝1 2 4 . (30) therefore, substitute for 𝑃 and 𝑘, from eq. (24) into eq. (30) and solve for 𝑝1. it is found that 𝑝1 = − √1−2𝑎0 √3 or √1−2𝑎0 √3 . (31) hence, for case ii, we get the following solutions: 𝑢5(𝑥, 𝑡) = 𝑎0 + 2𝑃(2𝑃𝑏2+𝑏1(2𝑃−𝑝1(𝑀+2tanh(𝜁𝑝1)))) (𝑝1(𝑀+2tanh(𝜁𝑝1))−2𝑃) 2 , (32) figure 1. 3d and contour plots of the solution (32) with 𝑎0 = −2 𝑃 = 5 and 𝑘 = 5. and 𝑢6(𝑥, 𝑡) = 𝑎0 + 2𝑃(2𝑃(𝑏1+𝑏2)−(𝑀+2coth(𝜁𝑝1))𝑏1𝑝1) ((𝑀+2coth(𝜁𝑝1))𝑝1−2𝑃) 2 , (33) in the same manner case iii, results in the solution 𝑢7(𝑥, 𝑡) = 𝑎0 + 4𝑃2𝑏2(𝑟+cosh(𝜁)) 2 (𝑀𝑟−2𝑃𝑟+(𝑀−2𝑃)cosh(𝜁)+sinh(𝜁)+√𝑟2−1) 2 − 2𝑃𝑏1(𝑟+cosh(𝜁)) 𝑀𝑟−2𝑃𝑟+(𝑀−2𝑃)cosh(𝜁)+sinh(𝜁)+√𝑟2−1 , (34) with the condition that 𝑝1 = 1. travelling wave solutions for fisher’s equation 27 figure 2. 3d and density plots of the solution (35) with 𝑎0 = −2, 𝑃 = 5 and 𝑘 = 5. for case iv, the solution form is 𝑢8(𝑥, 𝑡) = 𝑎0 + 2𝑃((𝑀+2𝑃+coth(𝜁)+csch(𝜁))𝑏1+2𝑃𝑏2) (𝑀+2𝑃+coth(𝜁)+csch(𝜁))2 , (35) with the condition that 𝑝1 = 1, 𝑢9(𝑥, 𝑡) = 𝑎0 + 2𝑃((−𝑀+2𝑃−2coth(𝜁))𝑏1+2𝑃𝑏2) (𝑀−2𝑃+2coth(𝜁))2 , (36) with the condition that 𝑝1 = 2. for the second set we are left only with solutions satisfying cases ii & iii & iv. since, the main criteria for these cases to be applicable is the compatibility condition, 𝑃𝑘 = 𝑀2−𝑝1 2 4 . (37) from (25), it is found that 𝑝1 = 1. (38) therefore, solutions to equation of the type (21), will be 𝑢10(𝑥, 𝑡) = 𝑎0 + 3 2 𝑝1 2(𝑀 + 2tanh(𝜁𝑝1)) 2 − 𝑎1𝑝1(𝑀+2tanh(𝜁𝑝1)) 2𝑃 , (39) and 𝑢11(𝑥, 𝑡) = 𝑎0 + 3 2 (𝑀 + 2coth(𝜁𝑝1 )) 2 𝑝1 2 − (𝑀+2coth(𝜁𝑝1))𝑎1𝑝1 2𝑃 , (40) in the same manner case iii, results in the solution 𝑢12(𝑥, 𝑡) = 𝑎0 + 3 2 (𝑀 + sinh(𝜁)+√𝑟2−1 𝑟+cosh(𝜁) ) 2 − 𝑎1(𝑀+ sinh(𝜁)+√𝑟2−1 𝑟+cosh(𝜁) ) 2𝑃 , (41) where 𝑝1 = 1, for case iv, the solution form is 𝑢13(𝑥, 𝑡) = 3 2 (𝑀 + coth(𝜁) + csch(𝜁))2 + 𝑎1(𝑀+coth(𝜁)+csch(𝜁)) 2𝑃 + 𝑎0, (42) with 𝑝1 = 1. 3.2 example 2. burgers-fisher equation consider burgers-fisher equation [24,25]. 𝑢𝑡 = 𝑢𝑥𝑥 + 𝑢𝑢𝑥 + 𝑢(1 − 𝑢). (43) apply the transformation 𝑢(𝑥, 𝑡) = 𝑈(𝜁), 𝜁 = 𝑥 − 𝜆𝑡 to eq. (43) then it is reduced to the following ordinary differential equation: mohammad m. fares et al. 28 −𝑈 + 𝑈2 − 𝜆𝑈′ + 𝑈𝑈′ − 𝑈′′ = 0. (44) balancing 𝑈′′ with 𝑈𝑈′ yields m=1. therefore, we are looking for the solution in the form 𝑈 = 𝑎0 + 𝑏0 + 𝑎1𝜔 + 𝑏1(1 + 𝜔) −1, (45) substituting eqs. (45) and (4) in eq. (44), we get a polynomial equation 𝜔. hence, equating the coefficient of 𝜔 𝑗 (i.e., 𝑗 = 0,1,2, . ..) to zero and solving the obtained system of overdetermined algebraic equations using the symbolic manipulation package mathematica, results in : 𝑀 = 2𝑃 + 1, 𝑘 = 𝑃 + 1, 𝑎1 = 0, 𝑃 ≠ 0, 𝑏1 = 𝑎0 𝑃 , 𝑏1 ≠ 0, 𝜆 = −𝑎0 + 𝑃𝑏1 + 2. (46) for the first set, as in the previous example , we apply the compatibility condition, in using the solutions satisfying cases ii & iii & iv. 𝑃𝑘 = 𝑀2−𝑝1 2 4 . (47) therefore, substitute for 𝑃 and 𝑘, from eq. (46), into eq. (47) and solve for 𝑝1. it is found that 𝑝1 = 1 or 𝑝1 = −1. (48) therefore, the solution to the equation of the type (43), will be 𝑢1(𝑥, 𝑡) = 𝑎0 (1 − 1 1+2tanh(𝑥−𝜆𝑡) ), (49) and 𝑢2(𝑥, 𝑡) = 𝑎0 (1 − 1 1+2coth(𝑥−𝜆𝑡) ), (50) figure 3. 3d and contour plots of the solution (51) with 𝑎0 = 0.03 𝑃 = 1 and 𝑟 = in the same manner, case iii results in the solution 𝑢3(𝑥, 𝑡) = (−𝑟−cosh(𝜁)+sinh(𝜁)+√𝑟2−1)𝑎0 𝑟+cosh(𝜁)+sinh(𝜁)+√𝑟2−1 , (51) with the condition that 𝑝1 = 1. for case iv, the solution form is 𝑢4(𝑥, 𝑡) = (4𝑃+coth(𝜁)+csch(𝜁)+3)𝑎0 4𝑃+coth(𝜁)+csch(𝜁)+1 , (52) with 𝑝1 = 1, 4. conclusion in summary, an extended homogeneous balance method with computerized symbolic computation is developed to deal with nonlinear partial differential equations (pdes). traveling wave solutions were formally derived for fisher’s equation and burgers-fisher equation. this method can be also applied to other nonlinear evolution equations. travelling wave solutions for fisher’s equation 29 conflict of interest the authors declare no conflict of interest. acknowledgment the 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"analytical wave solutions for foam and kdv-burgers equations using extended homogeneous balance method", mathematics 2019, 7(8), 729. 29. wazwaz, a. the tanh method for generalized forms of nonlinear heat conduction and burgers-fisher equations, applied mathematics and computation 2005, 169, 321-338. 30. wazwaz, a. analytic study on burgers, fisher, huxley equations and combined forms of these equations, applied mathematics and computation 2008, 195, 754-761. received 4 april 2020 accepted 24 november 2020 a new sparse quasi-newton update squ journal for science, 17 (1) (2012) 30-43 © 2012 sultan qaboos university 30 a new sparse quasi-newton update method minghou cheng*, yu-hong dai** and rui diao* institute of computational mathematics and scientific/engineering computing, academy of mathematics and systems science, chinese academy of sciences, beijing, china, *email: chengmh@lsec.cc.ac.cn; diaorui@lsec.cc.ac.cn. **email: dyh@lsec.cc.ac.cn. abstract: based on the idea of maximum determinant positive definite matrix completion, yamashita proposed a sparse quasi-newton update, called mcqn, for unconstrained optimization problems with sparse hessian structures. such an mcqn update keeps the sparsity structure of the hessian while relaxing the secant condition. in this paper, we propose an alternative to the mcqn update, in which the quasi-newton matrix satisfies the secant condition, but does not have the same sparsity structure as the hessian in general. our numerical results demonstrate the usefulness of the new mcqn update with the bfgs formula for a collection of test problems. a local and superlinear convergence analysis is also provided for the new mcqn update with the dfp formula. keywords: large-scale, matrix completion, quasi-newton methods, secant condition, sparsity, unconstrained optimization. المتناثرة نيوتنمتماثلة تحسين جديد لطريقة يوهونج داي و روي دياومنغو تشينج و نيوتن متماثلةلى فكرة إكمال المحدد األقصى لمصفوفة موجبة محددة، اقترح ياماشيتا تحسيناً لطريقة إباالستناد ص: خمل مسائل األمثليات غير المقيدة مع أصفار متناثرة في مصفوفة هس. يحافظ هذا وذلك لحل mcqnتناثرة وسماها الم mcqn التناثر في مصفوفة هس مع تخفيف شرط القاطع. نقترح في هذا البحث بديال عن تحسينالتحسين على هيكلية هيكلية التناثر لمصفوفة هس بشكل عام. تبين نفس لك تمحققة لشرط القاطع، ولكنها التم نيوتن متماثلةبحيث تكون مصفوفة . كذلك تم تجريبيةمجموعة من المسائل ال لحل bfgsقانونالجديد مع mcqn استخدام تحسينفائدة نتائجنا العددية .dfp قانونالجديد مع mcqn قانون الخطي الفائق لتحسينالموضعي وتحليل التقارب 1. introduction onsider the unconstrained optimization problem ( ) ,min n x r f x  (1) where : n f r r is continuously differentiable and its gradient ( )f x is available. if the dimension n is not c a new sparse quasi-newton update method 31 large, the quasi-newton method is one choice for solving problem (1) because of its superlinear convergence and the unnecessity to calculate the function hessian. assuming that kx is the current iterate and kh is the approximation to the inverse hessian, the quasi-newton method generates the next iterate by 1 = ( ) ,k k k k kx x h f x   (2) where > 0k is a stepsize obtained via some line search, and updates the approximation kh to 1kh  to meet the secant condition 1 = ,k k kh y s (3) where 1=k k ks x x  and 1= ( ) ( ).k k ky f x f x  if the dimension of the problem (1) is large, the direct use of the quasi-newton method is not possible due to the storage of an n n matrix. in order to overcome this difficulty, several methods have been proposed. the limited-memory bfgs (l-bfgs) method (liu and nocedal, 1989; nocedal, 1980) is only to store a few curvature pairs ( , )i is y in the construction of the hessian approximation. since there is no need to know any information about the hessian, the l-bfgs method is friendly to users and has been widely used in practice. for many large-scale problems, the function f can be written in the form =1 ( ) = ( ) , ne i i f x f x where each of the en element functions if depends only on a few variables. in this case, the partitioned quasinewton method, developed by griewank and toint (see griewank and toint, 1982a, 1982b; griewank and toint, 1984; and the references therein), performs very well in practice, and is now regarded as one of the important practical optimization algorithms. their basic idea is to update a hessian approximation i kb for each element function if and then to assemble these matrices to obtain an approximation kb to the whole hessian of f. further, they determine the search direction by solving the linear system =1 ( ) = ( ) . n ie k k ki b d f x their method was implemented with the trust region strategy since the matrix kb is not positive definite in general. there are also many large-scale problems where the function hessian 2 ( )f x is sparse and the sparsity structure is available. suppose that for all , n x r 2 ,[ ( )] = 0, ( , ) ,i jf x i j f  (4) where f is some subset of i i and = {1, 2, , }.i n in this case, it is possible to establish faster optimization methods by exploiting the sparsity structure of the hessian. toint (1977) and fletcher (1995) studied such updates and required 1kh  to meet the sparsity requirement, namely, 1 1 , 1 ,( ) = ( ) = 0k i j k i jh b    when ( , ) ,i j f and the secant equation (3) simultaneously. as a result, their methods involve the solution of a linear system or a convex program at each iteration. if some component of ks is zero, the obtained approximate hessian may be ill-posed (see sorensen's example (sorensen, 1982)). inspired by the successful use of positive definite matrix completion in (fukuda et al., 2000) for semidefinite programming, yamashita (2008) proposed a novel type of quasi-newton update for problem (1) satisfying the sparse hessian structure. let : n n r r   be a strictly convex function defined by ( ) =tr( ) ln det( )a a a  (5) (this function is introduced in (byrd and nocedal, 1989) as a powerful tool for the convergence analysis of minghou cheng, yu-hong dai and rui diao 32 quasi-newton methods). yamashita determines the new approximation matrix 1kh  from kh by two steps: (i) update kh to qn h by certain ordinary quasi-newton formula; (ii) obtain 1kh  by solving the following subproblem with h, 1/ 2 1/ 2 , , 1 , min ( ) s.t. = , ( , ) ( ) = 0 , ( , ) . k k qn i j i j i j h hh h h i j f h i j f h s         (6) here s  denotes the set of symmetric positive semidefinite matrices. notice that since step (ii) uses , , qn i j h ( , ) ,i j f we only have to update | |f elements of kh in step (i), where | |f means the cardinality of f. as in (yamashita, 2008), we call the above update mcqn (matrix completion quasi-newton). the use of dfp and bfgs methods in step (i) are considered in (yamashita, 2008). further, yamashita showed that, if the sparsity pattern of the hessian is such that there is not any fill-in in its cholesky factorization, or equivalently, the graph induced by the hessian is chordal (see (yamashita, 2008) for details), problem (6) is equivalent to finding a maximum-determinant positive definite matrix completion of , , qn i j h ( , )i j f : , , max det( ) s.t. = , ( , ) . qn i j i j h h h i j f h s    (7) the above problem can be easily solved by analyzing the clique tree of the graph induced by the hessian (see (yamashita, 2008) for details). in addition, it is shown in (yamashita, 2008) that the update does not suffer from the drawback in sorensen's example (sorensen, 1982). therefore by relaxing the secant equation, the mcqn update is easy to implement and is well-posed. the numerical experiments in (yamashita, 2008) show that, the mcqn update with bfgs obviously performs better than the mcqn update with dfp. as seen from the above procedure, the mcqn update by yamashita keeps the sparsity structure of the hessian, but does not satisfy the quasi-newton condition. nevertheless, local and superlinear convergence results are only established for an mcqn update with dfp. dai and yamashita (2007) extended the results to the mcqn update with broyden's family. in this paper, we propose an alternative of the mcqn update, in which the quasi-newton matrix satisfies the secant condition, but does not have the same sparsity structure as the hessian in general (see the next section). a local and superlinear convergence analysis is also provided for the new mcqn update with dfp (see section 3). our numerical results for a collection of test problems demonstrate that the new mcqn update with bfgs clearly outperforms the previous mcqn update with bfgs (see section 4). conclusions and discussions are presented in the last section. 2. the new mcqn method looking back to the mcqn update by yamashita (2008), the whole sequence of quasi-newton matrices, which were used for the calculations of search directions, keep the same sparsity structure as the function hessian. the intermediate matrix qn h satisfies the secant condition, but does not necessarily have the same sparsity structure as the function hessian. as an alternative of such an mcqn update, we may think of the possible use of those intermediate matrices in the calculations of search directions. in this paper, we explore this a new sparse quasi-newton update method 33 possibility and our numerical results in section 4 demonstrate the usefulness of such an idea. to describe the new mcqn update, we assume that the current quasi-newton matrix is ,kh which is symmetric and positive definite. since kh does not have the sparsity structure of the function hessian in general, we consider the optimal solution of the following subproblem as an intermediate matrix , s kh 1/ 2 1/ 2 , , 1 , min ( ) s.t. = ( ) , ( , ) ( ) = 0 , ( , ) , k k i j k i j i j h hh h h i j f h i j f h s         (8) where, again s  denotes the set of symmetric positive semidefinite matrices and f is some subset of i i such that (4) holds. if the graph induced by the hessian is chordal (otherwise, we extend the set f such that the induced graph has such property), we know that s kh possesses the sparse structure and has the following form of sparse clique factorization 1 2 1 2 1= , t t t l l lh p p p qp p p p (9) where , = 1, 2, ,ip i l and q are some sparse matrices (see (yamashita, 2008)). having obtained the intermediate matrix , s kh we can use for example the bfgs formula to generate a new quasi-newton matrix 1 = 1 , s t t s t s t s k k k k k k k k k k k k k t t t k k k k k k h y s s y h y h y s s h h s y s y s y            (10) which satisfies the secant condition 1 =k k kh y s and will be used for the calculation of search directions. in other words, we alter the two steps in the original mcqn method and determine the new approximation matrix 1kh  in the following way: (i) obtain s kh by solving problem (7); (ii) update s kh to 1kh  by certain quasi-newton formula. it is not difficult to see that the amount of computation of such a strategy is almost the same as that required by the original mcqn. however, since the new approximation matrix 1kh  satisfies exactly the secant condition, we think that the new quasi-newton matrix 1kh  contains more information about the function hessian. the numerical results confirm our idea. a description of the new sparse quasi-newton method is given as follows. algorithm 2.1 (nmcqn) step 1. obtain an extension of f (still denoted by f) such that ( , )g v f is chordal. choose 0 n x r and a positive definite matrix 0h with 1 0( ) = 0, ( , ) .ijh i j f    set := 0.k step 2. if kx satisfies the termination criterion, then stop. step 3. 1 = ( ).k k k kx x h f x   step 4. obtain the sparse clique-factorization formula (9) of . s kh step 5. obtain 1,kh  ( , )i j f by some ordinary quasi-newton update. step 6. set := 1k k  and go to step 2. minghou cheng, yu-hong dai and rui diao 34 we call the new mcqn method nmcqn. if, in step 5, the quasi-newton matrix 1kh  is obtained from s kh by (10), we denote 1 = bfgs( , , ) s k k k kh h s y and call the corresponding algorithm nmcqn-bfgs. if the dfp update formula is used, namely, 1 = , s t s t s k k k k k k k k t s t k k k k k h y y h s s h h y h y s y    (11) we denote 1 = dfp( , , ) s k k k kh h s y and call the corresponding algorithm nmcqn-dfp. 3. convergence analysis in this section, we show the local and superlinear convergence of nmcqn-dfp, namely, algorithm 2.1 with 1 = dfp( , , ). s k k k kh h s y the results are established in a manner similar to (yamashita, 2008). we give the following assumptions on the objective function, where  means the two-norm. assumption 3.1 let *x be a solution of (1) and let *= { : } n x r x x b   with a positive constant b. (i) the objective function f is twice continuously differentiable on . (ii) there exist positive constants m and m such that   12 22 ( ) , t n m z z f x z m z z r       for all .x  if the second-order sufficient optimality condition holds at the solution *x and b is sufficiently small, assumption 3.1(ii) holds. from assumption 3.1(i), 2 ( )f x is lipschitz continuous on . then, from lemmas 4.1.12 and 4.1.15 in (dennis and schnabel, 1983), there exist 1l and 2l such that for all 1, ,k kx x   22 * 1( )k k ky f x s l s  (12) and 2 * 2( ) ,k k k ky f x s l s  (13) where k is defined by  1 * *= max , .k k kx x x x    (14) moreover, there exists a positive constant 3l such that for all 1 2,z z  , 1 2 3 1 2( ) ( ) .f z f z l z z    (15) therefore, we have 1 3 1= ( ) ( ) , .k k k k k ky f x f x l s x x c      (16) from eq. (8.1.2) of (nocedal and wright, 1999) we have = ,k k ky g s (17) where kg is the average hessian defined by 1 2 0 = ( ) .k k kg f x ts dt  for convenience, the following notations are used in the analysis. 1 2 2 * * * *= ( ), = ( ) ,g f x h f x       1/2 1/2 * *= , = ,k k k ks h s y h y  a new sparse quasi-newton update method 35 1/2 1/2 1/2 1/2 * * * *= , = , s s k k k kh h h h h h h h     2 cos = , = , t s t s k k k k k k k ks k k k k y h y y h y q y h y y  2 = , = , t k k k k kt t k k k k s y s m m y s y y where k is the angle between ky and .k kh y firstly, we introduce the following two lemmas similarly to (yamashita, 2008). lemma 3.1 suppose that assumption 3.1 holds. then there exist (0, )c   and (0, )b  such that ln 2 , 1 . k k k k m c m c       whenever < .k  lemma 3.2 suppose that assumption 3.1 holds. consider algorithm 2.1 with 1 = dfp( , , ). s k k k kh h s y then we have ( ) ( ) , s k kh h  where ( ) = tr( ) ln det( ).a a a  by using the above lemmas, we show the following key inequality. lemma 3.3 suppose that assumption 3.1 holds. consider algorithm 2.1 with 1 = dfp( , , ). s k k k kh h s y let  be the constant specified in (13). if ,k  then we have 1 2 2 2 1 ( ) ln 1 ln ( ) 3 . cos cos cos k k k k k k k k q q h h c                  proof. by assumption 3.1(ii) and (17), we have = t t k k k k k t t k k k k y s y h y m y y y y  and = , t t k k k k k t t k k k k y y z h z m y s z z  where 1/2 =k k kz h y  and 1 = .k kh g  since 1kh  is obtained from s kh by the dfp formula, we have 1/ 2 1/ 2 1 * 1 * 1/ 2 1/ 2 1/ 2 1/ 2 * * * * 1/ 2 1/ 2 1/ 2 1/ 2 * * * * 1/ 2 1/ 2 1/ 2 1/ 2 1/ 2 1/ 2 * * * * * * = = = k k s t s t s k k k k k k k t s t k k k k k s t s t s k k k k k k k t s t k k k k k h h h h h y y h s s h h h h h y h y y s h h y y h h h s s h h y h h h h h y y h h s                         minghou cheng, yu-hong dai and rui diao 36 = . s t s t s k k k k k k k t s t k k k k k h y y h s s h y h y y s   (18) since 2 tr( ) = t zz z for , n z r it follows from (18) that 2 2 1tr( ) = tr( ) . s s k k k k k t s t k k k k k h y s h h y h y y s    (19) in a manner similar to the use of eqs. (8.45) in (nocedal and wright, 1999), we can show that 1det( ) = det( ) . t s k k k k t s k k k y s h h y h y  (20) moreover, simple calculations show that 2 2 = = t t kk k k k k t s t s kk k k k k kk yy s y s m qy h y y h yy (21) and 2 2 2 2 2 2 = = . ( ) cos s st s k k k k kk k k k t s t s kk k k k k kk h y h y yy h y q y h y y h yy  (22) it follows from (19), (20), (21) and (22) that 1 1 1 2 2 2 2 ( ) = tr( ) ln det( ) = tr( ) ln det( ) ln ln cos = ( ) ln 1 1 ln ln cos . cos cos k k k s sk k k k k k k s k k k k k k k k h h h q h m h m q q q h m m                      (23) lemmas 3.2 and 3.3 give ln 1 1 2 1 = 3k k k k km m c c c        and ( ) ( ) . s k kh h  then it follows from (23) that 2 1 2 2 ( ) ( ) 3 ln cos 1 ln . cos cos k k k k k k k k q q h h c             (24) therefore 1 2 2 2 1 ( ) ln 1 ln ( ) 3 , cos cos cos k k k k k k k k q q h h c                  (25) which completes the proof. □ using inequality (25), the local and superlinear convergence will be shown. theorem 3.1 suppose that assumption 3.1 holds. consider algorithm 2.1 with 1 = dfp( , , ). s k k k kh h s y then, for any (0,1),  there exist x and h such that 0 * xx x   and 0 * hh h   imply 1 * *k kx x x x    , for all k. a new sparse quasi-newton update method 37 proof. suppose that (0,1).  the following inequalities will be shown to hold for all k, 1 * * ,k kx x x x    (26) * 3 , 2 kh h l    (27) where 3l is the lipschitz constant of .f first, note that by choosing x to be sufficiently small, we have 1 < , , 2 x xl m     (28) where 1,l m and  are the constants specified in (12), assumption 3.1(ii) and (13), respectively. moreover, according to lemma 4 in (yamashita, 2008), by choosing x and h to be sufficiently small, there exists (0, )  such that 0( ) < , 2 h n    (29) * 3 ( ) < 2 h n h h l       (30) and 3 , 1 2 xc     (31) where h is a symmetric positive definite matrix, 1/2 1/2 * *= ,h h hh   and c is the constant specified in lemma 3.1. we prove the theorem by induction. when = 0,k the inequality (27) holds from (29) and (30). moreover, we have 1 * 0 0 0 * 0 * * 0 0 * 0 * * 0 * * 0 * 3 0 * 0 * 2 1 * 0 * 0 * 1 0 * 0 * = ( ) ( ) ( )( ( ) ( )) ( ( ) ( ) ( )) 2 ( ) 2 . x x x x h f x x x x h f x h h f x f x h f x f x g x x l h h x x l h x x x x l m x x x x                                  where the second inequality follows from (15), the third inequality follows from (12) and (30), the forth inequality follows from assumption 3.1(ii) and 0 * ,xx x   and the final inequality follows from (28) and < .  next, assuming (26) and (27) for = 0, 1, , 1,k l  we shall show they are also true for = .k l in fact, similarly to the case in which = 0,k we have minghou cheng, yu-hong dai and rui diao 38 1 * * * * * * * * * * 3 * * 2 1 * * * 1 * * ( ) ( ) ( )( ( ) ( )) ( ( ) ( ) ( )) 2 ( ) 2 l l l l l l l l l l l l l l l l x x x h f x x x x h f x h h f x f x h f x f x g x x l h h x x l h x x x x l m x x x x                                 and thus 1 * 1 * * ( ) 2 l l x l l x x l m x x x x            where the first inequality follows from the induction assumption. this shows the truth of (26) for = .k l in the following, we show (27) by (25) in lemma 3.3. summing up the inequality (25) with = 0, 1, , 1,k l  we have 1 1 02 2 2 =0 =0 1 ( ) ln 1 ln ( ) 3 . cos cos cos l l k k l k k kk k k q q h h c                       since 0 < cos 1k  and the term in the square brackets is nonpositive, we have 1 0 =0 ( ) ( ) 3 . l l k k h n h n c         (32) from (14) and the induction assumption, we have    11 * *= max , max , =k k kk k k x x xx x x x          for = 0, 1, , 1,k l  and thus 1 1 =0 =0 1 = . 1 1 ll l k x k x x k k                it then follows from (32), (29) and (31) that 0 3 ( ) ( ) < . 1 x l c h n h n           from (30), we have 2 1 * 3 ( ) , 2 lh f x l    which is (27) for = .k l thus by induction, (26) and (27) hold for all k. □ in order to show the superlinear convergence, we build the following relationship similarly to (yamashita, 2008), * *( ) ( ) = 0 = 0 .lim lim k k k k k kk k h h y b g s y s     (33) lemma 3.4 suppose that assumption 3.1 holds. consider algorithm 2.1 with 1 = dfp( , , ). s k k k kh h s y suppose also that 0 * xx x   and 0 * hh h   with the constants x and h specified in theorem 3.1 for sufficiently small (0,1).  then relationship (33) holds. a new sparse quasi-newton update method 39 proof. let , = 1, 2, , k i i n be the eigenvalues of .kh since the inequality (27) holds for sufficiently small , we can assume that there exists > 0min such that k i min  for all i and k. moreover, since * *= ( ) ,k k k ky g s g g s  we have * * * * * * * * * * * ( ) = ( ) ( )( ) ( ) ( ) . k k k k k k k k k k k k k min k k k k k h h y h h g s h h g g s h g b s h h g g s b g s h h g g s                it then follows from (16) that * * * * 3 3 ( ) ( ) ( ) . k k min k k k k k k h h y b g s h h g g y l s l       since 1 2 0 = ( )k k kg f x ts dt  and *kx x by theorem 3.1, the second term of the right-hand side of the inequality converges to 0 as .k  then, relationship (33) holds. □ in the following, we give the main result of this section. theorem 3.2 suppose that assumption 3.1 holds. suppose also that 0 * xx x   and 0 * hh h   hold for sufficiently small , > 0.x h  then the sequence { }kx generated by algorithm 2.1 with 1 = dfp( , , ) s k k k kh h s y converges to *x superlinearly. proof. from lemma 3.4, it suffices to show *( ) = 0 .lim k k k k h h y y  (34) notice by theorem 3.1 that for any (0,1),  relation (27) holds provided , > 0x h  are sufficiently small. then we must have that * = 0 ,lim k k h h   (35) otherwise there is a contradiction. therefore (34) is true since * *( ) .k k k kh h y h h y   by lemma 3.4, we conclude the superlinear convergence of the algorithm. □ comparing the proof of theorem 4 in (yamashita, 2008), the above proof is simpler and is directly obtained by one statement in theorem 3.1. 4. numerical results we tested the new mcqn algorithm with the dfp and bfgs formulas, namely, nmcqn-dfp and nmcqn-bfgs, by using matlab r2008a on core(tm)2 pc with windows-xp. we used the three problems in (yamashita, 2008) and two more problems in (dai and yamashita, 2007) in our numerical experiments. various dimensions, namely, = 10,n 100, 1000 and 10000, were chosen for the problems. all tested problems were tridiagonal. therefore, the chordal extensions of their sparsity pattern can easily be obtained. the details of the problems are given as follows, where inix means the used initial point. minghou cheng, yu-hong dai and rui diao 40 problem i (tridia (gould and toint, 2003)) 2 2 1 1 =2 ( ) = ( 1) ( 2 ) , = (1, 1, , 1) . n i i i t ini f x x x x x    problem ii (extended rosenbrock function (fletcher,1995)) 1 2 2 2 1 =1 ( ) = 100( ) (1 ) , = ( 1.2, 1, 1.2, 1, , 1.2, 1) . n i i i i t ini f x x x x x         problem iii (boundary value problem (fletcher,1995)) 2 =1 1 1 ( ) = (cos 2 ), 2 ( 1) 1 2 = ( , , , ) , 1 1 1 n t t n i i i t ini f x x tx e x x x n n x n n n        where = (1, 1, , 1) , t ne 2 1 1 2 1 = .1 2 1 1 2 t                  problem iv (extended powell singular function (moré et al., 1981)) /4 4 4 2 2 4 3 4 4 2 4 1 4 1 4 4 3 4 2 =1 ( ) = 10( ) ( 2 ) 5( ) ( 10 ) , = (3, 1, 0, 1, , 3, 1, 0, 1) . n i i i i i i i i i t ini f x x x x x x x x x x                   problem v (broyden tridiagonal function (moré et al., 1981)) 2 2 2 2 1 1 2 1 1 2 2 1 1 =2 ( ) = (3 2 2 1) (3 2 1) (3 2 2 1) , = ( 1, , 1) . n n n n i i i i i t ini f x x x x x x x x x x x x                   the following termination criterion is employed: 5( ) 10 or > 50000 . kf x k n   instead of step 3 in algorithm 2.1, we set 1 = ( )k k k k kx x h f x   with a step size k to improve the numerical performance. k is chosen to satisfy wolfe's rule : a new sparse quasi-newton update method 41 4 ( ) ( ) 10 ( ) , | ( ) | 0.9 ( ) . t k k k k k k k t t k k k k k k f x d f x f x d f x d d f x d              for convenience, we also list the numerical results reported for the mcqn update, as well as for the bfgs and l-bfgs methods, in (yamashita, 2008). see tables 1 and 2. for the l-bfgs method, = 5,m which is the number of stored curvature pairs of l-bfgs, and the scaling factor 2 1 1 1/ t k k ks y y   was employed. l-bfgs just stores the pairs of vectors ( , ), = 1, , ,k ks y k m while our method just stores a few entries of kh to exploit the sparsity structure of the hessian. therefore, both of them have fast implementation in practice. although nmcqn-dfp has a nice theoretical convergence property as shown in the previous section, its numerical performance is not very good. hence we only list the results of nmcqn-bfgs. the tables list the total number of iterations. the symbol "f" denotes that the number of iterations exceeds 50000 and "-" means that the bfgs method could not be implemented for = 10000.n table 1. results of problems i, ii and iii problem n bfgs l-bfgs mcqn-dfp mcqn-bfgs nmcqn-bfgs 10 15 31 20 29 47 i 100 108 126 167 72 75 1000 662 415 1498 192 195 10000 1191 11626 528 475 10 78 68 76 60 514 ii 100 487 527 665 341 1002 1000 4525 4979 6574 3207 690 10000 49580 f 31737 403 10 15 24 15 15 13 iii 100 107 299 49 50 18 1000 571 3117 86 54 23 10000 f 2600 402 25 table 2. results for problems iv and v problem n mcqn-bfgs nmcqn-bfgs 10 40 37 iv 100 211 324 1000 589 121 10000 998 97 10 30 52 v 100 56 54 1000 49 61 10000 56 52 the results in table 1 show that nmcqn-bfgs is the best among the methods compared. for problems iv and v, we only present numerical results for mcqn-bfgs by yamashita (2008) and nmcqn-bfgs. from tables 1 and 2, we can see that the nmcqn-bfgs method performs much better than mcqn-bfgs and bfgs and l-bfgs. minghou cheng, yu-hong dai and rui diao 42 for a further comparison between nmcqn-bfgs with mcqn-bfgs, we tested the new method with different choices of initial points. the initial points for the five test problems are ,inix 2 ,inix 4 ,inix 7 inix and 10 .inix the dimension of the test problems are fixed to be = 1000.n we list the number of iterations of the two methods for different test problems in table 3. the results show that nmcqn-bfgs is better than mcqnbfgs. therefore the new method, nmcqn-bfgs, is a promising alternative of mcqn-bfgs especially for large-scale problems. 5. conclusions and discussion in this paper, we have proposed an alternative to the sparse quasi-newton update method (mcqn) by yamashita (2008). the quasi-newton matrix in the new mcqn method (denoted by nmcqn) satisfies exactly the secant condition, but does not possess the same sparsity structure as the function hessian in general. we have established the local and superlinear convergence of nmcqn with the dfp updating formula, namely, nmcqn-dfp. the numerical experiments showed that nmcqn-bfgs is promising especially for large-scale problems. table 3. results with different initial points problem initial mcqn nmcqn problem initial mcqn nmcqn point -bfgs -bfgs point -bfgs -bfgs inix 192 195 inix 54 121 2 inix 210 202 2 inix 213 191 i 4 inix 213 199 iv 4 inix 210 249 7 inix 220 215 7 inix 228 370 10 inix 213 210 10 inix 294 252 inix 3207 690 inix 54 61 2 inix 4850 3753 2 inix 213 54 ii 4 inix 5056 3786 v 4 inix 210 90 7 inix 2157 813 7 inix 228 130 10 inix 4961 853 10 inix 294 62 inix 54 23 2 inix 213 24 iii 4 inix 210 24 7 inix 228 24 10 inix 294 25 it still remains under investigations how to provide a good combination of the mcqn update and the new nmcqn method by adaptively choosing one of them based on the property of the problems. when the sparsity dominates the performance, the mcqn update may be preferable; otherwise we could implement the nmcqn update. in addition, the new update method can obviously be extended to the whole broyden's convex family. a new sparse quasi-newton update method 43 6. acknowledgements this work was partly supported by the chinese nsf grants (no. 10831106), the cas grant (no. kjcx-yws7-03) and the china national funds for distinguished young scientists (no. 11125107) 7. references byrd, r. and nocedal, j. 1989. a tool for the analysis of quasi-newton methods with application to unconstrained optimization. siam journal on numerical analysis, 26: 727-739. dai, y.h. and yamashita, n. 2007. analysis of sparse quasi-newton updates with positive definte matrix completion. research report, academy of mathematics and systems science, chinese academy of sciences, beijing. dennis, j.e. and schnabel, r.b. 1983. numerical methods for unconstrained optimization and nonlinear equations, prentice-hall inc., new jersey. fletcher, r. 1995. an optimal positive definite update for sparse hessian matrices. siam journal on optimization, 5: 192-218. fukuda, m., kojima, m., murota, k. and nakata, k. 2000. exploiting sparsity in semidefinite programming via matrix completion i: general frameworks. siam journal on optimization, 11: 647-674. griewank, a. and toint, ph.l. 1982a. partitioned variable metric updates for large structure optimization problems. numerische mathematik, 39: 119-137. griewank, a. and toint, ph.l. 1982b. local convergence analysis of partitioned quasi-newton updates. numerische mathematik, 39: 429-448. griewank, a. and toint, ph.l. 1984. numerical experiments with partially separable optimization problems. numerical analysis: proceedings dundee 1983 (lecture notes in mathematics 1066) (d.f. griffiths, ed.), springer verlag, (berlin). pp. 203-220. gould, n.i.m. and toint, ph.l. 2003. cuter, a constrained and unconstrained testing environment: revisited. acm trans. math. softw., 29: 373-394. liu, d.c. and nocedal, j. 1989. on the limited memory bfgs method for large scale optimization. mathematical programming, 45: 503-528. moré, j.j., garbow, b.s. and hillstrom, k.e. 1981. testing unconstrained optimization software. acm trans. math. softw., 7: 17-41. nocedal, j. 1980. updating quasi-newton matrices with limited storage. mathematics of computation, 35: 773-782. nocedal, j. and wright, s.j. 1999. numerical optimization, springer, new york. sorensen, d.c. 1982. collinear scaling and sequential estimation in sparse optimization algorithm. mathematical programming study, 18: 135-159. toint, ph.l. 1977. on sparse and symmetric matrix updating subject to a linear equation. mathematics of computation, 31: 954-961. yamashita, n. 2008. sparse quasi-newton updates with positive definite matrix completion. mathematical programming, 115: 1-30. received 24 august 2011 accepted 29 november 2011 photovoltaic cells and systems: squ journal for science, 17 (1) (2012) 103-124 © 2012 sultan qaboos university 301 a superlinearly convergent penalty method with nonsmooth line search for constrained nonlinear least squares nezam mahdavi-amiri* and mohammad reza ansari** faculty of mathematical sciences, sharif university of technology, tehran, iran, *email: nezamm@sina.sharif.edu,**email: ansari.mr@gmail.com. abstract: recently, we have presented a projected structured algorithm for solving constrained nonlinear least squares problems, and established its local two-step qsuperlinear convergence. the approach is based on an adaptive structured scheme due to mahdavi-amiri and bartels of the exact penalty method. the structured adaptation also makes use of the ideas of nocedal and overton for handling the quasi-newton updates of projected hessians and appropriates the structuring scheme of dennis, martinez and tapia. here, for robustness, we present a specific nonsmooth line search strategy, taking account of the least squares objective. we also discuss the details of our new nonsmooth line search strategy, implementation details of the algorithm, and provide comparative results obtained by the testing of our program and three nonlinear programming codes from knitro on test problems (both small and large residuals) from hock and schittkowski, lukšan and vlček and some randomly generated ones due to bartels and mahdavi-amiri. the results indeed affirm the practical relevance of our special considerations for the inherent structure of the least squares. keywords: constrained nonlinear programming, exact penalty method, nonlinear least squares. nonsmooth line search, projected structured hessian update. مقيدةوطريقة جزاء فائقة التقارب مع خط بحث غير قابل لالشتقاق لمسائل مربعات صغرى غير خطية نظام مهداوي ومحمد رضا أنصاري لذمىا حذَثاً خىاسصمُت مشوبت ٌحً مغائً اٌمشبعاث اٌصغشي غُش اٌخطُت اٌممُذة، وأوذوا تماسبها اٌمىظعٍ :ملخص اٌفائك بخطىتُه. ولذ تم رٌه باالعتىاد إًٌ التباط خطت مهذاوٌ أمُشٌ و باستٍض ٌطشَمت اٌجضاء اٌذلُمت. رٌه االلتباط وُىته إلعماغاث هظ وعًٍ خىاص اٌخطت اٌتشوُبُت ت متماثٍحُح َغتىذ أَعا عًٍ أفىاس وىعُذاي وأفُشتىن فٍ وُفُت تص هذف ًٌ إاالعتىاد ، وعشض هىا خػ بحث معُه غُش لابً ٌالشتماق، بهزي اٌىتُجت ٌذوُظ وماستىُض وتابُت. وٌتأوُذ هُض وتائج ٍخىاسصمُت، وتجاٌتفاصًُ اٌتىفُزَت ٌ، وٍخػ اٌبحثهزا اٌاعتشاتُجُت تفاصًُاٌمشبعاث اٌصغشي. وزٌه وىالش ٌٍبشمجت غُش اٌخطُت (knitro)واَتشو بشوامج مماسوت تم اٌحصىي عٍُها بئختباس بشوامجىا مع ثالثت حاالث مهٌٍ فٍُه وبعط -شُتىىعىٍ وٌىوشان-صغُشة ووبُشة( تىتمٍ ٌمغائً هىن متبمُت راث أخطاءعًٍ مغائً ومىرجُت ) اٌعاللت اٌتطبُمُت الفتشاظاتىا اٌخاصت حىي اٌىتائج تٍه مهذاوٌ أمُشٌ. تؤوذ و باستٍضئُا بىاعطت اٌمختاسة عشىامغائً اٌ تشوُبت اٌمشبعاث اٌصغشي. mailto:nezamm@sina.sharif.edu mailto:ansari.mr@gmail.com n. mahdavi-amiri and m.r. ansari 300 1. introduction n exact penalty method is a sequential unconstrained minimization approach for solving general nonlinear programming (nlp) problems. some attractive features of the exact penalty methods are:  they overcome the difficulties posed by inconsistent constraint linearization (fletcher, 1987).  they are successful in solving certain classes of problems in which standard constraint qualifications are not satisfied (anitescu, 2005; benson et al., 2006; leyffer et al., 2006).  they are useful to enhance the robustness and ensure the feasibility of the subproblems produced in the iterations of the algorithm (byrd et al., 2004; gill et al., 2002). coleman and conn (1982a, 1982b, 1984) presented an effective exact penalty algorithm for solving generally constrained nonlinear minimization problems. mahdavi-amiri and bartels (1989) adapted the approach to develop an algorithm using projected structured hessian for solving constrained least squares problems. although computational results given in (mahdavi-amiri and bartels, 1989) showed a promising twostep superlinear asymptotic convergence, the authors did not provide an analytical proof. we presented a variant of the approach in (mahdavi-amiri and bartels, 1989) and established both the global and local superlinear convergence (mahdavi-amiri and ansari, 2011a, 2011b). our algorithm appropriates the ideas of dennis et al. (1989) in the unconstrained case to the projected structured hessian updating. here, we present the details of our new structurally adapted nonsmooth line search strategy, implementation details and more extensive computational results. the remainder of our work is organized as follows. section 2 gives the notation and relevant background on constrained nonlinear least squares problems, the exact penalty approach and projected structured hessian updating scheme for constrained nonlinear least squares problems. section 3 discusses the new nonsmooth line search procedure accounting for the structure in the nonlinear least squares objective. section 4 is devoted to the global and the local two-step superlinear convergence results. the practical issues relating to implementation are discussed in section 5. computational results in section 6 substantiate the theoretical results and show that the new algorithm is competitive as compared to the best methods tested in the collection of hock and schittkowski (1981) and three algorithms developed in knitro (byrd et al., 2006) integrated package. there, we also show the effectiveness of the algorithm on some larger test problems taken from (lukšan and vlček, 1999) and randomly generated test problems due to bartels and mahdavi-amiri (1986). finally, we conclude in section 7. throughout,  denotes the 2l norm for vectors or matrices. 2. constrained nonlinear least squares the problem to be solved is:           1 2 1 min 2 . . 0 , 0 , , t x i i x f x f x s t c x i m c x j m       (1) where       1 1, , , t f x f x f x x is an n-vector, and for each ,f  ic and jc are functions from n r to 1 ,r all assumed to be twice continuously differentiable. we refer to each f  as a residual. there are good reasons for numerical analysts to study least squares problems, mainly because of their applicability to many practical problems. almost anyone who formulates a parameterized model for a chemical, physical, financial, social or a a superlinearly convergent penalty method 301 economic application uses a problem of the form (1) to select values for the parameters that best match the model to the data. although the problem (1) can be solved by a general constrained nonlinear optimization method, in most circumstances the inherent structure of the objective function in (1) makes it worthwhile to use specialized techniques. notice that if  g x is the matrix with its columns being the gradients  ,f x then the gradient of  x is:      ,x g x f x  and the hessian of  x is:                2 2 1 : . lt t x g x g x f x f x g x g x s x           (2) in many applications, it is possible to calculate the first partial derivatives that make up the matrix  g x explicitly. these could be used to calculate the gradient  .x however, the distinctive feature of a least squares problem is that by knowing  ,g x we can compute the first part of the hessian  2 x for free. moreover, the term     t g x g x is often more important than the second summation term in (2), either because of near-linearity of the model near the solution (that is, the  2f x being small) or because of small residuals (that is, the f  being small). most algorithms for unconstrained nonlinear least squares exploit these structural properties of the hessian. newton's method uses the search direction p found by solving,           .tg x g x s x p g x f x   (3) for problems where,  s x is small compared to     t g x g x as x approaches a minimizer *,x the term  s x is dropped in (3) to yield the gauss-newton method. this method works well when  g x has full row rank and  s x is "sufficiently small", for discussions see (dennis, 1977; gill and murray, 1978). approximation for  s x in cases where it cannot be neglected is a recurring theme in the literature. in the unconstrained case, quasi-newton approximations to only the second term,  ,s x of the hessian matrix (2) have been developed (dennis et al., 1989; dennis and walker, 1981; engels and martinez, 1991). pertinent to our proposal is the work by dennis et al. (1981), who made investigations of quasi-newton updates to a matrix  .b s x this additive structure was analyzed by dennis et al. (1989), was used by al-baali and fletcher (1985) and was extended to an infinite dimensional setting by griewank (1987). these strategies are called "structured quasi-newton" methods. tapia (1988) extended the class of secant updates to equality constrained optimization utilizing the structure present in the hessian of the augmented lagrangian. local q-superlinear convergence of these structured secant methods were established by dennis and walker (1981). based on tapia's approach, huschens (1993) also presented an approach to exploit the nonlinear least squares structure. a hybrid method, linking the reduced successive quadratic programming (sqp) method with the ideas of fletcher and xu (1987), was proposed by tjoa and biegler (1991). mahdavi-amiri and bartels (1989) adjoined the reduced sqp method with the ideas developed by dennis et al. (1981) for the unconstrained structured quasinewton bfgs update to develop a projected structured approach for solving the problem (1). n. mahdavi-amiri and m.r. ansari 302 2.1 an exact penalty function here  ,x  denotes the 1 -exact penalty function,          1 2 , min 0, ,i j i m j m x x c x c x         where the penalty parameter  is a positive number. it is well known that for appropriate values of the penalty parameter , stationary points of  ,x  are either kkt points of the nonlinear program (1) or infeasible stationary points (byrd et al., 2005). pietrzykowski (1969) showed this penalty function to be exact in the sense that if *x is an isolated minimizer of (1) and the gradients of the active (binding) constraints at *x are linearly independent, then there exists a real number * 0  such that *x is also an isolated local minimizer of  , ,x  for each , 0 *.    luenberger (1970) determined, in the convex case, the threshold value of . the parameter 0  is used to determine the closeness of any constraint to zero, and hence to judge its activity. using the approach of mahdavi-amiri and bartels (1989), we define the index sets     1 2, iac x i m m c x     of active constraints,     1, ,ae x ac x m   of active equality constraints,     2, ,ai x ac x m   of active inequality constraints,    1, ,ve x m ae x   of violated equality constraints, and    2, ,vi x m ai x   of violated inequality constraints. thus, the minimization of  is carried out with the aid of an  -active merit function:               , , , sgn .i i j i v e x s j v i x s x x c x c x c x         this provides a differentiable approximation to the true merit function  in a neighborhood of x. it is trivial that  ,x  is equal in value to  ,x  when 0.  loosely speaking, step directions are determined using , but line searches and optimality tests use . a necessary condition for *x being an isolated local minimizer of  under the assumptions made above on , the ,ic and the jc is that there exist multipliers * ,r for ( *,0),r ac x such that * * 0 ( *,0) ( *, ) = ( *) = ( *) ,r r r ac x x c x a x       (4) and * 1 < < 1, ( *,0) ,r r ae x  (5) * 0 < < 1, ( *,0) ,r r ai x  (6) where ( )a x is the matrix with its columns being the gradients of the active constraints at x , for more details see (coleman and conn, 1980). a point x for which only (4) above is satisfied is said to be a stationary point of . if *x is an isolated minimizer, then it is necessary for *x to be a stationary point and satisfy (5) and (6). note that stationarity and optimality are determined using 0 , which is  with = 0. we estimate r of the numbers * r only in the neighborhoods of stationary points. in such neighborhoods, the numbers r are taken to be the least squares solution to: ( ) ( , ) ,min a x x     (7) and in practice, the qr decomposition of ( )a x is used to solve the least squares problem: a superlinearly convergent penalty method 303  ( ) = = . 0 0 r r a x q y z             (8) if the columns of ( )a x are linearly independent, then the columns of y and z, respectively, serve as bases for the range space of ( )a x and null space of ( ) ; t a x that is, ( ) = ,a x y r with r nonsingular, ( ) = 0, t a x z t y y and t z z are the identities. nearness to a stationary point is governed by the stationary tolerance > 0. the r are computed only if the projected gradient, ( , ), t zz x  is deemed "small enough" according to this tolerance. 2.2 the quadratic subproblem fundamental to the mahdavi-amiri and bartels (1989) approach is a particular unconstrained quadratic problem: 1 ( ( , )) .min 2 t t t z w z x w w h w   (9) the matrix zh is a positive definite approximation of one of two projected hessian matrices, 2 2 ( , ) ( ( , ) ( )) , t r r r ac x z x c x z         as explained next. when the algorithm is in its "local" state, that is in the proximity of a stationary point, the dual variables  are computed and in its "global" state, that is far from a stationary point, the value of the r are taken to be zero. for general nonlinear programming problems, a variety of projected quasi-newton updates is available. for the general constrained nonlinear least squares problems, we make use of the ideas in (dennis et al., 1989), in the unconstrained case, for structuring and in (nocedal and overton, 1985) for projecting. 2.3 the step directions the minimization of  is carried out using several alternative step directions derived from : (1) the global horizontal step direction; (2) the dropping step direction; (3) the newton step direction: (3a) the asymptotic horizontal step direction; (3b) the vertical step direction. the global horizontal step direction is :=gh z w where w is the solution of the quadratic problem (9). the matrix ,zh of course, approximates the global projected hessian. the asymptotic horizontal step direction ah is a component of the newton step direction, .ah v the newton steps are only attempted in close neighborhoods of stationary points that are expected to be minimizers. the step direction ah is computed as in the global case above. in this case, the matrix zh is to be an approximation of the local projected hessian. at ,ax h the constraints of ( , )ac x  may no longer be within  of zero. the vertical step is derived by taking a single newton step toward the value of v that solves the system of equations, ( , )( ) = ( ) , t ac x aa x v c x h  where ( , )ac xc  is the vector of the active constraint functions, ordered in accordance with the columns of ( ).a x n. mahdavi-amiri and m.r. ansari 304 the dropping step direction tries to drop a function ic from equalities or jc from inequalities of the collection of active constraints and provides a direction that gives a local first-order decrease in the penalty function value. it is the step direction d that satisfies the system of equations, ( ) = sgn( ) , t r ra x d e where ( , )r ac x  is chosen for whichever one of (5) or (6) is violated, and re is the rth unit vector. the steps described above are used, broadly speaking, as follows: (1) when ( , ) > , t zz x   then we set ,gx x h  where a line search is used to determine > 0. (2) when ( , ) , t zz x    then the multipliers ,r ( , ),r ac x  are approximated by the least squares solution of (7). (a) if (5) or (6) is not satisfied, then an index ( , )r ac x  is chosen for whichever one of (5) or (6) is violated, and we set ,x x d  where a line search is used to determine > 0. (b) if (5) and (6) are satisfied, then we set ax x h v   (no line search is used for ah or v ). under the standing assumptions on the ,f  ,ic and ,jc the steps incurred by the  -approximation to the penalty function produce descent for the penalty function if  and  are "correctly set". algorithm 1 below gives an outline of the classical 1 -penalty method. algorithm 1. classical 1 -penalty method. give 0 > 0 and starting point 0 ;sx for = 0, 1, 2,k find minimizer k x of ( , )x  , starting at ; k sx if k x is feasible then stop else choose new 1k  so that 1 <k k  (say, 1 = 8k k  ); set a new starting point 1k sx  (say, k x ); end if ; endfor. note that care must be taken to detect infeasibility or unboundedness. also, when the value of  is too large, in which case the optimal point for  may be infeasible, algorithm 1 reduces  and the minimization of  is repeated, for more details see the first two algorithms presented by mahdavi-amiri and bartels (1989). the details of how zb is to be managed will be given in section 2.4. 2.4 the projected least squares structure for computing the steps using (9), we intend to provide a quasi-newton approximation zh for 2 2 ( , ) ( ( , ) ( )) = [ ( ) ( ) ( , )] , t t t r r r ac x z x c x z z g x g x s x z            where a superlinearly convergent penalty method 305 2 2 =1 ( , ) ( , ) = ( ) ( ) ( ( )) ( ) l i i i v e x s x f x f x sgn c x c x           2 2 ( , ) ( , ) ( ) ( ) .j r r j v i x r ac x c x c x           in the rest of our work, we set ( ) ( ) ( ) ( ) ( ) t t zq x z x g x g x z x and in order to simplify the notation, the presence of a bar above a quantity indicates that it is taken at iteration 1,k  and the absence of a bar indicates iteration k. thus, we have = ( ) ,z z zh q x b  and intend to provide a quasi-newton approximation, ( , ) . t zb z s x z we interpret the multipliers r to be zero or estimated according to (7), whichever is appropriate at the kth iteration of the algorithm. following (mahdavi-amiri and bartels, 1989), the matrix zb is updated such that the new matrix zb satisfies the secant condition = ,zb s y where = ( ) , t s z x x (10) and y is an appropriate approximation to ( , ) . t z s x z s based on the structure principle given by dennis et al. (1989), engels and martinez (1991) derived the structured broyden family. according to this, we presented a scheme (mahdavi-amiri and ansari, 2011a) for updating the matrix zb and derived a bfgs zb -update scheme as ( ) = , t t z z z z t t z h s h s uu b b s h s u s      (11) and a dfp update formula as 2 ( ) ( ) ( ) = , ( ) t t t tz z z z z t t z h s z z z h s s z h s b b zz s z s z         (12) where = , z u q s y  and = .z z zh q b  later, we use the bfgs scheme for testing the problems, because of its generally satisfactory numerical behavior in other contexts. we also impose positive definiteness of ,zh if necessary, to guarantee descent, by use of the modified cholesky factorization. 3. the line search strategy here, we propose a nonsmooth line search strategy that makes use of the structure of least squares and is specially designed for exact 1 -penalty function ( , ).x  in a close neighborhood of *x (a point satisfying second-order sufficiency conditions), a step size of unity is always taken. therefore, the procedure to be explained here is to be used when 'far' from a solution. let x be the current iterate and h be the direction of search along which the step  is to be taken. we are interested in finding > 0 such that a sufficient reduction in  is imposed, that is, n. mahdavi-amiri and m.r. ansari 330 ( , ) < ( ( , ) ) ,x h x       where  is a given small positive constant to be specified by the following assumption. assumption 3.1 if h is a descent direction for  at x, then  is determined so that 2 1 1( , ) ( , ) ( ) := , > 0 , t x x h h g          (13) where ( , ) ( , ) = ( , ) ( ( )) ,i i i i v e x i v i x g x sgn c x c c             and  ( , ) = ( , ) | > 0 ,tiv e x i ae x c h    ( , ) = ( , ) | < 0 .tiv i x i ai x c h   we note that assumption 3.1 has also been used by coleman and conn (1980). it is a direct extension of a result of proposition 1 of conn and pietrzykowski (1977), to show that the above condition can be satisfied. for a function ( ),p x let ( ) = ( ).p p x h  it should always be clear from the context whether we are thinking of p, as a function of a vector or a step length value  . also, we denote the derivative of ( )p  along h, by ( ) = ( ) t p p x h h    and the left and right derivatives of ( ),p  by ( )p  and ( ),p  respectively, by 0 ( ) ( ) ( ) = ,lim t p t p p t         and 0 ( ) ( ) ( ) = .lim t p t p p t         then 1 2 ( ) = ( ) ( ) min (0, ( )) .i j i m j m c c           a point where the derivative of ( )  does not exist will be referred to as a breakpoint. note that the breakpoints occur at the zeros of the ( ).ic  since ( )  is a continuous function and bounded below, a minimizer * exists and a minimum occurs either at a breakpoint, where ( *) 0   and ( *) 0   or at a point where ( *) = 0.  we gain our motivation from the case when the f  and the ic are taken to be linear. a similar idea was suggested by coleman and conn (1982b) for the general nonlinear programming problems, but our approach is different in our consideration of the objective function. they make a linear approximation to the objective function and constraints but, in fact, we make a quadratic (sum of squares of linear functions) approximation of the objective function and a linear approximation of the constraints. clearly, this should provide a better approximation. in the new scheme, we try out a sequence of candidate values , stopping to accept one of these values when certain conditions are satisfied. the numerical results show the new strategy to do better than the general line search in (murray and overton, 1978) considered by mahdavi-amiri and bartels (1989). suppose that h is a descent direction for  so that ( ) < 0 t x h as an approximation of ( ),  we define 1 1 ( ) = ( ) ( ) ( ) min (0, ( ) ( ) ) , t t i i j j i m j m c x c x h c x c x h               where a superlinearly convergent penalty method 333 2 =1 ( ) = ( ( ) ( ) ) . l t f x f x h       note that the breakpoints of  occur at zeros of the 1 2( ) ( ) , . t i ic x c x h i m m    we can compute ' ( ),  ' ( )  or '( ),  for all  and without any new objective or constraint function evaluation, if needed. let  = | > 0, = 1, ,j j jx x h j r  be a sorted list (in nonincreasing order with respect to j ) of these breakpoints along h. now, an algorithm to determine the minimizer of ( )  is straightforward: by examining breakpoints sequentially, we find either a breakpoint as a minimizer (that is a breakpoint, at which ' 0   and ' > 0  ) or determine an interval (say, 1( , )j j  or ( , )r  ) on which   is continuous, containing the minimizer that is found by setting '( ) = 0.  next, we explain this strategy in more detail. we consider moving along the positive direction of h as long as the corresponding directional derivative of  along h is non-positive (in doing this, we may encounter breakpoints). later, we discuss how to compute ' ,  '  and '. now, suppose we are along the interval 1[ , ],i i  1' ( ) 0i    and a minimizer of  is yet to be determined. we compute ' ( ).i  if ' ( ) > 0,i  then the minimizer is in 1( , )i i  and we determine the step length  so that '( ) = 0,  for 1( , ).i i   but, if ' ( ) 0,i   then we compute ' ( ).i  now, if ' ( ) > 0,i  then clearly i is the desired step length and the breakpoint = i ix x h is a minimizer of  along h. in cases where ' ( ) 0,i   we expect more reduction along h, and thus the next interval 1[ , ]i i   is determined and the process is repeated. if we progress through the entire sorted list of breakpoints and  continues to reduce past the last breakpoint = , r rx x h then the step length  is determined by setting '( ) = 0,  for ( , ).r   now, we discuss the computational details. we compute breakpoints of  by = ( ) / ( ) > 0 .i j ji i c x c x  for computing the derivative and directional derivative of  , we note that for any > 0, we have '( ) '( ) = . t t x h x h gg h     inductively, consider we are in the interval 1[ , )i i  and 1' ( )i   is computed. along this interval, derivatives of the linearized constraints would remain unchanged. therefore, the change in ' is determined by the change in ' only. considering the above and 1 1= ( ) , i ix h x h       for 1( , ),i i   we have 1 1 1( ) = ( ) ( ) , ( , ) , t t i i i ih gg h                  (14) and 1 1( ) = ( ) = ( ) ( ) .lim t t i i i i i h gg h                      now, suppose i corresponds to ji c and 1 2 ( ) ( ) , if , ( ) = min (0, ( ) ( ) ), if . t j j ii i t j j ii i c x c x h j m c c x c x h j m               we have (by the fact that ( ) ( ) = 0 t j i ji i c x c x h  ), ' ( ) = ' ( ) sgn( ( )) ( ) ,i i j ji i c c c x c x     n. mahdavi-amiri and m.r. ansari 331 where 1 2 2, if , = 1, if . i i j m j m     (15) since at i the change in directional derivative of  is determined by the change in directional derivative of c only, we have ' ( ) = ( ) ' ( ) ' ( )i i i ic c           = ' ( ) sgn( ( )) ( ) ,i j ji i c x c x    where  is as defined by (15). finally, by (14), the solution of ( ) = 0,  for 1( , ),i i   is: 1 1( ) = ( ) ( ) = 0 , t t i i h gg h            and therefore, 1 1 ( ) = .ii t t h gg h           it is clear that if = 0, t g h then   is constant along each interval and therefore we are certain that the minimizer is a breakpoint. algorithm 2. line search procedure. input: x , the current point, h , a descent direction for  at x , 1 > 0 and > 0 . output: the step length  such that ( , ) < ( ( , ) )x h x       , where,  is a given small positive constant specified by (13). := 0l ; 1 :=x x ; while ( < 0) ; {determine , the minimizer of 1 ( , )x h   }; if ( = 0l ) then := min(1.0, )  ; else 1:= max( , )l    endif 1 :=x x h ; if 1 ( , ) < ( ( , )x x     then return  ; endif :=l  ; 1 := ( , ) t x h    ; endwhile; {perform the (murray and overton, 1978) line search with the initial step length  }; return  ; a superlinearly convergent penalty method 331 note that for ( , ),x  the resulting point x h may not necessarily satisfy the sufficient decrease. in this situation, if ( ) < 0,  then we repeat the above procedure with x replaced by .x h on the other hand, if ( ) 0,   then we have a good interval containing the minimizer and thus the approach of murray and overton (1978) can be performed conveniently using their successive polynomial interpolation with safeguard strategy (using the available information at the last point x and ,x h their algorithm works out more favorably; for details, see (murray and overton, 1978)). our numerical testing showed that an initial large value of  may harm the performance of the line search. thus, for the first trial, we adjust the choice of  by setting = min (1, ),  to ensure that the newton-like step is tried (if it gives enough reduction). for subsequent values of , when the first trial does not provide a sufficient decrease specified by (13), we adjust  by at least an 1 > 0 to ensure enough change in the value of and admit a finite termination of the algorithm. we are now ready to give our line search algorithm. in algorithm 2, the parameter 1 (we used 3 1 = 10  in our experiments in section 6) is used to avoid acceptance of a small correction to . our experiments showed that the usage of this parameter would accelerate the procedure. the parameter  is used to determine a sufficient decrease in  and is characterized by (line search) assumption 3.1 as specified by (3.1). it should be pointed out that our numerical experiments in section 6 showed that algorithm 2 often achieved adequate reductions inside the loop without needing to perform the murray and overton line search. 4. global and local convergence results here, we briefly state the global and the local two-step q-superlinear convergence results. the analysis of global convergence is based on the results of byrd and nocedal (1991), who studied convergence of the coleman and conn (1984) approach, with our necessary adjustments for the nonlinear least squares. let d denote a compact set so that k x d in d, for all k. let ( )acc x denote the vector of active constraints at x and ŝ denote the set of first-order points of  in d, see (coleman and conn, 1980) for justification of this terminology. assumptions 4.1 let d be a compact set. (a)  and 1 2, ,ic i m m  are twice continuously differentiable and their first and second derivatives are uniformly bounded in norm on d; (b)  kx is generated by algorithm 1 starting from an arbitrary initial point, and ,kx d for all k; (c) the gradients of the active constraints at any point in d are linearly independent. theorem 4.2 suppose that assumptions 4.1 hold and assume that (i) the number of stationary points of  in d is finite; (ii) all first-order points of  in d are strict second-order points of  ; (iii) if  k ix is a subsequence and x is a first-order point such that k ix x and ( , ) = ( , 0) , k i k i ac x ac x then there exists a sufficiently small positive constant  such that ,( ( , ) ) , kt i z k k k k kki i i i ii b z s x z s s   where ks is defined by (10); n. mahdavi-amiri and m.r. ansari 330 (iv) the proposed line search strategy produces a step length  satisfying assumption 3.1. then, (1) 0k . (2) ˆ k x x s  . (3) for k sufficiently large, ( , ) = ( , 0) k kac x ac x . (4) for k sufficiently large, the "newton step" is executed. proof. see theorem 3.4 in (mahdavi-amiri and ansari, 2011b). remark 4.3 it should be noted that a similar result for the general nonlinear case (see coleman and conn, 1982b, theorem 1) makes use of a stronger condition, , ( ) t z k li h z g x z as , k ix x where lg is the hessian of lagrangian function, while theorem 4.2 is proved under a weaker condition as specified by (iii). considering theorem 4.13 of mahdavi-amiri and ansari (2011a), our condition in (iii) is reasonable. now, we state a local two-step superlinear convergence of our method. the asymptotic analysis is developed adapting the approach of nocedal and overton (1985) to the nonlinear least squares. we will denote *x to be a local optimal solution of problem (1) and suppose the active set at *x to be  1, , .t furthermore, we assume that we are sufficiently close to *x so that the proper active set has been identified. we need the following assumptions. assumptions 4.4 assume that assumptions 4.1 hold, and that ( )y x and ( ),z x given by a particular implementation of (8), are lipschitz continuous in d. we assume that 2 , 2 ,ic ,i ac and ( )zq x are lipschitz continuous matrix functions. theorem 4.5 suppose that assumptions 4.4 hold. let the matrix ,z kb be updated by (12). then, the sequence  kx generated by algorithm 1 converges to *x with a local two-step q-superlinear rate. proof. see theorem 4.17 in (mahdavi-amiri and ansari, 2011a). 5. computational considerations here, we indicate the measures taken to implement algorithm 1. the reader is referred to (mahdavi-amiri and bartels, 1989) for more details. the test for nearness to stationarity has the form, 1( , ) ( , ( , ) ) , t z x reference x        (16) where, for given scalars  and val, we define 1reference to be a composite absolute-relative test, 2 1( , ) = .reference val val   this avoids underflow, or a stringent test, in either case that val becomes far from or close to zero. a much smaller tolerance, , of course, replaces  in (16) when the tests for convergence are made. by the same token, activity is determined by, 2( ) ( , ( )) ,r rc x reference c x a superlinearly convergent penalty method 331 and the violation of an equality constraint is determined by the reverse of this inequality. if  rc x defines an inequality constraint, it is regarded as violated if we have 2( ) < ( , ( )) .r rc x reference c x for any scalar , we define     1 2 2 1 1 2 ( , ( )) , , 1 i i m m r f x c x reference c x reference m m                in which the second term serves us as a general-purpose average function value. tests for feasibility are carried out exactly as for activity, except that a much smaller user-defined tolerance, , must be used in place of . the main difficulty in the context of exact penalty method is the strategy for choosing and updating the penalty parameter . the initial value of = 1 was used for most test problems, though we sometimes found that other values were more advantageous to use. these are noted in the reported results. only naive changes are made to  during the running of the program. the value of  is reduced through division by 8 each time a minimizer x for ( , )x  is found that is not feasible for (1). recently, byrd et al. (2008) proposed an effective penalty parameter update strategy appropriated for trust region approaches. of course, a possible adaptation to line search strategies is welcome. we have work in progress to consider a new penalty parameter updating strategy in the context of combined line search and trust region exact penalty methods. the value of r must be tested to determine whether it satisfies (5) or (6). we carried out this relative to a boundary tolerance  in analogy with the corresponding ones in (mahdavi-amiri and bartels, 1989). the value of  is regarded as being too small when   2 ( , ( )) ,rf x reference mascheps c x  where macheps is the unit round-off error. we regard  to be too small when ,  and  is regarded as being too small when .  the difference in penalty function values, ( , ) ( , ),x x    has to be tested to determine whether a sufficient decrease has been obtained. we choose the condition for a sufficient decrease on the newton step to be:     2 1 , 1 ( , ) , ( , ( , ) ) . t a ac xx h x reference z x c               a sufficient decrease for the other two steps (global and dropping) is demanded by setting the parameter 1 in the line search condition (13). the numerical positive definiteness of the matrix z h is enforced, if necessary, by using the modified cholesky factorization described in (fang and o'leary, 2008) during the process of solving (9) to guarantee descent. the requirements for optimality are that, for reasonable choices of reference values, (1) 1( , ) ( , ( , ) ) t z x reference x        , (2a) 1 1 , ( , ) ,i i ae x           (2b) 1 , ( , ) ,j j ai x         (3) 1( , ) ( , ) ( , ( , ) ) ,x x reference x          (4) 1( , ) .x x reference x  n. mahdavi-amiri and m.r. ansari 332 one might also be prepared to accept as a case of optimal termination the event that one or more of the above fail to be satisfied, but the user should be notified whenever this happens, for details see (mahdavi-amiri and bartels, 1989). 6. computational results here, we report the comparative results obtained on three sets of problems. first, thirty cnlls problems were taken from hock and schittkowski (1981): 1, 2, 6, 13, 14, 16, 17, 18, 20, 22, 23, 26, 27, 28, 30, 31, 32, 42, 46, 48, 49, 50, 51, 52, 53, 60, 65, 77 and 79. these were chosen because they were least squares problems or could be conveniently cast in that form. the number of variables in these problems varies from 1 to 5, and the number of constraints varies from 1 to 13. problems 28, 48, 50, 51, 52, and 53 have both linear constraints and linear residual functions and the other problems have at least a constraint or a residual function to be nonlinear. second, we considered seven problems generated from (bartels and mahdavi-amiri, 1986) who presented a program for random generation of general nonlinearly constrained nonlinear programming problems and also generated an example of a least squares problem where the dimensions and the curvature of the problem could be varied. these random test problems have both nonlinear constraints and residual functions. third, we used twelve larger test problems in the constrained nonlinear least squares form from (lukšan and vlček, 1999) as listed below: 1. chained rosenbrock function with trigonometric-exponential constraints. 2. chained wood function with broyden banded constraints. 3. chained powell singular function with simplified trigonometric-exponential constraints. 4. chained cragg-levy function with tridiagonal constraints. 5. chained hs46 (hock and schittkowski, 1981), problem number 46) problem. 6. chained hs47 problem. 7. chained modified hs48 problem. 8. chained modified hs49 problem. 9. chained modified hs50 problem. 10. chained modified hs51 problem. 11. chained modified hs52 problem. 12. chained modified hs53 problem. these problems were modified in such a way that a variable number of n may be used. in our tests we take 300n  (we were not able to consider larger n, since the free knitro package we are using is limited to problems with = 300n ). in all of these test problems the constraints and the residual functions are both nonlinear. the algorithm has successfully solved all of the considered problems quite efficiently. the local convergence on all problems clearly showed a two-step superlinear rate. moreover, the significant reduction in the number of global steps confirms the effectiveness of our proposed line search procedure (algorithm 2), as compared to the results obtained by mahdavi-amiri and bartels (1989) as well as methods reported by hock and schittkowski (1981) and results obtained by our testing of three algorithms (interior/direct, interior/cg and active-set) recently developed in the knitro 6.0 package. our calls to programs in knitro are managed by a c++ program to have the same testing environment as our program. our algorithm was coded in a portable subset of c++ and ran in double precision arithmetic on the microsoft visual c++ 6.0 compiler on an x86-based pc with an amd~1667mhz processor. the parameters of sections 2 and 5 were set as follows: 1 2 14 4 12 1= 1, = 10 , = 10 , = 10 , = 10 , = 10 ,           and 6 = 10 .  these values were determined by experience as ones that have worked well on most of the problems we had tried. a superlinearly convergent penalty method 333 tables 1 and 2 present the results on problems from (hock and schittkowski, 1981). the same initial points as in this reference were used. the function value obtained by our algorithm is found in the column headed by "fv" for comparison with those listed. it should be noted that our objective functions correspond to those reported in (hock and schittkowski, 1981) multiplied by .1 2 this was simply a matter of convenience for us in arranging the test problems in a least squares format. the number given in the "ni" column counts the cumulative number of steps through the for loop of the minimization for . the "nai" column counts the number of steps needed to be taken for termination after the identification of the correct active set at the solution and execution of the newton steps. the "nfe" column counts the number of times the value of the objective function was computed. the spread between the ni and the nfe provides an impression of how much work was required by the line search. indeed, the spread was not found to be significant and this points to the efficiency of our proposed line search scheme. the numbers listed in the column headed by "h&sh" give the number of function evaluations required by the best method tested in (hock and schittkowski, 1981) for attaining a function value at least as good as the one we attained. we list the number of function evaluations needed by the method of mahdavi-amiri and bartels (1989) in the column headed by "ma&b". for the three algorithms provided by knitro 6.0 (byrd et al., 2006) integrated package for general constrained nonlinear problems, we used the default parameter values without defining any special case for the objective function or constraints, and used the dense quasi-newton bfgs hessian approximation of the hessians. table 1. initializing with the zero matrix pn fv ni nai nfe h&sh ma&b d cg as 1 7.45045e-24 9 3 10 24 21 44 87 70 2 2.15624e-02 8 2 8 40 6 15 19 11 6 (1) 7.54965e-30 5 2 7 10 6 13 14 17 13 (2) 5.07423e-01 20 5 24 45 29 47 15 65 14 6.96732e-01 4 1 5 6 8 47 32 44 15 (3) 1.53250e+02 4 1 5 5 3 13 15 7 16 (3) 1.15723e+00 6 2 8 89 19 10 18 5 17 5.00000e-01 9 1 12 12 20 9 15 17 18 2.50000e+00 13 4 19 8 36 13 12 19 20 (3) 2.00994e+01 7 1 10 17 46 8 5 4 22 5.00000e-01 4 1 5 9 9 7 7 5 23 1.00000e+00 5 3 6 7 7 9 8 8 26 (1) 2.01655e-23 5 2 6 19 37 29 27 104 27 2.00000e-02 13 3 18 25 23 3588 22 26 28 5.23853e-32 2 1 2 5 2 11 9 10 30 5.00000e-01 2 1 3 14 2 9 7 21 31 3.00000e+00 9 5 11 10 15 13 10 22 32 5.00000e-01 4 1 3 3 9 8 9 4 42 6.92893e+00 7 3 8 10 14 13 10 18 46 5.84019e-09 16 9 16 14 40 44 32 94 48 5.54668e-32 2 1 2 7 2 11 12 28 49 1.35973e-07 11 6 11 9 11 23 26 26 50 1.70714e-30 2 1 2 18 8 9 8 10 51 3.69779e-32 2 1 2 5 2 13 7 13 52 2.66332e+00 3 1 3 8 7 7 9 10 53 2.04651e+00 3 1 3 8 8 9 9 8 60 (1) 1.62841e-02 12 3 14 9 29 11 16 100 65 (4) 4.76764e-01 11 3 13 20 11 19 21 77 (4) 1.20753e-01 15 4 17 16 39 39 19 25 79 3.93884e-02 12 4 15 10 29 13 12 17 n. mahdavi-amiri and m.r. ansari 334 table 2. initializing with the identity matrix pn fv ni nai nfe h&sh ma&b d cg as 1 9.59790e-18 9 4 10 24 29 44 87 70 2 2.15624e-02 7 2 7 40 8 15 19 11 6 (1) 4.48518e-23 8 2 11 10 13 13 14 17 13 (2) 5.03425e-01 22 6 28 45 30 47 15 65 14 6.96732e-01 4 1 5 6 8 47 32 44 15 (3) 1.53250e+02 3 1 4 5 3 13 15 7 16 (3) 1.15723e+00 6 2 8 89 9 10 8 5 17 5.00000e-01 9 1 12 12 20 9 5 17 18 2.50000e+00 13 4 19 8 32 13 12 19 20 (3) 2.00994e+01 7 2 10 17 32 8 5 4 22 5.00000e-01 4 1 5 9 11 7 7 5 23 1.00000e+00 5 3 6 7 34 9 8 8 26 (1) 2.41009e-24 7 4 8 19 15 29 27 104 27 2.00000e-02 14 8 16 25 18 3588 22 26 28 7.70372e-33 3 2 3 5 4 11 9 10 30 5.00000e-01 3 2 3 14 3 9 7 21 31 3.00000e+00 9 5 11 10 15 13 10 22 32 5.00000e-01 5 1 6 3 11 8 9 4 42 6.92893e+00 12 4 22 10 25 13 10 18 46 5.41352e-08 20 10 22 14 27 44 32 94 48 0.00000e-00 5 3 4 7 5 11 12 28 49 2.25804e-07 13 7 13 9 14 23 26 26 50 1.63935e-30 5 1 5 18 8 9 8 10 51 1.23260e-32 3 1 3 5 4 13 7 13 52 2.66332e+00 5 3 5 8 10 7 9 10 53 2.04651e+00 4 3 4 8 10 9 9 8 60 (1) 1.62841e-02 12 4 14 9 18 11 16 100 65 (4) 4.76764e-01 9 2 11 19 11 19 21 77 (4) 1.20753e-01 20 8 22 16 33 39 19 25 79 3.93884e-02 15 7 19 10 29 13 12 17 in tables 1 and 2, the columns headed by "d", "cg" and "as" respectively give the number of function evaluations required by interior/direct (barrier), interior/cg (barrier) and active-set algorithms in this package. our method of counting function evaluations was consistent with (hock and schittkowski, 1981; mahdavi-amiri and bartels, 1989; and knitro), so that these columns serve as a basis for comparison. obviously, the function evaluations are compared on cases where the algorithms have converged to the same solution point. the results for initialization of the projected matrix with the zero matrix are given in table 1 and those for initialization with the identity matrix are given in table 2. there is no entry in the "h&sh" column for problem 65, which serves to indicate that our program reached a minimum value significantly lower than that of any of the methods reported on in (hock and schittkowski, 1981). in the first column of tables 1 and 2, the superscript (1) or (4) indicates that the initial value of  was set to 100 or 10, respectively, rather than 1. the problems in question, i.e. 6, 26, 60, 65, and 77, had constraint function values at some points whose magnitudes dominated the magnitude of the penalty function, forcing the minimization process to take an unusually long time in attempting to maintain the constraints within feasibility. the larger value of  compensated for the imbalance in scale between the objective function and the constraints. the superscript (2) or (3) indicates that the initial value of a superlinearly convergent penalty method 335  was set to 0.01 or 0.001, respectively, instead of 1. in the problems for which this was done, i.e. 13, 15, 16, and 20, there was a reverse imbalance of scale. the magnitude of the objective function at some point was far larger than that of the constraints. this caused the minimization to waste time in finding a sequence of infeasible stationary points for a sequence of decreasing values of . the smaller value of  compensated for the imbalance in scale between the objective function and the constraints. it should be pointed out that we have work in progress to come up with a new automatic penalty parameter updating strategy in the context of combined line search and trust region exact penalty methods. despite this, the method we have described shows itself competitive in comparison with those tested by hock and schittkowski (1981) and those solved by knitro. it did, respectively, as well as, better than and poorer than the best of the methods in hock and schittkowski on approximately 40%, 50% and 10% of the test problems and in comparison with the method of mahdavi-amiri and bartels (1989), the corresponding results are 30%, 70% and 0%, respectively. in comparison with interior/direct algorithm, our algorithm did as well as, better and poorer on 13%, 70% and 17%, respectively. in comparison with interior/cg algorithm, the corresponding results are 13%, 74% and 13%, respectively. finally, in comparison with active-set algorithm, results are 37%, 50% and 13%, respectively. thus, our new code here with the modifications proposed along with the new line search strategy significantly outperforms the ones reported in (bartels and mahdavi-amiri, 1986; mahdavi-amiri and bartels, 1989), as well as the three general nonlinear algorithms of knitro (byrd et al., 2006), on the test problems. this should justify the appropriateness of our structural approach to nonlinear least squares. table 3. results on randomly generated test problems initializing with the zero matrix pn sp  fv ni nai nfe nce rfe 1 1 1 21.6541 19 5 19 24 e-12 1 10 1 21.6541 37 6 40 46 e-12 1 100 1 21.6541 39 7 40 47 e-13 2 1 -1 21.6541 24 6 25 31 e-12 2 10 -1 21.6541 39 7 45 52 e-11 2 100 -1 21.6541 41 6 42 48 e-11 3 1 -10 21.6541 33 7 37 44 e-12 3 10 -10 21.6541 39 7 45 52 e-11 3 100 -10 21.6541 36 7 37 44 e-12 4 1 1 99.3233 35 4 36 40 e-15 4 10 1 98.8173 51 4 56 60 e-14 5 1 -1 98.8173 51 4 55 59 e-16 5 10 -1 98.8173 115 8 117 125 e-15 6 1 1 862.628 105 3 113 116 e-15 6 10 1 862.628 116 4 117 121 e-16 7 1 -1 861.698 125 3 130 133 e-14 7 10 -1 861.698 140 5 152 155 e-14 in tables 3 and 4, we report the results obtained by our program on three sets of random problems (problems 1, 2 and 3 as set 1, problems 4 and 5 as set 2, and finally problems 6 and 7 as set 3) generated and tested by bartels and mahdavi-amiri (1986). each set of random problems are generated with all quantities ( *,x lagrange multipliers, 1,u etc.) being exactly the same, and only having different 2 l obtained by setting different values for  ( 2 l is definite if > 0 and is indefinite if 0  , for details see (bartels and mahdavi-amiri, 1986). the numbers of the equality constraints, the inequality constraints and the active constraints at solution for the three sets respectively are (2, 3, 4), (5, 5, 7) and (8, 12, 10). the results obtained by n. mahdavi-amiri and m.r. ansari 310 each algorithm provided by knitro 6.0 on these random problems are separately reported in table 5. in tables 3 and 4, the "sp" column shows the value to which all components of the starting point are set. the "  " column shows the value considered for . the "nce" column gives the count for the number of times the constraint function is computed. we compute the composite absolute-relative feasibility error at the final point x as: 1 2 1 ( ) (0, ( )) ( ) = , 1 ( ) mini j i m j m c x c x rfe x c x      where ( )c x denotes the vector of constraints evaluated at x. rounded value of ( )rfe x is shown in the column headed by "rfe". the other column headlines have the same meanings as those given for tables 1 and 2. table 4. results on randomly generated test problems initializing with the identity matrix pn sp  fv ni nai nfe nce rfe 1 1 1 21.6541 25 5 25 30 e-10 1 10 1 21.6541 45 6 47 53 e-12 1 100 1 21.6541 37 6 38 44 e-12 2 1 -1 21.6541 27 6 30 36 e-11 2 10 -1 21.6541 56 7 56 63 e-11 2 100 -1 21.6541 45 6 45 51 e-12 3 1 -10 21.6541 28 7 31 38 e-11 3 10 -10 21.6541 45 7 52 59 e-12 3 100 -10 21.6541 44 7 45 52 e-11 4 1 1 99.3233 38 6 40 46 e-15 4 10 1 98.8173 52 4 58 62 e-15 5 1 -1 98.8961 30 5 31 36 e-15 5 10 -1 98.9681 89 10 95 105 e-15 6 1 1 862.628 132 4 138 142 e-15 6 10 1 862.628 163 3 173 176 e-15 7 1 -1 861.698 152 7 157 164 e-15 7 10 -1 861.698 138 3 146 149 e-14 in table 5 for each algorithm of knitro we have three columns, and all column headlines have the same meanings as those given for other tables. note that on problems 4 (with starting point 10), 5 (with starting point 1), 6 and 7 our program reached a locally optimal solution having significantly smaller objective values than the values obtained by the other three algorithms. at these solutions, our program terminated with the active constraints set {1, … ,7,9} on problems 4 and 5, and with the active constraints set {1, … ,15,17,18,19} on problems 6 and 7. in table 6, we report the results obtained by our program and three programs of knitro 6.0 on problems taken from (lukšan and vlček, 1999). the same initial points as in this reference were used. the columns headed by "n" and "m" respectively give the number of variables and constraints. the superscript (in the first column) and the other column headlines have the same meanings as those given for table 1. the interior/direct program, on problems 2, 3, 4, 7 and 9 reached the iteration limit (of 10000) or failed to solve the problem and on problem 8 it found a local optimal solution having objective value 1.67453e+02, which is significantly smaller than the values obtained by the other three programs. on problem 3, the interior/cg program and the active -set program terminated with the objective values 3.40390e+02 and 7.08426e+00, respectively. on problem 1, the a superlinearly convergent penalty method 313 active-set program found a local optimal solution having the objective value 1.92827e+00, which is significantly larger than the values obtained by the other three programs. the results in tables 3, 4, 5 and 6 show the effectiveness of the proposed algorithm as compared to the three algorithms recently developed in knitro (byrd et al., 2006) on constrained nonlinear least squares problems. observing the low values of the number of local iterations under the column "nai" in all the tables, the local two-step superlinear convergence of our proposed algorithm is well supported. moreover, the overall performance of the proposed algorithm on the test problems attests to its robustness. table 5. results of knitro on randomly generated test problems d cg as pn sp  fv nfe rfe fv nfe rfe fv nfe rfe 1 1 1 21.6541 36 e-9 21.6543 45 e-8 21.6541 45 e-9 1 10 1 21.6544 58 e-9 21.6657 62 e-7 21.6542 327 e-10 1 100 1 21.6543 83 e-6 21.6562 77 e-5 22.8154 97 e-18 2 1 -1 21.6541 42 e-8 21.6543 45 e-8 21.6541 45 e-9 2 10 -1 21.6546 64 e-9 21.6565 76 e-8 21.6564 256 e-9 2 100 -1 21.6543 91 e-8 21.7348 72 e-5 21.8106 132 e-15 3 1 -10 21.6541 52 e-9 21.6541 69 e-8 21.6541 54 e-9 3 10 -10 21.6541 67 e-7 21.6665 77 e-7 21.6542 312 e-10 3 100 -10 21.6543 93 e-8 21.6546 87 e-8 21.8070 74 e-18 4 1 1 99.3281 266 e-8 99.3902 163 e-7 99.3281 151 e-11 4 10 1 99.3522 169 e-7 99.3531 130 e-7 99.3307 417 e-13 5 1 -1 99.3305 386 e-7 99.3304 139 e-9 99.3281 193 e-12 5 10 -1 98.8990 182 e-9 99.7139 99 e-8 99.3301 766 e-12 6 1 1 959.052 533 e-7 959.567 3096 e-7 959.327 406 e-12 6 10 1 959.061 8140 e-7 971.849 17787 e-14 959.327 406 e-12 7 1 -1 960.240 13174 e-6 959.517 423 e-10 960.210 127 e-15 7 10 -1 959.406 7835 e-5 959.514 255 e-9 959.040 3813 e-15 table 6. results on problems taken from (lukšan and vlček, 1999) pn n m fv ni nai nfe d cg as 1 (1) 300 298 1.12048e-14 30 5 40 36 34 31 2 (3) 300 290 2.62320e+03 250 9 340 186 699 3 300 2 2.00542e+02 27 6 34 544 189 4 300 296 7.15723e+02 50 8 65 35 180 5 (1) 299 198 2.34529e-13 30 4 38 25 23 37 6 297 222 2.22740e+02 35 5 48 25 27 174 7 299 198 1.18060e+03 32 6 39 41 80 8 299 198 7.79817e+02 75 8 125 159 183 184 9 (1) 297 222 1.67930e-06 115 8 135 194 588 10 297 222 5.06731e-14 29 7 38 91 24 10 11 (3) 297 222 2.11459e+02 50 9 75 55 56 121 12 (3) 297 222 1.77561e+02 40 6 53 19 27 71 remark 6.1 to investigate the effectiveness of projected structured updating schemes proposed by mahdaviamiri and bartels (1989) and (11) proposed here, we used alternative update rules instead of (11) in the local steps and ran the algorithm on all the test problems again. the asymptotic results showed a marginal n. mahdavi-amiri and m.r. ansari 311 outperformance of (11). thus, the overall clear outperformance of our new code to the one in (mahdavi-amiri and bartels, 1989) (as we mentioned before) should be attributed to our global steps and the use of our new nonsmooth line search strategy. with this observation, it is remarkable that the two-step superlinear convergence of the method in (mahdavi-amiri and bartels, 1989) is yet to be proved. 7. conclusions we presented a structurally projected exact penalty method adapted for solving constrained nonlinear least squares problems. the projected structure made appropriate use of the ideas of nocedal and overton (1985) for general nonlinear programs. numerical results showed our proposed algorithm to be efficient and reliable. for robustness, we devised a nonsmooth line search procedure accounting for the structure in the nonlinear least squares objective. we implemented the proposed algorithm and tested the program and three nonlinear programming codes from knitro on both small and large residual problems from (hock and schittkowski, 1981; lukšan and vlček, 1999) and some randomly generated ones due to bartels and mahdavi-amiri (1986). the results showed the practical relevance of our special line search and projected considerations for the sum of squares objective. 8. acknowledgment the first author thanks the research council of sharif university of technology for supporting this work. 9. references al-baali, m. and fletcher, r., 1985. variational methods for non-linear least squares. journal of the operational research society, 36: 405-421. anitescu, m., 2005. global convergence of an elastic mode approach for a class of mathematical programs with complementarity constraints. siam j. optim., 16(1): 120-145. bartels, r.h. and mahdavi-amiri, n., 1986. on generating test problems for 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kuwait; the gulf; conservation; reintroduction. دولة الكويت في قائمة بالحيوانات الثدية ج. كوان يترب الحيوانات الثدية في دولة الكويت بناءا على مواد بحثية منشورة، اتصاالت شخصية، الشبكة العنكبوتيةبلبحث قائمة اهذا يقدم :ملخص عة غير شائعة الوجود ربأمن الثديات باإلضافة الى ا ين نوعرم تسجيل خمسة و عشت. الباحث مالحظاتمدونات الكويت، و ،الكويتية ن في الراغبي هذه القائمة و اثنين مشكوك في مصدرها. يمكن ان تساعد موجودة في الماضي، بينما ستة كانت الزيارة للمنطقة و نادرةأ دخال الحيوانات في مشاريع المحميات الكويتية. إعمار الصحراء، وإعادة إ ليج ، المحافظة على النوع ، أعاده االدماج. مفتاح الكلمات : الحيوانات الثدية، الكويت ، الخ 1. introduction his annotated checklist of the non-domesticated mammals of kuwait is intended to be of use to those planning forthcoming desert rehabilitation, animal reintroduction and protected area projects there, funded by the united nations compensation commission (uncc, 2005), and to stimulate further field research, especially into kuwait‟s rodents (rodentia) and bats (chiroptera). harrison and bates‟ (1991) volume on the mammals of arabia is the single most useful source for kuwait‟s terrestrial mammals but otherwise the literature is scattered and often difficult to obtain. the scientific nomenclature and sequence i have used for terrestrial mammal species is that of harrison and bates (1991) with one exception. gazella saudiya (kingswood et al., 2001) was treated by harrison and bates (1991) as a subspecies of gazella dorcas. the cetacea follow the „conservation checklist‟ of shirihai (2006) and have been inserted before the artiodactyls. frequently cited references are abdulrahman al-sirhan‟s (2012) photographic website on the wildlife of kuwait, clayton (1983), clayton and wells (1987), harrison and bates (1991) and mike pope‟s (2012) photographic blog on the birds and other wildlife of kuwait. pjc stands for author‟s observations. thirty seven species are listed in the systematic list below. twenty five constitute the present kuwait mammalian fauna, indicated by pkmf after the authority citation of the scientific name. four species are uncommon or rare visitors to kuwait (rv), six used to occur in kuwait (ex) and two are of doubtful provenance (dp). 2. systematic list insectivora long-eared hedgehog hemiechinus auritus (gmelin 1770) pkmf fairly common resident (clayton, 1983; clayton and wells, 1987; harrison and bates, 1991; al-sirhan, 2012; pope, 2012; pjc). an inhabitant of eissa et al.‟s (1975) study area in southeast kuwait. t p.j. cowan 02 ethiopian hedgehog paraechinus aethiopicus (ehrenberg 1833) pkmf uncommon or rare resident (clayton, 1983; clayton and wells, 1987). one al-salmi, western kuwait, april 2007 (al-sirhan, 2009; al-sirhan, 2012). chiroptera naked-rumped tomb bat taphozous nudiventris cretzschmar 1830 pkmf rare visitor presumably from iraq (clayton, 1983; clayton and wells, 1987). large roost of ca. 500 or more found at a farm on outskirts of kuwait city 16 september 2002 (al-sirhan, 2007; al-sirhan, 2012). flying individuals there at sunset early december 2007 after “many bats erupted from one of the farm buildings” (pope, 2012). photographed at the farm april 2008 and 2009 and droppings found there november 2007 and december 2009, all suggesting it is a regular roost site and that the bats may well be resident (al-sirhan, 2009). trident leaf-nosed bat asellia tridens ( e. geoffroy 1813) rv uncommon or rare visitor presumably from iraq (clayton, 1983; clayton and wells, 1987). kuhl‟s pipistrelle pipistrellus kuhlii (kuhl 1819) pkmf fairly common urban resident (clayton and wells, 1987; harrison and bates, 1991). carnivora wolf canis lupus linnaeus 1758 ex occurred but apparently no longer present (clayton and wells, 1987; harrison and bates, 1991). red fox vulpes vulpes (linnaeus 1758) pkmf common resident (clayton and wells, 1987; harrison and bates, 1991; al-sirhan, 2012; pope, 2012; pjc). fennec fox vulpes zerda (zimmermann 1780) dp there are two specimens known from arabia if the sinai is excluded. one was obtained in kuwait and sent to london in 1935 and one from southern iraq was reported in 1982 (gasperetti et al., 1985; harrison and bates, 1991). a third, an animal captured live near jebel hafit (uae/oman border) and put in al-ain zoo, was actually a rüppell‟s fox vulpes rueppellii (harrison and bates, 1991). the fennec fox is a saharan species that occurs as far east as the sinai in egypt (asa et al., 2004) and is often kept in captivity. it is suspicious that there are no other arabian records, casting doubt on the provenance of the kuwait and iraq individuals (stuart and stuart, 2008). omar and abdulraheem (1996) stated that “red and fennec foxes (vulpes vulpes and fennecus zerda) have been seen in umm ar-rimman and jal az-zor [nearby sites in kuwait]…” and included the fennec fox in a list of species likely to be encountered within the jal az-zor national park. they presented no proof for these fennec fox records young red and rüppell‟s foxes in the field are easily mistaken for fennec fox (e.g. gasperetti et al., 1985). in an earlier publication on the jal az-zor national park, omar et al. (1986a) noted that kuwaiti senior citizens remembered the fennec fox and presented a photo captioned, “fennec fox, rare and endangered mammalian species”, which in fact depicts a red fox. omar et al. (1986b) proposed reintroducing [sic] the fennec fox into the jal az-zor national park. alsdirawi and faraj (2004) listed the presence of fennec fox in the kuwait border demilitarised zone without proof but presumably on the basis of the kuwait and iraq individuals. honey badger mellivora capensis (schreber 1776) pkmf rare resident (clayton, 1983; clayton and wells, 1987; harrison and bates, 1991). sighted occasionally in the sabah al-ahmad natural reserve (jal az-zor national park) (al-sirhan, 2007). captive individual photographed in 2002 (al-sirhan, 2012) apparently of african origin. indian grey mongoose herpestes edwardsi (e. geoffroy 1818) pkmf clayton and wells (1987) stated: “as recently as forty years ago they [indian grey mongooses] were reported as being very common in kuwait city. however, they are unlikely to be found in the modern city and nowadays have been relegated to outlying districts such as jahra or fahaheel.” they probably originated as stowaways on trading dhows or as escaped pets (clayton and wells, 1987). a specimen was obtained from kuwait (harrison and bates, 1991). wildcat felis silvestris (schreber 1777) pkmf recorded (clayton, 1983; clayton and wells, 1987; harrison and bates, 1991) and perhaps still present. sand cat felis margarita (loche 1858) pkmf kitten photographed at wafra on the kuwait border (harrison and bates, 1991). several live individuals, apparently caught in kuwait, were donated to the desert animal facility (kuwait institute for scientific research, an annotated checklist of the mammals of kuwait 02 kabd) and the scientific center (kuwait city) from 2001 (delima, 2006; bebehani, 2008; pjc). al-sirhan (2007) saw four in the jal az-zor national park 26 june 2003 and photographed two of them (al-sirhan, 2012). caracal caracal caracal (schreber 1776) ex recorded (clayton and wells, 1987; harrison and bates, 1991) but apparently no longer present. cheetah acinonyx jubatus (schreber 1776) ex reported from the kuwait area (though not necessarily from within what are the present-day boundaries of kuwait) but presumably now long extinct (clayton and wells, 1987; harrison and bates, 1991). cetacea sei whale balaenoptera borealis lesson 1828 rv in march 1999 a 10 m long whale carcass was washed ashore and eventually identified as b. borealis (bishop and alsaffar, 2008). blue whale balaenoptera musculus (linnaeus 1758) rv the skeleton of a whale stranded at kadhima in june 1963 and placed in the „natural history museum‟ was identified as that of b. musculus by al-robaae (1971b), who sent photographs of the skeleton and notes to f.c. fraser of the british museum (natural history). fraser replied “i…have no doubt about the genus of the animal concerned. it is balaenoptera, i am not quite certain of the species…i am inclined to say that it is balaenoptera musculus rather than balaenoptera physalus, basing this on the shape of the nasals” (al-robaae, 1971b). the skeleton is now in the „educational science museum‟ (visited april 2007). a second skeleton there is labelled as a blue whale length 6.5 m from the khowaysat area between kadmah and doha 10 october 1976. a third specimen, caught north of shuaiba industrial area on 26 december 1980 and measuring 7 m in length, is also on display there (nithyanandan, 2010a). indo-pacific humpback dolphin sousa chinensis (osbeck 1765) pkmf occurs (henningsen and constantine, 1992). observed year-round in the north off boubyan island with a maximum pod size of 30 individuals, and routinely observed in kuwait bay (bishop and alsaffar, 2008), though also recorded off fahaheel and in the south off khiran (willson, 2007). recent sightings between mina al-zour and khiran included calves (nithyanandan, 2010b; pope, 2012). indo-pacific bottlenose dolphin tursiops aduncus (ehrenberg 1833) pkmf farmer (1983) stated, “the commonest dolphin [of kuwait] is probably tursiops aduncus…” and included two photos of live t. aduncus. found year round though with fewer winter sightings, the majority seen in southern waters from fahaheel southwards (willson, 2007; pope, 2012). false killer whale pseudorca crassidens (owen 1846) rv a specimen was found south of kuwait city in 1964. its skeleton was mounted and displayed in the „natural history museum‟, kuwait (al-robaae, 1971a). finless porpoise neophocaena phocaenoides (g. cuvier 1829) pkmf farmer (1983) noted this species had been recorded and included a photo of a stranded individual. henningsen and constantine (1992) reported a group of two and a group of five in kuwait bay about 2 km from shore. andrew willson (2007) reported several sightings and strandings. artiodactyla arabian oryx oryx leucoryx (pallas 1777) ex o. leucoryx presumably occurred in the western and northwestern deserts of kuwait prior to 1900 (kingswood et al., 2001). reintroduction into kuwait has been recommended (omar et al., 1986b; omar and abdulraheem, 1996), though a protected area of considerable size would be needed, involving adjacent countries (kingswood et al., 2001; alsdirawi and faraj, 2004). mountain gazelle gazella gazella (pallas 1766) dp although intimated to have occurred (clayton and wells, 1987), it would seem most unlikely that this species, an inhabitant of the mountainous and nearby areas of the arabian peninsula, has ever occurred naturally in kuwait (harrison and bates, 1991; kingswood et al., 2001). saudi gazelle gazella saudiya (carruthers and schwarz 1935) ex this species has been recorded (harrison and bates, 1991) and suggested for reintroduction (omar et al., 1986b). however, saudi gazelle is now considered extinct in the wild and may well be extinct in captivity too, as certain claimed captive g. saudiya populations have been shown not to be so (kingswood et al., 2001; hammond et al., 2001). p.j. cowan 00 dunham et al. (2001) cast doubt on the existence of the species in the past in kuwait: “historically, this species was recorded on the western side of the arabian peninsula, with all records west of 47 °e except for one anomalous specimen from kuwait, which reached the british museum after a period of captivity at london zoo… recent dna studies indicate that a record for iraq (harrison and bates, 1991) refers to a sand gazelle [g. subgutturosa] (r. hammond, personal communication).” goitered gazelle gazella subgutturosa (guldenstaedt 1780) ex the taxon that occurred in kuwait was the arabian sand gazelle gazella subgutturosa marica (harrison and bates, 1991; kingswood et al., 2001). any reintroduction plan (omar et al., 1986b; omar and abdulraheem, 1996) needs to be aware of the genetic background of stock (harrison and bates, 1991; kingswood et al., 2001). lagomorpha cape hare lepus capensis (linnaeus 1758) pkmf recorded (harrison and bates, 1991) and perhaps still present. any reintroduction plan (omar et al.,1986b; omar and abdulraheem, 1996) would require geographically appropriate animals (harrison and bates, 1991). rodentia indian crested porcupine hystrix indica kerr 1792 pkmf a few quills were collected in the kuwait/saudi arabia border area in wadi al batin, february 1995 by s.t. spencer and c.w.t. pilcher (spencer, 2009). euphrates jerboa allactaga euphratica thomas 1881 pkmf occurs but apparently rare (clayton, 1983; harrison and bates, 1991). an inhabitant of eissa et al.‟s (1975) study area in southeast kuwait. one photographed (al-sirhan, 2008) in western kuwait april 2007. lesser jerboa jaculus jaculus (linnaeus 1758) pkmf common (clayton, 1983; harrison and bates, 1991; al-sirhan, 2012; pope, 2012; pjc). eissa et al. (1975) studied the ecology of this species at a site in southeast kuwait. at the jal az-zor escarpment, remains of jaculus jaculus were found in 18 of 97 little owl athene noctua pellets and jaculus jaculus hind limbs and tails at little owl feeding sites (clayton, 1991). black rat rattus rattus (linnaeus 1758) pkmf apparently present but declining (clayton, 1983). brown rat rattus norvegicus (berkenhout 1769) pkmf locally common (clayton, 1983; clayton and wells, 1987; harrison and bates, 1991). house mouse mus musculus linnaeus 1758 pkmf present (clayton, 1983; harrison and bates, 1991). baluchistan gerbil gerbillus nanus blanford 1875 pkmf present and commoner than g. dasyurus (clayton, 1983; clayton and wells, 1987; harrison and bates, 1991). wagner‟s gerbil gerbillus dasyurus (wagner 1842) pkmf present (clayton, 1983; clayton and wells, 1987). cheesman‟s gerbil gerbillus cheesmani thomas 1919 pkmf present (clayton, 1983; harrison and bates, 1991; al-sirhan, 2012; pjc). remains found in 13 of 97 little owl pellets collected at the jal az-zor escarpment (clayton, 1991). indian gerbil tatera indica (hardwicke 1807) pkmf present (alyan, 1989; harrison and bates, 1991). probably eradicated by the kuwait ministry of health (alsirhan, 2009). libyan jird meriones libycus lichtenstein 1823 pkmf common in some desert areas (clayton, 1983; clayton and wells, 1987; al-sirhan, 2012; pope, 2012; pjc). remains found in 44 of 97 little owl pellets collected at the jal az-zor escarpment (clayton, 1991). sundevall‟s jird meriones crassus sundevall 1842 pkmf present (clayton, 1983; harrison and bates, 1991; al-sirhan, 2012; pjc). an annotated checklist of the mammals of kuwait 02 3. discussion and conclusions kuwait‟s general environment has been described by el-baz and al-sarawi (2000) and al-yamani et al. (2004), its flora by omar (2000), insects by al-houty (1989) and birds by cowan and pilcher (2003), gregory (2005) and pope and zogaris (2012). the current paper presents an annotated checklist of the kuwait mammalian fauna. twentyfive species constitute the present kuwait mammalian fauna, 22 are terrestrial species and three marine (cetaceans). an additional four species are uncommon or rare visitors to kuwait (one bat, three cetaceans). six species used to occur in kuwait, either larger carnivores (wolf, caracal, cheetah) or ungulates (arabian oryx, saudi gazelle, arabian sand gazelle). the kuwait desert is in very poor condition with considerable vegetation degradation (brown, 2003) and uncontrolled hunting (pope and zogaris, 2012). the jal az-zor „national park‟, to the north of kuwait bay, is fenced and protected. otherwise there are some protected coastal wetland sites and some areas that receive inadvertent protection (military sites, airports, oil fields). more extensive areas need protection. they should be fenced first, a ranger service initiated and then inventoried. the marine environment also needs extensive reserves, which should include the coral islands. 4. acknowledgement dr jim bishop (kisr) supplied me with copies of several elusive marine mammal papers. 5. references al-houty, w. 1989. insect fauna of kuwait. university of kuwait, kuwait. al-robaae, k. 1971a. false killer whale pseudorca crassidens; a new record for arab gulf. bulletin iraq national history museum, 5(1): 31-34. al-robaae, k. 1971b. notes on a blue whale (balaenoptera musculus) skeleton in natural history museum, kuwait. bulletin iraq national history museum, 5(1): 43-44. alyan, s.m.h.h. 1989. biological studies of tatera indica (hardwicke, 1807), the indian gerbil, in kuwait desert. msc thesis (zoology). kuwait university, kuwait. asa, c.s., valdespino, c. and cuzin, f. 2004. fennec fox vulpes zerda (zimmermann, 1780). in canids: foxes, wolves, jackals and dogs. (eds.) sillero-zubiri, c., hoffmann, m. and macdonald, d.w. iucn, gland, switzerland. pp. 205-209. al-sirhan, a.r. 2007, 2008, 2009. personal communs. al-sirhan, a.r. 2012. wildlife of kuwait. www.alsirhan.com/animals. (last accessed 5 october 2012). al-yamani, f.y., bishop, j., ramadhan, e., al-husaini, m. and al-ghadban, a.n. 2004. oceanographic atlas of kuwait’s waters. revised edition. kuwait institute for scientific research, kuwait. alsdirawi, f. and faraj, m. 2004. establishing a transboundary peace park in the demilitarised zone (dmz) on the kuwaiti/iraqi borders. parks, 14(1): 48-55. bebehani, s. 2008. personal commun. bishop, j.m. and alsaffar, a.h. 2008. quantitative observations on marine mammals and reptiles of kuwait‟s boubyan island. zool. middle east, 43: 3-12. brown, g. 2003. factors maintaining plant diversity in degraded areas of northern kuwait. j. arid environments, 54: 183-194. clayton, d. 1983. mammals. in kuwait’s natural history: an introduction. (eds.) clayton, d. and pilcher, c. kuwait oil company, kuwait. 172-190. clayton, d.a. 1991. the little owl athene noctua and its food in kuwait. sandgrouse, 13: 2-6. clayton, d. and wells, k. 1987. discovering kuwait’s wildlife. fahad al-marzouk, kuwait. cowan, p.j. and pilcher, c.w.t. 2003. the status of desert birds in kuwait. sandgrouse, 25: 122-125. delima, e. 2006. personal commun. dunham, k.m., williamson, d.t. and joubert, e. 2001. saudi arabia. in antelopes. part 4: north africa, the middle east, and asia. (eds.) mallon, d.p. and kingswood, s.c. iucn, gland, switzerland. pp. 55-62. eissa, s.m., el-ziyadi, s.m. and ibrahim, m.m. 1975. autecology of the jerboa jaculus jaculus inhabiting aljalia desert area, kuwait. j. univ. kuwait (sci.), 2: 111-120. el-baz, f. and al-sarawi, m. (eds.). 2000. atlas of the state of kuwait from satellite images. kuwait foundation for the advancement of sciences, kuwait. farmer, t. 1983. marine life. in kuwait’s natural history: an introduction. (eds.) clayton, d. and pilcher, c. kuwait oil company, kuwait. pp. 192-246. gasperetti, j., harrison, d.l. and büttiker, w. 1985. the carnivora of arabia. fauna saudi arabia, 7: 397-461. gregory, g. 2005. the birds of the state of kuwait. gregory, skegness, uk. hammond, r.l., macasero, w., flores, b., mohammed, o.b., wacher, t. and bruford, m.w. 2001. phylogenetic reanalysis of the saudi gazelle and its implications for conservation. conservation biology, 15: 1123-1133. http://www.alsirhan.com/ p.j. cowan 02 harrison, d.l. and bates, p.j.j. 1991. the mammals of arabia. second edition. harrison zoological museum, sevenoaks, uk. henningsen, t. and constantine, r. 1992. cetaceans in the persian gulf: after the war. sixth annual conference european cetacean society, san remo, italy february 1992. 108-113. kingswood, s.c., cowan, p.j. and clayton, d.a. 2001. kuwait. in antelopes. part 4: north africa, the middle east, and asia. (eds.) mallon, d.p. and kingswood, s.c. iucn, gland, switzerland. pp. 84-87. nithyanandan, m. 2010a. personal commun. nithyanandan, m. 2010b. opportunistic sightings of indo-pacific humpback dolphin, sousa chinensis from kuwait waters with notes on their behaviour. j. of the marine biological association of india, 52(1): 19-23. omar, s.a.s. 2000. vegetation of kuwait. kuwait institute for scientific research, kuwait. omar, s.a.s. and abdulraheem, m.y. 1996. measures to conserve the wildlife of kuwait. in conservation of arabian gazelles. (eds.) greth, a., magin, c. and ancrenaz, m. national commission for wildlife conservation and development, riyadh. 149-158. omar, s.a., al-sdirawi, f., agarwal, v., hamdan, l., al-bakri, d. and al-shuaibi, f. 1986a. criteria for development and management of kuwait’s first national park/nature reserve. vol. 1 inventory and zoning. kuwait institute for scientific research, kuwait. omar, s.a., taha, f.k., al-sdirawi, f. and al-shuaibi, f. 1986b. criteria for development and management of kuwait’s first national park/nature reserve. vol. 2 reintroduction, management and legal land use. kuwait institute for scientific research, kuwait. pope, m. 2012. birding kuwait/kuwait birding. www.hawar-islands.com/blog/14_stub.php, http://kuwaitbirding.blogspot.com. (both last accessed 5 october 2012). pope, m. and zogaris, s. (eds.). 2012. birds of kuwait. kuwait foreign petroleum exploration company, kuwait and biodiversity east, nicosia. shirihai, h. 2006. whales, dolphins and seals. a and c black, london. spencer, s.t. 2009. personal commun. stuart, c. and stuart, t. 2008. a photographic guide to mammals of north africa and the middle east. new holland, london. uncc. 2005. decision concerning follow-up programme for environmental claims awards taken by the governing council of the united nations compensation commission at its 150th meeting, on 8 december 2005. s/ac.26/dec.258. united nations security council, www.uncc.ch/decision/dec_258.pdf. (accessed 5 october 2012). willson, a. 2007. personal commun. received 10 january 2012 accepted 16 june 2013 http://www.hawar-islands.com/ squ journal for science, 2021, 26(1), 58-66 doi:10.24200/squjs.vol26iss1pp58-66 sultan qaboos university 58 delineation of weathered layer using uphole and surface seismic refraction methods in parts of niger delta, nigeria mfoniso aka 1 , okechukwu agbasi 2 *, johnson ibuot 1 and chukwuemeka sampson 2 1 department of physics and astronomy, university of nigeria, nsukka, nigeria; 2 department of physics, michael okpara university of agriculture, umudike, nigeria. *email: agbasi.okechukwu@gmail.com. abstract: uphole and surface seismic refraction surveys were carried out in parts of the niger delta, nigeria, to delineate weathering thickness and velocity associated with aweathered layer. a total of twelve uphole and surface seismic refraction surveyswere shot, computed and analyzed. the velocity of the uphole seismic refraction ranged from 344.8 to 680.3 m/s with a thickness of 5.45 to 13.35 m. surface seismic refraction ranged from 326.6 to 670.2 m/s and 4.30 to 12.0 m, respectively. the average velocity and thickness ranged from 559.6 to 548.0 m/s and 9.43 to 8.63m with differences of 11.6 m/s and 0.83 m respectively. the vw/vs ratios ranged from 0.955 to 1.059. this indicates that the uphole velocity is higher than the surface refraction velocity leading to low vw/vs values. this is a direct experimental proof of a low velocity zone, confirming the weathered nature of the area. the results of both refraction methods are reliable; the differences in surface refraction values are due to shot point offsets. based on these findings, it is recommended that shots for seismic surveys should be located above 15.0 m in the area to delineate the effects associated with weathered layers to ensure that will be competent to withstand engineering structures. keywords: niger delta; surface seismic refraction; uphole and weathered layers. سطحي في أجزاء من دلتا النيجر ، نيجيرياتفكيك طبقة مجففة باستخدام طرق االنكسار الزلزالي ال شويميكا سامسونو مافينيسو أكا، أوكيشوكو أجباسي، جونسون أيبوت لتي تم إجراء مسوحات االنكسار الزلزالي والسطحي في أجزاء من دلتا النيجر ، نيجيريا ، لتحديد سماكة التجوية والسرعة المرتبطة بالطبقة ا:صلخمال . تم تصوير ما مجموعه اثني عشر مسًحا انكساًرا زلزاليًا في قاع البئر والسطح وحسابها وتحليلها. تراوحت سرعة االنكسار تعرضت للعوامل الجوية 4.80م / ث و ..3.0إلى 8.3.3م. تراوح االنكسار الزلزالي السطحي من 58.85إلى 5.45م / ث بسمك 330.8إلى 844.3الزلزالي في قاع البئر من م على 0.38م / ث و 55.3م بفارق 3.38إلى 9.48م / ث ومن 543.0إلى 559.3السرعة والسماكة من على التوالي. تراوح متوسط م 0..5إلى ، وهذا يوضح أن سرعة البئر أعلى من سرعة االنكسار السطحي مما يؤدي إلى انخفاض قيم 5.059إلى 0.955من vw/vsالتوالي. تراوحت نسب vw/vsيل تجريبي مباشر على منطقة سرعة منخفضة ، مما يؤكد الطبيعة المتجوية للمنطقة. ، نتائج كل من طريقتي االنكسار موثوقة ، . هذا دل متًرا 55.0ة فوق واالختالفات في قيم االنكسار السطحي ترجع إلى إزاحة نقطة التسديد. بناًء على هذه النتائج ، يوصى بأن تكون لقطات المسوحات الزلزالي .في المنطقة لتحديد التأثيرات المرتبطة بالطبقات التي تعرضت للعوامل الجوية ، والتي ستكون مؤهلة لتحمل الهياكل الهندسية .دلتا النيجر؛ االنكسار الزلزالي السطحي تمسك طبقات مجوية:مفتاحيةالكلمات ال delineation of weathered layer 59 1. introduction he niger delta region of nigeria comprises weathered layers of sedimentary materials and unconsolidated coastal plain underlain by, from bottom to top, akata, agbada and benin formations [1]. lack of proper understanding of the weathered layers’ characteristics creates problems such as poor data quality and statics in seismic surveys [2]. the weathered layer problems are result of large disparities in the velocities and thicknesses of the weather layers and the underlying strata in seismic data acquisition. small changes in the thickness of weathered layers make large differences in the arrival times of seismic data, which leads to false seismic imaging structures [3]. surface seismic refraction alone has been routinely used to delineate the effects of the weathered layer by previous researchers within the study area [1, 2]. this method has not provided a good definition of the weathered and consolidated layers, which has led to persistent cases of structural failure and environmental hazards encountered within the study area. the current research, therefore, combines both uphole and surface seismic refraction to better delineate the effects of weathered layers by taking advantage of the elevation and lithology of lateral formations coupled with the weathered layers’velocity and thickness. this is because differences in the elevation leads to differences in travel time of the geophone, which have an effect on the positioning of synclines, anticlines and fault formations. therefore, the weathered layer data acquired during seismic prospecting is corrected to take care of these anomalies [4]. the uphole seismic refraction method is the measurement of the near surface seismic velocity by generating a seismic source on or close to the surface, adjacent to a drilled borehole, and recording the travel times of its first arrival at intervals down the hole using a geophone [5]. the uphole technique measures the vertical changes in seismic velocity by placing a source at the top of a borehole and measuring travel times at multiple intervals in the borehole [6]. the p and s wave travel times for each geophone are combined and plotted for the uphole as travel time versus depth curves, respectively. this gives total velocity profiles from which various elastic moduli can be calculated from the borehole, thereby producing a true picture of the subsurface. weathered layers are characterized by high porosity, lack of cementation, low pressure and low bulk modulus, which are responsible for the low velocity encountered in them. comparing measurements obtained by uphole techniques with the surface method, reveals shortfalls in the determination of weathered layers and provides a way of inaccuracy in surveys. this proves that the method is viable for the delineation of the thickness and velocity of the weathered layer. 2. location and geology of study area the area under study is the southern part of the niger delta, nigeria. it is lies between the latitudes 4 0 33 1 and 4 0 45 1 n and from the longitudes 7 0 52 1 to 8 0 02 1 e as shown in figure 1. the sediments of the area are unconsolidated with a high variable thickness throughout the region [7]. the niger delta is characterized by fault-bounded sedimentation, extensive shale structures and weathered layers which are comprised of low velocity zones [8]. it is made up of fresh water swamps and mangrove swamps with relief that increases towards the north. it is composed of three sedimentary formations namely: benin, agbada and akata formations as shown in figure 2. the benin formation consists of coarse-grained sandstones with minor intercalations of shale. the agbada formation consists of alternating sandstones, marine shale and fluviomarine sandstone. the akata formation consists of shale with local interbedding of sands and siltstones [9]. figure 1. (a) map of nigeria showing the niger delta region and the study area (b) niger delta region showing the study area. t mfoniso aka et al. 60 figure 2. stratigraphic chart of the niger delta region, nigeria. 3.theoretical background the seismic refraction method is a geophysical technique used to determine thickness of weathered layers, depth to bedrock, depth of the water table and other seismic velocity boundaries [10]. for the seismic refraction method to be used effectively, subsurface determination, the travel times of the generated wave and the offset distance must be determined. the uphole method of seismic refraction is a seismic field technique which uses receivers on the ground surface and an underground source to obtain information about the subsurface lithology. it requires a drilling rig, pulley, water tank and man power and takes some time for the drilling process. it measures the travel times of primary and secondary waves from the energy source to the receivers. it also provides near surface information at the point of survey about the lithology of lateral formations [11]. in uphole refraction, the survey is performed in a single borehole in that a hole is drilled to the required depth at the survey location and a vibrating source is created to determine the velocity for various soil layers [6]. a single wave source is located on the ground and underground surfaces, a multiple receiver is fixed at known depth and the output is measured as a function of time and depth as shown in figure 3. the exact times of the source being produced and of the energy reaching the receivers need to be determined to analyze the first arrival times. the first arrival of seismic energy is always the direct wave or the refracted wave. the travel time versus depth and uphole survey time relationship are also shown in figures 4 and 5, respectively. the velocity of the weathered layer can be calculated from the reciprocal of the gradient of the direct arrivals. however, the velocity of the second layer can be calculated from the reciprocal of the gradient of refracted arrivals. a good knowledge of the thickness distribution of the layer is often of immense advantage to engineering geophysical studies as well as in seismic refraction data acquisition ventures. hence, the depth (thickness) of the interface can be calculated from the intercept of refracted arrivals along with the velocity [12], as shown in equations 1 and 2, respectively. on the other hand, the surface seismic refraction technique is slightly different from the uphole method as it measures the travel time of p and s seismic waves refracted at the interfaces between surface layers of different velocity. it also provides information about the near surface over the length of the laid spread. it requires the use of hammer and plates, weight drops or small explosive charges as energy sources, geophones as detectors and a seismograph as a recording unit. moreover, it is easy to accomplish, time efficient and more economical compared to uphole refraction. in surface seismic refraction, the survey is performed with a linear array of geophones connected to a seismograph at certain regular interval. seismic energy generated by a source located on the surface, radiating out from the shot point, penetrating into the subsurface is refracted at various interfaces, corresponding to geological boundaries [13]. however, the travel time is measured and plotted with respect to depth. the velocity and thickness are calculated in a similar way as in the case of uphole refraction. (1) delineation of weathered layer 61 (2) where z = the depth of the thickness, t = total time along refracted path, t1 = intercept time,v1 = velocity of the first layer and v2 is the velocity of the second layer. figure 3. direct and refracted waves in two layers. t t slope = 1/ v1 1 1 slope = 1/ v 2 t i x x 2 11 figure 4. travel time versus depth plot. time(s) depth(m) figure 5.uphole survey time depth relationship. 4. materials and method uphole refraction surveys were conducted at twelve different locations within the study area, using a td500 top drive drilling machine, a twelve channels enhancement seismograph and 48 hz geophones. during drilling, a deep hole was drilled at the intersection of the source and receiver line. dynamic charges were laid successively in the hole at 5 m intervals, starting from the greatest depth of 60 m. each charge extended to the surface with the depth written on it. the holes were tamped after each successful shot to prevent loss of energy at the hole during the shooting processes. mfoniso aka et al. 62 twelve geophones were laid on the surface at 5 m intervals from the hole to receive the seismic signal to the seismographs. after explosion, a single geophone was planted close to the hole surface to obtain an uphole pre-trigger time, which is the time elapsed between the shot and the reception by the geophone. surface seismic refraction surveys were also carried out at twelve different locations, covered by five traverses namely a, b, c, d and e, respectively. each of the traverses was 60 m long with an inter-geophone separation distance of 5 m. shot points were recorded on each profile. a twelve-channel enhancement seismograph was used to measure the refracted travel times of p and s waves along with the 48 hz frequency geophones. the seismic wave signals received by the geophones were converted from mechanical to electrical. however, parts of the signals that were undesirable (noise) were attenuated by a frequency filter. the outputs of the arrival times after filtration were displayed on the monitor and selected as shown in figure 6 and 7, respectively. in processing the data, the first break of arrival times were picked for various shots. the first break time is the first pick-up time recognized for any trace which is the parameter of interest in the interpretation of uphole data. the uphole data were normalized by subtracting the pre-trigger time from the first break time. by doing this, the pick-up time of the shot by each geophone was assumed to be the same [14]. moreover, the differences were due to time delays introduced by weathered layers with different lithology sediments. the recorded travel times were then plotted against geophone offset for each uphole point. the parameters of interest, that is, velocity and thickness, were calculated from the slope of travel times versus offset distance as the reciprocal and intersection points for all the shots, which constitutes the data set as shown in table 1. figure 6. surface monitor record in selected area. figure 7. uphole monitor record in selected area. delineation of weathered layer 63 table1. summary of weather red layer velocity and thickness for uphole and surface seismic refraction from each location. lat/long (m) elevation (m) locations uphole velocity vw(m/s) surface velocity vs(m/s) vw / vs (m/s) uphole thickness dw (m) surface thickness ds (m) dw / ds (m) 565568.5754/ 365103.2278 74.2054 a 680.3 670.2 1.015 13.35 12.00 1.113 570539.5123/ 360423.0335 85.2058 b 625.0 620.8 1.007 11.45 10.56 1.084 568627.2088/ 383721.0295 103.2058 c 588.2 568.6 1.034 10.60 10.00 1.060 557803.227/ 380138.3493 62.1058 d 531.0 525.0 1.011 9.90 9.20 1.076 514800.8760/ 386376.0214 24.4717 e 602.4 589.0 1.023 10.80 10.00 1.080 510781.3888/ 381888.5125 38.9448 f 549.5 537.5 1.022 9.25 8.20 1.128 573641.8600/ 381331.4300 0.0000 g 500.0 480.0 1.042 8.80 8.25 1.067 575130.5077/ 383323.1428 40.9058 h 476.1 448.0 1.063 7.25 6.95 1.043 565568.5754/ 365103.2278 74.2054 i 450.0 425.0 1.059 6.10 6.05 1.008 570539.5123/ 360423.0335 85.2058 j 672.0 703.5 0.955 12.95 12.10 1.070 568627.2088/ 383721.0295 103.2058 k 696.0 682.0 1.021 7.30 6.00 1.217 557803.227/ 380138.3493 62.1058 l 344.8 326.6 1.056 5.45 4.30 1.267 averages 559.6 548.0 9.43 8.63 5. results and discussion the results of the analyses are presented in table 1 and figures 8-12. the geophysical properties of interest are the seismic velocity and thickness variation competency of the weathered layer. uphole and surface seismic refraction survey data were collected from twelve different locations and analyzed. both methods show similar variations in velocity with uphole refraction having a slightly higher value for velocity than that of the surface refraction. these changes in velocity are the result of changes in lithology, cementation, fluid content and compaction of the formation, which determine the mechanical properties of the materials through which the seismic waves were propagated. figure 8. velocity and thickness ratio of the study area. the uphole velocity ranges from 344.8 to 680.3 m/s with an average velocity of 559.6 m/s. it is worthnoting that a reliable value of the uphole data is made only from shots taken well within the weatheredlayer. this is due to the fact mfoniso aka et al. 64 that the ray crosses the weathered layer twice, giving a more accurate representation of the ray path in the weathered layer than that of the surface data. for surface seismic refraction, the velocity ranged from 326.6 to 670.2 m/s with an average velocity of 548.0 m/s. figure 9. 2d contour map for surface thickness. figure 10. 2d contour map for uphole thickness. figure 11. 2d contour map for surface velocity. delineation of weathered layer 65 figure 12. 2d contour map for uphole thickness. the marginal variations in surface velocity are indicative of the high degree of homogeneity of the layer and data acquired in the study area. the differences in velocity of uphole and surface seismic refraction were 11.6 m/s, vw /vs ratios and <1.4142 indicating a negative poisson ratio which can occur only in the weathered layer formation [15]. hence, these results can be applied in near surface construction by removing the weathered organic layer of the top soil of the ground until finding vw /vs ratios that are >1.5 [12]. on the other hand, the thicknesses by uphole and surface seismic refraction are fairly uniformly thin in the area, ranging from 5.45 to 13.55 m, 4.30 to 12.0 m with an average of 9.43 and 8.63m, respectively. the disparity in the thickness values could be a result of shot point offset correction which could be caused by delayed arrival or low velocity formation, as observed in the surface seismic refraction which gives lower values than the uphole method. similarly, it is observed that the uphole thickness is slightly higher than that of surface refraction, by 0.83 m. this is because the uphole drilling process changes the lithology in the vicinity of the borehole due to the formation of mud cake, which affects the speed of seismic wave propagation in rock. 6. conclusion uphole and surface seismic refraction methods characterize the weathered layer by taking advantage of the lithology of the lateral formation, which can be used in comparison with drilled rock formations for better delineation of the weathered surface layer within the study area. the analysis is hinged on the determination of seismic velocity and thickness of the weathered layer as well as the elevation. the results show mainly a two-layer model in almost all the interpreted weathered layer data. the weathered layer velocity ranges from 344.8 to 680.3 m/s for uphole and 326.6 to 670.2 m/s for surface seismic refraction. thickness ranges from 5.45 to 13.35 m for uphole and 4.30 to 12.0 m for surface seismic refraction, respectively. comparatively, the average uphole velocity of 559.6 m/s is higher than the average surface velocity of 548.0 m/s. also, the average uphole thickness of 9.43 m is higher than 8.63 m of the surface refraction across twelve locations. however, seismic refraction work within the study area required substantial static corrections, due to high variability of the weathered layer seismic velocity and thickness. hence, uphole refraction is the better alternative. on the other hand, information obtained from both methods on weathered velocity, thickness and elevation will be of interest in determining the location of civil engineering structures and for the determination of the level of bedrock competence in the study area. conflict of interest the authors declare no conflict of interest. acknowledgements the authors are grateful to the department of physics, university of calabar and to akwaibom state rural water and sanitation agency for providing equipment for the field work. references 1. aka, m.u., okeke, f.n., ibout, j.c. and obiora, d.d. geotechnical investigation of near-surface structures using seismic refraction techniques in parts of akwaibom state, southern nigeria. modelling earth systems and environment. 2018, 4, 451-459. mfoniso aka et al. 66 2. ajulo, j.d., eze, c.l. and tamunobereton-ari, i. comparison of surface refraction anduphole refraction methods in the delineation of low velocity layer in parts of niger delta. international journal of scientific and engineering research.2018, 9(10), 572-582. 3. opara, a.i., agoha. c.c., okereke,c.n., adiela, u.p., onwubuariri, c.n, okpono,j.o. and nosiri,o.p.low velocity layer characterization in the niger delta: implications for seismic reflection data quality. journal of the geological society of india. 2017, 90(2), 187-195. 4. ofomola, m.o. uphole seismic refraction survey for low velocity layer determination over yom field, south east niger delta. journal of engineering and applied sciences. 2011, 6(4), 231-236. 5. sheriff, r.e.encyclopaedical dictionaryof exploration geophysics: 3 rd edition. society of exploration geophysicists, tulsa, oklahoma. 1991.p. 376. 6. das, b.m. downhole and crosshole tests: seismic wave evaluation. fundamentals of soil dynamics.1984, 115117. 7. igboekwe, m.u. and ohaegbuchu, h.e. investigation into the weathering layer using up hole method of seismic refraction. journal of geology and mining research. 2011, 3(3), 73-86. 8. osagie, e.o. weathering structure of southwestern niger delta, nigeria. pacific journal of science and technology. 2009, 10(2), 672-679. 9. igbokwe, m.u., gurundha, r.v. and okwueze, e.e. groundwater flow modeling of kwa ibo river watershed, south eastern nigeria.hydroelectric process. 2008, 3(11), 1523-1531. 10. agha, s.o., akpan, a.e. and okwueze, e.e. assessment of the strength of foundation materials in some part of afikpo, nigeria using seismic refraction method,abakaliki. nigerian journal of physics. 2006, 18(1), 33-37. 11. aka, m.u. and umoh, j.a. determination of weathering thickness and velocity of the near surface layers using uphole seismic refraction survey. proceedings of international conference on research, innovations and sustainable development.2013, 4(1), 10-17. 12. atat, j.g., akpabio, g.t., george, n.j. and umoren, e.b. geophysical assessment of elastic constants of top soil using seismic refraction compressional and shear wave velocity in the eastern niger delta, nigeria. international journal of modern applied science.2012, 1(1), 7-19. 13. george, n.j., akpan, a.e., george, a.m. and obot, i.b. determination of elastic properties of the overburden materials in parts of akamkpa, southeastern, nigeria using seismic refraction studies. archives of physics research.2010, 1(2), 58-71. 14. ogagarue, d.o.comparative study of the offset-geophone and down-deep hydrophone seismic refraction survey with application to the niger delta basin, nigeria. pacific journal of science and technology. 2007, 8(1), 49-58. 15. love, a.e.h. a treatise on the mathematical theory of elasticity. cambridge university press.cambridge. 1997, 78-123. received 28 november 2019 accepted 24 november 2020 photovoltaic cells and systems: 13-23 squ journal for science, 16 (2011) © 2011 sultan qaboos university 13 micellar enhanced ultrafiltration for the removal of polycyclic aromatic hydrocarbons (pahs) mixtures in underground contaminated water in oman mohamed aoudia*, amal al-sabahi**, salma al-kindy, mahfoodh al-sheily and fouzul marikar department of chemistry, college of science, sultan qaboos university, p.o. box 36, postal code 123, muscat, sultanate of oman,*email: aoudia@squ.edu.om.**ministry of education, muscat, sultanate of oman. حلقات فً المٌاه الجوفٌة الملوثةمتعددة ال معالجة الهٌدروكربونات األروماتٌةاستخدام طرٌقة الترشٌح الدقٌق المعزز بالمسٌل ل فً عمان فازول مارٌكارو أمل الصبحً، سلمى الكندي، محفوظ الشعٌلً ،محمد أودٌع فً منطقة الحلقات ةالمتعددتٌة اوكربونات األرومفً محاولة لتحلٌل المٌاه الجوفٌة الملوثة بكمٌات من الهٌدر :ملخص تٌة االهٌدروكربونات األروماستخدام الكروماتوجرافٌا الغازٌة المتزامنة مع طٌف الكتلة لتحدٌد تركٌز عناصر تم ،الرستاق ٌد زمن تحصلنا على تحد .الحلقات هٌدروكربونات متعددة 61الموجودة فً خلٌط معٌاري ٌحتوي على الحلقات ةالمتعدد ٌِّنات من تٌة اككل الهٌدروكربونات األروم رٌالمعاٌ ىومنحن االحتجاز المٌاه ثم اسُتـخدمت لمعرفة المركبات الموجودة فً ع الهٌدروكربونات " المستحدثة لمعالجةالّدقٌق المعّزز بوجود "المٌسل ها و قد استعملت طرٌقة الّترشٌحالجوفٌة الملوثة و تركٌز تٌة المتعددة امن الهٌدروكربونات األروم )فً البلٌونواحد جزء ( مائٌة ذات تركٌز منخفضال الحلقات ةددالمتعتٌة ااألروم ٌَة فقد لوحظ أنه تم .(tween 80)المنشط السطحً باستخدامالحلقات فً حدود الكشف األدنى .احتجاز العناصر بصفة كل قل أالمتبقٌة الحلقات ةالمتعددتٌة االهٌدروكربونات األروم ر( كان التركٌز لعناصجزء فً البلٌون 0.01 ±المستعمل ) عند تطبٌق هذه ، بطرٌقة مماثلة .موح بها فً المٌاه الصالحة للشربق التوصٌات المسبهذا ٌطاو جزء فً البلٌون 0.01من الحلقات ةالمتعددتٌة اونات األرومالهٌدروكربوجدنا أّن تركٌز عناصر ، تاق( الرس)التقنٌة لعٌنة من مٌاه جوفٌة ملوثة بالدٌزل .(البنزو)أ( بٌرانول بالنسبة للعنصر األكثر سمٌة )و هو الحد األدنى المقب جزء فً البلٌون0.01 قل منأإلى انخفض abstract: in an attempt to analyze polycyclic aromatic hydrocarbons (pahs) in diesel contaminated underground water in oman (rustaq), gas chromatography-mass spectrometry was first used to determine the different concentrations in a standard mixture containing 16 pahs. retention time and calibration curves were obtained for all aromatic compounds and were used to identify a given analyte as well as its concentration in the contaminated underground water. micellar enhanced ultrafiltration (meuf) was then used to treat standard aqueous solution mohamed aoudia et al. 41 of pahs at low concentration (~ 1 ppb) using an edible nonionic surfactant (tween 80). the totality of the mixture components was completely rejected. within the experimental detection limit ( 0.01 ppb), the residual pah concentrations were less than 0.01 ppb in accord with the allowed concentrations in drinking water. likewise, excellent rejections of pahs in meuf treatment of diesel contaminated underground water at an omani site (rustaq) were observed. the concentration of pahs was reduced to less than 0.01 ppb, the accepted limit for the most toxic member of the pah group (benzo(a)pyrene). keywords: surfactant; micelle; enhanced ultrafiltration; rejection; retention time. 1. introduction ontamination of aquifers by toxic and/or hazardous organic pollutants such as gasoline and diesel fuels is becoming a critical environmental issue in oman where about 14 contaminated sites have been identified by the ministry of regional municipalities and environment. diesel-range petroleum fractions are extremely complex mixtures containing a large number of organic compounds. polynuclear aromatic hydrocarbons (pahs) which may represent about 60% of volume in diesel are of particular concern as they are either known or suspected carcinogens (prak and pritchard, 2002). their removal presents a challenge to scientists and engineers owing to their low solubility in water and their great tendency to adsorb onto soil and sediments. therefore, conventional techniques such as pump and treat have proven to be of limited practical value, and significant efforts are being devoted to the development of efficacious approaches for the remediation of pah contaminated sites. surfactant flushing was recognized as one of the most promising in situ remediation techniques for contaminated underground water, generating a great deal of interest in surfactant-enhanced aquifer remediation (sear) processes (doung et al. 1996; volkering et al. 1995; zhao et al. 2005). overall, sear strategies are commonly characterized by two sequential process stages in situ, namely desorption of the contaminant from the sediment surface and subsequent incorporation of the pollutant into the bulk aqueous phase. ex-situ treatment can then be achieved by a surfactant-based process known as micellar enhanced ultrafiltration (meuf). in this process (baek and yang, 2004; aoudia et al. 2003), a surfactant at concentration higher than its critical micelle concentration (cmc) is added to the aqueous stream containing the dissolved hydrocarbons. the micelle causes the organic compounds to solubulize in the micellar core. the stream is then passed through an ultrafiltration membrane having pore sizes small enough to obstruct the passage of micelles, whereby the hydrocarbon molecules will be rejected. as a result, the permeate contains very low concentration of surfactant and organic solutes. compared to other conventional separation techniques, meuf is a relatively low energy, pressure driven, membrane-based separation process. anisotropic membranes ranging in molecular weight cut-off (mwco) from 5000 to 50,000 daltons are generally used to reject micelles from the surfactant stream. however, one major limitation of meuf is the inevitable leakage of monomer surfactant molecules into the effluent. since the monomers (surfactant molecules dispersed in the bulk phase in equilibrium with micelles) are not significantly rejected by the membrane, the total surfactant concentration in the permeate is equal or slightly less than the surfactant critical micelle concentration (cmc). indeed, this was clearly established by fillipi et al. (1999). one option to tackle this disadvantage is to use biodegradable, non toxic surfactants having extremely low critical micelle concentration. the other option is to use membranes having small mwco (e.g., 500-1000 daltons) to recover the monomers for reuse. the efficiency of meuf in water treatment is mainly determined by the extent of solubilization enhancement of organic pollutants in the presence of surfactant. thus, numerous studies have investigated water solubility enhancement of single pahs in the presence of surfactants above their critical micelle concentrations (zhu and feng, 2003; aoudia and al-shaaili, 2006; hill and ghoshap, 2002; aoudia et al. 2010). this solubility enhancement has been convincingly related to the surfactant and solute structure and to the pah-micelle interaction (prak and pritchard, 2002). however, only a limited number of investigations have been reported c micellar enhanced ultrafiltration 41 where effects of multiple solutes on micellar solubilization of an individual component were examined. thus, solubilization of binary mixtures of hydrocarbon (benzene and hexane) in anionic and nonionic surfactants systems was investigated by chaiko et al. (1984). the authors reported selective solubilization in some mixtures and a synergistic effect on the solubilization of hexane in the presence of small amounts of benzene. these studies showed evidence that the less hydrophobic solute (benzene) partitioned at the micellar core-water interface caused the interfacial tension to decrease, which consequently enabled the micellar core volume to increase, resulting in a greater solubility of the more hydrophobic compound (hexane). solubilization of pyrene, fluoranthrene, and phenantrene from binary and ternary mixtures in nonionic surfactant solutions were investigated by prak and pritchard (2002). the extent of solubilization was shown to be greatly influenced by the pah structure, pah-pah interactions, pah-micelle interaction, and pah packing within the micelle. using such simple binary and ternary pah mixtures, it was clearly demonstrated that the singlecomponent micellar partition coefficient cannot be used to predict the multicomponent micellar solubilization. in the presence of a co-solute, the concentration of organic compounds in micellar solutions may decrease, remain the same, or increase over single component systems depending on the co-solute and the surfactant structures (guha et al. 1998; jacobson and casassa, 1991; underwood et al. 1993). likewise, most meuf studies focused on the removal of single pah solutes from an aqueous stream (dunn et al. 1985; dunn et al. 1987; khandori and schechter, 1990; edwards et al. 1991; hong and yang, 1994; kim et al. 1998; jachowska et al. 2002; syamal and bhattacharya, 1997). very few addressed the rejection of pahs in mixtures (talens-alesson et al. 2001; bielska and szymanowski, 2004; jadhav et al. 2001) and evidence was found that removal of individual pahs and other organic compounds when solubilized in mixtures is not related in a simple manner to their single solute rejection from aqueous systems. for instance, the removal of phenol, p-cresol, xylenol in simultaneous micellar-enhanced ultrafiltration process showed that the highest rejection was observed with the most hydrophobic xylenol (witek et al. 2006). meuf of different phenolic derivatives including metanitrophenol (mnp), catechol (cc), paranitrophenol (pnp), and beta-napthol (bn) in their binary mixture has been studied by purkait et al. (2005). retention of solutes was found to be less in the case of the two-component feed solution compared to the single-component feed solution, suggesting that even for simple multiple systems (binary and ternary), the rejection of each cannot be predicted by its rejection from single-component system. clearly, binary and ternary pah mixtures are not realistic models for their solubilization in diesel contaminated sites where pahs mostly exist in mixtures containing a large number of organic compounds. therefore, the main objective of this work is to investigate the efficiency of meuf in removing pah pollutants from a standard aqueous pah mixture containing sixteen components using an edible surfactant (tween 80). this mixture can be considered to be a realistic model mixture of pah in the diesel-range petroleum fraction, a source of environmental concern in oman due to leakage of underground gasoline station storage tanks in many sites in the sultanate. the concentration of each pah component will be purposely limited to about 1 ppb in order to assess the efficiency of the meuf process in removing such extremely low amounts of organic solutes due to the fact that the recommended total pahs concentration in drinking water supply is ~ 0. 20 ppb whereas that of their most toxic member benzo(a)pyrene is 0.010 ppb (omani standards for unbotteled drinking water no. 245/1993). furthermore, the removal of pahs from diesel contaminated underground water in oman (rustaq) via micellar enhanced ultrafiltration will also be evaluated 2. experiment 2.1 materials surfactant tween 80 (molecular weight of 1310 g/mol, cmc = 0.0013 g/dliter) was purchased from sigma (usa) and used without further modification. standard mixtures of polycyclic aromatic hydrocarbons were purchased from ultra scientific (usa). the concentration of each mixture was 2000 μg/ml in methanol for each single compound. dichloromethane (ch2cl2, 99.5% pure) was supplied by s.d fine-chem ltd (usa). sodium hydroxide pellets (98.0 %) and sodium hypochlorite solution (12% chlorine) were obtained from qualigens and bdh, respectively. sodium sulphate anhydrous, 99 % (purchased from qualigens) was used as mohamed aoudia et al. 41 received. ultrapure water 18.2 m (millliq millipore corporation) was used to prepare standard solutions. the ultrafiltration membrane, supplied by millipore, was regenerated cellulose with mwco 10,000 daltons (type ym). the effective membrane area was 31.65 cm 2 . 2.2 methods ultrafiltration ultrafiltration experiments were performed at room temperature using an amicon 8200 batch stirred cell. the feed volume of the solution was 180 ml and the pressure in the batch cell was maintained at 80 –100 kpa by nitrogen gas. the ultrafiltration process began by placing the membrane with the glossy side facing upwards on the support at the bottom of the cell. the cell was then fixed tightly, filled with distilled water and pressurized with nitrogen gas. the water flux was measured to determine the permeability of the freshly used membrane. the feed solution was prepared by dissolving the required amount of surfactant in deionized water. the feed solution in the cell was stirred with a triangular stirrer at a constant stirring speed. the run was continued until 150 ml of the permeate (80% of the feed volume) had been collected, and the flux was monitored at different times during the entire ultrafiltration experimental run. after each run, the entire cell, stirrer and membrane were washed with distilled water to remove any deposition. the used membrane was rinsed with 0.1 m naoh, 100 ppm naocl for 30 minutes and then flushed with distilled water and stored in 10% ethanol /water (v/v) solution in the refrigerator. the water permeability of the membrane was measured before each run and was found to be similar to that measured for the freshly used membrane. preparation of standard solutions polynuclear aromatic hydrocarbons (pa) standard mixture (1.0 ppb) was prepared from the stock standard mixture (2000 ppm) by two successive dilutions. first, 5.0 l of the stock mixture was diluted to 750.0 ml with de-ionized water (this is called the working solution). then, 75.0 l of working solution was diluted to 1000.0 ml with de-ionized water to obtain the desired final concentration. the concentration of each pah component was then determined accurately from their corresponding calibration curves. liquid-liquid extraction pahs were extracted from aqueous solution by solvent extraction with dichloromethane. two 500 ml volumetric flasks were filled to the mark, one with the contaminated water and the other with the treated water (permeate). each entire sample was poured into a 500 ml separatory funnel and then extracted 5 times in dichloromethane with 10 ml increments each time. sodium sulfate anhydrous was added to the extractant to ensure the complete removal of water molecules. the drying agent was then removed by filtration in preweighed 100 ml round bottomed flasks. after extraction, the two samples were concentrated in a rotary evaporator but not to dryness, then weighed again to the nearest 0.1 mg. the volume left was calculated and adjusted to a final volume of 1 ml. analysis the analysis of the different samples was carried out with a varian cp 3800 gas chromatograph coupled with saturn 2000 ms/ms, a comboipal headspace, and spme autosampler. the column used was a cp sil 8 cb type column (30 m x 0.25 mm x 0.25 df). ultrapure helium was used as a carrier gas. the frit sample traps 5 ml of the sample and then purged it for 12 min. the gc-ms instrument was calibrated with the pah standard mixtures at different concentrations. the column temperature was set at 70 ºc for 1.50 min, then programmed to 200 ºc at 10.0 ºc/min, followed by increase to 270 ºc at a rate of 5.0 ºc/min and finally to 300 ºc at 10.0 ºc/min. the column was then held for 10.0 min with a total run time of 41.50 min. the sample analysis began with injecting of 2l of the extract to micellar enhanced ultrafiltration 41 the splitless injection port of the instrument and then processing the sample with the output referred to the appropriate calibration curve. 3. results and discussion 3.1 micellar enhanced ultrafiltration of a standard aqueous pah mixture gc-ms analysis was carried out for a prepared standard pah mixture containing 16 compounds. the retention time for each component was measured and reported in table 1. standard injections were performed with four different concentrations (1, 2, 5, and 10 ppb) for each pah component in the mixture to obtain different calibration curves. a typical calibration curve is shown in figure 1 for anthracene. peak size/10 6 figure 1. calibration curve for anthracene in the standard pah mixture. the micellar enhanced ultrafiltration process was then applied to treat a synthetic aqueous solution containing the standard pah mixture using an edible nonionic surfactant (tween 80). table 1. retention times rt (in minutes) for the different components in the standard pah mixture. no. compound name rt no. compound name rt 1 naphthalene 7.693 9 benz(a)anthracene 24.648 2 acenaphthylene 11.389 10 chrysene 24.793 3 acenaphthene 11.812 11 benzo(j)fluoranthene 29.025 4 fluorene 13.052 12 benzo(k)fluoranthene 29.025 5 phenenthrene 15.399 13 benzo(a)pyrene 30.099 6 anthracene 15.535 14 indeno(1,2,3-cd)pyrene 33.370 7 fluoranthene 19.063 15 dibenz(a,h)anthracene 33.497 8 pyrene 19.841 16 benzo(ghi)perylene 34.218 mohamed aoudia et al. 41 p e a k a re a obviously, there is a legitimate concern over adding surfactant to the contaminated water at surfactant concentration above its cmc and possibly trading one contaminant (pah) with another (surfactant). to allay this concern, the use of a food additive surfactant may be a relatively safe approach (schick, 1967). gc-ms analysis was carried out to estimate the concentration of each pah solute in permeate, using the appropriate calibration curve. the total ion chromatogram obtained is shown in figure 2 (green), along the total ion chromatogram for a similar non-treated synthetic aqueous standard pahs mixture (red). interestingly, all chromatogram peaks were significantly removed by meuf treatment. this finding strongly suggests that meuf by tween 80 surfactant micelles may be very efficient in removing pah solutes from the aqueous stream. figure 2 was used along the pah calibration curves (determined for standard pah mixture) to estimate the rejection percent (r%) of each pah component in the mixture from the following expression where c0 is the initial concentration of the pah solute in the feed standard mixture and cp is the permeate solute concentration. r% = [1 – (cp/c0)] (1) figure 2. overlaid total ion chromatogram of a non-treated standard pah mixture (red) and a meuf treated standard pah mixture (green) using tween 80 (10 × cmc). the detection limit of our gc-ms system used in this study is  0.010 ppb. thus, we decided to calculate a lower limit for the rejection percent by using a residual solute concentration equal to 0.010 ppb for those pahs that are completely removed. such lower limits are reported in table 2. time (minutes) micellar enhanced ultrafiltration 41 table 2. removal of pahs from a standard mixture of pahs by meuf using tween 80 (10 × cmc). no. compound name co (ppb) cp ± (0.010 ppb) r% 1 naphthalene 0.799 ud* 98.7 2 acenaphthyle 0.810 ud 98.8 3 acenaphthene 0.747 ud 98.7 4 fluorene 0.918 ud 98.9 5 phenenthrene 1.033 ud 99.0 6 anthracene 1.018 ud 99.0 7 fluoranthene 0.902 ud 98.9 8 pyrene 0.890 ud 98.9 9 benz(a)anthracene 0.873 ud 98.9 10 chrysene 0.872 ud 98.9 11 benzo(j)fluoranthene 0.784 ud 98.7 12 benzo(k)fluoranthene 0.844 ud 98.8 13 benzo(a)pyrene 0.842 ud 98.8 14 indeno(1,2,3-cd)pyrene 0.740 ud 98.7 15 benzo(ghi)perylene 0.915 ud 98.9 16 dibenz(a,h)anthracene 0.960 ud 98.9 *ud: undetected as clearly seen in this table, high pahs rejections (> 98.7 %) were obtained for all components, reflecting a significant efficiency of meuf in removing pahs from water. interestingly, because of the relatively low pah concentrations used in our experiments (0.800-1.000 ppb), these high pah rejections show that meuf is very effective at low solute concentration, an evident advantage over conventional separation techniques such as liquid-liquid extraction, adsorption onto activated carbon or distillation. it is worth noting that aromatic hydrocarbons have a great tendency to adsorb at surfaces and as a result, part of the rejection of aromatics may also be attributed to the solute-membrane interaction in addition to their solubility enhancements in the presence of tween 80 micelles. it is well recognized that pahs are very hydrophobic and have a very low solubility in water. for instance, their solubility ranges from 32.5 ppm for naphthalene to 0.14 ppm for pyrene. the recommended total pah concentration in drinking water supply is 0. 20 ppb whereas that of their most toxic member benzo(a)pyrene is 0.010 ppb (omani standards for unbottled drinking water no. 245/1993). it is, therefore, very essential to reduce the concentration of these hazardous chemicals present in contaminated water to 0.20 ppb total concentration as well as to less than 0.010 ppb for the most toxic ones. indeed, in the range of pah concentration investigated in this study (0.800-1.000 ppb), the residual concentration of each solute present in the standard pahs mixture was reduced to  0.010 ppb, in accord with the oman standards for unbottled drinking water. in fact, several water treatment methods can be used in order to go from high contaminant concentrations to low, but few effective methods can go from minute concentrations to nil or extremely low concentration. meuf is one of these methods in which efficiency increases as the contaminant concentration decreases. at this juncture, it is worth noting that in diesel contaminated underground water (a real concern for the sultanate of oman), pahs are generally found in mixtures with a considerable number of organic compounds with different: i) structure, ii) hydophobicity, iii) solubility locus in micelle, and iv) micelle-solute interaction. one may, therefore, assume that hydrocarbons with similar hydrophobicity and/or hydrophilicity could compete for a similar site of solubilization in the micelle. this mutual competitive solubilization within the micelle will certainly influence the solubilization behavior of the pahs (and therefore their rejection by meuf) in real diesel mohamed aoudia et al. 02 contaminated underground water relatively to their solubilization in pah standard mixtures. to elucidate this important issue, we investigated the rejection of pahs from diesed contaminated water in oman (rustaq) by meuf using tween 80 surfactant. 3.2 micellar enhanced ultrafiltration of pahs from diesel contaminated underground water (rustaq) meuf was applied to treat diesel contaminated underground water (rustaq, oman) using tween 80. total ion chromatograms are shown in figure 3. the red chromatogram corresponds to the non treated contaminated water sample, whereas the green chromatogram corresponds to the contaminated underground water sample treated by meuf. all the identified pah components in the non-treated contaminated water are shown in table 3 and their concentrations were estimated from their calibration curves. total ion chromatogram (figures 3) was used along the calibration curve for each identified pah to calculate the displayed percent rejection r% in table 3. figure 3 shows that, within the experimental error, our results indicate a complete removal of the identified pah components from the diesel contaminated water sample, indicating that meuf is also a very effective separation technique in the seldom-investigated extremely low pollutant concentration condition (less than 1 ppb). table 3. removal of identified pah diesel components from contaminated underground water (rustaq) by meuf using tween 80 ( 10 × cmc). no compound name co (ppb) cp ±0.010 ppb r% 1 naphthalene 0.413 ud* 97.6 2 2-methylnaphthalene 0.419 ud 97.6 3 2,6-dinitrotoluene 0.655 ud 97.5 4 dibenzofuran 0.353 ud 97.2 5 azobenzene 0.452 ud 92.3 6 phenanthrene 0.537 ud 98.1 7 anthracene 0.533 ud 98.1 8 carbazole 0.792 ud 98.7 9 flouranthene 0.482 ud 97.9 1 0 pyrene 0.527 ud 98.1 11 benz(a) anthracene 0.741 ud 98.7 12 chrysene 0.733 ud 98.6 13 benzo(b)flouranthene 0.801 ud 98.8 14 benzo(k) fluoranthene 0.801 ud 98.8 15 benzo(a) pyrene 0.814 ud 98.8 16 benzo(ghi) perylene 1.031 ud 99.0 *ud: undetected in treating contaminated water for drinking purpose by meuf, the main criteria (among others) imposed on the choice of surfactant is related to safety and toxicity considerations. as previously discussed, meuf treated water will inevitably contain surfactant at a concentration equal or slightly less than the surfactant cmc (fillipi et al. 1999). the cmc of tween 80 is 1.2 × 10 –5 m (aoudia and al-shuaily, 2006). this corresponds to a permeate surfactant concentration equal to 15.72 mg/l. toxicity and carcinogenecity studies of tween 80 indicated a recommended concentration acceptable for safe human daily consumption not exceeding 25 mg/kg of body weight. an average person can therefore ingest up to 1750 mg of tween 80 daily without any potential danger, thereby the concentration of tween 80 in the treated water is extremely low and safe. micellar enhanced ultrafiltration 04 p e a k a re a 4. conclusion micellar enhanced ultrafiltration (meuf) was applied to the treatment of a standard polycyclic aromatic hydrocarbon (pah) mixture containing 16 components and a diesel contaminated underground water in rustaq (sultanate of oman), using an edible nonionic surfactant (tween 80). gas-chromatography-mass spectrometry (gc-ms) was carried out to analyze solutes in the treated and untreated aqueous stream. within the experimental error ( 0.01 ppb), the totality of pah compounds in the standard mixture were substantially removed (% r > 98.1%), even though their initial concentrations in standard mixture were extremely low (< 1 ppb). this interesting result suggests that toxic solutes can be effectively removed by meuf at extremely low concentration. likewise, the concentration of the totality of pah identified in the diesel contaminated underground water was reduced to less than  0.01 ppb by meuf using tween 80 surfactant, which is below the recommended pah concentration in drinking water supply for the most toxic member of the pah group (benzo(a)pyrene,  0.010 ppb). the permeate surfactant concentration is 15.72 mg/l which corresponds to much less than the recommended maximum safe human daily consumption of 1750 mg of tween 80. figure 3. overlaid total ion chromatogram of a non treated contaminated underground water sample from rustaq (red) and a similar underground water sample treated by meuf (green) using tween 80 (10 × cmc). time (minutes) mohamed aoudia et al. 00 5. acknowledgment we thank sultan qaboos university, sultanate of oman for the financial support (grant: ig/ sci / chem / 03 /03). 6. references aoudia, m., allal, n., djennet, h., toumi, l., 2003. dynamic micellar enhanced ultrafiltration: use of anionic (sds)-nonionic (npe) system to remove cr 3+ at low surfactant concentration, j. membr. sci, 217: 181-192. aoudia, m., al-shaaili. m., 2006. solubilization of naphthalene and pyrene by sodium dodecyl sulfate (sds) and polyoxyethylenesorbitan monooleate (tween 80) mixed micelles, colloids and surfaces a: physicochem. eng. aspects, 287: 44-50. aoudia, m., al-haddabi, b., al-harthi, z., al-rubkhi, a., 2010. sodium lauryl ether sulfate micellization and water solubility towards naphthalene and pyrene: effect of the degree of ethoxylation, j. surfact detergtg, 13: 103-111. baek, k., yang, j.w., 2004. simultaneous removal of chlorinated aromatic hydrocarbons, nitrate and chromate using miceller-enhanced ultrafiltration, chemosphere, 57: 1091-1097. bielska, m., szymanowski, j., 2004. micellar enhanced ultrafiltration of nitrobenzene and 4nitrophenol, j. membr. sci, 243: 273-281. chaiko, m.a., nagarakjan, r., ruckenstein, e., 1984. solubilization of single components and binary mixtures of hydrocarbons in aqueous micellar solutions, j. colloid interface sci, 99: 168-182. doung, r.a., lei, w.g., chen, t.f., lee, c.y., chen, j.h., chang, w.h., 1996. effects of anionic surfactants on sorption and micellar solubilization of monoaromatic compounds. wat. sci. tech, 34: 327334. dunn, r.o., scamehorn, j.f., christian, s.d., 1985. use of micellar enhanced ultrafiltration to remove dissolved organics from aqueous streams, separ. sci. technol. 20: 257. dunn, r.o., scamehorn, j.f., christian, s.d., 1987. concentration polarization effects in the use of micellar enhanced ultrafiltration to remove dissolved organic pollutants from waste water, separ. sci. technol. 22: 763. edwards, d.a., luthy, r.g., liu, z., 1991. solubilization of polycyclic aromatic hydrocarbons in micellar nonionic surfactant solutions, environ. sci. technol, 25: 127. fillipi, b.r., brant, l.w., scamehorn, j.f., christian, s.d., 1999. use of micellar-enhanced ultrafiltration at low surfactant concentrations and with anionic-nomionic surfactant mixtures, j. colloid interface sci, 213: 68-80. guha, s., jaffe, p.r., peters, c.a., 1998. solubilization of pah mixtures by a nonionic surfactant, environ. sci. technol, 32: 930-945. hill, a., ghoshap, s. 2002. micellar solubilization of naphyhalene and phenanthrene fron nonaqueousphase liquids, environ. sci. tehnol. 36: 3901-3907. hong, j.j., yang, s.m., 1994. continuous separation of phenol from aqueous stream using micellar enhanced ultrafiltration (meuf), j. chem. eng. japan, 2 (3): 314. jacobson, a.m., cassassa, e.z., 1991. multicomponent solubilization in aqueous micelles of dodecyl and tetradecyltriammonium bromide: solubilization equilibria, j colloid interface 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influence of nonionic surfactants on bioavailability and biodegradation of polycyclic aromatic hydrocarbons. appl. environ. microbiol, 6: 1699-1705. witek, a., ko, a., kurczewski, b., radzejowska, m., and hatalski, m., 2006. simultaneous removal of phenols and cr3+ using micellar-enhanced ultrafiltration process, desalination, 191: 111116. zhao, b., zhu, l., li, w., chen, b., 2005. solubilization and biodegradation of phenanthrene in mixed anionic-nonionic surfactant solutions, chemosphere, 58: 33-40. zhu, l., feng, s., 2003. synergistic solubilization of polycyclic aromatic hyderocarbons by mixed anionicnonionic surfactants, chemosphere, 53: 459-467. received: 12 december 2010 accepted: 4 june 2011 squ journal for science, 2014, 19(1), 8-14 © 2014 sultan qaboos university 8 synthesis and spectroscopic properties of a fluorosensor for zn 2+ ions nawal k. al-rasbi*, bushra al-wihibi and nada al-nofali department of chemistry, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: nrasbi@squ.edu.om. abstract: the new schiff base ligand l: (e)-n'-(pyridin-2-ylmethylene)acetohydrazide, was synthesized, and its reaction with zn(ii) ions form the complex: [znl2](clo4)2, as confirmed by x-ray crystallography. this complex is stable in polar and non-polar solvents as proven by nmr. a significant enhancement in the fluorescence was observed from l upon coordination to zn(ii) ions over other transition metals such as fe(ii), co(ii), ni(ii), cu(ii), cd(ii) and ag(i). these results suggest that l can be used as a selective flourosensor for the detection of zn(ii) ions. keywords: schiff base; zinc(ii); crystal structure; flourosensor. ي أليونات الزنكطيفتركيب والخصائص الضوئية لحساس ال نوال الراسبي، بشرى الوهيبي و ندى النوفلي قذ دل نكما ثبج مه انخزكيب انبهُري. َ 2(clo4)[znl2] :مزكبانيُواث انشوك نخكُيه أَدراست حفاعهً مع lشيفهيجىذ زكيبحم ح ملخص: في ماوحنطيف انضُئي نهفي اقذ الحظىا سيادة ٌذا َقطبيت. انانزويه انمغىاطيسي انٍيذرَجيىي بأن انمزكب ثابج في انمحانيم انقطبيت َغيز ضُئي كحساص l ج حزشح انهيجىذئانحذيذ، انكُبانج، انىيكم، انىحاص َانفضت. ٌذي انىخا حخكُن مهفهشيت أخزِ زكباثمزكب انشوك مقاروت بم ُواث انشوك. السخكشاف أي صخخصم (، حزكيب بهُري، انطيف انضُئي.iiشيفهيجىذ، سوك)مفتاح الكلمات: 1. introduction n recent years, there was a great interest in schiff base ligands for their unusual photophysical properties. their compounds have potential significance in light emitting diodes [1], as models in bioinorganic chemistry [2] and as chemical sensors [3]. the schiff base ligands with polydentate donors such as imine are known for their selective detection of metal ions and other anions [4]. many research groups have designed extensive schiff base derivatives by incorporating fluorescent units. sensing of transition metal ions has become an important goal in chemistry because of their important biological and environmental roles [5]. zinc is an essential co-factor in many biological processes like brain function and pathology [6]. the main challenge in the design of an effective fluorescent probe for zn 2+ is to create a probe that responds selectively to zn 2+ over other metal ions such as ca 2+ , mg 2+ and cd 2+ [7]. a variety of zn 2+ sensors have been reported based on quinoline, [8] coumarin [9] and schiff base ligands [7]. i mailto:nrasbi@squ.edu.om synthesis and spectroscopic properties of a fluorosensor for zn 2+ ions 9 in this paper, we describe the synthesis and spectroscopic characterization of a tridentate schiff base ligand l (scheme 1). the ligand was designed by incorporating pyridyl and acetyl groups that have a strong affinity for metal ions. the ligand is poorly fluorescent due to excited state electron transfer in the c=n bond. upon complexation with metal ions, the structure’s rigidity inhibits the excited-state electron transfer process, and hence the fluorescence is produced. our work also includes an investigation of the selectivity of l to zn 2+ ions by exploring the fluorescence properties in solution. n h n o ph oh tbu but n n h n me o l sl scheme 1. a presentation of the schiff base ligand l used in this work. 2. results and discussion 2.1 synthesis and crystal structure studies the schiff base ligand used, l, was generated by the condensation reaction of stoichiometric,,amounts,,of, acetic hydrazide ,with picolinaldehyde according to the standard method used for the synthesis of schiff base ligands [10]. all of the spectroscopic and analytical data were consistent with the correct formulation of the ligand. the ir spectrum of l showed a strong imine absorption, vc=n at 1627 cm –1 . the reaction of l with zn(clo4)2 in 1:2 molar ratio afforded colorless crystals with the general empirical formula [znl2](clo4)2 by elemental analysis (scheme 2). the x-ray structure showed the simple mononuclear zn(ii) complex: [znl2](clo4)2∙meoh (znl) that is presented in figure 1 and table 1. initially, we thought that znl may adapt a dimeric structure similar to other related schiff base systems such as [zn2sl2(ch3co2)(c2h6oh)] reported by peng et al.[11] because the acetyl oxygen atoms are not basic enough to coordinate to two metal centers. n h o o me h n n o me h n etoh + h2n l + h2o n n o me h n n n o me n h n zn 2l + zn(no3)2.2h2o meoh znl scheme 2. schematic presentation of the synthetic routes for l and its zn(ii) complex znl. nawal k. al-rasbi et al 10 however, the zn(ii) ion was found to be in a 6-coordinate n4o2 environment, coordinating to two ligands in a meridional fashion. the bond distances to the zn(ii) ion were comparable to related zn(ii) compounds. the zn–n bonds to the imine donor (2.073(4) å) were slightly shorter than to the pyridyl donor (2.153(4) å). the zn–oac bond distances were the longest, 2.164(3) and 2.222(3) å. the angle between the two zn(nno)2 planes was 92.78°. the crystal packing for znl exhibited intermolecular interactions between the alternating pyridine rings forming parallel chains of alternating molecules. the remaining perchlorate ions and methanol molecules exhibited a combination of o···hc and nh···o hydrogen contacts within the molecules (figure 1 (b)). these have very important consequences on the emission properties of the complex. (a) (b) figure 1. (a) view of the complex cation of znl. the counter ions and solvent molecules are omitted for clarity. (b) the crystal packing of znl, showing the packing of molecules into parallel chains by hydrogen contacts of o···hc in the range 2.448–3.090 å and nh···o in the range of 2.482–2.527 å. table 1. bond lengths [å] and angles [] for znl. zn(1)-n(17) 2.071(4) zn(1)-n(7) 2.077(4) zn(1)-n(1) 2.148(4) zn(1)-n(12) 2.158(4) zn(1)-o(21) 2.164(3) zn(1)-o(11) 2.222(3) n(17)-zn(1)-n(7) 165.89(15) n(17)-zn(1)-n(1) 118.00(15) n(7)-zn(1)-n(1) 76.05(15) n(17)-zn(1)-n(12) 76.35(15) n(7)-zn(1)-n(12) 99.95(14) n(1)-zn(1)-n(12) 103.06(14) o(21)-zn(1)-o(11) 92.80(12) n(7)-zn(1)-o(21) 108.85(14) n(17)-zn(1)-o(11) 92.79(13) n(1)-zn(1)-o(21) 88.63(13) n(12)-zn(1)-o(21) 150.82(14) table 2. crystallographic data for znl. formula c17h22n6cl2o11zn formula weight 622.68 t (k) 100(2) k crystal system triclinic, p–1 a (å) 9.6126(11) b (å) 11.8491(13) c (å) 12.7991(15)  (°) 112.255(4)  (°) 111.853(4)  (°) 96.455(4) v(å 3 ), z 1196.5(2), 2 dcalc/ (mm -1) 1.728/ 1.321 crystal size (mm) 0.16 x 0.15 x 0.15 reflections collected 15386 data / restraints/ parameters 5857 / 0 / 283 goodness-of-fit on f2 1.050 final r indices r1 = 0.0725 wr2 = 0.1886 largest diff. peak and hole (e.å -3 ) 2.012 and -1.526 synthesis and spectroscopic properties of a fluorosensor for zn 2+ ions 11 2.2 1 h nmr studies the 1 h nmr spectra of re-dissolved crystals of zn(ii) complex znl, were investigated in cdcl3 and dmso-d6 (figure 2). the spectra exhibited the number of peaks expected for the molecular structure and confirmed the stability of znl in solution. in general, it was found that the complex znl exhibits a 2-fold symmetry, such that the two coordinating ligands are equivalent to one another. it was noticed in the 1 h nmr spectrum of znl in dmso-d6, that the n–h and ch3 signals are strongly downfield shifted to 11.50 and 3.40 ppm indicating that these protons are under a rich electronic zone via h-bonding with dmso molecules. the pyridine and ch=n protons are slightly down-field shifted when compared to those in cdcl3. these results suggest that the pyridine and ch=n protons of znl are under the shielding zone of -electrons of a conjugated system due to aggregation of molecules in non-polar solvents via – stacking interactions as referred from the crystal packing [12]. figure 2. the 1 hnmr spectra of re-dissolved crystals of znl a) in cdcl3 and b) dmso-d6 at ambient temperature. 2.3 luminescence properties the uv/vis absorption spectra of the ligand and its zn(ii) complex are shown in figure 3a. the ligand exhibited strong absorption in the uv region at 304 nm ( ~38,100 m –1 cm –1 ) and a shoulder at ca. 318 nm. these transitions could be attributed to –* transitions of the aromatic rings and the imine bonds present in the molecules [13]. upon complexation to zn(ii) ion, a distinct red shift of the high energetic band was observed at 313 nm ( ~47,500 m –1 cm –1 ). the band was highly intense and unresolved. however, a new weak band observed at 363 nm ( ~13,000 m –1 cm –1 ) contributed to the formation of the lowest-energy excited state of ligand centered –* transitions in l–zn(ii) bonds [14]. the ligand, l has no emissive chromophores and hence, is not luminescent. excitation of the complex znl in dcm at 363 nm, exhibited an enhanced emission centered at 468 nm (figure 3b). excitation at the highest energy absorption band, 313 nm, revealed very weak emission. normally in the presence of coordinating zn(ii) ions, the fluorescence of a ligand is enhanced by preventing the photo induced electron transfer (pet) process in the ligand [15]. this explains the intense emission of the complex at an excitation wavelength of 368 nm as this absorption is based on l–zn(ii) transition. in switching to more polar solvents such as thf, the effect of polarity is much more pronounced in the emission of znl (figure 3b). the emission spectrum showed an intense band with a large red-shift to 480 nm with respect to those in dcm. the 1 h nmr results suggest that znl molecules can form aggregates in a less polar dcm solution. in switching to a polar thf solution, the molecules of znl are under the influence of nawal k. al-rasbi et al 12 h-bonding with thf molecules. this would cause random aggregates of znl in thf, and hence the emission energy of znl is red shifted [16-17]. figure 3. (a) the absorption spectra of l (dashed line) and znl (solid line) in dcm at rt. (b) emission (solid line) and excitation (dashed line) spectra of znl in 1.0 x 10 –5 m dcm (black) and thf (red) solutions at rt. the selectivity of l towards zn(ii) ions was also investigated by the titration of the solution of l in dcm with a methanoic solution of zn(clo4)2 (0–1.5 equiv.). the bands of these spectra showed systematic enhancement in fluorescence which was very similar to that of znl complex after the addition of few equivalents of zn(ii) ions. the maximum fluorescence intensity was observed at a molar stoichiometry of 1:2 between zn(ii) ions and l. this is the point where all l molecules coordinate to zn(ii) ions to form the complex znl (1:2 molar ratio). further addition of zn(ii) ions revealed no enhanced emission. however, in switching to a polar thf solvent, addition of zn(ii) to l enhanced the emission in a similar manner to the complex znl, as the emission was red-shifted. the emission behavior of l upon titration with other d-metals such as fe(ii), co(ii), ni(ii) and cu(ii) was also investigated. the emission of their complexes did not enhance the emission of l. these metals exhibited electronic d-d transitions that caused the quenching of emission in their complexes. for zn(ii), the metal has a fully filled d-shell, d 10 and exhibits no such d-d transitions. instead, coordination to a zn(ii) center would enhance emission from the coordinating ligand. however, the emission of l was also studied with other d 10 metals such as cd(ii) and ag(i). these metals failed to induce the fluorescence from l, probably because these metals failed to form a suitable coordination environment around l to inhibit the pet process for their larger ionic radii. the high selectivity of l towards zn(ii) ions over other metal ions suggests that the ligand l can act as a fluorosensor for zn(ii). 3. conclusions the synthesis and crystal structure of the zn(ii) complex with a new tridentate schiff base ligand 'l' has been investigated and fully characterized. the structure of the complex: [znl2](clo4)2 is retained in polar and non-polar solvents as confirmed by nmr. it has been found that the emission of l is induced upon coordination to zn(ii) over other metal ions such as fe(ii), co(ii), ni(ii), cu(ii), cd(ii) and ag(i). these results suggest that l can be used as a selective fluorsensor for the detection of zn(ii) ions. 4. experimental 4.1 general details all organic reagents, metal salts and solvents were purchased from sigma-aldrich and were used as received without further purification. infrared spectra were recorded as kbr pellets on a perkin elmer ft-ir spectrometer bx in the range of 4000-400 cm –1 . electrospray (es) mass spectra were recorded on a vg autospec magnetic sector instrument. proton magnetic resonance ( 1 h-nmr) spectra were recorded using a 500 mhz avance bruker nmr spectrometer. chemical shifts (δppm) were recorded in parts per million 0 0.1 0.2 0.3 0.4 0.5 280 330 380 430 a b s o rb a n c e wavelength/nm (a) 0 100 200 300 400 270 370 470 570 f lu o re s c e n c e i n te n s it y wavelength/nm (b) synthesis and spectroscopic properties of a fluorosensor for zn 2+ ions 13 (ppm) downfield from tms (assigned as zero ppm). elemental analyses for carbon, hydrogen and nitrogen were performed using a perkin elmer 2400 chns/ o series ii elemental analyser. 4.2 preparation of ligand the ligand l was prepared according to the general method for preparation of schiff bases. a solution of pyridine-2-aldehyde (1.1 g; 10 mmol) in etoh (20 ml) was added dropwise to a solution of acetic hydrazide (0.65 g; 10 mmol) in etoh (20 ml) and refluxed at 85 c for four hours. the reaction mixture was concentrated under vacuum and cooled in the fridge to yield 1.40 g (86 %) of l. es-ms: m/z= 164.0 [m + ] 186.0 [na+m + ]. ir (kbr, cm -1 ) 3450, 3010, 2944, 1627, 1394-1600. 1 h nmr (cdcl3): 10.20 (1h, s, nh), 8.61 (1h, d, ch), 8.05 (1h, s, py h 6 ), 7.93 (1h, d, py h 3 ), 7.73 (1h, t, py h 5 ), 7.28 (1h, t, py h 4 ) and 2.40 (3h, s, me). c8h9n3o (163.01): calcd. c 58.88, h 5.56, n 25.75; found c 58.94, h 5.62, n 25.69%. 4.3 preparation of [znl2](clo4)2meoh, znl to a solution of l (0.27 g; 1.66 mmol) in meoh (10 ml) was added dropwise a solution of zn(clo4)2 (0.22 g; 0.83 mmol) dissolved in meoh (5 ml) at room temperature. the yellowish solution which formed was left for the solvent to slowly evaporate off. colorless needles formed within few days. yield 88%. esms: m/z 393.77. ir (kbr, cm -1 ) 1623. 1 h nmr (dmso-d6): 11.50 (1h, s, nh), 8.58 (1h, s, ch), 8.14 (1h, d, j= 9 hz py h 6 ), 7.80-7.93 (2h, m, py h 3 ,h 5 ), 7.35 (1h, dt, py h 4 ) and 3.28 (3h, s, me). znc16h18n6o10cl2 (590.64): calcd. c 32.54, h 3.07, n 14.23; found c 32.63, h 3.11, n 14.21%. 4.4 spectrofluorimetric measurements uv-visible spectra were recorded on a varian cary 50 conc uv-visible spectrophotometer in the range 250-800 nm. quartz cuvettes of 1 cm path length were used and solvent background corrections were applied. steady state luminescence spectra were recorded on a perkin-elmer ls50b fluorimeter. solution spectra were measured using 1 cm quartz cuvettes. the spectrofluorimetric titrations were performed as follows. stock solutions of the ligands (ca. 1.0 x 10 −5 m) were prepared by dissolving an appropriate amount of the ligand in a 50 ml volumetric flask and diluting it to the mark with dcm or thf. titrations were carried out by the addition of µl amounts of standard solutions of zn(clo4)2, fe(clo4)2, co(clo4)2, ni(clo4)2, cu(clo4)2, cd(so4)2 and agbf4 in meoh to a solution of l in dcm or thf. 4.5 crystallography single crystals of the complex were obtained as detailed above. the crystal structure of znl, [znl2](clo4)2∙meoh, was carried out at the university of sheffield. data was collected at 100 k, using a bruker apex-ii ccd diffractometer equipped with mo-kα radiation. absorption corrections were applied in each case using sadabs [18]. the structures were solved by direct methods and refined by full matrix least squares methods on f 2 using shelxl-97 [19,20]. the hydrogen atoms were generated geometrically with isotropic thermal parameters. some oxygen atoms in perchlorates were disordered and refined with isotropic displacement parameters. the meoh molecule was refined with isotropic displacement parameters to keep the refinement stable. crystallography data (excluding the structure factors) for the reported structure have been deposited with the cambridge crystallographic data centre ccdc 943597. 5. acknowledgements we would like to thank mrs. susan bradshaw (university of sheffield, uk) for recording the 1 hnmr spectra of the compounds. we also thank sultan qaboos university for financial support. references 1. yang, w., schmider, h., wu, q., zhang, y.-s and wang, s. syntheses, structures, and fluxionality of blue luminescent zinc(ii) complexes:  zn(2,2’,2’’-tpa)cl2, zn(2,2’,2’’-tpa)2(o2ccf3)2, and zn(2,2’,3’’-tpa)4(o2ccf3)2 (tpa = tripyridylamine). j. am. chem. soc. 2000, 39, 2397-2404. 2. lippard, s.j. and berg, j.m., principles of bioinorganic chemistry, university science books, mill valley, ca, usa, 1994. http://pubs.acs.org/doi/abs/10.1021/ic991436m?prevsearch=yang%252c%2bschmider%2bzhang%2bwang&searchhistorykey= http://pubs.acs.org/doi/abs/10.1021/ic991436m?prevsearch=yang%252c%2bschmider%2bzhang%2bwang&searchhistorykey= http://pubs.acs.org/doi/abs/10.1021/ic991436m?prevsearch=yang%252c%2bschmider%2bzhang%2bwang&searchhistorykey= nawal k. al-rasbi et al 14 3. fenton, d.e., metallobiosites and their synthetic analogues a belief in synergism tilden lecture. chem. soc. rev., 1999, 28, 159-168. 4. pedras, b., santos, h.m., fernandes, l., covelo, b., tamayo, a., bertolo, e., capelo, j. l., aviles, t. and lodeiro, c. sensing metal ions with two new azomethine–thiophene pincer ligands (nsn): fluorescence and maldi-tof-ms applications. inorg. chem. commun., 2007, 10, 925-929. 5. paul, b.k., kar, s. and guchhait, n. a schiff base-derived new model compound for 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chem., 2005, 44, 2018-2030. 10. schlecker, w., huth, a., ottow, e. and mulzer, j. regioselective metalation of pyridinyl carbamates and pyridine carboxamides with (2,2,6,6-tetramethylpiperidino)magnesium chloride. j. org. chem., 1995, 60, 8414-8416. 11. peng, x., tang, x., qin, w., dou, w., guo, y., zheng, j. liu, w. and wang, d. aroyl hydrazone derivative as fluorescent sensor for highly selective recognition of zn 2+ ions: syntheses, characterization, crystal structures and spectroscopic properties. dalton trans., 2011, 40, 5271-5277. 12. consiglio, g., failla, s., finocchiaro, p., oliveri, i.p. and bella, s.d. aggregation properties of bis(salicylaldiminato)zinc(ii) schiff-base complexes and their lewis acidic character. dalton trans. 2012, 41, 387-395. 13. seixas de melo, j., pina, j., pina, f., lodeiro, c., parola a.j., lima, j.c. albelda, m.t., clares, m.p., garcia-españa, e. and soriano, c. transport-limited recombination of photo carriers in dyesensitized nanocrystalline tio2 solar cells. j. phys. chem. a, 2003, 107, 11307-11315. 14. al-rasbi, n.k., sabatini, c., barigelletti, f. and ward, m.d., red-shifted luminescence from naphthalene-containing ligands due to -stacking in self-assembled coordination cages. dalton trans., 2006, 4769-4772. 15. konar, s., jana, a., das, k., ray, s., chatterjee, s., golen, j.a., rheingold a.l. and aar, s.k. synthesis, crystal structure, spectroscopic and photoluminescence studies of manganese(ii), cobalt(ii), cadmium(ii), zinc(ii) and copper(ii) complexes with a pyrazole derived schiff base ligand. polyhed., 2011, 30, 2801-2808. 16. lui ma, c.t. and maclachlan, m.j. twelve-connected net with face-centered cubic topology: a coordination polymer based on [cu12(μ4-sch3)6] 6+ clusters and cn − linkers. angew. chem. int. ed., 2005, 44, 4175-4178. 17. cai, y.b., zhan, j., hai, y. and zhang, j.l. molecular assembly directed by metal–aromatic interactions: control of the aggregation and photophysical properties of zn-salen complexes by aromatic mercuration. chem.a eur. j., 2012, 18, 4242-4249. 18. sheldrick, g.m. sadabs: a program for absorption correction with the siemens smart system. university of göttingen, göttingen, germany, 1996. 19. sheldrick, g.m. shelxs-97: a program for solution of crystal structures. university of göttingen, göttingen, germany, 1997. 20. sheldrick, g.m. shelxs-97: a program for refinement of crystal structures. university of göttingen, göttingen, germany, 1997. received 10 february 2014 accepted 3 april 2014 http://pubs.acs.org/action/dosearch?action=search&author=lim%2c+n+c&qssearcharea=author http://pubs.acs.org/action/dosearch?action=search&author=schuster%2c+j+v&qssearcharea=author http://pubs.acs.org/action/dosearch?action=search&author=porto%2c+m+c&qssearcharea=author http://pubs.acs.org/action/dosearch?action=search&author=tanudra%2c+m+a&qssearcharea=author http://pubs.acs.org/action/dosearch?action=search&author=yao%2c+l&qssearcharea=author http://pubs.acs.org/action/dosearch?action=search&author=freake%2c+h+c&qssearcharea=author http://pubs.acs.org/action/dosearch?action=search&author=br%c3%bcckner%2c+c&qssearcharea=author http://pubs.acs.org/doi/abs/10.1021/ic048905r http://pubs.acs.org/doi/abs/10.1021/ic048905r http://www.sciencedirect.com/science/article/pii/s0277538711005006 http://www.sciencedirect.com/science/article/pii/s0277538711005006 http://www.sciencedirect.com/science/article/pii/s0277538711005006 numerical experience with damped squ journal for science, 17 (1) (2012) 111 © 2012 sultan qaboos university 1 numerical experience with damped quasi-newton optimization methods when the objective function is quadratic mehiddin al-baali* and anton purnama** department of mathematics and statistics, sultan qaboos university, muscat, oman, *email: albaali@squ.edu.om and **email: antonp@squ.edu.om. abstract: a class of damped quasi-newton methods for nonlinear optimization has recently been proposed by extending the damped-technique of powell for the bfgs method to the broyden family of quasi-newton methods. it has been shown that this damped class has the global and superlinear convergence property that a restricted class of 'undamped' methods has for convex objective functions in unconstrained optimization. to test this result, we applied several members of the broyden family and their corresponding damped methods to a simple quadratic function and observed several useful features of the damped-technique. these observations and other numerical experiences are described in this paper. the important role of the damped-technique is shown not only for enforcing the above convergence property, but also for improving the performance of efficient, inefficient and divergent undamped methods substantially (significantly in the latter case). thus, some appropriate ways for employing the damped-technique are suggested. keywords: nonlinear optimization, quasi-newton methods, damped-technique, line search framework. في األمثليات عندما تكون دالة الهدف تربيعيةنيوتن متماثلة تخامد مع ةعددي ةخبر أنتون برناماو محي الدين البعلي باول إلى حزمة قنيةت رويطمثليات غير الخطية بتفي األ لمتماثلة نيوتنتخامدة ماقتراح حزمة طرق اتم حديث :خصمل التي تمتلكها الفائق أن هذه الحزمة المتخامدة تمتلك خاصية التقارب الخطي إثبات. وقد تم متماثلة نيوتنبرويدن لطرق ، لهدف محدبة. الختبار هذه النتيجةعندما تكون دوال ا المقيدة ة للطرق غير المتخامدة في األمثليات غيرحددالحزمة الم من عناصر حزمة برويدن وما يقابلها من الطرق المتخامدة على دالة تربيعية بسيطة والحظنا عددا من الصفات ا طبقنا عدد تم توضيح حيثالعددية األخرى في هذه الورقة. بارجتغيرها من الهذه المالحظات وشرح تم وقد التخامد. لتقنية الجيدة ، بل لتحسين سير الطرق السريعة والبطيئة وغير على التقارب فحسبمن أجل الحصول التخامد ليس لتقنيةالدور الرئيسي التخامد. قنيةتراح طرق مناسبة الستخدام تمتميز في الحالة األخيرة(. لذا تم اقوالمتقاربة بشكل كبير ) mehiddin al-baali and anton purnama 2 1. introduction onsider iterative quasi-newton methods with line search for solving the unconstrained optimization problem min ( ) ,f x where : n f r r is a smooth function. on each iteration k of these methods, an estimate of a solution kx and a positive definite hessian approximation kb are used to obtain a new estimate 1.kx  then, kb is updated to a new hessian approximation 1kb  by using a member of the broyden family in terms of the differences in points 1=k k ks x x  and gradients 1= ,k k ky g g  where kg denotes the gradient ( ).kf x this family consists of efficient, inefficient and divergent methods. the former two types of methods are usually defined sufficiently closely to the well known bfgs and dfp methods, respectively, while the latter type is defined sufficiently remotely away from these methods. for further details see for instance (fletcher, 1987; dennis and schnabel, 1996; nocedal and wright, 1999). al-baali and grandinetti (2009) show that the performance of the bfgs method can be improved if ky is modified before updating to the damped-technique ˆ = (1 ) ,k k k k k ky y b s   (1) where k is a parameter chosen appropriately and sufficiently large in the interval (0,1] . the resulting damped (d)-bfgs method is proposed by powell (1978) for the lagrangian function in constrained optimization and used many times with only values of 0.8k  , see for example (fletcher, 1987; nocedal and wright, 1999). the aim of this paper is to show that small values of k can be used to improve the behaviour of not only the bfgs method, but also all members of the broyden family of methods for unconstrained optimization. to illustrate this possibility, we applied several members of this family and their corresponding damped methods to a simple quadratic function of two variables, using certain initial point 1x and hessian approximation 1.b for particular choices of ,k it is shown that many damped methods work substantially better than the bfgs method. the analysis is organized in the following way. section 2 describes the broyden and d-broyden classes of methods, section 3 provides some numerical results and section 4 concludes the paper. 2. damped quasi-newton methods we now briefly describe the broyden and d-broyden classes of methods. on each iteration of these methods, the current point kx and a symmetric and positive-definite hessian approximation kb are available, given initially 1x and 1.b using these available data, a new point 1 1 =k k k k kx x b g    is calculated. here, k denotes a steplength which is usually chosen such that the wolfe conditions 1 0 t k k k kf f s g   (2) and 1(1 ) , t t k k k ks y s g   (3) where kf denotes ( ),kf x 0 (0, 0.5)  and 1 0( ,1),  are satisfied. then kb is updated to a new hessian approximation 1 ˆ ˆ ˆ ˆ= ( ) , ˆ t t t tk k k k k k k k k k k k k kt t k k k k k b s s b y y b b s b s v v s b s s y     (4) c numerical experience with damped quasi-newton methods 3 where k is a parameter, ˆ ˆ = ˆ k k k k t t k k k k k y b s v s y s b s  (5) and ˆky is defined by (1) for a suitable value of .k this class of damped updates is reduced to the broyden family if ˆ =k ky y (which corresponds to = 1k ). thus, if this equality holds for all iterations we obtain the broyden family of methods. otherwise, we obtain the d-broyden class of methods. in particular, the choices = 0k and = 1k yield the d-bfgs and d-dfp methods which correspond (for these choices and = 1k ) to the well known bfgs and dfp methods, respectively. although the restricted class of quasi-newton methods (defined for = 1k and < < 1,k k  where k is a certain negative value sufficiently close to zero) converges globally and q-superlinearly for convex functions, the performance of the class becomes worse as k increases. in general, the bfgs method is robust and the dfp method is inefficient, though the former method usually suffers from large eigenvalues of kb , see in particular (powell, 1986; byrd et al., 1992). therefore several modification techniques have been introduced to the bfgs method, see for example (yabe et al., 2007; gratton and toint, 2010). here, we test the d-broyden class of methods which is an extension of the d-bfgs update of powell (1978) in the augmented lagrangian and sqp methods for constrained optimization. for details on the latter case, see for instance (fletcher, 1987; nocedal and wright, 1999). this damped method was applied to unconstrained optimization problems for the first time by al-baali (2003) who considered 2 2 3 3 , < 1 1 = , > 1 1 1, otherwise , k k k k k                    (6) where = t k k k t k k k s y s b s  (7) and 2 3, 0.   if 3 ( 1) ,k c   where > 0,c then the bound k c  is guaranteed. this formula with damped-technique (1) ensures that ˆ t k ks y is sufficiently close to either the curvature t k ks y or approximate curvature t k k ks b s if k is sufficiently large or small, respectively. another useful feature of formula (6) is that ˆtk ks y remains sufficiently positive even when 0 t k ks y  (which may occur if the wolfe condition (3) is not enforced on ks ). we also observe that formula (6) is reduced to the choice of powell (1978) if 2 = 0.8 and 3 = .  for certain choices of these parameters, al-baali (2004) introduced formula (6) to the limited memory l-bfgs method of nocedal (1980) and reported encouraging numerical results in certain cases. other encouraging results for the d-bfgs method with formula (6) on unconstrained optimization have been reported by al-baali and grandinetti (2009). the authors also show that this formula works better than other modified bfgs formulae which modify ky to the form 1 1ˆ = [6( ) 3( ) ] , t k k k k k k k ky y f f g g s u     (8) for certain vectors , see for example (yabe et al., 2007) and the references therein. because this form is reduced to ky when the objective function is quadratic, the proposed modified bfgs methods maintain the difficulty mehiddin al-baali and anton purnama 4 associated with the bfgs method in this case. due to this feature and the above observations, we consider only formula (6) here and state the following investigations. in practice, we observed that formula (6) with 2 sufficiently close to 0.6 seems to work well in some cases, but generally worsens the performance of the d-bfgs method as 2 decreases. this observation illustrates that large values of 2 such as 0.8 or 0.9 are usually recommended when the d-bfgs update is employed in methods for constrained optimization, see for example (fletcher, 1987; nocedal and wright, 1999; powell, 1978, 2009). we will argue below that small values of k are also useful in some cases, although large values of k yield small changes in .ky al-baali (2011) extends the global convergence property of the restricted broyden class of methods to that of d-broyden, assuming that 21 2 1 (1 ) ,k k kk          (9) where 1 2, (0,1),   1 1 = , = , = 1 t t k k k k k k k k kt t k k k k k k s b s y b y b h b h s y s y    (10) and (0,1]k  is given by = . (1 ) k k k k kb      (11) we observe that < 0,k and that condition (9) hold for the choice = 0k (the bfgs option) and any values of 1 and 2. thus, this condition adds another useful feature to the bfgs method over the other methods. although prior to this result k was never chosen outside the interval ( ,1],k except for a well defined sr1 method (see for example fletcher, 1987), condition (9) allows any real number k for sufficiently small values of k (or k ). recently, for further restrictions on ,k al-baali (2011) extends the above superlinear convergence property to the damped methods and shows that ( 1) 0k k    and 2 ( 1) 0 ,k k kb h   (12) noting that = 1/ .k kb although this result suggests using a small value of < 1k when either term 1k  or 1k kb h  is sufficiently remotely away from zero, we use this value only when both terms satisfy the latter condition. this suggestion is due to the fact that the broyden family of updates is reduced to a single update if = 1k kb h (see for example al-baali, 1993). therefore, since the first limit in (12) yields formula (6) (see al-baali, 1993), we consider employing it only when the value of the product k kb h is sufficiently larger than one so that we obtain 2 2 4 3 3 4 , < min(1 , ) 1 1 = , 1 < < 1 1 1, otherwise , k k k k k k k h h                        (13) numerical experience with damped quasi-newton methods 5 where 4 0.  this modified formula ensures that the value of k or its modification lies in 2 3[1 , 1 ]   when 4> 1 .k kb h  if the value of 4 = 0 is used, then the damped-technique is always employed, except when the broyden family is reduced to a single update. in particular, this value with 2 = 0.8 and 3 =  reduces formula (13) to that of powell (1978) for d-bfgs, except when = 1k kb h and 2< 1 .k  indeed, for some choices of these parameters, we observed that formula (13) works better than (6). we now consider the second limit of (12) which suggests using 1/2 4= / ( 1)k k kb h   if 2 4> 1 ,k kb h  where 4 0,  which can be substituted into (11) to obtain the corresponding value of .k however, since 4 is chosen by the user and k k  if 1,k  we consider 4 4, > 1 1= 1, otherwise , k k k kk b h b h         (14) where, as above, 4 0.  if 4 = 0 is used, then as for formula (13), the damped-technique is always employed, except when the broyden family is reduced to a single update. since 2 ,k k  al-baali (2011) considers formula (14) with the denominator replaced by 1.k kb h  although other choices for k exist, formulae (13) and (14) are considered here for illustration. we note that the above formulae for k are independent of the updating parameter k , so that the global convergence condition (9) may not hold for sufficiently large values of | | .k therefore, in this case, this condition can be enforced by choosing k sufficiently small. for example, the equality in (9) could be solved for k which can be substituted into (11) to obtain the largest acceptable value of .k in this way, all the damped algorithms which we consider below for ( ,1)k k   (the divergent broyden options) solved the considered problem successfully. however, alternatively, replacing 1k kb h  by = ( 1) max(1,| |)k k k ka b h   (15) in formula (14), it follows that 4 4, > = 1, otherwise . k kk a a         (16) using formula (16), we observed that all the damped algorithms which we consider below for several values of k from inside and outside the convex interval solved the problem successfully with performance significantly better than that of bfgs. on the basis of the above discussions, we state the following outline for practical damped quasi-newton methods. we note that the strong wolfe conditions in step 3 yield the wolfe conditions (2)-(3). if, on every iteration, the choice ˆ =k ky y is used in step 5, which follows from (1) and (13) with values of 2 = 1, 3 =  and 4 = ,  then algorithm 2.1 is reduced to the 'undamped' broyden family of methods. in particular, this choice with = 0,k for all values of k, reduces the d-bfgs method to the standard bfgs method. in practice, we observed that several values for 2 > 1 2 improve the performance of the bfgs and dfp methods (the latter significantly). if k is chosen such that the usual positive definiteness property holds (which we consider here), then any value of k satisfies condition (9). indeed, we observed that sufficiently small mehiddin al-baali and anton purnama 6 values of k are sometimes useful, particularly when | |k is remotely away from zero. these features will be illustrated in the next section. algorithm 2.1 d-broyden class step 0: given a starting point 1,x a symmetric and positive-definite matrix 1,b positive values of 0 and 1, and a tolerance > 0. set = 1.k step 1: terminate if .kg  step 2: compute the search direction 1 = .k k kd b g   step 3: find a steplength k and a new point 1 =k k k kx x d  such that the following strong wolfe conditions hold: 1 0 1 1, | | . t t t k k k k k k k k kf f d g d g d g        (17) step 4: compute ,ks ,ky kb and .kh step 5: choose values for k and .k step 6: update ky to ˆky and hence kb to 1,kb  using (1) and (4), respectively. step 7: set := 1k k  and go to step 1. 3. a numerical example the question that has been most useful to the development of successful algorithms for unconstrained optimization is 'does the method work well when the objective function is quadratic?' this statement is given by powell (2009) who also states that the answer is very welcome and encouraging for the updating of second derivative matrices of quadratic models by a broyden family method. since this family usually suffers from illconditioned problems, we would like to apply some selected broyden family methods to a quadratic function with a very ill-conditioned hessian matrix. because quasi-newton methods are invariant under linear transformation, the difficulty is unchanged if we choose the simple quadratic function 21 ( ) = , 2 t f x x x x r which has the solution * = 0x and identity hessian 2 ( ) = ,f x i and the initial hessian approximation 1b is very ill-conditioned. in particular, powell (1986) uses 1 = diag(1, ) ,b  where > 0, and 1 1 = , = . 11 c x c c          the author simplifies the analytic derivation of 1kx  when calculated by either the bfgs or dfp method with = 1.k he shows that for large values of , bfgs performs badly and dfp is far worse, although ky is exact. note that the former performance is maintained for the modified bfgs methods which use (8). the derivation of powell (1986) for 1kx  has been extended to a restricted broyden class of methods by byrd et al. (1992) who also show that the performance of this class becomes worse as k increases. since these papers illustrate that numerical experience with damped quasi-newton methods 7 these methods usually suffer from large eigenvalues of kb rather than small ones, we will describe below the numerical results for a very large value of . in a similar manner, we have tested the d-broyden class of methods by applying algorithm 2.1 to the above problem. to define step 0 of this algorithm, we let 1x and 1b be given as above, using 10 = 10 and 7 = 10 .  we do not define 0 and 1 here, because = 1k was used in step 3 on all iterations whether this value satisfies the wolfe conditions or not. nevertheless, these conditions hold to the limit if a quasi-newton method converges superlinearly (dennis and moré, 1974). thus the algorithms we consider below differ only in the choices of k and k as required in step 5 of algorithm 2.1. all experiments were run in matlab. the damped-technique (1) with suitable values of k has the ability of correcting the hessian approximations successfully. here, we report the results for several choices of k and 7 7 { 10 , 100, 0.5, 0, 0.5,1,1.5,100,10 }k     which belong to the so called convex, preconvex and postconvex classes of methods (defined for 0 1,k   < 0k and > 0,k respectively). we will report the number of function evaluations ( nfe ) which is required to terminate algorithm 2.1 in step 1 with the euclidean norm .kg  this number is the same as that of the gradient evaluations as well as that of iterations. 'f' indicates the algorithm was terminated before the latter inequality held, ie the algorithm failed to solve the problem. we also consider the bfgs method for comparison, which required = 32nfe to solve the problem. table 1. d-bfgs with formula (6) 2 0.95 0.9 0.7 0.6 0.5 0.4 0.1 0.01 0.001 610  nfe 32 32 32 27 35 47 220 2107 18887 f we firstly tested the d-bfgs method with k  given by formulae (6), (13) and (14) for various choices of the parameters 2 and 4. we do not consider choices for 3 here, because the second case in (6) and (13) was not used as the inequality 3> 1k  was not satisfied for 3 > 0. the results expressed in terms of nfe are presented in table 1. we used (6) for 10 different values of 2 (0,1).  for sufficiently large values of 2 , d-bfgs required = 32nfe to solve the problem, which is the same as that required by bfgs. the reason is that using 2 = 1 in formula (6) yields = 1k which (by the damped-technique (1)) reduces the d-bfgs update to the bfgs one. we also note that d-bfgs works slightly better than bfgs when 2 is close to 0.6, while it becomes worse as 2 decreases in (0,0.5). indeed, d-bfgs also failed to solve the problem when values of 6 2 10   were used. this observation is somehow expected on the basis of some results from the literature, because (according to our knowledge) values of 2 = 0.8 or 0.9 have been used in the d-bfgs method for constrained optimization during the last three decades, see for example (powell, 2009). this drawback of formula (6) with choices of 2 0.5  can be avoided by employing it only when the bfgs update is sufficiently away from the rank one update, that is when k kb h is sufficiently away from 1. to illustrate this feature, we repeated the run using formula (13) with most of the above values of 2 and some values of 4 0.  the results are given in table 2. we do not report the results for 4 > 2 here, because we observed that d-bfgs required the same nfe as that required for 4 = 2. it is clear that the damped-technique mehiddin al-baali and anton purnama 8 improves bfgs substantially when 4 is defined sufficiently close to 0.5 and 2 0.6  and significantly for very small values of 2. it is rather surprising that d-bfgs with 6 2 = 10  and 4 < 2 required at most = 7nfe to solve the problem. this result shows that small values of 2 (and hence k ) are useful in practice. this table also shows that the choice of 4 = 0 (or nearly so) which yields that the damped-technique is employed on most iterations, is not desirable. table 2. d-bfgs with formula (13) 4 2\  0.95 0.9 0.7 0.6 0.5 0.4 0.1 0.01 310  6 10  2 32 32 32 32 32 32 32 32 32 32 1.5 32 32 32 20 18 17 12 8 7 6 0.95 32 32 32 20 18 17 12 8 8 6 0.5 32 32 32 20 18 17 12 8 8 5 0.1 32 32 32 20 19 18 12 8 8 5 0.001 32 32 32 22 20 19 13 8 8 5 6 10  32 32 32 24 21 19 14 9 8 5 0 32 32 32 27 27 25 87 625 3918 7 the damped-technique seems to work well if the left limit in (12) is enforced only when the term under the right limit, 1,k kb h  is sufficiently away from zero. therefore, it is worth testing formula (14) which enforces the right limit in (12). the results are given in table 3. we observe that the damped-technique improves over bfgs as 4 decreases. for example when 4 = 0.01, d-bfgs required only = 8nfe , which is very small compared to 32 as required by bfgs. table 3. d-bfgs with formula (14) 4 2 1 0.7 0.6 0.5 0.4 0.1 0.01 310  6 10  0 nfe 32 19 17 16 15 14 11 8 7 5 4 to see if the above encouraging numerical results for d-bfgs are generalised to other members of the dbroyden class, we repeated the run for formula (14) with the same values of 4 and several values of ;k some of them are very remotely away from 0 (the bfgs option). the numerical results are presented in table 4. in the first row of results, we used 4 =  to obtain = 1k for all k and, hence, the corresponding undamped quasi-newton methods were considered for comparison. the failures for < 0k and > 1k are expected, see for example (byrd et al., 1992). note that 10 = 10nfe  required for = 1k (the dfp option) is expected, see (powell, 1986). the remaining results in table 4 were obtained by testing condition (9) with 1 2= = 0.05.  if it does not hold for the computed ,k we reduce this value such that this condition holds with equality. in this way convergence is enforced to all algorithms which, indeed, solves the problem successfully. thus the second row numerical experience with damped quasi-newton methods 9 of results with 4 =  and condition (9) being enforced indicates that the damped-technique was employed for all algorithms defined with [0,0.95].k  table 4. d-broyden with formula (14) and enforcing condition (9) 4 \ k  710 -100 -0.5 0 0.5 1 1.5 100 7 10 * f f f 32 78 1010 f f f  16 21 16 32 78 411 118 150 18424 2 17 9 8 32 78 411 118 65 18425 0.95 17 9 13 19 22 30 30 65 18425 0.5 14 10 15 15 16 18 21 65 18425 0.1 11 19 10 11 11 12 15 66 18425 0.01 11 7 8 8 8 10 13 65 18425 0.001 11 7 7 7 7 9 12 64 18425 6 10  6 5 5 5 5 7 10 62 18425 0 7 7 7 7 7 9 12 79 22172 * condition (9) was not enforced. an examination of the other results in table 4 shows the following. the damped algorithms with 1.5k  and 4 0.1  work substantially better than bfgs. it is rather surprising that all algorithms with < 0,k which sometimes yields indefinite hessian approximations in the undamped algorithms, solved the problem successfully. although bfgs works much better than the algorithms for 100,k  it is also surprising that they solved the problem successfully. note that the slow convergence of these algorithms is avoided as described in the following paragraph. table 5. d-broyden with formula (16) 4 \ k  710 -100 -0.5 0 0.5 1 1.5 100 7 10 * f f f 32 78 1010 f f f  16 21 16 32 78 411 118 150 18424 0.95 20 16 13 19 22 27 23 16 18 0.5 13 11 15 15 16 17 16 12 12 0.1 12 8 10 11 11 10 10 8 34 0.01 820 7 8 8 8 8 8 8 1109 0.001 7 24 7 7 7 7 7 10 6 6 10  5 6 5 5 5 6 6 5 5 0 4 4 4 4 4 4 4 4 4 * condition (9) was not enforced. we now repeat the test with formula (16). the results are given in table 5. we observe the surprising results that all damped algorithms solve the problem successfully. for sufficiently small values of 4 , the mehiddin al-baali and anton purnama 10 algorithms performance is significantly better than that of bfgs, and the algorithms improve as 4 decreases. 4 = 0 means that the damped-technique is always employed, except when the broyden family of updating formulae is reduced to the sr1 update. all algorithms approach an optimal method with = 4nfe which is required to solve the problem by a well defined sr1 method. although 4 = 0 gives the best choice, the value of 4 = 0.95 might be typical for a general function, and further experiments on several test problems should be considered. it is worth reporting that an application of some algorithms to the above quadratic problem (or its linear transformation) with some choices for 1x and 10 1 = diag(1,10 )b  has been considered. we observed, as expected, that all the algorithms solved the problem successfully with = 2nfe or 3 whether the dampedtechnique was employed or not. to see if the above results are generalised to general functions, we applied algorithm 2.1, employing the strong wolfe conditions (17) with the usual values of 4 0 = 10  and 1 = 0.9, to some unconstrained optimization problems and observed the following. when k is sufficiently away from zero, the damped algorithms work significantly better than the undamped broyden methods. for = 0,k we observed that generally the standard bfgs method is preferable to the d-bfgs algorithm unless further restrictions on the damped parameter k are made or, similarly, the scalars 2 , 3 and 4 are appropriately chosen. indeed, albaali and grandinetti (2009) showed that the performance of the d-bfgs method with formula (6) for 2 = 0.9, 3 = 9 and further restrictions on k is substantially better than that of the bfgs method. this performance is improved further when both the damped and self-scaling techniques are combined in a certain sense (al-baali and khalfan, 2009). for large-scale problems, al-baali (2004) introduced the damped formula (6) to the limited memory l-bfgs method, see for example (nocedal and wright, 1999). using 2 = 0.6, 3 3  and sufficiently large values of ,k al-baali (2004) reported encouraging numerical results in certain cases. 4. conclusion it is shown that the d-broyden class of methods with appropriate choices for the damped-technique work very well when applied to the quadratic function of powell (1986). in particular, the damped parameter (16) improves the performance of robust methods (e.g. bfgs) substantially and inefficient methods (e.g. dfp) significantly and enforces fast convergence of divergent methods. the numerical results also demonstrate that small values for the damped parameter k are useful in some cases. since this finding contradicts the well known fact that large values of 0.8k  should be used in the dbfgs update of methods for the lagrangian function in constrained optimization (see for example fletcher, 1987; nocedal and wright, 1999; powell, 1978; powell, 2009; gill and leonard, 2003), it is worth noting that smaller values of k using formulae (13) and (14) which modify that of powell (1978) should also be further investigated. for a general function, these formulae can be used with ky replaced by the right hand side of (8) as in (albaali and grandinetti, 2009). 5. acknowledgment we would like to thank the two anonymous referees for making a number of valuable comments on a draft of this paper. numerical experience with damped quasi-newton methods 11 6. references al-baali, m. 1993. variational quasi-newton methods for unconstrained optimization. jota, 77: 127-143. al-baali, m. 2003. quasi-wolfe conditions for newton-like methods. 18th international symposium on mathematical programming, copenhagen, denmark, 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numerical methods for unconstrained optimization and nonlinear equations, siam publications, philadelphia. fletcher, r. 1987. practical methods of optimization (2nd edition). wiley, chichester, england. gill, p.e. and leonard, m.w. 2003. limited-memory reduced-hessian methods for large-scale unconstrained optimization. siam j. optim., 14: 380-401. gratton, s. and toint, p.l. 2010. approximate invariant subspaces and quasi-newton optimization methods. oms, 25: 507-529. nocedal, j. 1980. updating quasi-newton matrices with limited storage. math. comput., 35: 773-782. nocedal, j. and wright, s.j. 1999. numerical optimization. springer, london. powell, m.j.d. 1978. algorithms for nonlinear constraints that use lagrange functions. math. programming, 14: 224-248. powell, m.j.d. 1986. how bad are the bfgs and dfp methods when the objective function is quadratic?. math. programming, 34: 34-47. powell, m.j.d. 2009. on nonlinear optimization since 1959. optimization online, 11/2477. yabe, h., ogasawara, h. and yoshino, m. 2007. local and superlinear convergence of quasi-newton methods based on modified secant conditions. journal of computational and applied mathematics, 205: 617-632. received 20 april 2011 accepted 4 october 2011 squ journal for science, 2020, 25(2), 107-111 doi:10.24200/squjs.vol25iss2pp107-111 sultan qaboos university 107 dicyclic groups and frobenius manifolds yassir dinar and zainab al-maamari department of mathematics, college of science, sultan qaboos university, p.o. box 36, al-khod, pc 123, muscat, sultanate of oman. *email: dinar@squ.edu.om abstract: the orbits space of an irreducible representation of a finite group is a variety whose coordinate ring is finitely generated by homogeneous invariant polynomials. boris dubrovin showed that the orbits spaces of the reflection groups acquire the structure of polynomial frobenius manifolds. dubrovin’s method to construct examples of frobenius manifolds on orbits spaces was carried for other linear representations of discrete groups which have in common that the coordinate rings of the orbits spaces are polynomial rings. in this article, we show that the orbits space of an irreducible representation of a dicyclic group acquires two structures of frobenius manifolds. the coordinate ring of this orbits space is not a polynomial ring. keywords: differential geometry; frobenius manifolds; invariant theory; dicyclic group; orbifolds. ةالهندسيفروبينيس وفضاءات زمر مزدوجة الدورة زينب المعمري و ياسر دينار حدود من كثيرات تتشكل ةحداثية محدودالقة ح يمتلك متنوعفضاء محدودة هو لزمرةقابل لالختزال الغير لتمثيلل مداراتالفضاء إن :صلخمال .حدودالكثيرات ل الهندسية فضاءات فروبينيس تحتفظ ببنية لمتعاكسةا لزمرل يةالمدار اتفضاءال. أثبت بوريس دوبروفين أن وغير متبدلة متجانسة عامة في لها خاصية ،أخرى متقطعة لزمر اخطي تتمثل يةمدارفضاءات أمثلة لفضاءات فروبينيس على يمكن ايجاد ،طريقة دوبروفين باستخدام ثنائية زمرل لالختزال ةغير قابل تتمثيالل تمدارالأن فضاء ،في هذه المقالةنبين . حدودال كثيرةحلقات تكون ،الحلقات اإلحداثية للفضاءات المدارية .الحدودلكثيرات ةليست حلق ات المذكورفضاء المدارلاإلحداثية ةحلقإن ال .ات فروبينيستكتسب هيكلين من فضاء انالدور ، المدارات.راندوثنائية ال ة، مجموعفضاءات فروبينيس، النظرية الثابتةالهندسة التفاضلية، :مفتاحيةالكلمات ال 1. introduction he notion of a frobenius manifold was introduced by boris dubrovin as a geometric realization of a potential f satisfying a system of partial differential equations known in topological fields theory as wdvv equations [1]. besides topological fields theory, frobenius manifolds appear in many fields such as invariant theory, integrable systems, quantum cohomology and singularity theory. this article contributes to the relation between frobenius manifolds and invariant theory. let w be a finite group of linear transformations acting on a complex vector space v of dimention r. then the orbits space m = v/w of this group is a variety whose coordinate ring is the ring of invariant polynomials c[v ] w . the ring c[v ] w is finitely generated by homogeneous polynomials. if f1,f2,...,fm is a set of such generators then m ≥ r and the relation between them is called syzygies. the set of generators are not unique, nor are their degrees [2,3]. an element w ∈ w is called a reflection if it fixes a subspace of v of codimention one pointwise. the group w is called a complex reflection group if it is generated by reflections. then shephard-todd-chevalley theorem states that w is a reflection group if and only if the invariant ring c[v ] w is a polynomial ring [11], i.e. it is generated by r algebraically independent homogeneous polynomials (so there are no syzygies). furthermore, when w is a reflection group, the degrees of such a set generators of c[v ] w are uniquely specified by the group and we refer to them as the degrees of w. t yasir dinar and zainab al-maamari 108 let us assume w is a shephard group, i.e. a symmetry group of a regular complex polytope. then w is a reflection group. let f1,f2,...,fr be a set of algebraically independent homogeneous generators of c[v ] w . we assume that degree fi is less than or equal to the degree fj when i < j. then the inverse of the hessian of f1 defines a flat metric (·,·)2 on * t m [4]. there is another flat metric (·,·)1 on t∗m, which was studied initially by saito [5, 6], defined as the lie derivative of (·,·)2 along the vector field rf e   . the two metrics form what is called ‘a flat pencil of metrics’ (more details are given below). dubrovin used the properties of this flat pencil of metrics to construct polynomial frobenius manifolds [7] (see [8] and [9] for the case of coxeter groups). this article is about applying dubrovin’s method for other finite linear groups than shephard groups. dubrovin’s method to construct frobenius manifolds, through finding flat pencils of metrics on orbits spaces, was carried out for infinite linear groups like extended affine weyl groups [10, 11], jacobi groups [12] and recently a new extension of affine weyl groups [13]. they all have in common that the invariant rings are polynomial rings. moreover, even when considering a generalization of frobenius manifold structure on orbits spaces, many results were obtained under the assumption that the invariant ring is a polynomial ring [14]. it is then a natural question to ask about applying dubrovin’s method on orbits spaces of finite non-reflection groups. in this article we apply dubrovin’s method and construct frobenius manifolds on orbits spaces of dicyclic groups. the resulting frobenius manifolds can be obtained by using an ad-hoc procedure, but it is fascinating to find them on orbits spaces of some group. precisely, we will show that the orbits space of the dicyclic group of order 4n is endowed with two structures of frobenius manifolds which up to scaling has the following potential (1.1) where or . to make the article as self-contained as possible, we review in the next section the definition of the frobenius manifold and its relation with the theory of flat pencils of metrics. in the last section we obtain the promised frobenius manifolds by direct calculations. 2. preliminaries 2.1 frobenius manifolds a frobenius algebra is a commutative associative algebra with unity e and an invariant nondegenerate bilinear form < ·,· >. a frobenius manifold is a manifold m with a smooth structure of a frobenius algebra on the tangent space ttm at any point t ∈ m with certain compatibility conditions [6]. globally, we require the metric < ·,· > to be flat and the unity vector field e to be covariantly constant with respect to it. in the flat coordinates (t 1 ,...,t r ) where r e t    the compatibility conditions imply that there exists a function f(t 1 ,...,t r ) such that ηij =< ∂ti,∂tj >= ∂tr∂ti∂tjf(t) and the structure constants of the frobenius algebra are given by 1 ( )p i j k kp ij t t t p c t     where 1 ij  denotes the inverse of the matrix ηij. in this work, we consider frobenius manifolds where the quasihomogeneity condition takes the form 1 ( ) (3 ) ( ); 1.i r i i rt i d t t d t d      (2.1) this condition defines the degrees di and the charge d of the frobenius structure. the associativity of the frobenius algebra implies that the potential f(t) satisfies a system of partial differential equations which appears in topological field theory and is called witten-dijkgraaf-verlinde-verlinde (wdvv) equations: 1 1 , , ( ) ( ) ( ) ( ), , , , .i j k p q n n j k p q i kp kp t t t t t t t t t t t t k p k p t t t t i j q n                 (2.2) detailed information about frobenius manifolds and related topics can be found in [1]. 2.2 flat pencil of metrics and frobenius manifolds in this section we review the relation between the geometry of flat pencil of metrics and frobenius manifolds. see [15] for details. dicyclic groups and frobenius manifolds 109 let m be a smooth manifold of dimension r. a symmetric bilinear form (·,·) on * t m is called a contravariant metric if it is invertible on an open dense subset m0 ⊂ m. in local coordinates, if we set ω ij (u) = (du i ,du j ); i,j = 1,...,r (2.3) then the inverse matrix ωij(u) of ω ij (u) determines a metric < ·,· > on tm0. we define the contravariant christoffel symbols of (·,·) by γ where γ j sk are the christoffel symbols of < ·,· >. we say the metric (·,·) is flat if < ·,· > is flat. let 1 ( , )  and 2 ( , )  be two contravariant flat metrics on m and denote their christoffel symbols by 1; ( ) ij k u and 2; ( ) ij k u respectively. we say 1 ( , )  and 2 ( , )  form a flat pencil of metrics if 1 2 ( , ) : ( , ) ( , )          defines a flat metric on * t m for a generic  and its christoffel symbols are given by ; 2; 1;( ) ( ) ( ). ij ij ij k k k u u u       let 1 ( , )  and 2 ( , )  be two contravariant metrics on m and denote their matrices by 1 ( ) ij u and 2 ( ) ij u , respectively, in some coordinates 1 ( ,..., ) r u u . suppose that they form a flat pencil of metrics. this flat pencil of metrics is called quasihomogeneous of degree d if there exists a function on m such that the vector fields (2.4) satisfy the following relations [e,e] = e, liee( , )2 = (d − 1)( , )2, liee( , )2 = ( , )1, liee( , )1 = 0. here liex denote the lie derivative along a given vector field x. in addition, the quasihomogeneous flat pencil of metrics is called regular if the (1,1)-tensor is nondegenerate on m. the following theorem due to dubrovin gives a connection between the geometry of frobenius manifolds and flat pencils of metrics. theorem 2.1. [15] a quasihomogeneous regular flat pencil of metrics of degree d on a manifold m defines a frobenius structure on m of charge d. let us assume the flat pencil of metrics on m is regular quasihomogeneous of degree d. let 1 ( ,..., ) r t t be flat coordinates of 1 ( , )  where 1 , r t t e    and i i i t i e d t  . let ij denote the inverse of 1 ( ) ij t . then it turns out that the potential 1 ( ,..., ) r t t is obtained from the equations (2.5) it is well known that from a frobenius manifold we always have a flat pencil of metrics but it does not necessarily satisfy the regularity condition [15]. 3. dicyclic groups let n be a natural number greater than 1 and w be the matrix group generated by (3.1) where ξ is a primitive 2n-th root of unity. then σ and α satisfy the relations 2 2 1 1. 1, , n n            . (3.2) thus w is isomorphic to the dicyclic group of order 4n. the invariant ring of w is generated by the following homogeneous polynomials [2] (3.3) subject to the relation . (3.4) the orbits space m of w is a variety isomorphic to the hypersurface t defined as the zero set of equation (3.4) in c 3 . consider equation (3.4) as a quadratic equation in u3. then any point p out of the discriminant locus has a small yasir dinar and zainab al-maamari 110 neighbourhood up where u1 and u2 act as coordinates. in what follows we assume that we fix such the open set u ⊂ v with coordinates (u1,u2) and we omit the subscript p. let h be the hessian matrix of u1, i.e. and let h −1 denotes its inverse. then, by direct calculations, h −1 defines a flat contravariant metric (·,·)2 on u. this metric, in the coordinates u1 and u2, is given as follows . (3.5) let e be a vector field of the form f(u1)∂u2, where f(u1) is any smooth function. then, by direct calculations, the lie derivative (·,·)1 of (·,·)2 along e forms with (·,·)2 a flat pencil of metrics. this metric takes the value . (3.6) the guess for the vector field to take this from was inspired by [1]. in order to get a quasihomogeneous flat pencil of metrics, we need the lie derivative of (·,·)1 with respect to e to equal zero. this condition leads to the following differential equation for f(u) (3.7) which has two independent solutions and . (3.8) let us assume . then . (3.9) it turns out that the two metrics (·,·)2 and (·,·)1 form a quasihomogeneous flat pencil of metrics with degree . (3.10) in the notations of equations (2.4), we have and . (3.11) this flat pencil of metrics is also regular since the (1,1)-tensor ri j equals the nondegenerate matrix . (3.12) flat coordinates for (·,·)1 are obtained by setting . (3.13) in these coordinates we get . (3.14) the potential  of the corresponding frobenius manifold is . (3.15) let us take . then similar to the method above, we get a regular quasihomogenous flat pencil of metrics of degree (3.16) with . the resulting potential will be . (3.17) we repeat the calculation by taking (u1,u3) as coordinates instead of (u1,u2). it turns out that even though the middle steps may differ in values, the resulting frobenius manifolds are exactly the same as those given by the potentials (3.15),(3.17). dicyclic groups and frobenius manifolds 111 we observe that dubrovin computed by an ad hoc procedure all possible potentials of 2-dimensional frobenius manifolds [6]. the potentials found in this article, after scaling, are listed by dubrovin in the form (3.18) where or . however, finding this by using the method of a flat pencil of metrics on an orbits space of a finite group that is not a reflection group is a surprising result. 4. conclusion in this paper we prove that for a linear representation of dicyclic groups we can still use dubrovin's method to construct frobenius manifolds on its orbits spaces. in addition, the method leads to two structures of frobenius manifolds. the result reported in this article is a part of work in progress to apply dubrovin’s method on orbits spaces of finite groups to find interesting new examples of frobenius manifolds. in future, we will consider irreducible representations of coxeter groups which are not reflection representations [16]. conflict of interest the authors declare no conflict of interest. acknowledgment this work is funded by the internal grant of sultan qaboos university (ig/sci/doms/19/08). the authors thank hans-christian herbig for stimulating discussions and the anonymous reviewers for their comments and suggestions. references 1. dubrovin, b. geometry of 2d topological field theories. integrable systems and quantum groups, montecatini terme, 1993, lecture notes in math., springer, berlin, 1996, 1620, 120-348. 2. neusel, m. invariant theory, american mathematical society, student mathematical library (book 36), isbn: 978-0821841327, 2006, 3. derksen, h. and kemper, g. computational invariant theory. invariant theory and algebraic transformation groups, i. encyclopaedia of mathematical sciences, 130. springer-verlag, berlin, 2002. 4. orlik, p. and solomon, l. the hessian map in the invariant theory of reflection groups, nagoya mathematical journal, 1988, 109, 1-21. 5. saito, k. on a linear structure of the quotient variety by a finite reflexion group. publications of the research institute for mathematical sciences, 1993, 29(4), 535-579. 6. saito, k., yano, t. and sekeguchi, j. on a certain generator system of the ring of invariants of a finite reflection group, communication in algebra, 1980, 8(4), 373-408. 7. dubrovin, b. on almost duality for frobenius manifolds, geometry, topology and mathematical physics, american mathematical society, 2004, ser.2, vol.212, 75-132. 8. dubrovin, b. differential geometry of the space of orbits of a coxeter group, surveys in differential geometry iv: integrable systems, international press, 1998, 181-211. 9. zuo, d. frobenius manifolds associated to bl and dl, revisited, international mathematics research notices, 2007, 2007, rnm020. 10. dubrovin, b. and zhang, y. extended affine weyl groups and frobenius mainfolds, compositio mathematica, 1998, 111, 167-219. 11. dubrovin, b., strachan, ian a.b., zhang, y. and zuo, d. extended affine weyl groups of bcd-type: their frobenius manifolds and landau-ginzburg superpotentials, advances in mathematics, 2019, 351. 12. bertola, m. jacobi groups, jacobi forms and their applications. phd. thesis, sissa, trieste 1999. 13. zuo, d. frobenius manifolds and a new class of extended affine weyl groups w (k,k+1) (al). letters in mathematical physics, 2020, 110 (7), 1903-1940. 14. arsie, a. and lorenzoni, p. complex reflection groups, logarithmic connections and bi-flat f-manifolds. letters in mathematical physics, 2017, 107(10), 1919-1961. 15. dubrovin, b. flat pencils of metrics and frobenius manifolds. integrable systems and algebraic geometry kobe/kyoto, 1997, 47-72. 16. al-maamari, z. and dinar, y. frobenius manifolds from a few linear representations, in preparation. received 15 november 2019 accepted 16 july 2020 photovoltaic cells and systems: squ journal for science, 17(2) (2012) 232-244 © 2012 sultan qaboos university 232 a wavelet-based energetic approach for the analysis of electroencephalogram a.h. siddiqi* and h.k. sevindir** *department of mathematics, sharda university, 32-34 knowledge park-iii, greater noida201306, delhi ncr, india. **department of mathematics, university of kocaeli, umuttepe yerleskesi fen edebiyat fakultesi, izmit, kocaeli 41380, turkey, e-mail: hkodal@kocaeli.edu.tr. abstract: electroencephalography (eeg) is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. the main application of eeg is in the case of epilepsy, as epileptic activity can create clear abnormalities on a standard eeg study. eeg signals, like many biomedical signals, are highly non-stationary by their nature. wavelet analysis has found a prominent position in the investigation of biomedical signals for its ability to analyze such signals, in particular eeg signals. wavelet transform is capable of separating the signal energy among different frequency bands (i.e., different scales), achieving a good compromise between temporal and frequency resolution. the present study is an attempt to better understand the mechanisms causing epilepsy and accurate prediction of the occurrence of seizures. in the present paper we identify typical patterns of energy redistribution before and during a seizure using multi-resolution wavelet analysis. keywords: electroencephalography, epilepsy, multi-resolution, neuroscience, power spectral density, signal energy, wavelet. التخطيط الكهربي للدماغلتحليل اإلشارات موجيات على طاقة وطريقة معتمدة عبد الحسن صديقي و هوليا كودال سيفيندر إن الناتج عن إشارات الخالٌا العصبٌة. لدماغلفروة االكهربً تسجٌل النشاط هو التخطٌط الكهربً للدماغ :ملخص ٌسبب انحرافاً واضحاً عن ًالصرع كهربٌة الدماغ هو فً حاالت الصرع، إذ أن الحراك االستخدام األساسً لتخطٌط كهربٌة غٌر ثابتة بطبٌعتها كغٌرها من إشارات الطب الحٌوي. احتل هذه اللكهربٌة الدماغ. إشارات تخطٌط ةالنسق المعروف رته على تحلٌل هذه اإلشارات إذ ٌمكن فصل تحلٌل الموٌجات مكاناً بارزاً فً دراسة إشارات الطب الحٌوي وذلك لمقد اإلشارات إلى نطاقات ترددٌة مختلفة بٌن عرضً وثابت. تهدف هذه الدراسة إلى فهم أفضل لآللٌة المسببة للصرع وتكهن دقٌق بحدوث نوباته. نمٌز فً هذه الورقة أنماط قٌاسٌة إلعادة توزٌع الطاقة قبل وأثناء نوبات الصرع باستخدام تحلٌل لموٌجات متعددة القرارات. ا mailto:hkodal@kocaeli.edu.tr a wavelet-based energetic approach 233 1. introduction pilepsy is a common brain disorder associated with abnormal neuronal activity. about 1% of the world population suffers from epilepsy and 30% of epileptic patients are not cured by medicine (ninds 2001). its major manifestation is the epileptic seizure which may involve a discrete part of the brain (partial) or the whole cerebral mass (generalized). eeg is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. the main application of eeg is in the case of epilepsy, as epileptic activity can create clear abnormalities on a standard eeg study. careful analysis of eeg records can provide valuable insight and improved understanding of the mechanisms causing epileptic disorders. the fourier transform (ft) has been the traditional method applied to the analysis of time series signals for decades. fourier coefficients are determined by the entire signal support and frequencies are not localized in time, since the infinite basis functions are used in ft. consequently, fourier analysis provides only globally time-averaged information, whereas it lacks any local behavior within the signal. hence, it is suitable for extracting frequency information from stationary signals. eeg signals like many biomedical signals are non-stationary, and fourier transform does not give an effective analysis for such signals. for non-stationary signals one method to partly overcome this difficulty is the usage of short-time fourier transform, stft (the windowed fourier transform) in which the signal is multiplied by a sliding window of limited extent, considering the signal as quasi-stationary for such a short period. in essence, stft extracts several frames of the signal to be analyzed with a window that moves with time. if the time window is sufficiently narrow, each frame extracted can be viewed as stationary so that fourier transform can be used. with the window moving along the time axis, the relation between the variance of frequency and time can be identified. however the compromise between the temporal and frequency resolution, established by the window size, is the same for all frequencies. the wavelet transformation is well-suited to representing various aspects of eeg signals such as trends, discontinuities, and repeated patterns where other signal processing approaches fail. wavelet is an effective time/frequency analysis tool for analyzing transient signals. in the wavelet transform (wt) case, wt employs a windowing technique with variable-size windows. wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. they have advantages over traditional fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. the fundamental idea behind wavelets is to analyze according to scale. wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. approximation using superposition of functions has existed since the early 1800's; joseph fourier discovered that he could superpose sines and cosines to represent other functions. however, in wavelet analysis, the scale used to look at data has a special role. wavelet algorithms process data at different scales or resolutions. if we look at a signal with a large window, we can notice gross features, and if we look at a signal with a small window, we can catch small features. this makes wavelets interesting and useful. wavelets have been traced all the way back to alfred haar in 1910; however, the starting point of their modern history coincides with two publications in the 1980s by mallat (1989) and daubechies (1990) . mallat (1989) identified the important concept of multi-resolution analysis which is the corner stone of modern wavelet theory, while daubechies (1990) constructed the first orthogonal wavelet bases that were compactly supported. wavelets have become a tool of choice for scientists, leading to efficient solutions in time and space frequency analysis problems, as well as a number of other applications. nowadays wavelet methods of analysis and representation have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. wavelet applications in medicine include, but are not limited to, capillary pressure, coronary artery disease, auditory nerve models, blood flow velocity, ecg timing, distortions and noise detection of abnormalities, heart rate variability, cardiac arrhythmias, ecg data compression, evoke potentials, epileptic seizures and epileptogenic foci, classification of eeg, pathological sounds, ultrasounds, and vibrations (blood flow heart and lung sounds), medical imaging (ultrasonic, magnetic resonance, optical images, computed tomography and others) electromyography signals and sleep apnea (aldroubi and unser, 1996). e a.h. si̇ddi̇qi̇ and h.k. sevindir 234 it may be emphasized that wavelet transform has been extensively applied to eeg with different purposes: analysis and characterization of epileptic activity (such as spikes, slow waves, polyspikes, sharp waves, etc.), in the perspective of obtaining clues on the processes underlying the onset of an epileptic attack (attelis et al., 1997; bhandari et al., 2007; gigola et al., 2004; rosso et al., 2006), development of algorithms for the prediction and on-line/off-line automatic detection of epileptic seizures (attelis et al., 1997, gigola et al., 2004, latka et al., 2003) in order to assist clinitians in monitoring hospitalized patients and reviewing eeg recordings as well as to improve the quality of life of epileptic subjects. in inouye et al. (1990) a change of power spectrum in alpha frequency before the spike and wave complexes was reported. fisher et al. (1992) reported that frequencies above 40 hz are poorly visualized on conventional eeg scalp recordings, and that they have recorded frequency components up to 150 hz in digitally recorded eegs. high frequency increases were largely localized to the region of the seizure focus. in inouye et al. (1994) structural changes were observed just before spike occurance during seizure. in magosso et al. (2009) wavelet methods were applied to eeg data obtained from epileptic patients suffering from drug resistance temporal lobe seizures acquired at bellaria hospital (bologna). in this particular paper, magosso et al. (2009) analyzed the energy distribution of the eeg to determine if it is altered among the different scales of the wavelet representation and exhibits distinct patterns of energy redistribution. in the present work, we exploit the same approach for our data obtained at kocaeli university’s medical hospital in turkey to characterize the epileptic attack in quantitative terms and to obtain indications concerning the genesis of the seizure propagates among adjacent regions of the brain. we have obtained similar results for digitally recorded video eeg recordings for epileptic patients as magosso et al. (2009). we have shown that energy distribution of the eeg has altered among the different scales of wavelet representation at seizure onset and during the seizure. the paper is organized as follows. the first section gives an introduction. in the second section, wavelets and energy computation from wavelet coefficients will be introduced, while in the third section analysis of epileptic eeg will be discussed. in the last two sections, data, methodology, application to eeg and results are presented. 2. wavelet analysis and energy computation the wavelet is a quickly vanishing oscillation function localized both in frequency and time. in both continuous and discrete forms of wavelet analysis, the signal is decomposed into scaled and translated versions   ,a b t of a single function  t called the mother wavelet:   , 1 ,a b t a t ba         (1) where a and b are the scale and translation parameters, respectively, with ,a b  and 0.a  if a signal  f t is a square integrable function of time, i.e.   2 f l  (the space of finite energy signals), then the continuous wavelet transform (cwt) of the signal is defined as    , , 1 , * ,a b a b t b w a b c f t dt f aa              (2) where ,  means the inner product and the superscript * means complex conjugate. the factor 1 a is used to normalize the energy so that it stays at the same level for different values of a and b. the wavelet function   ,a b t becomes narrower when a is increased, and displaced in time when b is varied. therefore, a is called the scaling parameter which captures the local frequency content and b is called the translation parameter which localizes the wavelet basis function at time t b and its neighborhood. cwt at every possible scale a and translation b provides a redundant representation of the signal; hence cwt requires a heavy burden of a wavelet-based energetic approach 235 computations compared to the discrete wave transform (dwt). dwt provides sufficient information both for analysis and synthesis of the original signal, with a significant reduction in the computation time. the filters of different cutoff frequencies can be used to analyze the signal at different scales. the signal is passed through a series of high pass filters to analyze the high frequencies, and it is passed through a series of low pass filters to analyze the low frequencies (addison, 2002). the dwt is obtained by discretizing the parameters a and b. we may choose 2 , j a   2 j b k   with , .i j z by substituting this in (1) we get    2, 2 2 . j j j k t t k    (3) the dwt can be written as    2, ,2 2 , j j j k t kd f t t k dt f        (4) where ,j kd are known as wavelet (or detailed) coefficients at scale j and location k. the wavelet coefficients ,j kd measure the amount of fluctuation about the point 2 j t k   with a frequency determined by the dilation index j. appropriate selection of mother wavelet  lets the family   , ,j k t j k z  form an orthonormal basis for 2 ( )l  . in that case, the original signal can be reconstructed from the resulting wavelet coefficients accurately and efficiently without any loss of information (strang, 1996); the number of wavelet coefficients will be the same as the number of data points in the original signal. in other words, the dwt discards all redundant information in cwt by employing a set of orthogonal basis functions. furthermore, the dwt may be interpreted in terms of a multi-resolution analysis, where a hierarchy of approximation and details of the signal is constructed in nested subspaces of 2 ( )l  . multi-resolution scheme provides an effective way of implementing dwt (mallat, 1989). in this scheme, the square integrable space 2 ( )l  is decomposed into a direct sum of the subspaces ,jw j from  to , 2 3 2 1( )l w w w       0 1 2 3w w w w    . if the closed subspaces jv are defined as 1 2 3 ,j j j jv w w w      for all j  where  indicates direct sum, then the subspaces jv are a multi-resolution approximation of the square integrable space 2 l and can be obtained from dilation and translation of a single scale function , ( ).j k t thus, the subspaces jw are the orthogonal complementary of the subspaces jv : 1j j jv v w   for all .j  given a signal  ,f t its multi-resolution decomposition formula at level h is defined as / 2 / 2 , ,( ) 2 (2 ) 2 (2 ) ( ) ( ) , h h h h j j h k j k h j k j k j f t a t k d t k a t d t                     (5) ( )t is the mother wavelet, while  is a companion function, called the scaling function: / 2 , ( ) 2 (2 ) j j j k t t k      are scaled and translated versions of the original scaling function  .t ,h ka represent approximation or scaling coefficients at level h, and defined as , ,,h k h ka f  a.h. si̇ddi̇qi̇ and h.k. sevindir 236 extending decomposition over all resolution levels, the complete wavelet expansion can be obtained as / 2 ,( ) 2 (2 ) . j j j k j k f t d t k          (6) it expresses the synthesis of the original signal from wavelet coefficients. in each level j, the series in (6) has the property of complete oscillation (chui, 1992), which makes the decomposition useful in applications to time localization of events. by using down-sampling operations along with low-pass and high-pass filtering, signal decomposition as in (5) can be efficiently implemented (fast pyramid algorithm). it is important that the two filters are related to each other, and they are known as a quadrature mirror filter. the high-pass filters are associated with the wavelet functions , ( ),j k t while the low-pass filters are associated with the scaling functions , ( ).j k t at each decomposition step this pair of filters decomposes the signal into low-frequency components (approximation coefficients), and high-frequency components (details coefficients). filtering is applied first to the original signal, and then recursively, to the approximation series only. at every iteration, the output of each filter is down-sampled by a factor of 2 (decimation) halving the data each time. the down-sampling is done to give speed to the algorithm, reducing the computation at each iteration geometrically (after j iteration the number of samples being manipulated shrinks by 2 m ). let the signal be of finite length, say n and 2 . m n  let st denote the sampling time. theoretically, wavelet decomposition may involve all scales from negative to positive infinity as seen in (6). in practice, wavelet decomposition is applied to discrete signals. since there is not enough resolution between two consecutive samples to construct finer details at scales 0,j  the sample values of the signal are generally taken as the signal approximation coefficients at scale 0j  and the analysis is limited only to positive scales (siddiqi, 2004). the approximated and detailed signals at scale j will have only 2 m j samples each, because of the down sampling operation. coefficients at each scale j are placed at instant  , 2 0, , 2 1 . j m j j k st k t k     hence, the range of scales that can be investigated is 1 ,j m  since the decomposition can proceed only until the individual details contain a single coefficient. if the decomposition is done for all resolution levels m, the wavelet expansion will be 2 1 / 2 , 1 0 ( ) 2 (2 ) , m j m j j j k j k f t d t k          (7) where k starts from 0 since we assume, without loss of generality, that the signal starts from 0t  . scalograms are the graphical representation of the square of the wavelet coefficients for the different scales. they are an isometric view of the sequence of the wavelet coefficients versus wavelength. a scalogram clearly shows more details, identifies the exact location/time and detects low-frequency cyclicity of the signal. the scalogram surface highlights the location (depth) and scale (wavelength) of dominant energetic features within the signal. the combination of the various vectors of coefficients at different scales (wavelengths) forms the scalogram. the depths (location/time) with the largest (strongest) coefficients indicate the position where the particular wavelength change is taking place. the scalogram provides a good space-frequency representation of the signal. the scale 'a' is related to the frequency by 0f a f  (8) where 0f is the frequency of the mother wavelet. when the family     2, 2 2j jj k t t k    is an orthonormal basis in 2 ( )l  , the concept of energy is linked with the usual notions derived from the fourier theory, and the sum of the square of the coefficients of the series is the energy of the function, i.e. the energy series associated with coefficient series is given by a wavelet-based energetic approach 237 2 , ,| |j k j ke d (9) and the overall energy at resolution j is 2 1 2 , 0 | | m j j j k k e d      (10) the total energy associated with the entire signal can be obtained as 2 1 2 , 1 0 | | m j m tot j k j k e d        (11) energy coefficients as computed by (9) have a different localization and density over the temporal axis, depending on the scale: at scale j, the coefficients are placed at instants 2 , 0, , 2 1. j m j sk t k    thus, to study and to compare the temporal evolution of energy at different scales, it is necessary to recover for the halved time resolution at each scale due to the down-sampling operation. in the following, two methods which allow uniformly time distributed atoms of energy to be obtained across all scales will be intoduced. in the last section these methods will be applied to the analysis of the eeg data. 2.1 grouping and spreading-out energy coefficients in this method the original signal will be divided into non-overlapping temporal windows of fixed length 2 j sl t . here 2 j is the number of signal samples falling within the window, and an atom of energy within each window at every resolution level j will be computed. two different cases have to be considered: case a) j j : in this case, at each scale j ( 1, , ),j m the assigned window contains 2 j j energy coefficients. the atom of energy within the window n ( 0, 1, , 1)wn n  can be computed by grouping all the energy coefficients falling within the window: 1 , , 1 1 0 2 1, 0 , ˆ (2 1)2 (2 1)2 1, 1, , 2 1 j j j n j k j j j j m j k k n e e n k n n                       (12) the centre point of the corresponding time window will be set according to (12), so the first window will be centered on 0, and half of the coefficients contained in it are null. thus for each scale, a series of wn energy atoms are uniformly time distributed with a time resolution 2 . j j st t  case b) j j : this means that coefficients at some scale have a time resolution lower than l. in other words there is a scale *j within the decomposition  1 *j m  such that * .j j in this case again (12) can be used for each scale j j as before to group energy coefficients within a window. at scale *j j no processing is required for energy coefficients, because they have the desired time resolution. however for coefficients at scale j j we use , , ˆ round , 0, , 2 1 , 2 2 j k m j j n j j j j e n e k n             (13) where the function  round x rounds x to the nearest integer. therefore the total energy within a time window n can be obtained by , , 1 ˆ ˆ m tot n j n j e e    , (14) a.h. si̇ddi̇qi̇ and h.k. sevindir 238 and the relative energy associated with the resolution j in the time window n can be obtained by , , , ˆ ˆ ˆ j n j n tot n e e   (15) 2.2 averaging energy coefficients in this method atoms of moving average energy will be computed. series of moving average energy can be computed according to the following equation , , 0 2 1, 0 1 1 1 fix 1 fix 2 , 1, , 2 2 ,2 2 2 j j j n j k j j m jj j k j j k n e e n n k n                                 (16) where the functions  fix x rounds x to the nearest integer towards zero. the total means energy within a time window n  0, 1, , 2 2m jn   is given by , ,1 , m tot n j nj e e    (17) and the relative mean energy is defined as , , , ˆ j n j n tot n e e   (18) 3. analysis of epileptic eeg eeg is a record of electrical potential generated by cerebral cortex nerve cells (latka et al., 2003). careful analysis of eeg records can provide valuable insight and improved understanding of the mechanisms causing epileptic disorders. wavelet transformation, which is known as mathematical prism or microscope, is being exploited for the analysis and proper understanding of the eeg records (attelis et al., 1997; magosso et al., 2009; adeli et al., 2003; furati et al., 2006; gigola et al., 2004; mallat, 1989). siddiqi et al. (2009) have analyzed eeg’s of epileptic and normal persons through energy distribution among different approximate and detailed levels. any redistribution may indicate change in the characteristics of the eeg signal which in turn may represent specific events in the course of seizure. it may be remarked that if the information of a signal in general, or an eeg signal in particular, carrying specific information consists of different components, each individual component makes a different contribution to the total signal. for instance, each person’s voice is of different wavelet frequency scale characteristics; that is, the individual frequencies make a different contribution to the total energy of the voice. therefore the signal can be distinguished by the characteristics of its energy spectrum. to set up the correlation between target signal and the wavelet energy spectrum we must build up a model database (bhandari et al., 2007; furati et al., 2006; gencay et al., 2002; iske and randen, 2006; manchanda et al., 2007; percival and walden, 2000; rivera, 2003; siddiqi, 2004; siddiqi et al., 2007; yue et al., 2005; yue and tao, 2006) combining a series of specific models that are distinguished from one another. in the model database each model should have a group model signal. the energy spectrums of these model signals are obtained by applying wavelet transform. it may be emphasized that wavelet transform has been extensively applied to eeg with different purposes: analysis and characterization of epileptic activity (such as spikes, slow waves, polyspikes, sharp waves, etc.), in the perspective of obtaining clues on the processing underlying the onset of an epileptic attack (gigola et al., 2004; attellis et al., 1997; rosso et al., 2006). development of algorithms for the prediction and on-line/off-line automatic detection of epileptic seizures (attellis et al., 1997; gigola et al., 2004; latka et al., 2003) in order to assist clinitians in monitoring hospitalized patients and reviewing eeg recordings as well as to improve the quality of life of epileptic subjects. a wavelet-based energetic approach 239 in magosso et al. (2009) wavelet methods have been applied to eeg data obtained from epileptic patients suffering from drug resistance temporal lobe seizures acquired at bellaria hospital (bologna). the objective of this study is to analyse whether the energy distribution of the eeg is altered among the different scales of the wavelet representation and exhibit distinct patterns of energy redistribution. this information may be exploited to characterize the epileptic attack in quantitative terms and to obtain indications concerning the genesis of the seizure propagates among adjacent regions of the brain. figure 1. international 10-20 eeg recording system. 4. data and methodology in this study we collected data of 30 epileptic patients suffering from temporal lobe seizures at medical school's hospital of kocaeli university. data were recorded by the neurology laboratory of the hospital by using the international 10-20 recording system (see figure 1) using a digital eeg recording device. the scalp eeg recording was used since most hospitals have limited or no usage of intracerebral eeg recordings. using scalp eeg recordings we get the same major modifications of frequency and of energy distribution as with intracerebral eeg recording. the signals were sampled at 200 hz and stored on a 32–64 channel computerized video-eeg system. each patient was hospitalized for eeg video monitoring for several hours, and seizures in their eeg were detected visually. the data were cut into small pieces containing a few minutes before and after the seizures. the multi-resolution wavelet analysis was applied to all channels using the daubechies order 4 wavelet (db4). each eeg signal was decomposed into seven resolution levels, in order to consider all frequency bands which are commonly considered in the analysis of eeg signals. 5. application and concluding remarks figure 2 shows the 7-level decomposition of t6–o2 channel from one patient, with seizure activity starting at 115t  s. the signal(s), the seven levels of details (d1–d7) and the residual approximation (a7) are shown in the figure. the approximation and detail records are reconstructed from the scaling coefficients and wavelet coefficients, respectively. the original signal is the superimposition of details d1–d7 and approximation a7. figure 3 shows the power spectral density (psd) of the details and approximation estimated with the welch’s method. the frequency components captured by details move from the high-frequencies towards the low-frequencies as scale increases from 1 to 7 (35–100 hz at scale 1 vs. 0.75–1.5 hz at scale 7), whereas approximation a7 contains all the residual lower frequency information (<0.75 hz) of the signal for our data. from figure 3 the spectra clearly indicate the frequency content captured by each detail and the approximation. a.h. si̇ddi̇qi̇ and h.k. sevindir 242 figure 2. t6–o2 channel of the signal(s) and its wavelet decompositio using db4. figure 3. power spectrum density (psd) of the details and approximation. an important aspect in the analysis of eegs during epilepsy is the energy redistribution among the different details; this redistribution may indicate changes in the characteristics of eeg signals which, in turn, may represent specific events in the course of seizure. in order to characterize the temporal evolution of the energy redistribution of eeg signals, the signal was divided into moving average windows each with a duration 2 j sl t (where st is the sample time) and the energy of all details were computed within each window. in a wavelet-based energetic approach 242 particular, all energy atoms at the same resolution level, contained within the same window, were summed up to have energy at that particular level (see (14)). figure 4. total energy of the signal(s) and the relative energies contained in each detail d4–d7. 65s 70 s 75s 80s 85s 90s 95s 100s 105s 110s 115s 120s figure 5. snapshots of the relative energy distribution in all eeg channels for a patient with temporal lobe epilepsy. a.h. si̇ddi̇qi̇ and h.k. sevindir 242 figure 6. 2-d scalogram of t6–o2 channel of the signal(s). in figure 5 snapshots of the relative energy distribution in all eeg channels for a patient with temporal lobe epilepsy just before seizure ( 65t  s), at seizure beginning ( 105t  s), and during several seconds of seizure with reference to detail 4 can be seen. different colors indicate different relative energy; dark blue for colored pictures (light grey for black/white pictures) show values close to zero, while dark red (light grey) shows approximately 0.6 or higher values. figures 6 and 7 show, respectively, 2-d and 3-d scalograms of t6–o2 channel of the signal(s) and confirm the seizure. the depths (location/time) with the largest (strongest) coefficients indicate the position where the particular wavelength change is taking place. figure 7. 3-d scalogram of t6–o2 channel of the signal(s). our results show that eeg recordings of epileptic patients exhibit a rearrangement of relative energy among the different frequency bands just before and during seizure. our analysis confirms this result specifically for patients with temporal lobe epilepsy. however this relocation of the energy is not the same at all channels. a wavelet-based energetic approach 243 6. acknowledgement the work of the second author (h.k. sevindir) was supported by kocaeli university research foundation, project no. 2010/003. 7. references addison, p.s. 2002. the illustrated wavelet transform handbook – introductory theory and applications in science, engineering, medicine and finance. institute of physics publishing, bristol and philadelphia. adeli, h., zhou, z. and dadmehr, n. 2003. analysis of eeg records in epileptic patient using wavelet transform. j. neurosci methods, 123: 69-87. aldroubi, a. and unser, m.a. 1996. wavelets in medicine and biology. crc press. attelis, c.e., isaacson, s.i. and sirne, r.o. 1997. detection of epileptic events in electroencephalogram using wavelet analysis. ann. biomed. eng., 25: 286-293. bhandari, a., khare, v., santhosh, j. and anand, s. 2007. wavelet based compression technique of electroculogram signals. ifmbe proceedings 15: 440-443. chui, c.k. 1992. an introduction to wavelets. academic press, san diego, usa. daubechies, i. 1990. the wavelet transform: time-frequency localization and signal analysis. ieee trans. inform. theor. 36: 961-1005. fisher, r.s., webber, w.r., lesser, r.p., arroyo, s. and uematsu, s. 1992. high-frequency eeg activity at the start of seizures. j. clin. neurophysiol. 9: 441-448. furati, k.m., nashed, m.z. and siddiqi, a.h. 2006. (eds.) mathematical models and methods for real world system. chapman and hall icrc, taylor and francis group, boca raton, usa. gencay, r., seluk, f. and whichter, b. 2002. an introduction to wavelet and filtering methods in finance and economics. academics press, san diego, usa. gigola, s., ortiz, f., attelis, c.e.d., silva, w. and kochen, s. 2004. prediction for epileptic seizure using accumulated energy in a mra frame work. j. neurosci methods 138: 107-111. inouye, t., matsumoto, y., shinosaki, k., iyama, a. and toi, s. 1994. increases in the power spectral slope of background electroencephalogram just prior to asymmetric spike and wave complexes in epileptic patients. neuroscience letters 173: 197-200. inouye, t., sakamoto, h., shlnosaka, k., toi, s. and ukal, s. 1990. analysis of rapidly changing eegs before generalized spike and wave complexes. electroencephalography and chmcal neurophystology, 76: 205-221. iske, a. and randen, t. 2006. 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(eds). modern mathematical models, methods and algorithm for real world system. anshan and anamaya publishing, new delhi, india. ninds 2001. seizure and epilepsy: hope through research. national institute of neurological disorders and stroke (ninds). available from: http://www.ninds.nih.gov/health_and_medical/pubs/seizures_and_epilepsy_htr.htm. percival, d.b. and walden, a.t. 2000. wavelet methods for time series analysis. cambridge university press, cambridge, uk. a.h. si̇ddi̇qi̇ and h.k. sevindir 244 rivera, n. 2003. reservoir characterization using wavelet transform. ph.d. dissertation, texas a & m university. rosso, o.a., martin, m.t., figliola, a., keller, k. and plastino, a. 2006. eeg analysis using wavelet based information tools. j. neurosci. methods, 153: 163-182. siddiqi, a.h., 2004. applied functional analysis. marcel dekker, new york, usa. siddiqi, a.h., duff, i.s. and christensen, o. 2007. modern mathematical models, methods and algorithms for real world system. anshan and anamaya, new delhi, india. siddiqi, a.h., chandiok, a. and bhadouria, v.s. 2009. analysis and prediction of energy distribution in electroencephalogram (eeg) using wavelet transform. proc. 4 th international workshop on wavelets, kocaeli university, turkey, 5-6 june 2009. yue, w., tao, g. and liu, z. 2005. identifying reservoir fluids by wavelet transform of well logs. journal of petroleum technology, 57(5): 53-54. yue, w. and tao, g. 2006. identifying rreservoir fluids by wavelet transform of well logs. spe reservoir evaluation and engineering, 574-581. received 8 june 2011 accepted 30 november 2011 photovoltaic cells and systems: squ journal for science, 17 (2) (2012) 157-169 © 2012 sultan qaboos university 757 superstatistics in random matrix theory a.y. abul-magd department of basic sciences, faculty of engineering, sinai university, el-arish, egypt, email: aamagd@gmail.com. abstract: random matrix theory (rmt) provides a successful model for quantum systems, whose classical counterpart has chaotic dynamics. it is based on two assumptions: (1) matrix-element independence, and (2) base invariance. the last decade witnessed several attempts to extend rmt to describe quantum systems with mixed regular-chaotic dynamics. most of the proposed generalizations keep the first assumption and violate the second. recently, several authors have presented other versions of the theory that keep base invariance at the expense of allowing correlations between matrix elements. this is achieved by starting from non-extensive entropies rather than the standard shannon entropy, or by following the basic prescription of the recently suggested concept of superstatistics. the latter concept was introduced as a generalization of equilibrium thermodynamics to describe non-equilibrium systems by allowing the temperature to fluctuate. we review here the superstatistical generalizations of rmt and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments on billiards modeling systems in transition from order to chaos. keywords: chaotic dynamics, quantum systems, random matrix theory, superstatistics. اإلحصاء الفائق في نظرية المصفوفة العشوائية عادل يحيى أبو المجد دٌنامٌاكٌة الكالسٌكً على ٌحتوي نظٌره الكم الذي ألنظمة نموذجا ناجحا عشوائٌةال المصفوفة تقدم نظرٌة :خصمل العقد شهدلقد عدة الثابتة.القا (2) و مصفوفةعناصر ال استقالل (7): التالٌتٌن فرضٌتٌنال على ٌعتمد هذا النظام .االرتباك لفوضىل العادٌة دٌنامٌاكٌةوجود ال معٌة نظمة الكمألا لوصف عشوائٌةال المصفوفة نظرٌةتعمٌم محاوالت عدة ل الماضً العدٌد من قدم حدٌثا الثانً. االفتراض خالفتو االفتراض األول بقت علىقد أ ةحالمقتر التعمٌمات معظمن إ المختلطة. المصفوفة. الثانً مع السماح بوجود ارتباط بٌن عناصر بقت على االفتراضأالتً هذه النظرٌةلخرى أات الباحثٌن تعمٌم باتباع الوصفات الحدٌثة شانون، أولى إالتً ترجع نتروبٌااال بدال من وسعةم غٌر نتروبٌابا من خالل البدء هذا وٌتحقق عن طرٌق عدم التوازن لوصففً الدٌنامٌكا الحرارٌة توازنلل تعمٌم بمثابة المفهوم األخٌر تم إدخال. وصاءاتحإلل حسابب متهاٌونوضح ق عشوائٌةال المصفوفة صاءات فً نظرٌةحلإل تعمٌمات هنا نستعرض. فً التقلبحرارة السماح لل ى الفوضى.لإ النظام االنتقال من فً البلٌاردو نظم نماذج تجارب على حساب مع ومقارنة النتائج األقربللفضاء توزٌعات 1. introduction n classical mechanics, integrable hamiltonian dynamics is characterized by the existence of as many conserved quantities as degrees of freedom. each trajectory in the corresponding phase space evolves on an i a.y. abul-magd 758 invariant hyper-torus (lichtenberg and lieberman, 1983). in contrast, chaotic systems are ergodic; almost all orbits fill the energy shell in a uniform way. physical systems with integrable and fully chaotic dynamics are exceptional. typical hamiltonian systems show a mixed phase space in which regions of regular motion and chaotic dynamics coexist. these systems are known as mixed systems. their dynamical behavior is by no means universal. if we perturb an integrable system, most of the periodic orbits on tori with rational frequencies disappear. however, some of these orbits persist. elliptic periodic orbits appear surrounded by islands. they correspond to librational motions around these periodic orbits and reflect their stability. the kolmogorov-arnold (kam) theorem establishes the stability with respect to small perturbations of invariant tori with a sufficiently incommensurate frequency vector. when the perturbation increases, numerical simulations show that more and more tori are destroyed. for large enough perturbations, there are locally no tori in the considered region of phase-space. the break-up of invariant tori leads to a loss of stability of the system, to chaos. different scenarios of transition to chaos in dynamical systems have been considered. there are three main scenarios of transition to global chaos in finite-dimensional (non-extended) dynamical systems: via the cascade of period-doubling bifurcations, lorenz system-like transition via hopf and shil'nikov bifurcations, and the transition to chaos via intermittences (eckmann and ruelle, 1985; elnashaie and elshishini, 1996; bunimovich and venkatuyiri, 1997). it is natural to expect that there could be other (presumably many more) such scenarios in extended (infinitedimensional) dynamical systems. in quantum mechanics, the specification of a wave function is always related to a certain basis. in integrable systems eigenbasis of the hamiltonian is known in principle. in this basis, each eigenfunction has just one component, which obviously indicates the absence of complexity. in the nearly ordered regime, mixing of quantum states belonging to adjacent levels can be ignored and the energy levels are uncorrelated. the levelspacing distribution function obeys the poissonian,  exp ,s where s is the energy spacing between adjacent levels normalized by the mean level spacing. on the other hand, the eigenfunctions of a hamiltonian with a chaotic classical limit are unknown in principle. in other words, there is no special basis to express the eigenstates of a chaotic system. if we try to express the wave functions of a chaotic system in terms of a given basis, their components become on average uniformly distributed over the whole basis. they are also extended in all other bases. for example, berry (1977) conjectured that the wavefunctions of chaotic quantum systems can be represented as a formal sum over elementary solutions of the laplace equation in which real and imaginary parts of coefficients are independent identically-distributed gaussian random variables with zero mean and variance computed from the normalization. bohigas et al. (1984) put forward a conjecture (strongly supported by accumulated numerical evidence) that the spectral statistics of chaotic systems follow random-matrix theory (rmt) (mehta, 1991; guhr et al., 1998). this theory models a chaotic system by an ensemble of random hamiltonian matrices h that belong to one of the three universal classes, orthogonal, unitary and symplectic. the theory is based on two main assumptions: the matrix elements are independent identically-distributed random variables, and their distribution is invariant under unitary distributions. these lead to a gaussian probability density distribution for the matrix elements. the gaussian distribution is also obtained by maximizing the shannon entropy under constraints of normalization and existence of the expectation value of  †tr ,h h where tr denotes the trace and †h stands for the hermitian conjugate of h. the statistical information about the eigenvalues and/or eigenvectors of the matrix can be obtained by integrating out all the undesired variables from distribution of the matrix elements. this theory predicts a universal form of the spectral correlation functions determined solely by some global symmetries of the system (time-reversal invariance and value of the spin). time-reversal-invariant quantum systems are represented by a gaussian orthogonal ensemble (goe) of random matrices when the system has rotational symmetry and by a gaussian symplectic ensemble (gse) otherwise. chaotic systems without time reversal invariance are represented by the gaussian unitary ensemble (gue). among several measures representing spectral correlations, the nearest-neighbor level-spacing distribution function  p s has been extensively studied so far. for goe, the level spacing distribution function in the chaotic phase is approximated by the wigner-dyson distribution, namely, superstatistics in random matrix theory 759 2 4( ) 2 s p s s e     analogous expressions are available for gue and gse (mehta, 1991). the assumptions that lead to rmt do not apply for mixed systems. the hamiltonian of a typical mixed system can be described as a random matrix with some (or all) of its elements randomly distributed. here the distributions of various matrix elements need not be the same, may or may not be correlated and some of them can be non-random too. this is a difficult route to follow. so far in the literature, there is no rigorous statistical description for the transition from integrability to chaos. there have been several proposals for phenomenological random matrix theories that interpolate between the wigner-dyson rmt and banded rm ensemble with the (almost) poissonian level statistics, in which the level spacing distribution is given by the poisson distribution ( ) s p s e   the standard route of the derivation is to sacrifice basis invariance but keep matrix-element independence. the first work in this direction is that of (rosenzweig and porter, 1960). they modeled the hamiltonian of the mixed system by a superposition diagonal matrix of random elements having the same variance and a matrix drawn from a goe. therefore, the variances of the diagonal elements total hamiltonian are different from those of the off-diagonal ones, unlike the goe hamiltonian in which the variances of diagonal elements are twice of the off-diagonal ones. hussein and pato (1993) used the maximum entropy principle to construct such ensembles by imposing additional constraints. ensembles of band random matrices whose entries are equal to zero outside a band of width b along the principal diagonal have often been used to model mixed systems (casati et al., 1990). another route for generalizing rmt is to conserve base invariance but allow for correlation of matrix elements. this has been achieved by maximizing non-extensive entropies subject to the constraint of fixed expectation value of  †tr h h (evans and michael, 2002). recently, an equivalent approach is presented in abul-magd (2006), which is based on the method of superstatistics (statistics of a statistics) proposed by beck and cohen (2003). this formalism has been applied successfully to a wide variety of physical problems (beck and cohen, 2003). in thermostatics, superstatistics arise as weighted averages of ordinary statistics (the boltzmann factor) due to fluctuations of one or more intensive parameters (e.g. the inverse temperature). its application to rmt assumes the spectrum of a mixed system to be made up of many smaller cells that are temporarily in a chaotic phase. each cell is large enough to obey the statistical requirements of rmt but has a different distribution parameter  associated with it, according to a probability density  .f  consequently, the superstatistical random-matrix ensemble that describes the mixed system is a mixture of gaussian ensembles with a statistical weight  .f  therefore one can evaluate any statistic for the superstatistical ensemble by simply integrating the corresponding statistic for the conventional gaussian ensemble. 2. beck and cohen's superstatistics consider a complex system in a nonequilibrium stationary state. such a system will be, in general, inhomogeneous in both space and time. effectively, it may be thought to consist of many spatial cells, in each of which there may be a different value of some relevant intensive parameter. for instance, a system with hamiltonian h at thermal equilibrium is well represented by a canonical ensemble. the distribution function is given by 1 ( ) ( ) , h f h z e      where  is the inverse temperature. beck and cohen (2003) assumed that this quantity fluctuates adiabatically slowly, namely that the time scale is much larger than the relaxation time for reaching local equilibrium. in that case, the distribution function of the non-equilibrium system consists of boltzmann factors  exp h that are averaged over the various fluctuating inverse temperatures a.y. abul-magd 761 1 0 ( ) ( ) ( ) , h f h g z e d          where  1z  is a normalizing constant, and  g  is the probability distribution of . let us stress that 1  is a local variance parameter of a suitable observable, the hamiltonian of the complex system in this case. ordinary statistical mechanics are recovered in the limit    .g      in contrast, different choices for the statistics of may lead to a large variety of probability distributions  .f h several forms for  g  have been studied in the literature (beck and cohen, 2003; beck et al., 2005). beck and cohen (2003) have argued that typical experimental data are described by one of three superstatistical universality classes, namely, 2 , inverse 2 , or log-normal superstatistics. the first is appropriate if  has contributions from  gaussian random variables 1, ,x x  due to various relevant degrees of freedom in the system. as mentioned before, η needs to be positive; this is achieved by squaring these gaussian random variables. hence, 2 i   is 2  distributed with degree ,   /2 /2/2 1 0 0 1 ( / 2) 2 f e                (1) the average of  is  0 .f d     the same considerations are applicable if 1 ,  rather than , is the sum of several squared gaussian random variables. the resulting distribution  f  is the inverse 2 distribution given by /2 /2/2 20 0 0( ) , ( / 2) 2 f e                 (2) where again 0 is the average of . instead of being a sum of many contributions, the random variable  may be generated by multiplicative random processes. then 2 ln ln i   is a sum of gaussian random variables. thus it is log-normally distributed,   2 2 ln / 21 ( ) , 2 f e         (3) which has an average w and variance   2 1 ,w w  where  2exp .w  3. rmt within superstatistics the assumptions of rmt stated in the introduction lead to the following joint probability distribution function for the matrix elements in a random-matrix ensemble † 1 tr( ) ( ) ( ) , h h p h z e      where  is a parameter related the mean level density and  1z  is a normalizing constant. to apply the concept of superstatistics to rmt, assume the spectrum of a (mixed) system to be made up of many smaller cells that are temporarily in a chaotic phase. each cell is large enough to obey the statistical requirements of rmt but is associated with a different distribution of the parameter  according to a probability density  .f  consequently, the superstatistical random-matrix ensemble used for the description of a mixed system consists of a superposition of gaussian ensembles. the joint probability density distribution of its matrix elements is superstatistics in random matrix theory 767 obtained by integrating the distribution of the random-matrix ensemble over all positive values of  with a statistical weight  ,f  † 1 tr( ) 0 ( ) ( ) ( ) h h p h f z e d          (4) despite the fact that it is hard to make this picture rigorous, there is indeed a representation which comes close to this idea (caër and delannay, 1999). the new framework of rmt provided by superstatistics should now be clear. the local mean spacing is no longer uniformly set to unity but allowed to take different (random) values at different parts of the spectrum. the parameter  is no longer a fixed parameter but it is a stochastic variable with probability distribution  .f  instead, the observed mean level spacing is just the expectation value of the local values. the fluctuation of the local mean spacing is due to the correlation of the matrix elements which disappears for chaotic systems. in the absence of these fluctuations,    0f      and we obtain the standard rmt. within the superstatistics framework, we can express any statistic  e of a mixed system that can in principle be obtained from the joint eigenvalue distribution by integration over some of the eigenvalues, in terms of the corresponding statistic  ,g e  for a gaussian random ensemble. the superstatistical generalization is given by ( ) 0 (e) ( ) (e, ) g f d        (5) the remaining task of superstatistics is the computation of the distribution  .f  the time series analysis in (abul-magd et al., 2008) allows us to derive a parameter distribution  ,f  as we shall show now. 4. time-series representation in this section, we use the time series method for the study of the fluctuations of the resonance spectra of mixed microwave billiards. representing energy levels of a quantum system as a discrete time series has been probed in a number of recent publications (relaño et al., 2002). billiards are often used as simple models in the study of hamiltonian systems. a billiard consists of a point particle which is confined to a container of some shape and reflected elastically on impact with the boundary. the shape determines whether the dynamics inside the billiard is regular, chaotic or mixed. the best-known examples of chaotic billiards are the sinai billiard (a square table with a circular barrier at its center) and the bunimovich stadium (a rectangle with two circular caps) (bunimovich, 1974). neighboring parallel orbits diverge when they collide with dispersing components of the billiard boundary. elliptic and rectangular billiards are examples of regular billiards. the quantum-chaos group in darmstadt university carried out a series of experiments with microwave billiards (abul-magd et al., 2008; relaño et al., 2002; bunimovich, 1974; dietz et al., 2006). here we summarize the time-series analysis of the resonance spectra of the so-called limaçon billiard. the "time-series" analysis of the spectra of billiards of both families manifests the existence of two relaxation lengths in the spectra of mixed systems, a short one defined as the average length over which energy fluctuations are correlated, and a long one that characterizes the typical linear size of the heterogeneous domains of the total spectrum. this is done in an attempt to clarify the physical origin of the heterogeneity of the matrixelement space, which justifies the superstatistical approach to rmt. the second main result of this section is to derive a parameter distribution  f  . a.y. abul-magd 762 4.1 limaçon billiard the limaçon billiard is a closed billiard whose boundary is defined by the quadratic conformal map of the unit circle z to w, 2 ,w z z  1.z  the shape of the billiard is controlled by a single parameter  with 0  corresponding to the (regular) circle and 1 2  to the cardioid billiard, which is chaotic. for 0 1 4,  the limaçon billiard has a continuous and convex boundary with a strictly positive curvature and a collection of caustics near the boundary (robnik, 1983). at 1 4,  the boundary has zero curvature at its point of intersection with the negative real axis, which turns into a discontinuity for 1 4.  accordingly, there the caustics no longer persist (gutiérrez et al., 2007). the classical dynamics of this system and the corresponding quantum billiard have been extensively investigated by robnik and collaborators (prosen and robnik, 1994). they concluded that the dynamics in the limaçon billiard undergoes a smooth transition from integrable motion at 0  via a soft chaos kam regime for 0 1 4  to a strongly chaotic dynamics for 1 2.  in the darmstadt experiment (abul-magd et al., 2008), three de-symmetrized cavities with the shape of billiards from the family of limaçon billiards (see figure 1) were reported. they have been constructed for the values 0.125,  0.150, 0.300 and the first 1163, 1173 and 942 eigenvalues were measured, respectively. the latter billiard is chaotic while the other two have mixed dynamics. more details on these experiments are given in dembowski et al. (2001). figure 1. schematic representation of the billiards subject to the darmstadt experiment. 4.2 two spectral-correlation lengths the results of the previous subsection confirm the assumption that the spectrum consists of a succession of cells with different mean level densities. each cell is associated with a relaxation length , which is defined as that length-scale over which energy fluctuations are correlated. our basic assumption is that the level sequence within each cell is modeled by a random-matrix ensemble. the relaxation length  may also be regarded as an operational definition for the average energy separation between levels due to level repulsion. in the long term, the stationary distributions of this inhomogeneous spectrum arise as a superposition of the "boltzmann factors" of the standard rmt, i.e.  †tr . h h e  the parameter  is approximately constant in each cell for an eigenvalue interval of length t (see figure 2). in superstatistics this superposition is performed by weighting the stationary distribution of each cell with the probability density  f  to observe some value  in a randomly chosen cell and integrating over . of course, a necessary condition for a superstatistical description to make sense is the condition ,t  because otherwise the system is not able to reach local equilibrium before the next change takes place. the long time scale: first, let us determine the long time scale t. for this we divide the level-spacings series into n equal level-number intervals of size n. the total length of the spectrum is nn. we then define the mean local kurtosis  n of a spacing interval of length n by superstatistics in random matrix theory 761     4 , 2 21 , 1 ( ) n i n i i n s s n n s s       here  , 1 1 in i t k i n     denotes a summation over an interval of length n, starting at level spacing in, and s is either the local average spacing in each spacing interval or the global average 1s  over the entire spacing series. we chose the latter. in probability theory and statistics, kurtosis is a measure for the "flatness" of the probability distribution of a real-valued random variable. higher kurtosis means that a larger part of the contributions to the variance is due to infrequent extreme deviations, as opposed to frequent modestly sized ones. a superposition of local gaussians with local flatness three results in a kurtosis 3.  we define the superstatistical level-number scale t by the condition   3t  , (6) that is, we look for the simplest superstatistics, a superposition of local gaussians (beck et al., 2005). if n is chosen such that only one value of s is contained in each interval, then of course  1 1.  if on the other hand n comprises the entire spacing series, then we obtain the flatness of the distribution of the entire signal, which will be larger than 3, since superstatistical distributions are fat-tailed. therefore, there exists a level-number scale t which solves (6). figure 2 shows the dependence of the local flatness of a spacing interval on its length for the two mushroom and the three limaçon billiards. in the case of the chaotic limaçon billiard, in which 0.300,  the quantity  does not cross the line of 3  for the considered values of n. it is expected that t n in this case, since the fluctuations in a chaotic (unfolded) spectrum are uniform. the values of t for the mixed billiards with 0.125  and 0.150 are 12.5 and 15.4 respectively. for the chaotic billiard 0.300,  the curve of  n and the line 3  do not intersect as expected. figure 2. determination of the long correlation length t from (6) as the point of intersection of the curve of  n with the line 3  . a.y. abul-magd 761 figure 3. determination of the short correlation length  from the autocorrelation function  c n . the short time scale: the relaxation time associated with each of the n intervals, was estimated by beck et al. (2005) from the small-argument exponential decay of the autocorrelation function         21 1 ,c n s i s i n s    of the time series under consideration. figure 3 shows the behavior of the autocorrelation functions for the series of resonance-spacings of the two families of billiards. quite frequently, the autocorrelation function shows single-exponential decays,    exp ,c n n   where 0  defines a relaxation "time". a typical example is the velocity correlation of brownian motion (reif, 1984). the autocorrelation functions studied here clearly do not follow this trend. for the systems with mixed dynamics, they decay rapidly from a value of  0 1,c  change sign at some n becoming negative, then asymptotically tend to zero. in an attempt to quantify the dependence of c on n, we parameterized its empirical value in the form of a superposition of two exponentially decaying functions      1 1 2 2exp exp ,c n a n a n     and (arbitrarily) fixed the superposition coefficient as 1 1.5a  and 2 0.5.a   the curves in figure 3 show the resulting parameterization. the best fit parameters are  1 2,   (0.51, 1.9), (0.44, 2.1) and (0.2, 1.36) for. we may estimate  as the mean values of 1 and 2 and conclude that  has a value slightly larger than 1 for each billiard. this is sufficient to conclude that the ratio t  is large enough in each billiard to claim two well separated "time" scales in the level-spacings series, which justifies describing them within the framework of superstatistics. superstatistics in random matrix theory 765 figure 4. the values extracted from the time series for the superstatistical parameter  . figure 5. the parameter distributions obtained from the time-series analysis of the mixed limaçon billiards compared with the distributions in (1-3). a.y. abul-magd 766 4.3 estimation of the parameter distribution we represent the spectra of the three limaçon billiards as discrete time series, in which the role of time is played by the level ordering. the distribution  f  is determined by the dynamics of the entire time series representing the spectrum of each billiard. next, we need to determine which of these distributions fits best that of the slowly varying stochastic process  n described by the experimental data. since the variance of superimposed local gaussians is given by 1 ,  we may determine the process  t from the series 22 ,, 1 i i ti t s s    the result for the 1 2  billiard is shown in figure 4. figure 5 suggests that the extracted value of  (and thus the level density) shows rapid fluctuations superimposed over slower ones. this agrees with the picture described by the assumptions of the superstatistical rmt that the spectrum of the mixed system is composed of segments with different mean level density. the probability density  f  is determined from the histogram of the  i values for all i. the resulting experimental distributions are shown in figure 5. we compared them with the log-normal, the 2  and the inverse 2  distributions with the same mean  and variance 22 .  the inverse 2  distribution fits the data significantly better than the other two distributions. 5. nearest-neighbor spacing distribution this section focuses on the question whether the inverse 2  distribution of the superstatistical parameter η in (2) is suitable for describing the nearest-neighbor spacing distribution (nnsd) of systems in the transition out of chaos within the superstatistical approach to rmt. as mentioned above, the nnsd of a chaotic system is well described by that of random matrices from the goe, which is well approximated by the wigner surmise, if the system is chaotic and by that of poisson statistics if it is integrable. numerous interpolation formulas describing the intermediate situation between integrability and chaos have been proposed (guhr et al., 1998). one of the most popular nnsds for mixed systems is elaborated by berry and robnik (1984). this distribution is based on the assumption that semi-classically the eigenfunctions are localized either in classically regular or chaotic regions in phase space. accordingly, the sequences of eigenvalues connected with these regions are assumed to be statistically independent, and their mean spacing is determined by the invariant measure of the corresponding regions in phase space. the largest discrepancy between the empirical nnsds of mixed systems and the berry-robnik (br) distribution is observed for level spacing s close to zero. while the empirical nnsds of mixed systems almost vanish for 0,s  the berry-robnik (br) distribution approaches a constant and nonvanishing value for 0.s  it follows from (5) that the statistical measures of the eigenvalues of the superstatistical ensemble are obtained as an average of the corresponding  -dependent ones of standard rmt weighted with the parameter distribution  .f  in particular, the superstatistical nnsd is given by 0 ( ) ( ) ( , ) ,wp s f p s d      (7) where  ,wp s is the wigner surmise for the gaussian orthogonal ensemble with the mean spacing depending on the parameter , superstatistics in random matrix theory 767 21 ( , ) exp 2 wp s s s          (8) for a 2  distribution of the superstatistical parameter , one substitutes (1) and (8) into (7) and integrates over . the resulting nnsd is given by     0 2 1 /2 2 0 , 1 / p s s         (9) the parameter 0 is fixed by requiring that the mean-level spacing 0 ( )s s p s ds    equals unity. for an inverse 2  distribution of , given by (2), one obtains the following superstatistical nnsd   /2 0 2 0 /2 0 2 ( , ) , ( / 2) 2inv s s p s k s                   (10) where  mk x is a modified bessel function (gradshteyn and ryzhik, 1980),  x is a gamma function and 0 again is determined by the requirement that the mean-level spacing 1.s  finally, if the parameter  has a normal distribution (3), then the nnsd for this distribution,   2 2 ln / 2 log-norm 0 1 ( ) ( , ) , 2 wp s e p s d            (11) cannot be evaluated analytically and has to be calculated numerically. figure 6. experimental nns distributions for the two mixed limaçon billiards compared with the superstatistical distributions. a.y. abul-magd 768 we have compared the resulting nnsds given in (9), (10) and (11) with the experimental ones for the two limaçon billiards with mixed dynamics. in figure 6 the experimental results are shown together with the superstatistical and the br distributions (berry and robnik, 1984). 6. summary superstatistics has been applied to study a wide range of phenomena, ranging from turbulence to econophysics. among these applications is rmt, in which the parameter distributions of the random-matrix ensembles have been obtained by assuming suitable forms or applying the principle of maximum entropy. in this paper we use the time-series method to show that the spectra of mixed systems have two correlation scales as required for the validity of the superstatistical approach. the time-series analysis also shows that the best choice of the superstatistical parameter distribution for a mixed system is an inverse 2  distribution. we calculate the corresponding nns distribution of the energy levels and compare it with the spectrum of two microwave resonators of mushroom-shaped boundaries and two of the family of limaçon billiards, which exhibit mixed regular-chaotic dynamics. resonance-strength distributions for the limaçon billiards are also analyzed. in all cases the experimental data are found in better agreement with the corresponding distributions with i nverse-χ² superstatistics than all the other considered distributions including the celebrated brody nns distribution and the resonance-strength distribution that follows from the alhassid-novoselsky gamma distribution of transition intensities. 7. references abul-magd, a.y. 2006. 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transition from brody-like to berry-robnik behavior. j. phys., a27: 8059-8077. reif, f. 1984. fundamental of statistical and thermal physics. mcgraw-hill, singapore. relaño, a., gómez, j.m.g., molina, r.a., retamosa, j. and faleiro, e. 2002. quantum chaos and 1/f noise. phys. rev. lett., 89: 1-4. robnik, m.j. 1983. classical dynamics of a family of billiards with analytic boundaries. physica, a16: 3971 -3986. rosenzweig, n. and porter, c.e. 1960. repulsion of energy level in complex atomic spectra. phys. rev., 120: 1698-1714. received 25 april 2011 accepted 11 september 2011 squ journal for science, 2014, 19(2), 91-96 © 2014 sultan qaboos university 91 a test for dominance atsu s.s. dorvlo department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. email: atsu@squ.edu.om. abstract: in some selection situations a simple majority is not enough to indicate that one item dominates the others. in this paper we develop a simple procedure for testing the dominance of one item with respect to others in a multi option situation. expressions are given for computing the relevant p-values. the procedure is illustrated. keywords: dominance; modal class; categorical variable; hypothesis testing. سيطرةالاختبار اتسو دورفلو لقذ .العاهل الوسيطز هي بيي العواهل األخزىالوخخارة غيز كافيت لخذل علي أى عٌصزا واحذاً هو في بعض الحاالث إى األغلبيت البسيطت ملخص: لعٌصز واحذ بالوقارًت هع عٌاصز أخزى عٌذ وجود خياراث هخعذدة. لقذ حن وضع العاهل الوسيطز الخخياربسيطت طورًا في هذا البحث طزيقت يقت.ووضحج الطز pالصيغت الوٌاسبت لحساباث القين اخخبار الفزضياث. ،الوخغيز الحاسن ،الحزم الوشزوطت ،العواهل الوسيطزة: مفتاح الكلمات 1. introduction uppose that a categorical variable x can take on m possible values arbitrarily numbered 1 to m. let  i p p(x  category i), i =,…,m. are all these categories equally likely? is there a statistically dominant category? these two questions can be put formally as (i) are all the items equally likely versus (vrs) does at least one item occur more often. this hypothesis is that the probability of selecting each item is the same against the probability of selecting at least one item which is different from the others. that is  m ph i 1 : i, vrs. m ph i 1 :   for at least one i. secondly (ii) there is no dominant category vrs there is a dominant category. both hypotheses can be stated more generally as (iii) : , 1,..., i i h p p i m     where i p  are specified probabilities vrs at least one of them is different from the specified i p  . the rejection of the null hypothesis under (i) does not indicate which item is most preferred. also rejecting this hypothesis does not necessarily mean that a particular item is dominant. however, accepting the null hypothesis under (i) will imply that the null hypothesis under (ii) is true. the reverse is not necessarily true. the hypothesis (i) or (iii) can be tested using either the pearson chi-square statistic or the likelihood ratio statistic [1]. however the statement of dominance does not necessarily imply any particular probabilities under the null hypothesis. statistical dominance of g over f implies that ( ) ( )g x f x x   with strict inequality for some .x there are numerous kolmogorov-smirnov type tests for the dominance of g over f with many applications in financial mathematics [2-4]. tse and zhang [5] compared several tests for stochastic dominance using monte carlo simulation. this formulation of dominance implies a form of simple majority. instances where it is desired to know which item is most preferred occur frequently. in an opinion poll of say six politicians, which politician is the dominant one? in a restaurant that serves four types of deserts, which desert is the most patronized? when a group of seniors from a high school are asked to select a university from a list, which university will be the most selected? in an ‘eye-movement thought process experiment’, is there a dominant pattern for a particular thought process[6,7]? these examples and others like them often occur in practice. frequently a simple majority is enough to declare one option the favorite. the notion of dominance, however, involves a larger majority than a simple majority of the item where the simple majority item is not necessarily the dominant item. in this paper we propose a test that will indicate whether the modal item is dominant when there are m items/choices and the (selectors) s atsu s.s. dorvlo 92 sample size is n. to establish if a particular item is dominant we propose computing the probabilities associated with selecting an item i by j selectors out of n. 2. distribution of an item xi suppose xi is the number of subjects who have selected the i th item. this implies that 1 . m i i x n    the sample space for any xi is {0, 1, 2,..., n}. the null hypothesis of there being no dominant item implies that no particular item is favoured, hence without loss of generality we shall discuss the distribution of the number of subjects, x1, selecting item 1. the number of combinations such that x1 = j and the sum of the rest of the xis is equal to (n-j) is given by the binomial coefficient         2 2 m jnm , for m, the given number of items to be selected from, and n, the number of subjects doing the selection. then  1 21 , 0,1, 2,....., 2 n m m n j p x j j n mk           (1) where                   1 1 2 2 0 m nm m jnm k n j . after some simplification we have                    .,...,2,1, 1 1 1 1 0, 1 1 1 1 njfor tnm tn nm m jfor nm m jxp j t n m (2) table 1 gives an example of the frequency of x1, for various values of m from 3 to 10 and n = 10. table 2 gives the densities for x1. it is easy to prove that for fixed ,2m    jxpixp n m n m  11 for all i>j. also for a fixed i,    ixpixp n m n km   11 for positive integer k. these are illustrated in tables 1 and 2. table 1. frequency of x1 for given m and n=10. x1 3 4 5 6 7 8 9 10 0 11 66 286 1001 3003 8008 19448 43758 1 10 55 220 715 2002 5005 11440 24310 2 9 45 165 495 1287 3003 6435 12870 3 8 36 120 330 792 1716 3432 6435 4 7 28 84 210 462 924 1716 3003 5 6 21 56 126 252 462 792 1287 6 5 15 35 70 126 210 330 495 7 4 10 20 35 56 84 120 165 8 3 6 10 15 21 28 36 45 9 2 3 4 5 6 7 8 9 10 1 1 1 1 1 1 1 1 table 2. distribution of xi for a given m and n = 10. xi 3 4 5 6 7 8 9 10 0 0.1667 0.2308 0.2857 0.3333 0.3750 0.4118 0.4444 0.4737 1 0.1515 0.1923 0.2198 0.2381 0.2500 0.2574 0.2614 0.2632 2 0.1364 0.1573 0.1648 0.1648 0.1607 0.1544 0.1471 0.1393 3 0.1212 0.1259 0.1199 0.1099 0.0989 0.0882 0.0784 0.0697 4 0.1061 0.0979 0.0839 0.0699 0.0577 0.0475 0.0392 0.0325 5 0.0909 0.0734 0.0559 0.0420 0.0315 0.0238 0.0181 0.0139 6 0.0758 0.0524 0.0350 0.0233 0.0157 0.0108 0.0075 0.0054 7 0.0606 0.0350 0.0200 0.0117 0.0070 0.0043 0.0027 0.0018 8 0.0455 0.0210 0.0100 0.0050 0.0026 0.0014 0.0008 0.0005 9 0.0303 0.0105 0.0040 0.0017 0.0007 0.0004 0.0002 0.0001 10 0.0152 0.0035 0.0010 0.0003 0.0001 0.0001 0.0000 0.0000 a test of dominance 93 3. the joint distribution of two items x1 and x2 without loss of generality we consider the joint distribution of x1 = i and x2 = j. the sample space for the (x1, x2) combination is             0,,...,1,1,...,0,1,,0,...,1,0,0,0 nnn  . let k be the total combinations needed to fill the m items/choices. hence if x1 = i and x2 = j such that ,nji  for ix n  then the number of combinations for this set is         3 3 m jinm . therefore the joint distribution of x1 = i and x2 = j is  1 2 31 , , 3 n m m n i j p x i x j i j n mk              (3) where 0 3 3i j n m n i j k m              and the summation is over all possible i and j values such that the sum over all the items is n. this sum reduces to   0 3 1 1 1 . 3 1 n t m n t m n m n k t m n m                              (4) the probability in (3) can therefore be written in the computationally friendly form               1 2 1 1 2 , 0, 0 1 2 , 1 2 1 , 1 . 1 2 2 n m k t m m for i j m n m n p x i x j m m n t for i j n m n m n m n t                              (5) the joint distribution is dependent on only the sum of units selecting these two items. therefore if the interest is in the number of subjects, nk  , selecting any two items then the distribution is                1 2 1 1 2 , 0 1 2 1 1 2 1 , 1, 2,..., . 1 2 2 n m k t m m for k m n m n p x x k k m m n t for k n m n m n m n t                         (6) 4. the conditional distribution of xk given xl from the distribution of xk and the joint distribution of xk and xl we can derive the conditional distribution of say, .1 | xx k without loss of generality, the joint distribution of 1 2 |x x is given below.  1 2 1 1 ( 2) , 0, 0 ( 2) ( 2) , 0, 0, ( 2 ) | ( 2) 1 0, 0, ( 2) 2 ( 2) 1 0, 0, ( 2 ) 2 n m i t i j t j m for i j m n m for i j j n m n j p x i x j m n t for i j i n m n m n t m n t for i j i j n m n j m n t                                              (7) atsu s.s. dorvlo 94 5. a dominance test the acceptance of 1 : i h p i m    implies that there is no dominant item. however, the acceptance of the hypothesis of there being no dominant item does not necessarily imply 1 : i h p i m    . hence the first step in testing for dominance may be to perform the chi-square test for  m ph i 1 : i vrs m ph i 1 :   for at least one i. there may therefore be a dominant choice if the null hypothesis is rejected. in preference testing, one expects that the dominant item be the most selected. the item xi is said to be the modal item if the number of subjects that selected it is more than the number of subjects that selected any other item. we say that item xi is the modal item if xi >xj, for ji  for all j. in considering hypothesis (ii), it is intuitively clear that xi, the modal item, will be the dominant item the closer xi is to n. we can therefore base a test on the statistic xi the modal item. reject that there is no dominant item if xi is large. in fact, when the modal item is small, that means that the subjects are divided among the items equally except for random fluctuations. therefore the modal item is the dominant item if xi is greater than some y for which ( )ip x y   . from eq (2) the p-value can be computed from 1 1 1 ( ) , 1 1 jn i j y t m n t p x y m n m n t              where y is some observed modal value. when this p-value is less than some , then that particular item can be said to dominate the others. 6. discussion the proposed test checks if the modal item is the dominant one. however, suppose the interest is in determining if a particular item is dominant. the above test can still be used in one of two ways. 1. compute the p-value associated with the realization of this item. if it is less than  of choice, then the item is dominant. 2. compute the p-value associated with the modal item. if this is less than  , then the modal item is dominant. hence the item of choice cannot be said to be dominant, assuming there is only one dominant item. 7. an illustration twenty-five council members were asked to decide which of four amendments (m1, m2, m3 and m4) to a bill will be most favorable to their constituents. for example, suppose 14 voted for m1, 6 for m2, and 3 and 2 for m3 and m4 respectively. a chi-square test showed that not all the amendments are equally appealing to the councilors (  =14.2, p-value = 0.003). however no amendment is dominant (p-value = 0.111). for an amendment to be dominant, at 05.0 , it should have the vote of at least 18 out of the 25 council members. table 3 gives the critical values for some m and n at 05.0 . for m and n large, it is possible that this test will show that two or more items can be dominant. for example, suppose that m = 8 and n = 30, the critical value for dominance at 05.0 is 12. it is therefore possible that two items can have this number or more. however, the probability of this happening will be very small. the joint probability of two items having large values is generally small (eq (5) and (6)). in this example the probability of two items getting 12 or more at the same time is only 0.0023. also it can be shown that the conditional probability of a large item, xi given that xj is large, is small (eq (7)). an interesting application of the above formulation is to be able to compute the p-value corresponding to a particular modal value and thereby know ones position of strength. 8. acknowledgement i would like to acknowledge referees for suggestions which went to improve the readability of this paper. 9. appendix the following identities were useful in proving the distributions above. a test of dominance 95                    ba t ba a b ta t 0 2 )1(                          ba t ba a b a b ta 0 1 1 1                    ba t ba a a ba b ta t 0 2 2 table 3. critical values for dominance at 05.0 for some n and m. n/m 3 4 5 6 7 8 9 10 3 3 3 3 3 3 3 2 4 4 4 3 3 3 3 3 5 5 5 4 4 4 3 3 3 6 6 5 5 4 4 4 4 3 7 7 6 5 5 4 4 4 4 8 8 7 6 5 5 5 4 4 9 9 7 6 6 5 5 5 4 10 9 8 7 6 6 5 5 5 11 10 9 8 7 6 6 5 5 12 11 9 8 7 6 6 6 5 13 12 10 9 8 7 6 6 5 14 12 11 9 8 7 7 6 6 15 13 11 10 9 8 7 6 6 16 14 12 10 9 8 7 7 6 17 15 12 11 9 8 8 7 7 18 16 13 11 10 9 8 7 7 19 16 14 12 10 9 8 8 7 20 17 14 12 11 10 9 8 7 21 18 15 13 11 10 9 8 8 22 19 16 13 12 10 9 9 8 23 19 16 14 12 11 10 9 8 24 20 17 14 13 11 10 9 9 25 21 18 15 13 12 11 10 9 26 22 18 15 14 12 11 10 9 27 23 19 16 14 12 11 10 9 28 23 19 17 14 13 12 11 10 29 24 20 17 15 13 12 11 10 30 25 21 18 15 14 12 11 10 31 26 21 18 16 14 13 12 11 32 26 22 19 16 14 13 12 11 33 27 23 19 17 15 13 12 11 34 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dorvlo, a.s.s. and al-adawi, s. eye-movements and ongoing task processing. perceptual and motor skills., 2003, 96(3 pt. 2), 1330-1338. 7. zhou, y.h., gao, j.b., white, k.d., merk, i and yao, k. perceptual dominance time distributions in multistable visual perception. biol. cybernet., 2004, 90(4), 256-263. received 13 october 2013 accepted 4 november 2014 full page photo squ journal for science, 12 (2) (2007) 87-100 © 2007 sultan qaboos university 87 soft chemistry routes to new nanosize materials khaled melghit chemistry department, college of science, sultan qaboos university. p.o. box 36, postal code 123, sultanate of oman. e-mail: melghit@squ.edu.om. النانو في حجم جدیدة موادّ لتحضیر شبھ المستقرةیمیاء الك خالد ملغیت . تتلخص ھده الطریقة في خلط خزف أو تفاعل الحالة الّصلبةال ةھي طریق لالعضویةلطریقة الكالسیكیّة القدیمة إلعداد المواّد اا خالصة : ود، مجتمع علم المواّد منذ ثالثة عق . حتّى الیومالجدیدةّ إلعداد المواد ستخدمتفي حرارة عالیة . ھذه الّطریقة ّالمواد االولیة ثم تسخینھم كالسیكیّة، طرق الطریقة الر مجال تكنولوجیا النّانو . بدالً من وخاّصة مع ظھ ،)chimie douce ( شبھ المستقرة كیمیاءال رأى أھمیة و ئلالسا حرارةو phو یتم تغییر بعض عناصرالتحضیرمثل ئل ى الساذَاب فت . المواد االولیة حرارة أقلّ لستعمت شبھ المستقرةالكیمیاء على ,نانو متر 100 أقل منجزیئات بحجم یتكون من للحصول على المنتج المرغوب . باستخدام حرارة أقّل، المنتج زمن التّفاعل لككذ حجم مدى منحجم أكبربإلى جزیئات اھذ یؤّديمما ، الیةحرارة ع درجةستخدم التى ت( أو تفاعل الحالة الّصلبة ) ةعكس الّطریق الخزفیّ بالّطریقة ھاالّشبھ مستقّرة ) و غیر ممكن الوصول إلی مایسمى بالمواد( حرارة العالیة مستقّرة في الالغیر ھمةالم وادنانو . أیًضا بعض المال . زیادةائیّة مھّمةبنائیّة و خواّص فیزیلدیھا سمة بصفة عامة، ،الّشبھ مستقّرة وادھذه الم .شبھ المستقرةكیمیاء ة تحضر األن بالالكالسیكیّ .لىابمستوى نقاء ع ة تكونالمنتجمواد ذلك، ال على abstract : the old classical method for preparing inorganic materials is by the ceramic route or solid state reaction. it consists of mixing the starting materials at an elevated temperature. this method has been used for preparing numerous new materials until today. three decades ago, the materials science community was aware of soft chemistry synthesis or chimie douce, especially with the emergence of nanotechnology field. instead of the classical method, which involves high temperature, soft chemistry techniques use lower temperatures. in general, starting materials are dissolved in a liquid phase and different parameters such as ph, temperature and reaction time are adjusted in order to obtain the desired product. by using a lower temperature of preparation, the product obtained shows nanosize particles, with sizes lower than 100 nanometers. in contrast, the ceramic route (or solid state reaction) using higher temperatures leads to bigger particles size that are out of the nanosize range. also, some interesting phases that are not stable at elevated temperatures (named metastable phases) and are not accessible by the classical method, are now prepared by the soft chemistry technique. usually these metastable phases have interesting structural features and important physical properties. adding to that, the product is obtained with a higher level of purity. keywords : solid state reaction, soft chemistry, metastable phase, nanosize materials. 1. introduction khaled melghit 88 norganic materials (or mineral compounds) are important classes of chemistry. our development was not possible without these materials. it is recognized that many inorganic materials played a role in the history of human civilization; beginning from stone, copper, bronze, iron, aluminum and recently silicon which is the key to electronic and computer development. with new advanced inorganic materials being discovered, our life becomes easier and more technology is implemented in our daily life. let's take one example: the development of batteries leads to smaller mobile phones that can fit in our pocket. this has been possible because of new inorganic materials that can deliver high current energy with a smaller mass. the research is still going on to improve these materials in the hope to commercialize, in the future, an electrical car in the same manner as in the present oil-based cars. this goal can be reached if only new materials are discovered with the desired properties. this needed improvement on the techniques of preparation and new techniques should be tried. classical preparation or ceramic route was known from the old age as a fire preparation. although, until today, the method still remains proves its capability in preparing many new materials. however, it shows deficiency for preparing nanosize materials or metastable phases that usually show interesting properties and are needed for today’s applications. chimie douce or soft chemistry, that uses lower temperature, often room temperature, was found to be the alternative for ceramic preparation. the present review deals with such a preparation method. 2. ceramic route the classical method of preparation of inorganic materials is called solid state reaction or ceramic route. it is a very old method; it consists of mixing the starting materials in a container and heating the mixture at elevated temperature. the temperature used is often near to the melting point of the starting materials. in some reactions, one or more starting materials may melt. the reaction is based on the diffusion of atoms between the particles of starting materials to form the new product. this method has been used to prepare many new materials for a very long time, as it is said in the holy qur`an, chapter 18, verse 96: (bring me blocks of iron; until when he had filled up the space between the two mountain sides, he said: blow, until when he had made it (as) fire, he said: bring me molten brass which i may pour over it). the method used by prophet zul-qarnain (peace be upon him) is indeed a solid state reaction. until the present time, solid state reaction remains a powerful method and a choice for many researchers for preparing inorganic materials. in a typical solid state reaction the starting materials are mixed and ground in a pestle and mortar or using a ball milling system. then, the mixture is heated on a crucible at high temperature. usually different grinding at different stages of heating are needed followed by pelletization in order to increase the contact between starting materials. as the product is formed the constituents have to diffuse through the product phase which may be difficult without several grinding stages. figure 1 shows a good contact between crystallites of starting materials. starting reagents with large surface area are suitable. it is recommended to start with reagents that decompose prior to or during reaction like carbonates or nitrates. it is suitable to use reactants with crystal structures similar to that of the product (topotactic reactions: to enhance the rate of nucleation of the product phase). the diffusion coefficient increases with temperature, rapidly as you approach the melting point. this concept leads to tamman’s rule: extensive reaction will not occur until the temperature reaches at least 2/3 of the melting point of one or more of the reactants. it is important before starting a solid state reaction to have the knowledge of some parameters such as the phase diagram of the system under study in order to know the nature of the product that could be obtained at a given temperature. example of phase diagram is given on figure 2. at a given temperature, one or more than one phase could exist. to obtain a pure phase it is necessary to have knowledge of such phase diagram. i soft chemistry routes to new nanosize materials 89 figure 1. transmission electron micrograph (tem) showing the contact between the two starting materials (a and b) in a solid state reaction. figure 2. binary diagram of the v2o5-fe2o3 system. 2.1 examples of solid state reactions (a) preparation of zntio3 (chang et al, 2004): zntio3 was prepared by conventional solid state reaction using a mixture of zno with tio2. the starting materials were mixed in ethanol by ball milling for 24 hours and annealed at different temperatures: 700°c, 800°c, 900°c and 1000°c each for 24 hours. then the mixtures were pressed into discs and sintered at 800-940°c for 24 hours. khaled melghit 90 (b) preparation of la1-xfexvo4 (varma et al, 2004): for this preparation a mixture of oxides v2o5, la2o3 and fe2o3 was used. this mixture was heated at 900°c for 8-10 hours, and then it was pelletized into discs and heated at 600°c for 90 hours and at 800°c for 24 hours with grinding in between. (c) preparation of ba1-xcaxtio3 (chen et al, 2004): in this preparation, carbonate of baco3 and caco3 and tio2 powder were used. they were mixed by ball milling for 24 hours and then calcined at 1100°c in air for 3 hours. the calcined powder added with 8 wt. % of pva was pressed into discs and then sintered at 1350-1375°c for 3 hours. (d) also preparation of (ba, sr)-mn oxides (heiras et al, 2002): baco3, srco3 and mn2o3 in appropriate atomic ratios were mixed, ground and calcined at 850°c for 24h following two steps at 350 and 650°c for 3 hours each. the calcined powder was reground and pressed into 1 cm diameter pellets at a pressure of 650kg/cm2. pellets were sintered at 950°c for 24 hours following two pre-sintering steps at 650 and 750°c for 3 hours each. from these examples it is clear that the solid state reaction goes through a mixing and heating steps. thus, the english description: shake and bake. it is therefore necessary to put as much particles as possible in contact in order for the reaction to go to completion. in general many grinding, pressing and heating are needed. however in reality it is not possible that all starting materials will react completely and a small amount of reactant always exists with the product that could affect its physical properties. often, the use of high temperature in the method of preparation leads to sublimation of small amount of starting element, for instance oxygen which will affect the oxidation state of the final product. the use of high temperature reaction also does not allow the control of size and morphology of the product particles. high temperature leads to bigger particles with strong agglomeration that reduced the surface area and hence the reactivity of the product in chemical or physical applications. another inconvenience of the solid state reaction is the lack of preparing new metastable phases. in several systems a metastable phase could exist beside the stable phase (the known phase). the metastable phase has the same chemical composition as the known phase but with different crystalline structure. metastable phases are stable at relatively lower temperature; above this temperature the phase will transform to give the known stable phase that is usually obtained at higher temperature. because the solid state reaction uses high temperature in the method of preparation, it is not possible to prepare these phases. other inconvenience is the cost of preparation since a much higher temperature used requires a higher energy and therefore involves a higher cost. for this raison, about thirty years a go, the scientific community started to think of new methods of preparation whereby lower temperatures could be used. this new method will have the possibilities for preparing new advanced inorganic materials, in general metastable and nanosize phases, to meet the actual technological challenge. 3. soft chemistry (chimie douce) soft chemistry is a technique that uses low temperatures for preparing inorganic materials. historitically, soft chemistry or chimie douce was introduced by a french scientist three decades ago (j. livage, 1977). the idea comes from nature: the silicate which is prepared by industries at elevated temperatures (more than 1000°c) is found to be prepared at room temperature by the living organism diatoms and radiolarians in the marine area from the small amount of silica dissolved in the water with sophisticated, artistic and beautiful shapes figure 3. however, industry with the present development is not able to obtain similar shapes. it was important to study the mechanism involved for preparing such materials at lower temperatures. in such preparation, it is clear that a solution method or a wet method should be used instead of the dry method used by solid state reaction (j. livage, 2001). with time the scientific community was aware of the importance of soft chemistry in preparing new advanced inorganic materials which cannot be prepared by solid state techniques. different progresses were made in the field over the entire world especially in france, germany, england, japan and north american. presently, also many companies are dealing with soft chemistry techniques; their products are obtained at lower temperature especially with the emergence of nanotechnology and composite materials (inorganic-organic and inorganic-bioorganic composites). two major important benefits soft chemistry routes to new nanosize materials 91 of the soft chemistry techniques can be cited here: preparation of new metastable phase and preparation of nanosize materials. figure 3. sio2 formed by a living organism at normal temperature. 3.1 preparation of metastable phase one of the important advantages of soft chemistry is its capability in preparing new metastable phases which cannot be prepared by the classical techniques using high temperature. usually metastable phase presents open crystal structure and shows interesting physical and chemical properties. (poeppelmeier et al., 1994; rouxel, 1988, weiss, 1973; melghit et al, 1999). for example several years ago, a new metastable form of chromium orthovanadate was prepared (touboul and melghit, 1995 ); up to that time chromium orthovanadate crvo4 presents only one form which can be prepared by a solid state reaction at elevated temperature of 1000ºc from mixed oxide of vanadium and chromium. 1000°c v2o5 + cr2o3 → 2 crvo4 the solid state reaction cannot leads to preparation of new form of crvo4 if they exist because they are only stable at lower temperature (< 1000°c). a soft chemistry technique can be used starting from vanadium oxide dissolved in water and aqueous solution of chromium nitrate. 100ºc v2o5 1.8h2o + 2 cr(no3)3 9h2o → precipitate (aqueous) (aqueous) stirring the precipitate obtained was amorphous however it crystallized at 550°c to give a new phase. the new phase has a monoclinic crystal system different from the crystal system of the stable phase which is orthorhombic figure 4. if the new phase is heated at higher temperature it will leads to the stable phase orthorhombic crvo4. the two phases have the same chemical composition but different crystalline structures figure 5. the new metastable phase has shown good catalytic properties especially when it is mixed with other metals (song et al, 2002; shishido et al, 2003; song et al, 2003; zhaoxia et al, 2001). khaled melghit 92 figure 4. powder x-ray diffraction of crvo4 prepared by a soft chemistry technique and annealed at different temperatures (touboul and melghit, 1995). figure 5. polyhedral crystal representation of crvo4 metastable (monoclinic) and crvo4 stable (orthorhombic). similar to the chromium vanadate system a new metastable phase was also found on the indium vanadate system (touboul et al, 1995; touboul et al, 1994). also recently a new zinc pyrovanadate zn3v2o7(oh)2.2h2o was prepared at lower temperature using soft chemistry. it shows interesting open crystal structure figure 6 that can find potential application (zavalij et al, 1997; melghit et al, 1999; hoyos et al, 2005, melghit et al, 2007). soft chemistry routes to new nanosize materials 93 figure 6. polyhedral crystal representation of metastable zn3v2o7(oh)2.2h2o the question which can arise is why a solid sate technique cannot prepare the same metastable phases. in solid state reaction, the mixture must be heated at higher temperature to allow the diffusion between atoms; otherwise the reaction will not take place. the high temperature used exceeds in general the thermal stability of the metastable phase. solid state reaction aims to prepare a stable phase, obtained at higher temperature, which possesses a lower free energy. the metastable phase is not the phase which possesses the lowest free energy in view of thermodynamic (figlarz, 1994) however it is obtained mainly for kinetic reason. in each chemical reaction there are two parameters that affect the formation of product: kinetic and thermodynamic parameters. the metastable phase is not favorable in term of thermodynamics because its free energy is higher than the free energy of the stable phase but kinetically it is more favorable, it has lower activation energy. thus, higher rate compared to the stable phase that allows this phase to appear but with limited range of thermal stability. it will transform to the stable phase if it is heated at higher temperature. in the previous example chromium orthovanadate is initially obtained from the solution as an amorphous phase figure 4. when this precipitate is heated at 500°c a new metastable phase is formed (crvo4 monoclinic). this phase is not the stable phase in the chromium vanadate system; the stable phase is orthorhombic crvo4, but kinetically it is more favorable at that temperature 500ºc. if now the temperature is higher, 700ºc, the stable phase becomes favorable by both kinetic and thermodynamic; it will form and remain stable because it has the lowest free energy. 3.2 preparation of nanosize materials the other important point of soft chemistry that makes it attractive to the scientific community is its capability for preparing nanosize materials. nanosize materials show higher surface area, more reactivity and interesting physical properties compared to the usual bulk materials. nanotechnology is currently gaining interest from chemists, physists and biologists for its promising future. because solid sate reaction uses higher temperature, the particles obtained are bigger and out off the nanosize range. the effect of temperature on particle size is known as can be seen from the following example: indium orthovanadate invo4 can be obtained either from heating the metastable phase monoclinic at 600°c or by stirring the precursor obtained at room temperature for 6 hours (melghit, 1994). the two materials have the same chemical composition and the same crystalline structure deduced from the x-ray diffraction spectra. figure 7. the phase obtained at room khaled melghit 94 temperature clearly shows very fine particles figure 8 and broader x-ray diffraction peaks. in contrast the phase obtained by heating at 600ºc shows bigger particles and sharper x-ray diffraction peaks. figure 7. powder x-ray diffraction of invo4 iii (prepared by heating a precursor at 600°c) and invo4 iii* (obtained at room temperature). as the temperature of preparation is lowered the particles obtained are smaller. other example, such as spherical nanosize tin oxide, sno2·xh2o, figure 9 which can be obtained at room temperature using a simple soft chemistry technique starting from tin dichloride stirred in distilled water for several hours (k. melghit, unpublished data). 3.3 some comment techniques used in the soft chemistry preparation 3.3.1 sol-gel method a solution of molecular precursors is progressively transformed into an oxide network via inorganic polymerization reactions. most precursors are metal alkoxides m(or)z where r is an alkyl radical (r= ch˙3, c2h˙5,….) (bradley, 1978) we can have hydrolysis with h2o: m(or)z + x hoh → m(or)z-x(oh)x + x roh or condensation with a metal m'oh m(or)z + x m'oh → m(or)z-x(om')x + x roh if m'=organic or inorganic ligand, a complexation takes place soft chemistry routes to new nanosize materials 95 figure 8. scanning electron microscope (sem) of invo4 iii prepared by heating a precursor at 600°c and invo4 iii* obtained at room temperature. figure 9. tem micrograph of sno2·xh2o particles. khaled melghit 96 figure 10. flow chart showing preparation of nano-tio2 powders through a sol-gel process (qiu et al, 2006). the metal alkoxides continue its hydrolysis until the protonated roh ligand is finally removed. it is reported (livage, 1994) that the chemical reactivity of metal alkoxides toward hydrolysis and condensation mainly depends on the positive charge of the metal atom m and its ability to increase its coordination number n. as the general rule, as the electronegativity of metal atoms decreases and their size increases when going down the periodic table the corresponding alkoxides become progressively more reactive toward hydrolysis and condensation. silicon alkoxides are rather stable while alkoxides of electropositive metals must be handled with care under a dry atmosphere. this method is increasingly being used and many examples of such technique exists in the literature. some examples are given below a) preparation of anatase nanotubes as support for platinum nanocrystals (eder et al, 2006): the carbon nanotubes were coated by a sol-gel template method, followed by a hydrothermal treatment. the gel is formed from titanium alkoxide (such as titanium isopropoxide) which was dissolved in ethanol and slowly dropped into carbon nanotubes suspension. the titanium precursor hydrolyses with water to form hydroxyl group that will further condense in the process to build up a gel type ti-o-ti network. heating the sample at 500°c will removed the carbonaceous template. b) preparation of nanocrystalline titanium dioxide (qiu et al, 2006): the method is shown in the flow chart of figure 10. this method uses an organic sol-gel technique that leads to preparation of nanosize anatase tio2. an inorganic sol-gel method was recently used and the same product was obtained (melghit et al, in press). the method consists of dissolving titanium trichloride in water, after that hydrogen peroxide was added and the soft chemistry routes to new nanosize materials 97 mixture was stirred for several hours, then ammonium hydroxide was added. an amorphous yellow gel was obtained which crystallized to pure anatase after heating at 300°c figure 1. figure 11. powder x-ray diffraction of tio2 anatase obtained by using aqueous sol-gel method (melghit et al, in press). c) preparation of in2o3 nanorods (cheng et al, 2006): indium chloride was added to polyethylene octyl phenyl ether and stirred and then the ammonia was added. the gel obtained was heated at 500°c to obtain in2o3 nanorods. d) preparation of tio2 nanorods rutile (melghit and al-rabaniah, 2006): inorganic sol-gel method was also used for preparing nanorods tio2. ticl3 solution was stirred in water for several hours after that ammonium hydroxide was added. the gel obtained is formed from crystalline pure nanorods rutile tio2 figure 12. 3.3.2 precipitation method the precipitation method is widely used in recent years for preparing many new materials. in general, the product is obtained from a solution medium. the precipitate depends mainly on the experimental conditions like the ph, temperature and reaction time. the starting materials should be soluble in the solution and should be able to precipitate to form the new product. by changing the experimental conditions (ph, temperature, and reaction time) it is possible to find the optimum experimental parameters where a new phase can precipitate. for example, in preparing mixed oxide like zinc pyrovanadate zn3v2o7(oh)2.2h2o (melghit et al, 1999); two solutions should be prepared. the first solution will contain vanadium ions and the second solution will contain zinc ions. when the two solutions are mixed, a clear solution is formed. however by increasing the ph, using ammonium hydroxide, and heating to boiling temperature, a precipitate of zinc vanadium oxides was obtained. in other preparations, a precipitate is obtained without ph control. an example of such preparation is iron orthovanadate fevo4 (melghit and al-mungi). when the two solutions which contains iron ions and vanadium khaled melghit 98 ions, are mixed a precipitate is obtained immediately without ph control. sometime, in soft chemistry preparation, material formed presents a different composition compared to the initial composition of reactants; this is different to solid state reaction where the product composition usually has the composition of initial reactants. figure 12. tem micrograph of nanorods tio2 rutile (melghit and al-rabaniah, 2006). 3.3.3 hydrothermal method the term hydrothermal came from the earth sciences, where it implies a regime of high temperatures and water pressure. the technique uses a high temperature and pressure apparatus called autoclaves or bombs. hydrothermal synthesis usually involves water heated at higher boiling temperature (>100°c) with a higher pressure (> few atmospheres) compared to the normal atmosphere. many chemical hydrothermal experiments have led to many metastable phases that have open structure and interesting application. some time a templating ion was used in order to modify the product. also the ph was found to be important and affect the final product. for example if na2wo4 is acidified with hcl and is heated in an aqueous environment at 150°c, both a one dimension and three dimension tunnel structure are formed depending on the initial ph of the reaction medium (whittingham, 1994). beside that the technique was also used for preparing fine oxide powders (somiya et al, 2000). 3.3.4 intercalation and deintercalation usually these types of reaction take place in the lamellar compounds. for example li2fes2 (ouvrard et al, 1994) has hexagonal close packing layers of sulfur atoms with iron in tetrahedral sites. lithium atoms are found in equal proportions in octahedral sites between the s-fe-s layers and in tetrahedral sites inside these layers. lithium presents a high mobility it can be intercalated or deintercalated from the host chemical or electrochemically. it can be removed from the host by stirring the li2fes2 powder suspension in an iodine/acetonitrile solution or electrochemically by recharging a lithium battery. another similar example is deintercalated of lithium from limn2o4 (coowar et al, 1994). from these examples, by using soft conditions, soft chemistry preparation offer many advantages over classical method such as preparation of new interesting metastable phase. it leads also to the same material prepared by the solid state reaction but at lower temperature. this will save energy and lower the production soft chemistry routes to new nanosize materials 99 cost. in addition, the product obtained shows a higher level of purity and nanosize particles that lead to high surface area and hence higher reactivity. although the preparation using soft chemistry appears to be easy, it is not straightforward because starting reactants must be soluble in the solution which is not always the case. besides, the knowledge of behavior of reactant species in the solution with ph will be advantageous. for example in precipitation reaction, if two elements have to be obtained in the final product, it is important to find a common ph value where the two metals can precipitate in the same time. also it is important to give attention during experiment to other parameters such as temperature, stirring time and heating. such experiments are very sensitive to experimental conditions and a missed detail, even small, can be the cause of not getting the same product. for example a longer stirring time for few hours can instead affect the product to become crystallized which is obtained initially as amorphous phase (melghit, 1994). as its name indicates, the soft chemistry is soft and sensitive to experimental conditions and therefore care should be taken to record every experimental step. 4. conclusion although solid state reaction remains used in the laboratory until today, it presents less advantages in advancement of recent applications. the industries, which are under technological challenge, are more demanding for new materials with specific characteristic and better physical properties. often, these new materials are metastable phases that can be prepared only by soft chemistry techniques. the nanotechnology field takes more importance with time and becomes research area for many laboratories over the world. this is absolutely the domain of soft chemistry. by using high temperature that leads to bigger particles, solid state reaction cannot compete with soft chemistry in such area. in the recent years, soft chemistry or chimie douce was given more interest by the scientific community, indeed a sol-gel research journal was created in 1995, and several conferences on the subject took place. this indicates the role of such technique in chemistry of advanced inorganic materials. 5. references bradley, d.c., mehrotra, r.c., gaur, d.p. 1978. metal alkoxides, academic press, london. chang, y.s., chang, y.h., chen, i.g., chen, g.j., chai, y.l., fang, t.h., wu, s. 2004. synthesis, formation and characterization of zntio3 ceramics. ceram. international, 30: 2183-2189. chen, x.m., wang, t., li, j. 2004. dielectric characteristics and their field dependence of (ba, ca)tio3 ceramics. mater. sci. eng. b, 113: 117-120. cheng, z-x., dong, x-b., pan, q-y., zhang, j-c., dong, x-w. 2006. preparation and characterization of in2o3 nanorods. mater. lett., 60: 3137-3140. coowar, f., tarascon, j.m., mckinnon, w.r., guyomard, d. 1994. lithium deintercalation 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al-belushi, a.k., al-amri, i. 2007. short reaction time preparation of zinc pyrovanadate at normal pressure. ceram. international, 33: 285-288. melghit, k. 1994. thesis. universite of picardie france. melghit, k., al-mungi, a.s. 2006. new form of iron orthovanadate fevo4.1.5 h2o prepared at normal pressure and low temperature. mater. sci. eng. b. 136: 177-181 melghit, k., al-rabaniah, s.s. 2006. photodegradation of congo red under sunlight catalysed by nanorod rutile tio2. journal of photochem. and photobiol. a: chem. 184: 331-334. melghit, k., belloui, b., yahaya, a.h. 1999. room temperature preparation of zinc pyrovanadate zn3 (oh) 2v2o7.2h2o. j. mater. chem., 9(7): 1543-1545. melghit, k., rabaniah, s., al-ameri, i. 2006. low temperature preparation and characterization of nanospherical anatase tio2 and its photocatalytic activity on congo red degradation under sunlight. ceram. international. accepted. ouvrard, g., prouzet, e., brec, r., rouxel, j. 1994. some chalcogenides syntheses 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3-picoline. j. catal., 218: 32-41. touboul, m., melghit, k., benard, p. 1994. synthesis by chimie douce and characterisation of indium vanadates. eur. j. solid state inorg. chem., 31: 151-161. touboul, m., melghit, k. 1995. synthesis by chimie douce and properties of chromium (iii) vanadates (v). j. mater. chem., 5(1): 147-150. touboul, m., melghit, k., benard, p., louer, d. 1995 crystal structure of a metastable form of indium orthovanadate inv o4-i.. j. solid state. chem., 118: 9398. varma, s., wani, b.n., sathyamoorthy, a., gupta, n.m. 2004. on the role of lattice distortion in the catalytic properties of substituted orthovanadates la1-xfexvo4. j. phys. chem. solids 65: 1291-1296. whittingham, m.s., li, j., guo, j.d., zavalij, p. 1994. hydrothermal synthesis of new oxide materials using the tetrametyhyl ammonium. mater. sci. forum. 152-153: 99-108. weiss, p.b. 1973. zeolites-new horizons in catalysis., chemtech, p. 498. zhaoxia, s., kadowaki, e., shishido, t., wang, y., takehira, k. 2001. 3-picoline oxidation over monoclinic orthovanadate cr0.5al0.5vo4 catalysts. chem. letters 8: 754-755. zavalij, p.y., zhang, f., whittingham, m.s. 1997. a new zinc pyrovanadate, zn3(oh)2v2o7.2h2o, from x-ray powder data. acta crystallogr. sect. c: cryst. struct. communications 53:1738-1739. received 6 december 2006 accepted 24 june 2007 microsoft word math090915-f -edited_corrected.doc 81-86 squ journal for science, 15 (2010) © 2010 sultan qaboos university 81 formulas for the number of spanning trees in a chain of cycles thomas bier department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, postal code 123, muscat, sultanate of oman, email: tbier@squ.edu.om. لعدد األشجار المولدة في سالسل الدوراتصيغة بييروماسث ، اوجدنا صيغة لعدد اشجار المولدات في سلسلة الدورات و التي لها على االقل حافة واحدة مترابطة مشتركة :خالصة .هذه الصيغة تستعمل الخواص االولية للكسور الغير منتهية. و لكن بحجم دورات مختلف abstract: we give a formula for the number of spanning trees in a chain of cycles that have connected intersection of one edge but where the cycles have variable sizes. the formula uses basic properties of continued fractions. keywords: spanning trees, arboricity and continued fractions. 1. sequences of cycles onsider a graph which is a sequence of n cycles 123..nc where cycles (of variable size but larger than two) with adjacent labels share a single common edge. an example with 5n = is given in figure 1. figure 1. some sequences of cycles. c thomas bier 82 we should like to derive a formula for the tree complexity, i.e. the number of spanning trees, for such graphs that uses a continued fraction expansion rather than the matrix tree formula. if we glue two cycles of lengths 1g and 2g sharing one common edge, then the situation is easy, and there are precisely 1 2 1g g − spanning trees. indeed there are ( )( )1 21 1g g− − spanning trees containing the common edge and there are 1 2 2g g+ − spanning trees that do not contain the common edge. for example in the left of the above figure we will find 34 spanning trees. we may express this in the following arithmetic way. the fraction 1 2 1 2 2 11 g g g g g − − = has a numerator which is the number of spanning trees of the union of two cycles, and it has a denominator which is the number of spanning trees of a single cycle of length 2g . let us now consider a larger case as in the right hand side of the figure. let us assume that there are 5 cycles and they have sizes 1 2 3 4 5, , , , 2g g g g g > . thus for the example in the right hand side of figure we have 1 4g = , 2 6g = , 3 5g = , 4 4g = , and 5 7g = . we may then find the number of spanning trees of such a graph by first computing the numerator of the expression 1 2 3 4 5 1 1 1 1 x x x x x + + + + this turns out to be 3 4 5 3 5 1 1 1 4 5 2 3 4 5 2 3 2 5 4 5 2 2 5 3 4 5 3 5 3 4 5 1 1 1 1 1 1 x x x x x x x x x x x x x x x x x x x xx x x x x x x xx x x + + + = + = + + + + + ++ + + ++ + thus the numerator of the expression is just 1 2 3 4 5 1 2 3 1 2 5 1 4 5 3 4 5 1 3 5x x x x x x x x x x x x x x x x x x x x+ + + + + + + now to get the number of spanning trees we substitute ( )1 .kk kx g= − and take the absolute value. this yields the expression 1 2 3 4 5 1 2 3 1 2 5 1 4 5 3 4 5 1 3 5| |g g g g g g g g g g g g g g g g g g g g− + + + + − − − which is just the number of spanning trees of the graph under discussion. in our example in the right hand side of the figure we get for the number of spanning trees the positive integer 4 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 7 4 ⋅ 6 ⋅ 5 4 ⋅ 6 ⋅ 7 4 ⋅ 4 ⋅ 7 5 ⋅ 4 ⋅ 7 + 4 + 5 + 7 = 2836. let us state the result in the general case. formulas for the number of spanning trees 83 theorem: if we simplify the finite continued fraction in the n variables 1 2 3, , ,...., nx x x x as a simple quotient 1 2 3 1 2 3 2 3 1 [ , , , , ]1 1 [ , , , ] 1 1 n n n n x x x x x x x xx x x x− + = + + + … and if we substitute ( )1 .ii ix g= − then the absolute value of the numerator on the rhs of the above equation is the number of spanning trees in the chain of cycles 12...nc . for the proof of this formula we first remark that for the bracket [ ]1 2 3, , ,...., nx x x x defined by 1 2 3 1 2 3 2 3 1 [ , , , , ]1 1 [ , , , ] 1 1 n n n n x x x x x x x xx x x x− + = + + + … we have the well known relation (bier 1995) 1 2 3 1 2 3 3[ , , , , ] [ , , , ] [ , , ]n n nx x x x x x x x x x= ⋅ +… … … considering the substitution ( )1 .ii ix g= − this easily implies [ ] [ ]1 2 3, 3 1 2 3, , ..., ,..., . , ,...,n n ng g g g g g g g g g⎡ ⎤ + =⎣ ⎦ (1) now we can do a proof by induction on n. it is clear that for 1n = the result for both the formula and for the counting is g1, so we may start the induction. then for the induction step the right hand side of equation (1) is 1g times the number of spanning trees for the union of cycles 23...nc . we write this as a sum of four terms. 1 2 3 1 12 12 1 12 12[ , , , ] ( 1) ( ) ( ) ( 1) ( ) ( )ng g g g g m e m e g n e n e⋅ = − ⋅ + + − ⋅ +… (2) to explain this let 12 1 23...ne c c= ∩ be the common edge of the first and the second cycle. let ( )12m e be the number of spanning trees of 23...nc which contain e12 and let ( )12n e be the number of spanning trees of 23...nc which do not contain 12e . then (1) follows from the fact that [ ]2 3, ,..., ng g g is the number of spanning trees of 23...nc , and each such spanning tree either contains or does not contain 12e so that [ ] ( ) ( )2 3 12 12, ,..., ng g g m e n e= + . then multiply this equation by 1g and rearrange to get (1). we can thomas bier 84 now see by inspection that ( ) ( )1 121g m e− ⋅ is the number of spanning trees of 23...nc which contain 12e . indeed each spanning tree that contains 12e must miss precisely one other edge of 1c , and there are 1 1g − choices for these missing edges. we may now use the following obvious fact: assume that ,g h are two simple (connected) graphs and that g h∨ is the graph that is obtained by glueing these two graphs together at a single vertex. then the number ( )k g h∨ of spanning trees of this one point union g h∨ is the product of the number of spanning trees of the two parts: ( ) ( ) ( )k g h k g k h∨ = ⋅ . recall that for the complete graph we have cayley's formula ( ) 2nnk k n −= . for the n -cycle ncy obviously we have ( )nk cy n= . as a simple application of the above fact we have ( ) .nn n nk cy cy nκ ∨ ∨ = we can see by inspection, using the lemma twice and the induction hypothesis that the last term in (2) which is ( )12n e is just equal to [ ]3 4, ,..., ng g g . indeed ( )12n e is the number of spanning trees of { }23.. 12\nc e . let 1 2,t t be the two tail ends that remain from 2c after removing 12e . by using the above fact twice with 34.. 1 2,ng c t h t= ∨ = and with 34.. 1,ng c h t= = we get the equations: 23... 12 34... 1 2 34... 1 2 34... 1 2( \ { }) ( ) ( ) ( ) ( ) ( ) ( ) | | ,n n n n nc e c t t c t t c g g gκ κ κ κ κ κ κ= ∨ ⋅ = ⋅ ⋅ = = … where the second last step comes from ( ) 1k t = for any tree t , and the last step is the inductive assumption. finally we claim that the sum of the two central terms of (2) ( ) ( ) ( )12 1 121 .m e g n e+ − is the number of all spanning trees of 12...nc that do not contain 12e . to see this, distinguish the two cases when the spanning tree does or does not contain all the remaining edges of { }1 12\c e . the number of spanning trees of 12..nc that do contain all the edges of 1 12\c e are in bijective correspondence with the spanning trees of 23..nc and hence their number is ( )12m e . the trees that miss another edge of 1c are in bijective correspondence with the ordered pairs ( ),e t where e is the other missing edge, and where t is a spanning tree of 23..nc that does not contain the edge 12e . thus their total number is ( ) ( )1 121 .g n e− . both terms in ( ) ( ) ( )12 1 121 .m e g n e+ − have been accounted for. this proves the induction step by a counting argument, and hence (1) is true. note that the use of the matrix tree theorem may not be practical in this general case. 2. special cases and discussion let us consider the special case in which all cycles have the same length, say g. then from (1) we get for the number nk of such a union of n cycles the recursion relation 1 2n n nk g k k− −= ⋅ − formulas for the number of spanning trees 85 obviously we have the boundary conditions 0 11,k k g= = .we may the solve the recursion in the standard way by first finding the characteristic roots of the equation 2 1gλ λ∧ = ⋅ − which are 2 1,2 4 2 g g λ ± − = the general solution for 0k then has the form 2 24 4 ( ) ( ) 2 2 n n n g g g g a bκ + − − − = ⋅ + ⋅ and from the boundary conditions we get 2 2 2 2 4 2 4 2 ( ) and ( ) . 2 4 2 4 g g g g a b g g − + − − = = − − this then gives the general solution 2 2 1 1 2 4 41 [( ) ( ) ] . 2 24 n n n g g g g g κ + + + − − − = ⋅ − − for the cases 3g = in (bogdanowicz 1994) etc. and 4g = in (sedlacek 1970) etc., this solution already appeared in the literature for certain specific graphs, namely the fan and the ladder graphs. but from the approach given here it appears that for all graphs of the form 12..nc the results of these computations are the same, while most authors on the subject seem to restrict themselves to one particular family of graphs. figure 2. fan and related graph. for example (bogdanowicz 1994) gives results for the fan graph on the left of the figure 2, while the formulae are also correct for a graph as on the right side of that figure. similarly, various authors treat cases like the ladder on the left of the figure 3, but one rarely sees a graph like the one on the right side which again has the same number of spanning trees. perhaps the general theory of complexity (ihara 1966, hashimoto 1989, stark et al. 1995, northshield 1994) may help to explain such equalities. thomas bier 86 figure 3. two different graphs with the same number of spanning trees. similarly, various authors treat cases like the ladder on the left of the figure 3, but one rarely sees a graph like the one on the right side which again has the same number of spanning trees. perhaps the general theory of complexity (ihara 1966, hashimoto 1989, stark et al. 1995, northshield 1994) may help to explain such equalities. 3. references bier, t. 1995. eine charakterisierung zyklischer polytope durch kettenbrüche, archiv der mathematik 16: 545-554. bogdanowicz, z.r. 2008. formulas for the number of spanning trees in a fan, applied mathematical sciences 2: 781-786, hikari ltd. hashimoto, k. 1989. zeta functions of finite graphs and representations of p-adic groups, advanced study in pure mathematics, vol 15, academic press ny pp. 211-280. ihara, y. 1966. on discrete subgroups of the two by two projective linear group over p-adic fields, j. math soc japan 18: 219-235. northshield, s. 1994. several proofs of ihara's theorem, ima preprint series no 1459. sedlacek, j. 1970. lucas numbers in graph theory, in mathematics (geometry and graph theory) univ. karlova, prague p. 111-115. stark, h. and terras, a. 1995. zeta functions of finite graphs and coverings, msri preprint no 074-95. received 15 september 2009 accepted 21 february 2010 electromagnetic modeling of the propagation characteristics of satellite communications through composite precipitation layers science and technology, 18 (2013) 41-53 © 2013 sultan qaboos university 41 neorotalia omanensis and operculina musawaensis from the sultanate of oman abdul razak siddiq al-sayigh department of earth sciences, college of science, sultan qaboos university, p.o. box 36, alkhoud, 123 muscat, sultanate of oman, email: alsayigh@squ.edu.om. abstract: two new species of larger benthic foraminifera, neorotalia omanensis n. sp. and operculina musawaensis n. sp. are described and illustrated from the eastern oman mountains. n. omanensis n. sp. occurs in the musawa formation in association with the planktonic foraminifera morozovella edgari and truncarotaloides topilensis indicating an early to middle eocene age (p10p13). operculina musawaensis n. sp. occurs in the abat formation in association with the planktonic foraminifera acarinina esnaensis and a. soldadensis indicating an early eocene age (p6). this is the first known record showing the presence of genus neorotalia in the middle east. representatives of the larger foraminiferal genus linderina sp. are also described and illustrated from the musawa formation and compared with the published linderina species in the surrounding countries. keywords: neorotalia omanensis; operculina musawaensis; abat formation; musawa formation; oman. مع مالحظات على تصنيف الندرينا عمان من سلطنةاينس نيوروتاليا عمانينسس وابركيولينا موساونوعين جديدين من الصايغ صديق عبدالرزاق اٌنسسو ابركٌولٌنا موساو عمانٌنسسكبٌرة الحجم وهً نٌوروتالٌا المثقباتى نوعٌن جدٌدٌن من وصفتم فً هذا البحث :ملخص نٌوروتالٌا فً تكوٌن موساوا مترافقة مع المثقبات حٌث تم وصف وتوضٌح النوعٌن من المنطقة الشرقٌة لجبال عمان. تتواجد ذات النطق األٌوسٌن األوسط عصر توبلٌنسٌس مما ٌدل على عمر ٌتبع ترنكوروتالوٌدسطافٌة مثل مورزوفٌال ادجاري و مثقبات سس و اٌنسس تكوٌن األبات مترافقة مع مثقبات هائمة مثل أكارنٌنا إسناإنابركٌولٌنا موساوتتواجد (.p10 – p13)الحٌوٌة وهو ألول مرة سجلت وجود جنس نٌوروتالٌا فً منطقة الشرق (. p6سولدادنسٌس مما ٌدل على عمر األٌوسٌن المبكر ) وسط. وكذلك تم وصف مثقبات كبٌرة الحجم من تكوٌن موصاوى و مقارنتها مع أنواع الندرٌنا المنشورة فً الدول المجاورة. األ ، متكون ابات، متكون مصاوى ، عمان. نٌنسس وابركٌولٌنا موساواٌنس نٌوروتالٌا عما: مفتاح الكلمات 1. introduction he genus neorotalia sp. is poorly known from arabia. the only published record from the northern oman mountains is linderina rajasthanensis (singh, 1953), found by white (1989) in wadi rusayl. white (1989) synonymized all four of singh’s (1953) species (rajasthanensis, bikanerensis, kolayatensis, kirtharensis) under one name (rajasthanensis) stating that test size, and shape (globular to discoidal with central boss, depending on the amount of lateral thickening) are insignificant as the means of discriminating species. the geographic distribution of the recorded species is very broad, including southern europe (england to romania), the middle east, the indian sub-continent, indonesia, australia, western pacific and the caribbean, possibly reflecting the presence of different genera with similar features (ferrandex-canadell and serr-kiel, 1999). in this paper the author reports two new species of large foraminifera in the abat and musawa formations in the eastern part of the northern oman mountains. t a.r.s. al-sayigh 24 2. geological setting the section studied is located in the jabal ja’alan area of the sharqiyah region, in the foothills of the eastern oman mountains, north oman (figure 1). the samples studied were collected from the abat and musawa formations outcropping along the southern side of wadi musawa (figure 1). here a 1220 m thick mixed clastic-carbonate succession of tertiary age rests unconformably on an older granitic basement. the tertiary strata comprise, from bottom to top, the abat, musawa and tahwah formations (figure 2). the samples yielding the new taxa described herein were collected from unit d of the abat formation and unit h of the musawa formation (figure 2). the abat formation comprises interbedded marine limestone (mudstone to packstone) and shale. the musawa formation contains three fluvial units, each of which is ferruginous towards its base and contains coal towards its top. the fluvial units are overlain by marine limestone and shale. the abat formation is late palaeocene to early eocene and the musawa formation is early to late eocene based on planktonic foraminiferal assemblages. previous work in the area was mainly focused on geological mapping (villey et al., 1986; filbrandt et al., 1990; roger et al., 1991). although villey et al. (1986) include micropalaeontological data, these data are limited to faunal lists and broad age assignments and do not include illustrations and descriptions of the taxa recorded. figure 1. location map of the study area (modified after montenat et al., 1977). 3. lithostratigraphy this section describes the lithostratigraphic units containing the microfossils reported in the present study. 1. abat formation type-locality: wadi musawa latitude 22 0 19' n and longitude 58 0 23' e this unit unconformably overlies maastrichtian sandstone turbidite and marl of the fayah formation, and is conformably overlain by sandstone of the musawa formation within which it interdigitates in its upper part. the lower part of the abat formation consists of thinly interbedded shale and mudstone overlain by planktonic foraminiferabearing wackestone with interbeds of mudstone and calcarenite. these beds pass upwards (across a 9 m unexposed section) into resedimented wackestone and packstone comprising six depositional cycles. the middle part of the abat neorotalia omanensis and operculina musawaensis 24 formation is characterized by thinly bedded wackestone overlain by shale and followed by an upper unit of limestone and dolomite capped by a palaeosol horizon. figure 2. lithostratigraphic column of the wadi musawa section. planktonic foraminifera, including morozovella sp. and subbotina sp., are common in the mudstone and shale of the lower part of the formation. larger foraminifera, including discocyclina sp., daviesina sp., miscellanea sp., nummulites sp. and assilina sp. together with small rotaliids, textulariids, calcareous red algae, echinoids and corals are common in the limestone of the upper part of the abat formation (figure 3). the larger foraminifera commonly appear to have been penecontemporaneously redeposited and become progressively more abraded up section. reworked cretaceous radiolaria and charophytes also occur within this interval. the abat formation has been dated as late palaeocene to early eocene (thanetian to ypresian) on the basis of its planktonic foraminifera, and comprises a thick sequence of open-marine basinal sediments. common deep-marine planktonic-foraminiferal shale and mudstone form the lower part of the abat formation which shoals upwards into high-energy middle to outer shelf limestone. the latter is dominated by larger and smaller benthonic foraminifera with subordinate dasycladacean algae, calcareous red algae, echinoid plates and corals. the specimens of operculina musawaensis n. sp. described herein were collected from the lower part of unit d of the abat formation (figure 2). a.r.s. al-sayigh 22 n e o ro ta li a o m a n e n si s n . sp . l in d e ri n a s p . a l in d e ri n a s p . b n u m m u li te s d is c o rb in u s c o sk in o li n a b a ls il li d ic ty o c o n u s e g y p te in si s o p e rc u li n a m u sa w a e n si s n . sp . a lv e o li n a k a ti c a e m is c e ll a n e a p ri m it iv a d a v ie si n a i ra n ic a d a v ie si n a s h ir a ze n si s p z o n e s ; b lo w , 1 9 6 9 , 1 9 7 9 a n d b e rg g re n e t a l. , 1 9 8 8 f o r m a t io n e p o c h s t a g e a g e p13 m u sa w a e a r ly t o l a te e o c e n e priabonian m id d le e o c e n e p12 p11 bartonian p10 ypresian e a r ly e o c e n e p9 p8 e a r ly e o c e n e ypresian a b a t p5 a b a t l a te p a la e o c e n e thanetian l a te p a la e o c e n e p4 figure 3. distribution chart of the key taxa of benthonic foraminifera. neorotalia omanensis and operculina musawaensis 24 unit d description: this unit begins with packstone and mudstone separated by a very thin (7 cm thick) distinctive silicified mudstone from an overlying a 24 m thick massive larger foraminiferal limestone (wackestone-packstone). the basal part of unit d comprises bioturbated limestone (packstone) overlain by mudstone rich in planktonic foraminifera (acarinina sp. and morozovella sp.) and larger foraminifera including alveolina sp., nummulites sp., discocyclina sp. and operculina musawaensis n. sp. this passes upwards into shale containing nummulites and small rotaliids. the unit becomes more indurated up-section and rich in larger foraminifera, ostracods, corals, bivalves, gastropods and oysters. lithoclasts and foraminifera are less abundant in the uppermost part of the unit, where clasts of grey chert are common, together with rare silicified burrows. bivalves (often disarticulated) are also common in the uppermost part of the unit. the characteristic microfossils in the abat formation include larger foraminifera (alveolina sp., nummulites honogoensis, n. globulus, discocyclina sp., assilina ex. gr. exponens, somalina sp., actinocyclina sp., operculina musawaensis n. sp., ranikothalia sp.) together with planktonic foraminifera (acarinina esnaensis, a. soldadoensis and morozovella aragonensis) which occur in the basal part of this unit. other fossil fragments present include gastropods, and rare brachiopods, with smaller rotaliids, miliolids and textulariids. rare dasycladacean algae occur in the middle to upper part of this unit, together with ostracods (bairdia sp., cytherella sp., phalococythere sp. and xestoleberis sp.). age: an early eocene age is indicated by the presence of morozovella marginodentata, m. aragonensis, acarinina esnaensis, and a. soldadoensis along with associated larger foraminifera, including nummulites cf. globulus. although somalina is typically considered to be middle eocene in age, white (1989) found somalina hottingeri in late early – eocene rocks from the northern oman mountains. this unit corresponds to the morozovella aragonensis zone (p8) of blow (1969) and berggren and miller (1988). thickness: 33 m. environment: the unit shows a gradual change from deep marine basinal facies rich in planktonic foraminifera in its lower part into shallow marine mid-outer shelf limestone with nummulites sp., assilina sp. and discocyclina sp., and rare dasycladacean green algae (fragments) in its upper part. the abat formation is capped by non-fossiliferous shale of probable fluvial origin and palaeosols. ostracods (bairdia sp., cytherella sp., phalcocythere sp. and xestoleberis sp.) suggest a shallow marine environment. 2. musawa formation type-locality: wadi musawa latitude 22 0 19' n and longitude 58 0 23' e the early to late eocene (ypresian to upper bartonian) musawa formation comprises a regressive siliciclastic package at its base and a transgressive interval at its top. it contains fluvial sandstones, palaeosoland coal and shale, together with marine mudstone bearing planktonic foraminifera and re-deposited larger foraminifera and radiolaria. reworked radiolaria and charophytes tend to occur together, especially in the fluviatile, coal-bearing beds. the middle part of the musawa formation represents an outer shelf environment. the lower part of the musawa formation is characterised by deep, open marine planktonic foraminifera including morozovella sp.. its middle part is dominated by planktonic foraminifera (m. edgari, globigerinatheka sp., truncorotaloides sp. and turborotalia blowcentralis). the upper part of the musawa formation represents a shallow marine, outer shelf environment with common insitu larger foraminifera including nummulites sp., operculina sp., discocyclina sp., dictyoconus sp., coskinolina sp, and neorotalia omanensis n. sp. bivalves and gastropods, including bicorbula sp., lucinids and naticids (n. morris, 1998), are indicative of an intertidal to tidal-flat environment. the uppermost part of the formation consists of innershelf facies with miliolids and molluscs. it becomes more estuarine-dominated towards its top as indicated by the presence of coal seams and the presence of ostracods such as neocyprideis sp., bythocypris sp., hornibrookella sp. and paracosta sp. neorotalia omanensis n. sp. and linderina sp. specimens were collected from unit h of the musawa formation. unit h description: this unit consists of 75 m of marl overlain by 2-3 m of nodular grey limestone and marl. a three meter thick hummocky-cross-stratified limestone caps this unit. the marl layers contain abundant conical-shaped solitary corals and larger foraminifera, including alveolina sp., discocyclina dispansa, nummulites sp., neorotalia omanensis n. sp., miliolids and ostracods. the hummocky-cross-stratified limestone contains bicorbula sp., lucinids and naticids. planktonic foraminifera. including morozovella sp, truncorotaloides libyaensis, and globigerina sp., occur in the middle of the unit. the larger foraminifera include nummulites maculatus, nummulites cf. schaubi, discocyclina dispansa, assilina sp., alveolina sp., neorotalia omanensis n. sp., operculina sp., linderina sp., nonionella sp., pararotalia sp. and miliolids and rare ostracods. burrows and macrofossils, including gastropods (i.e. natica sp.), oysters and corals occur throughout. age: middle eocene (upper lutetian) age is indicated by the presence of the planktonic foraminifera: truncorotaloides libyaensis, truncorotaloides topilensis, morozovella bolivariana, globigerinatheka barri, globigerinatheka curryi and globigerinatheka sp.. benthonic foraminifera (nummulites schaubi and n. maculates) were recorded by racey (1995) from the middle eocene (lower and middle lutetian) of the northern oman mountains. the unit ranges within the a.r.s. al-sayigh 24 truncorotaloides topilensis zone to the truncorotaloides libyaensis/morozovella bolivariana zone, representing the local expression of the standard zones, the globigerinatheka subconglobata subconglobata zone to the orbulinoides beckmanni zone (p13), of blow (1969) and berggren and miller (1988). thickness: 81 m environment: this is an outer shelf environment which was deeper at the base of the unit. it is indicated by abundant and diverse planktonic foraminifera. the topmost part of the unit is characterized by a low-intertidal to sub-tidal molluscan assemblage (n. morris, personal commun. 1998). taxonomic notes systematic palaeontology order foraminiferida )eichwald, 1830( suborder rotaliina, )delage and hérouard, 1896( superfamily rotaliacea )ehrenberg, 1839( family rotaliidae )ehrenberg, 1839( type species: neorotalia mexicana nuttall, 1928 description: test low trochospiral. the umbilicus is filled with a simple plug and the wall is finely pillared dorsally and ventrally. in equatorial section the chambers are high and narrow and the intercameral septa are strongly doubled peripherally only. neorotalia omanensis al-sayigh n. sp. plate 1, figures 1-8 material: twenty three specimens found in samples wme 148 and wme 184 (unit h), from the musawa formation, wadi musawa section, se oman. latitude 22 o 19' 11" n and longitude 58 o 23' 10" e. typespecimens: holotype plate 1 , figures1-3, sample wme 184. paratypes plate 2 , figures 4-6, sample wme 148. depository: earth sciences department, college of science, sultan qaboos university, muscat, sultanate of oman ars – n1, ars – n2 and ars-n3 2005. etymology: after sultanate of oman country. diagnosis: a distinctive large (2.3 mm diameter) planoconvex species of neorotalia with 9-13 chambers in the last whorl. surface coarse and pustulate, umbilical region characterised by a rosette pattern of plugs. description: test trochoid, rounded planoconvex. periphery lobate to subcircular. there are 3-3.5 whorls with 9-13 triangular chambers in the last whorl in the equatorial section. umbilical side strongly convex with large pillars on the umbilical shoulder surrounded by fine pustules. spiral side flat to slightly convex with pustules coarser towards centre. aperture is extraumbilical-umbilical. dimensions: holotype diameter 2.3 mm. thickness 1.3 mm paratypes diameter 2.2 mm. thickness 1.1 mm neorotalia omanensis n. sp. specimens are slightly different from neorotalia aticantina, as described by colom (1954), which is biconvex and smaller in size (0.5 to 0.7 mm in diameter and 0.4 to 0.6 mm thick). the omani species have fine pustules at the periphery coarsening towards the centre on both sides, and a greater number of whorls than neorotalia aticantina (colom,1954) and neorotalia mexicana (nuttall, 1952). the n. omanensis shows a greater number of chambers in the last whorl than n. aticantina (colom, 1954) and has an equal number of chambers in the last whorl to n. mexicana (nuttall, 1952). the genus neorotalia shows some similarities with daviesina, although daviesina is restricted to the palaeocene and has a circular to subcircular, slightly trochospiral test with large pillars on umbilical shoulders. geographic distribution and stratigraphic range: the genus neorotalia is previously unknown from the middle east, having been reported from the oligocene of southern mexico (nuttall, 1952) and the ypresian/lutetian boundary in spain (colom, 1954). local range and faunal associations: the musawa formation containing truncorotaloides topilensis, morozovella edgari and globigerinatheka euganea, indicates a lower to middle lutetian age. this species ranges from the morozovella edgari/truncorotaloides topilensis zone (p10) to the truncorotaloides libyaensis/morozovella bolivariana zone (p13), which is equivalent to the hantkenina nuttalli zone (p10) and to the orbulinoides beckmanni zone (p13) of blow (1969) and berggren and miller (1988) respectively. genus operculina )d’orbigny 1826( type species lenticulites complanatus )defrance, 1822( description planispirally coiled, evolute with flat to flattened lenticular to compressed test; loosely coiled with rapidly opening spire, comprising few whorls and subdivided by numerous high chambers. wall calcareous, perforate with smooth or pustulose surface. neorotalia omanensis and operculina musawaensis 24 plate 1: figures 1-6 neorotalia omanensis n. sp. from samples wme 148 and wme 184, wadi musawa section, jabal ja’alan area, se oman. middle eocene. in spiral, edge and umbilical view, respectively, x65. figures 1-3 holotype figures 4-6 paratype. figures 7-8 neorotalia omanensis n. sp. paratypes from sample wme148, wadi musawa section, jabal ja’alan area, se oman. middle eocene. equatorial and axial sections, x50 and x55 respectively. a.r.s. al-sayigh 24 operculina musawaensis al-sayigh n. sp. plate 2, figures 5-8 material: 12 specimens of a-forms from sample wm35, abat formation (unit d), wadi musawa. grid reference lat. 22 0 19' n and long. 58 0 23' e. type species: holotype: plate 2. figure 4 paratypes: plate 2. figures 6-8 depository: earth sciences department, college of science, sultan qaboos university, muscat, sultanate of oman. ars – o1, ars – o2 and ars o3. 2005. etymology: after wadi musawa, se oman mountains, sultanate of oman country. diagnosis: a small heavily pustular species with a distinctive large polar pustule, relatively few chambers per whorl and a markedly tight spire (4 whorls in a radius of about 1 mm). description: a-form. test discoidal, flat with polar region thickened by secondary lamellation. marginal cord is well-developed with septal sutures radial and recurved towards the periphery. chambers are 1.5-2 times higher than wide with twenty four arcuate chambers in the last whorl. the spire is tight and opens uniformly. the proloculus has an internal diameter of 0.035-0.043mm. dimensions maximum minimum average diameter (mm) 1.7 1.6 1.65 height (mm) 0.22 0.17 0.19 d/t 7.7 16 8.68 a-form (paratype) b-form not found remarks: this species is similar to operculina campi, described by graham (1950) from the miocene meganos formation of california, but differs in possessing more whorls (6-7 whorls in o. campi) and has a flatter, more compressed test. o. campi is known only from the miocene. o. musawaensis also differs from o. jiwani, described by racey (1995) from the late palaeocene of oman, in that o. jiwani has a larger test diameter (1.26-2.37 mm) and a larger proloculus (0.063-0.094 mm). geographical distribution and stratigraphic range: previously unknown. local range and faunal associations: found in wadi musawa in the abat formation in association with acarinina esnaensis and a. soldadoensis within the acarinina soldadoensis zone (p6) indicating an early eocene age. other associated larger foraminifera are alveolina sp., nummulites honogoensis, n. globulus, discocyclina sp., assilina ex. gr. exponens, somalina sp., actinocyclina sp., operculina musawaensis n. sp. associated planktonic foraminifera are morozovella aragonensis and subbotina quadrata. family: linderinidae loeblich and tappan, 1964 genus linderina schlumberger, 1893 type species: linderina brugesi schlumberger, 1893 generic description of linderina test large up to 3.5 mm in diameter, discoidal, centrally thickened. periphery rounded, peripheral outline lobate, wall calcareous and test surface covered with small pustules. early chambers of microspheric test form an irregular cluster, rather than a distinct spire. megalospheric test with bilocular embryo followed by a nepionic ring of seven to eight small chambers with a concentric series of small arched chambers in a single equatorial layer. younger chambers are progressively larger and alternating in position. early stage is covered by numerous layers of calcite resulting in an inflated central region traversed by fine pores connecting the chambers to the exterior. apertures and intercameral openings occur at the base of the chamber against the chambers of the previous whorl. whorl # 1 2 3 4 radius (mm) 0.15-0.17 0.24-0.35 0.56-0.64 1.01 chambers number 7-8 11-16 17-19 22-25 neorotalia omanensis and operculina musawaensis 24 plate 2: figures 1-2 linderina sp. a. from sample wme 184, wadi musawa section, jabal ja’alan area, se oman. middle eocene. edge and side view, respectively, x50. figures 3-4 linderina sp b. from sample wme 148, wadi musawa section, jabal ja’alan area, se oman. middle eocene. edge and side view, respectively, x20. figures 5-8 operculina musawaensis n. sp. holotype (a-form). from sample wm 35 wadi musawa section, jabal ja’alan area, se oman. early eocene. side view, x30. figures 7-8 operculina musawaensis n. sp. paratypes a-forms from sample wm 35, wadi musawa section, jabal ja’alan area, se oman. early eocene. equatorial oblique and axial section, respectively, all x30. a.r.s. al-sayigh 45 plate 3: figures 1-4 linderina sp. a figure 5 linderina sp. b 4. discussion illustrations in the ellis and messina catalogue (1940) and observations during this study suggest that the globular forms with umbonal lamellar thickening (e.g. plate 2, figures 3-4; plate 3. figure 5) are all megalospheric, whereas the discoidal forms (without or with very little umbonal lamellar thickening e.g. plate 2, figures 1-2, plate 3, figures 1-4) appear to be microspheric. of the sixteen published species, four are now assigned to other genera: linderina douivillei (silvestri, 1948) to orbitoides (neumann, 1958); l. visserae (hofker, 1958) to hellenocyclina (macgillavry, 1963); l. ovata (halkyard, neorotalia omanensis and operculina musawaensis 45 1919) to droogerinella (popescu and brotea, 1994) and l. chapmani (halkyard, 1919) to halkyardia (neumann, 1958). of the remaining potentially valid species l. rajasthanensis (singh, 1953), l. kirtharensis (singh, 1953), l. kolayatensis (singh, 1953), l,. bikanerensis (singh, 1953), l. paronai, osimo, l. floridensis (colom,1954), and l. bihilensis (silvestri, 1948) are known only from megalospheric forms and pustules. l. nuttalli is known only from a microspheric form. two species, l. brugesi (schlumberger, 1893) and l. buranensis )nuttal and brighton,1930) are known from megalospheric and microspheric forms. all records appear to be from the middle eocene to the lower part of the upper eocene (bartonian). freudenthal (1969) further reduced these ten species to four: l. buranensis (within which he synonmised l. bihilensis and l. nuttalli), l. rajasthanensis (within which he synonymised l. bikanerensis, l. koyaltensis and l. kirtharensis), l. paranoi and l. floridensis. freudenthal (1969) also mentioned that l. floridensis may be a synonym of l. paranoi. this study refers to the globular form as sp. a and the discoidal form as sp. b. linderina sp. a plate 2, figures 1-2, plate 3, figures 1-4 material: fourteen specimens from wme 181 and wme 183 from the wadi musawa section. description: test small, biconvex, globular, stout with rounded periphery. central pillars are absent. the protoconch is circular in outline and the deuteroconch is crescentic. chambers in axial section are narrower at the center and increase gradually in thickness from the centre towards the periphery. wall finely perforated. the proloculus size varies between 0.04 and 0.07 mm in diameter. dimensions maximum minimum average diameter (mm) 1.40 1.02 1.21 height (mm) 0.81 0.49 0.65 d/t ratio 1.73 2.08 2.28 remarks: this species differs from linderina bikanerensis singh (1953) in having a larger and more globular test and circular protoconch, and can thus be distinguished externally and internally. geographic distribution and stratigraphic range: previously known from the middle east under a variety of names. the genus linderina is also known from the upper chocolate clay of sulieman range, pakistan (adams, 1970) and from rajistan, india (singh, 1953) and meghalaya (nagapa, 1956). local range and faunal associations: linderina sp. a is found at wadi musawa in association with globigerinatheka barri in strata of presumed middle eocene age, within truncorotaloides topilensis zone p11 and globigerinatheka barri zone, which is equivalent to globigerinatheka subconglobata subconglobata and morozovella lehneri zones (p11-p12) of blow (1969) and berggren and miller (1988). the associated fauna includes: the planktonic foraminifera truncorotaloides libyaensis, morozovella bolivariana, globigerinatheka barri, globigerinatheka curryi, globigerinatheka sp. benthonic foraminifera nummulites schaubi and n. maculatus were recorded by racey (1995). linderina sp. b. plate 2, figures 3-4, plate 3, figure 5 material: twenty five specimens from sample wme 182. description: test large, discoidal with rim encircling the central area and with a slightly wavy periphery. equatorial chambers arcuate, large and arranged overlapping alternately, increasing in size towards the center varying in size from 0.09 mm to 0.12 mm across. in axial section the test is thick at the centre and narrows towards the margins. pillars are fine, radial over most of the test. protoconch is about 0.11 mm in axial section, and 0.08 mm in equatorial section. dimensions maximum minimum average diameter (mm) 2.2 1.5 1.85 height (mm) 0.33 0.29 0.31 d/t ratio 6.66 5.17 5.97 remarks: this species is characterized by its discoidal test, wavy test periphery and distinctive equatorial chambers. geographic distribution and stratigraphic range: previously known from the middle east. local range and faunal associations: linderina sp. b is found in wadi musawa in association with truncorotaloides topilensis and morozovella sp., indicating a middle eocene age within the truncorotaloides topilensis zone (p11), equivalent to the globigerinatheka subconglobata subconglobata zone (p11) of blow (1969) and of berggren and a.r.s. al-sayigh 44 miller (1988). associated larger foraminifera include alveolina sp., discocyclina dispansa, nummulites and neorotalia omanensis n. sp. 5. conclusions two new larger foraminiferal species, operculina musawaensis n. sp., and neorotalia omanensis n. sp., are described and illustrated. the presence of neorotalia sp. represents the first record in the middle east. two forms of linderina sp. are also described and illustrated. it is concluded that of the sixteen published species, four (l. douvillei, l. visserae, l. ovata and l.chapmani) are referable to other genera and one (l. baldaci) is insufficiently described/illustrated to permit even a generic assignment. of the remaining species, two are known from both megalospheric and microspheric specimens (l. brugesi and l. buranensis), one is only known from a microspheric form (l. nuttalli) and the remainder are only known from megalospheric forms (l. bikinarensis, l. floridensis, l. glaesseneri, l. kirtharensis, l. kolayatensis, l. paronai, and l. rajahstanensis). of these, l. kolyatensis, l. bikanerensis l. kirtharensis and l. rajahstanensis are synonymous (with l. rajahstanensis having priority) and the status of l. glaessneri remains problematic. closer examination of the oman materials and published descriptions indicate that globular forms with umbonal lamellar thickening are megalospheric and discoidal forms without or with very little umbonal lamellar thickening are probably microspheric. because test size and shape (both dependent to a certain degree on the amount of lamellar thickening) are not species specific, many of the linderina species could be grouped under a single species. alternatively, the smaller globular forms may be juveniles. 6. acknowledgements the author thanks haynes, j.r. (university of wales), whittaker, j.e. (natural history museum, london), nasir, s. and hanna, s. (sultan qaboos university) for their support. 7. references adams, 1970. a reconsideration of the east indian letter classification. bulletin of the british museum (natural history) geology, 19:(3)1-13 berggren, w.a. and miller, k.g. 1988. paleogene tropical planktonic foraminiferal biostratigraphy and magnetobiochronology. micropaleontology, 34(4): 362-380. blow, w.h. 1969. late middle eocene to recent planktonic foraminiferal biostratigraphy. in: bronnimann, p. and renz, h.h. (eds.) proceedings of the first international conference on planktonic microfossils, geneva. 1: 199422. e.j. brill, leiden. colom, g. 1954. estudio de las biozonas con foraminiferos del terciario de alicante, espana. boletín, instituto geologico y minero, 6: 1-279. delage, y. and hérouard, e. 1896. lower aptian shallow water foraminiferal assemblages. traité de zoologe concrete, vol. 1, la cellule et les protozoaires. . pris: schleicher fréres. defrance, m.l. 1822. dictionnaire des sciences naturelles. minèralogie et géologie, 25. levrault, paris. d’orbigny, a. 1826. tableau, methodiane, de, la xlasse des cephalopoes: am. sci: nat., 7: 245-314. ehrenberg, c.g. 1839. uber die bildung der kreidefelsen und des kreidemergels durch unsichtbare organsmen. physikalische abh. kgl. akad. wiss. berlin, 59-147. eichwald, c.e. von. 1830. expositis animalibus tum vivis, tum. zoologia specialis, 2, velnae: d. e. eichwaldus, 1-323. ellis, b.f. and messina, a.r. 1940. catalogue of foraminifera. american museum of natural history. (+ supplements). ferrandex-canadell, c. and serra kiel, j. 1999. morphostructure and systematics of linderina brugesi schlumberger, 1893 (foraminifera, eocene), geobios, 32(4): 529-537. filbrandt, j.b., nolan, s.c. and ries, a.c. 1990. late cretaceous and tertiary evolution of jabal j a'alan and adjacent areas, n e oman. in: robertson, a.h.f., searle, m.p. and ries, c. (eds.) the geology and tectonics of the oman region. special publications of the geological society of london, 49: 697714. freudenthal, t. 1969. stratigraphy of neogene deposits in the khania province, crete, with special reference to foraminifera of the family planorbulinidae and the genus heterostegina. utrecht micropaleontological bulletin 1: 1–208. graham, j.j. 1950. new foraminifera from the type meganos formation (eocene) of california. j. paleontology, 24: 282-304. halkyard, e. 1919. the fossil foraminifera of the blue marl of the cote des. basques, biarritz. edited with additions by heron-after, e. and earland mem, a. proc. manchaster lit. phil soc. 62: 1-145. hofker, j. 1958 faraminifera from the cretaceous of limburg, netherlands, linderina, visserae nov. se natuurhistorisch, maandblad 47: 125-127. neorotalia omanensis and operculina musawaensis 44 loeblich, a.r.jr. and tappan, h. 1964. sarcodina, chiefly "thecamoebian': and foraminiferida. in: moore, r.c. (ed.) , treatise on invertebrate aleontology, part c, protista 2.2: pp. 511-900. geological society of america and university of kansas press. macgillavry, h.j. 1963. phylomorphogenesis and evolutionary trends of cretaceous orbitoidal foraminifera. in : koenigswald, g.h.r. von, emeis, j.d., buning, w.l. and wagner, c.w. (eds.) evolutionary trends in foraminifera. elsevier publishing company, amsterdam-london-new york 139-197. montenat, c., blondeau, a., bizon, g., peffeau, m., raju, d.s.n. and roman, j. 1977. premier apercu du tertiare d'oman (peninsule arabique orientale). bulletin de la societe geologique de france, 19: 1285-1295. morris, n. 1998. personal commun, british natural history museuum. london. nagapa, y. 1956. foraminifera of the genera fabiano and eorupertia from the sylnet limestone of assam. j. paleontit. soc. ndd. 1: 191-198. neumann, m. 1958. revision des orbitoidides du cretace et de eocene en aquilaine accidentale memories de la societe geologique de france, 83: 174. nuttall, w.l.f. 1928. notes on the tertiary foraminifera of southern mexico. j. paleontology, 2: 372-376. nuttall, w.l.f. and brighton, a.g. 1931. larger foraminifera from the tertiary of somaliland. geological magazine, 68: 49-65. nuttall, w.l.f. 1952 on the upper cretaceous and lower tertiary unicrofaunas of israel. israel, res, council, bult., 2: 37-50. popescu, gh. and brotea, d. 1994. evolution of the transylvanian foraminiferal assemblages during late oligocene and middle miocene. in: nicorici, e., bedelean, i., mészáros, n. and petrescu, i. (eds.), the miocene from the transylvaniann basin, romania. geological formations of transylvania, romania 4, cluj-napoca, romania, 119-124. racey, a. 1995. lithostratigraphy and larger foraminiferal (nummulitid) biostratigraphy of the tertiary of northern oman. micropaleontology, 41: 1-123. roger, j., béchennec, f., janou, d., le métour, j., wyns, r. and beurriér, m. 1991. geological map of ja’alan, sheet nf40-08e, scale 1:100,000 with explanatory notes. directorate general of minerals, oman. ministry of petroleum and minerals. schlumberger. c.m. 1893. note sur les genres trilling et linderina. bulletin la societe geologique de france, 3: 118-123. silvestri, a. 1948foraminifei dell, eocene della somalia, parte iii, 2 palaeontographia italica, 32(6): 277-331. singh, s.n. 1953 species of the genus linderina from the kirthars of kolayat, bikaner, india. proceedings of the natural academy of sciences, india, 23: 21-28. villey, m., le metour, j. and de garment, x. 1986. geological map of fanjah, sheet at 40-03f, with explanatory notes. bureau de recherches geologiques et minieres, orleans (for the ministry of petroleum and minerals, sultanate of oman). white, m.r. 1989. a new species of somalina (somalina hottingeri) with partially vacuolate lateral walls from the middle eocene of oman. j. micropalaeontology, 16: 131-135. received 13 february 2013 accepted 30 october 2013 squ journal for science, 2014, 19(1), 87-94 © 2014 sultan qaboos university 87 velocity profiles for flow of omani crude oils and other liquids sayyadul arafin* and sheikh m.m. rahman department of physics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: sayfin@squ.edu.om. abstract: velocity profiles of newtonian immiscible liquids undergoing laminar flow between two horizontal plates under pressure gradient are investigated using a momentum balance equation. the differential equation describing the flow has been solved and equations for the velocity profiles of a two-layer and three-layer liquid systems are presented. as examples, we show flow patterns of twolayer water-crude oil system and three-layer system involving water, tetrachloromethane, xylene, cyclopentane and hexane. a distinctive pattern is noticeable between the velocity profiles of heavy (api 19.19) and light (api 40.89) omani crude oils. keywords: multi-layer flow; immiscible liquids; velocity profiles. شكال انسرعة نتدفق اننفط انعماني انخاو وانسوائم األخرىأ سيد انعارفين و مجيب انرحمن جّثيً اٌسشعة ٌٍسىائً إٌيىجىٔية غيش اٌمابٍة ٌٍزوباْ رات االٔذفاق اٌصفحي بيٓ سطحيٓ أفمييٓ جحث جغيّش في اٌبحثيسحجٍى مهخص : سطحيٓ أو ِعادالت اٌسشعة بيٓ وزٌه اٌّعادالت اٌحفاضٍية اٌحي جصف اٌحذفك وجُ حً ححشن. اٌسحخذاَ ِعادٌة جىاصْ وّية إاٌضغظ ب . وّثاي عٍى رٌه، حشوة اٌّاء وإٌفظ اٌخاَ بيٓ سطحيٓ أو ثالثة باسحخذاَ اٌّاء و جيحشاوٍىسوِيثيٓ و صايٍيٓ و ثالثة أسطح ap1و api 19.19 ٌٍٕفظ اٌعّأي اٌخاَ اٌخفيف واٌثميً )اٌشىً اٌّحّيض بيٓ اٌسشعات يُّىٓ أْ يالحظ سايىٍىبيٕحيٓ واٌهيىسيٓ. 40.89.) شىً جغيش اٌسشعة. و ِحعذد اٌطبمات، سىائً غيش لابٍة ٌالخحالطجذفك : مفتاح انكهمات 1. introduction ulti-layer fluid flows span a wide field covering a multitude of various technological perspectives and a broad range of engineering disciplines. engineering applications of multi-layer flows of immiscible liquids are found in multi-layer extrusion of plastic films, multi-layer coating, lubricated squeezing flows and in the transportation of liquid hydrocarbon [1]. in the two-layer case, like an oil-water system, accurate prediction of flow characteristics, such as flow pattern, water holdup and pressure gradient is important in many engineering applications including petroleum engineering [2]. however, despite their importance, liquid-liquid flows have not been explored to the same extent as gas-liquid flows. in fact, gas-liquid systems represent a very particular extreme of two-fluid systems characterized by low-density and low viscosity ratios. in liquid-liquid systems the density difference between the phases is relatively low while the viscosity ratio encountered in liquid-liquid systems extends over a range of many orders of magnitude. the occurrence of annular flow in liquid-liquid systems is therefore more frequently encountered in oil-water systems of low density differential, and small diameter tubes. recently kumara et al. [3] used particle image velocimetry (piv) technique to characterize the flow structure of oil-water flow in horizontal and slightly inclined pipes. they observed stratified flow with some mixing at the interface at mixture velocity of 0.50 m/s for all pipe inclinations. in addition to these applications in chemical and petroleum engineering, the flow of multi-layered immiscible fluids is also important in the study of the evolution of magma within the earth. it has been suggested [4] that non-ideal mixing of silicate melts is the cause of liquid immiscibility in simple and naturally occurring systems. peridotite melts, constituent rock melts of the upper mantle of the earth, become immiscible as temperatures are raised above their liquidus. moreover, the kinematic and dynamic behavior of lava flows may dramatically change with lava temperature variations because of the strong temperature-dependence on viscosity [5,6]. flow during ascent and emplacement of magmas undergoing liquid immiscibility may have important consequences in magma rheology and differentiation. for m mailto:sayfin@squ.edu.om sayyadul arafin and s.m. mujibur rahman 88 example, strong elongation of liquid-liquid structures may have produced the fine lamination in domes of the piedra parada caldera in argentina [7]. it has been observed [8] in the study of multi-component geologically relevant systems that three-fluid immiscibility in the form of coexistence of an aluminosilicate melt with two hydrous fluids is common in natural magmatic systems. the earth’s outer core is 10% less dense than the pure metallic fe-ni liquid [9]. this led geophysicists and geochemists to assume that the outer core may have light elements like sulfur, carbon, oxygen, hydrogen and silicon to account for the 10% density reduction. the same argument is also directed to the study of the interior of other planets like mars and mercury. dasgupta et al. [10] investigated the near liquidus phase relations in the fe-c-s ternary system and concluded that liquid immiscibility could induce stratification of planetary cores that are entirely molten or at least have a molten outer core at pressures less than 6 gpa. such immiscibility is not expected at the molten outer core of the planets like the earth, venus and mercury where the relevant core pressures are much higher than 6 gpa. this observation contradicts an earlier prediction [11] that there exists immiscible layers of 12 km thickness at the outer liquid core of the earth. the presence of a thin layer at the top of the outermost core is of considerable importance for the geodynamic and geomagnetic behavior of the earth; however, detecting the presence of such a thin layer is difficult [12]. analytical solutions for two-layer flow have been obtained by several authors [13,14]. however, analytical expressions for more than two-layers are not available in the literature because of the 'tedious algebra' involved in deriving the equations for the velocity. owing to this difficulty it has been suggested [15] that the differential equations can best be solved by standard numerical techniques. in the present study we present exact solutions of the momentum balance equations involving velocity profiles for a three-layer liquid system having different viscosities and densities; this is one-step forward in understanding immiscible multi-layer fluid dynamics. we are, however, presently working towards finding a generalized solution for an n-layer liquid system, which will consider instability of the liquid interfaces. the layout of the paper is as follows: in section 2, we describe the mathematical formalism of the momentum balance equation and set up the equations for velocity profiles in terms of the unknown constants of integration for an n-layer liquid system. in section 3, we present the solutions of the relevant differential equations for twoand threelayer immiscible liquid systems. some examples of velocity profiles for two-layer systems involving water and omani crude oils, and three-layer systems involving water and some chemicals are given in section 4 which is followed by conclusions in section 5. 2. formalism the formalism is based on solving differential equations describing momentum balance and newton's equation for viscosity for an n-layer liquid system as shown in figure 1. it is assumed that the density of the liquids decreases progressively upwards with the bottom most layer being the most dense and the top the least dense. for steady state flow, the well-known momentum balance equation is [16] ∑ ( ) ( ) ( ) where p is the momentum and its time derivatives are the rate of change of momentum entering into and leaving the system respectively. the f’s are the pressure forces acting on the surface and gravity forces acting on the volume as a whole. we assume that (i) the liquid-liquid interface is a plane of constant x coordinate and (ii) tangential components of velocity vy, vz and of stress-tensor τxx, τxy, and τxz are continuous throughout an interface (i.e. there is no slip across an interface). the above boundary conditions imply that no material is diffusing through the interface. in other words there is no absorption, adsorption, dissolution, evaporation, melting or chemical reaction at the interface.  n  n-1     x n layer n: thickness, t n = x n x n-1 layer n-1: thickness, t n-1 = x n-1 x n-2 layer 3: thickness, t 3 = x 3 x 2 x n-1 x 3 x 2 -x 1 0,0 x n-2 z layer 1: thickness, t 1 = x 1 layer 2: thickness, t 2 = x 2 . . . .   figure 1. a schematic diagram for a multi-layer liquid system with varying viscosities and densities. velocity profiles for flow of omani crude oils and other liquids 89 the density of the layers is assumed to increase progressively downwards with the bottom most layer being the most dense and the top the least dense. when two or more immiscible fluids undergoing laminar flow are present in a horizontal thin slit of length l and width w under the influence of a pressure gradient, the velocity distribution can be obtained by solving two governing equations. one of these equations is the momentum balance equation given by: ( ) ( ) and the other one is the newton’s law of viscosity which is given by: ( ) here τxz is the viscous momentum flux component or simply the viscous stress component. τxz refers to the stress acting in the z direction on the face of a parallelepiped which is perpendicular to the x axis. δp/l is the pressure gradient, where δp is the pressure difference over a length l of the fluid surface, μ is the viscosity, and is the velocity. integration of (2) yields ( ) ( ) where c is a constant of integration. using the assumption of continuous throughout any of the interfaces, it can be shown that c is the same for all the interfaces within a given number of immiscible liquids. c changes if the number of given liquids changes and henceforth it will be denoted by n c. the index n is the number of liquids present in a system and its minimum value is 2, indicating the minimum number of layers required to constitute a liquid system in this study. substituting (3) in (4) and integrating, one can write the equation for velocity for an n-layer liquid system as: n ( ) n ( ) where μi and n viz are respectively the viscosity and velocity of liquid in the i th layer of an n-layer liquid system. the running index i takes on values 1, 2, 3, ....., n. the (n+1) constants of integration, n c and n di, are to be determined by applying the following three boundary conditions in (5) (i) at x = -x1, i.e. at the bottom solid surface, n v1z = 0 (ii) at x = 0, i.e. at the interface between layer 1 and layer 2 (see figure 1), n v1z = n v2z and (iii) at x = xk, i.e. for all interfaces between the 2 nd layer and the (n-1) th layer, n vkz = n v(k+1)z where k = 2, 3, 4, ...., n-1 and at x = xn, i.e. at the top solid surface, n vnz = 0 and solving the resulting (n+1) equations. applying boundary condition (i) in eq. (5) one gets ( ) ( ) the boundary condition (ii) at x = 0 gives: ( ) while the boundary condition (iii) at x = xk (i.e. the interface between k th and (k+1) th layers) gives ( ) ( ) ( ) likewise the boundary condition (iii) at x = xn, n vz = 0 yields ( ) ( ) the task is now to solve eqs. (6), (7), (8) and (9) to determine the (n+1) constants of integration such as c arising out of eq. (4) and the n di (i = 1, 2, 3, ... , n) arising out of eq. (5). we will restrict our investigations in this study to two and threelayer liquid systems only. our investigation for a generalized solution for an n-layer system is in progress. 3. solutions of the momentum balance equations we present here solutions of the momentum balance equations involving twoand threelayer liquid systems only. the constants (i.e. the c’s in eq. 4 and the d’s in eq. 5) of integration are first determined by solving eqs. (6), (7), (8) and (9) and then substituting back in eq. (5) to find the velocities within each layer. these velocities follow a pattern that can be represented by a mathematical series. we represent the velocity by n vi after dropping the subscript z. it is understood that all velocities considered in the present study are directed along the z-axis (see figure 1). the superscript, n indicates the total number of layers in a system and its minimum value is 2. the subscript, i (i =1, 2, 3, ..., n) represents an arbitrary layer for which the d's and v's are needed. sayyadul arafin and s.m. mujibur rahman 90 3.1 a two-layer liquid system for a two-layer liquid system n = 2. we will consider two simultaneous equations, eqs. 6 and 8 to find the constant 2 and either 2 or 2 (because 2 = 2 ). we present the constants and the velocities in terms of the thicknesses (figure 1) of the layers so that * + ( ) * ( )+ ( ) the superscript 2 represents the total number of layers in the liquid-liquid system and the subscripts represent an arbitrary layer within the system. we define numerator, num and denominator, deno for the 2-layer system as ( ) and ( ) so that the constant related to the viscous stress component can be denoted by 2 c by the equation ( ) where a = . the velocities in the two layers are ( )[( ) ] (10f) and ( )[( ) ] ( ) 3.2 a three-layer liquid system in the case of a three-layer system, n = 3. the numerator, num and denominator, deno for three layers are [ ( ) ] (11a) and ( ) (11b) the constants of integrations for a three-layer system are given by: (11c) [ ( )* ( ) + * ( )( )+ ] ( ) and [ ( ){ ( ) ( ) }] ( ) it may be recalled that the constant of integration, c arising out of momentum balance equation (eq. 2) is the same for all interfaces of an n-layer system because viscous stress component, is assumed to be continuous throughout the interfaces. the velocities for the three-layer system are given by ( ) *( ) + ( ) and ( ) [ ( ) ] (11g) velocity profiles for flow of omani crude oils and other liquids 91 where is the additional velocity term added to the velocity in the second layer of the 3-layer liquid system. it is given by: * ( ) ( ) + ( ) the velocity in the third layer is given by: ( ) *( ) + (11i) the superscript 3 indicates the number of liquids in the system and the subscripts 1, 2 and 3 represent the individual layers in which the velocities are to be found. 4. results and discussions we have used matlab to calculate the velocity profiles for twoand three-layer immiscible liquid systems. in all these cases we have assumed that the density of the liquids decrease upwards so that the most dense liquid is in the bottom most layer and the least dense liquid is in the top most layer. our entire analysis is based on stratified flow regime. we have used water, omani crude oils (erad and zal-41) and a number of chemicals such as tetrachloromethane, xylene, dichloromethane, cyclopentane and hexane to perform the model calculations of the velocity profiles in the liquids. the viscosities and densities of these liquids are given in table 1. the net pressure, δp between the ends of the horizontal plates is taken to be 5 pa for all the cases. table 1. densities and viscosities of liquids used in computing the velocity profiles for twoand three-layer systems. properties liquids density (g•cm -3 ) viscosity (mpa•s) tetrachloromethane 1.595 1.460 water 1.000 1.002 erad crude 0.933 580 xylene 0.880 0.812 zal-41 0.818 9.900 cyclopentane 0.751 0.440 hexane 0.655 0.294 4.1 omani crude oils we have chosen two representative samples of omani crude oils to study the flow dynamics in water -crude oil system. erad is described as a heavy crude oil (api 19.19) and has the largest viscosity (0.58 pa s) while zal – 41 is described as a light crude oil (api 40.89) with the smallest (0.0093 pa s) among the samples we have investigated [17,18]. the results for the simplest two-layer system consisting of water and omani crude oils are shown in figures. 2a, 2b, 2c and 2d for various crude oil and water thicknesses treated within stratified flow approximation. in the case of the erad-water system, the water thickness is kept at 1.0 mm (figures 2a and 2b) while the oil thickness is doubled (figure 2b). by doubling the oil thickness in figure 2b, the maximum velocity of the water layer has increased by about 29% but the velocity at the interface has increased by about 233%. the net pressure ∆p is kept at 5 pa in both the cases. figures 2c and 2d show the velocity distributions for zal-41 crude oil and water system. it may be noted that the zal – 41 sample has a very low viscosity (0.0093 pa s) in comparison with that of the erad sample (0.58 pa s). in this case the oil thickness was kept constant at 5 mm while the water thickness is different, 1 mm in figure 2c and 3 mm in figure 2d. an increase of water thickness by 300% has increased the maximum velocity by a factor of 10 for the same net pressure of 5 pa. figure 2a. velocity profile of erad (heaviest) crude oil-water system with an oil thickness 5 mm. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10 -5 -2 -1 0 1 2 3 4 5 x 10 -3 c o o rd in a te , x (m ) o f a p o in t w it h in l a y e rs velocity, v (m/s) oil-water interface erad crude oil water bottom plate top plate sayyadul arafin and s.m. mujibur rahman 92 figure 2b. velocity profile of erad (heaviest) crude oil-water system with an oil thickness 10 mm. figure 2c. velocity profile of zal-41 (lightest) crude oil-water system with a water thickness of 1mm and an oil thickness 5 mm. figure 2d. velocity profile of zal-4a (lightest) crude oil-water system with a water thickness of 3 mm and an oil thickness of 5 mm. 4.2 other liquids the effects of the viscosity of the top layer in a 3-layer system consisting of the liquids tetrachloromethane, water, xylene, cyclopentane and hexane are shown in figures 3 (a-c). thicknesses of the layers and the pressure difference are kept same in all these three cases. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 x 10 -5 -2 0 2 4 6 8 10 x 10 -3 c o o r d in a te , x ( m ) o f a p o in t w it h in l a y e r s velocity, v (m/s) oil-water interface bottom plate top plate water erad crude oil bottom plate 0 0.5 1 1.5 2 2.5 x 10 -5 -1 0 1 2 3 4 5 x 10 -3 c o o r d in a te , x ( m ) o f a p o in t w it h in l a y e r s velocity, v (m/s) top plate bottom platewater oil-water interface zal 41 crude oil 0 0.5 1 1.5 2 2.5 x 10 -4 -3 -2 -1 0 1 2 3 4 5 x 10 -3 c o o rd in a te , x (m ) o f a p o in t w it h in l a y e rs velocity, v (m/s) water zal 41 crude oil bottom plate oil-water interface top plate velocity profiles for flow of omani crude oils and other liquids 93 figure 3a. velocity profile of tetrachloromethane-water-xylene system. figure 3b. velocity profile of a tetrachloromethane-water-cyclopentane system. figure 3c. velocity profile of a tetrachloromethane-water-hexane system. the maximum velocity increases as the the viscosity of the topmost layer decreases. the maximum velocities are respectively 0.170, 0.207 and 0.241mm s -1 for xylene (figure 3a), cyclopentane (figure 3b) and hexane (figure 3c) as the topmost layer. the interface velocities also follow the same trend as that of the maximum velocity. 0 0.5 1 1.5 x 10 -4 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -3 c o o r d in a te o f a p o in t, x ( m ) w it h in l a y e r s velocity, v (m/s) tetrachloromethane water top plate xylene xylene-water interface water-tetrachloromethane interface bottom plate 0 0.5 1 1.5 2 2.5 x 10 -4 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -3 c o o r d in a te , x ( m ) o f a p o in t w it h in l a y e r s velocity, v (m/s) cyclopentane water tetrachloromethane top plate bottom plate cyclopentane-water interface water-tetrachloromethane interface 0 0.5 1 1.5 2 2.5 3 x 10 -4 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -3 c o o r d in a te , x ( m ) o f a p o in t w it h in l a y e r s velocity, v (m/s) water hexane hexane-water interface top plate bottom plate water-tetrachloromethane interface tetrachloromethane sayyadul arafin and s.m. mujibur rahman 94 5. conclusions the differential equations involving multi-layer flow of liquids under ideal conditions of newtonian liquids satisfying laminar and stratified flow have been set up for an n-layer liquid system and solutions for the velocity profiles of twoand three-layer systems are presented. these solutions are exact analytical expressions for the velocity profiles within the liquids. as examples, flow patterns of two-layer water-omani crude oil systems and three-layer systems involving tetrachloromethane, xylene, cyclopentane and hexane have been determined. the flow pattern for the heaviest erad crude oil is distinctively different from that of the lightest zal-41 crude oil. the viscosity data used in the calculation of the velocity profile are presented in table 1. for almost all of the model fluids the viscosity is lower than that of water at room temperature being the viscosity of the first layer i.e. tetrachloromethane (1.460 mpa s). it is relevant to mention here that in any real multi-layer system, the presence of absorption, adsorption dissolution, evaporation, melting or chemical reactions will complicate the situation. most of these processes are directly related to wetting and friction phenomena complicating the flow dynamics. in some circumstances interfacial instability occurs causing turbulence in the flow process. this real picture will certainly require modification of our approximations and in our future endeavor we will address the above issues, incorporating an extensive momentum balance equation along with exact solutions for n-layer liquid system. references 1. brennen, c.e. fundamentals of multiphase flow. cambridge university press, cambridge, 2005. 2. brauner, n. on the relation between two-phase flow under reduced gravity and earth experiment. int. comm. heat mass transfer, 1990, 17, 271. 3. kumara, w.a.s., halvorden, b.m. and melaaen, m.c. particle image velocimetry for characterizing the flow structure of oil-water 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birch, f. elasticity and constitution of the earth's interior. j. geophys. res., 1952, 57, 227-286. 10. dasgupta, r., buono, a., whelan, g. and walker, d. high pressure near-liquidus phase relations in fe-c-s systems and implications for composition, structure, and process of formation of metallic cores in planetary bodies. 40 th lunar and planetary science conference, 23-27 march, 2009, the woodlands, texas, usa. 11. helffrich, g. and kaneshima, s. seismological constraints on core composition from fe-o-s liquid immiscibility. science, 2004, 306, 2239-2242. 12. eaton, d.w. and kendall, j.m. improving seismic resolution of outermost core structure by multichannel analysis and deconvolution of broadband smks phases. phys. earth and planet. in. 2006, 155, 104-119. 13. yiantsios, s.g. and higgins, b.g. linear stability of plane poiseuille flow of two superposed fluids. phys. fluids, 1988, 31, 3225. 14. yih chia-shun. instability due to viscosity stratification. j. fluid mech., 1967, 27, pp. 337. 15. anturkar, n.r., papanastasiou, t.c. and wilkes, j.o. linear stability analysis of multilayer plane poiseuille flow. phys. fluids, 1990, 2, 530-541. 16. bird, r.b., stewart, w.e. and lightfoot, e.n. transport phenomena, john-wiley co., new york, 2002. 17. arafin, s., al-habsi, n. and rahman, s.m.m. transport properties and model-based dynamical properties of omani crude oils. arab j. geosci. 2012, 5, 1085-1092. 18. arafin, s. and rahman, s.m.m. dynamical properties of omani crude oils for flow through a vertical annulus and a cylindrical pipe. squ j. science. 2011, 16, 102-117. received 6 october 2013 accepted 21 november 2013 photovoltaic cells and systems: 68-81 squ journal for science, 16 (2011) © 2011 sultan qaboos university 68 on the existence of evolutionary learning equilibriums masudul alam choudhury department of economics and finance, college of commerce and economics, sultan qaboos university, muscat, sultanate of oman, international chair, postgraduate program in islamic economics and finance, trisakti university, jakarta, indonesia, email: masduc@squ.edu.om; masudc60@yahoo.ca. ات تعليمية تطوريةعن وجود توازندراسة ودرياشت العلم مسعود لا فا االقتصات ي النظريا تشار والتا تنتفسا تاوانن وجاو أسات علا المبنيا الثتبتا النقطا نظريات إن :ملخص نات را الشروط ذهه لكن. معكوس تصورا أو منظورا ذا و ومغلق محددة مجموعت عل فقط تعمل أن يمكن االقتصت ، التا التعلميا المجموعات فئا إن .المضاطرب والمتليا االقتصات ي واألوضات للتعقيا ا الاوقع عتلمال ف موجودة تكون مت الفر يا المساتويت علا ال ينتميكيا المفتضات تساببهت التا والتطاور والتكتمال التفتعال لسالوكيت المساتمر الحقاول تبينهات التعلميا لمجموعات فت لاذا .المعكوسا المحا المغلق األوضت فرضي احتيتجت تلب أن يمكن ال الجتمتعي وا والمؤسستتي والتطاور والكيتنت المتغيرا بين مت الواسع والمستهمت التكتمت توضحهت الت األنمتن، بين مت النظم متع والعتقت .ج ي منهجي طريق تتطل راس هكذا .تطوري تواننت لهت التعلم، بفعل ف التعلمي التواننت شمولي تبين وبتختصتر، ، التعلمي الفضتءا ف التطوري للتواننت المنهجي هذه تصوغ الورق هذه واألختق المست ام التنمي بين مت النظم مت اخل المتبت ل االعتمت الورق تبين مح وبشكل .الريتضي التراكي كل .التعليم للمجتل المح أو الختص الفهم ف قتصت واال abstract: the usual kinds of fixed-point theorems formalized on the existence of competitive equilibrium that explain much of economic theory at the core of economics can operate only on bounded and closed sets with convex mappings. but these conditions are hardly true of the real world of economic and financial complexities and perturbations. the category of learning sets explained by continuous fields of interactive, integrative and evolutionary behaviour caused by dynamic preferences at the individual and institutional and social levels cannot maintain the assumption of closed, bounded and convex sets. thus learning sets and multi-system inter-temporal relations explained by pervasive complementarities and participation between variables and entities, and evolution by learning, have evolutionary equilibriums. such a study requires a new methodological approach. this paper formalizes such a methodology for evolutionary equilibriums in learning spaces. it briefly points out the universality of learning equilibriums in all mathematical structures. for a particular case though, the inter-systemic interdependence between sustainable development and ethics and economics in the specific understanding of learning domain is pointed out. mailto:masduc@squ.edu.om on the existence of evolutionary learning equilibriums 96 keywords: economic theory; mathematical economics; evolutionary economics; economics and epistemology. 1. background: a brief review of the literature he theme of the existence of equilibrium in mathematical economics used to be a hot pursuit of researchers in the sixties and seventies, earlier and later on (brouwer, 1910; chichilnisky, 1993; kakutani, 1941; debreu, 1959, 1989; uzawa, 1964; quirk and saposnik, 1968; morishima, 1964; nikaido, 1989). this momentum has declined in recent years. but retrospectively, the steady-state and time-dependent optimal movements (pontryagin et al. 1965; intrilligator, 1971) of globally stable equilibriums have failed to produce the realism of a vastly unstable world of economics, finance and related areas that we have inherited. the real world of economics and finance is based on complexities and perturbations (bertuglia and vaio, 2005; casti, 1990) rather than on any visage of steady-state equilibrium or even time-dependent optimal states of equilibrium. there are deep epistemological issues in these theoretical questions. these were noted by shackle (1971). choudhury (2006) has formulated a description of a non-steady qua time-dependent equilibrium socioeconomic space and characterized it by the super-encompassing knowledge-induced learning states of the economic and finance space. this paper formalizes the existence of equilibrium in learning systems of state-variables and policy-variables under conditions of endogenous preferences and inter-systemic variable-vide relationships. indeed, without equilibrium, the predictability of a system even in the neighbourhood of occurrence of events, what i refer to as „near‟ points of occurrence of an event (choudhury, 2010), cannot take place. we would then be led into a chaotic world without order. this would not be to the social benefit of stabilizing the world-system as it prevails today, and thereby attaining well governed socioeconomic reconstructions out of a fallen world (krugman, 1996). yet the nature of such equilibriums, as they belong to a learning domain formed by complexities and perturbation, have been well studied by grandmont (1989), shell (1989) and thurow (1996). 2. objective the objective of this paper is firstly to formulate the important theme of existence of endogenously knowledge-induced equilibriums. secondly, the problem of existence of such overarching domains of equilibriums induced by learning processes within (intra-) and across (inter-) systems and of their state-variables is formalized. a simple problem on the existence of the resulting evolutionary learning forms of equilibrium intraand intersystems is proved. although the substance of the paper overarches across the entire socioscientific field, the topics here are narrowed down by invoking specific intraand intersystem problems in economics and finance. attention is given to the topic of endogenous development sustainability. the subject matter taken up as a whole is in the area of neural economics and complexity. 3. explaining evolutionary learning equilibriums we define evolutionary learning equilibrium as intraand intersystemic in respect of their intraand inter systemic variables and their relationships defined by the following expressions: 3.1 intra-systemic evolutionary learning equilibriums there exists a sequence of „temporary‟ equilibriums, * s e , in a given system denoted by s . this system is denoted by  * *s i s e e , where i = 1, 2, … within system s , denotes the number of events. every event is denoted by  *i s e in   s i s e e . in an applicable domain of intra-system interactive, integrative (ii)-learning t masudul alam choudhury 07 processes, the following is true: (1)   * ,s s se e   a small positive value conforming to corresponding numbered events  *i s e , i = 1, 2, … , for a given system numbered as s and events in s e and * s e belonging to .s intra-system iie evolution s s s inter -system iie domains of inter-systemic evolutionary sets of intra-systemic equilibriums evolution figure 1. intra-system and inter-system domains of evolutionary equilibriums elements of   s  can assume real continuous values or integer values when discrete depending upon the kind of event space s e s. (2) but none of the s is an indefinitely small positive value. this property of the equilibrium event allows for evolution at any state of knowledge before its exact convergence is attained. the same kind of institutional and social state is found in many instances. 1 convergence in the   s  -set for ___________________________________________________________________________ 1 the same rule complies with consensus in robert‟s rule of democratic procedure. it is also the basis of the principle of „irrelevant preferences‟ in social choice theory (arrow, 1951); enforcement of ethical preferences (hammond, 1989); and terminating of a rawlsian continuous mini-max game by an external preceptor (wolfe, 1977). also sudden great departures from the normal sciences are explained by scientific revolutions as of kuhn (1970), and complexity in historical change of the longue duree (braudel, 1980). 2 the usual definition of continuity around a point * of -values affecting an event es (say state variable) is this: es() – es(*)< , for  * < s, for (,s) as indefinitely small positive values. but in the case of an evolutionary equilibrium described by knowledge-trajectories over expanding knowledge-values {} across evolutionary events that are simultaneously intra-system and inter-systems, we have the result: es() – es(*)=(es() – es1(1)) + (es(1) – es2(2)) + … (es(n) – es(*))< 1 + 2 + … + n. this aggregate value is not an indefinitely small number by virtue of addition of finitely many positive small values to allow for finite time consensus without unanimity in agreement. along with this kind of a non-convergent learning process exactly to * (non-unanimity though consensus), we then also have,  * = ( 1) + ( 2) + … + ( n)< s1 + s2 + … + sn = {s}, which is not an indefinitely small number by virtue of the addition of small values that are not indefinitely small along expanding -values. hence {s} is a set of small positive numbers but these are not indefinitely small. thereby the same property is shared by {es()}. all these mean that there is no steady-state equilibrium in sets of evolutionary equilibriums. no exact equilibrium is reached. evolutionary equilibrium is only approximated to before next evolution takes off. 3 the negative value of the time derivative means the convergence of es to es* as learning continues, that is with   *. an example is the case of equilibrium by cobweb tatonement adjustment. the excess demand progressively diminishes with rounds of adjustment. su ch adjustments take place over time, although time is implied in the static form of the equilibrium tatonement process in excess demand (henderson and quandt, 1971). 4 the following expression is a misnomer: w = f(x(),t), for t is exogenous in this relation and does effect f(.) and its variables endogenously. rather, we would write the above functional relationship as, wt = f(xt(t)), for data observed and simulated at time t. here values of t could be discrete or continuous. in the latter case, 't' takes values on the real line  or real n-multidimensional space  n . 5 a non-compact or equivalently non-fixed point type topological set is an open, unbounded and not necessarily convex set in  n . for technical details see friedman (1982) and debreu (1959). {(,x())i}s {(,x())i}s on the existence of evolutionary learning equilibriums 07 * s s e e is continuous but only to the neighbourhood of * s e , which is not indefinitely small as in the standard definition of continuity. 2 because the   s e are knowledge-induced events caused by learning processes, such events are characterized by their variables denoted by    , i s x  {(,x())i}s. this means that there is a limiting learning parameter  intra-system that characterizes (endogenizes) the state-variables  x  of every event within that system. because of the learning nature of    , i s x  these occur out of consensus in every round of the interactive and integrative (ii) learning process within each given system of variables and entities in the learning system. therefore, every vector of events is defined by    ,s i se x  . consequently, the above characterization of learning equilibriums is taken up individually within a system, but attained by interrelations between the knowledge-flow variable   and the knowledge-induced vector of state-variables   x  in that system. in this case, the evolutionary equilibrium phenomenon is realized intra-system. this kind of intra-system movements occurring across domains of evolutionary equilibriums can be depicted in figure 1. but figure 1 also explains evolutionary inter-system equilibriums emerging from the intrasystemic ones. we now explain this second case of evolutionary equilibriums. every preference map in the learning space, which affects the event space, is formed by consciousness formed by continuous learning processes. consciousness is thus embedded in a socio-scientific state of knowledge-induction. thereby, consciousness that is invoked by dynamic endogenous preferences in the iilearning process is defined by the preference set,    , i s x  . note how the theme of consciousness assumes a great scientific meaning in our times, as it has been during the classical times marking great scientific contributions (heisenberg, 1958; kafatos and nadeau, 1990). we now summarize all the above-mentioned properties of equilibrium within an s-system in terms of its given preferences and events: the intra-systemic event-specific learning equilibriums are induced by the episteme of unity of knowledge. such an episteme characterizes the nature of convergence by complementarities and participation between entities and their representative variables along the ii-learning process within a given s -system. next we examine the second characteristic of figure 1 on evolutionary inter-systemic equilibriums. the inter-systemic evolutionary equilibriums emerge from the learning processes of the intra-systemic equilibriums. 6 define metric by a distance function d(x,y) that is explainable over any set described by the sequence of variables say {x,y}, for which there exist well-defined functions f(x) and f(y), respectively, such that the following postulates hold: (1) d(x,y) = 0 if and only if x = y; (2) d(x,y) = d(y,x); (3) dx,z)  d(x,y) + d(y,z), for z  (x,y}. all variables are real-valued. conformably, if the metric is a topology where order and mappings are preserved over {x,y}, then, f(x), f(y) and f(z) will maintain the above-mentioned properties for themselves and for the sequence of variables.clearly, the above definition of the metric is invalidated for learning spaces such as {, x(), y(), z()}. this is also true of the functional denoted by w(, x(), y(), z()) defined on {, x(), y(), z()};   n . the following properties of the learning space causes the invalidation of the metric-definition: {x()}  {y()} / {y()}  {x()} by an identical mapping (like i); the same is true of {z()}. likewise, dw/d > 0, without there being a value of  > 0, such that /w – wo/ < , for 0 < d(x(),y()) < . 7 brouwer‟s fixed point theorem, which is the genesis of all subsequent fixed-point theorems states: if f is a continuous function from a closed bounded convex set of euclidean space c into itself, then there exists x* c, such that f(x*) = x*. 8 the idea of the good things of life is exemplified by rawls‟ (1971) primaries and in his definition of the difference princip le for the wellbeing of the most underprivileged. masudul alam choudhury 07 3.2 definition of evolutionary learning equilibrium: from intra-system to inter-system the evolutionary learning equilibriums across system interrelations between state-variables is denoted by indexed   , i x  , i =1,2, (includes policy-variables in the x()-vector) that appear within an s-system. this dynamics is now defined as follows: for every member element i = 1,2,… within an s-system, there exist    * * * *, .s i s e x  the asterisked symbols denote limiting values where evolution across systems occurs. now for every i -tuple, evolutionary system-ensemble is defined by,        *, , , s s s si s e x e e     for each value in   0 s   , but not indefinitely small value in the neighbourhood of  *s se e . the intra-systemic events in s-system so taking place along the ii-learning process are driven by consciousness that is represented in preference maps    , i s x  as these are induced by the epistemic unity of knowledge . we write such events as   , i s x  occurring in recursive rounds of ii-learning intras -system but emerging across systems at the limiting values shown by asterisk. preference maps can only be implied as a matter of inducing and inculcating consciousness. yet they cannot be measured in the commensurate sense. therefore, the conceptual-empirical implication here is to subsume the entire definition and measurement of equilibrium intras -system with the primordial role of knowledge-flows derived from the episteme of unity of knowledge in the first place. knowledge-flows as observable variables reflect levels of attained consciousness. knowledge-flows alone can be commensurably ordinalized through social discourse and measurement in the conceptual-empirical problems under investigation. the intras -systemic evolutionary learning dynamics across sequences of evolutionary equilibriums is now defined by the complete interactive-integrative-evolutionary (iie)-learning processes intras -system by adding the following property of evolutionary equilibriums. evolution across systems as indicated in figure 1 has now taken place. define  *s s se = e -e , with    i,s,n n n n i se , x ,  , n denoting new evolutionary i -designated values of events when such values span across systems. s e are determined along the evolutionary learning processes by the predetermined limiting    * * *, i s x  -values intra-system for given s and i = 1,2,… events within system s . we therefore characterize such evolutionary equilibriums across i -variables within a given s -system now spanned across n -evolutionary systems as follows:                * * * * ** * * * ** * 0 s s n s n i s i s n n n s n i s n n dxd e e d e d d dx dxe dx                                                                                     (1) the governing property for determining the limiting convergence out of learning gives the negative sign of des/d* identically for each i -variable in s -system. we denote this simultaneous occurrence of variables in numbered system ( s ) by  i s . on the existence of evolutionary learning equilibriums 07 thus, (es/n) < 0 for  i s = 1,2,… values specific to s -system study; n denotes the evolutionary states of the new iterative e -values that become convergent to * e -values within  i s . liapunov (la salle & lefschetz, 1961) has formalized a dynamic condition of stable time-dependent equilibrium state to exist. the difference of the above-mentioned dynamic knowledge-induced evolutionary equilibrium from liapunov's condition is that there is no need for a neighbourhood of an indefinitely small positive size denoted by   i s ,n . expression (1) is thus indicative of progressive evolution of n -new inter-system values of {,x()}i(s), n being across phases of iie-learning processes, hence across systems (inter-systems). such a path of evolutionary iie-learning processes within s -system marks the path-dependency creative 'history' of the learning trajectory of {(n*,xn*(n*))i}s-values. expression (1) explains the conceptual part of the conceptio-empirical phenomenological model of learning processes in unity of knowledge. it need not be empirically computed. it is epistemologically invoked to establish consistency and sustainability of intraand intersystem-learning res extensa. thus, expression (1) characterizes the nature of evolutionary equilibrium within the s -system across  i s -state variables (including policy variables) pertaining to events, and spanned across n -iterative learning processes, hence inter-systems. this kind of bundles of evolutionary equilibriums determined by iie-learning processes establishes the sustainable 'history' of unity of knowledge intraand intersystems. 4. evolutionary equilibrium across intertemporal knowledge-induced paths of the iie-learning processes: learning dynamics in the knowledge-time-space dimension the intertemporal description of evolutionary learning equilibriums intras-system is obtained by differentiating (1) in respect of time. thus, 3 * 0 s d ed dt d            (2) expression (2) conveys two important meanings. firstly, over time the nature of intra-systemic equilibrium is retained. the growth of knowledge intensifies the occurrence of evolutionary learning equilibriums. hence sustainability of the endogenous circular causation relations of unity of knowledge is increasingly established along the intertemporal iie-learning processes. secondly, the changes of   , t x  -values over time t across  i s and n number of phases intras -system evolving into inter-systems means that time simply reads and records the state of the {,x()}t-values intertemporally. note that we have dropped the subscripts in the variables to ease the symbolization. such intertemporal recording of the   , t x  -values does not mean that time has anything to do with primal causation of change in these values. 4 only knowledge causes change. time records change that is caused by knowledge induction of the intraand intersystemic variables. 5. summarizing the analytics of the generalized form of evolutionary equilibriums we can now summarize the evolutionary learning equilibrium in terms of the following operator, (d/dn) (choudhury and zaman, 2006):     n n t i,s i,s nd/d w e 0, i 1, 2,...; 1, 2,...; 1, 2,....s n         (3) masudul alam choudhury 07 underlying the evaluation of w(.) there is the system of circular causation that reflects organic unity of knowledge according to the principle of pervasive complementarities between variables and entities. 6. fixed point theorem in non-compact topology 5 because of the openness of the learning domain of     , both for intra-systemic and inter-systemic changes over time, the equilibrium points on the trajectory of 'history' (i.e. such knowledge-induced changes recorded and read over time) belong to open and moving sets. such sets are thereby of the type having non-fixed equilibrium points (maddox, 1970) 6 . hence there must be a revision of the fixed point theorem in such a case of evolutionary learning equilibriums across non-compact topological spaces. for a characterization of such noncompact learning sets as topology see choudhury et al. (2006). we can now enunciate a theorem on evolutionary fixed-point theorem 7 for the case of noncompact evolutionary learning equilibrium points: 6.1 statement of theorem given all the properties of evolutionary learning equilibriums, there does not necessarily exist a diminishing metric in an evolutionary learning set, such that    0   has an indefinitely small value. thus any such set will not necessarily have a limiting point in   .e {e(.)}. a temporary limiting point will thus be pushed outside any particular -neighborhood of a point in the continuously evolutionary path of learning. since this condition of evolutionary learning equilibriums applies to all neighborhoods of   , t x  -variables over time t , there is no convergent limiting point in all of   .e . 7. towards proving the existence of evolutionary learning equilibriums to prove the existence of the consequential evolutionary learning equilibriums, the objective criterion   w e  needs to be evaluated by means of simulation of circular causation relations at the 'nearest' point of evaluation of the state of the targeted variables in accordance with the episteme of unity of knowledge. the 'predictor' values of the variables and  representing a wellbeing index are simulated by changes in the regression coefficients of the circular causation equations for attaining certain degrees of unity of knowledge between the variables. the resulting simulated learning equilibriums form „non-fixed point‟ type of sub-sets of  .e -event spaces across intraand intersystemic iie-learning processes over time. the proof of this theorem is given in the appendix. the footnote here explains the underlying idea of knowledge-induced magna of learning metrics. it is interesting to point out here that the same idea of the knowledge-induced metric also applies to the physical geodesic (wald, 1992) of the open-universe conjecture of popper (1988) upon which the realm of consciousness abides. thus the body of application of the formalism of evolutionary equilibriums that learn over 'non-fixed point' topological sets universally spans all socio-scientific domains. 8. what is the place of economics and finance in the e(.)-generalized system formalism? the formalism thus far on evolutionary learning equilibrium is of a generalized type. it can be used as mathematical formalism in modeling every problem of the socio-scientific category. in order to particularize to the special case of economics, finance, and related disciplines, we note in the general case signified by (3), that a on the existence of evolutionary learning equilibriums 07 vast nexus of interconnected complementary (participatory) variables arise across various domains specific to the problems at hand. 8.1 exemplar: sustainability in socioeconomic development by the learning paradigm some of the socioeconomic problems addressed by the evolutionary equilibrium paradigm are the following: the study of inter-temporal sustainable development can be done by means of dynamic coefficients input-output matrices of learning inter-sectorally linked (complementary). here, sectoral outputs can be complemented together to explain the evolutionary dynamics of an inter-sectorally connected joint production function. the same kind of intertemporal and inter-sectoral output matrix can be deconstructed into the matrices of derived demand and supply of productive factors. factor prices can thereby be simulated by considering the derived factor demand and supply functions with complementarities between the factor inputs and their relative prices in the presence of the learning impact of the knowledge-flow  -values to construct complementarities. indeed, intraand intersystemic complementarities are the sure mark of organic unity of knowledge in the „joint production function‟. the induction of  x  -vector by  -values across iie-learning processes signifies the endogenous nature of ethics in the problem under study. the fields of ethics and economics as endogenously embedded systems become a deep study of sustainability paradigm in development in learning systems. the sustainability concept in the realms of ethics and economics is now applied to the study of inter-systemic complementarities (systemic participatoriness) comprising economics, ethics (society), and development sustainability. learning models of unity of knowledge of the type presented here enable the study of interconnected learning systems with evolutionary learning equilibriums in them (choudhury et al. 2007a ; choudhury et al. 2007b). examples are sustainability in development paradigms and interlinking of money with real economy by development financing instruments (choudhury, 2009). inter-linkages by complementarities in the  x  -vector of variables in such studies are the result of ethico-economic formalism premised on the episteme of unity of knowledge. 9. development sustainability in the simulated domains of evolutionary learning equilibriums we define development sustainability here by simulated learning between appropriate technology (), induced output vector   x  and average cost of production   ,ac x  . goulet (1995) has given a succinct treatment of ethics as an endogenous force in sustainable development. in the learning model of sustainable development,  .ac will decline with the growth of   , x  ; and there will be a positive relationship between   and   x  . thus in a simulated domain of learning processes there will be systems of positive relations in the   , x  -tuples and negative relations between   .ac and each of the variables of the simulated    , x  -tuples. such simulated regions comprising the totality of      , , ,x ac x    are not necessarily convex. hence the fixed-point theorem cannot be used to prove the existence of equilibrium in evolutionary learning regions of simulation caused primordially by the effect of knowledge-flows   -values. such relations in the simulated      , , ,x ac x    -region bring out the property of pervasive complementarities between the good things of life 8 in a dynamic sense. simple technical details of the above example are examined below. the results of evolutionary equilibrium in simulated regions of sustainable development are shown in figure 2. masudul alam choudhury 09 in any given regime of development, hence in a given i(s)-stage of development with real gdp (x()) and technology variable  let,      2, . .ac x a b x c      (4) note that the coefficients , ,a b c are themselves functions of  because of the continuous shifts in the  induced simulated values      , , ,x ac x    . the properties of expression (4) in any intrasystemic      , , ,x ac x    -region followed by evolution for development sustainability inter-systems are worked out below 2 0, . 2 . . 0 dac da dx db dc b x c d d d d d                                 (5) by the effect of  -learning on the other variables and parameters we obtain the following results: dx/d > 0; da/d < 0; db/d < 0; dc/d < 0. there are no specific signs of a, b, c. but positive learning effect will make these shift-parameter enhancing wellbeing in the sustainable development model. resulting from expression (5) we note,  2. . dx b c d             where   2 0 da db dc x d d d                           expression (5) can be worked out with the help of the ancillary properties of learning effects as shown above, to show:        2 . 0 cdx d b                  (6) thereby,    *x     , for 0x  , for 0  of the learning type [see footnote 7]. if the variables of      , , ,x ac x    -region are taken in the natural logarithmic form then,    .x e     (7) figure 2 shows all the results of expressions (4), (6)/(7). according to endogenous development paradigm in this paper, the history ee is fully encapsulated in expression (3), which is limited subject to circular causation relations in  i s across {, x(), ac(,x())}region in  i s [see earlier notation].while ee is driven across systemic continuums by knowledge-flows and knowledge-induced state and policy variables   x  , and thus by circular causation relations between the inter-regional variables that enable evaluation of the wellbeing function, w(.), as shown above, yet the measurement of such system-evolutionary variables is recorded at specific time-periods. the resulting paradigm of endogenous development is different from the idea of endogenous economic growth (romer, 1986). this is on the existence of evolutionary learning equilibriums 00 due to the absence of circular causation in endogenous growth theory, which otherwise, is central to the endogenous -effect in evolutionary  i s -inter-systems. intra-systemic convergences e e inter-systemic evolution and convergence through intra-systemi linkages of the specific convergence on the evolutionary phases: the case of evolutionary average cost of production that never reaches a minimum point due to the technological effect of evolutionary learning. figure 2. development sustainability by endogenous technological induction. intra-inter-systemic convergence 'e' evolutionary equilibriums that describe what we refer to as evolutionary learning history. this is denoted along ee. along ee the knowledge-time-space evolution is described by the trajectory of the evolutionary bundle caused by the continuous effect of -values, {, x(), ac(,x())}-region in i(s) [see in text]. inward movement of {, x(), ac(,x())}-region denoted by the intra-inter-systemic gyration caused by learning affecting the continuously shifting curves under the primordial effect of -values, where shifts occur causing new evolutionary{, x(), ac(,x())}-regions moving inwards. the origin e of evolutionary convergence is one of many such temporary evolutionary intraand inter-systemic evolutionary fixed points (see figure 1). 10. conclusion: universalizing the evolutionary learning equilibriums the sustainable iie-learning system over knowledge-time-space dimension as explained by expression (2) can be generalized over any number of s -systems, with i -events and n -learning iterations of learning processes (hence inter-system evolutions). consequently, multivariate and multidimensional  i s -variables, intertemporally spanning any number of n -emergent iie-learning processes, inter-systems induce experience in synergistic symbiosis in evolutionary learning. the global pictures of evolutionary learning equilibriums are now established as a sustainable trajectory of „history‟ across knowledge-time-space dimension intra-systems and intersystems. such ensembles across history are explained by hubner et al. (1985). see appendix 2 for a formal explanation of the specific application of evolutionary learning equilibriums to the theme of development sustainability. masudul alam choudhury 07 (d/dn)[n=ti,sw(ei,s)[n] > 0, i = 1,2,…; s = 1,2,…; n = 1,2,…. {,x()}  n=ti,sei(s){,x()}n, intertemporally and across systems and their variables by means of the iielearning processes and multiple relations signified by events e(.) s1 s2 inter inter-systemic interaction s3 {,x()}  n=ti,sei(s){,x()}n inter-and intra-systems multiple variable i(s). „non-fixed point‟ properties of evolutionary spaces intraand intersystems are implied by the continuity of {,x()}values that make such learning spaces of the fuzzy-set type. mappings for wellbeing evaluation {w(,x())}{n=ti,sw(ei(s)(,x())n) by the property of toplogical preserving order of mappings on topological spaces of {,x() {dw/d > 0{n=ti,sdw(ei(s)(,x())n)/d}t subject to (d/dt)(des/d*) < 0 in this paper the continuity of the topological mapping on monotonically continuous functional relations implies that order-preserving properties hold on the evolutionary learning case. figure 3. geometry of evolutionary learning equilibriums. on the existence of evolutionary learning equilibriums 06 appendix 1 on the existence of equilibrium in non-fixed point’ type learning spaces a geometrical explanation and proof is presented here to explain the total picture of the existence of knowledgeinduced evolutionary equilibriums in a relevant form of the non-fixed point theorem. we deconstruct the following equation from the text of the paper that combines the entire nature of evolutionary equilibriums: dynamic equilibriums in evolutionary learning spaces are now defined by the following conditions:         , ,i s nx e x     , such that all the equations (1)-(3) in the paper hold true. appendix 2 algorithmic display of evolutionary systemic equilibriums simulate the wellbeing function given in the following form:                1, , , 0 ;n nx ac x ac n n w                   being numbered evolutionary learning systems};   0 d d     within the respective evolutionary regions in respect of an inestimable core convergent value   * n   . the evolutionary values of   n   do not compare between regions. ac() decreasing ac()-surface by virtue of learning  = 1  = 0.5 region of limiting ()-points by learning o  = 0.10 (>0), x()  x()-surface by learning figure 4. evolutionary learning phenomenon relating to {,x(),ac()}. masudul alam choudhury 77 as an example, in the region with  = 1, 2, 3, …10, leading respectively to  x  = 1,2,3,…10;  ac  = 1/1. 1/2, .., 1/10. the evolutionary system of wellbeing index is thus made up of regions bounded by the triplets, {(1,1,1, 1  ( =1) = 1), (2,2,0.5, 2  ( = 2) = 0.5), …, (10,10,0.10, 10  ( = 10) = 0.10)}. figure 4 shows the evolutionary learning phenomenon for the stated wellbeing function in reference to figures 2 and 3. 11. references arrow, k.j., 1951. social choice and individual values, new york, ny: john wiley and sons. bertuglia, c.s. and vaio, f. 2005. dynamical systems and the phase space, in nonlinearity, chaos & complexity, the dynamics of natural and social systems, oxford, uk: oxford university press, pp. 49-70. braudel, f., 1980. on history, chicago, ill: university of chicago press. brouwer, l.e.j., 1910. ube rein eindeutige, stetige transformation von flachen in sich, mathematische annalen, 69: 176-80. casti, j.l., 1990. mathematics of the unexpected , in his searching for certainty, pp. 61-68, new york,: william morrow & co. chichilnisky, g., 1993. topology and economics: the contribution of stephen smale, in hirsch, m.w. marsden, j.e. and shub, m (eds.), from topology to computation: proceedings of the smalefest, pp 147161, new york, springer-verlag. choudhury, m.a., 2006. evolutionary equilibrium in learning spaces of unity of knowledge, the middle east business and economic review, 18(2): 39-53. choudhury, m.a., 2009. money, finance, and the real economy in islamic banking and finance, unpublished msc dissertation, department of economics, university of stirling, uk. choudhury, m.a., 2010. islamic economics and finance, an epistemological inquiry, yorkshire, u.k.: emerald, in the series contributions to economic analysis 291. choudhury, m.a. and zaman, s.i., 2006. learning sets and topologies, kybernetes: international journal of systems and cybernetics, 35(7): 1567-1578. choudhury, m.a, zaman, s.i. and harahap, s.s., 2007a. an evolutionary topological theory of participatory socioeconomic development, world futures, 63(8): 584-598. choudhury, m.a. zaman, s.i. and nassar, y. 2007b. “a knowledge-induced operator model”, the journal for science, sultan qaboos university, 12(1): 19-40. debreu, g., 1959. theory of value, an axiomatic analysis of economic equilibrium, john wiley, new york. debreu, g., 1989. existence of general equilibrium, in eatwell, j. milgate, m and newman, p. eds. new palgrave: general equilibrium, pp. 131-138, new york, w.w. norton. friedman, a., 1982. compact metric spaces, in his foundations of modern analysis, pp. 107-109, new york, dover publications, inc. goulet, d. 1995. development ethics, new york: the apex press. grandmont, j-m., 1989. temporary equilibrium, in eatwell, j. milgate, m & newman, p. 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(eds.) the new palgrave: general equilibrium, pp. 274-280, new york: w.w. norton. thurow, l., 1996. plate two: an era of man-made brainpower industries, in his the future of capitalism, london, eng: nicholas-brealey. uzawa, h., 1964. optimal growth in a two-sector model of capital accumulation, review of economic studies, 31: 1-24. wald, r.m., 1992. space, time and gravity, chapters 2 and 3, chicago, ill; the university of chicago press. wolfe, r.p., 1977. a reconstruction of a critique of a theory of justice: understanding rawls, princeton, nj: princeton university press. received: 20 may 2011 accepted: 10 october 2011 squ journal for science, 2015, 20(2), 31-41 ©2015 sultan qaboos university 31 a priori error estimates for mixed finite element θ-schemes for the wave equation samir karaa department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, al-khod 123, muscat, sultanate of oman. email: skaraa@squ.edu.om. abstract: a family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. the mixed space discretization is based on the displacement form of the wave equation and the time-stepping method employs a three-level one-parameter scheme. a rigorous stability analysis is presented based on energy estimation and sharp stability results are obtained. a convergence analysis is carried out and optimal a priori 2 ( )l l  error estimates for both displacement and pressure are derived. keywords: energy technique; error estimation; mixed finite elements; wave equation. لمعادلت الموجت -العناصرالمحذودة المختلطت تقذيراث الخطأ المسبقت لطرق سمير القرعت رافل ح س راص ة ةت ة ةدة رض زم رم م ق ا را راعمحد ررالمختلم رالالضم ة ترال لم ة ت ي را سمق اضلدرة ل راع خل العحلا ة رال نع ملخصص رالس لاخمة عض ى رالدرةل راسممي عضى ثالثة مسل ةحت مرةبمة بللغ ر ترحخت ة ةمض رس لدررلرامراةعللخ تلعحلاة رال ةازرحة رإلبحالسلمحل إاى ححاة رألتاي ة ةمض رالدحلب تةدخةر راامأ كلح أسحش ةدخةررامحقة ترال د إاى نلحئج لق دةت 2 ( )l l  بشك مثحاي اك مق رإلزرحة ترالغطت . راعمحدررالمختلم رالالضمة ةدخةر راامأ ةدم ة رامحقةمعحلاة رال ة يتمفتاح كلماث 1. introduction he acoustic wave equation is used to model the effects of wave propagation in heterogeneous media. solving this equation efficiently is of fundamental importance in many real-life problems. in geophysics, it helps for instance in the interpretation of the seismograph field data and to predict damage patterns due to earthquakes. using finite element methods for its approximation is attractive because of the ability to handle complex discretizations and design adaptive grid refinement strategies based on error indicators. previous attempts on wave simulation by finite elements have used continuous galerkin methods [1-6], mixed finite element methods [7-13], and discontinuous galerkin methods [14-17]. in a mixed finite element formulation both displacements and stresses are approximated simultaneously. this approach provides higher-order approximations to the stresses. this property is important in many problems, in particular in modeling boundary controlability of the wave equation [18]. one of the main difficulties of the mixed finite element techniques is the requirement of compatibility of the approximating spaces for convergence and stability. given a bounded convex polygonal domain  in , m = 2,3m , with boundary = d n    , and unit outward normal , the general form of the wave equation is = (0, ), tt in t  u f (1) = 0 (0, ), d on t  u (2) = 0 (0, ), n on t  u (3) 0 ( , 0) = ,in u u (4) 0 ( , 0) = , t in u v (5) where u is the displacement,  is the density, and  is the stress tensor given by the generalized hooke's law = ( ) ( ( ) ) t       u i u u . here > 0 and  are the lamé coefficients characterizing the material. the function t samir karaa 32 f represents a general source term and 0 u and 0 v are initial conditions on displacements and velocities. we assume that f , 0 u and 0 v are sufficiently smooth that there is a unique solution 2 ((0, ) )c t u to (1)-(5), see [19]. the limiting case of (1) with = 0 is referred to as the acoustic wave equation, which is ( ( ) ) = . tt   u u i f (6) it is assumed that  and  are bounded below and above by the positive constants 0  , 1  , 0  , and 1  , respectively. this vector equation is equivalent to the scalar wave equation after making the substitution = ,p u . the mixed method is established by using this relationship, leading to the coupled system = (0, ), tt p in t  u f (7) 1 = (0, ),p in t   u (8) with the appropriate boundary and initial conditions. a priori error estimates for solving (7)-(8) were obtained in [7, 8, 9, 10]. in [9], geveci derived l  in-time, 2 l in-space error bounds for the continuous-in-time mixed finite element approximations of velocity and stress. in [7,8], a priori error estimates were obtained for the mixed finite element approximation of displacement which requires less regularity than was needed in [9]. stability for a family of discrete-in-time schemes was also demontratred. in [10], an alternative mixed finite element displacement formulation was proposed reducing requirement on the regularity on the displacement variable. for the explicit discrete-in-time problem, stability results were established and error estimates were obtained. the effectiveness of the method analyzed in [10] was demonstrated in [20] by providing simulations using both lowest-order and next-to-lowest-order raviart-thomas elements on rectangles [21]. the purpose of this paper is to analyze an implicit time-stepping method combined with the mixed finite element discretization proposed in [10]. we prove the stability of the proposed method by using energy estimation, and show in particular that it conserves certain energy. we also investigate the convergence of the method and prove optimal a priori 2 ( )l l  error estimates for both displacement and pressure. the rest of the paper is organized as follows. in sections 2 and 3, we introduce notations and describe the weak formulation of the problem. the fully discrete mixed finite element method is presented in section 4. stability results are established in section 4 and optimal a priori error estimates are obtained in section 5. conclusions are given in the last section. 2. notation we shall use the following inner products and norms in this paper. the 2 l -inner product over  is defined by ( , ) = ,u v uvd   inducing the 2 l -norm over , 1/ 2 2 ( ) || || = ( , ) l v v v  . the inner product over the boundary  is denoted by , =u v uvd     for ,u 1 2 ( )v h    with > 0 . we introduce the time-space norm:   1 22 2 2 2 2 2 (0, ; ( )) ( ) ( )0 || || =|| || = || || . t l t l l l l v v v dt   the time-space norm 2 ( ) || || l l   is similarly defined. in addition to the 2 l spaces, we use the standard sobolev space for mixed methods: 2 2 ( , ) = { : ( ( )) , ( )}, m div l l     h v v v with associated norm ( , ) 2 2 ( ) ( ) || || =|| || || || , div l l      h v v v where 1 2 2 2 2 ( ) ( ) =1 || || = || || . m i l l i v         v for the time discretization, we adopt the following notation. let n be a positive integer, = /t t n , and = n t n t . for any function v of time, let n v denote ( ) n v t . we shall use this notation for functions defined for all times as well as those defined only at discrete times. set   1 12 1 = , 2 n n n v v v      1 12 1 = , n n n t v v v t      a priori error estimates for mixed finite element  -schemes 33  1 1 1 = , 2 n n n t v v v t       1 12 1 = 2 , n n n n tt v v v v t       ; 1 1 = (1 2 ) , n n n n v v v v          where 0 1  . we also define the discrete l  -norm for time-discrete functions by 2 2 2 (0, ; ( )) ( ) ( )0 || || =|| || = || || .max n l t l l l ln nt v v v      3. weak formulation the finite element approximation of the wave problem is based on its weak formulation which is derived in the usual manner. integrating by parts and using the data on the boundary of  , we obtain the weak formulation [10], for any 0t  , find ( ( ), ( ))t p t w u v such that 0 ( (0), ) = ( , ) , u v u v v v (9) 0 ( (0), ) = ( , ) , t  u v v v v v (10) 1 0 ( (0), ) = ( , ) ,p w w w w    u (11) ( ( ), ) ( ( ), ) = ( ( ), ) , > 0, tt t p t t t    u v v f v v v (12) 1 ( ( ), ) ( ( ), ) = 0 , > 0,p t w t w w w t     u (13) where v and w are given by = { ( , ) : | = 0}, n div    v v h v 1 2= ( ) for any > 0.w h     the present formulation requires less regularity on the displacement than standard approaches. for instance in [7, 8] it is necessary that ( , )p div  h so that 2 ( )h  u . here, it is only required that 1 2h u , and it can be verified that the solution u of problem (1)-(5) with =p u is a solution to (12)-(13), see [10]. differentiate (13) with respect to time to obtain 1 ( , ) ( , ) = 0 . t t p w w w w     u (14) we next assume = 0f and choose = t v u and =w p in (12) and (14), respectively, so that ( , ) ( , ) = 0, tt t t p  u u u (15) 1 ( , ) ( , ) = 0. t t p p p   u (16) by adding the two equations, we find that 1 ( , ) ( , ) = 0, tt t t p p   u u (17) or 2 2 1 1 2 2 2 2 ( ) ( ) 1 1 = 0. 2 2 t l l d d p dt dt      u thus, in the absence of forcing, the (continuous) energy 2 2 1 1 2 2 2 2 ( ) ( ) 1 1 2 2 t l l p     u (18) is conserved for all time. it will be shown that a similar form of energy is conserved by the numerical solution of the wave problem. 4. finite element approximation for the finite element approximation, we let >0{ }h h be a quasi-uniform family of finite element partitions of  , where h is the maximum element diameter. let h h wv be any of the usual mixed finite element approximating subspaces of ,wv that is, the raviart-thomas-nedelec spaces [21, 22], brezzi-douglas-marini spaces [23], or samir karaa 34 brezzi-douglas-fortin-marini spaces [24]. for each of these mixed spaces there is a projection : ( , ) h h div  h v such that for any ( , )div z h ( , ) = ( , ) . h h w w w w   z z (19) we have the property that, if ( , ) ( ) k div   z h h , then 0 || || || || , 1 , j h j ch j k    z z z (20) where k is associated with the degree of polynomial and || || s  is the standard sobolev norm on ( ( )) s m h  . here and in what follows, c is a generic positive constant which is independent of h and t . for w  , we denote by h p  the 2l -projection of  onto h w defined by requiring that ( , ) = ( , ) . h h p w w w w    (21) if ( ) k w h    , then we also have || || || || , 0 , 0 . j s h s j p ch s k j k          (22) the semidiscrete mixed finite element approximation to ( ( ), ( ))t p tu is to seek ( ( ), ( )) h h t p t w u v satisfying 0 ( (0), ) = ( , ) , h h   u v u v v v (23) 0 ( (0), ) = ( , ) , t h h   u v v v v v (24) ( (0), ) = ( (0), ) , h p w p w w w  (25) ( ( ), ) ( ( ), ) = ( ( ), ) , > 0, tt h t p t t t    u v v f v v v (26) 1 ( ( ), ) ( ( ), ) = 0 , > 0. h p t w t w w w t     u (27) existence and uniqueness of a solution ( ( ), ( ))t p tu to the variational problem (23)-(27) is shown in [10]. the fully discrete mixed finite element -scheme is then defined by finding a sequence of pairs ( , ) n n h h p w u v , 0 n n  , such that 0 0 ( , ) = ( , ) , h h   u v u v v v (28) 0 0 ( , ) = ( , ) , h p w p w w w  (29) 1 1 1 2 0 0 22 2 2, , ( , ) = , 2 2 t t t t t t p p t                               u v v v f f v  0 , ,h h   v v v v (30) ; ; ( , ) ( , ) = ( , ) , n n n tt h p       u v v f v v v (31) 1 1/ 2 1/ 2 ( , ) ( , ) = 0 . n n h p w w w w       u (32) equation (30) is derived from the following expansion: 1 0 0 2 1 0 31 = ( ). 2 tt tt t t o t                  u u v u u the present scheme is explicit in time if = 0 and implicit otherwise. the existence and uniqueness of a solution to the resulting linear system for a nonzero value of  follows from the unisolvancy of the mixed formulation of the following elliptic problem: 2 1 ( ) = 0 ,in t          = 0 on . the explicit case has been considered in [10]. as expected from an explicit scheme, the method is conditionally stable. as a stability constraint, it requires the choice of = ( ).t o h in the next sections, stability and convergence properties of the proposed scheme are analyzed. 5. stability analysis we derive sharp stability bounds based on the energy technique and show that the proposed scheme conserves certain energy. we consider (31) and (32) for the homogeneous case ; ( , ) ( , ) = 0 , n n tt h p      u v v v v (33) 1 1/ 2 1/ 2 ( , ) ( , ) = 0 . n n h p w w w w       u (34) we will make use of the inverse assumption, which states that there exists a constant 0 c independent of h , such that 1 2 0 2 ( ) ( ) || || || || l l c h       (35) a priori error estimates for mixed finite element  -schemes 35 for all h w  . the following stability result holds. theorem 1 the fully discrete scheme (28)-(32) is stable if 2 2 0 1 2 0 1 1, 4 c t h            (36) and conserves the discrete energy 1 1 1 1 1 1 1 2 2 2 22 2 2 2 2 2 2 1 1 = || || || || || || . 2 4 n n n n h t t e t p p                      u (37) the scheme is unconditionally stable if 1/ 4  . proof. if we subtract (34) from itself, with 1/ 2n  replaced by 1/ 2n  , we find that 1 1 1 1 1 ( ( , ) ( ( ), ) = 0. n n n n p p w u u w          (38) as (33) holds for all h v v and (38) holds for all h w w , we choose = n t v u and ; = 2 n p w t   so that ; ( , ) ( , ) = 0, n n n n tt t t p     u u u (39) 1 ; ; ( , ) ( , ) = 0. n n n n t t p p p        u (40) by adding (39) and (40) we obtain 1 ; ( , ) ( , ) = 0. n n n n tt t t p p        u u (41) note that ; 2 = n n n tt p t p p     1 1 2 2 2 1 1 = . 4 2 n n n tt t p p p                (42) hence, (41) can be rewritten as 1 1 2 1 1 2 2 1 1 ( , ) ( , ) ( ), = 0. 4 2 n n n n n n n tt t tt t t t p p p p p                           u u (43) using that 1 1 1 1 2 2 2 2 = , = , 2 n n n n n nt t t t t tt t              u u u u u u we deduce that 1 1 1 1 2 2 2 2 1 ( , ) = ( , ) 2 n n n n n n tt t t t t t t                 u u u u u u 1 1 1 1 2 2 2 2 1 = ( , ) ( , ) , 2 n n n n t t t t t                 u u u u and similarly 1 1 1 1 1 1 12 2 2 2 1 ( , ) = ( , ) ( , ) . 2 n n n n n n tt t t t t t p p p p p p t                        we also have 1 1 1 1 1 1 1 1 12 2 2 2 2 2 1 ( ), = ( , ) n n n n n n n t p p p p p p p t                      1 1 1 1 1 12 2 2 2 1 = ( , ) ( , ) . n n n n p p p p t                hence, (43) is equivalent to 1 1 2 2 1 = 0, n n h h e e t         where 1 2 n h e  is the quantity defined by (37). this relation indicates that 1 2 n h e  is conserved for all time, which guarantees the stability of the scheme if and only if 1 2 n h e  defines a positive energy. a sufficient condition is that 2 2 1 1 1 1 22 2 2 2 1 0 4 n n t t t p                u samir karaa 36 for all 0n  . clearly, the scheme is unconditionally stable when 1/ 4  . now, using the cauchy-schwarz inequality and the inverse assumption (35), we obtain 1 1 1 2 2, = , n n t t p w w                 u 1 2 2 ( ) 2 ( ) || || n t l l w      u 1 0 2 2 ( ) 2 ( ) || || . n t l l c w h      u by setting 1 2= n t w p   , we see that 2 1 1 1 1 02 2 2 2 2 2 2 ( ) ( ) ( ) n n n t t t l l l c p p h            u 1 1 1 1 12 0 1 2 2 2 2 1 2 22 ( ) ( ) 0 n n t t l l c p h            u or 1 1 1 1 12 0 12 2 2 2 1 2 22( ) ( ) 0 . n n t t l l c p h             u hence, a sufficient condition for stability is given by 1 1 1 12 2 2 20 12 2 2 2 2 0 1 || || || || 0, 4 n n t t c t h                 u u which completes the proof. □ the case with = 1/ 4 is interesting because the form of the discrete energy in this case is similar to that of the continuous problem. in addition, one can verify that the time truncation error is minimized over the set of all 1/ 4  when = 1/ 4 . 6. convergence analysis in this section, we prove optimal convergence of the fully discrete finite element solution in the 2 ( )l l  norm. some of the techniques used in the proofs can be found in previous works [25, 26]. in order to estimate the errors in the finite element approximation, we define the auxiliary functions = , = , = , = , n n n n n n n n n n n h h h h p p p p p p      u u u u where h  and h p are defined in section 4. from (12-13) and (31-32), and the properties of the projections h  and h p , we arrive at ; ( , ) ( , ) = ( , ) ( , ) , 1, n n n n tt tt h v n             v v r v v v (44) 1 1/ 2 1/ 2 1 1/ 2 ( , ) ( , ) = ( , ) , 0, n n n h w w w w w n               (45) where ; = ( ) n n n tt tt   r u u . another equation has to be derived for the initial errors 1  and 1  . consider (12) at = 0n and = 1n , respectively, and subtract the resulting equations so that 1 1 1 2 2 2, , = , . t tt t t p                       u v v f v (46) a use of taylor's formula with integral remainder yields 1 3 0 0 22 30 1 = ( ) ( ) . 2 2 t t tt t t t t dt t t           u u v u (47) using (46) and (47), we readily obtain 1 1 1 1 2 2 22 2 2 2, , = , , t t t t tt t p t t                                      u v v f v u v a priori error estimates for mixed finite element  -schemes 37 0 0 ( , ) ( , ) 2 tt t     v v u v 3 2 30 1 ( ) , . 2 t t t dt t t              u v (48) subtracting (48) from (30) and taking into account (29) and (12) we arrive at     1 1 1 2 0 0 02 2 2 1 3 2 22 30 , , , = , ( ), 2 1 , ( ) , . 2 t t t h t t tt t t t t t dt t t                                                           v v v v v v v u u v v (49) note that 0 = 0 and 0 = 0 . we now state and prove our convergence result. theorem 2 if ( ( ; d ))l iv   u h , 3 1 2 3 ( ( ))l t     u l , 4 2 4 ( ( ))l t     u l , and 2 ( ( ))p l l    , then for { , } n n pu defined by (28)-(32) there exists a constant c independent of h and t such that if 2 2 1 0 2 0 1 1 < , 4 2 c t h           (50) then the following a priori error estimate holds: 1 1 2 2 2 2 ( ) ( ) 3 2 23( ) ( ) 2 ( ) ( ) ( ) ( ) || || || || , l l l l r r l h l l l l p p c h t p t                        u u u u (51) where r is associated with the degree of the finite element polynomial. proof. we first rearrange (44) in the form 1 1 2 2 2 1 1 ( , ) ( , ) , = ( , ) ( , ). 4 2 n n n n n n tt tt tt t v                             v v v r v (52) summing over time levels and multiplying through by t yields 1 1 1 1 22 2 2 2 1 1 1 1 2 2 2 2 =1 =1 1 ( , ) , 4 , = , , . 2 n n t t t t n n i i n i t t i i t t t v                                                               v v v v r (53) upon defining 11 0 2 =0 = 0, = , n i n i t       we verify that 1 1 1 1 2 2 2 2 =1 = . 2 2 n n i i i t t                taking into account (49) and that 1 1 2 2 2 = t t    , (53) becomes   1 1 1 1 22 2 2 2 1 ( , ) , , = , , , 4 n n n n n t t t t                                        v v v v r v (54) where 1 3 0 0 2 22 30 =1 1 = ( ) ( ) . 2 n t n i h t tt i t t t t dt t t                     u r r v v u since 1 1 2 2= n n t      , (45) reads 1 1 1 1 12 2 2, , = , . n n n t w w w                              (55) choosing 1 2= n v   and 1 2= n w   in (54) and (55), respectively, and adding the resulting equations, we arrive at samir karaa 38 1 1 1 1 1 1 2 12 2 2 2 2 2 1 1 1 1 1 12 2 2 2 2 1 ( , ) , , 4 = , , , . n n n n n n t t t n n n n n n t t                                                                       r (56) again, we choose 1 2= n t w    in (45) so that 1 1 1 1 1 1 1 12 2 2 2 2 2, = , , . n n n n n n t t t                                       substitution into (56) yields 1 1 1 1 1 1 2 1 12 2 2 2 2 2 1 1 1 1 2 1 2 2 2 2 1 1 1 12 2 2 1 ( , ) , , 4 1 , , 4 , , . n n n n n n t t t n n n n t t n n n n t t                                                                                             r (57) the terms on the right-hand side of (57) are bounded using cauchy-schwarz inequality as 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 ( ) ( ) , n n n n t t l l                         1 1 1 1 2 2 2 2 2 2 ( ) ( ) , n n n n t t l l                     1 1 2 2 2 ( ) 2 ( ) , n n n n l l             r r 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 ( ) ( ) , . n n n n l l                       we now distinguish the cases where 1 4   and 1 < 4  . in the first case, we sum on (57) over time levels and multiply through by 2 t . this results in 2 2 2 2 1 1 1 1 1 0 1 02 2 2 2 2 2 2 2 ( ) ( ) ( ) ( ) 2 2 1 1 2 1 02 2 2 2 ( ) ( ) 1 1 1 1 2 12 2 2 2 = 0 2 2 2 ( ) ( ) ( ) 1 1 2 2 = 0 2 2 ( ) ( 1 4 1 2 4 2 n n l l l l n l l n i i i i l l l n i i t i l l t t t                                                                                      2 ( ) ) 1 1 1 1 2 2 2 2 = 0 2 2 ( ) ( ) 2 . i l n i i i l l t                       r (58) since 1 1 2 2 2 2 ( ) ( ) i l l l          and 1 1 1 2 2 2 2 2 ( ) ( ) i l l l         , then a priori error estimates for mixed finite element  -schemes 39 2 2 2 1 1 1 1 1 2 12 2 2 2 2 2 ( ) ( ) ( ) 1 1 1 2 2 2 2 = 02 2 ( ) ( ) 1 1 2 2 21 ( ) = 0 = 02 22 ( ) ( ) 0 1 1 1 2 2 2 = 02 2 ( ) ( ) 1 4 1 4 4 2 2 n n n l l l n i i l l l n n i i t l i i l l l n i i l l l t t t t                                                                                   r .         (59) applying the algebraic inequality: 2 21 2 2 ab a b     to the right-hand side of (59) shows that 2 2 2 1 1 1 1 1 2 12 2 2 2 2 2 ( ) ( ) ( ) 2 2 1 1 11 2 2 2 2 = 02 2 ( ) ( ) 2 2 1 11 1 22 2 2 ( ) = 0 = 02 2 ( ) ( ) 1 2 1 4 1 1 1 8 2 4 4 1 2 1 2 n n n l l l n i i l l l n n i i t l i i l l l l t t t c t                                                                                         r 2 2 1 11 2 2 = 02 2 ( ) ( ) 4 . n i i l l t                  (60) if we take the supremum over n on the left-hand side and use the fact that =n t t , we conclude that 2 2 2 1 1 1 2 2 2 2 2 2 ( ) ( ) ( ) 2 211 1 2 22 2 ( ) = 0 = 02 ( ) . l l l l l l n n i i t l i i l c c t c t                                         r (61) for the case 1 < 4  , we can follow the analysis presented in [15,16] to derive error estimates similar to (61) under condition (50). to complete the proof, we need to bound each term on the right-hand side of (61). the first term can be bounded using the approximation properties. similarly, we have 1 31 22 3( ( )) =0 1 22 (0, ; ( ))( ) || || . n i k k l h i l t ll t c h t t                  u u for the last term on the right-hand side of (61), we have 1 2 2 ( ) ( ) =0 || || || || n i l l l i t c      r r 1 0 0 2 2 ( ) ( ) =1 || || || ( ) || n i h l l i c t c          r v v 1 3 2 22 30 22 ( )( ) 1 ( ) ( ) . 2 t t tt ll c t c t t t dt t t                u u to estimate 2 ( ) || || i l  r , we make use of the identity 4 3 2 4 1 = ( | |) ( ) . 6 t n n n tt tt t u t s t s ds t t            u u (62) samir karaa 40 from the taylor's expansions of 1n tt  u and 1n tt  u about n tt u ; 4 1 40 = ( | |) ( ) , t n n n n tt tt ttt t t s t s ds t            u u u u and 4 0 1 4 = ( | |) ( ) , n n n n tt tt ttt t t t s t s ds t           u u u u we obtain 4 ; 4 = ( | |) ( ) . t n n n tt tt t t s t s ds t            u u u (63) subtracting (62) from (63) yields 4 4 ; 3 2 4 4 1 = (| | ) ( ) (| | ) ( ) . 6 t t n n n n tt tt t t s t t s ds s t t s ds t t t                    u u u u hence,   2 2 1 14 4 2 ; 3 42 2 2 2 4 4( ) 2 2 ( ) ( ) || || =|| || ( ) , t i n n n tt tt l l t l l l c t t s ds c t t t                      u u r u u and therefore 1 14 4 2 2 22 2 2 4 4( ) =1 =12 2 ( ) ( ) || || . n n i l i i l l l l t c t t ct t t t                  u u r similarly, we have 2 2 22 1 1 13 3 3 3 42 2 2 3 3 30 0 22 2 2( )( ) ( ) ( ) = ( ) , t t t tt ll l l l t t dt c t dt c t t t t                       u u u u and 2 22 1 13 3 3 2 3 42 2 3 3 30 0 2 2 2( ) ( ) ( ) 1 ( ) ( ) . 2 t t l l l l t t t dt c t dt c t t t t t                       u u u finally, using the approximation property (20) and combining all the bounds, we arrive at 1 2 2 ( ) =0 || || ( ), n i k l i t c h t       r which completes the proof of the desired estimate. □ remarks. it is worthwhile to mention that the time discretization method is fourth-order accurate when = 1/ 12. to preserve the temporal accuracy of the finite element scheme one has to modify (30) carefully to obtain an appropriate initial value 1 u . the analysis presented in [25] can be used to derive optimal a priori error estimates in this case. 7. conclusions we proposed and analyzed a family of fully discrete mixed finite element schemes for solving the acoustic wave equation. we derived stability conditions for conditionally implicit stable schemes covering the explicit case treated by jenkins, rivière and wheeler [10]. the error estimates established provided optimal convergence rates for the use of mixed finite elements methods in solving the acoustic wave equation. references 1. baker, g.a. error estimates for finite element methods for second order hyperbolic equations. siam j. numer. anal., 1976, 13, 564-576. 2. bao, h., bielak, j., ghattas, o., kallivokas, l.f., o'hallaron, d.r., shewchuk, j.r. and xu, j. large-scale 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m.f. a priori estimates for mixed finite element approximations of second-order hyperbolic equations with absorbing boundary conditions. siam j. numer. anal., 1996, 33, 492-504. 9. geveci, t. on the application of mixed finite methods to the wave equation. rairo. modél. math. anal. numér.,1988, 22, 243–250. 10. jenkins, e.w., rivière, b. and wheeler, m.f. a priori error estimates for mixed finite element approximations of the acoustic wave equation. siam j. numer. anal., 2002, 40, 1698–1715. 11. pani, a.k. and yuan, j.y. mixed finite element methods for a strongly damped wave equation. numer. methods partial differential equations, 2001, 17(2), 105-119. 12. pani, a.k., sinha, r.k. and otta, a.k. an 1h -galerkin mixed method for second order hyperbolic equations. int. j. numer. anal. model., 2004, 1(2), 111-130. 13. vdovina, t. and minkoff, s.e. an a priori error analysis of operator upscaling for the acoustic wave equation. inter. j. numer. anal. model., 2008, 5, 543-569. 14. grote, m.j. and schötzau, d. optimal error estimates for the fully discrete interior penalty dg method for the wave equation. j. sci. comput., 2009, 40, 257-272. 15. johnson, c. discontinuous galerkin finite element methods for second order hyperbolic problems. comput. methods appl. mech. engrg., 1993, 107, 117–129. 16. rivière b. and wheeler, m.f. discontinuous finite element methods for acoustic and elastic wave problems. part i: semidiscrete error estimates. ticam report 01–02, university of texas, austin, tx, 2001. 17. rivière, b. and wheeler, m.f. discontinuous finite element methods for acoustic and elastic wave problems. in icm2002-beijing satellite conference on scientific computing, contemporary mathematics, ams, providence, 2003, 329, 271-282. 18. glowinski, r., kinton, w. and wheeler, m.f. a mixed finite element formulation for boundary controllability of the wave equation. int. j. num. meth. engng., 1989, 27, 623-635. 19. knops, r.j. and payne, l.e. uniqueness theorems in linear elasticity. springer tracts nat. philos, 19, springerverlag, berlin, 1971. 20. jenkins, e.w. numerical solution of the acoustic wave equation using raviart-thomas elements. j. comput. appl. math., 2007, 206, 420–431. 21. raviart, r.a. and thomas, j.m. mathematical aspects of the finite element method. lecture notes in mathematics, springer, berlin, 1997, 106, 292-315. 22. nedelec, j.c. mixed finite elements in n.numer. math., 1980, 35, 315–341. 23. brezzi, f., douglas, jr. j. and marini, l.d. two families of mixed elements for second order elliptic problems. numer. math., 1985, 88, 217–235. 24. brezzi, f., douglas, j., fortin, jr. m. and marini, l.d. efficient rectangular mixed finite elements in two and three space variables. rairo modèl. math. anal. numér., 1987, 21, 581-604. 25. karaa, s. finite element  -schemes for the acoustic wave equation. adv. appl. math. mech., 2011, 3, 181-203. 26. karaa, s. stability and convergence of fully discrete finite element methods for the acoustic wave equation. j. appl. math. comput., 2012, 40, 659-682. received 2 october 2014 accepted 26 march 2015 squ journal for science, 2014, 19(2), 8-16 © 2014 sultan qaboos university 8 the influence of diets containing phenols and condensed tannins on protein picture, clinical profile and rumen characteristics in omani sheep osman mahgoub a*, isam t.kadima, hamza a. babikerb and mohammed n. al-kindib a department of animal and veterinary sciences, college of agricultural and marine sciences, b department of biochemistry, college of medicine & health sciences, sultan qaboos university, p.o. box: 34, pc 123, al-khod, muscat, sultanate of oman. *email: osmahgob@squ.edu.om. abstract: a study was carried out to investigate the effects of feeding low quality non-conventional feeds (ncf) containing phenols and condensed tannins on health and performance characteristics in omani sheep. twelve omani sheep were fed one of two base roughages, urea-treated palm frond (utpf) or rhodesgrass hay, (rgh) plus a commercial concentrate for 63 days. haematological, serum biochemical and urine an alyses were used to assess sheep health. serum protein fractions were measured using electrophoresis. urea-treated palm frond contained higher levels of polyphenols and condensed tannins and fiber than rhodesgrass hay or concentrate feed. animals fed utpf had lower feed intake (p<0.05) and lower body gain (p<0.001) than those fed rgh. rumen liquor of utpf-fed animals had higher ph, ammonia-nitrogen and butyric fatty acid but lower acetic fatty acid (p<0.05). animals fed utpf had higher neutrophil (p<0.05) but lower lymphocyte (p<0.05) and monocyte (p<0.001) counts by the end of the trial than those fed rgh. there were no effects of diet on serum albumin or globulin fraction levels or albumin:globulin ratio. there were no major effects on urine analysis but there was a trend by control animals to have higher protein and specific gravity than treated ones. this study indicated that feeding low quality non-conventional feeds containing polyphenols or tannins would reduce body gain and may produce some effects on clinical parameters. although tannins are known to influence protein digestion and absorption in ruminants, it did not significantly affect the serum protein picture in sheep. keywords: phenols; tannins; hematology; protein; sheep. تأثير العلف الوحتوي على الفيٌوالث والتاًيي الوكثف على صورة البروتيي وصحت الحيواى وخصائص الكرش فً الضأى العواًً ًاصر الكٌديبي حوزة على بابكر وهحود ، عصام توفيق كاظن ، هحجوب واى ثع غٞش حقيٞذٝت راث ّ٘عٞت ٍخذّٞت ححخ٘ٛ عيٚ ٍشمباث اىفْٞ٘ه ٗاىخاِّٞ اىَشمض عيٚ طحت أعالفحٌ إجشاء حجشبت ىذساعت حأثٞش اىخغزٝت عيٚ هلخص: جشٝذ اىْخٞو اىَعاىج بَحي٘ه اىٞ٘سٝا أٗ دسٝظ أٛ ّ٘عِٞ ٍِ اىعيف اىَاىئ أحذحَج حغزٝت اثْٜ عشش ٍِ اىؼأُ اىعَاّٜ عيٚ . ٗأدائٔ اىؼأُ اىعَاّٜ ٍٝ٘اً. حٌ االعخعاّت بْخائج فح٘ص اىذً ٗحشمٞبٔ اىبٞ٘ مَٞٞائٜ ىخقٌٞٞ اىحاىت اىظحٞت 36ٛ ىَذة باإلػافت إىٚ غزاء ٍشمض حجاس ، حشٞشت اىشٗدط األىٞاف عِ حشٞشت اىشٗدط أٗ اىعيف اىَشمض. ٗاحخ٘ٙ جشٝذ اىْخٞو اىَعاىج عيٚ ٍغخ٘ٝاث أعيٚ ٍِ ٍشمباث اىفْٞ٘ه ٗاىخاِّٞ اىَشمض ٗقذ ىيحٞ٘اُ. فٜ اىحٞ٘اّاث اىخٜ حغزث عيٚ جشٝذ اىْخٞو أقو عِ حيل اىخٜ حغزث عيٚ حشٞشت اىشٗدط. ماُ األط ة اى٘صُ اىحٜ ٍٗعذه صٝادماُ ٍعذه حْاٗه اىغزاء ُ اىٖٞذسٗجْٜٞ فٜ عائو اىنشػ فٜ اىحٞ٘اّاث اىخٜ حغزث عيٚ جشٝذ اىْخٞو ٍٗحخ٘ٛ أٍّ٘ٞا اىْٞخشٗجِٞ ٗحَغ اىبٞ٘حٞشك اىذْٕٜ أعيٚ بَْٞا ما اىحٞ٘اّاث اىخٜ حغزث عيٚ حشٞؼ اىشٗدط. أحخ٘ٙ دً اىحٞ٘اّاث اىخٜ حَج حغزٝخٖا عيٚ جشٝذ اىْخٞو خ٘آ فٜ ٍغحَغ األعٞخٞل اىذْٕٜ أقو عِ ٜ حغزث عيٚ اىَعاىج عيٚ عذد أمبش ٍِ خالٝا اىعذالث فٜ اىذً ٗعذد أقو ٍِ اىخالٝا اىيَفاٗٝت ٗاألحادٝت عْذ ّٖاٝت اىخجشبت ٍقاسّت باىحٞ٘اّاث اىخ ٗاػحت أثش ىيخغزٝت عيٚ ٍغخ٘ٝاث اىضاله ٗاىغي٘بٞ٘ىِٞ بأّ٘اعٔ اىَخخيفت ٗال ّغبت اىضاله ىيغي٘بٞ٘ىِٞ. مَا ىٌ حالحظ آثاس حشٞشت اىشٗدط. ىٌ ٝالحظ ْ٘عٞت أعيٚ فٜ اىنثافت اىٗاىبشٗحِٞ ىيخغزٝت عيٚ ححيٞو اىب٘ه ٗىنِ ماُ ْٕاك إسٕاص بأُ اىحٞ٘اّاث اىخٜ غزٝج عيٚ حشٞؼ اىشٗدط ماُ ٍغخ٘ٙ دٛ إىٚ اىب٘ه. بْٞج اىخجشبت اىحاىٞت أُ حغزٝت اىؼأُ اىعَاّٜ عيٚ أعالف غٞش حقيٞذٝت ححخ٘ٛ عيٚ ٍعذالث عاىٞت ٍِ ٍشمباث اىفْٞ٘ه ٗاىخاِّٞ حؤ ٕؼٌ ٗاىبشٗحِٞاّخفاع فٜ ٍعذه ٗصُ اىحٞ٘اُ ٗسبَا ٝنُ٘ ىٖا حأثٞش عيبٜ عيٚ طحت اىحٞ٘اُ. باىشغٌ ٍِ أُ اىخاِّٞ ىٔ حأثٞش ٍعشٗف عيٚ عيٚ ط٘سة اىبشٗحِٞ فٜ اىذً.ٗاػح ىٌ ٝالحظ ىٔ حأثٞش ٗفٜ اىحٞ٘اّاث اىَجخشة ٗاٍخظاطٔ .ٍشمباث اىفْٞ٘ه، اىخاِّٞ، فحض اىذً، اىبشٗحِٞ، اىؼأُهفتاح الكلواث: mailto:osmahgob@squ.edu.om influence of diets containing phenols and condensed tannins 9 1. introduction nimals raised on natural range grazing in the dry tropics are customarily fed low quality non-conventional feeds such as agricultural by-products. these feeds are usually high in fibre and low in protein, minerals and vitamins. they may also contain secondary plant compounds such as polyphenols and condensed tannins which may have anti nutritional effects [1]. tannins which protect plants from degradation in the rumen are reported to significantly affect protein digestion and utilization. they form combinations with proteins in the rumen rendering them unavailable for digestion and consequently increasing their output in faeces [2,3]. in non-ruminants they interfere with nutrient digestion and promote excretion of endogenous nitrogen through the formation of tannin-enzyme complexes [4]. there are some reports that they might also cause physical damage to the digestive system [5] and other vital organs such as the kidney and liver [3]. however, there are no reports on the effects of these compounds on the blood protein picture. especially in growing animals, protein and amino acid metabolism which accounts for 20-30% of whole body protein turnover and energy expenditure, is a function of the gastrointestinal tract tissues which amounts to only 3-6% of body weight [6]. this is mainly because of their relatively high fractional rates of protein synthesis and oxygen consumption which is several fold higher than that of the peripheral tissues such as muscles [6]. maintaining an adequate feed supply to the intestine orally is essential to maintain the intestine’s major functions of digesting and absorbing nutrients and serving as a biological barrier against pathogens, toxins and antigenic molecules [6]. therefore, the oral route is extremely important in this regard especially in young animals. for instance, in non-weaned pigs the input of amino acids from the luminal route is far greater (67-90%) than the arterial circulation (11-21%), particularly for glutamate and glutamine. consequently, it might be hypothesized that agents which interfere with protein digestion and utilization, such as polyphenols and tannins, can influence the general protein picture including that of the serum. electrophoresis is a useful technique for studying serum protein and it can provide useful information for determining the cause of increased, decreased or disproportion serum protein , which is usually related to an increase in immunoglobulin, except in cases of dehydration [7]. feeding ncf to animals may not only reduce body weight growth rate but may also affect their health status and ability to withstand diseases. macro (energy and protein) and micro (vitamin and mineral) malnutrition negatively affects the immune system, rendering animals more prone to diseases [8]. feeding animals for extended periods on certain range land plants containing high levels of anti-nutritional compounds has been reported to produce detrimental effects on animal health [9,10]. studies on feeding feeds containing anti-nutritional factors mostly report effects on feed intake, body weight growth, digestibility of feeds, and rumen chemistry and biology. this study aimed to investigate the effects of feeding these feeds on the protein status, clinical profiles and rumen chemistry in sheep. 2. materials and methods twelve 1-year old male omani native sheep (body weight 31.8 ± 1.2 kg) were used in a 63-d feeding trial with a completely randomized experimental design including two types of roughages; rhodesgrass hay and urea-treated palm frond. the animals were also fed a commercial concentrate beside the roughage. animals were daily fed 300 g of the concentrate for the first month then 400 g thereafter plus ad libitum roughage. the utpf was prepared by adding a 4% commercial urea solution to the chopped palm fronds and ensiling for 60 days. water and mineral blocks were offered ad libitum. the blocks (frank wright ltd., uk) contained 400 mg/kg cupric sulphite, 200 mg/kg manganous oxide, 120 mg/kg zinc oxide, 124 mg/kg bmp-cobalt carbonate, 190 mg/kg calcium iodate, 10 mg/kg bmp-sodium selenite. they also contained 36% sodium, 1.3% calcium, 0.23% phosphorus, 0.30% magnesium and 40,000 iu/kg vitamin d3. daily feed intakes were determined and animals were weighed bi-weekly. the proximate chemical composition of the various components of feeds was determined according to the standard methods of aoac [11]. dry matter (dm) was determined by drying in an oven for 24 hours at 80 ºc (method 934.01). crude protein (cp) was determined using a foss tecator kjeltec 2300 nitrogen/protein analyser (method 976.05). fat (ee) was determined by soxhlet ether extraction of the dry sample, using petroleum ether (method 920.39). ash content was determined by ashing samples in a muffle furnace at 500 ºc for 24 hr (method 942.05). acid detergent fibre (adf) was determined using cetyl trimethyl ammonium bromide (ctab) and 1n h2so4 as described by roberston and van soest [12]. neutral detergent fibre (ndf) was determined using sodium sulphite and sodium lauryl sulphate as described by van soest et al. [13]. alpha amylase was not used to determine ndf. adf was expressed with ash whereas ndf was expressed without ash. calcium and phosphorus were measured with an atomic absorption spectrophotometer (philips model pu 9100, single beam). gross energy (ge) was measured using a bomb calorimeter. levels of phenols and condensed tannins were analysed following the methods of makkar [14]. condensed tannins were determined by extracting 200 mg samples overnight in 10 ml aqueous acetone (70:30 acetone:water) solution at 4 c. after centrifugation (3000× g at 4 c for 10 min), the supernatants were analysed for condensed tannins using leucocyanidin standard. total extractable phenols are expressed as gram equivalent tannic acid per kilogram dry matter. extractable condensed tannins are expressed as gram equivalent leucocyanidins per kilogram dry matter. a osman mahgoub et al 10 the use of experimental animals and methodology for the trial was approved by the college of agricultural and marine science research committee under project number: sr/agr/pint/01/01. rumen liquor was collected at slaughter, strained and ph was recorded. liquor was centrifuged and the clear top liquid used for the estimation of ammonia-n by reading against optical density at 540 nm in a uv-visible spectrophotometer (thermo spectronic corporation u.k.; type helios beta model). ten ml of blood samples were collected from each animal in plain glass vacutainers or with edta by jugular venipuncture on the last day of experiment. they were analyzed for: red blood cell count (rbc), packed cell volume (pcv), haemoglobin (hgb), mean corpuscular volume (mcv), mean cell haemoglobin (mch) and mean cell haemoglobin concentration (mchc) and differential white blood cell count (wbc) of neutrophils, lymphocytes, basophils, eosinophils and monocytes using a cell-dyn 3700 blood analyzer (cell-dyn 3700; abbott laboratories diagnostic division, abbott park, il 60064, usa). a giemsa stained blood smear was prepared for each sample. serum samples were analyzed for glucose, blood urea nitrogen (bun), albumin, creatinine, total protein, alanine aminotransferase (alt), gamma glutamyl transpeptidase (ggt), magnesium (mg), calcium (ca), phosphorus (p) and iron (fe) by spectrophotometric analysis using a cx7/cx7 serum chemistry analyser (synchron, beckman). total protein quantification was carried out using the bradford protein assay method which is a reliable procedure for determining the concentration of solubilized protein. it involves the addition of an acidic dye to a protein solution, and subsequent measurement at 595 nm with a spectrophotometer or microplate reader. a nanodrop® nd1000 spectrophotometer and bio-rad protein assay reagent were used to quantitate the total protein. serum protein electrophoresis (spe) was used to determine levels of two major protein groups, albumin and globulin in the blood serum. using protein electrophoresis, these two groups can be separated into five smaller groups (fractions): albumin, alpha-1 globulin, alpha-2 globulin, and gamma globulin. the paragon electrophoresis system (beckman, usa) was used to separate the two blood protein groups and the mobility pattern was visually interpreted and quantitated by densitometry at 600 nm, on a beckman appraise densitometer, in which the relative percent of each protein fraction is calculated automatically. urine samples were collected at the end of the experiment using a syringe to collect urine directly from the urinary bladder. they were analysed for blood, urobilinogen, bilirubin, protein, nitrite, ketones, ascorbic acid, glucose, ph, specific gravity and leucocytes using uryxxon® 200 equipment and combi 11 urine strips. data were subjected to the analysis of variance [15] to study the effects of diet using the general linear models procedure [16]. significant differences between treatment means were assessed using the least significant difference procedure at p<0.05 level. 3. results there were significant differences in chemical composition between the utpf and rhodesgrass hay. utpf contained higher levels of fibre, ash, ca and phosphorus but lower hemicellulose (table 1). it also contained four times the total extractable phenols and much higher condensed tannins compared to the conventional feeds (table 1). animals fed the utpf consumed similar daily amounts of concentrates (table 2) but less roughage than those fed rgh. the utpf-fed animals gained less body weight over the experimental period (3 vs. 70 g/d) than those fed the rgh. the utpf-fed animals maintained their weight throughout the trial. haematological values of experimental animals were within normal values reported for sheep. however, animals fed the utpf had higher neutrophil (p<0.01) but lower lymphocyte (p<0.01) and monocyte (p<0.05) counts at the end of the trial compared to the rgh-fed animals (table 3). there were no dietary effects on the serum biochemistry parameters measured (table 3). the serum protein profile is presented in figure 1 and table 4. serum protein electrophoretograms exhibited a normal pattern. the serum albumin in treated and control sheep averaged 7 g/dl, while the total globulin was 12.7 g/dl (table 4). the albumin proportion was higher (54%), resulting in an albumin/globulin ratio of 1.3. within the globulins, the highest proportion was made up of the gamma globulins (3 g/dl, 24%) followed by beta globulins (9%) and alfa 2 globulins (7.5%), whereas the smallest proportion was made by alpha 1 globulins (4.%). however, there were no significant treatment effects on the various protein fractions. however, there was a consistent trend of treated animals having higher albumin and gamma globulins (table 4). visual examination had shown that urine from ncf-fed animals was turbid and brownish in colour. urine analysis indicated a trend of elevated levels of protein, leukocytes and specific gravity in animals fed utpf compared to those fed rhodesgrass hay (table 5). influence of diets containing phenols and condensed tannins 11 fraction rel% g/dl fraction rel% g/dl fraction rel% g/dl albumin 53.8 4.52 albumin 51.7 9.77 albumin 58.9 7.07 alpha 1 3.3 0.28 alpha 1 3.1 0.59 alpha 1 3.2 0.38 alpha 2 7.8 0.66 alpha 2 7.2 1.36 alpha 2 7.5 0.90 beta 9.6 0.81 beta 9.9 1.87 beta 7.8 0.94 gama 25.4 2.13 gama 28.2 5.33 gama 22.6 2.71 total g/dl 8.50 a/g: 1.16 total g/dl 18.90 a/g: 1.07 total g/dl 12.00 a/g: 1.43 fraction rel% g/dl fraction rel% g/dl fraction rel% g/dl albumin 53.7 7.79 albumin 58.7 7.22 albumin 55.4 5.93 alpha 1 3.1 0.45 alpha 1 5.5 0.68 alpha 1 4.7 0.50 alpha 2 8.0 1.16 alpha 2 6.1 0.75 alpha 2 11.8 1.26 beta 9.3 1.35 beta 7.8 0.96 beta 7.2 0.77 gama 25.9 3.76 gama 21.9 2.69 gama 20.9 2.24 total g/dl 14.50 a/g: 1.16 total g/dl 12.30 a/g: 1.42 total g/dl 10.72 a/g: 1.24 figure 1. serum protein electrophoretograms of omani sheep fed rhodesgrass hay (control) and urea-treated palm frond (treated) plus general ruminant concentrate for nine weeks (top row, treated animals; bottom row, control animals). table 1. chemical composition of ingredients of experimental feeds. feed ingredient experimental diets commercial concentrate urea-treated palm frond rhodesgrass hay dm (g/kg) 862 892 916 crude protein (g/kg dm) 180 85 120 ether extract (g/kg dm) 21.5 11 15 neutral detergent fiber (g/kg dm) 182 740 614 acid detergent fiber (g/kg dm) 56 580 370 hemicellulose (g/kg dm) 126 160 243 ash (g/kg dm) 73 120 95 ca ++ (g/kg dm) 12 7.4 5 po4(g/kg dm) 8 1.1 0.20 ge (kj/g) 183 192 173 total extractable phenols a 16.6 112.6 32.1 extractable condensed tannins b 0 12.8 0 a expressed as gram equivalent tannic acid/kg dm. b expressed as gram equivalent leucocyanidins/kg dm. osman mahgoub et al 12 animals on utpf had higher rumen ammonia-n (p<0.05) levels and their rumen ph was higher (p<0.01) than those fed rhodesgrass hay (table 6). they also had significantly lower acetic acid but higher butyric fatty acids than the controls (table 6). table 2. feed intake and body weight gain of omani sheep fed rhodesgrass hay (control) and those fed urea-treated palm frond (treated) plus general ruminant concentrate for nine weeks. parameter treatment pse effect of diet treated control number of animals 6 6 days of experiment 63 63 daily roughage intake (g) 554 696 38 * daily concentrate intake (g) 365 365 0 ns daily feed intake (g) 919 1061 38 * starting body weight (kg) 31.60 31.88 0.519 ns final body weight (kg) 31.70 35.92 0.837 ** average daily gain (g) 3 69 7 *** pse, pooled standard error of means ns, p>0.05;*, p<0.05; **, p<0.01; ***, p<0.001. table 3. haematological and serum biochemistry values in omani sheep fed diets containing phenols and tannins. parameters experimental groups pse effect of treated control diet white blood cells (x10 3 /ml) 9.4 9.3 0.48 ns neutrophils (% of wbc) 61.1 46.9 1.82 *** lymphocytes (% of wbc) 30.0 39.9 2.24 * monocytes (% of wbc) 3.3 6.5 0.43 *** eosinophils (% of wbc) 1.7 1.8 0.44 ns basophils (% of wbc) 4.0 4.9 1.73 ns neutrophils (x10 3 /m) 5.8 4.4 0.42 * lymphocytes (x10 3 /m) 2.8 3.9 0.24 * monocytes (x10 3 /m) 0.3 0.6 0.04 *** eosinophils (x10 3 /m) 0.2 0.2 0.04 ns basophils (x10 3 /m) 0.3 0.5 0.14 ns red blood cells (x10 6 /ml) 13.4 13.6 0.40 ns hemoglobin (g/ll) 10.3 10.1 0.19 ns haematocrit (%) 43.8 44.7 1.61 ns mean corpuscular vol. (fl) 32.72 32.9 1.26 ns mean cell hemoglobin (pg) 7.7 7.4 0.17 ns mean cell hemoglobin (pg) 23.9 22.5 0.89 ns ck 75.7 89.8 24.8 ns ggt (µ/l) 62.9 90.5 5.57 ns got (µ/l)) 95.8 120.4 11.20 ns pse, pooled standard error of means ns, p>0.05;*, p<0.05; **, p<0.01; ***, p<0.001. 4. discussion feed composition analyses indicated that animals fed the urea-treated palm fronds were subjected to a lower nutritional regime compared to those fed the rhodesgrass hay as the utpf had much higher fibre contents than the rgh. utpf has been reported to have lower digestibility coefficients and sheep fed on it produced larger volumes of faeces and had lower viscosity of gut contents, a characteristic of highly fibrous diets [17]. moreover, the utpf also contained higher levels of phenols and condensed tannins that are known to have anti-nutritional effects [18, 2]. this would have further reduced its nutritive value, resulting in animals consuming less feed and gaining less body weight. although the nutritional insult was not severe enough to cause experimental animals fed the utpf to lose body weight, the diet characteristics indicated that animals that consumed them had been subjected to malnutrition. malnutrition was defined by [8] as an “inadequate or unbalanced diet, or a failure to absorb or assimilate dietary elements”. if severe enough, malnutrition may produce detrimental effects on the animal body. these may include macronutrient influence of diets containing phenols and condensed tannins 13 deficiencies that may lead to body cell mass depletion and micronutrient deficiencies that may impair body immune function [8]. animals fed the utpf would have ingested considerable amounts of condensed tannins as they had consumed approximately 550 g/d of utpf. similar levels of condensed tannins in sheep have been shown to reduce protein degradation in the rumen and increase protein flow to the intestine [19, 20]. a digestibility trial using utpf with sheep [17], indicated classical features of tannin-containing feeds in ruminants. a higher level of nitrogen in the faeces (less nitrogen retention) is a characteristic of dietary tannins, which bind to proteins in the rumen and consequently reduce digestion and absorption in the gut [4,5,2]. tannins also form complexes with carbohydrates and minerals and inhibit microbial and digestive processes in ruminants [2]. therefore, the presence of condensed tannins in the utpf in the current study could have resulted in depressed rumen digestibility [18]. the utpf-fed animals had higher rumen ph values than those fed rhodesgrass hay. ammonia-n and ph are indicators of rumen fermentation efficiency. this suggests that these animals had lower fermentation levels, which produced less volatile fatty acids, especially acetic fatty acid, as confirmed by chemical analyses of rumen liquor. contrary to the findings of mahgoub et al. [17], ammonia nitrogen levels in the current study were higher in utpf-fed animals than in rhodesgrass-fed animals. this could mainly be attributed to the fact that palm fronds in the current experiment had been ensiled in a solution of higher urea levels (4%) which must have increased non-protein nitrogen levels in the rumen. this was reflected in diet chemical composition. higher nitrogen levels in the faeces are usually accompanied by lower urine nitrogen level, a characteristic of animals fed condensed tannins [h.p.s. makkar, personal communication, 2007 and 17] most probably due to the higher proportion of nitrogen excreted through the faeces. generally the serum protein fractioning was of a normal picture, as indicated in the electrophoretograms and individual animal values. however, there was a pattern of lower albumin and higher globulin levels. albumin, produced by the liver, is major protein within the blood, and its levels are reduced by malnutrition and chronic liver disease such as cirrhosis. it appears that the utpf feeding did not produce enough insult to produce severe malnutrition or affect the liver of the experimental animals. globulins play an important role in immunity (e.g., iga, igg, ige). the trend of slightly higher globulins in treated animals may indicate some effects of tannins on the immune system, most probably indirectly through the leptin axis. this lack of effect on the protein picture suggests that, although tannins are known to interfere with protein digestion and utilization [2,17], apparently they did not affect the serum protein pattern in the current study. this could be due to the lower dosages and levels of tannins and polyphenols used in the present study. table 4. serum protein values in omani sheep fed diets of urea-treated palm frond or rhodesgrass hay plus a concentrate. 1 trt; t = treated (fed utpf); c = control (fed rhodesgrass hay) pse, pooled standard error of means ns, p>0.05;*, p<0.05; **, p<0.01; ***, p<0.001. although they did not gain much weight, utpf-fed animals did not show explicit signs of disease such as diarrhoea, constipation or anorexia. this could be mainly attributed to genetic disease resistance in such animals of the arid tropics, which have been naturally selected over generations for survival and ability to utilize low quality feeds. however, negative health effects may be produced and go unnoticed in animals fed under similar systems. the lower id trt1 albumin (%) albumin (g/dl) alpha 1 globulins (%) alpha 1 globulins (g/dl) alpha 2 globulins (%) alpha 2 globulins (g/dl) beta globulins (%) beta globulins (g/dl) gamma globulins (%) gamma globulins (g/dl) total globulins (g/dl)l albumin globulin ratio 2380 t 55.00 4.95 5.40 0.49 9.10 0.82 5.30 0.48 25.10 2.26 9.00 1.22 2400 t 51.70 9.77 3.10 0.59 7.20 1.36 9.90 1.87 28.20 5.33 18.90 1.07 2442 t 57.50 8.40 2.70 0.39 7.70 1.12 9.10 1.33 23.00 3.36 14.60 1.35 2467 t 53.80 4.52 3.30 0.28 7.80 0.66 9.60 0.81 25.40 2.13 8.40 1.16 2470 t 58.90 7.07 3.20 0.38 7.50 0.90 7.80 0.94 22.60 2.71 12.00 1.43 2494 t 58.00 7.83 4.50 0.61 3.80 0.51 7.70 1.04 26.10 3.52 13.50 1.38 mean 55.82 7.09 3.70 0.46 7.18 0.90 8.23 1.08 25.07 3.22 12.73 1.27 2401 c 55.30 6.91 6.20 0.78 5.50 0.69 8.00 1.00 24.90 3.11 12.50 1.24 2420 c 55.40 5.93 4.70 0.50 11.80 1.26 7.20 0.77 20.90 2.24 10.70 1.24 2466 c 53.70 7.79 3.10 0.45 8.00 1.16 9.30 1.35 25.90 3.76 14.50 1.16 2471 c 49.90 8.03 7.00 1.13 10.00 1.61 12.20 1.96 20.90 3.36 16.10 1.00 2486 c 46.00 4.69 3.10 0.32 8.50 0.87 18.30 1.87 24.20 2.47 10.20 0.85 2495 c 58.70 7.22 5.50 0.68 6.10 0.75 7.80 0.96 21.90 2.69 12.30 1.42 mean 53.17 6.76 4.93 0.64 8.32 1.06 10.47 1.32 23.12 2.94 12.72 1.15 pse 1.53 0.69 0.55 0.09 0.85 0.14 1.32 0.20 0.86 0.38 1.29 0.07 significance ns ns ns ns ns ns ns ns ns ns ns ns osman mahgoub et al 14 lymphocyte and monocyte and lower neutrophil counts in animals fed utpf could be an important indication of the health status of experimental animals. monocytes are essential for the immune system as they are precursors of macrophages and lymphocytes essential for humoral and cell-mediated immunity responses. similar findings had been reported by mahgoub et al. [17]. animals fed the utpf had lower body weights compared to those fed rgh [21]. although both control and treated animal groups started at similar weights (32.5 ± 1.13 kg), the group of sheep fed the rhodesgrass hay plus the commercial concentrate gained about 4 kg over the experimental period, whereas the utpf-fed group maintained their body weight. this indicates that the latter group had a lower body condition score and consequently lower body fat reserves. body composition may influence the immune system, with its effect most probably mediated by leptin [8]. leptin is a 16 da protein produced by adipocytes and released into systemic circulation which acts as a master hormone controlling energy acquisition and utilization processes as well as the immune/inflammatory response [22]. reduced level of leptin, a signal of energy reserve depletion (adipose tissue), appears to trigger the body to shut down non-essential body functions including those involved with immune and inflammatory responses [22]. leptin influences lymphocyte proliferation and cytokine secretion [23]. this is in line with the low lymphocyte and monocyte counts in the current study. pathological examination also indicated that animals fed utpf had shown signs of chronic inflammation in the small intestine and nephritis, another sign of immune system compromise [3]. low leptin levels caused by less adipose tissue in undernourished individuals reduced th1 immune response resulting in increased susceptibility to infections [24]. the trend of higher levels of protein in the urine of control than in that of treated animals is in line with findings of mahgoub et al. [17] and makkar (personal communication , 2007), that animals fed higher levels of tannins tend to produce higher levels of nitrogen in the faeces and lower nitrogen levels in the urine. this is probably the cause of the trend of higher specific gravity of urine in these animals. table 5. urine analyses of sheep fed urea-treated palm fronds containing higher levels of phenols and condensed tannins and those fed rhodesgrass hay. diet 1 id no blood urobilinogen bilirubin protein n ketones asc glucose ph specific leucocytes ery/µl mg/dl mg/dl mg/dl gravity leu/µl a 2380 250 norm neg neg neg neg neg neg 5 1.000 neg a 2400 50 norm neg neg neg neg neg neg 5 1.000 neg a 2494 250 norm neg 100 neg neg neg neg 6 1.010 neg a 2470 250 norm neg neg neg neg neg neg 5 1.005 neg a 2442 50 norm neg neg neg neg neg neg 5 1.005 neg b 2486 250 norm neg 100 neg neg 1+ neg 8 1.005 25 b 2466 50 norm neg 30 pos neg neg nor 6 1.010 neg b 2495 250 norm neg 100 pos neg neg neg 7 1.015 75 b 2401 250 norm neg 30 neg neg neg neg 5 1.015 neg b 2420 250 norm 1+ 100 neg neg neg neg 5 1.025 25 b 2471 50 norm neg 100 neg neg neg neg 8 1.010 neg 1 a: utpf; b: rhodesgrass hay norm: normal; neg: negative table 6. rumen chemistry values in omani sheep fed rhodesgrass hay (control) and those fed urea-treated palm frond (treated) plus general ruminant concentrate for nine weeks. parameters experimental groups pse effect of diet treated control rumen characteristics: ph 6.35 5.89 0.088 ** ammonia nitrogen (mg/l) 138.0 92.7 10.51 * volatile fatty acids acetic 1043 1399 116.9 * propionic 279 222 44.6 ns isobutyric 92 75 7.1 ns butyric 231 145 42.7 * isovaleric 51 52 8.0 ns pse, pooled standard error of means ns, p>0.05;*, p<0.05; **, p<0.01; ***, p<0. influence of diets containing phenols and condensed tannins 15 5. conclusions in general the present study indicated that feeds containing anti-nutritional factors such as polyphenols and tannins, commonly fed to livestock around the world, may produce negative effects on livestock health, welfare and productivity. they appear to affect animal health in a combination of ways. animals fed these feeds might have lower nutrient availability due to low digestibility resulting in macro and micro malnutrition. malnutrition as a result of a combination of the above mentioned factors may result in lower body weight and consequently lower adipose tissue. this could result in a compromise of the body’s immunity system, making the animal prone to infections and other ailments. the findings of this study did not show that there are significant effects of feeding sheep on diets containing tannins on the serum protein picture. 6. acknowledgment mr. musab al-busaidi, mrs. kanthi annamalai and mr. khalid al-habsi of the department of animal and veterinary sciences at sultan qaboos university provided technical help. dr hichem ben salem of inrat, tunisia, provided phenols and condensed tannin analyses. references 1. kumar, r. anti-nutritional factors, the potential risks of toxicity and methods to alleviate them. fao 102, animal production and health paper: 2005, pp.145-160. 2. robins, c. and brooker, j.d. the effects of acacia aneura feeding on abomasal and intestinal structure and function in sheep. anim. feed sci. & tech., 2005, 121, 205-215. 3. longstaff, m. and mcnab, j.m. the inhibitory effects of hull polysaccharides and tannins of field beans (vicia faba l.) on the digestion of amino acids, starch and lipids and on digestive enzyme activities in young chicks. brit. j. nutr., 1991, 65, 199-216. 4. mahgoub, o., kadim, i.t., tageldin, m.h., al-marzooqi, w.s., khalaf, s.q., al-amri, i. and ambu, a.a. pathological features in sheep fed rations containing phenols and condensed tannins. j. anim. & vet. adv., 2008b,7, 1105-1109. 5. walton, j.p., waghorn, g.c., plaizier, j.c., birtles, m. and mcbridge, b.w. influence of condensed tannins on gut morphology in sheep fed lotus pedunculatus. can. j. anim. sci., 2001, 81, 605-607. 6. burrin, d.g. gastrointestinal protein and amino acid metabolism in growing animals. in biology of the intestine in growing animals. eds, zabielski, r., gregory, p.c. and weström, b. elsevier, amsterdam. 2002, pp. 695-725. 7. meyer, d.j. and harvey, j.w. veterinary laboratory medicine. interpretation and diagnosis. 3 rd edition. saunders, usa, 2004. dekker, new york, basel, 1981. pp. 123-158. 8. hughes, s. and kelly, p. interactions of malnutrition and immune impairment, with specific reference to immunity against parasites. parasit. & immun., 2006, 28, 577-588. 9. adedapo, a.a., adegbayibi, a.y. and emikpe, b.o. some clinico-pathological changes associated with the aqueous extract of the leaves of phyllanthus amarus in rats. phytotherapy res., 2005, 19, 971-976. 10. tabosa, i.m., souza, j.c., graca, d.l. barbosa-filho, j.m., almeida, r.n. and rie correa, f. neuronal vacuolation of the trigeminal nuclei in goats caused by ingestion of prosopis juliflora pods. vet.& hum. toxic., 2000, 42,155-158. 11. aoac 2000. official methods of analysis. (17 th edition), association of official analytical chemists. gaithersburg, maryland, 20877-2417. usa. 12. roberston, j.b. and van soest, p.j. the detergent system of analysis, in: james, w.p.t. and theander, o. (eds.). the analysis of dietary fibre in food. marcel dekker, new york, basel, 1981, pp. 123-158. 13. van soest, p.j., roberston, j.b. and lewis, b.a. methods for dietary fibre ndf and non-starch polysaccharides in relation to animal nutrition. j. dairy sci., 1991, 74, 3583-3597. 14. makkar, h.p.s. quantification of tannins in tree and shrub foliage. a laboratory manual. makkar h.p.s. (ed.), kluwer academic publishers., 2003, pp 102. 15. ott, r.l. analysis of variance in some standard experimental designs. in: introduction to statistical methods and data analysis. duxbury press, belmont, ca. 1993, pp 842-928. 16. sas institute inc. sas user's guide: statistics. version 5, sas institute inc., cary, nc. usa, 1991. 17. mahgoub, o., kadim, i.t., tageldin, m.h. , al-marzooqi, w.s. , khalaf, s.q. and ambu, a.a. clinical profiles of sheep fed non-conventional feeds containing phenols and condensed tannins. small rumin. res., 2008a, 78, 115-122. 18. perez-maldonado, r.a. and norton, b.w. the effects of condensed tannins from desmodium intortum and calliandra calothyrsus on protein and carbohydrate digestion in sheep and goats. brit. j. nutr., 1996, 76, 515 533. 19. waghorn, g.c., jones, w.t. and shelton, i.d. the nutritive value of lotus corniculatus l. containing low and medium concentrations of condensed tannins for sheep. proc.new zealand soc. animal production., 1987, 47, 7580. osman mahgoub et al 16 20. waghorn, g.c. effect of condensed tannin on protein digestion and nutritive value of fresh herbage. proc. aust. soc. animal production., 1990,18, 412-415. 21. mahgoub, o., kadim, i.t., al-busaidi, m., naseeb, h., al-saqri, m. and annamalai, k. effects of feeding ensiled date palm fronds and a by-product concentrate on performance and meat quality of omani sheep. anim. feed sci. & tech., 2007, 135, 210-221. 22. fantuzzi, g. nourishment for immune system. euro. j. immun., 2006, 36, 3101-3104. 23. mattioli, b., straface, e., quaranta, m.g., giordani and l. viora m. leptin promotes differentiation and survival of human dentritic cells and licenses them for th1 priming. j. immun., 2005, 174, 6820-6828. 24. matarese, g., moshos, s. and mantzoros, c.s. leptin in immunology. j. immun., 2005, 173, 3137-3142. received 2 october 2013 accepted 11 december 2014 squ journal for science, 2014, 19(2), 29-36 © 2014 sultan qaboos university 29 a simple surfactant-free solution phase synthesis of flower-like in2s3 hierarchitectures and their photocatalytic activities rengaraj selvaraj 1*, kezhen qi2, uiseok jeong3, kholood al nofli1, salma al-kindy1, mika sillanpää 4 , and younghun kim 3 . 1 department of chemistry, college of science, sultan qaboos university, muscat, alkhodh 123, sultanate of oman. 2 college of chemistry and life science, shenyang normal university, shenyang, 110034, china. 3 department of chemical engineering, kwangwoon university, seoul 139-701, korea. 4 laboratory of green chemistry, lut savo sustainable technologies, lappeenranta university of technology, sammonkatu 12, fi-50130 mikkeli, finland.*email: rengaraj@squ.edu.om. abstract: flower-like in2s3 hierarchical nanostructures were successfully prepared via a facile solution-phase route, using thiacetamide as both sulfur source and capping agent. our experimental results demonstrated that the morphology of these in2s3 nanostructures can be easily modified by changing the ratio of in(no3)3/thiacetamide. with the ratio increasing from 1:1.5 to 1:6, the in2s3 crystals exhibited flower-like morphology of varying size. xrd and hrtem of the flowers revealed the cubic structure of in2s3; morphological studies examined by sem and tem showed that the synthesized in2s3 nanostructure was a flower-like hierarchitecture assembled from nanoscale flakes. xps and edx analysis confirmed the stoichiometry of in2s3 nanoflowers. the optical properties were investigated by uv-vis drs, which indicated that the in2s3 nanoflower samples possess a band gap from 1.90 to 1.97 ev. furthermore, photocatalytic activity studies revealed that the prepared in2s3 nanoflowers exhibit an excellent photocatalytic performance, degrading rapidly the aqueous methylene blue dye solution under visible light irradiation. these results suggest that in2s3 nanoflowers will be a promising candidate for a photocatalyst working under the visible light range. keywords: in2s3 nanoflowers; solution-phase synthesis; capping agent; photocatalyst. انىردي انشكم وانًتعانً انهُذسة عبر يحهىل خال يٍ انسطىح انفاعهة (in2s3طرٌقة بسٍطة نتركٍب كبرٌث األَذٌىو ) وظائف انًركب انتحفٍزٌة انضىئٍة. ٌىَغىٌ كٍى و يٍكاسٍالَبا ،ة، سهًى انكُذٌةسهفراج ، كٍزٌ كً، وٌسىك جٍىَغ، خهىد انُىفهٍ رَجراج thioacetamideانٕسدي انشكم ٔانًرعانً انرشكٍة انُإَي يٍ خالل طثقح انًذهٕل ٔرنك تاسرعًال in2s3ذى تُجاح ذشكٍة كثشٌد األَذٌٕو يهخص: ًكٍ ذعذٌهّ تسٕٓنح يٍ خالل ذغٍٍش ٌكًصذس نهكثشٌد ٔعايم يٕقف نهرفاعم. ٔقذ أثثرد َرائجُا االخرثاسٌح أٌ انشكم انعاو نٓزِ انًشكثاخ انُإٍََح "xشكهٓا انٕسدي تأدجاو يخرهفح. ٔخالل أشعح " in2s3، اذخزخ تهٕساخ 5:1انى 5: 5.1ٌادج انُسثح يٍ يع ص in(no3)3 /thioacetamideَسثح انُإَي انذجى يشكة تشكم ٔسدي يرعانً انرشكٍة ٔيؤنف يٍ ششائخ َإٍََح. ٔقذ أثثرد انرذانٍم أٌضاً in2s3ٔانًجٓش االنكرشًَٔ أثثرد انُرائج أٌ انٕسدي انُإَي ذرًرع تشفشج in2s3. ٔقذ أشاسخ أتذاثُا انضٕئٍح انًشئٍح ٔانًا فٕق انثُفسجٍح أٌ انخصائص انثصشٌح ل in2s3انعالقاخ انٕصٍَح فً أثثرد تأَٓا يًراصج األداء تعذ أٌ ذى تسشعح in2s3 إٌ انخصائص انرذفٍضٌح انضٕئٍح ل نى إ. إضافح electron volt 1.97انى 1.90ششٌطٍح يٍ انٕسدي انُإَي ْٕ يششخ in2s3األصسق انًزاب فً انًاء ذذد أشعح ضٕئٍح يشئٍح. ْزِ انُرائج ذقرشح تأٌ ال methyleneال ذقٌٕض ٔذكسٍش يادج ٔاعذ نهرذفٍض انضٕئً ذذد أشعح يشئٍح. َإَ ٔسدي انشكم، ذشكٍة يذهٕنً، انعايم انًٕقف انرذفٍض انضٕئً. in2s3: يفتاح انكهًات 1. introduction he rational design and fabrication of nanomaterials with special morphologies of nanostructures have attracted a great deal of attention because the properties of a material depend not only on its phase, shape and size, but also on its organization [1,2]. in particular, controlled hierarchical semiconductor nanostructures have attracted much attention because of their potential in new applications in catalysis [3], solar cells [4], chemical sensors [5], and supercapacitors [6]. thus, controllable synthesis of hierarchical nanostructures is of great interest and urgently called t rengaraj selvaraj et al 30 for. at present, scientists have been devoting considerable efforts to three dimensional (3d) hierarchical architectures assembled by the low dimensional nanoscale building blocks, such as nanoplates, nanoparticles, nanorods, and so forth [7,8]. however, it is still important, from the perspective of both science and industry, to develop a simple method to fabricate 3d hierarchical nanostructures with desired structures and properties and to explore their potential applications. indium sulfide (in2s3), as an important semiconductor material, has stimulated great interest because of its wide applications in optical [9], photoconductive [10], optoelectronic [11] and catalytic fields [12]. these applications result from its unique physicochemical properties, which depend not only on its phase but also on its shape and organization. for instance, liu et al. [13] have reported that β-in2s3 nanotubes showed high photocatalytic performance on the decomposition of rhodamine b under solar irradiation. du et al. [14] have synthesized ultrathin β-in2s3 nanobelts via an improved hydrothermal route, and found that these showed a good photocatalytic performance on the degradation of methylene blue (mb). moreover, β-in2s3 hollow microspheres also exhibited an excellent photocatalytic performance in degrading mb under visible light irradiation [15]. these results suggest that in2s3 with various morphologies is a promising candidate for photocatalysis under visible light. so far, considerable effort has been devoted to fabricating various morphologies, including particles [16], flakes [17], wires [18], tubes [19], belts [20], spheres [21], sheets [22], dendrites [23] and so on. despite these advances having been made, the ability to synthesize 3d in2s3 hierarchical architectures with fine morphology control still remains a significant challenge. in this paper, we present a facile solution-phase synthesis of 3d flower-like β-in2s3 hierarchical nanostructures, which are composed of two-dimensional (2d) nanosheets. flower-like in2s3 hierarchitectures can be obtained only using thiacetamide as both a sulfur source and a capping agent. the effect of molar ratios of precursors on the morphologies of flower-like in2s3 hierarchitectures and their formation mechanism are also discussed. furthermore, optical and photocatalytic properties of the flower-like nanostuctures are also reported. 2. experimental section 2.1 material preparation the flower-like in2s3 nanocrystals were synthesized using analytical grade indium nitrate in(no3)3.5h2o (sigma-aldrich 99%) and thioacetamide (taa) (c2h5ns) (sigma-aldrich 99%). as a typical synthesis, 10 mmol of in(no3)3.5h2o and 15-60 mmol (1:1.5 to 1:6 molar ratio of in(no3)3 to c2h5ns) of taa were dissolved in 100 ml of deionized water and continuously stirred for 30 min to form a homogenous solution. the above mixture was then transferred to a round bottomed flask and refluxed at 105 o c for 30 min, which yielded an orange precipitate. the product was collected by centrifugation, washed with deionized water and ethanol several times, and dried at 70 o c for 24 h. the final product was calcined at 350 o c for 2h for further characterization. 2.2 material characterization the products were characterized by x-ray diffraction (xrd) using a bruker (d5005) x-ray diffractometer equipped with graphite monochromatized cuk radiation ( = 1.54056 å). morphology observations were performed on a hitachi s-4800 field-emission scanning electron microscope. the morphologies and microstructures of the prepared products were analyzed by the transmission electron microscope (tem) (jeol jem-3010). the chemical states of the samples were studied by x-ray photoelectron spectroscopy (xps). the x-ray source was alk radiation (1.4867 ev). the photo-emitted electrons which escaped from the sample were analyzed in a hemispherical energy analyzer at a pass energy of ep = 20 ev. all spectra were obtained with an energy step of 0.1 ev and a dwell time of 50 ms. the absorption spectrum of the samples in the diffused reflectance spectrum (drs) mode was recorded in the wavelength range of 200 and 1000 nm using a spectrophotometer (jasco-v670), with baso4 as a reference. all photoreaction experiments were carried out in a photocatalytic reactor system, which consisted of a cylindrical borosilicate glass reactor vessel with an effective volume of 500 ml, a cooling water jacket, and a 150 w sodium vapor lamp (osram vialox nav-ts super 150 w) positioned axially at the center as a visible light source. the reaction temperature was kept at 20 o c by cooling water. a special glass frit was fixed at the reactor as an air diffuser to disperse air uniformly into the solution. photocatalytic activities of the prepared samples were examined by the degradation of methylene blue under visible light irradiation. for each run the reaction suspension was freshly prepared by adding 0.10 g of catalyst into 250 ml of aqueous methylene blue solution, with an initial concentration of 5 mg l -1 . prior to the photoreaction, the suspension was magnetically stirred under dark conditions for 30 min to attain the adsorption/desorption equilibrium condition. the aqueous suspension containing methylene blue and photocatalyst was then irradiated under visible light with constant aeration. at the 10-min intervals, the analytical sample was taken from the suspension, immediately centrifuged at 4000 revolutions per minute (rpm) for 15 min, and then filtered to remove the catalyst. the filtrate was analyzed by using an ultraviolet-visible (uv-vis) spectrophotometer (perkin-elmer lambda 45), and the concentration of mb was monitored at 664 nm. a simple surfactant-free solution phase synthesis 31 3. results and discussion 3.1 the morphology and crystal structure of the products figure 1a shows the xrd pattern of the prepared product from the in(no3)3/c2h5ns molar ratio of 1:6. the peaks were indexed to a cubic phase of β-in2s3 (jcpds card no. 65-0459). the morphologies and structures of the product were examined with tem and high-resolution tem (hrtem). figure 1b shows the flower-like β-in2s3 hierarchitecture in a large area, while an individual flower-like hierarchitecture shown in figure 1c is about 300-350 nm in diameter. it can be seen that the hierarchitecture is constructed from the aggregation of many thin petal-like building units. the nanopetals are of layered structure and consist of the nanoflakes growing on both sides uniformly. the hrtem image (figure 1d) of individual nanopetals indicates a high degree of crystallinity of in2s3 nanoflowers. the distance between adjacent lattice planes is about 0.27 nm, corresponding to the (400) plane. furthermore, the edx spectrum recorded from the highlighted region in figure 1c confirms that the components of the products are only in and s with a ratio of 2.02:3 (figure 3g), which is consistent with the xrd result above. the cu signal is attributed to the tem copper supporting grid. the elemental mapping of in and s did not show a strong composition variation (figures 1e and 1f). the contrast difference was contributed by the morphology of the selected petals only. to confirm the composition of the in2s3 nanoflowers, xps analysis was carried out (figure 2). the binding energies obtained in the xps analysis were corrected for specimen charging by referencing the c 1s to 284.6 ev. the survey xps spectrum is shown in figure 2a. no peak of any element other than c, o, in, and s was observed. the observed c peak is due to the carbon supporting film on the copper tem grid, and the o peaks can be attributed to the absorption of oxygen on the sample surface and the carbon supporting film. the xps spectra of the in2s3 sample is consistent with the typical in2s3 spectrum reported in the literature [24]. figures 2b and 2c show the high-resolution xps spectra of in 3d and s 2p, respectively. the two strong peaks at 445.3 and 452.6 ev are assigned to the binding energies of in 3d5/2 and in 3d3/2. the observed peaks at 160.9 and 162.4 ev are attributed to the binding energy of s 2p3/2 and s 2p. these values are in good agreement with the reported data [25]. according to the measurements of the in 3d and s 2p peak areas, the atomic ratio of in/s is 2:3, very close to the nominal composition of in2s3, which further confirms that the final products were stoichiometric in2s3 with no impurity. this result is consistent with the measurements of energy-dispersive x-ray (edx) and with the element map. (see figures 1e-g). figure 1. characterizations of prepared in2s3 nanoflowers from the in(no3)3/c2h5ns molar ratio of 1:6. (a) xrd patterns; (b) low-, and (c) high-magnification tem images; (d) hrtem image of the selected area marked with a yellow rectangle in (c); (e and f) the corresponding elemental mapping of in and s in the same area; (g) edx spectrum. 3.2 effects of precursor ratio on the morphology of in2s3 nanocrystals in order to investigate the influence of molar ratio of reactants on the morphology of in2s3 nanocrystals, the morphologic variety at different molar ratios of indium nitrate to thioacetamide was examined by sem (figure 3). when molar ratio of indium nitrate to thioacetamide is 1:1.5, the product is composed of the smallest flower-like nanostructures illustrated in figure 3a, with a diameter of about 400-650 nm. when the molar ratio is further decreased to 1:3.5, the diameters are 550-650 nm (figure 3b). when the molar ratio is 1:4.5, the diameters are 400-450 nm (figure 3c). when the molar ratio is 1:6, the diameters are 300-350 nm (figure 3d). these sem results indicate that the general flower-like morphology of these in2s3 nanostructures is almost the same. however, it is apparent that rengaraj selvaraj et al 32 the diameter of the individual flowers can be controlled by changing the concentration of thioacetamide. all the above samples of in2s3 have the same crystal structure, as confirmed by xrd (figure 4). figure 2. xps analysis of the sample in2s3-1:6: (a) survey spectrum, (b) in 3d and (c) s 2p bonding-energy spectrum. figure 3. sem images of the prepared products under different in(no3)3/c2h5ns molar ratios: (a, a1) 1:1.5, (b, b1) 1:3.5, (c, c1) 1:4.5, (d, d1) 1:6. a simple surfactant-free solution phase synthesis 33 3.3 growth mechanism of in2s3 nanoflowers as is well known, the morphology of nanocrystals can be determined by their intrinsic crystal structures [26]. figures 1a and 1d demonstrate that the crystal structure of the prepared in2s3 is cubic close packing. thus, in2s3 crystals usually present a morphology of 2d nanoplates. high concentration of in 3+ and s 2 could lead to fast nucleation and congregation of in2s3 in the early stages, resulting in sphere-like cores, which could then serve as heterogeneous nucleation sites, providing high-energy sites for crystalline growth. then a secondary nucleation would be favored, and cubic angular protuberances would grow into nanopetals combining with the remaining primary particles, finally forming the 3d flower-like hierarchitectures, a process which is similar to that described as “the terrace-step-kink model” [27]. this is similar to the formation process of those flower-like nanocrystals reported previously, such as cos [28], cuo [29], tis2 [30], in2o3 [31], alo(oh) [32], zno [33], bi2moo6 [34], ni(oh)2 [35] and so on. we observed that the sizes of in2s3 nanoflowers decreased with increasing the concentration of c2h5ns (figure 4). this can be explained as follows. the thioacetamide ions can be easily absorbed on the in2s3 surface, which slows down the rate of growth units moving to the growing crystal surface. this contributes to the growth units having enough time to move towards the lowest or favorite energy position. thermodynamics plays a dominant role in this process. the adsorbed thioacetamide ions can stabilize and protect the in2s3 exposed facet; this will be helpful to form a bigger nanoplate (figure 4a). however, as the concentration of thioacetamide increases, the higher concentration of s 2 leads to easier nucleation and a faster reaction rate, resulting in a lack of time to age and thus producing small sized nanoflowers (figure 4d). in this process kinetic growth dominates the strongest effect. this indicates that there is a synergistic effect between thioacetamide ions protecting the crystal facets and the nucleation rate, causing thioacetamide to tune the growth of in2s3 nanoplates. therefore, the growth rate and morphology of flower-like in2s3 crystals can be controlled by adjusting the thioacetamide concentration in the mixed solvent. figure 4. xrd of the prepared final in2s3 products under different in(no3)3/c2h5ns molar ratios: (a) 1:1.5, (b) 1:3.5, (c) 1:4.5. 3.4 optical properties the optical property of the obtained in2s3 nanoflowers was investigated by an uv-vis absorption spectrophotometer. as shown in figure 5, the absorption edges of the in2s3 nanoflowers were found between 652 and 630 nm, corresponding to the absorption edge of a semiconductor material. it is interesting that the absorption edges for all samples were very close to each other. however, the absorption edge for the samples from in2s3-1:1.5 to in2s31:6 showed a small blue shift, which can be attributed to the quantization size effect of the in2s3 nanoflowers [36]. for a crystalline semiconductor, the optical absorption near the band edge follows the equation αhv=a(hν-eg) n/2 , where α, ν, eg and a are the absorption coefficient, the light frequency, the band gap and a constant, respectively. among them, n decides the characteristics of the transition in a semiconductor [37]. the band gaps are calculated to be about 1.90, 1.92, 1.97, and 1.95 ev for in2s3-1:1.5, in2s3-1:3, in2s3-1:4.5 and in2s3-1:6, respectively, from the onset of the absorption edge (inset of figure 5). it should be noted that those values are smaller than the one reported in our previous studies (2.00 ev) [15]. the main reason may attribute to the large size of in2s3 nanoflowers. this indicates that the in2s3 nanoflowers have a suitable band gap for photocatalytic decomposition of organic contaminants under visible light irradiation. rengaraj selvaraj et al 34 figure 5. uv-vis diffuse reflectance spectra of in2s3 nanoflowers. 3.5 photocatalytic performance of in2s3 nanoflowers in order to study the photocatalytic degradation properties of the prepared in 2s3 samples, methylene blue was used as a probe pollutant to investigate the photocatalytic performance of in 2s3 nanoflowers (in2s3-1:6 sample, for example). the maximum absorptive energy of methylene blue was at 664 nm. figure 6 shows that the absorptive intensity of methylene blue at 664 nm gradually decreased with prolonging the irradiation time, when the mixed solution of methylene blue and in2s3 nanoflowers was exposed to visible light irradiation by a sodium vapor lamp at room temperature. this result indicates that methylene blue underwent degradation behavior under the catalysis of in2s3 nanoflowers. if the degradation ratio is defined as the ratio between the decreased absorptive intensity and that of the initial methylene blue solution, the degradation ratio was about 85% when the mixed solution was irradiated for 3 h. this implies that the prepared in2s3 nanoflowers have good photocatalytic activity for methylene blue and are likely to be an efficient photocatalyst. as to the photocatalytic mechanism of in2s3 nanoflowers on methylene blue, we assume that the electron injection from photoexcited methylene blue molecules to in 2s3 nanoflowers leads to oxidative decomposition of the consequently electron-deficient methylene blue. to the best of our knowledge, the photocatalytic performance of β-in2s3 nanoflowers has not been reported and the catalytic mechanism of β-in2s3 has not been well understood until now. figure 6. time-dependent uv-vis absorption spectra of methylene blue (5mg/l) degradation in in2s3 nanoflowers under visible light irradiation. [conditions: mb concentration – 5mg/l; amount of catalyst – 400 mg/l]. 4. conclusion in summary, we have reported a simple method to prepare flower-like β-in2s3 hierarchitectures by a solutionphase process, using (in(no3)2 and thioacetamide as the precursors. the xrd analysis confirmed that the in2s3 nanoflowers are in cubic phase. the sem and tem analysis revealed that the products are flower-like in shape, with a diameter from 300 nm to 650 nm. on the basis of the structural and morphological studies, a possible growth mechanism has been proposed to explain the formation of the in2s3 nanoflowers. the compositional analysis made by edx and xps measurements confirmed that the stoichiometric in/s ratio is approximately 2:3, which indicates highpurity in2s3. the uv-vis drs measurements demonstrated that the samples have the band gap from 1.90 to 1.97 ev a simple surfactant-free solution phase synthesis 35 and slightly change with varying crystal sizes. thus, the narrow band gap of our 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facile solvothermal synthesis of hierarchical flower-like bi2moo6 hollow spheres as high performance visible-light driven photocatalysts. j. mater. chem., 2011, 21, 887-892. 35. zhu, l.p., liao, g.h., yang, y., xiao, h.m., wang, j.f. and fu, s.y. self-assembled 3d flower-like hierarchical b-ni(oh)2 hollow architectures and their in situ thermal conversion to nio. nanoscale res lett., 2009, 4, 550557. 36. tawkaew, s., fujishiro, y., yin, s. and sato, t. synthesis of cadmium sulfide pillared layered compounds and photocatalytic reduction of nitrate under visible light irradiation. colloids surf. a., 2001, 179, 139-144. 37. zhang, j., shi, f.j., chen, d.f., gao, j.m., huang, z.x., ding, x.x. and tang, c.c. self-assembled 3-d architectures of biobr as a visible light-driven photocatalyst. chem. mater., 2008, 20, 2937-2941. received 8 september 2014 accepted 25 september 2014 squ journal for science, 2016, 21(1), 1-6 © 2016 sultan qaboos university 1 detection of unlabeled genetically modified soybean in the omani market nabila al-sadqi 1 * and aliya s. alansari 2 1* department of academic affairs, directorate general of technological education, ministry of manpower. 2 department of biology, college of science, sultan qaboos university, p.o.box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: nabila.al-sadqi@manpower.gov.om. abstract: this study aimed to screen for products containing genetically modified (gm) food in the omani market using detection methods for the presence of roundup ready soybean, bt176 and mon810 maize in food products and to quantify it in positive samples using real time polymerase chain reaction (pcr). a total of 100 food samples were collected randomly from markets in oman. out of 59 samples, 8 (13.5%) were successfully amplified with the maize plant specific pcr. gm screening showed negative for all samples, which indicated low or no gm maize in the samples tested. out of 57 soy containing samples, 40 (70%) were successfully amplified by the soybean plant specific pcr. six samples out of the 40 (15%) were found positive for gm using p35s-cf3/p35s-cr4 and hanos118-f/ha-nos118-r, primer pairs and using gmo5/gmo9 and gmo7/gmo8 primer pairs for specific detection of roundup ready soybean. real time pcr (taqman™ system) was carried out for the positive roundup ready soybean samples and results showed that 2 out of the positive gm soy samples contained more than 5%; a soy formula for infants (imported) sample contained 21% gm soybean and raw soybean seeds (imported in bulk amounts and packed in oman) contained 88% gm soybean. the results demonstrate for the first time the presence of gm-soy in food products in the omani market, reinforcing the need for the use of qualitative and quantitative methods for gm detection in food products. keywords: genetically modified food; gmo detection; pcr; soybean. الكشف عن الصويا المعذلة جينيا والغير معرفة في السوق العماني ةعلياء األنصاريية والصادق ةبيلن طرق جزٌئٌه الهدف من هذه الدراسة هو الكشف عن المواد المعدلة جٌنٌا فً المنتجات الغذائٌة المتواجدة فً األسواق العمانٌة, وذلك بإتباع : الملخص ( ونوعٌن من الذرة soybean roundup readyمعتمدة ودقٌقة للكشف عن تواجد ثالثة أنواع منها : نوع من حبوب الصوٌا المعدلة جٌنٌا ) (. وباإلضافة إلى ذلك فقد تم تقدٌر نسبه الصوٌا المعدلة جٌنٌا فً العٌنات الموجبة وذلك باستخدام تقنٌة mon810, bt176الصفراء المعدلة جٌنٌا ) real time pcr . جمعت مئة عٌنة عشوائٌا من األسواق المحلٌة فً السلطنة. بواسطه تفاعل البلمرة المتسلسل و كانت نسبه نجاح الكشف عن بلغث النسبة ( وبالنسبة إلى العٌنات التً تحتوي علً الصوٌا95من 8) %13.5غذائٌة التً تحتوي علً الذرة وجود الذرة فً عٌنات المواد ال (. لم ٌتم الكشف عن أي محتوي معدل وراثٌا بالنسبة لعٌنات المواد الغذائٌة التً تحتوي على الذرة, بٌنما أظهرت النتائج وجود 95من 04)70% و الزوج ha-nos118-f/ha-nos118-r و p35scf3/p35s-cr4 ستخدام الزوج التمهٌدي بأ( 04من 6% )59بنسبه صوٌا معدلة جٌنٌا من الصوٌا المعدلة جٌنٌا. و قدرت نسبه roundup ready soybeanنوع للكشف عن gmo5/gmo9 and gmo7/gmo8التمهٌدي % من 9. ووجد أن اثنٌن من هذه العٌنات تحتوٌان على نسبة أكبر من real time pcrمحتوى الصوٌا المعدلة فً العٌنات الموجبة بواسطة % و األخرى لحبوب صوٌا مستوردة بكمٌات كبٌره ومعبأة 65الصوٌا المعدلة جٌنٌا, أحداها لمسحوق حلٌب مستورد لألطفال وقدرت النسبة فٌه ب وبشدة الحاجة إلى استخدام طرق الكشف عن المنتجات المعدلة جٌنٌا ومشتقاتها نوعٌا %. وهذه النتائج تعزز 88فً السلطنة وقدرت النسبة فٌها ب وكمٌا لمراقبه المواد المعدلة جٌنٌا المستوردة والمتوافرة فً األسواق دون بٌانات. .الكشف عن المواد المعدلة جينيا ،المنتجات الغذائية ،المواد المعدلة جينيا: الكلمات المفتاحية 1. introduction echnological breakthroughs in plant genetic engineering have enabled scientists to directly introduce novel genes into a variety of economically important crops, such as soybean, corn, cotton, etc. [1]. genetically t nabila al-sadqi and aliya alansari 2 modified organisms (gmo) are produced to provide higher yield and nutritional and economic benefits to consumers, such as longer shelf-life, enhanced flavour, reduced allergenicity and enhanced health or wellness attributes. the new generation of gm foods with enhanced quality attributes or nutritional benefits elicits much greater public acceptance than previous products [2]. there are certain benefits of gm food; a study on bt-corn found that it has significantly reduced levels of fumonisin (which is amycotoxin derived from fusarium) when produced in a region where the european corn borer (ecb) is an important pest [3]. women who consume a diet heavy in unprocessed corn or lightly processed corn (e.g., corn meal) contaminated with fumonisin b1 or fb1 ( the most prevalent members of a family of toxins known as fumonisin) are at significantly higher risk of having a baby with neural tube defects (ntds) because fb1 interferes with the uptake of folate in maternal cells [3]. however, there are major concerns regarding gm foods, such as the risk of allergy in humans and the potential negative environmental effects of modified crops. a study was carried out on crop-to-crop gene flow using farm scale sites of fodder maize (zea mays l.) in the uk, and reported that gene flow was detected in 30% of the samples (40 out of 135) at 150 m from the gm source, and events of gm to non-gm gene flow were detected at distances up to and including 200 m from the gm source [4]. with increasing use of gm crops, expanding from 1.7 million hectares in 1996 to 44.2 million hectares in 2000, gene-flow is an important consideration in the contamination of conventionally or organically grown crops [5]. a further valid argument made about gm foods is that little is kno wn about the long-term effects of gm crops on the environment, microorganisms, animals, and humans [6]. therefore, there is a growing public demand for transparency and accountability in terms of gmos in the market place [1]. regulators and governments have come under pressure to strengthen labeling requirements for gm foods. more than 35 countries have developed some form of labeling requirement, including china (0% threshold), the european union (eu) (0.9% threshold), australia and new zealand (1% th reshold), south korea (3% threshold) and japan and taiwan (5% threshold) [1]. in order to support legislation, reliable, accurate methods for identification of gmos in raw materials and food products are required [5,7,8]. many analytical methods are available, including pcr methods for screening and for qualitative and quantitative detection of gmos [5,9,10,11]. a review of methods has been published [12]. oman was one of the countries that signed the cartagena protocol on biosafety at the convention on biological diversity in 2000. gmos are not grown in oman and the overall attitude of omani consumers to gmos is negative, although they are generally of the opinion that the government should allow importation of gm food if clearly labeled. when respondents were questioned about clearly labeled gm foods, the majority of respondents (59%) were happy to see them imported, if clearly labeled (unpublished results of phd study). there is, therefore, a need to label gm products in oman in order to fulfill consumer demand for clear labeling of gmos, to overcome the lack of gmo detection in oman and to meet the demand s of the biosafety protocol. the central laboratories for food and water in oman, which undertakes a range of analyses on food do not analyze for gmos or gm foods [13]. however, there is a proposal, prepared by the ministry of environment and climate affairs in collaboration with academic institutions and relevant organizations, for a national biosafety framework that will support the implementation of the biosafety protocol. in this study, dna extraction of different food products was performed . plant specific, screening of gmos and specific detection for roundup ready soybean, bt-176 maize and mon810 maize were carried out. in addition, the amount of gm soy in positive samples using quantitative real time pcr was semi-quantified. 2. materials and methods 2.1 sample collection a total of 100 food samples, including raw soybean, maize seeds and processed products containing soya and/or maize ingredients were collected during march april 2008. samples were collected randomly from four superstores in the capital area of oman (muscat). these stores are located in the districts of al-qurum, madinat as’sultan qaboos, al-hail and al-khod. the samples analyzed were: 8 varieties of baby foods, 2 types of burgers, 3 types of cake mixes, 5 types of canned foods, 2 types of cereals, 3 types of chips (fries), 1 type of chocolate drink mix, 5 varieties of confectionary, 3 types of cookies, 2 types of cornflour, 4 varieties of corn puffs, 4 types of corn seeds, 5 types of dried noodles, 1 type of fish cake, 2 types of franks, 2 types of fruit yoghurts, 2 types of frozen meals, 6 types of meal mixes, 2 types of sauces, 1 type of seasoning mix, 3 types of soup mixes, 1 type of soya bread, 1 type of soya cream, 3 types of soya milk, 1 type of soya pellets, 4 types of soya seeds, 1 type of spring rolls, 7 types of sweet biscuits (cookies), 7 types of sweet mixes, 2 types of sweet rolls, 1 type of thick cream and 4 types of tofu. the information on the labels detection of unlabeled genetically modified soybean in oman 3 of the food samples collected was checked, and it indicated that 59% of the samples collected contained maize and 57% contained soy. institute for reference materials and measurements (irmm)-certificated soybean and maize reference material was obtained commercially (sigma-aldrich, st. louis, mo). for mon 810 maize, crm was irmm-413, 77119 (0% gm), 79521 (0.5% gm) and 76182 (5% gm). for bt-176 maximizer maize, crm was irmm-422r, 91528 (0% gm), 14724 (0.5% gm) and 19074 (5% gm). for roundup ready soybean, crm was irmm-410s, 83063 (0% gm), 81751 (0.5% gm) and 93109 (5% gm). 2.2 dna extraction dna was extracted using the cetyltrimethyl ammonium bromide (ctab) method [11] with some modifications. the extraction buffer contained 1% ctab, 1.4m nacl, 0.1m tris-hcl (ph 8), 0.02m edta (ph 8), 0.5% w/v pvp and 0.1% v/v β-mercaptoethanol. dna from reference materials was extracted by the same method. dna concentration was measured for all samples (100) and the 9 controls using a nanodrop nd-000 spectrophotometer. the concentration of dna for pcr was diluted to 50 ng/µl. 2.3 plant specific pcr for maize and soybean due to the high risk of cross contamination of samples and reagents, individual pcr steps were performed separately in terms of physical space and equipment [5,11,13]. pcr reaction with water instead of dna extract was carried out with every mix as a reagent control and, with every set of samples, a series of positive and negative controls were run to ensure the accuracy of the results [5,11]. to confirm the presence and quality of dna extracted from maize and/or soybean containing samples, primers zein3/zein4 specific to the maize zein gene (ze 1, coding for a 10-kb protein) and gmo3/gmo4 specific to soybean lectin gene (le 1) were used [11]. the pcr master-mix was set up in a total volume of 50 µl using 26.25 µl milliq water, 2.5 µl glycerol (50%), 5 µl 10x buffer (of 1x concentration), 5µl mgcl2 (2.5 mm, applied biosystems, usa), 5µl dntps (0.2mm, promega, usa), 0.25µl taq. polymerase (0.025u/µl inno), 0.5 µl of each primer, (0.5 µm, sigma, usa) and 5 µl of dna (5 ng/µl). the pcr program for primer pair zein 3 & 4 was: initial denaturation for 3 min at 95ºc, denaturation for 1 min at 96 ºc, annealing for 1 min at 57 ºc, extension for 1 min at 72 ºc, number of cycles 50, final extension for 3 min at 72 ºc. the pcr program for primer pair gmo 3 & 4 was: initial denaturation for 3 min at 95 ºc, denaturation for 30 sec. at 95 ºc, annealing for 30 sec at 63 ºc, extension for 30 sec at 72 ºc, number of cycles 40, final extension for 3 min at 72 ºc. 2.4 screening for promoters and terminators the detection of the 35s promoter and nos terminator by pcr was carried out for screening. the identification of one of these regulatory sequences in soybean or maize containing samples indicates gmo presence. in roundup ready soybean, the identification of both 35s promoter and the nos terminator is possible, whereas only the 35s promoter is present in the bt-176 and mon810 maize [11]. the pcr master-mix was set up as detailed, with 0.5 µl of each primer, p35s-cf3 and p35s-cr4 for 35s and ha-nos 118-f and ha-nos 118-r for nos (0.5 µm, sigma, usa) and 5 µl of dna (5 ng/µl). the pcr program for primer pairs p35s-cf3, p35s-cr4 and ha-nos 118-f, ha-nos 118-r was: initial denaturation for 3 min at 95 ºc, denaturation for 25 sec at 95 ºc, annealing for 30 sec at 62 ºc, extension for 45 sec at 72 ºc; number of cycles 50, final extension for 7 min at 72 ºc. 2.5 detection of roundup ready soybean primer pairs gmo5/gmo9 and gmo7/gmo8 were used for specific detection of roundup ready® soybean [11]. the pcr master-mix was set up in a total volume of 25 µl with 0.1µl of each primer, gmo5 and gmo9 (0.5 µm, sigma, usa) and 2 µl of dna (5 ng/µl). the pcr program for primer pair gmo5 and gmo9 was: initial denaturation for 3 min at 95 ºc, denaturation for 30 sec at 95 ºc, annealing for 30 sec at 60 ºc; extension for 40 sec at 72 ºc, number of cycles 25, final extension for 3 min at 72 ºc. after amplification, 0.5 µl of the previous pcr product was added to 24.5 µl of the master-mix for a second pcr (nested pcr) with 0.1µl of each primer gmo7 and gmo8 (0.5 µm, sigma, usa). nabila al-sadqi and aliya alansari 4 the pcr program for primer pair gmo7 and gmo8 was: initial denaturation for 3 min at 95 ºc, denaturation for 30 sec at 95 ºc, annealing for 30 sec at 60 ºc, extension for 40 sec at 72 ºc, number of cycles 35, final extension for 3 min at 72 ºc. 2.6 quantification of roundup ready soybean using real time pcr rt-pcr was carried out to determine the ratio of target gm dna to the total of the species dna. applied biosystem abi prism ™ 7700 detector instrument (taqman tm ) was used. the primer pairs used for real time pcr were: reference gene primers and probe, le-f, le-r, le-probe and trans-gene primers and probe; rr-f, rr-r, rr-probe [11]. 2.7 agarose gel electrophoresis the extracted dna was subjected to electrophoresis on a 1% agarose gel at a constant voltage (75 v for 15 min); pcr products were checked on a 2% agarose gel (75v for 30 min) and nested pcr on a 2.5% agarose gel (100v for 30 min) containing ethidium bromide in 1xtbe buffer. the visualization was performed under uv light and the images were captured with a digital camera (casio, ex-z1000) for documentation. 3. results and discussion 3.1 dna extraction the modified ctab method yielded a good amount of dna for all controls and food samples. most of the samples under uv radiation showed a clear heavily illuminated area of dna. the dna extraction method used was satisfactory for most of the products, which ranged from raw seeds to processed food. the quantity of dna extracted ranged from 16.23 to 5454 ng/μl. 3.2 plant specific pcr for maize and soybean out of 57 samples containing soybean in their ingredients, 40 samples (70%) were positive for soybean plant specific pcr, and out of 59 samples containing maize in their ingredients (all were processed), 8 samples (13.5%) were positive for maize plant specific pcr. a study by cardarelli et al. showed that the analysis of products containing maize seemed to be more difficult, probably due to the low concentration of maize ingredients or to some processing steps in food production that strongly contributed to the failure of dna extraction [5]. in addition, the treatment during food production processes, such as heating, high pressure and the physical processing are known to affect the dna content. this was found in a study on maize samples screened for gm maize, where the corn samples investigated contained corn starch, corn grits, hydrolyzed corn starch, or corn flour [8]. 3.3 screening for promoters and terminators pcr was carried out for maize samples using primer pair p35s-cf3 and p35s-cr4. a band of 123bp indicates the presence of gm. six soybean samples out of 40 showed clear positive in both the 35s promoter and nos terminator reactions, 15% of soybean samples were gm soybean (table 1). although there were about the same number of samples containing maize (59) and soya (57), none of the maize-containing food were gm positive. the negative gm maize results in this study may indicate that oman’s source of maize is not a gm maize producer. however, having highly processed samples can potentially interfere with the pcr detection. this is clearly demonstrated by having only 5 samples detected out of 59 samples with the maize specific pcr. 3.4 detection of roundup ready soybean for specific detection of roundup ready soybean, standard controls, 2% gm and 5% gm, were used. the six samples, which were positive with both screening pcrs (35s and nos) were also positive for the specific pcr detection of roundup ready soybean. one was raw soybean seeds and five were processed foods (table 1). in previous studies where the primer pair gmo5/gmo9 and gmo7/gmo8 were used in the nested pcr the sensitivity was 0.01% [14]. the results of this study agree with these findings because all six gm soybean samples checked for roundup ready® soybean were positive. detection of unlabeled genetically modified soybean in oman 5 3.5 quantification of roundup ready soybean real time pcr real time pcr (taqman™ system) was carried out for the six roundup ready soybean samples and the controls, roundup ready soybean 0%, roundup ready soybean 2%, roundup ready soybean 5% and a dna negative control sample. two of the samples contained higher amounts of gm than the 5% control. one sample, raw soybean seeds imported and packed in oman, contained 88% gm soybean and the second sample, a soy formula for infants, contained 21% gm soybean (table 1). neither sample was labeled as containing gm, although analysis showed that the gm ingredients exceeded the legal threshold (1%) level of gm content in a food product. more of the samples could have contained gm, but with it failing to be detected due to method limitations, such as the quality of dna extracted from highly processed food products possibly being affected by degradation processes. the process of dna and protein detection faces difficulties when processed and highly refined food products are involved, e.g. starch, sugar or vegetable oils. sometimes food products are subjected to extensive food processing stages which could affect their ingredients and gmo origin. this can result in the possibility of nondetectable gm dna or proteins [15]. table 1. results of pcr for soybean samples product number of samples soybean plant specific screening detection rt pcr promoter terminator rr soybean gm % baby food 8 5 1 1 1 21 soya seeds 4 4 1 1 1 88 soya pellets 1 1 0 0 0 0 soya milk 3 3 0 0 0 0 soya bread 1 1 0 0 0 0 sweets 18 5 0 0 0 0 biscuits 10 8 1 1 1 0 tofu 4 4 0 0 0 0 frozen meals 5 1 1 1 1 0 canned meats 5 2 0 0 0 0 burgers 2 2 2 2 2 0 franks 2 2 0 0 0 0 mixes 11 1 0 0 0 0 noodles 5 1 0 0 0 0 4. conclusion using pcr-based methods we detected and quantified the presence of gm foods in a collection of 100 samples from the market. the results demonstrate the availability of unlabeled gm soybean products containing higher percentages than the limit for labeling (1%) in the omani food market. this indicates the need for better control and labeling of gm food products in oman, to address public concerns about gm foods and their potential health and environmental risks, the consumer right to choose, and also to support the implementation of the recently proposed national biosafety framework for oman. references 1. hai kang life corporation limited, 2010 (http://www.hkdnachips.com, 10th may 2010). 2. hossain, f. and onyango b. product attributes and consumer acceptance of nutritionally enhanced genetically modified foods. international journal of consumer studies, 2004, 28(3), 255–267. 3. kershen, d. health and food safety: the benefits of bt-corn. food and drug law journal, 2006, 61( 2). 4. weekes, r., allnutt, t., boffey, c., morgan, s., bilton, m., daniels, r. and henry, c. a study of crop-to-crop gene flow using farm scale sites of fodder maize (zea ays l.) in the uk. transgenic resources, 2007, 16, 203–211. 5. cardarelli, p., branquinho, m.r, ferreira, r.t.b., da cruz, f.p, and gemal, a.l. detection of gmo in food products in brazil: the incqs experience. food control, 2005, 16, 859–866. 6. daunert, s., deo, s., morin, x. and roda, a. the genetically modified foods debate: demystifying the controversy through analytical chemistry. analytical and bioanalytical chemistry, 2008, 392, 327–331. 7. abdullah, t., radu s., hassan, z. and hashim, j. detection of genetically modified soya in processed food sold http://www.hkdnachips.com/ nabila al-sadqi and aliya alansari 6 commercially in malaysia by pcr based method. food chemistry, 2006, 98(3), 575-579. 8. el sanhoty, r., broll2, h., grohmann, l., linke, b., spiegelberg, a., bogl, k.-w. and zagon, j. genetically modified maize and soybean on the egyptian food market. nahrung/food, 2002, 46(5), 360 – 363. 9. spiegelhalter, f., lauter f-r. and russell, j.m. detection of genetically modified food products in a commercial laboratory. journal of food science, 2001, 66(5), 634640. 10. randhawa, g., singh, m., chhabra r. and sharma, r. qualitative and quantitative molecular testing methodologies and traceability systems for commercialised bt cotton events and other bt crops under field trials in india. food analytical methods. 2010 (cited online on july1, 2010). 11. querci, m., jermini, m. and eede, g. the analysis of food samples for the presence of genetically modified organisms, training course user manual, 2006. isbn:92-79-02242-3, catalogue no.: lb-x1-06-051-en-c, european commission, directorate-general, joint research centre & institute for health and consumer protection. online publication: http://gmotraining.jrc.it/, september 2008. 12. marmiroli n., maestri e., gullì m., malcevschi a., peano c., bordoni r. and de bellis g.. methods for detection of gmos in food and feed. review. analytical bioanalytical chemistry, 2008, 392, 369-384. 13. ministry of regional municipalities, environment and water resource in oman and iucn–the world conservation union wescana in jordan. biosafety: national capacity assessment and work plan. december 2006. sultanate of oman. 14. viljoen, c.d., dajee, b.k. and botha, g.m. detection of gmo in food products in south africa: implications of gmo labelling. african journal of biotechnology, 2006, 5, 73-82. 15. brod, f.c.a & arisi, a.c.m. ‘quantification of roundup ready soybean in brazilian soy-derived foods by realtime pcr’. international journal of food science and technology, 2008, 43, 1027-1032. 16. anklam, e., gadani, f., heinze, p., pijnenburg, h. and eede, g. analytical methods for detection and determination of genetically modified organisms in agricultural crops and plant-derived food products. european food research technology, 2002, 214, 3–26. received 22 october 2014 accepted 8 june 2015 squ journal for science, 2015, 20(2), 12-18 ©2015 sultan qaboos university 12 a note on using partitioning techniques for solving unconstrained optimization problems on parallel systems mehiddin al-baali 1 and chefi triki 2 * ¹department of mathematics and statistics, sultan qaboos university, p.o. box: 36, pc 123, alkhod, muscat, sultanate of oman. email: albaali@squ.edu.om. 2 department of mechanical and industrial engineering,sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: chefi@squ.edu.om. abstract: we deal with the design of parallel algorithms by using variable partitioning techniques to solve nonlinear optimization problems. we propose an iterative solution method that is very efficient for separable functions, our scope being to discuss its performance for general functions. experimental results on an illustrative example have suggested some useful modifications that, even though they improve the efficiency of our parallel method, leave some questions open for further investigation. keywords: distributed systems; parallel algorithms; partitioning techniques; unconstrained optimization. مالحظت حول استخداو تقنياث انتجسئت نحم مسائم األمثهياث غير انمقيدة عهى أنظمت متوازيت تريكيانمحي اندين انبعهي و شافي طرٌقت حم تكرارٌت تكىٌ فعبنت َتعبيم يع تصًٍى خىارزيٍبث يتىازٌت ببستخذاو يتحىل تقٍُبث انتجسئت نحم يسبئم األيثهٍبث غٍر انخطٍت. َقترح :مهخص انًفٍذة. تجرٌبٍت عهى يثبل تىضٍحً، تى اقتراح بعض انتعذٌالثجذا نذوال يُفصهت، وَطبق عًهُب هى يُبقشت أدائهب عهى دوال عبيت. ببالستُبد إنى َتبئج بعض األسئهت غٍر انًحهىنت نًتببعت انبحث. تركعهى انرغى أَهب تحسٍ فعبنٍت طرٌقتُب نهتىازي، فإَهب ت األيثهٍبث غٍر انًقٍذة، انخىارزيٍبث انًتىازٌت، تقٍُبث انتجسئت، أَظًت يىزعت. :كهماث مفتاحيت 1. introduction he main aim of this work is to discuss the efficiency of solving nonlinear optimization problems on parallel systems when using partitioning techniques. consider the following unconstrained optimization problem ( )min n x r f x  (1) that we would like to solve on parallel systems not by, trivially, parallelizing a given sequential method, but rather by designing algorithms specifically intended for parallel computers. we want to show that even though such techniques are very successful for some problems there is still the risk that the convergence of certain numerical methods happens very slowly for other types of problems. our approach consists of developing an algorithm that solves nonlinear optimization problems by partitioning the optimization problem into a given number of subproblems, each of which is solved separately by a sequential method. we try to achieve the partitioning phase in such a way that all processors are efficiently utilized in doing useful work during most of the execution time. this strategy will be very fruitful when solving particular types of problems (e.g., separable functions) because, in this case, a solution of the original problem is obtained as soon as all subproblems are solved on the available processors of the parallel system. for general functions that are characterized by variable dependencies, however, convergence may be very slow, vanishing thus, any speedup deriving from the use of parallel technologies. the solution of optimization problems on parallel systems or on grids has, over the past decades, attracted the attention of several researchers [1-4]. if we ignore those contributions that simply used the automatic parallelization offered by the intelligent compilers embedded within the parallel systems, then most of the works can be classified into two different types: fine and coarse grain parallelization. fine grain parallelization acts directly on a matrix and vector t a note on using partitioning techniques 13 levels to split the workload among the processors [5, 6]. coarse grain parallelization tries to tackle the structure of the problem in order to split it among the available processors [7-10]. this last direction was the one chosen by ferris and mangasarian, whose seminal paper [11] proposed a general paradigm for solving nonlinear optimization problems based on splitting the decision variables among the processors. their method, called parallel variable distribution, involves, besides a concurrent phase, a synchronization phase based on calculating the affine hull of the generated partial solutions. their method was proved theoretically to converge under a set of mathematical conditions and their preliminary experimental results showed the potential for highly efficient parallelization by the method. after the seminal work of ferris and mangasarian many other methods have been proposed addressing parallelization of the problem's structure [12-15]. our work here goes in this same direction to propose a parallel algorithm that distributes the variables of a general problem among the available processors. then, unlike ferris and mangasarian's approach that uses an affine hull for the synchronization step, our iterative method simply restarts, whenever it is needed, the same method with a new initial point becoming available on some of the processors while running the sequential method independently. the rest of our work is organized as follows. in section 2, we describe our proposed parallel algorithm. in section 3, we describe how to redefine the initial point for the parallel numerical algorithm. in section 4, we apply the proposed parallel algorithm to a simple but challenging general function. then, in section 5 we suggest some modifications and discuss the numerical results. finally, in section 6, we give our concluding remarks. 2. parallel algorithms for unconstrained optimization we are interested in solving iteratively unconstrained optimization problems, as defined by (1), using a numerical method with a given initial point (1) x . for convenience, let the n variables of x be partitioned into groups that match the number p , say of processors of a parallel system. specifically, let [ ][ ][ ] [ ] 1 2= ( , ,..., ,..., ), nnn n pix x x x x where 1 2 .... = . p n n n n   the initial point (1) x can then be defined as: [ ,1][ ,1][ ,1] [ ,1](1) 1 2= ( , ,..., ,..., ). nnn n pix x x x x (2) the idea of designing a parallel algorithm consists of solving iteratively, using the available processors, p independent unconstrained optimization subproblems starting from the initial point (1) x . then, in each iteration we check the termination condition, ( ) ( ) , c g x  (3) where ( )g x is the gradient of ( )f x ,  is a tolerance parameter and c is an iteration counter. if condition (3) is satisfied, then the algorithm is terminated defining a proximate solution of (1). otherwise, the process is restarted, but with a new initial point ( 1) , c x  defined by using the solution obtained in iteration ,c as will be described in section 3.in the following, we refer to this repetitive process as outer iteration of the parallel method and use the index c for its identification, whereas the repetitive process inherent in the numerical method is referred to as inner iteration and denoted by the index k.throughout the paper, we will specify explicitly the index we are referring to whenever this is not made evident from the context. consequently, in each iteration c , we apply on each processor i p , = 1, 2,...,i p , a certain sequential method [16, 17], to optimize subproblem: [ , ] ( ) = ( ),min min i i n c i i i n n y r y r f y f x   (4) where [ , ][ , ] [ , ] [ , ][ , ] [ , ] 1 11 2= ( , ,..., , , ,..., ). n cn c n c n cn c n c pi i ix x x x y x x  (5) here all components of x are known quantities, except the partition y that represents the only set of variables of subproblem on i p specified as [ ] 1 2 = = ( , ,..., ) , n ti s s s n i y x x x x    where 0 1 2 1 = .... i s n n n n      and 0 = 0n . the starting point for a generic iteration c is, thus, given by [ , ]( ) ( ) ( ) ( ) 1 2 = = ( , ,..., ) . n cc c c c ti s s s n i y x x x x    after solving subproblem (4), we obtain on processor i p a solution [ ,*]* = n iy x that verifies [ ,*]* ( ) = ( ) n i i i f y f x . then by combining all the results deriving from all the processors, a new estimate for a solution of problem (1) is defined. mehiddin al-baali and chefi triki 14 it is worth noting that this algorithm is very efficient if the variables assigned to each processor i p are independent of the other variables, i.e., the original problem can be partitioned into a set of independent subproblems. in this case, the solution of the original problem (1) is obtained as soon as all the processors complete the required tasks of solving the assigned subproblems. this happens, for example, in the case of separable problems in which it is possible to group the variables to distribute among a certain number of processors as equally as possible, each requiring almost the same time for solving its assigned subproblem. subsequently, by combining all the obtained partial solutions we get the desired solution of (1). in this case, the time required to solve (1) is equal to the time required to solve the most difficult subproblem plus some data communication overhead. however, for general problems, it is usual to expect that the variables assigned to processor i p depend on some other variables handled by another processor j p with i j . in this case, the algorithm may converge very slowly, as shown in section 4, since it will be necessary to restart the algorithm by generating a new initial point at each (outer) iteration of our method. the way to generate a new initial solution is illustrated in the next section, and some improvements will be proposed in section 5. 3. obtaining a new starting point we assume here that, at a given iteration c , not all the processors terminated with a solution [ , ]n c ix of the assigned subproblem i which, once combined with the other partial results, does not constitute a valid solution to the original problem (i.e., condition (3) is not satisfied). in this case, we may exploit any solution [ , ]n c j x of another subproblem that is available on processor, say j p , and defined by (5) with i replaced by j , that is [ , ]n c j x . the idea is to make this value available to processor , i p which will restart the process of solving problem (4) with ( )c x as defined above, except that [ , ]n c j x is replaced by [ ,*]n j x . in addition, in order to improve the quality of the initial solution, it is also advantageous to replace [ , ]n c j x by [ , ]n c ix ,whenever we have [ , ] [ , ] ( ) < ( ). n c n cj i i i f x f x 4. illustrative example consider solving the (general) well-known rosenbrock problem 2 2 2 2 1 1 2 ( ) = 100( ) (1 ) ,min x r f x x x x     (6) starting with (1) = (0, 0) t x , as in [18]. it is easy to note that the optimal solution is * = (1,1) t x . assume that two processors, 1 p and 2 p , are available. in this case, 1 2 = = 1n n and (1) [1,1] [2,1] = ( , ) = (0, 0) t t x x x , but for simplicity of notation we will rename the two variables as (1) (1) (1) = ( , ) = (0, 0) t t x y z . consequently, the corresponding subproblem (4) to be solved on 1 p can be written as 2 2 2 1 ( ) = 100( ) (1 ) ,min y r f y z y y     (7) where [2,1] =z x is considered to be a known constant here (set initially to 0 ) and the starting point, for = 1c , is given by ( ) = 0 c y . similarly, processor 2 p should solve the subproblem 2 2 2 2 ( ) = 100( ) (1 ) ,min z r f z z y y     (8) where [1,1] =y x is a known constant (set initially to 0 ) and the initial point, for = 1c , is given by ( ) = 0 c z . while problem (8) can be solved on 2 p in one step exactly , easily yielding the solution * 2 =z y , we need to apply a numerical method to solve subproblem (7). here, we have implemented the newton-raphson method, which is known to be very efficient whenever the starting point is close enough to the optimal point [19]. by using the index k to denote the inner iterations of this iterative method, its termination criterion can then be defined by ( ) ( 1) , k k y y     (9) where 6 = 10  . numerical results for solving (7) on processor 1 p are reported in table 1. for each inner iteration ,k it includes the value of the variable ( ) , k y its corresponding value of ( ) 1 ( ) k f y and the initial value of ( )c z corresponding to the (outer) iteration c (recall that ( )c z is constant for problem 1 f ). a note on using partitioning techniques 15 table 1. solution of problem (7) on p1 for outer iteration = 1.c k ( )ky ( ) 1 ( ) k f y ( )c z 1 0 1 0 2 1 100 0 3 6.6722130× 19.929645 0 4 4.4688493× 4.294191 0 5 3.0373406× 1.3358733 0 6 2.1664151× 8.3392632× 0 7 1.7376816× 7.7383512× 0 8 1.6209454× 7.7112126× 0 9 1.6126604× 7.7110970× 0 10 1.6126202× 7.7110970× 0 from the results of table 1, it is clear that the newton-raphson method has terminated because of the satisfaction of condition (9). however, the whole algorithm is not terminated because condition (3) is not satisfied yet. for this reason, we need to restart a new outer iteration by using a new estimate of the initial solution (2) = (0.16126202, 0) t x as obtained from the solution of problem (1) as reported in table 1 (and from the exact solution of subproblem (8)). the results as summarized in table 2 show that condition (3) is not verified yet, and thus the iterative process should continue by using (3) = (0.2113389, 0.02600544) t x as a new initial solution. table 2. solution of problem (7) on 1 p for outer iteration = 2.c k ( )k y ( ) 1 ( ) k f y ( )c z 1 1.6126202× 7.0348137× 0 2 2.3482151× 6.7038702× 0 3 2.1393910× 6.5695530× 0 4 2.1137604× 6.5680104× 0 5 2.1133890× 6.5680104× 0 before proceeding, we want to note that the total number of function evaluations, say ,nf required to terminate the newton-raphson method is 10 in table 1 and 5 in table 2. this tradition of counting the number of function evaluations as a measure of the computing cost of a method is very important in nonlinear optimization. in fact it represents an alternative way (with respect to the cpu run time) of measuring the performance of a numerical algorithm without relating it to a specific hardware platform. for this reason, we will even use this measure to define a termination condition of the whole parallel algorithm. we decide for simplicityto stop our parallel algorithm on the basis of the following well-known condition, instead of using criterion (3): ( ) ( 1) 1 1 ( ) ( ) , c c f y f y     (10) where c is the outer iterations index and  is chosen to be, for example, 8 10  . a summary of the results of using condition (10) in the solution of our illustrative example is reported in table 3. this table, besides reporting k , ( )k y , ( ) 1 ( ) k f y and ( )c z as before, also shows the number of outer iterations, ,c and the number of function evaluations, nf.the first two lines of table 3 can be easily derived from the results of tables 1 and 2 and the value of (3) ,x as defined above, can be seen in the line corresponding to = 3c . mehiddin al-baali and chefi triki 16 table 3. outer and inner iterations for solving problem (7) on 1 .p c k nf ( )k y ( ) 1 ( ) k f y ( )c z 0 0 0 1 0 1 10 10 1.6126202× 7.7110970× 0 2 5 15 2.1133890× 6.5680104× 2.6005440× 3 4 19 2.4508301× 5.9362041× 4.4664126× 4 4 22 2.7112272× 5.4933041× 6.0065686× : : : : : : : : : : : : 10 4 47 3.6653980× 4.0873867× 1.2571033× 11 3 50 3.7761509× 3.9415559× 1.3435143× : : : : : : : : : : : : 208 3 641 8.0786871× 3.7055832× 6.5146273× 209 2 643 8.0860185× 3.6773699× 6.5265184× : : : : : : : : : : : : 1892 2 4009 9.9800324× 3.9970463× 9.9600046× 1893 2 4011 9.9800825× 3.9770370× 9.9601048× even though our parallel algorithm succeeds in generating the solution * (0.99800825, 0.99601048) t x = which is close to the optimal point (1,1) , t these results show that its performance, expressed in terms of the number of function evaluations, remains unsatisfactory. a positive comment that can be drawn from the results is that as the number of outer iterations increases, the quality of the initial solution improves and, consequently, the number of inner iterations required to solve 1 f decreases. 5. modified algorithm the example in the previous section highlighted the main drawback of solving nonseparable problems on parallel systems, namely the fact that some of the processors remain idle while others are doing useful work. in the previous example, indeed, processor 1 p was heavily utilized whereas 2 p solved its task in one step and remained idle most of the time. in order to rectify this inefficiency, we propose a modification of our algorithm consisting of calling upon any useful detail made available on any of the processors to update the initial solution and restart the process. we illustrate this idea by reconsidering the example of section 4. suppose that processor 2 p , once idle, calls upon any detail made so far available on 1 ,p i.e. ( =2) = 1 k y (see table 1). although ( =2) 1 ( ) = 100 k f y is much larger than ( =1) 1 ( ) = 1 k f y , this will result in getting (2) = 1*1 = 1z on 2 p and, surprisingly, in immediately obtaining the optimal solution of the original problem. since this case may happen rarely in practice, we propose another practical way of modifying our parallel method. while solving subproblem (7) on 1 p , we do not wait until the satisfaction of condition (9), but we stop the inner iterations earlier, i.e., whenever we note ( ) ( =1) 1 1 ( ) < ( ). k k f y f y (11) we then pass this newly generated value to the other processor to be used as a new initial value. the whole process will then terminate only when condition (10) holds. to understand how this modification affects the solution of our example, consider the results of table 1. by applying the new rule (11), processor 1 p does not need to run 10 inner iterations anymore, but stops at iteration 6, i.e., as soon as ( =6) 1 ( ) = 0.83392632 k f y , which turns to be less than ( =1) 1 ( ) = 1 k f y , thus reducing the time in which 2 p remains idle. hence, both processors terminate with the point (2) = (0.21664151, 0) t x .using this new estimate, we apply this procedure again in order to solve problem (8) and continue until obtaining the final estimate of the solution of (8) which yields that of (6). the results obtained are summarized in table 4. comparing these results with those reported in table 3, we note how our modification substantially reduced the number of inner iterations k required in each outer iteration and, consequently, the number of function evaluations nf( ) is reduced from 4011 to 1894. a note on using partitioning techniques 17 table 4. results of the modified algorithm for solving problem (7) on 1 .p c k nf ( )k y ( ) 1 ( ) k f y ( )c z 1 6 6 2.1664151× 8.3392632× 0 2 1 7 2.5625824× 5.8825087× 4.6933546× 3 1 8 2.8353419× 5.3500097× 6.5668290× 4 1 9 3.0514270× 4.9900761× 8.0391645× : : : : : : : : : : : : 10 1 14 3.8824373× 3.8099867× 1.4251556× 11 1 15 3.9822456× 3.6829531× 1.5073320× : : : : : : : : : : : : 208 1 212 8.1014949× 3.6180865× 6.5516895× 209 1 213 8.1086987× 3.5906568× 6.5634220× : : : : : : : : : : : : 1889 1 1893 9.9800360× 3.9956158× 9.9600118× 1890 1 1894 9.9800860× 3.9756095× 9.9601119× although this last modification has improved our parallel algorithm significantly, the high value of nf required to solve the problem remains unsatisfactory. the modified method seems to converge, but slowly indeed, since a large ,nf albeit smaller than before, is still required. a further reduction in the number of outer iterations (and thus in nf) can be observed only when larger values of  are used. in this case, however, the substantial reductions of the values of c and nf (that can be observed in table 5 for increasing values of  ) are counterbalanced by a deterioration in the quality of the solution obtained for problem (6). it is the responsibility of the decision maker to define the acceptable tradeoff between the solution's quality and the method's efficiency. table 5. results of the modified algorithm for different values of .  c k nf ( )ky ( ) 1 ( ) k f y ( )c z 8 10  1890 1 1894 9.9800860× 3.9756095× 9.9601119× 6 10  989 1 994 9.8044276× 3.8347995× 9.6116828× 4 10  244 1 249 8.3378845× 2.7725833× 6.9420540× 3 10  59 1 64 6.1549985× 1.4882825× 3.7569698× 6. concluding remarks we proposed a parallel algorithm based on a variable partitioning technique designed to efficiently solve separable problems, aiming to test its usefulness for general problems. we observed that, despite the proof of convergence demonstrated in [11], such a convergence may happen very slowly, probably vanishing the speedup deriving from the use of parallel systems. the main cause of this disadvantage is the fact that some of the processors remain idle while others are engaged with carrying out useful computations. we proposed some modifications that succeeded in reducing the effect of such inefficiency, but the results still turned out to be unsatisfactory. the solution of a simple (but not separable) function required a large number of function evaluations, while the use of the sequential newton method is known to require only 3 function evaluations [16]. on the basis of the above observations, the following points are made:  while our proposed method is efficient for separable problems, it converges slowly for general functions;  the illustrative example, a general function of a small size, faced the difficulty of having one of the two processors remaing idle during most of the computation time. this showed our original algorithm to be inefficient for solving nonseparable functions;  for well-structured general functions allowing a balanced distribution of the workload among the available processors, we expect better performance from our algorithm. moreover, tackling large scale problems will increase the workload, and thus reduce the effect of unavoidable waiting time of the idle processors;  the improvements that can be achieved by our method are clearly problem dependent and the remarkable speedup obtained in solving our illustrative example may prove to be significant for other problems. thinking about more general improvements tailored for nonseparable functions (such as considering load balancing techniques [20] or tasks scheduling [21]) may be of great benefit to speed up our parallel method. mehiddin al-baali and chefi triki 18 carrying out more intensive experiments and developing general purpose improvement techniques are beyond the scope of this paper. this contribution wanted, on the one side, to highlight the challenges faced when solving general problems by using partitioning techniques on parallel systems and, on the other side, to raise new problems of concern for further investigation. references 1. schnabel, r.b. a view of the limitations, opportunities, and challenges in parallel nonlinear optimization. parallel computing . 1995, 21(6), 875-905. 2. bertsekas, d.p. and tsitsiklis, j.n. parallel and distributed computation: numerical methods. athena scientific, belmont-usa, 1997. 3. triki, c. and grandinetti l. computational grids to solve large scale optimization problems with uncertain data. international journal of computing 2002, 1(1), 20-26. 4. migdalas, a., toraldo, g. and kumar, v. nonlinear optimization and parallel computing. parallel computing 2003, 29(4), 375-391. 5. beraldi, p., grandinetti, l., musmanno, r. and triki, c. parallel algorithms to solve two-stage stochastic linear programs with robustness constraints. parallel computing. 2000, 26(13-14), 1889-1908. 6. d'apuzzo, m. and marino, m. parallel computational issues of an interior point method for solving large boundconstrained quadratic programming problems. parallel computing 2003, 29(4), 467-483. 7. blomvall. j. a multistage stochastic programming algorithm suitable for parallel computing. parallel computing, 2003, 29(4), 431-445. 8. giraud, l., haidar, a. and pralet. s. using multiple levels of parallelism to enhance the performance of domain decomposition solvers. parallel computing, 2010, 36(5-6), 285-296. 9. argello, f., heras, d.b., bo, m. and lamas-rodrguez, j. the split-and-merge method in general purpose computation on gpus. parallel computing, 2012, 38(6-7), 277-288. 10. triki, c. solving the flood propagation problem with newton algorithm on parallel systems. squ journal for science, 2012, 17(1), 147-156, 11. ferris, m.c. and mangasarian, o.l. parallel variable distribution. siam journal on optimization, 1994, 4, 815832. 12. mangasarian, o.l. parallel gradient distribution in unconstrained optimization. siam journal on optimization, 1995, 33, 1916-1925. 13. rotiroti, d., triki, c. and grandinetti, l. combined mpi/openmp implementations for a stochastic programming solver. in parallel computing advances and current issues (edited by g. joubert, a. murli, f. peters and m. vanneschi), imperial college press, 2002. 14. zeng. d. parallel iterative methods for nonlinear programming problems. advanced materials research, 2010, 159,105-110. 15. li, w. a parallel multi-start search algorithm for dynamic traveling salesman problem. lecture notes in computer science, 2011, 6630, 65-75. 16. fletcher, r. practical methods of optimization. wiley, new york, 1987. 17. al-baali, m. and khalfan, h. an overview of some practical quasi-newton methods for unconstrained optimization. squ journal for science, 2007, 12(2), 199-209. 18. al-baali, m. solving optimization problems on parallel computers. technical report dmcs 1/95, uae university, uae, 1995 19. ruszczynski, a.p. nonlinear optimization. princeton university press, new jersey, 2006 20. grama, a. and kumar, v. load balancing for parallel optimization techniques. encyclopedia of optimization, 2008, 1905-1911. 21. sinnen, o. task scheduling for parallel systems. wiley-interscience, new jersey, 2007 received 19 june 2014 accepted 7 september 2014 squ journal for science, 2020, 25(2), 124-129 doi:10.24200/squjs.vol25iss2pp124-129 sultan qaboos university 124 magneto-optical kerr microscopy for nanostructures with perpendicular magnetic anisotropy suleiman al-risi 1 , rachid sbiaa 1 *, hanan mohammed 2 and jurgen kosel 2 1 department of physics, college of science, sultan qaboos university, p.o. box 36, al-khod, pc 123, muscat, oman; 2 king abdullah university of science and technology, thuwal, 23955-6900, saudi arabia. *email: rachid@squ.edu.om. abstract: magneto-optical kerr effect (moke) microscopy is a powerful imaging technique that can be employed to study the magnetization reversal of thin films and nanoscale structures. in this work, we describe the moke microscopy which is used to observe nanomagnetic domain structures of co/pt multilayers (mls) and plot hysteresis loops. we were able to image sub-micrometer size magnetic domains and trace their evolution in a s time scale with a lateral spatial resolution down to 300 nm. the magnetization reversal for co/pt mls is described by the expansion of the domains in all directions as dendritic domain wall propagation. for a fixed applied magnetic field, the evolution with time of magnetic domains started from many centers, then expanded without the appearance of new nucleated centers. when the applied magnetic field was applied perpendicular to the film plane, a square hysteresis loop was observed indicating that the film exhibits a perpendicular magnetic anisotropy. for the same material, the magnetic field needed to nucleate magnetic domains in sub-micrometer size wire is much larger compared to the thin films. the magnetization decay becomes faster as the applied field is closer to the coercivity of the sample for the thin films mls. the domain wall (dw) could be manipulated and pinned in a precise location in a stepped nanowire of co/pt mls induced by a consistent magnetic field. keywords: magnetic domain; moke microscope; magnetization reversal; perpendicular anisotropy; hysteresis loop. ستخدام مجهر كيير المغناطيسي الضوئي لدراسة حركة وشكل النطاقات المغناطيسية النانومترية القياس في المواد ذات مغنطةإ عمودية المغناطيسية كوسل ورجنسليمان الريسي، رشيد سبيع، حنان محمد و ج ومترية يعتبر مجهر كيير المغناطيسي الضوئي جهاز بكفاءة عالية لدراسة تركيب وحركة النطاقات المغناطيسة بكل القياسات النانومترية أو الميكر :صلخمال م منحنى ( ورسco/ni)12لعينات المواد المغناطيسية ، في هذه الدراسة تم صنع وبناء هذا المجهر لدراسة نوع وشكل النطاقات المغناطيسية لمادة . nm 300 المغناطيسية لها ، حيث تم تصوير حركة تغير المغناطيسية للمادة بتعريضها لمجال مغناطيسي يتزايد أو ثابت مع الوقت بدقة قياس تصل إلى ستمرار تعرضها للمجال أوضحت الدراسة أن المغنطة المغناطيسية لهذه المادة تبدأ بتشكل نطاقات نقطيه في أماكن مختلفة ، ثم تنمو بشكل عشوائي با أن المادة المغناطيسي، وتأخذ في نموها شكل مشابه لنمو جذور الشجرة حيث تكون متشابكه وتنتشر في كل االتجاهات. منحنى المغنطه المغناطيسية أوضح مغناطيسي أكبر لظهور النطاق هذه الدراسه كشفت أن السلك الميكرومتري يحتاج لمجال تمتلك اتجاه مغناطيسي عمودي على اتجاه سطح المادة. فيتي للماده كان المغناطيسي عن العينه ذات السطح األكبر مساحه لنفس الماده، وأيضا كلما كان المجال المغناطيسي المعرض للماده قريبا من قيمة الكوريس تري للمادة، وتم التحكم في توقيفه أو حركته باستخدام عدة وأخيرا تم دراسة حركة جدارالنطاق المغناطيسي للسلك النانومتغير المغنطه المغناطيسية سريعا، درجات عمودية على السلك وتعريضه لمجال مغناطيسي والذي يمكن استخدامه مستقبال في شرائح الذاكرة. مجهر كيير، النطاقات المغناطيسية، منحنى المغناطيسية، المغناطيسية العمودية. :مفتاحيةالكلمات ال magneto-optical kerr microscopy 125 1. introduction maging and modeling magnetic microand nanostructures are highly desirable due to the large number of applications in many areas. most of the techniques used for analyzing lateral magnetic nanostructures are powerful and highly advanced, and may have special requirements for sample conditions and thus have limitations. the tools available for imaging magnetic domains are lorentz microscopy, magnetic force microscopy (mfm), x-ray photoelectron emission microscopy (peem), magnetic transmission x-ray microscopy (mtxm) and kerr microscopy to quote only few of them. on the other hand, for sample characterization and signal detection/measurements, a superconducting quantum interference device (squid), the hall effect, the bragg-magneto-optic kerr effect, and polarized neutron reflectivity (pnr) are commonly used [1-2]. some of these have limitations and are not compatible with the study of magnetic response or reversal of magnetization. for instance, the magnetic force microscopy (mfm) is a high spatial resolution technique to image magnetic nanostructures. however, its main drawbacks are the slow scan speed, the existence of undesirable tip-sample interaction and limitation to the strength of the applied magnetic field as the magnetic tip could be affected by the same applied field. magneto-optical kerr effect (moke) microscopy is an efficient technique to get detailed and direct insight into the magnetic switching mechanism, as it combines fast measurements, flexibility, high-sensitivity and non-destruction of the sample [1], [3-5]. an additional advantage of this technique is mapping the evolution of the magnetization configuration at any magnetic field or electric current. hence the idea of building and developing it locally has attracted considerable interest [6]. its resolution could be enhanced using a short wavelength, oil immersion objective lens and high-resolution camera. magnetic materials based on co/pt multilayers (mls) with perpendicular magnetic anisotropy (pma) are promising candidates for ultrahigh density perpendicular recording [7-15] and magnetic random access memory [1416] due to their thermal stability in nano-scale devices. it is also easy to adjust these materials intrinsic properties. the coercivity hc, magnetic anisotropy ku, and domain size could be tuned either by varying the bilayer repetitions number n or the thicknesses of the sublayers. submicron sized magnetic domains in thin films and nanowires may play an important role in advanced magnetic storage schemes and thus, their dynamic magnetic properties are being studied experimentally and theoretically. for instance, the magnetic anisotropy, exchange stiffness and the saturation magnetization have an essential effect in defining the nature and stability of domain structure. for magnetic memory applications, as high storage densities are required, it is essential to have the capability to study small magnetic domains and have an insight into their dynamical behavior. in the present article, a high-resolution moke microscope devoted to studying the magnetization reversal induced by a magnetic field and magnetic properties for co/pt mls thin films is described. the unique performances of our set up will be illustrated and demonstrated by studying the domain motion of co/pt thin film and nanowire. then, and for the same material, we show the possibility of moving and pinning dw by a magnetic field for a stepped wire, which could open an avenue for high magnetic memory. 2. experimental the samples were deposited by direct current (dc)-sputtering in a high vacuum chamber on a thermally oxidized silicon (sio2) substrate. the multilayers consisted of [co (0.3 nm)/pt(0.8 nm)]. the seed layer was made of ta (5 nm) and pt (3nm) and the capping layer made of 3 nm pt followed by 5 nm ta to prevent oxidation. twelve bilayers (co/pt) were included. the magnetic measurements were carried out using the magneto-optic kerr effect microscope at room temperature and indicated that the sample had an easy perpendicular axis. the micro-sized wires were fabricated by electron-beam lithography (ebl) and direct-write laser (dwl) lithography with a width of 1 µm. the wire was patterned to be a stepped device with six nano-constrictions created by an off-set in x and y directions as described previously [15]. the wires were connected to a nucleation pad at one end (figure 4 (a-b)). figure 1 displays a schematic diagram of the moke microscope set up. the uniform red light is emitted by a high-intensity light-emitting diode led (670 nm, 700 mw). the output from the led is collimated and passes through an aperture to modulate the size of the light spot. the light is then linearly polarized by a polarizer and passes through a beam splitter to be focused on the objective lens by using a convex lens (f =12 cm). the light interacts and is reflected by the metallic surface to be captured again by the objective lens and then passes through the beam splitter. the beam splitter directs the light through an analyzer to be collected towards a charge-coupled-device (ccd) camera (if the imaging function is required) by a convex lens. the sample is placed on a holder attached to a high precision mounting stage that enables shifting the sample with a precision of 0.1 µm. a red laser could replace the led if hysteresis loop plotting is required and the light passes in the same path as described above. in the latter case, an optical chopper and a photodiode instead of the ccd camera are used. in the present polar geometry, the set-up is equipped with an electromagnet under the sample, which is controlled by a bipolar power supply and provides a magnetic field of up to 300 mt with typical increment steps of 0.001 mt. the ccd camera, the lock-amplifier and the power supply are controlled by computer. this configuration allows us to induce the magnetic field whether in-plane or in a perpendicular direction to the sample surface. mechanical stability and elimination of vibration are accomplished by using a vibration-free optical table. the polarizer and analyzer are aligned almost perpendicular to each other. i s. al-risi et al 126 figure 1. a schematic drawing of the moke microscope set up. this configuration yields to a very weak light intensity, hence the 12-bit and highly sensitive charge coupled device (ccd) camera was used. the direct domain observation was possible for thin film materials without applying any image process technique. 3. results and discussion magnetization reversal versus external magnetic field (m-h) curves of co/pt were measured and magnetic domains were imaged by moke microscopy at room temperature. figure 2 shows the m-h curves for the film under in-plane and out-of-plane magnetic fields. when the applied field is in the out-of-plane direction, a clear square hysteresis loop can be observed. on the other an almost s-like shape of the magnetization versus the applied field is revealed for the in-plane applied field case. these two curves indicate that the material exhibits a perpendicular magnetic anisotropy. the magnetization reversal takes place by domain nucleation at a few sites, and is followed by a fast domain wall motion, as shown in figure 2(a) from the hysteresis loop and inset kerr images. from the out-ofplane m-h curve, the value of the coercive field and the saturation magnetization extracted from magnetometry measurements are hc = 41 mt and ms = 491 emu/cm 3 , respectively. the perpendicular anisotropy ku = 2.73×10 6 erg/cm 3 for the film was calculated from m-h loops out-of-plane and in-plane using eq. (1). 𝐾𝑢 = ∫ 𝜇𝑜 𝐻𝑖𝑛 𝑑𝑀 − ∫ 𝜇𝑜 𝐻𝑜𝑢𝑡 𝑑𝑀 𝑀𝑠 0 𝑀𝑠 0 (1) where 𝐻𝑖𝑛 and 𝐻𝑜𝑢𝑡 are the in-plane and the out-of-plane magnetic fields, respectively, and 𝜇𝑜 is the permeability constant in a vacuum. the domains’ evolution under an applied magnetic field perpendicular-to-plane with different strengths and their time dependence under a constant magnetic field was performed at room temperature by moke microscopy using high magnification lenses and the images were recorded by a high-resolution camera with a speed of 65 frames/s. the sample was first fully saturated by a large perpendicular-to-plane magnetic field, then retained at the remanence state (no applied magnetic field) and followed by a reverse magnetic field. the selection of domain images is presented in figure 2(c) and figure 3(a), in which the bright and dark regions correspond to up and down magnetization states, respectively. it can be seen from figure 2(c) and figure 3(a) that the magnetization distribution is dominated by domain wall propagation as a dendritic structure starting from one small nucleation center, of less than one micrometer. both reversals, due to an incremented applied magnetic field or being time-dependent, look similar, i.e., the domain structures are irregular and the extension of the magnetic domain is along a preferred direction. moreover, the nucleation was observed in one center only when the lens magnification is more than 40x, which suggests that there are relatively few nucleation centers as described above. from one saturation state to the opposite saturation state, the reversed area was calculated (difference of contrasts). the magnetization decay from -ms to +ms was then measured as a function of time. this was repeated for several values of the applied magnetic field, giving relaxation times less than 300 s. as expected, by increasing the strength of the magneto-optical kerr microscopy 127 applied magnetic field, the magnetization reversal is much faster, but no new nucleation centers were observed figure 3(b). the change in the magnetization due to the rapid domain wall motion is linked to the quality of interfaces between co and pt sub-layers and the partial spin-polarization of non-magnetic pt. this behavior is similar to that observed previously in the pt(3.4 nm)/co(1.5 nm)/pt(6.5 nm) [10]. figure 2. (a) hysteresis loops of (co/pt)12 mls in the out-of-plane direction. the 300 µm × 300 µm using × 4 objective lens moke images (insert) of the magnetic domains’ nucleation were taken in the beginning of the evolution (b) hysteresis loops of (co/pt)12 mls in the plane to the surface of the film. (c) moke images of magnetic domains’ evolution with the magnetic field using × 40 objective lens; the field was increased in steps of 0.01 mt/s. figure 3. time-dependent magnetization (a) moke images of 10 µm × 11 µm captured after applying a magnetic field of 33 mt. (b) reversed area of the magnetic domains versus time curves plotted after the application of various reverse magnetic fields. in the second part of the study, we used the home-built moke microscope to image dw position in a stepped wire. the wire was made of the same material as discussed in the first part of this study figure 4. the constricted (stepped) area is very effective in pinning dw in precise positions as reported theoretically [14] and experimentally for both in-plane and perpendicular anisotropic materials [15-16]. the wire, made of (co/pt)×12, was patterned in 50 µm length and 1 µm width. along the wire, six nano-constrictions with off-set in x and y directions, represented by  and d, were created, as can be seen in figure 4(b), (c). the dw motion could not be observed in the wire under the application of a magnetic field until the wire was annealed at 300 °c for 30 minutes. the annealing process reduces the magnetic anisotropic energy for the wire which leads to a low magnetic field, as required to move the domain wall. the wire was first saturated at 100 mt in the direction perpendicular to the wire plane then a reversal field in continuous steps of 1 mt was applied in the opposite direction. as described in figure 4(d), it was possible to stabilize the dw at each step by a magnetic field in the stepped wire with d = 600 nm and  = 0 nm. the positions of dw in the wire were s. al-risi et al 128 captured using the moke microscopy described in figure 1 and the images presented in figure 4(c) were obtained by subtracting the actual image from a saturated one (no magnetic domain). to study the movement of dw in the wire by the magnetic field, we started by first applying -60 mt in the out-of-plane direction, which corresponds to the nucleation of magnetic domains in the pad. it is important to note that the nucleation magnetic field for the thin film was 28.4 mt figure 2(c), which is much smaller than within the pad in the wire. the dw could be moved to the first step by applying -65 mt. the strong pinning field of dw in the first step requires an applied field of -76 mt to de-pin it toward the second step. consequently, the positioning of dw to the third, the fourth and the fifth steps was achieved by applying magnetic fields of -84, -88 and -90 mt, respectively. finally, an applied field of -96 mt was needed to align all the domains in one direction (saturation). again, it was more than double that required for saturation in the case of the thin film. this way of controlling dw in the nano-wire could be used for multiple-bit-per-cell memory, as shown in figure 4(c). in this example, the device shows eight different states based on nano-constrictions. figure 4. (a) illustration of the staggered region with the x and y off-sets represented by = 0 and d = 600 nm, respectively. (b) the design of a staggered micro-wire with multi-steps is proposed to control the position of dw. the length and width of wire were fixed at 50 µm and 1 µm, respectively. (c) moke images of a fabricated device with six pinning regions. the polar moke images of different magnetic states at different applied perpendicular magnetic fields. the device was first saturated using a perpendicular magnetic field of 100 mt, then a reversed field was applied in the opposite direction to move the dw from one step to another. 4. conclusion we have demonstrated the magneto-optical kerr effect method for visualization of magnetic domain dynamics in thin films and nanowire of (co/pt) multilayers with 12 repeats. this method was used to image and plot the magnetization reversal process with polar geometry. this study shows that, as the sample size is reduced, there is a need for a higher magnetic field to nucleate magnetic domains and saturate the magnetization of the sample. from moke images, the magnetization reversal in (co/pt)×12 multilayers is initiated by small domains randomly distributed in all directions and evolves with time or magnetic field. we have studied the domain-wall motion using moke microscopy for a stepped nanowire. it is possible to move and block the domain-wall at a precise position within the (co/pt)×12 nanowire for a certain period of time. conflict of interest the authors declare no conflict of interest. acknowledgment the authors thank sultan qaboos university for the financial support under grant number ig/sci/phys/18/04. the authors would like to thank s. al harthi and m.t. zar myint from sultan qaboos university for their support and assistance in the magnetometry measurements. magneto-optical kerr microscopy 129 references 1. westphalen, a., lee, m.s., remhof, a., and zabel, h., review of scientific instruments, 2007, 78, 121301. 2. fischer, p., and young, m., ieee photonics journal, 2010, 2, 260. 3. cormier, m., fert, j., mougin, a., cromìres, j.p., and klein., v., review of scientific instruments, 2008, 79, 033706. 4. nikulina, e., idigoras, o., vavassori, p., chuvilin, a., and berger, a., applied physics letters, 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s.n., physical review applied, 2019, 11, 024023. 14. al bahri, m., and sbiaa., r., scientific reports, 2016, 6, 28590. 15. sbiaa, r., and al bahri., m., journal of magnetism and magnetic materials, 2016, 411, 113-115. 16. mohammed, h., al risi, s., jin, t.l., kosel, j., piramanayagam, s.n., and sbiaa., r., applied physics letters, 2020, 116, 032402. received 2 march 2020 accepted 27 july 2020 squ journal for science, 2020, 25(1),48-53 doi:10.24200/squjs.vol25iss1pp48-53 sultan qaboos university 48 mössbauer study of weathered h-meteorite from the desert of oman ahmed d. al-rawas 1,5,* , abbasher m. gismelseed 1 , subhi nasir 2 , ali a. yousif 1 , mohamed e. elzain 1 , hisham widatallah 1 , ali al-kathiri 3 , susan al-riyami 4 1 department of physics, college of science, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman; 2 department of earth sciences, college of science, squ box 36, pc 123, sultanate of oman; 3 directorate general of commerce and industry, ministry of commerce and industry, salalah, oman; 4 the research council, p.o. box 92, muscat 123, sultanate of oman; 5 present address: dhofar university, p.o box 2509, pc 211, salalah, sultanate of oman. *email: arawas@squ.edu.om. abstract: a number of meteorites from the desert of oman, classified as h-chondrites, with known and unknown ages, were studied by using 57 fe mössbauer spectroscopy to determine their fe 3+ -bearing compositions. mössbauer spectra measured at 78 k were composed of paramagnetic doublets superimposed on magnetic sextets. the doublets are assigned to the silicate minerals olivine and pyroxene and fe 3+ phases. the magnetic sextets in most samples showed the presence of at least three magnetic phases, namely troilite, magnetite and kamacite, which commonly exist in most ordinary chondrites. the relative amounts (area %) of fe 3+ in the known-age meteorites, determined from the mössbauer spectra, were plotted against their terrestrial ages. the plot was used to estimate the terrestrial ages of meteorites with unknown terrestrial age. keywords: oman meteorites; mössbauer spectroscopy; terrestrial age; meteorites weathering. في صحراء عمان عليهاذات تجوية تم العثور hكوندريتية دراسة موسباور لنيازك صبحي ناصر، علي يوسف، محمد الزين، هشام وداعة هللا، علي الكثيري و سوسن الرياميأبشر قسم السيد، أحمد الرواس، والتي عثر عليها في صحراء عمان باستخدام مطياف ذات األعمار المعلومة وغير المعلومة hتمت دراسة عدد من النيازك المصنفة كوندريتية :صلخمال كلفن تتكون من ثنائيات منطبقة على سداسيات 57أطياف موسباور المقاسة عند درجة حرارة .fe+ 3( لتحديد التركيبات الحاملة ل fe 75موسباور ) معظم العينات وجود ثالث + . وأظهرت السداسيات المغناطيسية فيfe 3تعيين الثنائيات على أنها سيليكات األوليفين و البيروكسين و أحد مغناطيسية. تم معظم الصخور الكوندريتة العادية إضافة لسداسيات المغنتيت الناتجة من مكونات مغناطيسية على األقل ، وهي التروليت ، الكاماسيت والتي توجد عادة في األرضية. تم النيازك معلومة العمر ، والتي تم تحديدها من أطياف موسباور ، ضد أعمارها+ في fe 3)المساحة٪( من التجوية. تم تحديد الكميات النسبية .استخدام المنحنى لتقدير األعمار األرضية للنيازك . العمر ،مطياف موسباور، العمانية :مفتاحيةالكلمات ال 1. introduction n recent years, oman has become one of the world centers of meteorite discovery. the omani meteorite recovery areas are mainly restricted to the flat carbonate plains and therefore meteorites have had a chance to accumulate over prolonged periods of time. the terrestrial ages of omani meteorites range from less than 1000 years to more than 50,000 years [1]. the majority of finds are ordinary chondrites (oc) [2]. the ordinary chondrites are divided into three groups, which have different amounts of metal and different amounts of total iron. the groups are named h (high iron), l (low iron), and ll (very low iron), with reference to the meteorite’s oxidation state and the amount of total iron they contain [3]. iron-bearing minerals (kamacite (fe-ni), troilite (fes), olivine (fe, mg)2sio4 and pyroxene (fe,mg)sio3) are important constituents of meteorites and can give important information about their type and origin and are important i mössbauer study of weathered h-meteorite 49 indicators of the environmental change of the local area since the date of impact. mössbauer spectroscopy has played an important role in the study and identification of these mineral phases through their mössbauer parameters derived from the best computer fit [4-6]. due to its sensitivity to fe 3+ and fe 2+ ions, mössbauer spectroscopy has been particularly useful to study weathering patterns of meteorites [7, 8]. weathering bearing concentrations have been used to estimate the terrestrial age of l-chondrite from arid australian deserts [9], and reveals an initial rapid weathering followed by much slower oxidation. the origin of magnetite is usually due to the length of time a meteorite has spent on the earth’s surface. a detailed study of the weathering of ordinary chondrites in oman [1] demonstrated the correlation of weathering parameters with terrestrial age. mineral analysis, classification and age determination of dho787, dho802 and uah02 were carried out by the swiss-omani team at bern university, switzerland [1, 10]. mineral analyses for dho1670 and dho1895 were carried out at stuttgart university using the wavelength-dispersive system of a cameca sx100 electron microprobe. x-ray analysis was carried at sultan qaboos university [11, 12] (table 1). table 1. data information of classification, petrographic weathering grades and carbon terrestrial ages of the studied meteorites. name classification weathering grade age (kyrs) dho787 h4 w4 19.6 dho802 h6 w2 17.8 uah2 h3 w1 9.4 dho1670 h4 w3 unknown dho1895 h5 w2 unknown in this paper, we aim to find the degree of weathering by using mössbauer spectroscopy on ordinary hchondrites found in the desert of oman. the fe-weathering products formed were used to estimate the unknown terrestrial ages of dho1670 and dho1895 meteorites. 2. experimental samples of five meteorites were prepared for mössbauer analysis in such a way that the fusion crust and the inner core were well mixed. mössbauer spectra were taken at 78 k for all five samples employing transmission geometry using a 50 mci, 57 co/rh source at sultan qaboos university. a spectrometer interfaced to a pc was used for collecting the data. the data were fitted by selecting the positions and intensities of the lorentzian lines; all other parameters were kept fixed. the center shifts of the doublets were then fitted assuming no coupling to the splitting. finally, the width of the lorentzian components was fitted. all parameters were allowed to vary during the final fits. isomer shifts (is) are referred to α-fe at 300 k. 3. petrography the studied meteorites consist of 50-60 vol% chondrules, 20-30 vol% matrix, and 5-10 vol% metals/opaque minerals. chondrules display porphyritic olivine or pyroxene, barred olivine and cryptocrystalline texture. the chondrule mineralogy is mainly olivine and orthopyroxene; however, the cryptocrystalline chondrules contain inclusions of pigeonite, augite, and metal. the matrix is recrystallized, transparent, and some grain sizes are visible. the diameter of the chondrules range between 0.7-0.8 mm. cracks, or veins, with altered material occur throughout the whole thin sections. many of the silicate grains have acquired a reddish, yellowish colour. small cracks go through both chondrules and individual grains. only a few olivine grains appear to show undulose extinction. some chondrules have a thin rim while others have a thick rim. the weathering has not influenced the silicates to any significant degree. heavy oxidation of metals and sulfides, abundant fe-oxide veinlets, and dominant rusty-staining of the specimens indicate moderate weathering (w2 to w3). the sample contains abundant irregular and planar fractures, a few undulatory extinction, opaque shock veins and some weakly mosaic olivine, indicating shock stage s3 to s4. 4. results and discussion the mössbauer spectra collected from the five meteorite samples viz. dho787, dho802, uah02, dho1670 and dho1895, at 78 k are presented in figure 1. all spectra depict the existence of central doublets flanked by magnetic sextets. the best fits to all mössbauer spectra were obtained using three doublets and several magnetic components. a summary of the mössbauer hyperfine parameters of the different spectral components and the minerals assigned to them are given in table 2. al-rawas, a.d. et al 50 figure 1. mössbauer spectra of ordinary chondrites dho787, dho802, uah02, dho1670 and dho1895 measured at 78 k. the mössbauer parameters of the central doublets are consistent with those reported in the literature for olivine pyroxene and superparamagnetic ultrafine particles containing fe 3+ with blocking temperature below 78 k [4-10]. accordingly, the isomer shifts in the range of 1.26-1.29 mm/s and the quadrupole splitting of the first doublet in the range of 3.11-3.16 mm/s are attributed to olivine [9]. the isomer shifts and quadrupole splittings of the second doublet in the ranges of 1.23-1.29 mm/s and 2.13-2.20 mm/s, respectively, are consistent with those reported for pyroxene [9]. the third doublet with isomer shifts and quadrupole splittings in the ranges of 0.40-0.76 mm/s and 0.945 0.960 0.975 0.990 1.005 r el at iv e t ra ns m is si on uah 002 0.954 0.965 0.975 0.986 0.996 dho 1670 0.973 0.980 0.988 0.995 dho-787 -10 -5 0 5 10 0.973 0.978 0.984 0.990 0.996 velocity (mm/s) dho 1895 0.987 0.990 0.993 0.996 0.999 dho 802 mössbauer study of weathered h-meteorite 51 0.40-0.86 mm/s, respectively, are consistent with those reported for superparamagnetic particles such as αfeooh(goethite) β-feooh (akaganite) γ-feooh (lapidocrocite) [13]. the spectral area percentages show variations spanning between 18-32 % for olivine, 10-15 % for pyroxene and 3-9 % for ultrafine particles containing fe 3+ . table 2. the mössbauer parameters for dho787, dho802, uah02, dho1670 and dho1895 measured at 78 k.  (±0.05) qs (±0.01) b (±1) a (±1) mms -1 mms -1 (t) (%) name components dho787 [1] 1.28 3.16 23 olivine 1.26 2.13 14 pyroxene 0.53 0.63 02 fe 3+ 0.44 -0.06 48 14 -feooh 0.51 -0.06 53 16 -fe2o3 0.53 -0.11 50 20 magnetite (b) 0.37 0.03 52 11 magnetite (a) dho802 [1] 1.26 3.16 22 olivine 1.24 2.13 12 pyroxene 0.80 -0.10 29.9 03 troilite 0.18 -0.10 32.7 05 kamacite 0.76 0.86 05 fe 3+ 0.46 -0.15 49.0 32 -feooh 0.44 -0.08 52.3 21 -fe2o3 uah002 [10] 1.29 3.11 29 olivine 1.29 2.14 15 pyroxene 0.95 0.02 31.8 09 troilite 0.18 0.00 33.3 07 kamacite 0.45 0.69 05 fe 3+ 0.50 -0.04 50.6 16 -feooh 0.52 0.04 52.7 07 -fe2o3 0.68 -0.04 46.8 08 magnetite (b) 0.34 0.04 48.2 04 magnetite (a) dho1670 [11] 1.26 3.13 32 olivine 1.23 2.19 12 pyroxene 0.78 -0.07 33.4 06 troilite 0.03 -0.10 34.5 05 kamacite 0.50 0.47 08 fe 3+ 0.48 -0.07 49.4 15 -feooh 0.46 -0.02 52.3 10 -fe2o3 0.52 -0.09 46.5 11 maghemite dho1895 [12] 1.26 3.15 18 olivine 1.26 2.13 11 pyroxene 0.49 0.65 06 fe 3+ 0.43 -0.02 52 16 -fe2o3 0.57 -0.13 47 33 magnetite [b] 0.36 -0.11 49 16 magnetite (a) the parameters are: : the isomer shift, qs: the quadrupole splitting, b: the magnetic field and a: area percentage on the other hand, the magnetic components of the spectra (table 1) have hyperfine parameters comparable to those reported for troilite, kamacite and weathering products magnetite, maghemite, -feooh, and -fe2o3 [7-10]. the magnetic spectral components of the dho802, uah02, dho1670 meteorites show the existence of iron sulfide (troilite fes) and iron nickel (kamacite feni) phases whose isomer shifts and quadrupole splitting are in good al-rawas, a.d. et al 52 agreement with corresponding literature values [5-10]. the troilite is identified by its hyperfine field and its large isomer shift of ~ 0.8 mm/s while kamacite is distinguished by its isomer shift of ~ -0.1 mm/s. the percent ranges of the troilite and kamacite in the different meteorites’ compositions were (3-9%) and (5-7%) respectively. the nonexistence of these two minerals in the dho787 and dho1895 meteorites could indicate high terrestrial weathering. as seen from the percentages of the weathering products (table 2), there exists a good correlation with the weathering grades determined by petrographic and probe analysis given in table 1 for all samples except that of dho1895. this particular sample shows a high weathering component (73%) which is not consistent with w2 grade of weathering. the reason could be associated with the sample preparation methods used in the two techniques. while in petrographic analysis only the inner core is probed, for the mössbauer measurements both the crust and core were mixed. so the dho1895 apparently has a higher weathering product on the surface relative to the other samples. the terresterial age of dho787, dho802, uah02 (table 1) was plotted against the fe 3+ percentages in the weathering products determined from the fits of the mössbauer spectra (table 2) assuming there was no fe 3+ (due to weathering) at the time of the impact on earth. the plotted graph shows an almost linear correlation. the fitting curve was used to estimate the terresterial ages of dho1670 and dho1895 that correspond to their fe 3+ percentages. these were found to be 11 ± 2 kyr and 23 ± 2 kyr, respectively. the almost linear variation of the fe 3+ percentage with terrestrial age (figure 2) found for these h-chondrites reflects an almost constant weathering rate. this is to be contrasted with that of l-chondrite [9] where the weathering at the initial stages is faster than later ones. further studies are required to elucidate this point. conclusion mössbauer spectroscopy was used to determine the weathering products of ordinary h-chondrites from the desert of oman. the terrestrial weathering products were identified. the terrestrial ages of dho1670 and dho1895 were estimated using figure 2 by considering the fe 3+ area percentages determined from the mössbauer spectra of dho787, dho802 and uah02, whose ages are known. the ages of dho1670 and dho1895 were found to be 11±2 kyr and 23±2 kyr respectively. the rather linear variation of fe 3+ spectral area with terrestrial age (figure 2) relative to that of an l-chondrite [9] reveals their weathering at the initial stages following their fall to the earth. h-chondrites have higher total fe concentrations and amounts of metals, which make them more susceptible to faster alteration following their fall. figure 2. terrestrial age of dho787, dho802, uah02 against the total percentage area of fe 3+ weathering products. conflict of interest the authors declare no conflict of interest. acknowledgment many thanks are due to drs. beda a. hofmann and edwin gnos, swiss-omani joint project for meteorite research in oman, for providing dho787 and dho802 samples. a.d. al-rawas thanks the college of arts and applied sciences at dhofar university for hosting him for a sabbatical year (september 2018-august 2019) during which the draft of this paper was prepared for publication. 0 5 10 15 20 25 0 10 20 30 40 50 60 70 p e rc e n ta g e a re a o f f e 3 + terrestrial age (kyr) mössbauer study of weathered h-meteorite 53 references 1. al-kathiri, a., hofmann, b.a., jull, a.j.t., and gnos, e., meteoritics and planetary science, 2005, 40, 1215. 2. norton, o.r., 2002: the cambridge encyclopedia of meteorites. cambridge university press uk. 352pp. 3. al-kathiri, a., studies on oman meteorites, phd thesis, university of bern (2006). 4. knudsen, j.m., hyperfine interactions, 1989, 47, 3-31. 5. rubin, a.e., meteoritics and planetary science. 1997, 32, 231-247. 6. gismelseed, a.m., bashir, s., worthing, m.a., yousif, a.a., elzain, m.e., al rawas, a.d., meteoritics and planetary science, 2005, 40, 255-259. 7. bland, p.a., sexton, a.s., jull, a.j.t., bevan, a.w.r., berry, f.j., thornley, d.m., astin, t.r., britt, d.t., and pillinger, c.t., geochimica et cosmochimica acta,1998, 62, 3169-3184. 8. bland, p.a., berry, f.j., jull, a.j.t., smith, t.b., bevan, a.w.r., cadogan, j.m., sexton, a.s., franchi, l.a., and pillinger, c.t., hyperfine interactions, 2002, 142, 481-494. 9. cadogan, j.m., rebbouh, l., mills, j.v.j. and bland, p.a. devlin ej, hyperfine interactions, 222, (suppl 2):s91s98, 2013. 10. al-rawas, a.d., gismelseed, a.m., yousif, a.a., elzain, m.e., worthing, m.a., al-kathiri, a., gnos, e., hofmann, b.a., and steele, d.a., planetary and space science, 2007, 55, 859-863. 11. meteoritical bulletin, no. 101, maps 50, 1661, september (2015). 12. meteoritical bulletin, no. 103, maps 52, 1014, may (2017). 13. buchwald, v.f. and clarke, r.s., american mineralogist, 1989, 74, 657-667. received 17 april 2019 accepted 30 october 2019 microsoft word chem140405-checked english5june.doc squ journal for science, 2014, 19(1), 54-63 © 2014 sultan qaboos university 54 a terbium sensitized luminescence method for the assay of flubiprofen in pharmaceutical formulations salma m.z. al-kindy*, arwa al-ghazali, fakhr eldin o. suliman and haidar a.j. al-lawati department of chemistry, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: alkindy@squ.edu.om. abstract: a sensitive time-resolved luminescence method for the determination of flubiprofen (flp) in methanol and in aqueous solution is described. the method is based on the luminescence sensitization of terbium (tb3+) by the formation of a ternary complex with flp in the presence of 4,7diphenyl1,10phenanthroline (dpp) as co-ligand, and tween-20 as surfactant. the signal for tb-flp-dpp was monitored at λex = 285 nm and λem = 552 nm. optimum conditions for the formation of the complex in an aqueous system were tris buffer, ph 8.0, dpp (2.5×10−7 m), tween-20 (0.30%) and 4×10-5 mol l-1 of tb3+ which allowed the determination of 20–1000 ng ml-1 of flp with a limit of detection (lod) of 10 ng ml-1. the relative standard deviations of the method ranged between 0.6 and 1.4% indicating excellent reproducibility of the method. the proposed method was successfully applied for the assays of flp in pharmaceutical formulations and spiked tap water samples with average recoveries of 87% – 95%. keywords: flurbiprofen; terbium; sensitized luminescence; drug formulation. التحلیل الكمي لفلوبیبروفین في المركبات الصیدالنیة باستخدام تحسیس ضیائیة سلمى الكندي، أروى الغزالي، فخر الدین سلیمان وحیدر اللواتي لطریقة على في المیثانول والمحالیل المائیة، وتعتمد ا (flp)تم وصف طریقة حساسة قائمة على التحلیل الزمني للضیائیة لتحدید الفلوبیبروفین :ملخص diphenyl 1,10phenanthroline -7 ,4بوجود مادة (flp)وذلك عن طریقة تكوین معقد ثالثي مع (+tb3)تحسیس ضیائیة ایون التربیوم (dpp) كمجموعة مرتبطات مرافقة ومادةtween-20 ولقد تم رصد مؤشر الضیائیة للمعقد . كمادة فاعلة سطحیاtbflp-dpp ة ثارإعن طریق كمحلول منظم tris: وكانت الظروف المثالیة لتكوین المعقد في المحلول المائي كما یلي. نانومتر 552نبعاث عند إنانومتر طول موجي و 285المعقد عند من (flp)موالریة ، حیث سمحت ھذه الظروف بتحدید تركیز tb3+ 4×10-5و %) 0.30( tween-20، )موالریة (ph 8 ،dpp 2.5×10−7عند ن الطریقة ألى إمما یشیر % 1.4لى إ 0.6نحراف المعیاري النسبي یتراوح بین وكان اإل. جزء بالبلیون كحد ادنى للكشف 10جزء بالبلیون مع 20-1000 حیث وجد أن نسب (flp)المضاف الیھا الشربفي التركیبات الصیدالنیة ومیاه (flp)وقد تم تطبیق الطریقة بنجاح تام لتحدید كمیة . تتمیز بدقة عالیة % . 95الى % 87ستعادة تتراوح بین اإل .ةالمركبات الصیدالنیوایون التربیوم فلوبیبروفین، التربیوم، تحسیس الضیائیة :مفتاح الكلمات 1. introduction lubiprofen (flp) [(±)-2-(2-fluoro-4-biphenylyl) propionic acid]) is a non-steroidal anti-inflammatory drug (nsaid), effectively used in the treatment of rheumatoid arthritis. it belongs to the profen derivatives, a class of phenyl propanoic acids that has anti-inflammatory effects in addition to antipyretic and analgesic activity. the antiinflammatory effect of flp is assigned to the inhibition of cox (cyclooxygenase) and, in particular, cox-2 activity that is known to block the conversion of arachidonic acid to prostaglandin, which is an indication of inflammation [1]. there is evidence that numerous nsaids, including flp, may help to reduce the severity of alzheimer's disease (ad). the beneficial effect is attributed to the reduction of the inflammation response of the ad brain which minimizes brain lesion and protects brain cells against damage, thus resulting in an improved memory and cognitive function [2]. f a terbium sensitized luminescence method 55 flp demonstrates comparable efficacy to other nsaids such as aspirin, ibuprofen, and naproxen in the treatment of rheumatoid arthritis. on the other hand, however, nsaids have some side effects; they may cause an increased risk of serious cardiovascular thrombotic events, myocardial infarction, stroke and serious gastrointestinal adverse events including bleeding, ulceration, and perforation of the stomach or intestines which can be fatal [3]. simple, accurate, precise and robust analytical techniques that could be applied directly and easily to pharmaceutical preparations are necessary, especially with the continuous production of new drugs every year and the increasing use of these drugs. several analytical techniques have been developed for the determination of flp; these include spectrophotometry [4], high performance liquid chromatography (hplc) [5,6], gas chromatography-mass spectrometry (gc-ms) [7] and capillary electrophoresis [8]. trace analysis requires the design of a method with high selectivity and sensitivity. a flourimetric method with very low detection limits and selectivity would be a suitable technique for trace analysis. fluorescence has two wavelengths (the excitation and emission wavelength); so the two wavelengths can be controlled to increase the degree of selectivity. however, some of the drugs are only weakly fluorescent in nature, the fluorimetric method is not of use in detecting them. on the other hand, the profen family has a carboxylic group which is known to form complexes with many metal ions that can form fluorescent products when linked to fluorogenic ligands. the use of lanthanide sensitization by chelate formation is one such approach which can be employed to determine the concentration of the organic ligand. the efficient intermolecular energy transfer process in a solution from the excited triplet state of the ligand to the emitting level of the lanthanide ion gives the lanthanide chelates unique luminescence properties, which are manifested in a narrow banded emission line that has a long decay life-time. the sensitizing ligand is referred to as sensitizing chromophere or "antenna". the decay time ranges between nanoseconds to milliseconds, with terbium and europium having the longest decay time. terbium-sensitized luminescence has been applied for the determination of benzoic acid and several derivatives such as anthranilic acid [9], salicylic acid [10], terephthalic acid [11], 1,4-diamino benzoic acid [12] and profen derivatives [13,14]. the efficiency of the energy transfer depends on several factors, these being the nature of the ion, the ligand type, the ligand-ion bond, the solvent, the rigidity of the molecular structure and the difference between the excited and the ground state levels [15]. in this study we report a method for the assay of flp in pharmaceutical formulation. the method is based on the luminescence enhancement and sensitization of terbium ions upon complexation with flp. the photosensitization was first carried out in organic solvents, and the effect of the type of solvent on the sensitization was thoroughly investigated. the effect of the concentration of metal to ligand and the stochiometry of the complex was also determined in the optimum solvent. furthermore, we studied the luminescence of a the flp-tb system in aqueous media. in order to apply the method developed in an aqueous medium, factors affecting sensitization such as ph, surfactant type and concentration, the ligand type and concentration, and different common interferences were investigated. using the optimized conditions established, a method was then designed and employed to determine the amounts of flp in pharmaceutical samples. 2. experimental 2.1 reagents flubiprofen (flp) was obtained from sigma (st. louis, mo, usa). methanol hplc grade was obtained from sigma-aldrich (germany). terbium(iii) chloride hexahydrate, 4,7-diphenyl-1,10-phenanthroline (97%) (dpp), trioctylphosphine oxide (topo), ethylenediaminetetraacetic acid (edta), 1,10-phenanthroline and tris(hydroxymethyl) methylamine (tris) were obtained from aldrich (germany). tween-20 was obtained from kanto chemical co, inc. (tokyo, japan). calcium chloride, sodium chloride, magnesium chloride, zinc chloride, ferric chloride, potassium chloride and urea were obtained from bdh chemicals ltd (pool, england). flp tablets (50 mg) were collected from the market; all other reagents and solvents were used without further purification. ultra pure water (milli-q, corporation) was used for the preparation of reagents. 2.2 apparatus luminescence measurements were performed using a perkin elmer ls-55 luminescence spectrometer (perkin elmer, beaconsfield, uk) equipped with a xenon discharge flash lamp. the operation and data processing were controlled by the fluorescence flwinlab software. the excitation and emission wavelengths were set at 250 nm and salma al-kindy et al 56 549 nm respectively (in the methanol system) and 285 nm and 552 nm respectively (in the aqueous system). a gate time of 1.00 ms and a delay time of 0.04 ms were used throughout. absorption spectra were recorded on a varian cary 50 conc uv visible spectrophotometer (connecticut, usa) with 1 cm matched quartz cell. measurement of ph was made with a wtw 320 ph meter (germany) using a combined electrode. 2.3 preparation of standard solutions flp stock solution (1.00×10-2 mol l-1) was prepared by dissolving 24.4 mg of flp in 10.00 ml of methanol. a working standard solution (1.00×10-3 mol l-1) was freshly prepared daily by appropriate dilution of the stock with deionized water. terbium(iii) chloride hexahydrate stock solution (0.010 mol l-1) was prepared by dissolving 37.3 mg of tb3+ in 10.00 ml of distilled water. working solutions were freshly prepared by appropriate dilution with distilled water. tris buffer solution (0.10 mol l-1) was prepared by dissolving 6.055 g of tris in 500 ml distilled water and the ph was adjusted by adding hydrochloric acid to the value of 8.00. stock solutions of various surfactants were prepared by dissolving 1.00 g each of the surfactant in 100 ml deionized water in a volumetric flask. the surfactants used in this study included tween-20, tween-80, triton x-100, sodium dodecylbenzene sulfonate (sdbs) and sodium dodecyl sulphate (sds). dpp, topo, edta and phenanthroline of concentration 1.0×10-2 mol l-1 were prepared by dissolving 33.2 mg, 38.6 mg, 29.2 mg and 18.0 mg of the reagents respectively in 10 ml methanol, and working solutions were freshly prepared by appropriate dilution with distilled water. a 1000 µg ml-1 of the cation of each solution of sodium chloride, calcium chloride, magnesium chloride hexahydrate, zinc chloride, iron chloride, potassium chloride and urea was prepared in a 25 ml volumetric flask. 2.4 preparation of drug samples the pharmaceutical sample was prepared by weighing flp tablets (50 mg). eight tablets were separately weighed and ground homogeneously. a portion of the powder equivalent to one tablet was accurately weighed and then sonicated with methanol for 30 min, filtered into a volumetric flask and completed to the mark with methanol to make a stock solution. a working solution of 500 µg ml-1 was prepared in methanol in a 100 ml volumetric flask. appropriate aliquots from the working solution were taken for the determination of flp in samples. 2.5 preparation of water samples tap water samples were filtered and spiked with convenient amounts of flp standard solution. the final flp concentration was in the range of 200-1000 ng ml-1. 2.6 procedure aliquots of the working solution were pipetted into 10 ml calibrated flasks. 1.0 ml of tb3+, 1 ml of dpp solution and 0.3 ml of tween-20 solution were added. the solution was diluted to the mark with 0. 10 m tris solution. the ph of the tris solution was adjusted to 8. the flp concentration range was 0-1000 ng ml-1. the luminescence was measured at 552 nm, using an excitation wavelength of 285 nm. the concentration of flp in the sample was determined from a calibration curve prepared under identical conditions. 3. results and discussion 3.1 spectral characteristics the uv-visible absorption spectra of the flp and tb complex were measured in methanol and are shown in figure 1. the absorption spectra of the flp and flp-tb complex exhibited absorption in the region 210 – 280 nm. however, a slight increase in the absorptivity was observed for the complex when compared to the ligand alone, especially at longer wavelengths accompanied by a slight blue shift of the wavelength of maximum absorbance indicating complex formation. the fluorescence emission of the flp solution (1  10-6 mol l-1) in methanol was measured. a moderate fluorescence signal was observed for flp at λem 350 nm when excited at 251 nm. the fluorescence signal in the shorter wavelength region has a limited analytical usefulness as it may be subjected to the interference from the matrix especially for the determination of the drug in biological samples. a terbium sensitized luminescence method 57 figure 1. absorption spectrum of flp and flp-tb3+ complex in methanol. [flp] = [tb3+] = 1×10-5 m. in order to obtain better analytical characteristics for the determination of flp in pharmaceutical formulations, the system of flp-tb in methanol was investigated where flp was used to sensitize the luminescence of the terbium ion as shown in figure 2. a weak time resolved signal was observed for the tb3+; the ligand on the other hand exhibited no native time resolved emission. however, on adding flp to tb3+, the well known structured emission spectrum of tb3+ was obtained (figure 2). figure 2. luminescence emission spectra of: (1) tb3+ in methanol. (2) tb3+-flp in methanol [tb3+]= 1×10-5 m, λem= 549 nm, λex= 251 nm. the fluorescence enhancement of the tb3+ ion in the presence of flp and the shift in the wavelength suggests complex formation between the drug and the terbium ions. similar shifts have been reported previously for the complexation of tb3+ with other arylpropanoic acid derivatives [13,14]. the luminescence enhancement of the tb3+ ion upon complexation with flp is attributed to the efficient transfer of excitation energy from the flp moiety to the encapsulated tb3+ ion which can overcome the low ion extinction coefficient. for the sensitization process to be successful, the sensitizing moiety should be excited in the near ultraviolet region since the triplet energy state should have sufficient energy to provide efficient energy transfer to the ion. this excitation is well satisfied by the flp-tb complex which exhibits absorption at 251 nm in methanol. it has been reported that the longest excited wavelength of tb3+ is at 341 nm [16]. the luminescence emission spectrum of the flp-tb complex when excited by the π-π* absorption band at 251 nm revealed the well-known bands of terbium, based on the 5d4-7f6 (490 nm), 5d4-7f5 (550 nm), 5d4-7f4 (590 nm) and 5d4-7f3 (620 nm) and they can be seen as peaks in figure 2. the most intense peak is at a wavelength of 550 nm which indicates the 5d4-7f5 transition, so it is more convenient to base the study on this peak. although this emission band overlaps the second order scatter from the excitation wavelength, the use of time resolved mode eliminates the scattering effect as these systems have a large salma al-kindy et al 58 luminescence life time. furthermore, a stoke shift > 250 nm was observed indicating that there is no overlap between the tb3+ emission band with the antenna chromophore absorption band. the close resemblance of absorption spectrum of flp (245 nm) and the excitation spectrum of the flp-tb (251 nm) indicates that the excitation of the antenna chromophore may be the only photophysical pathway leading to the observable luminescence in the system [17]. the hypersensitive emission line of tb3+ at 551 nm requires the optimization of different factors that affect the coordination environment. 3.2 complex stoichiometry the optimal molar ratio of flp:tb3+ was determined by measuring the luminescence intensity of various mol ratios of flp:tb3+. the ratio of metal to ligand that will give a maximum complex was determined by using two different methods, the molar ratio method and the mole fraction method (job's plot). in the molar ratio method, the concentration of flp was maintained constant at 1×10-5 mol l-1 while the concentrations of tb3+ were varied, ranging from 0.5×10-5 to 9×10-5 mol l-1. the luminescence intensity increased with an increase in the concentration of tb3+ till it reached a stable value. upon extrapolating the linear part of the curve it intersects at a ratio of 4:1, which suggests a stoichiometry of 4:1. therefore the concentration of terbium was maintained at a four fold excess of flp. the stochiometry of the complex was confirmed further by using job's plot of continuous variation as demonstrated in figure 3. the experimental results also indicated that the maximum fluorescence intensity was obtained at a mole fraction of 4:1. figure 3. job's plot of continuous variation for complexation of tb3+ with flp, λex= 265 nm, λem = 550 nm. the stiochiometric study was repeated many times to confirm the flp:tb ratio since 1:4 is an unusual result, where the common ratio of terbium-sensitized luminescence that had been reported in the literature for the determination of benzoic acid and several derivatives is 3: 1 [12,13,14]. this unusual behavior may be due to the presence of a halogen atom (f) in flp which probably binds to the extra tb atoms. 3.3 effect of solvent since the type of solvent used influences the luminescence intensity of the molecule, an investigation was made to study the effect of solvent on the luminescence intensity of the tb-flp complex. the results of the effect of solvent on the luminescence emission of the complex are shown in figure 4. while investigating a series of alcohols, the maximum enhancement was observed in methanol, which has the highest dielectric constant (ɛo of 32.6), and the minimum intensity was observed in the presence of butanol (ɛo = 17.1) accompanied by a slight blue shift in the emission wavelength from 557 nm to 550 nm. these results indicate that the solvent polarity affects the luminescent intensity of the complex. similar results were previously reported by dang et al.[18], qin et al.[19] and al-kindy et al. [14] for terbium and europium complexes, where maximum sensitization was observed in methanol. this behavior is explained by the higher coordination between methanol and terbium [18]. furthermore it has been reported that as the alkyl chain in the alcohol increases, the emission intensity decreases [20]. on the other hand, low sensitization was observed in water, this being due to the effect of quenching of the excited state of the lanthanide ions by interaction with high energy vibration associated with o-h bonds. solvent molecules usually replace coordinated water and avoid high frequency of o-h bond vibration, thus greatly decreasing the energy loss by coordination of water molecules. this results in an increase in the emission of the lanthanide ion. a terbium sensitized luminescence method 59 figure 4. effect of type of solvent on terbium sensitized luminescence emission spectra, [tb3+] = 4×10-5 m [flp] = 1×10-5 m, λex = 250 nm, λem = 550 nm. other organic solvents such as acetonitrile, ethyl acetate and chloroform were also investigated. acetonitrile (ɛ = 37.5) showed extremely high sensitization where ethyl acetate (ɛ = 6.0) and chloroform (ɛ = 4.8) did not show any complexation; only the tb3+ peaks where observed and the reason can also be referred to the solvent polarity dielectric constants (ɛ) [18]. 3.4 study in aqueous system we extended this study further to include the determination of flp in biological samples; therefore we investigated the complexation behavior of flp-tb in an aqueous system. hence factors that affect complexation such as ph, concentration ratios of the ligand to metal, effect of surfactant and type of co-ligand were investigated. the luminescence of the tb-flp complex in an aqueous system revealed a band at 550 nm emission with an excitation at 285 nm. these results showed a red shift in both excitation and emission wavelength when compared to the spectra in methanol, where an excitation of 250 nm and emission of 549 nm were observed. the addition of a surfactant (tween 20) increased the luminescent intensity by the removal of the quenching effect of water, and a further enhancement was achieved when the co-ligand (dpp) was added (figure 5). figure 5. the effect of a co-ligand on the luminescence spectra of tb3+-flp system. [tb3+] =2.25 610 m, [flp] 1×10-5 m, [coligand ] = 1×10-5 m, [tw-20] =0.30% (1) tb3+ (2) tb3+ and flp (3) tb3+, flp and tw-20 and (4) tb3+, flp ,tw-20 and dpp, λex= 251 nm, λem= 549 nm. salma al-kindy et al 60 3.5 effect of ph the ph of the medium has a great effect on the existing form of the ligand and hence affects the complex formation. therefore, it is necessary to determine the ph of the system that will give maximum complex formation. the effect of ph on the luminescence properties of the flp-tb complex was studied by measuring the luminescence of the complex in buffers of various ph values from 2 to 10. an increase in the luminescence intensity was observed when the ph increased in the range 2 to 8.5 reaching a maximum at a ph of 8.0. on increasing the ph further, a decrease in the luminescence intensity was observed. this is a typical result, as dissociation of the carboxylic group is necessary for complexation to occur. it has been reported that the pka of flp is 4.2. at higher ph, the luminescence intensity decreased due to the competitive hydrolysis of terbium forming tb(oh)3 which is expected to predominate at a ph > 8.0. similar results were previously reported for the complex formation between benzoic acid and terbium [12] and ibuprofen and terbium [13]. 3.6 effect of surfactant surfactants are known to lower the surface tension of a liquid, allowing an easier spreading. furthermore, the addition of micelles (aggregate of surfactant molecules) allows the removal of the efficient quenching effect of water in an aqueous system by forming an aggregate with the hydrophilic "head" regions in contact with surrounding solvent. as a result, the possibility of the complexation is more rapid. in addition, micelles allow the removal of the efficient quenching effect of water in the aqueous system [11]. in a previous study, it was suggested that micelles provide a discrete volume region for inclusion of the lanthanide ion and the ligand so that an energy transfer process is possible [21]. a number of surfactants were used (tween-20, tween-80, triton x-100, (ctab), (sdbs), (sds). the concentration of surfactants was maintained at 0.1%, which is above the critical micelle concentration (c.m.c.) of all of the surfactants used. among these surfactants, tween 20 gave the highest intensity of the luminescence signal. since tween-20 gave the highest enhancement of the signal, its concentration was optimized to enhance the signal even further. the luminescence intensity was observed to increase with an increase in concentration of tween-20 from 0.1 to 0.3% and then to drop when the concentration of tween-20 was increased. the drop in the intensity may be explained as follows; as the concentration of tween-20 increases the number of micelles increases until it reaches the required to solublize the whole compound. after that, the excess amount of the surfactant causes a reduction in the rate of solubilization. therefore the concentration of tween-20 in this study was maintained at 0.3%. 3.7 effect of co-ligand one of the possible strategies to improve the luminescence properties of flp-tb chelates is the substitution of water molecules in the coordination sphere with synergetic agents. several co-ligands were investigated in this study, including topo, edta, 1,10-phenanthroline and dpp with a concentration of 1×10-5 mol l-1. the highest fluorescence sensitization was observed in the presence of dpp, the phenanthroline had the second highest intensity, and the lowest was observed in the presence of edta. since dpp is insoluble in water, it was dissolved using a surfactant. next, the optimum concentration of dpp was investigated by monitoring the luminescence intensity of the complex in various concentrations of dpp which varied from (0-5) ×10-7 mol l-1. the luminescence intensity of dpp increased between the range 0-2.5 ×10-7 m and it reached a maximum at 2.5×10-7 mol l-1. after the latter concentration, a decrease in the luminescence intensity was observed. dpp acts as a co-ligand to promote the formation of flp-tb complex by coordination to the terbium ion through the lone pair of its nitrogen atoms. dpp has the ability to remove water molecules from the coordination sphere. a high concentration of dpp results in competition between flp and dpp for tb3+ ions and hence will result in a greater enhancement of the terbium blank relative to the flp-tb complex. 3.8 concentration ratios of tb in aqueous system since luminescence intensity results through complex formation between terbium and flp, it is important to recheck the maximum concentration ratio of flp to terbium that forms the maximum complexation in an aqueous system as it was first studied only in methanol. the optimum concentration of tb(iii) was obtained by varying its concentration in the range 2×10-5 to 8×10-5 mol l-1 while maintaining the flp constant at 1×10-5 mol l-1 as shown in figure 6. from the figure it is obvious that the intensity increased with an increase in tb3+ concentration, reaching a maximum at 4×10-5 mol l-1, then a slight decrease in intensity was observed. this result suggests that an optimum concentration of tb3+ is required for maximum complexation. the decrease in the intensity that was observed when adding an excess amount of tb3+ is attributed to the decrease in the protective power of dpp, and the surfactant for flp singlet state against radiation a terbium sensitized luminescence method 61 brought about collision with free tb3+ ions. similar behavior was observed previously for ibuprofen complexation with terbium [13]. figure 6. influence of [tb3+] on sensitized luminescence. [flp] = 1×10-5 m, [tb] = 4× 10-5 m, [dpp] = 2.5×10-6 m, [tween-20] = 0.3%, [tris] = 0.1 m, ph = 8.0, λex = 285nm, λem = 552 nm. 3.9 effect of interference different kinds of species are commonly present in real samples; these species are known to interfere with the complex formation. the interference can affect positively where it enhances the signal or negatively where it inhibits the signal. the effect of interference by these species was studied with a constant concentration 0.4 µg ml-1 for flp as shown in table 1. from the table we can conclude that for most of the interfering species, the recovery percentage increases as the concentration of the substance interfering decreases. this is especially so in the case of ferric chloride, due to the paramagnetic character of the iron, which results in quenching the signal. on the other hand, the opposite occurs with zinc chloride and magnesium chloride. both have a positive interference effect where the recovery percent increases as the concentration of the interference species increases. in order to improve the recovery of the sample, ion exchange chromatography may be used to eliminate the interference effect. table 1. effect of interference on recovery of flp. interfering species recovery % ± r.s.d flp : interfering species nacl (100 g ml-1) 92.8 ± 0.3 1 : 40 kcl (100 g ml-1) 81.9± 0.2 1 : 40 zncl2 (50 g ml -1) 156.9 ± 0.1 1 : 5 mgcl2 (75 g ml-1) 113.9 ± 0.8 1 : 20 cacl2 (12.5 g ml-1) 78.9 ± 0.1 1 : 5 fecl3 (2.5 g ml-1) 19.2 ± 0.2 1 : 1 urea (150 g ml-1) 92.3 ± 0.2 1 : 60 3.10 analytical figures of merit the luminescence intensity (i) versus flp concentration (c) was found to be linear for a specific range. two calibration curves were constructed, one in the organic medium (methanol) and the other in the aqueous medium. the calibration equation for the medium (methanol) was: i = 552.71c + 46.56, with a correlation coefficient r2 of 0.996 salma al-kindy et al 62 and for the aqueous medium it was: i = 36.51c – 0.35, with a correlation coefficient r2 of 0.998. the detection limit (signal to noise ratio of 3) was 10 ng ml-1, and the quantification limit was 33 ng ml-1 in aqueous media. this method offered an advantage over other luminescence methods, in that its emission is at a longer wavelength, free from interference from short-emitting species present in the matrices. the reproducibility of the method was obtained for standard solutions of flp and was found to be less than 2.0% (n = 7) showing excellent precision. 3.11 application the applicability of the method was then tested for the determination of the flp in aqueous media. analysis was made with pharmaceutical samples and spiked water samples. the results in table 2 show that reasonable recoveries were obtained. these results suggest that the method is applicable to the determination of the drug in pharmaceutical samples and in water. table 2. application of the proposed method to the assay of commercially available dosage forms and water samples. concentration of flp claimed flp concentration found % recovery  rsd 0.10 g ml-1 water sample 0.09 g ml-1 95.32 ± 1.40 0.30 g ml-1 0.50 g ml-1 flp genus 50 mg 0.26 g ml-1 0.46 g ml-1 49 mg 86.87 0.56 92.41 ± 0.62 98.0 ± 0.52 4. conclusion in this study it has been demonstrated that terbium-sensitized luminescence offers a simple, selective and sensitive procedure to determine flp in pharmaceutical formulation. the enhancement of the terbium luminescence upon complexation with flp has enabled the assay of this drug with high sensitivity and selectivity where short-lived emissions were efficiently eliminated. the method was applied to the assay of flp in tablets and in aqueous systems with high recovery and reproducibility. references 1. cipriano, m., björklund, e., wilson, a., congiu, c., onnis, v. and fowler, c.j. inhibition of fatty acid amide hydrolase and cyclooxygenase by the n-(3-methylp yridin-2-yl)amide derivatives of flubiprofen and naproxen. eur. j. 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free convection; magnetic field; stream function; vorticity. على الحمل الحراري الحر فً تجوٌف مستطٍل العمودي مغناطٍسًالمجال التأثٍر انانذ كومار واشوك سٍنج وباالث شانذران و نٍرمال ساشٍتً حدٕٚف ثُائٙ األبعاد ٔٔخٕد ٙحى دساست حذفق انحًم انحشاس٘ انحش انثابج بانُسبت نهًٕائع انهزخت غٛش انقابهت نهضغظ ٔقابهت نخٕصٛم انكٓشباء ف : ملخص: ، بًُٛا ٚفخشض أٌ اندذساٌ األفقٛت ُٕعحسخٍٛ اندذساٌ عًٕدٚت اندٕاَب نهخدٕٚف بشكم يخ. حى انعادٖ٘ انخدٕٚف حقم يغُاطٛسٙ حى حطبٛقّ عهٗ يسخٕ ٔحم انًعادالث انُاحدت بششٔط حذٚت عذدٚا باسخخذاو طشٚقت حٛاس. دانتعادة صٛاغت انًعادالث انخٙ ححكى ْزا انًُٕرج فٙ صٕسة دٔايت ٔإيعزٔنت. ٔحى adi ًُٛإنٗ رنك، فقذ باإلضافتخٛاس ٔعهٗ دسخت انحشاسة. شكال انًُحُٛاث نخٕضح حأثٛش عذد ْاسحًاٌ ٔعذد سٚهٛت عهٗ سشعت انأ. ٔعشض عذد يٍ تانض عُذ حطبٛق يدال يغُاطٛسٙ عهٗ طٕل ٔحى يقاسَخٓا يع َخائح يُشٕسة ٔانحذ األقصٗ انشايم نذانت اندشٚاٌ، انشقًَٙسهج انحصٕل عهٗ َخائح نًعذل حى حدٕٚف فٙ االحداِ األفقٙ. .تايخٛاس، انذٔانانحًم انحشاس٘ انحش، يدال يغُاطٛسٙ، حذفق فٙ خٕف، دانت :كلمات مفتاحٍة 1. introduction he theoretical and experimental studies of laminar free convective flows in channels and enclosures have a number of applications, for instance in the cooling of reactors and electronic equipment, crystal growth in liquids, storage systems and solar technology, etc. batchelor [1] initiated investigations on natural convection in an enclosure heated and cooled from side walls. he concluded that the flow is determined by three key dimensionless parameters, namely, the prandtl number, the rayleigh number and the aspect ratio of the cavity. following batchelor's work, a number of researchers carried out experimental and numerical investigations related to natural convection in vertical enclosures. eckert and carlson [2] and elder [3] experimentally studied natural convection in a rectangular cavity across which a temperature differential occurred. elder [4] subsequently obtained numerical solutions of steady free convective flow in a vertical slot and compared the numerical results with the experimental findings [2,3]. gill [5] presented approximate solutions of equations governing natural convection in a rectangular cavity for the case of large values of prandtl number. he found his results in satisfactory agreement with the experimental results of elder [3]. wilkes and churchill [6] and later de vahl davis [7] introduced a numerical computation model to discuss free convection in a rectangular cavity. kimura and bejan [8] discussed the free convective flow in a rectangular cavity assuming uniform t anand kumar et al 50 heat influx from one side of the cavity. in this work, the importance of heat flux wall thermal condition was highlighted and described in detail. numerical and theoretical investigations of the transient natural convection in a 2-dimensional rectangular enclosure were carried out by hall et al. [9]. these authors assumed one of the side walls to be heated suddenly while keeping the remaining three walls insulated. some other aspects of convection in electrically nonconducting fluids in vertical channels and enclosures-mixed convection, porous media flow, stability, anisotropy were discussed by straughan [10], hill and straughan [11], barletta et al. [12], oztop et al. [13], and tiwari et al. [14]. a detailed exposition of stability and nonlinear convection is also available in the research monograph of straughan [15]. in the above studies, the flow features in the cavities were reported in the absence of a magnetic field. flows of electrically conducting fluids subject to the influence of an externally applied magnetic field have been analyzed in the literature extensively due to their applications, for instance, in the manufacturing industry. this has led to a number of researchers carrying out investigations on the hydromagnetic free convective flows taking place inside rectangular enclosures or in vertical channels, albeit with some simplifying assumptions. oreper and szekely [16] carried out a numerical investigation for transient flow in a rectangular cavity in the presence of an imposed magnetic field and noted that the magnetic field suppresses the natural convection. garandet et al. [17] carried out an analytical study for hydromagnetic free convection in a rectangular cavity. rudraiah et al. [18] considered the effect of a transverse magnetic field while assuming the vertical walls of the rectangular cavity to be isothermal and horizontal walls to be insulated. a similar study to that in [18] was reported by alchaar et al. [19]. kanafer and chamkha [20] investigated the effect of heat generation on hydromagnetic natural convection from an inclined porous square enclosure. pirmohammadi et al. [21] have dealt with the effect of an applied magnetic field on a buoyancy-driven flow in a differentially heated square cavity. these authors have obtained solutions of the flow problem for wide-ranging values of rayleigh and hartmann numbers assuming the applied magnetic field to be along the plane of the flow. the transient nature of such a flow has heen discussed by these authors in a subsequent work [22]. in order to analyse the effect of the inclination of a rectangular vertical cavity on the buoyancy driven flows of electrically conducting fluids in the presence of applied magnetic field, a number of researchers have carried out numerical studies [23-26]. another aspect of magneto-free convective flow in a partitioned enclosure has been dealt with by pirmohammadi and ghassani [27]. they have shown that the partition of an enclosure can cause the flow to separate and then form vortices inside the cavity. in a subsequent work, pirmohammadi et al. [28] have extended some of their previous works on hydromagnetic convection in a rectangular enclosure to include the temperature dependent variations of thermal conductivity, specific heat capacity, fluid viscosity and electrical conductivity. in the present work, we analyze the free convective flow of an electrically conducting fluid in a rectangular vertical cavity under the influence of a magnetic field applied normal to the plane of the cavity. it is worth mentioning here that in most of the experimental or theoretical two-dimensional natural convection studies involving a magnetic field, the magnetic field has been assumed to be applied in the plane of the flow-either perpendicular to or along the direction of gravity. thus, the flow configuration considered herein results in the magnetic coupling of the momentum equations, necessitating the consideration of both the horizontal and vertical components of the velocity. it is assumed that the magnetic reynolds number is small. the governing hydromagnetic equations, under boussinesq approximation, are solved numerically by using a computationally stable adi method. the effects of the transport parameters on the streamlines, isotherms, and also the velocity and temperature are analyzed. the results of the present study are compared with those of pirmohammadi et al. [21], and have enabled us to highlight the distinguishing effect of the direction of application of the magnetic field. the results reported here have particular relevance to applications involving control of convection. it may be mentioned here that in [21], the authors used a control-volume based finite volume method to solve the field equations directly. however, in our case, we have used a vorticity-stream function formulation of the governing equations which, in turn, has been solved using an appropriate adi method, as explained above. 2. mathematical formulation consider a steady free-convective flow of a viscous incompressible and electrically conducting fluid in a rectangular cavity of length l and width .h the ' x axis is taken along the lower horizontal wall and ' y axis transverse to it in the plane of the cavity, having origin at the lower end of the left wall as shown in figure 1. a constant magnetic field of magnitude 0 b is applied normal to the cavity in the ' z direction. as stated earlier, the flow is at small magnetic reynolds number so that the induced magnetic field can be neglected. the top and bottom walls of the cavity are thermally insulated while the vertical left and right walls are maintained at constant but different temperatures ' h t and , ' c t respectively. furthermore, the viscous and ohmic dissipation terms are assumed to be negligible. effect of perpendicular magnetic field on free convection 51 figure 1. physical configuration. under the boussinesq approximation, the governing equations continuity, momentum and energy in dimensional form, can be written as = 0, ' ' ' ' u v x y      (1) 2 2 01= , ' ' ' ' ' ' ' ' ' ' bu u p u v u u x y x                (2) 2 2 01= ( ) , ' ' ' ' ' ' ' ' ' c' ' ' bv v p u v v g t t v x y y                   (3) 2 = , ' ' ' ' ' ' ' t t u v t x y        (4) where ' u and ' v are the velocity components in the ' x and ' y directions, respectively, ' p the pressure, 't the temperature,  the kinematic viscosity,  the thermal diffusivity,  the electrical conductivity and  is the coefficient of volumetric expansion. for the flow model considered, the boundary conditions for the velocity and temperature fields are given by = = 0 for 0 , 0 , ' ' ' ' u v x l y h = at = 0, = at = , ' ' ' ' ' ' h c t t x t t x l (5) = 0 at = 0 and = . ' ' ' ' t y y h y   in order to recast the momentum equations (2) and (3) in terms of vorticity '  and stream function , '  we introduce = , ( , ) = , . ' ' ' ' ' ' ' ' ' ' ' v u u v x y y x                 (6) introducing the nondimensional variables 2 ( , ) = ( , ) / , ( , ) = ( , ) / , = / , ' ' ' ' ' x y x y l u v u v l l    = / , = ( ) / ( ), ' ' ' ' ' c h c t t t t t     (7) the quantities in (6) take the dimensionless forms = , ( , ) = , v u u v x y y x                 (8) while (2)-(4) can be expressed as 2 2 = pr ra pr ha pr , t u v x y x               (9) anand kumar et al 52 2 = , t t u v t x y       (10) 2 = .   (11) in (9)-(11), we have introduced a number of well-known nondimensional parameters, namely, the rayleigh number (ra), prandtl number (pr) and hartmann number (ha). these are defined as 3 ra = ( ) / ( ), pr = / , ' ' h c g t t l    2 2 2 0 ha = / ( ).b l  (12) in view of (7), the set of boundary conditions (5) can be shown to transform to = 0 on = 0, 1; = 0, = arx y y (13) 2 2 on = 0 and = 1x x x      (14) 2 2 on = 0 and = ary y y      (15) = 1 on = 0 and = 1t x x x (16) = 0 on = 0 and = ar t y y y   (17) where the aspect ratio ar is defined as ar = / .h l 3. numerical procedure the transport equations (9)-(11) are highly nonlinear, and their solutions, subject to the boundary conditions (13)-(17), are obtained numerically. to facilitate this, the partial differential equations are first transformed into the parabolic form by adding false transient terms [29]. the solutions of the transformed equations are obtained by employing a uniform grid discretization and then solving the resulting finite difference equations by a well-known alternating direction implicit (adi) method [30]. finally, the system of linear algebraic equations, expressed tridiagonally, has been solved. in the computational procedure, we have taken the square grid, 101 101 , in order to obtain accurate results. in each iteration process, firstly the temperature field is obtained by using the values of the temperature and velocity components obtained in the previous iteration. these values are then used to compute the vorticity and the stream function, respectively. finally, the velocity components are obtained by using the newly obtained values of the stream function. the solution procedure from the initial state is iterated until a quasi-steady state is approached by satisfying the convergence criterion 1 , , 6 1 , , < 10 . n n i j i j n i j i j        (18) in the above expression  may stand for the temperature, vorticity or stream function. the superscripts denote the values of the dependent variables after the n th and ( 1)n  th iterations, respectively, whereas the subscripts i and j indicate grid location in the xy-plane. in order to validate the accuracy of our computational procedure, we have compared our results in the absence of a magnetic field with the corresponding results reported by pirmohammadi et al. [21], and found good agreement. in engineering applications, one of the important characteristics of the flow is the rate of heat transfer across the cavity, and this is estimated by computing the values of the nusselt number, nu. the local nusselt number on the left wall of the cavity is defined by = nu = x t x         0 (19) the overall heat transfer rate across the cavity, expressed by the average nusselt number at the left vertical wall, is a av 0 nu nu d r y (20) 4. results and discussion in this section, we present numerical results for two-dimensional hydromagnetic natural convection in an electrically conducting fluid inside a cavity caused by differentially heated vertical walls in the presence of a magnetic field applied normal to the plane of the cavity. it may be observed that the dimensionless equations which govern the behavior of the considered model contain four physical parameters, namely ra, ha, pr and ar. the presence of all four physical parameters in a model makes the computation and the subsequent analysis a tedious job. as we are effect of perpendicular magnetic field on free convection 53 mainly interested in examining the effects of the magnetic field and buoyancy force on the convective flow, we have carried out computations for the rayleigh number ra ranging from 4 10 to 6 10 and the hartmann number ha from 0 to 100, for specific values of the prandtl number pr = 0.733 and aspect ratio ar = 1. figure 2. streamlines and isotherms. 4 r = 10a , ha = 0, 10, 50, 100 (a-d). figure 2 shows the effect of an applied magnetic field on the streamlines and isotherms as ha increases from 0 to 100, with ra fixed at 4 10 . in the absence of the applied magnetic field [figure 2a], the flow shows a typical circulating pattern with the centre of circulation being in the middle of the cavity. the isotherms, particularly in the central portion, i.e., away from the boundaries, exhibit appreciable effects of the convection currents. however, with a moderate increase in the magnitude of the magnetic field [figure 2b], the streamlines begin to distort from their circular shape tending to be slightly elliptic. however, the plots of streamlines and isotherms in figure 2 seem to suggest that at this chosen level of buoyancy (ra =10 4 ) , isotherms are more affected in comparison to streamlines as we transit from a weak magnetic field domain to a relatively stronger magnetic field zone. in particular, at ha = 50 or 100, the flow is dominated by conduction, as clearly evidenced from the isotherms being almost parallel to the vertical walls. in other words, the temperature stratification, apparently visible in the case of a weak magnetic field, is no longer there, having been significantly suppressed by the applied magnetic field corresponding to higher values of ha. this last observation is broadly similar to those reported by rudraiah et al. [18] and pirmohammadi et al. [21] although these studies considered the applied magnetic field to be along the cavity, parallel and transverse to the direction of gravity, respectively. however, the typical feature related to the elongation of the innermost streamline and leading to the formation of two secondary loops (see [18] and [21]), at higher values of ha, is not observed in our work. apparently, this difference can be attributed to the direction of the applied magnetic field being normal to the plane of the cavity in our present work as opposed to the field being along the cavity, as stated above. anand kumar et al 54 figure 3. streamlines and isotherms. 6 r = 10a , ha = 0, 10, 50, 100 (a-d). the contours of isotherms and streamlines, for a relatively high rayleigh number (ra = 10 6 ), are shown for the same set of values of ha in figure 3. for a weak magnetic field, the presence of thermal boundary layers along the vertical side walls is quite conspicuous. furthermore, there is thermal stratification in the vertical direction indicating the predominance of convection currents in the heat transfer process. as regards streamlines, the circular pattern observed earlier for 4 ra = 10 is quite distorted [see figure 3a or 3b]. also, there is a strong upward or downward flow near the isothermal walls. for high values of ha (50 or 100), the streamlines appear to gradually head towards circulating pattern through elongated ellipses (see figure 3c or 3d]. interestingly, the temperature stratification, referred to earlier for the weak magnetic field case, seems to lose its intensity in the central core region of the cavity along with the disappearance of thermal boundary layers near the side vertical walls. effect of perpendicular magnetic field on free convection 55 figure 4. velocity profiles u at = 0.5x (ra = 10 4 ). figure 5. velocity profiles u at = 0.5x (ra = 10 6 ). figure 6. velocity profiles v at = 0.5x (ra = 10 4 ). anand kumar et al 56 figure 7. velocity profiles v at = 0.5x (ra = 10 6 ). since the magnetic field is applied normal to the plane of the cavity, we need to discuss the variation of both components of velocity, u and .v in figures 4 and 5, we show how the xcomponent of velocity, u , changes with the vertical coordinate y at the cross-section = 0.5,x for 4 ra = 10 and 6 10 , respectively. these sketches show that u is oscillatory in nature, with values peaking near the lower and upper adiabatic walls. the seemingly suppressive effect of the applied magnetic field on this component is quite visible for 4 ra = 10 (figure 4). however, for larger values of ra (10 6 ), we notice a mixed response of the magnetic field. in order to assess the combined effect of buoyancy and the magnetic forces on the velocity, we show profiles of the ycomponent of velocity v . the curves are shown at a vertical cross-section = 0.5x for 4 ra = 10 (figure 6) and 6 ra = 10 (figure 7). as observed in a similar study [18], the effect of the increase of magnetic field is to suppress the magnitude of the velocity. as buoyancy force increases from 4 ra = 10 to 6 ra = 10 , we observe that there is an appreciable variation in the velocity near the adiabatic walls. however, in the central region, the fluid is nearly stagnated for the higher rayleigh number. from the profiles of u and v , we notice that the magnitude of the vertical component of the velocity is relatively much more influenced by the magnetic field of the type considered here normal to the plane of the cavity. furthermore, the flow suppression due to the magnetic field, usually observed in hydromagnetic convective studies, is clearly visible in the velocity component .v this, in turn, shows that the convective heat transfer is reduced in the region away from the adiabatic boundaries. the non-dimensional temperature profiles at the vertical cross-section = 0.5x are shown in figure 8 for the same set of values of ra and ha, as above. interestingly, at higher values of the hartmann number (ha = 50 or 100), the temperature varies rather linearly with y when 4 ra = 10 , although showing little variation with the magnetic field. however, for a weak magnetic field, the temperature profiles oscillate about this linear profile, showing opposite behaviour before and after the mid-point = 0.5.y as the buoyancy force becomes larger (ra = 10 6 ), we observe broadly similar features, although in this case the effects of a weak as well as a strong magnetic field are quite clearly manifested. effect of perpendicular magnetic field on free convection 57 figure 8. temperature profiles t at = 0.5x for 4 r = 10a and 6 r = 10 .a in figure 9, we show the effect of the applied magnetic field on the local nusselt number nu. the curves are selfexplanatory. in particular, we note that when the rayleigh number is low and the hartmann number high, nu is nearly constant. figure 9. local nusselt number at 0x  for 4 r = 10a and 5r = 10 .a in table 1, we show the computed values of two parameters of practical importance in applications the average nusselt number on the heated wall, a n , v u and the maximum absolute value of the stream function, m | | ax  for a range of values of the rayleigh and the hartmann numbers. the practical utility of m | | ax  stems from the fact that it quantifies the intensity of the natural convection in the flow domain. we see from the tabulated values that for a fixed ha, the effect of increase in ra is to increase a n v u as well as m | | ax  . on the other hand, when ra is fixed, m | | ax  and a n v u decrease with ha. moreover, for relatively small values of ra, 4 510 r 10 ,a  a n 1 v u  with increasing ha. anand kumar et al 58 table 1. numerical values of m | | ax  and a n v u . present work previous work [21] ra ha m | | ax  a n v u m | | ax  a n v u 4 10 0 5.0552 2.2879 5.05 2.29 10 2.9159 1.7091 3.35 1.97 50 0.2696 1.0105 0.47 1.06 100 0.0707 1.0008 0.12 1.02 5 10 0 9.6884 4.5761 9.75 4.62 10 8.1514 4.1950 – – 50 2.2038 1.5975 – – 100 0.6901 1.0710 1.14 1.37 6 10 0 16.961 8.9214 17.0 8.90 10 16.318 8.7685 – – 50 9.0776 5.6404 10.51 6.39 100 4.4136 2.8784 – – this indicates that the heat transfer at high hartmann number is dominated by conduction which further implies, inter alia, the absence of convection currents in the cavity. on the other hand, for larger values of buoyancy force and weak magnetic field, m | | ax  attains high values showing the dominance of heat transfer by the convection mode. finally, in order to assess the effect of the nature of application of the magnetic field normal to the plane of the cavity vis-à-vis along the plane of the cavity we have compared our results with that of pirmohammadi et al. [21]. the broader conclusions drawn above in our analysis are qualitatively very similar to those reported in [21]. as regards the comparative effect due to different modes of application of the magnetic field, we observe that for given ra and ha, the values of m | | ax  and a n v u are lower in our work as compared to the corresponding values in [21]. this important result of our study shows that the suppression of natural convection in the cavity is enhanced when the magnetic field is applied perpendicular to the cavity in contrast to when it is applied along the cavity in the horizontal direction. 5. acknowledgment a. k. is thankful to the council of scientific and industrial research, new delhi, india for financial assistance in the form of a senior research fellowship. references 1. batchelor, g.k. heat transfer by free-convection across a closed cavity between vertical boundaries at different temperature. quart. j. appl. math, 1954, 12, 209–233. 2. eckert, e.r.g. and carlson, 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(2) (2012) 200-213 © 2012 sultan qaboos university 200 weakly orthogonal spherical harmonics in non-polar spherical coordinates and its application to functions on cubed-sphere m.a.a.m. faham * and h.m. nasir ** * department of mathematics, south eastern university, sri lanka, email: faham75@yahoo.com ** department of mathematics, university of peradeniya, sri lanka, email: nasirh@pdn.ac.lk abstract: in a recent paper a set of weakly orthogonal and completely orthogonal spherical harmonics in a non-polar spherical coordinate system based on a cubed-sphere was constructed. in this work, we explore some linear relations between these two sets of spherical harmonics. moreover, a power representation for the set of weakly orthogonal spherical harmonics corresponding to a mode is presented. we also determine the norm of the orthogonal spherical harmonics and hence the inner products for the weakly orthogonal spherical harmonics. as an immediate application of these properties, we present a fourier series formulation of spherical functions defined on the cubedsphere. keywords: non-polar spherical coordinate system, cubed sphere, spherical harmonics. كروي مكعب فً على دوال وتطبٍقاتها قطبٍةغٍر التىافقٍات الكروٌة ضعٍفة التعامد فً إحداثٍات كروٌة حنيفة ناصرو محمد فهم ٌةًضعٌفةًالتعامدًوأخرىًكاملةًالتعامدًفًًإحداثٌاتًكروٌةًغٌرًقطبٌة.مجموعةًمنًالتوافقٌاتًالكروتكوٌنًًحدٌثا ً تم :خصمل نستكشفًفًًهذاًالعملًبعضًالعالقاتًالخطٌةًبٌنًهاتٌنًالمجموعتٌنًمنًالتوافقٌاتًالكروٌة.ًإضافةًإلىًذلك،ًفقدًتمًعرضًمتمٌزً حددًنظٌمًالتوافقٌاتًالكروٌةًالمتعامدةًوبالتالًًلمجموعةًمنًالتوافقٌاتًالكروٌةًضعٌفةًالتعامدًمتوافقةًمعًنموذجًالعرض.ًكذلكًن الضربًالداخلًًللتوافقٌاتًضعٌفةًالتعامد.ًكتطبٌقًفوريًلهذهًالخواص،ًنناقشًصٌغةًمتسلسالتًفورٌهًلدوالًكروٌةًمعرفةًعلىً .مكعبًكروي 1. introduction umerical computations on the sphere in solving problems defined on the sphere suffer from many difficulties near the poles with a spherical polar coordinate system for the spherical surface. for example, in the computations of global weather prediction models, concentrated grid points near the poles increase the amount of computations in the pole region where quantities of interest are of less importance than in other parts n weakly orthogonal spherical harmonics 201 of the globe (nasir, 2007), non-smoothness and unbounded derivatives of bounded functions on the sphere at the poles (gomez et al., 1997; phillips, 1957; reisswig et al., 2007; rockmore et al., 2003) and unbounded entries in the matrices of finite element approximations (swartzrauber, 1979,1981) are some example problems faced near the poles. these are collectively called the ‘pole problems’. searching for remedies for pole problems have attracted some researches in the recent past (archibald et al., 2011; chen and xiao, 2008; gomez et al., 1997; nasir, 2007; nasir and kako, 2001; nasir et al., 2003; rockmore at al., 2003; ronchi et al., 1996; swartzrauber, 1979,1981). one of the developments in this direction is to define a grid mesh on the sphere that does not contain polar concentrated points. among these the ‘cubedsphere’ defined from the surface of a unit cube has been used by some authors for approximating weather prediction models by finite difference and finite element methods (phillips, 1957; reisswig et al., 2007; ronchi et al., 1996). for some latest papers in this direction, see for example archibald et al. (2011), chen and xiao (2008) and lauritzen et al. (2010). in a recent paper nasir (2007), one of the present authors has defined a non-polar coordinate system based on the cubed-sphere concept and constructed sets of weakly orthogonal and completely orthogonal spherical harmonic functions. these spherical harmonics can be used as basis functions for representing functions defined on the cubed-sphere by fourier series expansion. in the fourier series expansion, one encounters the evaluation of inner products of these basis functions. in nasir (2007), numerical quadrature was used to approximately compute these inner products. in this paper, we establish more properties and results for the weakly orthogonal and completely orthogonal spherical harmonics. we use these properties to obtain explicit formulas for inner products of the completely orthogonal and hence weakly orthogonal spherical harmonics on the cubed-sphere. the rest of the paper is organized as follows: section 2 recalls the results in nasir (2007) and establishes some notations and conventions for the spherical harmonics. section 3 presents a power representation for the weakly orthogonal spherical harmonics. section 4 determines the inner product for the orthogonal spherical harmonics. section 5 establishes some linear relations between the weakly orthogonal and orthogonal spherical harmonics. section 6 gives a fourier series form using the weakly orthogonal spherical harmonics and finally, section 7 draws a conclusion. figure 1. mapping from the cube surface to spherical surface. 2. preliminaries and notations in this section, we briefly list the main results presented in nasir (2007). let c be the surface of the cube 3 [ 1, 1] in the xyz coordinate system. the surface c of the cube with its six faces of the cube are denoted by the six-tuple ( , , , , , ),c x y z x y z       where, for example, x  denotes the face across the positive xaxis.  x  z  y  x  y  z   d c 2 s m.a.a.m. faham and h.m. nasir 202 each face of the cube is assigned a two-dimensional local coordinate system. the cube is then transformed to the unit sphere 2 s by a mapping (figure 1). this divides the surface of the unit sphere into six 'faces', each of which corresponds to a face on the cube. the cubed-spherical coordinate system for the three dimensional space is defined as a six-tuple of the local coordinate systems for the cube faces and is given by 1 2 1 2( , , ) ( ( , )),r t t r t t   where  is the mapping from the domain d of two-dimensional faces to the cube and is given by 1 2 1 2 1 2 2 1 1 2 1 2 2 1 1 2( , ) {(1, , ), ( ,1, ), ( , ,1), ( 1, , ), ( , 1, ), ( , , 1)} , 1 , 1 ,t t t t t t t t t t t t t t t t           r is the standard radial coordinate and  is the transformation mapping from the cube to the sphere. the coordinate signs are chosen according the orientation of the local coordinate systems as shown in figure 2. each triplet in the six-tuple is defined on the six faces of the cubed-sphere by ( ) / , .c  p p p p the function  maps each face on c to a corresponding surface on the sphere 2 .s for convenience, where there is no ambiguity, these mapped faces on the sphere are also denoted by 2 ( , , , , , ).s x y z x y z       for a detailed discussion on the construction of the cubed-spherical coordinate system, we refer to nasir (2007). figure 2. orientation of local coordinate parameters. a spherical function defined on the unit 2-sphere 2 s is described in the cubed-spherical coordinates as a six-tuple of functions defined for each face with respect to its local coordinates 1 2 1 2 1 2 1 2 1 2 1 2 1 2( , ) : ( ( , ), ( , ), ( , ), ( , ), ( , ), ( , )) .x y z x y zf t t f t t f t t f t t f t t f t t f t t      (1) the laplace-beltrami operator on the unit 2-sphere is given by 2 2 2 2 2 1 1 2 2 1 22 2 1 2 1 21 2 (1 ) 2 (1 ) 2 2s ts t t t t t t t t t tt t                       for all faces of 2 ,s where 2 2 1 21 .ts t t   the eigenvalue problem for spherical harmonics is given by ( 1)s u l l u    (2) where l is an integer. 2.1 spherical harmonics a set of linearly independent solutions for the eigenvalue problem (2) is given by ( , ) ( , ) /2 , 1, m n m n l l l t p y m n l l s     (3) where ( , ) 1 2( , ) m n l p t t are polynomials satisfying the differential equation weakly orthogonal spherical harmonics 203 2 2 2 2 2 1 1 2 2 1 22 2 1 2 1 21 2 (1 ) 2 (1 ) ( 1) 2 2 0 . p p p p p t t t t l t t lp t t t tt t                        (4) the polynomials ( , )m n l p are explicitly given by the non-zero real or imaginary parts of ( , ) ( ) 1 2 2 2 1 2 1 1 ( ) / 2 ( , ) i , 1, , ( ) / 2 , m n m n p q l p q l p m q n m p n q l p t t t t m n l l m p p q                     (5) where 1 1mod 2, mod 2, i -1,m m n n   the subscript 2 in the summation notation indicates that the index variables increase with step 2, and ! !( )! a a b b a b       and ! , ! !( )! a a b c b c a b c        are the binomial and trinomial coefficients respectively. the degree of the polynomial ( , ) 1 2( , ) m n l p t t is ( , )m n with total degree .m n the leading coefficient of ( , )m n l p is ( , ) . , m n l l a m n        the polynomials display many symmetric properties. one property is that they are either odd or even functions with respect to the parameters. that is, ( , ) ( , ) 1 2 1 2( , ) ( 1) ( 1) ( , ). m n m nm n l l p t t p t t     the same symmetric property holds for the spherical harmonics as well. that is, ( , ) ( , ) 1 2 1 2( , ) ( 1) ( 1) ( , ). m n m nm n l l y t t y t t     another symmetric property is that the polynomial gives another independent solution for the same mode when the parameters are switched, ( , ) ( , ) 1 2 2 1( , ) ( , ). n m m n l l p t t p t t the same holds for the spherical harmonics as well. that is, ( , ) ( , ) 1 2 2 1( , ) ( , ). n m m n l l y t t y t t a set of continuous spherical harmonics can be constructed from the eigenfunctions of one face forming a six-tuple of functions 2 1 2 1 1 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 1 1 ( , ) : ( , ), , , , , ( , ), , , , , t t t t y t t y t t y y y t t y y t t t t t t t t                                    (6) where each component in the six-tuple is an eigenfunction obtained from the eigenfunction 1 2( , )y t t of the face .x  details of the continuity of 1 2( , )y t t can be found in nasir (2007). for spherical harmonics in a spherical polar coordination system, see (macrobert, 1967). the inner product on the space of square integrable functions 2 2 ( )l s is given by { , , } , ,s f f x y z u v u v          , (7) where 1 1 3/2 1 2 1 1 , f f f tu v u v s dt dt         are the inner products for the functional components for one face { , , , , , }.f x x y y z z       the spherical harmonics ( , )m n l y are weakly orthogonal in the sense that they are orthogonal for distinct modes because the laplace-beltrami operator is self-adjoint but are not orthogonal among the 2 1l  functions for a given mode .l 2.2 completely orthogonal spherical harmonics a set of completely orthogonal spherical harmonics can be constructed from the eigensolutions in the form m.a.a.m. faham and h.m. nasir 204 ( ) ,( ) 1 2, /2 ( , ) : , 0, 1, , , 0,1 k l rk l r l t q z t t r l k k s     (8) with polynomials ( ) ( ) 1 1, ( ) ( ) ( , ), k k l r r l rl r q p t t q l    where ( ) 1( ) and ( , ) k r l rp t q l  are polynomials in the variables 1t and  respectively with degrees , ( 0, 1)l k k  and l r respectively satisfying the differential equations 2 2 1 12 11 (1 ) 2( 1) ( 1) 0 d p dp t r t r r p dtdt       (9) and 2 2 2 (1 ) (2 1) ( )( ) 0 d q dq l l r l r q dd           (10) respectively, and 2 1/2 1 1 2 1( ) (1 ) , / ( ).t t t t     for orthogonal polynomial solutions of differential equations, see (krall and sheffer,1967; kwon et al., 2001; lee and littlejohn, 2006; and the references therein). the differential equations we have in (9) and (10) are slightly different from the equations treated by the authors in those papers. nevertheless, their approach can be directly applicable to equations (9) and (10). the polynomials ( ) 1( ) k rp t can be obtained from (0) (1) 1i ( i) r r rp p t   and the polynomials ( , )l rq l  are given by ( ) ,1 ( , ) , l r nl r l r l nn r q l a       where the coefficients ( ) , l r l n a  satisfy the recurrence relation ( ) ( ) 1, , 2 ( 1)( 2) / ( )( ) , 2, 4, , , l r l r l n l n a n n l r n l r n a n l r l r r                 where 1 ( ) mod 2.r l r  the polynomials ( , )l rq l  are normalized such that the leading coefficient ( ) , . l r l r l a l r         hence, we get ( )/2 ( ) 1, ( 1) , 2, 4, , . ( ) / 2,2 l r n l r l l n l r n l a n l r l r r l r n n                   (11) (11 the polynomials ( ) 1 2, ( , ) k l r q t t have, in expanded form, degrees ( , )r k l r  for with total degree .l k the orthogonal spherical harmonics are then given by the six-tuple formed by ( ) 1 2, ( , ) k l r z t t as in (6). the set of polynomials corresponding to the weakly orthogonal and completely orthogonal spherical harmonics for the face x  are given in table 1 for the first five modes. 3. a power representation in this section, we establish a representation of the weakly orthogonal spherical harmonics for a given mode l as a monomial power of a simple linear expression. theorem 3.1 let s, j be symbolic (indeterminate) variables connected by the s-j relation 2 2 (1 ).j s   for a mode l, the 2 1l  polynomials ( , )m n l p in (5) can be given by the coefficients of the powers of s of the expansion of (1) (2) 1 2(1 ) ( ) ( ), l l l t s t j p s jp s    where, in the expansion of the trinomial, the even powers of j weakly orthogonal spherical harmonics 205 are substituted by the s j relation. proof. expanding the trinomial power and substituting the s-j relations for even powers of j we get, 1 2 1 2 (1) (2)1 1 2 1 2 ( ) , : . , , p ql q r p q r l p q p qq r q r l l p q r l p q r l r even r odd l t t s j t t s j p q l l t t s j j t t s j p jp p q p q                                       considering the first term with even r , /2 (1) 2 /2 2 1 2 1 2 0 / 2 ( ) (1 ) . , , r p q p qq r r r q k l p q r l p q r l k r even r even l l r p s t t s s t t s p q p q k                              i i now, collecting the coefficients of n s where 2n q k  or ( ) / 2,k n q  and noting that n and q must be of same parity for k to be an integer and hence that m and p must be of same parity, we have (1) 2 2 1 2 0 1 1 ( ) / 2 ( ) , ( ) / 2 l m n p q l p q n l n p m q n l m n p q p s t t s p q n q                        i , m n l  , where 1 mod 2m m and 1 mod 2n n to force the parity of p and q to conform with that of those m and n respectively. similarly, for the second term, we have 1 (2) 2 2 1 2 0 1 1 ( ) / 2 ( ) , ( ) / 2 l m n p q l p q n l n p m q n l m n p q p s t t s p q n q                         i , 1.m n l   the coefficients of (1) ( ) l p s and (2) ( ) l p s are the polynomials ( , )m n l p for 1, .m n l l   we now show that the polynomials can be computed by the convolution products of lower order polynomials. theorem 3.2 let (1) (2) 1 2( ) ( ) ( ). l l l t t s j p s jp s    then the polynomials for mode 1 2l l are given by (1) (2) (2) (2) (2)2 1 2 1 2 1 2 (1 ) l l l l l l p p p s p p     and (2) (1) (2) (2) (1) 1 2 1 2 1 2 . l l l l l l p p p p p    proof. expansion of the powers gives (1) (2) (1) (2) (1) (1) (2) (2) (1) (2) (2) (1)21 2 1 2 1 1 2 2 1 2 1 2 1 2 1 2 ( ) ( )( ) (1 ) ( ) . l l l l l l l l l l l l l l t t s j p jp p jp p p s p p j p p p p            again we have (1) (2)1 2 1 2 1 2 1 2 ( ) . l l l l l l t t s j p jp        equate the coefficients of .j the polynomial multiplications are the convolution products involving the coefficients ( , ) , m n l p m n l  for (1) l p and ( , ) , 1 m n l p m n l   for (2) . l p thus, if we denote the sequence of coefficients of the polynomials with the same notation, we have (1) (1) (1) (2) (2) (2) (2) 2 1 2 1 2 1 2 1 2 * * ( * ) l l l l l l l l p p p p p p p     and (2) (1) (1) (2) (1) 1 2 1 2 1 2 * * l l l l l l p p p p p    , where (2) (2) 2 1 2 ( * ) l l p p is the sequence shifted two places to the right. m.a.a.m. faham and h.m. nasir 206 table 1. polynomials for weakly orthogonal and completely orthogonal spherical harmonics (sh). l ( , )m n polynomials ( , ) 1 2( , ) m n l p t t for weakly orthogonal sh [ , ]r k polynomials ( ) 1 2, ( , ) k l r q t t for completely orthogonal sh 0 (0,0) 1 [0,0] 1 1 (1,0) (0,0) (0,1) 1t 1 2t [1,1] [0,1] [1,0] 1t 1 2t 2 (1,0) (0,1) (2,0) (1,1) (0,2) 12t 22t 2 11 t  1 22t t 2 21 t  [2,1] [1,1] [2,0] [1,0] [0,0] 12t 22t 2 11 t  1 22t t 2 2 1 21 / 2 / 2t t   3 (2,0) (1,1) (0,2) (3,0) (2,1) (1,2) (0,3) 2 11 3t  1 26t t 2 21 3t  3 1 13t t  2 2 1 23 3t t t  2 1 1 23 3t t t  3 2 23t t  [3,1] [2,1] [1,1] [3,0] [2,0] [1,0] [0,0] 2 11 3t  1 26t t 2 2 1 23 / 4 3 / 4 3t t   3 1 13t t  2 2 1 23 3t t t  2 2 1 1 2 1 23 / 4 3 / 4 3t t t t t   2 3 2 1 2 23 / 2 3 / 2t t t t   4 (3,0) (2,1) (1,2) (0,3) (4,0) (3,1) (2,2) (1,3) (0,4) 3 2 14 4t t  2 2 1 24 12t t t  2 1 1 24 12t t t  3 2 24 4t t  2 4 1 11 6t t  3 1 2 1 212 4t t t t  2 2 2 2 1 2 1 22 6 6 6t t t t   3 1 2 1 212 4t t t t  2 4 2 21 6t t  [4,1] [3,1] [2,1] [1,1] [4,0] [3,0] [2,0] [1,0] [0,0] 3 2 1 4 4t t  2 2 1 24 12t t t  3 2 1 1 1 22 2 12t t t t   2 3 2 1 2 23 3 4t t t t   2 4 1 11 6t t  2 1 2 1 212 4t t t t  4 2 2 2 1 2 1 21 6 6t t t t   3 3 1 2 1 2 1 23 3 4t t t t t t   2 4 2 2 2 4 1 1 2 1 2 23 / 8 3 / 4 3 / 8 3 3 4t t t t t t     5 (4,0) (3,1) (2,2) (1,3) (0,4) (5,0) (4,1) (3,2) (2,3) (1,4) (0,5) 2 4 1 11 10 5t t  3 1 2 1 220 20t t t t  2 2 2 2 1 2 1 22 10 10 30t t t t   3 1 2 1 220 20t t t t  2 4 2 21 10 5t t  3 5 1 1 15 10t t t  2 4 2 1 2 1 25 30 5t t t t t  3 2 3 2 1 1 1 2 1 2 10 10 30 10t t t t t t   2 3 2 3 2 1 2 2 1 210 30 10 10t t t t t t   2 4 1 1 2 1 25 30 5t t t t t  3 5 2 2 25 10t t t  [5,1] [4,1] [3,1] [2,1] [1,1] [5,0] [4,0] [3,0] [2,0] [1,0] [0,0] 2 4 1 1 1 10 5t t  3 1 2 1 2 20 20t t t t  2 4 2 2 2 1 1 2 1 2 5 / 4 5 / 2 5 / 4 10 30t t t t t    3 3 1 2 1 2 1 2 10 10 20t t t t t t   2 4 2 2 2 4 1 1 2 1 2 2 5 / 8 5 / 4 5 / 8 15 / 2 15 / 2 5t t t t t t     3 5 1 1 15 10t t t  2 4 2 1 2 1 25 30 5t t t t t  3 5 2 3 2 1 1 1 1 2 1 215 / 4 5 / 2 5 / 4 30 10t t t t t t t    4 3 2 3 2 1 2 2 1 2 5 5 10 10t t t t t t   3 5 2 3 2 4 1 1 1 1 2 1 2 1 2 5 / 8 5 / 4 5 / 8 15 / 2 15 / 2 5t t t t t t t t t     2 4 3 2 3 5 2 1 2 1 2 2 1 2 2 15 / 8 15 / 4 15 / 8 5 5t t t t t t t t t     weakly orthogonal spherical harmonics 207 4. inner products for completely orthogonal spherical harmonics in the fourier series expansion of spherical functions on a cubed-sphere by weakly orthogonal spherical harmonics, one needs to evaluate the inner products of those spherical harmonics. a method for doing this, however, is not explicitly available. the problem is handled in connection with the inner products of the completely orthogonal spherical harmonics. in this section, we obtain an explicit form for the inner products of the completely orthogonal spherical harmonics. these are then used in the evaluation of the inner products of the weakly orthogonal spherical harmonics by means of the linear relations to be established in section 5. the inner product of the completely orthogonal spherical harmonics ( ) , k l r z are given by ( )( ) 1 1( ) ( ) 1, , 2 2 3 0 01 ( ) ( ) ( , ) ( , ) , 8 ( ) ( ) kk rk k r l r l r sl r l r r r l p t p t q l q l z z dt d t                                (12) where r r is even and 0,1.k  the inner products of the other distinct combinations of the indices ,r r  vanish (nasir, 2007). by the transformation 1 tan ,t  the first integral is evaluated to ( )( ) 1 1 12 0 1 0 ( ) ( ) / 2 0 ( ) / 4 0 kk r r r r r r p t p t dt r r t r r                 which makes ( ) , { , 0,1, 2, ; 0,1, 2, , ; 0,1} k l r z l r l k k    a fully orthogonal set of spherical functions. to evaluate the inner product (12), we now need to evaluate the second integral for .r r lemma 4.1 the polynomials ( , ), 0,1, 2, ,l rq l r l  are orthogonal in the weighted hilbert space 2 0(0, , ),l  where 2 ( 1/2) 0 (1 ) . l       thus, ( , )l rq l  is orthogonal to any lower order polynomials. proof. differentiating (10) k times, we get 2 ( ) ( ) 2 ( ) 2 (1 ) (2( ) 1) ( )( ) 0 k k kd q dq l k l r k l r k q dd              . writing in self-adjoint form, we get ( 1) ( ) 1( ) ( )( ) 0 k k k k d q l r k l r k q d            or ( ) ( 1) 1 1 ( ), 0,1, 2, , ( )( ) k k k k d q q k l r k l r k d            where 2 1 (1 ) , 0,1, 2, ,k k k l      with 2 ( 1/2) 0 (1 ) , ( , ). l l rq q l        by repeated application of this relation starting with the case 0,k  we have (0) ( ) 0 ( 1) (2 )! ( ) . ( )!( )! l r l r l r l rl r l rl r r d q q l r l r d             since ( ) , , l r l r l r l l r q a lots       where, and in other places, ‘lots’ stands for ‘lower order terms’, we have ( ) ( ) , ( )!, l r l r l r l l r q a l r       which gives the rodrigue’s type formula for ( , ) :l rq l  m.a.a.m. faham and h.m. nasir 208 2 1/2 2 ( 1/2) , ( 1) (2 )! ( , ) (1 ) (1 ) . ( )! l r l r l r l r l r l l r l r r d q q l a l r d                    (13) for ',r r multiplying (13) by 2 ( 1/2) ' (1 ) l l rq      and integrating over (0, ) with repeated integration by parts, we get 2 ( 1/2) 0 (1 ) 0. l l r l rq q d         this gives the orthogonality of the polynomials ( , ).l rq l  since any polynomial of degree n can be expressed as a linear combination of the polynomials ( , ), 0,1, , ,kq l k m  it is orthogonal to any ( , ), .nq l n m  we now evaluate the norm of ( , ).l rq l  for convenience, let 2 0 ( ) (1 ) c i c d        and 2 2 0 ( ) (1 ) . c l rj c q d        we need to evaluate 2 3/2 2 3/2 0 ( ) (1 ) .r l rj q d        when ,r r using the orthogonality of l rq  with lower order polynomials, rodrigue’s type formula (13) and integration by parts, we have ( )2 ( 1/ 2) 2 2 ( 1/ 2) 1/ 2 , 0 0 ( ) ( )2 2 ( 1/ 2) 2 2 ( 1/ 2) , , 0 0 ( , ( ) (1 ) (1 ) ( 1) (2 )! (2 )! ( ) (1 ) ( ) ( )! (1 ) ( )! ( )! ( l rl l r l l l r l rl l r l r l r l r l rl r r r l l r l l rl r l l l r j q d a q d r d r a d a l r d l r l rd a                                                   ) 2 1/ 2 (2 )! ) ( )! ( ) . ( )! r r r l r i l r    (14) for the evaluation of 1/2 ( ),ri   we use the identity 2 2 2 1 1 1 (1 2 ) 2 . (1 ) (1 ) (1 ) d d                  (15) we shall evaluate 3/2 ( )rj   separately for 0r  and 1.r  we first consider the case 1.r  integrating (15) over the positive real line (0, ), we get the recurrence relation 1( ) (2 1) ( ) / (2 )i i       for 1/ 2  and 1 3/2( ) ( ) 1i i     when 1/ 2.  hence, by repeated application of this recurrence relation starting with 1/ 2, 1r r    and ending with 1/ 2,  we get 2( 1) 2 2 2 2 1/2 3/2( ) 2 (( 1)!) ( ) / (2 1)! 2 (( 1)!) / (2 1)!. r r ri r i r r r            therefore, (14) becomes, with the substitution of ( ) , , l r l l r l a l r          ( ) 2 2 1 2 2 1 2 ' 1/2 2 ( ) 2 ( !) 2 ( !) ( ) , 1 . ( )!( )! ( )!( )! l r r r l l r l a l l j r l r l r r l r l rl r l r                   in order to evaluate the integral 3/2 ( ),lj   again multiplying the identity (15) by 2 l rq  with 1/ 2,l   integrating over a large interval (0, c) and integration by parts, we have weakly orthogonal spherical harmonics 209 2 3/2 1/2 2 1/2 2 1/2 00 2 ' (2 1) ( ) 2 ( ) . (1 ) (1 ) c c l r l r l r l l l l q q q l j c l j c d                    (16) as ,c  the boundary limit vanishes for 1.r  by writing ( ) , ( ) l r l r l r l l r q l r a lots          and using (14), we get 3/2 1/2 1/2(2 1) ( ) 2 ( ) 2( ) ( ).l l ll j lj l r j          hence, 2 2 3/2 1/2 2 2 ( !) ( ) ( ) , 1 . 2 1 2 1 ( )!( )! r l l r l j j r l l l r l r           now, for the case 0,r  the second terms in both sides of (16) become equal when c  and get cancelled. however, the boundary limit becomes 2 , .l la thus we have ( ) 2 , 3/2 ( ) 1 ( ) . 2 1 2 1 l l l l a j l l       this is consistent with the case for 1.r  substituting these in (12), we have the inner product for the completely orthogonal spherical harmonics as 2 1 2 ( ) ( ) , , 2 , 02 ( !) , , 0,1, 2, , 0,1 . , 02 1 ( )!( )! r k k l r l r rl z z l k r ll l r l r               (17) 5. linear relations and inner product in this section, we establish linear relations between the weakly orthogonal spherical harmonics ( , )m n l y and completely orthogonal spherical harmonics ( ) , , k l r z and use these relations to obtain the inner product of the weakly orthogonal spherical harmonics. by virtue of equations (3) and (8), it is enough to establish the relations between their corresponding polynomials ( , )m n l p and ( ) , . k l r q we define the column vector 1p of size 2 1l  of the polynomials ( , ) , 1, m n l p m n l l   for mode l and the column vector of polynomials 1q of the polynomials ( ) , , 0,1, , , 0,1. k l r q r l k k   let ls be the space of eigenfunctions ( , ) , 1, m n l y m n l l   for the face x  on the sphere with the face inner product 1 1 3/2 1 2 1 1 , .x tp q p q s dt dt          since the weakly orthogonal and completely orthogonal eigenfunctions are in the same eigenspace, they are linearly related. since both set of eigenfunctions have the same factor / 2l ts  with their corresponding polynomials, the polynomials are also linearly related with the same linear coefficients. moreover, since the spherical harmonics are either odd or even in the coordinate parameters 1 2, ,t t the face inner product vanishes for two spherical harmonics components with different parities making them 'locally orthogonal'. since there are four combinations of parity differences namely ( , ),ev ev ( , ),ev od ( , )od ev and ( , )od od for the coordinate parameters, the spherical harmonics for a given mode l can be grouped into four blocks of mutually locally orthogonal sets. the above observation is valid for both weakly orthogonal and completely orthogonal spherical harmonics. the difference is that, for the completely orthogonal spherical harmonics, the functions within a set block are m.a.a.m. faham and h.m. nasir 210 also orthogonal (with respect to the inner product (7)), while the weakly orthogonal spherical harmonics are not, whence the name weakly orthogonal. define ( , ) ( , ) { : , } ev k m n l l p p m even m n l k     , ( , ) ( , ) { : , }, 0,1 , od k m n l l p p m odd m n l k k      ( , ) ( ) 1 2, { : deg( ) , deg( ) } ev k k l l r q z m t even t l m k      and ( , ) ( ) 1 2, { : deg( ) , deg( ) } ev k k l l r q z m t odd t l m k      so that the column vectors lp and lq with their four blocks are        , 0 , 0 ,1 ,1 ; ; ; ev od ev od l l l l l      p p p p p and        , 0 , 0 ,1 ,1 ; ; ; ev od ev od l l l l l      q q q q q respectively. also let ly and l be the column vectors of their spherical harmonics respectively. any linear relations between the functions in lp and lq are limited to the functions in their corresponding block counterparts as the blocks of different locations are mutually orthogonal, as observed above, and hence linearly independent. the key points in establishing the linear relations are the leading coefficients of the polynomials involved. the polynomials ( , )m n l p have the leading coefficient ( , )m n l a corresponding to the higher degree term 1 2 . m n t t then, we may write ( , ) ( , ) 1 2 m n m n m n l l p a t t lots  or ( , ) ( , ) 1 2 / . m n m nm n l l t t p a lots  (18) for the polynomials ( ) , k l r q corresponding to the orthogonal spherical harmonics, we have (0) (1) ( )(0) (1) 1 ( ) 1 1 2, , , 1 ( ) 2 ( )/2 1 2 2 1, 1 i ( i ) ( ) ( , ) ( i) ( ) ( i) (1 ) . l r l rr l r r l r n r r l rl r l r l n n r l r l rr n l r n l n n r q q p p t q l t t a t a t t                        being l r n  even, expanding this and separating the real and imaginary parts, we see that ( ) , , 0,1 k l r q k  are polynomials of total degree l k (see also table 1). we may write them, with their leading coefficients, as (0) ( ) 2 1 2, , 1 (1) ( ) 1 2 1 2, , 1 . l r l r l n n l r l n n r l r l r l n n l r l n n r q a t t lots q r a t t lots              note that while ( , ) 1 2( , ) m n l p t t has only one leading coefficient, ( ) 1 2, ( , ) k l r q t t has many leading coefficients for highest total degree .l k substituting (18) and using the orthogonality of ( , )m n l p with lower order polynomials, we have  (0) ( ) ( , ) ( , )2, , 1 ( )/2 ( , ) 2 ( ) 1 / ( 1) ( ) / 22 l r l r l n n l n n l r l n l l n r l r nl r l n n ll r n n r q a a p l n p l r n                       (19) weakly orthogonal spherical harmonics 211 and  (1) ( ) ( 1 , ) ( 1 , )2, , 1 ( )/2 ( 1 , ) 2 ( ) 1 / ( 1) . ( ) / 22 l r l r l n n l n n l r l n l l n r l r nl r l n n ll r n n r q r a a p l nr p l r nl n                           (20) from this, we obtain the matrix form of the linear relations between the sets of polynomials and hence between the weakly and completely orthogonal spherical harmonics as l l lq t and l l l t y (21) respectively, where lt is a square matrix of size 2 1l  consisting of the coefficients of the linear relations in (19) and (20). according to the choice of blocks of the column vectors lp and lq , the structure of the matrix lt is given in the block diagonal matrix form  , , , ,l l l l ldiag a b c dt (22) where , ,l l la b c and ld are upper triangular matrices with sizes , ( 1) / 2 ,a ln l    , , / 2b l c ln n l     and , ( 1) / 2d ln l    respectively, and with  x denoting the smallest integer such that .x x    the coefficients of the matrices are given by 2 2 2 11 1 ( , ) , ( , ) , 4 4 j i j i l l j j a i j b i j j i j i                             2 1(2 1) 1 ( , ) (2 1) 4 j i l ji c i j j ij                and 21 ( , ) 4 j i l ji d i j j ij              respectively for ,j i and zeros otherwise. the indices i, j range up to their respective matrix sizes. these coefficients can be obtained successively by the relations 1 (2 ) (2 1) ( ) (1,1) 1, ( , 1) ( , ), ( 1, ) 4 ( , ) 4 ( 1 ) ( 1) 1 l l l l l j j j i a a i j a i j a i j a i j j i j i i j                2 1 2 1 ( , ) ( , ), ( , ) ( , ) 1 1 l l l l j i b i j a i j c i j a i j i j i j         and ( , ) ( 1, 1)l l i d i j a i j j    for their respective sizes. it is also noted that for even mode 0,l  1 1 1, ,l l l l l la a b b c c     and 1.l ld d  when the matrices change sizes in alternative modes, their sizes increase by only one row and column. the entries of the row are all zero except the last, which is one. therefore, by appending one column, we may obtain the matrices for the next mode. the coefficients of , andl l lb c d can also be obtained from the simplified relations with constant coefficients as       1 1 ( , ) ( , ) 1, , ( , ) ( , ) 1, , ( , ) 2 ( , ) 1, 1 . 4 4 l l l l l l l l lb i j a i j a i j c i j a i j a i j d i j b i j a i j          the matrices, therefore, are obtained from the matrix la only, and by using the above relations. the entries of matrix la can be easily evaluated column wise by the recurrence formula , 1 2 ( , ) 1, ( 1, ) ( , ), , 1, ,1, 1, 2, , . 4 1 l l a l j i a j j a i j a i j i j j j n j i            m.a.a.m. faham and h.m. nasir 212 the inner product for the weakly orthogonal spherical harmonics is determined using the linear relations established between the two sets of spherical harmonics and the inner product of the completely orthogonal spherical harmonics. since the matrices in (22) are upper triangular matrices, they can be easily inverted. the relation between the inner products of the two sets of spherical harmonics is then given in matrix form as , , t t t t l l l l l l l l l l l l  t y y t t y y t from which we obtain the matrix of inner products for the weakly orthogonal spherical harmonics for model l as 1 , , t l l l l l l   y y t t (23) note that the matrix of inner products for the completely orthogonal spherical harmonics is a diagonal matrix. further, matrix lt consists of upper triangular block matrices. they can be easily inverted. 6. spherical fourier series on cubed-sphere the fourier series of a spherical function 1 2( , )f t t is written in terms of the weakly orthogonal spherical harmonics as  1 2 0 , i i i f t t m     y where im are row vectors of sizes 2 1l  of coefficients given by 1 , , .i i i if  m y y y . it is interesting to note that the inverse matrix of inner products 1 ,l l  y y can be evaluated without inverting the matrix it in fact, we have from (23) that 1 1 , , . t l l l l l l   y y t t since ,l l , being the matrix of inner products of completely orthogonal spherical harmonics for model l, is diagonal, its inverse is also diagonal with the reciprocals of the diagonal entries. the vector of coefficients , lf y consists of entries of the form { , , } , , f f f x y z f y f y          , where ( , )m n l y y and fy is its restriction on one face of the cubed-sphere. the local inner product is given by 1 1 3/2 1 2 1 2 1 2 1 1 , ( , ) ( , ) .f f f lf y f t t y t t s dt dt         7. conclusion we have established linear relations between weakly orthogonal and orthogonal spherical harmonics and their inner products, and a power representation for the weakly orthogonal spherical harmonics. spherical functions can be decomposed by fourier series using the weakly orthogonal spherical harmonics. application of these weakly orthogonal spherical harmonics in problems in areas of science, such as weather prediction models, is a subject 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analysis, 18(2): 191-210. received 25 april 2011 accepted 7 march 2012 squ journal for science, 2015, 20(2), 42-48 ©2015 sultan qaboos university 42 mapping methods to solve a modified korteweg-de vries type equation edamana. v. krishnan department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al khod, muscat, sultanate of oman. email: krish@squ.edu.om. abstract: in this paper, we employ mapping methods to construct exact travelling wave solutions for a modified korteweg-de vries equation. we have derived periodic wave solutions in terms of jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions. keywords: jacobi elliptic functions; korteweg-de vries equation; solitary wave solutions; travelling wave solutions. يس المعذلةرلحل معادلة كورتيج دو ف الخرائط طرق رسم ادمنان كرشنان حلول الموجة الذوسية بذاللة أوجذنانتقال التامة لمعادلة كوستيج دو فشيس المعذلة. الإلنشاء حلول ا طشق سسم الخشائطوظف في ىزه الوسقة ن ملخص: ة بذاللة الذوال الزائذية.شارحلول كينك وحلول الموجو الودوال جاكوبي التناقصية، .ةنتقاليالحلول الموجة ا، ةشارال موجةال حلول، معادلة كوستيج دو فشيس ،دوال جاكوبي التناقصية :كلمات مفتاحية 1. introduction ravelling wave solutions (twss) of nonlinear evolution equations have been extensively studied due to their significant applications in mathematical theory and other fields in physical sciences. the advantage of using travelling wave solutions is that the governing partial differential equation (pde) reduces to an ordinary differential equation (ode) which makes it easier to solve. several methods using twss have been proposed such as the tanh method [1], the exponential function method [2], the jacobi elliptic function (jef) method [3], mapping methods [47] etc. solitary wave solutions (swss) of different types of korteweg-de vries (kdv) equations have been a field of intense study in many branches of physics over several decades [8-11]. a variety of kdv equations have been proposed since the discovery of solitons. because of the rich structures of the solutions, both mathematicians as well as physicists have been attracted to this field of research. in this paper, we derive periodic wave solutions (pwss) of a modified kdv equation in terms of jefs [12] and deduce their infinite period counterparts in terms of hyperbolic functions such as shock wave solutions and singular wave solutions using mapping methods. the mapping methods employed in this paper give a variety of solutions, such as hyperbolic function solutions, different types of jefs etc., which other methods cannot do. 2. mathematical analysis in this section, we give an analysis of the mapping methods which will be employed in this paper. the analysis given below is, in general, for a system of pdes [13] but in this paper we have applied it for a single pde. consider a nonlinear coupled pde with two dependent variables u and v and two independent variables x and t given by ( , , , , , , , ,...) = 0, t t x x xxx xxx f u v u v u v u v (1) where subscripts denote partial derivatives with respect to the corresponding independent variables, and f is a polynomial function of the indicated variables. t mailto:krish@squ.edu.om mailto:krish@squ.edu.om mapping methods to solve a modified korteweg-de vries type equation 43 step 1: assume that (1) has a travelling wave solution in the form 1 2 =0 =0 ( , ) = ( ) = ( ), ( , ) = ( ) = ( ), l l i i i i i i u x t u a f v x t v b f     (2) where = ,x t  , i i a b and  are arbitrary constants, 1 l and 2 l are integers and i f represents integer powers of .f the first derivative of f with respect to  denoted by 'f can be expressed in powers of f in the form 2 2 41 = , 2 ' f p f qf r  (3) where ,p q and r are arbitrary constants. the motivation for (3) was that the squares of the first derivatives of jefs can be expressed in even powers of themselves. step 2: substituting (2) into (1), the pde reduces to an ode. balancing the highest order derivative term and the highest order nonlinear term of the ode, the values of 1 l and 2 l can be found. step 3: substituting for u and v and using (3), the ode gives rise to a set of algebraic equations by setting the coefficients of various powers of f to zero. step 4: from the values of the parameters , , , i i a b p q and r , the solution of (1) can be derived. thus a mapping relation is established through (2) between the solution to (3) and that of (1). it is to be noted that if the values of 1 l and 2 l are integers, we can use the method directly to get a variety of solutions in terms of hyperbolic functions or jefs. if they are non integers, the equation may still have solutions as rational expressions involving hyperbolic functions or jefs. the jefs and their main properties have been described in appendix. 3. a modified kdv-type equation in this paper, we derive a variety of solutions in terms of jefs and their infinite period counterparts, which are kink solutions, swss or singular swss for a modified kdv-type equation derived in [14]. in a study by wazwaz [15], he has derived kink solutions and single and multi swss for this equation using hirota's method. the equation under consideration is 3 3 4 4 4 16 = 0. xxt x xt t xxx x xx x u u u u u uu u u u u     (4) we search for travelling wave solutions of (4) in the form ( , ) = ( ).u x t u  (5) substitution of (5) into (4) gives rise to the ode 3 (4 ) (4 ) 4( 4) = 0.uu u u u u            (6) dividing by 2 (4 )u and integrating with respect to  , we arrive at the equation 3 2 = 0,u ku u    (7) where k is the integration constant. 3.1 mapping method applying the mapping method it can be seen that 1 = 1l and so we assume that (7) has the solution of the form 0 1 ( ) = ( ),u a a f  (8) where f satisfies (3) and 0 a and 1 a are constants to be determined. cases in which 1 > 1l have been considered in [16]. substituting (8) into (7) and using (3), we arrive at the following algebraic equations: 3 1 1 2 = 0,qa a (9) 2 0 1 6 = 0,a a (10) 2 1 0 1 ( ) 6 = 0,p k a a a  (11) 3 0 0 2 = 0.ka a  (12) edamana. v. krishnan 44 solving these equations, we get 0 1 = 0, = , = . 2 q a a k p (13) for illustration, we consider the following cases. case 1. = 2, = 2, = 1.p q r now, (7) has the solution ( ) = tanhf   (see [4,5]). therefore, (4) has the kink solution ( , ) = tanh( ).u x t x t  (14) case 2. 2 2 = (1 ), = 2 , = 1.p m q m r  now, (7) has the solutions ( ) = snf   and ( ) = cdf   (see[4,5]). so, (4) has the pwss ( , ) = sn( )u x t m x t  (15) and ( , ) = cd( ).u x t m x t  (16) as 1m  , the kink solution (14) is recovered from (15), and (16) gives a trivial constant solution. case 3. 2 2 = 2 , = 2, = 1 .p m q r m  in this case, (7) has the solution ( ) = cs .f   therefore, (4) has the pws ( , ) = cs( ).u x t x t  (17) as 1m  , (17) gives rise to the singular sws ( , ) = csch( ).u x t x t  (18) case 4. 2 2 = (1 ), = 2, = .p m q r m  here, (7) has the solutions ( ) = nsf   and ( ) = dc .f   thus, (4) has the pwss ( , ) = ns( )u x t x t  (19) and ( , ) = dc( ).u x t x t  (20) as 1m  , (19) leads us to another singular sws ( , ) = coth( ).u x t x t  (21) in the infinite period limit, (20) gives a trivial constant solution. it is worth mentioning that for case 1, ( ) = cothf   is also a solution which is a special case of case 4 when 1m  . 3.2 modified mapping method this method gives a combination of a hyperbolic function or jef and its reciprocal as solutions. in this case, we consider the solution of (7) in the form 1 0 1 1 ( ) = ( ) ( ),u a a f b f      (22) where f satisfies (3) and 0 1 ,a a and 1 b are constants to be determined. also, 1 f  is the reciprocal of .f when 1 = 0,b this method reduces to the mapping method. substituting (22) into (7) and using (3), we obtain the following algebraic equations: 3 2 1 1 1 0 2 2 = 0, 6 = 0,rb b b a  (23) 2 2 1 1 1 0 1 1 6 6 = 0,pb kb b a b a   (24) 3 0 0 1 0 1 2 12 = 0,ka a b a a   (25) 2 2 1 1 0 1 1 1 6 6 = 0,pa ka a a b a   (26) 2 3 0 1 1 1 6 = 0, 2 = 0.a a qa a  (27) these equations lead us to 0 1 1 = 0, = , = , = 3 2 . 2 q a a b r k p qr   (28) mapping methods to solve a modified korteweg-de vries type equation 45 we now consider some choices for the parameters, as the first three cases of section 3.1, to obtain the following cases. case 1. = 2, = 2, = 1.p q r here, (7) has the solution ( ) = tanhf   . so, ( ) = tanh( ) coth( )u    satisfies (7) with = 8.k  therefore, (4) has the solution  ( , ) = tanh( ) coth( ) .u x t x t x t     (29) case 2. 2 2 = (1 ), = 2 , = 1.p m q m r  so, equation (7) has the solutions ( ) = snf   and ( ) = cdf   with 2= (1 6 )k m m   (see [4,5]). therefore, (4) has the pwss ( , ) = sn( ) ns( )u x t m x t x t     (30) and ( , ) = cd( ) dc( ).u x t m x t x t     (31) as 1m  , the solution (29) is recovered from (30), and (31) gives a trivial constant solution. case 3. 2 2 = 2 , = 2, = 1 .p m q r m in this case, (7) has the solution ( ) = csf   with 2 2 = 2 6 1k m m   . thus, (4) has the pws 2 ( , ) = cs( ) 1 sc( ).u x t x t m x t      (32) as 1m  , (32) gives rise to the singular sws (18). 3.3 extended mapping method this method gives a combination of two different jefs as solutions. here, we consider the solution of (7) in the form 0 1 1 ( ) = ( ) ( ),u a a f b g    (33) where f satisfies (3), 0 1 ,a a and 1 b are constants to be determined, and g satisfies 2 2 2 1 2 3 4 = ( ), = . '' g g c c f g c c f  (34) when 1 = 0,b this method also reduces to the mapping method. the motivation for (34) was the relationship of the second derivative of any jef with itself and another jef for some constants 1 2 3 , ,c c c and 4 .c as in (3), prime denotes differentiation with respect to  in (34) as well. substituting (33) into (7) and using (3) and (34), we obtain the following algebraic equations: 3 2 1 1 4 1 1 2 6 = 0,qa a c a b  (35) 2 3 2 1 1 1 4 1 6 2 = 0,c b a b c b  (36) 2 2 0 1 4 0 1 2(3 3 ) = 0,a a c a b  (37) 0 1 1 12 = 0,a a b (38) 2 2 1 1 0 1 3 1 1 2(3 3 ) = 0,pa ka a a c a b   (39) 2 3 1 1 1 0 1 3 1 2(3 ) = 0,c b kb a b c b   (40) 3 2 0 0 3 0 1 2( 3 ) = 0.ka a c a b   (41) solving these equations, we obtain 0 1 2 1 1 3 1 3 1 = 0, = 3 , = , = 4 6 2 2 p k a a c q b k c p c      (42) with the constraint relation 2 3 3 4 3 9 8 ( ) = 0.c c qc c p k   (43) so, we can deduce from (42) that 1 1 3 1 = . 2 p c b c   (44) we consider the case 2 2 = (1 ), = 2, =p m q r m  . edamana. v. krishnan 46 case 1. 2 1 2 3 4 = , = 2, = 1, = 1.c m c c c  so, (7) has the solutions ( ) = nsf   and ( ) = csg   with 21 = 2 k m . therefore, (4) has the pws   1 ( , )= ns( ) cs( ) . 2 u x t x t x t     (45) as 1m  , (45) gives rise to the singular solution   1 ( , )= coth( ) csch( ) . 2 u x t x t x t     (46) case 2. 2 1 2 3 4 = 1, = 2, = , = 1.c c c m c  so, (7) has the solutions ( ) = nsf   and ( ) = dsg   with 21 = 1 2 k m  . therefore, (4) has the pws   1 ( , ) = ns( ) ds( ) . 2 u x t x t x t     (47) as 1m  , (47) gives rise to the same singular solution (46). case 3. 2 1 2 3 42 2 1 = 1, = 2, = , = . 1 1 m c c c c m m     in this case, (7) has the solutions ( ) = dcf   and ( ) = ncg   with 21 = 1 2 k m  . therefore, (4) has the pws 21 ( , ) = dc( ) 1 nc( ) . 2 u x t x t m x t         (48) in this case, as 1m  , (48) will lead to a trivial constant solution. case 4. 2 1 2 3 42 2 1 1 = , = 2, = , = . 1 1 c m c c c m m     here, (7) has the solutions ( ) = dcf   and ( ) = scg   with 21 = 2 k m . thus, (4) has the pws 21 ( , ) = dc( ) 1 sc( ) . 2 u x t x t m x t         (49) in this case also, as 1m  , (49) will lead to a trivial constant solution as in the previous case. in order to illustrate the properties of the travelling wave solutions, we draw some plots of the kink wave solution, as in figure1, and singular wave solution, as in figure2. figure 1. kink wave solution (14) with = 1 . mapping methods to solve a modified korteweg-de vries type equation 47 figure 2. singular wave solution (18) with = 1 . . 4. conclusion the modified kdv-type equation under consideration was found to have shock wave solutions and singular wave solutions. it was not possible to derive solitary wave solutions in terms of sech functions using the method. it is worth investigating the possibility for such solutions as future research. acknowledgement i would like to express my sincere gratitude to the unknown referees whose suggestions added to the value of the paper to a great extent. references 1. malfliet, w. the tanh method: 1. exact solutions of nonlinear evolution and wave equations. physica scripta, 1996, 54, 563-568. 2. he, j.h. and wu, x.h. exp-function method for nonlinear wave equations. chaos solitons and fractals, 2006, 30, 700708. 3. liu, j., yang, l. and yang, k., jacobi elliptic function solutions of some nonlinear pdes. physics letters a, 2004, 325, 268-275. 4. peng, y. exact periodic wave solutions to a new hamiltonian amplitude equation. journal of the physical society of japan, 2003, 72, 1356-1359. 5. krishnan, e.v. and peng, y. a new solitary wave solution for the new hamiltonian amplitude equation. journal of the physical society of japan, 2005, 74, 896-897. 6. krishnan, e.v. and biswas, a., solutions to the zakharov-kuznetsov equation with higher order nonlinearity by mapping and ansatz methods. physics of wave phenomena, 2010, 18, 256-261. 7. alzaidy, j.f. extended mapping method and its applications to nonlinear evolution equations. journal of applied mathematics, 2012, article id 597983, 14 pages. 8. hirota, r. and satsuma, j. soliton solutions of a coupled korteweg-de vries equation. physics letters a, 1981, 85, 407-408 . 9. dodd, r. and fordy, a.p. on the integrability of a system of coupled kdv equations. physics letters a, 1982, 89, 168-170 . 10. krishnan, e.v. remarks on a system of coupled nonlinear wave equations. journal of mathematical physics, 1990, 31, 1155-1156. 11. wang, m.l., solitary wave solutions for variant boussinesq equations. physics letters a, 1995, 199, 169-172 12. lawden, d.f., elliptic functions and applications, springer verlag, 1989. 13. peng, y.z. and krishnan, e.v. exact travelling wave solutions to the (3+1)-dimensional kadomtsev-petviashvili equation. acta physica polonica, 2005, 108, 421-428. 14. gurses, m. and peckcan, a. 2+1 kdv(n) equations. journal of mathematical physics, 2011, 52, 1-14. edamana. v. krishnan 48 15. wazwaz, a.m. a modified kdv-type equation that admits a variety of travelling wave solutions: kinks, solitons. peakons and cuspons, physica scripta, 2012, 86, 1-6. 16. ebadi, g., krishnan, e.v., labidi, m. zerrard, e. and biswas, a. analytical and numerical solutions to the davey-stewartson equation with power law nonlinearity. waves in random and complex media, 2011, 21, 559590. appendix consider the function 0 2 2 ( , ) = = . 1 sin d f m m       (a.1) letting = sint  , we obtain sin 0 2 2 2 = . (1 )(1 ) dt t m t      (a.2) this is called legendre's standard elliptical integral of the first kind. when 1 0 2 = 0, = = sin 1 x dt m x t     , where = sinx  . when 1 20 = 1, = = tanh 1 x dt m x t     , where = sinx  . for 0 < < 1,m we define  as the inverse of a function which is known as jacobi sine elliptic function, expressed in the form 1 = sn x  so that = snx  or sn =sin  . here, m is known as the modulus of the jefs (see [12]). we define two other elliptic functions as 2 2 cn = 1 = 1 sn ,x   (a.3) and 2 2 2 2 dn = 1 = 1 sn .m x m   (a.4) cn is known as jacobi cosine elliptic function and dn is known as jef of the third kind. as 0m  , sn sin , cn cos     and dn 1.  as 1m  , sn tanh , cn sech     and dn sech  . note that ns , nc and nd are the reciprocals of the three jefs and sc , cd , ds , cs , dc and sd are the ratios of the corresponding jefs. received 14 august 2014 accepted 28 january 2015 photovoltaic cells and systems: 82-101 squ journal for science, 16 (2011) © 2011 sultan qaboos university 82 chiral polyhedra derived from coxeter diagrams and quaternions mehmet koca, nazife ozdes koca* and muna al-shueili department of physics, college of science, sultan qaboos university, p.o.box 36, alkhoud, 123 muscat, sultanate of oman, *email: nazife@squ.edu.om. متعددات السطوح اليدوية المستمدة من أشكال كوكزتر والرباعيات مهمت كوجا، نزيفة كوجا و منى الشعيلي الكتالنٌة أشكالها مع المسطوح األسطح والثنعشري المسطوح المكعب: أرخمٌدٌان ٌدوٌان أسطح تمتعددا هناك :صخمل برسم نقوم البحث هذا فً. الخماسٌة السداسٌة السطوح باعٌاتر مع الخماسٌة العشرونٌة السطوح رباعٌات: المزدوجة اتلمجموع الحقٌقٌة الدورانٌة الجزئٌة المجموعة باستخدام نقوم. منظمة بطرٌقة مزدوجاتها مع الٌدوٌة السطوح متعددات كوكستر 1 1 1 3 3 ( ), ( ), ( )w a a a w a w b  و 3 ( )w h تقودنا الطرٌقة هذه. اللألشك الممثلة المدارات الشتقاق المسطوح السطوح الثنعشري و المسطوح المكعب و الوجوه وعشرونً الوجوه رباعً: التالٌة األسطح المتعددات رسم إلى الثمانٌة بالمجموعة المرآتٌة صورتها إلى التحول الوجوه وعشرونً الوجوه رباعً بإمكان أنه أثبتنا لقد. التوالً على الحقٌقٌة الدورانٌة 3 2 ( ) /w b c .المكعب رؤوس أن أٌضا المالحظ من. ٌدوٌة أسطح كمتعددات تصنٌفها ٌمكن ال لذلك وذلك البسٌطة الجذور من خطٌا المجموعة المتجهات من اشتقاقها ٌمكن المسطوح السطوح الثنعشري ورؤوس المسطوح الحقٌقٌة الدوران مجموعة باستخدام 3 2 ( ) /w b c و 3 2 ( ) /w h c بجمع مزدوجاتها رسم الممكن من. التوالً على متعددات بربط عام بشكل منتظمة الشبه األسطح متعددات بإنشاء نقوم أٌضا. االهتمام قٌد المجموعة من مدارات ثالثة مجموعة من جزئٌة كمجموعة الالبٌروهٌدر مجموعة على نحصل لذلك كنتٌجة. المرآتٌة صورها مع الٌدوٌة األسطح الكوكزتر 3 ( )w h الرباعٌات على تعتمد نستخدمها التً الطرٌقة. البحث فً ونناقشها. abstract: there are two chiral archimedean polyhedra, the snub cube and snub dodecahedron together with their dual catalan solids, pentagonal icositetrahedron and pentagonal hexacontahedron. in this paper we construct the chiral polyhedra and their dual solids in a systematic way. we use the proper rotational subgroups of the coxeter groups 1 1 1 3 3 ( ), ( ), w( ),w a a a w a b  and 3 w( )h to derive the orbits representing the solids of interest. they lead to the polyhedra tetrahedron, icosahedron, snub cube, and snub dodecahedron respectively. we prove that the tetrahedron and icosahedron can be transformed to their mirror images by the proper rotational octahedral group 3 2 ( )w b c so they are not classified in the class of chiral polyhedra. it is noted that vertices of the snub cube and snub dodecahedron can be derived from the vectors, which are linear combinations of the simple roots, by the actions of the proper rotation groups 3 2 ( )w b c and 3 2 ( )w h c respectively. their duals are constructed as the unions of three orbits of the groups of concern. we also chiral polyhedra derived from coxeter diagrams and quaternions 38 construct the polyhedra, quasiregular in general, by combining chiral polyhedra with their mirror images. as a by-product we obtain the pyritohedral group as the subgroup the coxeter group 3 ( )w h and discuss the constructions of pyritohedrons. we employ a method which describes the coxeter groups and their orbits in terms of quaternions. keywords: coxeter diagrams; chiral polyhedral; quaternions; snub cube; snub dodecahedron. 1. introduction t seems that the coxeter groups and their orbits (coxeter and moser, 1965) derived from the coxeter diagrams describe molecular structures (cotton et al. 1999), viral symmetries (caspar and klug, 1962; twarock, 2006), crystallographic and quasi crystallographic materials (jaric, 1989). chirality is a very interesting topic in molecular chemistry and physics. a number of molecules display one type of chirality; they are either leftoriented or right-oriented molecules. in fundamental physics chirality plays a very important role. for example a massless dirac particle has to be either in the left handed state or in the right handed state. no lorentz transformation exists which can transform one state to the other state. the weak interactions which are described by the standard model of high energy physics are invariant under one type of chiral transformations. in three dimensional euclidean space, which will be the topic of this paper, chirality is defined as follows: an object which cannot be transformed to its mirror image by other than the proper rotations and translations is called chiral. for this reason the chiral objects lack the plane and/or central inversion symmetry. in two previous papers we have constructed the vertices of the platonic-archimedean solids (koca et al. 2007) and the dual solids of the archimedean solids, the catalan solids (koca et al. 2010), using the quaternionic representations of the rank-3 coxeter groups. two of the 13 archimedean solids, the snub cube and snub dodecahedron are the chiral polyhedra whose symmetries are the proper rotational subgroups of the octahedral group and the icosahedral group respectively. in this paper we use a similar technique as that in (koca et al. 2007; koca et al. 2010) to construct the vertices of the chiral archimedean solids, snub cube, snub dodecahedron and their duals. they have been constructed by employing several techniques (huybers and coxeter, 1979; weissbach and martini, 2002) but it seems that the method in what follows has not been studied earlier in this context. we follow a systematic method for the construction of the chiral polyhedra. first we begin with the coxeter diagrams 1 1 1 a a a  and 3 a that lead to the tetrahedron and icosahedron respectively and prove that they possess larger proper rotational symmetries which transform them to their mirror images and so demonstrate that they are not chiral solids. we organize the paper as follows. in sec.2 we construct the coxeter groups 1 1 1 ( ), w a a a  3 ( ), w a 3 ( )w b , and 3 ( ) w h in terms of quaternions. in sec.3 we obtain the proper rotation subgroup of the coxeter group 1 1 1 ( ),w a a a  and determine the vertices of the tetrahedron by imposing some conditions on the general vector expressed in terms of simple roots of the diagram 1 1 1 . a a a  we prove that the tetrahedron can be transformed to its mirror image by the proper octahedral rotation group 3 2 ( ) .w b c in sec.4 we discuss a similar problem for the coxeter-dynkin diagram 3 a leading to an icosahedron and again prove that it can be transformed by the group 3 2 ( )w b c to its mirror image which indicates that neither tetrahedron nor icosahedron are chiral solids. here we also discuss the properties of the pyritohedral group and the constructions of the pyritohedrons. sec.5 deals with the construction of the snub cube and its dual pentagonal icositetrahedron from the proper rotational octahedral symmetry 3 2 ( )w b c using the same technique employed in sec.3 and sec.4. in i mehmet koca et al. 38 32e22e12e sec.6 we repeat a similar operation for the constructions of the snub dodecahedron and its dual pentagonal hexacontahedron from the proper icosahedral group 3 2 5 ( )w h c a which is isomorphic to the group of even permutations of five letters. in the conclusion, sec.7, we point out that our technique can be extended to determine the chiral polyhedra in higher dimensions. 2. construction of the groups 1 1 1 3 3 3 ( ), ( ), w( ) and w(h )w a a a w a b  in terms of quaternions let 0 i i q q q e  , ( 1, 2, 3)i  be a real unit quaternion with its conjugate defined by 0 i i q q q e  and the norm 1qq qq  . the quaternionic imaginary units satisfy the relations: i j ij ijk k e e e    , ( , , 1, 2, 3)i j k  (1) where ij  and ijk  are the kronecker and levi-civita symbols and summation over the repeated indices is implicit. the unit quaternions form a group isomorphic to the unitary group (2)su . with the definition of the scalar product: 1 1 ( , ) ( ) ( ) 2 2 p q pq qp pq qp    , (2) quaternions generate the four-dimensional euclidean space. the coxeter diagram 1 1 1 a a a  can be represented by its quaternionic roots in figure 1 with the normalization 2 . figure 1. the coxeter diagram 1 1 1 a a a  with quaternionic simple roots. the cartan matrix and its inverse are given as follows 2 0 0 0 2 0 0 0 2 c           , 1 1 0 0 1 0 1 0 2 0 0 1 c            . (3) for any coxeter diagram, the simple roots i  and their dual vectors i  satisfy the scalar product (carter, 1972; humpherys, 1990). 1 ( , ) , ( , ) ( ) , ( , ) i j ij i j ij i j ij c c           ; , 1, 2, 3i j  . (4) we note also that they can be expressed in terms of each other: 1 , ( ) i ij j i ij j c c       . (5) let be an arbitrary quaternionic simple root. then the reflection of an arbitrary vector  with respect to the plane orthogonal to the simple root  is given by (koca et al. 2001). chiral polyhedra derived from coxeter diagrams and quaternions 38 21 ee  23 ee  12 ee  2 2 2 2 [ , ]r             . (6) our notations for the rotary reflections and the proper rotations will be [ , ]p q  and [ , ]p q respectively where p and q are arbitrary quaternions. the coxeter group 1 1 1 ( )w a a a  is generated by three commutative group elements 1 1 1 2 2 2 3 3 3 [ , ] , [ , ] , [ , ]r e e r e e r e e          . (7) they generate an elementary abelian group 1 1 1 2 2 2 ( )w a a a c c c     of order 8. its proper rotation subgroup elements are given by 1 2 3 3 2 3 1 1 3 1 2 2 [1,1], [ , ], [ , ], [ , ] i r r e e r r e e r r e e    . (8) the next coxeter group which will be used is the tetrahedral group 3 4 ( ) d w a t s  . its diagram 3 a with its quaternionic roots is shown in figure 2. figure 2. the coxeter diagram 3 a with quaternionic simple roots. the cartan matrix of the coxeter diagram 3 a and its inverse matrix are given respectively by the matrices 2 1 0 1 2 1 0 1 2 c               , 1 3 2 1 1 2 4 2 4 1 2 3 c            . (9) the generators of the coxeter group 3 ( )w a are given by 1 1 2 1 2 2 2 1 1 [ ( ), ( )]r e e e e      , 2 3 2 3 2 2 2 1 1 [ ( ), ( )]r e e e e      , 3 2 1 2 1 2 2 1 1 [ ( ), ( )]r e e e e      . (10) the group elements of the coxeter group which is isomorphic to the tetrahedral group of order 24 can be written compactly by the set (koca et al. 2003; koca et al. 2006a; koca et al. 2006b). 3 ( ) {[ , ] [ , ] }w a p p t t    , , p t t t  . (11) mehmet koca et al. 38 21 ee  32 ee  32e 4 2e 5   321 2 1 eee  1e here t and t represent respectively the binary tetrahedral group of order 24 and the coset representative t o t  where o is the binary octahedral group of quaternions of order 48 (koca et al. 2003; koca et al. 2006a; koca et al. 2006b). the coxeter diagram 3 b leading to the octahedral group 3 ( ) h w b o is shown in figure 3. figure 3. the coxeter diagram 3 b with quaternionic simple roots. the cartan matrix of the coxeter diagram 3 b and its inverse matrix are given by 2 2 2 1 0 1 2 0 2 c               , 1 2 2 2 2 1 1 1 1 2 1 3 2 c                 . (12) the generators, 1 1 2 1 2 2 2 1 1 [ ( ), ( )]r e e e e      , 2 2 3 2 3 2 2 1 1 [ ( ), ( )]r e e e e      , 3 3 3 [ , ]r e e    (13) generate the octahedral group which can be written as 3 3 4 2 ( ) ( ) {[ , ] [ , ] [ , ] [ , ] }w b aut a s c p p p p t t t t          , ,p t t t  . (14) a shorthand notation could be 3 ( ) {[ , ] [ , ] [ , ] [ , ] }w b t t t t t t t t         . note that we have three maximal subgroups of the octahedral group 3 ( ),w b namely, the tetrahedral group 3 ( ),w a the chiral octahedral group consisting of the elements 3 2 ( ) {[ , ] [ , ]}w b c t t t t   , and the pyritohedral group consisting of the elements 4 2 {[ , ] [ , ] } h t a c t t t t      . the pyritohedral symmetry represents the symmetry of the pyritohedron, an irregular dodecahedron, with irregular pentagonal faces which occurs in iron pyrites. the coxeter diagram 3 h leading to the icosahedral group is shown in figure 4. figure 4. the coxeter diagram of 3 h with quaternionic simple roots.(it is assumed that the simple roots are multiplied by 2 ). the cartan matrix of the diagram 3 h and its inverse are given as follows: chiral polyhedra derived from coxeter diagrams and quaternions 38 2 0 2 1 0 1 2 c                 , 2 3 3 1 3 2 2 3 2 3 2 1 2 4 2 2 2 2 c                       . (15) the generators, 1 1 1 [ , )]r e e    , 2 1 2 3 1 2 3 1 1 [ ( ), ( )] 2 2 r e e e e e e           , 3 2 2 [ , ]r e e    (16) generate the icosahedral group 3 5 2 ( ) {[ , ] [ , ] } , ( , ) h i w h p p p p a c p p i        , (17) or in a shorter form, 3 ( ) {[ , ] [ , ] }w h i i i i    . here 5 51 1 , 2 2       and i is the set of 120 quaternionic elements of the binary icosahedral group (koca et al. 2001). the chiral icosahedral group is represented by the set 3 2 5 ( ) / {[ , ]}w h c a i i  which is isomorphic to the even permutations of five letters. note also that the pyritohedral group is a maximal subgroup of the coxeter group 3 ( )w h . all finite subgroups of the groups (3)o and (4)o in terms of quaternions can be found in (conway and smith, 2003). a general vector in the dual space is represented by the vector 1 1 2 2 3 3 1 2 3 ( )a a a a a a       . we will use the notation 1 2 3 ( ) ( ) ( )o w g o a a a    for the orbit of the coxeter group ( )w g generated from the vector  where the letter g represents the coxeter diagram. we follow the dynkin notation to represent an arbitrary vector 1 2 3 ( )a a a  in the dual space and drop the basis vectors , 1, 2, 3. i i  in the lie algebraic representation theory the components 1 2 3 ( )a a a of the vector  are called the dynkin indices (slansky, 1981) which are non-negative integers if it represents the highest weight vector. here we are not restricted to the integer values of the dynkin indices. they can be any real number. when the components of the vector in the dual space are non integer values we will separate them by commas otherwise no commas will be used. for an arbitrary coxeter diagram of rank 3 we define the fundamental orbits as 1 2 3 ( ) (100), ( ) (010), and ( ) (001)o o o o o o     . (18) any linear combination of the basis vectors i  over the real numbers will, in general, lead to quasi regular polyhedra under the action of the coxeter group. in the next four sections we discuss a systematic construction of chiral polyhedra and their dual solids. in our construction, a tetrahedron and icosahedron will also occur but we prove that they are not chiral polyhedra. 3. the orbit 2 2 1 2 3 ( ) ( )( )o c c a a a   as a tetrahedron the proper rotation subgroup of the coxeter group 1 1 1 ( )w a a a  applies on an arbitrary vector 1 1 2 2 3 3 2 1 ( )a e a e a e    as follows: mehmet koca et al. 33 1 2 1 1 2 2 3 3 2 1 ( )r r a e a e a e     , 2 3 1 1 2 2 3 3 2 1 ( )r r a e a e a e    , 3 1 1 1 2 2 3 3 2 1 ( )r a e a e a er      . to obtain a tetrahedron from these four vertices the dynkin indices should satisfy the relations 2 2 2 2 1 2 3 , , 1, 2, 3. i a a a a a a i      (19) we take 2 1 a  and start with a vector 1 2 3 1 ( ) 2 i e e e    then the orbit ( ) i o  will be given by 1 2 3 1 2 3 1 2 3 1 2 3 1 1 1 1 ( ) { ( ), ( ), ( ), ( )} 2 2 2 2 i e e e e e e e e e e e eo             . (20) the tetrahedron with these vertices is shown in figure 5. figure 5. the tetrahedron with the vertices given in equation (20). these are the vertices of a tetrahedron invariant under the rotation group given in (8). of course, the full symmetry of the tetrahedron is a group of order 24 isomorphic to the permutation group 4 s generated by reflections of the coxeter-dynkin diagram 3 a (koca et al. 2010). now the mirror image of the tetrahedron of (20) can be determined by applying the same group of elements in (8) on the vector 1 1 2 3 1 ( ) 2 i ii r e e e       . then the second orbit which is the mirror image of the set in (20), is determined to be 1 2 3 1 2 3 1 2 3 1 2 3 1 1 1 1 ( ) { ( ), ( ), ( ), ( )} 2 2 2 2 ii o e e e e e e e e e e e e            . (21) chiral polyhedra derived from coxeter diagrams and quaternions 38 of course we know that the union of two orbits in (20) and (21) determines the vertices of a cube. the point here is that if we were restricted to the group 2 2 c c of (8) then the tetrahedron in (20) would be a chiral solid. however this is not true because there exist additional rotational symmetries which exchange these two orbits of (20) and (21) proving that the tetrahedron is not a chiral solid. now we discuss these additional symmetries. it is obvious that the coxeter diagram in figure 1 has an additional 3 s symmetry which permutes three 1 a diagrams. indeed this symmetry extends the group 2 2 c c to the proper octahedral rotation group as will be explained now. one of the generators of this symmetry 2 3 2 3 2 2 [ , ] e e e e d     is a 2-fold rotation leading to the transformation 1 1 2 3 3 2 , ,e e e e e e    . it is straightforward to see that ( ) ( ) i ii do o   .this proves that by a proper rotation the tetrahedron can be transformed to its mirror image, and therefore that it is not a chiral solid. the generator d and those elements in (8) enlarge the symmetry to a group of order 8 which can be concisely written as the set of elements 0 0 1 1 {[ , ] [ , ]}v v v v (koca et al. 2003; koca et al. 2006a; koca et al. 2006b), where the sets 0 v and 1 v are defined by 0 1 2 3 { 1, , , }v e e e     , 2 31 1 2 2 1 { , } e ee v     . (22) a cyclic subgroup 3 c of the symmetric group 3 s permutes three sets like those in (22) extending the group 2 2 c c of order 4 to a group of order 24. actually the larger group obtained by this extension is the chiral octahedral group of order 24 which can be symbolically written as 4 3 2 {[ , ] [ , ]} ( )t t t t s w b c    . (23) this is the proper rotational symmetry of the octahedron whose vertices are represented by the set of quaternions 1 2 3 ( , , )e e e   and the cube whose vertices are the union of the orbits ( ) ( ) i i i o o   . 4. the icosahedron derived from the orbit 3 2 1 2 3 ( ) ( ( ) ) ( )o w a c a a a  the proper rotational subgroup of the coxeter group 3 4 ( )w a s is the tetrahedral group 4 a , the even permutations of the four letters, of order 12. they can be generated by the generators 1 2 a r r and 2 3 b r r which satisfy the generation relation 3 3 2 ( ) 1.a b ab   let 1 2 3 ( )a a a  be a general vector. the following sets of vertices form equilateral triangles: 2 2 1 2 1 2 2 3 2 3 ( , , ( ) ), ( , , ( ) )r r r r r r r r      (24) with the respective square of edge lengths 2 2 1 1 2 2 2( )a a a a  and 2 2 2 2 3 3 2( )a a a a  . we have another vertex 1 3 3 1 r r r r   as shown in figure 6. mehmet koca et al. 89 23rr 21rr 12rr 31rr 32rr  1 3 54 2 figure 6. the vertices connected to the general vertex  . then one can obtain three more triangles by joining 1 3 r r  to the vertices 1 2 r r  and 3 2 r r  and by drawing a line between 2 1 r r  and 2 3 r r  . if we require that all these five triangles be equal to each other then we obtain the relations: 2 2 2 2 2 2 1 1 2 2 2 2 3 3 1 3 ( ) ( ) ( )a a a a a a a a a a       . (25) factoring by 2 2 a and defining 1 2 a x a  and 3 2 y a a  one obtains yx  and a cubic equation 3 2 0x x x   . assuming 0x  we get the solutions x  and x  this leads to two vectors 2 1 2 3 ( + ) i a      and 2 1 2 3 ( + ) ii a      here 2 a is an overall scale factor which can be adjusted accordingly. the 0x  solution represents an octahedron which is not a chiral solid anyway. let us study the orbit which is obtained from the vector i  . when expressed in terms of quaternions it will read 2 2 3 ( ). i a e e    we choose the scale factor 2 2 a   for convenience. to obtain the orbit 3 2 ( ) ( ( ) ) i i o w a c   we use the generators of the tetrahedral group of interest in terms of quaternions, namely, 1 2 3 1 2 3 1 1 1 1 [ (1 ), (1 )], d [ , ] 2 2 c e e e e e e e e         . (26) they act on the quaternionic units as follows: 1 2 3 1 1 1 2 2 3 3 : ; : , , c e e e e d e e e e e e        . (27) applying the generators c and d several times on the vector 2 3 1 ( ) 2 i e e   we obtain the set of vectors 1 2 2 3 3 1 1 1 1 ( ) { ( ), ( ), ( )} 2 2 2 i o e e e e e e          (28) which constitute the vertices of the icosahedron shown in figure 7. chiral polyhedra derived from coxeter diagrams and quaternions 89 figure 7. the icosahedron obtained from tetrahedral symmetry 4 a . similarly if we use the solution x  we will get the vector 2 3 1 ( ) 2 ii e e    after a suitable choice of the factor 2 a . applying the generators in (27) repeatedly on the vector ii  we get the orbit 1 2 2 3 3 1 1 1 1 ( ) { ( ), ( ), ( )} 2 2 2 ii o e e e e e e          . (29) this is another icosahedron which is the mirror image of the icosahedron of (28). indeed one can show that 1 1 ( ) ( ) ( ) i i ii r o o r o     . before we proceed further we note the fact that the coxeter-dynkin diagram 3 a has the diagram symmetry 1 3   and 2 2   , in other words, 1 3   and 2 2   . it is clear that this symmetry does not alter the orbits since under the diagram symmetry the vectors i  and i i  remain intact. the diagram symmetry acts on the quaternions as 1 1 2 2 , e ee e   and 3 3 e e . this transformation can be obtained by the action of the element 1 1 [ , ]e e   which is not an element of the group 3 4 ( )w a s . the proper rotation group 4 [ , ]a t t can then be extended by the generator 1 1 [ , ]e e   to the pyritohedral group 4 2 {[ , ] [ , ] }. h t a c t t t t      actually in a previous paper (koca et al. 2010) we have shown that the orbit ( ) i o  is invariant under a larger group h i of (17) which admits the pyritohedral group as a maximal subgroup. it is straightforward to see that the element 1 1 2 2 1 1 [ , ] e e d    exchanges the two icosahedral orbits; i ii : o( ) o( )d    . one can see that the element d represents a rotation around the first axis by 90 and extends the group 4 [ , ]a t t to the proper octahedral rotation group 4 4 2 : {[ , ] [ , ]}.s a c t t t t    this proves that two mirror images of the icosahedron are transformed to each other by rotations therefore the icosahedron is not a chiral solid rather it is achiral. when two orbits of (28) and (29) are combined one obtains a quasi regular polyhedron which can be obtained as the orbit of the group 3 ( )(1, , 0)w b  (koca et al. 2011a). the quasi regular polyhedron represented by the combined vertices of (2829) is shown in figure 8 . it consists of two types of faces, squares of side  and isogonal hexagons of sides 1and . mehmet koca et al. 89 figure 8. the quasi regular polyhedron represented by the vertices of (28-29). although we know that the dual of an icosahedron is a dodecahedron (koca et al. 2010) here we show how the vertices of the dodecahedron can be obtained from the vertices of the icosahedron, say, from the vertices of ( ) i o  given in (28). we have to determine the centers of the planes in figure 6. we can choose the vector 1  as the vector representing the center of the face #1 because it is invariant under the rotation represented by 2 3 r r . in other words the triangle #1 is rotated to itself by a rotation around the vector 1  . for the same reason the center of the face #3 can be taken as the vector 3  . we note that the line joining these vectors is orthogonal to the vector i  , namely, 1 3 ( ). 0 i     . the centers of the faces #2, #4 and #5 can be determined by averaging the vertices representing these faces: 1 2 3 4 1 2 1 3 5 3 1 3 22 2 1 1 ), ( ), ( ) 3 3 1 ( 3 i i i i i i i ii r r r b r r r r b r r r rb r                  (30) since we have the following relations among these three vectors 1 2 2 4 r r b b , 3 2 4 5 r r b b and 3 2 2 5 ,r r b b they are in the same orbit under the group action 4 2 4 4 4 5 ( ) ( ) ( ).a b a b a b  therefore it is sufficient to work with one of these vectors, say, with 2 b . in terms of the quaternionic units it reads 2 2 2 3 ( ) 6 b e e     . a quick check shows that 2 1 b  is not orthogonal to the vector i  rather 2 1 ( ). 0 i b    provided 2 3  . then we obtain three orbits: 4 2 1 2 2 3 3 1 1 1 1 ( ) { ( ), ( ), ( )}, 2 2 2 a b e e e e e e             4 1 1 2 3 1 2 3 1 2 3 1 2 3 1 1 1 1 ( ) { ( ), ( ), ( ), ( )}, 2 2 2 2 a e e e e e e e e e e e e            (31) 4 3 1 2 3 1 2 3 1 2 3 1 2 3 1 1 1 1 ( ) { ( ), ( ), ( ), ( )} 2 2 2 2 .a e e e e e e e e e e e e            note that the last two orbits represent the vertices of two dual tetrahedra which, when combined, represent a cube. these 20 vertices which decompose as three orbits under the tetrahedral group represent the vertices of a dodecahedron as shown in the figure 9 which is also an achiral solid. so far we have shown that, although, a chiral polyhedra derived from coxeter diagrams and quaternions 88 2 2b 1 3 54 2 2 2 2 22 2 2 2 2 tetrahedron and icosahedron can be obtained as chiral solids there exist additional proper rotational group elements that convert them to their mirror images. therefore they are not chiral solids. figure 9. dodecahedron represented by the vertices of (31). although our main topic is to study the chiral objects systematically using the coxeter diagrams, here with a brief digression, we construct the pyritohedron, a non regular dodecahedron, made by 12 irregular pentagons. if we plot the solid represented by the orbit 4 2 ( )a b in the first line of (31) we obtain an irregular icosahedron as shown in figure 10. figure 10. irregular icosahedron represented by the vertices of the orbit 4 2 ( )a b . let us recall that the vector 2 1 2 3 1 ( ) 2 b      differs from the vector i  by the sign in front of 2  . in figure 11 we show the faces joining to the vector 2 b . figure 11. faces of the irregular icosahedron joined to the vertex 2 b . mehmet koca et al. 88 there we see that two of the triangles are equilateral and the remaining three are isosceles triangles. we determine the centers of the faces of this irregular icosahedron. the faces #1 and #3 can be represented again by the vectors 1  and 3  respectively. the centers of the faces of the #2, #4 and #5 can be determined, up to a scale factor, by averaging the vectors representing the vertices of the isosceles triangles. they can be obtained, up to a scale factor, as: 2 2 3 4 3 1 5 3 1 ( 2 ) , ( 2 ) , ( 2 )d e e d e e d e e                 . (32) these three vertices determine a plane which can be represented by its normal vector 2 3 5 (7 )d e e   up to a scale factor. now, we can determine the scale factor  so that 2 1 ( ). 0d d   determines the five vertices lying in the same plane. we obtain 205 280 1210     . the particular edge represented by the vector 4 5 1 2d d e  leads to an orbit of size 6 given by 1 2 3 2 { , , }e e e    . this shows that the pyritohedral group transforms this type of edges to each other. the vertices of the pyritohedron are given by the set of quaternions: 1 2 2 3 3 1 { ( 2 ) , ( 2 ) , ( 2 ) }, e e e e e e                  1 3 1 2 3 1 ( ) ( ) { ( )} 2 o o e e e      (33) which leads to the pyritohedron as shown in figure 12. its symmetry is represented by pyritohedral group 4 2 {[ , ] [ , ] }a c t t t t     of order 24. the 20 vertices of the pyritohedron lie in three orbits 20=12+4+4 as shown in (33). figure 12. the pyritohedron consisting of irregular pentagonal faces. a variety of pyritohedra can be constructed. if two orbits of the tetrahedron leading to the vertices of a cube are chosen to be the set of quaternions 1 2 3 ( )e e e   then one can build the orbit of size-12 which depends on a single parameter. indeed the following sets of 12 quaternions are invariant under the pyritohedral group h t : 1 2 2 3 3 1 { , , } ae be ae be ae be      (34) where a and b are arbitrary real parameters. here now, three vectors 2 3 3 1 , ae be ae be  determine a plane whose normal can be represented by the vector 2 3 ( )a b e ae  . the condition that five points represented by the vectors 1 2 3 ( ),e e e  chiral polyhedra derived from coxeter diagrams and quaternions 88 32rr  2 23 )( rr 31rr 23rr 12rr 21rr  1 5 4 3 2 1 2 3 ( )e e e   and 2 3 3 1 , ae be ae be  are in the same plane determines that 2 2b a a  . therefore the set of vertices of a pyritohedron has an arbitrary parameter and includes also the dodecahedron and the rhombic dodecahedron (koca et al. 2010), a catalan solid, as members of the family for a  and 2a  respectively. the pyritohedron is face-transitive since the normal vectors of the faces form an orbit of size 12 under the pyritohedral group. it is an achiral solid. 5. the snub cube derived from the orbit 3 2 1 2 3 ( ) ( ( ) ) ( )o w b c a a a  the snub cube is an archimedean chiral solid. its vertices and its dual solid can be determined employing the same method described in sec.3 and sec.4. the proper rotational subgroup of the coxeter group 3 4 2 ( )w b s c  is the octahedral group 3 2 4 ( )w b c s , isomorphic to the symmetric group of order 24. they can be generated by the generators 1 2 a r r and 2 3 b r r which satisfy the generation relation 3 4 2 ( ) 1 a b ab   . let 1 2 3 ( )a a a  be a general vector. the following sets of vertices form an equilateral triangle and a square respectively: 2 2 3 1 2 1 2 2 3 2 3 2 3 ( , , ( ) ), ( , , ( ) , ( ) )r r r r r r r r r r       (35) with the respective square of edge lengths 2 2 1 1 2 2 2( )a a a a  and 2 2 2 2 3 3 22( )a a a a  . we have another vertex 1 3 3 1 r r r r   as shown in figure 13. figure 13. the vertices connected to the vertex  . similar to the arguments discussed in sec.4 we obtain four equilateral triangles and one square sharing the vertex 1 2 3 ( )a a a  (see figure 13) provided the following equations are satisfied 2 2 2 2 2 2 1 1 2 2 2 2 3 3 1 3 2( ) ( ) ( )a a a a a a a a a a       . factoring by 2 2 a and defining again 1 2 a x a  and 3 2 y a a  one obtains 2 2 1 y x   and the cubic equation 3 2 1 0x x x    . this equation has one real solution 1.8393.x  now the first orbit can be derived mehmet koca et al. 88 from the vector 2 1 2 3 ( + ) i a x y     and its mirror image can be defined as 1 2 1 1 2 3 ( ( ) + ). ii i r a x y        in terms of quaternionic units the vectors read: 2 12 1 2 3 ( 1) ( +e ) 2 i a x xe x e      , 2 12 1 2 3 2 ( 1) ( ) ii a x e xe x e      . (36) deleting the overall scale factor in (36) the set of vectors constituting the orbits can be easily determined (koca et al. 2010) as 1 1 1 1 2 3 2 3 1 3 1 2 ( ) {( e ), ( e ), ( e )}, i o xe x e xe x e xe x e               1 1 1 1 2 3 2 3 1 3 1 2 ( ) {( e ), ( e ), ( e )}. ii o e x x e e x x e e x x e               (37) the snub cubes represented by these sets of vertices are depicted in figure 14. note that no proper rotational symmetry exists t transforms these two mirror images to each other so that they are truly chiral solids. (a) (b) figure 14. two snub cubes (a) ( ) i o  and (b) ( ) ii o  (mirror image of each other). one can combine the vertices of these two chiral solids in one solid which is achiral and it is depicted in figure 15. this quasi regular solid can be obtained from the vector 2 1 2 3 ( + ) i a x y     by applying the octahedral group 3 ( )( ) i w b  . figure 15. the quasi regular polyhedron consisting of two chiral orbit ( ) i o  and ( ) ii o  . chiral polyhedra derived from coxeter diagrams and quaternions 88 the dual of the snub cube can be determined by determining the centers of the faces as shown in figure 13. similar arguments discussed in sec. 4 can be used to determine the centers of the faces in figure 13. the faces #1 and #3 are represented by the vectors 1  and 3  respectively. the vectors representing the centers of the faces #2, #4 and #5 can be determined and they lie in the same orbit under the proper octahedral group. the vector representing the center of the face #2 can be given, up to a scale factor, in terms of the quaternionic units as: 2 2 1 2 3 (2 1) +e . c x e x e   (38) the scale factors multiplying the vectors 1 3 ,   and 2 c can be determined as 2 x   and 2 2 x    when i  represents the normal of the plane containing these five points. then 38 vertices of the dual solid of the snub cube, the pentagonal icositetrahedron, are given in three orbits as follows: 3 1 2 3 1 1 2 3 2 2 2 2 2 1 2 3 2 3 1 3 1 2 1 ( ) ( ), 2 2 ( ) { , , }, ( ) {[ (2 1) ], [ (2 1) ], [ (2 1) o e e e x o e e e x o c x e e x e x e e x e x e e x                          2 ]}.e (39) the pentagonal icositetrahedron is shown in figure 16. figure 16. the pentagonal icositetrahedron, a catalan solid, dual of the snub cube. 6. the snub dodecahedron derived from the orbit 3 2 1 2 3 ( ) ( ( ) ) ( )o w h c a a a  the snub dodecahedron is the second archimedean chiral solid. its vertices and its dual solid can be determined employing the same method described in section 5. the proper rotational subgroup of the coxeter group 3 5 2 ( )w h a c  is the icosahedral group 3 2 5 ( )w h c a , which is the simple finite group of order 60 representing the even permutations of five letters. they can be generated by the generators 1 2 a r r and 2 3 b r r which satisfy the generation relation 5 3 2 ( ) 1.a b ab   let 1 2 3 ( )a a a  be a general vector. the following sets of vertices form a pentagon and an equilateral triangle respectively 2 3 4 2 1 2 1 2 1 2 1 2 2 3 2 3 ( , , ( ) , ( ) , ( ) ), ( , , ( ) )r r r r r r r r r r r r        (40) mehmet koca et al. 83 1 2 3 4 5 32rr 23rr 21rr 31rr 12rr  2 21 )( rr  3 21 )( rr  with the respective square of edge lengths 2 2 1 1 2 2 2( )a a a a  and 2 2 2 2 3 3 2( )a a a a  we have another vertex 1 3 3 1 r r r r   which is depicted in figure 17. figure 17. the vertices connected to the vertex  . the only difference of this from the one in figure 13 is that in the present case the face #1 is an equilateral triangle whose center is represented by the vector 1  and the face #3 is a regular pentagon whose center is represented by the vector 3  . assuming that face #1, face #2, face #4 and face #5 are equilateral triangles which lie in the same orbit of size 60 one obtains the following equations: 2 2 2 2 2 2 1 1 2 2 2 2 3 3 1 3 ( ) ( ) ( ).a a a a a a a a a a       (41) factoring by 2 2 a and defining 1 2 a y a  and 3 2 a x a  one obtains 2 1 y 1 x x       and the cubic equation is 3 2 0x x x     . this equation has the real solution 1.94315x  . now the first orbit can be derived from the vector 2 1 2 3 ( + ) 1 i a x x        and its mirror image can be defined as 1 2 1 1 2 3 ( ( ) + ). 1 ii i r a x x           in terms of the quaternionic units these vectors read: 2 32 1 2 3 2 [ ( 1) e (1 ) ], i a x e x x e       2 32 1 2 3 2 [ ( 1) e (1 ) ]. ii a x e x x e        (42) two snub dodecahedra obtained using these vectors are shown in figure 18(a) and (b). one can combine the vertices of these two chiral solids in one solid which is achiral and it is depicted in figure 18(c). this quasi regular solid (quasi regular great rhombicosidodecahedron) can be obtained from the vector 2 1 2 3 ( + ) 1 i a x x        by applying the icosahedral group 3 ( )( ). i w h  chiral polyhedra derived from coxeter diagrams and quaternions 88 (a) (b) (c ) figure 18. the snub dodecahedron (a) ( ) i o  and (b) its mirror image ( ) ii o  , (c) quasi regular great rhombicosidodecahedron. the vertices of the dual solid (pentagonal hexecontahedron) of the snub dodecahedron represented by ( ) i o  can be given as the union of three orbits of the group 3 2 5 ( ) .w h c a the orbit 1 ( )o  consists of 20 vertices of a dodecahedron. the second orbit consists of 12 vertices of an icosahedron 3 ( )o  where 2 2 3 2 (2 ) 1 . x x x x              (43) the third orbit 2 ( )o c involves the vertices including the centers of faces #2, #4 and #5 where the vector 2 c is given by 2 3 2 2 122 1 3 2 {[(2 1) 1] (21 20) (21 17) 21 11 x x c x x e x x                      (44) 2 3 3 2 3 ( 3 3) ( ) }.x x e x e        applying the group 5 [ , ]a i i on the vector 2 c one generates an orbit of size 60. the 92 vertices consisting of these three orbits constitute the dual solid (pentagonal hexecontahedron) of the snub dodecahedron represented by the orbit ( ). i o  the pentagonal hexecontahedron is shown in figure 19. figure 19. the pentagonal hexacontahedron, the dual of the snub dodecahedron. mehmet koca et al. 999 the pentagonal hexacontahedron is one of the face transitive catalan solid which has 92 vertices, 180 edges and 60 faces. 7. concluding remarks in this work we presented a systematic construction of the chiral polyhedra, the snub cube, snub dodecahedron and their duals using proper rotational subgroups of the octahedral group and the icosahedral group. we used the coxeter diagrams 3 b and 3 h respectively. employing the same technique for the diagrams 1 1 1 a a a  and 3 a we obtained the vertices of a tetrahedron and icosahedrons which are not chiral solids because they can be transformed to their mirror images by the proper rotational subgroup of the octahedral group. as a by-product we also constructed the orbit of the pyritohedron using the pyritohedral group which is the symmetry of the iron pyrites. this method can be extended to the higher dimensional coxeter groups to determine the chiral polytopes. for example, the snub 24-cell, a chiral polytope in the 4d euclidean space can be determined using the 4 d coxeter diagram (koca et al. 2011b). 8. references carter, r.w., 1972. simple groups of lie type, john wiley & sons ltd. caspar, d.l.d. and klug, a., 1962. physical principles in the construction of regular viruses. cold spring harbor symp. quant. biol. 27:1-24. conway, j.h. and smith, d.a., 2003. on quaternion’s and octonions: their geometry, arithmetics, and symmetry, a.k.peters, ltd, natick, ma. cotton, f.a., wilkinson, g., murillo, c.a. and bochmann, m., 1999. advanced inorganic chemistry (6 th ed.) wiley-interscience, new york. coxeter, h.s.m. and moser, w.o.j., 1965. generators and relations for discrete groups, springer verlag. humphreys, j.e., 1990. reflection groups and coxeter groups, cambridge university press, cambridge. huybers, p and coxeter, h.s.m., 1979. a new approach to the chiral archimedean solids. c.r. math. reports acad. sci. canada. 1: 259-274. jaric, m.v. 1989. introduction to the mathematics of quasicrystals, academic press, new york. koca, m., koc, r. and al-barwani, m., 2001. noncrystallographic coxeter group h4 in e8. j. phys. a: math. gen. 34: 11201-11213. koca, m., koc, r. and al-barwani, m., 2003. quaternionic roots of so(8), so(9), f4 and the related weyl groups. j. m. phys. 44: 03123-03140. koca, m., al-barwani, m. and koc, r., 2006a. quaternionic root systems and subgroups of the aut(f4). j.m. phys. 47: 043507-043521. koca, m., koc, r. al-barwani, m. and al-farsi, s., 2006b. maximal subgroups of the coxeter group w(h4) and quaternions. linear alg. appl. 412: 441-452. koca, m., al-ajmi, m., koc, r., 2007. polyhedra obtained from coxeter groups and quaternions. j. math. phys. 48: 113514-113527. koca, m., koca, n.o. and koc, r. 2010. catalan solids derived from 3d-root systems. j. math. phys. 51: 043501-043513. koca, m., al-ajmi, m. and al-shidhani, s., 2011a. quasi regular polyhedra and their duals with coxeter symmetries represented by quaternions-ii. the african review of physics, 6: 0007 53-67. chiral polyhedra derived from coxeter diagrams and quaternions 999 koca, m., koca, n.o. and al-barwani, m., 2011b. snub 24-cell derived from the coxeter-weyl group w(d4), arxiv:1106.3433. slansky, r., 1981. group theory for unified model building. phys. rep.79 (1): 1-128. twarock, r., 2006. a mathematical physicist's approach to the structure and assembly of viruses phil. trans. r. soc. a365, 3357-3374. weissbach, b. and martini, h., 2002. on the chiral archimedean solids. beitrage zur algebra und geometrie -contributions to algebra and geometry, 43 (1): 121-133. received: 1 october 2011 accepted: 16 november 2011 photovoltaic cells and systems: squ journal for science, 18 (2013) 25-32 © 2013 sultan qaboos university 25 synthesis of doped and non-doped nano mgo ceramic membranes shiraz labib nuclear chemistry department, hot laboratories center, atomic energy authority, cairo, egypt, email: dr_sh_labib@yahoo.com. abstract: doped and non-doped mgo coated thin films on alumina substrates were prepared using a chelating sol-gel method under controlled conditions to prepare nanomaterials with unprecedented properties. the effect of doping of zno on thermal, surface and structural properties was investigated using dta-tg, bet and xrd respectively. also microstructural studies and coating thickness measurements of mgo thin film were conducted using sem. an increase in the thermal stability of mgo with increasing zno doping percent was observed. the increase of zno doping percent showed a marked decrease in the average particle size of mgo powder as a result of the replacement of some mg 2+ by zn 2+ which has similar ionic radius as mg 2+ . this decrease in particle size of mgo was also related to the decrease of the degree of mgo crystalinity. the increase of zno doping also showed a marked decrease in coating thickness values of the prepared membranes. this decrease was related to the mechanism of zno doping into a mgo crystal lattice. keywords: mgo; mgo-zno; polymeric sol-gel; doping mechanism; nano properties; thin films. تحضير أغشية سيراميكية مطعمة وغير مطعمة من نانو أكسيد الماغنيسيوم شيراز لبيب الخارصيٌن كطبايار رقٌايط مطي بأكسٌدكسٌد الماغنٌسٌوم المطعم أكسٌد الماغنٌسٌوم و أفى هذا البحث تم تحضٌركل من :ملخص ظروف تحضٌر محكميط و ذليل لتحضيٌر ميواد نانومترٌيط عند sol-gelكسٌد األلومنٌوم باستخدام طرٌاط أعلى دعامار مصنعط من الخصياص و السيطحٌط و ذار مواصفار غٌر مسبوقط. تم عمل دراسط تأثٌر التطعٌم بأكسٌد الخارصٌن عليى المواصيفار الحرارٌيط حٌود و حط السطوحقٌاس مسا و الوزنًو التفاضلً يالتحلٌل الحرار ألكسٌد الماغنٌسٌوم و ذلل بدراسط الظاهريالبللورٌط و الشكل لٌط تطعٌم أكسٌد الماغنٌسيٌوم بأكسيٌد آ. تم استنتاج ع قط بٌن لألغشٌط المحضر اإللكترونًوسكوب الماسح راألشعط السٌنٌط و المٌك الثبيار الحيرارأل ألكسيٌد الماغنٌسيٌوم المطعيم ماارنيط فيًالخارصٌن و النتاصج المختلفيط للاٌاسيار المعنٌيط. هيذا و قيد ليوحظ تحسيٌن لألغشيٌط المحضير بزٌياد نسيبط التطعيٌم. يجسٌمار و السيلول البلليورالحجم فًلوحظ وجود ناصان و قد ألكسٌد الغٌر المطعم. با ن العنصيرٌن لمميا قيٌم أالخارصٌن خاصيط و بأٌونارٌونار الماغنٌسٌوم أبعض بإح لحجم الجسٌمار له ع قط فًوهذا الناصان تقليل سمك الطبقاث المحضرة لألغشيت بزيادة نسبت التطعيم. ٌضا السبب وراء أبا كما ٌوضح تارٌ األٌونًمماثلط لنصف الاطر ، الماغنيسيم المطعم ، مواد نانومتريت ، طبقاث رقيقت. sol-gel: اكسيذ الماغنيسيم ، اكسيذ الخارصين ، طبقاث مفتاح الكلمات 1. introduction go is a highly ionic crystalline solid, which crystallizes into a cubic rock salt structure. it is characterized by a large band gap (7.8 ev), high thermal conductivity and stability (raj et al., 2007). it has extensive applications in the area of toxic waste remediation, refractory, paint and superconductor products. it also shows excellent adsorption properties in enhanced surface areas and intrinsically higher surface reactivity (niu et al., 2006). due to its superior electronic properties, it can be used as a substrate for high temperature superconductor film deposition. it has a wide application in microwave devices (raj et al., 2007). mgo thin films are of scientific and technological importance due to their applications in optical and electronic devices, in catalytic reactions, as protective coatings on metals and in gas sensors (raj et al., 2007). therefore, mgo is considered an important applied and economical material. nano mgo ceramic membranes are prepared by a sol-gel process that offers enhanced homogeneity and better control for the size, the shape and the degree of agglomeration of the resulting nanocrystals, as well as simple compositional control and low processing temperature (maensiri et al., 2007; iyer et al., 2009; desai et al., 2007; caruntu, 2006; cernea, 2005; m shiraz labib 62 willard et al., 2004). a better control of precursor reactivity may be achieved through the addition of chelating agents such as ß-diketones, carboxylic acids or other complex ligands (cernea, 2005; sanchez et al., 1988). this paper deals with the preparation of doped and non-doped nano mgo membranes using a polymeric sol-gel method that offers the possibility of controlling the synthesis of thin film hierarchical internal structure (crisan et al. 2000). doping mgo with zno is studied in order to create doped nanocrystals and nanostructures with unprecedented properties (yang et al., 2010). the effect of zno doping on thermal, surface and structural properties is studied. also microstructural studies and coating thickness measurements of mgo thin film are conducted. the relationship between the mechanism of zno doping into a mgo crystal lattice and the properties studied is discussed. 2. experimental 2.1 substrate preparation disk alumina substrates of thickness (0.1cm), diameter (10 cm), pore size distr ibution (0.1 µm), and porosity (18.42 vol. %) (labib, 2006) were used for doped and non-doped mgo coating thin films. these substrates were synthesized by a polymeric sol-gel process using aluminium tri-second butylate (99.9 % merck, germany), distilled water, isopropyl alcohol (99.8 % scharlau, spain) and glacial acetic acid (98 % merck, germany). the precursors used were of a.r. grade. glacial acetic acid (2 mol), as a chelating agent, was added to the alcoholic solution of aluminium tri-second butylate having the molar ratio (isopropyl alcohol/aluminium tri-second butylate: 5:1 respectively). this solution was stirred for ten minutes, then it was exposed to a controlled rate of hydrolysis with a diluted solution of isopropyl alcohol having the molar ratio (isopropyl alcohol/distilled h2o: 5:0.5 respectively). the prepared polymeric sol was stirred for ten minutes and then aged at room temperature for 48 h. the aged polymeric sol was dried at 120 o c for 1h, calcined at 500 o c for 1h, ground for 15 min, pressed uniaxially at 12 k.n using (poly vinyl alcohol) as a binder and then sintered at 1100 o c for 1h (labib, 2006). 2.2 membrane preparation doped and non-doped mgo ceramic membranes were initially prepared using magnesium nitrate hexahydrate [99% winlab, england], zinc nitrate hexahydrate [99% merck, germany], isopropyl alcohol [99.8% scharlau, spain], acetylacetone [≥ 99% merck, germany] and distilled water. all the reagents used were of a.r. grade. the composition of the prepared samples is shown in table 1. table 1. composition of the prepared samples. sample mgo % zno % m100 100 00 m99 99 01 m95 95 05 m90 90 10 polymeric magnesium oxide sol was prepared by drop-wise addition of an alcoholic mixture of isopropyl alcohol (5.0 mol) and distilled water (1.0 mol) to the stirred alcoholic solution of magnesium nitrate hexahydrate and acetyl acetone having the molar ratio (isopropyl alcohol /magnesium nitrate /acetyl acetone: 10:0.8:1.6 respectively). the different doped mgo-zno sols were prepared by adding 1, 5 and 10% of zinc nitrate hexahydrate to each of the alcoholic solutions of 99, 95 and 90% of magnesium nitrate hexahydrate, followed by adding acetyl acetone. the mixed polymeric sols were prepared by drop-wise hydrolysis with the alcoholic mixture of isopropyl alcohol and distilled water. the different prepared polymeric sols were stirred vigorously for 20 min. the dip coat process was performed at room temperature by immersing alumina substrates into the different polymeric sols for 2 h (peters et al., 2005), (immersion and withdrawal rate: 0.5 mm 1 s  ). after dip coating, the different ceramic membranes were left overnight to be dried at room temperature. the different prepared membranes and the unsupported membranes were dried at 200 o c for 1h with a heating rate of 3 o c 1 min  . the process of dipping, withdrawing and drying was repeated 6 times to obtain suitable coating thicknesses (sekulic et al., 2006) and then the membranes were sintered at 400 and 600 o c for 6 h with a heating rate of 3 o c 1 min  . 2.3 membrane characterization the thermal degradation behaviors of the unsupported membranes were studied using differential thermal analysis (dta) and thermogravimetric (tg) analysis (shimadzu 60, japan). dta/tg studies were performed by heating the sample from room temperature to 400 o c in an air atmosphere with a heating rate of 3 o c 1 min .  specific surface area measurements were taken, applying the brunauer-emmet-teller (bet) method, using (nova 3200 series, synthesis of doped and non-doped nano mgo ceramic membranes 62 usa). prior to the analysis, the different samples were evacuated at 300 o c for 2h. particle size values of the unsupported membranes were calculated from: dbet = 6/ssabet.ρsample (1) where, ρsample is the density of the samples used (mikhail and robens, 1975), ρsample was calculated from the density of mgo (ρmgo ) = 3.58 x 10 3 kg/m 3 and the density of zno (ρzno) = 5.61 x 10 3 kg/m 3 taking into consideration the appropriate amount of both components (samerjai et al., 2009). the crystal structures of the different unsupported membranes were identified using x-ray diffraction (xrd) (philips x’pert multi-purpose diffractometer, usa). a copper-tube x-ray tube operating at 40 kv and 30 ma was used, and the wavelength kα1 used was 1.54056 a 0 . the scan was performed over the range 2 (40-70). the identification of the crystalline phases present was done using the jcpds database cards. the microstructures and coating thicknesses of the prepared membranes were studied using a scanning electron microscopy (sem) (jeol jsm-5600, japan). prior to sem analysis, the samples were sputtered with a thin layer of gold using jeol fine coat (jfc-1500 ion sputtering device, japan). 3. results and discussion 3.1 unsupported membranes 3.1.1 differential thermal analysis-thermogravimetric analysis (dta-tg) thermal properties of the unsupported membranes were investigated using dta/tg analysis and the corresponding curves are shown in figure 1. owing to the low heating rate used (3 o c 1 min  ), the samples were heated only to 400 o c. tg curve for the sample m100 shows two weight losses at t< 300 oc. the gradual mass loss below 300 o c could be assigned to the evaporation and the elimination of the bonded water, residual organic solvents as well as to the burning of nitrate groups from the metal nitrate precursor. this result was correlated to the two endothermic peaks of the dta curve at t<100 oc (li et al., 2008; anas et al., 2010). the third distinct weight loss ~37.83% at 100400 o c was due to the crystallization of mg(oh)2 to cubic mgo as indicated from the weight loss value (37.83%). figure 1. dta-tg analysis for (a) m100 and (b) m90 membranes in air with a heating rate of 3 o c/min. the theoretical weight loss for mg(oh)2 transformation to mgo is (30.8%) (niu et al., 2006). the exothermic peaks at 400 o c in the dta curve demonstrated the occurrence of the reaction (li et al., 2008). on the other hand, the tg curve for m90 shows four distinct weight loss regions at temperatures (20-400 o c): two weight losses ~ 13.8 and shiraz labib 62 20.4% from 20 to 250 o c corresponding to the combined evaporation of bonded water, residual organic solvents and the nitrate groups from both magnesium nitrate and zinc nitrate. this explained the increase in weight loss percent with respect to the pure material. the two weight losses ~ 16.5 and 8.7% at 250-400 o c correspond to the transformation to mgo and zno respectively taking in mind the stoichiometric ratio of the metal precursor used. an important feature which was observed was the shift of weight loss to higher temperature with respect to the case of pure material. this result indicated the role of dopant (zno) in increasing the thermal stability of the mgo phase (han et al., 2007). also, the presence of two weight losses at 250-400 o c confirmed the presence of two phases: cubic mgo and hexagonal zno wurtzite structures. 3.1.2 specific surface area measurements (ssa) table 2 shows the specific surface area values of the unsupported membranes thermally treated at 600 o c for 6h. a marked increase in specific surface area values was observed with increasing zno doping percent. this increase was accompanied by a decrease in particle size as shown in table 2. the decrease in particle size means a decrease in the crystalline behavior of the cubic mgo by incorporating zno. this result was explained as follows: since the ionic radius of zn 2+ (0.083) nm is similar to that of mg 2+ (0.078) nm, the position of mg 2+ can be occupied by zn 2+ (huang et al., 2008; saraiva et al., 2010). mgo structure is similar to the well-known nacl structure. the o 2 anions are in a cubic closest packing and the mg 2+ cations fill all the octahedral sites (saraiva et al., 2010). the increase in doping percent of zno indicated that the octahedral positions occupied by mg 2+ ions were replaced by zn 2+ ions and when the doping percent reached 50% the structure became unstable and a disappearance of mgo structure was observed (saraiva et al., 2010). in general, the mgo structure was determined under thermodynamic conditions, the increase of doping percent can decrease the mobility of adatoms (zno atoms) within the structure. so, the structure became kinetically not thermodynamically determined (saraiva et al., 2010). this result was confirmed by the increase in the mgo peak broadness given in xrd results. table 2. specific surface area and particle size values of the unsupported membranes thermally treated at 600 o c for 6h. sample specific surface area (ssa) (m 2 /g) particle size dbet (nm) m100 m99 m95 m90 26.56 74.37 106.70 121.54 63.0 22.4 15.0 13.0 3.1.3 x-ray diffraction analysis (xrd) figure 2 shows the xrd patterns of doped and non-doped mgo powder thermally treated at 600 o c for 6 h. the characteristic peak of pure mgo (200) was presented at 2 ~ 43 degrees as indicated from (jcpds-card n0 45-0946). the development of zno peak (103) at 2 ~ 62 degree (jcpds-card n0 36-1451) was observed with increasing zno doping percent. a marked increase in the peak broadness of mgo, as marked by the arrow, was observed which confirms the decrease in the particle size and the crystallinity of mgo with adding zno, as given previously. two important features were observed: ithe increase of mgo peak broadness and its shift to a higher angle with increasing zno doping percent. this shift was due to the variation of the lattice parameters confirming that zno was alloyed with mgo forming a mg(zn)o solid solution. this trend was known as vergard's law which states that the lattice parameters depend on the composition (saraiva et al. 2010). from this behavior, it was concluded that mg(m)o systems can be treated as solid solutions (saraiva et al., 2010). this means that the replacement of mg by a cation with smaller radius was accompanied by a decrease in the lattice parameter and the opposite was noticed with a replacement by a larger cation (saraiva et al., 2010). iithe development and the intensity increase of zno peak (103) with increasing the doping percent indicated the presence of zno as a secondary phase. this result was also confirmed from tg results. so, not all zno was alloyed with mgo. synthesis of doped and non-doped nano mgo ceramic membranes 62 figure 2. xrd patterns of doped and non-doped mgo membranes thermally treated at 600 o c for 6h. (a) m100, (b) m99, (c) m95 and (d) m90. 3.2 supported membranes 3.2.1 scanning electron microscopy (sem) figures 3 (a-d) show the sem, at a magnification power of 8000 x, of doped and non-doped mgo thermally treated at 600 o c for 6h. a dense film of nanoparticles (200 nm) was shown in m100. the aggregated nanoparticles were in fact formed from tiny nanocrystallites within the size range of a few nm. the increase in the doping percent of mgo film with zno shows the development of a porous structure with slight variation in the average particle size. this decrease in structure density with increasing the doping percent can be attributed to the low mobility of the adatoms on the surface of the mgo films (park et al., 2005). the decrease in adatom mobility on the mgo surface leads to the decrease in mgo (200) orientation, i.e. the decrease of the degree of crystallinity (park et al., 2005). this result confirmed the result obtained in the ssa and xrd results. the adatoms acted as a grain growth inhibitor and influenced the grain growth kinetics either by pinning grain boundary or by changing the thermodynamic factors such as surface and grain boundary energies respectively (suzuki et al., 2002). the energy necessary for the movement of mgo grain boundary increased and the driving force for the grain boundary migration decreased (he et al., 2002) leading to an inhibition of the grain growth. similar behavior was reported in mgo-doped al2o3 (suzuki et al., 2002). the reduction in the spread of dihedral angles leading to a homogeneous microstructure was observed because of the presence of dopants (suzuki et al., 2002). 3.2.2 coating thickness coating thickness measurements were done to give a detailed explanation of the kinetic role of zno incorporation into the mgo system, the mechanism of the film formation and the limit mobility of zno into mgo crystal lattice. coating thickness measurements were calculated for the prepared membranes thermally treated at 200, 400 and 600 o c using cross sem investigations. figure 4 shows the plot of coating thickness values for the different prepared membranes versus thermal temperatures. the decrease of coating thickness layer with increasing temperature was due to the release of organic by-products and the crystalline formation of the final product, leading to a uniform coated film over the substrate. shiraz labib 03 figure 3. sem of doped and non-doped mgo membranes thermally treated at 600 o c for 6h. (a) m100, (b) m99, (c) m95 and (d) m90. the marked decrease of coating thickness values of the prepared thin films were observed with increasing zno doping percent. this behavior was interpreted as follows: the thickness per deposited layer was dependent on several parameters: the concentration of the precursors, the sol viscosity and the density of the deposited film (liebrecht, 2006). in a (mgo-zno) system, the mobility of the adatoms is more dependent on the film thickness than the other parameters (guillén and herrero, 2010). a direct correlation coexists between the mobility increase and both the coating layer thickness and grain size increase (guillén and herrero, 2010). on the other hand, the decrease in mobility occurs as a result of the strong interfacial interaction between the deposited film and the substrate leading to the decrease in coating thickness value (park et al., 2005). it is certain that the adatomic mobility was an important factor affecting the coating thickness as well as the microstructure of the deposited films. figure 4. coating thickness values for doped and non-doped mgo membranes at different thermal temperatures. 4. conclusion doped and undoped mgo membranes were prepared using a chelating sol-gel process. zno was chosen as a dopant to mgo in different proportions. the addition of zno to mgo increased the thermal stability of mgo, as synthesis of doped and non-doped nano mgo ceramic membranes 03 investigated from dta-tg results. the marked increase in specific surface area and decrease in particle size values, with increasing doping percent, was due to the decrease of the adatom mobility within the structure when increasing the percent of zn 2+ replacing mg 2+ ions. the increase of mgo peak broadness with increasing doping percent confirms the bet results. the decrease of adatom mobility affected the microstructure of the obtained films by increasing the porous structure of the obtained films, as shown in sem investigations, and decreasing the coating thickness values. this was attributed to the strong interfacial interaction created between the deposited film and the substrate as a result of the decrease in adatom mobility. therefore, the mechanism of increasing the percent of zn 2+ replacing mg 2+ ions played an important role in obtaining nano-coated thin film membranes. the aim of this paper was to understand the true role of doping zno into mgo matrix because this system is very important and opens the key of knowing the link between the mechanism of doping and the resultant properties. as concluded, the above results are compatible together leading to an improvement in mgo thin film microstructure with increasing zno doping percent and the field allows for other systems that have similar trends to be studied and applied. 5. references anas, sh., mukundan, p., sanoj, a.m., mangalaraja, v.r. and ananthakumar, s. 2010. synthesis of zno based nanopowders via a non-hydrolytic sol-gel technique and their densification behaviour and varistor properties. process. and appl. ceram. 4: 7-14. caruntu, d. 2006. nanocrystalline transition metal ferrites: synthesis, characterization and functionalization. ph.d. thesis, university of new orleans, louisiana, usa. cernea, m. 2005. sol-gel synthesis and characterization of batio3 powders. j. optoelectronics and advanced materials 7: 3015-3022. crisan, m., jitianu, a., crisan, d., balasoiu, m., dragan, n. and zaharescu m. 2000. sol-gel monocomponent nano-sized oxide powders. j. optoelectronics and advanced materials 2: 339-342. desai, r., mehta, r.v., upadhyay, r.v., gupta, a., praneet, a. and rao, k.v. 2007. bulk magnetic properties of cadmium ferrite in nano regim. bull. mat. sci. 30: 197-203. guillén, c. and herrero, j. 2010. optical, electrical and structural characteristics of al:zno thin films with various thicknesses deposited by dc sputtering at room temperature and annealed in air or vacuum. vacuum 84: 924-929. han, z-d., diao, ch., dong, l. and zhang, x. 2007. thermal stability and combustion behaviors of lldp/silica nanocomposites. 16 th international conference on composite materials, 8-13 july 2007, kyoto, japan. he, ch., yu, y., hu, x. and larbot, a. 2002. influence of silver doping on the photocatalytic activity of titania films. app. surface sci. 200: 239-247. huang, ch-l., hou, j. l., pan, ch-l., huang, ch-y., peng, ch-w., wei, ch-h. and huang, y-h. 2008. effect of zno additive on sintering behavior and microwave dielectric properties of 0.95mgtio3-0.05catio3 ceramics. j. alloys and compounds 450: 359-363. iyer, r., desai, r. and upadhyay, r.v. 2009. low temperature synthesis of nanosized mn1-xcdxfe2o4. indian j. pure and applied physics 47: 180-185. labib, sh. 2006. preparation, characterization and formulation of nano-ceramic materials to be used for the separation of some heavy metals. ph.d. thesis, ain shams uni., egypt. li, m., xu, m., liang, h., li, x. and xu, t. 2008. preparation and dielectric properties of mn-doped ba0.6sr0.4tio3-mgtio3 composite ceramics. acta physico-chimica sinica 24: 1405-1410. liebrecht, l.j.h. 2006. sol-gel derived barium titanate thin films. m.sc. thesis, uni. of twente, the netherlands. maensiri, s., masingboon, ch., boonchom, b. and seraphin, s. 2007. a simple route to synthesize nickel ferrite (nife2o4) nanoparticles using egg white. scripta materialia 56: 797-800. mikhail, r.sh., robens, e. 1975. microstructure and thermal analysis of solid surfaces. john wiley & sons. chichester, new york, brisbane, toronto, singapore. niu, h-x., yang, q., yu, f., tang, k-b. and zhou, w. 2006. simple synthesis of single-crystalline nanoplates of magnesium oxide. chin. j. chem. phys. 19: 438-442. park, s.y., lee, m.j., kim, h.j., moon, s.h., kim, s.g. and kim, j.k. 2005. relationship between the microstructure and the discharge characteristics of mgo protecting layer in alternating current plasma display panels. j. vac. sci. technol. a. 23: 1162-1166. peters, t.a., fontalvo, j., vorstman, m.a.g., benes, n.e., van dam, r.a., vroon, z.a.e.p., van soest-vercammen, e.l.j. and keurentjes, j.t.f. 2005. hollow fibre microporous silica membranes for gas separation and pervaporation. synthesis, performance and stability. j. memb. sci. 248: 73-80. raj, a.m.e., nehru, l.c., jayachandran, m. and sanjeeviraja, c. 2007. spray pyrolysis deposition and characterization of highly (100) oriented magnesium oxide thin films. cryst. res. technol. 42: 867-875. samerjai, th., liewhiran, ch. and phanichphant, s. 2009. characterization of zno/mgo nanocomposites synthesized by flame spray pyrolysis. j. microscopy soc. thailand 23: 87-90. shiraz labib 06 sanchez, c., livage, j., henry, m. and babonneau, f. 1988. chemical modification of alkoxide precursors. j. non-crystalline solids 100: 65-76. saraiva, m., georgieva, v., mahieu, s., aeken, k.v., bogaerts, a. and depla, d. 2010. compositional effects on the growth of mg(m)o films. j. appl. phys. 107: 1-10 sekulic, j., luiten, m.w.j., elshof, j.e.t., benes, n.e. and keizer, k. 2006. microporous silica and doped silica membrane for alcohol dehydration by pervaporation. desalination 148: 19-23. suzuki, t., kosacki, i. and anderson, h.u. 2002. microstructure-electrical conductivity relationships in nanocrystalline ceria thin films. solid state ionics 151: 111-121. willard, m.a., kurihara, l.k., carpenter, e.e., calvin, s. and harris, v.g. 2004. chemically prepared magnetic nanoparticles. int. mat. rev. 49: 125-170. yang, y., jin, y., he, h., wang, q., tu, y., lu, h. and ye, z. 2010. dopant-induced shape evolution of colloidal nanocrystals: the case of zinc oxide. j. am. chem. soc. 132: 13381-13394. received 7 august 2012 accepted 3 september 2012 squ journal for science, 2015, 20(1), 11-19 © 2015 sultan qaboos university 11 antibacterial and antifungal activities of cyanobacterial strains isolated from hot springs in oman neelam sherwani 1 , raeid m.m. abed 1 *, sergey dobretsov 2 and sheji mary 1 1 department of biology, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. 2 department of marine science and fisheries, college of agricultural and marine sciences, sultan qaboos university, p.o. box: 36, pc 123, alkhod, muscat, sultanate of oman. *email: rabed@squ.edu.om. abstract: in this study, cyanobacterial microbial mats from five hot springs in oman, namely al kasfah rustaq, al thwara nakhl, al–ali hammam, gala and bowsher, were characterized using direct microscopy. nine monoclonal cyanobacterial cultures were obtained and their extracts in butanol, dichloromethane (dcm) and hexane were screened for antibacterial and antifungal activities. direct microscopy revealed the presence of 12 different unicellular and filamentous morphotypes, with different distribution in the various mats. temperature seems to be one of the most important parameters that accounts for the differences in cyanobacterial composition of the mats. cells of the nine isolates and their aqueous supernatants were subsequently extracted with butanol, dcm and hexane. dried extracts were tested against nine bacterial (i.e. gram +ve staphylococcus aureus, bacillus subtilis and gram –ve, escherichia coli, klebsiella pneumoniae, salmonella choleraesuis, s. enterica, psuedomonas aeruginosa, providencia stuartii, and acinetobacter calcoaceticus) and two fungal pathogens (rhizoctonia solani and pythium sp.). all isolates exhibited antibacterial and antifungal activities, which depended mainly on the type of cyanobacterial culture, type of solvent used and the pathogen tested. the highest antibacterial activity was observed in phormidium species, and butanol was found to be the most appropriate solvent to extract bioactivity from these cyanobacterial species. the results of this study suggest that thermal springs in oman harbor diverse types of cyanobacteria, which may constitute an important source of antibacterial and antifungal compounds. further investigation is needed to purify these compounds and find their chemical compositions and modes of action. keywords: cyanobacterial mat; antibacterial; antifungal. تيرية و الفطرية التي تفرزها السياووبكتيريا المعسولة مه اليىابيع الساخىة في عمانفاعلية المضادات البك عابذ، سيرجي دوبرتسوف و شيجي مارى رائذويلم شرواوي، انبكخٍزٌت فً خًس ٌُابٍع ساخُت فً عًاٌ وهى عٍٍ انكسفت فً انزسخاق و انثىارة فً انسٍاَىبكخٍزٌت انخجًعاث فحصفً هذِ انذراست حى ملخص: فزاس أَخم و انحًاو و غال وبىشز باسخخذاو انًجهز. يٍ هذِ انخجًعاث حى انحصىل عهى حسع سالالث يٍ انسٍاَىبكخٍزٌا و انكشف عٍ قذرحها عهى َىع يخخهف يٍ انسٍاَىبكخٍزٌا وحٍذة انخهٍت و خٍطٍت يىسعت بشكم يخخهف 21يزكباث نقخم انبكخٍزٌا و انفطزٌاث. باسخخذاو انًجهز حى انكشف عٍ ذاو انًاء و درجت انحزارة هً انًسؤونت عٍ هذِ االخخالفاث .وقذ حى انحصىل عهى يسخخهص يٍ هذِ انسالالث باسخخٌ أفً هذِ انخجًعاث. كًا حبٍٍ انبٍىحاَىل و انذاي كهىرويٍثٍٍ و انهٍكسٍٍ .وقذ جزبج انًسخخهصاث انجافت ضذ حسع أَىاع يٍ انبكخٍزٌا و َىعٍٍ يٍ انفطزٌاث و هى : staphylococcus aureus, bacillus subtilis and gram –ve, escherihia coli, klebsiella pneumoniae, salmonella choleraesuis, s. enterica, psuedomonas aeruginosa, providencia stuartii, and acinetobacter calcoaceticus) (rhizoctonia solani and pythium sp.) جًٍع هذِ انسالالث كاٌ نها انقذرة عهى إبادة انبكخٍزٌا و انفطزٌاث حسب َىع انسٍاَىبكخٍزٌا و َىع. .َخائج هذِ انذراست حقخزح أٌ انٍُابٍع انساخُت فً عًاٌ ححخىي عهى سالالث يٍ انسٍاَىبكخٍزٌا نها انقذرة عهى إبادة انبكخٍزٌا انضارة وَىع انًذٌباث انٍخها.انفطزٌاث و انبكخٍزٌا انضارة.و فً انًسخقبم ٌجب انقٍاو بأبحاد يفصهت نخُقٍت هذِ انًزكباث و انكشف عٍ حزكٍبها انكًٍٍائً و طزٌقت فع . و عًاٌ ،انخجًعاث انبكخٍزٌت وانٍُابٍع انساخُت انسٍاَىبكخٍزٌا، يضاداث انبكخٍزٌا، يضاداث انفطزٌاث: كلمات مفتاحية 1. introduction errestrial geothermal springs are characterized by a dominance of microbial mats comprising a diversity of prokaryotic organisms, principally cyanobacteria [1-4]. the biodiversity of thermophilic cyanobacteria in t neelam sherwani et al. 12 geothermal springs has long attracted the attention of microbial ecologists because of their unique adaptations to these harsh environments [3, 5-8]. however, their value as a source of thermo-stable bio-compounds and unusual metabolic products for biotechnological applications has received much less attention [9, 10]. in recent decades, the search for bioactive compounds has been more directed towards the exploration of new environments and the screening of less exploited microbial groups endowed with a more versatile secondary metabolism such as cyanobacteria [11]. therefore, the exploration of bioactive compounds from thermophilic and thermotolerant cyanobacteria of hot springs is an important step towards these goals. cyanobacteria produce a wide variety of compounds including 40% lipopeptides, 5.6% amino acids, 4.2% fatty acids, 4.2% macrolides and 9% amides [12]. lipopeptides are biochemically active, having cytotoxic, anticancer, antibiotic, enzyme inhibitor, antiviral and antifungal activities [11]. numerous screening programs have revealed the potential of cyanobacteria in the production of novel antimicrobial [13-19], antifungal [20-22], antiviral [23], anticancer or cytotoxic [24] and antifouling compounds [10]. cyanotoxins like the hepatotoxic microcystins and nodularins or the neurotoxic anatoxins and saxitoxins have been isolated from cyanobacteria [25, 26]. thermotolerant cyanobacteria have also been reported to produce bioactive compounds [9,11]. the thermotolerant phormidium sp. has produced an antimicrobial compound against candida albicans and cladosporidium resinae [27]. anticancer drugs have also been made from thermophilic cyanobacteria [28]. the thermophilic synechococcus sp. is a potential producer of poly-hydroxybutyrate, which is the basis of biologically degradable plastics [29]. in this study, we identified five locations in northern oman with active thermal springs, dominated by cyanobacteria mats [9]. it was previously demonstrated that microbial mats from these springs had antimicrobial activity in vivo [9]. the aim of this study was to identify the common mat-forming cyanobacteria in these hot springs using direct microscopy, and to isolate cyanobacterial cultures and investigate their antibacterial and antifungal activities. 2. material and methods 2.1 physical and chemical characteristics of the sampling sites mat samples were collected from al-kasfah spring rustaq, al-thwara nakhl spring, al-ali hammam spring, and gala and bowsher springs in sterile plastic boxes. al-ali hammam spring, located in the huge fault structure separating triassic dolomite from ophiolite, had the highest temperature range recorded (60-67 o c), while gala and bowsher had the lowest temperatures (table 1). air-shade and water temperatures were taken in the field using an electronic thermometer (spring celsimeter, model super-k). the ph of the samples was measured by a digital ph meter (orion; thermo fisher scientific, waltham, ma, usa) and electrical conductivity was determined using a conductivity bridge (systronics, norcross, ga, usa). ammonium concentration [nh4 + ] was measured using a multiparameter nh4 + electrode (orion) as described in [30]. table 1. environmental conditions from the five investigated hot springs. hammam rustaq nakhal boshwer ghala lat/long coordinates 23 o 28’10.5"n 23 o 23’27"n 23 o 23’n 23 o 55'76"n 23 o 55'05"n 58 o 19' 13"e 57 o 25' 28"e 57 o 49'e 58 o 40' 96"e 58 o 38'33"e temperature ( o c) 60-67 46-47 37-40 35-38 35-37 ph 6.98 6.93 7.9 7.1 7.1 conductivity 1900 1300 800 1100 1200 (ω –1 cm 2 mol –1 ) n (mg/l) 0.2 1.1 1.4 0.6 0.6 no3 (mg/l) 1 4.8 6 2.5 3 2.2 isolation and identification of cyanobacteria cyanobacterial species were observed under the microscope within 24 hours of collection. identification was performed using morphological variation studies and taxonomical approaches [31-34]. cyanobacterial communities at different hot springs were compared using cluster analysis of the bray-curtis similarity index [35] with the help of primer software (plymouth marine laboratory). for construction of a similarity matrix, the presence of particular morphotypes was denoted as 1 and their absence was set as 0, and the data were square root transformed. fourteen cyanobacteria species belonging to twelve cyanobacterial genera were identified . monoclonal cultures were prepared using subculturing methods in bg11 medium (atcc medium 616) with and without nitrate [34]. the bg 11 medium was prepared by adding nano3 (1.5 g), k2hpo4 (0.04 g), mgso4·7h2o (0.075 g), cacl2·2h2o (0.036 g), ferric ammonium citrate (0.006 g), edta (disodium salt) (0.001 g), na2co3 (0.02 g) and trace metal mix a5 (1.0 ml) per bioactive compounds from hot spring cyanobacteria 13 litre distilled water. each isolated cyanobacterium was cultured in a 500 ml flask containing 250 ml of bg11 medium for 30 days. the cultures were incubated at 30-35 o c and illuminated for 16 hrs. biomass was harvested at the end of the linear growth phase, filtered on nylon net and carefully washed with sterile bg11 media. these cultures were used for further investigations. 2.3 preparation of cell extracts the cultures were harvested after 30 days of growth by centrifugation at 5000 rpm for 15 minutes. extracts of the cyanobacterial pellets were prepared, in each of 100 ml butanol, 100 ml dcm and 100 ml hexane. these extracts were dried under reduced pressure at 40 °c and were stored at −10 °c for further study. 2.4 determination of antibacterial and antifungal activities the extracts from the isolates were screened for antibacterial activity on nine different pathogenic bacterial strains and for antifungal activities on two fungal strains. four of the pathogenic strains used were american type culture collection (atcc) of bacteria: escherichia coli (atcc 9637), klebsiella pneumoniae (atcc 37853), staphylococcus aureus (atcc 29213) and salmonella choleraesuis (atcc 14028), whereas salmonella enterica, pseudomonas aeruginosa, providencia stuartii, acinetobacter calcoaceticus, bacillus subtilis were obtained from the sultan qaboos university hospital (kind contribution from dr. akbar rafay). the fungal plant pathogens of rhizoctonia solani and pythium sp. were obtained from prof. mike deadman, squ. the bacteria were subcultured on nutrient agar (oxoid, hampshire, england) at 37 °c for 24 hrs and the fungi were grown on potato dextrose agar (pda; oxoid, hampshire, england) at 25 °c for 5 days. the dried extracts were dissolved in their extraction solvent (final concentration = 1 mg/ml), and antibacterial and antifungal activities were determined by the disc diffusion method. filter paper discs (6.4 mm) were saturated with 100 μl of the test solution, dried under laminar air flow, and placed on either the nutrient agar plate for bacteria or the potato dextrose agar plate for fungi, both of which had been inoculated with a lawn of the test microorganisms. plates were incubated at 37 °c for a period of 24 hrs for bacteria, and at 25 °c for 5 days for fungi. discs treated only with 100 μl butanol, or hexane or dcm, were used as negative controls. the extracts containing antibacterial and antifungal components produced distinct, clear, circular zones of inhibition around the discs, and the diameters of the clear zones were determined and used as an indication of antibacterial and anti-fungal activity. the experiment was run three times in triplicate and the mean inhibition zones were calculated for each extract/treatment. 3. results and discussion the ph of the samples was between 7 and 7.9 and electrical conductivity was between 800-1900 µs/cm in all samples (table 1). ammonium concentrations were between 1 and 6 mg/l, with the highest value in nakhl spring and lowest in hammam spring. direct microscopy examinations revealed the presence of 14 unicellular and filamentous cyanobacterial morphotypes, in the microbial mats of the studied geothermal springs. morphotypes like synechococcus, aphanocapsa, anabeana, gloeocapsa, chroococcus, aphanizomenon, leptolyngbya, oscillatoria, phormidium, spirulina, lyngbya and nostoc (table 1) were observed. the highest number of cyanobacterial morphotypes (7) was recorded for hammam and bowsher hot springs. cluster analysis demonstrated that the cyanobacterial communities present in nakhl and gala were similar to each other, while those found in rustaq thermal spring were completely different (figure 1). temperature differences in the mats were found to be one of the most important parameters that accounted for the differences in cyanobacterial composition (table 1), with synechoccus and aphanocapsa observed in hammam spring (6067 o c) and filamentous genera of phormidium, leptolyngbya and lyngbya constituting most of the cyanobacterial mats in bowsher (35-38 o c), gala (3740 o c) and nakhl (37-40 o c). previous studies have also revealed the presence of unicellular forms like synechococcus in cyanobacterial mats at thermal gradients from 50 o c to 75 o c [36,37], whereas those mats occurring at the lower end of thermophily (35-50 °c) are often dominated by filamentous cyanobacteria such as phormidium, lyngbya, oscillatoria, pseudoanabaena, calothrix and fischerella [3,37,38]. on the other hand, nitrogen also affects the species distribution in cyanobacterial mat communities below ~60 °c [3,38]. diazotrophic cyanobacteria are able to colonize springs where nitrogen levels are too low to support other taxa, but they may be outcompeted by non-diazotrophic cyanobacteria in springs with sufficient combined nitrogen [38]. our results also support this assumption since heterocystous species were not detected in nakhl spring, where the ammonium level was the highest (table 1), while heterocystous species like nostoc sp. were observed in bowsher spring which has a comparatively low nitrogen concentration. neelam sherwani et al. 14 figure 1. cluster analysis of the presence and absence of cyanobacterial morphotypes in the studied hot springs, based on bray-curtis similarity matrix. similarity between communities is in %. nine different monoclonal cyanobacterial isolates were obtained from all the mats (figure 2). based on their morphological features, the cultured strains were identified as species of genera phormidium, chroococcus, anabeana, gloeocapsa, lyngbya, leptolyngbya and nostoc (figure 2). all these strains were endowed with antibacterial activity (table 2). the diameter of the inhibition zone depended mainly on the type of cyanobacterial species, type of solvent used and the pathogen tested. almost all the tested extracts of cyanobacteria were highly effective against e.coli and s. aureus, but few extracts inhibited growth of a. calcoaceticus and b. subtilis (table 2). butanol was found to be the most appropriate solvent to obtain bioactive extracts from cyanobacterial biomasses. this solvent allows the extraction of relatively polar bioactive compounds. extracts prepared in hexane (which extracts highly non-polar compounds) did not show bactericidal activity against any of the tested microorganisms except for e. coli (table 2).this observation was in agreement with other studies [39], which state that hexane extracts show little antibacterial activity, and this could be due to the chemical nature of the active compounds [20]. figure 2. photomicrographs of cyanobacterial isolates cultured from the microbial mats of the active thermal springs of northern oman. the identification of these morphotypes can be found in table 2 with the same letter code indicated in brackets. rustaq hammam bowsher nakhl gala 1 0 0 8 0 6 0 4 0 2 00 similarity gala nakhl bowsher hammam rustaq 0 20 40 60 10080 % similarity 20µm 20µm a b c d e g h f 20 µm 15 µm 20 µm 20 µm 10 µm 20 µm 20 µm 20 µm 20 µm i bioactive compounds from hot spring cyanobacteria 15 table 2. cyanobacterial morphotypes observed from the five investigated hot springs. hammam rustaq nakhl bowsher gala cyanobacterial morphotypes synechoccus + aphanocapsa + + aphanothece + + chroococcus + + gleocapsa + + + aphanizomenon + + lyngbya + leptolyngbya + + + + oscillatoria + phormidium + + + + spirulina + + nostoc + total number 7 3 5 7 3 + present; absent among butanol extracts, the highest antibacterial activity was detected in phormidium species, which had the ability to inhibit the growth of all tested pathogens (table 2). the largest inhibition zone for butanol extracts of phormidium species was observed in the case of gram-negative p. stuartii, s. enterica and p. aeruginosa respectively (table 2). the second highest inhibition zone was detected in the case of k. pneumoniae, b. subtilis and e.coli. phormidium spp. have been previously reported to produce compounds that inhibit growth of different gram-positive and gram-negative bacterial strains, yeasts, and fungi [40-42]. butanol extracts of lyngbya sp. exhibited the highest antibacterial activity against k. pneumoniae (figure 3). lyngbya species are known for the production of antimicrobial, anticancer and quorum sensing inhibitory compounds [10]. significant antimicrobial activity was observed by using chroococcus sp. against all pathogens. these results are congruent with previous reports that detected high biological activity of cyanobacterial species belonging to the genera of phormidium, chroococcus, lyngbya and leptolyngbya [22,38,4345]. the butanolic extracts of nostoc sp.1 and nostoc sp. 2 strains strongly inhibited the growth of s. choleraesuis, p. stuartii and p. aeruginosa (table 2). studies on the antarctic cyanobacterium nostoc ccc537 have shown that methanolic extracts of this strain inhibit the growth of mycobacterium tuberculosis, enterobacter aerogenes, salmonella typhi, e. coli, p. aeruginosa and s. aureas [46]. an intracellular biomolecule similar to an anthraquinone (indane) derivative of a diterpenoid was hypothesized to be the active compound. some of the active substances screened from nostoc include nostocyclyne, nostofungicidine, nostocin [47,48], 4,4’-dihydroxybiphenyl [21], cryptophycin-a and nostodione-a, which inhibit microtubule assembly or function [49]. figure 3. inhibition of klebsiella pneumoniae growth by dcm extracts of nostoc, leptolyngbya, anabeana species. in the present study, we observed that the different isolates of the genus anabeana exhibited different antimicrobial activities. extracts of anabeana sp.1 were more effective against e.coli and k. pneumonia compared to anabeana sp. 2 (table 2). it has been shown hat different species of cyanobacteria produce extracellular compounds neelam sherwani et al. 16 with different antimicrobial activities, such as amino acids, peptides, lipopeptides, amides, fatty acids, indoles, nucleosides, alkaloids, polyketides and sterols [50,51]. calothrix brevissima and oscillatoria redekei have antibacterial activity and produce bromophenols [52] and fatty acids [51], respectively. two depsipeptide bioactive compounds, scyptolin a and b have been isolated from the axenically grown terrestrial cyanobacterium scytonema hofmanni [53]. the cyanobacterial antibacterial compounds inhibit the growth of gram-positive pathogens by destabilizing their cytoplasmic membrane [54]. in the gram-negative bacteria, the outer membrane of the bacteria shows the hydrophilic surface on the side chains of lipopoly-saccharides, which prevents the entrance of hydrophobic substances to the cellular membrane [55]. however, certain molecules, such as terpenoid and phenolic compounds, can destabilize the lipopolysaccharide layer [56]. bioactive compounds have not been isolated through this study and the isolation of antibacterial compounds from thermal spring cyanobacteria should be a priority in future investigations. all cyanobacterial isolates showed antifungal activity against rhizoctonia solani and phythium species (table 3). table 3. inhibition of growth of bacterial pathogens by buthanol, dichloromethane (dcm), and hexane extracts of cyanobacterial isolates. data are the mean diameters ± standard deviation (sd) of inhibition zones (mm). cyanobacterial buthanol, dcm and hexane extracts were applied to sterile paper disks (diameter = 6.4 mm ). inhibition zones in the presence of the positive control ie. streptomycin antibiotic was between 15-32 mm. table 4. antifungal activity of cyanobacterial isolates. data are the mean diameters of inhibition zones (mm). cyanobacterial butanol, dcm and hexane extracts were applied to sterile paper disks (diameter = 6.4 mm). fungal pathogens cyanobacterial spp. rhizoctonia solani phythium sp. butanol dcm hexane butanol dcm hexane phormidium sp. 15.4 14.4 15.4 15.4 15.4 15.4 gleocapsa sp. 15.4 15.4 15.4 15.4 15.4 15.4 anabeana sp.1 15.4 15.4 15.4 15.4 15.4 15.4 anabeana sp. 29.9 14.4 15.4 14.4 15.4 15.4 chrocodiopsis sp. 15.4 15.4 15.4 15.4 15.4 15.4 lyngbya sp. 15.4 15.4 15.4 15.4 15.4 15.4 leptolyngbya sp. 14.7 15.4 15.4 15.3 15.4 15.4 nostoc sp.1 10.4 15.4 15.4 15.4 15.4 15.4 nostoc sp.2 15.4 15.4 15.4 15.4 15.4 15.4 cyanobacterial spp. solvent s. aureus e. coli k. pneumonia s. choleraesuis s. enteritidis p. aeruginosa p. stuartii a. calcoaceticus b. subtilis phormidium sp. (a) butanol 14.4±2.2 18.4±4 18.4±3 17.4±.3.5 24.3±3.5 22.6±1.2 24.6±2 9.4±0.8 18.6±2 dcm 10.4±1 9.4±0.8 r 12.5±1.5 r 15.8±1.8 9.4±0.4 11.8±1.5 10.4±1 hexane r 13.4±2 r r r r r r r chroococcus sp. (b) butanol 15.4±2.3 12.4±1.5 16±3 13.2±1 22.5±2.5 22.4±2.8 24.3±3 7.4±0 18.7±3.2 dcm 8.4±0 10±1 r 10.4±0.95 11.4±1.2 r 11.4±0.5 13.3±1.2 11.4±0.8 hexane r r r r r r r r r aphanizomenon sp.1 butanol 16.4±.22 14.4±1.5 15.4±2.2 17.6±2.8 8.1±0 21.1±3 22.2±2 r r dcm r 10.4±0.8 r 9.3±0.8 9.4±0.5 r 10.5±0.75 13.6±1.5 na hexane r r r r r r r r r aphanizomenon sp.2 butanol 15.9±2 10.4±1 7.3±0 8.4±0.5 18.2±2 22.4±2.2 16±2 8.4±0.5 r dcm 9.4±1 8.4±0 9.2±0.8 10.2±1 10.4±1.2 11.5±0.95 3±0.25 11.6±0.8 11.4±0.5 hexane r r r r r r r r r gleocapsa sp.(e) butanol 13.4±1.2 10.6±0.8 16.4±2 11.4±1.2 20.6±2 21.4±3.2 21.6±2.5 r r dcm 10.4±0.5 9.4±0.3 11.4±0.56 9.3±0.2 12.2±1 15.5±1.1 12.6±1.5 r 8.4±0.5 hexane r 9.4±0.3 r r r r r r r butanol 13.4±0.5 11.4±1.2 19.3±0.56 12.8±0.2 22.5±1 19.4±1.1 20.5±1.5 r 8.5±0.5 lyngbya sp. (f) dcm 8.4±0.5 8.3±0.5 10.4±1.5 11.4±0.8 8.4±0.5 9.4±0.5 10.4±0.8 9.5±1 8.5±0.5 hexane r r r r r r r r r leptolyngbya sp. (g) butanol 14.4±2.1 12.4±2.2 15.4±1.5 12.6±2.1 19.2±2.3 20.5±2.5 19.3±2 r 12.4±2.5 dcm 8.4±0.5 9.3±0.5 10.6±1 8.2±0.5 10.4±1.5 11.4±1.5 11.4±2.1 8.4±0.5 9.5±1 hexane r r r r r r r r r nostoc sp. 1 (h) butanol 11.4±0.95 18.4±2.1 14.4±1.8 21.5±1.6 14.5±2.2 20.3±3.2 19.4±2 r 8.4±0.5 dcm 10.4±0.95 10.2±0.5 12.2±2.2 10.4±1.8 9.7±0.6 9.4±0.95 11.3±1.6 13.8±2.1 na hexane r r r r r r r r r nostoc sp. 2 (i) butanol 13.5±1.6 16.4±1.5 16.4±.2.1 18.8±3.4 11.4±0.85 19.4±2 20.6±1.8 r 16.4±1.1 dcm 12.4±2.2 13.4±1.5 12.8±2.5 11.2±1.6 11.4±1.5 13.8±2 8.4±0.5 10.4±0.95 na hexane 12.2±1.5 12.4±0.7 r r r r r r r r: resistant and no inhibition zone is formed na: data not available bioactive compounds from hot spring cyanobacteria 17 the diameters of the inhibition zones were bigger than the antibacterial halos, revealing greater antifungal activity of the cyanobacterial extracts. most of the extracts (in butanol, hexane and dcm) had similar activity (table 3). minimum activity was observed in strains collected from bowsher hot spring. various investigations have confirmed the antifungal properties of different cyanobacterial strains [20, 57-61]. various antifungal compounds have been isolated from cyanobacteria including fisherellin a, hapalindole, carazostatin, phytoalexin, tolytoxin, scytophycin, toyocamycin, tjipanazole, nostocyclamide and nostodione [62], which supports the present findings. 4. conclusion the results obtained in the present investigation clearly demonstrate that cyanobacteria from thermal springs have strong antibacterial and antifungal properties. in particular, cyanobacterial isolates belonging to phormidium and gleocapsa genera have promising antibacterial and antifungal activities. further knowledge of the composition, analysis and properties of these cyanobacteria with respect to antimicrobial compounds may be useful in various future biotechnological and pharmaceutical applications. further research should be done, and bioactive compounds from these 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natural sciences, matica srpska novi sad, 2007, 112, 57-66. 62. abed, r.m.m., kohls, k., schoon, r. scherf, a–k.schacht, m., palinska, k.a., al-hassani, h., hamza, w., rullkotter, j. and golubic, s. 2008. lipid biomarkers, pigments and cyanobacterial diversity of microbial mats across intertidal flats of the arid coast of the arabian gulf (abu dhabi, uae). – fems microbial ecology, 2008, 65, 449-462. received 31 may 2014 accepted 8 march 2015 squ journal for science, 2021, 26(1), 31-39 doi:10.24200/squjs.vol26iss1pp31-39 sultan qaboos university 31 boolean zero square (bzs) semigroups g.a. pinto department of mathematics, college of science, sultan qaboos university, p.o. box 36, al-khoud, pc 123, muscat, sultanate of oman. email: goncalo@squ.edu.om abstract: we introduce a new class of semigroups, that we call bzs boolean zero square-semigroups. a semigroup s with a zero element, 0, is said to be a bzs semigroup if, for every 𝑥 ∈ 𝑆, we have 𝑥 2 = 𝑥 or 𝑥 2 = 0. we obtain some properties that describe the behaviour of the green’s equivalence relations ℛ, ℒ, ℋ and 𝒟. necessary and sufficient conditions for a bzs semigroup to be a band and an inverse semigroup are obtained. a characterisation of a special type of bzs completely 0-simple semigroup is presented. keywords: bzs semigroup; green’s relations; regular; completely 0-simple; inverse and band. أشباه الزمر البوالنية ذات المربع الصفري ج. أ. بينتو , 0الذي يحتوي على صفر sاشباه الزمر البوالنيه ذات المربع الصفري". شبه الزمرة جديدا من اشباه الزمر و أطلقنا عليه اسم "لقد اوجدنا نوعا :صلخمال x xيحقق اما sفي xشبه زمرة البوالنيه ذو مربع صفري اذا كان كل يسمى 2 xاو = 2 . لقد اوجدنا بعض الصفات التي تصف تصرف عالقة جرين 0 = شبه زمره باندية , شبه زمرة معاكسة. كما اوجدنا . كما اوجدنا الشروط الالزمة و الشروط الكافية ليكون شبه الزمرة هذا 𝒟 و ℛ, ℒ, ℋالتكافؤية اشباه الزمر البوالنيه ذات المربع الصفري وهو شبه الزمرة الصفري البسيط التام.التوصيف الكامل تنوع خاص من البوالنيه ذو مربع صفري، عالقة جرين، منتظم، الصفري البسيط التام، معكوس و فرقة. شبه زمرة :مفتاحيةالكلمات ال mailto:goncalo@squ.edu.om g.a. pinto 32 1. introduction e shall use standard semigroup notation, that can be found, for example, in [1]. if s is a semigroup, 𝐸(𝑆) represents the set of idempotents of s, and 𝑉(𝑥) denotes the set of inverses of an element x in s. we recall that the natural order ≤𝑛 on the idempotents of a regular semigroup is defined by 𝑒 ≤𝑛 𝑓 ⟺ 𝑒 = 𝑒𝑓 = 𝑓𝑒 in [2], farag and tucci introduced the notion of a boolean zero square (bzs) ring as an associative ring, not necessarily commutative and not necessarily with identity, such that every non-zero element of r is either idempotent or nilpotent of index 2, that is, (∀𝑥 ∈ 𝑅) 𝑥 2 = 𝑥 ∨ 𝑥 2 = 0 the structure of bzs rings is investigated, in [2] and in [3]. it is possible to find in the literature several papers in boolean zero rings, and as a sample we refer to [4] in order to several constructions in this structure. here we present a generalisation of these notions to semigroup theory, starting by introducing the following concept, that follows naturally from ring theory. definition. a semigroup 𝑆, with element zero 0, is said to be a bzs semigroup if, for every element 𝑥 in s, we have 𝑥 2 = 𝑥 or 𝑥 2 = 0. in the ring case, there are more tools available due to the presence of two operations: addition and multiplication. this fact has, as a consequence, that the majority of the results obtained in [2] and [3] cannot be replicated to the semigroup case. one of the results obtained in [2] is that in a bzs ring, the set of nilpotent elements, is an ideal of the ring. this property does not hold in a general bzs semigroup, as it can easily be seen in example 2 below. this happens because the result only mentions the multiplicative operation, although its proof uses the additive operation heavily. we obtain in theorem 8 that in a bzs commutative semigroup the set of its nilpotent elements, is an ideal of the semigroup. in what follows, unless otherwise stated, s will always denote a bzs semigroup. we denote 𝐸 = {𝑥 ∈ 𝑆|𝑥 2 = 𝑥} and 𝑁 = {𝑥 ∈ 𝑆|𝑥 2 = 0} respectively, the set of idempotent elements and the set of nilpotent elements of s. let us present some basic properties that hold in any such semigroup s. (∀𝑥 ∈ 𝑆) 𝑥 3 = 𝑥 2 (1) for any 𝑥 ∈ 𝑆, we have two cases to consider: i) 𝑥 2 = 𝑥 ⟹ 𝑥 ⋅ 𝑥 2 = 𝑥 ⋅ 𝑥 ⟹ 𝑥 3 = 𝑥 2 ii) 𝑥 2 = 0 ⟹ 𝑥 ⋅ 𝑥 2 = 𝑥 ⋅ 0 ⟹ 𝑥 3 = 0 ⟹ 𝑥 3 = 𝑥 2 which proves the result. (∀𝑥 ∈ 𝑆) 𝑥 4 = 𝑥 2 and 𝑥 2 ∈ 𝐸(𝑆) (2) this follows immediately from (1). 𝐸 ∩ 𝑁 = {0} (3) in fact, if 𝑥 ∈ 𝐸 ∩ 𝑁, we have 𝑥 = 𝑥 2 = 0, and the result follows. (∀𝑥, 𝑦 ∈ 𝑆) 𝑥𝑦 ∈ 𝐸\{0} ⟺ 𝑦𝑥 ∈ 𝐸\{0} (4) let us, assume that 𝑥𝑦 ∈ 𝐸\{0}, that is, (𝑥𝑦)2 = 𝑥𝑦, with 𝑥𝑦 ≠ 0. if 𝑦𝑥 = 0 then, 𝑦𝑥 = 0 ⟹ 𝑥 ∙ 𝑦𝑥 ∙ 𝑦 = 𝑥 ∙ 0 ∙ 𝑦 ⟹ (𝑥𝑦)2 = 0 w boolean zero square (bzs) semigroups 33 which is a contradiction, and therefore we can conclude that 𝑦𝑥 ≠ 0. also, if (𝑦𝑥)2 = 0 then, using (1), we have (𝑦𝑥)2 = 0 ⟹ 𝑥(𝑦𝑥)2𝑦 = 𝑥 ∙ 0 ∙ 𝑦 ⟹ (𝑥𝑦)3 = 0 ⟹ ⟹ (𝑥𝑦)2 = 0 𝑥𝑦 = 0 which is also a contradiction. so, (𝑦𝑥)2 = 𝑦𝑥 ≠ 0, which means that, 𝑦𝑥 ∈ 𝐸\{0}. similarly, we prove the reverse implication. (∀𝑥, 𝑦 ∈ 𝑆) 𝑥𝑦 ∈ 𝑁 ⟺ 𝑦𝑥 ∈ 𝑁 (5) if 𝑥𝑦 ∈ 𝑁 then, by (3), 𝑥𝑦 ∉ 𝐸\{0} and therefore by (4), 𝑦𝑥 ∉ 𝐸\{0}, that is 𝑦𝑥 ∈ 𝑁. the converse implication follows similarly. now, let us present some examples to illustrate this concept, which show that they can be found in a wide variety of very well-known classes of semigroups, such as bands, completely 0-simple semigroups and inverse semigroups. example 1. any band, b, with zero is clearly, a bzs semigroup, with 𝐸 = 𝐵 and 𝑁 = {0}. example 2. in a context of ordered semigroup theory, blyth and mcfadden presented in [5] a semigroup which has proved to be very helpful in describing several classes of ordered semigroups. more details of the relevance and properties of this semigroup can also be found in [6]. it can be defined by 𝑁5 = {𝑢, 𝑒, 𝑓, 𝑎, 𝑏} with the following cayley table: u e f a b u u u f f b e e e a a b f u b f b b a e b a b b b b b b b b it follows directly from the table that 𝑁5 is a bzs semigroup, b is its zero element, 𝑁 = {𝑎, 𝑏} and 𝐸 = {𝑢, 𝑒, 𝑓, 𝑏}. this semigroup appears in a different context, as an example of a completely 0-simple semigroup that it is not orthodox. routine calculations show that it is 0-simple 𝑁5 = 𝑁5𝑢𝑁5 = 𝑁5𝑒𝑁5 = 𝑁5𝑓𝑁5 = 𝑁5𝑎𝑁5 and, for example, 𝑓 is a primitive idempotent. since 𝑒𝑓 ≠ 𝑓𝑒, we can state that 𝑁5 is not an orthodox semigroup. example 3. consider the completely 0-simple semigroup 𝑆 = (𝐼 × 𝐺 × λ) ∪ {0} with operation (𝑖, 𝑎, 𝜆)(𝑗, 𝑏, 𝜇) = { (𝑖, 𝑎𝑝𝜆𝑗 𝑏, 𝜇) if 𝑝𝜆𝑗 ≠ 0 0 if 𝑝𝜆𝑗 = 0 (𝑖, 𝑎, 𝜆)0 = 0 = 0(𝑖, 𝑎, 𝜆) = 00 where 𝐺 0 = 𝐺 ∪ {0} is a zero group, with 𝐺 = 〈𝑥〉 an order two cyclic group, 𝐼, λ are non-empty index sets and 𝑃 = [𝑝𝜆𝑖 ] is a λ × 𝐼 sandwich matrix with entries in 𝐺 0, and all the non-zero entries of 𝑃 are equal to x. recall that every row and column of p has at least a non-zero entry. consider 𝑇 = {(𝑖, 𝑥, 𝜆) ∈ 𝑆} ∪ {0} a subset of s, and let (𝑖, 𝑥, 𝜆), (𝑗, 𝑥, 𝜇) ∈ 𝑇. we have the following possibilities for the element 𝑝𝜆𝑗 : if 𝑝𝜆𝑗 ≠ 0, then (𝑖, 𝑥, 𝜆)(𝑗, 𝑥, 𝜇) = (𝑖, 𝑥𝑝𝜆𝑗 𝑥, 𝜇) = (𝑖, 𝑥𝑥𝑥, 𝜇) = (𝑖, 𝑥, 𝜇) ∈ 𝑇 if 𝑝𝜆𝑗 = 0, then (𝑖, 𝑥, 𝜆)(𝑗, 𝑥, 𝜇) = 0 ∈ 𝑇 g.a. pinto 34 and we can say that 𝑇 is a semigroup, with the induced semigroup operation. also, for any (𝑖, 𝑥, 𝜆) ∈ 𝑇, we have that (𝑖, 𝑥, 𝜆)2 = { (𝑖, 𝑥, 𝜆) if 𝑝𝜆𝑖 ≠ 0 0 if 𝑝𝜆𝑖 = 0 therefore, 𝑇 is a bzs semigroup. example 4. consider the following set of 2 × 2 real matrices 𝑆 = {𝐼, 𝐴, 𝐸11, 𝐸12, 𝐸21, 𝐸22, 𝑂} = {[ 1 0 0 1 ] , [ 0 1 1 0 ] , [ 1 0 0 0 ] , [ 0 1 0 0 ] , [ 0 0 1 0 ] , [ 0 0 0 1 ] , [ 0 0 0 0 ]} it is well known that s with the usual matrix multiplication is an inverse semigroup (see, for example [7, section 7.6, exercise 1]). s is not a bzs semigroup, since 𝐴2 = 𝐴𝐴 = 𝐼 ≠ 𝐴, 𝑂. but if we consider the subset 𝑇 = {𝐼, 𝐸11, 𝐸12, 𝐸21, 𝐸22 , 𝑂}, it gives us the following cayley table 𝐼 𝐸11 𝐸12 𝐸21 𝐸22 𝑂 𝐼 𝐼 𝐸11 𝐸12 𝐸21 𝐸22 𝑂 𝐸11 𝐸11 𝐸11 𝐸12 𝑂 𝑂 𝑂 𝐸12 𝐸12 𝑂 𝑂 𝐸11 𝐸12 𝑂 𝐸21 𝐸21 𝐸21 𝐸22 𝑂 𝑂 𝑂 𝐸22 𝐸22 𝑂 𝑂 𝐸21 𝐸22 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 it follows immediately from the table that t is a subsemigroup of s which is a bzs inverse semigroup, with 𝐸 = {𝐼, 𝐸11, 𝐸22, 𝑂} and 𝑁 = {𝐸12 , 𝐸21, 𝑂}. 2. green’s relations let us now obtain some basic properties on the green’s relations ℛ, ℒ, ℋ, 𝒥 and 𝒟 on a bzs semigroup s. 𝑅0 = 𝐿0 = 𝐻0 = 𝐷0 = 𝐽0 = {0} (6) for any 𝑥 ∈ 𝑅0, we have that 𝑥 = 𝑥 ∙ 1 ∈ 𝑥𝑆 1 = 0𝑆1 = {0}, which immediately implies that 𝑅0 = {0}. the other equalities follow similarly. for 𝑥, 𝑦 ∈ 𝐸 or 𝑥, 𝑦 ∈ 𝑁 (7) 𝑥ℛ𝑦 ⟹ 𝑥𝑦ℛ𝑦𝑥 in fact, if 𝑥, 𝑦 ∈ 𝐸, then, since ℛ is a left congruence [1, proposition 2.1.2], 𝑥ℛ𝑦 ⟹ { 𝑥𝑥ℛ𝑥𝑦 𝑦𝑥ℛ𝑦𝑦 ⟹ { 𝑥ℛ𝑥𝑦 𝑦𝑥ℛ𝑦 ⟹ 𝑥𝑦ℛ𝑦𝑥 and, if 𝑥, 𝑦 ∈ 𝑁 then 𝑥ℛ𝑦 ⟹ { 𝑥𝑥ℛ𝑥𝑦 𝑦𝑥ℛ𝑦𝑦 ⟹ { 0ℛ𝑥𝑦 𝑦𝑥ℛ0 ⟹(6) 𝑥𝑦 = 0 = 𝑦𝑥 ⟹ 𝑥𝑦ℛ𝑦𝑥 for 𝑥, 𝑦 ∈ 𝐸 or 𝑥, 𝑦 ∈ 𝑁 (8) 𝑥ℒ𝑦 ⟹ 𝑥𝑦ℒ𝑦𝑥 this follows similarly as in (7). boolean zero square (bzs) semigroups 35 note that properties (7) and (8) do not hold if one element is in e and the other is in n. to see this, consider 𝑁5 in example 2, where the ℛ classes of 𝑁5 are 𝑅𝑢 = {𝑢, 𝑓}, 𝑅𝑒 = {𝑒, 𝑎} and 𝑅𝑏 = {𝑏}, while its ℒ classes are 𝐿𝑢 = {𝑢, 𝑒}, 𝐿𝑓 = {𝑓, 𝑎} and 𝐿𝑏 = {𝑏}. from property (7) we have that 𝑒 ∈ 𝐸, 𝑎 ∈ 𝑁, 𝑒ℛ𝑎 but 𝑒𝑎 = 𝑎 which is not ℛ related with 𝑎𝑒 = 𝑏. similarly, for property (8). theorem 1. let s be a bzs semigroup. (1) if 𝑎 ∈ 𝐸, then 𝑅𝑎 ∩ 𝐸 is a subsemigroup of s, which is a right zero semigroup. in particular, if 𝑅𝑎 ⊆ 𝐸 then 𝑅𝑎 is a right zero semigroup. (2) if 𝑎 ∈ 𝑁, then 𝑅𝑎 ∪ {0} is a subsemigroup of s. proof. (1): it is clear that 𝑅𝑎 ∩ 𝐸 is non-empty, since 𝑎 ∈ 𝑅𝑎 ∩ 𝐸. for any 𝑏, 𝑐 ∈ 𝑅𝑎 ∩ 𝐸, we have, 𝑏ℛ𝑎 and 𝑐ℛ𝑎 ⟹ 𝑏ℛ𝑐 ⟹ 𝑏 = 𝑏𝑏ℛ𝑏𝑐 ⟹ 𝑏𝑐 ∈ 𝑅𝑏 = 𝑅𝑎 which means that, 𝑅𝑎 is a subsemigroup of s. since 𝑏 and 𝑐 are idempotents, we have by [1, proposition 2.3.3], that 𝑏𝑐 = 𝑐 and therefore 𝑅𝑎 is a right zero semigroup. (2): it is clear that 𝑅0 = {0} is a subsemigroup of s. so, it is enough to consider 𝑎 ∈ 𝑁\{0}, that is, 𝑎 ≠ 0 and 𝑎 2 = 0. for 𝑏, 𝑐 ∈ 𝑅𝑎, there exist 𝑥, 𝑦, 𝑧, 𝑤 ∈ 𝑆 1 such that 𝑎 = 𝑏𝑥, 𝑏 = 𝑎𝑦, 𝑐 = 𝑎𝑧 and 𝑎 = 𝑐𝑤 if, on one hand 𝑏2 = 0 , then 𝑎 = 𝑏𝑥 ⟹ 𝑏𝑎 = 𝑏(𝑏𝑥) = 𝑏2𝑥 = 0 ∙ 𝑥 = 0 ⟹ 𝑏𝑎 = 0 and 𝑏𝑐 = 𝑏(𝑎𝑧) = (𝑏𝑎)𝑧 = 0 ∙ 𝑧 = 0 if, on the other hand 𝑏2 = 𝑏, then by [1, proposition 2.3.3], 𝑏𝑐 = 𝑐 ∈ 𝑅𝑎. therefore, 𝑅𝑎 ∪ {0} is a subsemigroup of s. note that in general, an ℛ class, 𝑅𝑥, is not a subsemigroup of s. in fact, if we consider the semigroup 𝑁5 of example 2, and its ℛ class, 𝑅𝑒 = {𝑒, 𝑎}, where 𝑒 ∈ 𝐸 and 𝑎 ∉ 𝐸, then we have that 𝑎𝑒 = 𝑏 ∉ 𝑅𝑒, which means that, 𝑅𝑒 is not a subsemigroup of 𝑁5. theorem 2. let s be a bzs semigroup. (1) if 𝑎 ∈ 𝐸, then 𝐿𝑎 ∩ 𝐸 is a subsemigroup of s, which is a left zero semigroup. in particular, if 𝐿𝑎 ⊆ 𝐸 then, 𝐿𝑎 is a right zero semigroup. (2) if 𝑎 ∈ 𝑁 then, 𝐿𝑎 ∪ {0} is a subsemigroup of s. proof. similar to the proof of theorem 1. like in the note to theorem 2, we can use example 2 to illustrate that an ℒ class of a bzs semigroup is not, in general, a subsemigroup of s. theorem 3. let s be a bzs semigroup. (1) if 𝑎 ∈ 𝐸, then 𝐻𝑎 is a group with only one element. (2) if 𝑎 ∈ 𝑆\𝐸, then 𝐻𝑎 ⊆ 𝑆\𝐸, (𝐻𝑎 ) 2 = {0} and 𝐻𝑎 ∪ {0} is a subsemigroup of s. (3) if a 𝒟 class of s contains an idempotent, all its ℋ classes are singleton. proof. (1): in fact, by [1, corollary 2.2.6], 𝐻𝑎 is a subgroup of s. we need to prove that 𝐻𝑎 has a unique element. for 𝑎 = 0 this is obvious, by (6). let us now assume that 𝑎 ∈ 𝐸\{0}, and consider 𝑏 ∈ 𝐻𝑎 . we have that 𝑏ℋ𝑎 ⟹ { 𝑏ℛ𝑎 𝑏ℒ𝑎 ⟹ { 𝑏𝑏ℛ𝑏𝑎 𝑏𝑎ℒ𝑎𝑎 ⟹ { 𝑏2ℛ𝑏𝑎 𝑏𝑎ℒ𝑎 if 𝑏2 = 0 then 𝑏ℋ𝑎 ⟹ { 0ℛ𝑏𝑎 𝑏𝑎ℒ𝑎 ⟹ { 𝑏𝑎 = 0 𝑎 ∈ 𝐿𝑏𝑎 ⟹ 𝑎 ∈ 𝐿𝑏𝑎 = 𝐿0 = {0} ⟹ 𝑎 = 0 which is a contradiction. therefore, we can conclude that 𝑏2 = 𝑏, and 𝑏 is an idempotent. using again [1, corollary 2.2.6], we conclude that 𝑏 = 𝑎, and 𝐻𝑎 is a singleton subgroup of s. (2): let 𝑎 ∈ 𝑆\𝐸, and consider 𝑦 ∈ 𝐻𝑎 , which cannot be equal to 0, by (6). then, 𝑦ℋ𝑎 ⟹ { 𝑦ℛ𝑎 𝑦ℒ𝑎 ⟹ { 𝑦𝑦ℛ𝑦𝑎 𝑦𝑎ℒ𝑎𝑎 ⟹ { 𝑦2ℛ𝑦𝑎 𝑦𝑎ℒ0 ⟹ 𝑦2 ∈ 𝑅0 = {0} ⟹ 𝑦 ∈ 𝑁 g.a. pinto 36 and therefore 𝐻𝑎 ⊆ 𝑆\𝐸. again, with 𝑎 ∈ 𝑆\𝐸 we have that 𝑏ℋ𝑎 ⟹ { 𝑏ℛ𝑎 𝑏ℒ𝑎 ⟹ { 𝑎𝑏ℛ𝑎𝑎 𝑏𝑎ℒ𝑎𝑎 ⟹ { 𝑎𝑏ℛ0 𝑏𝑎ℒ0 ⟹ { 𝑎𝑏 = 0 𝑏𝑎 = 0 therefore, for 𝑏, 𝑐 ∈ 𝐻𝑎 , we can say that 𝑎𝑏 = 0, 𝑏𝑎 = 0, 𝑎𝑐 = 0 and 𝑐𝑎 = 0 since 𝑏ℋ𝑐, we have that 𝑏ℛ𝑐, and 𝑏ℛ𝑐ℛ𝑎 ⟹ 𝑐𝑏ℛ𝑐𝑐ℛ𝑐𝑎 = 0 ⟹ 𝑐𝑏ℛ0 ⟹ 𝑐𝑏 = 0 from which, we conclude that (𝐻𝑎 ) 2 = {0} and that 𝐻𝑎 ∪ {0} is a subsemigroup of s. (3): this follows by [1, lemma 2.2.3] and (1). note, that in theorem 3(2) we verified that, for every 𝑎 ∈ 𝑁, the ℋ class 𝐻𝑎 is a subset of n. the same property does not hold for the ℛ and ℒ classes. in fact, the semigroup 𝑁5 of example 2 is such that 𝑎 ∈ 𝑁, but 𝑅𝑎 = {𝑒, 𝑎} ⊄ 𝑁, as well as 𝐿𝑎 = {𝑓, 𝑎} ⊄ 𝑁. theorem 4. let s be a bzs semigroup. (1) if 𝑎 ∈ 𝑆\{0} and 𝐷𝑎 ⊆ 𝐸, then 𝐷𝑎 is a subsemigroup of s. (2) if 𝑎 ∈ 𝑆\𝐸, then 𝐷𝑎 ∪ {0} is a subsemigroup of s. proof. (1): for any 𝑎 ∈ 𝑆\{0}, we have by (6), that 𝐷𝑎 ≠ {0}. the fact that 𝐷𝑎 ⊆ 𝐸 therefore implies that 𝐷𝑎 ⊆ 𝐸\{0}. considering any 𝑏, 𝑐 ∈ 𝐷𝑎 , there exist 𝑑 ∈ 𝑆, such that 𝑏ℒ𝑑ℛ𝑐. by [1, propositions 2.1.2 and 2.3.3], we have that 𝑑ℛ𝑐 ⟹ 𝑏𝑑ℛ𝑏𝑐 ⟹ 𝑏ℛ𝑏𝑐 ⟹ 𝑏𝑐 ∈ 𝑅𝑏 ⊆ 𝐷𝑎 thus, 𝐷𝑎 is a subsemigroup of s. (2) consider any 𝑎 ∈ 𝑆\𝐸, that is, 𝑎 ≠ 0 and 𝑎2 = 0. for any 𝑏, 𝑐 ∈ 𝐷𝑎 , there exist 𝑑 ∈ 𝑆, such that 𝑏ℒ𝑑ℛ𝑐, which means, in particular, that 𝑏 = 𝑥𝑑 and 𝑐 = 𝑑𝑦 for some 𝑥, 𝑦 ∈ 𝑆1. also, 𝑑ℛ𝑐 implies 𝑏 = 𝑥𝑑ℛ𝑥𝑐 and therefore 𝑥𝑐 ∈ 𝑅𝑏. then, 𝑏𝑐 = (𝑥𝑑)(𝑑𝑦) = 𝑥(𝑑𝑑)𝑦 if 𝑑2 = 𝑑, then 𝑏𝑐 = 𝑥𝑑2𝑦 = 𝑥𝑑𝑦 = 𝑥𝑐 ∈ 𝑅𝑏 ⊆ 𝐷𝑎 . if 𝑑2 = 0, then 𝑏𝑐 = 0. thus, 𝐷𝑎 ∪ {0} is a subsemigroup of s. 3. special classes of bzs semigroups we now devote our attention to obtaining necessary and sufficient conditions for a bzs semigroup s to be a band or an inverse semigroup. a characterisation of some bzs completely 0-simple is presented. also, the commutativity property will be approached. theorem 5. let s be a bzs semigroup. the following statements are equivalent: (1) s is a band; (2) (∀𝑥 ∈ 𝑆) 𝑥 3 = 𝑥. proof. (1) ⟹ (2): the definition of a band tells us that 𝑥 2 = 𝑥 for all 𝑥 ∈ 𝑆. then, 𝑥 3 = 𝑥 2 ∙ 𝑥 = 𝑥 ∙ 𝑥 = 𝑥 and the result follows. (2) ⟹ (1): take an element 𝑥 ∈ 𝑆. since s is bzs, 𝑥 2 = 𝑥 or 𝑥 2 = 0. if 𝑥 2 = 𝑥, there is nothing to prove. if 𝑥 2 = 0, then 𝑥 = 𝑥 3 = 𝑥 2𝑥 = 0 ∙ 𝑥 = 0 which, immediately implies that 𝑥 2 = 𝑥, for every element of s, that is, s is a band. in the following theorem and its proof, we use the identification provided from rees theorem [1, theorem 3.2.3], for a completely 0-simple semigroup s. such s is isomorphic to (𝐼 × 𝐺 × λ) ∪ {0}, boolean zero square (bzs) semigroups 37 where g is a group, 𝐼 and λ are non-empty index sets, and 𝑃 = [𝑝𝜆𝑖 ] is a λ × 𝐼 sandwich matrix with entries in the zero group 𝐺 0 = 𝐺 ∪ {0}. also, every row and column of p has at least a non-zero entry. the semigroup operation is defined by (𝑖, 𝑎, 𝜆)(𝑗, 𝑏, 𝜇) = { (𝑖, 𝑎𝑝𝜆𝑗 𝑏, 𝜇) if 𝑝𝜆𝑗 ≠ 0 0 if 𝑝𝜆𝑗 = 0 theorem 6. let s be a bzs semigroup. the following statements are equivalent: (1) s is a completely 0-simple semigroup with no zero entries in the sandwich matrix; (2) s is a rectangular 0-band. proof. (1) ⟹ (2): let s be a completely 0-simple semigroup. considering an arbitrary element 𝑥 in 𝐺, for any 𝜆 ∈ λ and 𝑖 ∈ 𝐼, we have that 𝑝𝜆𝑖 ≠ 0. then, (𝑖, 𝑥, 𝜆)2 = (𝑖, 𝑥, 𝜆)(𝑖, 𝑥, 𝜆) = (𝑖, 𝑥𝑝𝜆𝑖 𝑥, 𝜆) ≠ 0, which therefore implies, since s is a bzs semigroup, that (𝑖, 𝑥, 𝜆)2 = (𝑖, 𝑥, 𝜆). thus, (𝑖, 𝑥, 𝜆)(𝑖, 𝑥, 𝜆) = (𝑖, 𝑥, 𝜆) ⟺ (𝑖, 𝑥𝑝𝜆𝑖 𝑥, 𝜆) = (𝑖, 𝑥, 𝜆) ⟺ 𝑥𝑝𝜆𝑖 𝑥 = 𝑥 ⟺ 𝑝𝜆𝑖 = 𝑥 −1 in particular, if we replace x by the identity element of the group 1𝐺 , we obtain 𝑝𝜆𝑖 = 1𝐺 , and therefore 𝑥 −1 = 1𝐺 which, is equivalent to 𝑥 = 1𝐺 . so, g is the trivial group. then, 𝑆 is isomorphic to {(𝑖, 1𝐺 , 𝜆): 𝑖 ∈ 𝐼 and 𝜆 ∈ λ} ∪ {0} , whose elements verify (𝑖, 1𝐺 , 𝜆)(𝑗, 1𝐺 , 𝜇) = (𝑖, 1𝐺 , 𝜇) and (𝑖, 1𝐺 , 𝜆) ∙ 0 = 0 = 0 ∙ (𝑖, 1𝐺 , 𝜆) that is, s is a rectangular 0-band. (2) ⟹ (1): if s is a rectangular 0-band, then (∀𝑎 ∈ 𝑆)(∀𝑏 ∈ 𝑆\{0}) 𝑎2 = 𝑎 and 𝑎𝑏𝑎 = 𝑎 . then, for any 𝑎, 𝑏 ∈ 𝑆 and 𝑏 ∈ 𝑆\{0}, we have that, 𝑎 = 𝑎𝑏𝑎 ∈ 𝑆𝑏𝑆 which implies that 𝑆 ⊆ 𝑆𝑏𝑆. since, the reverse inclusion is always true, we can conclude that s is a 0-simple semigroup. also, if in 𝑆\{0}, 𝑎 ≤𝑛 𝑏, then 𝑎𝑏 = 𝑏𝑎 = 𝑎. we have that 𝑎𝑏 = 𝑏𝑎 ⟹ { 𝑎𝑏𝑎 = 𝑏𝑎𝑎 𝑏𝑎𝑏 = 𝑏𝑏𝑎 ⟹ { 𝑎 = 𝑏𝑎 𝑏 = 𝑏𝑎 ⟹ 𝑎 = 𝑏 which, means that all non-zero idempotents are primitive, and therefore s is completely 0-simple. also, if 𝑎, 𝑏 ∈ 𝑆\{0}, then if 𝑎𝑏 = 0 then 𝑎𝑏𝑎 = 0 ≠ 𝑎, which is a contradiction. so, all the entries of the sandwich matrix are not zero. it follows from the previous theorem and its proof that for a bzs semigroup to be completely 0-simple where the sandwich matrix has no zero entries, it is necessary to have a singular group in the middle component of the rees representation. in fact, we can say that a bzs semigroup is completely 0-simple where the sandwich matrix has no zero entries if, and only if, it is a completely simple semigroup with a zero adjoined. theorem 7. let s be a bzs semigroup. s is an inverse semigroup if, and only if, the following conditions hold: (1) s is regular; (2) (∀𝑥 ∈ 𝑆) 𝑥 ′𝑥 2𝑥′ = 𝑥 2, for any inverse 𝑥′ of 𝑥. proof. let s be an inverse semigroup. any element x in s has a unique inverse denoted by 𝑥 −1. by [1, theorem 5.1.1], an inverse semigroup is a regular one, where the idempotents commute. so, by (2), 𝑥 2 is an idempotent that, therefore, commutes with 𝑥𝑥 −1 and with 𝑥 −1 𝑥. thus, 𝑥 4 = 𝑥 2 ⟹ 𝑥 −1𝑥 4 = 𝑥 −1𝑥 2 ⟹ 𝑥 −1𝑥 ∙ 𝑥 2 ∙ 𝑥 = 𝑥 −1𝑥 2 ⟹ 𝑥 2 ∙ 𝑥 −1𝑥 ∙ 𝑥 = 𝑥 −1𝑥 2 ⟹ 𝑥(𝑥𝑥 −1𝑥)𝑥 = 𝑥 −1𝑥 2 ⟹ 𝑥 3 = 𝑥 −1𝑥 2 ⟹ 𝑥 3𝑥 −1 = 𝑥 −1𝑥 2𝑥 −1 ⟹ 𝑥 2 ∙ 𝑥𝑥 −1 = 𝑥 −1𝑥 2𝑥 −1 ⟹ 𝑥𝑥 −1 ∙ 𝑥 2 = 𝑥 −1𝑥 2𝑥 −1 ⟹ 𝑥 2 = 𝑥 −1𝑥 2𝑥 −1 g.a. pinto 38 conversely let us, assume that (1) and (2) hold. let 𝑒 be an idempotent of s and 𝑒′ any inverse of 𝑒. by (2), we have that 𝑒 ′𝑒 2𝑒′ = 𝑒 2, that is, 𝑒 ′ = 𝑒. thus, we can conclude that each idempotent in s has a unique inverse. now, considering an element 𝑥 in 𝑆 and 𝑥 ′, 𝑥′′ inverses of 𝑥, we have that 𝑥𝑥 ′ and 𝑥𝑥 ′′ are idempotents and inverses of each other, as well as 𝑥 ′𝑥 and 𝑥 ′′𝑥. thus, 𝑥𝑥 ′ = 𝑥𝑥 ′′ and 𝑥 ′𝑥 = 𝑥 ′′𝑥 and we can deduce that 𝑥 ′ = 𝑥 ′(𝑥𝑥 ′) = 𝑥 ′(𝑥𝑥 ′′) = (𝑥′𝑥)𝑥 ′′ = (𝑥′′𝑥)𝑥 ′′ = 𝑥′′ the result follows, since by [1, theorem 5.1.1], a regular semigroup where each element has a unique inverse is an inverse semigroup. theorem 8. let s be a bzs commutative semigroup. then, (1) e is a subsemigroup of s; (2) n is an ideal of s; (3) if s is inverse then 𝑥 3 = 𝑥, for every 𝑥 ∈ 𝑆. proof. consider any elements 𝑥, 𝑦 ∈ 𝑆. (1): if, on one hand, both belong to e, we have 𝑥 2 = 𝑥 and 𝑦2 = 𝑦, and therefore (𝑥𝑦)2 = (𝑥𝑦)(𝑥𝑦) = 𝑥(𝑦𝑥)𝑦 = 𝑥(𝑥𝑦)𝑦 = (𝑥𝑥)(𝑦𝑦) = 𝑥 2𝑦2 = 𝑥𝑦 which means that 𝑥𝑦 ∈ 𝐸 , and therefore e is a subsemigroup of s. (2): if, on the other hand, for example 𝑥 ∈ 𝑁, we have that (𝑥𝑦)2 = (𝑥𝑦)(𝑥𝑦) = 𝑥(𝑦𝑥)𝑦 = 𝑥(𝑥𝑦)𝑦 = (𝑥𝑥)(𝑦𝑦) = 𝑥 2 ∙ 𝑦2 = 0 ∙ 𝑦2 = 0 thus, 𝑥𝑦 ∈ 𝑁 and we can conclude that n is an ideal of s. (3): if s is an inverse commutative semigroup, any 𝑥 ∈ 𝑆 has a unique inverse, 𝑥 −1, and we have by theorem 7 (2), that 𝑥 = 𝑥𝑥 −1𝑥𝑥 −1𝑥 = 𝑥(𝑥 −1𝑥𝑥𝑥 −1) = 𝑥 ∙ 𝑥 2 = 𝑥 3 we have seen previously that 𝑥 3 = 𝑥 for all 𝑥 ∈ 𝑆 holds in any bzs semigroup that it is also a band, or a commutative inverse semigroup. it also holds for a bzs completely 0-simple semigroup, where the sandwich matrix has no zero entries. however, this property does not hold for all the bzs semigroups. to see this, let us consider 𝑇 = {𝐼, 𝐸11, 𝐸12, 𝐸21, 𝐸22, 𝑂} of example 4, which is an inverse bzs semigroup. note that we have 𝐼3 = 𝐼, 𝐸11 3 = 𝐸11, 𝐸22 3 = 𝐸22, 𝑂 3 = 𝑂, 𝐸12 3 = 𝑂 ≠ 𝐸12, 𝐸21 3 = 𝑂 ≠ 𝐸21 from which, we can deduce that the mentioned property does not hold in all the bzs semigroups. 4. conclusion in this paper, we introduce a new class of ordered semigroups: bzs boolean zero square semigroups. several basic properties on green’s relations are obtained. necessary and sufficient conditions for a bzs semigroup to be a band and to be an inverse semigroup are obtained. a characterisation of a special type of bzs completely 0-simple semigroup is presented. conflict of interest the author declares no conflict of interest. acknowledgment i thank sultan qabbos university for providing facilities and to the referees for their comments that improved the qulity of this paper. boolean zero square (bzs) semigroups 39 references 1. john, m. howie, fundamentals of semigroup theory, l.m.s. monographs, 12, oxford university press, oxford, 1995. 2. farag, m. and tucci, r. bzs rings, palestine journal of mathematics 2019, 8(2), 8-14.doi:10.7151/dmgaa.1243. 3. farag, m. bzs rings ii, 2020 (preprint). 4. bhavanari, s., lungisile, g. and dasari, n. ideals and direct product of zero square rings, east asian mathematics journal 24, 2008, 4, 377-387. 5. blyth, t.s. and mcfadden, r. naturally ordered regular semigroups with a greatest idempotent, proceedings of the royal society of edinburgh, 91a, 1981, 107-122. doi:10.1017/s0308210500012671. 6. blyth, t.s. lattices and ordered algebraic structures, (springer 2005). doi:10.1007/b139095. 7. clifford, a.h. and preston, g.b. the algebraic theory of semigroups, volume ii, a.m.s. mathematical surveys, 1967. doi: 10.1090/surv/007.2. received 25 june 2020 accepted 18 january 2021 squ journal for science, 2016, 21(1), 41-47 ©2016 sultan qaboos university 41 two dimensional short time hartley transforms narasimman sundararajan 1* , alaeddin ebrahimi 1 and nannappa vasudha 2 1 department of earth science, college of science, sultan qaboos university, p.o.box: 36, pc 123, al-khod, muscat, sultanate of oman. 2 department of mathematics, vasavi college of engineering, hyderabad, india.*email: visvid12@squ.edu.om. abstract: the hartley transform, as in the case of the fourier transform, is not suitably applicable to nonstationary representations of signals whose statistical properties change as a function of time. hence, different versions of 2-d short time hartley transforms (stht) are given in comparison with the short time fourier transform (stft). although the two different versions of stht defined here with their inverses are equally applicable, one of them is mathematically incorrect/incompatible due to the incorrect definition of the 2-d hartley transform in literature. these definitions of sthts can easily be extended to multi-dimensions. computations of the stft and the two versions of sthts are illustrated based on 32 channels (traces) of synthetic seismic data consisting of 256 samples in each trace. salient features of sthts are incorporated. keywords: fourier transform; hartley transform; wavelet transform; time; frequency and window. تحويالت هارتلي ثىائية األبعاد للزمه القصير وارسيمان ساوذراراجان و عالءالذيه ابراهيمي واواباراجا فاسودا كما ٌُ انحال بانىسبت نخحُیم فُریيً، ال یىطبق بشكم مىاسب نهخمثيم غيز انثابج نإلشاراث انخي خصائصٍا اإلحصائيت حخغيز ححُیم ٌارحهی ان :الملخص ( حقارن مع ححُیم فُریيً نهشمه انقصيز ) stht) كذانت في سمه؛ بانخاني إصذاراث مخخهفت مه ححُیالث ٌارحهي نهشمه ثىائي األبعاد نهشمه انقصيز stft بانزغم مه َجُد اصذاریه مخخهفيه مه .)stht ي انخطبيق، فان احذٌما غيزصحيح/ مخُافقً ریاضيا انمعّزفً ٌىا مع معکُسٍا انذیه مخساَیان ف ح بسٍُنت إنى أبعاد مخعذدة؛ َقذ حم حُضي sthtsَمه انممکه حُسيع حعزیفاث .بسبب انخعزیف انغيز صحيح نخحُیم ٌارحهي نهبعذیه في انمىشُراث عيىت في كم أثز. کما حم دمج 352)أثز( مه انبياواث انسيشميت انمؤنفت حخأنف مه 23بااالسخىاد انی قىاة sthtsاإلصذاریه ل حعزیف َ stftحسابان .sthtsانخصائص انبارسة ل .ححُیم فُریيً، ححُیم ٌارحهي،ححُیم انمُجاث، انشمه، فزیکُوسی َانىافذي: الكلمات المفتاحية 1. introduction t is well known that the elegant mathematical tools, the fourier transform (ft) and hartley transform (ht), were invented in 1807 and 1942 respectively. subsequently, the theory of spectral analysis began with the breakthrough of tukey in 1949 [1]. however, the computational feasibility of the ft was a reality only when the great breakthrough occurred in the form of the fast fourier transform (fft) algorithm that was brought out in 1965 by cooley and tukey [2]. in general, the ft gives the spectral content of the signal, devoid of any information regarding the time at which those spectral components appear. such a result is appreciable only for stationary signals [3], whose frequency content does not change with time. in most of the cases, a particular spectral component occurring at a specific time instant can be more useful and interesting, as in the case of seismological data which is non-stationary, and in which the frequency of the signal varies with time. mathematicians and researchers are aware that the fourier transform is best suited to process stationary signals; however, most of the information and data we come across in our day to day life are not stationary. to achieve time localization of frequency of a non-stationary signal while using the ft, it is necessary that the signal be subjected to narrow windows, narrow enough that the portion of the signal seen from these windows is indeed stationary. this approach is called the short time fourier transform (stft), which is a modified version of the ft. in the stft, the given signal is divided into small segments, such that each segment of the signal can be assumed to be stationary. for this purpose, a window function is chosen, so that the width of the window is equal to the segment of the signal, in which its stationarity is valid. thus, the one dimensional stft can be defined as [4-6]:       2 w , w i t stft f t g t e dt         (1) i narasimman sundararajan et al. 42 where ‘g’ is the window function and ‘ ’ is the width of the window. in analogy with the stft, the short time hartley transform (stht), is the real version of its complex fourier counterpart. a time varying hartley representation of signal for analyzing the time varying signal f(t) can be defined [5] in its one dimension as:        , w 2 wstht f t g t cas t dt       (2) where ‘g’is the window function and ‘ ’ is the width of the window. further, the kernel in equation (2) represents a 45 degrees phase shifted sine wave and is given as: )w2(sin)w2(cos)w2( tttcas   it may be emphasized here that the ht is an attractive alternative and real replacement for the well-known complex ft in all its applications. it is identical in its 1-d representation with the ft wherein the amplitude is the same as that of fourier amplitude. further, the ht is fully equivalent to the ft with the same physical significance in that both ft and ht furnish a pair of numbers that represent the physical oscillations in amplitude and phase and hence may be termed as a mathematical twin [7]. the theory and applications of this now well-known tool are found in the literature [813]. although the conventional fourier and hartley transforms are more appropriate to represent periodic, transient and stationary random signals, direct applications of these elegant tools fail in case of signals whose properties vary markedly as a function of time. in such cases, the time varying fourier and hartley transforms which are referred to as the stft and stht are employed to overcome the drawbacks of the ft and ht [14]. the effects of windows may be realized by computing the stht of a non-stationary signal with windows of two different lengths. for example, the gaussian function may be used as a window function of the form:   2 2 w a t t e   (3) where ‘a’ determines the length of the window and ‘t’ is the time. two different window functions can be generated for two different values of ‘a’. generally, a narrower window function (a=0.01) may yield very good time resolution, but a relatively poor frequency resolution. on the other hand, a wider window function may result in a poor time resolution but does ensure better frequency resolution. a window function of infinite length yields the ft and ensures perfect frequency resolution, but no time resolution. thus, the window length needs to be optimized in applications, according to the desired results. 2. frequency and time resolutions short time hartley transforms (stht), as in the case of the stft, obey the ‘heisenberg uncertainty principle’, which holds good for the time frequency information of a signal. according to this principle, one cannot know what spectral components exist at what specific times but one can know the time intervals at which certain bands of frequencies exist. this is known as time frequency resolution. in stft, if a window function of infinite length is used, we get the ft, which gives perfect frequency resolution, but no time information. in order to obtain stationarity, the narrower the width of the window function, the better the time resolution but the poorer the frequency resolution. therefore, choice of window function length becomes a tradeoff between frequency resolution and time resolution. resolution in time and frequency cannot arbitrarily be small, because their product is lower bounded, and hence time localization and frequency resolution cannot simultaneously be determined to an arbitrary precision. this can be stated in terms of a redefinition of the heisenberg uncertainty principle as: 1. 4 t f     (4) where t and f are the uncertainties in time and frequency [13]. so, to analyze various types of behavior in a signal, the stht would have to be taken several times, each time with a different size of window function. this is especially problematic when the location and/or duration of transient behavior are unknown, which is normally the case [15]. however, it ensures better resolution than the use of either the ft or hts [16]. 2-d fourier and hartley transforms the well-known complex 2-d fourier transform of an image represented by a real function f(x, y) and its inverse are given [17, 12] as:      2 , , i ux vy f u v f x y dx dye           (5) two-dimensional short time hartley transforms 43 and      2 , , i ux vy f x y f u v du dve          (6) where u and v correspond to x and y and are referred to as wave numbers. on the other hand, two different versions of 2-d hartley transforms exist [12], and are given here. the 2-d hartley transform of an image represented by f(x,y) and its inverse are given [17,12] as:       , , 2h u v f x y cas ux vy dx dy        (7) and       , , 2f x y h u v cas ux vy du dv        (8) where cas(ux+ vy) = cos (ux+ vy) + sin (ux+ vy). equations (7) and (8) (version i) are defined in many applications in analogy with the 2-d fourier transform [8]. the other version (version ii) of the 2-d ht can be written as [12]:        , , 2 2h u v f x y cas u x cas v y dx dy         (9)        , , 2 2f x y h u v cas u x cas v y du dv         (10) where,      xuxuxucas  2sin2cos2  and      yvyvyvcas  2sin2cos2  . equation (9) is sometimes referred to as the cas-cas transform. perkins [17] called it a ‘hartley like’ transform. on the other hand, equation (7) is dubbed the ‘fourier like’ 2-d ht. according to sundararajan, equations (7) and (9) give rise to the same frequency information [12]. furthermore, equation (9) is mathematically more appropriate than the conventional representation given by equation (8), which is mathematically incorrect since: exp[-(x u + y v)] ≠ cas(x u). cas(y v) the discrete counterpart of 2-d hartley transforms (dht) of an image f(x,y) of size m x n and their inverses given by equations (5), (8), (6) and (9) can be expressed as [12]:        1 , , 2h u v f x y cas ux vy mn   (11)       , , 2f x y h u v cas ux vy  (12)         1 , , 2 2h u v f x y cas u x cas v y mn    (13)        , , 2 2f x y h u v cas u x cas v y   (14) 2-d stft and sthts it may be noticed that the ht (stht) and its inverse possess the same kernel, unlike its progenitor, the ft, or any other integral transform. this is an exclusive characteristic associated with the ht [18]. the concept of the stht can easily be introduced to 2-d and multi-dimensions. accordingly, the 2-d stft and the 2-d stht of both the versions narasimman sundararajan et al. 44 (equation (7) and equation (9)) can be defined as:           dydxeyyxxgyxfvuyxstft y)vx(uπ2i ,,, (15)         , , 2, x y f x y g x x y y cas u x v y dx dystht x y u v        (16)          , , 2 2, yx f x y g x x y y cas u x cas v y dx dystht x y u v        (17) it is also to be noted that most of the signals we come across in our day to day life are real, and hence their spectral studies can better be realized using a real tool like a ht/stht rather than a complex tool like the ft/stft which is computationally more expensive, since one complex and one real mathematical operation have a cpu time ratio of 4:1. 2.1 computational examples the 2-d stft and the two different versions of the sthts are illustrated with the computation of a set of 32 synthetic seismic traces (figure 1) consisting of 256 samples in each trace making a data size of 256 32 . each trace (figure 1) represents the variation of amplitude with respect to time and all the traces are separated by a fixed interval of distance. thus, the set of 32 seismic traces make the spacetime function f(x,t). the computations of the stft and the two versions of sthts that yield the spectral amplitude versus frequency/wavenumber over each window are based on equations (15, 16) and (17) and are shown in figures (2, 3) and (4) respectively. the normalized spectral amplitudes are given in figures (2-4). figure 1. a set of 32 synthetic seismic traces represented by f(x, t). two-dimensional short time hartley transforms 45 figure 2. amplitude of short time fourier transform (stft) of f(x, t). figure 3. amplitude of short time hartley transform (stft) of f(x, t)-version-i. narasimman sundararajan et al. 46 figure 4. amplitude of short time hartley transform (stft) of f(x, t)-version-ii. 3. discussion in general ft/stfts can be replaced by their real versions called ht/stht in all their applications without any loss of information, but with certain computational advantages. although sthts ensure better resolutions than their hts, the optimization of window length for a desired result is again a cumbersome exercise. therefore, what is needed is a mapping that uses one initial window function which varies its size automatically so that all frequency behavior can be analyzed with just one pass (narrow window function at high frequencies and wide window function at low frequencies). this is where the wavelet transform comes in. the wavelet transform may address some of the shortcomings of the stft/sthts. instead of fixing the time and the frequency resolutions t and f , one can let both resolutions vary in time frequency plane in order to obtain a multi-resolution analysis. this variation can be carried out without violating the heisenberg inequality given in the equation (4). in this case, the time resolution must increase as frequency resolution decreases, and the frequency resolution must increase as time resolution decreases. this can be obtained by fixing the ratio of f over f to be equal to a constant c as: c f f   (18) with this approach, the time resolution becomes arbitrarily good at high frequencies, while the frequency resolution becomes arbitrarily good at low frequencies. the wavelet transform allows analysis of a signal that can locate energy in both time and frequency within the constraints of the uncertainty principle. perhaps the wavelet transform plays a significant role in signal analysis, overcoming the drawbacks encountered in the ft/stft and ht/stht, when carried out with appropriate mother wavelets [19]. therefore, the wavelet transform can be understood as being the natural extension of the hartley transform. the wavelet transform leads to automatic windowing instead of fixed windows as in sthts. two-dimensional short time hartley transforms 47 4. conclusion the appropriate choice between complex and real mathematical tools like the stft and stht, the stht is ideal for studying non-stationary signals, and has the added advantage of computational efficacy. 5. acknowledgment the authors record their sincere thanks to the reviewers for their useful suggestions to improve the manuscript as presented. references: 1. tukey, j.w. the sampling theory of power spectrum estimates. paper presented at the symposium on applications of autocorrelation analysis to physical problems, 1949. 2. cooley, j.w. and tukey, j.w. an algorithm for the machine calculation of complex fourier series. mathematics of computation., 1965, 19(90), 297-301. 3. brigham, e. the fast fourier transform. englewood cliffs, 1974. 4. gabor, d. theory of communication. part 1: the analysis of information. journal of the institution of electrical engineers part iii: radio and communication engineering, 1946, 93(26), 429-441. 5. allen, j.b. and rabiner, l. a unified approach to short-time fourier analysis and synthesis. proceedings of the ieee., 1977, 65(11), 1558-1564. 6. cohen, l. time-frequency analysis. prentice hall ptr englewood cliffs, nj., 1995, 1, 995,299. 7. sundararajan, n. fourier and hartley transforms-a mathematical twin. indian journal of pure and applied mathematics, 1997, 28, 1361-1366. 8. bracewell, r.n. discrete hartley transform. josa., 1983,73(12), 1832-1835. 9. bracewell, r.n. aspects of the hartley transform. proceedings of the ieee., 1994, 82(3), 381-387. 10. villasenor, j. and bracewell, r. optical phase obtained by analogue hartley transformation, nature, 1987, 330(6150), 735-737. 11. villasenor, j. and bracewell, r. lensless microwave imaging using the hartley transform. 1988, 617-619. 12. sundararajan, n. 2-d hartley transforms. geophysics, 1995, 60(1), 262-267. 13. sundararajan, n. and vijayachitra, s. multidimensional fourier and hartley transforms-are they same?, iete j res, 2000, 46(3), 125-127. 14. liu, j.c. and lin, t. short-time hartley transform. radar and signal processing, iee proceedings f, 1993, 140(3), 171-174. 15. chui, c. k. an introduction to wavelets analysis and its applications. academic, san diego, 1992. 16. zhao, z., xu, j. and horiuchi, s. differentiation operation in the wave equation for the pseudospectral method with a staggered mesh. earth, planets and space, 2001, 53(5), 327-332. 17. perkins, m. g. a separable hartley-like transform in two or more dimensions. proceedings of the ieee., 1987, 75(8), 1127-1129. 18. duhamel, p. and vetterli, m. improved fourier and hartley transform algorithms: application to cyclic convolution of real data. ieee transactions on acoustics, speech and signal processing,1987, 35(6), 818-824. 19. sundararajan, n. and vasudha, n. genesis of wavelet transform types and applications. wavelets and fractals in earth system sciences, 2013, 93-116. received 20 august 2014 accepted 1 november 2015 squ journal for science, 2014, 19(2), 97-100 © 2014 sultan qaboos university 97 some improved estimators in double sampling using two auxiliary variables mohammad s. ahmed department of mathematics and statistics, college of science, sultan qaboos university, p.o.box 36, al-khoud, 123 muscat, sultanate of oman. email: msahmed@squ.edu.om. abstract: dash and mishra [1] suggested an improved class of estimators without defining the optimum estimator. however, they gave the wrong taylor’s series expression of their class of estimator and their minimum mean squared error expressions are also incorrect. here we show that ahmed et al.’s [2] class of chain estimators is more efficient than dash and mishra’s [1], with minimum mean squared error. keywords: chain based estimator; double sampling; auxiliary variable; mean square error. بعض المقذراث المتطىرة في العيىبث المزدوجت ببستخذام اثىيه مه المتغيراث المسبعذة ص. أحمذ حمذم للفئه المقذرة متطىرة للمقذراث بذون تحذيذ المقذر األمثل ولكه لألسف أعطىا التعبير الخبطئ لسلست تبيلى تاقترحب فئ [1] داش وميشرا :ملخص هي أكثر [2] وآخرون.ن فئت مه سلسلت المقذراث ألحمذ أ وقذ بيىب هىبيضب غير صحيحه. أوأيضب تعببير الحذ األدوى لمتىسظ الخطأ التربيعي لهب .مع الحذ األدوى لمتىسظ الخطأ التربيعي [1]ميشرا كفبءة مه داش و .متىسظ الخطأ التربيعي ،المتغير المسبعذ ،عيىبث المزدوجتالتقذير حلقي، مفتاح الكلمات: 1. introduction uppose one is interested in estimating the population mean of a study variable y from a finite population of size n. if the information on an auxiliary variable x which is highly correlated with y is readily available on all the units of the population, it is well known that ratio and regression type estimators can be used for increased efficiency, incorporating the knowledge of ̅. however, in certain practical situations ̅ is not known a priori, in which case the technique of double sampling is fruitfully applied. the values of x are assumed to be known over a large simple random sample of size . now suppose that information on yet another auxiliary variable z is available on all units of the population ( ̅ is the population mean of z). then we observe the study variable y from a simple random subsample of that large sample of size ( ) to estimate the population mean ( ̅) of study variable . the first phase sample of size ( ) is selected to observe and , and the second phase sample of size is selected to observe and . suppose ̅ and ̅ are the unbiased estimators of ̅ and ̅, respectively, based on first phase sample ; ̅, ̅ and ̅ are the unbiased estimators of ̅, ̅ and ̅, respectively, based on second phase sample, . thus, a specific class of estimators can be suggested by suitably choosing the auxiliary information. over a period, a large number of estimators were proposed under different assumptions which can be classified as a particular member or case of some general class of estimators. in section 2, we critically evaluate some of these estimators. 2. some classes of estimators using information on two closely related auxiliary variables, x and z, a good number of classes of improved estimators were suggested by chand [3], kiregyera [4, 5], srivastava et al. [6], sahoo et al. [7], tripathi and ahmed [8], and mishra and rout [9]. a brief review of these estimators may be referred to das and mishra [1]. dash and mishra [1] suggested an improved class of estimators as defined ̅ ̅ ̅ ̅ ̅ (1.1) s mohammad s. ahmed 98 ahmed [10] proposed a wider class of estimators as ̅ (1.2) where ̅ ̅ , ̅ ̅ and ̅ ̅ ; is a function such that ̅ ̅ satisfying some regularity conditions. tripathi and ahmed [8] suggested the general class of estimator: ̅ ̅ ̅ ̅ ̅ ̅ ̅ (1.3) where and are suitably chosen statistics such that or . with suitable choices of and , tripathi and ahmed [8] showed that chand [3], kiregyera [4, 5], mukerjee et al. [11] and sahoo et al. [7] are the particular cases (1.3). further, ahmed [12] also showed that the recent estimators of mishra and rout [9], upadhyay and singh [13], samiuddin and hanif [14] and hanif et al. [15] are also the particular case of (1.3). the optimum values of , and are respectively , and , where and are partial regression coefficients and is a the total regression coefficient (see tripathi and ahmed [8]). the optimum estimator (1.3) is ̅ ̅ ̅ ̅ ̅ ̅ ̅ (1.4) where and are sample partial, and is the sample total, regression coefficients respectively. ahmed et al. [2] suggested another general class of estimators: ̅ ( ̅ ̅ ) ( ̅ ̅ ) ( ̅ ̅ ) (1.5) where , and are suitable chosen constants. the optimum values of , and are respectively, , and ( ̅ ̅ and ̅ ̅ ) the optimum estimator (1.3) is ̅ ( ̅ ̅ ) ( ̅ ̅ ) ( ̅ ̅ ) (1.6) where , , ( ̅ ̅ and ̅ ̅ ) it can be shown that the suggested estimators of chand [3], srivastava et al. [6], samiuddin and hanif [14] and hanif et al. [15] are the particular cases of the class of estimators (1.5) and that it has minimum mean squared error (mse). ahmed et al.[16] showed that both general classes of estimators (1.3), (1.5) and that of singh et al. [8] are a subclass of (1.2). the minimum mse of (1.2), (1.3) and (1.5) is the same and it is *( ) ( ) ( ) ( )+ (1.7) where is the population correlation coefficient between y and z, and is the multiple correlation coefficient of y on x and z ( √ . some improved estimators in double sampling 99 it can be easily shown that the proposed improved class of estimators of dash and mishra [1] as given in (1.1) does not accommodate the estimator (1.5), as the known mean ̅ does not contain in (1.1). they were not able to provide a correct taylor series expression of the estimator (1.1), which is a parametric function. besides this, they failed to present an explicit estimator for population mean. in their article, dash and mishra [1] presented an incorrect expression of the minimum variance of sahoo et al.’s [7] estimator [see the expression (2.2) in dash and mishra [1], pp. 4349 (which may be a typographical error)]. the correct minimum mse expression should be *( ) ( ) ( ) ( )+ (1.8) dash and mishra [6] derived a wrong expression for minimum mse of their estimator as [( ) ( ) ( ) ] (1.9) it is true that estimator (1.7) is more efficient than (1.8), as we have ( ) ( ) (1.10) which is the same as [dash and mishra [6], eq. 3.1)] but expressions (1.9) and (1.7) are totally different. 3. conclusion this paper provides an overview of classes of estimators in double sampling using two auxiliary variables. some limitations and errors of an improved class of estimators recently suggested by dash and mishra [1] have been pointed out. the reviews suggest that although a lot of improved classes of estimators have been presented in recent time, they are equivalent or particular cases of the general class of estimators suggested by tripathi and ahmed [8] and ahmed et al. [2]. diana and tommassic [18] argued that the regression type of estimators as given by ahmed et al.[2] is one of the best estimators, at least at the first order of approximation. they further suggested that no new estimators be proposed, since no estimator can be more efficient than the best estimators proposed by ahmed et al. [2], and some others, at least at the first order of approximation. references 1. dash, p.r. and mishra, g. an improved class of estimators in double sampling using two auxiliary variables. commu. stat.-theo. meth., 2011, 40(24), 4347-4352. 2. ahmed, m.s., rahman, m.s. and ahmed, r. general class of chain estimators for a finite population mean using double sampling. j. appl. statist. sci., 1998, 7, 185–190. 3. chand, l. some ratio-type estimators based on two or more auxiliary variables. ph.d. thesis, iowa state university, ames, iowa., 1995. 4. kiregyera, b. a chain ratio-type estimator in finite population two phase sampling using two-auxiliary variables. metrika, 1980, 27, 217-223. 5. kiregyera, b. regression type estimators using two-auxiliary variables and the model of double sampling from finite populations. metrika, 1984, 31, 215-226. 6. srivastava, s.rani., khare, b.b., and srivastava, s.r. a generalized chain ratio estimator for mean of a finite population. j. ind. sco. ag. stat., 1990, 42, 108-117. 7. sahoo, j., sahoo, l.n. and mohanty, s. a regression approach to estimation in two-phase sampling using two auxiliary variables. current sci., 1993, 65(1), 73-75. 8. tripathi, t.p. and ahmed, m.s. a class of estimators for a finite population mean based on multivariate information and double sampling. cal. stat. asso. bull., 1995, 45(179-180), 203-218. 9. mishra, g. and rout, k. a regression estimator in two phase sampling in presence of two auxiliary variables. metron, 1997, 12, 177–186. 10. ahmed, m.s. 1997. the general class of chain estimators for the ratio of two means using double sampling. commu. stat.-theo. meth., 1997, 269, 2247-2254. 11. mukerjee, r., rao, t.j. and vijayan, k. regression-type estimators using multiple auxiliary information. aust. j. stat., 1987, 29(3), 244-254. mohammad s. ahmed 100 12. ahmed, m.s. some recent works on two phase sampling for ratio and regression estimation. 12th islamic countries conference on statistical sciences iccs-12, december 19-22, 2012, qatar university, doha, qatar. 13. upadhyaya, l.n. and singh, g.n. chain type estimators using transformed auxiliary variable in two-phase sampling. adv. model. anal., 2001, 38, 1-2, 1-10. 14. samiuddin, m. and hanif, m. estimation of population mean in single and two phase sampling with or without additional information. pak. j. stat., 2007, 232, 99-118. 15. hanif, m., ahmed, z. and ahmad, m. generalized multivariate ratio estimators using multi-auxiliary variables for multi-phase sampling. pak. j. stat., 2009, 254, 615-629. 16. ahmed, m.s., khan, s.u. and tripathi, t.p. two general classes of chain ratio and product estimators for a finite population mean based on double sampling and multivariate information. j. stat. studies., 1994, 14, 86-99. 17. singh,v.k., singh, hari p., singh, housila p., and shukla, d. a general class of chain estimators for ratio and product of two means of a finite population. commu. stat.-theo. meth., 1994, 235, 1341-1355. 18. diana, g. and tommassic, c. estimation for finite population mean in double sampling. atti della xli riunione scientifica della sis. 599-602, padova:cleup "coop. libraria editrice università di padova, milano, 5-7 june, 2002. received 14 august 2014 accepted 8 december 2014 cg versus minres: an empirical comparison squ journal for science, 17 (1) (2012) 44-62 © 2012 sultan qaboos university 44 cg versus minres: an empirical comparison david chin-lung fong* and michael saunders** *icme, stanford university, california, usa, email: david3.14159@gmail.com. **systems optimization laboratory, department of management science and engineering, stanford university, california, usa, email: saunders@stanford.edu. abstract: for iterative solution of symmetric systems = ,ax b the conjugate gradient method (cg) is commonly used when a is positive definite, while the minimum residual method (minres) is typically reserved for indefinite systems. we investigate the sequence of approximate solutions kx generated by each method and suggest that even if a is positive definite, minres may be preferable to cg if iterations are to be terminated early. in particular, we show for minres that the solution norms kx are monotonically increasing when a is positive definite (as was already known for cg), and the solution errors * kx x are monotonically decreasing. we also show that the backward errors for the minres iterates kx are monotonically decreasing. keywords: conjugate gradient method (cg), conjugate residual method (cr), iterative method, krylov subspace method, linear equations, minimum residual method (minres), sparse matrix, trust-region method. مقارنة تجريبية بين طريقتي التدرج المترافقة والخطأ المتبقي األصغر لونج فونج و ميخائيل سوندرز-ديفيد تشن ax=من المعتاد استخدام طريقة التدرج المترافقة لحل جملة من المعادالت الخطية المتناظرة :خصمل b تكرارياً، عندما لحل جملة غير محددة. ندرس في هذا نموذجية األصغر الخطأ المتبقي طريقة كونموجبة محددة، بينما ت a المصفوفة تكون األصغر أفضل من الخطأ المتبقي أن طريقة نبين و تين،طريقنتج عن الالتي ت kxيةتقريبال الحلولمن البحث متسلسلة أنموجبة محددة، إذا توقف التكرار مبكراً. نبرهن بشكل خاص a عندما تكون المصفوفة طريقة التدرج المترافقة، حتى هو معروف اموجبة محددة )كم a المصفوفة عندما تكون ستمرارتزايد باياألصغر الخطأ المتبقي طريقة في kxيمنظال أخطاء الحلأن في حالة طريقة التدرج المترافقة( و * kx x لتكرارات سابقةأن األخطاء ال بانتظام. كذلك نبين تناقصت .ستمرارباناقص تتاألصغر الخطأ المتبقي طريقة cg versus minres: an empirical comparison 45 1. introduction he conjugate gradient method (cg) (hestenes and stiefel, 1952) and the minimum residual method (minres) (paige and saunders, 1975) are both krylov subspace methods for the iterative solution of symmetric linear equations = .ax b cg is commonly used when the matrix a is positive definite, while minres is generally reserved for indefinite systems (van der vorst, 2003, p85). we re-examine this wisdom from the point of view of early termination on positive-definite systems. we assume that the system =ax b is real with a symmetric positive definite (spd) and of dimension .n n the lanczos process (lanczos, 1950) with starting vector b may be used to generate the n k matrix  1 2k kv v v v and the ( 1)k k  hessenberg tridiagonal matrix kt such that 1=k k kav v t for = 1, 2, ,k and =av v t for some ,n where the columns of kv form a theoretically orthonormal basis for the kth krylov subspace 2 1 ( , ) span{ , , , , }, k k a b b ab a b a b   and t is  and tridiagonal. approximate solutions within the kth krylov subspace may be formed as =k k kx v y for some k-vector .ky as shown in (paige and saunders, 1975), three iterative methods cg, minres, and symmlq may be derived by choosing ky appropriately at each iteration. cg is well defined if a is spd, while minres and symmlq are stable for any symmetric nonsingular a. as noted by choi (2006), symmlq can form an approximation 1 1 1=k k kx v y   in the (k+1)th krylov subspace when cg and minres are forming their approximations =k k kx v y in the kth subspace. it would be of future interest to compare all three methods on spd systems, but for the remainder of this paper we focus on cg and minres. with different methods using the same information 1kv  and kt to compute solution estimates =k k kx v y within the same krylov subspace (for each k), it is commonly thought that the number of iterations required will be similar for each method, and hence cg should be preferable on spd systems because it requires somewhat fewer floating-point operations per iteration. this view is justified if an accurate solution is required (stopping tolerance  close to machine precision  ). we show that with looser stopping tolerances, minres is sure to terminate sooner than cg when the stopping rule is based on the backward error for ,kx and by numerical examples we illustrate that the difference in iteration numbers can be substantial. 1.1 notation we study the application of cg and minres to real symmetric positive-definite (spd) systems = .ax b the unique solution is denoted by *.x the initial approximate solution is 0 0,x  and k kr b ax  is the residual vector for an approximation kx within the kth krylov subspace. for a vector v and matrix a, v and a denote the 2-norm and the frobenius norm respectively, and 0a indicates that a is spd. 2. minimization properties of krylov subspace methods with exact arithmetic, the lanczos process terminates with =k for some .n to ensure that the approximations =k k kx v y improve by some measure as k increases toward , the krylov solvers minimize some convex function within the expanding krylov subspaces (freund et al., 1992). t david chin-lung fong and michael saunders 46 2.1 cg when a is spd, the quadratic form 1 ( ) 2 t t x x ax b x   is bounded below, and its unique minimizer solves = .ax b a characterization of the cg iterations is that they minimize the quadratic form within each krylov subspace (freund et al., 1992; meurant, 2006, §2.4; watkins, 2010, §8.8-§8.9): = , where = arg min ( ) . c c c k k k k k y x v y y v y with = *b ax and 2 ( ) = 2 *, t t k k k kx x ax x ax  this is equivalent to minimizing the function * ( * ) ( * ), t k k ka x x x x a x x    known as the energy norm of the error, within each krylov subspace. for some applications, this is a desirable property (steihaug, 1983; sun, 2003; arioli, 2004; meurant, 2006; watkins, 2010). 2.2 minres for nonsingular (and possibly indefinite) systems, the residual norm was used in (paige and saunders, 1975) to characterize the minres iterations: = , where = arg min . m m m k k k k k y x v y y b av y (1) thus, minres minimizes kr within the kth krylov subspace. this was also an aim of stiefel's conjugate residual method (cr) (stiefel, 1955) for spd systems (and of luenberger's extensions of cr to indefinite systems (luenberger, 1969, 1970)). thus, cr and minres must generate the same iterates on spd systems. we use this connection to prove that kx increases monotonically when minres is applied to an spd system. 2.3 cg and cr the two methods for solving spd systems =ax b are summarized in table 1. the first two columns are pseudocodes for cg and cr with iteration number k omitted for clarity; they match our matlab implementations. note that =q ap in both methods, but it is not computed as such in cr. termination occurs when = 0r ( = = 0  ). to prove our main result we need to introduce iteration indices; see column 3 of table 1. termination occurs when = 0kr for some index =k n ( = = 0,  = = = = 0r s p q ). note: this is the same as the at which the lanczos process theoretically terminates for the given a and b. theorem 2.1 the following properties hold for algorithm cr: (a) = 0 t i jq q ( i j ) (b) = 0 t i jr q ( 1i j  ) proof. given in luenberger (1970, theorem 1). theorem 2.2 the following properties hold for algorithm cr: (a) 0i  (b) 0i  (c) 0 t i jp q  cg versus minres: an empirical comparison 47 (d) 0 t i jp p  (e) 0 t i jx p  (f) 0 t i jr p  proof. (a) here we use the fact that a is spd. the inequalities are strict until =i (and = 0r ). = = 0 ( 0) t t i i i i ir s r ar a  (2) 2 1 1= / 0i i iq     (b) and again: 1= / 0 (by (2))i i i     (c) case i: =i j = 0 ( 0) t t i i i ip q p ap a case ii: = > 0i j k 1= = t t t t i j i i k i i k i i i kp q p q r q p q    1= (by theorem 2.1(b)) t i i i kp q   0 , where 0i  by (b) and 1 0 t i i kp q   by induction as ( 1) ( ) = 1 < .i i k k k    case iii: = > 0j i k = = t t t i j i i k i i kp q p q p ap  1= ( ) t i i k i k i kp a r p    1= t t i i k i k i i kq r p q    1= (by theorem 2.1(b)) t i k i i kp q    0 , where 0i k   by (b) and 1 0 t i i kp q    by induction as ( 1) = 1 < .i k i k k    (d) at termination, define 0 1 1span{ , , , }p p p  and 0 1span{ , , }.q q  by construction, 1 = span{ , , , }b ab a b  and = span{ , , }ab a b (since =i iq ap ). again by construction, ,x  and since = 0r we have = .b ax b  we see that . by theorem 2.1(a), 1 =0{ / }i i iq q  forms an orthonormal basis for . if we project ip   onto this basis, we have 1 =0 = , t i k i kt k k k p q p q q q   where all coordinates are non-negative from (c). similarly for any other ,jp < .j therefore 0 t i jp p  for any , < .i j (e) by construction, david chin-lung fong and michael saunders 48 1 1 1 0 =1 = = = ( = 0) i i i i i k k k x x p p x     . therefore 0 t i ix p  by (d) and (a). (f) note that any ir can be expressed as a sum of iq : 1 1=i i i ir r q  = 1 1= l l l i ir q q     1 1= .l l i iq q    thus we have 1 1= ( ) 0 , t t i j l l i i jr p q q p     where the inequality follows from (a) and (c). □ table 1. pseudocode for algorithms cg and cr we are now able to prove our main theorem about the monotonic increase of kx for cr and minres. a similar result was proved for cg by steihaug (1983). theorem 2.3 for cr (and hence minres) on an spd system = ,ax b kx increases monotonically. proof. 2 2 1 1 1 1 1= 2 0, t t i i i i i i ix x x p p p       where the last inequality follows from theorem 2.2(a), (d) and (e). therefore 1 .i ix x  □ * kx x is known to be monotonic for cg (hestenes and stiefel, 1952). the corresponding result for cr is a direct consequence of (hestenes and stiefel, 1952, theorem 7.5). however, the second half of that theorem, 1* > * , c m k kx x x x  rarely holds in machine arithmetic. we give here an alternative proof that does not depend on cg. cg versus minres: an empirical comparison 49 theorem 2.4 for cr (and hence minres) on an spd system = ,ax b the error * kx x decreases monotonically. proof. from the update rule for ,kx we can express the final solution = *lx x as 1 1 1=l l l lx x p   = 1 1 1= k k k l lx p p      (3) 1 1 1 1 1= .k k k k k l lx p p p          (4) using equations (3) and (4), we can write 2 2 1 1 1= ( ) ( ) ( ) ( ) t t l k l k l k l k l k l kx x x x x x x x x x x x          2 1 1 1 1 1 1= 2 ( ) t t k k k k l l k k kp p p p p           0 , where the last inequality follows from theorem 2.2 (a), (d). □ the energy norm error * k a x x is monotonic for cg by design. the corresponding result for cr is given in (hestenes and stiefel, 1952, theorem 7.4). we give an alternative proof here. theorem 2.5 for cr (and hence minres) on an spd system = ,ax b the error in energy norm * k a x x is strictly decreasing. proof. from (3) and (4), we can write 2 2 1l k l ka a x x x x   1 1= ( ) ( ) ( ) ( ) t t l k l k l k l kx x a x x x x a x x      2 1 1 1 1 1 1= 2 ( ) t t k k k k l l k k kp a p p p ap           2 1 1 1 1 1 1= 2 ( ) t t k k k k l l k k kq p p q p           > 0 , where the last inequality follows from theorem 2.2 (a), (c). □ 3. backward error analysis for many physical problems requiring numerical solution, we are given inexact or uncertain input data (in this case a and/or b). it is not justifiable to seek a solution beyond the accuracy of the data (dongarra et al., 1979). instead, it is more reasonable to stop an iterative solver once we know that the current approximate solution solves a nearby problem. the measure of "nearby'' should match the error in the input data. the design of such stopping rules is an important application of backward error analysis. for a consistent linear system = ,ax b we think of kx coming from the kth iteration of one of the iterative solvers. following titley-péloquin (2010) we say that kx is an acceptable solution if and only if there exist perturbations e and f satisfying ( ) = , ,k e f a e x b f a b      (5) for some tolerances 0,  0  that reflect the (preferably known) accuracy of the data. we are naturally david chin-lung fong and michael saunders 50 interested in minimizing the size of e and f. if we define the optimization problem , , s.t. ( ) = , ,min k e f e f a e x b f a b       to have optimal solution ,k ,ke kf (all functions of ,kx , and  ), we see that kx is an acceptable solution if and only if 1.k  we call k the normwise relative backward error (nrbe) for .kx with = ,k kr b ax the optimal solution ,k ,ke kf is shown in (titley-péloquin, 2010) to be 2 (1 ) = , = , tk k k k k k k b e r x a x b x        (6) = , = . k k k k k k r f r a x b       (7) see (higham, 2002, p12) for the case = 0 and (higham, 2002, §7.1 and p336) for the case = .  3.1 stopping rule for general tolerances  and , the condition 1k  for kx to be an acceptable solution becomes ,k kr a x b   (8) the stopping rule used in lsqr for consistent systems (paige and saunders, 1982a, p54, rule s1). f igure 1. comparison of distribution of the condition number for matrices used for cg vs minres, before and after diagonal preconditioning. cg versus minres: an empirical comparison 51 3.2 monotonic backward errors of interest is the size of the perturbations to a and b for which kx is an exact solution of = .ax b from (6)-(7), the perturbations have the following norms: = (1 ) = , k k k k k k r a r e x a x b       (9) = = . k k k k k b r f r a x b     (10) since kx is monotonically increasing for cg and minres, we see from (6) that k is monotonically decreasing for both solvers. since kr is monotonically decreasing for minres (but not for cg), we have the following result. theorem 3.1 suppose > 0 and > 0 in (5). for cr and minres (but not cg), the relative backward errors /ke a and /kf b decrease monotonically. proof. this follows from (9)-(10) with kx increasing for both solvers and kr decreasing for cr and minres but not for cg. □ 4. numerical results here we compare the convergence of cg and minres on various spd systems =ax b and some associated indefinite systems ( ) = .a i x b the test examples are drawn from the university of florida sparse matrix collection (davis, 2007). we experimented with all 26 cases for which a is real spd and b is supplied. in matlab we computed the condition number for each test matrix by finding the largest and smallest eigenvalue using eigs(a,1,'lm') and eigs(a,1,'sm') respectively. for this test set, the condition numbers range from 1.7e+03 to 3.1e+13. since a is spd, we apply diagonal preconditioning by redefining a and b as follows: = diag( )d a , = diag(1. / sqrt( )),d d ,a dad ,b db / .b b b thus in the figures below we have diag( ) =a i and = 1.b with this preconditioning, the condition numbers range from 1.2e+01 to 2.2e+11. the distribution of the condition number of the test set matrices before and after preconditioning is shown in figure 1. the stopping rule used for cg and minres was (8) with = 0 and 8 = 10 .  that is, 8 8 10 = 10kr b    (but with a maximum of 5n iterations for spd systems and n iterations for indefinite systems). 4.1 positive-definite systems in plotting backward errors, we assume for simplicity that > 0 and = 0 in (5)-(7), even though it doesn't match the choice of  and  in the stopping rule (8). this gives = 0k and = /k k ke r x in (9). thus, as in theorem 3.1, we expect ke to decrease monotonically for cr and minres but not for cg. david chin-lung fong and michael saunders 52 figure 2. comparison of backward and forward errors for cg and minres solving two spd systems = .ax b cg versus minres: an empirical comparison 53 figure 3. comparison of backward and forward errors for cg and minres solving two more spd systems = .ax b david chin-lung fong and michael saunders 54 in figures 2 and 3, we plot / ,k kr x * k a x x (the quantity that cg minimizes at each iteration), and * kx x against iteration number k for cg and minres for four different problems. for cg, the plots confirm that * k a x x and * kx x are monotonic. for minres, the plots confirm the prediction of theorems 3.1, 2.5, and 2.4, that / ,k kr x * ,k a x x and * kx x are monotonic. figure 2 (left) shows problem schenk_afe_af_shell8 with a of size 504855 504855 and cond( )a = 2.7e+05 (minres stops significantly sooner than cg). from the plot of backward errors / ,k kr x we see that both cg and minres converge quickly at the early iterations. then the backward error of minres plateaus at about iteration 80, and the backward error of cg stays about 1 order of magnitude behind minres. a similar phenomenon of fast convergence at early iterations followed by slow convergence is observed in the energy norm error and 2-norm error plots. figure 2 (right) shows problem cannizzo_sts4098 with a of size 4098 4098 and cond( )a = 6.7e+03 (minres stops slightly sooner than cg). minres converges slightly faster in terms of backward error, while cg converges slightly faster in terms of both error norms. figure 4. comparison of residual and solution norms for cg and minres solving two spd systems = .ax b figure 3 (left) shows problem simon_raefsky4 with a of size 19779 19779 and cond( )a = 2.2e+11. because of the high condition number, both algorithms hit the 5n iteration limit. we see that the backward error for minres converges faster than for cg as expected. for the energy norm error, cg is able to decrease over 5 orders of magnitude while minres plateaus after a 2 orders of magnitude decrease. for both the energy norm cg versus minres: an empirical comparison 55 error and 2-norm error, minres reaches a lower point than cg for some iterations. this must be due to numerical error in cg and minres (a result of loss of orthogonality in kv ). figure 3 (right) shows problem benelechi_benelechi1 with a of size 245874 245874 and cond( )a = 1.8e+09. the backward error of minres stays ahead of cg by 2 orders of magnitude for most iterations. around iteration 32000, the backward error of both algorithms goes down rapidly and cg catches up with minres. both algorithms exhibit a plateau on energy norm error for the first 20000 iterations. the error norms for cg start decreasing around iteration 20000 and decrease even faster after iteration 30000. figures 4 and 5 show kr and kx against iteration number k for cg and minres on four different problems. the solution norms grow somewhat faster for cg than for minres. both reach the limiting value *x significantly before kx is close to *.x figure 4 (left) shows problem simon_olafu with a of size 16146 16146 and cond( )a = 4.3e+08, and (right) shows problem cannizzo_sts4098 with a of size 4098 4098 and cond( )a = 6.7e+03. we see that kx is monotonically increasing for both solvers, and the kx values rise fairly rapidly to their limiting value, with a moderate delay for minres. figure 5. comparison of residual and solution norms for cg and minres solving two more spd systems = .ax b figure 5 (left) shows problem schmid_thermal1 with a of size 82654 82654 and cond( )a = 3.0e+05, and (right) shows problem benelechi_benelechi1 with a of size 245874 245874 and cond( )a = 1.8e+09, in which the residual decrease and the solution norm increase are somewhat slower than typical. the rise of kx david chin-lung fong and michael saunders 56 for minres is rather more delayed. in the second case, if the stopping tolerance were 6 = 10  rather than 8 = 10 ,  the final minres kx ( 10000)k  would be less than half the exact value * .x it will be of future interest to evaluate this effect within the context of trust-region methods for optimization. 4.1.1 why does k r for cg lag behind minres? it is commonly thought that even though minres is known to minimize kr at each iteration, the cumulative minimum of kr for cg should approximately match that of minres. that is, 0 .min c m i k i k r r    however, in figures 2 and 3 we see that kr for minres is often smaller than for cg by 1 or 2 orders of magnitude. this phenomenon can be explained by the following relations between c kr and m kr (greenbaum, 1977, lemma 5.4.1; titley-peloquin, 2011): 2 2 1 = . 1 / m k c k m m k k r r r r  (11) from (11), one can infer that if m kr decreases a lot between iterations k-1 and k, then c kr would be roughly the same as . m kr the converse also holds, in that c kr will be much larger than m kr if minres is almost stalling at iteration k (i.e., m kr did not decrease much relative to the previous iteration). the above analysis was pointed out by titley-peloquin (2011) in comparing lsqr and lsmr (fong and saunders, 2011). we repeat the analysis here for cg vs minres and extend it to demonstrate why there is a lag in general for large problems. with = 0 in stopping rule (8), cg and minres stop when .kr b if this occurs at iteration l, we have =1 1 = . l k l k k r r r b    thus on average, 1/ m m k kr r  will be closer to 1 if l is large. this means that the larger l is (in absolute terms), the more cg will lag behind minres (a bigger gap between c kr and m kr ). 4.2 indefinite systems a key part of steihaug's trust-region method for large-scale unconstrained optimization (steihaug, 1983) (see also (conn et al., 2000)) is his proof that when cg is applied to a symmetric (possibly indefinite) system = ,ax b the solution norms 1, , kx x are strictly increasing as long as > 0 t j jp ap for all iterations 1 .j k  (we are using the same notation as given in table 1.) from our proof of theorem 2.2, we see that the same property holds for cr and minres as long as both > 0 t j jp ap and > 0 t j jr ar for all iterations 1 .j k  in case future research finds that minres is a useful cg versus minres: an empirical comparison 57 solver in the trust-region context, it is of interest now to offer some empirical results about the behavior of kx when minres is applied to indefinite systems. first, on the nonsingular indefinite system 2 1 1 0 1 0 1 = 1 , 1 1 2 1 x                     (12) minres gives non-monotonic solution norms, as shown in the left plot of figure 6. the decrease in kx implies that the backward errors /k kr x may not be monotonic, as illustrated in the right plot. figure 6. for minres on the indefinite problem (4.2), kx and the backward error /k kr x are both slightly non-monotonic. more generally, we can gain an impression of the behavior of kx by recalling from (choi et al., 2011) the connection between minres and minres-qlp. both methods compute the iterates = m m k k kx v y in (1) from the subproblems 1 1 1 1= arg min and possibly = . m m k k k y y t y e t y e    when a is nonsingular or =ax b is consistent (which we now assume), m ky is uniquely defined for each k  and the methods compute the same iterates m kx (but by different numerical methods). in fact they both compute the expanding qr factorizations 1 1 = , 0 k k k k k r t q t e           (with kr upper tridiagonal) and minres-qlp also computes the orthogonal factorizations =k k kr p l (with kl lower tridiagonal), from which the kth solution estimate is defined by = ,k k kw v p = ,k k kl u t and = . m k k kx w u as shown in (choi et al., 2011 §5.3), the construction of these quantities is such that the first 3k  columns of kw are the same as in 1,kw  and the first 3k  elements of ku are the same as in 1.ku  david chin-lung fong and michael saunders 58 since kw has orthonormal columns, = , m k kx u where the first 2k  elements of ku are unaltered by later iterations. as shown in (choi et al., 2011, §6.5), it means that certain quantities can be cheaply updated to give norm estimates in the form 2 2 2 2 2 2 2 2 1ˆ , = , m k k k kx          where it is clear that 2  increases monotonically. although the last two terms are of unpredictable size, 2 m kx tends to be dominated by the monotonic term 2  and we can expect that m kx will be approximately monotonic as k increases from 1 to . figure 7. residual norms and solution norms when minres is applied to two indefinite systems ( ) = .a i x b experimentally we find that for most minres iterations on an indefinite problem, kx does increase. to obtain indefinite examples that were sensibly scaled, we used the four spd ( , )a b cases in figures 4 and 5, applied diagonal scaling as before, and solved ( ) =a i x b with = 0.5 and where a and b are now scaled (so that diag( ) =a i ). the number of iterations increased significantly but was limited to n. figures 7 and 8 show residual norms 10log kr and and solution norms kx against iteration number k cg versus minres: an empirical comparison 59 when minres is applied to the four indefinite systems ( ) = ,a i x b where = 0.5 is large enough to make the systems indefinite. figure 7 (left) shows problem simon_olafu with = 16146,n and (right) shows problem cannizzo_sts4098 with = 4098n (where a is the spd matrices in figure 4). the values of kx are essentially monotonic. the backward errors /k kr x (not shown) were even closer to being monotonic (at least for the first n iterations). during the = 16146n iterations of simon_olafu, kx increased 83% of the time and the backward errors /k kr x (not shown) decreased 96% of the time; and during the = 4098n iterations of cannizzo_sts4098, kx increased 90% of the time and the backward errors /k kr x (not shown) decreased 98% of the time. figure 8. residual norms and solution norms when minres is applied to two more indefinite systems ( ) = .a i x b figure 8 (left) shows problem schmid_thermal1 with = 82654,n and (right) shows problem benelechi_benelechi1 with = 245874n (where a is the spd matrices in figure 5). the problem schmid_thermal1 reveals a definite period of decrease in ,kx and there is a mild but clear decrease in kx over an interval of about 10000 iterations. nevertheless, during the = 82654n iterations, kx increased 83% of the time and the backward errors /k kr x decreased 91% of the time. the problem benelechi_benelechi1 is more like those david chin-lung fong and michael saunders 60 in figure 7, where the solution norms and backward errors are essentially monotonic. during the = 245874n iterations, kx increased 88% of the time and the backward errors /k kr x (not shown) decreased 95% of the time. 5. conclusions for full-rank least-squares problems min ,ax b the solvers lsqr (paige and saunders, 1982a, 1982b) and lsmr (fong and saunders, 2011, 2010) are equivalent to cg and minres on the (spd) normal equation = . t t a ax a b comparisons in (fong and saunders, 2011) indicated that lsmr can often stop much sooner than lsqr when the stopping rule is based on stewart's backward error norm / t k ka r r for least-squares problems (stewart, 1977). table 2. comparison of cg and minres properties on an spd system =ax b [11]=hestenes and stiefel (1952); [18]=paige and saunders (1975); [21]=steihaug (1983) table 3. comparison of lsqr and lsmr properties on min ax b [7]=fong (2011); [8]=fong and saunders (2011); [19]=paige and saunders (1982) our theoretical and experimental results here provide analogous evidence that minres can often stop much sooner than cg on spd systems when the stopping rule is based on the backward error /k kr x for =ax b (or the more general backward errors in theorem 3.1). in some cases, minres can converge faster than cg by as much as 2 orders of magnitude (figure 3). on the other hand, cg converges somewhat faster than minres in terms of both * k a x x and * kx x (same figure). for spd systems, table 2 summarizes properties that were already known by hestenes and stiefel (1952) and steihaug (1983), along with the two additional properties we proved here (theorems 2.3 and 3.1). cg versus minres: an empirical comparison 61 these theorems and experiments on cg and minres are part of the first author's phd thesis (fong, 2011), which also discusses lsqr and lsmr and derives some new results for both solvers. table 3 summarizes the known results for cg and minres in (paige and saunders, 1982a) and (fong and saunders, 2011), respectively, and the newly derived properties for both solvers in (fong, 2011). 6. acknowledgements we kindly thank professor mehiddin al-baali and other colleagues for organizing the second international conference on numerical analysis and optimization at sultan qaboos university (january 3-6, 2011, muscat, sultanate of oman). their wish to publish some of the conference papers in a special issue of squ journal for science gave added motivation for this research. we also thank dr sou-cheng choi for many helpful discussions of the iterative solvers, and michael friedlander for a final welcome tip. the first author (david fong) was partially supported by a stanford graduate fellowship. the second author (michael saunders) was partially supported by office of naval research grant n00014-08-1-0191 and nsf grant dms-1009005, and by the u.s. army research laboratory, through the army high performance computing research center, cooperative agreement w911nf-07-0027. 7. references arioli, m. 2004. a stopping criterion for the conjugate gradient algorithm in a finite element method framework. numerical mathematics, 97: 1-24. choi, s.-c. 2006. iterative methods for singular linear equations and least-squares problems. phd thesis, stanford university, stanford, california, usa. choi, s.-c., paige, c.c. and saunders, m.a. 2011. minres-qlp: a krylov subspace method for indefinite or singular symmetric systems. siam j. sci. comput., 33: 1810-1836. conn, a.r., gould, n.i.m. and toint, ph.l. 2000. trust-region methods, vol. 1. siam, philadelphia, usa. davis, t.a. 2007. university of florida sparse matrix collection. http://www.cise.ufl.edu/research/sparse/matrices. dongarra, j.j., bunch, j.r., moler, c.b. and stewart, g.w. 1979. linpack users’ guide. siam, philadelphia, usa. fong, d.c.-l. 2011. minimum-residual methods for sparse least-squares using golub-kahan bidiagonalization. phd thesis, stanford university, stanford, california, usa. fong, d.c.-l. and saunders, m.a. 2010. lsmr software for linear systems and least squares. http://www.stanford.edu/group/sol/software.html. fong, d.c.-l. and saunders, m.a. 2011. lsmr: an iterative algorithm for sparse least-squares problems. siam journal on scientific computing, 33: 2950-2971. freund, r.w., golub, g.h. and nachtigal, n.m. 1992. iterative solution of linear systems. acta numerica, 1: 57-100. greenbaum, a. 1997. iterative methods for solving linear systems. siam, philadelphia, usa. hestenes, m.r. and stiefel, e. 1952. methods of conjugate gradients for solving linear systems. journal of research of the national bureau of standards, 49: 409-436. higham, n.j. 2002. accuracy and stability of numerical algorithms. (second edition) siam, philadelphia, usa. lanczos, c. 1950. an iteration method for the solution of the eigenvalue problem of linear differential and integral operators, journal of research of the national bureau of standards, 45: 255-282. luenberger, d.g. 1969. hyperbolic pairs in the method of conjugate gradients. siam journal on applied mathematics, 17: 1263-1267. david chin-lung fong and michael saunders 62 luenberger, d.g. 1970. the conjugate residual method for constrained minimization problems. siam journal on numerical analysis, 7: 390-398. meurant, g.a. 2006. the lanczos and conjugate gradient algorithms: from theory to finite precision computations, vol. 19 of software, environments, and tools, siam, philadelphia, usa. paige, c.c. and saunders, m.a. 1975. solution of sparse indefinite systems of linear equations. siam journal on numerical analysis, 12: 617-629. paige, c.c. and saunders, m.a. 1982a. lsqr: an algorithm for sparse linear equations and sparse least squares. acm transactions on mathematical software, 8: 43-71. paige, c.c. and saunders, m.a. 1982b. algorithm 583; lsqr: sparse linear equations and least-squares problems. acm transactions on mathematical software, 8: 195-209. steihaug, t. 1983. the conjugate gradient method and trust regions in large scale optimization. siam journal on numerical analysis, 20: 626-637. stewart, g.w. 1977. research, development and linpack, in mathematical software iii, j.r. rice, ed., academic press, new york, usa, 1-14. stiefel,e. 1955. relaxationsmethoden bester strategie zur l¨osung linearer gleichungssysteme. comm. math. helv., 29: 157-179. sun, y. 2003. the filter algorithm for solving large-scale eigenproblems from accelerator simulations. phd thesis, stanford university, stanford, california, usa. titley-peloquin, d. 2010. backward perturbation analysis of least squares problems. phd thesis, school of computer science, mcgill university, canada. titley-peloquin, d. 2011. convergence of backward error bounds in lsqr and lsmr. private communication. van der vorst, h.a. 2003. iterative krylov methods for large linear systems. (1st edition) cambridge university press, cambridge, uk. watkins, d.s. 2010. fundamentals of matrix computations. (3rd edition) pure and applied mathematics, wiley, hoboken, new jersey, usa. received 20 october 2011 accepted 29 november 2011 microsoft word biol041016-proof.doc 1-30 squ journal for science, 10 (2005) © 2005 sultan qaboos university 1 harmful algal blooms: physiology, behavior, population dynamics and global impactsa review al-ghelani, h.m.*, alkindi, a.y.a**, amer, s.* and al-akhzami, y.k*. *ministry of agriculture and fisheries, p.o.box 467, al khuwair 113, muscat, sultanate of oman,** department of biology, sultan qaboos university, p.o.box 36, alkhod 123, muscat, sultanate of oman, **email: aakindy@squ.edu.om. الجوانب الفيزيولوجية والسلوكية لها ونموها وتأثيرها العالمي : إزدهار الطحالب الضارة حمد بن محمد الغيالني ، عبدالعزيز الكندي ، شهلة عامر و يونس بن خلفان االخزمي رة تحظي إن الطحالب السامة تعد واحدة من أكبر العوامل الحيوية التي بدأت تظهر كمؤثرات بيئية ضا:خالصة وإن االزدياد الواضح للطحالب الضارة أصبح يمثل مشكلة لالستزراع السمكي وللمصائد البحرية ، ولم . باالهتمام يقف أثر هذه الظاهرة السلبية المتنامي على الصحة العامة وعلى اآلثار االقتصادية السيئة لها في السنوات األخيرة ي تتأثر بهذه الظاهرة الخطرة ، ويبدو أن هناك سببان رئيسيان لهذه بل تعداه إلى اتساع الرقعة الجغرافية الت الظاهرة أحدهما طبيعي كالتغيرات المناخية واآلخر من صنع اإلنسان كإلقاء المخلفات الصناعية في مياه البحار، وضع ومع ذلك ال نستطيع إغفال ظاهرة االحتباس الحراري ومدى تأثيرها على نمو هذه الطحالب، مما يتطلب خطط عملية إلدارة ومراقبة هذه الظاهرة ، وهناك جهود تبذل من أجل التقليل من تأثيرها ببرامج الرقابة الساحلية، واكتشاف أنواع الطحالب وتحديد السام منها والتنبؤ بها قبل ازدهارها مما يعكس مدى االهتمام العالمي بها ة مما سيكون له تأثير سريع وحقيقي على مدى اكتشاف سمية هذه واستخدام التكنولوجيا الحديثة كالتحاليل الجزيئي .الكائنات وأسباب تأثيرها abstract: harmful, toxic algae are now considered as one of the important players in the newly emerging environmental risk factors. the apparent global increase in harmful algal blooms (habs) is becoming a serious problem in both aquaculture and fisheries populations. not only has the magnitude and intensity of public health and economic impacts of these blooms increased in recent years, but the number of geographic locations experiencing toxic algal blooms has also increased dramatically. there are two primary factors causing habs outbreaks. the natural processes such as upwelling and relaxation, and the anthropogenic loading resulting in eutrophication. however, the influence of global climate changes on algal bloom phenomenon cannot be ignored. the problem warrants development of effective strategies for the management and mitigation of habs. progress made in the routine coastal monitoring programs, development of methods for detection of algal species and toxins and coastal modeling activities for predicting habs reflect the international concerns regarding the impacts of al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 2 habs. innovative techniques using molecular probes will hopefully result in development of rapid, reliable screening methods for phycotoxins and the causative organisms. keywords: harmful algal blooms, phycotoxins, eutrophication, toxigenic algae, biotoxin, upwelling. 1. introduction arine phytoplankton develops over various scales of space and time (harris, 1986), one of which includes the massive, relatively sudden and local or geographically restricted outbursts of one or sometimes a few species. such phenomena are given one of a few names: ‘red tides’, ‘brown water’, ‘discoloured waters’, ‘colored waters’. all these terms imply that algal proliferation is so intense as to modify the appearance of the sea surface as perceived by human eye. red tides refer to the bio optical phenomena and rely implicitly on a threshold of a plant biomass or light extinction; several attempts have been made to estimate this threshold in terms of cell numbers, total cell volume and carbon content (kim et al. 1993) or chlorophyll content (allen, 1946; saunders and glenn, 1969; tett, 1987). on the other hand, blooms (originally, the regular spring growth in temperate waters) are ecophysiological rather than bio-optical in meaning; being typically harmless. phyoplankton or single celled marine plants are organisms at the base of the food chain that are the food for many higher organisms. these microscopic planktonic algae are critical food for filter-feeding bivalve fish as well as the larvae of commercially important crustaceans and finfish. in most cases, the proliferation of planktonic algae, so-called (‘algal blooms’, up to millions of cells per litre) is therefore beneficial for aquaculture and wild fisheries operations (hallegraeff, 1993). in some situations algal blooms can have a negative effect, causing severe economic losses to aquaculture, fisheries and tourism operations and having major environmental and human health impacts. red tides may be harmless or harmful to the surrounding fauna, man included, and they can be dramatically harmful when the causative organism produces a toxin (sournia, 1995). however, toxin-producing microalgae may be deleterious even when present in low or moderate concentrations. therefore: (i) red tides are not all toxic (ii) toxic phytoplankters do not all produce red tides. 2. definition generally, approximately 1 million cells per liter of seawater equals a bloom which may also produce biotoxins. these events are termed harmful algal blooms or habs. attendees at the 1984 ices exceptional plankton blooms meeting concluded that exceptional blooms should be defined in terms of the deviation from the normal cycle of phytoplankton biomass (parker, 1987). habs were defined as phytoplankton blooms where the effects are noticeable and or harmful. the term ‘harmful’ algal blooms (habs) referred to as ‘red tides”, has been applied to a class of blooms increasingly thought to have unique properties (smayda, 1997). this emergent bloom phenomenon is rapidly expanding in global coastal waters (anderson, 1989; smayda, 1990; hallegraeff, 1993). richardson (1989) defined a bloom as an outburst resulting in ‘high biomass’, stating also that ‘a red tide is an exceptional bloom’. according to richardson (1997), phytoplankton (also called “microalgal or algal”) bloom is the rapid growth of one or more species leading to an increase in biomass of the species. exceptional phytoplankton blooms have also been defined as “those which are noticeable, particularly to the general public, directly or indirectly through their effects such as visible discoloration of water, foam production, fish or invertebrate mortality or toxicity to human (ices, m harmful algal blooms 3 1984). reid et al. (1987) applied the term “exceptional” to blooms of microalgae, accompanied by ‘deleterious side-effects.’ cellular abundance levels have also been used to define red tide blooms. kim et al. (1993), classify blooms as ‘red tides’ (in korean waters) when abundance of the causative species (>30 µm) exceeds 1000 cells ml-1. this criterion results in about 200 diatom species being classified as red tide species, which represents about two thirds (65%) of the total number of species classified as such (sournia, 1995). blooms, as a phenomenon collectively have properties other than biomass, numerical population density, and the potential of the bloom species to inflict harm. harmful effects may therefore accompany very high (~108 cells l-1) or very low (<103 cellsl-1) biomass. furthermore, bloom events may occur at very low (<103 cells l-1) or very high (~108 cells l-1) cellular abundance, and may be due to very small or very large species’ size. in both cases same species may be simultaneously inimical to several trophic components or have multiple effects and for different reasons. the presence of a toxic species does not necessarily lead to a deleterious impact. such effects require a threshold population density level, above which it becomes inimical. the population level at which this occurs need not be accompanied by seawater discolouration, contrary to anecdotal perceptions of red tides. 3. harmful algal blooms 3.1 history it is often cited that the first written record (1000 b.c.) of a harmful algal bloom appears in the bible: ‘…all the waters that were in the river were turned to blood. and the fish that was in the river died; and the river stank, and the egyptians could not drink of the water of the river’ (exodus: 20-21, moore, 1977; hallegraeff, 1995). however, there is fossil evidence that harmful algal blooms were occurring long before this. noe-nygaard et al. (1987) have suggested, on the basis of the distribution of dinoflagellate cysts and bivalve shells in fossil sediments taken from island of bornholm in the baltic sea, that toxic dinoflagellates caused mass mortalities of bivalves on several occasions dating back to about 130 million years ago. dale et al. (1993) have also studied the distribution of fossil dinoflagellate cysts and presented evidence suggesting bloom formation by the toxic dinoflagellate gymnodium catenatum in the kattegat-skagerrak long before anthropogenic activities could have influenced these waters. the species first appeared in the region about 6000 years ago and achieved a minor peak in production about 4500 years ago. after that it occurred in relatively low numbers until about 2000 years ago. during the next 1500 years periodic blooms of the species took place. in the sediment records for the last 300 years these workers found no evidence of this dinoflagellate. the fossil records emphasize two important points with respect to exceptional algal blooms (richardson, 1997): i. the occurrence of such blooms is not a recent phenomenon i.e., anthropogenic perturbation of the environment is not a necessary prerequisite for all exceptional blooms ii. phytoplankton species are not necessarily permanent residents of a given body of water. 3.2 causative organisms the numbers of species within each phytoplankton class implicated in the formation of harmful bloom or red tides have been estimated by sournia (1995). according to him the dinoflagellates (dinophyceae) comprise the class which is numerically the largest and it is also within this class that one finds the greatest numbers of both exceptional / harmful bloom forming and toxic species. estimates show that 5.5–6.7% of the known phytoplankton species in the world’s oceans, i.e. about 200 species, have been identified as causing exceptional or harmful blooms (sournia, 1995; skulberg et al. 1993; steidinger, 1996; hasle and syvertsen, 1996; throndsen, 1993; taylor et al. 1995; landsberg, 2002). about half of these species are dinoflagellates, while diatoms are probably the second most important algal class in terms of causing exceptional or harmful blooms (sournia, 1995). al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 4 however, toxic species are about four times less numerous (60-78) than red tide species, but still represent 1.8-1.9% of the world flora (sournia, 1995), with numbers increasing by not more than 2030 species (bomber, 1991; shimizu, 1987; elbrachter, 1990; hawser et al. 1991). approximately 75% of the species that have been identified as being toxic belong to the dinophyceae and most of these belong to the order peridiniale, gymnodiniales and dinophysales. four genera (alexandrium, dinophysis, gymnodium and prorocentrum) dominate in terms of causing toxic blooms (white, 1979; skulberg et al. 1993; steidinger, 1996; steidinger et al. 1996; taylor et al. 1995). 3.3 impacts of harmful algal blooms there is an increase in phytoplankton events in number, geographical extent, frequency, number of species, intensity and damages (boalch, 1983; anderson, 1989; smayda, 1990; sournia et al. 1991; hallegraeff, 1993). three modes of negative impact have resulted in characterrising certain species as ‘harmful’. they are described as : ‘toxic’ (anderson et al. 1985), ‘noxious’ (horner et al. 1990) or ‘nuisance’ (hallegraeff, 1993). the three major impacts of the harmful blooms are: 1. a number of toxins produced by phytoplankton that affect humans also affect fish (white, 1977; gosselin et al. 1989; riley et al. 1989; robineau et al. 1991; noga, 1998). in addition, however some bloom forming phytoplankton species that have not been shown to be toxic to human produce toxins that affect fish or other marine organisms (moshiri et al. 1978; granmo et al. 1988; heing and campbell, 1992; eilertsen and raa, 1994). phytoplankton species which cause fish-poisoning (ciguatera) and shell-fish vectored poisoning of humans are clearly harmful (hallegraeff, 1993). public health concerns over-bloom related, shellfish borne diseases affecting seafood safety are an emergent global concern. 2. species whose blooms induce die-offs of farmed fish and cultivated shellfish leading to aquacultural financial losses are also harmful. gelatinous secretion during an unusual bloom of the diatom coscinodiscus wailessi in the north sea was so great that the weight of the slime tore fishing nets and impaired the fishery (boalch and harbour, 1977). deflections of migratory routes (savage, 1930), emigrations (lenanton et al. 1985) and other avoidance reactions (potts and edwards, 1987) of commercially important fish during harmful blooms also occur. 3. the third major category of impact-field and experimental evidence reveals at least eight different modes and mechanisms by which harmful species cause mortality or physiologically impair target victims (table 1). these fall in two general types: i. non-chemical effects: effects, which lead to starvation or cause harmful mechanical and physical damage. ii. chemical effects: attributable to physical-chemical reaction, phycotoxins or other metabolites. starvation impaired growth and fecundity resulting from nutritional and prey size mismatches are well-known experimental results, (smayda, 1997). excess prey density (> 250 x 106 l-1) of the brown tide species, aureococcus anophagefferens, led to a spawning failure and mortality of the mussel, mytilus edulis (tracey, 1988; nuzzi and waters, 1989; smayda and villareal, 1989). this organism has also been shown to reduce or stop filter feeding in some shellfish (tracey, 1988; gallager et al. 1989; gainey and shumway, 1991). mechanical damage leading to death of larval fish can result from collisions (“bumping”) with dinoflagellates at high bloom population densities (ho and zubkoff, 1979). lethal piercing of gill filaments of penned and feral population of fish and crustaceans by the setae of chaetoceros diatoms also can occur (horner et al. 1997; rensel, 1993; yang and albright, 1992; tester and mahoney, 1995). respiratory failure, haemorrhaging, or bacterial infection resulting from such particle irritation can cause mortality. extra cellular polymer secretions of harmful species can induce mortality in three physical ways; as a viscosity barrier (partensky et al. 1989; potts and edwards, 1987); by forming a gelatinous barrier (taylor et al. 1985) and through mucoid layer reduction (endo et al. harmful algal blooms 5 1985). gill clogging, elevated shear stress, which tears gill filaments and osmoregulatory failure can lead to death (endo et al. 1985, 1992). table 1. mortality modes and impact mechanisms of harmful species and their blooms (source : smayda, 1997). modes impact starvation nutritionl mismatch size mismatch excess prey density mechanical “bumping” particle irritation (chaetoceros spp.) physical viscosity barrier (gyrodinum areolum) gelatinous barrier (ceratulina pelagica) mucoid layer reduction (chattonella marina) anoxia ceratium blooms nh4 toxicity noctiluca blooms phycotoxins direct vs. vectored toxicity saxitoxin brevetoxins hemolysins cytotoxins allelopathic ambush predation pfiesteria piscicida unresolved aureococcus anophaghagefferens among the chemically harmful mechanisms die off due to anoxia or hypoxia following blooms of large, relatively ungrazed species such as ceratium are well-known (graneli et al. 1989; mahoney and steimle, 1979). noctiluca produced a remarkably simple ichthyotoxin: nh4 (okaichi and nishio, 1976). in contrast phycotoxins have much more elaborate effects. mortality can occur through direct ingestion of endotoxin of the harmful species (carmichael, 1996), upon exposure to secreted toxins (exotoxins; hansen et al. 2000) or from toxin vectoring through the food web, accompanied by conformational changes in the toxic principles and their potencies (shimizu, 1987; shimizu et al. 1989; yasumoto and murata, 1993). the impact may be on a directly targeted predator or may lead to indiscriminate die-offs and physiological impairment during food web vectoring (landsberg, 2002). specific toxins are water or lipid soluble and have cytolytic, haemolytic (hansen et al. 2000) or neurotoxic activity (perovic et al. 2000; daugbjerg et al. 2000). allelopathic substances are distinguished from phycotoxins in being secondary metabolites (subba rao et al. 1995; wright and cembella, 1998; naviner et al. 1999) and both can co-occur within a given harmful species. allelopathic substances tend to be directly targeted and may physiologically impair, stun, repel, induce avoidance reactions or kill grazers (plumley, 1997; wyatt and jenkinson, 1997, fistarol et al. 2004). examples of these diverse modes of impact have been demonstrated by smayda (1992). a relatively newly discovered, remarkable ambush predatory behavior of the harmful dinoflagellate pfiesteria piscicida has been presented by burkholder and glasgow (1995, 1997), burkholder et al. (1992, 1999, 2001), and berry et al. (2002) and vogelbein et al. (2002). al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 6 3.4 types of harmful algal blooms harmful and toxic species are a small subset of the total phytoplankton flora and little is known about the inter-annual variability with respect to the relative frequency of occurrence of different phytoplankton species. the three different types of harmful habs are: 1. in some cases, a non-toxic bloom forming alga becomes so densely concentrated that it can generate anoxic conditions resulting in indiscriminate kills of both fish and invertebrates due to oxygen depletion. for example, dinoflagellates, gonyaulax polygramma (lam, 1988) noctiluca scintillans. (okaichi and nishio, 1976; chen and qi, 1991; ho and hodgkins, 1992; xie, et al. 1993; hong and huang, 1989; qi et al. 1992, 1993, 1995; qi and li, 1994) and cynobacterium: trichodesmium erythraeum (endean et al. 1993). 2. species that produce potent toxins that can find their way through the food chain to humans (table 2), cause a variety of gastrointestinal and neurological illnesses such as paralytic shellfish poisoning (psp; lush and hallegraeff, 1996). for example, dinoflagellates, alexandrium acatanella (cembella et al. 1987), alexandrium minutum (chen and chou, 2001) alexandrium fundyense (anderson et al. 1990). most humans who experience paralytic shellfish poisoning have consumed toxic bivalves (shumway, 1990) and toxic gastropods and crustaceans (shumway, 1995). whales and porpoises can also become victims when they receive toxins through the food chain via contaminated zooplankton or fish (geraci et al. 1989). 3. the third type of harmful algal bloom has been apparent only as a result of the increased interest in intensive aquaculture systems for finfish. some algal species can seriously damage fish gills, either mechanically (berry et al. 2002) or through production of haemolytic substances (hansen et al. 2000). table 2. potency of some algal blooms (source: wyatt, 1998) toxin source toxicity cyanide 1 muscarin amanita muscaria, fungus 9 okadaic acid algae, dinflagellates (e.g. dinophysis spp.) 50 domoic acid algae, diatoms (pseudo-nitzschia spp.) 80 prymnesium algae, haptophytes (e.g. prymnesium parvum) 350 cobra toxin cobra snake 500 saxitoxin algae, dinoflagellates (e.g. alexandrium spp., pyrodinum bahamense) 1 100 ciguatoxin algae, dinoflagellates (gambierdiscus toxicus) 22 000 tetanus toxin bacterium (clostridium tetani) 100 000 000 4. harmful algal events upwards of ten thousand named species of plank-toxic algae are found in the upper layers of the oceans and continental waters. excluding those which respond to eutrophication and associated processes and which can give rise to biomass problems, less than a hundred of these have so far been recorded as harmful (wyatt, 1998). three distinct periods of harmful algal events can be distinguished: 1. events due to accumulation of biomass of microplanktonic cells (larger than 20 µm in diameter), often associated with natural or anthropogenic eutrophication, which are normally composed of different species. in these cases, unrestrained growth of algae can lead to very high cell concentration. if these populations are neither grazed nor dispersed by winds and tides, their death and decay can lead to deoxygenation in the sediments where they settle harmful algal blooms 7 (okaichi and nishio, 1976; onoue, 1990; olsgard, 1993) in the lower water column and consequent mortalities of other components of the ecosystem are affected. anoxia and or bacterial infection in combination with the damaged gill tissue leads to mortality of the fish (jones and rhodes, 1994; tester and mahoney, 1995). hypoxia or anoxia resulting from the respiration or decay of dense blooms of phytoplankton can also, on its own, lead to fish or shellfish killsespecially of caged fish that are unable to swim from the affected area (steimle and sindermann1978; taylor et al. 1985). events of this kind are common, often annual, in many parts of the world, especially in shallow, semi-enclosed and poorly furnished estuaries and lagoons but less frequently in open sea areas such as the northern adriatic sea or the new york bight, when the balance between nutrient supplies and flushing rates tips in favour of such events (wyatt, 1998) 2. there are blooms of single microplanktonic species with particular morphological, physiological or biochemical features which interact in negative ways with other organisms in the environment, either directly or through the food web. for example, (i) some diatoms in the genus chaetoceros cause much damage to the gills of caged fish (ianora et al. 1995); (ii) the diatom coscinodiscus wailesii, a water blooming species competes for nutrients with the red microalgae porphyra which is farmed in japan and other countries; and (iii) the dinoflagellate gyrodinium aureolum, (frequently referred to as gymnodium), (mahoney et al. 1990) can cause potentially lethal respiratory distress in fish and other organisms brought about by secretion of large quantities of mucilaginous materials (wyatt, 1998). but many harmful species in this group are poisonous and produce compounds which can cause paralytic, neurotoxic, diarrhetic and other effects when transmitted through the food web to vertebrates including man. 3. events due to accumulation of biomass of ultraplanktonic cells (between 0.2 and 20 µm in diameter). events of this kind are less common, but can be very persistent as in the case of the texas ‘brown tide’ which has persisted in laguna madre for more than seven years (wyatt, 1998). 5. rise of algal blooms the issue of a global increase in harmful algal blooms has been raised previously in conference proceedings (anderson 1989; hallegraeff et al. 1990; smayda, 1990), while the biology of toxic dinoflagellates has been reviewed by steidinger (1993) while the facts of algal blooms on aquaculture have been summarized by shumway (1990). four possible explanations for the apparent rise of algal blooms are: • increased scientific awareness of toxic species • increased utilization of coastal waters for aquaculture • stimulation of plankton blooms by cultural eutrophication • unusual climatologic conditions and transport of dinoflagellate resting cysts either in ships ballast water or associated with movements of shellfish stocks from one area to another. 5.1 increased scientific awareness of toxic species reports of harmful algal blooms associated human illnesses or damage to aquaculture operations are receiving increased attention in media and scientific literature. concerns about aquatic biotoxin, particularly from micro-organisms, stems from an increased dependency on aquatic environments for food and potable water as well as on their potential source for drugs and other chemicals and modern aspects of genetic engineering (colwell. 1983). these potent materials from natural sources are of more than just academic interest, since they may cause massive animal mortalities, as well as legal, al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 8 recreational and human health problems (hashimoto, 1979: carmichael, 1981, 1986; white, 1982; baden, 1983; ragelis, 1984; van dolah, 2000). until 1988, the type of species a.minutum was known to be in egypt only (halim, 1960). but it has recently been reported in australia, france, spain, portugal, italy, turkey and the east coast of north america (hallegraeff et al. 1991). 5.1.1 toxic algal blooms relatively few species among the primary producers produce potent materials which may affect organisms at other trophic levels in the food chain. in general a biotoxin is a harmful substance synthesized by one species and adversely affects other species when present in extremely small quantities. toxins are characterized by their potency (µg toxin kg-1 body mass), their specificity of action (e.g. ion channels in membranes) and, in some cases, their reversibility. the latter characteristic has attracted the attention of physiologists and pharmacologists who study basic phenomena at the membrane level (hashimoto, 1979; adelman et al. 1982; kao and walker, 1982; baden, 1983; sasner et al. 1984). in general, the major producers of toxins are the dinoflagellate and diatom groups in the marine environment and cyanobacteria in fresh and brackish waters. dinoflagellates constitute the most prevalent of the toxic marine algae and their effects are widespread and disastrous. the effects may be generally classified as paralytic shellfish poisoning, diarrhetic shellfish poisoning, ciguatera poisoning and ichthyotoxicity. 5.1.2 diarrhetic shellfish poisoning the phenomenon of diarrhetic shellfish poisoning (dsp) was first documented in 1976 from japan where it caused major problems for the scallop fishery (yasumoto et al. 1978). the first dinoflagellate to be indicated was dinophysis fortii (in japan). it was soon followed by the d. acuminata (in europe), d. nutra, d. rotunda and the benthic dinoflagellate prorocentrum lima (aune and yndestad, 1993) and prorocentrum excavata (rausch de traubenberg and morlaix, 1995). the dsp toxins include okadaic acid and polyether toxins, dinophysistoxins (dtx1-4) (aune and yndestad, 1993), pectenotoxins and yessotoxins (yasumoto, 1985; who, 1984). a number of dinoflagellate species (hallegraeff, 1993), especially from the genus dinophysis, have been identified as producing these toxins. the detection of dsp toxins in the heterotrophic dinoflagellates protoperidinium occanicum and p. pellucidum (lee et al. 1991) may reflect their feeding on dinophysis. the symptoms of dsp include stomach pain, nausea, vomiting and diarrhoea (who, 1984). no fatalities directly associated with dsp have ever been recorded (richardson, 1997). however, some of the toxins associated with dsp may promote the development of stomach tumours (suganuma et al. 1988). 5.1.3 amnesic shellfish poisoning amnesic shellfish poisoning (asp) gets its name from the fact that one of the symptoms of the poisoning is loss of memory. it was first recognized in 1987 on prince edward island on canadian east coast when a serious incident occurred which caused three human fatalities and 105 cases of acute poisoning following the consumption of blue mussels mytilus edulis (bates et al. 1989). clinical symptoms of asp are nausea, vomiting, abdominal cramps, diarrhea, memory loss, decreased level of consciousness, seizures, confusion and disorientation (wright et al. 1989; perl et al. 1990; todd, 1990; nijjar and nijjar, 2000). the cause of this poisoning was traced to a bloom dominated by the pinnate diatom, pseudo-nitzschia multiseries (formerly pseudonitzschia pungens f. multiseries) which produces the neurotoxin domoic acid (da) (subba rao et al. 1998; bates et al. 1989, 1995). lundholm et al. (1994) have shown that the diatom pseudo-nitzschia seriata also produces domoic acid at levels similar to those observed with pseudo-nitzschia multiseries. this diatom is common in harmful algal blooms 9 colder waters of the northern hemisphere. there is also an indication in the literature that several other common diatom species may produce domoic acid e.g., fragilaria spp (pauley et al. 1993), amphora coffeaeformis (maranda et al. 1990), nitzchia pungens .f. multiseries, n.pseudo delicatissima and n. pseudo seriata (pseudonitzchia australis frenguelli) (subba rao et al. 1998, martin et al. 1990, work et al. 1992; 1993). the production of da has been identified in nine species of pseudonitzschia and one species of nitzschia (bates et al. 1989; bates, 2000). these diatoms produce toxins only after the onset of the stationary growth phase which is induced by either phosphate or silicate deficiency (bates et al. 1991). 5.1.4 paralytic shellfish poisoning existence of paralytic shellfish poisoning (psp) has been recognized for many centuries. this form of shellfish poisoning induces muscular paralysis and in severe cases can lead to death through paralysis of respiratory muscles. psp is caused by toxins often referred to collectively as “psp toxins”. the structure of the most potent component of the psp toxin is called saxitoxin and referred to as stx. its structure was determined about 30 years ago. it is now known that psp is caused not by just one toxin but a group of toxins, based on the backbone structure of the saxitoxin molecule (cembella et al. 1987; hall et al. 1990). psp is caused by one or more of about 18 different toxins which, include saxitoxins, neosaxitoxins and gonyautoxins (fremy, 1991). with the exception of the african and parts of the south american coasts, psp is a worldwide problem (hallegraeff, 1993), although some evidence (baddyr, 1992) suggests that psp incidents have occurred along the morrocan coast during the 1980s and 1990s. paralytic shellfish toxins are produced by dinoflagellates – approximately 11 alexandrium species, gymnodium catenatum, and pyrodinium bahamense var. compressumand by cyanobacteria anabena circinalis, aphanizomenon flos-aquae, cylindrospermopsis raciborskii, lyngbya wollei and planktothrix sp. (scholin, 1998; balech, 1995). anderson et al. (1990) examined different psp producing dinoflagellates (alexandrium fundyense and a. tamarense) and identified differences in toxin production that were directly related to changes in growth rate associated with the various stages of the life cycle. shellfish are the usual vectors of psp to human consumers. however, crustaceans can also accumulate psp toxins (desbiens and cembella, 1995). psp toxins have been found in the zooplankton and guts of dead and diseased fish in the vicinity of blooms (white, 1977). some psp toxins have also been found in the muscle of the affected fish and there is at least circumstantial evidence that psp toxins may be implicated in mortalities of marine animals (hofman, 1989; anderson and white, 1992). a number of studies have indicated reduced grazing rates by copepods on psp containing phytoplankton (ives 1985, 1987; huntley et al. 1986; turriff et al. 1995). 5.1.5 neurotoxic shellfish poisoning blooms of the dinoflagellate ptychodiscus breve (formerly gymnodium breve) have been associated with human poisoning which is characterized by airborne bronchial irritation and neurological symptoms but no paralysis (baden, 1989; schulman et al. 1990). brevetoxins, which have been isolated in pure form (chou et al. 1985; baden and mende, 1982), have high molecular weight, and are lipid soluble, non-nitrogen containing complex polyethers. 5.1.6 ciguatera ciguatera poisoning has been known for centuries in subtropical and tropical areas (swift and swift, 1993; lewis et al. 2000). during the period, 1960-1984, over 24,000 cases were reported in french polynesia alone (hallegraeff, 1993). ciguatera is caused by benthic dinoflagellates such as gambierdiscus toxicus, (faust, 1995; chinain et al. 1999); ostreopsis siamensis, coolia monotis, prorocentrum lima and related species (anderson and lobel, 1987; hallegraeff, 1993, hu et al. al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 10 1996). these toxins are transported through the food chain and usually reach humans through the consumption of finfish (lewis and holmes, 1993). there are chemical similarities between ciguatoxin and brevetoxins and the toxic effects of both these types of toxins are apparently caused by the changes in sodium ion influx in the affected organisms (baden, 1989, 1995; trainer et al. 1990). many of the symptoms associated with ciguatera poisoning also resemble nsp and in severe cases, death can result from circulatory collapse or respiratory failure due to nsp (who, 1984). ciguatoxins have also been implicated in marine mammal kills (hofman, 1989). 5.1.7 cyanobacterial toxins toxic cyanobacteria (blue-green algae) blooms are most often associated with fresh waters. however, it has been recently shown that blooms of the cyanobacterium trichodesmium thiebautii occurring in the open ocean of the us virgin islands can be toxic (hawser and codd, 1992). toxicity tests conducted with trichodesmium sp. cells on the copepod acartia tonsa demonstrated that intact cells were not toxic to a. tonsa, but the homogenized cells were (guo and tester, 1994). thus the authors suggested that the alga contained one or more intracellular biotoxins. brackish waters can also harbour toxic cyanobacteria blooms. some australian estuaries and inlets (huber and hamel, 1985; lenanton et al. 1985; blackburn and jones, 1995) and the baltic sea (kononen, 1992) are examples of brackish areas where the toxic cyanobacterium nodularia spumigena frequently forms blooms. nodularin, the toxin associated with nodularia spumigena which is hepatotoxic (kiviranta et al. 1991; de mott et al. 1991) may promote tumours with chronic exposure (falconer, 1991). given the discovery that some cyanobacterial toxins may stimulate tumour formation (falconer, 1991; carmichael, 1992), it is likely that there will be increasing awareness directed towards this type of phytoplankton bloom in coming years. 5.1.8 other types of toxic bloom toxic blooms of prymnesiophytes are frequently reported to be a problem for aquaculture facilities. for example, a massive bloom of chrysochromulina polylepis in the skaggerak / kattegat during may-june, 1988, caused havoc with salmon raising facilities along the swedish norwegian coasts (moestrup, 1994). this bloom also affected wild stocks of a number of different genera (olsgard, 1993) and in addition to causing mortalities of mature animals, it has been shown that the presence of the phytoplankton inhibits the reproduction process in the ascidian, ciona intestinalis and the mussel mytilus edulis (granmo et al. 1988). thus granmo et al. (1988) suggested that the phytoplankton bloom might have had long term effects in the affected area by reducing larval settlement and recruitment for these and possibly other species. other plankton organisms were also shown to be affected by this chrysochromulina bloom (nielsen et al. 1990). chrysochromulina leadbeatri caused mortalities in caged salmon among the northern norwegian coast in 1991 and the two prymnesium (p. patelliferum and p. parvum) have also caused mortalities in aquaculture facilities for salmon and rainbow trout (aune et al. 1992; meldahl et al. 1994, 1995). there can be mechanical interaction between phytoplankton and the gills which leads to gill damage and ultimately suffocation of the fish. diatoms are often implicated in such events (bell, 1961; taylor et al. 1985; farrington, 1988; rensel, 1993; kent et al. 1995; tester and mahoney, 1995). the raphidophyte heterosigma akashiwo presents a serious problem for aquaculture in many parts of the world including japan, north america, asia and new zealand (haigh and taylor, 1990; change et al. 1990; black et al. 1991; mackenzie, 1991; qi et al. 1993; honjo, 1994). affected salmon shows signs of gill and intestinal pathology and death has been attributed to impairment of the gills’ respiratory and osmoregulatory functions (change et al. 1990). it has been suggested that the toxic effects elicited by this organism on salmon may be brought about by the formation of toxic concentrations of oxygen radical and hydrogen peroxide (yang and albright, 1994). dinoflagellate harmful algal blooms 11 gyrodinium aureolum has been recognized as fish killer for many years (tangen, 1977). gill histopathology in affected fish has been reported to be similar to that observed in fish exposed to heterosigma (change et al. 1990). it is now generally accepted that toxin production by g. aureolum is at least in some cases involved in mortalities caused by this organism (boalch, 1983; bullock et al. 1985; heinig and campbell, 1992). jenkinson, (1989, 1993) suggested that gymnodium aureolum and some other bloom forming flagellates may alter seawater characteristics through the production of extracellular organic material. this extracellular material should increase the viscosity of the medium surrounding the fish so that the energy expended in filtering water through the gills exceeds that which can be supported by the oxygen uptake. phaecystis spp. are also considered to be harmful because they extrude protein-rich compounds that can be whipped into a stiff foam by wave action and which under certain hydrographic conditions can accumulate along beaches (richardson, 1997). a relatively new toxic dinoflagellate, pfiesteria piscicida (steidenger et al. 1996), was described by burkholder et al. (1992). according to burkholder et al. (1995) this dinoflagellate requires live finfish or their excrement in order to excyst and to release its potent neurotoxin. but more recently, research reports (berry et al. 2002; vogelbein et al. 2002) say that in the pfiesteria shumwayee, the strain they have examined shows no signs of toxin. instead, the single celled dinoflagellate alga kills by swarming over a fish and eating away its skin (berry et al. 2002; vogelbein et al. 2002; kaiser, 2002; rutherford, 2002). 5.1.9 marine algal toxins: biochemistry and molecular biology the production of toxic compounds is a common, but not universal characteristic of harmful algal blooms (habs). only a few hab toxins have been characterised and these are synthesised by only a limited number of algal species (steidinger, 1993). toxigenic algae may not have significant impacts on ecosystem processes as toxins affect viability, growth, fecundity and recruitment of a wide range of organisms. the most widely known marine hab toxins produce poisonous syndromes known as diarrhetic, paralytic, neurotoxic, and amnesic shellfish poisoning (dsp, psp and asp). planktonic dinoflagellates synthesise the toxins associated with each of these poisoning events except that the asp toxin, domoic acid is produced primarily by diatoms. ciguatera, fish poisoning, another type of massive hab toxin event is caused by benthic dinoflagellates. from a chemical standpoint, the common marine hab toxins are either alkaloids, poly ethers or substituted amines (plumley, 1997). there are other toxins associated with hab species such as superoxide and (or) hydroxyl radicals (oda et al. 1992; tanaka et al. 1992), lipoteichoic acids with hemagglutinin activity (ahmed et al. 1995) and pentacyclic derivatives with a fuzed azine (seki et al. 1995). other toxic effects of hab algae have been documented but the toxins remain to be elucidated (burkholder and glasgow, 1997). it is likely that many more marine hab toxins will be identified and characterized as both utilization of marine resources and our ability to detect the toxins increases. hab toxins have complex chemical structures and they seem to be the end products of elaborate pathways and some of the enzymatic reactions are likely to entail highly unique and (or) specialized reactions (plumley, 1997). very little is known about the biochemistry of toxin synthesis. one of the difficulties is that hab algae, which produce toxins are extremely difficult to culture (shilo and ashner, 1953) and remain largely resistant to most contemporary protocols routinely used with other microbes. at present rapid progress in understanding hab algae at the molecular and biochemical levels is dependent on technological innovation. some innovative analytical techniques developed promise to provide rapid and reliable detection of the causative organism and the toxins produced. molecular probes are being applied to distinguish species-specific rna and dna sequences (pierce and kirkpatrick, 2001) for identification of habs causing organisms. 5.2 increased utilisation of coastal waters for aquaculture al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 12 with the increased problems of over fishing of coastal waters more and more countries are looking toward aquaculture as an alternative. aquaculture operations act as sensitive ‘bioassay systems’ for harmful algal species and can bring to light the presence in water bodies of problem organisms known to exist there before. the increase in shellfish farming worldwide is leading to more reports of paralytic, diarrhetic and amnesic shellfish poisoning. on the other hand, increased finfish culture is drawing attention to algal species which can cause damage to the fishes delicate gill tissues (taylor, 1988; rensel et al. 1989). the diatoms long, hollow spines (setae) are studded with smaller barbs along their length. the setae can break off and penetrate the gill membranes of fish, with the smaller barbs preventing them from coming out (tester and mahoney, 1995; rensel, 1993). fish death may be caused by capillary haemorrhage, dysfunction of gas exchange at the gills, suffocation from an overproduction of mucus, or even from secondary infection of the damaged tissue (bell, 1961, bruno et al. 1989; rensel, 1991; yang and albright, 1992, 1994). a more widespread problem for fish farmers is the production by various algal groups of fatty acids or galactolipids (bass et al. 1983; bodennec et al. 1995) which damage the epithelial tissue of the gills. in experimental assay systems, these substances destroy red blood cells and therefore have been provisionally termed ‘hemolysins’ (yasumoto et al. 1990). algal species as diverse as the raphidophytes (hetersigma akashiwo and chatonella antique, the prymnesiophytes chrysochromulina polylepis (yasumoto et al. 1990) and prymnesium parvum (kozaki et al. 1982) and the dinoflagellate gymnodium mikimotoi (arzul et al. 1995; parrish et al. 1998) have been implicated (change et al. 1990). the two prymnesiophyte flagellates chrysochromulina. and prymnesium produce substances that affect gill permeability leading to a disturbed ion balance (yasumoto et al. 1990). toxicity by these species is promoted by phosphorous deficiency. a massive bloom (60000km2, 107-108 cells l-1) of chrysochromulina polylepis occurred in may-june 1988 in the skagerrak, the kattegat, the beltarea and the sound between denmark, norway and sweden (rosenberg et al. 1988, kaas et al. 1991). fish deaths occurred due to damage of gill membranes which produced a lethal increase in the chloride concentration in the blood (dahl and tangen, 1993) and fish cages moved into less saline fjords were therefore less affected. 5.3 increase of algal blooms by cultural eutrophication eutrophication as defined by nixon 1995 “is an increase in the rate of supply of organic matter to an ecosystem”. eutrophication can occur via natural processes or as a result of human activities (cultural eutrophication). correlations with eutrophication and human industrial development are of serious concern (smayda, 1990, sournia et al. 1991). a number of workers have suggested that there has been an increase in harmful blooms in recent years (anderson, 1989; smayda, 1990; hallegraeff, 1993) and is often argued that the apparent increase in the occurrence of “harmful blooms” is linked to eutrophication. indeed in some areasespecially those with limited water exchange such as fjords, estuaries and inland seasthere does seem to be good evidence for a stimulation of the number of algal blooms occurring by eutrophication. however, the relationship between the occurrence of harmful phytoplankton blooms and environmental conditions is complicated and anthropogenic perturbation of the environment is certainly not a pre-requisite for all harmful algal blooms (richardson, 1997; sellner et al. 2003). thus, the occurrence of a harmful bloom may or may not have as one of its underlying causes a change in human activities or behavior. eutrophication from domestic, industrial and agricultural wastes can stimulate harmful algal blooms (lam and ho, 1989). in hong kong, this increase (mainly gymnodium nagaskiense, gonyaulx polygramma, nocticula scintillaus and prorocentrum minutum, shows a striking relationship with a 6-fold increase in human population in hong kong and the concurrent 2.5 fold increase in nutrient loading mainly contributed by untreated domestic and industrial waste (okaichi, 1989, lam and ho, 1989). there is considerable concern (ryther and dunstan, 1971, officer and harmful algal blooms 13 ryther, 1980, smayda, 1990) regarding the altered nutrient ratios in coastal waters. improved wastewater treatment has been causing increases in the ammonia nitrate ratio of river rhine discharge (riegman and noordeloos, 1991). the nutrient composition of treated wastewater is never the same as that of coastal waters in which it is being heavily discharged. such altered nutrient ratios in coastal waters may favour blooms of nuisance flagellate species which replace the normal spring and autumn blooms of siliceous diatoms (smayda, 1990). the remarkable increase of foam producing blooms of the prymnesiophyte phaeocystis pouchetti which first appeared in dutch coastal waters in 1978 is probably the best studied example of this phenomenon (lancelot et al. 1987). algals species which are not normally toxic (chrysochromulina, nitzschia pungens .f. multiseries, prymnesium parvum) may be rendered toxic when exposed to typical nutrient regimes (for example phosphate deficiency) resulting from cultural eutrophication (shilo, 1981, edvardsten et al. 1990, bates et al. 1991). the 1998 bloom in the kattegat of prymnesiophyte, chrysochromulina polylepis, is not usual in terms of biomass but in terms of its species composition and toxicity, has been related to a change in the nutrient status from nitrogen to phosphorus limitation (maestrini and graneli, 1991). in the black sea, a long term decrease in the si:p ratio has been associated with an increase in the dinoflagellate blooms of prorocentrum cordatum (bodeanu and usurelu, 1979). changed patterns of land use, such as deforestation, can also cause shifts in phytoplankton species composition by increasing the concentrations of humic substances in land runoff. acid precipitation can further increase the mobility of humic substances and trace metals in soils (graneli and moreira, 1990). agricultural run-off of phosphorus can also stimulate cyanobacterial blooms, for example nodularia spumigena in the baltic sea and in the peel harvey estuary, australia. these species produce hepatotoxic peptides. nodularia microcystis and neurotoxic alkaloids (anabena aphanizomenon) can kill domestic and wild animals that drink from the shores of eutrophic ponds, lakes and reservoirs (edler et al. 1985). cyanobacteria also pose public health problems through the production of teratogens and tumour promoters, which are not acutely toxic (carmicheal, 1989). the toxins accumulate in mussels and have been reported to contaminate drinking water. a neurotoxic factor has also been associated with some strains of the common marine, bloom forming tropical cyanobacterium trichodesmium thiebautii (hawser et al. 1991). while this organization can thrive under nutrient impoverished oceanic conditions, it is possible that coastal eutrophication can prolong or enhance bloom phenomena (hallegraeff, 1993). 5.4 stimulation of algal blooms by unusual climatological conditions the global change forcasts for the period 1990-2100 in climate has been predicted to lead to a projected rise in temperature of 1.4-5.8°c with a 90% probability interval of 1.7-4.9% (ipcc 2001; wigley and raper, 2001). a direct consequence of global warming is thermal expansion of water and hence a rise in the sea level in 2100 by 0.1-0.9m (ipcc, 2001). photosynthesis and plankton growth are basic processes to the marine ecosystem, and in general both rates double when temperature increases by 10°c (raven and geider, 1988). the qualitative conclusion from investigations by peperzak (2003) on the effects of climate change in the marine ecosystem indicate that the risk of harmful dinoflagellate and raphidophyte blooms will increase rather decrease due to climate change. increased temperature leads to decreased viscosity (vogel, 1996), which theoretically leads to (i) increased nutrient diffusion towards the cell surface, which is important when interspecific competition for nutrients takes place (ii) increased sedimentation rates, which will be important for nonflagellate species such as diatom. at the present, the dinoflagellate pyrodinium bahamense is confined to tropical mangrove fringed coastal water of the atlantic or indo-west pacific. according to mcminn (1989), a survey of fossil occurrences of its resting cyst polysphaeridium zokaryi found in records going back to eocene 50 million years ago, recorded by bujak and others, indicated a much wider range of distribution in the past. at present, the dinoflagellate does not extend further south than al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 14 papua new guinea but in the pleistocene, it ranged as far south as sydney harbour (mcminn, 1989). the first harmful implications of pyrodinium blooms became evident in 1972 in papua, new guinea. red brown water discolouration coincided with the fatal food poisoning of three children and mouse bioassays on shellfish from a house in the affected village subsequently established pyrodinium bahamense as a source of paralytic shellfish poison (maclean 1977). maclean (1989) presented strong circumstantial evidence for a coincidence between pyrodinium blooms and el nino southern oscillation (enso) climatoligical events. summer marine climate is dominated by the succession of periods of upwellings and other relaxation or downwellings. during the upwellings, water masses from as low as 60-70m are brought close to the surface, indicated by the lowering of the temperature to 23-25oc. these cool waters are also poor in oxygen (o2) and rich in nutrients. rich nutrient water is susceptible to trigger development of phytoplankton blooms (claereboudt et al. 2001). phytoplankton and other marine biota have relatively short life spans (roughly 1-3 days), under the right conditions they have the capacity to reproduce, or ‘bloom’ into exceptionally large numbers in a matter of days (herring, 2002). 5.5 transport of dinoflagellate cysts in ship’s ballast water or associated with the transfer of shellfish stocks dissemination of toxic species in the ballast water of commercial ships adds another concern (hallegraeff and bolch, 1991; hallegraeff, 1993). cargo vessel ballast water was first suggested as a vector in dispersal of non-indigenous marine plankton more than 90 years ago (ostenfeld, 1908). the diatom odontella sinesis, well known from the tropical and subtropical coasts of the indo-pacific, had not been reported in european waters until 1903, when it produced dense plankton blooms in the north sea. ostenfeld (1908) suggested that this species was introduced via the water or sediment contained in the ship’s ballast tanks. subsequently, hallegraeff et al. (1990) confirmed this possibility by culturing the related diatom species odontella aurita from a ballast water sample collected at the end of a voyage from japan to australia. the evidence of ballast water transfer of marine organisms other than microscopic algae is considerable and includes species of fish, crustaceans, polychaete worms and molluscs (carlton, 1985). the most effective measure to restrict spreading of dinoflagellate cysts via ship’s ballast water would be to avoid ballasting during toxic dinoflagellate blooms in ports. other options using heat or chemical treatment (chlorine, hydrogen peroxide) of ballast water either in hold or in onshore facilities have also been investigated (rigby et al. 1991; bolch and hallegraeff, 1990). another anthropogenic vector for the dispersal of algae (especially their resting cysts) is with transfer of shellfish stocks containing phytoplankton in their digestive organs from one area to another (hallegraeff, 1993). 6. bloom dynamics 6.1 bloom initiation generally, unusual wind/ weather/hydrographic conditions have been identified as factors preceding or accompanying the harmful algal blooms (maestrini and graneli, 1991; rhodes et al. 1993). according to fraga (1993) regions with coastal upwellings and river discharge areas are vulnerable to phytoplankton blooms. in some cases, wind, weather, tidal or other hydrographic conditions have been related to initiation of nearshore blooms by delivery of the organisms into the bloom region (balch, 1981; lindahl, 1983; taylor et al. 1994). in some other cases, transport of phytoplankton blooms from offshore to inshore regions, longshore transport of blooms from one coastal region to another has also been documented (franks and anderson, 1992). 6.2 bloom composition harmful algal blooms 15 individual phytoplankton species have different requirements and responses to the physical environment. marine microalgae use inorganic nutrients such as nitrate, phosphates and sulphur, and convert them into the basic building blocks of living organismsproteins, fats, carbohydrates. they also need trace elements such as silicon, iron and calcium (kiørboe, 1993). the overall understanding of various phytoplankton species requirements and tolerances with respect to micronutrients is at a primitive stage. however, it is known that there are differences between species in terms of requirements for vitamin (guillard et al. 1991; graneli and moreira, 1990; graneli et al. 1993; honjo, 1993) and trace metals (price and morel, 1991; honjo, 1993). 6.3 bloom maintenance bloom maintenance requires the growth rate of the phytoplankton in a bloom to exceed the rate of loss of phytoplankton in a population. phytoplankton loss usually occurs by grazing or through cell lysis sinking or advection away from the bloom site (richardson, 1997). grazing impacts can be important in the development of harmful algal blooms. limited grazing pressure often on toxic phytoplanktons may allow development of large biomasses of these phytoplankters. grazing pressures can also be reduced by acting as a selection factor in phytoplankton species (olsson et al. 1992) or by reduction in loss through advection (crawford and purdie, 1992) or by vertical migration of the phytoplankton in the water column. the blooming organism can also be maintained by reduction of competition for limiting resources. if nutrients are limiting, then inhibition of other phytoplankters competing for the same nutrients will serve to optimize growth conditions for the bloom organism. several harmful bloom forming species have been shown to have a repressing effect on other phytoplankton species, such as, gyrodniium aureolum (arzul et al. 1993); heterosigma akashiwo (honjo, 1993). thus, more than one mechanism may be contributing towards maintenance of some phytoplankton blooms. 6.4 bloom termination a phytoplankton bloom will terminate or decline when the loss factors exceed the increase factors. the immediate effect is usually a decrease in the growth rate of bloom forming phytoplankton species, brought about by a change in the environmental conditions, including light and / nutrients. the decaying phytoplankton cells can either sink out of the water column or lyse and release their contents to the surrounding water column (richardson, 1997). flagellate blooms are often degraded in the water column (boekel et al. 1992), while diatom blooms often sink out of the water column (cushing, 1992). different diatoms have different sinking rates, which are probably influenced by cell volume and the physiological states, expressed as respiration rates (waite et al. 1992). according to jackson (1990) a given phytoplankton population will grow exponentially until it reaches an equilibrium concentration : “critical concentration”. at this stage, growth and coagulation will balance. applying the coagulation theory to phytoplanktons, it has been suggested that aggregation may be an important mechanism in terms of sudden disappearance of diatom blooms (jackson, 1990; jackson and lochmann, 1992). the phytoplankton cells are believed to possess a certain degree of adhesiveness or stickiness that allows them to aggregate or stick together (kiørboe et al. 1990). under laboratory conditions, different phytoplankton species exhibit different degrees of “stickiness” (kiørboe et al. 1990). moreover, age (physiological state) can influence stickiness within an individual species. a better understanding of these mechanisms will help to elucidate the bloom dynamics. 7. summary and conclusions marine phytoplankton blooms occur intermittently, within 100 km of coastal regions near all the major continents. the common denominators associated with phytoplankton blooms are (a) seed al-ghelani, h.m., alkindi, a.y.a, amer, s. and al-akhzami, y.k. 16 population of organisms; (b) proper chemical environment of organic and inorganic nutrients; and (c) suitable physical and hydrographic conditions for concentration and maintenance of nutrient organisms. phytoplankton blooms are natural phenomena that develop over various scales of space and time including the massive, sudden and local outbursts of one or more species. such phenomena have also been termed “red tides”, “brown tides”, “colored waters” or “discolored waters”. there are about 4000 different species which constitute the world’s flora. approximately 6% (about 200 species) have been indicated to cause red tides or are regarded as harmful. about 2% of the world’s phytoplankton are implicated in toxin production. according to a number of workers, there has been a considerable rise in harmful algal blooms due to anthropogenic activities in recent years. these activities include eutrophication, distribution and transport of harmful species from one region to another via ballast water or in connection with aquacultural activities. despite several common features habs are very diverse in terms of causative organisms, dynamics of blooms and type of blooms. 8. references adleman, w.j., jr., fohlmeister, j.f., sasner, j.j., jr. and ikawa, m. 1982. sodium channels blocked by aphantoxin obtained from the blue-green alga. aphanizomenon flos-aquae. toxicon. 23: 513-516. ahmed, m.s., arakawa, o. and onoue, y. 1995. toxicity of cultured chatonella marina. in: harmful marine algal blooms (lassus, p., arzul, g., erard-le-denn, e., gentien, p. and marcillou-le-baut, c., eds.) pp 499-504, paris, lavoisier. allen, w.e. 1946. “red water” in la jolla bay in 1945. trans. amer. microsc. soc. 65 (2): 149153. andersen, d.m. 1989. toxic algal blooms and red tides: a global perspective. in: red tides: biology, environmental science and toxicology. proc. 1st int. symp. on red tides. pp. 11-16, elsevier. anderson, d.m., white, a.w. and baden, d.g. 1985. toxic dinoflagellates. pp. 561. elsevier, new york. anderson, d.m. 1989. toxic algal blooms and red tide: a global perspective. in: red tides: biology, environmental science and toxicology. 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mathematics, university of cairo, giza, egypt, email: nsweilam@sci.cu.edu.eg, n_sweilam@yahoo.com. **faculty of science, department of mathematics, university of um-alqura, saudi arabia, email: r_ieda@hotmail.com. abstract: in this paper, the space fractional wave equation (sfwe) is numerically studied, where the fractional derivative is defined in the sense of caputo. an explicit finite difference approximation (efda) for sfwe is presented. the stability and the error analysis of the efda are discussed. to demonstrate the effectiveness of the approximated method, some test examples are presented. keywords: fractional order wave equation, caputo's derivative, stability condition, stability matrix analysis. تحليل خطأ تقريب الفروق المحدودة الظاهرة عند حل المعادالت الموجية في فضاء الرتب الكسرية ناصر حسن سويلم و تغريد عبدالرحمن عسيري الرتب الكسرية، حيث تم تعريف المشتقة من لقد تم في هذا البحث دراسة عددية لمعادالت موجية في فضاء :ملخص ة للمعادلة الموجية. كما ييجاد حلول تقريبإلرة ظاهتب الكسرية باستخدام تعريف كابوتو. وتم استخدام الفروق المحدودة الالر بعض األمثلة ة، فقد تم عرض يالتقريب فعالية هذه الطريقة توضيحل الفروق.االستقرار وتحليل الخطأ لتلك تم مناقشة االختبارية. 1. introduction ractional derivatives in mathematics are natural extension of integer-order derivatives, where the order is non integer. fractional order differential equations have been the focus of many studies due to their frequent appearance in various applications especially in the fields of fluid mechanics, viscoelasticity, biology, physics and engineering (bagley and torvik, 1984; mainardi, 1995; mainardi and paradisi, 1997; podlubny, 1999; 2002). consequently, considerable attention has been given to the solutions of fractional ordinary/partial differential equations (sweilam et al., 2011). numerical approximations are the main tool to simulate and study the behaviour of the solutions of such model problems (fix and roop, 2004; meerschaert and tadjeran, 2004; sweilam et al., 2007; sweilam and khader, 2010; tenreiro machado, 2003; yuste, 2011; yuste and acedo, f mailto:nsweilam@sci.cu.edu.eg mailto:n_sweilam@yahoo.com,**%20faculty%20of%20science,%20department%20of%20mathematics,%20university n.h. sweilam and t.a. assiri 542 2005). difference methods and, in particular, explicit finite difference methods, are an important class of numerical methods for solving fractional differential equations (morton and mayers, 1994; west and seshadri, 1982; xu et al., 2001). the usefulness of the explicit method and the reason why they are widely employed is based on their particularly attractive features (yuste, 2011; yuste and acedo, 2005). in this paper, an efda scheme is designed for solving a fractional order wave equation where the fractional derivative is in the caputo sense. moreover, since the explicit methods may be unstable, then, it is crucial to determine under which conditions, if any, these methods are stable. we will use here a kind of fractional von neumann stability analysis to derive the stability conditions. we consider in this paper the following sfwe model:   2 2 , 0, 1 2 , ( , ) ( , ) , 0 ,x t t u x t u x t d x l t t             (1)     1 2( ,0) , ( ,0) , 0 ,tu x f x u x f x x l    (2)    (0, ) , ( , ) ,u t t u l t t   (3) where the variable coefficient ( , ) 0.d x t  the parameter  refers to the fractional order of spatial derivatives, and the caputo's fractional derivative ( ),xd u x  is defined as follows (podlubny, 1999).          1 0 , , , , ( , ) ,1 , 1 , m m x mx m m x t d u x t m n u x t dx d u x u t x d m m m                              (4) where  . is the gamma function. 2. explicit finite difference approximation for sfwe let us consider ,h l k where k is a positive integer, by using a second order difference approximation and (4), we get for 2m  that                                      2 1 2 0 211 1 2 0 11 1 2 0 1 2 2 0 , ,1 2 ,1 2 1 , 2 , 1 ,1 2 1 , 2 , 1 , 1 . 3 x x j hk j jh j hk j jh k j x t u t d u x d u x z t z dz z u x j h t u x jh t u x j h t z dz h h u x j h t u x jh t u x j h t j j                                                                       let 0t    be the grid step in time, ,nt n 0 ,nt t  0, , 1,n n  n t  and 0x h   be the grid step in space, ,kx kh 0 ,kx l  1, , 1,k k  so that  , n ku u kh n and  , 0 .k kd d x applying the forward finite difference formula to the initial conditions (2), we obtain error analysis of an explicit finite difference approximation 542      0 11 1 2, .k k k k ku f x u f x f x   now the discrete form of (1) using the explicit finite difference scheme can be written as     1 1 1 2 2 1 12 0 2 [ 2 ][ 1 ] , 3 n n n k n n nk k k k k j k j k j j u u u d h u u u j j                          and 1 1 1 1 1 1 1 1 2 [ 2 ] [ 2 ] , k n n n n n n n n n k k k k k k j k j k j k j j u u u s u u u s g u u u                    (5) where   , 3 kd ss     2 ,s h      2 2 1 .jg j j       the general form of (5) with initial conditions, can take the following form  1 0 1 12 , , n n n ku u f x u au u       (6) where  1 2 1, , , t n n n n ku u u u  and a is the coefficients matrix with elements ija obtained from (5). 3. stability analysis of efda it is well known that the explicit difference schemes are not always stable for integer order differential equations. then, for any , there are always choices of t and x for which the numerical schemes may become unstable. therefore, it is important to determine under which conditions, if any, the explicit method presented here is stable. to analyze the stability of the numerical scheme (6), we will use here a kind of fractional von neumann stability analysis. theorem 1 the explicit finite-difference scheme (6) for sfwe is conditionally stable if        1 3 1 2 2 2 2 . 3 xs s              proof. let us analyze the stability of (5) by substituting in a separated solution n iqj x j nu e   where q is a real spatial wave-number. inserting this expression we get 1 1 1 1 1 1 2 [ 2 ] [ 2 ] k iq x iq x n n n n j n j n j n j j s e e s g                           , where ( )x means the riemann zeta function. the stability will be determined by the behaviour of .n if we write 1n n   and assume that ( )q  is independent of time, then we can obtain 1 1 1 1 2 ( 2 ) ( 2 ) k j j j iq x iq x j j s g s e e                      . inserting the extrema value 1   into this equation, we obtain the following stability bound on s: n.h. sweilam and t.a. assiri 542 2 2 2 1 sin ( ) 1 ( 1) [( 1) ] 2 nn j x j q x s s j j            , with     2 2 1 1 1 , j x j s j j              or, in terms of the riemann zeta function    32 1 2 2 .xs        then, the method is stable when        1 3 1 2 2 2 2 . 3 xs s              □ table 1. the exact and efda solutions at 0.05t  when 0.005, 0.0025.h   ix 2  1.8  0.0000 0.00000000 0.00000000 0.0500 0.43696211 0.49019405 0.1000 0.83115133 0.92270888 0.1500 1.14398166 1.25716135 0.2000 1.34483109 1.46300554 0.2500 1.41403909 1.52125246 0.3000 1.34483109 1.42692326 0.3500 1.14398166 1.18975019 0.4000 0.83115133 0.83331667 0.4500 0.46696211 0.39279598 0.5000 0.00000000 -0.08846503 0.5500 -0.43696211 -0.56317267 0.6000 -0.83115133 -0.98470522 0.6500 -1.14398166 -1.31166940 0.7000 -1.34483109 -1.51194717 0.7500 -1.41403909 -1.56583600 0.8000 -1.34483109 -1.46797473 0.8500 -1.14398166 -1.22786629 0.9000 -0.83115133 -0.86894593 0.9500 -0.43696211 -0.43396401 1.000 -0.00000000 0.00000000 theorem 2 the truncation error of sfwe is       2 , .t x t o t o x    proof. evaluating (1) at the point  ,k nx t gives 2 ( , )2 [ ] 0x tk n u u d t x         , by the difference equation 2 1 ( , ) n n t k x k k nu d u t x t    . (7) error analysis of an explicit finite difference approximation 542 neglecting the truncation error term  , ,k nt x t we get the explicit difference scheme (5). from (1) and (7), we get 2 2 12 ( , ) ( , ) [ ] [ ] ( , ) n n t k x k k n x t x tk n k n u u u d u t x t t x            , 2 2 2 2 ( , ) ( , ) ( )k n t k nu x t u x t o t t      , (8) 2 1 ( , ) ( ) n x k x tk n u u o x x         , 2 ( , ) ( , ) ( , )1 ( )x x t x t x tk n k n k n u u d u o x dxx x x                   . so that 2 1 ( ) ( ) n n x k x ku u o x o x      . from this result and from (8), we claim that       2 , .t x t o t o x    □ 4. numerical results example 1. consider the space fractional wave equation 2 1.8 2 1.8 0 1 , ( , ) ( , ) , 0 1, t u x t u x t x t x          (9)        ,0 sin 2 , ,0 2 sin 2 ,tu x x u x x    (0, ) (1, ) 0 .u t u t  when 2  (instead of 1.8 in (9)), the exact solution is ( , ) sin 2 (cos 2 sin 2 )u x t x t t    . (10) figure 1. efda solutions when 0.005h  and 0.0025  : (left) comparison with the exact solution for 2  at 0.05t  , (right) for 1.8  at 0.125.t  n.h. sweilam and t.a. assiri 522 the numerical studies are given as follows: the exact solutions for 2  (as given by (10)) and the efda solution for 1.8  at 0.05t  when 0.005h  and 0.0025  are given in table 1. in order to test the numerical scheme, we also plot in figure 1 the exact and approximate solutions for integer case 2.  moreover, the approximate solution for 1.8  at 0.125t  when 0.005h  and 0.0025  is also shown in figure 1. to study the behaviour of these solutions, figure 2 is plotted to show the 3d-efda solutions for 2  and 1.8  respectively. figure 3 shows the unstable solutions behaviour when 0.157h  and , 0.001  where the value of s is larger than the stability bound .xs for more details see theorem 1. figure 2. 3d-efda solutions for: (left) 2,  (right) 1.8.  figure 3. unstable efda solutions when 0.157h  and 0.001  : (left) comparison with the exact solution, (right) 3d-efda solutions. example 2. consider the space fractional wave equation 2 1.6 2 1.6 ( , ) ( , ) , 0 5, 0 1 , u x t u x t x t t x          (11) ( , 0) sin , ( , 0) 0,tu x x u x     (0, ) 0, (5, ) sin 5 cos .u t u t t  error analysis of an explicit finite difference approximation 522 when 2  (instead of 1.6 in (11)) the exact solution is ( , ) sin cosu x t x t . (12) figure 4. efda solutions when 0.002h  and 0.001  : (left) comparison with the exact solution for 2  at 0.01,t  (right) for 1.6  at 0.01.t  figure 5. 3d-efda solutions for: (left) 2  , (right) 1.6.  the numerical studies for example 2 can be presented as follows: the exact solutions for 2  (as given by (12)) and the efda solution for 1.6  at 0.01t  where 0.002h  and 0.001  are given in table 2. in order to test the numerical scheme, we also plot in figure 4 the exact and approximate solutions for integer case 2.  moreover, the approximate solution for 1.6  at 0.01t  when 0.002, 0.001h   is also shown in figure 4. to study the behaviour of these solutions, figure 5 is plotted to show the 3d-efda solutions for 2  and 1.6  respectively. figure 6 shows the unstable solutions’ behaviour when 0.008h  and 0.001,  where the value of s is larger than the stability bound .xs for more details see theorem 1. n.h. sweilam and t.a. assiri 525 figure 6. unstable efda solutions when 0.008h  and 0.001  : (left) comparison with the exact solution, (right) 3d-efda solutions. table 2. the exact and efda solutions at 0.01t  when 0.002, 0.001.h   ix 2  1.6  0.0000 0.00000000 0.00000000 0.2000 0.19866128 0.19866128 0.4000 0.38940257 0.38940432 0.6000 0.56461961 0.56462215 0.8000 0.71732704 0.71733027 1.0000 0.84143691 0.84144069 1.2000 0.93200134 0.93200553 1.4000 0.98540982 0.98541426 1.6000 0.99953312 0.99953762 1.8000 0.97380819 0.97381257 2.0000 0.90926060 0.90926469 2.2000 0.80846366 0.80846730 2.4000 0.67543582 0.67543886 2.6000 0.51548049 0.51548281 2.8000 0.33497458 0.33497609 3.0000 0.14111429 0.14111493 3.2000 -0.05837178 -0.05837204 3.4000 -0.25553075 -0.25553190 3.6000 -0.44250252 -0.44250451 3.8000 -0.61183311 -0.61183586 4.0000 -0.75677158 -0.75677525 error analysis of an explicit finite difference approximation 522 5. conclusions an explicit finite difference approximation for sfwe has been explored, where the fractional derivative was in the caputo sense. error analysis and stability of the explicit numerical method for sfwe were discussed by means of a fractional version of the von neumann stability analysis. finally, some numerical results of efda were presented. these numerical results demonstrate that the efda is a computationally simple and efficient method for sfwe. 6. acknowledgments the authors wish to express their gratitude to the referees for their valuable suggestions and comments that have improved the paper. matlab has been used for computations in this paper. 7. references bagley, r.l. and torvik, p.j. 1984. on the appearance of the fractional derivative in the behavior of real materials. j. appl. mech., 51: 294-298. fix, g.j. and roop, j.p. 2004. least squares finite element solution of a fractional order two-point boundary value problem. comput. math. appl., 48: 1017-1044. mainardi, f. 1995. fractional diffusive waves in viscoeslastic solids. nonlinear waves in solids, j.l. wegner and f.r. norwood, eds., asme/amr, fairfield, nj, pp. 93-97. mainardi, f. and paradisi, p. 1997. a model of diffusive waves in viscoelasticity based on fractional calculus. proceedings of the 36th conference on decision and control, o.r. gonzales, ed., san diego, ca, pp. 4961-4966. meerschaert, m.m. and tadjeran, c. 2004. finite difference approximations for fractional advection-dispersion flow equation. j. comput. applied math., 172: 65-77. morton, k.w. and mayers, d.f. 1994. numerical solution of partial differential equations. cambridge university press, cambridge, uk. podlubny, i. 1999. fractional differential equations. academic press, new york. podlubny, i. 2002. geometric and physical interpretation of fractional integration and fractional differentiation. fractional calculus and applied analysis, 5(4): 367-386. sweilam, n.h., khader, m.m. and al-bar, r.f. 2007. numerical studies for a multi-order fractional differential equation. phys. lett. a, 371: 26-33. sweilam, n.h. and khader, m.m. 2010. a chebyshev pseudo-spectral method for solving fractional order integro-differential equations. anziam j., 51: 464-475. sweilam, n.h., khader, m.m. and nagy, a.m. 2011. numerical solution of two-sided space fractional wave equation using finite difference method. j. comput. applied math., 235: 2832-2841. tenreiro machado, j.a. 2003. a probabilistic interpretation of the fractional-order differentiation. fractional calculus and applied analysis, 6(1): 73-80. west, b. and seshadri, v. 1982. linear system with levy fluctuations. physica a, 113: 203-216. xu, k., zhang, z., leng, g. and lu, q. 2001. matrix theory. scientific publishing house. yuste, s.b., 2011. an explicit difference method for solving fractional diffusion and diffusion-wave equations in the caputo form. j. comput. and nonlinear dynamics, 6:1-6. yuste, s.b. and acedo, l. 2005. on an explicit finite difference method for fractional diffusion equations. siam j. numer. anal., 42: 1862-1874. received 14 january 2011 accepted 20 november 2011 http://landau.unex.es/public_html/santos/publications/a11quiyus.jcnd.pdf squ journal for science, 2014, 19(2), 17-20 © 2014 sultan qaboos university 17 facile and surfactant-free synthesis of hierarchical zno microstructures kezhen qi 1*, ruidan wang2, jiaqi fu3, ke chen4 and chunying zuo5 1 college of chemistry and life science, shenyang normal university, shenyang, 110034, china, 2 the department for discipline and scientific research, shenyang normal university, shenyang, 110034, china, 3 college of chemistry and molecular engineering, peking university, beijing 100871, china, 4 the school of teacher education, shenyang normal university, shenyang, 110034, china, 5 the science college of heilongjiang bayi agricultural university, daqing, 163319, china.*email: qikezhen2003@gmail.com. abstract: hierarchical zno crystals with flower-like microstructures were successfully synthesized via a facile hydrothermal route without using any surfactants. the morphology of these microstructures can be easily controlled by adjusting the ph of the reaction solution. the products were characterized by x-ray powder diffraction (xrd) and scanning electron microscope (sem). furthermore, a possible growth mechanism of zno hierarchical microstructures was proposed. keywords: zinc oxide; hierarchical microstructures; hydrothermal synthesis; free-surfactant. تحضير أشكال ميكروويت هرميت ألكسيد الخارصيه بطريقت مباشرة خاليت مه المحفساث السطحيت كيشه كي* 1 ، رويدن واوج 2 ، جايكي فو 3 ، كي جيه 4 شوويىج زو* و 5 انهشيٍة رات انتشكٍة انًٍكشوتً انضهشي تى تذضٍشها تُجاح تىاسطة انًساس انذشاسي انًائً انسهم وتذوٌ استخذاو أٌة znoتهىسات ملخص: يذهىل انتفاعم. تى دساسة خىاص ph))يُشطات سطذٍة. ًٌكٍ انتذكى تًىسفىنىجٍا هزِ انتشكٍثات انًٍكشوتٍة يٍ خالل ضثط دسجة دًىضة . تاإلضافة إنى رنك، تى اقتشاح (sem) انًاسخ وجهاص انًٍكشوسكىب االنكتشوًَ (xrd)عة انسٍٍُة نذٍىد انًسذىق انًىاد انُاتجة تاستخذاو األش .znoآنٍة نًُى انتشكٍثات انًٍكشوتٍة انهشيٍة ألكسٍذ انخاسصٍٍ يُشطات سطذٍة. -أكسٍذ انخاسصٍٍ، انتشكٍثات انًٍكشوتٍة انهشيٍة، انتذضٍش انذشاسي انًائً، تذوٌ مفتاح الكلماث: 1. introduction n the past few decades, hierarchically structured materials have attracted a great deal of attention because they provide a potential opportunity to explore the utility of their novel properties [1]. synthesis of these hierarchical structures with controlled size and quality is surely significant to tune their physical properties, and will help to further broaden their application. hydrothermal synthesis is regarded as the mainstream morphology-controlled synthetic method, because it is easy to control the shape and size of the materials produced. however, there are some drawbacks of the original method, especially in the use of toxic surfactants [2]. moreover, these surfactants are difficult to remove, and appropriate solvents are usually needed to wash them off. thus, morphology-controlled synthesis of well aligned hierarchical structures via a simple, surfactant-free method is of great importance. zinc oxide (zno), as an important semiconductor material, has been extensively investigated because of its great potential applications in electronics, photoelectronics, optics, sensors and catalysis [3-7]. these applications result from its unique properties, which depend not only on the phase but also on the morphology and organization. for instance, ko et al. reported that zno nanowires present high efficiency in dye-sensitized solar cells [8]. arya et al. demonstrated that zno crystals exhibit different biosensor properties corresponding to their different shape changes [9]. up to now, many different zno nano/micro nanostructures have been reported [10-15]. however, to develop a facile, environment-friendly method to synthesize zno crystals with well defined complex morphology is still a major challenge. herein, we present a facile hydrothermal method for synthesis of hierarchical zno microstructures without using any surfactant. the effects of the solution’s ph on the morphology of the zno crystal were systemically i kezhen qi et al 18 investigated. furthermore, a possible growth mechanism of the zno hierarchical microstructures is proposed on the basis of the experimental results. 2. experimental section 2.1 sample preparation the zno microflowers were synthesized by a simple hydrothermal process. in a typical synthesis procedure, 0.744 g zn(no3)2·6h2o and 0.6 g naoh were dissolved in a reaction solution containing 15 ml ethanol and 20 ml water under vigorous stirring for 10 min. then, the above mixture was transferred to a 30 ml teflon-lined stainless steel autoclave and heated at 120 °c for 24 h. the autoclave was taken out and allowed to cool naturally to room temperature. the as-prepared product was separated by centrifugation, washed several times with distilled water and ethanol, respectively, and finally dried at 60 °c in air for 5 h. 2.2 characterization of the samples the xrd patterns of the products were collected on a rigaku d/max 2500v/pc x-ray diffractometer with cukα radiation (λ =1.5406 å), employing a scanning rate of 0.017° s -1 . the morphology of the as-synthesized products was examined by field emission scanning electron microscope (fe-sem, jeol jsm-6700f). 3. results and discussion 3.1 morphology and structure of the zno products figure 1a shows the xrd pattern of the prepared zno hierarchical microstructures. all diffraction peaks can be indexed to the hexagonal wurtzite structure of zno (jcpds no. 36-1451). no other noticeable peaks of impurities are detected, which indicates a high purity of the prepared zno. the morphologies of the product were examined by sem. figure 1b shows a typical sem image of the zno microflowers, constructed of interleaved thin plates or nanosheets. the microflowers are about 2 μm in diameter. figure 1. characterization of the zno samples obtained when the ph of the reaction solution is 13.8: (a) xrd pattern and (b) sem image. 3.2 effects of solution’s ph on the morphology of zno crystals in this section, we report our results of the ph effects on the morphology of zno crystals. when the ph of the solution is 13.1, the product is composed of nanoparticles about 200-400 nm in diameter (figure 2a). when the ph of the solution is increased to 13.6, nanoplates with a size of 150-350 nm are synthesized (figure 2b). when the ph of the solution is further increased to 13.7, the formed nanosheets become thinner and gather together to form flowerlike microstructures (figure 2c). these complex structures are made of nanosheets which grow continuously from one layer to another in a helical fashion. the above experimental results show that the solution’s ph has a strong influence on the morphology of zno crystals. the possible growth mechanism of zno microflowers is illustrated in figure 3. first, zn 2+ and oh can react easily and lead to fast nucleation and congregation, resulting in sphere-like cores, which would probably provide high-energy sites for crystalline primary particles to grow. then a secondary growth stage could occur at the protuberances of the primary particle and grow into the nanopetals, finally forming the flower-like hierarchitectures. facile and surfactant-free synthesis 19 figure 2. sem images of zno samples obtained with different ph values of the reaction solution. figure 3. illustration of the possible growth mechanism of the zno microflowers. we also changed the zinc source to zn(ch3coo)2·2h2o to study the effect of the precursor on the morphology of zno crystals (fig. 4). when the ph of the solution is 13.1, nanoplates with varying sizes are formed (fig. 4a). when the ph of the solution increases to 13.6, nanoplates with size of 500-600 nm are synthesized (fig. 4b). when the ph of the solution is increased to 13.7 (fig. 4c), microflowers with diameter of 2-4 μm are observed. the morphology of the zno crystals is slightly different from that resulting from using zn(no3)2·6h2o as the zinc source, but the ph effects on the shape evolution are similar in that, as the ph value increases, the shape transforms from the nanosheet to the microflowers. figure 4. sem images of zno crystals obtained by using zn(ch3coo)2·2h2o as the zinc source with different ph values of the reaction solutions: (a) 13.1, (b) 13.6, (c) 13.7. 4. conclusion hierarchical zno microstructures were successfully synthesized via a facile hydrothermal route. the ph of the solution plays an important role in determining the final morphology of these microstructures. based on these results, a possible growth mechanism of the hierarchical zno microstructures has been proposed. this simple route is expected to enable the fabrication of other metal oxides with hierarchical microstructures. 5. acknowledgment this work was supported by financial support from shenyang normal university (grant no. 05455440109035). kezhen qi et al 20 references 1. qi, k.z., yang, j.q., fu, j.q., wang, g.c., zhu, l.j. and zheng, w.j. morphology-controllable zno rings: ionic liquid-assisted hydrothermal synthesis, growth mechanism and photoluminescence properties. cryst. eng. comm., 2013,15, 6729-6735. 2. jung, s., cho, w., lee, h.j. and oh, m. self-template-directed formation of coordination-polymer hexagonal tubes and rings, and their calcination to zno rings. angew. chem. int. ed., 2009, 48, 1459-1462. 3. zhang, j., sun, l., yin, j., su, h., liao, c. and yan, c. control of zno morphology via a simple solution route. chem. mater., 2002, 14, 4172-4177. 4. gao, p.x. and wang, z.l. mesoporous polyhedral cages and shells formed by textured self-assembly of zno nanocrystals. j. am. chem. soc., 2003, 125, 11299-11305. 5. wang, x.d., summers, c.j. and wang, z.l. large-scale hexagonal-patterned growth of aligned zno nanorods for nano-optoelectronics and nanosensor arrays. nano lett., 2004, 4, 423-426. 6. lao, j.y., wen, j.g. and ren, z.f. hierarchical zno nanostructures. nano lett., 2002, 2, 1287-1291. 7. kurtz, m., strunk, j., hinrichsen, o., muhler, m., fink, k., meyer, b. and wöll, c. active sites on oxide surfaces: zno-catalyzed synthesis of methanol from co and h2. angew. chem., int. ed., 2005, 44, 27902794. 8. ko, s.h.,lee, d.,kang, h.w., nam, k.h.,yeo, j.y.,hong, s.j.,grigoropoulos, c.p. and sung, h.j. nanoforest of hydrothermally grown hierarchical zno nanowires for a high efficiency dye-sensitized solar cell. nano lett., 2011, 11, 666-671. 9. arya, s.k.,saha, s.,ramirez-vick, j.e., gupta, v., bhansali, s. and singh, s.p. recent advances in zno nanostructures and thin films for biosensor applications: review. anal. chim. acta., 2012, 737, 1-21. 10. zhai, t., li, l., ma, y., liao, m.,wang, x., fang, x.,yao, j., bando, y. and golberg, d. one-dimensional inorganic nanostructures: synthesis, field-emission and photodetection. chem. soc. rev., 2011, 40, 2986-3004. 11. peng, y., xu, a.w., deng, b., antonietti, m. and cölfen, h. polymer-controlled crystallization of zinc oxide hexagonal nanorings and disks. j. phys. chem. b., 2006, 110, 2988-2993. 12. boal, a.k., ilhan, f., derouchey, j.e., thurn-albrecht, t., russell, t.p. and rotello, v.m. self-assembly of nanoparticles into giant spherical arrays. nat., 2000, 404, 746-749. 13. shi, r.x.,yang, p.,wang, j.r., zhang, a.y., zhu, y.n., cao, y.q. and ma, q. growth of flower-like zno via surfactant-free hydrothermal synthesis on ito substrate at low temperature. cryst. eng. comm., 2012, 14, 5996-6003. 14. wen, m.w.,yang, b.f.,yan, h.w., fu, z.p., cai, c., liu, k.p., chen, y.j., xu, j., fu, s.q. and zhang, s.y. morphology-controlled synthesis of flowerlike zno nano/microstructures and their photocatalytic property. j nanosci. nanotechnol., 2009, 9, 2038-2044. 15. cauda, v., pugliese, d., garino, n., sacco, a., bianco, s., bella, f., lamberti, a. and gerbaldi, c. multifunctional energy conversion and storage electrodes using flower-like zinc oxide nanostructures. energy, 2014, 65, 639-646. received 22 march 2014 accepted 30 june 2014 photovoltaic cells and systems: squ journal for science, 18 (2013) 54-59 © 2013 sultan qaboos university 54 dihedral groups as epimorphic images of some fibonacci groups abdullahi umar a* and bashir ali b a department of mathematics and statistics, sultan qaboos university,al-khod, pc 123 – oman, *a email: aumarh@squ.edu.om. b department of mathematics and computer science, nigerian defence academy, kaduna – nigeria. abstract: the fibonacci groups are defined by the presentation ),( nrf ,,,:,,, 213212121    rrrrn aaaaaaaaaaa , 11 rrn aaaa    where 0r , 0n and all subscripts are assumed to be reduced modulo n . in this paper we give an alternative proof that for 0r  , (2 , 4 2)f r r  , (4 3, 8 8)f r r  and (4 5, 8 12)f r r  are all infinite by establishing a morphism (or group homomorphism) onto the dihedral group n d for all 2n  . 1 keywords: group; fibonacci group; dihedral group; (homo) morphism. مجموعات دايهيدرل كصورة متماثلة لمجموعات فيبوناتشى يبشير علو عبدهللا عمر انتمثيم بىاسطت تعسف مجمىعاث فيبىناتشيتعّسف ملخص : 1 2 1 2 3 1 2 1 1 ( , ) , ,..., : , , ... ,..., ... n r r n r r f r n a a a a a a a a a a a a       ,0 عندما تكىن 0n r  ، r r n a a   1نكم, ...,r n. 2) بأن، في هرا انبحث بسهانا بديلا نعطي , 4 2)f r r  ،( 4 3, 8 8)f r r  4)و 5, 8 12)f r r  في جمعيها ال منتهيت 0r حانت بىاسطت إيجاد دانت شمسة متماثهت وفىقيه عهى انصمسة وذنك n d 2 نكمn . : مجمىعاث ، مجمىعاث فيبىناتشي ، مجمىعاث دايهيدزل ، تشابه شكهي. مفتاح الكلمات 1. introduction for 1r  and 1n  the fibonacci group ( , )f r n is defined by the presentation: 1 2 1 2 1 2 3 1 2 1 1 ( , ) , , , : , , , n r r r r n r r f r n a a a a a a a a a a a a a a a         , where all subscripts are assumed to be reduced modulo n , if necessary. these groups were first introduced by conway (1965) and have been studied over the last few decades. for a nice survey article see (thomas, 1991) or (campbell et al., 1992). the dihedral group of order 2n denoted by n d is usually defined by .,1:, 12 xyyxyxyxd n n   (1) it is well known that x and y in dn satisfy the relations summarized in the next lemma. lemma 1.1 for all 0 1k n   we have 1 msc2010 : 20f05 fibonacci groups 55 (a) ; knk xx   (b) ; 1 yy   (c) ;yxyx knk   (d) ;1)( 2 yx k (e) ;yyxx kk  (f) . knk xyyx   thus we may write the elements of n d uniquely as k x or yx k for 0, 1, 2, , 1.k n  campbell et al. (2004) explored the connection between the fibonacci groups and finite groups via the concept of fibonacci length. in the case where the finite groups were dihedral they obtained satisfactory results. in this note we further explore the connection between the fibonacci groups and dihedral groups in a different manner. in particular, we establish epimorphisms between fibonacci groups in certain classes and all finite dihedral groups of order greater than 4, thus giving alternative proofs regarding the infiniteness of the groups in these classes of fibonacci groups. for basic concepts in group theory we refer the reader to (gallian, 1998). the following lemma for ),( nrf is indispensable for our discourse. lemma 1.2 for all 0r  and 2m  we have 1 2 1 1m r m m r a a a       in ( , )f r n . proof. 1211 1 111 )(     rmrmmmmmrmmmrm aaaaaaaaaa  . 2 1 1 1     rmm aa 2. morphic images first we consider the fibonacci groups (2 , 4 2).f r r  theorem 2.1 let 0.r  there exist morphisms from (2 , 4 2)f r r  onto n d for all 3n  . hence (2 , 4 2)f r r  is infinite. we are going to prove this theorem via a sequence of lemmas. however, we first define a mapping from the first 2r generators of (2 , 4 2)f r r  onto the generators of n d by xa x  and ( 2, 3, ... , 2 ). i a y i r (2) then the next lemma gives the images of the remaining generators: .,,, 142212  rrr aaa  lemma 2.2 (a) );1( 12   rxya r  (b) );1( 1 22    rxa n r  (c) );1( 2 32   ryxa r  (d) 2 ( 2 r i ra y   and 4 2 1).i r   proof. using lemma 1.2 we see that (a) );1( 12 22112    rxyxyaaaa r rr  (b) );1()( 1212 12 1 122      rxxyxaaa n rr  (c) );1()( 22112 22 1 232      ryxxyaaa n rr  (d) this proof is by induction. basis step: by lemma 1.2 and (c) above, we see that .)( 2212 32 1 342 yyxyaaa rr       inductive step: suppose that ya ir 2 (for some 4 2i r  ). using lemma 1.2 again we see that 1 2 1 2 2 1 2 , r i i r i a a a y y y        abdullahi umar and bashir ali 55 as required. lemma 2.3 for 1r  we have (a) );1(24  rxya r  (b) ;341 xaa r  (c) 2 4 (4 2 2). i r i i ra a y      proof. using lemmas 1.2 and 2.2 we see that (a) ;)( 212 14 1 1224 xyyxyaaa rrr       (b) ;)( 22 24 1 2234 xxyxaaa rrr      (c) this proof is by induction. basis step: by lemma 1.2 and (b) above, we see that .)( 2122 34 1 3244 yxyxaaa rrr       inductive step: suppose that ya ir  4 (for some 4 2 1i r   ). using lemma 1.2 again we see that , 212 4 1 214 yyyaaa iririr       as required. it is now clear from lemmas 2.2 and 2.3 that the mapping defined in (2) is indeed a morphism onto n d , which preserves all the relations of (2 , 4 2)f r r  and so theorem 2.1 is proved. next we consider the fibonacci groups (4 3, 8 8).f r r  theorem 2.4 let .0r there exist morphisms from (4 3, 8 8)f r r  onto n d for all 3n  . hence (4 3, 8 8)f r r  is infinite. as in the previous case, we are going to prove this theorem via a sequence of lemmas. first, we define a mapping from the first 34 r generators of (4 3, 8 8)f r r  onto the generators of n d by xaa ri  32 ,  and ,ya i  (3) where 32,342  riri and 0r . then the next two lemmas give the images of the remaining generators: .,,, 885444  rrr aaa  lemma 2.5 for 0r we have (a) ; 44 ya r   (b) ; 1 54   n r xa  (c) ; 2 64 yxa r   (d) 4 (7 2 6). r i i ra y     proof . using lemma 1.2 we see that (a) 2 1 2 4 4 1 2 4 3 ; r r r r a a a a xy xy y      (b) 1 2 1 2 1 4 5 1 4 4 ; n r r a a a x y x        (c) ;)( 22112 54 1 264 yxxyaaa n rr       (d) this proof is by induction. basis step: by lemma 1.2 and (c) above, we see that 1 2 1 2 2 4 7 3 4 6 ( ) . r r a a a y x y y       inductive step: suppose that ya ir 4 (for some 7 2 5i r   ). using lemma 1.2 and the induction fibonacci groups 55 hypothesis we see that , 212 4 1 314 yyyaaa iriir       as required. lemma 2.6 for 0r we have (a) ; 1 76   n r xa  (b) ; 2 86 yxa r   (c) 6 (9 2 8). r i a y i r     proof. using lemmas 1.2 and 2.5 we see that (a) ; 1212 66 1 3276      n rrr xyxaaa  (b) ;)( 22112 76 1 4286 yxxyaaa n rrr       (c) this proof is by induction. basis step: for 9i  , we see tha .)( 2212 86 1 5296 yyxyaaa rrr       inductive step: suppose that ya ir  6 (for some 9 2 7i r   ). then using lemma 1.2, the fact that 9i  and induction hypothesis we see that , 212 6 1 )32(16 yyyaaa iririr       as required. lemma 2.7 for 0r  we have (a) ; 981 xaa r    (b) 8 8 (10 2 10). i r i a a y i r       proof. using lemmas 1.2, 2.5 and 2.6 we see that (a) ;)( 2112 88 1 5498 xyxaaa n rrr       (b) for 10 2 10,i r   we use induction. basis step: for 10i  , we see that .)( 2122 1)88( 1 642)88( yxyxaaa rrr       inductive step: suppose that 8r i a y  (for some 10 2 9i r   ). then using lemma 1.2, (a) above and the induction hypothesis we see that 1 2 1 2 8 1 4 3 8 , r i r i r i a a a y y y          as required. lemma 2.8 for 0r we have (a) ; )112(832 xaa rrr    (b) 8 8 (2 12 4 11). i r i r i ra a y       proof. using lemmas 1.2, 2.6 and 2.7 we see that (a) ;)( 2112 )102(8 1 )72(4)112(8 xyxaaa n rrrrrr       (b) for 2 12 4 11r i r    we use induction. basis step: for 2 12,i r  we see that .)( 2122 )112(8 1 )82(4)122(8 yxyxaaa rrrrrr       abdullahi umar and bashir ali 55 inductive step: suppose that ya ir  8 (for some 2 12 4 10r i r    ). then using lemma 1.2 (a) above and the induction hypothesis we see that , 212 8 1 3418 yyyaaa iririr       as required. it is now clear from lemmas 2.5, 2.6, 2.7 and 2.8 that the mapping defined in (3) is indeed a morphism onto , n d which preserves all the relations of (4 3, 8 8)f r r  and so theorem 2.4 is proved. finally we consider the fibonacci groups (4 5, 8 12)f r r  . theorem 2.9 let 0r . there exist morphisms from (4 5, 8 12)f r r  onto n d for all 3.n  hence (4 5, 8 12)f r r  is infinite. as in the previous cases, we are going to prove this theorem via a sequence of lemmas. however, since the proofs are similar to the previous case we are going to state the corresponding results without proofs. we first define a mapping from the first 4 5r  generators of  4 5, 8 12f r r  onto the generators of nd by 1 2 3 , r a a x  and , i a y (4) where 32,542  riri and 0r . analogously to lemma 2.5 we have lemma 2.10 for 0r  (a) ; 64 ya r   (b) ; 1 74   n r xa  (c) ; 2 84 yxa r   (d) ).829( 4   riya ir  analogously to lemma 2.6 we have lemma 2.11 for 0r  we have. (a) ; 1 96   n r xa  (b) ; 2 106 yxa r   (c) 6 (11 2 12). r i i ra y     analogously to lemma 2.7 we have lemma 2.12 for 0r  we have (a) ; 1381 xaa r    (b) 12 8 (14 2 14). i r i i ra a y      analogously to lemma 2.8 we have lemma 2.13 for 0r  we have (a) ; )152(832 xaa rrr    (b) 12 8 (2 16 4 17). i r i r i ra a y       it is now clear from lemmas 2.10, 2.11, 2.12 and 2.13 that the mapping defined in (4) is indeed a morphism onto n d , which preserves all the relations of (4 5,8 12)f r r  and so theorem 2.9 is proved. fibonacci groups 55 3. acknowledgements bashir ali acknowledges the support and hospitality of sultan qaboos university in spring 2011 during which period this work was completed. bashir ali also thanks the nigerian defence academy for research leave and etf nigeria for financial support. we also thank the referees for helpful comments and suggestions, which greatly improved the exposition of this paper. 4. references campbell, c.m., doostie, h. and robertson, e.f. 2004. on the fibonacci length of powers of dihedral groups. applications of fibonacci numbers 9, ed. f.t. howard, kluwer, dordrecht, 69-85. campbell, c.m., robertson, e.f. and thomas, r.m. 1992. fibonacci groups and semigroups. technical report csd-50, department of computing studies, university of leicester. conway, j.h. 1965. solution of advanced problem 5327. american mathematical monthly 72(8): 915. gallian, j.a. 1998. contemporary abstract algebra, houghton mifflin, boston/new york. thomas, r.m. 1991. the fibonacci groups revisited. in proceedings of groups st andrews 1989, volume 2 (london math. soc. lecture note series 160, cambridge university press, 1991). (eds.) campbell, c.m. and robertson, e.f. 445-454. received 12 april 2011 accepted 16 june 2012 squ journal for science, 2020, 25(2), 78-84 doi:10.24200/squjs.vol25iss2pp78-84 sultan qaboos university 78 determination of toxic metals in tobacco from selected imported cigarette brands and local tobacco in iraqi markets wedad h. al-dahhan 1 , emad yousif 1* and hassan hashim 2 1 department of chemistry, college of science, al-nahrain university, baghdad, iraq; 2 department of physics, college of science, al-nahrain university, baghdad, iraq; *email: emad_yousif@hotmail.com. abstract: metals are essential in many physiological processes in the human body, but can also be detrimental to our health when the concentration is not within recommended permissible limits. various types of cigarettes were selected from the local markets in iraq in addition to the iraqi tobacco from sulaymaniyah governorate to conduct tests of the elements in these species. the selected samples were tested using edx instrument. results proved the presence of dangerous elements such as cr, ni, zn, as, al, p, s, pb, cd, sn and sb in quantities which could greatly affect the health of the smoker and have negative effects to the environment. the real danger is the result of the accumulation of these elements in the smoker's body, in the lungs, liver, blood or brain, the effects of which are chronic and dangerous, and can threaten the life of the person in the future. an acid digestion method was used to break down the organic matter in tobacco to release these elements, and solutions to measure their concentrations were prepared using an atomic absorption device. keywords: heavy metals; cigarette; toxic elements; carcinogenic elements; tobacco. سواق العراقيةائرالمستوردة والتبغ المحلي في األجتحديد العناصر السامة للتبغ لنماذج من الس وداد حمد الدهان ، عماد يوسف و حسن هاشم المعادن ضرورية لعدد من العمليات الفسيولوجية في جسم اإلنسان، لكن يمكن أيضا أن تكون ضارة لصحتنا عندما يكون التركيز ليس ضمن :صلخمال اء نية إلجرحدود المسموح بها. تم اختيار أنواع مختلفة من السجائر من األسواق المحلية في العراق باإلضافة إلى التبغ العراقي من محافظة السليماال . أثبتت النتائج وجود نسب من العناصر الخطيرة مثل )الكروم، (edxجهاز )اختبارات العناصر في هذه األنواع. تم اختبار العينات المختارة باستخدام صحة المدخن وآثاره ( والتي تؤثر بشكل كبير علىاالنتمونو ، الكادميوم، الخارصين، الرصاصاللمنيوم ،الفسفور، الكبريت، الزرنيخالنيكل، الزنك، ا يكمن الخطر الحقيقي نتيجة تراكم هذه العناصر في الرئتين ، الكبد ،الدم او الدماغ للشخص المدخن مع الزمن.استخدمت طريقة الهضم السلبية على البيئة. للتبغ باستخدام الحامض لكسر المواد العضوية وتحرير العناصر لغرض الفحص بجهاز االمتصاص الذري. .التبغ العناصر المسرطنة، العناصر السامة، ائر،جالس الثقيلة، المعادن :مفتاحيةالت كلماال 1. introduction s discussed in our papers on safety measures which affect human health [1-6], metals are essential for a number of physiological processes in the human body, but can also be detrimental to our health when the concentration is not within the world health organization/food and agricultural organization of the united nations/joint expert committee on food additives (who/fao/jecfa) recommended permissible limits [7]. although there is no clear definition of what a heavy metal is, density is in most cases taken to be the defining factor. heavy metals are thus commonly defined as those having a density of more than 5 g/cm 3 [8]. the heavy metals are widely dispersed in the environment, and at excessive levels are very toxic to humans [9]. chronic exposure to these substances may also be hazardous. although these metals occur naturally, exposure may be increased by human activities that release them into the air, soil, water and food, and from by-products containing them. certain plants also can accumulate heavy metals that have no known biological function [10]. plants, among them the tobacco plant [11-13] are amenable to absorbing and accumulating heavy metals from the soil into their leaves. the factors governing heavy metals speciation, adsorption and distribution in soil are ph, a toxic metals determination of tobacco 79 soluble organic matter content and soil type, and the presence of organic and other metal ions. trace amounts of heavy metals accumulate in tobacco leaves, and they are known to transfer in trace quantities from the cured and processed tobacco to mainstream cigarette smoke. these metals include cadmium, lead, arsenic, iron, copper, chromium, nickel, and selenium [14-17]. the most abundant redox inactive metals in cigarette smoke generally are cadmium, lead and arsenic. the cigarette smoke contains both organic and inorganic human carcinogenic compounds. containing 4000 identified chemical compounds, cigarette smoke is very harmful and toxic for human health [18]. some of these toxic materials are heavy metals, particularly cadmium and lead. several heavy metals found in tobacco smoke, such as cd, cr, pb, and ni, can also accumulate in tissues and fluids through smoking [1925]. tobacco smoking is the most important single source of cd exposure in the general population. according to al-bader et al. [21], the most important sources of cd in humans are smoking and food. cadmium can enter the body through tobacco smoking, diet, drinking water, and inhaling it from the air. small amounts of cd taken over many years may cause kidney damage and fragile bones, since cd is mainly stored in bone, liver, and kidneys [26]. the scientific literature is filled with evidence of the harmful health effects of carbon monoxide, nicotine, tar, irritants and other noxious gases emitted in tobacco smoke. not enough attention, however, has been paid to the presence of heavy metals and other toxic and trace elements in tobacco smoke and their possible effects on biochemical processes in the human body. once inhaled through smoking, heavy metals have a long biological half-life. chronic adverse effects on human health may, therefore, result in later years from prolonged intake of such toxic elements, some of which are powerful carcinogens. several of them accumulate in bone and may trigger disorders of mineral metabolism, e.g. osteoporosis. the body burden of heavy metals increases as a result of occupational exposure, and tobacco smoking enhances the adverse effects of such exposure. table 1 illustrates some of the main trace and heavy elements in some american brands of cigarette tobacco [27]. table 1. concentration range for main trace and heavy elements in cigarette tobacco of american brands. element concentration range (µg/g) al 699-1200 as > 1 ba 40.7-56.6 ca 1.39-1.96 (mg/100g) co > 0.01-.94 cr > 0.1-0.345 fe 325-520 mg 0.13-.54(mg/100g) mn 155-400 ni >2-200 se >0.007-0.091 sr 29.7-49.5 zn 16.8-30.5 tobacco smoking not only affects human health, but it is also associated with environmental pollution. most of the environmental problems associated with tobacco smoking have been attributed to the tobacco smoke itself, commonly regarded as environmental tobacco smoke (ets). however, several researchers have reported environmental contamination by smoked cigarette butts. several other smoking devices also need the attention of environmental monitoring studies. these devices include kretek, bidi and shisha which are not just a human health problem, but also contaminate the air by releasing smoke which is classified as ets and is a source of soil and water pollution by the water which is discarded after every smoking session. [28]. this research spans a series of research specialized in safety aspects to lay the groundwork for improvements in human health and that of environment [29-33]. the work aims to determine the toxic metals in tobacco from selected imported cigarette brands and local tobacco in iraq using an acid digestion method to break organic matter in tobacco down to release elements to determine their concentrations using energy-dispersive x-ray spectroscopy and atomic absorption devices. 2. experimental 2.1 sampling samples of three common brands of cigarettes (1-3) were purchased, along with one of molasses tobacco and one raw local tobacco sample. the raw sulaimaniyah tobacco sample was selected from the market as the major origin of tobacco in iraq. emad yousif et al 80 2.2 digestion of tobacco samples a 2 g sample of each type of tobacco was weighed and placed separately into a 500 ml and 20 ml mixture of hno3 and hclo4 of ratio 9: 4, and the contents were well mixed by swirling thoroughly [34]. each with its contents was then placed on a hot plate in a fume chamber and heated to boiling; heating continued until the production of red nitrous oxide fumes ceased. the contents were further heated until the volume was reduced to 8-10 ml and the mixture became colorless or yellowish, but not dry. this was done to reduce interference by organic matter and to convert metal associated particulates to a form (the free metal) that could be determined by the atomic absorption spectrophotometer (aas). contents were cooled and filtered through whatman. no.1 filter paper and the volume made up with deionized water to 100 ml. the resulting solution was used for spectrophotometric determination of various metals (see figure 1). a semi-digested tobacco b fully digested tobacco figure 1. tobacco acid digestion. 2.3 atomic absorption spectrophotometry (aas) analysis atomic absorption spectrophotometer (agilent) model fs240 was used in determining the content of heavy metals and their concentrations in the previously acid digested tobacco samples. standard solutions were prepared in different concentrations for each element to establish the calibration curve, according to the detection limit concentration defined in the instrument. an air-acetylene burner was used for spectrophotometric determination of the various metal concentrations in the range of (ppm). fe, mg, cr, cd, zn, k, as and pb metals were tested in the aas spectrophotometer. 2.4 energy-dispersive x-ray spectroscopy (edx) analysis energy-dispersive x-ray spectroscopy (edx) bruker model xflash6i10, sometimes called energy dispersive x-ray analysis (edxa), is an analytical technique used for the elemental analysis or chemical characterization of a sample. tobaccos from the selected types of cigarettes were tested in this instrument. 3. results and discussion 3.1 edx results samples of three common brands of cigarettes (1-3) were tested, along with one of molasses tobacco and one of raw local tobacco in an edx instrument for elemental analysis. results obtained from these tests are illustrated in figures (2, 3,4,5,6 and 7) respectively. figure 2. edx spectrum of sample -1 cigarette tobacco. toxic metals determination of tobacco 81 figure 3. edx spectrum of sample 2 cigarette tobacco. figure 4. edx spectrum of sample 3 cigarette tobacco. figure 5. edx spectrum of molasses tobacco. emad yousif et al 82 figure 6. edx spectrum of raw local tobacco. 3.2 atomic absorption test some selected elements were tested using atomic absorption apparatus (see tables 2, 3 and 4). table 2. concentration of selected elements in (µg/g) for some prepared samples. sample cr mg fe cd zn k pb 1 <1 29.7 <1 <1 0.12 50.00 <1 2 <1 3.38 <1 <1 0.06 25.00 <1 3 <1 15.3 <1 <1 0.82 55.00 <1 molasses <1 3.38 <1 <1 0.06 25.00 <1 local tobacco <1 13.2 <1 <1 0.03 18.00 <1 table 3. weight of selected elements in (mg) for some prepared samples in the total extracted solutions. sample mg zn k total extracted solution(ml) 1 14.85 0.06 25.00 500 2 1.69 0.03 12.50 500 3 7.65 0.41 27.50 500 molasses 1.69 0.03 12.50 500 table 4. weight % of selected elements for some prepared samples with respect to total sample weight. sample mg zn k total sample weight(g) 1 7.40 0.03 12.50 2 2 0.85 0.015 6.25 2 3 3.82 0.20 13.75 2 molasses 0.85 0.015 6.25 2 local tobacco 3.30 0.0075 4.50 2 4. discussion results of the energy-dispersive x-ray spectroscopy tests for the samples (1,2) clearly showed the presence of mg, ca, al, si, p, mo, cl, sb and k in high percentages compared with the elements cd, ni, zn, na, as, s, sn, and pb which were found at low concentration while the third sample (3) showed a large proportion of elements mg, ca, al, si, p, mo and sb. except for k, these were found at a lower percentage than in samples (1,2). low percentages were found for ni, zn, na, as, sn and pb. as for the molasses used in shisha (also known as narghile), the test results for the elements al, k, si and ca were the highest for this sample, but much less than in samples (1 and 2). the results for local iraqi tobacco from sulaymaniyah governorate were very close to the results for molasses, which contained limited concentrations of the elements found in samples 1 and 2 except for ca, which is the metal found in the highest percentage in this type of tobacco. an atomic absorption device was used to determine the accurate concentrations of some trace elements that showed high and low ratios in the energy-dispersive x-ray spectroscopy test used to find the approximate concentrations of the other elements. the results showed the low concentrations of pb, fe, cd and cr, in the level of toxic metals determination of tobacco 83 (µg/g). this is clearly what we found in the percentages of these elements in the energy-dispersive x-ray spectroscopy test. these results can be used to determine the approximate concentrations of sn, s, as, na, zn and ni by means of approximate comparison. the results of the atomic absorption test of the molasses and local tobacco in iraq coincided with the results from the energy-dispersive x-ray spectroscopy in terms of the lowest percentage being found in the content of these samples. 5. conclusion three selected varieties of cigarette tobacco and a type of molasses for shisha, in addition to iraqi tobacco were digested using nitric acid to break down the organic substances to release the elements in the tobacco components. the prepared samples were tested using energy-dispersive x-ray spectroscopy. the results proved the presence of dangerous elements such as cr, ni, zn, na, as, al, p, s, pb, cd, sn and sb, which greatly affect the health of the smoker and have negative effects on the environment. the real danger results from the accumulation of these elements in the smoker's body in the lungs, liver, blood or brain, and the effects of this are chronic and threaten the life of the person in the future. conflict of interest the authors declare no conflict of interest. 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problems mats andersson*, oleg burdakov**, hans knutsson* and spartak zikrin** *department of biomedical engineering, linköping university, linköping, sweden. **department of mathematics, linköping university, linköping, sweden, email: oleg.burdakov@liu.se abstract: the multilinear least-squares (mlls) problem is an extension of the linear leastsquares problem. the difference is that a multilinear operator is used in place of a matrix-vector product. the mlls is typically a large-scale problem characterized by a large number of local minimizers. it originates, for instance, from the design of filter networks. we present a global search strategy that allows for moving from one local minimizer to a better one. the efficiency of this strategy is illustrated by the results of numerical experiments performed for some problems related to the design of filter networks. keywords: filter networks, global optimization, global search strategies, multilinear leastsquares. ائل المربعاث الصغرى الخطيت المتعذدةسلحل م شاملاستراتيجياث البحث ال ماتس أندرسون و أولج بورداكوف و هانس ناتسون و سبارتك زكرين بينهما في استعمال الفرق ويكمن . امتداد لمسألة المربعات الصغرى الخطية هي مسألة المربعات الصغرى المتعددة :خصمل تتميز و ،حجمكبيرة ال مسألة المربعات الصغرى المتعددة تكون عادة بدالً من ضرب مصفوفة بشعاع.متعدد الخطية معامل استراتيجية بحث هذه الدراسة قدمتبعدد كبير من النهايات الدنيا الموضعية. إنها تنتج، مثآل، من تصميم شبكات الترشيح. بنتائج فعالية هذه االستراتيجية وسيتم توضيحأخرى أفضل منها. إلى ن نهاية دنيا موضعية شامل تسمح بالتحرك م بعض المسائل التي لها عالقة بتصميم شبكات الترشيح.عددية مطبقة على اترباتاخ 1. introduction onsider the following multilinear least-squares (mlls) problem in which u v denotes the componentwise product of vectors u and v. given a vector m b r and matrices , m ni ia r   = 1, 2, , ,i l find * n x r that solves the problem 2 1 1 2 2( ) ( ) ( ) ,min l l n x r b a x a x a x   (1) c global search strategies 13 where , ni ix r = 1, 2, , ,i l 1 2= ln n n n   and 1 2= ( , , , ) . t t t t lx x x x for the sake of simplicity, we consider here the standard euclidean norm, although the subsequent reasoning holds also for the weighted euclidean norm. note that if = 1,l then (1) is a linear least-squares problem. the mlls problem occurs, for instance, in factor analysis, chemometrics, psychometrics (leardi et al., 2000; leurgans and ross, 1992; lopes and menezes, 2003; paatero, 1997; wang et al., 2003). we will study this problem in relation to the design of filter networks (andersson et al., 1999; norell et al., 2011; svensson et al., 2005), specifically the sequential connection of sparse sub-filters presented by figure 1. in this case, ix stands for individual characteristics (design parameters) of sub-filter i, whose frequency response is .i ia x the ideal (desired) frequency response of the sub-filter sequence and the actual one are represented in (1) by b and 1 1 2 2( ) ( ) ( ),l la x a x a x respectively. it is common for the design of filter networks that << .n m mlls is a non-convex, typically large-scale, optimization problem with a very large number of local minimizers. each of the local minimizers is singular and non-isolated. the most typical approach to solving the mlls problem consists in generating randomly a number of starting points for their further refinement with the use of local optimization methods. one major shortcoming of this approach is that a very large number of starting points is required to be generated in order to find a reasonably good fit in problem (1). another major shortcoming is that the convergence of local methods is too slow in this problem. figure 1. sequential connection of l sub-filters the most popular of the local algorithms used for solving the mlls problem is called ‘alternating least squares’ (als). it exploits the feature of problem (1) that, if to fix all the vectors 1 , , t t lx x but one, say ,ix then the resulting sub-problem of minimizing over ix is a linear least-squares problem. in the als algorithm, the linear least-squares sub-problems are solved for the alternating index i. this algorithm is also known as ‘block-coordinate relaxation’ or ‘nonlinear gauss-seidel algorithm’ (ortega and rheinboldt, 2000). the mentioned major shortcomings of the local search algorithms are inherent in als. the main aim of our work here is to develop an effective global optimization approach to solving the mlls problem and justify it theoretically. our work is organized as follows. in section 2, we consider a new constrained optimization problem introduced in norell et al. (2011). it is similar, in some sense, to the mlls problem, and its solution gives a good starting point for running the local search in the mlls problem. global optimality conditions for the new problem are derived in section 3. these conditions are then used in section 4 for constructing a global search algorithm. in section 5, we report and discuss results of applying our global search algorithm to solving mlls problems related to the design of filter networks. in section 6, we draw conclusions and discuss future work. 2. problem reformulation problem (1) can be written in the equivalent form 2 1 , min s.t. = , = 1, , , l n ml x r y r i i i b y y a x y i l    mats andersson, oleg burdakov, hans knutsson and spartak zikrin 14 where , m iy r = 1, , ,i l 1 2= ( , , , ) t t t t ly y y y and 's.t.' stands for 'subject to'. this problem is characterized by the relations 1 , and = , = 1, , .l i i ib y y a x y i l following norell et al. (2011), we consider a similar, conceptually close, problem in which 1= , and , = 1, , .l i i ib y y a x y i l we formulate it as: 2 =1 , 1 min s.t. = . l i i i n ml ix r y r l y a x y y b    after solving this problem in x, we obtain =1 1 min s.t. = , l t i i i ml iy r l y p y y y b   (2) where ip is the matrix of orthogonal projection defined by .ia in the numerical implementation, it may not be reasonable to compute ip explicitly, but instead, it can be treated as a linear operator defined by ia in one of the standard ways (björk, 1996). moreover, since this problem may admit trivial asymptotic solutions, it must be regularized. this can be done by adding 2 iy with a small  to each term in the objective function. we assume further that all matrices ip have been slightly perturbed in this way, and hence they are positively definite. observe that the regularized objective function in (2) is strictly convex with a unique minimizer in the origin. unlike (1), this problem does not suffer from the bad property of having non-isolated minimizers. however, it inherits the multi-extremal nature of problem (1). without loss of generality, we can assume that 0b  in (1) and (2). indeed, if any component of b is negative, the change of its sign to positive can be compensated by the change of sign in the corresponding row of, for instance, 1.a in (norell et al., 2011), it is discussed how to treat the case of zero components. from now on, we assume that > 0.b note that the feasible set in problem (2) consists of disjoint subsets. each of these subsets is connected. it is characterized by a certain feasible combination of signs of 1, , .ly y the total number of the subsets is determined by the number of the feasible combinations of signs which is equal to ( 1) 2 . m l  consider how to solve problem (2) on a given isolated subset of the feasible set, for instance, the subset associated with the positive orthant = { : > 0}. ml ml r y r y  the problem in this case takes the form >0, , >0 =11 1 min s.t. = . l t i i i y y il l y p y y y b  (3) the substitution = exp( )i iy w reduces this problem to: , , =11 1 exp( ) exp( )min s.t. = ln , l t i i i w w il l w p w w w b    (4) where exp( ) and ln( ) are component-wise operations. this linear equality constrained problem can be global search strategies 15 efficiently solved by the conventional methods (nocedal and wright, 2006) that are able to take advantage of using the easily available derivatives of the objective function and the simple structure of the linear constraints in (4). in (norell et al., 2011), the computational time for solving this problem was approximately half the time for one run of the als algorithm on problem (1). to study the general case of sign combinations, we divide problem (2) into an outer binary problem to deal with the signs of y and an inner subproblem, similar to (4), in which the minimization is performed on the corresponding subset of the feasible set. notice that the feasible vectors 1, , ly y in (2) have no zero components, because > 0.b following norell et al. (2011), we present problem (2) as a specially enumerated set of subproblems of the form (3). we will use the following notations: = sign( ), = , = diag( ) diag( ) .i i i i i i i i is y y s y p s p s (5) let m s be the set of all vectors in m r whose elements equal 1 or 1. if iy is feasible, then m is s and > 0.iy furthermore, for all feasible vectors 1, , ly y in (2) we have 1 = ,ls s e where = (1, , 1) . t m e r it is easy to verify that problem (2) is equivalent to 1 , ,1 1 ( , , )min s.t. = , l m m s s s sl l s s s s e    (6) with the objective function 1 >0, , >0 =11 1 ( , , ) = min s.t. = . l t l i i i y y il l s s y p y y y b   (7) here, the dependence of ip on is is given by (5). note that the substitution 1 1=l ls s s  is able to eliminate the equality constraint in outer problem (6), which is a binary problem with ( 1) 2 m l  feasible points. this number of feasible points defines the number of all inner problems (7). the important feature of problem (6) is that it performs a partitioning of the feasible set in (2) and reduces this problem to a finite number of easy-to-solve inner problems (7) of the same form as (3). this allows us to capture the nature of the local minimizers of problem (2) and to enumerate them efficiently by combining the signs. any optimal or close to optimal solution y to problem (6), or equivalently, to problem (2), can be used as an initial point in problem (1), to be further refined by local search algorithms like als. given y, the initial point x is computed by the formula † = , = 1, , ,i iix a y i l where † i a is the pseudo-inverse of ia (björk, 1996). in our numerical experiments in (norell et al., 2011), we compared the performance of the als for the initial point generated by our approach and for randomly generated points. it was required to run the als from at least 500 random points in order to get a local minimizer in (1) with the approximation error comparable with only one run of the als from the point generated by solving problem (6). thus, the approach introduced in (norell et al., 2011) achieved the overall network design speedup factor of several hundreds. moreover, the randomly generated initial points did not guarantee any success. this speaks for the robustness of the approach. it should be emphasized that binary problems are, in general, difficult to solve, but fortunately, the nature of signs in the sub-filter outputs are often well understood. prior knowledge of the filter’s characteristics and its structure helps to facilitate substantially the solution process of the outer problem by focusing on a relatively small number of sign combinations (see (norell et al., 2011) for details). mats andersson, oleg burdakov, hans knutsson and spartak zikrin 16 3. theoretical background for global search given an approximate solution to problem (2), our global search is aimed at finding a new combination of signs in (6) with a better value of the objective function defined by (7). it is based on solving problem (2) under the assumption that all components of given feasible vectors 1, , ly y are fixed, except for their kth components denoted here by 1, , ,lu u respectively. the value of k changes in the process of global minimization. to justify our approach, we will consider problem (2) rewritten in terms of these components. let ˆiy coincide with iy in all the components, but the kth one which equals zero in ˆ .iy let ( )i kp and ( )i kkp stand for the kth column and diagonal element of the matrix ,ip respectively. it can be easily verified, for = 1, , ,i l that 2 = ( ( ) ) , t i i i i i k i iy p y y    where 2ˆ ˆ ˆ= ( ) , = ( ) / , = . t t i i kk i i i k i i i i i ip y p y p y      (8) thus, the minimization over 1= ( , , ) t lu u u in (2) results in the problem: 2 =1 1 ( )min s.t. = , l i i i l iu r l u u u c       (9) where c denotes the kth component of b. it is worth noting that this problem has at least one global minimizer, because the level sets of the objective function are compact and the function defining the constraint is smooth. let * u stand for the set of all global minimizers in problem (9). for this problem, the following notations will be used: * * * * = { : = sign( ), }, = { : sign( ) = } , l l l ss s s s u u u r u r u s   1 , 1= ( , , ) = ( , , ) . t t l l      let the multivariate function ( )  be defined as the product of the signs of all the variables, for instance, 1( ) = sign( ) sign( ) .lu u u   note that the feasible set in problem (9) consists of disjoint subsets. each of these connected subsets belongs to the corresponding orthant l sr determined by sign( ).u since such subsets are characterized by ( ) = 1,u their total number is 12 .l  it grows exponentially with l. this is indicative of a highly multi-extremal nature of problem (9). the result presented in theorem 1 allows one to effectively locate the optimal combination of signs * s or, equivalently, to find the orthants that contain the connected subsets of the feasible set on which the global optimum of problem (9) is attained. theorem 1 let the coefficients c and  in problem (9) be positive. then, * * s s if and only if * ( ) = 1s and one of the following conditions holds: (i) ( ) 0   and * = sign( ),i is  for all i such that 0;i  (ii) ( ) = 1   and there exists *i i such that ** * sign( ), if = , = = 1, , , sign( ), otherwise, i i i i i s i l      global search strategies 17 with the set 1 = | | .min i i l i arg    proof. we start by proving the "if'' part. suppose that * *.s s let * * u u be such that * * sign( ) = .u s the feasibility of * u implies that * ( ) = 1.s consider the linear space transformation given by the formula * = .v s u this nonsingular transformation is aimed at easing our analysis because, in the new space, the objective function takes the form of a squared euclidean distance between the two points 1= ( , , ) t lv v v and * 1= ( , , ) = . t la a a s  note that 1 | |= .min i i l arg a i   another important feature of the transformation is that it does not change the multiplicative type of the constraint. the problem in the new space takes the form: 2 1 min s.t. = , l v r l v a v v c     (10) where 1= .lc c     thus, the reformulated problem (10) is to find the shortest distance from a to the feasible set. let * * * 1= ( , , ) t lv v v be the image of * u in the new space, i.e., * * * = .v s u clearly, * v is a global minimizer for problem (10). then, in the view of the fact that * > 0,v conditions (i) and (ii) can be reformulated in the new space as follows: (i') if ( ) 0,a  then 0;a  (ii') if ( ) < 0,a then there exists *i i such that > 0,ia for all *,i i and * < 0.ia we first show that there is no more than one negative component of a. suppose, to the contrary, that at least two components of a are negative, say, ia and .ja it can be verified easily that the open linear segment * ( , )v a intersects the hyperplane = { : = 0} l i jv r v v   at the point * = (1 ) ,v a v    (11) where (0,1)  is given by the formula * * * * = . ( ) ( ) i j i j i j v v v v a a      (12) consider the point 1= ( , , ) t lv v v   defined as follows: (13) this point is obviously feasible. the triangle inequality gives * * * , if = , = , if = , = 1, , . , otherwise, j l i l v l i v v l j l l v         mats andersson, oleg burdakov, hans knutsson and spartak zikrin 18 < ,v a v v v a       where * = ,v v v v    because ,v  * ( ) / 2v v   and * ( ) .v v   then, we obtain * * < = ,v a v v v a v a           (14) since * ( , ).v v a hence, the feasible point v  gives a better objective function value in (10) than *.v this contradicts the assumption that * v is a global minimizer for problem (10) and proves that a can have at most one negative component. this result immediately proves (i') for ( ) = 1.a for ( ) = 0,a suppose, contrary to (i'), that there exists < 0.ia such a component must be unique. there must exist index j such that = 0.ja for these indices i and j, consider the points v  and v  defined by formulas (11), (12) and (13). one can show, as above, that (14) holds for the two points. this contradicts the assumption that * v is a global minimizer. thus, statement (i'), and consequently part (i) of the theorem, hold. consider now the case ( ) < 0.a as shown above, exactly one component of a must be negative, say, < 0.ia suppose, contrary to (ii'), that .i i for this i and any ,j i consider the point v  defined by (13). for the point v  defined by (11) and (12), the condition (0,1)  is satisfied, because < 0.i ja a for v  and v  one can show, as above, that (14) holds, which contradicts that *v is a global minimizer. this proves (ii') and accomplishes the proof of the "if'' part of the theorem. for the "only if'' part, let * s satisfy the sufficient conditions. we choose any * u u and construct a point * * * 1= ( , , ) t lu u u individually for each of the cases (i) and (ii). suppose that (i) holds. consider * u defined as follows: * * = | |, = 1, , .i i iu s u i l obviously, * * sign( ) =u s and *u is a feasible point. as proved in the "if'' part, sign( )u must satisfy (i). thus, * =sign( ),i is u for all i such that 0.i  therefore, * u has the same objective function value in (9) as u. suppose now that (ii) holds. let * i i be such that * * *= sign( ). i i s  it must satisfy (ii). suppose j i is the index for which sign ( ) = sign( ).j ju  this means that *| |=| | .j i   if * = ,i j then we define * = .u u otherwise, we define * u as follows: * * * * * * * | | / , if = , = | | / , if = , = 1, , . , otherwise, j ji i l j i ji l s u l i u s u l j l l u          it can be easily seen that sign * * ( ) =u s and also that *u is feasible and has the same objective function value in (9) as u. in each of the two cases, * * ,u u and consequently * *.s s this completes the proof of the theorem. □ this result suggests ways in which the sign combinations intrinsic in the global minimizers of problem (9) can be effectively constructed for any given . our algorithm presented in the next section is based on this result. global search strategies 19 4. global search algorithm theorem 1 implies that * s is not unique when either of the following two cases occurs: •  has more than one zero component. • ( ) = 1   and the set i consists of more than one element. given  , the set *s can be constructed based on the optimality conditions as follows. • if ( ) = 1,  then the set * = {sign( )}s  is a singleton. • if ( ) = 0,  then *s is composed of all vectors * ls s whose components * = sign( ),i is  for all i such that 0,i  and the rest of the components ensure * ( ) = 1.s • if ( ) = 1,   then *s is composed of the same number of elements as i. each * i i determines * *s s in such a way that * * *= sign( ), i i s  and the remaining components of *s are the same as in sign( ). note that it is not necessary to construct the whole set * s when it is required to find only one * * .s s the same principles as above can be employed in this case. we propose below a global search algorithm. it uses procedures optsign, local and als. procedure optsign( , )y k computes  by formula (8), and then it returns an *s arbitrarily chosen from the set *.s another task of this procedure is to verify if a given l s s is optimal for problem (9). the optimality conditions given by theorem 1 can be used for checking if optsign( , )s y k holds. procedure 1local( , , )ls s returns y that solves problem (7) for a given sign combination 1, , .ls s procedure 0 als( )x returns the result of running the als algorithm from a given starting point 0.x the derived optimality conditions open the way to a successive improvement of the sign combination in outer problem (6). the resulting global search strategies admit various implementations. the one that we present below is based on a sequential checking of the components in 1, , ls s for a possible improvement. it starts from a given sign combination 1, , ls s , and it returns an approximate solution for problem (1). our global search proceeds as follows: in algorithm 1, an initial sign combination 1, , ls s is required to be given. for this purpose, the choice of signs proposed in norell et al. (2011) can be used. an alternative is to choose as the initial sign combination the best one produced by als, starting from a number of randomly generated points. mats andersson, oleg burdakov, hans knutsson and spartak zikrin 20 5. numerical experiments for generating mlls test problems of the form (1), we considered two-dimensional filters of the monomial class (knutsson et al., 2011) with the lognormal (granlund and knutsson, 1995; knutsson, 1982) and logerf (knutsson and andersson, 2005; norell et al., 2011) radial parts. we shall use the abbreviations lp, bp and hp standing for the low-pass, first-order band-pass and first-order high-pass filters, respectively. they were approximated by a sequence of = 5l sub-filters. the total number of coefficients n of the sub-filters and the number of components m of the discretized ideal frequency responses b are specified in table 1 for each filter. our numerical experiments were performed on a pc with a 2.27ghz intel xeon e5520 processor and 32bit windows xp operating system. the results are shown in table 1. the matlab routine fmincon was used to solve problem (4) which is a reformulation of (7). as mentioned earlier, the objective function in (2) is required to be regularized. for the regularization parameter value, we used = 0.5. we shall use the term approximation error to refer to the objective function value in (1) and denote it by . in table 1, min( )j stands for the best approximation error obtained by running als from 500 randomly generated starting points. the cpu time (in seconds) spent on performing these 500 runs is denoted by .alst we shall use the term local search to refer to solving problem (7) only once for the sign combination chosen as proposed in (norell et al., 2011). the approximation error loc is the result of one run of als from the starting point produced by the local search. our global search strategy is aimed at improving the local search results. to initialize it, we used the same sign combination as in the local search. the global search, as proposed in algorithm 1, took globt seconds of cpu time and yielded a relative improvement, calculated by the formula = 100% , loc glob loc        where loc and glob are the values of the regularized objective function in (2) produced by the local and global search, respectively. als started from the point generated by our global search resulted in the error .glob the set of filters used in our experiments included also zeroand second-order band-pass and high-pass filters. for these filters, the initial sign combination proposed in (norell et al., 2011) was nearly optimal in the sense that there was practically no difference between the approximation errors loc and min( ).j for this reason, our global search strategy was unable to improve the initial sign combination. table 1. performance of the als, local and global search strategies filter n m min( )j loc glob  alst globt lp, lognorm 15 361 1.94e-4 3.44e-4 3.31e-4 0.01 1262.4 73.0 bp, lognorm 13 360 1.66e-3 3.16e-3 1.66e-3 0.19 1226.3 21.9 bp, logerf 13 360 1.23e-4 5.63e-4 1.23e-4 0.19 1251.5 21.1 hp, logerf 13 360 1.05e-3 3.19e-3 1.05e-3 0.10 1246.2 23.4 the results presented in table 1 refer to the filters for which the global search strategy was able to improve local search solutions in terms of objective function values in problems (7) and (1). in the case of high-pass and band-pass filters, the solution produced for problem (1) was as good as the best of those produced by 500 runs of als, but for achieving this, the global search required a cpu time that was over 50 times shorter. these results demonstrate the efficiency of our global search strategy and its capability for substantially speeding up the filter design process. global search strategies 21 6. conclusions the derived optimality conditions open up possibilities to perform a global search for a better sign combination. the implemented global search strategy is not a very computationally demanding procedure. its efficiency was demonstrated by the results of numerical experiments. for some filters, our global search ensured a faster process of optimizing sub-filter parameters with an overall speedup factor of over fifty. we plan to extend our approach to solving optimal filter design problems having more general sub-filter network structures. 7. acknowledgment this work was supported by the swedish research council; the linnaeus center for control, autonomy, and decision-making in complex systems (cadics); the swedish foundation for strategic research (ssf); strategic research center (moviii); the linköping univ. center for industrial inf. technology (ceniit). 8. references andersson, m., wiklund, j. and knutsson, h. 1999. filter networks. in n.m. namazi, editor, signal and image processing (sip), proceedings of the iasted international conferences, october 18-21, 1999, nassau, the bahamas, pages 213–217. iasted/acta press. björk, å. 1996. numerical 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(scia’05), pp. 1086–1095, joensuu, finland, june 2005. wang, j.h., hopke, p.k., hancewicz, t.m. and zhang, s.l. 2003. application of modified alternating least squares regression to spectroscopic image analysis. analytica chimica acta, 476(1):93–109. received 27 october 2011 accepted 29 november 2011 squ journal for science, 2021, 26(1), 1-7 doi:10.53539/squjs.vol26iss1pp1-7 sultan qaboos university 1 parasitic contamination of local drinking water sources in aba metropolis, abia state, nigeria blessing u. ejike 1,2 , carmelita c. ohaeri 2 and ebube c. amaechi 3* 1 department of biology/microbiology, abia state polytechnic, aba abia state, nigeria; 2 department of zoology and environmental biology, michael okpara university of agriculture, umudike, abia state, nigeria; 3 department of zoology, faculty of life sciences, university of ilorin, ilorin, nigeria. *email: ebubeamechi@yahoo.com. abstract: water-borne parasitic infections have become a source of concern in recent times due to the contamination of various water sources. a survey on the parasitic contamination of local drinking water sources in aba metropolis was carried out between august and october 2018. this was done to evaluate the extent of contamination of these water sources and their public health implications. a total number of eighty (80) water samples were investigated from five (5) major water sources within the study area using the standard sedimentation method and examined for parasite cysts, eggs and larvae. physical/macroscopic examination was done to determine the ph, colour, odour, temperature and presence/absence of particles. among the water sources analyzed, stream water samples had the highest rate of parasite contamination 27 (44.3%) followed by river water 14 (22.9%) while the least contaminated was borehole 7 (11.5%). rainwater was found free from parasitic infestation. the differences in the level of contamination among the water sources analyzed were found to be statistically significant (p<0.05). five parasites entamoeba histolytica, giardia lamblia, ascaris lumbricoides of entamoeba coli and hookworm were observed. each of the sample sources except rainwater harbored at least one of these. among these parasites, giardia lamblia had the highest rate occurrence of 15 (24.6%), followed by entamoeba histolytica 14 (22.9%) and the least frequently occurring parasite was hookworm 8 (13.1%). most of the identified water sources are utilized by the populace who lack access to potable water. the detection of protozoan and helminthic parasites in drinking water sources is a serious public health concern, hence the proper implementation of a supply of safe drinking water is vital. keywords: parasitic; contamination; local sources; drinking water and aba metropolis. تلوث الطفيلي لماء الشرب في أباميتروبوليس، والية أبيا، نيجيرياال كارميليتا شيما أوهاري، إيبوبي شارلز أماتشي بليسينج أوزوماكا إيجايك، جرينا دراسة للتلوث الطفيلي لمصادر مياه الشرب المحلية في أبا ميتروبوليس بين يشكل التلوث الطفيلي في مصادر المياه مشكلة حيوية. ولذلك أ :صلخمال من مياهعينة 21تم جمع لقد م. الغرض من الدراسة تقييم مستوى التلوث لمصادر المياه وتأثيرها على صحة األفراد. 8102 للعام ربشهري أغسطس وأكتو ، اللون، phتم تحديد الخواص الفيزيائية مثل لقد . المتواجد بها تم اختبار عدد الطفيليات، البيض و اليرقاتومن ثم محلية مياهخمسة مواقع لمصادر بأن المياه الجارية تحتوي على أعلى معدل للتلوث الطفيلي بنسبة اكتشف العلماءفي كل عينة. الصلبة جسيمات الالرائحة، درجة الحرارة وتواجد طفيليات ألمطار على أيالجدير بالذكر ال تحتوي مياه او(. 00.1)%2( بينما احتلت اآلبار أقل معدل للتلوث 88.2).0( ثم يلحقها مياه النهر 4...%)82 اإلنتاميبا والجيارديا واإلسكارس التالية الطفيليات نوع . لقد حددنا1.11ة خطأ أقل من نسبالمختلفة لها ياه. إن نسبة معدل التلوث في عينات الم1.1بنسبة % ن أمياه الشرب يشكل كارثة مجتمعية بين السكان و . إن تواجد هذه الطفيليات في(b.1%) 01تتواجد الجيارديا بأعلى معدل بحيث وإيكولي وهوك وورم توفير مصادر مياه نظيفة للشرب ضرورة حتمية. مصادر محلية، مياه الشرب، أباميترو بوليس. التلوث، ،طفيليات :مفتاحيةالمات كلال blessing uzoamaka ejike et al. 2 1. introduction ater is universal and fundamental to the survival and wellbeing of living organisms. water-borne diseases are usually acquired by the consumption of polluted water containing human and animal faecal matter from patients or healthy carriers and they remain a major source of morbidity and mortality in the world causing more than 2.2 million deaths per year [1]. sources of water for human use include boreholes, well water, dams, rivers, streams, lakes, municipal water and rain water [2]. most of these water sources are located some distance away requiring transportation to homes. these different sources of water need to be protected from pollution and contamination by potential parasites, micro-organisms and harmful chemical substances [3]. most urban and rural communities in the developing countries do not have adequate disposal systems for human waste, and many inhabitants defecate indiscriminately in places not far from their dwelling places, including the sides of streams, home ponds, wells, and in some cases into the streams [4]. furthermore, excreta from children and free roaming animals are particularly hazardous and a potential source of health problems in both urban and rural communities [5]. according to water aid (2012) over 2000 children die of diarrhea in africa daily. epidemics associated with water-borne diseases are common in most developing countries where access to basic amenities, especially safe drinking water, is lacking. potable water should be free from biological or chemical contaminants. it must be colourless, tasteless and odourless in accordance with the recommendations of world health organization [6]. however, according to [7], in most developing countries like nigeria, dangerous and very toxic wastes are disposed of by dumping them in rivers and streams with total disregard for aquatic life and rural dwellers. lack of information about the parasitic and pathogenic microorganisms in drinking water sources in our rural communities creates uncertainties in our understanding of the overall quality of the drinking water in these areas, and as a result, has prompted the need to undertake this research in accordance with the goal of the who on safe drinking water. to the best of our knowledge, no documented report has been made on parasitic contamination of local sources of drinking water in aba metropolis, abia state, nigeria and its public health implications. 2. materials and method 2.1 study area the study was carried out in aba metropolis. aba is a major settlement and commercial centre surrounded by small villages and towns in the southeast of nigeria. it is the largest clan and the main trading centre in abia state. aba is divided into two local government areas namely aba south and aba north. other local government areas are abosisioma and obingwa local government areas. aba has a population of 2,434, 265 as at the 2006 census [8] and is located between latitudes 5 o 07’n and longitude 7 o 22’e. aba north has its headquarters located in the town of eziama. aba south has its headquarter in the city of aba. it is characterized by a tropical climate with distinct dry and rainy seasons spanning from november to march and april to october respectively. the average temperature is 27 o c, the average humidity 90% and the annual rainfall 2,400 mm. the major crops cultivated in the area are yam, cassava, plantain and vegetables. the area is still developing, hence, adequate social and infrastructural amenities are lacking. sources of water for drinking and other domestic activities in the area include boreholes, streams, rivers, rain water and in some villages, well water. 2.2 ethical approval a letter of introduction was obtained from the head of the department of biology/ microbiology, abia state polytechnic, aba, abia state before the commencement of this work. permission of the authorities in charge was obtained for collection of water samples, after explaining the aim of the study. 2.3 sample collection ten samples each from five (5) different water sources were collected using sterile 500 ml glass bottles. each of the samples was collected at a different location within the different communities in 10 trips except for the rainwater which was collected each time rain fell during the period of the study. the samples which were collected between the months of august and october, 2018 include borehole water from randomly selected sampling sites in osusu, umungasi and eziama, in aba north local government area; stream water from okpulo–umobo and eziama in osisioma ngwa and aba north local government area respectively; shallow and deep well water, from umuocheala village in osisioma ngwa local government area, river water from ogbor hill, in aba south local government area and rain water from umuocham community, aba south local government area, all in aba metropolis. samples of water from the stream and river were collected during the early hours of the day (at about 9:00 am in the morning). the base of the sample bottle was held in one hand and the cap was carefully opened with the other hand covered with gloves and then plunged downwards below the surface of the water. samples of water from the boreholes were obtained by first sterilizing the mouth of the tap and allowing water to run for a few minutes before collecting water into the sample bottles. samples of water from the wells were obtained with help of the villagers who were given clean gloves to fetch water from each of the wells. the base of the sample bottle was held in one hand, the cap was carefully opened with the other hand and some of the water was carefully poured into the sample bottle. a total of 80 water w parasitic contamination of local drinking water sources 3 samples (30 borehole water samples from three different communities, 20 stream water samples from two communities, 10 river and well water samples from one community each and 10 samples of rain water from an autonomous community) were collected for the study and were transported to the department of biology/microbiology laboratory within two (2) hours (maximum transit time) of collection to abia state polytechnic aba, abia state for examination and analysis. 2.4 parasitological analysis each of the water samples was first subjected to macroscopic and physical examination to determine the ph using a ph meter, the temperature using a thermometer, the colour, the odour and the presence/ absence of debris. the water samples in each labeled container were shaken and passed through a filter sieve of 0.5 mesh size according to who guidelines. the filter was removed and particulate materials present discarded. the filtrate was poured into 10ml centrifuge tubes and centrifuged at 2500 rpm per minutes for 10 minutes. the test tubes were allowed to settle for a while after which the supernatant was discarded. a drop of the suspended sediment was placed on a clean grease free glass slide with a drop of lugol’s iodine solution using a pasteur pipette. the mixture was covered with a cover slip and examined microscopically using x10 and x 40 objective lenses to identify parasite eggs, larvae and cysts[9]. 2.5 data analysis comparative analysis of parasites in the various water samples was done using spss package version 22.0. the statistical analysis for significant differences was done using chi-square (x 2 ) placed at a significant level of p < 0.05. 3. results a total of eighty (80) water samples were collected from streams, boreholes, rivers, wells and rain water, out of which five (5) different parasites (protozoan and helminthes) were found. the species of parasites were in various stages of development, ranging from eggs and cysts to larvae. the macroscopic and physical examination of the various water samples showed that the temperatures of all the water samples were within the range of 27 º c and 29 º c and the ph values were within the range of 6.0–7.1. all the water samples analyzed except the well water were colourless and odourless. the stream, river and the well-water samples contained particles while the others were clear and particle-free (table 1). all the water sources except the rainwater from umuocham recorded at least two waterborne parasites. out of the five (5) different parasites encountered in this study, giardia lamblia was observed to have the highest rate of occurrence 15 (24.6%) followed by entamoeba histolytica which occurred at the rate of 14 (22.9%), hookworm was the least frequently occurring parasite 8 (13.1%) as shown in table 2. among the water sources, the streams had the highest rate of contamination with parasites 27 (44.3%) followed by the rivers 14 (22.9%) while the least contaminated were the boreholes 7 (11.5%). rain water had no parasite contamination 0(0.0%) as shown in figure 1. the differences in the level of contamination among the water sources were statistically significant (p < 0.05). figure 1. percentage occurrence of parasites in the drinking water sources. 11.5 44.3 21.3 22.9 0 0 5 10 15 20 25 30 35 40 45 50 borehole stream well river rain p e rc e n ta g e o cc u rr e n ce o f p a ra si te s (% ) sources of water blessing uzoamaka ejike et al. 4 table 1. macroscopic/physical parameters of the local water sources in aba metropolis. water sources temperature ph colour odour clear/ particles borehole (osusu) 28 ºc 7.1 colourless odourless clear without particles stream (okpu–umobo) 27 ºc 7.0 colourless odourless clear with brownish particles borehole (eziama) 28 ºc 6.9 colourless odourless clear without particles borehole (umungasi) 28 ºc 6.9 colourless odourless clear without particles stream (eziama) 27 ºc 6.5 colourless odourless clear with particles well (umuocheala) 27 ºc 6.5 pale yellowish brown odourless not clear with brownish particles rain (umuocham) 26 ºc 6.9 colourless odourless clear without particles river (ogbor-hill) 27 ºc 6.0 colourless odourless clear with whitish particles table 2. rate of occurrence of parasites in relation to the water sources in the study area. water sources no of samples ascaris lumbricoides e. coli g. lamblia e. histolytica hook worm total percentage occurrence (%) borehole (osusu) 10 `0 0 2 1 0 3 4.9 stream (okpu– umobo) 10 3 3 4 3 2 15 24.6 borehole (eziama) 10 0 0 1 0 1 2 3.3 borehole (umungasi) 10 0 0 1 1 0 2 3.3 stream (eziama) 10 3 3 2 2 2 12 19.7 well (umuocheala ) 10 3 4 2 3 1 13 21.3 rain (umuocham) 10 0 0 0 0 0 0 0 river (ogbor-hill) 10 2 3 3 4 2 14 22.9 total 80 11 13 15 14 8 61 100 (%) 18.0 21.3 24.6 22.9 13.1 4. discussion water sources contaminated with parasites are a threat to millions of people in developing countries, which result in severe morbidities and mortalities [1]. the prevalence of water-borne diseases is determined by the quality of drinking water. in this study, most of the drinking water sources were contaminated with water-borne parasites. these parasites were found in the different sources of drinking water at various rates of occurrence. the rural communities of the study area are therefore at risk of water-borne diseases due to the high rate of parasitic infestation of these water sources. this finding agrees with the reports of [10] and [11] who recorded degrees of contamination of local sources of drinking water in ebonyi state and nassarawa state, respectively. this is explained by the fact that natural bodies of water such as lakes, rivers and groundwater normally contain nutrients and certain microorganisms (bacteria, viruses, etc.) which have evolved to take advantage of this environment [12]. surface and ground water are subject to contamination by enteric water-borne pathogens which may come from leaking septic systems or improperly protected parasitic contamination of local drinking water sources 5 well heads. the presence of water-borne parasites in natural water bodies helps explain the tolerance adaptation of these parasites even to harsh conditions. the public health implication of these results is that water-borne parasites pose a serious hazard to human health and may result in outbreaks of water-borne diseases among the community dwellers. with the exception of well water and the river water, the physical parameters (temperature and ph) of the different water sources were slightly below the recommended limits of who [1] and nigerian standard for drinking water quality (nsdwq) [13] which is a ph range of 6.5-8.5. the river water with a ph of 6.0 suggests slight acidity of the water sample which could likely be due to the presence of organic matter such as microorganisms which generate excessive levels of carbon (iv) oxide [14]. the importance of water ph is to keep the body in balance and regulate metabolic processes. water with ph values less than or greater than 7 may cause aesthetic problems, hence the body is constantly working to achieve a balanced ph level [4]. the health implication of this is that the physical appearance of water, especially groundwater and surface water, does not guarantee its safety for drinking. the temperature values of all the water samples recorded ranged from 27 º c to 29 º c; these values were lower than the who stipulated maximum temperature level of 40 º c for potable water [1]. aside from the temperature and ph, colour in drinking water indicates the presence of organic substances such as humic substances while odour in water is caused by increased biological activity [1]. some of the water samples contained dirt and particles while others contained some coloured particles, as a result making the water unfit for drinking. the activities that go on within the area of these water sources, in addition to erosion and influx of surface water, could be reasons for their contamination [10]. three (3) water-borne protozoan parasites, entamoeba coli, giardia lamblia, entamoeba histolytica and two (2) helminth parasites, hookworm, and ascaris lumbricoides were identified in this study. the parasites were seen as fertilized eggs, cysts and larvae. the identification of these parasites agrees with the studies carried out by [10] in ebonyi state, nigeria and [14] in ankara, turkey on their drinking water sources. the public health implication of this finding is that water-borne parasite infections are considered a re-emerging threat. in developing countries like nigeria, water-borne parasites and protozoan pathogens such as cryptosporidium parvum, giardia lamblia, entamoeba histolytica, and many others are frequently associated with morbidity particularly in children. theses parasites are also the most common cause of infections worldwide [15, 16]. the world health organisation estimates that 88% of the burden of water related infections is attributed to unsafe water supply, sanitation and hygiene [2]. of all the water sources analyzed, the stream, river and well water were the most contaminated. this is not surprising because contaminants gain access into water bodies through human and animal faecal matter from patients and healthy carriers of parasitic diseases [4]. most of the inhabitants of eziama community, particularly those who live few meters away from the stream do not have adequate disposal systems for human waste, and as such defecate indiscriminately in places not far from their dwelling places, including directly on the soil or by the sides of the streams. this finding is similar to the report of [17] who observed that well water, pond and stream were the most contaminated water sources in some local government areas of plateau state, nigeria and [11] who also found out that a well water source had the highest prevalence rate of parasites in lafia local government area, nasarawa state, nigeria. transmission of parasites occurs when water is contaminated with the parasites [15]. excreta-related communicable diseases have also become a major problem in areas where untreated human faeces are used as manure as they are regularly washed into the communities’ water bodies [5]. unprotected surface water (such as rivers) or ground water (such as shallow wells) can become contaminated by human or animal faeces or agricultural effluent [15]. the data from this study also showed that borehole water was not completely free from water-borne parasites. the recovery of protozoan cysts in the samples analyzed clearly demonstrated the continued deterioration of the environment brought about by poor planning and uncontrolled property development in the area. a borehole that was sunk below 10 meters is more prone to faecal pollution from landfill and septic tank seepages and this is particularly true if the recharge point is located very close to the pit [16]. samples from rain water were found to be free from parasites; this is because water obtained from rainfall is usually covered after collection and was not fetched directly under the roof of the houses. this does not agree with the fact that parasitic infestation of water is contaminative. human parasites do not directly use water bodies for their life cycle development, rather, their vectors inhabit and associate their transmission with these water bodies [14]. giardia lamblia accounted for the most frequently occurring parasites in this study. giardia lamblia cysts may remain viable in water for long periods of time under typical environmental conditions depending on source water characteristics and water treatment practices [18]. its survival in water is dependent primarily on decreased water temperature [19]. protozoan cysts like entamoeba histolytica cysts can survive in water for several weeks [20,21,22].ascaris lumbricoides eggs and hookworm larvae were observed in this study. according to [20,21] helminthic ova can remain alive in cold water for months. the occurrence of intestinal parasites in water sources is prevalent among poor people in remote rural communities who lack proper toilet facilities, an adequate supply of potable drinking water and poor sewage and waste disposal systems [22]. the implications of these findings suggest that parasitic organisms are maintained by a viable ecosystem in remote settlements in nigeria, where toilet facilities, pipe borne water, poor sewage disposal, and illiteracy thrive the most. blessing uzoamaka ejike et al. 6 5. conclusion the results showed the extent of parasitic contamination of the various drinking water sources in aba metropolis and the susceptibility of the population to water-borne diseases. since almost all the water samples had varying levels of parasitic contamination, provision of well-treated potable water combined with the application of adequate operational practices are of utmost importance within the area and the state in general. the inhabitants of the area should also stop activities that lead to the contamination of the water bodies and boil their drinking water before consumption. infections by these parasites can result in serious parasitic diseases such as amoebic dysentery and gastrointestinal infection which may pose health risks as well as result in economic losses. conflict of interest the authors declare no conflict of interest. acknowledgement the authors are sincerely grateful to the technical staff at the microbiology laboratory, department of biology/microbiology, abia state polytechnic, aba, where this research was conducted, for their effort towards making it a success. references 1. world health organization. guidelines for drinking water quality. water safety and quality. 4 th edition incorporating the 1 st addendum by world health organisation. 2011 retrieved 2019-08-02. 2. world health organization 2008. guidelines for drinking water quality. safe water and global health. 3 rd edition by world health oragnisation. 2008. retrieved 2019-08-05. 3. yousefi, z., ziaei-hezarjaribi, h., enayati, a.a. and mohammadpoor, r.a. parasitic contamination of wells drinking water in mazandaran province. iranian journal of environmental health science and engineering, 2009, 6(4), 241-246. 4. adegoke, a. the challenges of environmental management in africa. the nigeria experience. an international journal of medical science, 2000, (2), 3. 5. ukoli, f.a. m. sanitation in africa: nigeria. an international journal of medical science, 2000, (2), 25-28. 6. world health organisation.who guidelines for drinking water quality. 2015. retrieved july 21 st 2019, from https://www.whoguidelinesfordrinkingwaterquality. 7. curry, a. and smith, h.v. emerging pathogens: isospora, cyclospora and microsporidia. parasitology, 1998, 117, 143-159. 8. national population commission of nigeria (2006). volume 1 of the national population census, pp 15. accessed december 15, 2019, from http://www.population.gov.ng/index.php/80-puplications. 9. cheesbrough, m. district laboratory practice in tropical countries part i. cambridge university press, united kingdom, 2004, 178-209. 10. odikamnoro, o.o., omowaye, o.s. and udu-ituma, s.o. parasitic survey of drinking water source in ohaukwu local government area, ebonyi state, nigeria. european journal of nursing, 2014, 1(1), 1-5. 11. gyang, p.r., uzoigwe, n.r., ayim, j.o., ombugadu, a. and ahmed, h.o. evaluation of local drinking water sources to determine their possible contamination with parasite in lafia local government area nasarawa state, nigeria. european journal of basic and applied sciences, 2017, 4(1), 63-68. 12. world health organization. guidelines for the safe use of waste water, excreta and greywater-volume; waste water use in agriculture who, geneva, 2006. 13. standards organization of nigeria (son), nigerian standard for drinking water quality, son publication, abuja, nigeria, 2007, 15-16. 14. bakir, b., tanyukseel, m., saylam, f., tanriverdis, s., araz, r.e., hacim, a.k. and hasde, m. 2003. investigation of waterborne parasites in drinking water source of ankara, turkey. journal of microbiology, 2003, 41(2), 148-151. 15. efstratiou, a., ongerth, j.e. and karanis, p. water-borne transmission of protozoan parasites: review of worldwide outbreaks – an update 2011-2016. water research, 2017, 114, 14-22. 16. tanyuksel, m., tachibana, h. and petro, w.a. amoebiasis, an emerging disease. american society of microbiology, 2001, 1, 197-212. 17. chollom, s.c., iduh, m.u., gyang, b.j., idoko, m.a., ujah, a., aga, g.o., peter, j., akele, y.r. and okwori, j. a. 2013. parasitological evaluation of domestic water sources in a rural community in nigeria. british microbiology research journal, 2013, 3(3), 393-399. 18. jones, j.g. freshwater ecosystems-structure and response. ecotoxicology and environmental safety, 2001, 50, 107-13. 19. centers for disease control and prevention. safe water system for the developing world: a handbook for implementing household-based water treatment and safe storage projects, atlanta, g.a., usa, p187. 2000. https://www.whoguidelinesfordrinkingwaterquality/ http://www.population.gov.ng/index.php/80-puplications parasitic contamination of local drinking water sources 7 20. aroh, k.n., sagay, h.o., obieze, c.c., ubong, i.u., eze, c.l. and abam, t.k.s. a survey of bore hole water quality for possible water-borne parasites in diobu community in southern nigeria. african journal of environmental pollution and health, 2006, 5(1), 16-22 . 21. arnold, b.f. and colford, j.m. treating water with chlorine at pointof -use to improve water quality and reduce child diarrhea on developing countries. a systematic review and meta analysis. american. journal of tropical medicine and hygiene, 2007, 76, 354-365. 22. eseigbe, a.p., ibhadode, o., ayoola, a.r. and sosanolu, o.m. experimental determination of drinking water quality in abeokuta metropolis, south-western nigeria. international journal of advances in scientific research and engineering, 2018, 4(12), 241-6. received 31 august 2020 accepted 14 january 2021 squ journal for science, 2015, 19(2), 55-61 © 2014 sultan qaboos university 55 a unique common coupled fixed point theorem for four maps in partial b-metriclike spaces mohammad s. khan 1 *, konduru p.r. rao 2 and kandipalli v.s. parvathi 3 1 department of mathematics and statistics, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. 2 department of mathematics, acharya nagarjuna university, nagarjuna nagar -522 510, a.p., india. 3 department of applied mathematics,krishna university-m.r.appa row p.g.center, nuzvid-521 201, andhra pradesh, india. *email: mohammad@squ.edu.om. abstract: we prove the existence of a unique common coupled fixed point theorem for four mappings satisfying a general contractive condition on partial b-metric-like spaces. we also give an example to illustrate our main theorem. our theorem generalizes and improves the theorem of [1]. keywords: b-metric-like space; coupled fixed point; w-compatible maps. ب الجزئي الفراغ شبه فيالربعة اقترانات العامة المزدوجة الثابتة النقطة نظرية كانذورو ب.ر.راو و كانذيبالي ف.س. برافاثي ، محمذ سعيذ خان تحقق شزوط االنقباض العامة على شبو الفزاغ الجزئي ألربعة إقتزانات نظزية وجود نقطة ثابتة مزدوجة عامة بإثبات في ىذه الورقة قمنا ملخص: .[1]نظزيتنا ىي تعميم و تحديث للنظزية المثبتة في .مثاال لتوضيح نظزيتنا الزئيسيةأحضزنا ب. و قد w.المتوافقة توافق الدوال و مزدوجة ثابتة نقطة ، الجزئي ب الفزاغ شبو : كلمات مفتاحية 1. introduction and preliminaries he concept of b-metric space was introduced by czerwik [2] as follows: definition 1.1 [2]: a b-metric on a non-empty set x is a function d : x × x → [0, ∞) such that for all x, y, z ε x and a constant k ≥ 1 the following three conditions hold true: (i) d(x, y) = 0 if and only if x = y, (ii) d(x, y) = d(y, x), (iii) d(x, y) ≤ k [d(x, z) + d(z, y)] . the triad (x, d, k) is called a b-metric space. alghamdi et al. [3] introduced the concept of b-metric -like spaces and proved some fixed point theorems for a single map. definition 1.2 [3]: a b-metric-like on a non-empty set x is a function d : x × x → [0, ∞) such that for all x, y, z ε x and a constant k ≥ 1 the following three conditions hold true: (i) d(x, y) = 0 implies x = y, (ii) d(x, y) = d(y, x), (iii) d(x, y) ≤ k[d(x, z) + d(z, y)] . the triad (x, d, k) is called a b-metric-like space. mathews [4] introduced the concept of a partial metric space as follows: definition 1.3 [4]: a mapping p : x × x → [0, ∞), where x is a non-empty set, is said to be a partial metric on x if for any x, y, z ε x the following are satisfied: (i) x = y if and only if p(x, x) = p(x, y) = p(y, y), (ii) p(x, x) ≤ p(x, y) , (iii) p(x, y) = p(y, x), t mailto:mohammad@squ.edu.om mohammad s. khan et al. 56 (iv) p(x, y) ≤ p(x, z) + p(z, y) − p(z, z). the pair (x, p) is called a partial metric space. now we give the following definition by combining the definitions 1.2 and 1.3. definition 1.4: a partial b-metric-like on a non-empty set x is a function p : x × x → [0, ∞) such that for all x, y, z ε x and a constant k ≥ 1 the following are satisfied: (p1) p(x, y) = 0 implies x = y, (p2) p(x, x) ≤ p(x, y), p(y, y) ≤ p(x, y), (p3) p(x, y) = p(y, x), (p4) p(x, y) ≤ k[p(x, z) + p(z, y) − p(z, z)]. the triad (x, p, k) is called a partial b-metric-like space. definition 1.5: let (x, p, k) be a partial b-metric-like space and let {xn} be a sequence in x and x ε x. the sequence {xn} is said to be convergent to x if n lim p(xn, x) = p(x, x). definition 1.6: let (x, p, k) be a partial b-metric-like space. (i) a sequence {xn} in (x, p, k) is said to be a cauchy sequence if mn, lim p(xn, xm) exists and is finite . (ii) a partial b-metric-like space (x, p, k) is said to be complete if every cauchy sequence {xn} in x converges to a point x ε x so that mn, lim p(xn, xm) = p(x, x) = n lim p(xn, x). one can prove easily the following remark. remark 1.7: let (x, p, k) be a partial b-metric-like space and {xn} be a sequence in x such that n lim p(xn, x) = 0. then (i) x is unique , (ii) k 1 p(x, y) ≤ n lim p(xn, y) ≤ k p(x, y) for all y ε x , (iii) p(xn, x0) ≤ kp(x0, x1) + k 2 p(x1, x2) + ··· + k n−1 p(xn−2, xn−1) + k n p(xn−1, xn) whenever  kx n k 0 ε x. let (x, p, k) be a partial b-metric-like space and f, g : x × x and f, g : x → x. for x, y, u, v ε x, we denote x,y u,v p(fx, gu), p(fy, gv), p(fx, f (x, y)), p(fy, f (y, x)), p(gu, g(u, v)), p(gv, g(v, u)), 1 min [p(fx, g(u, v)) + p(gu, f (x, y))], 2k 1 [p(fy, g(v, u)) + p(gv, f (y, x))] 2k .m                    and , , p(fx, f (x, y)), p(fy, f (y, x)), p(gu, g(u, v)), p(gv, g(v, u)), 1 1 max p(fx, g(u, v)), p(gu, f (x, y)), k k 1 1 p(fy, g(v, u)), p(gv, f (y, x)) k k . x y u vm                    recently bhaskar and lakshmikantham [5] introduced the concept of coupled fixed point and discussed some problems of the uniqueness of a coupled fixed point and applied their results to the problems of the existence and uniqueness of a solution for the periodic boundary value problems. later lakshmikantham and ciric [6] proved some coupled coincidence and coupled common fixed point results in partially ordered metric spaces. a unique common coupled fixed point theorem 57 definition 1.8 [6] an element (x, y) ε x × x is called (i) a coupled coincident point of mappings f : x×x → x and g: x → x if gx = f (x, y) and gy = f (y, x). (ii) a common coupled fixed point of mappings f : x × x → x and g : x → x if x = gx = f (x, y) and y = gy = f (y, x) . definition 1.9 [7] the mappings f : x × x → x and g : x → x are called w-compatible if g(f (x, y)) = f (gx, gy) and g(f (y, x)) = f (gy, gx), whenever gx = f (x, y) and gy = f (y, x). recently, abbas et al. [8] proved a common fixed point theorem for two maps of jungck type satisfying generalized condition (b) in metric spaces (see theorem 2.2, [8]). as a generalization of theorem 2.2 of [8], kaewcharoen et al. [1] obtained a common fixed point theorem for four maps satisfying a generalized condition in partial metric spaces. in this paper, we obtain the existence of a unique common coupled fixed point theorem for four mappings satisfying a general contractive condition on partial b-metric-like spaces. we also give an example to illustrate our main theorem. our theorem generalizes and improves the theorems of [1] and [8]. 2. main result theorem 2.1: let (x, p, k) be a complete partial b-metric-like space, f, g : x × x → x and f, g : x → x be mappings satisfying (2.1.1) f (x × x)  g(x), g(x × x)  f(x), (2.1.2) k p(f(x,y),g(u,v)) ≤ δ , , x y u vm + l , , x y u vm for all x, y, u, v ε x, where δ > 0 and l ≥ 0, k l < 1, where l = max         l l   , 1 , (2.1.3) f(x) or g(x) is closed, (2.1.4) the pairs (f, f), and (g, g) are w-compatible. then f, g, f and g have a unique common coupled fixed point. proof. let (x0, y0) ε x × x. since f (x × x)  g(x), there exist x1, y1 ε x such that gx1 = f (x0, y0) and gy1 = f (y0, x0). since g (x × x)  f(x), there exist x2, y2 ε x such that fx2 = g(x1, y1) and fy2 = g(y1, x1). continuing this process, we construct sequences {xn} and {yn} in x such that gx2n+1 = f (x2n, y2n) = z2n, gy2n+1 = f (y2n, x2n) = w2n, fx2n+2 = g(x2n+1, y2n+1) = z2n+1, fy2n+2 = f (y2n+1, x2n+1) = w2n+1, n = 0, 1, 2, 3, ··· now consider p(z2n, z2n+1) ≤ k p(f (x2n, y2n), g(x2n+1, y2n+1)) ≤ 2 2 2 1 2 1 2 2 2 1 2 1 , , , , n n n n n n n n x y x y x y x y lm m     (1) where 2 2 2 1 2 1 , , n n n n x y x ym   2 1 2n 2 1 2n 2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 2 1 2n+1 2n 2n 2 1 2n+1 2n 2n p(z , z ), p(w , w ), p(z , z ), p(w , w ), p(z ,z ), p(w ,w ), 1 max [p(z , z ) + p(z , z )], 2k 1 [p(w , w ) + p(w , w )] 2k n n n n n n                    ≤ max 2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 p(z , z ), p(w , w ), p(z ,z ), p(w ,w ) n n -      from k ≥ 1 and from (p4) mohammad s. khan et al. 58 2 2 2 1 2 1 , , n n n n x y x ym   2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 2 1 2n+1 2n 2n 2 1 2n+1 2n 2n p(z , z ), p(w , w ), p(z ,z ), p(w ,w ), 1 1 min p(z , z ) , p(z , z ), k k 1 1 p(w , w ), p(w , w ) k k n n n n                    2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 2 1 2n 2 2n+1 2n 2n 2 1 2n 2 2n+1 2n 2n p(z , z ), p(w , w ),p(z ,z ), min p(w ,w ), p(z , z ) p(z , z ) , p(z , z ),p(w , w ) p(w , w ), p(w , w ) n n n n n n              = min {p(z2n, z2n), p(w2n, w2n)}, from (p2) ≤ max {p(z2n, z2n), p(w2n, w2n)} ≤ max {p(z2n, z2n-1), p(w2n, w2n-1)}, from (p2). thus p(z2n, z2n+1) ≤ δ max 2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 p(z , z ), p(w , w ), p(z ,z ), p(w ,w ) n n -      + l max{p(z2n, z2n-1), p(w2n, w2n-1)}. similarly p(w2n,w2n+1) ≤ δ max 2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 p(z , z ), p(w , w ), p(z ,z ), p(w ,w ) n n -      + l max{p(z2n, z2n-1), p(w2n, w2n-1)}. thus max 2 2n 1 2n 2n+1 p(z , z ), p(w ,w ) n       ≤ δ max 2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 p(z , z ), p(w , w ), p(z ,z ), p(w ,w ) n n -      + l max 2 2n 1 2n 2n-1 p(z , z ), p(w ,w ) n       (2) if max 2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 p(z , z ), p(w , w ), p(z ,z ), p(w ,w ) n n -      ≤ max 2 2n 1 2n 2n+1 p(z , z ), p(w ,w ) n       , then from (2) max {p(z2n, z2n+1), p(w2n, w2n+1)} ≤ 1 l  max { p(z2n−1, z2n), p(w2n−1, w2n)}. if max 2 1 2n 2 1 2n 2n 2n+1 2n 2n+1 p(z , z ), p(w , w ), p(z ,z ), p(w ,w ) n n -      ≤ max 2 1 2n 2n-1 2n p(z , z ), p(w ,w ) n       , then from (2) max{ p(z2n, z2n+1), p(w2n, w2n+1)} ≤ (δ + l) max{ p(z2n−1, z2n), p(w2n−1, w2n)}. hence max {p(z2n, z2n+1), p(w2n, w2n+1) } ≤ l max {p(z2n−1, z2n), p(w2n−1, w2n)} where l = max  , 1 l l    < 1. similarly we can show that max{p(z2n−1, z2n), p(w2n−1, w2n) } ≤ l max { p(z2n−2, z2n−1), p(w2n−2, w2n−1)}. hence max {p(zn, zn+1), p(wn, wn+1)} ≤ l max { p(zn−1, zn), p(wn−1, wn)} , n = 1, 2, 3, ··· thus max{ p(zn, zn+1), p(wn, wn+1) } ≤ l n max{ p(z0, z1), p(w0, w1)}. (3) from (3), it follows that lim n p(zn, zn+1) = 0 = lim n p(wn, wn+1). (4) for m > n, consider max {p(zn, zm), p(wn, wm)} ≤ max 2 m-n-1 m-n-1 n n 1 n 1 n 2 m-2 m-1 m-1 m 2 m-n-1 m-n-1 n n 1 n 1 n 2 m-2 m-1 m-1 m k p(z ,z ) k p(z ,z ) ... k p(z ,z ) k p(z ,z ), k p(w ,w ) k p(w ,w ) ... k p(w ,w ) k p(w ,w )                     ≤ k max {p(zn, zn+1), p(wn, wn+1)} + k 2 max {p(zn+1, zn+2), p(wn+1, wn+2)} + .... + k m−n−1 max {p(zm−2, zm−1), p(wm−2, wm−1)} + k m−n−1 max {p(zm−1, zm), p(wm−1, wm)} a unique common coupled fixed point theorem 59 ≤  112112 ....   mnmmnmnn lklklkkl max 0 1 0 1 p(z , z ), p(w ,w )       =  1222221 ....1   nmnmnmnmn lklklkklkl max 0 1 0 1 p(z , z ), p(w ,w )       ≤  1122221 ....1   nmnmnmnmn lklklkklkl max 0 1 0 1 p(z , z ), p(w ,w )       ≤ 1 n kl kl max 0 1 0 1 p(z , z ), p(w ,w )       , since kl < 1. hence , iml n m p(zn, zm) = 0 = , lim n m p(wn, wm). (5) thus {zn} and {wn} are cauchy in (x, p, k). since x is complete, the sequences {zn} and {wn} converge to some α and β in x respectively such that , iml n m p(zn, zm) = p(α, α) and , iml n m p(wn, wm) = p(β, β). also lim n p(zn, α) = p(α, α) and lim n p(wn, β) = p(β, β). now from (5), we have p(α, α) = 0 = p(β, β). (6) suppose f(x) is closed. since fx2n+2 = z2n+1 → α and fy2n+2 = w2n+1 → β, it follows that α = fu and β = fv for some u, v ε x. consider p(α, f (u, v)) ≤ kp(α, z2n+1) + kp(f (u, v), g(x2n+1, y2n+1)) ≤ kp(α, z2n+1) + δ 2 1 2 1 , ,n n u v x ym   + l 2 1 2 1 , ,n n u v x ym   2 1 2 1 , ,n n u v x ym   2n 2n 2n 2n+1 2n 2n+1 2n+1 2n 2n+1 2n p(fu, z ), p(fv, w ), p(fu, f(u, v)), p(fv, f(v, u)), p(z ,z ), p(w ,w ), 1 max [p(fu, z ) + p(z , f(u, v))], 2k 1 [p(fv, w ) + p(w , f(v, u)] 2k                    0, 0, p( , f(u, v)), p( , f(v, u)), 0, 0, 1 max [0 + p( , f(u, v))], 2k 1 [0 + p( , f(v, u)] 2k                        , from (4) and remark 1.7 (ii) = max { p(α, f (u, v)), p(β, f (v, u))}. also 2 1 2 1 , ,n n u v x ym   → 0. thus p(α, f (u, v)) ≤ δ max {p(α, f (u, v)), p(β, f (v, u))} . similarly we can show that p(β, f (u, v)) ≤ δ max {p(α, f (u, v)), p(β, f (v, u))} . hence max {p(α, f (u, v)), p(β, f (v, u))} ≤ δ max {p(α, f (u, v)), p(β, f (v, u))}, which in turn yields that α = f (u, v) and β = f (v, u). thus fu = α = f (u, v) and fv = β = f (v, u). since the pair (f, f) is wcompatible, we have fα = f (α, β) and fβ = f (β, α). (7) since α = f (u, v) ε f (x × x)  g(x), there exists r ε x such that α = gr. since β = f (v, u) ε f (x × x)  g(x), there exists t ε x such that β = gt. mohammad s. khan et al. 60 now p(α, g(r, t)) ≤ s p(f (u, v), g(r, t)) ≤ δ , , u v r tm + l , , u v r tm , , u v r tm p(fu, gr), p(fv, gt), p(fu, f(u, v)), p(fv, f(v, u)), p(gr, g(r, t)), p(gt, g(t,r)), 1 max [p(fu, g(r, t)) + p(gr, f(u, v))], 2k 1 [p(fv, g(t, r)) + p(gt, f(v, u)] 2k                    0, 0, 0, 0 p( , g(r, t)), p( , g(t,r)), 1 max [p( , g(r, t)) + p( , f(u, v))], 2k 1 [p( , g(t, r)) + p( , f(v, u)] 2k                          = max{ p(α, g(r, t)), p(β, g (t, r))}. , , u v r tm = 0. thus p(α, g(r, t)) ≤ δ max {p(α, g(r, t)), p(β, g(t, r))} . similarly we can show that p(β, g(t, r)) ≤ δ max {p(α, g(r, t)), p(β, g(t, r))} . hence max {p(α, g(r, t)), p(β, g(t, r))} ≤ δ max {p(α, g(r, t)), p(β, g(t, r))} which in turn yields that gr = α = g(r, t) and gt = β = g(t, r). since the pair (g, g) is w-compatible, we have gα = g(α, β) and gβ = g(β, α). now consider p(fα, α) ≤ k p(f (α, β), g(r, t)) ≤ δ , ,r tm   + l , ,r tm   , ,r tm   p(f , gr), p(f , gt), p(f , f( , )), p(f , f( , )), p(gr, g(r, t)), p(gt, g(t,r)), 1 max [p(f , g(r, t)) + p(gr, f( , ))], 2k 1 [p(f , g(t, r)) + p(gt, f( , ))] 2k                                  p(f , ), p(f , ), 0, 0, 0, 0, 1 max [p(f , ) + p( , f ) ], 2k 1 [p(f , ) + p( , f )] 2k                               . = max { p(fα, α), p(fβ, β)}. also , ,r tm   = 0. thus p(fα,α) ≤ δ max {p(fα, α), p(fβ, β)}. similarly we can show that p(fβ, β) ≤ δ max {p(fα, α), p(fβ, β)} . hence max {p(fα, α), p(fβ, β)} ≤ δ max {p(fα, α), p(fβ, β)} which in turn yields that fα = α and fβ = β. similarly we can show that gα = α and gβ = β. thus a unique common coupled fixed point theorem 61 f (α, β) = fα = α = gα = g(α, β) and f (β, α) = fβ = β = gβ = g(β, α). hence (α, β) is a common coupled fixed point of f, g, f and g. uniqueness of this common coupled fixed point follows easily from (2.1.2). now, we give an example to illustrate our main theorem 2.1. example 2.2 let x = [0, 1] and p(x, y) = max{x 2 , y 2 }. then (x, p, k) is a complete partial b-metric-like space with k = 2. define f, g : x × x → x and f, g : x → x as f(x, y) = 0, g(x, y) = 4 x , fx = 2 x and gx = x. then k p(f(x, y), g(u, v)) = 2 max 2 0, 16 u      = 2 8 u , p(gu, g(u, v)) = max 2 2 , 16 u u       = u 2 . thus p(f (x, y), g(u, v)) = 1 8 u 2 = 1 8 p(gu, g(u, v)) ≤ 1 8 , , x y u vm + 0 , , x y u vm . here δ = 1 8 , l = 0, k l = 1 4 < 1. clearly (2.1.1), (2.1.3) and (2.1.4) are satisfied and (0, 0) is the unique common coupled fixed point of f, g, f and g. theorem 2.1 is a generalization and improvement of the following: theorem 2.3 (theorem 2.1, [1]): let (x, p) be a complete partial metric space. suppose that f, g, f, g : x → x satisfying the following conditions (2.3.1) f(x)  g(x) and f (x)  g(x), (2.3.2) there exist δ > 0 and l ≥ 0 with δ + 2l < 1 such that p(fx, fy) ≤ δ m(x, y) + l min{p(gx, fx), p(gy, fy), p(gx, fy), gy, fx)} for all x, y ε x, where m(x, y) = max{p(gx, gy), p(gx, fx), p(gy, fy), 1 2 [p(gx, fy) + p(gy, fx)]}, (2.3.3)f(x) or g(x) is closed and (2.3.4) the pairs (f, g) and (g, f ) are w-compatible. then f, g, f and g have a unique common fixed point in x. acknowledgement the authors are thankful to the referees for their valuable suggestions in improving the manuscript. references 1. kaewcharoen, a. and yuying, t. unique common fixed point theorems on partial metric spaces. j. nonlinear sciences and applications, 2014, 7, 90-101. 2. czerwik, s. contraction mappings in b-metric spaces. acta math. inf. univ. ostraviensis, 1993, 1, 5-11. 3. alghamdi, m., ali hussain, n. and salimi, p. fixed point and coupled fixed point theorems on b-metric-like spaces. j. inequalities and applications, 2013, 402, 25 pages. 4. matthews, s.g. partial metric topology, proc. 8th summer conference on general topology and applications. ann. new york acad. sci., 1994, 728, 183-197. 5. bhaskar, t.g. and lakshmikantham, v. fixed point theorems in partially ordered metric spaces and applications. nonlinear anal., 2006, 65(7), 1379-1393. 6. lakshmikantham, v. and ciric, lj. coupled fixed point theorems for non-linear contractions in partially ordered metric spaces, nonlinear analysis: theory, methods and applications, 2009, 70(12), 4341-4349. 7. abbas, m.a.. khan, m. and radenovic, s. common coupled fixed point theorems in cone metric spaces for w-compatible mappings. appl. mathematics and computation, 2010, 217(1), 195-202. 8. abbas, m. babu, g.v.r. and alemayelu, g.n. on common fixed points of weakly compatible mappings satisfying generalized condition(b). filomat, 2011, 25(2), 9-19. received 24 august 2014 accepted 20 december 2014 squ journal for science, 2016, 21(1), 7-15 © 2016 sultan qaboos university 7 comparison of chemical composition and antioxidant activity of four essential oils extracted from different parts of juniperus excelsa saleh n. al-busafi*, salim h. al-saidi, amani i. al-riyami and nawal s. al-manthary department of chemistry, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman.*email: saleh1@squ.edu.om. abstract: the chemical contents and compositions of four essential oils extracted from leaves, branches, fruits and gum-resin of juniperus excelsa from jabal al-akhdhar in the sultanate of oman were studied using infra-red (ir) spectroscopy and gas chromatography-mass spectrometry (gc-ms). ir analysis revealed the presence of c-h, o-h, c=c and c=o functionality bonds with varied intensities. the gc-ms study showed the occurrence of 35 different monoterpenes of which 11 (31.43%) monoterpenes were shared by the four oils. α-pinene was detected in branches and gum-resin oils as a major compound with different proportions (80.50% in gum oil and 79.03% in branches oil). the major component in leaf and fruit oils was the monoterpene limonene with proportions of 50.46% and 42.51%, respectively. sesquiterpenes exist in leaf, branch and fruit essential oils but not in gum-resin oil. the essential oil of the leaves showed stronger antioxidant and radical scavenging activities than the other oils. keywords: juniperus excelsa; essential oil; gc-ms analysis; monoterpenes; antioxidant; dpph radical scavenging. مقاروت المحتوى الكَمَائٌ ودراست القذرة علي تثبَط التأكسذ ألربعت سٍوث عطزٍت مستخلصت مه أجشاء مختلفت مه شجزة العلعالن ، سالم السعَذً، أماوٌ الزٍامٌ، ووال المىذرًصالح البوصافٌ (juniperus excelsa)حن دراست الوحخْٓ الكيويائي ألربؼت سيْث ػطزيت هسخخلصت هي أّراق ّأغصاى ّثوار ّلباى شجزة الؼلؼالى :الملخص الغاس الوزحبظ بجِاس كشف الكخلت. لقذ كشف لٌا الوٌخشزة في الجبل األخضز في سلطٌت ػواى باسخخذام طيف األشؼت ححج الحوزاء ّ كزّهاحْجزافيا بٌسب هخفاّحَ. بيٌوا c-h, o-h, c=c, c=oجِاس طيف األشؼت ححج الحوزاء ػي ّجْد الزّابظ الكيويائيت الخاليت في هزكباث الشيْث الؼطزيت: هزّكب 11ث في الشيْث الؼطزيت األربؼت هٌِا هزكب كيويائي هخخلف هي ًْع الوًْْحيزبيٌا 53كشف جِاس الكزّهاحْجزافيا الغاسيت ػي ّجْد %79.03في سيج لباى الؼلؼالى ّ 5008.بيٌيي يْجذ في سيج األغصاى ّاللباى كجشء اساسي بكوياث هخخلفت: % -( هشخزك. هزّكب الفا31.43%) . يوخاس سيج لباى %42.5يج الثوار بٌسبت ّفي س% 50.46 في سيج أغصاى الٌباث بيٌوا يْجذ هزّكب الليوًْيي بكثزة في سيج األّراق بٌسبت لؼلؼالى الؼلؼالى بؼذم ّجْد هزّكباث السيسكْيخزبيي بيٌوا حْجذ ُذٍ الوزكباث بٌسب هخفاّحت في الشيْث الثالثت األخزٓ. يظِز سيج أّراق شجزة ا ًشاط أكبز ػلٔ كبح الخأكسذ هقارًت هغ الشيْث األخزٓ. .الؼلؼالى، سيْث طيارة، الكزّهاحْجزافيا الغاسيت، الوًْْحيزبيٌاث، حثبيج الخأكسذشجزة :الكلماث المفتاحَت 1. introduction he juniper tree (juniperus excelsa) grows at an altitude of about 2,300 m on jabal al-akhdar (sultanate of oman) in an open dry mountain forest under suitable conditions [1]. in addition, j. excelsa can be found throughout the eastern mediterranean from northeastern greece and southern bulgaria across turkey to syria [2], and in the mountains of iran, pakistan, saudi arabia, and yemen [3]. traditionally, j. excelsa is used in folk medicine to treat different ailments such as abdominal rigidity, asthma, fever, headache, diabetes and leucorrhoea [4,6]. in other parts of the world, the plant is considered useful as an antihypertensive, diuretic, appetizer, carminative, stimulant, anticonvulsant, flavoring agent, and as a remedy for tuberculosis [7,8]. bioactivity studies performed on j. excelsa have revealed antibacterial [9], antifungal [10], and bronchodilatory activities [11]. sandracopimaric acid, a diterpene isolated from j. excelsa was found to exhibit significant antibacterial activity against bacillus subtilis, staphylococcus aureus and streptococcus durans [12]. t mailto:saleh1@squ.edu.om mailto:saleh1@squ.edu.om saleh n. al-busafi et al. 8 moreover, hexane extract of the berries of j. excelsa exhibited potent activity against a human colon cancer cell line [13]. chemical compositions of essential oil of j. excelsa leaves and fruits have revealed diverse ratios of monoterpenes and sesquiterpenes from one region to another. in this regard, chemical analysis of the essential oil of the leaves of j. excelsa from the crimea revealed the presence of -pinene (56.2%), limonene (10.4%), -3-carene (3.1%), camphene (2.9%), -pinene (1.2%), -terpinene (1.9%) and terpinolene (0.8%) [14]. the essential oil (eo) extracted from the leaves of j. excelsa from jammu (india) was reported to contain sabinene (36.1%) and cedrol (26.8%) as the major components [15]. chemical analysis of the leaf oil of j. excelsa from greece revealed the presence of cedrol (28.1%), -pinene (22.5%) and limonene (22.7%) as the major components [16]. the essential oil extracted from the j. excelsa fruits of iran origin showed -pinene (89.5%), myrcene (2.6%), germacrene (2.2%), and limonene (1.3%) with other minor components [17]. essential oil of the leaves of j. excelsa from oman has been found to possess limonene (49.6%), germacrene (9.6%), -3-carene (5.9%), αpinene (4.81%) and γ-cadinene (3.76%) [18]. in addition, the juniper tree produces gum-resin that appears on the surface of the branches. the chemical compositions of the essential oil extracted from the gum-resin of j. excelsa have not yet been described in the literature. in this study we analyzed the chemical contents and compositions of the essential oil of the gum-resin of j. excelsa along with essential oils of the leaves, branches and fruits using ir spectroscopy and gc-ms spectrometry. additionally, the four extracted materials were subjected to antioxidant and radical scavenging activity tests. 2. materials and methods 2.1 plant materials gum resin, leaves, branches and fruits of j. excelsa were collected in october 2013 at jabal al-akhdhar, sultanate of oman. the plant was botanically identified by dr. amina al-farsi at the botanical section of the life science unit, college of science, sultan qaboos university. 2.2 extraction of volatile oil fresh 70.2 g, 152.0 g, 212.0 g and 230.4 g samples of gum-resin, leaves, branches and fruits, respectively, of j. excelsa were subjected to hydro distillation using clevenger’s apparatus until complete exhaustion to yield 3.1 g (4.4%), 0.41 g (0.27%), 0.68 g (0.32%) and 1.2 g (0.52%) of essential oils respectively. the obtained oils were collected, dried over magnesium sulphate and kept at 4 0 c until analysis. the isolation percentage was calculated based upon the weight of the fresh materials used. ir spectra were obtained using the neat liquid method with a nicolet model magna 560 spectrometer; absorption bands are recorded in wave number (cm -1 ). 2.3 gas chromatography-mass spectrometry the gc-ms analyses were carried out with a shimadzu gc-ms-qp/5050a apparatus equipped with a quadrupole mass spectrometer and a j&w scientific db-5ms (5% phenyl / 95% dimethylpolysiloxane) fused-silica capillary column (30 m x 0.25 mm i.d. x 0.25 mm film thickness). the oven temperature was programmed to increase from 31˚c to 271˚c at 3 ˚c /min. injector and interface temperatures were kept at 275 ˚c and 300 ˚c respectively. helium was used as carrier gas with a linear velocity of 44.6 cm/s, column flow rate of 1.5 ml/min and total flow rate of 36 ml/min. the split ratio was 1:21. mass spectra were continuously recorded over the mass range 35 to 501 amu. the ms operating parameters were as follows: ionization voltage 70 ev and scan rate 500 amu/s. the oil constituents were identified by comparison of their kovat’s relative retention indices (ris), determined relative to the retention times (tr) of a homologous series of n-alkanes (c8 – c30), with those reported in the literature. additionally, the mass spectra obtained were compared to those recorded in the computer ms library (wiley 229,000 database). the percentage composition was determined by using the single area percentage method without considering corrections for response factors. 2.4 evaluation of total antioxidant activity by the phosphomolybdenum method the antioxidant activity of the essential oils was evaluated by the phosphomolybdenum method according to the procedure of prieto et al. [19]. an aliquot of 0.3 ml of sample solution (1 mm in methanol) was combined in a 4 ml vial with 3 ml of reagent solution (0.6 m sulfuric acid, 28 mm sodium phosphate and 4 mm ammonium molybdate). the vials were capped and incubated in a water bath at 95 °c for 90 min. after the samples had cooled to room temperature, the absorbance of the mixture was measured at 695 nm against a blank. triplicate measurements were made and the antioxidant activity was expressed as ascorbic acid (aa) equivalent using the following linear equation established using ascorbic acid as standard: [a = 0.0013 c + 0.049; r 2 = 0.974] where a is the absorbance at 695 nm and c the concentration of ascorbic acid (mg/l). the values are presented as the means of triplicate analysis. comparison of chemical composition and antioxidant activity 9 2.5 free radical scavenging activity (dpph, 2,2-diphenyl-1-picrylhydrazyl) the free radical scavenging activity of the essential oils was determined by the dpph free radical method [20]. a 2.0 ml methanolic solution of dpph (0.1 mm) was mixed with 0.1 ml of oil solution (0.1 mg/ml) in methanol and, after standing for 60 min, the absorbance of the mixture was measured at 517 nm against methanol as the blank. triplicate measurements were made and the radical scavenging activity was calculated by the percentage of dpph that was scavenged using the following formula: % reduction = [(ab – aa)/ab] x 100, where ab is the absorption of blank sample and aa is the absorption of tested oil solution. 3. results and discussion the essential oils of different parts of j. excelsa were obtained by conventional hydrodistillation of the crushed fresh materials. the essential oil of the gum-resin of j. excelsa (4.4%) was a colorless oil which solidified with time to a white solid. this behavior can be attributed to the high percentage of oxygenated monoterpenes compared with other essential oils (table 2). the essential oil of the leaves of j. excelsa (0.27%) was colorless oil which stayed liquid on standing. the essential oils of the branches of j. excelsa (0.32%) and of the fruits (0.52%) were light yellow. 3.1 ir analysis ir analysis of the essential oils of different parts of j. excelsa revealed the presence of four characteristic symmetrical stretching bands for o-h, c-h, c=o and c=c bonds (table 1). the stretching frequency of the c-h bond ranged from 2916 cm -1 in fruits and leaves to 2965 cm -1 in gum-resin. the o-h stretching band varied from strong frequencies as in the essential oils of branches and fruits, at 3430 cm -1 and 3524 cm -1 respectively, to moderate and weak frequencies as in the essential oils of gum-resin and leaves. the c=o stretching frequency ranged from 1700 cm -1 in fruit oil to 1753 cm -1 in branch oil. such frequency ranges indicate the presence of saturated carbonyl compounds. table 1: ir data of essential oils of different parts of j. excelsa [s: strong; m: medium; w: weak] functional group wavenumber (cm -1 ) gum-resin leaves branches fruits o-h 3439 (m) 3418 (w) 3430 (s) 3524 (s) c-h 2965 (s) 2916 (s) 2941 (s) 2916 (s) c=o 1731 (m) 1740 (w) 1753 (w) 1700 (w) c=c 1685 (w) 1645 (s) 1654 (s) 1644 (s) 3.2 gc-ms analysis twenty-five components, comprising 97%, were detected in the essential oil of j. excelsa gum-resin using gcms (table 2, figures 1 & 2). the major compound in the j. excelsa gum oil was α-pinene (80.50%); other compounds that were identified in minute proportions were e-pinocarveol (2.85%), limonene (2.46%) and e-verbenol (2.09%). among the identified components, twelve compounds, comprising 48%, were monoterpene hydrocarbons and thirteen compounds, comprising 52%, were oxygenated monoterpenes. the oil was characterized by the absence of sesquiterpenes. the essential oil of the branches of j. excelsa contained 39 compounds. the major component in the branch oil was α-pinene (79.03%), followed by limonene (2.20%), myrcene (1.53%), and β-pinene (1.20%). amid the revealed compounds, twelve, comprising 31%, were monoterpene hydrocarbons and ten, comprising 26%, were oxygenated monoterpenes. the essential oil of the branches of j. excelsa was distinguished by the presence of seventeen sesquiterpenes (44%). thirty-seven compounds, comprising 98%, were identified in the eo of the leaves of j. excelsa. limonene (50.46%) and α-pinene (31.67%) were the major compounds. other compounds found to exist in minor proportions were myrcene (2.53%) and 3-carene (1.87%). twelve compounds, comprising 32%, were monoterpene hydrocarbons and ten compounds, comprising 27%, were oxygenated monoterpenes. fifteen sesquiterpenes, comprising 41%, of the oil were identified. the eo of the fruits of j. excelsa contained thirty-four components, comprising 98% of the oil. the major compounds were limonene (42.51%) and α-pinene (35.09%) followed by myrcene (3.09%), β-eudesmol (2.16%), -3-carene (2.14%) and α-humulene (2.11%). twelve compounds, comprising 35%, were identified as monoterpene hydrocarbons and five compounds comprising 15% were oxygenated monoterpenes. the oil was characterized by the presence of seventeen sesquiterpenes comprising 50% of the oil. saleh n. al-busafi et al. 10 table 2. chemical composition of essential oils of different parts of juniperus excelsa compounds ri percentage in gum-resin branches leaves fruits tricyclene 928 0.77 0.36 0.29 0.09 α-thujiene 932 0.19 0.22 _ _ α-pinene 942 80.50 79.03 31.67 35.09 α-fenchene 951 0.36 0.31 0.23 0.20 camphene 955 0.57 0.45 0.32 0.22 thuja-2,4(10)-diene 960 0.96 0.27 0.12 _ sabinene 977 0.22 0.41 0.05 0.04 β-pinene 982 1.03 1.20 0.96 1.73 myrcene 994 0.14 1.53 2.53 3.09 -phellandrene 1005 _ _ 0.13 _ -3-carene 1011 _ 0.15 1.87 2.14 α-terpinene 1019 _ _ _ 0.05 p-cymene 1027 0.46 0.26 _ 0.42 limonene 1033 2.46 2.20 50.46 42.51 z--ocimene 1040 0.10 _ _ _ -terpinene 1062 _ _ 0.11 0.25 α-terpinolene 1088 0.25 0.79 0.24 0.94 α-pinene oxide 1097 0.33 _ _ _ linalool 1098 0.13 _ _ _ α-campholenal 1127 1.31 0.30 0.15 _ trans-pinocarveol 1141 2.85 0.92 0.36 _ camphor 1143 _ _ _ 0.09 trans-verbenol 1144 2.09 0.34 _ _ trans-pinocamphone 1161 0.38 _ _ _ pinocarvone 1168 _ 0.13 _ _ α-phellandren-8-ol 1170 _ 0.28 _ _ terpinene-4-ol 1179 0.11 0.31 0.25 0.08 p-cymen-8-ol 1188 0.55 0.39 _ _ cis-piperitol 1194 _ 0.86 0.28 0.15 myrtenal 1197 0.47 _ _ _ verbenone 1204 0.44 _ 0.13 _ trans-carveol 1229 0.26 _ 0.50 _ cis-carveol 1230 _ _ 0.14 _ carvone 1242 _ _ 0.35 _ bornyl acetate 1285 0.49 1.20 0.56 0.08 -elemene 1339 _ 0.11 _ _ α-copaene 1376 _ _ 0.49 _ -bourbonene 1384 _ _ 0.16 _ -elemene 1393 _ 0.18 0.29 0.12 β-caroyophyllene 1418 _ 0.78 0.61 1.79 -elemene 1430 _ 0.87 0.18 0.51 α-humulene 1452 _ 0.10 0.50 2.11  -gurjunene 1473 _ _ 0.17 _ germacrene d 1480 _ 0.26 _ 0.79 -selinene 1485 _ 0.39 0.73 0.11 α-selinene 1493 _ 0.33 _ 0.23 α-muurolene 1499 _ 0.16 0.30 0.08 α-amorphene 1506 _ _ 0.32 0.08 -cadinene 1512 _ 0.19 _ 0.34 -cadinene 1516 _ 0.78 0.85 0.53 cis-calamenene 1521 _ 0.26 0.94 0.21 elemol 1547 _ 0.28 0.15 0.22 germacrene b 1556 _ 1.19 0.23 0.68 caryophylene oxide 1573 _ 0.53 0.33 0.50 α-cedrol 1604 _ 0.84 _ _ comparison of chemical composition and antioxidant activity 11 -cadinol 1636 _ _ _ 0.09 β-eudesmol 1651 _ _ _ 2.16 α-cadinol 1652 _ 0.19 _ _ total identified (%) 97% 99% 98% 98% gc-ms analysis of the four oils of j. excelsa show some similarities and differences in their monoterpene and sesquiterpenes chemical composition. the essential oil of the gum-resin contains the lowest number of components (25 compounds) whilst the essential oil of the branches contains the highest number of components (39). each one of the four oils contains twelve monoterpene hydrocarbons but they differ in the number of oxygenated monoterpenes. the four essential oils share 11 monoterpenes and differ in 24 monoterpenes. the identity of the major component also differs among the four oils; while the essential oils of the gum and branches contain α-pinene as the major compound (80.50% and 79.03% respectively) the oils of leaves and fruits contain limonene as the major component (50.46% and 42.51% respectively). in terms of composition of sesquiterpenes, the essential oils of leaves, branches and fruits contain varied proportions of sesquiterpenes while that of gum-resin contains no sesquiterpenes. tricyclene thujene pinene fenchene camphene thuja-2,4(10)-diene sabinene pinene myrcene phellandrene carene terpinene pcymene limonene z-ocimene terpinene terpinolene pinene o linalool ho cho campholenal trans-pinocarveol oh o pinocarvone phellandren-8-ol oh terpinene-4-ol oh pcymene oh oh cis-piperitol ho myrtenal verbenone o trans-carveol ho cis-carveol ho carvone o bornyl acetate o o camphor o trans-verbenol oh trans-pinocamphone o figure 1. monoterpenes from the essential oils of the j. excelsa. saleh n. al-busafi et al. 12 elemene elemene elemene h h h bourbonene h h copaene h h caroyophyllene humulene h gurjunene germacrene d selinene selinene h h murrolene h h amorphene h h cadinene h cadinene cis-calamenene oh elemol germacrene b h h caryophylene oxide o cedrol h oh cadinol ho eudesmol oh hh cadinol ho figure 2. sesquiterpenes from the essential oils of the j. excelsa. 3.3 total antioxidant activity the antioxidant activity of the essential oils of different parts of j. excelsa was evaluated by using the phosphomolybdenum method which is based on the reduction of mo(vi) by the sample analyte and the subsequent formation of green phosphate mo(v) complex with a maximum absorption at 695 nm. total antioxidant activity of the four essential oils, expressed as ascorbic acid equivalent (mg of aa per g of the oil), was obtained from the calibration curve of ascorbic acid (aa) as shown in figure 1. the essential oil of j. excelsa leaves showed higher total antioxidant activity compared to the other three oils scoring 385.0 mg ascorbic acid (aa) equivalents followed by the eo of gumresin with total antioxidant activity of 277.0 mg (figure 3). the eo of the fruits showed the lowest activity with 108.0 mg aa. comparison of chemical composition and antioxidant activity 13 figure 3. antioxidant activity of j. excelsa essential oil. 3.4 dpph radical scavenging activities another standard method to quantify antioxidant activity of essential oils is to measure their hydrogen donating ability to a dpph radical. in this study, essential oils of different parts of j. excelsa were investigated for their radical scavenging activity and compared with that of ascorbic acid (aa) (figure 4). the scavenging activity of the four essential oils, as well as that of ascorbic acid, increases as the concentration increases. the four oils, however, showed lower activity than ascorbic acid. figure 5 exhibits the ic50 values which describe the concentration of antioxidant required to inhibit 50% of dpph radicals. the smaller the ic50 value, the stronger the antioxidant activity obtained. the data obtained showed that the radical scavenging of the four essential oils decreased in the following order: leaves (ic50 = 20.47) > fruits (ic50 = 30.27) > resin-gum (ic50 = 36.77) > branches (ic50 = 40.46). figure 4. dpph radical inhibition activity of j. excelsa essential oils compared with ascorbic acid (aa) activity. a: ascrorbic acid; b: j.excelsa leaves oil; c: j. excelsa branches oil; d: j. excelsa fruits oil; e: j.excelsa gum oil. 0 50 100 150 200 250 300 350 400 450 leafs gum branches fruits a n ti o x id a n t a c ti v it y 0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 100 120 d p p h s ca ve n g in g concentration a b c d e saleh n. al-busafi et al. 14 figure 5. ic50 values of ascorbic acid (aa) and j. excelsa essential oils. 4. conclusion the chemical content and compositions of four essential oils extracted from resin-gum, leaves, branches and fruits of j. excelsa from jabal al-akhdhar (sultanate of oman) were analyzed by the gc-ms method. the analysis showed some variations as well as similarities in their chemical contents and compositions. out of a total of 35 different monoterpenes existing in the four essential oils, 11 monoterpenes are shared by the four oils. the essential oil of the resin-gum of j. excelsa is characterized by the absence of sesquiterpenespinene was found to be the major compound in the essential oil of resin-gum and branches with 80.50% and 79.03%, respectively, while limonene is the major compound in the essential oil of leaves and fruits with 50.46% and 42.51%, respectively. the essential oil of the leaves of j. excelsa shows stronger antioxidant activity and radical scavenging activity than other essential oils, but all four oils show lower antioxidant and radical inhibition activities when compared to ascorbic acid (aa). 5. acknowledgment we acknowledge, with thanks, financial support from the sultan qaboos university. the authors are grateful to professor fakhreldin suliman for his valuable help. 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and petroleum studies, rabat international university, technopolis, morocco. *email: rachid@squ.edu.om. abstract: a study on spin transfer torque switching in a magnetic tunnel junction with perpendicular magnetic anisotropy is presented. the switching current can be strongly reduced under a spin torque oscillator (sto), and its use in addition to the conventional transport in magnetic tunnel junctions (mtj) should be considered. the reduction of the switching current from the parallel state to the antiparallel state is greater than in the opposite direction, thus minimizing the asymmetry of the resistance versus current in the hysteresis loop. this reduction of both switching current and asymmetry under a spin torque oscillator occurs only during the writing process and does not affect the thermal stability of the free layer. keywords: magnetic random access memory; spin transfer torque; magnetization reversal; magnetic tunnel junction; spin torque oscillator. المشتقة مه (fcc)( والمكعب مركسي الوجه bccوالمكعب مركسي الجسم ) (scشبكات المكعب البسيط ) ويل والكواتيرويون -مجموعات كوسيتر بوزيان خالدو شيد سبيعر انًغُاطٍسً ُفقًانجهاص ان تقاطع فً نتبذٌم انًغُاطٍس (sto) اإلنكتشوٌ دوساٌكًٍت انتحشك انُاتج عٍ اَتقال انىسقت هً دساست عٍملخص : هذا( sto) اإلنكتشوٌ دوساٌ يزبزب َاتجت عٍ ًٌكٍ أٌ ٌتى باستعًال اتجاِ انًغُاطٍس نتبذٌم انكهشبائٍتتخفٍض فً انطاقت ( . mtjانعًىدي) انتقهٍم يٍ وبانتانً االتجاِ انًعاكسانى يىاصٌت حانت انًغُاطٍس يٍ نتبذٌم انكهشبائٍتتخفٍض انطاقت . mtj فً انتقهٍذٌت وسائم انُقم باإلضافت إنى انكتابت فقط أثُاء عًهٍت ٌحذث sto فً ظمعذو انتًاثم انحانً و انتحىل كم يٍ هزا االَخفاض. انتباطؤ فً حهقت انتٍاس ضذ فً انًقاويت انتباٌٍ .انزواكش انعشىائٍتحشكت فً انًتطبقت نهانحشاسي االستقشاسعهى تؤثش، وال mtj فً انًعهىياث .اإلنكتشوٌ دوساٌ و انًغُاطٍسً ُفقًانجهاص ان ،تبذٌم انًغُاطٍس ،عضو انذوساٌ تذوس َقم ،انىصىل انعشىائً انًغُاطٍسٍت راكشة :كلمات مفتاحية 1. introduction pin transfer torque (stt)-based magnetic random access memory (mram) is considered as a potential future memory due to its non-volatility, good scalability, fast reading and writing processes and its reasonably low writing current [15]. the key part of stt-mram device is made of a magnetic tunnel junction (mtj) where a magnetically soft layer, also called the free layer, is separated from a magnetically hard layer called the reference layer by a non-conductive tunnel barrier, as can be seen in the top part of figure 1(a). recently, materials with perpendicular magnetic anisotropy for the free and reference layers have been intensively investigated [6-17]. these materials have larger anisotropy energy and better thermal stability than their counterparts with in-plane anisotropy which are required for devices below 20 nm diameter. for magnetic memory to be competitive with static random access memory (sram) and dynamic random access memory (dram), the critical switching current for the free layer magnetization has to be reduced. although current densities below 5 ma/cm 2 have been reported [9,18-21], the scalability problem still remains, as these values are for switching the magnetization of the free layer from the antiparallel state to the parallel state with respect to the reference, which has a fixed magnetization direction. in magnetoresistance devices, it is known that the free layer magnetization switching by stt effect represents a strong asymmetry, i.e. the switching current density from antiparallel state to parallel state (jc app ) is much smaller than the one for switching from opposite states (jc pap ). this phenomenon is mainly due to the unbalanced rate between the polarized majority of electrons and the minority responsible for magnetization reversal. it is also important to note that in the case of perpendicular mtj, the magnetostatic field from the reference layer could reach values larger than 0.1 mt, thus favoring parallel state and causing a strong asymmetry [11, 22]. it is crucial to reduce both jc app and jc pap , though mainly the later , as it is the s sbiaa and bouziane 78 higher with a factor of two or more [9,11,14]. different studies have aimed to reduce jc without solving the issue of the asymmetry of the signal. in this paper, a new structure based on incorporating a spin torque oscillator (sto) to an mtj device to reduce the switching current density of fl magnetization m and the asymmetry of the hysteresis loop is proposed. moreover, it is found that for a frequency range around 2 ghz, it is possible to further reduce the value of jc pap . minimizing the writing current and the asymmetry of the writing signal using a sto is an efficient way to make stt-mram competitive with other future memories. for the same applied current, both rl and sto devices induce complementary effects in reducing stt current. 2. theoretical model the proposed structure is shown in figure 1(a), where an mtj is separated from an sto by a non-magnetic spacer. in this study only the magnetization dynamics of the free layer will be discussed and no details of the sto will be presented. it is assumed that the sto is made of a perpendicular magnetic anisotropy ferromagnetic layer with a fixed magnetization direction and an oscillating magnetic layer (osl) with magnetization mosc as sketched in figure 1(a). when a polarized electric current is applied, mosc forms an angle  from z-axis perpendicular to the film plane and rotates with an angular frequency  = 2 f. in this geometry, the free layer magnetization is under two stt effects, hst1 and hst2, originating from the reference layer and the oscillating layer, respectively. the current is assumed to flow perpendicularly to the layers and to have a uniform distribution. the dynamics of the free layer magnetization is described by the landau-lifshitz-gilbert (llg) equation: )()( eff s t α m γ t      m mhm m (1) where  is the gyromagnetic ratio and α is the effective damping constant. the effective field heff in eq. (1) includes the anisotropy field, the exchange field and the magnetostatic field, as well as hst1 and hst2. the two stt fields can be expressed as: )( 1(2)st1(2))2(1 pmh  h st (2) j dem h 2 )2(1 s st1(2) 2   (3) the mtj device in figure 1(a) is the main part, and the oscillating layer functions only to assist the switching of m. to avoid a reduction of read-back signal due to the existence of the sto, the spacer between the mtj and sto parts is of cu, which helps in writing and will not affect the tunnel magnetoresistance signal (tmr). the thickness of the cu spacer between the free layer and oscillating layer is about 2 nm, but could be made slightly larger. this range of thickness is enough to reduce the magnetostatic field from the oscillating layer which could change the magnetization dynamics of the free layer. in the case of the spin valve, 1.8 nm cu was is used to minimize the magnetostatic field between rl and fl [23]. because there is a conductive spacer between the oscillating layer and the free layer, the magnetoresistance signal from this part (osl/cu/fl) is much smaller than the tmr signal from fl/tunnel barrier/rl. in eq. 3, ms and d are the saturation magnetization and the thickness of the free layer, which were fixed to 800 emu/cm 3 and 2 nm, respectively. the efficiencies of spin polarization from rl and osl, 1 and 2 were also fixed in this work to 0.5 and 0.4, respectively. this difference was because the efficiency of a stt in a mtj is larger than in all conductive magnetoresistive devices, as reported by switching current values in both structures. for the calculation of the magnetization dynamics using eq. 1, the anisotropy field hk and exchange constant were kept constant at 9 koe and 1.610 6 erg/cm, respectively. these values are similar to those for materials commonly used for perpendicular mtjs, such as cofeb single layer or a laminated cofeb with ta [9,24,25]. finally,  = 0.007, as reported from ferromagnetic resonance measurements in the case of cofeb [26], was used throughout this study. in this simulation, the lateral size of the device, which includes fl, rl and osl, was fixed to 40 nm by 40 nm. 3. results and discussions firstly, the out-of plane component of the normalized free layer magnetization, mz, when there is only a reference layer (polarizer p1) was evaluated. for an electric current with a pulse duration  of 2 ns, mz decays with the current density, as can be seen from figure 2. it is important to note that mz was calculated at time t = 2ns. a critical value jc app of about 12 ma/cm 2 for switching m was obtained. this value is about 2.5 times smaller than jc pap . before considering the case where a sto is added, the case where the magnetic layer is below the free layer (figure 1) was studied. it can be seen from figure 2 that the switching of m occurs at a lower jc app of about 6 ma/cm 2 , but is not sensitive to the angle  (up to 30 investigated in this study). if one could make a fixed magnetization direction spin torque oscillator for high performance magnetic memory 79 instead of a sto device, the reduction of the electrical current for switching the free layer magnetization could still be improved. however, practically, it is challenging to have a good thermal stability with a tilted angle of more than15. in the proposed scheme, conventional perpendicular anisotropy materials could be used for an osl with good thermal stability and it would then only be when the current is applied, that mosc starts to oscillate, thus forming an angle  from the z-axis. in a second part of this study, we investigate the effect of frequency f on m dynamics. from eq. (2), the three components of hst2 are ).2sin.sin..(cos 22 zyst x st mfmhh   (4.a) ).cos.2cos..(sin 22 xzst y st mmfhh   (4.b) myfhh st z st .2cos.sin. 22  (4.c) figure 1. (a) schematic diagram of the proposed structure made of a magnetic tunnel junction (top part) and a spin torque oscillator (bottom part). the order of the two parts could be reversed. the free layer and reference layer have perpendicular magnetic anisotropy and (b) the oscillating magnetization in the spin torque oscillator part is shown in spherical coordinates. the current is flowing perpendicular to the film plane. these components are added to hst1 leading to an increase of the efficiency of the stt effect in reversing m. figure 3 shows the dependence of mz on the frequency f of sto for two applied current densities. as mentioned earlier, we did not investigate the dynamics of mosc but it is assumed that for a given current density j a frequency f could be reached. this is possible by adjusting the intrinsic properties of sto such as saturation magnetization, anisotropy field and damping constant. in addition, the efficiency of stt from the in-plane layer and spin polarization of the two magnetic layers of a sto are two other parameters that could tune the frequency f [2729]. for j = 12 ma/cm 2 , fl magnetization has a z-component of 0.7 and could not be reversed from p state to ap state with respect to reference layer magnetization. values of j = 12 ma/cm 2 and 14 ma/cm 2 for this part of the study were selected so as not to have a switching of fl magnetization without sto. figure 2. out-of-plane component of free layer magnetization as a function of the current density j for cases where there is only polarizer p1, and for both p1 and p2 with  = 15 and 30. in this calculation, the current pulse duration is 2 ns and p2 is considered not oscillating (f = 0). sbiaa and bouziane 80 figure 3. out-of-plane component of free layer magnetization versus frequency f of spin torque oscillator for different current densities. the current pulse duration is fixed to 2 ns and the switching is from parallel state to antiparallel state. as shown in figure 3, to reverse m either a large j should be applied to improve stt efficiency or mosc should be allowed to oscillate with a frequency f around 2 ghz under our calculation conditions. it is difficult to correlate between f and fl resonance frequency fr. heinonen et al. reported that fr decreases linearly with the bias voltage or applied current [30]. more interestingly, from ferromagnetic resonance (fmr) measurements they showed that fr is higher for a negative bias voltage compared to positive voltage. in the case of cofeb with 2 nm, it was found that fr is around 2.5 ghz without applying an electric current [26]. nevertheless, the intrinsic properties such as hk and ms may have a strong effect on f, in addition to the device size and applied current magnitude. in fact, while m is precessing under stt from rl, an additional stt from sto helps m to become reversed. the z-component of fl magnetization evolves with time t as mz ~ exp(t).cos(t) for a small amplitude limit and with no sto (only rl as a polarizer) [31]. when a sto is added to assist magnetization switching  should be synchronized with f of m, but this is not straightforward, as can be seen from eq. 4, where both t and the three components of m which are also time dependent exist. in figure 3, it can be seen that for a larger frequency (f > 3 ghz), the oscillation of mosc is not effective in the reversal process, and thus mz drops to an even lower value than where f = 0. similar behavior of mz versus f was observed for j = 14 ma/cm 2 . by plotting the calculated hysteresis loop for each value of applied current density, it can be seen from figure 4 that there is a strong asymmetry  for the case of conventional mtj (only polarizer p1). a jc pap of 28.5 ma/cm 2 is required to reverse m from p state to ap state, which leads to a change of device resistance from low value to high value, respectively (plotted as normalized resistance in figure 4). it we assume that the sto is replaced by a layer with fixed magnetization direction  = 30 without any oscillation (f = 0), a reduction of both jc pap and jc app to 13.6 ma/cm 2 and 9.9 ma/cm 2 , respectively, could be achieved. the strong reduction of jc pap compared to jc app leads to a minimization of asymmetry . when a sto is acting on the free layer magnetization, a further reduction of jc pap with almost no change in jc app value was is observed. for f = 2 ghz, jc pap was further reduced to 10.7 ma/cm 2 which represents an approximately 60% reduction. in fact, for a/the sttmram application, it is mainly the reduction of jc pap which remains a challenge, thus causing an asymmetry between jc from parallel and antiparallel states. it is known that m takes less time to switch from antiparallel to parallel states than for the reverse case. the sto is then more effective for reducing jc pap than jc app . figure 4. normalized resistance versus current density for cases where there is only p1, and when p2 is added with no oscillation (f = 0), and with a frequency of oscillations of 2 ghz. the magnetization of the oscillating layer has a fixed angle  = 30 around the z-axis. spin torque oscillator for high performance magnetic memory 81 4. conclusion integrating a spin torque oscillator to a magnetic tunnel junction with perpendicular anisotropy could help to improve the efficiency of the stt effect. the study revealed a stronger reduction of switching current from parallel state to antiparallel state compared to the reverse transformation. this is important in reducing the asymmetry in the resistance-current hysteresis loop. it is also shown from this study that the critical switching current is not very sensitive to the opening angle of sto oscillations. more interestingly, the oscillation frequency is another key parameter to further reduce the current from parallel state to antiparallel state. the proposed structure does not require an additional lithography process or special electrical circuit and 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a statistical analysis on forecasting prices of some important food commodities in bangladesh mohammad abdullah al-mamun1, sheikh mohammad sayem1, khondaker mohammad mostafizur rahman 1 and mohammad zakir hossain 2* 1 department of agricultural statistics, bangladesh agricultural university; mymensingh, bangladesh. 2 department of operations management and business statistics, college of economics and political science, sultan qaboos university, p.o. box 20, al-khod, pc 123, muscat, sultanate of oman. *email: mzhossain@squ.edu.om. abstract: this paper investigates the best possible forecasting price models for three important agricultural products in bangladesh namely potato, onion and garlic using time-series and secondary data from january 2000 to december 2014. the main objective of this paper is to find out the appropriate time series models using some of the latest selection criteria that could describe the best price patterns of the above mentioned three crops. to forecast the prices of the crops, the arima models were used, based on model selection criteria and error statistics among the competing models. the overall findings of the study indicate that the fitted models are satisfactory for the respective commodities. the study observed increasing trends in forecasted prices of all three commodities. in particular, the increase in the price of garlic has been observed to be very high compared to that of potato and onion. the study also found that the best fitted sarima model for potato is sarima (1,0,0) (0,1,2)12, for onion sarima (2,0,0) (0,1,1)12, and for garlic sarima (2,1,3) (0,1,3)12. keywords: box-jenkins methodology; forecasting price; autocorrelation function; arima model; sarima model; estimation; identification; akaike information criterion; bayesian information criterion. بعض المنتجات الغذائية الهامة في بنغالديش للتنبؤ بأسعارتحليل إحصائي مصطفى الرحمن حمدوخندكر م اكر حسينزعبد هللا المأمون وشيخ محمد صايم، ومحمد حمدم والثوم، ممكنة للتنبؤ حول ثالثة منتجات زراعية مهمة في بنغالديش وهي البطاطا والبصل درست هذه الورقة البحثية أفضل نماذج أسعار :صلخمال . تهدف هذه الدراسة إلى ايجاد نماذج متسلسالت زمنية مناسبة، 0202إلى ديسمبر 0222الت زمنية وبيانات ثانوية اعتبارا من يناير لسباستخدام متس ه. من ألل التنبؤ بسسعار باستخدام بعض المعايير المختارة حديثا والتي يمكن أن توصف أفضل أنماط األسعار للمحاصيل الزراعية الثالثة المذكورة أعال استناداً على معايير نماذج مختارة وإحصاء األخطاء بين النماذج المتنافسة. وقد أشارت النتائج (arimaالمحاصيل، فقد تم استخدام نماذج أريما ) ة في األسعار المتوقعة لجميع السلع الثالث. وعلى اإللمالية للدراسة إلى أن النماذج المركبة مناسبة للسلع المعنية. والحظت الدراسة أن االتجاهات متزايد مناسب وله الخصوص مادة الثوم، حيث لوحظ أن الزيادة في سعرها مرتفعة للغاية مقارنة بالبطاطا والبصل. وولدت الدراسة أيًضا أن أفضل نموذج وللثوم هو sarima(2,0,0)(0,1,1)12صل هو وللب sarima(1,0,0)(0,1,2)12للبطاطا هو ( يتم الداللة عليه كما يلي:sarimaلساريما ) .sarima(2,1,3)(0,1,3)12 ، نموذج ساريما (arimaأريما ) (، سعر التنبؤ، وظيفة االرتباط التلقائي، نموذجbox-jenkinsمنهجية صندوق لينكنز ) :مفتاحيةالكلمات ال (sarimaالتقدير، التعريف، معيار معلوما ،)( ت أكيكakaike) معيار معلومات ،( بايزbayesian.) 1. introduction angladesh is predominantly an agriculture-based country where more than 80% of the population are engaged in agriculture, of which 70% are purely in the labor force. the agriculture sector is one of the main important sectors for the economic development of the country which contributes 16.33% of the total gross domestic product (gdp) in bangladesh (bangladesh bureau of statistics (bbs)) [1]. potato is one of the most important vegetables in b a statistical analysis on forecasting prices 131 bangladesh. it contributes 55% of the country’s total vegetable production [2]. the market price of potatoes decreases from tk. 1164/100 kg to tk. 1077/100 kg (department of agriculture marketing (dam)) [3]. the onion is also a very important spice crop for the people of bangladesh. the market price of onion increases from tk. 1403/100 kg to tk. 2806/100 kg [3]. garlic is another important spice crop of the country, which is used for medicinal purposes as well. the market price of garlic decreases from tk. 3730/100 kg to tk. 2806/100 kg [3]. forecasting prices of the heavily consumed major commodities is very essential for the businessmen, planners and policymakers of a developing country like bangladesh where approximately 40% of the people are living below the poverty line. for many developing countries, primary commodities remain an important source of export earnings, and commodity price movements have a major impact on overall macroeconomic performance. hence, commodity-price forecasting is a key input to macroeconomic policy planning and formulation [4]. the fluctuation of the prices of vegetable and spice crops always makes the government anxious and it has great impact on the millions of the country’s producers and consumers. early forecasting of the probable prices of vegetable and spice crops could help the policy makers to predict the probable fluctuations in their prices [5]. forecasting prices of commodities is very important in decision making at all levels and sectors of the economy. this is particularly true in the agriculture sector where policy decisions are characterized by risks and uncertainty, largely due to uncertain yields and relatively low price elasticity of demand for most agricultural commodities in order to make good decisions and policies [6]. the farmers are emotionally and financially affected by the fluctuation in prices of agricultural commodities and its adverse effect on the gdp of a country. prediction of the prices may help the agriculture supply chain in making necessary decisions in minimizing and managing the risk of price fluctuations [7]. future prices are also used by crop insurance programs to decide their first-stage and harvest prices [8]. price forecast therefore, is vital to facilitate efficient decisions and it will play a major role in coordinating the supply and demand of farm products. hence, forecasting cereal prices will be useful to producers, consumers, processors, rural development planners and other stake holders and agencies/institutions involved in the market [9]. the main objective of this paper is to forecast the monthly prices of the selected three most useful agricultural commodities namely, potato, onion and garlic. four different models on time series data, namely autoregressive (ar) model, moving average (ma) model, autoregressive integrated moving average (arima) model and seasonal autoregressive integrated moving average (sarima) model (popularly known as box-jenkins methodology) [10] are extensively used in this study. 2. data and methodology data collection: the monthly secondary data of the prices of the three commodities namely potato, onion and garlic were collected from dam, bbs and the food planning and monitoring unit (fpmu) under the ministry of food and disaster management of bangladesh. in order to find out the best possible models for forecasting prices of the three items, we used tabular and graphical approaches under descriptive statistics and boxjenkins methodology. time series analysis: time series analysis was chosen to analyze the data because this particular analysis requires absolute values of forecast, and it usually produces a better result. the arima process is a mathematical model generally used for forecasting. under this process, the forecasts are based on linear functions of the sample observations in order to find the simplest models that provide an adequate description of the observed data. the time series process, when differenced, follows both ar and ma models and is known as the autoregressive integrated moving averages (arima) model. the model is often abbreviated as arima (p, d, q) where ‘p’ stands for ar part, ‘d’ for integrated part and ‘q’ for ma part. the arima model as used in this study required a sufficiently large data set and involves four steps within the framework of box-jenkins methodology, these being identification, estimation, diagnostic checking and forecasting[11]. identification: t h e m a i n t o o l s i n i d e n t i f i c a t i o n a r e t h e autocorrelation f u n c t i o n ( a c f ) , t h e p a r t i a l autocorrelation function (pacf), and the resulting correlations, which are simply plots of acfs and pacfs against the lag length. the acf and pacf are estimated from the sample data. this estimated acf and pacf are used as a guide to choose appropriate models. the decision regarding transformation is necessary to stabilize the variance of the series through a time plot and it shows data scattered horizontally around a constant mean; the acf and pacf drop to, or near to, zero quickly which indicates that the data are stationary. if the time plot is not horizontal, or the acf and pacf do not drop to zero, then nonstationary is to be implied. estimation: at this stage precise estimates of the coefficients, the ar and ma parameters, seasonal and non-seasonal, of the tentative model chosen at the identification stage have to be determined. in other words, having selected appropriate values for non-seasonal (p, d, q) and seasonal (p, d, q) of the model, parameters are estimated, typically using simple least squares. diagnostic checking: after choosing a particular arima model and having estimated its parameters, the next step is to see whether the chosen model fits the data reasonably well by performing some diagnostic tests. at the diagnostic test one sample test of the chosen model is to see if the residuals estimated from the model are white noise. in this regard, the portmanteau test can be applied to the residuals as an additional test of fit. the box-pierce q test and ljung-box q tests are the popular portmanteau tests for testing the statistical significance of autocorrelation coefficients. if the portmanteau test is found to be significant, then the model will be inadequate. in such a case, mohammad zakir hossain et al 132 another arima model needs to be considered. besides the pattern of significant spikes in the acf and pacf of the residuals, we cannot improve the model. for example, the significant spikes at the small lags suggest increasing the non-seasonal ar or ma component of the model. similarly, significant spikes at the seasonal lags suggest adding a seasonal component to the chosen model. forecasting: if the residuals of the selected model are white noise then the model can be used for forecasting purposes. the reason for the general acceptability of the arima model is its wide successes in forecasting. in this study, we have used the autoregressive (ar) model, moving average (ma) model, autoregressive integrated moving average (arima) model and seasonal autoregressive integrated moving average (sarima) in order to find the best suited model and to increase the accuracy of the forecast. 3. the model the first-order autoregressive disturbance or ar (l) process is of the form [12] 𝑌𝑡 = 𝜌𝑌𝑡−1 + 𝑢𝑡 where 𝑢𝑡 ~ n (0, 1). similarly, the second-order ar (2) process is of the form 𝑌𝑡 = 𝜌1𝑌𝑡−1+ 𝜌2𝑌𝑡−2 + 𝑢𝑡 . in general, the pth-order ar (p) process is considered as 𝑌𝑡 = 𝜌1𝑌𝑡−1+ 𝜌2𝑌𝑡−2+ ∙∙∙ + 𝜌𝑝𝑌𝑡−𝑝 + 𝑢𝑡 . (1) the first order moving average or ma (1) process is expressed as 𝑌𝑡 = 𝑢𝑡 + 𝜃𝑢𝑡−1. the secondorder moving average ma (2) process is of the form 𝑌𝑡 = 𝑢𝑡 + 𝜃1𝑢𝑡−1+ 𝜃2𝑢𝑡−2. the general form of moving average or ma (q) process is considered as 𝑌𝑡 = 𝑢𝑡 + 𝜃1𝑢𝑡−1+ 𝜃2𝑢𝑡−2 + ∙∙∙ + 𝜃𝑞 𝑢𝑡−𝑞 . (2) for time series analysis, the general autoregressive integrated moving average (arima) (p, d, q) model in terms of backward shift operator b is as follows: (1-𝜑1b− ∙∙∙ − 𝜑𝑝𝐵 𝑝)𝑊𝑡 = (1−𝜃1b− ∙∙∙ −𝜃𝑞 𝐵 𝑞 )𝐴𝑡 (3) where, 𝑤𝑡 = (1 − 𝐵) 𝑑 𝑒𝑡 is the first difference of the original time series 𝑌𝑡 and 𝐴𝑡 is the random shock which forms a white noise process with mean zero [13]. similarly, the seasonal arima, often called sarima (p, d, q) (p, d, q)s in terms of the backward shift operator b can be expressed as (1−𝜑𝑠 𝐵 𝑠 −∙∙∙ −𝜑𝑠𝑝𝐵 𝑠𝑝 ) 𝑊𝑡 = (1−𝜃𝑠 𝐵 𝑠 −∙∙∙ −𝜃𝑠𝑄 𝐵 𝑠𝑄 ) 𝐴𝑡 (4) where, 𝑤𝑡 = (1 − 𝐵 𝑠 )𝑑 𝑌𝑡 , s = 12 for monthly data and s = 4 for quarterly data. contrary to (1.3), here the random shocks 𝐴𝑡 do not form a white noise process. combining (1.3) and (1.4) we obtain (1-𝜑1b− ∙∙∙ − 𝜑𝑝𝐵 𝑝) (1−𝜑𝑠 𝐵 𝑠 −∙∙∙ −𝜑𝑠𝑝𝐵 𝑠𝑝 )𝑊𝑡 =(1−𝜃1b− ∙∙∙ −𝜃𝑞 𝐵 𝑞 ) (1−𝜃𝑠 𝐵 𝑠 −∙∙∙ −𝜃𝑠𝑄 𝐵 𝑠𝑄 ) 𝐴𝑡 . (5) as a final generalization, a constant term 𝜃0 needs to be added to the model (1.5) in order to accommodate the possibility that the variables 𝑤𝑡 may have a non-zero mean. thus the resulting model can be written as (1-𝜑1b− ∙∙∙ − 𝜑𝑝𝐵 𝑝) (1−𝜑𝑠 𝐵 𝑠 −∙∙∙ −𝜑𝑠𝑝𝐵 𝑠𝑝 )𝑊𝑡 = 𝜃𝑜+(1−𝜃1b− ∙∙∙ −𝜃𝑞 𝐵 𝑞 ) (1−𝜃𝑠 𝐵 𝑠 −∙∙∙ −𝜃𝑠𝑄 𝐵 𝑠𝑄 ) 𝐴𝑡 (6) where, 𝑤𝑡 =(1 − 𝐵) 𝑑 (1 − 𝐵𝑠 )𝐷 𝑌𝑡 . therefore, the equation (1.6) stands as (1-𝜑1b− ∙∙∙ − 𝜑𝑝𝐵 𝑝)(1−𝜑12𝐵 12 −∙∙∙ −𝜑12𝑝 𝐵 12𝑝 )𝑊𝑡 = 𝜃𝑜+(1−𝜃1b− ∙∙∙ −𝜃𝑞 𝐵 𝑞 ) (1−𝜃12𝐵 12 −∙∙∙ −𝜃12𝑄 𝐵 12𝑄 ) 𝐴𝑡 (7) where, 𝑤𝑡 =(1 − 𝐵) 𝑑 (1 − 𝐵12)𝐷 𝑌𝑡 . this is the multiplicative model of order (p, d, q) (𝑃, 𝐷, 𝑄)12. here the term (1-𝜑1b− ∙∙∙ − 𝜑𝑝 𝐵 𝑝) is known as the regular autoregressive operator of order p, the term (1−𝜑12𝐵 12 −∙∙ ∙ −𝜑12𝑝𝐵 12𝑝) is known as seasonal autoregressive operator of order p, the term (1−𝜃12𝐵 12 −∙∙∙ −𝜃12𝑄 𝐵 12𝑄 ) is the seasonal moving average operator of order q. the multiplicative model (1.7) represents a common form of most of the seasonal time series models considered in practice. the best model is obtained with the following diagnostics, by lowest values of akaike’s information criteria (aic) and schwartz bayesian criteria (sbc or bic). to check the adequacy for the residuals, q statistic is used. a modified q statistic is the box-ljung q statistic as given below: q'= n (n+2)∑ 𝑟𝑘² (𝑛−𝑘) 𝑝 𝑘=1 . the q statistic is compared to the critical value of chi-square distribution. if the p-value associated with the q statistic is small, the model is considered as adequate. forecasting the future periods using the parameters for the tentative model has been selected. trend fitting: for evaluating the adequacy of ar, ma, arima and sarima processes, various reliability statistics like r 2 , root mean square error (rmse), mean absolute percent error (mape), mean absolute error (mae) and bic were used. the smaller the various reliability statistics, the better the efficiency of the model in predicting the future production. a statistical analysis on forecasting prices 133 4. results and discussion accuracy of forecasting depends on the time series data which must be stationary. apart from the graphical method of using acf and pacf for determining whether the time series is stationary, a very popular method of determining this is the augmented dickey fuller (adf) test. in the present study the adf tests of the three different agricultural commodities such as potato, onion and garlic prices were conducted using eviews software. the most suitable models were selected based on their ability for reliable prediction. lower values of rmse and mape were preferable whereas for normalized bic, higher values were preferable. furthermore, the ljung-box test (portmanteau test) was conducted to see if the residual acf at different lag times was significantly different from zero, where not being different from zero was expected. after the best model was identified, forecasts for future values from january 2000 to december 2014 were made. the best fitting model was determined for the three different commodities based on secondary data from january 2000 to december 2014 by using the statistical software spss 20. from the following tables, it can be seen that the best sarima model for forecasting the wholesale price of potato is sarima (1,0,0)(0,1,2)12, for onion it is sarima (2,0,0)(0,1,1)12 , and for garlic it is sarima (2, 1, 3)(0,1,3)12. in the three best models, the acf and pacf of residuals have no significant spikes and the residuals are found to be white noise. after fitting the best selected models, the prices of three selected commodities were forecasted for january 2015 to december 2015 based on the collected secondary data from january 2000 to december 2014. overall, the forecast prices of the selected commodities were found to be consistent with some few upturns and downturns of the observed series. table 1. model selection criteria for tentatively selected sarima models for onion. model r 2 rmse bic mae mape ljung-box(q statistics) p-value sarima(2,0,0)(0,1,1)12 .853 478.97 12.49 329.02 16.21 19.88 .176 sarima(2,0,1)(0,1,2)12 .854 480.24 12.56 327.56 16.15 18.74 .131 sarima(2,0,1)(0,1,3)12 .853 483.14 12.60 328.94 16.23 16.87 .155 sarima(2,0,1)(0,1,4)12 .855 480.84 12.62 325.26 16.03 16.22 .133 sarima(3,0,1)(0,1,2)12 .857 476.40 12.57 327.78 16.26 13.87 .309 sarima(3,0,1)(0,1,3)12 .858 475.81 12.60 319.63 15.78 13.11 .286 table 2. model parameters of sarima (2, 0, 0) (0,1,1)12 for onion. type coefficient standard error pvalue ar(1) 1.1364 .0724 0.00 ar(2) -0.3923 .0729 0.00 sma(12) 0.8587 .0615 0.00 constant 39.319 6.785 0.00 table 3. model selection criteria for tentatively selected sarima models for garlic. model r 2 rmse bic mae mape ljungbox(q statistics) pvalue sarima(1,1,4)(1,1,5)12 .904 973.622 14.16 519.00 10.86 10.00 .188 sarima(2,1,5)(1,1,5)12 .906 971.621 14.21 511.59 10.61 8.11 .150 sarima(2,1,3)(0,1,3)12 .906 953.208 14.02 513.93 10.64 10.54 .394 sarima(2,1,4)(0,1,3)12 .905 964.886 14.08 519.80 10.84 7.81 .553 sarima(2,1,4)(0,1,4)12 .905 968.313 14.11 518.50 10.81 7.77 .456 sarima(2,1,4)(0,1,5)12 .907 959.466 14.13 506.96 10.48 7.24 .404 table 4. model parameters of sarima (2, 1, 3) (0,1,3)12 for garlic. type coefficient standard error p-value ar(1) 0.3127 0.0730 0.00 ar(2) -0.8822 0.0631 0.00 ma(1) 0.2857 0.1000 0.00 ma(2) -o.8862 0.0629 0.00 ma(3) -0.1551 0.0856 0.07 sma(12) 0.9894 0.0822 0.00 sma(24) 0.1812 0.1276 0.15 sma(36) -0.3005 0.1105 0.00 constant 16.87 -0.18 0.85 mohammad zakir hossain et al 134 table 5. model selection criteria for tentatively selected sarima models for potato. model r 2 rmse bic mae mape ljung-box(qstatistics) pvalue sarima(0,1,1)(0,1,1)12 .829 217.159 10.884 138.89 13.70 16 .453 sarima(0,1,2)(0,1,2)12 .844 208.651 10.865 132.20 13.12 7.78 .900 sarima(0,1,3)(0,1,2)12 .844 209.210 10.901 132.41 13.14 7.69 .863 sarima(0,1,4)(0,1,3)12 .846 209.102 10.961 131.46 13.21 7.40 .765 sarima(0,1,5)(0,1,3)12 .846 209.658 10.997 131.35 13.20 7.46 .681 sarima(1,0,0)(0,1,2)12 .848 205.002 10.779 134.58 13.22 10.84 .764 table 6. model parameters of sarima (1, 0, 0) (0,1,2)12 for potato. type coefficient standard error pvalue constant 6.080 1.704 0.00 ar(1) 0.893 0.035 0.00 sma(12) 1.268 0.086 0.00 sma(24) -0.3608 0.091 0.00 figure 1. residual of acf and pacf for the best sarima models for potato, garlic and onion. the actual and fitted prices using the best fitted model of the respective commodities are presented below for one year (march 2009 – february 2010) to check the validity of the models employed in our study. table 7. comparison of actual and fitted price of the commodities per 100 kg. potato onion garlic month actual price fitted price actual price fitted price actual price fitted price jan-14 632 1068 3430 5703 7898 7767 feb-14 1514 548 1938 1896 6951 7695 mar-14 784 1579 2166 1535 4658 4516 apr-14 1124 983 2156 2208 4650 4550 may-14 1264 1329 1928 2624 4522 5683 jun-14 1511 1406 2825 2071 5795 5034 jul-14 1713 1619 3251 3496 6279 6107 aug-14 1756 1768 3380 3581 5812 6370 sep-14 1760 1808 3472 3584 6853 5824 oct-14 1847 1830 3252 3900 7566 7367 nov-14 1850 1893 3299 3554 7218 7731 dec-14 1952 1818 2752 3003 6970 7083 a statistical analysis on forecasting prices 135 figure 2. plot of actual and predicted prices of potato, onion and garlic. the forecasted prices of the selected commodities are given below table 8. 0 1000 2000 3000 4000 5000 6000 o n io n p r ic e month actual price predicted price 0 2000 4000 6000 8000 10000 g a r li c p r ic e month actual price predicted price 0 500 1000 1500 2000 2500 p o t a t o p r ic e month actual price predicted price mohammad zakir hossain et al 136 table 8. forecasted prices per 100 kg of potato, garlic and onion. forecasted price per 100kg month potato onion garlic jan-15 1700 2167 7034 feb-15 1170 2360 6306 mar-15 1370 2579 4339 apr-15 1454 2546 4607 may-15 1600 2896 5159 jun-15 1664 3099 5364 jul-15 1738 3453 5793 aug-15 1780 3730 6231 sep-15 1799 3932 6589 oct-15 1822 4280 6905 nov-15 1940 4554 6858 dec-15 1898 4038 6655 4. conclusion during the last few decades, a huge amount of work has been done by using time series data on the major crops of bangladesh such as rice, wheat, tea, jute, lentil, etc. see for example, [14] and [15]. we used three important food crops, i.e. potato, onion and garlic, for our analysis. we observed from table 8 that the forecasted price for potato rose from tk.1700 per 100 kg in january 2015 to tk.1898 by the end of the year 2015. for onion, the forecasted price of onion rose from tk. 2167 per 100 kg in january 2015 to tk. 4038 by the end of the year 2015. the table reveals that the price fluctuations had erratic trends in nature. the forecasted price of garlic decreased greatly from tk. 7034 per 100 kg in january 2015 to tk. 5793 in july 2015. after this, the price slightly increased from tk. 5793 per 100 kg in july 2015 to tk. 6655 in december 2015. based on the above numerical figures, we may conclude that the overall prices for the selected three important food commodities are expected to increase in the next one year. this could be very helpful information to businessmen, policy makers and planners in order to make future economic decisions regarding these types of agricultural food commodities. the seasonal autoregressive integrated moving average model traces out the seasonal effect of the desired variable. the current research identified sarima (1,0,0) (0,1,2)12 for potato, sarima (2,0,0) (0,1,1)12 for onion and sarima (2,1,3) (0,1,3)12 for garlic have been proved to be the best possible models for forecasting purposes on the basis of the latest model selection criteria. the forecasting performances of the chosen models were found to be satisfactory, as shown by figure 2. as we know, more reliable results on forecasting accuracy mainly depend on accuracy of data on the selected variables. thus, we recommend that data banks in bangladesh should be better organized and of better quality in order to obtain the best possible outcomes through forecasting models. conflict of interest the authors declare no conflict of interest. acknowledgment mzh thanks the college of economics and political science for infrastructural support. the authors would like to thank the anonymous reviewers for their constructive suggestions which helped to improve the quality of the paper. references 1. bangladesh bureau of statistics. yearbook of agricultural statistics of bangladesh, ministry of planning, government of the people’s republic of bangladesh, dhaka, 2014. 2. bangladesh bureau of statistics. yearbook of agricultural statistics of bangladesh, ministry of planning, government of the people’s republic of bangladesh, dhaka, 2009. 3. department of agricultural marketing. the monthly data collection of the selected commodity (potato, onion, garlic) prices in bangladesh from january 2000 to december 2014, dhaka, 2014. 4. chakriya, b. and husain, a. forecasting commodity prices: futures versus judgment”, imf working paper 04/41, 2004. 5. hassan, m.f., islam, m.a., imam, m.f. and sayem, s.m. forecasting wholesale price of coarse rice in bangladesh: a seasonal autoregressive integrated moving average approach. a working paper, 2013. 6. ali, m.z., hossain, m.z. and samad, q.a. historical, ex-post and ex-ante forecasts for three kinds of pulse prices in bangladesh: masur, gram and khesari. jahangirnagar university journal of science, 2002, 25, 255-265. a statistical analysis on forecasting prices 137 7. kiron, m. sabu, t.k. and manoj, k. predictive analytics in agriculture: forecasting prices of arecanuts in kerala, procedia computer science, 2020, 171, 699-708. 8. hongbing, o., xiaolu, w. and qiufeng, w. agricultural commodity future prices prediction via longand shortterm time series network, journal of applied economics, 2019, 22(1), 468-483. 9. jadhav, v., chinnappa, r.b.v. and gaddi, g.m. application of arima model for forecasting agricultural prices, journal of agricultural science and technology, 2017, 19(5), 981-992. 10. box, g.e.p. and jenkins, g.m. time series analysis: forecasting and control, holden-day, san francisco, ca, 1976. 11. schwarz, g. estimating the dimension of a model. annals of statistics, 1978, 6(2), 461-464. 12. makridakis, s., wheelwright, s. and hyndman, r.j. forecasting methods and applications. 3rd edition, john willey and sons, new york, 1998. 13. pankratz, a. forecasting with univariate box-jenkins models: concepts and cases, john wiley, new york, 1984. 14. hossain, m.z., samad, q.a. and ali, m.z. arima model for forecasting the prices of field pea, blackgram and mungbean in bangladesh. bangladesh journal of agricultural research, 2004, 29(2), 289-303. 15. samad, q.a. an econometric model for the world market of tea. ph.d. thesis, university of belefield, germany. received 20 february 2019 accepted 1 st july 2020 robust resistance network topology design by conic optimization squ journal for science, 17 (1) (2012) 125-146 © 2012 sultan qaboos university 125 robust resistance network topology design by conic optimization c. roos*, y. bai** and d. chaerani*** *faculty of information technology and systems, delft university of technology, p.o. box 5031, 2600 ga delft, the netherlands, email: c.roos@tudelft.nl. **shanghai university, shanghai, china, email: yanqin.bai@gmail.com. ***jurusan matematika, fmipa, universitas padjadjaran, bandung, indonesia, email: d_chaerani@yahoo.com. abstract: after a brief introduction to the field of conic optimization we present an application to the (robust) resistor network topology design problem, where the goal is to design an electrical network containing resistors, such that the dissipation is minimal, given the external current values at the nodes of the network and assuming that the conductance values satisfy some normalizing constraint. we present a linear model for the single-current case and semidefinite models for multicurrent cases. all models are illustrated by examples. keywords: conic optimization, network topology design, conic quadratic optimization, semidefinite optimization, robust optimization. تصميم طوبولوجيا متينة لشبكات المقاومة باستخدام األمثليات المخروطية روس، ي. باي و د. تشايراني س. لحل مسألة تصمٌم طوبولوجٌا متٌنة لشبكات بعد مقدمة وجٌزة عن موضوع األمثلٌات المخروطٌة، نقدم تطبٌقا :ملخص ،ن الهدف من هذه المسألة هو تصمٌم شبكة كهربائٌة تحتوي على مقاومات بحٌث ٌكون التبدد فٌها أقل ما ٌمكنإالمقاومة. . وبافتراض أن قٌم التوصٌل الكهربً تحقق بعض شروط التطبٌع ،باعتبار قٌم التٌارات الخارجٌة على مستوى عقد الشبكة كما نرفق أمثلة توضٌحٌة مع .ةتعددم نصف محددة فً حالة تٌارات نماذجخطً فً حالة وجود تٌار وحٌد و نموذجنقدم المقترحة. النماذجكل 1. introduction very general mathematical setting of an optimization problem is the following:  0 ( ) : ( ) 0, = 1, , .min i x x f x f x i m   (p) in this problem, we are given an objective function 0 ( )f x and finitely many functional constraints ( ) 0, = 1, , .if x i m the functions ( )if x are real-valued functions of an n-dimensional design vector x a c. roos, y. bai and d. chaerani 126 varying in a given domain x. the goal is to minimize the objective over the feasible set of the problem, i.e., the set which is cut off the domain x by the system of inequalities ( ) 0, = 1, , .if x i m in general, this is a very hard problem to solve. the situation is much better if the set x and all functions ( ), = 0,1, ,if x i m are convex. in that case (p) is called a convex optimization problem. but even then, the problem might be hard to solve. in this paper we restrict ourselves to a special class of convex optimization problems, namely conic optimization (co) problems. co addresses the problem of minimizing a linear objective function over the intersection of an affine set and a convex cone. the general form is as follows:  : .min t n x c x ax b k    r (conp) the objective function is , t c x where n c  r is called the objective vector. furthermore, ax b represents an affine function from n r to m r and k denotes a convex cone in . m r usually a is given as an m n (constraint) matrix, and . m b r the importance of this class of problems is due to two facts: many nonlinear problems can be modelled as a co problem, and, secondly, under some weak conditions on the underlying cone k, co problems can be solved efficiently. the easiest and most well known case occurs when the cone k is the nonnegative orthant of , m r i.e. when = m k r :  : .min t m n x c x ax b     r r (lo) this is nothing but one of the forms of the well known linear optimization (lo) problem. thus it becomes clear that lo is a special case of co. it is well known that lo models cover numerous applications. whenever applicable, lo allows useful quantitative and qualitative information on the problem at hand to be obtained. the specific analytic structure of an lo problem gives rise to a number of general results which in many cases provide valuable insight and understanding. at the same time, this analytic structure underlies some specific computational techniques for lo; these techniques, which by now are perfectly well developed, allow quite large lo problems (with tens/hundreds of thousands of variables and constraints) to be solved routinely. nevertheless, in practice, many situations arise that cannot be covered by lo models. to handle these essentially nonlinear cases, there is a strong need to extend the basic theoretical results and computational techniques known for lo beyond the bounds of lo. when passing from a generic lo problem to its nonlinear extensions, we should expect to encounter some nonlinear components in the problem. historically, this was done by putting the nonlinearity in the functions defining the problem, as done above in problem (p). in co, however, we replace the cone m r in (lo) by a convex cone k, and hence the nonlinearity is now captured in the cone. in the next section we discuss some basic properties of relevant convex cones and we introduce two special cones that play a prominent role in the context of co. in the recent years, a lot of attention has been devoted to co. the reason is that the interior-point methods developed in the three last decades for lo, and which revolutionized the field of lo, could be naturally extended to obtain polynomial-time methods for co (see, for example ben-tal and nemirovski (2001), nesterov and nemirovski (1994), roos et al. (2005), terlaky (1973), wright (1997) and ye (1997)). this opened the way to a wide spectrum of new applications which cannot be captured by lo, e.g. in control theory, combinatorial optimization, etc. for a complete survey both of the theory of co and its applications, we refer to the recent book by ben-tal and nemirovski (2001). the aim of this paper is to introduce the reader to the theory of co, and to illustrate its use. lo has a beautiful duality theory. we will see that much of this theory can be generalized to co. in ben-tal and nemirovski (2001), the authors dealt with one of the important applications of co, namely truss topology design. we apply a similar approach to the topology design of electrical networks consisting of resistances only. robust resistance network topology design 127 we call it the resistor network topology design (rntd) problem. as far as we know this is a new application of topology design problems by co. the paper is organized as follows. section 2 introduces the theory of co including the main duality results for co. section 3 is devoted to the rntd problem. after introducing some notation in section 3.1, we derive a nonlinear and a linear model of the single-current rntd problem in section 3.2 and section 3.3, respectively. in section 3.3 we present the solution of of a simple rntd problem and we show that the resulting design is very unstable with respect to small perturbations of the current for which it is designed. based on a simple variational principle, introduced in section 3.4.1, we derive a model for the rntd problem that enables us to deal with the multi-current case, i.e., the case where we want to design a network that best withstands a finite set of different external currents. the model is a co model, of the semidefinite type. it is shown that by using this model a more stable design can be obtained, but also that the new design may be still sensitive to small occasional currents. to make the design less sensitive to such perturbations in the design current, in section 3.4.3 we make use of a recently developed modelling technique that yields a very robust design (see, for example, ben-tal et al. (1999, 2000), ben-tal and nemirovski (1997, 1998, 1999, 2000, 2001, 2002a, 2002b), el ghaoui and lebret (1997), el ghaoui et al. (1999) and soyster (1973)). the paper concludes with some final remarks in section 4. a preliminary version of this paper gave rise to example 8.2.6 in ben-tal et al. (2009). this paper can be seen as a worked out version of this example. 2. conic optimization the general form of a co problem is as given by (conp). in this section we start with a discussion of the conditions on the cone k, and we review the three most important cones. then we deal with the main duality results for co. it will become clear that, under some mild conditions, the duality theory for co closely resembles the well known duality theory for lo. 2.1 more on convex cones recall that a subset k of m r is a cone if , 0 ,a k a k     (1) and the cone k is a convex cone if moreover , .a a k a a k     (2) we will impose three more conditions on k. recall that co is a generalization of lo. to obtain duality results for co similar to those for lo, the cone k should inherit three more properties from the cone underlying lo, which is the nonnegative orthant:  1= = ( ; ; ) : 0, = 1, , . m m ix x x x i m r this cone is called the linear cone. the linear cone is not only a convex cone; it is also pointed, it is closed and it has a nonempty interior. these are exactly the three properties we need. we describe these properties now. a convex cone k is called pointed if it does not contain a line. this property can be formalized as follows: , = 0 .a k a k a    (3) a convex cone k is called closed if it is closed under taking limits: ( = 1, 2, ), = .limi i i a k i a a a k     (4) finally, denoting the interior of k as ,int k we require that .int k   (5) this means that k is full-dimensional, i.e., there exists a vector x k such that a ball of positive radius centered at x is contained in k. in co we only deal with cones k that enjoy the three above properties. so we always assume that k is a pointed and closed convex cone with nonempty interior. apart from the linear cone, two other relevant examples of such cones are c. roos, y. bai and d. chaerani 128 1. the lorentz cone 2 2 1 1= { : } . m m m mx x x x    l r this cone is also called the second-order cone, or the ice-cream cone. 2. the positive semidefinite cone . m s this cone 'lives' in the space m s of m m symmetric matrices (equipped with the frobenius inner product ,, = tr( ) = i j ij ija b ab a b   ) and consists of all m m matrices a which are positive semidefinite, i.e.,  = : 0, .m m t ma x ax x    s s r we assume that the cone k in (conp) is a direct product of the form 1 = , m k k k  where each component i k is either a linear, a lorentz or a semidefinite cone. if x k we also denote this as 0,kx and if x int k then we write 0.kx if this gives no confusion we omit the argument k in these notations. for example, if a is a square matrix, then 0a means that a is positive semidefinite. 2.2 conic duality before we derive the duality theory for co, we need to define the dual cone of a convex cone k:  * = : 0, .m tk a a k    r (6) we recall the following result from ben-tal and nemirovski (2001). theorem 2.1 let m k  r be a nonempty cone. then (i) the set *k is a closed convex cone; (ii) if k has a nonempty interior (i.e., int k   ) then *k is pointed; (iii) if k is a closed convex pointed cone, then *int k   ; (iv) if k is a closed convex cone, then so is *k , and the cone dual to *k is k. corollary 2.2 if m k  r is a closed pointed convex cone with nonempty interior then so is *k , and vice versa. if * = ,k k then k is called self-dual. we leave it to the reader to verify that the three cones introduced in section 2.1 are self-dual. moreover, the dual of a direct product of convex cones is the direct product of their duals, i.e., 1 1 * * *= = . m m k k k k k k     as a consequence, any direct product of linear, lorentz and semidefinite cones is self-dual. now we are ready to deal with the problem dual to a conic problem (conp). we start with observing that whenever x is a feasible solution for (conp) then the definition of *k implies   0, t ax b   for all *,k and hence x satisfies the scalar inequality *, . t t ax b k     it follows that whenever *k satisfies the relation = t a c (7) robust resistance network topology design 129 then one has = ( ) = = t t t t t t c x a x ax b b    for all x feasible for (conp). so, if *k  satisfies (7), then the quantity t b  is a lower bound for the optimal value of (conp). the best lower bound obtainable in this way is the optimal value of the problem  *: = , .max t t m b a c k       r (condd) by definition, (cond) is the dual problem of (conp). using theorem 2.1(iv), one easily verifies that the duality is symmetric: the dual problem is conic and the problem dual to the dual problem is the primal problem. indeed, from the construction of the dual problem it immediately follows that we have the weak duality property: if x is feasible for (conp) and  is feasible for (cond), then 0 . t t c x b   the crucial question is, of course, whether we have equality of the optimal values whenever (conp) and (cond) have optimal values. differently from the lo case, however, this holds only if some additional conditions are satisfied. the following theorem clarifies the situation. for its proof we refer again to ben-tal and nemirovski (2001). we call the problem (conp) solvable if it has a (finite) optimal value, and this value is attained. before stating the theorem it may be worth pointing out that a finite optimal value is not necessarily attained. for example, the semidefinite problem , 1 : 0min 1x y x x y           r has optimal value 0, but one may easily verify that this value is not attained. we need one more definition: if there exists an x such that ax b int k  , then we say that (conp) is strictly feasible. thus we have similar, and obvious, definitions for (cond) being solvable and strictly feasible, respectively. theorem 2.3 let the primal problem (conp) and its dual problem (cond) be as given above. then one has i. (a) if (conp) is below bounded and strictly feasible, then (cond) is solvable and the respective optimal values are equal. (b) if (cond) is above bounded and strictly feasible, then (conp) is solvable, and the respective optimal values are equal. ii. suppose that at least one of the two problems (conp) and (cond) is bounded and strictly feasible. then a primal-dual feasible pair ( , )x  is comprised of optimal solutions to the respective problems (a) if and only if = t t b c x (zero duality gap) and (b) if and only if [ ] = 0 t ax b  (complementary slackness). note that this result is slightly weaker than the corresponding result for the lo case. in the lo case the same theorem holds by putting everywhere 'feasible' instead of 'strictly feasible'. however, the adjective 'strictly' cannot be omitted here. for a more extensive discussion and some appropriate counter-examples we refer to ben-tal and nemirovski (2001). 3. the resistance network topology design problem a resistance network is an electrical network comprised of resistors only. the resistors are linked to each other; the points at which they are linked to each other are called the nodes of the network. we consider the situation where the input and output currents at the nodes are given. our aim is to design a resistance network that minimizes the dissipation, i.e., the energy consumption, of the network. we call this the resistance network topology design problem (rntd) problem). c. roos, y. bai and d. chaerani 130 3.1 preliminaries we assume that some of the nodes are connected to earth. these nodes are called fixed nodes; the remaining nodes are called free nodes. let  v v denote the set of (free) nodes in the network. for each node ,v v vy will denote the potential of v. if v is a fixed (i.e., grounded) node then = 0vy , so vy can be nonzero only if v is a free node. to each resistor we associate a directed arc ( , )v w connecting the nodes of the resistor. the set of all arcs is denoted as a. the node-arc incidence matrix of the resulting directed network is denoted as .b so b is a v a matrix. if u v and = ( , )a v w a then ( , ) = 1b u a if = ,u v ( , ) = 1b u a  if = ,u w and ( , ) = 0b u a otherwise. in other words,   1, if = , ( , , ) = 1, if = , , ( , ) . 0, otherwise . u v b u v w u w u v v w a        (8) the matrix obtained by removing the rows of b corresponding to fixed nodes is called the structural matrix of the network and denoted as b. in belevitch (1968), matrix b is called the partition matrix of the network. the vector of external currents is denoted as a vector . v f r so ( )f v denotes the external current in the free node v; ( )f v may be either positive, negative or zero. the currents on the arcs in the network are denoted as ,vwx and x is the vector of all currents. so . a x r kirchhoff's first law gives the balance equations in the free nodes, which are simply = .bx f (9) we assume that for every free node v such that ( ) 0f v  there exists some path in the network to a fixed node. then (9) certainly has a solution. we denote by  y y the vector of the potentials at the (free) nodes. so = 0vy if v is fixed, and otherwise = .v vy y by ohm's law, on each arc = ( , )a v w a we must have = ,vw vw v wx r y y where vwr denotes the resistance value of the arc. in other words, since = , t v w vwy y b y where vwb denotes the column of b corresponding to arc ( , ),v w = , t b y rx where r denotes the diagonal matrix of size a a with the resistance values on the diagonal, i.e. = diag( ).r r since = 0vy for all fixed nodes, we have = . t t b y b y thus we obtain = . t b y rx (10) note that if = 0vwr , then we may identify the nodes v and w. thus we may assume without loss of generality that > 0vwr for all arcs ( , ).v w we allow resistance values to be  (if the corresponding nodes are not connected). the conductance value of arc ( , )v w is denoted as .vwg so, letting 1/ = 0 , = 1 ,vw vwg r for each arc. defining = diag( ),g g where g is the vector of conductance values, we have 1 = ,g r  and equation (10) is equivalent to = . t gb y x (11) substitution into (9) yields = . t bgb y f (12) robust resistance network topology design 131 the matrix t bgb is called the conductance matrix of the network. this is a v v matrix. note that the conductance matrix depends linearly on the conductance values. without loss of generality we assume that the conductance matrix is nonsingular. from a physical point of view, it is obvious that whenever (12) has a solution then this solution is unique. in fact, one may prove that the matrix t bgb is positive definite if and only if the (undirected) subgraph consisting of all edges with positive conductance values is connected (gosh et al., 2008). to complete our model, we note that the dissipation of the network is a function of the external current vector f and the conductance vector g. we denote it as diss ( ).f g one has   2 , diss ( ) = = . t f vw vw v w a g x r x rx   using (10), (9) and (12), respectively, this can be reduced as follows:    diss ( ) = = = = .tt t t tf g x rx x b y bx y f y (13) purely to illustrate the use of the above relations, we include some elementary examples. example 3.1 (replacement resistance of a ladder network) with the tools developed so far we can easily derive both well known and new formulae for replacement resistances. obviously, when entering a unit current ve at a free node v, the replacement resistance from node v to earth is equal to the potential vy at the same node. due to (12), we conclude that the replacement resistance at any free node is equal to the corresponding element on the diagonal of the inverse matrix of the conductance matrix . t bgb as an example we consider the network drawn in figure 1. the nodes are numbered as indicated and the resistance values at the drawn arcs all are equal to 1. the nodes 5 to 9 are taken to be fixed. the nonzero elements in the matrix b are as follow below. (in this paper, we orient the arcs such that the node numbers are increasing along the arcs, but any other choice is admissible.)                0,1 1, 2 2,3 3, 4 1, 6 2, 7 3,8 4,9 0 1 1 1 1 1 12 1 1 13 1 1 14 1 . 5 16 17 18 19 b                                 removing the rows corresponding to fixed nodes we get the structural matrix b: c. roos, y. bai and d. chaerani 132                0,1 1, 2 2,3 3, 4 1, 6 2, 7 3,8 4,9 0 1 11 1 1 .1 12 1 1 13 1 1 14 b                 since r is the unit matrix i, we have =g i and hence the conductance matrix satisfies = t t bgb bb : 1 1 1 3 1 = .1 3 1 1 3 1 1 2 t bgb                    the inverse matrix is   1 34 13 5 2 1 13 13 5 2 1 1 = .5 5 10 4 2 21 2 2 4 10 5 1 1 2 5 13 t bgb                  if we want to know the resistance matrix at node 0, we just take  = 1;0;0;0;0 ,f which gives  = 34;13;5;2;1 / 21,y whence 1 = 34 / 21.y we conclude, that the replacement resistance at node 0, i.e., the resistance from node 0 to earth, equals 34 21. similarly, at nodes 1 and 4 the replacement resistance is 13 21, and at nodes 2 and 3 the replacement resistance is 10 21. figure 1. ladder network of length 5. in the above example we dealt with a ladder network of length 5. we can easily compute the replacement resistance nr of the ladder network of length n ( 2n  ) by using the recursive formula 1 2 1 = 1 , = 2 . 1 n n n r r r r     from this one easily deduces that 5 = 34 / 21,r as it should, and also that nr converges to (1 5) / 2 if n goes to infinity. robust resistance network topology design 133 example 3.2 (resistance between two adjacent points in a rectangular grid) an old question is to find the resistance between two adjacent grid points of an infinite square lattice in which all the edges represent identical resistances r. the result is 2,r and an elegant and elementary solution of the problem is given by aitchison (1964). we consider a grid of size m n with m odd and n even. for = 3m and = 4n the network is depicted in figure 2. we assume = 1.r we want to know the resistance between nodes 6 and 7; these are the end nodes of the resistance in the heart of the network. this resistance is equal to the potential at node 6 when connecting node 7 to earth and entering a unit current at node 6. figure 2. example of a grid network. as in the previous example, we use a value which is precisely the value of the element on the diagonal of the inverse matrix of the conductance matrix t bgb corresponding to element 6. table 1 gives the results for some small values of m and n: table 1. replacement resistance of 'central' arc in a grid network \m n 2 4 6 8 10 12 1 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 3 0.600000 0.565217 0.563636 0.563567 0.563564 0.563564 5 0.578947 0.526882 0.522166 0.521701 0.521652 0.521647 7 0.577465 0.519923 0.512364 0.511120 0.510897 0.510856 9 0.577358 0.518430 0.509238 0.507202 0.506696 0.506566 11 0.577351 0.518098 0.508154 0.505538 0.504735 0.504477 table 2. replacement resistance of 'central' arc when k increases k m n replacement resistance 1 1 2 1.0000000000000000 2 3 4 0.5652173913043479 3 5 6 0.5221664118803231 4 7 8 0.5111196478156734 5 9 10 0.5066959790643568 6 11 12 0.5044767482078642 7 13 14 0.5032046931553875 8 15 16 0.5024076601669391 9 17 18 0.5018752216213316 10 19 20 0.5015018885720043 by taking = 2 1,m k  and = 2n k we found the values in table 2 for = 1, ,10.k if k goes to infinity the value converges to 0.5, in agreement with the aforementioned result of aitchison (1964). c. roos, y. bai and d. chaerani 134 3.2 nonlinear model for the rntd problem with the results of the previous section we can now build a mathematical model for the rntd problem. we assume that the nodes are given and also which of these nodes are fixed. furthermore, the external current f is given. we want to find conductance values in such a way that the dissipation is minimized. mathematically speaking, this amounts to solving the following minimization problem in the vector y of the potentials and the vector g of conductance values:   , : = , 0 ,min t t g y f y bgb y f g  where = diag( ).g g if y and g are feasible, and > 0, then g  and y are feasible as well, whereas the objective value is multiplied by . hence, letting  decrease to zero, the objective value approaches to zero, but then all conductance values go to infinity, which means that all resistance values go to zero. to prevent this pathological situation, we add a normalizing constraint which requires that the sum of the conductances is bounded above by some positive constant . we may think of the number  as a measure for the amount of copper that is available for connecting the nodes. the more the amount of available copper the larger the sum of the conductance values can be and the smaller the dissipation in the network. thus we arrive at the following model:  , , : = , 0, .min t t vw g y v w a f y bgb y f g g            below we use the shorthand notation ( )a g for the conductance matrix . t bgb thus we reformulate the above problem as   , : ( ) = , , 0 ,min t t g y f y a g y f e g g  (14) where e denotes the all-in-one vector in . a r note that as a consequence of the above argument the constraint t e g  will always be tight at an optimal solution. moreover, if *g and *y are optimal solutions for = 1, then for other values of  the optimal solutions are *g and * / .y  also, since ( )a g is linear in g, the equality constraints in (14) are nonlinear (they are in fact bilinear in g and y). as a consequence, from a practical point of view, the model (14) cannot be solved efficiently. in the next section we present a much simpler, linear and hence computationally tractable, model. example 3.3 consider a network with 4 nodes, numbered from 1 to 4. we take node 1 to be fixed and the external currents in the nodes 2, 3 and 4 to be 4, -8 and -16 respectively. thus we have            1, 2 1,3 1, 4 2,3 2, 4 3, 4 2 1 1 1 4 1 13 1 , 8 . 1 1 14 16 b f                        with = 6, we computed the dissipation for two different values of g. the results were as depicted in figure 3. if = 0vwg , then arc ( , )v w is not drawn. the numbers next to the arcs show the entries of the current vector x, and those next to the nodes the entries of the potential vector y. the dissipations are 184 and 96, respectively. as will become clear later on, the last network is an optimal solution of the nonlinear problem (14). robust resistance network topology design 135 3.3 linear model for the rntd problem the voltage over resistor vwr is given by = = , t vw v w vwy y y b  where vwb denotes the column of b corresponding to arc  , .v w in practice, it is desired that the voltages do not exceed a threshold value. therefore, it becomes natural to impose an upper bound on the voltage values. taking figure 3. several 4-node networks for = 6 and = (0;4; 16; 4).f   this upper bound to be equal to 1, we therefore consider the following maximization problem:   : 1, , .max t t vw y f y y b v w a   (15) in this section we deal with the surprising fact that any optimal solution of the linear problem (15) and its dual problem can be used to construct an optimal solution to the nonlinear model (14). the nonlinear constraint 1 t vwy b  can be replaced by 1 1, t vwy b   which makes the problem a linear optimization problem. also note that the constrains in (15) can be written as 1. t b y   the dual problem of (15) is given by     1 , , = : = .min vw vw vw x v w a v w a x x x b f            (16) the constraint in the dual problem can be written simply as = .bx f since this equation has a solution, the dual problem is feasible. the primal problem is feasible as well (take = 0y ). hence, by the duality theorem for linear optimization, both problems have optimal solutions and their optimal values are equal. if y is primal feasible and x dual feasible, then we may write       1 , , , = = , t t t vw vw vw vw vw v w a v w a v w a f y x y b x y b x x        c. roos, y. bai and d. chaerani 136 which is nothing else than the weak duality property in the current situation. hence, y and x are optimal, for (15) and (16) respectively, if and only if the above two inequalities hold with equality, and this holds if and only if  = , , .tvw vw vwx y b x v w a  (17) it is worth pointing out an important consequence of this result, namely that if y is primal feasible and x dual feasible, then these solutions are optimal for (15) and (16) if and only if: for every arc( , ) with nonzero current the voltage | | equals 1. t vwv w y b (18) also note that (17) is equivalent to  diag = .tx b y x (19) 3.3.1 correctness of the linear model in this section we show that if *y and *x satisfy (17) (i.e., are optimal for (15) and (16) respectively) then ** 1 * * 1 := , := xx g y y x   (20) is an optimal solution to the nonlinear model (14). we first show that these g and y are feasible for (14), and after this that they are also optimal. one obviously has 0.g  the inequality t e g  holds with equality, because we may write * * 1 = = , t t e x e g x   (21) showing that the normalizing constraint is tight. furthermore,        20 19 16 * * *( ) = d ( ) = diag = = .t t ta g y b iag g b y b x b y b x f thus we have shown that g and y are feasible for (14). it remains for us to show that the objective value t f y is minimal. we start by computing this value for the solution given by (20). one has        2 * * * *20 19(16) 1 1 1 1* * * *= = * * = diag = = .t t t t t t x x x x f y y bx y bx e x b y e x     thus we must further show that if g and y are arbitrary feasible solutions to (14), then 2 * 1 ,t x f y   (22) where *x is any optimal solution of (16). to show this we define, according to (11), := . t x gb y then, since g and y are feasible solutions of (14), we have = = ( ) = , t bx bgb y a g y f demonstrating that x is feasible for (16). since *x is optimal for (16), we conclude that * 1 1 .x x (23) the last step in this analysis consists of proving that (23) implies (22). we have   2 1 2= ( ) = = = ( ) ( ) = = . t t t t t t t t t tf y bx y bgb y y y bgb y gb y r gb y x rx r x on the other hand, using 1 1 2 2= =e rg r g and the cauchy-schwarz inequality we obtain robust resistance network topology design 137 2 2 2 1 1 1 1 1 2 2 22 2 2 2 2 1 = ( ) = [( ) ( )] = ( ) ,t t t tx e x g r x g r x e g r x f y  (24) where the last equality follows since t e g  and 2 1 2= .tf y r x hence, also using > 0 and (23), we obtain 2 2 1 1 * , t x x f y     proving (22). thus we have shown that optimal solutions of the linear problem (15) and its dual (16) contain all the information we need to obtain an optimal solution of the nonlinear problem (14). the above proof makes clear that in any optimal solution we have 2 1 = , t x f y and due to (24) this holds if and only if 2 2 1 1 1 1 22 2 2 2[( ) ( )] = and = .t tg r x g r x e g  since the vectors 1 2g and 1 2r x are nonzero we deduce from the first equality that > 0vwg implies > 0vwx and, moreover, for all such arcs ( , )v w the products vw vwr x have the same value. since vw vwr x is equal to the voltage over arc ( , )v w we conclude that g is optimal if and only if = , if > 0 then 0 and | | is constant. t vw vw v we g g x y y   (25) using this one easily verifies that the second network in figure 3 is optimal. 3.3.2 stability with respect to small perturbations in this section we consider an optimal network g for a given external current f. one may wonder how the network behaves when it is fed with a current that differs slightly from the current f for which it is designed. we will demonstrate in this section that very small perturbations in the design current f may have a disastrous effect on the dissipation. to make this clear, let z be a nonzero eigenvector of ( )a g with eigenvalue > 0. so we have ( ) = 0.a g z z  let f denote the design current of the network and y the corresponding potential vector. without loss of generality we assume that =z f and 0. t z f  now consider the situation that the design current is replaced by ( ) :=f f z  for some 0.  then the potential vector ( )y  under the new current follows by solving the equation ( ) ( ) = .a g y f z  since ( ) =a g y f and ( ) = ,a g z z this gives ( ) = .y y z     the new dissipation then satisfies   2 ( )diss ( ) = = t t t t t f g f z y z f y z y f z z z                   . one has = diss ( ) t ff y g , 0 t f z  , 2 = t z z f and = ( ) = ( ) = ( ( ) ) = 0 , t t t t t z y y z y a g z z a g y z f   whence 0. t z y  thus we obtain c. roos, y. bai and d. chaerani 138 2 2 ( )diss ( ) diss ( ) .f fg g f     (26) it thus follows that the effect on the dissipation of a small perturbation of the design current may be large if the eigenvalue  is small. figure 4. a 5-node network with given external currents in the free nodes. example 3.4 by way of example we consider the 5-node grid shown in figure 4 with = 10, the nodes are numbered as indicated. node 1 is fixed and the values of the input currents in the remaining nodes are as shown. the matrix b and the input vector, which we denote as 1f , are as follows.                     1 1, 2 1,3 1, 4 1,5 2,3 2, 4 2,5 3, 4 3,5 4,5 2 0.00100 0 0 0 0 01 1 1 1 3 1 1 10.00000 0 0 0 0 01 1 , . 4 1 1 1 0.01000 0 0 0 0 0 1 5 1 1 1 1 0.01000 0 0 0 0 0 b f                                  for the optimal solution of (14) the following holds: 1 0.000571 0.000572 9.981628 9.992608 0.007812 0.007820 0.000000 0.000000 0.000000 0.000000 := = , = 0.000000 0.000000 0.000428 0.000428 0.000000 0.000000 0.007384 0.007392 0.002177 0.0 g g x                                  1.001100 1.001100 , = . 1.001100 0.000000 02180 y                                      moreover, the dissipation equals 10.022012 . the matrix ( )a g is given by robust resistance network topology design 139 0.000999 0.000000 0.000000 0.000428 0.000000 9.989012 0.000000 0.007384 ( ) = diag( ) = , 0.000000 0.000000 0.009989 0.002177 0.000428 0.007384 0.002177 0.009989 t a g b g b                      (27) whose eigenvalues are 0.000977, 0.007822, 0.012172, and 9.989018. so the smallest eigenvalue is = 0.000977, and a corresponding eigenvector u such that 1=u f and 1 0 t f u  is given by 9.986587 0.000372 = . 0.121645 0.503471 u             using (26) we derive that 2 2 2 ( ) 11 1 1 diss ( ) diss ( ) diss ( ) 102317 .f f fg g f g        hence, for = 0.1 , the dissipation becomes about 1023. thus we conclude that a perturbation of the design current of only 10% may lead to an increase of the dissipation by as much as a factor 100. for future reference we give the perturbed external current yielding this increase in the dissipation: 2 1 1 0.999659 10.000037 := (0.1) = 0.1 = . 0.022165 0.040347 f f f u             (28) the actual dissipation for 2f is given by 1035.225318. the above example makes clear that a small perturbation of the design current may cause a large increase of the dissipation. in practice, this phenomenon may cause the network to be burned. so it is a an important question if we can find a network that is more robust with respect to small perturbations of the design current. 3.4 robust models for the rntd problem in this section we start by showing that the rntd problem can also be modelled as a semidefinite optimization (sdo) problem. an advantage of the sdo model is that it naturally extends to the multi-current case, i.e., the case where we want to design a network that is able to withstand a finite set of different currents in the best possible way. this enables us to improve the robustness of a network considerably. 3.4.1 semidefinite model for the rntd problem it has become clear in the previous section that for a given network g with external current f the dissipation equals , t f y where y follows from the equation ( ) = .a g y f hence we have 1 diss ( ) = = ( ) . t t f g f y f a g f  (29) theorem 3.5 diss ( )f g  holds if and only if 0 . ( ) t f f a g        (30) proof. by (29), diss ( )f g  is equivalent to 1 ( ) 0. t f a g f    c. roos, y. bai and d. chaerani 140 by lemma 5.1 this is equivalent to (30), proving the theorem. recall that the matrix ( ) = t a g bgb is linear in g. this means that (30) is an lmi. due the semidefinite representation of the dissipation, as given by theorem 3.5, we can formulate the rntd problem as the following semidefinite optimization problem: , : 0, , 0 .min ( ) t t g f e g g f a g                 (31) 3.4.2 semidefinite model for the multi-current rntd problem a big advantage of the above model is that it can be easily adapted to obtain a rntd that can best withstand a finite number of currents ,jf 1 j k  (not acting at the same time). we simply need to solve the following semidefinite problem: , : 0, = 1, , , , 0 .min ( ) t j t g j f j k e g g f a g                   (32) the design variables are the components of the conductance vector g and . r a crucial issue is that the matrices in (32) depend linearly on these variables. the corresponding inequalities in (32) are therefore called linear matrix inequalities (lmi's). they express that the highest dissipation, over the currents 1, , kf f , of the network determined by g does not exceed , while the linear inequalities t e g  and 0g  express that 1= ( , , )ng g g is an admissible network. a natural question is whether we can solve this model efficiently. the answer is affirmative, as may be clear from section 1. so we are ready to give an example. example 3.6 we turn back to the problem considered in example 3.4. there we considered a network for the single design current 1,f and we also subjected the resulting network to the current 2 ,f as given by (28). these forces are given by 1 2 0.0010 0.999659 10.0000 10.000037 = , = . 0.0100 0.022165 0.0100 0.040347 f f                         (33) our aim is to optimize the network with respect to both currents by solving (32) for = 2k and 1f and 2f , as just given. the optimal solution turns out to be 2 2 0.903687 9.039812 0.020035 0.036466 0.000000 = , = 12.237244 . 0.000000 0.000000 0.000000 0.000000 0.000000 g                                 robust resistance network topology design 141 the resulting network has a topology different from the network in example 3.4, where 1f was the design current. the dissipation of the new network with respect to 1f is 11.069912. in example 3.4 the dissipation was 10.022012. so the dissipation in the new network, when loaded with 1f , is about 10% higher than the minimal dissipation. this is the price we pay for more robustness, as becomes clear by computing the dissipation with respect to 2 ,f which is now 12.237244, an increase of only 22%. this is an enormous improvement with respect to the network of example 3.4 where 2f gave rise to an increase of the dissipation with a factor of more than 100. note that this result does not necessarily imply that the new network is stable with respect to other small perturbations of the current. we investigate the instability using the same approach as in section 3.3.2. for the new network the smallest eigenvalue of ( )a g is = 0.020035 and the corresponding (normalized) eigenvector u such that 1=u f and 1 0 t f u  is given by 0.000000 0.000000 = . 10.000010 0.000001 u             if we replace the design current by 1 1( ) = ,f f u  with = 0.1, we get 3 1 1 0.001000 10.000000 := (0.1) = 0.1 = . 1.010001 0.010000 f f f u             (34) the dissipation in the network then becomes 61.981951, an increase with more than a factor of 6 with respect to the minimal dissipation for 1.f of course, we then can solve the multi-current model (32) for the input currents 1,f 2 ,f and 3,f which gives 3 3 0.532924 8.769407 0.496593 0.016689 0.000000 := , := 13.003520 . 0.170698 0.000000 0.000000 0.000000 0.013690 g                                  the dissipations with respect to the respective input currents are now 11.406625, 13.003521 and 13.003521, which is a significant improvement. note that the last two numbers are (a little) larger than 3; this must be due to inaccuracy in the computations. for future use, we computed also a worst-case input current for this network, in the same way as before, which gives c. roos, y. bai and d. chaerani 142 4 0.004708 10.000000 = . 0.012523 1.009731 f             it still may happen that some unforseen small perturbation of one of the three input currents if in the last example may drastically increase the dissipation. in the next section we present a model which yields a network that withstands every perturbation of the design vector 1,f provided that the norm of the perturbation does not exceed a prescribed fraction of 1 .f 3.4.3 a more generic rntd model when dealing with robust optimization models for the rtnd problem the most natural situation to consider is the case where the input current may be modified by arbitrary small perturbations. we therefore consider the situation where the set of external currents f has the form  = = : 1 , ,n t m pf f f qz z z q   m (35) where n f is the design current and the ellipsoid  : 1tqz z z  contains all perturbations that might occur. the matrix q has to be chosen such that f contains all possible external currents that the network has to withstand. since the set f is infinite, we meet a difficulty not present in the case of finite f, namely that the objective now is to minimize diss ( ) := diss ( ) ,supf f f f g g  (36) which is the supremum of infinitely many semidefinite representable (sdr) functions. fortunately, it is easy to get a semidefinite representation for diss ( ).f g in the next theorem pi denotes the unit matrix of order p. theorem 3.7 let f be as given by (35). then one has diss ( )f g  for each f f if and only if ( ) 0 ( ) 0 . 0 n t n t p f f a g q q i                proof. due to theorem 3.5 we have diss ( )f g  if and only if   0, , t f f f f a g         or, equivalently, if and only if    0, : 1 . ( ) t n t n f qz z z z f qz a g             we have the following chain of equivalent statements, each being equivalent to the above property:    2 2 ( ) 0, , , : 1 t n t v t f qz a g z z z                r r robust resistance network topology design 143    2 2 ( ) 2 0, , , : 1 t n t t t v t f a g z q z z z                   r r  2 : 1 2 ( ) 2 0, ,min t n t t t v t z z z f a g z q                   r r  2 2 ( ) 2 0, , t n t t v f a g q                 r r  2 22 ( ) 2 0, , , ( : ) . t n t t t v t f a g q                       r r thus it becomes clear that diss ( )f g  holds if and only if, for all , ,   :  2 2 2 ( ) 2 0 . t t n t t t f a g q                by the s-lemma (lemma 5.2) this holds if and only if there exists 0  such that    2 22 ( ) 2 , t n t t t t f a g q                which can be written as    2 2 ( ) 2 0 . t n t t t t f a g q                this implies the statement in the theorem. □ an immediate consequence of the above theorem is that , ( ) 0 diss ( ) = : ( ) 0, , 0 .min 0 n t n t f g t f g f a g q e g g q i                            (37) example 3.8 in order to get a 5-node network with design current 1,f and = 10, which is robust with respect to arbitrary perturbations u, with 10.1u f we solve (32) with 1= n f f and q the identity matrix. this gives 4 = 14.414417 and 4 4 0.417292 8.741458 0.424783 0.408135 0.000000 = , = 14.414417 . 0.000000 0.000005 0.000000 0.008310 0.000019 g                                 c. roos, y. bai and d. chaerani 144 this network admits perturbations up to 10% of the design current, while the dissipation will never exceed 14.414417. the dissipations for 1,f 2 ,f 3f and 4f are 11.429114, 13.830830, 13.830830, and 13.831614, respectively. these values are all well below 4. table 3. optimal networks and their dissipations 0 g 1g 2g 3g 4g 1 12g 0.000571 0.903687 0.532924 0.417292 2 13g 9.981628 9.039812 8.769407 8.741458 3 14g 0.007812 0.020035 0.496593 0.424783 4 15g 0.000000 0.036466 0.016689 0.408135 5 23g 0.000000 0.000000 0.000000 0.000000 6 24g 0.000000 0.000000 0.170698 0.000000 7 25g 0.000428 0.000000 0.000000 0.000005 8 34g 0.000000 0.000000 0.000000 0.000000 9 35g 0.007384 0.000000 0.000000 0.008310 10 45g 0.002177 0.000000 0.013690 0.000019 11 design dissipation  10.022012 12.237244 13.003520 14.414417 12 dissipation w.r.t 1f 10.022012 11.069912 11.406625 11.429114 13 dissipation w.r.t 2f 1035.225318 12.237244 13.003521 13.830830 14 dissipation w.r.t 3f 117.229046 61.981951 13.003520 13.830238 15 dissipation w.r.t 4f 118.800746 39.028988 45.311988 13.831614 16  min ( )a g 0.000977 0.020035 0.030070 0.416460 3.4.4 summary of the results let us summarize the results of this section. in section 3.2 we started by presenting the basic model (14) for the rntd problem. this model contains the bilinear equality constraint 1( ) = ,a g y f which makes it hard to solve. surprisingly enough it became clear in section 3.3 that the solution of (14) can be constructed from the solution of the linear optimization problem (15) and its dual problem (16). the bad news of section 3.3.2 is that the network thus obtained may suffer from serious instability. we showed in example 3.4 that a 10% perturbation in the design current 1f may multiply the dissipation by a factor of 1000. the good news is in section 3.4. we first presented the multi-current model (32) in section 3.4.2, which already gave a substantially improved robustness. next, in section 3.4.3 we derived the model (37), which yields a network that is stable with arbitrary perturbations of prescribed size. we demonstrated this in some examples. table 3 summarizes the results of the examples in section 3.4. the last four columns in table 3 correspond to the networks ,ig 1 4,i  that we found in these examples. the zero entries in ig refer to edges that are not used. note that arcs (2, 3) and (3, 4) are never used. the table shows the dissipations for these networks for the input currents 1,f 2 ,f 3f and 4.f one has 1 1= 0.1if f f for 3.i  in other words, each if with 3i  is a 10% perturbation of 1.f recall that 1g is optimal for 1f and 2g is optimal for  1 2, .f f the network 3g is optimal for  1 2 3, , ,f f f and 4g is such that for all 10% perturbations of 1f the dissipation will be at most 4 = 14.414417. the last row gives the smallest robust resistance network topology design 145 eigenvalue of the conductance matrices ( ).ia g we saw in section 3.3.2 that this eigenvalue can be considered as a measure for the robustness of a network. indeed, the last row shows that this eigenvalue is increasing in i. 4. concluding remarks it is now well-known that co is a powerful tool for the mathematical modelling of inherently nonlinear problems. the subject thanks its existence to the development of efficient solution methods for co problems in the last decade. in particular, the possibility of modeling robustness of a design in a computationally tractable way opens up many new applications. a major source for the techniques used in this paper is ben-tal and nemirovski (2001), where one of the striking examples concerns the development of co models for robust truss topology design. in the present paper we apply the same approach to the inherently more simple case of the robust resistor network topology design problem. it is shown that, by using semidefinite models, the robustness of the design can be significantly improved. the extension to more general electrical networks, with inductances and capacitors, seems to be a promising subject for future research. 5. appendix to make the paper self-supporting we list in this appendix two lemmas that are used in the paper. for the proofs we refer to the literature. the first lemma is known as the schur complement lemma. lemma 5.1 (lemma 4.2.1, page 148 in (ben-tal and nemirovski, 2001)) let = t b c a c d        be a symmetric matrix with k k block b and  block d. assume that b is positive definite. then 1 t d cb c   is called the schur complement of b in a. one has 1 0 0 . t a d cb c    we conclude with the so-called s-lemma. lemma 5.2 (theorem 4.3.3, page 176 in ben-tal and nemirovski (2001)) let a and b be symmetric n n matrices, and assume that > 0 t x ax holds for some x. then 0 0 t t x ax x bx   holds for all x if and only if there exists a 0  such that .b a 6. references aitchison, r.e. 1964. resistance between adjacent points of liebman mesh. am. j. phys., 32: 566-566. belevitch, v. 1968. classical network theory. holden-day, san francisco, california, usa. ben-tal, a., el ghaoui, l. and nemirovski, a. 2000. robustness. in handbook of semidefinite programming, internat. ser. oper. res. management sci., 27: 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(ed.) 1996. interior point methods of mathematical programming, volume 5 of applied optimization. kluwer academic publishers, dordrecht, the netherlands. wright, s.j. 1997. primal-dual interior-point methods. siam, philadelphia, usa. ye, y. 1997. interior point algorithms. wiley-interscience series in discrete mathematics and optimization. john wiley & sons inc., new york, usa. received 11 april 2011 accepted 12 september 2011 squ journal for science, 2016, 21(1), 69-81 © 2016 sultan qaboos university 69 thermal and transport properties of mafic and ultramafic rocks of oman ophiolite sayyadul arafin* and ram n. singh department of physics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: sayfin@squ.edu.om. abstract: thermal and other physical properties of rocks and minerals are of considerable significance for deriving mineralogical and compositional models of the earth's mantle. we have determined these properties for the mafic rock such as gabbro and ultramafic rock like harzburgite of the oman ophiolite suite by utilizing the debye characteristic property . forms the basis of our present investigation and allows us to evaluate their melting temperature tm, thermal conductivity kl and diffusivity d. their seismic velocities and the density data are used, a priori, to determine the debye temperature of these rocks. different thermoelastic and thermodynamic relations are further used to investigate the above properties as a function of temperature, t. our analysis shows that is temperature dependent, indicating the presence of vibrational modes other than the debye distribution in the gabbro and harzburgite of the oman ophiolite. results suggest that the thermal properties such as , tm and specific heat capacity and transport properties such as kl, d and viscosity, of ultramafic rock (harzburgite) are higher than those of mafic rock, indicating the influence of an olivine content in the former. decreases with increasing temperature but increases with increasing pressure, p. similarly, compressibilities increase for both rocks with increasing t but decrease with increasing p. the trends of variation of thermal conductivity and diffusivity with temperature and pressure are opposite. kl and d decrease with increasing t but are found to increase with increasing p. keywords: debye temperature; melting temperature; specific heat capacity; thermal conductivity; diffusivity; ophiolite. فويالت العمانيةالخواص الحرارية واالنتقالية للصخور القاعدية وفوق القاعدية من األ سيد العارفين و رام سنج سضيت. نقذ اسخخشخىا انمعذويت َانخشكيبيت نهقششة األٌميت َاضحت في اسخىباط انىمارج أانخُاص انحشاسيت َ انفيضيائيت نهظخُس َانمعادن نٍا :الملخص اسخخذاو انخُاص انخشكيبت نذسخت بفيُاليج انعماويت َرنك بعض انخُاص نهضخُس انقاعذيت مثم انقابشَ َانظخُس فُق انقاعذيت مثم انٍاسصبيشقايج في األ َكزنك klيداد دسخً حشاسة االوظٍاس دسخت انحشاسة انخُطيهيت إٌزا انبحث ساعذث في ساط فّأباسخخذامٍا ك . دسخت حشاسة ديباِ حشاسة ديباِ مه قيمت سشعاث انضالصل َ انكثافت. كزنك اسخخذمج االخخالفاث في عالقاث انحشاسة انيىاميكيت . نقذ اسخىبطج دسخت حشاسة ديباِ dعامم االوخشاسيت حعخمذ عهي دسخاث انحشاسة مما يعضَ ن دسخت حشاسة ديباِ أثبخج ححانيهىا أص اعالي بذالنت دسخت انحشاسة. َ انحشاسة االسخطانيت في اسخىخاخاث انخُا َ سعت tmَ ن كم مه أَضحج انىخائح أ فيُاليج انعماوي.ني َخُد حانت اٌخضاصيت خالف حُصيع ديباِ فّ كم مه انقابشَ َ انٍاسصَبيشقايج في األإ ّفي انظخُس فُق انقاعذيت اعهّ مه رنك في انظخُس انقاعذيت مما يذل عه عامم انهضَخت kl َ dَكزنك انخُاص االوخقانيت َ cpانحشاسة انىُعيت p .kl َdَ نكىٍا حضداد بضيادة انضغظ tباصدياد دسخت انحشاسة َنفيه في انظخُس فُق انقاعذيت.حخىاقض دسخت حشاسة ديباِ حاثيش معذن األ .pَنكىٍما يخضايذان بضيادة انضغظ tيخىاقظان باصدياد دسخت انحشاسة فيُاليج.األ ، دسخت انحشاسة انخُطيهيت ،سعت انحشاسة انىُعيت ، دسخت حشاسة االوظٍاس ، دسخت حشاسة ديباِ : الكلمات المفتاحية 1. introduction ur present understanding of the deep interior of the earth in terms of a thin crust, a mantle, a liquid outer core and a solid inner core is largely based on seismologoical data recorded at the network of seismic stations distributed all over the globe. however, thermal properties along with geochemical data have become increasingly important lately in the understanding of the interior of the earth. they are of considerable significance for deriving the mineralogical and compositional models of the earth's mantle. at depth levels of less than 700 km, thermophysical properties can help determine the tectonic and petrogenic processes involved in the generation of oceanic lithosphere. besides providing information on the interior of the earth, thermoelastic properties can enhance our knowledge about o sayyadul arafin and ram n. singh 70 the formation and transformation of rocks and minerals. the rate of deformation increases strongly with temperature but decreases with pressure at modest pressures. thermal and transport properties of planetary materials as functions of temperature and pressure are the key to the understanding of the dynamics and evolution of terrestrial planets. in recent years, a good deal of interest has been shown in the literature [1-6] in the study of the thermal properties of the mantle and the core. the debye temperature, , is one of the important ingredients in geophysical studies and has facilitated the characterization of rocks, minerals, and even geological processes such as metamorphism [7]. any change in the external condition of rocks, and other material formation and transformation, can lead to a change in . the debye temperature is a physical constant of matter that characterizes numerous properties of solids, such as specific heat, electric conductivity, thermal conductivity, broadening of x-ray spectral lines, and elastic properties. in debye theory, , is the temperature of a crystal's highest normal mode of vibration, i.e. the highest temperature that can be achieved due to a single normal vibration. the concept was first introduced by peter debye in his theory of specific heat. the debye temperature is defined by the equation, ⁄ , where k is boltzmann’s constant, h is planck’s constant, and is the maximum frequency of the vibrations of the atoms of a solid. it gives a relative idea for a temperature scale, above which vibrations within a solid behave basically according to the dulong-petit law and the heat capacity is given by 3r, r being the gas constant. below the debye temperature quantum effects are important, and the heat capacity is reduced considerably at low temperatures. at the specific heat is proportional to ( ⁄ ) (the debye t 3 approximation). the difference between the debye temperatures of the separated facies of the metamorphic rocks is maximum in the case of regional metamorphism, is lower at an intermediate level of metamorphism, and is a minimum in the case of extremely altered rocks. similarly, melting temperature and its pressure dependence, tm(p), are important items of information required for the thermal characterization of materials, including minerals and rocks. on the other hand, the dependence of thermal and transport properties on temperature and pressure is important information on the physical properties of rocks for understanding the driving forces in geodynamics. in the present work we have used the seismic velocity and the density data [8, 9] to obtain useful properties such as debye temperature, melting temperature, compressibilities, specific heat capacities, gruneisen parameter, viscosity, thermal conductivity and diffusivity of harzburgite and gabbro by making use of thermoelastic and thermodynamic equations. gabbro and harzburgite rock (a type of peridotite rock) of the oman ophiolite are of considerable interest to geophysicists and geologists. the available measured density and seismic velocities of these rocks, which are the basic input of the present analysis, are uniform and consistent. a brief description of the relevant rocks of the oman ophiolite is given in section 2. section 3 discusses the basic formalism for determining the temperature dependence of debye temperature, specific heats, compressibilities and diffusivity. the melting criterion and viscosity are discussed in section 4. section 5 describes the pressure dependence of thermal properties, and is followed by a summary and conclusion in section 6. 2. oman ophiolite ophiolite is an integral part of many mountain belts. study of ophiolites aids in understanding the formation of mountains and the history of sea-floor spreading [10,11] in past ocean basins. the samail ophiolite in southeastern oman (see figures 1 and 2 [12, 13] ) provides the best opportunity [14] to investigate the oceanic lithosphere exposed on land. from base to top, the oman ophiolite sequence is made up of peridotite, layered gabbro, massive gabbro, dikes and volcanic rocks. the entire sequence is about 13 km thick. harzburgite forms the bottom-most rock of the oman ophiolite, which is a sequence of rocks representing oceanic crustal and upper mantle material that has been pushed up onto the continents. olivine is the major constituent mineral of the upper mantle, with an average composition of 90% mol mg2sio4 and 10% mol fe2sio4 [10]. about 80% of the harzburgite of the oman ophiolite suite is olivine. the thermoelastic properties of harzburgite will, therefore, provide us with a better understanding of the composition and dynamics of the upper mantle. harzburgite is a type of peridotite rock, abundantly found in the upper mantle and predominantly composed of the minerals olivine and orthopyroxene, and relatively low proportions of basaltic ingredients. it has a uniform mineralogy of 80% olivine ((fe, mg)2sio4), 17–19% orthopyroxene ((mg, fe)2si2o6), 1% chrome spinel ((mg, fe) (al, cr)2o4) and 1% clinopyroxene ((ca, mg, fe, al)2(si, al)2o6). gabbro, an igneous rock, is another major constituent of the oman ophiolite suite. the gabbroic layer is interlayered between the mantle peridotite and the sheeted dyke complex. it represents the crustal succession of the oman ophiolite with a thickness ranging from about 1.5 km to 4 km. it is believed to have been generated in a magma chamber beneath an ancient fast-spreading ocean ridge. the largest part of the gabbroic layer is composed of troctolite, olivine gabbro and gabbro with minor wehrlite and dunite. gabbro is mainly composed of calcium plagioclase, pyroxene and olivine minerals. the percentage of olivine present in the gabbro of the oman ophiolite ranges from 18% to 44% [15]. http://scienceworld.wolfram.com/physics/debyetheory.html http://scienceworld.wolfram.com/physics/temperature.html http://scienceworld.wolfram.com/physics/normalmode.html http://scienceworld.wolfram.com/physics/temperature.html thermal and transport properties of mafic and ultramafic rocks 71 figure 1. geology of oman showing semail ophiolite in pink [12] figure 2. exposed rocks of the oman ophiolite and its associates [13] sayyadul arafin and ram n. singh 72 3. temperature dependence of thermophysical properties 3.1 debye temperature the debye theory connects the heat capacity of a poly-atomic solid with its elastic constants, and paves the way for calculating the characteristic temperature from the measured data of density and velocities of primary (p-wave) and secondary or shear (s-wave) ultrasonic waves in the solid. here we have used acoustical data [8] to obtain debye temperature. in terms of acoustic velocities, , also known as acoustic debye temperature in geophysical literature, takes the simplified form [16]: ( ) . ( ) ( ) / ⁄ ( ) (1)  is the density (g cm-3) and  is the mean atomic mass given by ⁄ ; m is the molecular weight (g mol-1) and p is the atomic number. for composite materials like harzburgite and gabbro, the mean atomic mass, μ is taken as 21 g mol -1 [17]. m v is the generalized mean velocity (km s -1 ) given by: ( ) 0 ( ( ) ( ))1 ⁄ (2) where vp and vs are the acoustic velocities of the primary (longitudinal) and secondary (transverse) waves. we have used experimentally determined values of vp, vs, ρ and an empirical value of mean atomic mass 21 amu in eqs. (1) and (2) to calculate θd [8, 9]. 400 800 1200 1600 2000 2400 2800 450 500 550 600 650 700 d e b ye te m p e ra tu re ,  d (k ) temperature, t(k) gabbro harzburgite figure 3: variation of debye temperature ( ) of gabbro and harzburgite with temperature we have calculated the temperature dependence of density and velocity of the mafic and ultramafic rocks from the available data [8, 9]. the values of obtained at different temperatures of gabbro and harzburgite are plotted in figure 3, which shows that decreases linearly with increasing temperature of the rock. typical values of at room temperature (293.15k) for gabbro and harzburgite are found to be 548 k and 693k. for harzburgite is about 26% higher than that of gabbro. the higher value for harzburgite may be due to the abundance of olivine in it.there are hardly any data on of these rocks availalable in the literature. it may be recalled that gabbro and harzburgite are composed of 40% and 80% olivine respectively. for olivine is found to be 731 k [18]. in view of this, the computed for gabbro and harzburgite are well within the expected range. 3.2 specific heat as a function of temperature the debye theorywas originally developed for monatomic solids for which the vibrational phonon density of states is given by debye frequency spectrum. the theory can be applied to polyatomic solids like rocks and minerals provided the density of states can be approximated by the frequency spectrum[19]. taking into account all the possible modes of acoustic vibrations, the total phonon energy , d u becomes [19] : ( ) ∫ ( ) ( ) the upper limit of integration, d x refers to: (4) where h is the planck's constant, d  is the debye angular frequency and b k is the boltzmann's constant. differentiating eq. (3) with respect to t , one obtains specific heat at constant volume: thermal and transport properties of mafic and ultramafic rocks 73 ( ) ∫ ( ) ( ) the integral has been evaluated here numerically by using the value of (=548 k) as determined in section 3.1. a plot of against the ratio, ⁄ is shown in figure 4. the curve approaches the maximum value of 11 25  kmolj at higher temperatures, which is the highest limiting value of r3 ( r being the gas constant) due to dulong petit'slaw. at low temperature ( ), vc increases with increasing temperature as per debye's 3 t law. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 5 10 15 20 25 s p e c if ic h e a t c a p a c it y , c v (j .m o l-1 .k -1 ) reduced temperature, t/t d harzburgite gabbro figure 4. the computed values of the debye specific heat ( ) of gabbro and harzbutgite plotted against t/ 3.3 compressibilities 3.3.1 isothermal and adiabatic compressibilities specific heat capacities are related to isothermal compressibility, t  and the coefficient of volume expansion, β through a thermodynamic relation: (6) specific heats and compressibilities are also related as: (7) where s  is the isentropic compressibility. from eqs. (6) and (7) one has: (8) s  and t minerals have been determined here from acoustic data. the adiabatic compressibility s is determined [20] from the measured values of density (ρ),and longitudinal (vp) and transverse (vs) velocities by using the relation: ( ) ( )0 ( ) ( )1 (9) further, the isothermal compressibility, t  is related to poisson ratio  , density  and p-wave velocity by the equation: ( ) , ( ), ( ) (10) where  is expressed in terms of the two velocities by the equation: ( ) [ ( ) ( )] [ ( ) ( )] (11) the computed values of s  and t for gabbro and harzburgite are plotted in figures 5 and 6, respectively, as functions of temperature. s  and t are found to increase with increasing temperature. t is slightly higher than s  . at room temperature the difference between s  and t is small, but the difference increases with increasing temperature. is determined using the values of s  and t in eq. (7). it is found to be 1.009296 and exhibits very sayyadul arafin and ram n. singh 74 little dependence on temperature. the results given in figures 5 and 6 suggest that s  and t of gabbro are higher than those of harzburgite. at ambient condition, s  of gabbro is 36% higher than that of harzburgite. 0 500 1000 1500 2000 2500 3000 0.0075 0.0080 0.0085 0.0090 0.0095 0.0100 0.0105 0.0110 0.0115 0.0120 0.0125 0.0130 0.0135 a d ia b a ti c c o m p re s s ib ili ty ,  s (g p a -1 ) temperature, t(k) g ab br o ha rzb ur git e figure 5. comparison of of temperature dependent adiabatic ( s  ) compressibility of gabbro and harzburgite 0 500 1000 1500 2000 2500 3000 0.007 0.008 0.009 0.010 0.011 0.012 0.013 0.014 is o th e rm a l c o m p re ss ib ili ty ,  t (g p a -1 ) temperature, t(k) g ab br o ha rzb urg ite figure 6. comparison of of temperature dependent isothermal ( t  ) compressibility of gabbro and harzburgite 3.3.2 specific heat at constant pressure from thermodynamic relations it may be noted that  for most solid rocks is very close to unity.  is used in eq. 8 to determine . the thermodynamic values of for mafic rock (gabbro) and ultramafic rock (harzburgite) are calculated as 678.1 and 795.7 j kg -1 k -1 respectively at room temperature of 293.15 k. this yields the specific heat at constant volume, as 671.0 j kg -1 k -1 for gabbro and 787.5 j kg -1 k -1 for harzburgite. these values are in very good agreement with the measured values [21] of 650 j.kg -1 .k -1 for gabbro and 771 j kg -1 k -1 for harzburgite. in the case of gabbro a variation in specific heat capacity value of 650-1000 j kg -1 k -1 is reported [21]. by using the value of mean atomic mass of21.0 amu, and reduce to 14.24 and 14.1 j mol -1 k -1 for gabbro and 16.71 and 16.54 j mol -1 k -1 for harzburgite respectively. we may recall that, from debye theory, at room temperature has been computed to be 21.1 for mafic and 19.1 j.mol -1 .k -1 for ultramafic rocks, figures which are about 50% and 15.5% higher than the thermodynamic values. the difference increases at higher temperatures. it was argued [17] that the similarity between heat capacities obtained thermodynamically and from debye theory can be used as a criterion for a material to be classified as a debye-like solid. we can see that the two values are far from being close to each other, indicating that the mafic and ultramafic rocks of oman ophiolite are not debye-like solids. 3.4 thermal conductivity from the striking linearity of a plot of θd against kl for silicate minerals, an empirical relation has been proposed by horai and simmons [22] connecting the two as: ( ) ( ) ( ) thermal and transport properties of mafic and ultramafic rocks 75 where kl is measured in w m −1 k −1 and in k. although the above equation was proposed for silicate minerals, the effect of chemical composition was taken into consideration in establishing eq. (12), and hence, it has been suggested [22] that it can be applied to a wide range of materials. equation (12) can be used for evaluating kl, provided is known. the thermal conductivity for gabbro determined from eq. (12) is found to be 2.68 w m -1 k -1 , which compares well with the measured value of 2.47 w m -1 k -1 [23], while it is 5.07 w m -1 k -1 for harzburgite which is higher than the value 2.69 w m -1 k -1 reported in [23]. rocks of similar genesis may have quite different thermophysical properties because of their origin from different geological provinces and their different ages [24]. 300 600 900 1200 1500 1800 2100 2400 2700 0 1 2 3 4 5 6 t h e rm a l c o n d u ct iv ity , k l (w .m -1 .k -1 ) temperature, t(k) harzburgite gabbro figure 7. dependence of thermal conductivities of gabbro and harzburgite on temperature according to wiedemann-franz law the ratio of the thermal conductivity, kl to the electrical conductivity, is given by: ( ) where is the electrical conductivity and l w -2 is the lorentz constant. this yields the electrical conductivity for gabbro, si m -1 and for harzburgite, si m -1 at normal temperature 300 k. our results of and suggest that harzburgite is a better conductor for heat and electricity than gabbro. 3.5 thermal diffusivity and activation energy in the heat transfer analysis, thermal diffusivity, d plays an important role which measures the ability of a material to conduct thermal energy relative to its ability to store thermal energy. it is defined as the ratio of the thermal conductivity, kl to the product of the density, ρ and the specific heat capacity, , i.e.: ( ) ( ) ( ) ( ) ( ) where kl is the lattice thermal conductivity, is the specific heat capacity at constant pressure, and ρ is the density. the magnitude of thermal diffusivity dictates how fast heat moves through a material. we have used our determined values of ( ), ( ) and ( ) to determine temperature dependence of the diffusivity. the thermal diffusivity value of the ultramafic rock (harzburgite) determined in this study is 2.15 mm 2 s -1 which is close to the measured value of peridotite (also a an ultramafic rock and similar to harzburgite in composition) from oman ophiolite is 2.27 mm 2 s -1 [24]. the thermal diffusivity value of 1.3 mm 2 s -1 determined here for the mafic rock (gabbro) is slightly higher than the experimental value of 0.97 mm 2 s -1 [21]. d(t) of both mafic and ultramafic rocks fall with increasing temperature. the decrease in d(t) for ultramafic rock is much sharper that of gabbro in the lower range of temperature. at high t, d(t) tends towards a constant value. sayyadul arafin and ram n. singh 76 400 800 1200 1600 2000 2400 2800 0.0 0.5 1.0 1.5 2.0 d if fu s iv it y , d (m 2 .s -1 ) temperature, t(k) harzburgite gabbro figure 8. dependence of diffusivities of gabbro and harzburgite on temperature the formation of mafic and ultramafic rocks at the deep interior of the earth involves complex chemical reactions and phase changes under the influence of high temperature and pressure. the activation energy δe is a measure of the energy necessary for a chemical reaction to occur. the repulsive energy emerging due to the overlap of electron clouds needs to be overcome by the activation energy. the computed values of d(t) have been fitted to as arrhenius type equation, ( ) where r is the gas constant. taking the natural logarithm, one has: ( ) ( ) the plot of ln d vs 1/t results in a linear variation. the slope has been used to determine δe. for gabbro δe is found to be 1.4 kj which is much lower than that (4.3 kj) of harzburgite. 4. melting temperature and viscosity 4.1 melting criterion we suggest a simple approach to determine the melting temperature from the knowledge of the debye temperature, , which we obtained in section 3.1. lindemann [25] proposed that the amplitude of the atomic vibrations increase with increasing temperature and that melting occurs when the amplitude of vibrations reach a critical fraction, m y of the mean atomic radius, a r . mott and jones [20] used the debye model to show that the mean square amplitude of vibration of each atom is given by . / . / ⁄ approximately. using this expression, lindemann's formula can be written [26]: . / (17) where m y is the maximum amplitude of vibration [27] which is taken as 0.2. is the debye temperature (k), mr the mean atomic radius and m the mean atomic mass. the value of m is taken 21 amu for gabbro and harzburgite. b k is the boltzmann's constant and h is the planck's constant. the mean atomic radius is calculated from the relation: . / ⁄ (18) the melting temperature of gabbro and harzburgite calculated from the above relations are 1201 k and 1695 k, which are much higher than the corresponding debye temperatures, 548 k and 693 k. m t is, in general, sensitive to the values of m r , and my as can be seen from eq. (17). thermal and transport properties of mafic and ultramafic rocks 77 4.2 viscosity the viscosity, of gabbro and harzburgite at their melting points can be determined [27, 28] from the values of m, tm and i.e. * + ⁄ ⁄ ( ) where viscosity, is given in mpa s. is the atomic volume at melting and m is the molecular weight. equation (19) is found to reproduce the experimental viscosity data for liquid metals at their melting points with great success. we have collected the values, , tm, , , d and η determined in this work at normal t and p in table 1. the viscosity values for the melting phase of gabbro and harzburgite determined from eq. (19) are found to be 2.21 mpa s and 2.63 mpa s.at their corresponding melting points (1201 k and 1695 k) respectively. it may be noted that all the values of thermal properties of harzburgite are larger than those of gabbro except for thermal conductivity. table 1. debye temperature (k), melting temperature (k), specific heat capacity (j kg .-1 k -1 ), thermal conductivity (w m -1 k -1 ), diffusivity d (mm 2 s -1 ) and viscosity η (mpa s) of gabbro and harzburgite; published values for each rock are shown in bracket. properties rocks (k) (k) (j kg -1 k -1 ) (w m -1 k -1 ) d (mm 2 s -1 ) (mpa s) gabbro 548 1201 678.0 2.66 1.30 0.00221 1123 [9] 650.0 [21] 2.47 [21] 0.97 [21] harzburgite 693 1693 796.0 5.07 1.8 0.00263 731 [18]** 2163 * ,1473 $ 771 [21] 2.69 [21] 2.27 [24] *melting temperature of mg2sio4; $ melting temperature of fe2sio4. it may be noted that for our model mg2sio4 constitutes 90% of olivine, which is about 80% of oman harzburgite. fe2sio4 constitutes about 10% of olivine. ** debye temperature of olivine 5. pressure dependence of thermal properties of gabbro the pressure dependence of debye temperature, specific heat capacity, adiabatic compressibility, isothermal compressibility, thermal conductivity, and diffusivity can be determined from the various equations developed in the previous sections, provided that the pressure dependence data for density and seismic velocities are known. the basic input data (seismic velocities) available for gabbro are taken from reference [8]. the sample of gabbro for which these measurements exist was taken from a depth of 5.5 km. there are no pressure dependent velocity data available for harzburgite in the literature. in this section, we have therefore restricted our discussions of pressure dependent properties to those of gabbro only. 5.1 pressure dependence of density and velocity the pressure dependence of the densities of gabbro and harzburgite are determined using the murnaghan equation [29]: ( ) [ ] ⁄ ( ) where is the density at atmospheric pressure, the bulk modulus, the pressure gradient of and p the pressure. the pressure dependent density and velocity data of gabbro are plotted in figs. 9 and 10. the density data show a linear relationship but the velocity data show a non-linear relationship with pressure. sayyadul arafin and ram n. singh 78 0.0 0.1 0.2 0.3 0.4 0.5 0.6 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 v e lo c it ie s , v p a n d v s ( k m s -1 ) pressure, p(gpa) compressional velocity, v p transverse velocity, v s figure 9. plot of density of gabbro as a function of pressure figure 10. variation of longitudinal and transverse wave velocity of gabbro with pressure 5.2 numerical results for debye temperature, compressibilities, specific heat capacity, thermal conductivity and diffusivity as a function of pressure the pressure dependence of debye temperature, specific heat capacity, compressibilities, thermal conductivity, and diffusivity are plotted in figures 11-15. the value of of gabbro increases from its value of 548 k at ambient temperature and pressure to a value of 574 k at 0.60 gpa. it can be seen from figure 11 that θd increases with increasing p but does not exhibit a linear variation like -t variation as found in figure 3. at high pressures, the gradient ⁄ is much smaller than that at low pressures. it is expected to be lower at higher pressures bcause various vibrational modes are likely to be compressed resulting in a lower gradient of ⁄ . 0.0 0.1 0.2 0.3 0.4 0.5 0.6 545 550 555 560 565 570 575 d e b y e t e m p e ra tu re ,  d (k ) pressure, p(gpa) figure 11. variation of debye temperature ( d  ) of gabbro with pressure. the pressure dependence of specific heat capacity, , is shown in figure 12. it is determined from eq. (5) using the values of (p) as shown in figure 11. with increasing pressure, decreases nonlinearly from its value of 21.1 j mol -1 k -1 at ambient pressure to about 19.6 j mol -1 k -1 at a pressure of 0.6 gpa. this amounts to a decrease of by 7.5%. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 3039.9 3040.0 3040.1 3040.2 3040.3 3040.4 3040.5 3040.6 3040.7 d e n s it y ,  (k g m -3 ) pressure, p(gpa) thermal and transport properties of mafic and ultramafic rocks 79 0.0 0.1 0.2 0.3 0.4 0.5 0.6 19.6 19.8 20.0 20.2 20.4 20.6 20.8 21.0 21.2 s p e ci fic h e a t c a p a ci ty , c v( j. m o l-1 .k -1 ) pressure, p(gpa) figure 12. variation of specific heat capacity, , of gabbro as a function of pressure. the computed values of and are plotted in figure 13 as a function of p. is approximately equal to at ambient conditions but the difference between them increases as p increases. is smaller than at high p which suggests that the specific heat ratio, , slowly increases with increasing pressure. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0098 0.0100 0.0102 0.0104 0.0106 0.0108 0.0110 0.0112 0.0114 c om pr es si bi lit ie s,  s a nd  t (g p a1 ) pressure, p(gpa) adiabatic compressibility isothermal compressibility figure 13. adiabatic and isothermal compressibilities of gabbro shown as a function of pressure. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 2.6 2.7 2.8 2.9 3.0 3.1 3.2 t h e rm a l c o n d u c ti v it y , k l (w .m -1 .k -1 ) pressure, p(gpa) figure 14. variation of thermal conductivity, kl of gabbro as a function of pressure. sayyadul arafin and ram n. singh 80 the thermal conductivity kl and diffusivity d of gabbro as a function of pressure are plotted in figures 14 and 15. both kl and d increase with increasing p. like ⁄ , the gradients ⁄ and ⁄ are large at lower pressures and decrease as p increases. kl and d increase by 10% and 61% respectively as p increases to 0.6 gpa from 0 gpa. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 1.0 1.5 2.0 2.5 3.0 3.5 4.0 d iff u si vi ty , d (m m 2 .s -1 ) pressure, p(gpa) figure 15. diffusivity, d of gabbro as a function of pressure. 6. conclusion the seismic velocities and the density data are used to determine the temperature dependence of debye temperature, ( ) and other thermodynamic and thermoelastic functions, such as specific heat capacity ( and ), compressibilities ( and ), thermal conductivity (kl), and the diffusivity (d) of gabbro and harzburgite. as determined here, was further used to compute the melting temperature tm and the viscosity ( ). the availability of experimental data for the seismic wave velocities [25] for gabbro over a wide pressure range of 0 to 6 kbar has made it possible to also compute the pressure dependence of , , . and d of gabbro. computed at ambient conditions for gabbro is 548 k and for harzburgite is 693 k. for harzburgite is about 26% higher than that of gabbro. for both rocks falls linearly with increasing temperature. the specific heat ratio ( ) for gabbro and harzburgite at normal p and t are found to be around 1.009 and 1.0103 respectively. this value of is consistent with the observation [21] that is nearly unity for rocks and minerals. is found to depend weakly on t. the value of  has been utilized to calculate the specific heat capacities, and , through thermodynamic relations. the values of and for gabbro are found to be 14.33 j mol -1 k -1 and 14.20 j mol -1 k -1 respectively at room temperature, 293.15 k. additionally, we have estimated from debye theory where occurs as an input. the value of at room temperature is obtained as 21.12 j mol -1 k -1 and the as 21.31 j mol -1 k -1 . it may be noted that and cv of gabbro determined from thermodynamic relation is about 33% lower than that determined from debye theory. and values for harzburgite determined from thermodynamic relation are 16.71 j mol -1 k -1 and 16.54 j mol -1 k -1 and those determined from debye theory are 19.31 j mol -1 k -1 and 19.11 j mol -1 k -1 respectively. in this case, specific heat capacity determined from thermodynamic relations is 13% lower than that computed from debye theory. specific heat capacities are found to increase with increasing temperature. the crucial criterion for determining [2] whether or not a polyatomic solid is a debye-like solid is the closeness between the thermodynamic value of and its value calculated from debye theory. these values exhibit little or no closeness indicating that the gabbro and harzburgite of the oman ophiolite suite are not debye-like solids. melting point has been calculated from modified lindemann's formula by making use of debye temperature as input. tm of harzburgite at ambient conditions is found to be 1693 k compared to 1201 k for gabbro. it may be noted that tm for harzburgite is about 40% higher than that of gabbro. the computed value of viscosity of molten gabbro (0.00221 mpa s) is smaller than that of the molten harzburgite (0.00263 mpa s) by about 16%. we may recall that mg, fe and si are the main constituent elements of these rocks. it is interesting to observe that the viscosities of these rocks fall within the range of the experimental values [30] of viscosity of mg (1.25 mpa s), fe (5.5 mpa s) and si (0.94 mpa s). the pressure dependence of , , , and d for gabbro have been computed as a function of pressure. this was possible by virtue of available experimental seismic velocity data for gabbro. the computed value of , kl and d are found to increase with increasing p, unlike their temperature dependence. however, specific heat (cv) and compressibilities ( and ) of gabbro decrease with increasing pressure. , tm, , , , and d are smaller in mafic rocks (gabbro) than those of ultramafic rocks (harzburgite) except for the thermal conductivity, . this behavior indicates the influence of the olivine content (80% in harzburgite and up to 40% in gabbro) on the thermal and transport properties of these rocks. the higher thermal conductivity of gabbro is likely to cause its solidification faster than is the case for harzburgite. 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(edited), smithshells metals reference book (7 th edition), butterworthheinemann, oxford, 1992. received 6 december 2015 accepted 29 february 2016 quaternionic root systems and subgroups of the squ journal for science, 2014, 19(1), 95-104 ©2014 sultan qaboos university 95 fcc, bcc and sc lattices derived from the coxeter-weyl groups and quaternions nazife özdeş koca*, mehmet koca and muna al-sawafi department of physics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *e-mail: nazife@squ.edu.om. abstract: we construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended coxeter groups 3 3 3 ( ) and w( ) ( )w a b aut a . it is naturally expected that these rank-3 coxeter-weyl groups define the point tetrahedral symmetry and the octahedral symmetry of the cubic lattices which have extensive applications in materials science. the imaginary quaternionic units are used to represent the root systems of the rank-3 coxeter-dynkin diagrams which correspond to the generating vectors of the lattices of interest. the group elements are written explicitly in terms of pairs of quaternions which constitute the binary octahedral group. the constructions of the vertices of the wigner-seitz cells have been presented in terms of quaternionic imaginary units. this is a new approach which may link the lattice dynamics with quaternion physics. orthogonal projections of the lattices onto the coxeter plane represent the square and honeycomb lattices. keywords: coxeter groups; lattices; quaternions. ( المشحقة مهfcc( والمكعب مركزي الىجه )bcc( والمكعب مركزي الجسم )scشبكات المكعب البسيط ) لكىاجيرويىنويل وا -مجمىعات كىسيحر وظيفة كىجا، مهمث كىجا و مىى الصىافية يٍ انشبكت (fcc( وانًكعب يشكضي انىخه )bcc( وانًكعب يشكضي اندسى )sc: نقذ حى بُاء شبكاث انًكعب انبسٍط ) ملخص (affine extended coxeterانًًخذة )انًخشابطت واألساسٍت وانشبكت انخثاقهٍت نًدًىعاث كىسٍخش ( راث انًشحبت انثانثت حًخهك حُاظش )حًاثم( سباعً coxeter-weylوٌم ) -.إٌ يدًىعاث كىسٍخش و ( quaternionsوثًاًَ نشبكت انًكعب وانخً نذٌها حطبٍقاث واسعت فً يدال عهى انًىاد. إٌ وحذاث انعذد انًشكب انخخٍهً كىاحٍشٍَىٌ ) انًشحبت انثانثت إلٌداد يخدهاث انشبكت. عُاصش و( رcoxeter-dynkinدٌُكٍ )-و األساسً نًخططاث كىسٍخشُظااناسخخذيج نخًثم صٌخض -انًدًىعت كخبج بذالنت أصواج يٍ كىاحٍشٍَىٌ حشكم انًدًىعت انثًاٍَت انثُائٍت. كًا حى حًثٍم سؤوط )قًى( خالٌا وٌدُش (wigner-seitzٍبذالنت وحذاث انعذد انًشكب انخخ )( ٌهً كىاحٍشٍَىquaternions وهزا انُهح اندذٌذ قذ ٌشبط بٍٍ دٌُايٍكٍت انشبكت .) ( ًٌثم شبكت انًشبع وانشبكت انسذاسٍت )خهٍت انُحم(.coxeterيع فٍضٌاء انكىاحٍشٍَىٌ. اإلسقاط انعًىدي نهشبكت عهى سطح كىسٍخش ) انًشكبت. يدًىعاث كىكسخش، انشبٍكت انفشاغٍت و انشباعٍاث مفحاح الكلمات: 1. introduction he lie groups based on the coxeter-weyl groups [1] have had a great impact in high energy physics, describing its standard model [2-4] and its extension to the grand unified theories [5-7]. the coxeter-weyl groups acting as discrete groups in the 3d euclidean space generate certain orbits [8-9] which describe the molecular structures [10] and viral symmetries [11-12]. higher dimensional lattices described by the affine extension of the coxeter-weyl groups can be used to describe the quasicrystal structures when projected into lower dimensions [13-16]. the rank-3 coxeter-weyl groups 3 3 3 ( ) and w( ) ( )w a b aut a define the point tetrahedral and octahedral symmetries of the cubic lattices which have an enormous number of applications in materials science. in this paper we explicitly show that the root lattice and the weight lattice of the affine coxeter group 3 ( ) a w a describe the fcc and bcc lattices respectively. we point out that there is a natural correspondence between the octahedral symmetry of the fcc and bcc lattices and the binary octahedral group of quaternions. the paper is organized as follows. t mailto:nazife@squ.edu.om nazife ozdes koca et al 69 in section 2 we explore how the honeycomb lattice and the square lattice in two dimensions are respectively described by the affine extensions of the coxeter-weyl groups 2 2 ( ) and ( )w a w b respectively. section 3 is devoted to the construction of the coxeter-weyl group 3 ( ) w a and its extension 3 ( )aut a by dynkin diagram symmetry in terms of quaternions. we explicitly display how those polyhedra possessing tetrahedral symmetry can be constructed as the orbits of the group 3 ( ) w a and prove that the root lattice and the weight lattice describe the fcc and the bcc lattices respectively. in section 4 we point out that the regular polyhedra can be obtained as the orbits of the coxeter-weyl group 3 ( )w b and furthermore we demonstrate that its affine extension 3 ( ) a w b describes the sc and the bcc lattices as the root and the weight lattices of 3 b expressed in terms of quaternions. in section 5 we study the orthogonal projections of 3 3 and a b lattices onto the coxeter plane, displaying respectively the square and hexagonal lattices and emphasize the importance of the dihedral subgroups of the coxeter-weyl groups in projection techniques. some conclusive remarks will be presented in section 6 regarding the applications of the quaternionic constructions of the 3d lattices. 2. construction of the honeycomb and square lattices as the affine coxeter-weyl groups wa (a2) and wa (b2) the coxeter-weyl groups are generated by reflections with respect to some hyperplanes represented by vectors (also called roots in the literature of lie algebras). if 1 2 , ,..., n r r r represent the reflection generators, then the presentation of the coxeter-weyl group ( ) w g is given by 1 2 ( ) , ,..., ( ) 1ij m n i j w g r r r r r    (1) where ij m is an integer label with 1, 2, 3, 4 ii ij m m  and 6 for i j representing respectively no line, one line, two lines (or label 4) and three lines (or label 6) between the nodes of the coxeter-dynkin diagrams which determine the crystallographic groups. in case ij m takes other positive integer values they correspond to non-crystallographic coxeter groups which are out of the scope of this work. the coxeter-dynkin diagrams representing the groups 2 2 ( ) and ( )w a w b that we will study in this section are given in figure 1. (a) (b) figure 1. the coxeter-dynkin diagrams (a) for 2 2 and (b) for a b . the vectors 1 2 and   (hereafter called „roots‟) orthogonal to the planes with respect to which the reflection generators reflect an arbitrary vector  as 2( , ) , 1, 2. ( , ) i i i i i r i           (2) the cartan matrix c with the matrix elements 2( , ) ( , ) i j ij j j c      and the metric g defined by matrix elements 1 ( , ) ( ) 2 j j ij ij g c     are important for the description of the coxeter-weyl groups and the corresponding lattices. the cartan matrix and the matrix g represent the gram matrices of the direct lattice and the reciprocal lattice respectively [17]. we take the roots i  as the generating vectors of the direct lattice. the weights i  spanning the dual space and satisfying the scalar product 2 ( , ) and ( , ) with ( , ) j i j ij i j ij j j j g             correspond to the generating vectors of the reciprocal lattice. now we discuss the lattices associated with each coxeter-weyl group. 2.1 the lattice determined by the affine group wa(a2) the cartan matrix c and the metric g are given as follows 2 1 2 11 , 1 2 1 23 c g              . (3) fcc, bcc and sc lattices 69 the plot of the polygons (triangle or hexagon) described by the orbits of the group 2 ( )w a will be given in orthonormal basis which can be obtained by using the eigenvectors of the cartan matrix [18] 1 1 2 2 1 2 1 1 ˆ ˆ( ), ( ) 2 6 x x       (4) and in the orthonormal basis the roots read as 1 2 1 3 1 3 ( , ), ( , ) 2 22 2     . (5) the group generators act on the roots as: 1 1 1 1 2 2 1 2 1 1 2 2 2 2 , , ,r r r r                 which generate the group 2 ( )w a of order 6, which is isomorphic to the dihedral group 3 d . including the dynkin diagram symmetry which implies 1 2 :   , the generators generate a group of order 12, which is isomorphic to the dihedral group 6 d . the matrix representations of the generators in the root space can be written as 1 2 1 0 1 1 0 1 , , 1 1 0 1 1 0 r r                         . (6) the affine coxeter group 2 ( ) a w a includes another generator 0 r which reflects the vectors with respect to a plane bisecting the vector 1 2   . this corresponds to a translation on an arbitrary vector  , as 1 2 ( )     . the repeated applications of the generators will generate the root lattice 2 a , where an arbitrary lattice vector is given by 1 1 2 2 , p b b   with 1 2 , b b  (the set of integers). the root system consisting of the vectors 1 2 1 2 , , ( )       determines the primitive cell of the direct lattice which is an hexagon. the whole lattice is the infinite set of hexagons as shown in figure 2. it is interesting that the honeycomb lattice does in fact exist as graphene made of carbon atoms [19]. figure 2. the honeycomb lattice. the weight vectors can be determined from the relation 2 1 i ij j j g     where the reciprocal lattice 2a  (weight lattice) vectors are given by 1 1 2 2 1 2 ( , ) q a a a a    with 1 2 , a a  . we will define an orbit in the dual space (reciprocal space) as 22 1 2 1 2 ( )( , ) ( , ) a w a a a a a which represents an isogonal hexagon with two edge lengths in general. when we have 1 2 a a , the orbit is a regular hexagon 2 (1,1) a determined by the root system which is invariant under the group 2 2 2 ( ) ( ) :aut a w a c generated by the matrices in (6). the orbits 2 21 2 ( , 0) and (0, ) a a a a represent triangles. the union of the orbits 2 2 (1, 0) (0,1) a a  , each representing an equilateral triangle, constitutes another hexagon dual to the hexagon 2 (1,1) a and describes the primitive cell of the weight lattice. since both the root lattice and the weight lattice are made of hexagons they can be transformed to each other by a change of scale and the lattice point symmetry. note that the hexagon described by two triangles is invariant under the group 2 ( )aut a which involves the dynkin diagram symmetry. we assume that the reader is familiar with the concept of nearest neighbor region which is called the wignerseitz cell or brillouin zone by the crystallographers, but is also known as the voronoi cell or drichlet region by mathematicians. the wigner-seitz cell of the root lattice 2 a is the cell 2 2 (1, 0) (0,1) a a  which can be determined from its primitive cell (see figure 3). the wigner-seitz cell 2 2 (1, 0) (0,1) a a  is a scaled copy of the dual of the primitive cell 2 (1,1) a after a 0 30 rotation. it is obvious that the primitive cell of the weight lattice is the hexagon 2 2 (1, 0) (0,1) a a  . nazife ozdes koca et al 69 it can be shown that the wigner-seitz cell of the weight lattice is the orbit 2 1 (1,1) 3 a , which is a scaled copy of the root polyhedron (hexagon in this case) by the coxeter number 3 of the group 2 ( )w a . we will see that this is a general property of the n a series of the coxeter-weyl groups. figure 3. the wigner-seitz cell 2 2 (1, 0) (0,1) a a  inscribed in the primitive cell of the root lattice. 2.2 the lattice determined by the affine group wa (b2) the roots of 2 b consist of long and short roots; in a particular orthonormal system with ( , ) i j ij l l  , the simple roots can be written as 1 1 2 2 2 ,l l l    . the cartan matrix, its inverse and the matrix g are given by 1 1 1 1 1 2 2 2 , ,1 1 2 1 11 2 2 2 c c g                           . (7) the group generators 1 2 and r r act in the root space as 1 1 1 1 2 1 2 2 1 1 2 2 2 2 , , 2 ,r r r r                 (8) which can be represented by the matrices 1 2 1 0 1 2 , 1 1 0 1 r r              . (9) they generate the dihedral group 4 d of order 8, which is the symmetry of the square. the root system consists of two orbits 2 1 2 1 1 2 { , ( + )} and { , ( +2 )}         which can also be written in the orthonormal basis as 1 2 1 2 { , } and { }l l l l    , corresponding to the centers of the edges and the vertices of a square respectively. it is clear that the root lattice is generated by the short roots of 2 b .the primitive cell is the square represented by the vectors 1 2 { , }l l  . the translation generator is obtained as the addition of the highest short root 1 2 1 + l   to any vector. therefore the root lattice is represented either by the vectors 1 1 2 2 1 2 + ; ,b b b b   or, equivalently, by 1 2 2 1 2 + ; , l m l m l m m  . then the wigner–seitz cell is a square with the vertices 2 1 2 1 1 (0,1) { } 2 2 b l l   as shown in figure 4. figure 4. the square lattice as the root lattice of 2 b . the weight lattice is represented by the vectors 1 1 2 2 1 2 +a , , a a a   . then the lattice vectors in the orthonormal basis will be 1 2 2 1 2 + ; 2 , 2 l m l m l m m  so that it involves the union of the sets with 1 2 and m m are either both fcc, bcc and sc lattices 66 integers or both half integers. this indicates also that the root lattice is a sublattice of the weight lattice. since the weight lattice and the root lattice are equivalent to each other up to a scale transformation and a rotation by 0 45 , it suffices to talk about the root lattice only. 3. construction of the fcc and the bcc lattices as the affine coxeter-weyl group wa (a3) a brief introduction is necessary for those readers not familiar with the quaternions. the quaternions are the extension of the complex number system discovered by hamilton in 1853 [20] with three imaginary units , ,i j k satisfying the well-known relations 2 2 2 1, 1i j k ijk      . in what follows we will use a different notation for the quaternionic units 1 2 3 , ,i e j e k e   . let 0 i i q q q e  , ( 1, 2, 3)i  be a real unit quaternion with its conjugate defined by 0 i i q q q e  and its norm 1qq qq  . the quaternionic imaginary units now satisfy the relations i j ij ijk k e e e    , )3,2,1,,( kji (10) where ij  and ijk  are the kronecker and levi-civita symbols, and summation over the repeated indices is understood. the unit quaternions form a group isomorphic to the special unitary group (2)su . with the definition of the scalar product 1 1 ( , ) ( ) ( ) 2 2 p q pq qp pq qp    (11) quaternions generate the four-dimensional euclidean space and the unit quaternions 1 2 3 1, , and e e e form an orthonormal basis. from now on it is understood that a quaternion is a 4d-euclidean vector. the coxeter-dynkin diagram of 3 a with the quaternionic simple roots is given in figure 5. 21 ee  23 ee  12 ee  figure 5. the coxeter diagram 3 a with quaternionic simple roots. an arbitrary quaternion  when reflected by the operator r with respect to the hyperplane orthogonal to quaternion  is given in terms of quaternion multiplication [21] as [ , ] 2 2 2 2 r             . (12) the bracket on the right of the equation (12) is self explanatory and should not be confused with the commutator notation. the cartan matrix of the coxeter-dynkin diagram 3 a and its inverse matrix are given respectively by the matrices 2 1 0 1 2 1 0 1 2 c             , 1 3 2 1 1 2 4 2 4 1 2 3 c            . (13) the generators of the coxeter group 3 ( )w a are then given in the notation of (12) by 1 1 2 1 2 1 1 [ ( ), ( )] 2 2 r e e e e      , 2 3 2 3 2 3 2 1 2 1 1 1 1 1 [ ( ), ( )] , [ ( ), ( )] . 2 2 2 2 r e e e e r e e e e           (14) the reflection generators operate on the quaternionic imaginary units as follows: 1 1 2 3 3 2 1 1 2 3 3 1 2 3 3 : , ; : , ; : , .r e e e e r e e e e r e e e e       they generate the coxeter group 3 ( )w a of order 24 isomorphic to the tetrahedral group, the elements of which can be written compactly by the set 3 ( ) {[ , ] [ , ] }w a p p t t    , , p t t t   . (15) nazife ozdes koca et al 011 here and t t  are the sets of quaternions {t 1 2 3 1 2 3 1 1, , , , ( 1 )} 2 e e e e e e        , 1 1 1 1 1 1 1 2 3 2 3 1 3 1 22 2 2 2 2 2 { ( 1 ), ( ), ( 1 ), ( ), ( 1 ), ( )}e e e e e e e e et              (16) where t represents the binary tetrahedral group of order 24, and the union of the set o t t   represents the binary octahedral group [22] of order 48 . when the simple roots are chosen 1 1 2 2 3 2 3 2 1 , ,e e e e e e        as in the figure 5 then the weight vectors are determined from (13) as 1 1 2 3 2 3 3 1 2 3 1 1 (1, 0, 0) ( ), (0,1, 0) , (0, 0,1) ( ) 2 2 e e e e e e e             . (17) the orbits generated by these vectors would lead to the set of vectors 3 3 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 1 1 1 (1, 0, 0) { ( ), ( ), ( ), ( )}, 2 2 2 2 (0,1, 0) { , , }, 1 1 1 1 (0, 0,1) { ( ), ( ), ( ), ( )}. 2 2 2 2 a a a e e e e e e e e e e e e e e e e e e e e e e e e e e e                           (18) they respectively represent the vertices of a tetrahedron, an octahedron and another tetrahedron. the orbits 3 3 (1, 0, 0) and (0, 0,1) a a together represent the vertices of a cube. therefore the symmetry of the union of the orbits 3 3 (1, 0, 0) (0, 0,1) a a  requires the dynkin diagram symmetry 1 1 [ , ]e e    which extends the coxeter group 3 ( )w a to the octahedral group 3 3 2 ( ) ( ) :aut a w a c whose quaternionic representation is given by 3 ( ) {[ , ] [ , ] [ , ] [ , ]}aut a t t t t t t t t         . (19) note that from now on we are using the group notation instead of (15), but with the same meaning. it can be proved that the coxeter-weyl group 3 ( )w a given by (15) is isomorphic to tetrahedral group 3 4 ( ) d w a t s  where the notation d t is used by crystallographers and 4 s represents the symmetric group of four objects which permutes the vertices of a tetrahedron. to understand this better, let us denote the vertices of the tetrahedron by letters; 1 2 3 1 2 3 1 2 3 1 2 3 1 1 1 1 ( ), ( ), ( ), ( ). 2 2 2 2 a e e e b e e e c e e e d e e e              it is clear now that the reflection generators can be written in the permutation notations 1 2 3 , , a b c d a b c d a b c d r r r c b a d a b d c a d c b                      . (20) in this notation they represent the generators of the group 4 s , permuting the four letters. to see a few examples, note that 1 2 r r fixes b but permutes acd. similarly 2 3 r r leaves a invariant but permutes bdc. the coxeter element 1 2 3 r r r permutes all four letters in the order acdb. the group 3 ( )aut a has three maximal subgroups, each is of order 24. a) the usual one is the 3 ( ) {[ , ] [ , ] }w a t t t t    tetrahedral group derived from the coxeter-dynkin diagram and it is the symmetry of a tetrahedron as we have seen. b) the group 3 2 ( ) {[ , ] [ , ]}w a c t t t t   is the proper rotational subgroup of the octahedral group 3 ( )aut a . in another paper [23] we have proved that it is the symmetry of the snub cube, a chiral polyhedron, and one can construct the vertices of the snub cube by the action of the group on a vector. the group 4 2 {[ , ] [ , ] } h t a c t t t t      is the pyritohedral group representing symmetry of a pyritohedron, an irregular dodecahedron with irregular pentagonal faces which occurs in pyrites. for the interested reader we give here the matrix representations of the generators of the group 3 ( )aut a acting on the quaternionic imaginary units. fcc, bcc and sc lattices 010 1 2 3 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 , 0 0 1 , 1 0 0 , 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 r r r                                                (21) 3.1 the fcc lattice as the root lattice of a3 the group generators of the affine 3 ( ) a w a are the three reflection generators 1 2 3 0 , , and r r r r , where 0 r acts like a translation by the highest root 1 2 3 2 3h e e        , that is, 0 h r    . a general vector of the root lattice is then given by 1 1 2 2 3 3 1 2 3 ; , ,p b b b b b b      which can be written in terms of quaternions as 1 1 2 2 3 3 1 2 3 ; , ,p m e m e m e m m m    . (22) the root system of 3 a is the orbit 3 1 2 2 3 3 1 (1, 0,1) { , , } a e e e e e e       consisting of 12 quaternions representing the centers of the edges of a cube. including the orbit 3 (0, 0, 0) a which corresponds to the origin, the root system represents the “non-conventional” face centered cubic cell [24]. it is easy to prove that the wigner-seitz cell of the fcc lattice is the catalan solid, the rhombic dodecahedron, dual to the archimedean solid cuboctahedron determined by the root system of 3 a . the vertices of the rhombic dodecahedron which constitutes the wigner-seitz cell can then be written as the union of the orbits 3 3 3 (1, 0, 0) (0,1, 0) (0, 0,1) a a a   whose quaternionic vertices are given in (18). the rhombic dodecahedron represented by the set of vertices is depicted in figure 6. the centers of the faces of the rhombic dodecahedron are the vertices given by 3 1 2 2 3 3 1 1 1 (1, 0,1) { , , } 2 2 a e e e e e e       . note that the rhombic dodecahedron tiles the 3d euclidean space, however, it is not vertex transitive under the group 3 ( )aut a , but rather face transitive. figure 6. the rhombic dodecahedron, wigner –seitz cell of the fcc lattice. 3.2 the bcc lattice as the weight lattice of a3 the weight lattice 3 a  is generated by three weight vectors 1 2 3 (1, 0, 0), (0,1, 0), (0, 0,1).     a general vector of the lattice is given by 1 1 2 2 3 3 1 2 3 , , ,q a a a a a a      . in terms of quaternions, a weight lattice vector consists of the linear combinations of the quaternionic units; the coefficients of the unit vectors are either all integers or half integers. recall that the root lattice consists of the quaternions obtained as the linear coefficients of the quaternionic imaginary units with integer coefficients only. we note that the orbits 3 3 3 (1, 0, 0) (0, 0, 0) (0, 0,1) a a a   form the body centered cubic cell where the origin represents the central lattice point. one can easily prove that the nearest lattice points to the origin are the orbits 3 3 3 (1, 0, 0) (0,1, 0) (0, 0,1) a a a   . from (18) we deduce that the distance to the lattice points represented by the vertices of the square 3 3 (1, 0, 0) 0, 0,1) a a  is 3 0.866 2  , but the next nearest points are on the orbit 3 (0,1, 0) a at a distance 1. as usual, the walls of the wigner-seitz cell bisect the lines joining these nearest points to the origin. it is easy to show that the intersections of these planes determine the vertices of the wigner-seitz cell as the orbit 3 1 (1,1,1) 4 a , which is a truncated octahedron as shown in figure 7, and the vertices of which are given by 3 1 2 2 3 3 1 1 2 2 3 3 1 1 1 (1,1,1) { 2 , 2 , 2 , 2 , 2 , 2 } 4 4 a e e e e e e e e e e e e             . (23) nazife ozdes koca et al 011 figure 7. truncated octahedron. 4. construction of the sc and the bcc lattices as the affine coxeter-weyl groups wa (b3) the coxeter-dynkin diagram of 3 b leading to the octahedral group 3 ( ) h w b o is shown in figure 8. figure 8. the coxeter-dynkin diagram of 3 b with quaternionic simple roots. the cartan matrix of the coxeter-dynkin diagram of 3 b and its inverse matrix are given by 2 1 0 1 2 2 0 1 2 c             , 1 1 1 1 1 1 1 2 1 2 2 , 1 2 1 1 3 1 3 1 1 2 2 2 4 c g                          . (24) the generators, 1 1 2 1 2 1 1 [ ( ), ( )] 2 2 r e e e e      ; 2 2 3 2 3 1 1 [ ( ), ( )] 2 2 r e e e e      ; 3 3 3 [ , ]r e e    (25) generate the octahedral group which can be written as 3 3 4 2 ( ) ( ) {[ , ] [ , ] [ , ] [ , ] }w b aut a s c p p p p t t t t          , ,p t t t  . (26) where the shorthand notation 3 ( ) {[ , ] [ , ] [ , ] [ , ] }w b t t t t t t t t         is given in (19). the weight vectors 1 2 3 , and    are determined from the simple roots 1 1 2 2 2 3 3 3 , ,e e e e e       as 1 3 2 1 2 3 1 2 3 1 , , ( ) 2 e e e e e e         . (27) the orbits 3 3 (1, 0, 0) , (0,1, 0) , b b and 3 (0, 0,1) b represent an octahedron, a cuboctahedron and a cube respectively. here the orbit 3 (1,1, 0) b represents the truncated octahedron which is obtained as the orbit 3 (1,1,1) a under the group 3 ( )w a . note that 3 b consists of long roots and short roots of norms 2 and 1 respectively. the octahedral group 3 ( ) h w b o in (26) generates a root system consisting of the roots 3 3 1 2 3 1 2 2 3 3 1 (1, 0, 0) (0,1, 0) { , , } { , , } b b e e e e e e e e e            . (28) it is clear from (28) that they constitute two different orbits; however the second set is merely a linear combination of the first set of vectors. by the affine extension of 3 b we note that the quaternionic highest root is 1 2h e e   . therefore the generator 0 r corresponding to the highest root 1 2h e e   leads to a translation 0 1 2 r e e     . this represents a reflection of the origin with respect to the plane bisecting the vector 2  at the point 2 2  . a general root lattice vector is then given by 1 1 2 2 3 3 , p b b b     with 1 2 3 , , b b b  . fcc, bcc and sc lattices 012 4.1 the sc lattice as the root lattice of b3 the root lattice is generated by the short roots 1 2 3 , ,e e e of 3 b and a general root lattice vector is given in terms of quaternionic units as 1 1 2 2 3 3 1 2 3 ; , ,p m e m e m e m m m    . including the origin the simple cube has the vertices 1 2 3 1 2 2 3 3 1 1 2 3 0, , , , , , , e e e e e e e e e e e e     . (29) the reciprocal lattice has the same generator vectors 1 2 3 , , e e e . the wigner-seitz cell can be determined around the origin by bisecting the lines joining the origin to the vertices 1 2 3 , ,e e e   . intersecting planes determine the vertices of the wigner-seitz cell which represents the cube given by the orbit 3 1 2 3 1 (0, 0,1) ( ) 2 b e e e    . (30) 4.2 the bcc lattice as the weight lattice of b3 the weight lattice is exactly the same lattice as determined by the weight lattice 3 a  , since the weight vectors will be the linear combinations of the quaternionic imaginary units with either integer coefficients or half integer coefficients. here the nearest neighbors of the origin are the vectors 1 2 3 1 ( ) 2 e e e   and 1 2 3 { , , }e e e   . as we have seen in the case of 3 a  , the wigner-seitz cell is the truncated octahedron whose vertices are determined as the orbit 3 1 (1,1, 0) 4 b . 5. projections of the a3 and b3 lattices onto their coxeter planes projection of higher dimensional lattices to lower dimensional spaces is an interesting technique in the description of quasicrystallography. in reference [18] we proposed that in the projection technique the coxeter number and the coxeter integers play important roles. we here describe the technique in applying it to 3 a and 3 b lattices although the result is not a quasi crystal. every coxeter group has a maximal dihedral subgroup of order 2h where h is the coxeter number. it goes as follows: partition the simple roots into two sets of roots so that each set consists of orthogonal roots. in the case of 3 a and 3 b these sets are 1 3 2 { , } and    . we now consider the case of 3 a where we define the coxeter plane determined by the vectors given by 1 1 3 2 2 2 2 3 1 ( } 2e , 2 e e          (31) which is orthogonal to the vector 3 1 3 1 1 ( } 2e 2      . we now define the generators 1 1 3 2 2 and r r r r r  which satisfy the relation 4 1 2 ( ) 1r r  .orthogonal projection will be made onto the coxeter plane determined by the vectors 1 2 and   in which 1 2 and r r act as reflection generators. 1 2 and r r do in fact generate the dihedral subgroup 4 d of 3 a of order 8. the orthogonal set of vectors in the coxeter plane can be taken as the quaternionic unit vectors 2 3 and e e . let us recall that the root lattice vectors are given by 1 1 2 2 3 3 ;p m e m e m e   1 2 3 , ,m m m  . the orthogonal projection of the 3 a lattice means one takes only the set of vectors 2 2 3 3 2 3 ; ,m e m e m m  which constitutes a square lattice, or in other words, the root lattice of the coxeter-weyl group 2 b as shown in figure 4. projection of the weight lattice onto the coxeter plane also includes the set of quaternions 2 3 and e e with half integer coefficients as shown in figure 4. for the orthogonal projection of the lattice 3 b , we follow the same technique; however the group generated by the generators 1 2 and r r is the dihedral group 6 d of order 12 since 6 1 2 ( ) 1r r  . here the coxeter plane is determined by the vectors 1 1 2 3 1 ( 2 ) 3 e e e    and 2 2 3 e e   . since the angle between them is 0 150 , the reflection generators generate the dihedral group 6 d of order 12. this is the symmetry of a hexagon. the third vector 3 1 2 3 1 ( ) 3 e e e     is orthogonal to the coxeter plane. the projection of the 3 b lattice onto the coxeter plane will lead to a honeycomb lattice as shown in figure 2. nazife ozdes koca et al 013 6. conclusion the crystallographic coxeter groups, in other words, the coxeter-weyl groups, are the skeleton of the lie groups which may have many applications in quasicrystallography. we have shown in this paper that the coxeter-weyl groups acting in 2d and 3d directly describe the square, hexagonal, sc, fcc and bcc lattices. the advantage here is that they can be associated with some finite subgroups of quaternions and the vertices can be represented by quaternionic imaginary units. the symmetries of all these lattices have been explicitly demonstrated. this is a novel aspect of the quaternionic lattices in which not only the lattice vectors but also the group elements are represented by the quaternions. since the quaternions can be used to describe the spin 2 1 states of electrons or some atoms we anticipate that the lattice structures in 2d and/or 3d with explicit spin dependence can be described by the quaternionic lattice structures. another interesting aspect of this work is that we have developed an orthogonal projection technique of the 3 3 and a b lattices leading to the square and the honeycomb lattices respectively. it is an interesting observation that, if one views the 3d lattices from the coxeter plane, one may observe the square or honeycomb lattice behaviors in the 3 3 and a b lattices respectively. references 1. coxeter, h.s.m. and moser, w.o.j. generators and relations for discrete groups springer-verlag, 1965. 2. weinberg, s. a model of leptons. phys. rev. lett., 1967, 19, 1264-1266. 3. salam, a. elementary particle theory: relativistic groups and analyticity. eighth nobel symposium, stockholm (ed. svartholm, n.), 1968, 367-377. 4. fritzsch, h., gell-mann, m. and leutwyler, h. advantages of the colour octet gluon picture. phys. lett.b, 1973, 47, 365-368. 5. georgi, h. and glashow, s. unity of all 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duneau, m. quasiperiodic patterns and icosahedral symmetry. j. phys. france, 1986, 47, 181196. 14. elser, v. the diffraction pattern of projected structures. acta cryst. a, 1986, 42, 36-43. 15. baake, m., joseph, d., kramer, p. and schlottmann, m. root lattices and quasicrystals. j. phys. math.and gen. a, 1990, 23, l1037-l1041. 16. baake, m., kramer, p., schlottmann, m. and zeidler, d. planar patterns with fivefold symmetry as sections of periodic structures in 4-space. int. j. mod. phys. b, 1990, 4, 2217-2268. 17. conway, j.h. and sloane, n.j.a. sphere packings, lattices and groups, springer-verlag, new york, 1988. 18. koca, m., koca, n.o. and koc, r. 12-fold symmetric quasicrystallography from higher dimensional lattices. 2013, arxiv: 1306.3316v2. 19. geim, a.k. and novosolev, k.s. the rise of graphene. nat. mat., 2007, 6(3), 183-191. 20. hamilton, s.w.r. lectures on quaternions london: whittaker, 1853. 21. koca, m., koc, r., al-barwani, m. noncrystallographic coxeter group h4 in e8. j. phys. a: math. gen. a, 2001, 34, 11201-11213. 22. conway, j.h. and smith, d.a. on quaternions and octonions: their geometry, arithmetics, and symmetry a.k. peters, ltd. natick, m.a., 2003. 23. koca, m., koca, n.o. and al-shueili, m. chiral polyhedra derived from coxeter diagrams and quaternions. squ j. for sci., 2011, 16, 82-101. 24. ashcroft, n.w. and mermin, n.d. solid state physics, w.b. saunders company, 1976. received 20 october 2013 accepted 9 december 2013 first steps in mesh wifi network squ journal for science, 17 (2) (2012) 214-223 © 2012 sultan qaboos university 214 first steps in mesh wifi network design by genetic algorithm m.b. reed* and s. nash department of mathematical sciences, university of bath, bath, england, u.k., *email: m.b.reed@bath.ac.uk. abstract: given a mesh of wireless nodes for wifi customers covering a city district, we describe a genetic algorithm-based approach to the problem of selecting a small fixed number of nodes as gateways to the internet, and linking the remaining nodes to the gateways either directly or by 'hopping', to create an efficient mesh network structure. the algorithm uses a modification of kmeans clustering to allocate nodes to gateways. keywords: genetic algorithms, mesh wifi network. متشابكة بواسطة خوارزمية وراثية (wifi)فاي -الخطوات األولية في تصميم شبكة واي يوارت ناش مارتن ريد و ست ، نصف ما تغطً منطقة فً مدٌنة (wifi)فاي -مستخدمً شبكة وايلنقاط السلكٌة ةبافتراض وجود شبك :ملخص خوارزمٌة وراثٌة لمسألة اختٌار عدد ثابت وصغٌر من نقاط الشبكة كبوابات إخراج إلى الشبكة العنكبوتٌة مع ربط باقً تجمع k لمتوسطات لشبكة. تستخدم الخوارزمٌة تعدٌالفعالة لتكوٌن هٌكلٌة ل" لقفزشبكة إما بطرٌقة مباشرة أو "باالنقاط .وذلك لتحدٌد نقاط بوابات الخروج 1. introduction mesh wifi network is a city-wide wireless network providing broadband connections for consumer equipment such as laptops and smartphones. coverage is provided by wifi nodes attached to masts, lampposts and other street furniture. connecting each of these nodes directly to the wired internet would be prohibitively expensive, so a mesh network is formed, where only a small proportion of nodes are directly connected (these are called gateway nodes), and the remaining nodes transmit their data to a gateway, either directly or by 'hopping' via one or more intermediate nodes. we are given the nodes' locations, and a list of which nodes have the potential for being gateways, as in figure 1. we also know, for each node, a list of those other nodes which it can 'see', i.e. would be able to transmit to. these links are limited by distance and also by line-of-sight; two nearby nodes may not be able to connect to each other because of an intervening building. the initial graph contains the potential connections as edges; see for example figure 2. the task is to design an efficient mesh structure by identifying a small number of nodes which will be used as gateways, and the route by which each of the other nodes will link to a gateway. an efficient network is one which is feasible (each node is connected to a gateway, directly or indirectly, using valid links), and in which: a first steps in mesh wifi network design 215 • the number of gateways g is relatively small; • each gateway services approximately the same number of nodes, i.e. the load or bandwidth is balanced among gateways; • the amount of data-hopping from nodes to gateways is minimised. figure 1. example 1: node locations. figure 2. example 1: all possible connections. a search of the literature in particular of the relevant institute of electrical and electronic engineers (ieee) conferences has not revealed any published algorithmic approaches to this problem. as will be seen in section 4 below, it is straightforward to evaluate a cost function for a given mesh wifi network structure. however, the structure itself is complex, consisting of a division of the initial graph into g separate subgraphs, each having one of its nodes designated as a gateway and (direct or indirect) connections from the other nodes to the gateway node. two general approaches to algorithm design for this combinatorial problem might be: i. first assign the nodes to g clusters, then within each cluster select the gateway node and hence choose m.b. reed and s. nash 216 the edges needed to connect the other nodes to it; or ii. first select the g gateway nodes, then 'grow' the subgraphs from each gateway until all nodes are included in a subgraph. a combinatorial optimization problem with characteristics similar to the mesh wifi problem, is the vehicle routing problem (vrp). in a vrp, a fleet of vehicles must be routed to deliver goods from a central depot to a distributed set of customers. the vrp thus involves the interdependent tasks of associating each vehicle with a cluster of customers, and for each vehicle determining the most efficient route by which the vehicle can visit those customers, all routes beginning and ending at a central depot. the customers are treated as nodes on a graph, and we seek a shortest-path route for each vehicle such that each customer node is visited by exactly one vehicle. here we also find two general categories of heuristic constructive algorithms which have been proposed in the literature, namely 'cluster-first, route-second' and 'route-first, cluster-second'. for example beasley (1983) gives an example of a route-first cluster-second algorithm. this categorisation of algorithms also applies to the more complicated capacitated arc routing problem (carp), where the customers are distributed along arcs of a graph, and each customer has a demand quantity ;wj the total demand on a given route must not exceed the vehicle capacity w. in the first approach, the graph is partitioned into clusters containing adjoining arcs, each cluster having a total demand not exceeding w, using a greedy algorithm or general assignment algorithm; then for each cluster a shortest-path route around the arcs is required (a standard problem in operations research known as the chinese postman problem). the second approach may involve first constructing an euler 'grand tour' over all the arcs, which is then partitioned into feasible sub-tours, each satisfying the capacity constraint. eiselt et al. (1995) review published algorithms for the carp. practical applications include the routing of street sweeping and road-gritting, postal delivery and waste and recycling collection. the carp is an np-hard (non-deterministic polynomial-time hard) problem. when comparing it to the mesh wifi problem, however, we see an additional level of complication in the latter: within each cluster we do not have to find a route around the arcs/nodes starting and finishing at a central depot node, but we need to efficiently link the nodes to a gateway node which must itself be chosen from among the cluster nodes as part of the problem. the carp can be extended to the multiple depot vrp. in the mdvrp a fixed number of depot locations are prescribed. practical applications include consumer goods distribution and newspaper delivery. a recent paper by ho et al. (2008) approaches the mdvrp using genetic algorithms. if the optimal location of the depots (and possibly also the optimal number of depots) must be determined as part of the problem, we have the location routing problem (lrp). the lrp is an extension of the mdvrp in which a (prescribed or optimal) number of depot facility sites must be chosen from a set of potential depot locations, and a cluster of customers built around each facility, which can then be routed. this is the routing problem closest to the mesh wifi problem. the lrp comprises a facility location problem and a vrp as sub problems, each of which is np-hard. a review of lrp algorithms by tuzun and burke (1999) suggests that the most profitable approach to this problem is an integrated or two-phase algorithm, which iterates between the location and routing sub-problems. a practical lrp problem solved numerically involved location of regional blood-banks serving hospitals in a region. a recent development in solving combinatorial optimization problems is the use of metaheuristics, which provide a general framework for directed search within the set of feasible solutions. under this heading we may mention simulated annealing, tabu search, neural networks, and evolutionary computation methods. in the last category the most well-established metaheuristic is genetic algorithms, although the power of ant colony optimisation (dorigo and stuetzle, 2004) is becoming increasingly recognized. this paper proposes a genetic algorithm (ga) based method for the mesh wifi problem. an individual in the ga is defined just by the unordered list of its gateway nodes; from these, the allocation of nodes to gateways is done by a clustering algorithm. the clustering algorithm is also used to create the initial population of feasible solutions. very simple crossover and mutation operators are used; crossover is performed essentially by picking low-cost gateways from the two parent solutions. the ga was run for 50 generations. it was tested on randomly-generated mesh layouts of up to 100 nodes. first steps in mesh wifi network design 217 2. genetic algorithms genetic algorithms were first proposed by holland (1975), and popularised in the textbook by goldberg (1997). they are used to find single or multiple optima of a fitness function f. they are zero-derivative methods, and require no smoothness conditions on f. they work with an encoding of feasible solutions, for example as binary strings, ordered or unordered lists of letters or integers, or real-valued vectors. each encoded solution is called an individual, or chromosome, and its individual elements are genes. the ga algorithm starts from an initial population of n individuals, usually randomly-generated. the fitness of each individual is evaluated. the ga then proceeds to develop a next-generation population by first copying all the current population. it then augments and refines this population using combination, mutation and selection, as follows: i. combination: two parent individuals are selected by weighted roulette wheel selection (individuals of higher fitness have a greater chance of being selected), and combined to produce one or more offspring. the possible combination operations usually include a variant of the biological process of genetic crossover; ii. mutation: the fittest of the offspring is chosen, but before being added to the new population a process of random mutation is applied to its genes; typically each gene has a 0.01 chance of being mutated (e.g. by flipping between 0 and 1 in a binary string). the combination+mutation process is repeated k times, creating k new population members; iii. selection: the new, augmented population of size n k is reduced to size n by a 'survival of the fittest' process. the above procedure is repeated with the new population, and iterated until a population containing individuals of sufficiently high fitness is obtained. in line with the simple genetic algorithm (sga) of goldberg, we create two offsprings from each combination using crossover, and perform the selection process using binary tournament: in each tournament, two individuals are picked at random, and the individual with the lower fitness is marked for deletion. as with the location routing problem discussed above, the mesh wifi problem is not amenable to a standard implementation of ga. it involves two sub-problems: the gateway location problem (glp) and the mesh routing problem (mrp), both of which are np-hard, and which are interdependent. the fitness of a selected set of gateways cannot be assessed without forming a mesh routing solution, and mesh routing can only be performed on the basis of a set of gateways. a complete feasible solution, prescribing the gateway locations and the routing, is too complicated a phenotype to be expressible as a genotype such as a binary string. our solution to this problem is to solve the glp using a genetic algorithm, in which the chromosome is just an unordered list of gateway nodes. from such a glp solution a mrp solution is grown using a clustering algorithm. the following three sections describe features of the ga applied to the mesh wifi problem. we denote the number of nodes by n, and the number of gateways by g; typically 0.1 < < 0.2 .n g n 3. features i: encoding and the clustering algorithm the success of a ga for a particular situation depends greatly on the way that solutions are encoded. a full encoding of a mesh network could be done using a vector of n integers, where the ith integer either indicates that node i is a gateway node (by using a value of 0, for example), or gives the number of the node to which node i will transmit its data. however such an encoding does not reflect the geometric properties of the network; the primary property is the allocation of nodes to gateways, i.e. the partition of the n nodes into g clusters, each cluster containing a gateway node and the nodes which transmit to it either directly or indirectly. we therefore chose a simpler partial encoding which just contained the g gateway node numbers, in an unordered list. from this list, the full network would be constructed using a clustering algorithm. the principle of k-means clustering (lloyd, 1982) is to partition a set of n data-points into k clusters, such that each point is in the cluster whose centroid is closest to it. the clustering process is usually performed by an m.b. reed and s. nash 218 iterative algorithm (lloyd's algorithm) involving two steps, starting from an initial partition whose cluster centroids have been calculated: i. assignment: assign each point to the cluster with the closest centroid; ii. update: re-calculate the centroids of the clusters. the iteration continues until no re-allocation of nodes is occurring. while the general principle of this algorithm is relevant to the mesh wifi problem, there is a difficulty. as was already observed, two nodes may be close together spatially, but unable to link due to an intervening building. the clustering should thus be done on the basis of the potential connections, rather than spatial distances. in our variant of k-means clustering, the distance from node i to the centroid of cluster m was replaced by the proportion = imim m v p s where imv is the number of nodes in cluster m which node i can 'see' (i.e. is connected by an arc on the initial graph), and ms is the number of nodes in cluster m. in the iterative algorithm, node i is assigned to the cluster with the highest value of .imp the gateway nodes themselves do not get reassigned. once the iteration has converged, the network connections within each cluster are formed. first, all nodes in the cluster which can see the gateway node, are routed directly to it. then all unconnected nodes which can see an already-connected node, are routed to that node and so on, until all nodes in the cluster are routed by pathways to the gateway. this approach is also used to grow the initial clusters from the gateways, at the start of the k-means clustering algorithm. the initial population of the ga consists of solutions formed by choosing g gateways at random from among the potential gateway nodes, and then applying the clustering algorithm. 4. features ii: fitness function the fitness function used was 1 = 1 f c where the cost function c is the sum of the costs for each gateway cluster. this is given by =1 = max(0, ) . g m m c c c here, c is the average nodal bandwidth, defined as the total bandwidth b for the network divided by n, and the cost mc of the mth cluster is = ( 1)( 1) m m m cn c g r s  (1) where cluster m has mr nodes connected directly to its gateway, and ms nodes connected indirectly (through hopping). it can be checked that = 0c in the ideal network of equal numbers of nodes in each cluster, and no hopping. the optimal fitness is thus = 1,f and the range is 0 < 1.f  5. features iii: genetic operations in the combination step of the ga, a pair of offsprings are formed from two parent solutions (a 'mother' and a 'father'), chosen by roulette-wheel selection. each parent consists of an unordered list of g gateway nodes. the list of gateways defining the first offspring ('child 1') is formed by first including all gateways which appear in both the mother and the father. then we look at the cluster costs (as defined in the fitness function) of the first steps in mesh wifi network design 219 remaining gateways in the mother, and include the maternal gateway associated with the least cost. any remaining gateways in child 1 are obtained from the father, again using the lowest-cost principle. child 2 is formed in the same way but using the least-cost paternal gateway, and filling with low-cost gateways from the mother. the fitness of each child is then calculated. note that this operation may produce infeasible solutions as offsprings if the initial graph is not fully connected. mutation is applied to the fitter offspring before it is added to the augmented population. each gateway node is considered in turn, and has a 0.03 probability of being mutated. where a mutation occurs, the node is replaced by a node which it can see, selected randomly. after mutation, the clustering is re-performed with the new gateway nodes. figure 3. example 1: 10 gateways: best initial connections. figure 4. example 1: 10 gateways: best final connections. 6. results the algorithm is in the early stages of development, but has already produced encouraging results on small m.b. reed and s. nash 220 sets of artificial data. to generate the data, one hundred nodes were first positioned randomly over a unit square, and each of these had a 0.5 probability of being identified as a potential gateway (see figure 1). potential connections were also assigned with a random probability, between nodes sufficiently close together (figure 2). an initial population of 50 solutions was then created by randomly selecting 10 gateways, and growing the clusters as described in section 3. the fitness of each solution was calculated, and figure 3 shows the highest fitness solution in the initial population. the ga was then run for 50 iterations, and figure 4 shows the best solution in the final population. a more even distribution of nodes into clusters is observed in figure 4, although the cost has only decreased from 4.91 to 4.55. figures 5 and 6 show the best initial and best final structures when 17 gateways are allowed. here the cost has decreased from 2.00 to 1.27. in the second example, figures 7 and 8, two exclusion zones were imposed in the domain, to represent adjoining buildings which prevent line-of-sight communication between nodes. in this case 17 gateways were specified, and the best initial and final structures are shown in figures 9 and 10. figure 5. example 1: 17 gateways: best initial connections. figure 6. example 1: 17 gateways: best final connections. 7. conclusions initial results indicate that a genetic algorithm, utilising clustering, is a possible technique for assisting the first steps in mesh wifi network design 221 design of a mesh wifi network. improvements could be made in many of the features of the current algorithm. techniques from graph theory could be applied, in particular the dijkstra algorithm for determining the shortestpath route between two given nodes, and the matrix-based algorithm finding the matrix of shortest path lengths between node pairs (chen, 2003). this information could be used to check that the initial graph is fully connected, and to construct higher-fitness solutions for the initial population of the ga. the following are some further possibilities: figure 7. example 2: node locations. figure 8. example 2: all possible connections. i. the clustering algorithm may be improved by using a different connection-based metric. for example, a node may be associated with the cluster for which the average path length to the other nodes in the cluster is smallest. ii. the fitness function is insensitive to poor internal construction of a cluster, when the size of the cluster is lower than average; there is thus no incentive for the ga to find the best node to act as the gateway. there should also be greater penalizing of paths involving more than one hop to reach the gateway, for example by replacing (1) by m.b. reed and s. nash 222 2 = ( 1)( 1)( 1) m m m m cn c g r s t   where ms nodes need one hop, and mt nodes need two or more hops to reach the gateway. iii. from looking at the initial graph showing all possible connections, it is clear that some nodes are more suitable as gateways than others, because of their high number of connections; this information could be used in the algorithm, by computing the degree of each node. the crossover and mutation operations, and the initial clusterings could be improved using this information. iv. once a mesh routing has been grown from a given set of gateways, the selection of the gateway node within each cluster could be optimized, by choosing the node with the lowest maximum path length to other nodes in the cluster, before redrawing the routes as described in section 3. figure 9. example 2: 17 gateways: best initial connections. figure 10: example 2: 17 gateways: best final connections. first steps in mesh wifi network design 223 a further development would be to treat the number of gateways g as a variable to be minimised. following the practice with vrps, this could be achieved by starting with a small value for g and re-running the algorithm with increasing values of g until feasible solutions of acceptable cost are found. 8. acknowledgements we are grateful to mike ratford of motorola uk, who was industrial supervisor of the msc dissertation (nash, 2007). 9. references beasley, j.e. 1983. route first-cluster second methods for vehicle routing. omega, 11:403-408. chen, w-k. 2003. net theory and its applications: flows in networks. imperial college press, london, uk. dorigo, m. and stuetzle, t, 2004. ant colony optimization. mit press, cambridge, massachusetts, usa. eiselt, h.a., gendreau, m. and laporte, g. 1995. arc-routing problems, part ii: the rural postman problem. operations research, 43(3): 399-414. goldberg, d.e. 1997. genetic algorithms in search, optimization and machine learning. addison wesley. ho, w., ho, g.t.s., ji, p. and lau, h.c.w. 2008. a hybrid genetic algorithm for the multi-depot vehicle routing problem. engineering applications of artificial intelligence, 21(4):548-557. holland, j. 1975. adaption in natural and artificial systems. the university of michigan press, ann arbor. lloyd, s.p. 1982. least squares quantization in pcm. ieee transactions on information theory, 28:129137. nash, s. 2007. motorola: mesh wifi gateway optimisation. m.sc. dissertation, dept. of mathematical sciences, university of bath, uk. tuzun, d. and burke, l.i. 1999. a two-phase tabu search approach to the location routing problem. european journal of operations research, 116(1):87-99. received 2 june 2011 accepted 6 january 2012 squ journal for science, 2022, 27(1), 74-76 doi:10.53539/squjs.vol27iss1pp74-76 sultan qaboos university 74 a compiled synoptic table of the standard microfacies and facies zone system of flügel (2010): a practical tool frank mattern department of earth sciences, college of science, sultan qaboos university, p.o. box 36, al-khod, muscat, sultanate of oman, email: frabk@squ.edu.om. abstract: a synoptic table, compiling the most important information of flügel’s (2010) [1] complex standard microfacies and facies zone system, is shared with the public. on one page, it contains all standard microfacies (smf) types, all facies zones (fz) and which smfs are associated with which fzs. this table provides the user with a quick and convenient reference/overview, serving students and professionals as an effective teaching/learning and research tool. keywords: overview; quick reference; rimmed tropical carbonate platform. ع للسحنات الدقيقة القياسية ونظام منطقة السحنة من فلوجل ) (: أداة عملية0202جدول شامل ُمجمَّ فرانك مارتن الخاصة بالسحنات الدقيقة القياسية المعقدة ونظام منطقة السحنة. [1]( 0202يتم مشاركة العامة بجدول شامل يجمع أهم المعلومات من فلوجل ) :صلخمال لسحنة. (، وأي السحنات الدقيقة مرتبطة بأي مناطق اfz(، وجميع مناطق السحنة )smfصفحة واحدة تحتوي على جميع أنواع السحنات الدقيقة القياسية ) سيوفر هذا الجدول للمستخدم مرجع / استعراض عام سريع ومالئم، يخدم الطالب والمهنيين كأداة تعليم / تعلم وبحث فعالة. .مراجعة عامة؛ مرجع سريع؛ منصة كربونات استوائية؛ نموذج : مفتاحيةالكلمات ال 1. introduction in 1975, james lee wilson [2] published his book carbonate facies in geologic history, which was printed seven times by 1986. one of the main features of this book is figure xii-1, redrawn in excerpts (fig. 1). it depicts the names and numbers of all nine facies zones (facies belts) associated with a rimmed tropical carbonate platform as well as the names and numbers of all 23 standard microfacies (smf) types associated with each facies zone (fz). wilson’s (1975) [2] concept of facies zones and smf was further developed by flügel (2010) [1]. in his book microfacies of carbonate rocks, he not only subdivided both fzs 1 and 9 into a and b, but also increased the number of fzs to ten by adding the zone of “meteorically affected carbonate rocks”. he also raised the number of smf types to 26 and distinguished numerous variants. in addition, he updated the names of both fzs and smf types. a compiled synoptic table of the standard microfacies and facies zone system of flügel 75 figure 1. excerpt of wilsons’s (1975) [2] figure xii-1, showing the nine fzs (facies belts) and their associated smf types. redrawn. while [2] (wilson, 1975 fig. xx-1) produced a handy synoptic diagram for quick reference at one glance, summarizing the different facies zones and their associated smf, no equivalent diagram is provided in [1] although the book, in general terms, hosts a trove of excellent illustrations. instead, one has to laboriously piece together the corresponding information. the facies zones are illustrated, numbered, named and defined on pages 662 and 663. the revised smf types are listed with their names and numbers on page 681. which smf types are assigned to which fzs must be gathered from pages 682 to 716. obviously, this is of limited practicality and has the potential to make some people hesitant to use the advanced system of [1], while at the same time, it keeps the model by [2], which “has passed the test of time” [1], more attractive. to make the work of geoscientists and students easier, the author compiled the above-mentioned information from [1] (pages 662-663, 681-716) and summarized it as much as possible in a “wilson-style” overview diagram (fig. 2). the new figure should allow the users to access key facies distribution information quickly and conveniently. thus, the author has reason to believe that it could encourage students and geoscientists to use the advanced system of [1] more frequently. the new figure also facilitates a direct comparison of the original and the updated model. for the application of figure 2 and numerous illustrated examples and case studies, the reader is referred to flügel (2010). 2. result figure 2 is a synoptic compilation of flügel’s (2010) [1] revised wilson (1975) [2] model, showing all facies zones and associated smf types for a rimmed tropical carbonate platform, using the updated terminology. it is not feasible to create the perfect analogue of wilson’s (1975) [2] original design as the new smf names [1] are too numerous and too long for it to be possible to place them all in a readable way into the vertical columns of the microfacies scheme. still, it was possible to place the most important information into one diagram (figure 2). for definitions of the fzs and well-illustrated examples of smf types, see [1] (pages 662-663, 682-710). frank mattern 76 figure 2. compilation of the most important smf and fz information according to [1]. the upper part provides the names and numbers of the facies zones as well as the facies profile. the central part lists the occurrences of smf types in the different fzs. the lower part lists the smf types and their variants. not all variants have been assigned to fzs by [1]. conflict of interest the author declares no conflict of interest. acknowledgement the author gratefully acknowledges talal al-hosni for the arabic translations. he is also indebted to anonymous reviewers for their constructive comments and to sarah mattern for having reviewed the english. references 1. flügel, e. microfacies of carbonate rocks, analysis, interpretation and application. 2 nd ed., springer, berlin, 2010. 2. wilson, j.l. carbonate facies in geologic history. springer, new york, 1975. received 24 october 2021 accepted 17 february 2022 the induction of electric currents in a squ journal for science, 17 (2) (2012) 170-186 © 2012 sultan qaboos university 170 the induction of electric currents in a conducting spherical cap with geomagnetic applications: a semi-analytical approach for the axisymmetric case a.a. ashour, m.s. abou-dina and a.f. ghaleb* department of mathematics, faculty of science, cairo university, giza, egypt, *email: afghaleb@gmail.com. abstract: the objective is to introduce a semi-analytical method for solving axisymmetric problems of electromagnetic induction in thin spherical caps placed in a time-varying magnetic field due to an axial magnetic dipole or in a time-varying uniform axial magnetic field. this method provides approximate solutions to mathematically difficult mixed boundary-value problems governing the induction of electric currents in thin sheets, for arbitrary angles of the cap. numerical results are given and discussed. the best approximations were obtained for sheets with integrated conductivity decreasing to zero towards the edge of the sheet. the case of uniform conductivity, characterized by weak singularities of the induced magnetic vector potential at the rim of the cap, yielded relatively large errors and is dealt with separately within an improved model. the method may be adequately extended to deal with other problems involving more complicated geometries, arbitrary electric conductivity distributions and inducing magnetic fields, in two or three dimensions, for various geophysical applications. keywords: spherical cap, geomagnetic applications, axisymmetric case. :ومغنطٌسٌةمع تطبٌقات جٌ بالحث فً غطاء كرويتولٌد التٌارات الكهربائٌة طرٌقة حل شبه تحلٌلٌة للحالة ذات التماثل المحوري مصطفى صابر أبو دٌنة وأحمد فؤاد غالبعطٌة عبدالسالم عاشور، موضوع فً المجال غطاء كروياقتراح طرٌقة شبه تحلٌلٌة لحل مسائل الحث الكهرومغنطٌسً فً هودف اله :خصمل المغنطٌسً المتغٌر مع الزمن لمزدوج كهربائً، فً حالة وجود تماثل محوري. ُتمكن هذه الطرٌقة من الحصول على تكون حلول تقرٌبٌة لمسائل الشروط الحدٌة المعقدة التً تصف تولٌد التٌارات الكهربائٌة فً الرقائق الموصلة للكهرباء التً . ٌضم البحث نتائج عددٌة ومناقشة لهذه النتائج. ٌتبٌن أن أفضل النتائج كانت فً الحاالت التً رويغطاء كعلى شكل ، بٌنما كانت أسوأ النتائج فً حالة التوصٌلة الكهربائٌة الثابتة التً الغطاءتؤول فٌها التوصٌلة الكهربائٌة للصفر عند حافة ٌمكن ، ولذلك تم التعامل مع هذه الحالة من خالل نموذج معدل.اءالغطتنفرد بوجود نقاط شاذة ضعٌفة للحل عند حافة كذلكأكثر تعقٌدا ولتوزٌعات أعم للتوصٌلة الكهربائٌة، و ٌةتطوٌر الطرٌقة المقترحة بشكل مناسب للتعامل مع مسائل هندس .لتطبٌقات جٌوفٌزٌائٌة مختلفة ألنواع متعددة من المجاالت الحاثة، فً بعدٌن أو ثالثة induction of electric currents in a conducting spherical cap 171 1. introduction any of the geomagnetic phenomena of electromagnetic induction in earth and in the surrounding ionosphere are investigated through mathematical models involving the solution of difficult boundaryvalue problems in three-dimensional regions of different geometries. these formulations are considerably simplified by introducing the so-called "thin sheet'' approximation, within which numerous applications can be considered. early studies of induction of electric currents in uniformly conducting infinite, or finite plane sheets were undertaken within simplified models by lamb, maxwell and others. the mathematical problem of electromagnetic induction in thin sheets was first formulated by price (1949) in terms of the scalar magnetic potentials of the inducing and the induced magnetic fields. a method suggested by price was realized by ashour (1950) to investigate the problem of induction of electric currents in a uniformly conducting circular disk. the method of multiform potentials was used by ashour (1952) to resolve the induction problem in a uniform circular disk by the sudden creation of magnetic poles, which has application in the study of magnetic storms. price's formulation found numerous geophysical applications, such as the investigation of the variations of the magnetic currents induced in the oceans and in the ionosphere. the sheet boundary condition derived by price, however, involves the gradient along the sheet of the function representing the integrated conductivity. this renders the use of the condition most inconvenient when dealing with models involving discontinuities in the integrated conductivity, such as induction in uniform infinite strips and spherical or spheroidal caps, etc. it is such geometries, among others, which have direct geophysical application, for example when studying the coast line effect and simulating vast oceans, either as part of a spherical shell or of a plane sheet. motivated by this limitation in price's formulation, ashour (1965) proposed a sheet boundary condition in terms of the vector potential, in which only the conductivity of the sheet appears, but not its gradient. this formula is specially useful for axisymmetric and for two-dimensional problems, whether the conductivity of the sheet is continuous or not, as the vector potential has only one non-vanishing component involving two of the coordinates. an early attempt to resolve the induction problem while avoiding dual integral or dual series equations was undertaken by ashour (1950). the same author, ashour (1971), deduces an integral equation for the current density induced in a thin, uniformly conducting circular disk or in an infinite plane sheet with a circular hole, and obtains solutions for the infinitely conducting sheet. the fredholm integral equation giving the density of the induced currents in a thin spherical cap was also deduced in (ashour, 1971) from the case of the disc and a solution was found for the infinitely conducting cap for certain special conductivity distributions. doss and ashour (1971) investigated the electric currents induced in a hemispherical cap by axisymmetric time-varying fields and discussed the case of highly conducting caps. the case of two thin half-sheets was considered by weidelt (1971) who succeeded in unveiling the logarithmic singular behaviour of the normal component of the magnetic field at the line of separation for the considered two-dimensional configuration. hutson et al. (1972) obtained an integral equation for the density of the induced currents in sheets of arbitrary shapes and for a wide class of conductivity distributions. they discussed the existence and uniqueness of the solution and the convergence of the proposed iteration method. they also noticed the necessity for introducing a scalar electric potential together with the vector potential, in accordance with the general rules of electrodynamics. these authors produced numerical results for the induced currents in a hemisphere of constant electric conductivity and compared their results with an exact solution. however, they did not show results at the immediate vicinity of the rim, neither have they produced results for the magnetic field components. ashour (1974a) further investigated this scalar electric potential and showed that it reduces to a constant for axisymmetric and for twodimensional problems. he deduced a generalized boundary condition on the sheet. exact solutions for certain axisymmetric problems of induction in thin non-uniform sheets with special distributions of conductivity were given by ashour (1974b) using inversion. three-dimensional modelling and inverse problems were discussed by hewson-browne and kendall (1976). these authors pointed out the importance of developing theoretical investigations in order to produce new methods of solution for the induction problems. fainberg (1980) gave an m a.a. ashour, m.s. abou-dina and a.f. ghaleb 172 ample survey of the state of global investigations of electromagnetic induction in geophysics. for those problems where the sheet is uniform and forms a part of a closed coordinate surface (spherical cap, oblate or prolate spheroidal cap, disc, infinite strip, half-plane, etc), the mathematical problem reduces to finding the solution of dual (triple, etc) integral equations or series equations. the analytical solution in closed form of such equations is not usually available and runs into serious mathematical difficulties, especially in those cases where the conductivity function has a discontinuity at the edge of the sheet. the anomalous behaviour of the normal magnetic field was discussed by many authors. ashour (1965) and later on raval et al.(1981) noticed that the normal component of the magnetic field at the egde of the perfect conductor behaves like 1/2 r  , where r denotes the distance from the edge. as stated above, weidelt (1971) uncovered the logarithmic singularity at the edge of two half-plane conductors. wolf (1983a, 1983b) discussed this issue. he notes that the model of a perfect conductor is poor at low frequencies and induction ceases to be important, hence the limitatio n of this model for geophysical applications. rigorous solutions to induction problems in thin sheets of finite electric conductivity could be obtained only in few cases of axisymmetric and two-dimensional problems (see, for example (ashour, 1971), (doss and ashour, 1971), (hewson-browne and kendall, 1976) and (hutson et al., 1972)). the significance of configurations involving perfect conductors as useful idealizations of real conductors was underlined in (hewson-browne and kendall, 1976). the difficulty of the mathematical problem and the constant need for more elaborate mathematical models to deal with modern geophysical observations boosted research towards iterative techniques and purely numerical methods, in particular for 3d modelling. review articles may be found in (chave and booker, 1987; gainberg et al., 1990; tarits, 1994; varentsov, 1983). siew and hurley (1988) treated the problem of the disc under a non-axisymmetric inducing field by an orthogonal expansion method. for applications of spherical cap harmonic analysis, one may refer to (thebault et al., 2004, 2006a, 2006b). the aim of the present work is to fill the existing gap between analytical and numerical approaches by presenting an efficient, semi-analytical procedure capable of handling models of arbitray angle of the cap and for a wide class of the conductivity function and the inducing magnetic field. the method can be adequately extended to cover other geometries of the sheet. the essence of the method is to use a boundary expansion for a function representing the error between the actual boundary conditions and those resulting from the proposed formula for the approximate solution. the method is a variant of trefftz's collocation method and was earlier initiated and implemented for efficiency in a series of test problems by two of the authors (abou-dina and ghaleb, 2004). in the present case, this is used in combination with the usual collocation technique. the problem under consideration is that of a thin, spherical cap of electric (integrated) conductivity, placed in the time-varying magnetic field due to an axisymmetric magnetic dipole. the case of a time-varying axial uniform magnetic field is also considered. other types of axisymmetric inducing fields may be treated within the same formulation. our treatment, however, will be confined to those cases of practical interest, when the effects of induction are appreciable in size. the solution of the considered problem may be used to evaluate the currents induced in the earth by the change of the ionospheric currents, as well as the components of the induced magnetic field. this model was previously investigated by doss and ashour (1971), who reduced the problem of a hemispherical shell to that of a non-uniform circular disc, then resolved the resulting dual integral equations by successive approximations, only for high values of a non-dimensional physical parameter characterizing the problem, corresponding to high conductivity or/and to very rapid variations of the inducing magnetic field. in our formulation, the conductivity takes on finite values, not necessarily high, and the time variations of the inducing magnetic field may also be taken to be arbitrary. the angle of the cap can also vary arbitrarily, but not be larger than 90 o . the case of uniform conductivity is treated separately. thus, the solutions obtained from the present formulation are expected to provide a better description of the geophysical phenomenon. 2. statement of the problem consider a thin, spherical cap defined by =r a and 0    with respect to a system of spherical polar induction of electric currents in a conducting spherical cap 173 coordinates  , ,r   with the elevation angle  measured from the upward vertical. the integrated electric conductivity    of the cap is an arbitrary continuous function of the angle . the cap is surrounded by a dielectric medium. a time varying magnetic dipole of moment  m t k is situated at a distance c from the origin, on the negative part of the z-axis  = .  here t denotes the time. accordingly, a system of electric currents is induced in the cap and it is required to calculate the intensity of the resulting current in the cap and the magnetic field everywhere in space. the case of an inducing, time varying, uniform axial magnetic field is also treated in the numerical examples. 3. basic equations and boundary conditions the problem of electromagnetic induction in thin sheets was initiated by price (1949) using a formulation through the magnetic scalar potential function. the sheet boundary condition derived within this formulation involves the derivatives of the electric conductivity of the sheet. this makes the procedure incapable of dealing with models involving discontinuities in the conductivity. a remedy to this situation was proposed by ashour (1965), who replaces the magnetic scalar potential by the magnetic vector potential, thus making the new sheet boundary condition derivative-free. ashour's formulation could handle two-dimensional problems, as well as problems with axial symmetry. a generalization of the sheet boundary condition was later suggested by ashour (1974) to cover the general case. many applications may be found in the literature (ashour, 1974). figure 1. geometry of the problem. the basic field equations to be used are those of classical electrodynamics in the quasi-static approximation, expressed through the magnetic vector potential (no scalar magnetic potential is needed here due to axial symmetry), together with the usual boundary conditions. these relations may be found in standard textbooks (jackson, 1962). in what follows, we use the rationalized mks system of units and the magnetic permeability in the dielectric is taken as equal to unity. let us assume that the function of electrical conductivity has the form  0= , = cosu u    a.a. ashour, m.s. abou-dina and a.f. ghaleb 174 in the used system of spherical polar coordinates  , ,r   in which the sheet is part of a coordinate surface. for these special choices of the conductivity and the inducing magnetic fields, the problem under consideration presents axial symmetry about the axis of the cap. in such cases, it is well-known (doss and ashour, 1971) that the vector potential a for any of the inducing and the induced magnetic fields, as well as the electric current in the cap, have only one non-vanishing component in the direction of  -increasing as shown on figure 1. these components are independent of the angle . hence  = , ,a r a e (1) where e is the unit vector in the direction of  -increasing. hereafter, the superscripts (e) and (i) refer to quantities belonging to the inducing and to the induced fields respectively. for the considered inducing fields, an axial dipole or an axial uniform field, it is well-known that the function    , e a r  is given by wolf (1983b, p.143)           0 03/2 2 2 sin , = , = 4 2 cos e iptm t r a r m t m e r cr c       (2a) for the magnetic dipole of moment  m t with magnetic field components           2 2 2 5/2 2 2 2 2 cos 3 sin , = , 4 2 cos e r r cr c crm t h r r cr c           (2b)         2 2 5/2 2 2 sin cos 2 , = , 4 2 cos e m t r cr c h r r cr c           (2c) and      0 0 , = sin , 2 e h t a r r    (3a) for the axial uniform field of intensity  0 ,h t with magnetic field components      0, = cos , e rh r h t  (3b)      0, = sin e h r h t    (3c) in both cases, the magnetic field component in the direction of  -increasing vanishes. the directions of the other two non-vanishing components are shown on figure 1. as for the vector potential of the induced magnetic field, it must be everywhere finite and continuous, and satisfies the vectorial laplace's equation  2 = i  a 0 (4) from the above equations and conditions, and using the well-known representations of harmonic functions in the system of spherical polar coordinates, one may write down the solution for the case of the axial magnetic dipole (doss and ashour, 1971)           1 10 2 1 1 1 , , , = 4 , > , n n n i n n n n n r a p u r a m t a a r a r a p u r a a                            (5a) induction of electric currents in a conducting spherical cap 175 where , = 1, 2,na n are coefficients to be determined, 1 np is the associated legendre function of degree n and order 1. for the uniform inducing field,  m t is replaced by  3 04 .a h t it is known that      1/21 2 = 1 n n dp u p u u du  (5b) and  np u is the legendre polynomial of degree n given by rodrigues' formula    2 1 = 1 2 ! n n n n n d p u u n du  (5c) the sheet boundary condition as given by ashour (1965) reduces in the present case to:         0 0= , = , 0 i i e ia a d a a r a r r                             (6) where   and   signs refer to the quantities calculated on the sheet for = 0r a  and = 0r a  respectively, d denotes the operator of differentiation with respect to the time t and 0 is the magnetic permeability of free space with value 7 -1 0 = 4 10 hm    on the remaining part of the sphere, i.e. for = ,r a < ,   the normal derivative  i a r  is continuous, which is equivalent to the no current condition. from equations (5) and (6) and the continuity of the magnetic field outside the sheet, the coefficients , = 1, 2,na n are found to satisfy the dual series equations:          1 1 2 1 = , , cos 1 , e n n n n u a p u u a a u u              (7a)    1 1 2 1 = 0, 1 < cos ,n n n n a p u u       (7b) where 0 0= ad  (8) the term involving  in the denominator in (7a) may be interpreted, as usual, as an inverse operator and evaluated according to the rules of operational calculus. without loss of generality, the dependence of the inducing field on time may be taken as a multiplicative term i te  with constant . thus, the inducing field has a periodic time variation of frequency = 2 ,   in which case the operator  acting on a function of time will be replaced by a multiplicative, dimensionless factor 0 0 0= .i a   an advantage of the above formulation of the sheet boundary condition is that the case of a perfect conductor is obtained as a limiting case when .  the only non-vanishing components of the induced magnetic field are given in terms of the coefficients , = 1, 2,na n by the expressions         0 1 1 , = cot i i i r a h r a r             a.a. ashour, m.s. abou-dina and a.f. ghaleb 176             3 1 2 3 1 1 1 , < , 4 = 1 1 , > 4 n n n n n n n n r m t n n a p u r a aa r m t n n a p u r a aa                             (9a)         0 1 1 , = i i ia h r a r r                       1 1 3 1 2 1 3 1 1 1 , , 4 = 1 , > 4 n n n n n n n n r m t n a p u r a aa r m t na p u r a aa                            (9b) the current density in the sheet is found from ampère's circuital relation as             0 1 = = i i i i a a i h h r r                                      1 3 1 = 2 1 cos , 0 . 4 n n n m t n a p a          (10) the dual series equations (7a,b) were previously solved in certain particular cases, usually by transforming them through lengthy manipulations to a single fredholm integral equation for an auxiliary function which, in turn, is solved either analytically in a very restraint number of cases (fainberg, 1980) or by further reduction to an infinite system of linear algebraic equations solved numerically. an alternative method is proposed here below. this is a variant of a more general method developed earlier by two of the authors (m.s. abou-dina and a.f. ghaleb), relying on a boundary fourier expansion (wolf, 1983a). 4. the method looking for an approximate solution to the dual series equations (7), we start by considering the truncated dual series equations        1 1 2 1 , = 0, cos 1 , n n e n n n n a p u a a u u             (11)      1 1 2 1 = 0, 1 < cos , n n n n n n a p u u      where   , = 1, 2, , n na n n are the unknowns and n is a predetermined, sufficiently large positive integer. as ,n  system (11) tends to system(7) and  n n na a for all = 1, 2,n . earlier work on two-dimensional problems or three-dimensional axisymmetric problems of electromagnetic induction in finite thin sheets of uniform conductivity (doss and ashour, 1971; weidelt, 1971) indicates a singular behaviour of the induced magnetic field at the boundary of the sheet. the component  i rh of the magnetic field has a singularity when crossing the cap along the  -direction (the corresponding singularity for plane problems is of logarithmic nature at the edge of discontinuity of the electrical conductivity, induction of electric currents in a conducting spherical cap 177 cf (doss and ashour, 1971), while the component  i h  has a jump there. the method presented here below cannot deal efficiently with such a situation, which will be treated separately in a later section. thus, for the moment, it is assumed that the function defining the conductivity is bounded and continuous on the sheet and that it decreases to zero towards the edge of the cap. let us denote the functions in the left-hand sides of equations (11) by    1 n f u and    2 n g u respectively, with 1cos 1u   and 21 cos .u    these two functions are expanded in their domains of definition in terms of two orthogonal families of functions  1rp w and   1 sp z respectively, = 0, 1, 2,r and = 1, 2, ,s as:        11 1 1 =11 = , 1 1 , nn m m m f u w r p w w        (12a) and        12 2 2 1 = , 1 1 , nn m m n g u z s p z z         (12b) with    1 2 1 cos 1 cos = 1 1 , = 1 1 . 2 2 u w u z         (12c) one has          1 11 1 11 11 1 1 2 1 = , = 1, 2, 2 1 n n mm m r f u w p w dw m m m        (13a) and          1 12 2 21 22 2 2 2 1 = , = 1, 2, . 2 1 n n mm m s g u z p z dz m m m        (13b) as n  (for the exact solution), the coefficients   1 n m r and   2 n m s tend to zero for all values of 1m and 2.m however, for an approximate solution, one needs only set to zero a finite number of these coefficients, i.e. one sets      1 11 1 11 1 = 0, = 1, 2, , n mf u w p w dw m m     (14a) and      1 12 2 21 2 = 0, = 1, 2, , n mg u z p z dz m m     (14b) for some prefixed 1m and 2.m let 1 2=m m m insertion of expressions (12) for    1 n f u w   and    2 n g u z   into conditions (14) yields the following system of linear, algebraic equations in the unknowns   , = 1, 2, , n na n n , written in matricial form as = ,ax b (15a) where x is the vector formed by the unknown coefficients   , n na a is an  m n matrix, b is an  1m  vector defined blockwise by a.a. ashour, m.s. abou-dina and a.f. ghaleb 178         1 1 2 2 = , = , a b a b a b                 (15b) where  1 ,a  2 ,a  1 b and  2 b have respective dimensions  1 ,m n  2 ,m n  1 1m  and  2 1 ,m  and       1 1 1 1 11 11 2 1 = n mm n n a p u w p w dw             1 1 11 1 1 11 1 , = 1, 2, ,n mu w p u w p w dw m m         (15c)         2 1 1 1 2 2 21 22 = 2 1 , = 1, 2, , ,n mm n a n p u z p z dz m m       (15d)           1 1 1 1 1 1 11 11 = , , = 1, 2, , , e mm b u w a a u w p w dw m m           (15e) and  1 2 2 2 = 0, = 1, 2, , m b m m (15f) for finite n, 1,m 2 ,m the resulting values of the unknown coefficients are denoted  , ,1 2 . n m m na the functions f and g defined above are correspondingly denoted  , ,1 2n m mf and  , ,1 2 . n m m g 4.1 accuracy criterion we introduce the quantities       2 , , , ,11 2 1 2 11 1 = n m m n m m e f u w dw      (16a) and       2 , , , ,11 2 1 2 21 2 = n m m n m m e g u z dz      (16b) clearly,  , ,1 21 n m m e and  , ,1 22 n m m e measure the error in satisfying the boundary conditions of the problem. they are generally non-zero, but tend to zero as ,n  hence they may be taken as criteria for the accuracy of the method. the best results are not necessarily obtained with a square matrix a, i.e. when = .m n therefore, we will assume that .m n when > ,m n the system (15) is overdetermined and the matricial equation (15a) is either solved by gaussian elimination, or else reduced to a square system by matrix multiplication from the left by the transpose matrix t a :   =t ta a ax b (17) the solution of which is obtained by any adequate method for the required approximate values of the coefficients  , ,1 2 , = 1, 2, , n m m na n n . from the computationl point of view, n cannot be increased without limit to improve the solution. alternatively, the process to be followed is: (i) n is given an initial value, then 1 m and 2m are varied until the best result is obtained according to a prefixed criterion. (ii) the value of n is then increased by 1 and the steps in (i) are repeated. (iii) the process is terminated when the optimal values of 1 2,m m and n are reached, meaning that the induction of electric currents in a conducting spherical cap 179 next iterations do not add substantially to the results. an accuracy criterion may be conveniently taken in the form:    , , , ,1 2 1 2max( 1 , 2 ) < , n m m n m m e e  (18)  is chosen sufficiently small according to the needed accuracy. 5. numerical results for the case of conductivity decreasing to zero towards the edge as stated earlier, the method allows to consider a wide range of values for the geometrical and the physical parameters of the problem. for geophysical applications, however, one usually sets: 6 4 -1 0 2 = 6.48 10 m , = 2 10 s , = s , 24 60 60 a       corresponding to a spherical cap on the earth's surface, an integrated conductivity of saline water in an ocean of depth 5 km, and a 24-hour period for the inducing field.this gives the estimate 12 . for definiteness, the function of electrical conductivity is taken in the form       1 cos( ) if > cos = 2 cos 1 0 otherwise u u u           (19) and = , = 1 (for the dipole) 2 c   we have plotted the current density distribution  ,i  the induced magnetic vector potential and the magnetic field components    0, , i rh a     , i h a   on the sphere =r a using the optimal values of m and n when the inducing field is produced by an axial magnetic dipole or by an axial uniform magnetic field. the function of electrical conductivity is also shown on the same graph as  .i  the computations were carried out for the values = 12, 100 the latter value corresponds to relatively high electrical conductivities and/or relatively rapid variations of the inducing magnetic field. for the best results: 1 2= 35, = 50n m m we have noticed, however, that the results are improved if direct collocation is used on the part of the sphere defined by =r a and < .   the optimal number of points placed on that interval was about 400. the error in satisfying the dimensionless sheet boundary condition as given in (18) was of the order of 0.001 in all four cases shown below on figures 2-5. a.a. ashour, m.s. abou-dina and a.f. ghaleb 180 figure 2. the results for conductivity decreasing to zero under a uniform axial magnetic field with = 12. figure 3. the results for conductivity decreasing to zero under a uniform axial magnetic field with = 100. as expected, each of the functions    , , i a a     , i h a   and  i  has one relative extremum on the sheet. the behavior of  i  and    , i h a   is almost the same, except for the fact that the tangential component of the magnetic field is not required to vanish identically outside the sheet. it is worth noting and comparing the behavior of the normal component    , i rh a  around the rim of the cap in the two cases of the axial dipole and the axial magnetic field. an extrapolation to the case of uniform electrical conductivity seems to predict the following singular behavior in the vicinity of the rim: induction of electric currents in a conducting spherical cap 181    , when 0 i rh a       for the axial uniform magnetic field and    , when 0 i rh a       for the axial magnetic dipole. this result was confirmed by our calculations involving different functions of electrical conductivity with steeper descents towards the zero at the rim of the cap. figure 4. the results for conductivity decreasing to zero under a axial magnetic dipole with = 12. figure 5. the results for conductivity decreasing to zero under a axial magnetic dipole with = 100. a.a. ashour, m.s. abou-dina and a.f. ghaleb 182 6. an improved version for the uniform conductivity when the cap is of uniform electrical conductivity, the conductivity function is   1 if > cos = 0 otherwise u u      the method explained above does not yield good results. in order to simulate the singular behaviour of the magnetic field at the edge of the cap, we enrich the expansion (5a) with a solution of laplace's equation on space, having a singularity at those points. such a solution may be constructed as an expansion in the associated legendre polynomials 1 (cos )np  using the function  sgn .  other possibilities are currently under investigation. thus,               1 1 1 1 1 cos , , , , = cos , , > , n n n i n n n n n r a p q g r r a a a r m t r a p q g r r a a                                 (19a) with    1 1 , = cos , k k k k r g r d p a             (19b)     1 1 1 , = cos k k k k r g r d p a              (19c) with properly chosen coefficients kd and q is a multiplicative constant to be determined simultaneously with the coefficients .na in the new truncated dual series equations, the constant q is identified with the coefficient  n n a and the dual series equations themselves take the form          1 1 1 1 2 1 cos = , 0 n nn e n n n n n a p a g a               (20a)        1 1 2 1 2 1 cos = 0, < , n nn n n n n n a p a g         (20b) with      11 1 = cos , ,k k k g d p g a        (20c)      2 1= ,g g g a   (20d) induction of electric currents in a conducting spherical cap 183 figure 6. the singular solution on the sphere = .r a figure 6 shows the function      , = , = , .g a g a g a    7. numerical results for the case of uniform conductivity this improved version of the method was used to study the case of a hemisphere 2  under a uniform, axial magnetic field previously investigated in (chave and booker, 1987) with = 12 . the results of this improved version are shown on figure 7. figure 7. the results for a uniform conductivity under a uniform axial magnetic field with = 12. figure 8 compares our result for the real and imaginary parts of the electric current density,  re i and  ,im i with that of hutson et al. (1972). the adjustment of the angle measure to degrees was made to match the reference. a.a. ashour, m.s. abou-dina and a.f. ghaleb 184 figure 8. comparison of present results with those of chave and booker (1987) for the real and imaginary parts of the current density. the solid lines represent the exact solutions (this solution is not produced in (hutson et al., 1972)) for the real and the imaginary parts of the electric current density, the dotted lines represent the numerical results of hutson et al. (1972), while the dashed lines are those of the present work. the results obtained by the proposed method clearly deteriorate as one gets closer to the edge of the cap. as expected, the error in satisfying the sheet boundary condition is now of the order of 0.025, i.e. much larger than for the case of the conductivity decreasing towards zero at the edge, and is concentrated towards the edge of the cap. also, the number of points used for the collocation doubled in comparison to the previous case. we have considered the case of the axial magnetic dipole as well. the results are qualitatively similar to those of the uniform axial magnetic field, with a comparable order for the error. 8. conclusions the following conclusions were reached, concerning the efficiency of the present approach: a. the proposed method, together with its improvement, can deal efficiently with the axisymmetric problem of magnetic induction in the spherical cap to generate approximate solutions to a difficult boundary-value problem for which very few exact solutions are known. b. the method is flexible in what concerns the nature of the inducing magnetic field and the function of electrical conductivity in the cap, provided it is bounded and continuous. c. there is room for increasing the accuracy by associating the usual collocation method with the one proposed above. d. the error strictly decreases initially, but fails to keep this behavior after a threshold value of the number of degrees of freedom n is reached: an oscillatory character generally establishes beyond this stage. this is probably due to the accumulation error. induction of electric currents in a conducting spherical cap 185 e. the method is more efficient for larger angles of the cap, as the induction effects become more pronounced. however, further studies are necessary when the cap exceeds the hemisphere. f. the method becomes less efficient for larger , i.e for higher electrical conductivity or/and faster time variations of the inducing magnetic field. g. the level of accuracy is strongly affected by the presence of weak singularities located at the rim of the cap, in which case the expression for the approximate solution has to include additional terms accounting for these singularities. h. adequate harmonic functions with singularities at the edge could be introduced into the expansion set of functions in order to obtain improved approximate solutions. such harmonic functions with boundary singularities may be efficiently used in other problems with more complicated geometries of the boundary. i. the effect of the additionally introduced harmonic functions is to improve the accuracy and, simultaneously, to decrease significantly the number of terms in the expansion for the approximate solution and the number of zeroed fourier coefficients. j. the obtained results with geophysical applications yield results which are in qualitative agreement with the data scattered throughout the literature. 9. references abou-dina, m.s. and ghaleb, a.f. 2004. a variant of trefftz's method by boundary fourier expansion for solving regular and singular plane boundary-value problems. j. comp. appl. math. (c.a.m.), 167: 363-387. ashour, a.a. 1950. the induction of electric currents in a uniform circular disk. quart. j. mech. appl. math., 3(1): 119-128. ashour, a.a. 1952.the induction of electric currents in a uniformly conducting circular disk by the sudden creation of magnetic poles. quart. j. mech. appl. math., 5(3): 379-384. ashour, a.a. 1965. electromagnetic induction in finite thin sheets. quart. j. mech. appl. math., 18(1): 7386. ashour, a.a. 1971. electromagnetic induction in thin finite sheets having conductivity decreasing to zero at the edge, with geomagnetic applications. geophys. j. r. astr. soc., 22: 489-498. ashour, a.a. 1974a. research note: the condition at the surface of a thin conductor in which currents are induced. geophys. j. r. astr. soc., 36: 235-237. ashour, a.a. 1974b. exact solutions for certain axisymmetric problems of induction in thin non-uniform sheets. j. geophys. res., 79(16): 2479-2486. chave, a.d. and booker, j.r. 1987. electromagnetic induction studies. reviews of geophysics, 25(5): 9891003. doss, s.s. and ashour, a.a. 1971. some results on the magnetic field of electric currents induced in a thin hemispherical shell of finite conductivity, with geomagnetic applications. geophys. j. r. astr. soc., 22: 385-400. fainberg, e.b. 1980. electromagnetic induction in the world ocean. geophysial surveys, 4: 157-171. gainberg, e.b., kuvshinov, a.v. and singer, b.sh. 1990. electromagnetic induction in a spherical earth with non-uniform oceans and continents in electric contact with the underlying medium. geophys. j. int., 102: 273-281. hewson-browne, r.c. and kendall, p.c. 1976. magnetotelluric modelling and inversion in three dimensions. acta geodet., geophys. et montanist. acad. sci. hung., 11(3-4), 427-446. hutson, v.c.l., kendall, p.c. and malin, s.r.c. 1972. computation of the solution of geomagnetic induction problems: a general method, with applications. geophys. j. r. astr. soc., 28: 417-443. jackson, j.d. 1962. classical electrodynamics. john wiley & sons, inc., new york, london. price, a.t. 1949. the induction of electric currents in non-uniform thin sheets and shells. quart. j. mech. a.a. ashour, m.s. abou-dina and a.f. ghaleb 186 appl. math., 2(3): 283-310. raval, u., weaver, j.t. and dawson, t.w. 1981. the ocean coast-effect re-examined. geophys. j. r. astr. soc., 67: 115-123. siew, p.f. and hurley, d.g. 1988. electromagnetic response of thin disks. j. appl. math. and phys. (zamp), 39: 619-633. tarits, p. 1994. electromagnetic studies of global geodynamic processes. surveys in geophysics, 15: 20238. thebault, e., schott, j.j., mandea, m. and hoffbeck, j.p. 2004. a new proposal for spherical cap harmonic modeling. geophys. j. int., 159: 83-103. thebault, e., schott, j.j. and mandea, m. 2006a. revised spherical cap harmonic analysis: validation and properties. j. geophys. res.-solid earth, 111(5): b01102, 1-17. thebault, e., mandea, m. and schott, j.j. 2006b. modelling the lithospheric magnetic field over france by means of revised spherical cap harmonic analysis. j. geophys. res.-solid earth, 111: b05102, 1-13. varentsov, iv. m. 1983. modern trends in the solution of forward and inverse 3d electromagnetic induction problems. geophysical surveys, 6: 55-78. weidelt, p. 1971. the electromagnetic induction in two thin half-sheets. zeitschrift für geophysik, 37: 649665. wolf, d. 1983a. inductive coupling between idealized conductors and its significance for the geomagnetic coast effect. j. geophys., 52: 22-33. wolf, d. 1983b. singular solutions to maxwell's equations and their significance for geomagnetic induction. geophys. j. r. astr. soc., 75: 279-283. received 10 february 2011 accepted 21 november 2011 model calibration in option pricing squ journal for science, 17 (1) (2012) 84-102 © 2012 sultan qaboos university 84 model calibration in option pricing andre loerx* and ekkehard w. sachs** department of mathematics, university of trier, trier, germany. *email: loerx@uni-trier.de and **email: sachs@uni-trier.de abstract: we consider calibration problems for models of pricing derivatives which occur in mathematical finance. we discuss various approaches such as using stochastic differential equations or partial differential equations for the modeling process. we discuss the development in the past literature and give an outlook into modern approaches of modelling. furthermore, we address important numerical issues in the valuation of options and likewise the calibration of these models. this leads to interesting problems in optimization, where, e.g., the use of adjoint equations or the choice of the parametrization for the model parameters play an important role. keywords: adjoints, calibration, jump models, local volatility models, mixed models, partial differential equation (pde), stochastic differential equation (sde), stochastic volatility models. معايرة النماذج في تسعير الخيارات أندريه لوركس و إكهارد زاكس فً التموٌل الرٌاضً. نناقش طرق متنوعة كاستخدام التسعٌر التً تظهر اتنفترض مسائل المعاٌرة لنماذج مشتق :خصمل التطورات المنشورة مسبقا ونعطً عرضأو المعادالت التفاضلٌة الجزئٌة لعملٌة النمذجة. نالعشوائٌة المعادالت التفاضلٌة تلك النماذج. ةنعالج مواضٌع عددٌة هامة فً تقٌٌم الخٌارات ومعاٌر ،آفاق حول الطرق الحدٌثه للمعاٌرة. إضافة إلى ذلك ا فً ماها دور تلعب تم معادالت مساعدة أو اختٌار معامالااستخدأن حٌث، مثآل، ٌاتمثلاألهذا ٌؤدي إلى مسائل مهمة فً .نموذج المعامالت 1. introduction inancial derivatives, like options and futures, have gained considerable importance since the chicago board options exchange (cboe), the first exchange to list standardized exchange-traded stock options, was founded in 1973. starting with 911 contracts on 16 underlying stocks on the first trading day on april 26, 1973, the cboe reported a total number of over 1.1 billion traded contracts in 2009, which corresponds to an average volume of more than 4.5 million contracts a day. 1 the rapid growth over the last 40 years of financial derivative markets, certainly owes its success to the publication of black and scholes (1973) and its extension by merton (1973), since they laid the foundation of preference-free valuation of contingent claims. particularly, they developed a simple, but powerful model that governs the price of european-style call and put options over time. the main achievement, however, was not only the derivation of a valuation formula in closed form but also the idea of building a (hedge) portfolio by buying and selling the underlying asset and a risk-free bond in such a 1 source: http://www.cboe.com/aboutcboe/history.aspx & http://www.cboe.com/data/marketstats-2009.pdf f model calibration in option pricing 85 self-financing way that it perfectly matches the payoff (at maturity) of the option to be priced. consequently, the amount of initial capital needed for building up the hedge portfolio coincides with the price of the considered european-style option. these publications form the cornerstone of today's financial industry. but not only the total number of contracts, also the variety have grown in a remarkable way. nowadays, in addition to standard european-style plain vanilla call and put options, exotic derivatives like digital or barrier options of americanor bermudan-type, asian-style options like lookbacks, or chooser options, cliquets or any reasonable combination, are frequently traded on financial derivative markets. however, it has been shown (in a variety of publications and text books) that due to its simplicity the classical black-scholes model cannot properly capture the real market dynamics. the black-scholes model is, unfortunately, not suitable to adequately price and hedge exotic options. in the literature, a multiple of models can be found subsequently relaxing the assumptions of the classical black-scholes model, for instance, by adding another degree of freedom to the process of the underlying asset. in order to extract accurate market dynamic information to price and hedge exotic options, practitioners, e.g., traders and risk managers, need to adapt their models to the current market situation, i.e. the models have to be calibrated to a set of liquidly traded standard instruments like plain vanilla options. the pricing of options as well as model calibration are interesting mathematical problems from various points of view. they pose challenges in several areas like mathematical modeling, stochastic processes, partial differential equations, optimization and numerical analysis. in section 2, we briefly review the fundamentals of smile-consistent option pricing and its numerical pricing techniques like biand trinomial trees, monte carlo methods, and pde pricing, for the case where no closed form solution is available. we will focus mostly on european-style call options and briefly discuss some pros and cons of the main classes of smile-consistent volatility models proposed in the literature. more precisely, we consider stochastic volatility models, local volatility models, jump models, as well as mixed volatility models and emphasize their relevance in practice. section 3 gives an exhaustive survey of publications on the calibration of financial market models. although several references on monte carlo calibration are given, we focus mostly on literature concerning the reconstruction of the local volatility function. we distinguish parametric and non-parametric approaches and briefly illustrate three categories of calibration procedures proposed in the literature. in doing so, we closely follow the distinction of bouchouev and isakov (1999), i.e. optimization-based algorithms, extraand interpolation schemes, and iterative methods. 2. option pricing starting with the black-scholes model, today's price of a european-style call (put) option with maturity t and strike k under some risk-neutral measure q is defined as 0call: ( , 0) = (max( , 0)), rt q tc s e s k   (1) 0put: ( , 0) = (max( , 0)), rt q tp s e k s   (2) where ts denotes the asset price at maturity t given the asset price process 0( )t t ts   as a solution of the black-scholes stochastic differential equation (sde) = ( )t t t tds r d s dt s dw  (3) with 0 (0, )s   and [0, ].t t the (constant) instantaneous drift term consists of the risk-less interest rate r and the dividend yield d of the underlying. 2 furthermore,  denotes the (constant) instantaneous volatility function and 0( )t t tw   represents a brownian motion (or wiener process) defined on a probability space ( , , )q with  -algebra over the set =  and q the unique risk-neutral measure (or martingale measure). the brownian motion 0( )t t tw   is adapted to an adequate filtration 0( ) ,t t t  where the filtration 0( )t t t  2 for simplicity, we assume constant interest rates and dividend yields and further omit equity premiums. andre loerx and ekkehard w. sachs 86 satisfies some 'technical' conditions (see (karatzas and shreve, 2008) for details). as already mentioned, one of the key achievements of black and scholes (1973) was to provide an explicit valuation formula (known as the black-scholes formula 3 ) for european-style call and put options, namely ( ) ( ) 1 2( , ; , ; , , ) = ( ) ( ) , bs d t t r t t t tc s t k t r d e s e k          (4) ( ) ( ) 2 1( , ; , ; , , ) = ( ) ( ) , bs r t t d t t t tp s t k t r d e k e s            (5) where 2 1 2 1 1 ln( / ) ( )( ) 2= , = ts k r d t t t t t t              with ( )x the cumulative distribution function of the standard normal distribution, i.e. 2 2 1 ( ) = . 2 y x x e dy    hence, the black-scholes option price at time [0, ]t t depends on the current value of the underlying ,ts i.e. the spot price, the time the option expires t, i.e. the maturity, the exercise price or strike price k, the interest rate r, dividend yield d and finally the (constant) volatility . a well-known model-free relationship between calls and puts on the same underlying asset, with equal strike and maturity, is the put-call parity ( ) ( ) ( , ; ) ( , ; ) = . bs bs d t t r t t t t tc s t p s t e s e k       it is easy to show that given a fixed black-scholes price c satisfying reasonable non-arbitrage conditions, i.e. ( ) ( ) ( ) max( , 0) , d t t r t t d t t t te s ke c e s          the mapping ( )c c   has a unique root , impl  called implied volatility. conversely, in the classical black-scholes model the option price ( , ; , ; , , ) bs impl tc s t k t r d  depends uniquely on its implied volatility , impl  where impl is assumed to be constant in time t, stock price ,ts strike k and maturity t. this assumption, however, cannot be observed on the market. if one plots the observed market implied volatility against the strike k, the resulting graph will usually be downward sloping in equity markets, while it is typically valley-shaped in currency markets or for equity index options. this behavior is referred to as 'volatility skew' or 'volatility smile', respectively. furthermore, it can be observed that the volatility skew or smile usually flattens for long term maturities. the change of implied volatilities with respect to different maturities is called 'term structure' of the implied volatility surface. finally, the implied volatility surface also changes dynamically over time. a more detailed introduction to this topic is given, e.g., in (hull, 2011). although, the classical black-scholes model lacks on realism, implied volatility serves as a standardized (or normalized) value (usually quoted in %) of market volatility. in sticky-moneyness markets 4 , the implied volatility provides more stability than the black-scholes option price. practitioners use implied volatility as a language, rather than as a model. a lot of research has been done over the last 40 years, trying to explain this strike deviation from the black-scholes constant volatility assumption. many factors have been investigated as being possibly responsible for the smile and term structure of the implied volatility surface. they range from the existence of transaction costs or liquidity constraints, to stochastic volatility and jump processes for the underlying asset price process. in the following we focus on the latter ones. 3 in fact, black and scholes (1973) derived their valuation formula by solving the black-scholes partial differential equation, which will be introduced later on. 4 moneyness is defined as the quotient between stock price ts and strike price k. model calibration in option pricing 87 2.1 smile-consistent pricing models the idea behind the development of new pricing models, so called 'smile-consistent pricing models', is to directly extract information about the asset price and volatility dynamics from frequently traded standardized plain vanilla options in order to price and hedge exotic options. this is done by assuming the coefficients of (3) to be some deterministic function of the spot price ts and the time t, by adding new sources of randomness or by adding all of it. since the sources of randomness are usually added to the volatility [cf. gatheral (2006)] the generalized framework (or extension) of the black-scholes model is given by replacing (3) by = ( , ) ( , )t t t t t tds a s t s dt b s t s dw (6) with 0 (0, ).s   the asset price 0( )t t ts   is, therefore, modeled by a 0( )t t t  adapted stochastic process, driven by the sde (6), where ( , )ta s t and ( , )tb s t are the instantaneous drift and the volatility, respectively. fengler (2005) assumed that the instantaneous volatility ( , , )t tb s t  follows some 0( )t t t  adapted arbitrarily depending stochastic process, where the ' t -dependence' simply emphasizes that ( , , )t tb s t  may also depend either on the history of ,ts i.e. 1 = , , ,t t tn s s for 0 <nt t for all n, or some other sources of randomness. furthermore, the absence of arbitrage, i.e. the existence of some risk-neutral measure under which a discounted asset price 0( )t t ts   is a martingale, is assumed. however, the martingale measure needs not to be unique (see (björk, 2004, p. 150)). to the knowledge of the authors, at least two main lines can be identified. 'stochastic volatility models' impose a new source of randomness to the volatility, while 'local volatility models' treat the volatility as a deterministic function of ts and t. adding jumps as a new source of randomness leads to 'jump diffusion models'. most recently, 'stochastic local volatility models' have become very attractive, since they allow a perfect fit while preserving the advantages of stochastic volatility models. 2.1.1 stochastic volatility models the most prominent stochastic volatility (sv) model was introduced by heston (1993), = ( ) , = ( ) s t t t t t v t t t t ds r d s dt v s dw dv v v dt v dw      (7) with 0 0, (0, )s v   and , = , s v t tdw dw  where r d denotes the (deterministic) instantaneous drift of stock price returns,  the volatility of volatility,  the speed of reversion of tv to its long-term mean v and  the correlation between s tw and , v tw the brownian motions driving the stock price process and variance process, respectively. the latter one is a special case of the square root process proposed by cox et al. (1985) to model interest rates, known as the cir model. other stochastic volatility models have been proposed in the literature, e.g., (hagan et al., 2002, sabr; bollerslev, 1986, garch; stein and stein, 1991), just to name a few of them. however, it is proven, for instance, in (duffie et al., 2000) that the heston model has a quasi-closed form solution for european-style options. although other, possibly more realistic, stochastic volatility models are available, the existence of a quasi-closed form solution contributed substantially to the outstanding success of heston's model in practice. this is due to the fact that computational efficiency becomes essential when calibrating the model to observed market data. furthermore, according to gatheral (2006), all stochastic volatility models generate roughly the same shape of implied volatilities and thus the same implications for the valuation of non-vanilla derivatives. on the other hand, he shows that, although the heston model fits observed implied volatility for longer expirations, this is, unfortunately, not true for shorter-dated options. this motivates the use of 'jump diffusion models', since, loosely speaking, introducing jumps has very little impact for long term maturity options, while jumps are strongly noticeable in terms of implied volatility for short-expiration options. andre loerx and ekkehard w. sachs 88 2.1.2 adding jumps jump diffusion models were first considered by merton (1973) and later by kou (2002) as an extension of one-dimensional processes. duffie et al. (2000) proved that 'affine jump diffusion' (ajd) processes, which consist, roughly speaking, of a jump diffusion process for which the drift vector, the 'instantaneous' covariance matrix, and the jump intensities all have affine dependence on the state vector, are in general analytically tractable. in case of a two-dimensional process we have =1 =1 = ( ) 1 , = ( ) n st zs n t t t t t n n n tv v t t t t n n ds r d k s dt v s dw d s e dv v v dt v dw d z                           (8) with 0 0, (0, )s v   and , = , s v t tdw dw  where r, d, , , ,v and  are as in (7). further, tn denotes a poisson process with jump intensity > 0 and drift compensation k. the jump sizes in stock price and volatility, i.e. s nz and , v nz respectively, for = 1, , ,tn n are assumed to be i.i.d. (independent and identically distributed). finally, := lim t tnn s s  denotes the stock price at n right before the jump occurs. thus, (8) denotes a stochastic volatility model with simultaneous jumps in stock price and volatility (svjj). note that heston's stochastic volatility model is a jump-free special case, i.e. = = 0 s v n nz z for all n, of an ajd process and as such has at least a quasi-closed form solution as mentioned before. 5 the merton and heston approaches were combined by bates (1996), who proposed a model with stochastic volatility and jumps (svj). bates' model is also incorporated in (8) as a special case, where = 0 v nz for all n. gatheral (2006) shows that svj models perform empirically as well as svjj, but they have less parameters. therefore, svj models like heston's model are frequently used in practice. an extensive discussion about jump diffusion models can be found in (cont and tankov, 2004). we now turn our focus onto 'local volatility (lv) models'. they became quite popular in the past due to their simplicity, however, they have also gained a lot of criticism in financial literature (cf., e.g., (ayache et al., 2004; hagan et al., 2002)). 2.1.3 local volatility models following fengler (2005), 'local variance' may be defined as the risk-neutral expectation of the instantaneous variance conditional on =ts k and time filtration ,t i.e. 2 2 ,ˆ ( , ) := ( ( , , )| = , ) , q k t t t t t ts t b s t s k  where ( , , )t tb s t  is as before. then, 'local volatility' (also called 'forward volatility') is given as the square root of local variance. the main advantage of this definition of local volatilities is that it naturally implies the purely deterministic case, but also offers some insights into the concept of stochastic volatility. within this framework of local volatilities, for some market level = tk s at = ,t t the instantaneous volatility is given by ,ˆ( , ) = ( , ) ,t s t tt s t s t  such that (with ( , ) := ,ta s t r d for simplicity) ,ˆ= ( ) ( , )t t s t t t tt ds r d s dt s t s dw  (9) 5 in fact, the heston's formula is given as a linear combination of two integrals of real-valued functions. model calibration in option pricing 89 defines the stock price process, which generalizes the classical black-scholes theory as desired. the intrinsic stochasticity is integrated out and we are left with a one-factor diffusion process. however, if by assumptions the instantaneous volatility is deterministic in spot and time, i.e. ( , , ) = ( , ),t t tb s t s t  both concepts of instantaneous and local variance coincide, since 2 2 ,ˆ ( , ) := ( ( , , )| = , ) q k t t t t t ts t b s t s k  2 2 = ( ( , )| = , ) = ( , ) . q t t ts t s k k t  the local volatility assumption is the easiest way of relaxing the constant volatility case and it introduces much more flexibility. in contrast to stochastic volatility models, the concept of local volatility preserves the assumption of market completeness. 6 originally, dupire (1994) and derman and kani (1994a) 7 have shown that given the distribution of the final stock price ts for each time t conditional on some starting price 0 ,s there exists a unique risk-neutral diffusion process (9) consistent with these distributions. the reason is that there exists a 'dual' or 'adjoint' pde to the classical black-scholes pde (cf. section 2). the remarkable observation that local volatility can be seen as the market expectation of future volatility, known as 'markovian projection', was independently derived by dupire (1996) and by derman and kani (1998). different assumptions on the special shape of the local volatility function have been made in the literature. they are either motivated by model calibration in order to reduce the number of unknowns (see section 3.3.2), or by empirical observations (see, e.g., (dumas et al., 1998; coleman et al., 2001)) in order to properly capture the dynamics of the underlying asset. a prominent example is the 'constant elasticity of variance model' (cev) introduced by cox and ross (1976), where 1 ( , ) =t ts t s     with , > 0.  the cev model attempts to heuristically capture the stochastic volatility, where  controls the relationship between volatility and price. when < 1, commonly observed in equity markets, the volatility of the underlying increases as its price falls. conversely, in commodity markets, the volatility of the underlying tends to increase as its price increases. note that for = 1 we obtain the black and scholes case. ingersoll (1997) and rady (1997) introduced the class of bounded quadratic diffusion models, i.e. ( , )ts t which is considered to be a bounded quadratic function in asset price and/or time. zühlsdorff (2001) has proven the existence and uniqueness of the solution of the underlying sde and provided explicit formulas for call options assuming that the deterministic local volatility function can be split in a strictly positive and bounded function  and a quadratic polynomial p such that ( , ) = ( ) ( ).t ts t p s t  option pricing in the quadratic volatility model is a rather delicate issue, since it touches the limits of no-arbitrage theory. andersen (2011) clarified some confusion in literature and further extended the range of existing pricing formulas. coleman et al. (2001) published empirical evidence that a spline representation can provide a more accurate representation in terms of hedging compared to the quadratic model considered by dumas et al. (1998). although the deterministic local volatility function may look very complicated, considering local volatilities can be a questionable model simplification. ayache et al. (2004) and hagan et al. (2002) doubt that a one-factor diffusion model delivers an adequate description of the asset price behavior. hagan et al. (2002) illustrated that the model delta of deterministic local volatilities is wrong or at best very misleading. this, however, is a crucial issue in terms of the dynamic hedging performance of the model. furthermore, another undesirable feature of the local volatility model is that it predicts flat future smiles, such that forward-start options or cliquets are likely to be mispriced. beside these pricing and hedging problems, ayache et al. (2004) criticized that local volatility models reveal no reasonable explanation for the existing smile phenomenon. despite all criticism, local volatility models are widely used in practice. common problems arising from using complex models like 'jump diffusion models' or even 'mixed volatility models' are the additional 6 note that volatility is not a tradeable asset, which implies that the completeness of the market, i.e. the ability to hedge options with the underlying asset only, is lost. 7 while dupire (1994) developed a continuous time theory, derman and kani (1994a) used a discrete binomial tree approach. andre loerx and ekkehard w. sachs 90 computational effort, the high implementation costs, the loss of intuition, and a potential decrease in calibration stability. hence, 'practitioners may, and in fact often do, favor a simple and intuitive model', see (coleman et al., 2011). furthermore, it is most likely that dupire (1994) and derman and kani (1994a) did not introduce the local volatilities as a model of its own, but instead they intended to propose an intuitive way to price exotic derivatives under certain market circumstances. 2.1.4 mixed or hybrid volatility models as jump processes have been added to stochastic volatility models to provide a better fit of model implied volatilities to market implied volatilities (especially for short term maturities), the local volatility framework has been applied to stochastic volatility models. so-called 'stochastic local volatility (slv) models' were proposed by blacher (2001) and lipton (2002) and were studied further, e.g., in (ren et al., 2007; piterbarg, 2007; alexander and nogueira, 2008; henry-labordère, 2009). as an example, the governing sdes for a 'heston-type stochastic local volatility model' are: = ( ) ( , ) = ( ) s t t lv t t t t v t t t t ds r d s dt s t v s dw dv v v dt v dw        (10) with 0 0, (0, )s v   and , = , s v t tdw dw  where again r, d, , , ,v and  are as in (7) and lv denotes the local volatility function. then, in the framework of local variance, the instantaneous 'hybrid' variance takes the form: 2 2 ,ˆ ( , ) = ( , ) ( | = , ) . q k t t lv t t ts t k t v s k   (11) because of this particular form of (11), it is not possible to separate the influence of the stochastic component from the local component in an intuitive manner. thus, tavella et al. (2005) prefer to define the instantaneous hybrid volatility as a weighted sum of a stochastic component and a local component. it is worth mentioning that lipton (2002) and lipton and mcghee (2002) further extended (10) by adding jumps to the stock price process .ts among others, this extension of (10), called the 'universal model', was strongly criticized by ayache et al. (2004). it is argued that, roughly speaking, there is no chance to reveal the true market smile dynamics, since the freedom of the local volatility function can nearly compensate every dynamics introduced by the stochastic or jump component. in practice, this problem is usually addressed by separately calibrating the model parameters to extract plausible dynamics from the market. 2.2 numerical evaluation of smile-consistent pricing models fast model evaluation is a crucial issue in practice. in order to be competitive with other market participants, very complex derivatives need to be priced nearly on-the-fly. additionally, a fast and stable pricing scheme is essential when calibrating a financial market model to a large number of market data. therefore, it is not surprising that models, which provide a closed or quasi-closed form solution, have become popular in practice. a survey of most of the existing market models with closed (or quasi-closed) form solutions has been given , e.g., in (kolb and overdahl, 2010, chap. 27; hull, 2011; andersen, 2011), especially for unbounded quadratic local volatility models. in the early years, bior trinomial trees have been a typical approach to price path-independent and path-dependent options in consistence with the prevailing volatility smile. this valuation method, which can be seen as a discrete version of black-scholes pricing pde, was pioneered by cox et al. (1979) (crr). 8 a very natural way to price complex derivatives are monte carlo or quasi-monte carlo methods. they are based on the continuous time models, i.e. the fundamental pricing formula (1) or (2) and the considered market model: 8 more precisely, it can be easily shown that, for instance, the trinomial method is an example of an explicit finite difference scheme of blackscholes pricing pde and therefore it inherits certain stability properties of finite difference methods, cf. (duffy, 2006, chap. 13) model calibration in option pricing 91  0 0 ( , 0) = ( , ) s.t. = ( , ) ( , , ) , (0, ) , rt q t t t t t t t t t c s e s ds a s t s dt b s t s dw s         (12) where ( , )t ts  denotes the payoff function, depending on the asset price ts at maturity t and possibly on some history 1 = , ,t t tn s s (0 <nt t for all n). as discussed, the general market model in (12) may be replaced by a specific one like (7), (8), (9), or (10). thus, in case of a european-style call option under local volatility we obtain  0 0 ( , 0) = max( , 0) s.t. = ( ) ( , ) , (0, ) . rt q t t t t t t c s e s k ds r d s dt s t s dw s        (13) in order to generate monte carlo samples, the stochastic differential equation in (14) is usually discretized by a euler-maruyama or milstein scheme (see (kloeden and platen, 1999)) which is then used to approximate the expected value functional. following the well-known law of large numbers, the pricing problem (14) can be formulated as 0 =1 1 0 0 1 ( , 0) max( , 0) s.t. = ( ) ( , ) , = , = 0, , 1, = 1, , , m rt m n m m m m m m m n n n n n n n n m c s e s k m s s r d s t s t s w s s n n m m            (14) where m, sufficiently large, denotes the number of random samples. further, m ns is the m-th realization of the solution of (9) at time nt given a time discretization 0 10 = < < <t t t with step size 1:=n n nt t t  for = 0, , 1.n n  accordingly, 1:= ( )n n nw w w  are the discrete increments of the brownian motion tw at time .nt due to their flexibility to changes in either the payoff function or the considered market model, (quasi)monte carlo methods are widely used in practice. they further allow the computation of path-dependent derivatives with relatively small extra costs. moreover, monte carlo methods are very easy to parallelize, such that the use of modern graphics processors (gpus) allows a tremendous speed-up in computation time. consequently, high dimensional problems can be solved in a reasonable time. an exhaustive discussion of (quasi)-monte carlo methods can be found in (glasserman, 2003). while (quasi)-monte carlo methods are quite meaningful in high dimensions, they can be very slow for low dimensional problems. representation theorems like feynman-kac's theorem (cf. (karatzas and shreve, 2008)) show that, for instance, in the case of european-style call options, the price process of a plain vanilla call option follows some parabolic partial differential equation, i.e. 2 21 ( , ) = ( , ) ( , ) ( ) ( , ) ( , ) , 2 ( , ) (0, ) [0, ) , ( , ) = max( , 0), (0, ) . c s t s s t c s t r d sc s t rc s t s t t c s t s k s           (15) to put it differently, under reasonable assumptions of the existence of unique solutions of the local volatility model, i.e. sde (9) and black-scholes pricing pde (15), the unique solution ( , )tc s t of (15) admits for all (0, )ts   and [0, ]t t the stochastic representation  ( )( , ) = max( , 0) s.t. = ( ) ( , ) , (0, ) r t t q t t t c s t e s k ds r d s d s s dw s               (16) with ( , ].t t  similar results can be obtained for, among others, barrier-, digital-, or plain vanilla call and put options with local or stochastic volatility. while basket options and models with stochastic volatility and/or andre loerx and ekkehard w. sachs 92 stochastic interest rate lead to multidimensional pdes (see (wilmott, 2006)), an integral term is added in the pde when considering jump diffusion models (see (cont and tankov, 2004)). thus, the latter one requires the numerical solution of a partial integro-differential equation (pide). pricing american-style options yields the challenge of solving free-boundary value problems (see (wilmott, 2006)). asian-style options can be modeled using oneor two-dimensional pdes, depending on special payoff characteristics (see (zvan et al., 1998)). in either case, numerical methods like finite difference or finite element methods need to be applied, when no analytic solution is available. among multiple standard textbooks on numerical methods for pdes, an exhaustive discussion on robust, accurate and efficient finite difference methods particularly for pricing various derivative products can be found in (duffy, 2006;tavella and randall, 2000). topper (2005) and achdou and pironneau (2005) focus on finite element methods used in quantitative finance. a current survey of efficient numerical methods for solving those types of pides is given in (feng and linetsky, 2008; sachs and strauss, 2008). beside the fact that under risk-neutrality there is a unique diffusion process consistent with the prevailing market smiles, dupire (1994) and derman and kani (1994a) discovered that european-style option prices in the local volatility model satisfy a certain forward pde, in which the independent variables are the options' strike k and maturity t, i.e. 2 2 max 0 1 ( , ) = ( , ) ( , ) ( ) ( , ) ( , ) , 2 ( , ) (0, ) (0, ] , ( , 0) = max( , 0), (0, ) . d k t k k t d k t r d kd k t d d k t k t t d k s k k           (17) this forward evolution equation, called 'dupire's equation', is of twofold importance: (i) dupire's equation in a local volatility framework is used to explicitly determine the underlyings' instantaneous volatility function, see section 3. (ii) once volatility function is known, the forward pde can be solved numerically to efficiently price a collection of european-style options of different strikes and maturities all written on the same underlying asset. due to its significance in option pricing and model calibration, several extensions, also called 'forward equations', have been proposed in financial literature. andersen and andreasen (1999) derived and andreasen and carr (2002) further extended, forward equations for european-style options in jump diffusion models. it is straightforward to develop the relevant forward equation for barrier or digital options (see, e.g., (pironneau, 2006; pironneau, 2007; carr and hirsa, 2007)). buraschi and dumas (2001) give a forward representation of compound option prices for general diffusion processes with deterministic volatility. forward equations for american-style put options with jump diffusion processes are derived in (carr and hirsa, 2003; amster et al., 2009) and are considered dupire-like equations for multi-asset options, while bentata and cont (2010) further generalized dupire's forward equation to a large class of non-markovian models with jumps. basically two lines of techniques to derive dupire-like forward equations can be found in the literature. either a generalization of itô's formula, called 'tanaka-meyer formula' (see (karatzas and shreve, 1998, p. 220)), is applied to the underlying sde, or classical adjoint calculus is used to formulate the 'dual' problem of black-scholes pricing pde. the first approach is explained, for instance, in (bentata and cont, 2010), while adjoint calculus (see, e.g., (friedman, 1964)) is applied in (pironneau, 2006; pironneau, 2007; pironneau, 2009). a comparison of both approaches for the original dupire's equation can be found in (fengler, 2005). 3. model calibration one of the key issues in quantitative finance is model calibration. practitioners, like traders or risk managers, need to extract accurate market dynamic information, in order to correctly price and hedge derivatives. usually, this is done by calibrating the relevant financial market model to a set of frequently traded standard instruments. in this section, we shortly review the common techniques used in practice. due to its considerable importance, we start with restricting our attention to the calibration of local volatility models. in the literature, mainly three groups of approaches are proposed: extraand interpolation model calibration in option pricing 93 schemes, iterative procedures on analytic approximations, and optimization-based methods. 9 in the last part, however, we extend our view to the calibration of other models as well, since optimization-based methods naturally allow more flexibility in terms of changing the considered model. 3.1 extraand interpolation techniques the concept of 'implied biand trinomial trees' is aligned with the option pricing scheme introduced by cox et al. (1979). instead of setting up a smile-consistent pricing tree in advance using, e.g., parameters inferred from a separate calibration routine, implied trees are directly recovered from observed market data approximating all necessary risk-neutral transition probabilities. binomial trees, proposed by derman and kani (1994b) and barle and cakici (1998), however, suffer from a number of fundamental problems. according to boyle and lau (1994), binomial trees may encounter unpredictable convergence behavior when pricing options with discontinuous payoffs (like barriers or digitals). secondly, and more importantly, negative transition probabilities may occur, from which arbitrage opportunities ensue. in contrast to derman and kani (1994b) and barle and cakici (1998), who construct the tree using a forward recursion formula, rubinstein (1994) and jackwerth (1997) propose to inductively build up the tree beginning from a risk-neutral distribution at the terminal node. this, by construction, prevents the probabilities becoming negative. derman and kani (1994b) suggest the use of trinomial trees, which are somehow equivalent to a simple explicit finite difference approximation of dupire's equation (17). trinomial trees provide a more flexible approximation to the state space than a binomial tree, but suffer from many of the same problems as the binomial tree and are prone to instability. andersen and brotherton-ratcliffe (1997/1998), therefore, use the well-known (semi-implicit) cranknicolson approximation, since it exhibits much better stability and convergence properties. in any tree or tree-related approach, it is assumed that plain vanilla options are available for every strike and time to maturity. therefore, option prices need to be interand extrapolated into regions where no market data are observable. this becomes even more relevant when considering the time continuous theory. having built the bridge to dupire's equation (17) earlier, practitioners sometimes prefer a slightly different view on (17), i.e. 2 2 ( , ) ( ) ( , ) ( , ) ( , ) = 2 . ( , ) d k t r d kd k t d d k t k t k d k t     (18) in this approach, calibration is meant to find a continuous and sufficiently smooth option price function ( , )d k t with respect to strike k and maturity t, such that the local volatility function can be recovered from (18), known as 'dupire's formula'. therefore, again some interand extrapolation techniques are required, in order to obtain a continuous and smooth price function for market data information. aside from the smoothness requirements, the challenge is to guarantee that no standard arbitrage bounds are violated and that the local variance remains positive and finite. due to the fact that, under no-arbitrage conditions, there is a unique implied volatility given an option price and vice versa (see section 2), the necessary interand extrapolation is usually done on the implied volatility side. kahalé's interpolation procedure (see (kahalé, 2004)), for instance, is based on piecewise convex polynomials, which mimics the black-scholes formula. if the input data are free of arbitrage, so will be the resulting implied volatility surface. fengler (2009) used natural cubic splines in space and finite differences in time to parametrize the local volatility function. the idea is to solve a sequence of small quadratic programs (qp) arising from a least-squares formulation (lsq) of the spline representation under additional no-arbitrage constraints. calender arbitrage is avoided by imposing transfer conditions through the iterates of the sequence of qps. in contrast to kahalé (2004), the main advantage of fengler (2009) is that the input data need not to be free of arbitrage. benko et al. (2007) suggest estimating the implied volatility surface with local quadratic polynomials. arbitrage is ruled out by forcing the state-price density to be non-negative. hanke and rösler (2005) solve a normal equation to get an equivalent minimal norm solution of a lsq problem using the 9 see also (bouchouev and isakov, 1999). andre loerx and ekkehard w. sachs 94 discretized dupire's formula and cubic splines in space and finite differences in time to parametrize the local volatility function. an extensive review about useful smoothing techniques is given in (fengler, 2005, chap. 4). calibration using dupire's formula (18) requires an interpolation method for either the implied volatility surface or the option price function. however, practitioners have stated that the resulting local volatility surface is very unstable and that the option prices are very sensitive to the interpolation method (see, e.g., (lipton, 2001)). furthermore, a difficulty is the extraand interpolation into areas where no market data are observed. for instance, it is not clear how to extrapolate prices for options that mature before the closest expiration date. 3.2 analytic approximations (and iterative methods) bouchouev and isakov (1999) apply the classical parametrix technique for pdes to derive an analytic approximation of the option premium as a sum of its black-scholes price and an integral correction for the nonconstant volatility, which explicitly shows the nonlinear relationship between the option price and volatility. the resulting integral equation is then discretized and iteratively solved at the points where observed option prices are available. a second iterative algorithm is applied directly to the fundamental solution of the underlying pde. both algorithms proposed are straightforward to implement. however, they should only be used for short term maturities, since the algorithm is applied for a single time period and then repeated for all consecutive maturities. therefore, it might not be able to capture the term structure of the local volatility surface. analytic approximation formulae for one-dimensional local volatility models using the parametrix methods are also derived in (corielli et al., 2010), but not considered in the context of calibration. 3.3 optimization-based calibration while usually very fast, the methods described above are only applicable to a quite small class of financial market models. optimization-based calibration methods offer more flexibility and are applicable to almost any financial market model. trying to minimize the distance between model data and observed market data, for instance, in a least-squares formulation (lsq), i.e. 2 0 =1 1 ( ( ; , 0) ) ,min 2 m mod obs m m a m c a s c   (19) the model prices can either be given in closed form or as a solution of the underlying sde or pde model. nonlinear constrained and unconstrained optimization problems arise in many sciences, and numerous methods exploiting the special structure have been proposed to efficiently solve them. an introduction to state-of-the-art numerical methods for constrained and unconstrained optimization problems can be found in (nocedal and wright, 1999). as an example, to calibrate the time-dependent heston call option model, gerlich et al. (2010) designed a special sequential quadratic programming (sqp) optimization algorithm for the constrained least-squares problem (19), where n a r denotes the vector of heston parameters, 0( ; , 0) mod mc a s and , obs mc for = 1, , ,m m and the model, respectively, market data with maturity t and strike k given an initial stock price 0s of the option's underlying at 0 = 0.t the feasible set arises from additional constraints on the heston parameters a, for example, by assuming that the variance of the underlying stochastic process remains strictly positive. the model prices 0( ; ,0), mod mc a s for = 1, , ,m m are evaluated using the closed form solution. as mentioned before, closed form solutions are only available for a small class of models. in the following, we consider the least-squares calibration of financial market models in a more general setting. 3.3.1 sde constrained optimization (monte carlo calibration) since financial market models are often characterized by the sde of their underlying asset, calibration problem (19) may be written (for example, for a local volatility model) as model calibration in option pricing 95   2 0 =1 0 0 1 ( ) := ( ( ; , 0) )min 2 where ( ; , 0) = max( , 0) , s.t. = ( ) ( , ) , (0, ) , m mod obs m m m mod rt q m t mm f c s c c s e s k ds r d s d s s dw s                      (20) where is an appropriate set of volatility functions. sde constrained optimization problems have not been much considered in financial market literature, since monte carlo methods are known to be very slow. giese et al. (2007), for instance, use the euler-maruyama scheme to simulate the underlying stock price process in the heston framework and combine it with a multi-layer method related to multigrid methods from the solution of pdes as proposed, e.g, in (kelley and sachs, 1994). further acceleration is achieved by parallelization of the price evaluations. recently, adjoint techniques have proven to be quite successful to accelerate monte carlo pricing. adjoint techniques have their origin in the field of optimal control (see (giles and pierce, 2000)) and were recently introduced into finance in the context of automatic differentiation to compute derivatives (greeks) (see (giles and glasserman, 2006)). kaebe et al. (2009a) applied adjoint calculus combined with a multi-layer approach to gain a tremendous speed-up in the calibration of a very general setting of systems of sdes. furthermore, kaebe et al. (2009b, unpublished data) extended their consideration of monte carlo calibration of sde models by adding jump components and proposed the use of a semi-analytical adjoint framework, which is based on a decomposition of the sensitivity computation into a sufficiently smoothed diffusion and jump part. groß and sachs (2011, unpublished data) derived an adjoint approach for the milstein scheme (a second order discretization scheme) in connection with predictor-corrector methods. the feasibility and efficiency of monte carlo calibration for financial market models is discussed in (käbe, 2010). monte carlo calibration using adjoints provides at least two main considerable advantages. beside its flexibility, it allows a strong parallelization and thus the use of gpus (see section 2) to gain remarkable speed ups. secondly, second order information can easily be obtained due to pathwise use of adjoints (cf. (kaebe et al., 2009a)). hence, the number of necessary optimization iterations can be reduced tremendously. 3.3.2 pde constrained optimization we again consider the nonlinear lsq problem (19) as an example for the calibration problem using the pde framework (15), i.e.   2 0 =1 1 ( ) := ( , 0)min 2 m mod obs m m m f c s c     (21) 2 21 s.t. = ( , ) ( ) , ( , ) , 2 m m m mc s s t c r d sc rc s t     ( , ) = max( , 0), (0, ), for 1, , .m m mc s t s k s m m    with max= (0, ) [0, ).t   a drawback of (21) is the fact that m pdes need to be solved in order to obtain one function evaluation of f. since market data are given with different strikes k and maturities t, one can substantially reduce the computational effort replacing the m black-scholes equations (15) in (21) by, whenever available, one single dupire's equation (17). hence, the optimization problem (21) becomes   2 =1 1 ( ) := ( , )min 2 m obs m m m m f d k t c     (22) 2 21 s.t. = ( , ) ( ) , ( , ) , 2 d k t k d r d kd d d k t     ( , 0) = max( , 0), (0, ) ,d k s k k   andre loerx and ekkehard w. sachs 96 with max= (0, ) (0, ].t   the main tasks, when solving pde constrained optimization problems like (21) or (22), are: (i) the discretization of the model pde, (ii) the parametrization of the parameter functions, for instance, the local volatility function ( , )   and (iii) the type of regularization to overcome the potential ill-posedness of the problem. finally, (iv) the efficient computation of derivative information is a crucial issue to apply standard optimization routines. a gradient evaluation at low cost accelerates the calibration procedure tremendously and makes the calibration problem amenable for the application in practice. since (i) is more a pricing issue, references on proper discretization schemes of the model pde are already given in section 2. as mentioned earlier (cf. section 2.1), the parametrization of model functions can either be motivated by desired model properties in terms of hedging performance and implied volatility behavior or by reducing the number of unknowns in the calibration procedure. while in the time-dependent heston model the corresponding parameter functions are usually parametrized via piecewise constant or piecewise linear functions, the type of parametrization of the local volatility function varies strongly in the financial market literature. beaglehole and chebanier (2002), for example, used piecewise quadratic functions, whereas brown and randall (1999) applied hyperbolic trigonometric functions. mcintyre (2001) considered hermite polynomials and bsplines were used by hamida and cont (2005). bicubic splines were applied to parametrize the local volatility function, for instance, in (coleman et al., 1999; jackson et al., 1999; pironneau, 2009). spline representations, however, require rectangular parametrization grids. orosi (2010), glover and ali (2011) and coleman et al. (2011) use radial basis functions like gaussian, multi-quadratic and thin-plate splines, a popular choice for reconstruction surfaces from sparse data. the main advantage is the arbitrary placement of parametrization knots, which allows the number of parameters to be kept to a minimum. according to glover and ali (2011), thin-plate splines seem to perform best in terms of showing accurate and robust solutions to parametrize the local volatility function. a clever parametrization strategy can be very helpful to stabilize the calibration procedure, since it reduces the number of unknowns. however, the right choice can be a difficult task. as an example, parametrizing the local volatility function with cubic splines (as in (coleman et al., 1999)) is very difficult to automate, since one is faced with the trade-off between a lack of stability and unrealistic oscillations. thus, in case of a high number of unknowns, usually some regularization is needed to overcome the ill-posedness of the optimization problem. the best-known stabilization method for ill-posed nonlinear inverse problems is the tikhonov regularization introduced by tikhonov (1963). bodurtha (2000) and bodurtha and jermakyan (1999), for instance, minimize the sum of squared deviations from the black-scholes constant variance 2 0 , i.e. 2 2min ( , ) , l f x t where 2 2 0( , ) = ( , ).x t f x t   10 lagnado and osher (1997a, 1997b), jackson et al. (1999) and coleman et al. (2001) suggest regularizing the ill-posed inverse problem by additionally minimizing the 2 l -norm of the gradient of the volatility function, i.e. 2 2min ( , ) , l x t subject to a finite number of constraints. theoretical stability and convergence results for the calibration problem of local volatility models can be found in (jiang and tao, 2001; crépey, 2003; egger and engl, 2005). egger and engl (2005) prove convergence rates for the case of timeindependent volatilities, i.e. = ( ),s  under simple and interpretable smoothness assumptions. the results can be generalized to a class of local volatility functions, where the term structure is assumed to be known, more precisely, where ( , ) = ( ) ( )s t s t   and the function ( )t is known. purely time-dependent volatilities are extensively studied in (hein and hofmann, 2003) and the ill-posedness of the inverse problem is proven. uniqueness for state-dependent volatilities and the relation of optimal control problems corresponding to timediscrete and time-continuous observations are investigated in (jiang and tao, 2001). as mentioned before, the efficient derivative evaluation is crucial when applying existing optimization routines. coleman et al. (1999) use a trust region / interior point method and formulate the box-constrained 10 note that bodurtha (2000) and bodurtha and jemarkyan (1999) used a trinomial tree model (cf. section 3.1) to compute the option prices. model calibration in option pricing 97 nonlinear least-squares problem, 2 2 1 ( ) := ( )min 2p f r    r (23) s.t. ,l u  where 1= ( , , ) t p   is the vector of a cubic spline parameterization of the local volatility function ( , ),x t l and u the vectors of lower and upper bounds on , respectively, and ( )r  the residual function defined as 1 1 1( ) := ( ( ; , ) , , ( ; , ) ) , obs obs t m m mr d k t c d k t c    where ( ; , )d    is the solution of dupire's equation (21). 11 in (coleman et al., 1999) two possibilities to efficiently compute the jacobian of r are explored, i.e. the use of automatic differentiation (ad) (see (griewank and walther, 2008; coleman and verma, 1996)) and an approximation of the jacobian via a secant update formula. he et al. (2006) extended the calibration method of coleman et al. (1999) to a jump diffusion model coupled with local volatilities. when applying a classical steepest decent algorithm or quasi-newton approach, the use of adjoint equations to compute the gradient of f at low costs is proposed in (achdou and pironneau, 2005; egger and engl, 2005; loerx et al., 2010, unpublished data). an optimal control framework also using adjoints is applied by jiang et al. (2003) to recover the local volatility surface. turinici (2008) chose an sqp method to solve optimization problem (21). note that the sqp method already needs some second order information of f which comes at a cost of solving 1m  black-scholes pdes. according to coleman et al. (1999), optimization approaches, which do not require the calculation of second order information, typically converge very slowly, such that the additional computational effort to obtain at least some second order information can be profitable in the overall computation time of the optimization routine (see also (loerx, 2011)). schulze (2002) developed an inexact gauss-newton method to recover a non-parametric local volatility function. since, in general, the jacobian of the residual function cannot be stored in the non-parametric setting, the gauss-newton subproblems are solved with an iterative method (cg method). the matrix-vector products, which are needed within the cg framework, can be provided via sensitivity and adjoint equations. this approach was further improved in terms of computational efficiency by loerx et al. (2011, unpublished data). a reduced order model technique, known from fluid dynamics, is used in (pironneau, 2009) and applied to the local volatility framework. in (sachs and schu, 2008, 2010) reduced order models using proper orthogonal decomposition (pod) are used to solve the pide problem of jump diffusion models including local volatility. based on berestycki et al. (2002), turinici (2008, 2009a, 2009b) discovered other forms of cost functionals, for instance, including implied volatilities and proved convergence and stability properties. originally, berestycki et al. (2002) derived a new cost functional based on results of asymptotic relations between implied and local volatility. the new functional is close to a convex functional at least for short term maturities and therefore exhibits a more stable minimizer. more precisely, berestycki et al. (2002) proved that near expiry, the implied volatility can be represented as the spatial harmonic mean of the local volatility. furthermore, they showed that, for deep inand out-of-the-money options under certain assumptions, the squared implied volatility can be expressed as a time weighted average of squared local volatilities. these results can either be exploited to regularize the ill-posed inverse problem in a least-squares framework (as in (turinici, 2008, 2009a, 2009b)), or it can be used to continuously extrapolate the implied volatility surface into regions, where no observed implied volatilities are available. therefore, one is able to overcome one of the main drawbacks of extraand interpolation approaches using dupire's formula. another interesting approach, known from the field of 'dynamic programming', is to consider the calibration of financial market models in the framework of a 'stochastic control problem'. the method was proposed by avellaneda et al. (1997) and studied in a deeper way by samperi (2002). in contrast to the previous methods, this approach does not rely on any parametrization of the volatility. it leads to an unconstrained 11 note the equivalence of calibration problem (22) and (23). andre loerx and ekkehard w. sachs 98 optimization problem at the cost of solving nonlinear hamilton-jacobi-bellman equations. as a regularizer avellaneda et al. (1997) minimize the relative-entropy distance to a prior given distribution. some further details can also be found in (achdou and pironneau, 2005, chap. 8). 4. conclusion to capture realistic asset price behavior and volatility dynamics, a variety of financial market models has been developed over the last 40 years. in practice smile-consistent models are used to extract this market information from frequently traded standardized options in order to price and hedge exotic derivative products. we introduced the most common models and briefly discussed their characteristics from different perspectives. from the modeling side, for instance, we saw that despite all criticism simple models are widely used in practice, due to smaller computation and implementation costs and a better intuitiveness for risk-takers. numerical methods are needed whenever no closed form solution is available. we discussed pros and cons of common numerical methods, like the monte carlo method or pde methods. dupire or dupire-like equations have proven to be particularly useful for pricing and calibration purposes, since they provide option prices for different strikes and maturities with a computational effort of one pde evaluation. the main objective of this paper, however, was to illustrate one of the key issues in quantitative finance and that is model calibration. thus, we reviewed the existing literature on extraand interpolation techniques as well as iterative methods applied to analytic approximation. whereas the previous methods are mostly restricted to the calibration of local volatility models, optimization-based calibration methods offer more flexibility and are applicable to almost any financial market model. hence, we introduced sde and pde constrained optimization and addressed issues like parameter parameterization and problem regularization. the efficiency of optimizationbased methods strongly depends on the computational effort necessary to compute derivative information. we emphasized that adjoint techniques for derivative computations, recently introduced in financial market literature, have the potential to substantially speed-up optimization-based calibration procedures. 5. references achdou, y. and pironneau, o. 2005. computational methods for option pricing. siam, philadelphia. alexander, c. and nogueira, l.m. 2008. stochastic local volatility. available at ssrn: http://ssrn.com/abstract=1107685. amster, p., de napoli, p. and zubelli, j.p. 2009. towards a generalization of dupire's equation for several assets. journal on mathematical analysis and its applications, 355(1): 170-179. andersen, l. 2011. option pricing with quadratic volatility: a revisit. fin. and stochastics, 15(2): 191-219. andersen, l. and andreasen, j. 1999. jumping smiles. risk, 12(11): 65-68. andersen, l. and brotherton-ratcliffe, r. 1997/1998. the equity option volatility smile: an implicit finite-difference approach. journal of computational finance, 1(2): 5-38. andreasen, j. and carr, p. 2002. put call reversal. manuscript, new york university, new york, usa. avellaneda, m., friedman, c., holmes, r. and samperi, d. 1997. calibrating volatility surfaces via relative-entropy minimization. applied mathematical finance, 4(1): 37-64. ayache, e., henrotte, p., nassar, s. and wang, x. 2004. can anyone solve the smile problem? 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(2nd edition) john wiley & sons, chichester, uk. zühlsdorff, c. 2001. the pricing of derivatives on assets with quadratic volatility. applied mathematical finance, 8(4): 235-262. zvan, r., forsyth, p.a. and vetzal, k.r. 1998. robust numerical methods for pde models of asian options. journal of computational finance, 1(2): 39-78. received 15 january 2012 accepted 7 february 2012 microsoft word earth140317_02jun14.docx squ journal for science, 2014, 19 (1), 64-73 ©2014 sultan qaboos univeristy 64 late cretaceous sub-marine fan system in batain mélange zone, the fayah formation in northeastern oman iftikhar a. abbasi1*, abdulrahman al-harthy2 and yahya k. al-subhi3 1department of earth science, college of science, sultan qaboos university,p.o.box: 36, pc 123, al-khod, muscat, sultanate of oman; 2geo-consultancy center, al-khod, muscat, sultanate of oman; 3petrogas e & p llc, sultanate of oman. *email: iftikhar@squ.edu.om. abstract: the batain coast along the northeastern margin of oman between ra’s al-hadd and ra’s jibsch, is comprised of permian to late cretaceous complex stratigraphy in a tectonically deformed area recording permian rifting to late cretaceous tethys closure events. these rocks are thrust over mesozoic and older autochthonous sedimentary cover in the form of a major nappe structure known as the batain nappe. the uppermost part of the batain nappe is comprised of isolated outcrops of early maastrichtian siliciclastic fayah formation dominated by gravity flow deposits. the fayah formation in the jabal fayah area is over four hundred meters thick and comprised of five distinct facies associations; namely, i) coarsening-up sandstone, ii) conglomerate, iii) debrisflow, iv) turbidite, and v) inter-bedded sandstone and shale lithofacies. these lithofacies associations are repeated many times in the section. the sandstone lithofacies association exhibits a coarsening-upward trend making sequences tens of meters thick in various parts of the formation. waterscape structures are common along with occasional sandstone dykes and convolute bedding, reflecting fluidized conditions of deposition. the conglomerate lithofacies association is comprised of a series of interbedded coarsening-upward pebble to gravel size conglomerates containing chert, limestone, granite and volcanic clasts ranging a few mm to cm in diameter. occasionally these are interbedded with sandstone lithofacies. the conglomerate lithofacies was deposited by a high-energy channelized flow in a sub-aqueous setting. the debris-flow lithofacies association is a matrix supported chaotic mixture of clay and boulders of granite, limestone and volcanic rocks, some of which are meter-sized in diameter, and possibly derived from the nearby basement rocks such as the jabal ja’alan basement rocks. it constitutes the most dominant part of the formation. these sediments were deposited along a slope setting, possibly as olistostrome formed due to submarine slumping and sliding. the turbidite lithofacies association is comprised of monotonous grayish-green to brown coloured clays tens of meters thick interbedded with thin, clean, well-sorted sandstone. the interbedded sandstone and shale lithofacies association is comprised of a half to one meter thick cross-bedded, burrowed arkosic sandstone and plane laminated shale. the sandstone constitutes about 25% of the association with ripple lamination in the upper part of the unit indicating a fining-upward trend. dewatering structures are common. this association constitutes the upper 100 m of the formation. these sediments were deposited in shallow water conditions by channelized flows. based on the lithofacies associations described above, especially the dominance of debris-flow units and turbidites, the greater part of the fayah formation are interpreted as having been deposited under a sub-marine fan setting. only the upper part of the formation was deposited in a shallow water setting before the onset of overlying carbonate deposits. the sub-marine fan system was active during the last stages of the tethys ocean closure at the time of onset of the batain nappe. keywords: batain mélange; late cretaceous; jabal fayah; turbidite; sub-marine fan. late cretaceous sub-marine fan system 65 رواسب مرواح البحر العمیق من العصر الطباشیري في شرقیة عمان افتخار احمد عباسي، عبدالرحمن الحارثي ویحیى خلیفة الصبحي العصر البرمي تجاه الجنوب على تشكیالت صخریة متنوعة و تترواح أعمارھا من إرأس الحد و ب الممتد منمن عمان یحتوي الساحل الشرقي: ملخص و تشوھت ھذه الطبقات بفعل الحركات التكتونیة مسجلة بذلك التصدع المصاحب لتكون محیط التیثش في العصر البرمي . المتأخر إلى العصر الطباشیري سفر عن أبواسطة صدوع عكسیة مما ) مجموعة البطین(وتم دفع ھذه الصخور قید الدراسة .واخر العصر الطباشیريألى مراحل إنغالق ھذا المحیط في إ و یتكون الجزء العلوي من مجموعة البطین من . كثر قدماألى عصور إستقرارھا فوق صخور القاعدة الرسوبیة والتي یترواح عمرھا من الدھر الوسیط إ معزولة یعود عمرھا الى أوائل العصر المستریخي و یتكون من رواسب فتاتیة ترسبت بفعل تیارات تكوین الفیاح الذي یظھر على شكل منكشفات صخریة رواسب -3. الرصیص 2. سحنات رملیة-1:ربعمئة متر وھي كالتاليو تحتوي رواسب تكوین الفیاح على سحنات متنوعة یزید سمكھا على األ. الجاذبیة ن سحنات الحجر الرملي أو یالحظ . وتتكرر ھذه السحنات بشكل مستمر في التكوین. ت الطین الصفحي و الرملمتتالیا-5. رواسب المیاه العكرة-4. ركامیة و تحتوي ھذه السحنة على طبقات تشوھت بفعل التدفقات المائیة . على و یبلغ سماكة الطبقات عشرات األمتارلى األإسفل زدیاد حجم الحبیبات من األإتتمیز ب ما سحنة الرصیص فتحتوي على الصوان والحجر أ. عملیة تمییع للرواسبا وسریعة جدً نثناءات طبقیة تشیر الى عملیة ترسیب إرملیة ویضا قواطع أو بھا حیان تتعاقب سحنتا الرصیص و الحجر و في بعض األ. الجیري و الجرانیت و مفتاتات بركانیة یتراوح قطرھا من بضع ملیمترات إلى سنتیمرات معدودة من التكوین وھي الجزء األبرز ما السحنات الركامیة فھيأ. ن سحنة الرصیص ترسبت من تیارات مائیة عالیة السرعةأما من ناحیة البیئة فیعتقد أ. الرملي وربما لى المتر، إالصخور البركانیة، حیث یصل قطر بعضھا ریة من الجرانیت والحجر الجیري وخلیط غیر منتظم من الطین و مفتاتات صخعبارة عن ومن حیث الترسیب فھي رواسب المنحدرات التي تتكون بفعل .الدراسةجعالن القریبة من منطقة البحث و تكون مصدرھا صخور القاعدة البلوریة لجبل والتي تتعاقب مع طبقات عشرات األمتار لىإما سحنات المیاه العكرة فتتكون من طبقات طینیة یصل سمكھا أ .نھیارات الصخریة تحت الماءنزالقات و اإلاإل رتفاع إو التموج التي یصل أخیرا سحنة المتتالیات من الطین الصفحي و الرمل و تحتوي على صخور رملیة بھا عالمات النیم أو. رملیة ممتازة الفرز ً أثار ألى نصف المتر وبھا إبعضھا كبر فھو طین صفحي األ ءا الجزمأوتشكل الرمال ما مجموعھ ربع السحنة . حافیر في الرمل الفلدسباري خصوصا و . ن ھذه السحنة تكونت في میاه بحریة ضحلةأویعتقد . وتوجد سحنة المتتالیات من الطین الصفحي و الرمل في المئة متر العلویة من التكوین. فقیاأمتراص نھا إه السحنات السالفة الذكر وعالقتھا ببعضھا فقد توصل على على الدراسات التفصیلیة لھذ من متتالیات الطین الصفحي و الرمل وبناءً ھذه السحنة ستثناءإب .نغالق محیط التیثسإرضیة في فترة عماق السیحقة للبحر نتیجة الجاذبیة األح مائیة تدفقت نحو األواعبارة عن راوسب لمر . و بطین میالنج لیت كریتشیوس ،سب مارین فان :الكلماتمفتاح توربیدایت ، جبل فیاح ، 1. introduction he batain coast in northeastern oman in ash-sharyqiah region (figure 1) is comprised of diverse stratigraphy due to complex deformation related to the late cretaceous-paleogene deformation of the arabian plate and closure of the tethyan ocean [1,2,3]. the area is part of a tectonic mélange known as the batain mélange [1], comprising permian to late cretaceous rocks later described as the batain group of the batain nappe [4]. the batain nappe was thrust westward onto the eastern oman margin at the cretaceous-tertiary transition. the batain mélange, though initially mapped as the hawasina mélange [5], was subsequently identified as a separate unit [6] possibly separated by jabal ja'alan uplift. the rocks exposed along the batain coast in the mélange sequence are comprised of permian age qarari limestone, pink limestone, greenish fossiliferous grits, and limestone megabreccias and associated basalt; triassic age white, pink and red bioclastic lime-mudstones and framestones, claciturbidites; late jurassic to early cretaceous pillow lava and limestone assemblage; triassic to cenomanian cherts and argillites; cretaceous ophiolitic rocks and late cretaceous fayah sandstone (fayah formation). this study deals with the upper-most unit of the batain mélange sequence, the fayah formation and describes the lithofacies association in order to interpret the depositional system of the formation and its tectonic significance during the closure of tethys ocean along the northeastern margin of oman. a number of thin-sections from the sandstone units of the formation are studied to interpret the modal composition and probable provenance of the formation. the study was carried out along a section near jabal fayah (type-section) (figure 2). the stratigraphic thickness was measured along the section located at coordinates 21° 41/ 03// n 59° 21/ 33// e, and dominant lithofacies were described and rock samples collected for thin-section preparation (figure 2). 2. lithofacies association of the fayah formation the fayah formation is exposed in isolated outcrops along the batain coast. the study area is located near jabal fayah where the formation is a siliciclastic sequence, about 400 m thick comprising five main lithofacies associations i) coarsening-up sandstone, ii) conglomerate, iii) debris-flow, iv) turbidite, and v) inter-bedded sandstone and shale (figure 3). the outcrops are covered with migrating dunes in places but the mutual relationship of the lithofacies can be worked out on composite outcrop sections. the most significant feature of the fayah formation in the study area is the dominance of the debris flow deposits constituting the major part of the formation. details of each of the lithofacies association are given below. i) coarsening-up sandstone lithofacies association: this lithofacies association constitutes the lower 60 m of the formation (figure 3) and is comprised of green coloured coarse-grained arkosic sandstone, micaceous sandstone, buff coloured coarse to pebbly sandstone, gray coloured siltstone, and distinct red coloured matrix-rich beds of rhyolite and granite clasts. the sandstone grains are medium-to coarse-grain, well-cemented, well-sorted and moderately rounded. sandstone in the upper part of the association shows t iftikhar ahmed et al 66 plane and cross-lamination (figure 4a, b). most of the sandstone units show a coarsening-up trend, occasionally passing into conglomerate lithofacies. bioturbation and water escape structures are common features of this lithofacies (figure 4c). there are some units (at 30 m level figure 3) which contain large boulders over 1 m in diameter of granite composition in a sandy matrix (figure 4d). figure 1. location map of the study area in jabal fayah located in northeast the of oman, shown as batain mélange in ashsharyqiah region (modified after [7]). the lithofacies association is interpreted to have been deposited under shallow water marine conditions [8]. coarsening-up sequences show an active supply of sediments and high sedimentation rates. water escape structures also indicate high sedimentation rates in highly fluidized conditions [9]. the exotic boulder clasts and beds were formed due to debris flows contributed from nearby uplifted terrains. ii) conglomerate lithofacies association: the conglomerate lithofacies association is 15-20 m thick in the lower and middle part of the formation (figure 3). figure 2. location of fayah formation outcrops in batain mélange shown on google image. late cretaceous sub-marine fan system 67 the lithofacies association in the middle part of the formation is interbedded with thick debris flow deposits. this association is comprised of coarsening-upward conglomerate interbedded with plane bedded arkosic sugary textured white coloured sandstone (figure 4e). each coarsening-up sequence is about 2 m thick. the sandstone beds show occasional cross-bedding and burrowing. the clasts in the conglomerate beds are pebble sized and angular to subangular in shape (figure 4f ). the clasts are comprised of rhyolite, granite, green and red chert and limestone. water escape structures are common in the facies association. convolute bedding and sedimentary dykes (sandstone) are also present in the lithofacies association. the conglomerate lithofacies association was deposited by channelized flows associated with distributary channels draining into the proximal part of a submarine fan system. the sediments were derived from nearby basement escarpments. abundant chert is derived from obducted oceanic floor sediments of the batain nappe [10]. abundant water escape structures, convolute bedding and sandstone dykes were formed due to liquefied conditions and abundant sediment supply in the depositional site. another possibility is that deposition of the lithofacies along unstable slopes generated slumping. figure 3. detailed measured section of the fayah formation in the jabal fayah area. iii) debris flows lithofacies association: the debris flows lithofacies association (debrites) is the most significant rock type in the fayah formation, constituting most of middle part of the formation where it is over 150 m thick. it also occurs in the lower and upper parts of the formation being interbedded with other lithologies, such as sandstone lithofacies. the debris flow deposits contain 1-2 m in diameter sized angular boulders of granite and rhyolite floating in the sand-to-mud matrix. most of the matrix has now been removed, and the boulders are scattered over a large area (figure 4g). in the middle part of the formation iftikhar ahmed et al 68 where it constitutes the bulk of the formation, it is interbedded with coarsening-up conglomerate lithofacies. the debris flow lobes are exposed over 200 m in lateral extent and can be traced out at the outcrop scale. the debris flow deposits (debrites) were formed by mass flow processes in the proximal part of the submarine fan system during high discharge events in streams draining through a nearby source terrain, possibly an escarpment surface, exposing basement rocks. iv) turbidite lithofacies association: the turbidite lithofacies consists of grey to greyish-green coloured mudstone interbedded with thin sandstone (figure 4h). the lithofacies association occurs throughout the formation, and is interbedded with other lithofacies, such as debris flow lithofacies. it occurs dominantly at the 60-80 m level, interbedded with debris flows at the 90-220 m level and also occurs in the upper part of the formation (220-340 m level) (figure 3). shale and siltstone constitute about 75% of the association, the rest being the sandstone. the sandstone beds are 0.5 to 1 m thick, arkosic in composition, and fineto medium-grained. occasional conglomerate beds are also present. graded beds, dewatering structures, convolute bedding and trace fossils, such as bedding parallel burrows (planolites), are common in this lithofacies (figure 4i, j). figure 4…. continued this lithofacies association is interpreted as having been formed by mass flows deposited by density currents in deep water conditions most probably below the shelf margin [11]. v) interbedded sandstone and shale lithofacies association: this lithofacies association consists of interbedded green and brown coloured sandstone and shale. the sandstone is medium to coarse-grained. this lithofacies association is common in the upper 100 m or so of the formation (figure 3). d a c e f b late cretaceous sub-marine fan system 69 figure 4. field photographs of various lithofacies in the fayah formation; a) cross-bedded sandstone common in coarsening-up sandstone lithofacies associations, b) plane-bedded sandstone with water-escape structures, c) water-escape structures in various sandstone lithofacies, d) meter sized (~1m in diameter) pink granite boulders in debris flows lithofacies, e) coarsening-up conglomerate. light coloured clasts are granitic and dark coloured clasts are volcanic and carbonate in composition, f) angular to sub-angular clasts in conglomerate facies, g) pink coloured large clasts of granite in debris flow lithofacies associations. matrix has been removed and clasts are scattered over the outcrop scale usually in lobe shape, h) interbedded shale and sandstone of the turbidite lithofacies association, i) convolute bedding in turbidite facies, j) extensive bioturbation in shale beds of turbidite facies, k) oxidized red clays in the upper part of the formation in interbedded sandstone and shale lithofacies association, l) ridge-forming sandstone beds in the upper part of the formation. the lower 40 m of the lithofacies association is dominated by green coloured sandstone interbedded with shale, whereas the upper 40 m are dominated by brown coloured coarse-grained sandstone interbedded with siltstone. in its uppermost part, the depositional site was occasionally exposed to surface conditions, as shown by oxidized red coloured sandstone and conglomerate beds (figure 4k). the sandstone in this lithofacies association constitutes about 75% of the unit. the brown coloured sandstone is ridge forming. however it is difficult to trace laterally due to outcrop limitations (figure 4l). this lithofacies association was deposited under shallow water conditions by distributary channels during a drop in sea-level. the sediments were deposited in a shallow marine setting. sandstone was deposited by distributary channels while shale and siltstone were deposited in inter-distributary areas. 3. modal composition and provenance: detailed petrographic analyses were conducted on selected samples from various lithofacies, especially sandstone sequences, for detailed modal compositional analyses and to identify probable source terrain for the sediments of the fayah formation. a total of 14 thin-sections from the selected samples from bottom to top of the formation were prepared and studied. texturally and mineralogically the sandstone is immature, having poor sorting, a high percentage h i l k j g iftikhar ahmed et al 70 of feldspar and sub-angular grains. the modal composition shows that the sandstone is composed of quartz, feldspar, rock fragments, mica and occasional heavy minerals. the modal composition of these samples is presented in table 1, whereas a brief summary of the various components is given below. table 1. modal composition and texture of sandstone of the fayah formation. cement sorting/ roundnes texture other mica rock fragment feldspars quartz sample no silica, well sorted, subangular coarse-grain %2 5% 3% 35% 55% f1 not visible poorly sorted, angular subangular mediumcoarse-grain 1% 5% 4% 40% 50% f2 calcite poorly sorted, angular fine-medium grain 1% 3% 15% 45% 35% f3 calcite angular-subangular mediumgrain 1% 1% 10% 28% 60% f4 not visible angularsubangular very coarse grain 2% 1% 8% 47% 42% f5 silica, calcite subangular subrounded very coarse grain 3% 2% 10% 45% 40% f6 silica well sorted, subangular subrounded mediumcoarse-grain 2% 1% 12% 35% 50% f7 mudstone angular-subangular coarse-grain 2% 3% 5% 40% 50% f8 mudstone subangular coarse-grain 3% 2% 10% 45% 40% f9 silica poorly sorted, subangular fine-medium grain 5% 1% 9% 40% 45% f10 silica moderately sorted subangular subrounded mediumcoarse-grain 3% 3% 4% 40% 50% f11 not visible poorly sorted angular subangular fine-grained 3% 7% 10% 35% 45% f13a iron oxide, calcite poorly sorted subangular subrounded mediumcoarse-grain 2% 8% 5% 40% 45% f14 not visible poorly sorted angular subangular coarse -rain 3% 7% 5% 30% 55% f15 quartz: quartz grains form the major part of the framework component of the sandstone, constituting on average about 45% (table 1). quartz occurs both in mono-crystalline and poly-crystalline form (figure 5a,b). the quartz grains are sub-angular to sub-rounded in shape, reflecting short transportation distances. the amount of quartz varies from 35-60%, but without any trend in variation from the lower to the upper part of the formation. feldspar: feldspar constitutes the second most dominant part (on average about 40%) of the framework component (table 1). however, in a few samples, it is the most dominant grain type. it occurs as plagioclase, orthoclase and microcline (figure 5c,d). plagioclase and orthoclase are common in all thin sections with a minor amount of microcline. most of the orthoclase and plagioclase grains are altered (figure 5c). late cretaceous sub-marine fan system 71 rock fragment: rock fragments are the third major framework population, constituting on average about 10% (table 1). chert is the most dominant type of the lithic grains (figure 5e). granite, rhyolite, mudstone and limestone are other major lithic types in the formation. the lithic clasts are angular to sub-angular. mica: mica is present in small amounts (up to about 5%) in all samples. muscovite, biotite and chlorite are common types (figure 5f). chlorite is the major mica type in many sandstone samples particularly is most common in the green coloured sandstone. heavy minerals/others: minute amounts (<1%) of heavy minerals and other opaque minerals are present in all samples. a few grains of zircon and epidote are present in many samples. figure 5. microphotographs of sandstone sections, a & b) mono-and poly-crystalline quartz, c) diagenetically altered feldspar (oorthoclase & p-plagioclase) grains, d) microcline (mi) grain, e) chert (ch) fragments, f) chlorite (cl) grains. cement: calcite cement occurs in patches in many samples. silica, clay minerals and iron oxide also act as cement in some samples. in many samples the cement has been leached out. the composition of the framework components of the fayah formation shows that the clasts were derived mainly from the basement rocks exposed in the vicinity. textural immaturity, especially the grain angularity, reflects short transportation distances. high feldspar and quartz content in the formation is contributed by the basement granitic rocks exposed in the jabal ja’alan area [12]. however, large size granitic boulder clasts, over a meter in diameter, in the formation reflect a source area closer to the depositional site. the only alternative to the jabal ja’alan basement outcrops are the al-khlata formation outcrops as a probable nearby source area. the al-khlata formation has a large proportion of granitic and rhyolitic boulders, some of which are many meters in diameter. reworking of these boulder clasts could be a possible source terrain. the al-khlata formation is not exposed in the nearby area; however the formation may have been exposed during late cretaceous time and remnants of it are now buried under a migrating dunes. chert fragments are derived from oceanic floor sediments obducted along the batain coast as part of the batain mélange [3]. these sediments are rich in red and green coloured chert. the limestone clasts were contributed by a number of carbonate units, such as the qarari limestone and the guwayza formation exposed in the batain mélange. it is, therefore, interpreted that the source area for the fayah formation sediments is the jabal ja’alan basement sequence and the batain mélange thrust nappe. 4. depositional system and discussion the northeastern margin of oman between ra’s al hadd and ra’s jibsch is characterized by a complex stratigraphic setting recording major tectonic events, such as the opening of the tethys ocean and the obduction of the iftikhar ahmed et al 72 masirah ophiolites and associated mélange sequence [2,3]. the batain mélange formed due to the closure of the batain basin and the obduction of the masirah ophiolite along the northeastern margin of the arabian plate during late maastrichtian-early paleocene time. the fayah formation was deposited in the uppermost part of the batain basin during the emergence and erosion of the eastern oman margin, providing siliciclastic sediments in the basin [13]. the lithofacies association of the fayah formation, especially the debris flows and turbidite lithofacies associations suggest relatively deep water depositional conditions. the debris flows interbedded with other lithofacies associations, especially the turbidite lithofacies association, were deposited as sediment lobes which are laterally discontinuous even at outcrop scale. large meter sized boulders of pink granite suggest a major detritus input from the continental basement rocks exposed in the nearby source area. these mass flows were triggered during episodic uplifts associated with some faults or unusually wet conditions. the ophiolitic detritus in the mass flow deposits suggest a contribution from advancing ophiolite nappe such as the masirah ophiolites. the debris flow deposits in outcrops have lost their clay matrix and cement, resulting in scattered boulders and pebbles. in contrast to the debris flow deposits, the conglomerate lithofacies association is comprised of pebbles of granite and rhyolite which are only centimeter to few decimeters in size. the small size of the detritus in the conglomerate lithofacies association suggests that the continental basement was providing small size clasts during most of the deposition of the fayah formation, except during events of unusual uplift associated with the gravity flow. the interbedded sandstone and shale facies association in the upper part of the formation was deposited by submarine stream flows in shallowing-upward conditions associated with sea-level fall. the late cretaceous/early paleogene carbonate deposition started in the area once the distributary channels seized to exist. the fayah formation is age-equivalent to the qahlah and thaqab formations in the oman mountains which were deposited as a result of the samial ophiolite and hawasina nappe obduction during late cretaceous time [14]. the sediments of the fayah formation are interpreted as having been deposited under a marine setting by submarine fans (figure 6). the sediments were shed by the west-northwestward advancing masirah ophiolite nappe and uplifted basement and/or older formation, such as al-khlata formation rocks. figure 6. proposed depositional model for the submarine fan system of the fayah formation (modified from [15] ). 5. conclusions 1. the sediments of the fayah formation in jabal fayah were deposited in the batain mélange during late cretaceous time during closure of the neo-tethys ocean due to the masirah ophiolite obduction. 2. the sediments were deposited as a submarine fan system which developed during the final phase of ocean closure. various lithofacies associations were deposited in different parts of the fan system. 3. the detritus was contributed from advancing nappe and uplifted basement rocks, such as the jabal ja’alan rock sequence. since jabal ja’alan basement rocks are located far away from jabal fayah, large basement clasts in the alkhlata formation might be a possible alternative source rock. late cretaceous sub-marine fan system 73 6. acknowledgements financial support for this work was provided by the college of science, sultan qaboos university, oman through internal grant # ig/sci/eths/08/01. hilal al-zidi and hamdan al-zidi prepared thin-sections. comments from two referees helped to improve the manuscript. references 1. shackleton, r.m. and ries, a.c. tectonics of the masirah fault zone and eastern oman. in the geology and tectonics of the oman region, (eds. robertson, a.h.f., searle, m.p. and ries, a.c.), geological society of london special publication, london. 1990, 49, 715-724. 2. shackleton, r.m., ries, a.c., bird, p.r., filbrandt, j.b. lee, c.w. and cunningham, g.c. the batain melange of ne oman. in the geology and tectonics of the oman region, (eds. robertson, a.h.f., searle, m.p. and ries, a.c), geological society of london special publication, london. 1990, 49, 673-696. 3. immenhauser, a., schreurs, g., gnos, e., oterdoom, h.w. and hartmann, b. late palaeozoic to neogene geodynamic evolution of the northeastern oman margin. geol. mag., 2000, 137(1), 1-18. 4. immenhauser, a., schreurs, g., peters, t., matter, a., hauser, m. and dumitrica, p. stratigraphy, sedimentology and depositional environments of the permian to uppermost cretaceous batain group, eastoman. eclogae geologicae helvetiae, 1998, 91, 217-35. 5. glennie, k.w., hughes-clarke, m.w., boeuf, m.g., pilaar, w.f. and reinhardt, b.m. geology of the oman mountains. verhandelingen koninklijk nederlands geologisch mijnbouwkundig genootschap, 1974, 31, p423. 6. graham, g.m. evolution of a passive margin and nappe emplacement in the oman mountains. proceedings of the international ophiolite symposium, nicosia, cyprus, 1980, 414-423. 7. loosveld, r.j.h., bell, a. and terken j.j.m. the tectonic evolution of interior oman. geoarabia, 1996, 1(1), 28-51. 8. reading, h.g. sedimentary environments: processes, facies and stratigraphy, (3rd edition) wileyblackwell, london, 1996, p704. 9. reineck, h.e. and singh, i.b. depositional sedimentary environments. with reference to terrigenous clastics. springer verlag, berlin, heidelberg, new york, 1973, p439. 10. ries, a.c. and shackleton, r.m. structures in the huqf–haushi uplift, east central oman. in the geology and tectonics of the oman region (eds. robertson, a.h.f., searle, m.p. and ries, a.c), geological society of london special publication, london. 1990, 49, 653-664. 11. walker, r.g. turbidites and submarine fans. in facies models: response to sea-level changes (eds. walker r.g. and james n.p.) geotext1 canada, 1992, 239-263. 12. roger, j., béchennec, f., janjou, d., le métour, j., wyns, r. and beurrier, m. explanatory notes to the geological map of ja’alan, sheet nf 40–8e, scale:1:250,000. muscat, oman directorate general of minerals, oman ministry of petroleum and minerals, 1991, p84. 13. gnos, e., immenhauser, a. and peters, t. late cretaceous/early tertiary collision between the indian and arabian plates recorded in ophiolites and related sediments. tectonophys., 1997, 271, 1-19. 14. abbasi, i.a., salad-hersi, o. and al-harthy, a. late cretaceous conglomerates of the qahlah formation, north oman. in tectonic evolution of the oman mountains (ed. rollinson, h.r). 15. searle, m.p., abbasi, i.a., al-lazki, a. and al kindi, m.h. geological society london special publication, london. 2014, 392, 325-341. 16. normark, w.r. fan valleys, channels and depositional lobes on modern submarine fans: character for recognition of sandy turbidite environment. am. assoc. petrol. geol. bull., 1978, 62, 912-931. received 17 march 2014 accepted 11 may 2014 squ journal for science, 2015, 20(2), 19-30 ©2015 sultan qaboos university 19 numerical wave solutions for nonlinear coupled equations using sinc-collocation method kamel al-khaled department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. e-mail: kamel@squ.edu.om abstract: in this paper, numerical solutions for nonlinear coupled korteweg-de vries(abbreviated as kdv) equations are calculated by the sinc-collocation method. this approach is based on a global collocation method using sinc basis functions. the first step is to discretize time derivative of the kdv equations by a classic finite difference formula, while the space derivatives are approximated by a -weighted scheme. sinc functions are used to solve these two equations. soliton solutions are constructed to show the nature of the solution. the numerical results are shown to demonstrate the efficiency of the newly proposed method. keywords: nonlinear coupled kdv equations; sinc-collocation method; soliton solutions. التجميعية-حلول الموجة العذدية لمعادالت الذوال غير الخطية باستخذام طريقة سينك كامل الخالذ انتجًيعيح. -( تطزيقح سينكkdvتى في هذا انثحث إيجاد انحهىل انعذديح نًعادالخ انذوال غيز انخطيح وانًسًاج كىرتيج دو فزيس )يختصز ملخص: ح وفقا نصيغ kdvيستنذ هذا اننهج عهى طزيقح تجًيعيح شايهح تاستخذاو دوال انسينك األساسيح. تى في انخطىج األونى تقطيع يشتقح انشين نهًعادالخ و دوال سينك. كًا تى إيجاد افزق انًحذود انكالسيكيح، تينًا تى تقزية انًشتقاخ انفضائيح تطزيقح نظاو انًىاسنح. وتى حم هاتين انًعادنتين تاستخذ وحساب حهىل انًىجح انًنعشنح إلظهار طثيعح انحم. وأظهزخ اننتائج انعذديح كفاءج انطزيقح انًقتزحح. انتجًيعيح.-خطيح، حهىل انًىجح انًنعشنح، طزيقح سينكانانًقزونح غيز kdvيعادالخ :كلمات مفتاحية 1. introduction onlinear partial differential equations appear in many branches of physics, engineering and applied mathematics. the coupled kdv equations, recently, have been an attractive research area for scientists, because of their many applications in scientific fields and many studies have been reported in the literature, see for example [1-5]. in this paper, we study the coupled kdv equations that were introduced by hirota-satsuma [6] = 6 2 , = 3 , t xxx x x t xxx x u u uu vv v v uv         (1) subject to the initial conditions ( , 0) = ( ), ( , 0) = ( ),u x f x v x g x a x b  (2) and boundary conditions 1 2 1 2 ( , ) = ( ), ( , ) = ( ), ( , ) = ( ), ( , ) = ( ),u a t f t u b t f t v a t g t v b t g t (3) where ( , )u x t and ( , )v x t are real-valued scalar functions, t is time, and x is a spatial variable. the equations (1)(3) describe interactions of two long waves with different dispersion relations. many powerful methods have been developed to find solutions (exact, or numerical) of such nonlinear evolution equations. these include the adomian decomposition method [7] and the collocation method [8]. the soliton solutions for this system are constructed by fan [9]. mesh-free methods are the topic of recent research in many areas of computational science and approximation theory. over the past several years mesh-free approximation methods have found their way into many different application areas ranging from engineering to the numerical solution of differential equations. a meshless method does not require a grid, and only makes use of a set of scattered collocation points. in [10,11], the authors propose a meshn kamel al-khaled 20 free collocation method and formulate simple classical radial basis functions for the numerical solution of the kdv equation, and coupled kdv equations. in [12], the authors employ a mesh-free technique for the computational solution of the two-dimensional coupled burgers' equations. they combine the collocation method using the radial basis functions with first-order accurate forward difference approximation to obtain a mesh-free solution of the coupled burgers' equations. a mesh-free technique was presented in [13] for the solution of the generalized regularized long wave equation, the collocation being founded using sinc function basis. the purpose of this paper, and following [11], is to elaborate a special collocation method based on sinc function basis for spatial derivatives, and classic finite difference formulae for time derivatives, to obtain numerically the traveling wave solutions of the kdv system in (1)(3). the sinc-collocation method will be used in the space direction. the main idea is to replace derivatives by their sinc approximations. the ease of implementation coupled with the exponential convergence rate have demonstrated the viability of this method. sinc functions are discussed in stenger [14] and by lund and bowers [15]. the layout of the paper is as follows. in section2, we briefly review some general concepts of the sinc function that are necessary for the formulation of the discrete system. in section 3, we discuss the mesh-free method together with the sinc-collocation discretization of the coupled kdv equations. section 4 is devoted to the stability of the method, by using a linearized stability analysis. finally, numerical experiments are presented and some comparisons are made in section 5. some concluding remarks are given in the final section 6. 2. sinc-collocation the goal of this section is to recall notations and definitions of the sinc function that will be used in this paper. these are discussed in [14,10]. the sinc function is defined on the whole real line r by sinc ( ) = sin( ) , 0 1, 0 x x x x x         (4) recall that a radial basis function is a function whose value depends only on the distance of its input to a central point. for a series of nodes equally spaced h apart, the sinc function can be written as a radial basis function: ( ) = sinc , = 0, 1, 2,... j x jh s x j h       ( 5) the whittaker cardinal function ( , )c f h of a function f is defined as = ( , )( ) = ( ) ( ). j j c f h x f jh s x    whenever this series converges, f is approximated by using the finite number of terms. so, for positive integer ,n define = ( , )( )= ( ) ( ). n n j j n c f h x f jh s x (6) definition 2.1 let > 0d , and let dd denote the region { = ,| |< }z x iy y d in the complex plane c , and  the conformal map of a simply connected domain d in the complex plane domain onto dd such that ( ) =a  and ( ) =b  , where a and b are the boundary points of .d let  denote the inverse map of  , and let the arc  , with end points a and b ( ,a b  ), be given by = ( , ).   for > 0h , let the points kx on  be given by = ( ) , k x kh z z  and ( ) = exp( ( ))z z  . hence, the numerical process developed in the domain containing the whole real line can be carried over to infinite interval by the inverse map. the approximation of the th n derivatives of ( )f x by the sinc expansion is given by ( ) = ( ) [ ( )]. nn n jn j n d f f jh s x dx   (7) the derivatives of sinc functions evaluated at the nodes will be needed [14,15]. in particular, the following convenient notation will be useful in formulating the discrete system. (0) = = [ ( )] | 1, = = 0, jk j x x k s x j k j k     (8) numerical wave solutions for nonlinear coupled equations 21 (1) = = [ ( )] | = 0, = ( 1) , ( ) k j j x x k jk d s x dx j k j k h k j        (9) 3 (3) =3 2 2 3 = [ ( )] | = 0, = ( 1) [6 ( ) ] , ( ) k j j x x k jk d s x dx j k k j j k k j          (10) where the collocation points are = . k x x in practice, we need to use a finite number of terms in the series (7), say = ,..., ,j n n where n is the number of sinc grid points. for a restricted class of functions known as the palyweiner class, which are entire functions, the sinc interpolation and quadratic formulas are exact [14]. a less restrictive class of functions which are analytic only on an infinite strip containing the real line and which allow specific growth restrictions have exponentially decaying absolute errors in the sinc approximation. in order to state the convergence theorem of the sinc-collocation method, we introduce the following notation and definition. definition 2.2 for all 0 < < 1 , let ( )dd  be defined by ( ) = { :| |< 1 / , | |< (1 )}. d d z c rez imz d    (11) let ( )db d be the hardy space over the region dd , i.e., the set of all functions such that 0 | ( ) | | |< .lim ( )d d f z dz    (12) the properties of functions in ( )db d and detailed discussions are given in [14]. we recall the following theorem for our convergence purposes. theorem 2.1[14] let ,  and d be positive constants. assume that 1. ( )df b d 2. f decays exponentially on the real line, that is, | ( ) | exp( | |), .f x x x r    then, we have ( ) ( ) ( 1)/ 2 1 = sup | ( ) ( ) | exp( ) n n n n j j j n f x f s x c n d n       for some constant 1c , where the mesh size h is taken as = / ( ).h d n  the above theorem states that if f is an analytic function on an infinite strip containing the real line, and satisfies some kind of decaying conditions, then the function f together with it derivatives can be approximated by sinc function methodology with error of exponential order. therefore, in order to approximate the solution of the kdv system (1) using sinc basis, we should start with the assumption that the initial conditions in (3) belong to class ( ) d b d . the matrices (0) (1) (3) , ,i i i will appear in the final discrete system, and in order to study the stability of the sinc-collocation method, we should find some bound for the eigenvalues of these matrices. the matrix (0) i is just the identity matrix which has eigenvalue1. for eigenvalue bounds for the toeplitz matrices (1) (3) , ,i i we state the following theorem. theorem 2.2[14] 1. the m m matrix (1) i is a singular skew-symmetric matrix, if its eigenvalues are denoted by (1) = { } n j j n i   , then (1) (1) ... . n n           2. the m m matrix (3) i is a singular skew-symmetric matrix, if its eigenvalues are denoted by (3) = { } n j j n i   , then 3 (3) (3) 3 ... . n n           kamel al-khaled 22 3. construction of the method consider the nonlinear coupled kdv equations in (1), subject to the initial and boundary conditions (2)-(3). to implement the sinc-collocation method, we discretize the time derivative of the nonlinear coupled kdv equations using the classic finite difference formula, and space derivatives by the weighted (0 1)  scheme successive two time levels n and 1n  1 1 1 1 = ( (1 )( ) 6 ( ) 6 (1 )( ) 2 ( ) n n n n n n n xxx xxx x x x u u u u uu uu vv t                    (13) and, 1 1 = ( ) (1 )( ) 3 ( ) n n n n n xxx xxx x v v v v uv t            (14) where = ( , ) n n u u x t is the value of the solution at the th n time step, and 1= ,n nt t t  where t is a time step size. the nonlinear term 1 ( ) n x uu  must be linearized before continuing. this can be accomplished by using the following formula which is obtained by applying the taylor expansion, as follows thus, 1 2 ( ) ( ) [( ) ( ) ] ( ) n n n n n n x x t x xt uu uu t u u u u o t       (15) which can be simplified to 11 1 2( ) ( ) ( ) ( ) [ ] ( ) n nn n n n n n x x x x x u uu u uu uu t u u o t t t             (16) finally, we arrive at the linearization 1 1 1 ( ) ( ) n n n n n n n x x x x uu u u u u u u       (17) so that equations (14)-(15) can be rewritten as 1 1 1 1 ( ) 6 ( ) = (1 ) 6 (1 ) 6 2 n n n n n n xxx x x n n n n n n n n xxx x x x u t u t u u u u u t u t u u t u u tv v                         (18) and 1 1 ( ) = (1 )( ) 3 n n n n n n xxx xxx x v t v v t v tu v           (19) where n u and n v are the th n iterates of the approximate solutions. now the space variable is discretized upon the use of sinc-collocation at the points 1 | | { = ,..., ( 1) ,..., = }, = . 1 i n b a x a x a i h x b h n      (20) the solution of equation (13) is interpolated and approximated by means of the sinc functions as =1 =1 ( ) = ( ), ( ) = ( ) n n n n n n j j j j j j u x u s x v x v s x  (21) where ( 1) ( ) = sinc( ). j x j h a s x h    (22) the unknown parameters , j j u v in equation (21) are to be determined by the collocation method. therefore, for each collocation point ix in (20), equation (22) can be written as =1 =1 ( ) = ( ), ( ) = ( ), = 1,..., . n n n n n n i j j i i j j i j j u x u s x v x v s x i n  (23) substituting equation (23) into equations (18) and (19), we get 1 1 2 ( ) ( ) ( ) n n n n x x x x u u u u t o t t           numerical wave solutions for nonlinear coupled equations 23 1 1 1 =1 =1 =1 =1 1 =1 =1 =1 =1 =1 =1 =1 ( ) ( ) 6 [ ( ) ( ) ( ) ( )] = ( ) (1 ) ( ) 6 (1 ) ( ) ( ) 6 n n n n n n n n j j i j j i j j i j j i j j j j n n n n n n n n j j i j j i j j i j j i j j j j n n n n j j i j j i j j j u s x t u s x t u s x u s x u s x u s x u s x t u s x t u s x u s x t                                   =1 =1 =1 ( ) ( ) 2 ( ) ( ). n n n n j j i j j i j n n n n j j i j j i j j u s x u s x t v s x v s x       (24) and 1 1 =1 =1 =1 =1 =1 =1 ( ) ( ) = ( ) (1 ) ( ) 3 ( ) ( ) n n n n n n j j i j j i j j i j j j n n n n n n j j i j j i j j i j j j v s x t v s x v s x t v s x t u s x v s x                    (25) equations (24) and (25) are used for all interior points = , = 2,..., 1ix x i n  , where primes in these equations denote differentiation with respect to the variable x . the boundary condition given by equation (17) for the boundary points = , = 1,ix x i n can be written as 1 1 1 1 1 2 =1 =1 ( ) = ( ), ( ) = ( ) n n n n n n j j i j j i j j u s x f t u s x f t       (26) and 1 1 1 1 1 2 =1 =1 ( ) = ( ), ( ) = ( ). n n n n n n j j i j j i j j v s x g t v s x g t       (27) to obtain matrix representation of the expression in equation (24) and (25), we introduce the following matrix and vector notations 1 2 (0) (1) (3) = [ , , ..., ] , = ( ), , = 1,..., , = ( ), , = 1,..., , = ( ), , = 1,..., . n n n n t n j i j i j i u u u n i s x i j n i s x i j n i s x i j n   (28) note that the matrices (1) (3) ,i i are skew symmetric. the system of equations (24)-(27) can be solved for unknown parameters , j j u v in equation (21) simultaneously, and then the solutions for u and v can be obtained from equation (21). equations (24)-(27) can be written in matrix form as (0) (3) (1) (0) 1 [ 6 [ ]] n n n x i t i t u i u i u          (0) (3) (1) (1) (1) 1 = [ (1 ) 6 (1 ) 6 2 ] n n n n n i ti tu i t u i tv i u f                    (29) and (0) (3) 1 (0) (3) (1) 1 [ ] = [ (1 ) 3 ] n n n n i t i v i ti tu i v g              (30) where  stands for component by component multiplication, and 1 1 1 1 2 = [ ( ), 0,..., 0, ( )] n n n t f f t f t    , and 1 1 1 1 2 = [ ( ), 0,..., 0, ( )] n n n t g g t g t    . equations (29) and (30) can be written in a more compact form as 1 1 1 1 = n n n a u b u f    (31) and 1 1 2 2 = , n n n a v b v g    (32) where kamel al-khaled 24 (0) (3) (1) (0) 1 (0) (3) (1) (1) (1) 1 (0) (3) 2 (0) (3) (1) 2 = 6 [ ], = (1 ) 6 (1 ) 6 2 , = , = (1 ) 3 . n n x n n n n a i t i t u i u i b i ti tu i t u i tv i a i t i b i ti tu i                                       equation (21) can written in matrix form as (0) (0) = , = . n n n n u i u v i v (33) from equation (31), we get 1 1 1 1 1 1 1 = . n n n u a b u a f      combining the above equation together with equation (33), we arrive at 1 (0) 1 (0) 1 1 1 1 1 = . n n n u i a b u i a f      (34) similarly, using equations (32) and (33) we arrive at 1 (0) 1 (0) 1 1 2 2 2 = . n n n v i a b v i a g      (35) we can obtain the coefficients of the approximate solution by solving the system in equations (34)-(35) using any iterative technique. for the convergence of the method, we state the following two theorems. theorem 3.1 let the function ( , )u x t be as in equation (1) with the initial condition as in equation (2), and let the matrix u be defined as in (34). then for a sufficiently large ,n there exists a constant c independent of n such that   2 , || ( , ) || exp( ).sup n j n j x t u x t u cn d n    theorem 3.2 given a constant > 0r , there is a constant > 0t such that if 1 0 || || / 2u u r  , then the iterative scheme (34) converges to the unique solution. the proof of the above two theorems are immediate from [16,17]. we would like to mention here that for theorem 3.1, we use the second part of theorem 2.1 for = 1n and = 3n , which is a simple modification of theorem 3.2 in [2]. for theorem 3.2, we use contraction mapping of the iteration scheme given in equation (34) and apply fixed point theorem to prove convergence. interested readers may follow [16] for a detailed analysis 4. stability analysis in this section, we present an analysis of the stability of the sinc-collocation method for solving the coupled kdv system using spectral radius matrices. following the method outlined in [11], let ,u v be the exact, and ,u v be the numerical solutions of the coupled system in (1). define the error vectors = , n u u u  and = . n v v v  using equations (34) and (35) the errors , n n u v   can be written as 1 1 1 (0) 1 1 1 1 (0) 1 1 1 2 2 = = , = = . n n n n n n n n u u v v u u i a b v v i a b              (36) for stability of the method, we need 0 n u   , and 0 n v   for large values of n . therefore, the scheme is considered numerically stable if (0) 1 1 1 ( ) < 1i a b  , and (0) 1 2 2 ( ) < 1i a b  , where (.) denotes the spectral radius. the sinc matrices (1) (3) ,i i are contained in the matrices 1 2 1, ,a a b and 2b , where the bounds for the eigenvalues of these matrices are given in theorem 2.2. therefore, stability is assured if 3 1 2 3 1 1 1 < 1 1 6 [ ] 1 (1 ) 6 (1 ) 6 2 n n n n n t t t t t t                            (37) and numerical wave solutions for nonlinear coupled equations 25 3 3 1 1 < 1 1 (1 ) 3 n t t t             (38) where we have used the numbers 1 , 1 3 1 2, , ,n n    being eigenvalues of the matrices (0) (1) (3) (1) (0) , , , , n n i i i u i u i  respectively. using the upper bound for the eigenvalues in theorem 2.2, together with the fact that 1 1 = | |i  , 3 3 = | |i  , and if 1 2 , n n   are complex, then after algebraic manipulation (see, [13,10,11]), the conditions (37) and (38) must hold for all eigenvalues of the respective matrices. having 1/ 2 < 1 is necessary, but not sufficient, to guarantee the stability of the sinc collocation method. 5. numerical results choosing examples with known solutions allows for a more complete error analysis. in order to assess the advantages of the proposed method, in terms of accuracy and efficiency for solving nonlinear coupled kdv equations, the following examples are presented in this section. example 5.1 in this example, we have to apply our scheme to solve equation (1) with = 1, 1/ 2   , and > 0 , with the initial conditions 2 2 2 2 1 ( , 0) = 4 , ( , 0) = 3 6 (1 ) (1 ) kx kx kx kx e me u x k k v x e e         (39) where 224 =m k   , and k is an arbitrary constant. the exact solution is given by [7] ( ) ( ) 2 2 ( ) 2 ( ) 2 1 ( , ) = 4 , ( , ) = 3 6 (1 ) (1 ) k x ct k x ct k x ct k x ct e me u x t k k v x t e e              (40) the computations associated with the example were performed using mathematica. in our computational work, we take = 1.5, = 0.1, = 0.1, = 0.1c k  , and two different time step sizes = 0.1t and = 0.05t through the interval [ 30, 30] and = 160n for the set of collocation points as in equation (20). the accuracy of the scheme is measured by using the following two error norms [1, 11] 2 2 2 1=1 =|| || = | | , =|| || = | |max n j j j j j nj l u u h u u l u u u u         where u and u represent the exact and approximate solutions, respectively, and h is the minimum distance between any two points in equation (21), similarly for the v solution. the pointwise rate of convergence in time is also calculated by using the following formula [1,11] 10 1 110 (|| || / || ||)log order = ( / )log exact t exact t j j j j u u u u t t         where exactu is the exact solution, and t j u  is the numerical solution with time step size j t . in table 1, the number of collocation points is = 160n , and the time step size = 0.8, 0.4, 0.2, 0.1, 0.05, 0.025, 0.01t is varied to compute the time rate of convergence when = 1/ 2 . it can be noted from table 1 that the method has order of convergence 2 . the accuracy of the proposed method is demonstrated for the absolute errors for solution of (1) with their exact solutions. table 2 reports the supremum norm error between the exact solution (40) and our approximate solution compared with the results in [11]. a clear conclusion can be drawn from the numerical results in figures 1, 2 and table 2 that sinc methodology provides highly accurate numerical solutions. kamel al-khaled 26 figure 1. the exact and approximate solutions for ( , )u x t in example 5.1. figure 2. the exact and approximate solutions for ( , )v x t in example 5.1. table 1. time rate of convergence solution of equation (1): = 16, = 1/ 2, = 160, 30 30t n x     t l  order 2 l order 0.8 33.10524 10    2 1.10518 10    0.4 31.22201 10   1.96166 3 3.22148 10   1.96453 0.2 45.35209 10   1.99086 4 8.35020 10   1.99486 0.1 41.49743 10   1.99748 4 4.49278 10   1.99782 0.05 58.66014 10   1.99835 4 1.65082 10   1.99892 0.025 56.84252 10   1.99809 5 5.82611 10   1.99212 0.010 52.04701 10   1.98971 5 1.02058 10   1.98775 table 2. numerical results for example 5.1when = 0.001.t x | |u u | |u u as in [13] | |v v | |v v as in [13] 4 82.039 10   7 1.766 10   8 9.672 10   8 1.239 10   3 81.565 10   6 1.368 10   8 7.423 10   8 9.832 10   2 81.060 10   5 1.056 10   8 5.031 10   7 8.829 10   1 95.356 10   5 2.966 10   8 2.540 10   5 1.023 10   0 132.485 10   4 1.367 10   12 1.179 10   6 2.001 10   1 95.353 10   5 3.897 10   8 2.540 10   5 1.195 10   2 81.060 10   5 1.241 10   8 5.031 10   6 1.252 10   3 81.565 10   5 1.666 10   8 7.423 10   6 1.182 10   4 82.039 10   6 7.380 10   8 9.672 10   7 5.219 10   numerical wave solutions for nonlinear coupled equations 27 example 5.2 in this example, we solve the problem = 2 , = t xxx x x t xxx x u u uu vv v v uv     (41) subject to the initial conditions 2 2 3 1 1 3 1 1 1 ( , 0) = s [ ], ( , 0) = [ ],tanh 4 2 2 4 2 2 2 u x ech x v x x a x b  (42) and boundary conditions ( , ) = ( , ) = 0, ( , ) = ( , ) = 0u a t u b t v a t v b t as a and b both approaches  . the exact solution is known as [7] 2 2 3 1 1 1 3 1 1 1 1 ( , ) = s [ ( )], ( , ) = [ ( )].tanh 4 2 2 2 4 2 2 2 2 u x t ech x t v x t x t  (43) the numerical solutions are shown in figures 3 9 . these solutions are the bell-shaped waves, which agree with the results of [7]. from figures 3 and 5, we understand that in both cases of u and ,v the solutions are a solitary wave pattern. also, from figures 4 and 6 , we see that for 0.5t  , the solution starts to bifurcate into three waves. figures 7, 8 show both the approximate and exact solutions for both ( , )u x t and ( , )v x t , while figure 9 shows the absolute error when finding the solution of ( , )u x t . figure 3.three profile solutions for ( , )v x t when 160,n  t =0.1, 0.2, 0.3 and 0.05t  . figure 4. two profile solutions for ( , )u x t when 160,n  t =0.5, 0.6 and 0.05t  . 5 5 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 5 5 x 0.2 0.4 0.6 0.8 1.0 kamel al-khaled 28 figure 5. three profile solutions for ( , )v x t when 160,n  t =0.1, 0.2, 0.3 and 0.05t  . figure 6. two profile solutions for ( , )v x t when 160,n  t =0.5, 0.6 and 0.01t  . figure 7. the exact and approximate solutions of ( , )u x t in example 5.2. 5 5 x 0.1 0.2 0.3 0.4 0.5 4 2 2 4 x 0.2 0.4 0.6 0.8 numerical wave solutions for nonlinear coupled equations 29 figure 8. the exact and approximate solutions of ( , )v x t in example 5.2. figure 9. the error in our approximate solution for ( , )u x t in example 5.2. table 3. the absolute error in finding both ( , )u x t and ( , )v x t in example 5.2 for t = 0.1. x | |u u | |v v 5 62.6530 10   4 2.8135 10   4 51.7980 10   3 1.0097 10   3 59.9222 10   3 3.1410 10   2 42.6240 10   3 7.1015 10   1 41.6752 10   3 7.6237 10   0 44.8000 10   4 1.8600 10   1 53.9810 10   3 7.1700 10   2 41.7891 10   3 6.5813 10   3 59.5560 10   3 3.3004 10   4 52.5442 10   3 1.1990 10   5 64.7766 10   4 3.6223 10   kamel al-khaled 30 6. conclusions the fundamental goal of this paper wasto propose an efficient algorithm for the solution of coupled kdv equations. the sinc-collocation method was described in detail, and implemented to compute a numerical solution to the system in (1). a brief stability analysis was provided, which produced a necessary condition for stability of the method. the efficiency of the method wastested on one example of soliton type, and the accuracy examined in terms of the 2,l l error norms. the results obtained by the sinc collocation method were very close to analytical ones, and were found to be more accurate than other numerical schemes [12,17]. the algorithm has been found to be stable, exponentially convergent in space and a reliable numerical method for solving coupled kdv equations. references 1. alquran, m. and al-khaled, k. sinc and solitary wave solutions to the generalized benjamin-bona-mahonyburgers equations. phys. scr, 2011, 83, 6. 2. alquran, m. and al-khaled, k. the tanh and sine–cosine methods for higher order equations of korteweg-de vries type. phys. scr, 2011, 84. 3. wazwaz, a.m., the tanh and the sine-cosine methods for the complex modified kdv and the generalized kdv equations. comput. and math. with appl., 2005, 49, 1101-1112. 4. wazwaz, a.m. travelling wave solutions of generalized forms of burgers, burgers-kdv and burgers-huxley equations, appl. math. and comput., 2005, 169, 639-656. 5. triki, h., taha, t. and wazwaz, a.m., solitary wave solutions for a generalized kdv-mkdv equation with variable coefficients. math. and comput. simul., 2010, 80(9), 1867-1873. 6. hirota, r. and satsuma, j. soliton solutions of a coupled korteweg-de vries equations. phys. lett. a, 1981, 85, 407-408. 7. kaya, d. and inan, i.e., exact and numerical travelling wave solutions for nonlinear coupled equations using symbolic computation. appl. math. comput., 2004, 151, 775-787. 8. khare, a.h., temsah, r.s. and callebaut, d.k. numerical solutions for some coupled nonlinear evolution equations by using spectral collocation method. math. computer model., 2008, 48, 1237-1253. 9. fan, e. soliton solutions for a generalized hirota-satsuma coupled kdv equation and a coupled mkdv equation. phys. lett. a, 2001, 282, 18-22. 10. siraj-ul-islam, haq, s. and uddin, m. a meshfree interpolation method for the numerical solution of kdv-burgers equation. appl. math. model. 2009, 33, 3442-3449. 11. siraj-ul-islam, haq, s. and uddin, m. a meshfree interpolation method for the numerical solution of the coupled nonlinear partial differential equations. engineering analysis with boundary elements, 2009, 33, 399-409. 12. arshed, a., siraj-ul-islam and haq, s. a computational meshfree technique for the numerical solution of the twodimensional coupled burgers' equations. intern. j. of comput. eng. sci. mech., 2009, 10(5), 406-422. 13. mokhtari, r. and mohammad, m. numerical solution of grlw equation using sinc-collocation method. computer phys. commun., 2010, 181, 1266-1274. 14. stenger, f. numerical methods based on sinc and analytic functions. springer-verlag, new york, (1993). 15. lund. j. and bowers, k.l.sinc methods for quadrature and differential equations,siam, philadelphia, (1992). 16. al-khaled, k. numerical study of fisher's reaction-diffusion equation by the sinc collocation method. j. comput. appl. math., 2001, 137, 245-255. 17. al-khaled, k. sinc numerical solution for solitons and solitary waves. j. comput. appl. math., 2001, 130(1-2), 283-292. received 28 august 2014 accepted 24 february 2015 squ journal for science, 2021, 26(1), 67-75 doi:10.24200/squjs.vol26iss1pp67-75 sultan qaboos university 67 comparing science and engineering students using the force concept inventory in introductory physics courses nazife koca* and nidhal sulaiman department of physics, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *email: nazife@squ.edu.om. abstract: this work is intended to analyze and compare the performances of two groups of students on the understanding of force and motion concepts using the force concept inventory (fci). the fci test serves questions on basic newtonian concepts where the answers include the correct response and commonly misconceived alternatives. the fci test was implemented twice as pre and post-tests for two introductory calculus-based physics courses offered at the sultan qaboos university (squ) in oman for students mainly from the colleges of science, education and agriculture and the students from the college of engineering in the spring 2017 and spring 2018 semesters. these courses cover the traditional first-year level kinematics and dynamics in translational and rotational motions based on the same syllabus and the same textbook. hake’s normalized gain, defined as the change in class averages divided by the maximum possible increase, was used to compare the students’ performances. the normalized gains for both groups of students were in the low gain category. female students in both courses performed better on the fci in general, but the difference was only statistically significant in the course offered to science students. keywords: force concept inventory (fci); gender; physics and engineering education research and hake’s normalized gain. مقارنة بين طالب كلية العلوم وكلية الهندسة في استخدام المفهوم المكتسب عن القوة في المواد التمهيدية للفيزياء نضال سليمانو اكنزيفا كو مفاهيم القوة والحركة بإستخدام مقياس مفهوم القوة المكتسب في أداء مجموعتين من الطالب في فهمالهدف من هذا العمل المقارنة والتحليل :صلخمال (fci) امتحان مقياس مفهوم القوة المكتسب .(fci) يقدم أسئلة في مفاهيم نيوتن األساسية حيث أن اإلجابات تحتوي على استجابات صحيحة وأخرى تم تطبيقه مرتين قبل وبعد امتحانات مادتين تمهيدية للحسابات المعتمدة على الفيزياء في جامعة السلطان (fci)خاطئة. امتحان مقياس مفهوم القوة المكتسب 7102عظم الطالب من كليات العلوم والتربية والزراعة ومن كلية الهندسة. تم تطبيق المقياس مرتين في فصل ربيع قابوس في سلطنة عمان حيث كان م . هذه المواد تحتوي على مواضيع الحركة التقليدية الخطية والدائرية مع استخدام نفس مخطط المنهج ونفس الكتاب. تم استخدام 7102وفي فصل ربيع عي لمقارنة أداء الطالب والذي يعرف على أنه الفرق بين المتوسطات في الصف مقسوم على أعلى زيادة محتملة. معدل الكسب مقياس هاك للكسب الطبي للجنس في المادتين يظهر تقدم اإلناث بشكل عام ولكن إحصائيا يظهر تقدم بارز (fci)الطبيعي للمفهوم للمجموعتين في الفئة الدنيا. مستوى األداء في .ي المادة المطروحة لطلبة كلية العلوملإلناث ف ، الجنس، بحث تعليم الفيزياء والهندسة، مقياس هاك للكسب الطبيعي(fci)مقياس مفهوم القوة المكتسب :مفتاحيةالكلمات ال mailto:nazife@squ.edu.om nazife koca and nidhal suliman 68 1. introduction oncept inventories are research-based assessment techniques that study students’ understanding of certain physics concepts. they are designed mainly to measure the effectiveness of teaching by determining students’ performances in the given course. the force concept inventory (fci) [1] is a multiple-choice test to measure the students’ understanding of newton’s concepts and related kinematics, and in addition to identifying the misconceptions of the students in these topics. the fci is one of the most reliable tests that has been implemented in physics education and is used in educational institutions all over the world. the questions in the fci involve concepts only and avoid problem solving. in this work we used the original version of fci [1] consisting of 29 multiple-choice questions that are classified into six conceptual dimensions, kinematics, newton’s first, second and third laws, the superposition principle and kinds of forces. the questions are intentionally designed in such a way that, while the correct answer shows a certain newtonian concept, the remaining four answers give some information on the common-sense alternatives or misconceptions, and the fci was designed to examine each one of them [2]. martin-blas et al. [3] and bani-salameh [4-5] analyzed their data to identify dominant misconceptions of their students. caballero et al. [6] compared two different curricula at georgia institute of technology in the usa using the fci and found that post instruction fci averages were significantly higher for their traditional curriculum than for the matter & interactions (m&i) curriculum where both were taught with similar interactive pedagogy. we administered the fci for students in sultan qaboos university who took two calculus-based physics courses, namely, physics 1 (phys2101) and physics for engineers 1 (phys2107). phys2101 is offered to students from the colleges of science, education and agriculture. students from other colleges are also enrolled in phys2101 in order to be able to major in stem (science, technology, engineering, and mathematics) subjects. phys2107 is offered to students from the college of engineering. each course is coordinated by one of the instructors who are involved in teaching the courses. these courses cover the traditional first year level kinematics and dynamics in translational and rotational motion. in both courses, the same textbook by walker, halliday and resnick, “principles of physics”, 10 th edition is used. each course has typically 250-300 students, divided into 3-4 sections. these sections are taught by several instructors from the physics department, in two time slots per week, each one running for one hour and twenty minute lectures, conducted in large lecture halls. in addition, each student attends a 3h laboratory and 3h tutorial session in alternating weeks within groups of maximum 60 students. attendance of lectures, labs and tutorials is mandatory. tutorials are conducted on problem solving by two instructors, with one-to one discussions with the students. the total period of instruction is 15 weeks per semester. we present the fci results for spring 2017 and spring 2018 semesters. we calculated the normalized gain [7], defined as the change in class averages divided by the maximum possible increase, for two groups of students and compared it with the results obtained in the other institutions in the gulf region. for example, in uae g.w. hitt et al. [8] obtained the average normalized gain on fci as 0.16 ± 0.01 over several semesters of traditional instruction, and in saudi arabia a normalized gain of 0.10 was found (more details are given in [4]). we compared the fci performances between genders by using the normalized gains. results obtained for the gender difference in phys2101 and phys2107 groups are not in tune with most of the studies performed using the fci. normandeau et al [9] reported the presence of gender disparity on the fci in a sample of canadian undergraduate students. madsen et al. [10] reviewed the literature and reported that a gender gap exists in fci scores and gains in favor of males across several institutions from the usa and uk. docktor and heller [11] from university of minnesota, usa, found a significant gender gap in pre-test fci scores that remained post-instruction, wherein male students outperformed females. bates et al. [12] investigated the gender gap in conceptual understanding of newtonian mechanics in three uk universities and found that there is a statistically significant gender gap, with males outperforming females. bani-salameh et al. [13] in saudi arabia measured the performance gap among male and female college students with the fci, showing a gender gap in favor of male students. further studies compare the performances of the male and female students on in-class exams versus those on the fci. when examining the performance of male and female students in the final exam scores in our two courses, we found that female students outperform the males. in contrast, docktor et al. [11] found that the male final exam scores of 15 semesters were higher by 3.9 % while bates et al. [12] found no statistically significant difference in final exam scores between men and women at three universities for a single semester. research in a canadian university shows that there is no apparent gender bias in the in-course assessments [9]. we organize the paper as follows: in section 2 we introduce the students’ background. section 3 deals with details of the method used. analysis of the fci results is covered in section 4. section 5 presents the discussions and conclusions. 2. students’ background students taking phys2101 and phys2107 courses come to the university from high schools where the education is mostly in arabic with some english background. they enroll in different colleges, each having different entry requirements. the phys2101 group consists of students from the colleges of science (60%), agriculture (30%) and education (10%). at times, students from other colleges (about 1%) also enroll in phys2101. before admittance c comparing science and engineering students 69 to the university, the students who enroll in phys2101 should satisfy the following requirements. the students of colleges of science and of education are supposed to have studied four subjects (mathematics, chemistry, physics and biology) in high school and to have obtained a minimum of 65 % grade in any of these three subjects. the students of the college of agriculture have to score at least a 65 % grade in mathematics and also to study and pass with at least a 65% grade in any two of the courses, chemistry, physics and biology. on the other hand, the students from the college of engineering register to phys2107. their admission criteria to the college requires a minimum of a 65 % grade in mathematics, physics and chemistry. in addition, at least a 65% grade in basic english language in high school is a must for all students who are admitted to the above-mentioned colleges. the number of female and male students admitted to the colleges is equal, except for the college of engineering. most students go through a one-year foundation program taking mathematics, information technology and english language and then they register either in phys2101 or phys2107 courses depending on their colleges. the medium of instruction in these courses is english. despite an intensive one-year training in the foundation program, some students still struggle in understanding the language of the textbook and terminology. in general, there are a higher proportion of male than female students in phys2107 as compared to phys2101. the male/female ratio in the randomly sampled phys2101 group was 1:3 and in phys2107 group was 4:1. 3. method the fci test was given twice to the same students in spring 2017 and spring 2018 semesters; the pre-test was administered at the beginning of the semester, during the first week, and the post-test towards the end of the semester, after newton’s force and motion concepts had been covered. a total of 249 students from randomly selected sections of phys2101 groups, in which 24.5% were male and 75.5% were female, took the preand posttests over two semesters of traditional instruction. the phys2107 group consisted of 218 students, in which 81.2% were male and 18.8% were female. these sample sizes represented 44.9% of the total populations of phys2101 and 39.4% of phys2107 groups, respectively. the reported statistics are for matching individual students who took part in both pre and posttests. the fci test has usually been conducted for between 30 and 45 minutes in many institutions. we gave our students 45 minutes to finish the test. this was due to the fact that phys2101 and phys2107 courses are two of the first science courses that are taught in english, and for many of our students’ language proficiency is still developing. our students had neither prior information about the test dates, nor were introduced to the fci test in their mother language. students were informed that the fci results would not affect their final grade in these two courses and there were no alternative incentives given for taking the fci. 4. results 4.1 performance of student groups table 1 shows the fci preand posttests mean values and standard deviations (s) in percentages, number of students n and t-test results for the group of phys2101 and phys2107 students. the low mean values in the pretest for both groups of students reflect poor knowledge and misconceptions in physics prior to any instruction; this is particularly true for the students of the college of agriculture since in their admittance physics is not a compulsory requirement. the mean percentage of correct answers in the posttest is 32.7% for the phys2101 group and 36.9% for phys2107 group. the t-test is performed for the preand posttest scores with unequal variances for the two independent groups and obtained a t-value (with significance level of 0.05). the results are shown in table 1. the difference in the averages is greater for phys2107; they are statistically significant as verified by the t-tests. table 1. fci preand posttest mean values for phys2101 and phys2107 groups. ni is the number of students and 𝑆𝑖 the standard deviation (i = pre, post) group pre-test post-test t-test npre mean (%) 𝑺𝒑𝒓𝒆 (%) npost mean (%) 𝑺𝒑𝒐𝒔𝒕 (%) tvalue p value phys2101 249 22.6 9.4 249 32.7 11.6 10.80 < 10−4 phys2107 218 26.0 11.6 218 36.9 13.0 9.26 < 10−4 the results can be compared with similar data from different institutions from a number of countries. preand posttest fci scores range from 27% 52% and 48% 77% respectively in usa [1] depending on the methods of nazife koca and nidhal suliman 70 instruction [7]. reported preand posttest scores were obtained as 28 % and 69 % in finland [14-15] and 22 % and 30.4 % in saudi arabia [4] respectively. we find that our results of the post tests for the phys2101 and phys2107 groups are within the range reported by [3] for the forestry engineering school (euitf) in spain and bani -salameh [4] in saudi arabia. figure 1 (a) and (b) shows the overall performance in terms of the number of correct answers (a maximum of 29 correct answers) by the students in preand posttest in phys2101 and phys2107. we normalized the frequencies to the number of students per group. the highest grades obtained by the students for post-test are 22 in phys2101 and 25 in phys2107. it can be seen that there is a clear shift towards the right, indicating that there is an obvious increase in the number of correct answers in the post-test in both groups. similar analysis has been done by [3] and [4]. figure 1. the number of correct answers by the students normalized to number of students in preand post-tests in (a) phys2101 (b) phys2107. dashed lines represent the trend line. figure 2 shows the percentage of students who answered a particular question correctly versus the question number for pre-test (grey) and post-test (blue) for both phys2101 (a) and phys2107 (b). in the pre-test less than 20 % of students in each group answered the questions 2, 8, 9, 13, 18, 24 and 26 correctly. in the posttest, questions 6, 9, 16, 20, 22, 24 and 26 were still only answered correctly by 20 % of phys2101 students. here question 26 was about the newton’s first law which was also answered correctly by less than 20 % of phys2107 students. figure 2 also clearly shows that a few questions, namely, questions 1, 4, 10, 12 and 16, were answered correctly by more than 50 % of both groups of students in the post-test. in particular, more than 70% of students correctly answered question 12, which deals with newton’s third law of motion. more analysis on each question will be done in the gain per question section below. figure 2. percentage of students obtaining pre(grey) and post(blue) test correct answers per question in the fci test for the groups (a) phys2101 and (b) phys2107. the fci averages are shown as horizontal dashed lines. 0 5 10 15 20 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 n o rm a li ze d f re q u e n ci e s (% ) number of correct answers (a) phys2101 pre post 0 5 10 15 20 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 n o rm a li ze d f re q u e n ci e s (% ) number of correct answers (b) phys2107 pre post comparing science and engineering students 71 4.2 normalized gain per group to measure the improvement in students’ conceptual understanding, hake’s normalized gain, 〈g〉, [7], [16] is extensively used in many studies and given by 〈g〉 = 〈a𝑝𝑜𝑠𝑡〉 −〈a𝑝𝑟𝑒〉 100%−〈a𝑝𝑟𝑒〉 (1) where 〈a𝑝𝑟𝑒 〉 and 〈a𝑝𝑜𝑠𝑡 〉 are pre-test and post-test class averages. the normalized gain is accepted high for 〈g〉 ≥ 0.7, medium for 0.3 < 〈g〉 < 0.7 and low for 〈g〉 ≤ 0.3. we used the following equation for the pooled standard error of 〈g〉 in terms of the standard deviations of both the preand posttest data [17]: se〈g〉 = 1 100 √ (𝑁𝑝𝑟𝑒−1)𝑆𝑝𝑟𝑒 2 +(𝑁𝑝𝑜𝑠𝑡−1)𝑆𝑝𝑜𝑠𝑡 2 𝑁𝑝𝑟𝑒+𝑁𝑝𝑜𝑠𝑡−2 × ( 1 𝑁𝑝𝑟𝑒 + 1 𝑁𝑝𝑜𝑠𝑡 ) 1 2⁄ (2) where 𝑁𝑝𝑟𝑒 and 𝑁𝑝𝑜𝑠𝑡 are the same since we have matched data sets. table 2 shows the average normalized gain for each group of students whose 〈g〉 values remain in the low gain category. although 〈g〉 of the phys2101 group is slightly lower than that of the phys2107, there is no statistical difference between them (p = 0.28) at 95% confidence level. table 2. normalized gains for phys2101 and phys2107 groups. group n 〈g〉 se〈g〉 tvalue pvalue phys2101 249 0.13 0.01 1.08 0.28 phys2107 218 0.15 0.01 4.3 normalized gain per question in order to have a better understanding of students’ performances on the fci questions for both groups, we calculated the gain per question [6], which is basically hake’s gain for a single question. the histograms of the gain per question are shown in figure 3. the highest item gain obtained is 0.55 on question 12 for phys2101 and 0.46 on question 4 for phys2107. gains above 0.3 are achieved on questions 2, 11, 12 for phys2101 and questions 4 and 12 for phys2107. question 2 related to newton’s third law and question 12 dealt with kinds of forces. as can also be noticed, the gains are negative for questions 7, 15, 22 and 26 for both groups of students. these questions are on “kinds of forces” and “newton’s first law”. figure 3. gain per question for phys2101 (orange) and phys2107 (green). the average gains are shown as horizontal dashed lines. 4.4 normalized gain per category we calculated the students’ performances on the groups of questions which cover certain fci force and motion concepts per category, these being kinematics, newton’s first, second and third laws, superposition and kinds of forces nazife koca and nidhal suliman 72 as listed in [1]. “the kinematics” category includes the questions on position, velocity, and acceleration and their relationships excluding the dynamical effects. questions in the “newton’s first law” category concern the relationship between motion and applied forces. the “newton’s second law” category deals with the questions on contact forces and resolving unknown forces, and the “newton’s third” law category covers the questions related to action-reaction principles and contact forces. the “superposition” category includes the questions in which the direction and relative strength of forces acting on a body or set of bodies are represented by diagrams (i.e., force-body diagrams). the “kinds of force” category deals with the questions including solid and fluid contacts and gravitation. figure 4 shows the average normalized gain in each fci concept category for phys2101 (orange) and phys2107 (green) groups. each category consists of more than one question from the fci inventory items. the highest normalized gain is obtained for the “newton’s third law” category for both groups, it is in the medium gain region for phys2101 group. in the “kinematics” and “newton’s second law” categories the average normalized gains are less than the overall normalized gain as shown in table 2. the lowest normalized average gain is observed in the “newton’s second law” category for both groups of students, where the gain is negative or very low. this shows a persistent misconception despite the instruction. figure 4. normalized gain per concept category for phys2101 (orange) and phys2107 (green) (error bars of the mean are shown). the horizontal dashed lines indicate the average gains. 4.5 normalized gain per gender we also compared the fci performances between genders. it should be noted that more than 75% of registered students in phys2101 are females, while the majority of phys2107 students are male. table 3 (see also figure 5) shows the fci preand posttest scores for male and female students in both groups. our results point to a small gender gap, where the average pretest gender gap is 2.3% (favoring males) for phys2101 and 0.14 % (favoring females) in phys2107. on the other hand, the gender gap in the post-test for both groups is in favor of females and the gap is 3.7% for the phys2101 group and 2.7% for the phy2107 group. the gender gap increased from preto post tests, with an absolute increase favoring females of about 1.4% for phys2101 and 2.8% for phys2107. this is in contrast to the usual gender gap on the post test for the fci that ranges from 1.5% to 24.6% [10] , favoring the male students. table 3. average preand postinstruction fci scores for female and male students in phys2101 and phys2107 groups. ni is the number of students and 𝑆𝑖 the standard deviation (i = pre, post). group gender pretest posttest ttest npre mean (%) 𝑺𝒑𝒓𝒆 (%) npost mean (%) 𝑺𝒑𝒐𝒔𝒕 (%) tvalue pvalue phys2101 female 188 22.00 9.35 188 33.64 11.51 10.76  10 -4 male 61 24.31 9.22 61 29.90 11.31 2.99 0.0034 phys2107 female 41 26.07 12.24 41 39.02 12.40 4.76  10 -4 male 177 25.93 11.47 177 36.37 13.09 7.98  10 -4 comparing science and engineering students 73 0 10 20 30 40 50 pre post pre post phys2101 phys2107 f c i s co re s (% ) male female figure 5. average fci scores for male (blue) and female (orange) students in the phys2101 and phys2107 groups (error bars of the mean are shown). the normalized gain 〈g〉 per gender for each group is also calculated. as shown in table 4, it is larger for females in both groups. in phys2101 it is 0.15 ± 0.01 for females compared to 0.07 ± 0.02 for males, while in phys2107 〈g〉 is 0.18 ± 0.03 and 0.14 ± 0.01 for females and males, respectively. the difference in the normalized gain between females and males is 0.08 ± 0.02 and is statistically significant in phys2101 (p < 10 -3 , at 95% confidence level) indicating that the females are performing better than the males. on the other hand, the difference in the normalized gain between males and females is 0.04 ± 0.01 in the phys2107 group with (p = 0.26). table 4. average normalized gains for phys2101 and phys2107 groups. group gender hake’s normalized gain 〈g〉 ttest n 〈g〉 se〈g〉 tvalue pvalue phys2101 female 188 0.15 0.01 3.46 0.0006 male 61 0.07 0.02 phys2107 female 41 0.18 0.03 1.13 0.2597 male 177 0.14 0.01 figure 6. final exam scores of female (grey) and male (blue) students for (a) phys2101 and (b) phys2107 groups. 0 5 10 15 20 25 30 1 0 0 9 0 9 0 8 0 8 0 7 0 7 0 6 0 6 0 5 0 5 0 4 0 4 0 3 0 3 0 2 0 2 0 1 0 < 1 0 n o rm a li ze d f re q u e n ci e s (% ) final exam scores (a) phys2101 female male 0 5 10 15 20 25 30 1 0 0 9 0 9 0 8 0 8 0 7 0 7 0 6 0 6 0 5 0 5 0 4 0 4 0 3 0 3 0 2 0 2 0 1 0 < 1 0 n o rm a li ze d f re q u e n ci e s (% ) final exam scores (b) phys2107 female male nazife koca and nidhal suliman 74 we also examined the performances of male and female students in the final exams of the two courses. we noted that, when the average scores are compared, female students outperformed the males by 11 % in phys2101 and 15% in phys2107. in addition, as can be seen from figure 6, 27 % of female and 4 % of male students scored 70 and above out of 100 in phys2101 while in phys2107 these numbers correspond to 53 % of females and 16 % of males. furthermore, the general secondary final exams certificates in oman (higher education admission statistics for the academic year 2015/2016) indicate that, on the average, females score better than males. 5. discussion and conclusion the fci test was implemented on two groups of students who enrolled in introductory physics courses in squ, oman. the hake’s normalized gain remained in the low range for both groups of students. this indicates that there is not much improvement in the conceptual understanding of the students of the newton’s force concept and the related topics of mechanics. from the analysis of each question in the fci and the categories, we noted that the students have difficulties in understanding and interpreting the questions when the questions involved diagrams and graphs. we observed a significant gender gap on fci normalized gains, with females achieving better gains than males in phys2101 but no significant difference in phys2107. moreover, according to the final exam scores in these courses, female students outperformed male students, supporting our findings in the fci test results. this could be due to the fact that females tend to have better study habits and that they are accommodated in better living conditions as they are hosted at the university hostels. conflict of interest the authors declare no conflict of interest. acknowledgment we would like to thank the staff of the physics department for their contributions and a special thanks to sheikha al majrafi, an msc student, for entering part of the data. references 1. hestenes, d., wells, m. and swackhamer, g. force concept inventory, the physics teacher, 1992, 30, 141-158. 2. halloun, a. and d. hestenes, d. common sense concepts about motion, american journal of physics., 1985, 53(11), 1056-1065. 3. martin-blas, t., seidel, l., serrano-fernandez, a. enhancing force concept inventory diagnostics to identify dominant misconceptions in first-year engineering physics. european journal of engineering education, 2010, 35(6), 597-606. 4. bani-salameh, h.n. using the method of dominant incorrect answers with the fci test to diagnose misconceptions held by first year college students. physics education, 2017, 52, 015006. 5. bani-salameh, h.n. how persistent are the misconceptions about force and motion held by college students? physics education, 2017, 52, 014003. 6. caballero, m.d., greco, e.f., murray, e.r., bujak, k.r., marr, m.j., catrambone, r., kohlmyer, m.a., and schatz, m.f. comparing large lecture mechanics curricula using the force concept inventory: a five thousand student study, american journal of physics, 2012, 80(7), 638-644. 7. hake, r.r. interactive-engagement versus traditional methods: a six-thousand-student survey of mechanics test data for introductory physics courses, american journal of physics, 1998, 66 (1), 64-74. 8. hitt, g.w. isakovic, a.f., fawwaz, o., bawa’ach, m.s., el-kork, n., makkiyil, s. and qattan, i. a. secondary implementation of interactive engagement teaching techniques: choices and challenges in a gulf arab context, physical review special topics physics 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among male and female college students measured with the force concept inventory. iosr journal of applied physics, 2017, 9(2), 11-12. comparing science and engineering students 75 14. savinainen, a. and scott, p. the force concept inventory: a tool for monitoring student learning. physics education, 2002, 37(1), 45-52. 15. savinainen, a. and scott, p. using the force concept inventory to monitor student learning and to plan teaching. physics education, 2002, 37(1), 53-58. 16. coletta, v.p. and phillips, j.a. interpreting fci scores: normalized gain, pre-instruction scores, and scientific reasoning ability. american journal of physics, 2005, 73(12), 1172-1182. 17. smith, t.i., wittmann, m.c. and carter, t. applying model analysis to a resource-based analysis of the force and motion conceptual evaluation. physical review special topics physics education research, 2014, 10, 020102. received 23 july 2020 accepted 10 november 2020 squ journal for science, 2014, 19(2) 53-76 © 2014 sultan qaboos university 53 hydromagnetic boundary layer flow and heat transfer characteristics of a nanofluid over an inclined stretching surface in the presence of a convective surface: a comprehensive study mohammad m. rahman* and mohammed m. al-hatmi department of mathematics and statistics, college of science, sultan qaboos university, po box 36, al-khod, pc 123, muscat, sultanate of oman. *email: mansur@squ.edu.om. abstract: in this paper we investigate numerically the hydromagnetic boundary layer flow and heat transfer characteristics of a nanofluid using three types of nanoparticles (copper, aluminium oxide and titanium dioxide) having various shapes (spherical, cylindrical, arbitrary, etc) by considering three kinds of base fluids (water, ethylene glycol and engine oil) over a nonlinear inclined stretching surface, taking into account the effect of convective surface condition. using similarity transformations, the governing nonlinear partial differential equations of the physical model are transformed into non-dimensional ordinary differential equations which are solved for local similar solutions using the very robust computer algebra software, maple 13. the numerical simulation is carried out to investigate the role of the pertinent parameters on the flow and temperature fields as well as on the rate of heat transfer and on the rate of shear stress. the results show that the addition of nanoparticles to the base fluid may not always increase the rate of heat transfer. it depends significantly on the surface convection, type of base fluid and nanoparticles. the finding of this study will open a gate for better understanding of nanofluid characteristics. keywords: nanofluid; convection; boundary layer; stretching surface; similarity solution. خصبئص السوائل التً تذتوي على جزٌئبث متنبهٍت الصغز وتأثٍزهب على التذفقبث المغنبطٍسٍت والنقل الذزاري فً الطبقت الذذودٌت المجبورة لسطخ منفذ للذزارة ومبئل و متمذد: دراست شبملت .م. الذبتمً .م. ردمبن و مذمذ ذمذ م مت فً ٕزٓ اى٘سقت قَْب سٌبضٍبً ببعخخذاً طشٌقت اىخحيٍو اىعذدي بذساعت حأثٍش اىَجبه اىَغْبطٍغً ٗاىْقو اىحشاسي فً طبقت اىغبئو اىَخحش :ملخص ٗ إثٍيٍِ حشكٗاىَجبٗسة ىغطح )ٍبئو ٗ ٍخَذد( ٍع األخز فً االعخببس اىْفبرٌت اىحشاسٌت ىيغطح. حٌ اعخخذاً ثالثت ع٘ائو فً رىل ًٕٗ اىَبء ٗ صٌج اىَ ٍبً مغٍذ األىًٍَّ٘٘ ٗ اىخٍخبًٍّ٘.أجالٌن٘ه ٍضبفبً إىٍٖب ثالثت أّ٘اع ٍِ اىجضٌئبث اىذقٍقت ٍثو جضٌئبث اىْحبط ٗ حَج صٍبغت اىَشنيت اىفٍضٌبئٍت سٌبض دىج . maple13بعخخذاً بشّبٍج بَعبدالث حفبضيٍت جضئٍت غٍش خطٍت ثٌ قَْب بعذ رىل بخحٌ٘يٖب إىى ٍعبدالث حفبضيٍت عبدٌت غٍش خطٍت ٍِٗ ثٌ حيٖب ب ت اىضغظ اىَحبمبة اىعذدٌت عيى اىذٗس اىزي حيعبٔ اىَعبٍالث راث اىصيت فً عشعت اىغبئو ٗدسجت حشاسحٔ عالٗة عيى حأثٍشٕب فً اىْقو اىحشاسي ّٗغب شفع ٍقذاس اىْقو اىحشاسي ىيغبئو ٗإَّب حعخَذ أُ ح ةاىذقٍقت فً اىغ٘ائو ىٍظ ببىضشٗس اىجبّبً ىيغبئو ، حٍث أظٖشث اىْخبئج أُ صٌبدة مٍَت اىجضٌئبث ضبفت اىجذٌذة اإلأُ حنُ٘ ٕزٓ ّشج٘ ميٍبً ٗ بشنو ٗاضح عيى اىْفبرٌت اىحشاسٌت ىيغطح ٗ عيى ّ٘ع اىغبئو ٗمزىل عيى ّ٘ع اىجضٌئبث اىذقٍقت. خخبٍب ًٕ بَثببت فخح ب٘ابت ىفٌٖ أٗعع ىخ٘اص اىغ٘ائو اىخً ححخ٘ي عيى جضٌئبث صغٍشة جذاً. . اىحو اىَشببٔ، عطح ٍخَذد، اىطبقت اىحذٗدٌت،، اىحَو اىحشاسي، عبئو ٌحخ٘ي عيى جضٌئبث ٍخْبٍٕت اىصغش: مفتبح الكلمبث 1. introduction anotechnology plays a vital role for the development of 21 st century modern microand nano-devices. cooling of these devices is very important for their proper functionality. increasing the heat transfer efficiency of high -tech devices is desirable as it reduces processing time of work and lengthens the working life of equipment. there are several ways to improve the heat transfer efficiency, such as extended surfaces, application of vibration to the heat transfer surfaces, and usage of micro channels [1]. heat transfer efficiency can also be improved by increasing the n mohammad m. rahman and mohammed m. al-hatmi 54 thermal conductivity of the working fluid [2]. commonly used heat transfer fluids such as water, ethylene glycol, and engine oil have relatively low thermal conductivities compared to the thermal conductivity of solids [3]. the high thermal conductivity of solids can be used to increase the thermal conductivity of a fluid by adding small solid particles to that fluid [4]. the feasibility of using of such suspensions of solid particles with sizes of the order of millimeters or micrometers has been investigated by several researchers and significant drawbacks have been observed (see for example, [5]). these drawbacks are sedimentation of particles, clogging of channels, erosion in channel walls, and formation of agglomerate particles, all of which have prevented the practical application of suspensions of solid particles in base fluids as advanced working fluids in heat transfer applications [1,6]. recent advances in nanotechnology have allowed researchers to study the next generation heat transfer nanofluids, which consist of a base fluid containing a suspension of ultra-fine nanometer-sized (usually less than 100 nm) solid particles. nanoparticles used in nanofluids have been made of various materials, such as oxide ceramics (al2o3, cuo), nitride ceramics (aln, sin), carbide ceramics (sic, tic), metals (cu, ag, au, fe), semiconductors (tio2, sic), carbon nanotubes, and composite materials such as alloyed nanoparticles (al70cu30) or nanoparticle core–polymer shell composites [7]. ‘nanofluids’ is the term coined [8] to describe this new class of nanotechnology based heat transfer fluid that exhibits thermal properties superior to those of their host fluids or of conventional particle fluid suspensions. nanofluids offer several benefits; for example, higher cooling rates, smaller and lighter cooling systems, reduced inventory of heat transfer fluids, decreased pumping-power needs, reduced friction coefficient, and improved wear resistance [7]. the references on nanofluids can be found in the book [7,9], and in the review papers [10-15], among others. numerous researchers have studied and reported results on convective heat transfer in nanofluids considering various flow and thermal conditions in different geometries; these include tiwari and das [3], abu-nada [16], oztop and abu-nada [17], nield and kuznetsov [18], abu-nada and oztop [19], congedo et al. [20], kuznetsov and nield [2122], muthtamilselvan et al. [23], bachok et al. [24], ahmad and pop [25], khan and pop [26], beg et al. [27], gorla et al. [28], gorla and chamka [29], rashidi et al. [30], rahman et al. [31], rahman and aziz [32], rahman and eltayeb [33], rahman et al. [34-36], to mention a few only. the objective of this paper is to extend the very recently published paper [36] on the boundary layer flow of a nanofluid over an inclined nonlinear stretching sheet in the presence of an applied magnetic field and convective boundary condition. it should be mentioned that the flow and heat transfer characteristics due to the stretching sheet has been of great interest to the researchers. a variety of technical processes are involved in the production of sheeting material, including both metal and polymer sheets. the rate of heat transfer at the sheet is largely dependent on the quality of the final product. the dynamics of the boundary layer flow over a stretching sheet became a popular area of research after the pioneering work of crane [37], due to its engineering applications in polymer technology and metallurgy, as creating a final product with the desired characteristics depends on the rate of cooling and on the process of stretching. in fact crane’s problem, in which the sheet is stretched with the velocity linearly proportional to the distance from the origin, has been considered for several other features such as viscoelasticity, heat and mass transfer, porosity and magnetic field [38]. several authors have studied the thermal boundary layer flow and heat transfer of a viscous (regular) fluid, with or without the convective boundary condition, over a nonlinear stretching surface. yao et al. [39] studied the boundary layer flow near a stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid in the presence of heat generation and absorption, considering the usual viscous fluid model [40]. in their model the effects of brownian diffusion and thermophoresis were neglected. following this rahman and aziz [32] studied natural convection heat transfer in a nanofluid over a stretching cylinder. they have shown that the presence of nanoparticles reduces the thickness of the hydrodynamic boundary layer and enhances the heat transfer rate. on the other hand, a literature survey indicates that the flow analysis of a nanofluid over a nonlinear stretching sheet has been less studied. thus the aim of this work is to present a theoretical study of a hydromagnetic boundary layer flow and convective heat transfer of a nanofluid over an impermeable nonlinear stretching sheet with convective boundary condition at the surface. in certain polymeric (plastic films, artificial fibers) and metallurgical processes, nonlinear stretching effects are very important, as the final product is strongly influenced by the stretching rate. thus, the main focus of the analysis is to investigate how the flow and temperature fields of a nanofluid within the boundary layer are influenced by the nonlinearity of the sheet, applied magnetic field, buoyancy force, empirical shape factor of the nanoparticles, and convective boundary condition, varying different base fluids and nanoparticles. in this respect this study is unique and the results are more realistic and practically useful. the organization of the remainder of the paper is as follows. in section 2 we describe the physical model and governing equations, and discuss the non-dimensionalization of the governing equations. section 3 discusses the solution method for finding the local similarity solution of the non-dimensional governing equations which are derived in section 2. here we also present the detailed worksheet of maple 13 used to solve our problem. the numerical results obtained in section 3 are illustrated graphically and presented in section 4, where we discuss important hydrodynamic and thermal features of the flow. the results are also discussed from the physical and engineering points of view. section 5 highlights the important conclusions derived from the present study. hydromagnetic boundary layer flow and heat transfer characteristics 55 2. physical model in the boundary layer analysis of nanofluids two types of models, buongiorno [10] and tiwari and das [3] (herein and after referred as td), are widely used. in the buongiorno model the effects of thermophoresis and brownian motion are taken into account, while in the td model no such effects are considered, due to the smallness of such parameter values. the td model is more useful and applicable because of the availability of most of the data relating to the thermal properties of the nanofluid. thus, the principal aim of this work is to investigate the dynamics of nanofluids over an inclined nonlinear stretching surface in the presence of a convective surface under the action of an applied magnetic field, taking into account viscous dissipation and joule heating, using the td model. three types of nanoparticles, ,cu 2 3 al o and tio2, having different shapes (cylindrical, spherical and arbitrary) are dispersed in three base fluids, water (h2o), ethylene glycol (eg), and engine oil (eo), to produce nanofluids. in this section we formulate the physical model with appropriate boundary conditions and non-dimensionalization of the governing equations and, discuss the significance of the important physical and engineering parameters related to the model. 2.1 governing equations consider the steady two-dimensional boundary layer flow of a nanofluid in the region 0y  moving with uniform velocity u  driven by the pressure gradient over a heated stretching sheet. the surface of the sheet is inclined with an acute angle  to the horizontal. the x-axis is taken along the sheet along the downstream direction, and the yaxis is taken normal to it. two equal and opposite forces are applied to the sheet to keep the origin fixed. the physical regime is illustrated in figure 1. the lower surface of the sheet is heated by convection currents from a hot fluid that is different from the studied nanofluid at temperature 0 t which provides the heat transfer coefficient h. a magnetic field of uniform strength 0 b is applied in the y -direction, i.e., normal to the flow direction. the magnetic reynolds number is assumed to be small, so the induced magnetic field can be neglected. 0 b figure 1. flow configurations and coordinate system. the external velocity u  and pressure gradient p x   of the free stream are given by: m u b x   (1) e nf e dup u x dx     (2) the surface velocity w u of the sheet is considered to be: ( ) m w u u x a x  (3) 0 x y y x horizontal line convective hot fluid v e rt ic a l li n e boundary layer stretching sheet mohammad m. rahman and mohammed m. al-hatmi 56 where a is a dimensional positive constant known as the stretching coefficient, b is defined as a function of the flow geometry and m is an arbitrary positive constant. under the boundary layer approximations, the governing equations of the problem become (rahman et al. [31, 36]): 0 u v x y       (4) 2 2 2 * * 0 ( )1 sin ( ) (1 )( ) nf nf nf sp bf nf t tu u p u u v g x y x y b u                               (5) 2 22 2 0 2 ( ) ( ) ( ) nf nf p nf p nf b ut t t u u v x y y c y c                 (6) where u, v are the velocity components along x, y coordinates, respectively. here nf nf nf     is the kinematic coefficient of viscosity of the nanofluid, nf  is the viscosity of the nanofluid, nf  is the density of the nanofluid, nf  is the thermal diffusivity of the nanofluid, nf  is the thermal conductivity of the nanofluid, ( ) p nf c is the heat capacity of the nanofluid, t is temperature of the nanofluid within the boundary layer,  is the magnetic permeability, and *  is the volume expansion coefficient of the nanofluid. the term  * *sin ( ) ( ) (1 )( )sp bfg t t           in equation (5) accounts for thermal buoyancy due to the thermal expansion of the base fluid and due to the difference in density of the nanoparticles. the last term in the right-hand side of equation (5) 2 0 b u   is due to the applied magnetic field. the interaction of the fluid velocity ( )u and applied magnetic field ( )b creates a lorentz force, j b , where the electric current density follows the generalized ohm’s law, ( )  j e bu ,  is the electrical conductivity, and e is the electric field. for an applied magnetic field 0 (0, , 0)bb , fluid velocity ( , , 0)u vu , and in the absence of any electric field ( e 0 ) (since the surface is electrically non-conducting), the x -component of the lorentz force yields 2 0 ( )b u . equation (6) states that heat can be transported in a nanofluid by convection the left-hand side t t u v x y         , by conduction first term on the right-hand side 2 2nf t y        and by virtue of viscous dissipation 2 ( ) nf p nf u c y        , and also by joule heating 2 2 0 ( ) p nf b u c   . the effective dynamic viscosity nf  , density nf  , volumetric coefficient of thermal expansion * nf  , thermal diffusivity nf  , and the heat capacitance ( ) p nf c of the nanofluid are given by: 2.5 (1 ) bf nf      (brinkman [41]) (7) (1 ) nf bf sp        (xuan and li [42]) (8) ( ) (1 )( ) ( ) p nf p bf p sp c c c       (xuan and li [42]) (9) hydromagnetic boundary layer flow and heat transfer characteristics 57 * * * ( ) (1 ) nf bf bf sp sp           (mansour and ahmed [43]) (10) ( ) nf nf p nf c     (11) ( 1) ( 1)( ) ( 1) ( ) n nsp spnf bf bf nsp spbf bf bf                       (rana and bhargava [44]) (12) the subscripts bf and nf , respectively, stand for base fluid and nanofluid, whereas sp stands for solid particles, and n is the empirical shape parameter. 2.2 boundary conditions the boundary conditions for the above-stated model are (i) on the surface of the sheet ( 0y  ) m w u u a x  , 0v  , 0 ( ) nf t h t t y       (13) (ii) matching with the free stream ( y  ) , m u u b x t t      (14) where the subscript w refers to the sheet surface, and  refers to the boundary layer edge. 2.3 introduction of dimensionless variables in order to make equations (4)-(6) and (13)-(14) dimensionless, we introduce the following dimensionless variables: 0 21 , ( , ) ( ) and ( ) 2 1 w bf w bf u x u t tm y x y f x m t t                   (15) where  is the stream function and bf bf bf     is the kinematic viscosity of the base fluid. the function f is the nondimensional stream function. the stream function  satisfies the relations andu v y x         (16) so as to satisfy the continuity equation (4). from equations (15) and (16), we obtained the following expressions ( ) w u u f  (17) ( 1) 1 2 1 bf w um m v f f x m               . (18) 2.4 non-dimensional governing equations now substituting equations (7)-(12) and (15)-(18) into equations (5)-(6), we obtain 2 2 22 2 ( ) (sin ) 0 1 1 1 m f a f f a f ab c ha f m m m                                  (19) 1 2 22 0 1 pr d e f pr e ec c f pr ec ha e f m               (20) where the constants a, b, c, d , and e are defined by 2.5 (1 ) 1 sp bf a                     (21) mohammad m. rahman and mohammed m. al-hatmi 58 * * 1 1 sp sp bf bf sp bf b                                    (22) 2.5 (1 )c   (23)     1 p sp p bf c d c        (24) ( 1) ( ) ( 1) ( 1) ( ) bf sp bf bf sp nf sp bf bf sp n e n n                        (25) the dimensionless parameters which appear in equations (19)-(20) are as follow: 2 (re ) bf bf gr   is the thermal buoyancy parameter, * 3 0 2 ( ) bf bf bf g t t x gr      is the local thermal grashof number corresponding to the base fluid, re w bf bf u x   is the local reynolds number corresponding to the base fluid, 2 0 bf w b x ha u    is the modified hartmann number or local magnetic field parameter, b a   is the ratio of the external free stream velocity to the velocity of the stretching surface, bf bf pr    is the prandtl number, and 2 0 ( ) ( ) w p bf u ec c t t    is the eckert number. 2.5 non-dimensional boundary conditions the boundary conditions (13)-(14) in their nondimensional form become (0) 0f  , (0) 1f   , 1 1 (0) 1 (0) 2 m e bi           (26) ( )f    , ( ) 0   (27) the dimensionless parameter bi is defined by 1 2re bf bf h x bi    (28) the biot number ( bi ) signifies the ratio of the convection at the surface to conduction within the body, otherwise it is the ratio of the internal resistance of a body to heat conduction to its external resistance to heat convection. therefore, a small biot number represents low resistance to heat conduction, and thus small temperature gradients within the body. 2.6 rate of shear stress and rate of heat transfer 2.6.1 skin-friction coefficient the boundary layer normally generates a drag on the surface as a result of the viscous stresses which are developed at the wall. this drag is normally referred to as skin friction. skin friction occurs from the interaction between the fluid and the skin of the body, and is directly associated with the wetted surface, and the area of the face of the body that is in contact with the fluid. therefore, skin friction is the force resisting the relative motion of fluid layers and material elements sliding against each other. the skinfriction coefficient (rate of shear stress) is defined by 2 2 f bf w c u    (29) where the shear stress at the surface  is defined as: hydromagnetic boundary layer flow and heat transfer characteristics 59 0 nf y u y           (30) by using (15) and (17), equation (29) becomes 1 2 2.5 1 2 (0) 2 (1 ) f bf m f c r     (31) 2.6.2 nusselt number the nusselt number is the ratio of convective to conductive heat transfer across (normal to) the boundary of the surface. the nusselt number (or rate of heat transfer) is defined as 0 ( ) w bf x q nu t t    (32) where the surface heat flux w q is given by 0 w nf y t q y          (33) by using (12) and (15), equation (32) can be written as:   1 1 2 2re ( 1) / 2 (1/ ) (0) bf nu m e      (34) 3. numerical technique a similarity solution is one in which the number of variable can be reduced by one or more by some analytical means, usually by a coordinate transformation. the benefit of a similarity analysis is to reduce the set of governing partial differential equations (pdes) of a physical model into a set of ordinary differential equations (odes). in section 2, the governing equations (4)-(6) of the physical model have two-independent variables, namely x and y. to find a similarity solution, we introduced a new variable  (eq. (15) which replaced both x and y in the system. with this substitution, the number of independent variables reduced from two to one and the pde system (4)-(6) became a system of ordinary differential equations (19) and (20). 3.1 the numerical code and maple worksheet in this section we discuss in detail the technique to solve the system (19)-(20) together with the boundary conditions (26)-(27). the set of equations (19)-(20) is highly nonlinear and coupled and cannot be solved analytically. thus, the numerical solutions of them subject to the boundary conditions, (26)-(27) are obtained using the very robust computer algebra software, maple 13. this software uses a fourth-fifth order runge-kutta-fehlberg method as the default to solve the boundary value problems numerically following the code dsolve. in maple 13, dsolve is a built-in command which solves the boundary value problems with a certain level of accuracy ( 6 10  as default). the ‘infinity’  in the boundary conditions (27) is replaced by a finite value  . we started the computation at small value of  , then subsequently increased the value of  until the boundary conditions were verified. for a detailed maple worksheet see al-hatmi [45]. 3.2 validity of the numerical results to check the validity of our numerical results we calculated the values of   1/ 2 2 / ( 1) bf f re m c and 1 2( 1) / 2 bf m re nu     for various values of m and  keeping all other parameter values fixed. if we consider 0, 0, 0ha ec    , then the non-dimensional governing equations (19) and (20) become 22 (1 ) 0 1 m f a f f a f m            , (35) 0pr d e f    . (36) mohammad m. rahman and mohammed m. al-hatmi 60 table 1. comparison of the values of    1 22 / 1 bf f re m c and 1 2( 1) / 2 bf m re nu     with yacob et al. [46] for different values of m and  . m     1 22 / 1 bf f re m c 1 2( 1) / 2 bf m re nu     present yacob et al. [46] present yacob et al. [46] 0 0.1 0.7181 0.7179 1.1102 1.1100 0.2 0.9993 0.9992 1.3343 1.3342 0.5 0.1 1.5882 1.5881 1.3473 1.3472 0.2 2.2106 2.2105 1.6048 1.6048 1 0.1 1.8843 1.8843 1.4043 1.4043 0.2 2.6227 2.6226 1.6693 1.6692 these equations exactly match with those of yacob et al. [46]. now replacing the boundary conditions (26)-(27) with the following (0) 0, (0) 0 , (0) 1 ( ) 1, ( ) 0 as f f f                (37) we calculated the reduced shear stress    1 22 / 1 bf f re m c and reduced nusselt number 1 2( 1) / 2 bf m re nu     to match with yacob et al. [46] keeping pr = 6.2 fixed and default nanofluid as cu-h2o. from table 1 we see that the data produced by our maple code and those of yacob et al. [46] are in excellent agreement, and give confidence to use the present code. 4. results and discussion in section 3, we discussed the code for solving the coupled dimensionless momentum and energy equations (19)(20), subject to the dimensionless boundary conditions (26)-(27). in this section, we discuss the effects of the various non-dimensional parameters, namely angle of inclination  , magnetic field parameter ha , nanoparticle volume fraction parameter  , thermal buoyancy parameter  , empirical shape factor ,n stretching index m and biot number bi on the velocity and temperature distributions. we also discuss the effects of the same parameters on the nusselt number and skin-friction coefficient. we carry out the numerical simulations for three different types of base fluids namely: water 2 ( ),h o engine oil (eo) and ethylene glycol (eg) with three different kinds of nanoparticles, namely cu, al2o3 and tio2. the thermophysical properties of the base fluids and solid nanoparticles (oztop and abu-nada [17], rahman et al. [31], al-hatmi [45]) are given in table 2. table 2. thermophysical properties of the base fluids and solid nanoparticles. physical properties water h2o ethylene glycol eg engine oil eo cu al2o3 tio2 p c [j/kgk] 4179 2382.1 1880.3 385 765 686.2  [kg/m3] 997.1 1117.48 888.23 8933 3970 4250  [w/mk] 0.613 0.2492 0.145 400 40 8.9538  [ns/m2] 0.001003 0.022 0.8451 * 5 10   [1/k] 21 57 70 1.67 0.85 0.9 7 , 10 bf nf   [m2/s] 1.47 0.94868 0.868 1163.1 131.7 30.7 pr 6.8377 210.2978 10958.9 hydromagnetic boundary layer flow and heat transfer characteristics 61 4.1 computational results for fluid velocity and temperature distributions 4.1.1 velocity profiles in cu-h2o nanofluid the numerical values of the nondimensional x-component of the translational velocity as a function of  are illustrated in figures 2 to 6 for different values of the angle of inclination  , magnetic field parameter ha , nanoparticle volume fraction parameter  , thermal buoyancy parameter  , empirical shape factor ,n stretching index m and biot number bi respectively. since there is almost no experimental data, the choice of the values of the parameters was dictated by the values chosen by previous investigators. the default values of the parameters are considered as / 4  , 0.5ha  , 2%  , 5  , 3n  , 2m  , and 0.5bi  . in the simulation we also consider 2 cu h o as default nanofluid unless otherwise specified. the value of the prandtl number pr is kept 6.8 (at the room temperature). in figure 2 we present the nondimensional x-component of the translational velocity profiles against  for different values of the angle of inclination  keeping all other parameter values (stated above) fixed. the value 0  corresponds to a flat horizontal surface, whereas / 2  corresponds to a vertical surface. it is found that the nondimensional velocity of the nanofluid increases with the increase of the angle of inclination  while the thickness of the hydrodynamic boundary layer is found to decrease with the increase of  . this is due to the fact that, as  increases, the thermal buoyancy of the fluid increases, which in turn induces the fluid velocity. from equation (19) we see that the buoyancy force is multiplied by sin , which attains its maximum value when / 2.  thus, the velocity profiles squeeze closer and closer to the boundary layer. figure 3 presents the impact of the applied magnetic field on the nanofluid flow keeping all other parameter values fixed. the magnetic field parameter (or modified hartmann number) ha is a ratio of the electromagnetic force to the viscous force, which measures the strength of the applied magnetic field. figure 2. velocity profiles for different values of . figure 3. velocity profiles for different values of ha. mohammad m. rahman and mohammed m. al-hatmi 62 figure 4. velocity profiles for different values of . figure 5. velocity profiles for different values of . figure 6. velocity profiles for different values of m. figure 7. temperature profiles for different values of . an increase in ha intensifies the strength of the applied magnetic field. figure 3 reveals that maximum fluid flow occurs in the absence of the magnetic field (ha = 0). in the presence of a magnetic field, fluid velocity reduces. this is due to the fact that an applied magnetic field on the flow domain creates a lorentz force which acts like strings to retard the fluid motion. thus, fluid velocity may be controlled by just controlling the strength of the applied magnetic field. hydromagnetic boundary layer flow and heat transfer characteristics 63 in figure 4 we present the variations of the nanoparticle volume fraction on the flow field. the value 0  corresponds to a clear fluid, i.e. without nanoparticles. it is found that the velocity of the nanofluid increases with the increase of the nanoparticle volume fraction. figure 4 also shows the significant effect of  on the hydrodynamic boundary layer thickness, i.e., the thickness of the hydrodynamic boundary layer of the nanofluid decreases with the increase of the nanoparticle volume fraction. the effect of the thermal buoyancy parameter  on the nondimensional x-component of the translational velocity of the nanofluid within the boundary layer is presented graphically in figure 5. in this figure we observe the remarkable increasing effect of  on the nanofluid velocity. as the buoyancy force intensifies, the thickness of the hydrodynamic boundary layer decreases. the effect of the stretching parameter m on the nanofluid velocity is displayed in figure 6. in this figure we observe again the remarkable effect of m on the nanofluid velocity, i.e. the nondimensional velocity increases very rapidly with the increase of m. the thickness of the hydrodynamic boundary layer decreases with the increase of m. thus, by changing the nonlinearity of the stretching surface we may control the growth of the boundary layer. 4.1.2 temperature profiles in cu-h2o nanofluid the effects of the pertinent parameters on the temperature profiles of the water-based nanofluid containing cu nanoparticles are presented in figures 7 to 13. figure 7 displays the nondimensional temperature profiles within the boundary layer for different values of the angle of inclination: 0  (flat plate), / 6  ( 0 30 ), / 4  ( 0 45 ), / 3  ( 060 ), / 2  ( 0 90 ) (stagnation flow). from this figure, it can be seen that the temperature of the nanofluid increases with the increase of  . it is also found that the maximum temperature of the nanofluid is obtained for a stagnation point flow and the minimum value is obtained for the flow over a flat plate. the temperature of the nanofluid within the boundary layer decreases monotonically with the increase of η. figure 8 shows temperature profiles for different values of the magnetic field parameter, i.e. modified hartmann number ha. it is found that the temperature of the nanofluid increases monotonically as ha increases. the thickness of the thermal boundary layer also increases with the increase of the strength of the applied magnetic field ha. thus the surface temperature of the sheet can be controlled by controlling the strength of the applied magnetic field. an applied magnetic field retards the fluid motion, which results in an increase of the fluid temperature. in figure 9 we present the effect of the nanoparticles volume fraction  on the temperature profiles within the boundary layer. here we varied the nanoparticle volume fraction from 0% to 20% of the total volume of the fluid. it is found that the temperature of the nanofluid increases with the increase of nanoparticles volume fraction  . it can further be noted that the temperature of the base fluid ( 0  ) is lower than the temperature of the nanofluid since the thermal conductivity of the base fluid increases with the addition of solid nanoparticles in it. as their volume fraction increases, the nanoparticles absorb more heat from the surface of the sheet, and as a consequence, the fluid temperature increases in the vicinity of the wall. the thermal buoyancy parameter  is a ratio of the buoyancy force to the viscous force. the value  << 1 corresponds to forced convection in which viscous forces are dominant compared to the buoyancy forces, whereas  =1 corresponds to mixed convection in which viscous forces and buoyancy forces are of comparable size. on the other hand  >> 1 corresponds to free convection, or the so-called natural convection, in which buoyancy forces are dominant. the effect of the thermal buoyancy parameter on the nondimensional temperature profiles within the boundary layer is presented in figure 10. figure 10 shows that temperature within the boundary layer increases monotonically irrespective of the types of convection. we further notice that the thickness of the thermal boundary layer increases with the increase of the value of  . this is due to the fact that as  increases, the thermal state of the fluid also increases, which in turn increases the heat transfer rate from the surface of the sheet to the fluid. figure 11 represents the temperature profiles for various values of the empirical shape factor n of the nanoparticles. it can be seen that the nanofluid temperature decreases as the empirical shape factor increases when 0 0.3  . as the shape factor increases, the nanoparticles absorb more heat from the surface of the sheet, and as a consequence, the fluid temperature decreases in the vicinity of the sheet. on the other hand, away ( 0.3  ) from the surface of the sheet, the temperature of the nanofluid increases with the increase of empirical shape factor. the value 3 / 2n  represents cylindrical shaped nanoparticles, whereas 3n  represents spherical shaped ones. the other values correspond to arbitrary shaped nanoparticles. we notice that, in the vicinity of the surface, nanofluid temperature is higher for cylindrical shaped nanoparticles than for spherical shaped nanoparticles. it is worth mentioning that nanofluid velocity was not affected by the shape of the nanoparticles, hence is not depicted. figure 12 depicts the variation of the temperature profiles within the boundary layer for various values of the stretching index m. the value m = 0 corresponds to a uniformly moving surface. here, we consider only the positive values of m (stretching surface). figure 12 reveals that the temperature profiles within the boundary layer decrease quite rapidly with the increase of the stretching index m. from figure 6 we noted that nanofluid velocity increases with the increase of the stretching index m. thus, fast fluid motion carries less heat from the surface of the sheet to the mohammad m. rahman and mohammed m. al-hatmi 64 boundary layer, and as a consequence, fluid temperature within the boundary layer decreases. the thickness of the thermal boundary layer decreases with the increase of the stretching index. figure 8. temperature profiles for different values of ha. figure 9. temperature profiles for different values of . figure 10. temperature profiles for different values of . figure 11. temperature profiles for different values of .n hydromagnetic boundary layer flow and heat transfer characteristics 65 figure 12. temperature profiles for different values of .m figure 13. temperature profiles for different values of .bi the effect of the biot number (or surface convection parameter) bi = 0.1, 0.5, 1, 1.5, and 2 on the temperature profiles against η is displayed in figure 13. from this figure, we notice that the temperature profiles within the boundary layer increase with the increase of the biot number. the surface convection parameter (or biot number) is a ratio of the hot fluid side convection resistance to the cold fluid side convection resistance on a surface. for fixed cold fluid properties and fixed free stream velocity, the surface convection parameter is proportional to the heat transfer coefficient h associated with the hot fluid. the thermal resistance on the hot fluid side is inversely proportional to h. we further notice that throughout the boundary layer the temperature profiles decrease monotonically with the increase of η. from this figure it is also noticed that for large values of bi, i.e. bi→∞, the temperature profile attains its maximum value of 1. it is important to note that we observed a negligible effect of the biot number on the velocity profiles. this is due to the fact, as can be seen from equation (26), that bi appears only in the thermal boundary conditions and thus has a negligible effect on fluid velocity. 4.2 effect of base fluids and nanoparticles here we investigate the effects of different base fluids and nanoparticles on the flow and temperature fields, as can be seen from figures 14 to 20. figure 14 presents velocity profiles considering aluminium oxide nanoparticles (al2o3) with different base fluids (water, engine oil, and ethylene glycol) within the boundary layer. in this figure, we notice that variation in the base fluids has no significant effect on the velocity profiles, but it can clearly be seen from a magnified part of the curve that ethylene glycol-al2o3 nanofluid has the lowest value of velocity while water-al2o3 nanofluid has the highest value of velocity, followed by engine oil. a similar result is also noticed for various base fluids considering cu and tio2 nanoparticles, as depicted in figures 15 and 16. the effects of different base fluids and nanoparticles on temperature profiles are shown in figures 17 to 19. figure 17 shows how base fluids with al2o3 nanoparticles affect the temperature profiles. it is clearly seen that the temperature of engine oil-al2o3 nanofluid is higher than those of the wateral2o3 and ethylene glycolal2o3 nanofluids in the vicinity of the surface. this is due to the high prandtl number of engine oil, which means the molecules of engine oil absorb more heat from the surface of the sheet compared with the other base fluids. this phenomenon is true for the limiting value of η in which 0.1  . for 0.1  , the behavior of the temperature profiles is reversed. we further notice that the thickness of the thermal boundary layer is lower when the base fluid is water. in figures 18 to 19 we present temperature profiles in different base fluids considering cu and tio2 nanoparticles. similar patterns are observed for cu and tio2 nanoparticles as for al2o3 nanoparticles in various base fluids. from these figures we may conclude that a base fluid having a high prandtl number absorbs more heat from the surface of the sheet. figures 20 and 21 show the comparison between the effects of cu and al2o3 nanoparticles, using different base fluids on the velocity and temperature profiles when 0.02  , 0.5bi  , 5  , 0.5ha  , and 0.05ec  . in figure 20, we observe that a nanofluid containing cu nanoparticles has higher velocity than a nanofluid having al2o3 nanoparticles. from figure 21 we notice that nanofluids with cu nanoparticles show higher temperature than the nanofluids having al2o3 nanoparticles. mohammad m. rahman and mohammed m. al-hatmi 66 4.3 computational results for rate of heat transfer and shear stress the variation of rate of heat transfer in terms of nusselt number and rate of shearing in terms of skin friction coefficient in three types of base fluids for different solid nanoparticles are displayed in the figures 22 to 39, to investigate the effects of the physical parameters m ,  , bi , and pr on them. 4.3.1 the nusselt number 4.3.1.1 nusselt number in different base fluids with cu nanoparticles the influence of the nonlinear stretching index m on the nusselt number considering cu-h2o, cu-eg, cu-eo nanofluids for different values of nanoparticle volume fraction  is shown in figure 22. it can be noticed that the rate of heat transfer in the water-based nanofluids is higher than those of the ethylene glycol and engine oil based nanofluids for all variations of the stretching index m. it is also clear that the rate of heat transfer in cu-h2o nanofluid increases with the increase of the stretching index m, whereas it decreases in the cu-eg, and cu-eo nanofluids with the increase of m . in figure 23 we have presented the nusselt number against  for the cu-h2o nanofluid for different values of the angle of inclination  , keeping all other parameter values fixed. figure 23 reveals the effect of the angle of inclination on the nusselt number, i.e. an increase in the value of  produces a decrease in the nusselt number. figure 24 shows that the rate of heat transfer from the surface of the sheet to the fluid in cu-water nanofluid increases with the increase of the biot number bi. it is also noted that the rate of heat transfer increases with the increase of the nanoparticles volume fraction  when biot number bi  1, whereas it decreases when bi1.thus, the addition of nanofluid to the base fluid may not always increase the rate of heat transfer. in cu-ethylene glycol (eg) nanofluid the rate of heat transfer decreases for all increasing values of the stretching index as well as for the increase of the nanoparticles volume fraction, as can be seen from figure 25. therefore, the rate of heat transfer significantly depends on the base fluids as well as on the surface convection parameter. the nusselt number versus the nanoparticles volume fraction  is plotted in figure 26 for several values of the biot number bi, considering cu-engine oil (eo) nanofluid. from this figure it is observed that the value of the nusselt number increases with the increase of the biot number when 0 0.03  . beyond this range of  , the behavior of heat transfer changes, in that the nusselt number decreases with the increase of the biot number. thus, addition of nanoparticles to the base fluid may not always increase the rate of heat transfer. it significantly depends on the biot number. the effects of the different values of the inclination angle  and biot number bi on the nusselt number for cuh2o, cu-eg, and cu-eo nanofluids are presented in figures 27 to 28, respectively. from figure 27, it is clear that the water-based nanofluids have a higher value of nusselt number than the ethylene glycol and engine oil based nanofluids for all variations of the angle of inclination . this phenomenon might be caused by features of the base fluid; for example, water has a lower value of prandtl number than the engine oil and ethylene glycol. in addition, the hydrogen bond in a hydrocarbon (engine oil and ethylene glycol) is much weaker than the hydrogen bond in water. in figure 28 we compare the nusselt number in different base fluids, considering cu as nanoparticles and varying bi and  . this figure shows that heat transfer in nanofluid not only depends on the base fluids and nanoparticles, but significantly on the surface convection too. 4.3.1.2 nusselt number for water based nanofluids the comparisons between the nusselt numbers for water-based nanofluids such as cu-h2o, tio2-h2o, and al2o3-h2o for various values of m , bi and  are presented in figures 29 to 33, respectively. it is found that the nusselt number increases with the increase of the stretching index for all types of nanoparticles as shown in figure 29. it is also found that al2o3-h2o nanofluid provides the highest rate of heat transfer. figure 30 shows that change in the nusselt number is higher for large values of the biot number bi. it is observed that for fixed values of bi and  the cu-h2o nanofluid has the lowest value of nusselt number, while al2o3h2o nanofluid has the highest value of nusselt number, followed by tio2-h2o nanofluid. from figure 31 it is found that the nusselt number decreases with the increase of the value of angle of inclination for different kinds of nanofluids. 4.3.1.3 nusselt number in different base fluids with different nanoparticles the variations of nusselt numbers in different base fluids with different nanoparticles for various values of  and 0.5bi  , 1.0, 2.0 are shown in figures 32 to 34, respectively. these figures clearly indicate that large values of bi (when the external thermal resistance of the surface is lower than the internal thermal resistance) may significantly change the heat transfer characteristics of a nanofluid. in figure 34 we notice that for   crit, ethylene glycol-based nanofluids have higher values of nusselt number than those of water and engine oil based nanofluids. outside this range of  (i.e. crit), the behavior of the nusselt number is similar to the cases of 0.5bi  and 1bi  . hydromagnetic boundary layer flow and heat transfer characteristics 67 figure 14. velocity profiles in different base fluids with al2o3 nanoparticles. figure 15. velocity profiles in different base fluids with cu nanoparticles. figure 16. velocity profiles in different base fluids with tio2 nanoparticles. figure 17. temperature profiles in different base fluids with al2o3 nanoparticles. mohammad m. rahman and mohammed m. al-hatmi 68 figure 18. temperature profiles in different base fluids with cu nanoparticles. figure 19. temperature profiles in different base fluids with tio2 nanoparticles. figure 20. velocity profiles for comparison between cu and al2o3 nanoparticles in different base fluids. figure 21. temperature profiles for comparison between cu and al2o3 nanoparticles in different base fluids. cu-water cu-eo cu-eg al2o3-water al2o3-eo al2o3-eg cu-water cu-eo cu-eg al2o3-water al2o3-eo al2o3-eg hydromagnetic boundary layer flow and heat transfer characteristics 69 figure 22. nusselt number for different values of m and  in cu-h2o, cu-eg, cu-eo nanofluids. figure 23. nusselt number for different values of  and  for cu-h2o nanofluid. figure 24. nusselt number for different values of bi and  for cu-h2o nanofluid. figure 25. nusselt number for different values of bi and  for cu-eg nanofluid. mohammad m. rahman and mohammed m. al-hatmi 70 figure 26. nusselt number for different values of bi and  for cu-eo nanofluid. figure 27. nusselt number for different values of  and  in cu-h2o, cu-eg, and cu-eo nanofluids. figure 28. nusselt number for different values of bi and  in cu-h2o, cu-eg, and cu-eo nanofluids. figure 29. nusselt number for different values of m and  in cu-h2o, tio2-h2o, and al2o3-h2o nanofluids. hydromagnetic boundary layer flow and heat transfer characteristics 71 figure 30. nusselt number for different values of bi and  in cu-h2o, tio2-h2o, al2o3-h2o nanofluids. figure 31. nusselt number for different values of α and  in cu-h2o, tio2-h2o, al2o3-h2o nanofluids. figure 32. nusselt number for different base fluids using different nanoparticles when 0.5bi  . figure 33. nusselt number for different base fluids using different nanoparticles when 1bi  . mohammad m. rahman and mohammed m. al-hatmi 72 figure 34. nusselt number for different base fluids using different nanoparticles when 2bi  . figure 36. skin-friction coefficient for different base fluids using cu nanoparticles for different values of m. figure 37. skin-friction coefficient for different base fluids using cu nanoparticles for different values of bi. figure 35. skin-friction coefficient for different base fluids using cu nanoparticles for different values of . hydromagnetic boundary layer flow and heat transfer characteristics 73 figure 38. skin-friction coefficient for water based nanofluid for different values of m. figure 39. skin-friction coefficient for water based nanofluids for different values of bi. figure 40. skin-friction coefficient for water based nanofluid for different values of . 4.3.2 skin-friction coefficient 4.3.2.1 skin-friction coefficient for different base fluids with cu nanoparticles the variation of the shear stress in terms of the skin-friction coefficient for different values of  ,  , m , and bi considering three different base fluids with cu nanoparticles is shown in figures 35 to 37, respectively. it is found that the skin-friction coefficient increases with the increase of the angle of inclination  , as well as with the increase of the nanoparticle volume fraction, as can be seen from figure 35. it is also found that the values of the skin-friction coefficient in cu-eo nanofluid are higher than those of the other base fluids containing al2o3 and tio2 nanoparticles. it can be noticed from figure 36 that the skin-friction coefficient increases with an increase in the stretching index m, irrespective of the choice of nanofluids. however, it is higher for cu-eo nanofluids, which means that the base fluids mohammad m. rahman and mohammed m. al-hatmi 74 are very important in the cooling and heating processes. the effect of bi on the skin-friction coefficients is very similar to those of and m , as can be found from figure 37. 4.3.2.2 skin-friction coefficient for water-based nanofluids figures 38 to 40 respectively display the behavior of the skin-friction coefficient under the effects of stretching parameter m, biot number bi, and angle of inclination  , using water-based nanofluids having different nanoparticles. from these figures we see that the skin-friction coefficients for 2 cu h o nanofluids are higher than the values corresponding to those of 2 2 tio h o and 2 3 2 al o h o nanofluids for all values of the stretching index m , bi , and . 5. conclusions in this paper we have studied numerically the convective heat transfer mechanism of nanofluids over a nonlinear inclined stretching surface using the three different base fluids, water, ethylene glycol, and engine oil, and considering three different nanoparticles, ,cu 2 3 al o and 2 tio . a magnetic field of uniform strength was applied along the normal direction of the flow. the lower surface of the sheet was heated by a convection current of a hot fluid different from the studied nanofluids. various shapes (cylindrical, spherical and arbitrary) of the nanoparticles were also considered to investigate their influences on the flow and temperature fields. following our numerical computations it is concluded that addition of nanoparticles to the base fluid may not always increase the rate of heat transfer; it is significantly controlled by the surface convective parameter. the type of nanofluid is a key factor for heat transfer enhancement. nanofluid velocity increases with an increase of the inclination angle parameter, thermal buoyancy parameter, nanoparticle volume fraction and nonlinear stretching index. nanofluid velocity decreases with the increase of the hartmann number. the velocity of the nanofluid is higher than the velocity of the base fluid. the velocity of the ethylene glycol-al2o3 nanofluid has the lowest value for velocity, while wateral2o3 nanofluid has the highest value for velocity followed by engine oil-al2o3. the temperature of a nanofluid increases with the increase of the angle of inclination, hartmann number, nanoparticle volume fraction parameter, thermal buoyancy parameter and biot number. the temperature of a nanofluid decreases with the increase of the nonlinear stretching index and empirical shape factor. the temperature in the engine oil-based nanofluid is higher than the temperature in the water and ethylene glycol-based nanofluids. a nanofluid with cu nanoparticles has a higher temperature than nanofluids containing al2o3 nanoparticles. the rate of heat transfer decreases with the increase of the stretching index, except in the water-based nanofluids. the rate of heat transfer in tio2-water nanofluid is higher than the rate of heat transfer in cu-water and al2o3-water nanofluids. shear stress increases significantly with the increase of the inclination angle of the surface. shear stress in the engine oil-based nanofluid is higher than the shear stress in the waterand ethylene glycol-based nanofluids. 6. acknowledgement this research work was supported by the grant ig/sci/doms/13/05, college of science, sultan qaboos 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transition metals; magnetic susceptibility measurements. الفينانثرولين 10,1-أو ثنائي البيريدين -2,'2 و تكوين ودراسة خصائص بعض المعقدات الخماسية الحلقة من األندول ادويه كوويستابلو، ووال الراسبية محمذ خان -1,01 أو ينثنائي انبيريذ-2',2 بين ثنائي هايذرازين انخكاثف حفاعالث من انمشخقتحم حكىين معقذاث من انمخرابطاث انخماسيت انحهقت ملخص: ( وأخيرا انسنك ii( واننيكم )ii( وانكىبانج )ii( و انحذيذ )iiمن انمنجنيس) انحهقت جذيذة خماسيت معقذاثمع أنذول أنذيهايذ. وحم حكىين انفينانثرونين (ii كما حمج دراست خصائصها عن طريق انخحهيم انخقني وانخىصيم انكهربائي وانخصائص .).انمغناطيسيت خماسيت انحهقت، انعناصر االنخقانيت، قياش انقابهيت انمغناطيسيت. معقذاث: كلمات مفتاحية 1. introduction n the past six decades macrocyclic ligands and complexes incorporating an enormous variety of functional groups have been prepared and investigated [1, 2]. there has been particular interest in macrocyclic systems incorporating heterocyclic subunits, which may provide donor atoms for a metal ion and also act as rigid structure formers. metal complexes of polydentate macrocyclic ligands have also attracted interest because of their potential for providing molecules capable of mimicking various aspects of biological systems [3]. in the early to late 1980s, lewis and constable reported a variety of macrocyclic systems incorporating 1,10phenanthroline, 2,2'-bipyridine [4-29], 2,2':6',2"-terpyridine [30-34] and 2,2'-biquinoline [35] moieties into the cyclic structure. more recently, the group of constable and housecroft have designed a series of dinuclear macrocyclic ligands containing multiple bipyridines or terpyridines coordinated to fe(ii) [36]. metal-directed self-assembly of macrocyclic compounds bearing terpyridine pendants bound to fe(ii), ru(ii) and pt(ii) [37-43] have also been investigated. as an extension to these studies, in this paper, we investigate the utility of indoledialdehyde for the preparation of macrocycles. we describe the preparation and characterization of cyclic hydrazones formed from a 2,7-diformylindole. we also investigate their coordination chemistry with some d-block metal ions such as mn(ii), fe(ii), co(ii), ni(ii), cu(ii) and zn(ii). 2. experimental 2.1 general details all reactions were performed under a dry nitrogen atmosphere using standard schlenk techniques. solvents were pre-dried and distilled before use by standard procedures. all chemicals were obtained from sigma aldrich and used as received. infra-red spectra were recorded in compressed kbr pellets on a perkin-elmer 1710 ft spectrophotometer. i synthesis and characterization of some macrocyclic complexes 21 i h nmr spectra were recorded on a brüker wm-250 or a am-400 spectrometer. mass spectra were recorded on a kratos ms 890 mass spectrometer by the fast atom bombardment (fab) technique. microanalyses were performed in the university chemical laboratory, university of cambridge. cyclic voltammograms were conducted in a princeton applied research electrochemistry system, model 170. a pt wire sealed in glass was the auxiliary electrode with a second pt wire serving as the working electrode, and a ag/agno3 as the reference electrode. measurements were made in acetonitrile solution with 0.1 m [ tbu4n]bf4] as the base electrolyte. a cdm 210 conductivity meter was used to measure conductivity in nitromethane solution. magnetic susceptibility measurements were done using a sherwood scientific mki model gouy balance. the bis(hydrazines) l 2 -l 7 [4-29] and 2,7-indoledildehyde (hl) [4549] were prepared as reported in the literature. 2.2 preparation of complexes preparation of [nil 8 ][bf4] a solution of ni(oac)2.4h2o (0.100 g, 0.4 mmol) in meoh (15 cm 3 ) was added to a solution of hl (0.100 g, 0.4 mmol) in meoh (15 am 3 ) at 70 °c under an inert atmosphere. after 5 minutes, a solution of l 2 in meoh (15 cm 3 ) was added, and the mixture heated to reflux for 5 h, during which period it turned orange-yellow. the solution was concentrated in vacuo to one third volume and na[bf4] (0.04 g) added to the hot solution. after cooling, an orange microcrystalline solid was precipitated. recrystallisation from meoh followed by drying in vacuo gave [nil 8 ][bf4] as an orange solid (65% yield). anal. found: c, 49.1; h, 4.3; n, 14.9. calc. for c27h28n7o4nibf4: c, 49.1; h, 4.2; n, 14.9%. fab-ms: m/z 574.65 {nil 8 } + . i.r. (kbr), 1590m, 1530m, 1260m, 1225w, 1180w, 1151s, 1090br, 960br, 844s, 830m, 750s cm -1 . preparation of [col 8 (h2o)][pf6] a solution of co(oac)2.4h2o (0.100 g, 0.4 mmol) in meoh (15 cm 3 ) was added to a solution of hl (0.100 g, 0.4 mmol) in meoh (15 cm 3 ) at 70 °c under an inert atmosphere. after 5 minutes, a solution of l 2 in meoh (15 cm 3 ) and triethylamine (0.041 g, 0.4 mmol) were added, and the mixture heated to reflux for 5 h, during which period it turned orange-yellow. the solution was concentrated in vacuo to one third volume and [nh4][pf6] (0.064 g) was added to the hot solution. after cooling [col 8 (h2o)][pf6] was precipitated as an orange microcrystalline solid (65% yield). anal. found: c, 44.2; h, 4.1; n, 13.8. calc. for c27h30n7o4copf6: c, 44.0; h, 4.1; n, 13.3%. fab-ms: m/z 574.02 {col 8 } + . i.r. (kbr), 3500br, 1660w, 1593s, 1262m, 1230w, 1174w, 1148s, 1094br, 960br, 849s cm -1 . all other complexes were prepared in similar manners. analytical data for the complexes are presented in table 1. the 1 h nmr data of the zn(ii) complexes are presented in table 2. table 1. analytical data for metal macrocyclic complexes. compound found calc conductivity c h n cl c h n cl ω –1 cm 2 mol –1 [nil 8 ][bf4] 49.1 4.3 14.9 49.1 4.2 14.8 121 [nil 9 ][bf4] 52.8 4.3 17.0 52.9 4.3 17.3 126 [nil 10 ][bf4] 51.1 3.8 18.1 51.2 3.7 18.0 127 [nil 11 ][bf4] 50.8 4.0 14.2 50.9 4.1 14.3 123 [nil 12 ][bf4] 54.6 4.1 16.5 54.8 4.1 16.6 124 [nil 13 ][bf4] 53.3 3.6 17.3 53.2 3.6 17.4 127 [cul 8 ][bf4] 48.9 4.2 14.6 48.8 4.2 14.8 125 [cul 9 ][bf4] 52.5 4.2 17.0 52.4 4.2 17.1 125 [cul 10 ][bf4] 50.6 3.7 17.8 50.7 3.7 18.0 123 [cul 11 ][bf4] 50.5 4.0 14.2 50.6 4.1 14.2 125 [cul 12 ][bf4] 54.2 4.0 16.4 54.3 4.0 16.4 128 [cul 13 ][bf4] 52.7 3.6 17.2 52.8 3.6 17.2 126 [col 8 (h2o)][pf6] 44.2 4.1 13.4 44.0 4.1 13.3 123 [col 9 ][pf6] 48.0 3.9 15.6 47.9 3.9 15.7 124 [col 10 ][pf6] 46.2 3.3 16.3 46.2 3.4 16.4 124 [col 11 (h2o)][pf6] 48.9 4.2 14.6 48.8 4.2 14.8 123 [col 12 ][pf6] 49.8 3.7 15.0 49.9 3.7 15.1 122 [col 13 ][pf6] 48.3 3.3 15.6 48.2 3.2 15.8 124 [znl 8 cl] 52.8 4.6 15.7 52.7 4.5 15.9 [znl 11 cl] 54.5 4.4 15.2 54.4 4.3 15.3 [mnl 8 cl] 53.7 4.7 16.2 53.6 4.6 16.2 [mnl 9 cl] 58.4 4.7 19.0 6.9 58.5 4.7 19.1 6.9 [mnl 10 cl] 57.0 4.2 20.1 7.3 57.0 4.1 20.2 7.3 [mnl 11 cl] 55.2 4.5 15.4 55.4 4.4 15.6 [mnl 12 cl] 60.4 4.5 18.2 6.6 60.4 4.5 18.3 6.6 [mnl 13 cl] 59.0 4.0 19.2 6.9 59.0 4.0 19.3 7.0 [fel 9 cl] 58.5 4.7 18.9 6.9 58.5 4.7 19.1 6.9 [fel 10 cl] 56.9 4.2 20.1 7.3 56.9 4.2 20.2 7.3 [fel 12 cl] 60.2 4.4 18.1 6.6 60.3 4.5 18.2 6.6 [fel 13 cl] 58.8 3.9 19.2 6.9 58.9 4.0 19.2 7.0 muhammad s. khan et al. 22 table 2. summary of 1 h nmr data of zn(ii) macrocyclic complexes. compound 1 h nmr in dmso-d6 [znl 8 cl] 1.06 (3h, s, ch3); 1.69 (2h, m, ch2); 1.90 (3h, dt, 2ch); 2.73 (4h, m, ch); 3.20 (6h, s, 2och3); 3.35 (4h, t, 2ch2); 3.79 (4h, t, 2ch2); 7.63 (2h, s, 2hc=n); 7.10-7.62 (6h, m, arh). [znl 11 cl] 1.04 (3h, s, ch3); 1.68 (2h, m, ch2); 1.92 (3h, dt, 2ch); 2.75 (4h, m, ch); 3.18(6h, s, 2och3); 3.36 (4h, t, 2ch2); 3.75 (4h, t, 2ch2); 7.87 (2h, s, 2hc=n); 7.10-7.62 (6h, m, arh). 3. results and discussion there have been very few reports of macrocyclic ligands which incorporate indole moieties within the cyclic framework. the condensation of dicarbonyls with diamines or bis(hydrazines) provides a facile route to ring closure, and indoledialdehydes or indolediketones are obvious candidates for such cyclisation reactions. indoles differ from related pyridines in possessing an acidic nh functionality, which allows the preparation of macrocycles which may bind metals with concomitant deprotonation. black and co-workers developed an effective synthetic route to 2,7diformyl-3-methyl-4,6-dimethoxyindole (hl) (chart 1) and demonstrated that macrocyclic complexes may be obtained from template condensations with α,ω-diamines [45,46]. black also demonstrated the facile preparation of other macrocyclic ligands containing three indolyl subunits [47] and 2,2'-biindolyl moieties [48]. the similarity in behaviour between (hl) and 2,6-diformylpyridine led us to investigate the reactions of hl with 6,6'-bis(hydrazino)2,2'-bipyridines and 2,9-bis(hydrazino)-1,10-phenanthrolines in an attempt to prepare hydrazone-based macrocycles incorporating an indolyl functionality. n hmeo hl ome h o oh chart 1. 2,7-diformyl-3-methyl-4,6-dimethoxyindole. the dialdehyde hl was prepared by the literature method in 44% overall yield from 3,5-dimethoxyaniline and ethyl oxomalonate [45]. the reactions of the bis(hydrazines) l 2 -l 7 (chart 2) with the dialdehyde hl in the absence of metal-ions were briefly investigated. in all cases, reaction in meoh in the presence or absence of acid resulted in the formation of intractable, dark-coloured polymeric materials and none of the desired macrocycles hl 8 -hl 13 . we did not further pursue this synthetic method, and concentrated instead upon metal-directed template assembly of the macrocyclic systems. synthesis and characterization of some macrocyclic complexes 23 nn n nh2 n nh2 r r nn n nh2 n nh2 r r l5 r = ch2ch2oh l6 r = ch3 l7 r = h l2 r = ch2ch2oh l3 r = ch3 l4 r = h chart 2. 2,2’-bipyridine and 1,10-phenanthroline bis-hydrazines. we concentrated upon template reactions involving hl and l 2-7 . the reaction of the hyrazines with hl in refluxing meoh in the presence of manganese(ii) acetate, cobalt(ii) acetate, copper(ii) acetate or zinc(ii) acetate resulted in the formation of coloured solutions from which coloured solids were precipitated upon the addition of ammonium hexafluorophosphate or sodium tetrafluoroborate. in some cases, triethylamine was added to the reaction mixture and it was observed that the colour changes occurred more rapidly in the presence of the base. this is consistent with the formation of metal complexes of the deprotonated macrocyclic ligands hl 8-13 (chart 3). nn n n n n r r meo h n h ome nn n n n n r r meo h n h ome l8 r = ch2ch2oh l9 r = ch3 l10 r = h l11 r = ch2ch2oh l12 r = ch3 l13 r = h h h chart 3. macrocyclic ligands incorporating indoledialdehyde. in the case of the nickel(ii) templated reactions, the final reaction solutions were orange-yellow in colour. concentration of these solutions followed by the addition of methanolic na[bf4] solution resulted in the precipitation of orange-brown solids in 50-70% yield. recrystallisation from meoh or dmf-meoh gave orange microcrystalline products which analysed for [nil 8-13 ][bf4] after prolonged drying in vacuo. these complexes are soluble in muhammad s. khan et al. 24 nitromethane to give orange solutions which behave as 1:1 electrolytes. the infra-red spectra of the complexes exhibit no amine absorptions and no carbonyl absorptions in the range 1600-2000 cm -1 , but do show strong absorptions at 1590-1580 cm -1 assigned to imine stretching modes. the strong nh stretching mode observed in the free ligand hl is absent from these complexes. all of these data are fully in accord with the formation of nickel(ii) complexes of the deprotonated macrocyclic ligands. repetition of the above reactions with copper(ii) acetate or cobalt(ii) acetate resulted in the formation of the complexes [cul 8-13 ][bf4] or (col 813 (h2o)n][pf6] (n = 0,1). the copper(ii) complexes were obtained as dark-brown microcrystalline solids whereas the cobalt(ii) species were orange-brown. in each case, the i.r. spectra showed no carbonyl or nh absorptions, but strong imine stretches in the range 1590-1595 cm -1 . those of the cobalt(ii) complexes which analysed as containing a water molecule also showed absorptions in the 1630-1640 cm -1 region assigned to coordinated water. the cobalt(ii) complexes are all electrochemically active, and in acetonitrile solution exhibit a reversible or quasi-reversible oxidation (co ii /co iii ) at +0.1-+0.2 v vs. ag/agcl. the magnetic moments of the cobalt(ii) complexes are in the range 4.50-4.70 b.m., in accord with the spin-only formula. these complexes all behave as 1:1 electrolytes in nitromethane solution. slightly different behaviour is observed in the template condensation of hl with l 2-7 with zinc(ii) or manganese(ii) acetate in meoh solution. in these cases, orange or yellow solids were precipitated from the reaction mixture, but these did not behave as pure macrocyclic products and were contaminated with metal hydroxides. in order to avoid the precipitation of metal hydroxides, the solutions were buffered by substitution of the salts [hl 2-7 ]cl in the presence of triethylamine. this resulted in the formation of clean products, for which microanalysis indicated the formulations [znl 8,11 cl] and [mnl 8-13 cl] respectively. these molecular species exhibited parent ions in their mass spectra all showing the correct isotopomer distributions. all of these complexes behave as non-electrolytes in dmso solution. once again, the i.r. spectra showed no carbonyl or nh absorptions, but strong imine stretches in the range 1590-1595 cm -1 . similar complexes, [fel 9,10,12,13 ci], are obtained by the use of iron(ii) chloride as a template. the manganese(ii) and iron(ii) complexes are high-spin and each possesses magnetic moments of 5.8-6.0 b.m. the 1 h nmr spectra of the zn(ii) complexes [znl 8 cl] and [znl 11 cl] have been investigated in strong polar solvents such as dmso–d6. the spectra are concentration independent and exhibited the number of peaks expected for each molecular structure, which suggests that the discrete anionic macrocycle complexes remain intact in solution. repeated attempts to obtain x-ray quality crystals of any of these complexes were unsuccessful. in every case, very small microcrystals or powders were obtained. in the absence of crystallographic data, we can only propose tentative structures for these complexes. the i.r. data strongly supports the formation of complexes of the desired macrocyclic ligands rather than of the acyclic precursors or acyclic reaction products. the absence of carbonyl absorptions is particularly indicative, as is the appearance of bands assigned to imine c=n stretches. in all cases, the metal complexes contain the deprotonated ligands. once again, the i.r. data supports this and shows the loss of the pyrrolic nh absorption. the overall stoichiometry of the complexes also supports this, with the formation of monocationic (ml 8-13 ) species. the neutral zinc(ii), iron(ii) and manganese(ii) complexes contain coordinated chloride, and the most likely structure is a six-coordinate one containing a pentagonal-based pyramidal metal center, with the macrocyclic ligand occupying the basal plane and the chloride the axial site (figure 1). this is strikingly reminiscent of the pentagonalbased pyramidal structures we have previously described for chlorocomplexes of the pentadentate macrocyclic ligands obtained from the template condensation of l 2 -l 7 with 2,6-pyridinedicarbonyls in the presence of metal chlorides [4-29]. cl figure 1. proposed structure of the six-coordinate zinc(ii), iron(ii) and manganese(ii) complexes, [ml 8-13 ]cl. synthesis and characterization of some macrocyclic complexes 25 (a) x (b) x x figure 2. (a) proposed structure of the six-coordinate nickel(ii), cobalt(ii) and copper(ii) complexes, [ml 9/10 ][bf4]; (b) proposed structure of the seven-coordinate nickel(ii), cobalt(ii) and copper(ii) complexes, [ml 9/10 ][bf4]. the structures of the nickel(ii), cobalt(ii) and copper(ii) complexes is less certain. drying the complexes to obtain analytically pure samples results in solvent loss and the formation of complexes analyzing as [ml 9/10 ][bf4]. in the light of our structural studies with related ligands [4-29] we suggest that these complexes are six(figure 2a) or seven-coordinate (figure 2b) species, but in the absence of further structural data, we cannot make unambiguous assignments of their structures. in the case of some of the cobalt(ii) complexes, we have evidence for the presence of one strongly associated water molecule, and cannot eliminate a structure such as shown in figure 3, in which the condensation has resulted in the formation of one imine and aminol functionality. nn n n n hn r r meo h n ome h h oh figure 3. proposed structures of some cobalt(ii) complexes containing one imine and an aminol functionality. muhammad s. khan et al. 26 4. conclusion the indoledialdehyde (hl) is a versatile dicarbonyl for incorporation into macrocyclic ligands which may be deprotonated to yield anionic species. although clean macrocyclic complexes may be obtained from template condensations, we have been unable to grow x-ray quality crystals to unambiguously confirm the structures. 5. acknowledgement msk acknowledges sultan qaboos university, oman for financial support (ig/sci/chem/13/01). references 1. lindoy, l.f. the chemistry of macrocyclic ligand complexes, (ed), cambridge university press, 1990. 2. curtis, n. and melson, g. coordination chemistry of macrocyclic compounds. plenum press, new york, 1979, 230. 3. constable, e.c., sacht, c., palo, g., tocher, d.a. and truter, m.r. lead(ii) as a template for the synthesis of a [1+1] 18-membered hexadentate n4s2-donor macrocycle; crystal and molecular structure of (acetato-o, o′)[3,13dithia-6,10-diaza-1,8 (2,6)-dipyridinacyclotetradecaphane-6,9-diene] lead(ii) hexafluorophosphate. j. chem. soc., dalton trans., 1993, 8, 1307-1312. 4. chung, l., constable, e.c., khan, m.s., lewis, j., raithby, p.r. and vargas, m.d. structural characterisation of a pentagonal bipyramidal macrocyclic chromium (iii) complex; an explanation of a chromium-mediated ‘transienttemplate’ effect. j. chem. soc., chem. commun., 1984, 21, 1425-1426. 5. constable, e.c., chung, l.-y., lewis, j. and raithby, p.r. the first stable lithium complex of a pentadentate macrocycle incorporating sp2-nitrogen donor atoms only; the x-ray crystal structure of [li (l2)(meoh)][pf6]{l2= 6,13-(bis-2-hydroxyethyl)-6h,13h-tripyrido[cd,fg,lm][1,2,4,7,9,10,13] heptazapentadecine. j. chem. soc., chem. commun., 1986, 23, 1719-1720. 6. lewis, j. and wainwright, k.p. synthesis of a macrocyclic ligand derived from 6, 6′-dihydrazino-2, 2′-bipyridyl. ibid., 1974, 5, 169-170. 7. ansell, c.w.g., lewis, j., raithby, p.r., ramsden, j.n. and schröder, m. x-ray crystal structure of the pentagonal bipyramidal nickel(ii) complex [ni ii(l)(h2o)2](bf4)2 and the selective stabilisation of the nickel(i) oxidation state by a quinquedentate macrocyclic ligand. ibid., 1982, 10, 546-547. 8. bishop, m.m., lewis, j., o'donoghue, t.d. and raithby, p.r. some metal complexes of macrocyclic ligands incorporating the 1,10-phenanthroline group. x-ray crystal structure of the manganese(ii) complex. ibid., 1978, 11, 476-478. 9. bishop, m.m., lewis, j., o'donoghue, t.d., raithby, p.r. and ramsden, j.n. x-ray crystal structure of a planar, high-spin iron(ii) complex of a pentadentate unsaturated macrocycle formed by reaction of 2,9-di(1methylhydrazino)-1,10-phenanthroline monohydrochloride with 2,6-diacetylpyridine. ibid., 1978, 19, 828-829. 10. chung ,l.-y., constable, e.c., dale, a.r., khan, m.s., liptrot, m.c., lewis, j. and raithby, p.r. the transient template effect: chromium (iii)-directed syntheses of metal-free macrocyclic ligands and crystal structure of 1,11bis(2′-hydroxyethyl)-4,8;12,16;17,21-trinitrilo-1,2,10,11-tetra-azacyclohenicosa-2,4,6,9,12,14,18,20-octaene hydrochloride tetrahydrate. j. chem. soc., dalton trans., 1990, 4, 1397-1404. 11. lewis, j. and wainwright, k.p. chemistry of polydentate ligands. part 2. the mode of co-ordination of 6,6′dihydrazino-2,2′-bipyridyl ligands with nickel(ii) and zinc(ii) in octahedral complexes. ibid., 1977, 8, 739-744; lewis, j. and wainwright, k.p. chemistry of polydentate ligands .part 3. ring closures effected by the reaction of β-diketones with 6,6′-dihydrazinoand 6,6′-di(n-methylhydrazino)-2,2′-bipyridylnickel(ii) diperchlorate. ibid., 1978, 5, 440-446. 12. lewis, j., o'donoghue, t.d., haque, z.p. and tasker, p.a. chemistry of polydentate ligands. part 9. preparation and properties of group 2b cation complexes with multidentate ligands based on 2,2′-bipyridyl. ibid., 1980, 9, 1664-1 666. 13. ansell, c.w.g.,lewis, j.,raithby, p.r. and ramsden, j.n. synthesis and x-ray structure of a macrocyclic pentagonal bipyramidal complex of cobalt(ii). ibid., 1982, 10, 2127-2129. 14. ansell, c.w.g., lewis, j., liptrot, m.c., raithby, p.r. and schröder, m. the stabilisation of low oxidation state transition metal complexes. preparation and electrochemistry of cobalt(ii) unsaturated macrocyclic complexes and the stabilisation of a cobalt(i) derivative. crystal and molecular structures of [coii(l)(ch3oh)2][bf4]2 and [coi(l){p(och3)3}][bf4]. ibid., 1982, 8, 1593-1601. 15. ansell, c.w.g., lewis, j., raithby, p.r. and o'donoghue, t.d. synthesis of a macrocyclic metal complex incorporating peripheral hydroxyethyl tails: the x-ray structure of [mn(l1)cl][bf4]·4h2o. ibid., 1983, 1, 177179. 16. bishop, m.m., lewis, j., o'donoghue, t.d., raithby, p.r. and ramsden, j.n. chemistry of polydentate ligands. part 8. preparation and properties of iron(ii) complexes with quinquedentate macrocyclic ligands. crystal and molecular structure of a compound where high-spin feii sits in the ligand cavity. electrochemistry of a series of complexes with the macrocycles. ibid., 1980, 8, 1390-1396. synthesis and characterization of some macrocyclic complexes 27 17. lewis, j., o'donoghue, t.d. and raithby, p.r. chemistry of polydentate ligands. part 7. synthesis, characterisation, and properties of some manganese(ii) complexes of quinquedentate macrocyclic ligands based on 1,10-phenanthroline. crystal and molecular structure of a complex with pentagonal-pyramidal coordination geometry about the mn(ii). ibid., 1980, 8,0383-0381. 18. lewis, j. and o'donoghue, t.d. chemistry of polydentate ligands. part 5. complexes of 2,9-di-hydrazino-derivatives of 1,10-phenanthroline. dependence of co-ordination number of a ligand on the anion present. ibid., 1980, 5, 736-742. 19. constable, e.c., lewis, j., liptrot, m.c., raithby, p.r. and schröder, m. synthesis, molecular structure and electrochemistry of pentagonal bipyramidal nickel(ii) complexes of quinquedentate macrocylic ligand incorporating a 2,2′:6′,2″-terpyridyl moiety. polyhed., 1983, 2(4), 301-302. 20. ansell, c.w.g., lewis, j., ramsden, j.n. and schröder, m. the preparation and electrochemistry of manganese(ii) complexes of an unsaturated pentadentate macrocyclic ligand. polyhed., 1983, 2(6), 489-491. 21. constable, e.c.,corr, s. and lewis, j. the hydrolytic behaviour of some pentadentate schiff-base type macrocycles. inorg. chim. acta., 1986, 116(2), 95-97. 22. constable, e.c.,khan, m.s.,liptrot ,m.c.,lewis, j. and raithby, p.r. silver(i)-silver (i) interactions in complexes of pentadentate macrocyclic ligands; crystal and molecular structure of [ag2l2][bf4]2(l1,11-bis (2′-hydroxyethyl)-4, 8; 12, 16; 17, 21-trinitrilo-1, 2, 10, 11-tetraazacyclohenicosa-2,4,6,9,12,14,18,20-octaene). ibid., 1991, 179(2), 239-244. 23. constable, e.c.,khan, m.s.,lewis, j.,liptrot, m.c. and raithby, p.r. iron complexes of derivatised pentadentate macrocyclic ligands; the crystal and molecular structure of dichloro (6, 13-(bis-2-hydroxyethyl)-6h, 13h-tripyrido [cd, fg, lm][1, 2, 4, 7, 9, 10, 13] heptaaza-pent adecine) iron (iii) chloride. ibid., 1991, 181(2), 207-212. 24. lewis, j. and wainwright, k.p. chemistry of polydentate ligands. part 4. the oxidative denitrogenation of dichloro-6, 6′-dihydrazino-2, 2′ bipyridyliron (ii). ibid., 1979, 34, 57-60; lewis, j. and o'donoghue, t. folding of a macrocyclic ligand induced by hydrogenation of part of the ring: the effect of rigidity in the system. ibid., 1978, 30, l339-l340. 25. ansell, c.w.g., egert, e., lewis, j. and raithby, p.r. [2, 9-bis (n-methylhydrazino)-1, 10-phenanthroline] dichlororhodium (iii) tetrafluoroborate sesquihydrate[, rhcl2 (c14h16n6)]bf4.1.5h2o. acta cryst. sect. c: cryst. struct. commun., 1984, 40(3), 359-362. 26. ansell, c.w.g., lewis, j., raithby, p.r., kabir, a., khan, f.k., malik, k.m.a., khan, m.s. and haider, s.z. coordination chemistry of polydentate macrocyclic ligands. part 1. synthesis, characterization, spectral, thermal, electrochemical and electrolytic properties of ag(i), pt(ii) and rh(iii) complexes of 2,9-bis(n-methyl hydrazino)1,10-phenanthroline, l1; crystal and molecular structure of rh(l1)cl2.2h20 j. bangladesh acad. sci., 1986, 10, 215229. 27. khan, f.k., malik, k.m.a., khan, m.s., haider, s.z., lewis, j., liptrot, m.c. and raithby, p.r. coordination chemistry of polydentate macrocylic ligands. part 2. synthesis, characterization, spectral, electrolytic and electrochemical properties of some quinquedentate macrocycles derived from 1,10-phenanthroline dihydrazines and 2,6-pyridine dicarbonyls; crystal structure of a novel n5-macrocycle ibid., 1987, 11, 43-54. 28. constable, e.c. and lewis, j. the preparation and coordination chemistry of 2,2′:6′,2″-terpyridine macrocycles-1. polyhed. ,0182, 1(3), 303-306; constable, e.c. and holmes, j.m. the preparation and coordination chemistry of 2,2′:6′,2″-terpyridine macrocycles-vi. planar hexadentate macrocycles incorporating 2,2′: 6′,2″-terpyridine. ibid., 1988, 7(24), 2531-2536. 29. constable, e.c., lewis, j., liptrot, m.c. and raithby, p.r. the preparation and co-ordination chemistry of 2,2′: 6′,2″terpyridine macrocycles. part 3. transient template effects involving dimethyltin(iv). j. chem. soc., dalton trans., 1984, 10, 2177-2185. 30. constable, e.c., khan, f.k., lewis, j., liptrot, m.c. and raithby, p.r. the preparation and co-ordination chemistry of 2,2′:6′,2″-terpyridine macrocycles. part 4. structural characterisation of an intermediate in a transient template reaction. ibid., 1985, 2, 333-335. 31. constable, e.c., holmes, j.m. and mcqueen, r.c.s. the preparation and co-ordination chemistry of 2,2′: 6′,2″terpyridine macrocycles. part 5. unsubstituted fifteen-membered-ring macrocycles containing 2,2′: 6′,2′-terpyridine. ibid., 1987, 1, 5-8. 32. constable, e.c., doyle, m.j., healy, j. and raithby, p.r. alkali metal complexes of planar pentadentate macrocycles; a unique environment for lithium in the crystal and molecular structure of (lil1][pf6] {l1 = 1,6-dimethyl-1,2,5,6-tetraaza[6.0.0](2,6)pyridinophane-2,4-diene}. j. chem. soc., chem. commun., 1988, 18, 1262-1264. 33. chung, l,. constable, e.c., lewis, j., raithby, p.r. and kaye, p.t. transition metal complexes of substituted 2,2′biquinolines. part 1. the crystal and molecular structures of [8,8′-bis(aminomethyl)-2,2′biquinoline]dichloromanganese(ii) and [8,8′-bis(aminomethyl )-2,2′biquinoline]chlorocopper(ii) chloride. j. chem. soc., dalton trans., 1988, 8, 2121-2125. 34. constable, e.c., housecroft, c.e. and smith, c.b. self-assembly of two discrete polynuclear iron(ii) metallomacrocycles from a ligand containing two 2, 2′:6′,2″-terpyridine binding domains. inorg. chem. commun., 2003, 6(8), 1011-1013. 35. chow, h.s., constable, e.c., housecroft, c.e. and neuburger, m. metal-directed assembly of a conformationally restricted metallomacrocycle. dalton trans., 2003, 24, 4568-4569. muhammad s. khan et al. 28 36. constable, e.c., dunphy, e.l., housecroft, c.e., kylberg, w., neuburger, m., schaffner, s., schofield, e.r. and smith, c.b. structural development of free or coordinated 4′-(4-pyridyl)-2, 2′:6′,2′-terpyridine ligands through nalkylation: new strategies for metallamacrocycle formation. chem. a eur. j., 2006, 12(17), 4600-4610. 37. constable, e.c., housecroft, c.e., neuburger, m. and schmitt, c.x. platinamacrocycles containing 2,5thiophenediyl and poly(2,5-thiophenediyl)-linked azaaromatic ligands: new structural paradigms for metallosupramolecular chemistry. polyhedron, 2006, 25(8), 1844-1863. 38. constable, e.c. and schofield, e. metal-directed assembly of a box-like structure. chem. commun., 1998, 3, 403404. 39. constable, e.c., king, a.c. and raithby, p.r. synthesis, coordination chemistry and crystal structures of [2+2] macrocycles incorporating 2,6-bis(thiomethyl)pyridine sub-units. polyhedron, 1998, 17(23-24), 4275-4289. 40. constable, e.c. and housecroft, c.e. supramolecular approaches to advanced materials. chimia, 1998, 52(10), 533-538. 41. constable, e.c., harris, k., housecroft, c.e. and neuburger, m. when is a metallopolymer not a metallopolymer? when it is a metallomacrocycle? dalton trans., 2011, 40(7), 1524-1534. 42. constable, e.c., housecroft, c.e., prescimone, a.,vujovic, s. and zampese, j.a. environmental control in the assembly of metallomacrocycles and one-dimensional polymers with 4,2′:6′:4′′-terpyridine linkers and zinc(ii) nodes. cryst. eng. comm., 2014, 16(37), 8691-8699. 43. black, d.s.c., rothnie, n.e. and wong, l.c.h. synthesis of macrocyclic ligands containing the indole ring system. tet. lett., 1980, 21(19), 1883-1886. 44. black, d.s.c., rothnie, n. and wong, l. metal template reactions. xx. macrocyclic metal complexes derived from 4, 6-dimethoxy-3-methylindole-2, 7-dicarbaldehyde and some primary diamines with additional nitrogen donor atoms. aust. j. chem., 1983, 36(12), 240 6-2402. 45. black, d.s.c., craig, d.c. and kumar, n. synthesis of a new class of indole-containing macrocycles. j. chem. soc., chem. commun., 1989, 7, 425-426. 46. black, d.s.c., kumar, n. and wong, l.c.h. synthesis of macrocyclic nickel(ii) complexes containing the 2,2′-biindolyl moiety. ibid., 1985, 17, 1174-1175. 47. constable, e.c., khan, m.s. and lewis, j. chromium(iii) complex of a pentadentate macrocycle containing 2,2’bipyridine. in synthetic methods of organometallic and inorganic chemistry., hermann, w.a., salzer, a. (eds.), thieme, stuttgart, 1996, 1, 126. 48. constable, e.c., khan, m.s. and lewis, j. chromium(iii) directed synthesis of a planar pentadentate macrocycle containing 2,2’-bipyridine. in synthetic methods of organometallic and inorganic chemistry., hermann, w.a., salzer, a. (eds.), thieme, stuttgart, 1996, 1, 128 received 22 january 2015 accepted 22 march 2015 squ journal for science, 2017, 22(1), 48-52 doi: http://dx.doi.org/10.24200/squjs.vol22iss1pp48-52 2017 sultan qaboos university 48 theorems on fixed points for asymptotically regular sequences and maps in 𝒃-metric space mohammad s. khan1* and pankaj k. jhade2 1department of mathematics and statistics, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman; 2department of applied science, sagar institute of science, technology and engineering, bhopal, india. *email: mohammad@squ.edu.om. abstract: in this paper, we present some fixed point theorems for asymptotically regular sequences and asymptotically regular maps in complete 𝑏metric spaces. our results extend and generalize the well-known fixed point theorems of hardyroger [1] and reich [2]. keywords: b-metric space; fixed point; asymptotically regular sequence; asymptotically regular maps. سقاط في فضاء متريإنقاط ثابتة لمتتالية عادية متقاربة وحول نظريات ادهبونكاج كومار جو محمد سعيد خان تعتبر نتائجنا . بعض نظريات النقطة الثابتة لمتتاليات عادية متقاربة واسقاط عادي متقارب في فضاءات مترية متكاملةنقدم في هذه الورقة ملخص:ال [.1]وريخ [ 2]روجر -توسيع وتعميم لنظريات النقطة الثابتة المعروفة لكل من هاردي .سقاط عادي متقاربإالفضاء المتري، النقطة الثابتة، متتالية عادية متقاربة، : مفتاحيةالكلمات ال 1. introduction etric fixed point theory was born with the well-known banach contraction principle that was initially published in 1922. this principle states that on a complete metric space(𝑋, 𝑑) , a self mapping 𝑇 for which 𝑑(𝑇𝑥, 𝑇𝑦) ≤ 𝑘𝑑(𝑥, 𝑦), for all 𝑥, 𝑦 ∈ 𝑋, 0 < 𝑘 < 1, has a unique fixed point. several generalizations and extensions of this celebrated result have been appeared in the last few decades. the fixed point theorem in metric spaces plays a significant role to construct methods to solve the problems in mathematics and sciences. metric fixed point theory is a vast field of study and is capable of solving many equations. to overcome the problem of measurable functions with respect to a measure and their convergence, [3] needed an extension of metric space. using this idea, he introduced the concept of 𝑏-metric space and presented the contraction mapping in 𝑏-metric spaces that is generalization of the banach contraction principle in metric spaces [4-7]. after that, several papers have dealt with fixed point theory or the variational principle for single-valued and multi-valued operators in 𝑏metric spaces [8-14]. in this paper our aim is to show the validity of some fixed point theorems for asymptotically regular sequences. we also present results on fixed points of asymptotically regular mappings. 2. preliminaries: consistent with [3] and [4,15], we recall some definitions and properties for 𝑏-metric space. definition 2.1. let 𝑀 be a nonempty set and the mapping 𝜌: 𝑀 × 𝑀 → ℝ+ (ℝ+ stands for nonnegative reals) satisfies: (i) 𝜌(𝑥, 𝑦) = 0 if and only if 𝑥 = 𝑦 for all 𝑥, 𝑦 ∈ 𝑀; (ii) 𝜌(𝑥, 𝑦) = 𝜌(𝑦, 𝑥) for all 𝑥, 𝑦 ∈ 𝑀; (iii) there exists a real number 𝑠 ≥ 1 such that 𝜌(𝑥, 𝑦) ≤ 𝑠[𝜌(𝑥, 𝑧) + 𝜌(𝑧, 𝑦)] for all 𝑥, 𝑦, 𝑧 ∈ 𝑀. then 𝜌 is called a b-metric on 𝑀 and the pair (𝑀, 𝜌) is called a 𝑏metric space with coefficient 𝑠. remark 2.1. the class of 𝑏-metric spaces is larger than the class of metric spaces since any metric space is a 𝑏metric space 𝑠 = 1. therefore, it is obvious that 𝑏-metric spaces generalizes metric spaces. we present an example which shows that introducing a 𝑏-metric space instead of a metric space is meaningful since there exists 𝑏-metric space instead of a metric space which are not metric spaces. m mailto:mohammad@squ.edu.om theorems on fixed points for asymptotically regular sequence 49 example 2.1. let 𝑀 = [0, ∞) and 𝜌: 𝑀 × 𝑀 → ℝ+ defined by 𝜌(𝑥, 𝑦) = |𝑥 − 𝑦|𝑝, where 𝑝 is a real number such that 𝑝 > 1. let 𝑥, 𝑦, 𝑧 ∈ 𝑀. by taking 𝑢 = 𝑥 − 𝑧 and 𝑣 = 𝑧 − 𝑦 we have |𝑥 − 𝑦|𝑝 = |𝑢 + 𝑣|𝑝 ≤ (|𝑢| + |𝑣|)𝑝 ≤ (2max{|𝑢|, |𝑣|})𝑝 ≤ 2𝑝(|𝑥 − 𝑧|𝑝 + |𝑧 − 𝑦|𝑝), which implies that 𝜌(𝑥, 𝑦) ≤ 2𝑝[𝜌(𝑥, 𝑧) + 𝜌(𝑧, 𝑦)]. therefore (𝑀, 𝜌) is a 𝑏-metric space with coefficient 2𝑝. on the other hand, for 𝑥 > 𝑧 > 𝑦, we have |𝑥 − 𝑦|𝑝 = |𝑢 + 𝑣|𝑝 = (𝑢 + 𝑣)𝑝 > 𝑢𝑝 + 𝑣 𝑝 = (𝑥 − 𝑧)𝑝 + (𝑧 − 𝑦)𝑝 = |𝑥 − 𝑧|𝑝 + |𝑧 − 𝑦|𝑝, which implies that 𝜌(𝑥, 𝑦) > 𝜌(𝑥, 𝑧) + 𝜌(𝑧, 𝑦). therefore (𝑀, 𝜌) is not a metric space. definition 2.2. let (𝑀, 𝜌) be a 𝑏-metric space. then {𝑥𝑛} in 𝑀 is called 1. a cauchy sequence if and only if for all 𝜖 > 0 there exists 𝑛(𝜖) ∈ ℕ such that for each 𝑛. 𝑚 ≥ 𝑛(𝜖), we have 𝜌(𝑥𝑛 , 𝑥𝑚 ) < 𝜖. 2. a convergent sequence if and only if there exists 𝑥 ∈ 𝑀 such that for all 𝜖 > 0 there exists 𝑛(𝜖) ∈ ℕ such that for every 𝑛 ≥ 𝑛(𝜖), we have 𝜌(𝑥𝑛 , 𝑥) < 𝜖. definition 2.3 if (𝑀, 𝜌) is a 𝑏-metric space then a subset 𝐿 ⊂ 𝑀 is called (i) compact if and only if for every sequence of elements of 𝐿 there exists a subsequence that converges to an element of 𝐿. (ii) closed if and only if for each sequence {𝑥𝑛 } in 𝐿 which converges to an element 𝑥, we have 𝑥 ∈ 𝐿. (iii) the 𝑏-metric space is complete if every cauchy sequence in 𝑀 converges in m. definition 2.4 [13] let (𝑀, 𝜌) be a 𝑏-metric space. a sequence {𝑥𝑛} in 𝑀 is said to be asymptotically t-regular if lim 𝑛→∞ 𝜌( 𝑥𝑛, 𝑇𝑥𝑛 ) = 0. example 2.2. let 𝑀 = [0, ∞) and 𝜌: 𝑋 × 𝑋 → ℝ+ defined by 𝜌(𝑥, 𝑦) = |𝑥 − 𝑦|𝑝, 𝑝 ≥ 1 then clearly (𝑀, 𝜌) is a 𝑏metric space with coefficient 2𝑝. now let 𝑇 be a self map of 𝑀 such that 𝑇𝑥 = 𝑥 2 and choose a sequence {𝑥𝑛}, 𝑥𝑛 ≠ 0 for any positive integer 𝑛, which converges to zero in metric in 𝑀 . we deduce that lim 𝑛→∞ 𝜌( 𝑥𝑛 , 𝑇𝑥𝑛 ) = lim 𝑛→∞ |𝑥𝑛 − 𝑇𝑥𝑛 | 𝑝 = lim 𝑛→∞ |𝑥𝑛 − 𝑥𝑛 2 | 𝑝 = lim 𝑛→∞ | 𝑥𝑛 2 | 𝑝 = 0. hence {𝑥𝑛 } is an asymptotically t-regular sequence in(𝑀, 𝜌). definition 2.5 [17] let (𝑀, 𝜌) be a 𝑏-metric space. a mappings 𝑇 of 𝑀 into itself is said to be asymptotically regular at a point 𝑥 in 𝑀 if lim 𝑛→∞ 𝜌(𝑇𝑛𝑥, 𝑇𝑛+1𝑥) = 0. example 2.3. let (𝑀, 𝜌) be a 𝑏-metric space as defined in example 2.2 and let 𝑇: 𝑀 → 𝑀 be such that 𝑇𝑥 = 𝑥 4 where 𝑥 ∈ 𝑀. then we have lim 𝑛→∞ 𝜌( 𝑇𝑛𝑥, 𝑇 𝑛+1𝑥) = lim 𝑛→∞ |𝑇𝑛𝑥 − 𝑇𝑛+1𝑥|𝑝 = lim 𝑛→∞ | 𝑥 4𝑛 − 𝑥 4𝑛+1 | 𝑝 = lim 𝑛→∞ | 3𝑥 4𝑛+1 | 𝑝 = 0. hence t is an asymptotically regular map at all points in m. 3. main results theorems 3.1. let (𝑀, 𝜌) be a complete 𝑏-metric space with the coefficient 𝑠 ≥ 1 and 𝑇 be a self mapping of 𝑀 satisfying the following inequality 𝜌(𝑇𝑥, 𝑇𝑦) ≤ 𝑎1𝜌(𝑥, 𝑇𝑥) + 𝑎2𝜌(𝑦, 𝑇𝑦) + 𝑎3𝜌(𝑥, 𝑇𝑦) + 𝑎4 𝜌(𝑦, 𝑇𝑥) + 𝑎5𝜌(𝑥, 𝑦), for all 𝑥, 𝑦 ∈ 𝑀, where 𝑎𝑖 ( 𝑖 = 1,2,3,4,5) are non-negative real numbers with 𝑚𝑎𝑥{(𝑎1𝑠 + 𝑎4𝑠 2), (𝑎3𝑠 3 + 𝑎4𝑠 2 + 𝑎5)} < 1 for 𝑠 ≥ 1. if there exists an asymptotically 𝑇-regular sequence in 𝑀, then 𝑇 has a unique fixed point. proof. let {𝑥𝑛 } be an asymptotically 𝑇-regular sequence in 𝑀. then for 𝑛, 𝑚 ∈ ℕ 𝑤𝑖𝑡ℎ 𝑚 ≥ 𝑛 , we have 𝜌(𝑥𝑛 , 𝑥𝑚 ) ≤ 𝑠[𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + 𝜌(𝑇𝑥𝑛 , 𝑥𝑚 )] mohammad s. khan and pankaj k. jhade 50 ≤ 𝑠[𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + 𝑠𝜌(𝑇𝑥𝑛 , 𝑇𝑥𝑚 ) + 𝑠𝜌(𝑇𝑥𝑚 , 𝑥𝑚 )] ≤ 𝑠 𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + 𝑠 2𝜌(𝑇𝑥𝑛 , 𝑇𝑥𝑚 ) + 𝑠 2𝜌(𝑇𝑥𝑚 , 𝑥𝑚 ) ≤ 𝑠 𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + 𝑠 2𝜌(𝑇𝑥𝑚 , 𝑥𝑚 ) + 𝑠 2[𝑎1𝜌(𝑥𝑛, 𝑇𝑥𝑛 ) + 𝑎2𝜌(𝑥𝑚 , 𝑇𝑥𝑚 ) +𝑎3 𝜌(𝑥𝑛, 𝑇𝑥𝑚 )+𝑎4𝜌(𝑥𝑚 , 𝑇𝑥𝑛 ) + 𝑎5𝜌(𝑥𝑛 , 𝑥𝑚 )] ≤ (𝑠 + 𝑎1𝑠 2 + 𝑎4𝑠 3)𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + (𝑠 2 + 𝑎2𝑠 2 + 𝑎3𝑠 3)𝜌(𝑥𝑚 , 𝑇𝑥𝑚 ) +(𝑎3𝑠 3 + 𝑎4 𝑠 3 + 𝑎5)𝜌(𝑥𝑛 , 𝑥𝑚 ). thus, we get 𝜌(𝑥𝑛 , 𝑥𝑚 ) ≤ { (𝑠+𝑎1𝑠 2+𝑎4𝑠 3) 1−(𝑎3𝑠 3+𝑎4𝑠 3+𝑎5) } 𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + { (𝑠2+𝑎2𝑠 2+𝑎3𝑠 3) 1−(𝑎3𝑠 3+𝑎4𝑠 3+𝑎5) } 𝜌(𝑥𝑚 , 𝑇𝑥𝑚 ). taking the limit as 𝑛 → ∞, we get lim 𝑛→∞ 𝜌( 𝑥𝑛 , 𝑥𝑚 ) = 0, which shows that {𝑥𝑛 } is a cauchy sequence. since 𝑀 is a complete 𝑏-metric space, the sequence {𝑥𝑛 } converges in 𝑀. so let lim 𝑛→∞ 𝑥𝑛 = 𝑧 for some 𝑧 ∈ 𝑀. now we show that 𝑧 is a fixed point of t. consider, 𝜌(𝑇𝑧, 𝑧) ≤ 𝑠[𝜌(𝑇𝑧, 𝑇𝑥𝑛 ) + 𝜌(𝑇𝑥𝑛 , 𝑧)] ≤ 𝑠𝜌(𝑇𝑧, 𝑇𝑥𝑛 ) + 𝑠 2𝜌(𝑇𝑥𝑛 , 𝑥𝑛 ) + 𝑠 2𝜌(𝑥𝑛 , 𝑧). ≤ 𝑠[𝑎1𝜌(𝑧, 𝑇𝑧) + 𝑎2𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + 𝑎3𝜌(𝑧, 𝑇𝑥𝑛 ) + 𝑎4𝜌(𝑥𝑛 , 𝑇𝑧) + 𝑎5𝜌(𝑧, 𝑥𝑛 )] + 𝑠2𝜌(𝑇𝑥𝑛 , 𝑥𝑛) + 𝑠 2𝜌(𝑥𝑛 , 𝑧) ≤ 𝑎1𝑠𝜌(𝑧, 𝑇𝑧) + 𝑎2 𝑠𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + 𝑎3𝑠 2𝜌(𝑧, 𝑥𝑛 ) +𝑎3𝑠 2𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + 𝑠 2𝑎4𝜌(𝑥𝑛 , 𝑧) + 𝑠 2𝑎4𝜌(𝑧, 𝑇𝑧) +𝑎5𝑠𝜌(𝑧, 𝑥𝑛 ) + 𝑠 2𝜌(𝑇𝑥𝑛 , 𝑥𝑛 ) + 𝑠 2𝜌(𝑥𝑛 , 𝑧). therefore, (1 − 𝑎1𝑠 − 𝑠 2𝑎4)𝜌(𝑇𝑧, 𝑧) ≤ (𝑠 2 + 𝑎2𝑠 + 𝑎3𝑠 2)𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) +(𝑠2 + 𝑎3𝑠 2 + 𝑎4𝑠 2 + 𝑎5𝑠)𝜌(𝑥𝑛 , 𝑧), which implies that 𝜌(𝑇𝑧, 𝑧) ≤ { (𝑠2+𝑎2𝑠+𝑎3𝑠 2) (1−𝑎1𝑠−𝑠 2𝑎4) } 𝜌(𝑥𝑛 , 𝑇𝑥𝑛 ) + { (𝑠2+𝑎3𝑠 2+𝑎4𝑠 2+𝑎5𝑠) (1−𝑎1𝑠−𝑠 2𝑎4) } 𝜌(𝑥𝑛 , 𝑧). since t is asymptotically t-regular, letting limit 𝑛 → ∞ we get 𝜌(𝑇𝑧, 𝑧) = 0 𝑖. 𝑒. 𝑇𝑧 = 𝑧. hence z is a fixed point of t. uniqueness: let 𝑢 be another fixed point such that 𝑧 ≠ 𝑢. then, 𝜌(𝑧, 𝑢) = 𝜌(𝑇𝑧, 𝑇𝑢) ≤ 𝑎1𝜌(𝑧, 𝑇𝑧) + 𝑎2𝜌(𝑢, 𝑇𝑢) + 𝑎3𝜌(𝑧, 𝑇𝑢) + 𝑎4𝜌(𝑢, 𝑇𝑧) + 𝑎5𝜌(𝑧, 𝑢). from the last inequality, we have (1 − 𝑎3 − 𝑎4 − 𝑎5) 𝜌(𝑧, 𝑢) = 0. since 𝑎3 + 𝑎4 + 𝑎5 < 1, therefore 𝑧 = 𝑢,. next, we discuss the problem of the existence of a fixed point of an operator without using any contractive condition. we shall first consider the situation in a metric space. theorem 3.2. let (𝑀, 𝜌) be a metric space, and 𝑇 be a continuous self-mapping on 𝑀. if there exists an asymptotically 𝑇-regular sequence {𝑥𝑛 } such that lim 𝑛→∞ 𝑥𝑛 = 𝑧, then 𝑧 is a fixed point of 𝑇. proof. let us consider the inequality 𝜌(𝑇𝑧, 𝑧) ≤ [𝜌(𝑇𝑧, 𝑇𝑥𝑛 ) + 𝜌(𝑇𝑥𝑛 , 𝑧)] ≤ 𝜌(𝑇𝑧, 𝑇𝑥𝑛 ) + 𝜌(𝑇𝑥𝑛 , 𝑥𝑛) + 𝜌(𝑥𝑛 , 𝑧). taking the limit as 𝑛 → ∞, we obtain 𝜌(𝑇𝑧, 𝑧) ≤ 0 giving thereby 𝑇𝑧 = 𝑧. now, let us see the similar situation in a b-metric space. theorem 3.3. let (𝑀, 𝜌) be a 𝑏-metric space with the coefficient 𝑠 ≥ 1 , and 𝑇 be a self-mapping of 𝑀. if there exists an asymptotically 𝑇-regular sequence {𝑥𝑛 } with lim 𝑛→∞ 𝑥𝑛 = 𝑧, then 𝑧 is not necessarily a fixed point. proof. using the triangle inequality twice in a b-metric space, we obtain 𝜌(𝑇𝑧, 𝑧) ≤ 𝑠[𝜌(𝑇𝑧, 𝑇𝑥𝑛 ) + 𝜌(𝑇𝑥𝑛 , 𝑧)] ≤ 𝑠 𝜌(𝑇𝑧, 𝑇𝑥𝑛 ) + 𝑠 2𝜌(𝑇𝑥𝑛 , 𝑥𝑛 ) + 𝑠 2𝜌(𝑥𝑛 , 𝑧). taking the limit as 𝑛 → ∞, we obtain (1 − 𝑠2)𝜌(𝑇𝑧, 𝑧) ≤ 0 , which is equivalent to the inequality (𝑠2 − 1)𝜌(𝑇𝑧, 𝑧) ≥ 0, which provides no definite information. thus z may or may not be a fixed point of t. theorems on fixed points for asymptotically regular sequence 51 remarks 3.1. 1. even if t is continuous in theorem 3.3, we cannot get any information from it about the existence of a/ the fixed point of t. 2. from theorem 3.2 and theorem 3.3, we notice yet another difference between the behavior of the two types of metrics defined on a set. theorem 3.4. let (𝑀, 𝜌) be a complete 𝑏-metric space with the coefficient 𝑠 ≥ 1 and 𝑇 be a self mapping of 𝑀 satisfying the inequality 𝜌(𝑇𝑥, 𝑇𝑦) ≤ 𝑎1𝜌(𝑥, 𝑇𝑥) + 𝑎2𝜌(𝑦, 𝑇𝑦) + 𝑎3𝜌(𝑥, 𝑇𝑦) + 𝑎4𝜌(𝑦, 𝑇𝑥) + 𝑎5𝜌(𝑥, 𝑦), for all 𝑥, 𝑦 ∈ 𝑀, where 𝑎𝑖 ( 𝑖 = 1,2,3,4,5) are non-negative real numbers with 𝑚𝑎𝑥{(𝑎1𝑠 + 𝑎4𝑠 2), (𝑎3 + 𝑎4 + 𝑎5)} < 1 for 𝑠 ≥ 1. if 𝑇 is asymptotically regular at some point 𝑥0 ∈ 𝑀, then there exists a unique fixed point of 𝑇. proof. let 𝑇 be an asymptotically regular mapping at 𝑥0 ∈ 𝑀. considering the sequence {𝑇 𝑛 𝑥0} and 𝑚, 𝑛 ∈ ℕ, we have 𝜌(𝑇𝑚 𝑥0, 𝑇 𝑛 𝑥0) ≤ 𝑎1𝜌(𝑇 𝑚−1𝑥0, 𝑇 𝑚 𝑥0) + 𝑎2𝜌(𝑇 𝑛−1𝑥0, 𝑇 𝑛𝑥0) + 𝑎3𝜌(𝑇 𝑚−1𝑥0, 𝑇 𝑛𝑥0) +𝑎4𝜌(𝑇 𝑛−1𝑥0, 𝑇 𝑚 𝑥0) + 𝑎5𝜌(𝑇 𝑚−1𝑥0, 𝑇 𝑛−1𝑥0) ≤ 𝑎1𝜌(𝑇 𝑚−1𝑥0, 𝑇 𝑚 𝑥0) + 𝑎2𝜌(𝑇 𝑛−1𝑥0, 𝑇 𝑛𝑥0) +𝑎3𝑠𝜌(𝑇 𝑚−1𝑥0, 𝑇 𝑚 𝑥0) + 𝑎3𝑠𝜌(𝑇 𝑚 𝑥0, 𝑇 𝑛𝑥0) +𝑎4𝑠𝜌(𝑇 𝑛−1𝑥0, 𝑇 𝑛𝑥0) + +𝑎4𝜌𝑠(𝑇 𝑛 𝑥0, 𝑇 𝑚 𝑥0) +𝑎5𝑠𝜌(𝑇 𝑚−1𝑥0, 𝑇 𝑚 𝑥0) + 𝑎5𝑠 2𝜌(𝑇𝑚 𝑥0, 𝑇 𝑛𝑥0) + 𝑎5𝑠 2𝜌(𝑇𝑛𝑥0, 𝑇 𝑛−1𝑥0), which implies that 𝜌(𝑇𝑚 𝑥0, 𝑇 𝑛𝑥0) ≤ { 𝑎1+𝑎3𝑠+𝑎5𝑠 1−(𝑎3𝑠+𝑎4𝑠+𝑎5𝑠 2) } 𝜌(𝑇𝑚−1𝑥0, 𝑇 𝑚 𝑥0) + { 𝑎2+𝑎4𝑠+𝑎5𝑠 2 1−(𝑎3𝑠+𝑎4𝑠+𝑎5𝑠 2) } 𝜌(𝑇𝑛−1𝑥0, 𝑇 𝑛𝑥0) . since 𝑇 is asymptotically regular, as 𝑚, 𝑛 → ∞, the above inequality yields lim 𝑚,𝑛→∞ 𝜌(𝑇𝑚 𝑥0, 𝑇 𝑛 𝑥0) = 0 . this shows that {𝑇𝑛𝑥0} is a cauchy sequence. since 𝑀 is complete, lim 𝑛→∞ 𝑇𝑛 𝑥0 = 0 = 𝑧 for some 𝑧 ∈ 𝑀. next we will show that 𝑧 is a fixed point of 𝑇. consider, 𝜌(𝑇𝑧, 𝑧) ≤ 𝑠𝜌(𝑇𝑧, 𝑇 𝑛𝑥0) + 𝑠𝜌(𝑇 𝑛𝑥0, 𝑧) ≤ 𝑎1𝑠𝜌(𝑧, 𝑇𝑧) + 𝑎2𝑠𝜌(𝑇 𝑛−1𝑥0, 𝑇 𝑛 𝑥0) + 𝑎3𝑠𝜌(𝑧, 𝑇 𝑛𝑥0) +𝑎4𝑠𝜌(𝑇 𝑛−1𝑥0, 𝑇𝑧) + 𝑎5𝑠𝜌(𝑧, 𝑇 𝑛−1𝑥0) + 𝑠𝜌(𝑇 𝑛𝑥0, 𝑧) ≤ 𝑎1𝑠𝜌(𝑧, 𝑇𝑧) + 𝑎2𝑠𝜌(𝑇 𝑛−1𝑥0, 𝑇 𝑛 𝑥0) + 𝑎3𝑠𝜌(𝑧, 𝑇 𝑛𝑥0) +𝑎4𝑠 2𝜌(𝑇 𝑛−1𝑥0, 𝑇 𝑛𝑥0) + 𝑎4𝑠 2𝜌(𝑇𝑛𝑥0, 𝑇𝑧) +𝑎5𝑠 2𝜌(𝑧, 𝑇𝑛 𝑥0) + 𝑎5𝑠 2𝜌(𝑇𝑛 𝑥0, 𝑇 𝑛−1𝑥0) + 𝑠𝜌(𝑇 𝑛𝑥0, 𝑧). letting the limit be 𝑛 → ∞ and since {𝑇𝑛−1𝑥0} is a subsequence of {𝑇 𝑛 𝑥0} , we obtain 𝜌(𝑇𝑧, 𝑧) ≤ 𝑎1𝑠𝜌(𝑧, 𝑇𝑧) + 𝑎4𝑠 2𝜌(𝑧, 𝑇𝑧) which gives 𝜌(𝑇𝑧, 𝑧) = 0 i.e. 𝑇𝑧 = 𝑧. hence 𝑧 is a fixed point of 𝑇. the uniqueness of the fixed point follows from theorem 3.1. theorem 3.5. let (𝑀, 𝜌) be a complete 𝑏-metric space with coefficient 𝑠 ≥ 1 and 𝑇 be a self mapping of 𝑀 satisfying the inequality 𝜌(𝑇𝑥, 𝑇𝑦) ≤ 𝑎1𝜌(𝑥, 𝑇𝑥) + 𝑎2𝜌(𝑦, 𝑇𝑦) + 𝑎3𝜌(𝑥, 𝑇𝑦) + 𝑎4𝜌(𝑦, 𝑇𝑥) + 𝑎5𝜌(𝑥, 𝑦), for all 𝑥, 𝑦 ∈ 𝑀, where 𝑎𝑖 ( 𝑖 = 1,2,3,4,5) are non-negative real numbers with 𝑚𝑎𝑥{(𝑎2 + 𝑎3)𝑠 2, (𝑎3 + 𝑎4𝑠 + 𝑎5𝑠)} < 1 for 𝑠 ≥ 1. if 𝑇 is asymptotically regular at some point 𝑥 ∈ 𝑀 and the sequence {𝑇𝑛𝑥} of iterates has a subsequence {𝑇𝑛𝑘 𝑥} converging to a point 𝑧 of 𝑀, then 𝑧 is a unique fixed point of 𝑇 and {𝑇 𝑛𝑥} also converges to 𝑧. proof. let lim 𝑘→∞ 𝑇𝑛𝑘 𝑥 = 𝑧, then 𝜌(𝑧, 𝑇𝑧) ≤ 𝑠𝜌(𝑧, 𝑇𝑛𝑘 𝑥) + 𝑠2𝜌(𝑇𝑛𝑘 𝑥, 𝑇𝑛𝑘+1𝑥) + 𝑠2𝜌(𝑇𝑛𝑘+1𝑥, 𝑇𝑧) ≤ 𝑠𝜌(𝑧, 𝑇𝑛𝑘 𝑥) + 𝑠2𝜌(𝑇𝑛𝑘 𝑥, 𝑇𝑛𝑘+1𝑥) + 𝑎1𝑠 2𝜌(𝑇𝑛𝑘 𝑥, 𝑇𝑛𝑘+1𝑥) + 𝑎2𝑠 2𝜌(𝑧, 𝑇𝑧) +𝑎3𝑠 2𝜌(𝑇 𝑛𝑘 𝑥, 𝑇𝑧) + 𝑎4𝑠 2𝜌(𝑧, 𝑇𝑛𝑘+1𝑥) + 𝑎5𝑠 2𝜌(𝑇𝑛𝑘 𝑥, 𝑧). letting 𝑘 → ∞, we get 𝜌(𝑧, 𝑇𝑧) ≤ (𝑎2𝑠 2 + 𝑎3𝑠 2)𝜌(𝑧, 𝑇𝑧) which gives 𝑧 is a fixed point of 𝑇. now, 𝜌(𝑧, 𝑇𝑛 𝑥) = 𝜌(𝑇𝑧, 𝑇 𝑛𝑥) ≤ 𝑎1𝜌(𝑧, 𝑇𝑧) + 𝑎2𝜌(𝑇 𝑛−1𝑥, 𝑇𝑛𝑥) + 𝑎3𝜌(𝑧, 𝑇 𝑛𝑥) + 𝑎4𝜌(𝑇 𝑛−1𝑥, 𝑇𝑧) + 𝑎5𝜌(𝑧, 𝑇 𝑛−1𝑥) ≤ 𝑎1𝜌(𝑧, 𝑇𝑧) + 𝑎2𝜌(𝑇 𝑛−1𝑥, 𝑇𝑛𝑥) + 𝑎3𝜌(𝑧, 𝑇 𝑛𝑥) +𝑎4𝑠𝜌(𝑇 𝑛−1𝑥, 𝑇𝑛 𝑥) + 𝑎4𝑠𝜌(𝑇 𝑛 𝑥, 𝑇𝑧) +𝑎5𝑠𝜌(𝑧, 𝑇 𝑛𝑥) + 𝑎5𝑠𝜌(𝑇 𝑛 𝑥, 𝑇𝑛−1𝑥) which implies that (1 − 𝑎3 − 𝑎4𝑠 − 𝑎5𝑠)𝜌(𝑧, 𝑇 𝑛𝑥) ≤ (𝑎2 + 𝑎4𝑠 + 𝑎5𝑠)𝜌(𝑇 𝑛−1𝑥, 𝑇𝑛𝑥). mohammad s. khan and pankaj k. jhade 52 since 𝑇 is asymptotically regular at 𝑥 ∈ 𝑀 and using the fact that 𝑚𝑎𝑥{(𝑎2 + 𝑎3)𝑠 2, (𝑎3 + 𝑎4𝑠 + 𝑎5𝑠)} < 1 for 𝑠 ≥ 1 implies that the sequence {𝑇𝑛 𝑥} converges to 𝑧 in 𝑀. this completes the proof. example 3.1. let 𝑀 = ℝ and 𝜌: 𝑀 × 𝑀 → ℝ + be defined by 𝜌(𝑥, 𝑦) = |𝑥 − 𝑦|𝑝, where 𝑝 > 1. then (𝑀, 𝜌) is a 𝑏metric space. define a self map 𝑇 on 𝑀 as follows 𝑇𝑥 = 𝑥 2 for all 𝑥 ∈ 𝑀. clearly 𝑇 is asymptotically regular for all 𝑥 ∈ 𝑀. if we take 𝑎1 = 𝑎2 = 𝑎3 = 𝑎4 = 0 and 𝑎5 = 1 2𝑝 , then the contractive condition used here holds and 0 is the unique fixed point of 𝑇. remark 3.2. the asymptotic regularity of the mapping 𝑇 satisfies the hardy-roger’s contraction condition. it is actually a consequence of ∑ 𝑎𝑖 < 1 5 𝑖=1 . thus theorem 3.3 and theorem 3.4 extend results due to hardy-roger [1] in 𝑏metric space. it is also worth mentioning that our condition on control constants says that ∑ 𝑎𝑖 5 𝑖=1 may exceed 1. 4. conclusion it has been demonstrated that one can use asymptotically regular sequences rather than sequences of iterates to 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matematica-informatica, xlviii, 2010, 3, 125-137. 13. mehmet kir and hukmi kiziltunc, on some well-known fixed point theorems in b-metric spaces, turkish journal of analysis and number theory, 2013, 1( 1), 13-16. 14. memudu o. olatinwo and christopher o. imoru, a generalization of some results on multi-valued weakly picard mappings in b-metric spaces, fasciculi mathematici, 2008, 40, 45-56. 15. mishra, p.k. sachdeva, s. and banerjee, s.n., some fixed point theorems in b-metric spaces, turkish journal of analysis and number theory, 2014, 2(1), 19-22. 16. heinz w. engl, weak convergence of asymptotically regular sequences for nonexpansive mappings and connection with certain chebyshef-centers, nonlinear analysis: theory, methods and applications, 1977, 1(5), 495-501. 17. browder, f.e. and petryshyn, w.v., the solution by iteration of nonlinear functional equations in banach spaces, bulletin of american mathematical society, 1966, 72, 571-575. received 9 november 2015 theorems on fixed points for asymptotically regular sequence 53 accepted 5 january 2017 squ journal for science, 2016, 21(2), 89-101 © 2016 sultan qaboos university 89 computational study of geometry, solvation free energy, dipole moment, polarizability, hyperpolarizability and molecular properties of 2-methylimidazole mohammad firoz khan1, ridwan bin rashid2, shahidul m. islam3* and mohammad a. rashid4* 1computational laboratory, department of pharmacy, state university of bangladesh, dhaka 1205, bangladesh; 2department of microbiology, university of dhaka, dhaka-1000, bangladesh; 3department of chemistry, college of science, sultan qaboos university, p.o. box 33, alkhoud, pc 123, muscat, sultanate of oman; 4department of pharmaceutical chemistry, university of dhaka, dhaka1000, bangladesh. *email: shahidul321@gmail.com; rashidma@du.ac.bd abstract: ab initio calculations were carried out to study the geometry, solvation free energy, dipole moment, molecular electrostatic potential (mesp), mulliken and natural charge distribution, polarizability, hyperpolarizability, natural bond orbital (nbo) energetic and different molecular properties like global reactivity descriptors (chemical hardness, softness, chemical potential, electronegativity, electrophilicity index) of 2methylimidazole. b3lyp/6-31g(d,p) level of theory was used to optimize the structure both in the gas phase and in solution. the solvation free energy, dipole moment and molecular properties were calculated by applying the solvation model on density (smd) in four solvent systems, namely water, dimethylsulfoxide (dmso), n-octanol and chloroform. the computed bond distances, bond angles and dihedral angles of 2-methylimidazole agreed reasonably well with the experimental data except for c(2)-n(1), c(4)-c(5) and n(1)-h(7) bond lengths and n(1)c(5)-c(4) bond angle. the solvation free energy, dipole moment, polarizability, first order hyperpolarizability, chemical potential, electronegativity and electrophilicity index of 2-methylimidazole increased on going from nonpolar to polar solvents. chemical hardness also increased with increasing polarity of the solvent and the opposite relation was found in the case of softness. these results provide better understanding of the stability and reactivity of 2-methylimidazole in different solvent systems. keywords: 2-methylimidazole; solvation free energy; dipole moment;polarizability; solvation model. ميثيل ايميدازول-2الدراسة النظرية للتركيب الهندسي، والطاقة الحرة لإلذابة، والعزم القطبي، واإلستقطاب، والخصائص الجزيئية لـ محمد فيروز خان1، رضوان بن راشد2، شهيدول م. إسالم3* ومحمد أ. راشد4 تم تنفيذها لدراسة التركيب الهندسي والطاقة الحرة لإلذابة والعزم القطبي والطاقة الكهروستاتيكية الجزيئية وتوزيع مليكان حسابات آب انيشيو :ستخلصم لليونة، الكمونوالطبيعي للشحنات واإلستقطاب وطاقة الربط المداري والخصائص الجزيئية المختلفة كاألوصاف التفاعلية الكونية ) الصالبة الكيميائية، ا استخدم لتحسين التركيب في b3lyp/6-31g(d,p). المستوى النظري ميثيل ايميدازول -2إلى الكيميائي، السالبية الكهربائية، مؤشر األلفة الكهربائية( (smd)الكثافة الحالة الغازية وفي المحلول. الطاقة الحرة لإلماهة، والعزم القطبي، والخصائص الجزيئية تم حسابها من خالل تطبيق نموذج اإلذابة على طول الروابط الكيميائية والزوايا المحسوبة ، واألوكتانول، والكلورفورم.(dmso)في نظام من أربعة مذيبات وهي الماء، وثنائي ميثيل السلفوكسيد والزاوية في n(1)-h(7)و c(2)-n(1), c(4)-c(5)ميثيل ايميدازول تتوافق بشكل معقول مع النتائج التجريبية ماعدا لطول الرابطة في -2للمركب n(1)-c(5)-c(4)،2والسالبية الكهربائية، ومؤشر األلفة الكهربائية للجزيء . الطاقة الحرة لإلذابة، والعزم القطبي، واإلستقطاب، والكمون الكيميائيلنسبة للليونة. نتائج هذه ميثيل ايميدازول يزيد كلما اتجهنا من أقل المذيبات قطبية إلى أكثرها. الصالبة الكيميائية أيضا تزيد بزيادة قطبية المذيب والعكس با ميثيل ايميدازول في أنظمة مختلفة المذيبات. -2للجزيء الدراسة تساعد في فهم مدى الثبات والقدرة التفاعلية ميثيل ايميدازول، الطاقة الحرة لإلذابة، العزم القطبي، اإلستقطاب، نموذج اإلذابة. -2: كلمات مفتاحية mailto:shahidul321@gmail.com mailto:rashidma@du.ac.bd shahidul m. islam et al 90 1. introduction he 2-methylimidazole (figure 1) is a nitrogen-containing heterocyclic organic compound. it is structurally related to imidazole with the chemical formula c4h6n2. it is a solid substance with high solubility in polar solvents. the 2-methylimidazole is commonly used as a chemical intermediate in the production of pharmaceuticals, dyes and pigments, photographic and photothermographic chemicals, agricultural chemicals, and rubber [1]. it is formed by the ammoniation of sugars and considered a by-product of food and forage colored with caramel. the n-substituted derivatives of imidazole and of the 2-methylimidazole exhibit a wide range of pharmacological properties, such as antiparasitic [2], antifungal [3], and antimicrobial activities [4], which has made it a subject of interest to organic and medicinal chemists [5]. this compound was explored against e. coli, s. aureus and p. aureginosa for antibacterial activity [6]. because of its wide presence and lack of carcinogenic information, the toxicity studies of this compound were carried out in rats and mice [7-9]. the 2-methylimidazole has also been detected in mainstream and side-stream cigarette smoke as a result of pyrolysis [10]. the length of the alkyl chain on the imidazole ring is very important for biological activity, i.e. 1-alkylimidazoles require a hydrocarbon chain of 12 carbons to exhibit antifungal and cytotoxic activity and 10 carbons for inhibition of microsomal oxidation [3,6,11]. the thermochemical investigation has revealed that the standard molar enthalpies of formation for crystalline and gas phase of 2-methylimidazole are 1.4 and 89.8 kj/mol, respectively, and standard molar enthalpies of sublimation is 88.4 kj/mol [12]. figure 1. structure of 2-methyimidazole. fewer computational and theoretical studies of 2-methylimidazole have previously been reported. yu et al. reported the experimental and theoretical study of interactions between the diperoxovanadate complexes and histidinelike ligands, namely imidazole, 2-methylimidazole, carnosine, 4-methylimidazole and histidine [13]. the reactivity (coordination capability) of the ligands were found in the order of imidazole >2-methylimidazole>carnosine ≈ 4methylimidazole >histidine. theoretical study of the formation of complexes between co2 and imidazole derivatives has also been reported [14]. the most stable complex between 2-methylimidazole and co2 is formed due to the charge transfer from the ring of 2-methylimidazole to the co2. the variation in solvent polarity and the type of solute-solvent interaction(s) can affect the calculated geometry, dipole moment, polarizability, hyperpolarizability and other molecular properties [15,16] due to variable interactions with the frontier molecular orbitals [15,17], and hence, can influence the stability and reactivity of the molecule. density functional theory (dft) calculations provide a greater detail of molecular characteristics and interactions which lead to a good understanding of molecular properties [18]. in the present investigation, computational studies have been carried out to better understand geometry, solvation free energy, dipole moment, molecular electrostatic potential (mesp), charge distribution, polarizability, hyperpolarizability and global reactivity descriptor properties such as the chemical hardness, softness, chemical potential, electronegativity, electrophilicityindex of 2-methylimidazole in different solvent systems, which could potentially be helpful for the development of pharmaceutical and (bio)chemical products. 2. methodology computational methods all calculations were conducted with the gaussian 09 software package [19]. from previous work [20,21], it was found that geometries, solvation free energies, dipole moment and molecular properties of similar systems obtained using the b3lyp/6-31g(d,p) showed better agreement with experiments. therefore, methylimidazole geometries were optimized at the b3lyp electronic structure method [22-24] using the 6-31g(d,p) basis set. frequencies were calculated to ensure the absence of imaginary frequencies in the lowest energy state. the solvation model on density t n h n h3c computational study of geometry 91 (smd) [14] as implemented in gaussian 09 was used for all calculations involving the solvents, water, dmso, noctanol, and chloroform. the smd model is highly parameterized, uses the original polarizable continuum model (pcm), and the charge density of the solute molecule interacts with the dielectric medium of the solvent through surface tension at the solute-solvent boundary. all calculations involving solvation were performed using the optimized solution-phase structures. the free energy of solvation (∆g) is calculated from the difference in gas phase and solvent phase free energies of a molecule as represented below, ∆g = g(sol) g(gas) where g(gas) is the gas phase free energy which is obtained as follows: g(gas) = sum of electronic and thermal free energies (1) + thermal correction to gibbs free energy (2). (1) and (2) are readily obtained from the gaussian output file. similarly, g(sol) is also calculated from a solvent phase simulation of the same molecule. 3. results and discussion equilibrium geometries the optimized geometrical parameters such as bond lengths, bond angles, and dihedral angles of 2-methyimidazole obtained by the b3lyp/6-31g (d,p) are listed in tables 1 and 2. the computed bond distances and bond angles were also compared with the x-ray crystallographic data [5]. from the tables, it has been found that the calculated bond distances, bond angles and dihedral angles agreed well with the experimental data, except for the c(2)-n(1), c(4)-c(5) and n(1)-h(7) bond lengths and the n(1)-c(5)-c(4) bond angle. the mean absolute deviation (mad) is used to calculate the differences between the computed and experimental geometrical parameters and the mad values for bond distances, bond angles and dihedral angles are 0.030 å, 0.6˚ and 0.4ᵒ, respectively. table 1. theoretical (gas phase) and experimental (x-ray diffraction) bond distances (å) of 2-methylimidazole. assignment theoretical bond distances (å) experimental [5] bond distances (å) c(2)-n(1) 1.372 1.347 c(2)-n(3) 1.319 1.327 c(4)-c(5) 1.370 1.356 c(4)-n(3) 1.379 1.384 c(5)-n(1) 1.382 1.370 c(2)-c(6) 1.494 1.487 c(4)-h(8) 1.081 c(5)-h(9) 1.079 n(1)-h(7) 1.008 0.870 c(6)-h(10) 1.096 c(6)-h(11) 1.096 c(6)-h(12) 1.091 mad 0.030 shahidul m. islam et al 92 table 2. theoretical (gas phase) and experimental (x-ray diffraction) bond angle (ᵒ) and dihedral angles (ᵒ) of 2methylimidazole. assignment theoretical bond angle (ᵒ) experimental [5] bond angle (ᵒ) assignment theoretical dihedral angles (ᵒ) experimental [5] dihedral angles (ᵒ) c(2)-n(1)-h(7) 126.3 c(2)-n(1)-c(5)-c(4) 0.0 0.1 c(2)-n(1)-c(5) 107.7 107.4 c(2)-n(1)-c(5)-h(9) -180.0 h(7)-n(1)-c(5) 126.0 h(7)-n(1)-c(5)-h(9) 0.0 n(1)-c(5)-h(9) 122.2 h(7)-n(1)-c(5)-c(4) 180.0 n(1)-c(5)-c(4) 104.9 106.2 n(1)-c(5)-c(4)-n(3) 0.0 0.3 n(1)-c(2)-c(6) 123.3 123.0 n(1)-c(5)-c(4)-h(8) 180.0 h(9)-c(5)-c(4) 132.8 h(9)-c(5)-c(4)-h(8) -0.1 c(5)-c(4)-h(8) 127.9 h(9)-c(5)-c(4)-n(3) 180.0 c(5)-c(4)-n(3) 110.8 109.9 c(5)-c(4)-n(3)-c(2) 0.0 0.4 h(8)-c(4)-n(3) 121.4 h(8)-c(4)-n(3)-c(2) -180.0 c(4)-n(3)-c(2) 105.8 105.0 c(4)-n(3)-c(2)-n(1) 0.0 -0.3 n(3)-c(2)-n(1) 110.8 111.5 c(4)-n(3)-c(2)-c(6) 180.0 179.4 n(3)-c(2)-c(6) 125.8 125.5 c(5)-n(1)-c(2)-c(6) -180.0 -179.2 c(2)-c(6)-h(10) 112.0 n(3)-c(2)-n(1)-c(5) 0.0 0.0 c(2)-c(6)-h(11) 112.0 n(3)-c(2)-n(1)-h(7) -180.0 c(2)-c(6)-h(12) 108.3 n(3)-c(2)-c(6)h(10) 119.4 h(10)-c(6)h(11) 107.7 n(3)-c(2)-c(6)h(11) -119.5 h(10)-c(6)h(12) 108.3 n(3)-c(2)-c(6)h(12) -0.1 h(11)-c(6)h(12) 108.3 h(7)-n(1)-c(2)-c(6) 0.0 mad 0.6 n(1)-c(2)-c(6)h(10) -60.6 n(1)-c(2)-c(6)h(11) 60.5 n(1)-c(2)-c(6)h(12) 179.9 mad 0.4 solvation free energy the most important properties of a chemical system (solute) with surrounding solvent can best be described by means of free energy variation [25]. the solvation free energies of 2-methylimidazole calculated with the smd model [26] are summarized in table 3. the solvation energies of methylimidazole in water, n-octanol, chloroform and dmso are -33.36 kj/mol, -33.76 kj/mol, -36.01 kj/mol and -38.09 kj/mol, respectively. the highest solvation free energy is found in polar aprotic solvent (dmso) followed by nonpolar (chloroform) and polar protic solvents (n-octanol and water). therefore, the hydrogen bond plays an important role in the solvation of 2-methylimidazole. dipole moment the dipole moment of 2-methylimidazole in different solvents is found to be higher than that of the gas phase. table 4 presents the dipole moments computed in the gas phase and different solvents (water, dmso, n-octanol and chloroform) at the b3lyp/6-31g(d,p) using smd solvation model. the dipole moments are 3.6d, 4.6d, 4.8d, 5.0d, and 5.1d in the gas phase, chloroform, n-octanol, dmso and water, respectively. therefore, there is a gradual increase in dipole moment on going from a lower to higher dielectric constant of the solvent. in other words, the dipole moment increases with the increasing polarity of the solvent (figure 2). computational study of geometry 93 table 3.solvation free energy (kj/mol) of 2-methylimidazole in different solvents with smd. medium (dielectric constant) solvation free energy (kj/mol) water (78.3) -33.36 dmso (46.8) -38.09 n-octanol (9.9) -33.76 chloroform (4.7) -36.01 table 4. dipole moment (debye, (d)) of 2-methylimidazole in gas phase and in different solvents using smd. medium (dielectric constant) dipole moment (d) gas 3.6 water (78.3) 5.1 dmso (46.8) 5.0 n-octanol (9.9) 4.8 chloroform (4.7) 4.6 figure 2. effect of solvent polarity on dipole moment (d) of 2-methylimidazole. 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 chloroform (4.7) n-octanol (9.9) dmso (46.8) water (78.3) d ip o le m o m e n t (d ) solvents (dielectric constant) shahidul m. islam et al 94 figure 3. electrostatic potential contour of 2-methylimidazole. molecular electrostatic potential (mesp) the molecular electrostatic potential (mesp) represents the net electrostatic effect of a molecule which is generated from the total charge distribution in the molecule. the mesp correlates very well with the partial charges, electronegativity, dipole moments and chemical reactivity of the molecule [27-29]. in the case of chemical reactivity, the region of the molecule susceptible to electrophilic or nucleophilic attack can be identified by the total electron density surface mapped with the electrostatic potential. the mesp contour map of 2-methyimidazole calculated at the b3lyp/6-31g(d,p) is shown in figure 3. the red (negative) and blue (positive) color regions in the mesp surface represent the regions susceptible to the attack of electrophiles and nucleophiles, respectively. the map reveals that the most possible sites for nucleophilic attack are c2 and h7 and electrophilic attack are n1 and c4. mulliken and natural population analysis the mulliken population analysis (mpa) and natural population analysis (npa) show the simplest picture of charge distribution. the mulliken and natural charges present net atomic charges in the molecule; while electrostatic potentials are generated by the electric field of internal charge distribution. thus, in the reactivity studies, population analysis (mpa or npa) and mesp are complementary tools, and correlation between the schemes is expected [30]. in this study, both mpa and npa have been carried out to clearly understand the charge distribution among the atoms in 2-methylimidazole. npa is less dependent on the choice of basis set compared to the original mpa. atomic charges obtained from mpa and npa are found to be consistent with each other (table 5). however, according to mpa, among all the carbon atoms only c(6) has negative charge, while in the case of npa the c(6) along with c(4) and c(5) possess negative charges. the presence of two nitrogen atoms n(1) and n(3) imposes large positive charges on the c(2) atom. the mpa and npa show that all the hydrogen and nitrogen atoms have positive and negative charges, respectively. among all the h atoms, the h(7) possesses the highest positive charge. this shows that the charge distribution and the mesp information are concordant. polarizability and first order hyperpolarizability polarizability is the measure of distortion of a molecule in an electric field. it is a tensor and can be represented in a 3 × 3 real symmetric matrix i.e. the off-diagonal elements are equal. the polarizability (α) was calculated using the following equation: 𝛼 = 1 3 (𝛼𝑥𝑥 + 𝛼𝑦𝑦 + 𝛼𝑧𝑧 ) (1) the quantities αxx, αyy and αzz are known as the principal values of the polarizability tensor. this property measures the strength of molecular interactions (e.g., long-range intermolecular induction, dispersion forces, etc.), the cross sections of different scattering and collision processes, and the optical properties of a system [17]. the calculated polarizability of 2-methylimidazole in different solvents is presented in table 6, which shows that polarizability (αtot) of 2methylimidazole in these solvents ranged from 60.81 to 66.20 a.u. the plot of polarizability vs. solvent is shown in figure 4. it is clear from the figure that the polarizability gradually increases on going from lower to higher dielectric constant. computational study of geometry 95 table 5. atomic charges of 2-methylimidazole obtained from mulliken population analysis (mpa) and natural population analysis (npa). atom b3lyp/6-31g(d,p) mpa npa n(1) -0.517 -0.579 c(2) 0.451 0.378 n(3) -0.474 -0.502 c(4) 0.022 -0.104 c(5) 0.064 -0.119 c(6) -0.384 -0.735 h(7) 0.260 0.435 h(8) 0.085 0.232 h(9) 0.103 0.236 h(10) 0.120 0.244 h(11) 0.120 0.244 h(12) 0.150 0.271 the first order hyperpolarizability (β) is the measure of the nonlinear optical activity which can be of different types such as βvec (β vector), β|| (β parallel) and βtot (β total). it is a third rank tensor that can be described by a 3 × 3 × 3 matrix. the kleinman symmetry enables the reduction of the 27 components of 3d matrix into 10 components [31]. gaussian provides 10 components of this matrix as βxxx, βyxx, βxyy, βyyy, βxxz, βxyz, βyyz, βxxz, βyzz, βzzz, respectively, from which all x, y and z components of β can be calculated. the hyperpolarizability (βtot) can be calculated using the following equation: 𝛽𝑡𝑜𝑡 = (𝛽𝑥 2 + 𝛽𝑦 2 + 𝛽𝑧 2) 1 2⁄ (2) where, βx = βxxx + βxyy + βxzz βy = βyyy + βxxy + βyzz βz = βzzz + βxxz + βyyz figure 4. effect of solvent polarity on polarizability of 2-methylimidazole. 23.50 24.00 24.50 25.00 25.50 26.00 26.50 27.00 27.50 28.00 28.50 water (78.3) dmso (46.8) n-octanol (9.9) chloroform (4.7) a .u . solvents (dielectric constant) shahidul m. islam et al 96 figure 5. effect of solvent polarity on first order hyperpolarizability of 2-methylimidazole. the βtot for different solvents has been listed in table 6, which shows that the hyperpolarizability in different solvents ranges from 24.24 to 28.22 a.u. moreover, the hyperpolarizability increases on going from lower to higher dielectric constant i.e. from non-polar to polar solvents (figure 5). table 6. effect of solvent polarity on polarizability (a.u.) and first order hyperpolarizability (a.u.). medium (dielectric constant) αxx αyy αzz αtot βx βy βz βtot gas phase 67.01 54.00 27.57 49.53 1.33 19.57 0.00 19.62 water (78.3) 88.04 74.91 35.67 66.20 -0.09 28.22 0.00 28.22 dmso (46.8) 87.91 74.58 35.52 66.00 0.03 28.03 0.00 28.03 n-octanol (9.9) 85.16 71.46 34.17 63.60 -0.16 26.74 0.00 26.74 chloroform (4.7) 81.88 67.87 32.68 60.81 -0.37 25.24 0.00 25.24 natural bond orbital analysis the natural bond orbital (nbo) analysis provides structural insight of a conformer by a set of localized bonding, anti-bonding, and rydberg extra valence orbitals [32]. the nbo analysis is a tool used to study delocalization of electrons from a lone pair or a filled donor to an unfilled acceptor within the molecule. the second-order fock-matrix is used to calculate the donor–acceptor interactions in the nbo scheme. the interactions cause the delocalization of electrons from the occupied orbital to an empty anti-bonding or rydberg extra valence orbital. for each donor (i) and acceptor (j) the delocalization of i → j is determined by the stabilization energy. 𝐸(2) = ∆𝐸𝑖𝑗 = 𝑞𝑖 (𝐹𝑖𝑗) 2 (𝐸𝑗−𝐸𝑖) (3) here, qi is the occupancy of donor orbital, ei and ej are the diagonal elements and fij is the off diagonal nbo fock matrix element. table 7 shows the results of the nbo analysis of 2-methylimidazole. the large value of e(2) (written as ie(2) in the table) suggests strong interaction between electron donor and acceptor, and a greater extent of conjugation of the system. from table 7, it is clear that strong hyper conjugative interactions are formed by orbital overlap between lp(n) and π*(c–n), π*(c–c), σ*(c–n), σ*(c–c) with ie(2) values of 201.96, 129.41, 41.25 and 23.47 kj/mol, respectively, between π(c2-n3) and π*(c4–c5) with ie(2) of 90.75 kj/mol, between π(c4-c5) and π*(c2–n3) with ie(2) of 55.69 kj/mol and between σ (c6-h12) and σ*(c2–n1) orbitals with ie(2) values of 27.11 kj/mol. these strong hyper conjugative interactions result in intra-molecular charge transfer (ict) leading to the stabilization of the system. in the presence of solvent, these orbitals are most likely to be affected and will give rise to the instability or stability of the system. 58.00 59.00 60.00 61.00 62.00 63.00 64.00 65.00 66.00 67.00 water (78.3) dmso (46.8) n-octanol (9.9) chloroform (4.7) a .u . solvents (dielectric constant) computational study of geometry 97 table 7. second order perturbation theory analysis of fock matrix in nbo basis for 2-methylimidazole. donor (i) ed/e acceptor (j) ed/e ie(2) kj/mol iie(j)-e(i) kj/mol iiif(ij) kj/mol σ(c2-n1) 1.98934 σ*(c5-h9) 0.01275 10.96 3386.90 136.53 σ(c2-n3) 1.98384 ivry*(2)c(4) 0.00416 10.17 4883.43 157.53 π(c2-n3) 1.85698 π*(c4-c5) 0.29818 90.75 840.16 204.79 σ(c2-c6) 1.98606 σ*(c4-n3) 0.00975 9.50 3019.33 120.77 σ*(c5-n1) 0.01340 8.95 2888.05 112.90 σ(c4-c5) 1.98619 σ*(n1-h7) 0.01725 17.45 3019.33 162.78 π(c4-c5) 1.87391 π*(c2-n3) 0.37552 55.69 761.40 154.90 σ(c4-n3) 1.97739 ry*(2)c(2) 0.00558 10.46 4437.10 152.28 σ*(c2-c6) 0.02211 31.46 3071.84 220.54 σ*(c5-h9) 0.01275 14.73 3203.11 154.90 σ(c5-n1) 1.98522 σ*(c2-c6) 0.02211 17.91 3176.86 168.03 σ(c5-n1) 1.98522 σ*(c4-h8) 0.01564 14.27 3386.90 154.90 σ(c6-h10) 1.98086 π*(c2-n3) 0.37552 15.10 1417.77 112.90 σ(c6-h11) 1.98088 π*(c2-n3) 0.37552 15.06 1417.77 112.90 σ(c6-h12) 1.98441 σ*(c2-n1) 0.04740 27.11 2546.74 186.41 lp(1)n(1) 1.59317 ry*(2) c(5) 0.00230 14.10 3386.90 173.28 π*(c2-n3) 0.37552 201.96 761.40 280.93 π*(c4-c5) 0.29818 129.41 787.65 231.04 lp(1)n(3) 1.92543 ry*(1) c(2) 0.00943 27.03 3334.39 215.29 σ*(c2-n1) 0.04740 41.25 2126.66 210.04 σ*(c4-c5) 0.01960 23.47 2494.23 173.28 ie(2)means energy of hyper conjugative interactions iienergy difference between donor and acceptor i and j nbo orbital iiif(i,j) is the fock matrix element between i and j nbo orbitals ivry = rydberg extra valence orbital global reactivity descriptors the electrical transport properties of a molecule depend on the energy gap of homo and lumo orbitals. the values of the homo-lumo energy gap in various solvents are presented in table 8 and their trend is shown in figure 6. from figure 6, it is clear that the homo-lumo energy gap decreases on going from polar solvent (water) to nonpolar solvent (chloroform). table 8. molecular orbital energy (ev) (homo and lumo) of 2-methylimidazole in different solvents with smd. medium (dielectric constant) molecular orbital energy (ev) homo lumo ∆e gas phase -5.841 0.942 6.783 water (78.3) -5.891 1.009 6.900 dmso (46.8) -5.883 1.012 6.895 n-octanol (9.9) -5.870 1.010 6.880 chloroform (4.7) -5.852 1.008 6.860 shahidul m. islam et al 98 figure 6. effect of solvent polarity on the homo-lumo energy gap of 2-methylimidazole. this suggests that the molecule is stabilized with increasing polarity of the solvent i.e. the molecule is less likely to be kinetically reactive, which is in agreement with the calculations of chemical softness. the global chemical reactivity descriptors, such as softness, hardness, chemical potential and electrophilicity index, can be calculated from the homo-lumo energy gap of a molecule [33-37]. using koopman’s theorem for closed-shell molecules, the hardness (η), chemical potential (µ), electronegativity (𝝌) and softness (s) are defined as follows: 𝜂 = 𝐼−𝐴 2 (4) µ = − 𝐼+𝐴 2 (5) 𝜒 = 𝐼+𝐴 2 (6) 𝑆 = 1 𝜂 (7) where i and a are the ionization potential and electron affinity of the molecule, respectively. the ionization energy and electron affinity can be quantified as i = -ehomo and a = -elumo. parr et al. [36] defined and calculated the global electrophilic power of a molecule as electrophilicity index (𝜔) as follows [34]: 𝜔 = µ2 2𝜂 (8) these new reactivity descriptors can be used to understand the toxicity of various pollutants in terms of their reactivity and site selectivity [38-40]. the molecular properties of 2-methylimidazole in different solvent media are presented in table 9. on going from polar to non-polar solvent, the chemical potential, electrophilicity index and electronegativity are decreased (figure 7 and 8). chemical hardness also decreases on going from polar to non-polar solvent, while the opposite relation is found in the case of chemical softness. table 9. effect of solvent polarity on molecular properties of 2-methylimidazole. medium (dielectric constant) chemical hardness (η) softness (s) chemical potential (µ) electronegativity (𝝌) electrophilicity index (𝜔) water (78.3) 3.450 0.290 -2.441 2.441 0.863 dmso (46.8) 3.447 0.290 -2.435 2.435 0.860 n-octanol (9.9) 3.440 0.291 -2.430 2.430 0.858 chloroform (4.7) 3.430 0.292 -2.422 2.422 0.855 6.840 6.850 6.860 6.870 6.880 6.890 6.900 6.910 water (78.3) dmso (46.8) n-octanol (9.9) chloroform (4.7) ∆ e ( e v ) solvents (dielectric constant) computational study of geometry 99 figure 7. effect of solvent polarity on the electronegativity of 2-methylimidazole. figure 8. effect of solvent polarity on the electrophilicity index of 2-methylimidazole. 4. conclusion to understand the structure and reactivity of 2-methylimidazole and related molecules, we have carried out an extensive study of the geometry, solvation free energy, dipole moment, molecular electrostatic potential (mesp), atomic charge distribution, polarizability, hyperpolarizability, chemical potential, electrophilicity, chemical hardness and chemical softnesses of 2-methylimidazole using the b3lyp/6-31g(d,p) level of theory. geometries obtained from b3lyp/6-31g(d,p) are found to be very similar to those obtained from x-ray crystal structure. the solvation free energy is highest in the polar aprotic solvent (dmso) and is lowest in the polar protic solvents (n-octanol and water). the dipole moment of 2-methylimidazole increases with increasing polarity of the solvent. similarly, polarizability and hyperpolarizability of 2-methylimidazole also increase with the polarity of the solvent. molecular electrostatic potential (mesp), mulliken population analysis (mpa) and natural population analysis (npa) reveal that the most possible sites for nucleophilic attack are c2 and h7 and for electrophilic attack are n1 and c4 among the atoms in 2methylimidazole. the chemical potential, electrophilicity index and electronegativity increase with the increase of solvent polarity. 0.850 0.852 0.854 0.856 0.858 0.860 0.862 0.864 0.866 water (78.3) dmso (46.8) n-octanol (9.9) chloroform (4.7) solvents (dielectric constant) 2.410 2.415 2.420 2.425 2.430 2.435 2.440 2.445 water (78.3) dmso (46.8) n-octanol (9.9) chloroform (4.7) 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september 2016 squ journal for science, 2017, 22(1), 56-62 doi: http://dx.doi.org/10.24200/squjs.vol22iss1pp56-62 2017 sultan qaboos university 56 effect of nano sb2o3 on the dispersive optical constants of pmma films wasan a. al-taa'y1, mohammed t. abdul nabi1, saad f. oboudi2*, emad yousif3* 1department of physics, college of science, university of baghdad, baghdad, iraq; 2department of physics, college of science, university of al-nahrain, baghdad, iraq; 3department of chemistry, college of science, university of al-nahrain, baghdad, iraq. *email: ch@sc.nahrainuniv.edu.iq; emad_yousif@nahrainuniv.edu.iq. abstract: pure and antimony trioxide sb2o3 doped pmma films were prepared by the casting method. optical absorption measurements in the wavelength range 200-800 nm were studied by using a computerized uvvis spectrophotometer (shimadzu uv-1601 pc) and these confirmed that pmma films have a direct band gap that decreases from 5.15 to 4.66 ev as the doping concentration increases to 5wt%. the increase in the density of localized states from 8.9 to 74.5 mev causes an expansion in the urbach tail and consequently decreases the energy gap. the dispersion of the refractive index was analyzed using the concept of a single oscillator. the values of the single oscillator energy were 32.70, 13.59, 7.06, and 4.58 ev, while the dispersion energy values were 4.36, 49.04, 21.76 and 14.15 ev for the pure, and 3%, 4% and 5% sb2o3 for the doped pmma films respectively. the single-term sellmeier were determined, and the average oscillator position was investigated, the value of which decreased with increasing doping concentration. the value of average oscillator strength increased with increasing sb2o3 concentration to 5wt%. skin depth and optical conductivity could be calculated, and results show a decrease in skin depth with an increasing impurity percentage, but an increase of optical conductivity with greater impurity keywords: pmma polymer; optical dispersion parameters. pmmaغشية على ثوابت التشتت البصرية أل 3o2sbنانو تأثير عماد يوسفو عبد النبيمحمد طارق ،سعد فرحان العبيدي ،ئيوسن علي الطا درست قياسات االمتصاص تقنية الصب.حضرت باستخدام 3o2sbيموان الثالثيالنقية والمشوبة بمادة اكسيد االنت pmmaغشية أ :ملخصال uv-vis spectrophotometer (shimadzu uv-1601 pc).باستخدام جهاز nm(800-200البصرية ضمن مدى االطوال الموجية ) الزيادة . wt% 5 الى كيز التطعيمربزيادة ت 4.66evالى 5.15ذات فجوة طاقة مباشرة تنخفض من pmmaغشية أن أ الى توصلنا في هذا البحث تحدث توسيع في ذيول اورباخ وبالتالي انخفاض في فجوة الطاقة. تم تحليل تشتت معامل االنكسار 74.5mevالى 8.9في المستويات الموضعية من 21.76, 49.04, 4.36تشتت , بينما قيم طاقة ال4.58evو 7.09, 13.59, 32.70 قيم طاقة المذبذب االحادي هيباستخدام مفهوم المذبذب االحادي. ن قيمته أعلى التوالي. حسب معدل موقع المذبذب ووجد 3o2sbالنقية والمشوبة بمادة pmmaغشية أل %5% و 4%, 3 ,0بنسب ev 14.1و تم حساب عمق االختراق والتوصيلية . wt5%وصوال الى 3o2sb. زادت قيم معدل قوة المذبذب مع تركيز انخفضت مع زيادة تركيز التطعيم مع نسب التشويب بينما تزداد التوصلية البصرية مع هذه النسبة.بينت النتائج حدوث انخفاض في عمق االختراق ،البصرية .عامالت التشتت البصريةم ، pmmaبوليمر : مفتاحيةالكلمات ال 1. introduction ilms of poly methyl methacrylate (pmma) as a polymeric waveguide has steadily gained attention for use in optical components and in optoelectronic devices. recently, some researchers have reported optical components such as an optical switch, a coupler, a splitter and a transceiver [1,2]. polymeric composites of pmma are very popular due to their low cost, volume productivity, high strength to weight ratio, noncorrosive properties and simple fabrication methods. they are known for their importance in technical applications [3]. composites containing two materials with different physical properties often exhibit new properties. the composites can provide improved characteristics that are not obtainable in any of the original components alone; they not only combine the advantageous properties of dopant and polymers but also exhibit many new properties that single-phase materials do not have [4], and they are used in a wide variety of industrial products. a variety of additives are used in the composites to improve these materials’ properties, aesthetics, manufacturing processes, and performance. f mailto:ch@sc.nahrainuniv.edu.iq mailto:emad_yousif@nahrainuniv.edu.iq effect of nano sb2o3 on the dispersive optical constants 57 the structural, optical, and electrical properties of these polymeric materials can be enhanced by incorporation of filler into a polymer matrix, because dispersed filler will enhance various physical properties of the host polymer [5]. in this paper, we report and discuss the optical characterization of pmma films doped with different concentrations of sb2o3 nanoparticles by uv-vis spectra. 2. experimental details pmma films doped with different weight concentration (3,4 and 5) wt% of nano antimony trioxide (sb2o3) were prepared by dissolving the dispersed polymer in 100 ml chloroform. different polymer solutions (volumetric solutions) were cast as films and dried at room temperature for 24 hours. the thickness of the prepared films were measured using an indicating micrometer and found to be in the range of 150 μm. these films were clear, transparent, and free from any noticeable defect and of a light bluish color. optical transmittance and absorbance were recorded in the wavelength range 200-800 nm using a computerized uv-vis spectrophotometer (shimadzu uv-1601 pc). optical transmittance and absorbance were reported in order to study the effect of doping on the parameters under investigation. 3. results and discussion the study of the optical absorption for the films under investigation, particularly the absorption edge, has proved to be very useful for elucidation of the electronic structure of these materials. the optical absorption spectra of the tested films as a function of dopant concentration are shown in figure 1. the absorption at higher wavelengths in the visible region is low, but at wavelength 280–380 nm an intense absorption can be seen. moreover, it can be noticed that the absorbance tends to increase as the doping concentration rises to 5 wt%. figure 1. absorbance of pure and sb2o3 doped pmma films versus wavelength: eda = is pure pmma, b = pmma/3% sb2o3, c = pmma/4% sb2o3, d = pmma/5% sb2o3. the tail of the absorption edge is exponential, indicating the presence of localized states in the energy band gap. the amount of tailing can be predicted to a first approximation by plotting the absorption edge data in terms of an equation originally given by urbach [6]. the absorption edge gives a measure of the energy band gap and the exponential dependence of the absorption coefficient, in the exponential edge region urbach rule is expressed as [7,8]. α = α° exp (hυ / eu) (1) where α is the absorption coefficient, hυ is photon energy, α° is a constant, and eu is the urbach energy, which characterizes the slope of the exponential edge. figure 2 shows urbach plots of the films. the value of urbach energy was obtained from the reciprocal gradient of the linear portion of the plot. lnα vs. hυ is given in table 1. urbach energy values change inversely with the optical band gap. the urbach energy values of the films increases with an increase of doping concentration. the increase of urbach energy suggests that the atomic structural disorder of doped films is increased by increasing the doping ratio. this behavior can result from increasing the grain size. the size of the grains varies with the doping and influences the value of the optical energy gap; this increase leads to a redistribution of states from band to tail and may be attributed to the improved of crystallinity. as a result, both a decrease in the optical gap and expansion of the urbach tail take place. 0 20 40 60 80 100 120 100 300 500 700 900 a b c d a b so rb a n ce wavelength (nm) wasan a. al-taa'y et al 58 table 1. the optical parameters. sample eu (mev) eg (ev) ed (ev) eo (ev) λo nm so *10-5 cm-2 pure pmma 60 5.15 4.36 32.70 254.90 0.26 pmma/3% sb2o3 83 5.03 49.04 13.59 79.17 57.11 pmma/4% sb2o3 40 4.82 21.76 7.067 129.18 17.43 pmma/5% sb2o3 217 4.66 14.15 4.58 378.95 2.66 figure 2. lnα versus photon energy for pure and doped pmma films: a is pure pmma, b is pmma/3% sb2o3, c is pmma/4% sb2o3, d is pmma/5% sb2o3. according to the inter-band absorption theory, the optical band of the films can be calculated using tauc's relation [9,10] (αhυ) = a(hυ–eg)n (2) where a is a constant, eg the optical band gap, and n an index which could take different values according to the electronic transition. for allowed direct transitions the coefficient n = 1/2, and for allowed indirect transitions n = 2. the curve (αhυ)1/2 for the allowed indirect transition does not present evident linearity; this seems to suggest that pmma films have a direct band gap. the extrapolation of the linear part of the curve (αhυ)2 to the energy axis is shown in figure 3. the direct bandgap energy for the pure pmma film is 5.15 ev. it can be seen that the energy gap of the films tends to decrease with an increase of sb2o3 concentration; this decrease can be attributed to a decrease in crystallinity disorder of the films. the optical band gap of the pmma films is obviously affected by defects and by the crystallinity. such a decrease in the energy gap due to doping was also obtained by other researchers [11-15]. 0 1 2 3 4 5 6 4.65 4.7 4.75 4.8 4.85 4.9 a b c d ln α (c m )1 photon energy (ev) effect of nano sb2o3 on the dispersive optical constants 59 figure 3. (αhυ)2 versus photon energy for pure and doped pmma films. a is pure pmma, b is pmma/3% sb2o3, c is pmma/4% sb2o3, d is pmma/5% sb2o3. wemple and didomenico [16,17] used a single-oscillator description to define dispersion energy parameters. the refractive index dispersion plays an important role in optical communication and the design of optical devices. therefore, it is a significant factor. the relation between the refractive index n, and the single oscillator strength is given by the expression: n2 = 1 + [ed eo / eo 2− (hυ) 2] (3) where ed and eo are single oscillator constants, eo is the energy of the effective dispersion oscillator, and ed the socalled dispersion energy, which measures the intensity of the inter band optical transitions. the oscillator energy e o is an average of the optical band gap, and can be obtained from the wemple–didomenico model. this model describes the dielectric response for transitions below the optical gap. experimental verification of eq. (3) can be obtained by plotting (n2−1)−1 versus (hυ)2, as illustrated in figure 4, which yields a straight line for normal behavior having the slope (eoed) -1 and the intercept with the vertical axis equal to eo/ed. eo and ed values were determined from the slope, (eoed) −1 and intercept (eo/ed) on the vertical axis. eo values decrease as the optical band gap decreases as shown in table 1. according to the single-oscillator model, the single oscillator parameters eo and ed are related to the imaginary part of the complex dielectric constant. figure 4. variation in (n2 – 1)−1 as a function of (hυ)2 for pure and doped pmma films.: a is pure pmma, b is pmma/3% sb2o3, c is pmma/4% sb2o3, d is pmma/5% sb2o3. the values obtained for the dispersion parameters eo, ed, and eu are listed in table (1). for the definition of the dependence of the refractive index (n) on the light wavelength (λ), the single-term sellmeier relation can be used [16]: 0 2.1 4.2 6.3 8.4 6.56 6.76 6.96 7.16 7.36 (hυ)2 (ev)2 (n 2 1 )1 wasan a. al-taa'y et al 60 n2 (λ)− 1 = soλo 2 / 1 − (λo/λ) 2 (4) where λo is the average oscillator position and so is the average oscillator strength. the parameters so and λo in eq. (4) can be obtained experimentally by plotting (n2 – 1)−1 versus λ−2 as shown in figure 5; the slope of the resulting straight line gives 1/so, and the infinite-wavelength intercept gives 1/ so λo 2. after doped the average oscillator position values decreased and with increasing doping concentration to 5wt%, the average oscillator strength increased with impurity percentage as shown in table 1. figure 5. variation in (n2 – 1)−1 as a function of (λ)-2 for pure and doped pmma films. a is pure pmma, b is pmma/3% sb2o3, c is pmma/4% sb2o3, d is pmma/5% sb2o3. the skin depth x could be calculated using the following relation [18]: x = λ / 2πk (5) where k is the extinction coefficient. figure 6 shows the variation of skin depth as a function of wavelength for all films. it is clear from the figure that the skin depth increases as the wavelength increases; this behavior could be seen for all samples (a, b, c and d). however, the skin depth decreases as the sb2o3 concentration increases to 5wt%, which means that the skin depth is transmittance related. figure 6. skin depth versus wavelength for pure and doped pmma films: a is pure pmma, b is pmma/3% sb2o3, c is pmma/4% sb2o3, d is pmma/5% sb2o3. 0 2.1 4.2 6.3 8.4 4.4e-06 4.5e-06 4.6e-06 a b c d (λ )-2(nm)-2 (n 2 1 )1 effect of nano sb2o3 on the dispersive optical constants 61 the optical conductivity σ was calculated using the relation [19]: σ = α n c / 4π (6) where c is the velocity of light. figure 7 shows the variation of optical conductivity with the wavelength. it can be seen that the optical conductivity for pure film decreases with the increase of wavelength; this decrease is due to the low absorbance of the films in that region. after films are doped, this decrease is gradually changed to the increasing down to percentage of 5wt%. also, it can be noticed that the optical conductivity increases with an increase in doping concentration. this suggests that the increase in optical conductivity is due to electrons excited by photon energy. the origin of this increase may be attributed to some changes in the structure of the film due to the doping and the charge ordering effect. figure 7. optical conductivity versus wavelength for pure and doped pmma films. a is pure pmma, b is pmma/3% sb2o3, c is pmma/4% sb2o3, d is pmma/5% sb2o3. 4. conclusion pure and sb2o3 doped pmma films were successfully prepared by the solution casting method. the optical absorption spectra were calculated and were found to increase progressively after doping with increasing concentrations. the type of optical transition responsible for optical absorption was found to be direct allowed transitions. the energy gap values obtained from the wemple–didomenico model were close to those determined from the tauc model, and were found to decrease with an increase in doping concentration, having the values of 5.15, 5.03, 4.82, and 4.66 ev for the pure pmma, 3,4, and 5wt% respectively. the optical dispersion parameters were characterized and found to obey the single oscillator model. the single oscillator parameters and the single-term sellmeier were determined, the change in dispersion and the average oscillator position was investigated and its values decreases with increasing doping concentration to 5wt%. values of dispersion energy and average oscillator strength increase with the concentration of sb2o3 impurity. skin depth and optical conductivity could be calculated, with results showing a decrease in skin depth with impurity percentage while optical conductivity increases with increasing impurity. 5. acknowledgements the authors thank al-nahrain university and baghdad university for their financial support. references 1. kobayashi, j., matsuura, t., hida, y., sasaki, s and maruno, t. fluorinated polyimide waveguides with low polarization – dependent loss and their application to thermooptic switches. journal lightwave technology, 1998, 16, 1024-1029. 2. ojima, s., hatano, t; kintaka, k and nishii, j. extended abstracts, the 49th spring meeting. the japan society of applied physics and related societies, 2002, 28a-zs-9. wasan a. al-taa'y et al 62 3. tawansi, a and zidan, h.m. tunneling and thermally stimulated phenomena in highly filled pmma composites. international journal of polymer materials, 1991, 15(2), 77-83. 4. podgrabinski, t., svorcik, v., mackova, a., hnatowicz, v., and sajdl, p. dielectric properties of doped polystyrene and polymethylmethacrylate. journal of materials science, 2006, 17, 871-875. 5. el-khodary, a., oraby, a.h., and abdelnaby, m.m. characterization, electrical and magnetic properties of pva films filled with fecl3-mncl2 mixed fillers. journal of magnetism and magnetic materials, 2008, 320, 1739-1746. 6. urbach, f. 1953. the long-wavelength edge of photographic sensitivity and of the electronic absorption of solids. physics review, 2008, 92, 1324-1325. 7. j. tauc, “amorphous and liquid semiconductors”, plenum press, new york, 1974. 8. mohammed, s.a., hasan, a., al-taa'y, w.a., ahmed, a., khalaf, m., yousif, e. optical properties study of new film drived from poly (vinyl chlorid)-n-(4-hydroxy-phenyl)-acetamide. reasearch journal of pharmaceutical, biological and chemical sciences, 2016, 7(4), no.1064. 9. ismael, m., hamood,a.b., shaalan,n., al-taa'y,w.a; hasan, a., ali,m; ahmed,a., yousif, e. study of optical properties study of pvc-2-5di (2-pyrrole hydrazine)1,3,4-thiadiazole complexes. reasearch journal of pharmaceutical, biological and chemical sciences, 2016, 7(5), no.2347. 10. al-taa'y, w.a., abdul nabi, v., yusop, r.m., yousif, e., abdullah, b.m., salimon, j., salih, n and zubairi, s.i. effect of nano zno on the optical properties of poly (vinyl chloride) films. international journal of polymer science, 2014, 1-6. 11. kurt, a. influence of alcl3 on the optical properties of new synthesized 3-armed poly(methyl methacrylate) films. turkish journal of chemistry, 2010, 34, 67-79. 12. mahasin, f; wafaa, h and abaas, h. optical properties of crystal violet doped pmma films, research and reviews in polymer. 2013, 4(2), 45-51. 13. zidan, h.m and abu-elnader, m. structural and optical properties of pure pmma and metal chloride-doped pmma films. physica, 2005, b 355, 308-317. 14. deshukh, s.h., burghate, d.k., shilaskar, s.n., chaudhari, g.n and deshmukh, p.t. optical properties of polyaniline doped pvc-pmma thin films. indian journal of pure and applied physics, 2008, 46, 344-348. 15. hasan, b.a. effects of doping with (mathylene blue and methel red) on the optical properties of polymethyl methacrylate (pmma). journal of education college, 2005, 5(3), 449-464. 16. oboudi, s.f., abdul nabi, m.t., al-taa'y, w.a., yusop, r.m., derawi, d and yousif, y. dispersion characterization of conductive polymer. international journal of electrochemical science, 2015, 10, 1555 1562. 17. wemple, s.h and didomenico. behavior of the electronic dielectric constant in covalent and ionic materials. physical review, b3, 1971, 1338-1351. 18. al-taa'y, w. a., oboudi, s.f., yousif, e., abdul nabi, m.t., yusop, r. m. and r.m. derawi. fabrication and characterization of nickel chloride doped pmma films, advance in material science and engineering. article id 913260, 2015. 19. hamad, t.k., yusop, r.m., al-taa'y, w.a., abdullah, b and yousif, e. co2 laser enhanced modification of the optical properties of nano zno doped pvc films, international journal of polymer science, 2014, 1-8. received 4 january 2016 accepted 13 september 2016 squ journal for science, 2017, 22(1), 1-9 doi: http://dx.doi.org/10.24200/squjs.vol22iss1pp1-9 2017 sultan qaboos university 1 composition of solid waste in al jabal al akhdar, a mountain region undergoing rapid urbanization in northern oman abdullah i. al-mahrouqi and reginald victor* department of biology, college of science, sultan qaboos university, p.o. box: 36, pc 123, alkhoud, muscat, sultanate of oman. *email: rvictor@squ.edu.om. abstract: there is a lack of data on the generation and composition of waste in rural areas worldwide. the present study analyzed the composition of solid waste in al jabal al akhdar, a rural mountain region in the sultanate of oman, which is presently experiencing a rapid rate of urbanization due to tourism development. the solid wastes here are generated by the municipality collecting waste from residential, commercial, institutional and recreational areas, the military from a training camp and a few non-governmental private companies from their camps and hotels. the whole load from each of the three sources was manually segregated each month from june 2013 – may 2014. the results indicated that plastic is the dominant category in the wastes collected by the municipality and accounts for 26.7%, followed by paper (17.9%) and then food (14.4%). food is the dominant category in the wastes collected by the military and private companies and accounts for 36.5% and 45.5% respectively. management issues associated with solid waste are briefly considered. the study concluded that the municipality should implement an improved system for the collection of plastic waste and initiate a system for recycling it; the military and private companies should reduce the quantities of food waste by improved planning and management of the catering services. keywords: solid waste; rural areas; al jabal al akhdar; oman; statistical analysis; composition. مكونات النفايات الصلبة في منطقة الجبل االخضر الجبلية في شمال عمان التي تتطور بسرعة نحو التحضر ريجنالد فيكتوروعبدهللا المحروقي يكون هناك نقص في البيانات الخاصة بكمية النفايات المتولدة ومكوناتها في المناطق الريفية. في هذه الورقة تم تحليل مكونات النفايات غالبا ما :ملخصال جمع يتم الصلبة في نيابة الجبل األخضر، وهي منطقة جبلية ريفية في شمال سلطنة عمان. تشهد في الوقت الحاضرنموا سريعا بسبب التنمية السياحية. ا بالنسبة لمعسكر النفايات عن طريق ثالث جهات رئيسية وهي البلدية، التي تجمع النفايات من المناطق السكنية والتجارية واألماكن العامة والترفيهية. أم ات الخاصة والفنادق فتقوم بجمع التدريب القتالي التابع للجيش السلطاني العماني فيتم جمع النفايات بواسطة شاحنة مخصصة من قبلهم. أما مخيمات الشرك من تم فرز النفايات الواردة من المصادر الثالثة المشار إليها بطريقة يدوية شهريا ولمدة سنة كاملةونقل النفايات إلى مردم البلدية بواسطة سيارات مستأجرة. ٪ يليها النفايات 26.7أكثر النفايات التي تم جمعها من قبل البلدية وتمثل بينت نتائج الدراسة أن النفايات البالستيكية هي . 2014إلى مايو 2013شهر يونيو ٪. في حين تمثل نفايات الطعام الفئة األبرز في النفايات التي تم جمعها من قبل معسكر التدريب القتالي 14.4٪ ثم مخلفات األطعمة بنسبة 17.9الورقية نتائج البينت توالي. كما تم التطرق إلى إدارة النفايات الصلبة في الجبل األخضر بصفة مختصرة.٪ على ال45.5٪ و 36.5والشركات الخاصة والتي تمثل اتباع إدارة البلدية أن تتبع نظام جديد متطور لجمع النفايات البالستيكية وتدويرها. أما بالنسبة للشركات الخاصة ومعسكر التدريب القتالي فعليهم أن على فات األطعمة.متطورة في التخلص من مخل .و المكونات، التحليل اإلحصائي النفايات الصلبة، المناطق الريفية، الجبل األخضر، عمان: مفتاحيةالكلمات ال 1. introduction he amount of solid waste generated throughout the world is increasing dramatically and continues to be a major problem in most of the developing countries affecting the environment, human and other organisms [1]. waste composition differs from one place to another even in the same country or same district or sub-district [2]. it is influenced by many factors such as the income of the people, economic development, eating habits and consumption patterns [3]. al jabal al akhdar of the western hajar mountains is rapidly developing as a popular tourist destination in oman. this area had restricted access until about two decades ago and was populated by remote rural communities. in 1993, the number of households in the area was 547 and the population was about 5227 people. al jabal al akhdar t abdullah i. al-mahrouqi and reginald victor 2 branch of the nizwa municipality was responsible for the solid waste management and even donkeys were used to transport solid waste from remote areas. the infrastructure available for managing solid waste at that time was considered adequate. from 1995, the area opened up for urban development and the promotion of tourism. by 2010, the number of households had increased to 803 with 8000 people. the projected estimate for 2016 at the same conservative rate of increase is over 1000 households and about 10000 people excluding the transient population of military personnel and tourists. the associated increase in the solid waste, as evidenced by observation, has not been subjected to any scientific study. open dumps are the most common waste disposal systems in oman. these dumps, particularly if uncontrolled, are associated with human and environmental hazards due to foul odor, loss of amenity value, toxic leachate and contamination of drinking water sources [4]. leachate is a liquid associated mainly with open dumps and it is produced when rainwater percolates through waste dumped in a disposal site [5]. sources such as electronic goods, electroplating waste, paint waste, used batteries, ceramics, newspapers, motor oils, plastics, etc., when dumped with municipal solid waste increase the heavy metal concentrations in dumpsites [6]. al jabal al akhdar has one small open dump that receives all solid waste except the construction and demolition waste. to our knowledge there is no study on the qualitative and quantitative composition of the waste generated in this area. for the efficient management of solid waste including strategies for recycling and disposal, this information is needed [3], and therefore this study investigates the composition of solid waste as the first step toward integrated solid waste management. 2. study area the study area, al jabal al akhdar (figures 1a and b) which is the largest structural domain in the western hajar mountain range, is located in al dakhliah governorate of the sultanate of oman between latitudes 16°39′ and 26°30′ n and longitudes 52°00′ and 59°30′ e. it is 150 km southwest of muscat and has a total land area of 26 sq. km. it is around 2000 3000 m above sea level (masl). figure 1a. the location of the al jabal al akhdar region in oman. (source: oman environmental services holding company; be'ah). composition of solid waste 3 the geology of al jabal al akhdar is unique and all rock groups found in the oman mountains are represented. the detailed geology of these mountains is given by glennie [7] and hanna [8]. the dump site is located on the triassic mahil formation of around 600 m in thickness. the formation is composed mainly of thick alternations of pinkish and yellowish dolomite rocks characterized by high permeability. beds in the area are steeply dipping eastward toward the izki area [8]. al jabal al akhdar (figure 1a) is moderately cool in summer (20-25 °c) and very cold in winter (< 0-10 °c). when the average summer temperature in nizwa (500 masl) is 49 °c, in saiq, the main village on the plateau (20003000 masl) temperature averages around 25 °c [9]. the annual rainfall occurs normally between june and august in summer and between december and january in winter although this varies from one place to another. the annual precipitation ranged from 115-413 mm for the period of 2000-2009 [9]. figure 1b. main villages in al jabal al akhdar (source: oman environmental services holding company; be'ah). al jabal al akhdar supports 48 small villages (figure 1b). agricultural farming inclusive of raising livestock is the most important activity of the local residents, and employ about one quarter of the population. pomegranate, apricot, fig, grape, walnut, apple, plum, pear and peach are the most cultivated crops. many animal fodders such as corn, oats and alfalfa are also cultivated. most families raise livestock in private fens attached to their homes, particularly goats and sheep for food, the sale of wool and to provide fecal matter as a source of fertilizer for the crop production. some villages produce rosewater in late spring of each year when the damascus rose (rosa damascena) is in bloom. because of the intensive urban development in recent times, there has been a steady increase in the number of residents in certain parts of the jabal. many citizens who were originally from al jabal al akhdar but had become residents in the lower plains are returning to be a part of this urban development. tourists and locals visit al jabal al akhdar to experience the cool weather, to camp, for landscape photography and to visit farming areas and traditional villages. the number of hotels has increased from one in 2006 to four in 2014, and another large hotel which belongs to the ministry of defense is still under construction. in addition, there are other apartments and rest-houses and some organizations such as the municipality have their own accommodation for their staff. the number of tourists has increased from 85,000 in 2006 to 134,000 in 2013[10]. the majority of the inhabitants are concentrated in saih katanah representing 26% of the population, and the rest are distributed in other villages. the population growth rate of al jabal al akhdar is 3.5% per year [11]. the only open dumpsite in al jabal al akhdar has an area of 6223 m2. it is under the ownership of nizwa municipality. the method used to dispose of the waste is burning in order to reduce the volume because the area is small. the ash, with other unburnt waste, is transferred once annually to another site at a distance of 500 m. different wastes are not sorted, and at times, special wastes (clinical, industrial, and electronic) are also deposited in the municipal dump. the dumpsite is located on a dry river bed from where waste can be washed away during rains and flash floods. the dump has no engineered measures for waste processing. it is not fenced off properly and has no leachate management or plans for landfill gas management or liners. similarly, there are no operational measures, such as registration of users, control of the number of loads, or compaction of waste. abdullah i. al-mahrouqi and reginald victor 4 3. materials and methods there are three different stakeholders for carrying solid waste to the dumpsite. the main collector is nizwa municipality (al jabal al akhdar branch) which collects the waste from residential, commercial, institutional and recreational areas. they use either mini trucks (2 -3 m3) or tippers (18 m3). the military bring their waste by their own compactor truck (9 m3). normally they bring only one load daily except when they have special occasions. the third class of collector is non-governmental companies, which collect the waste from other private organization’s camps and hotels. they use mini-trucks or pickups (2-3 m3). these three sources of waste were kept separate for assessing the composition. the sampling program was carried out for one year at monthly intervals from june 2013 to may 2014. klee [12] recommended that the solid waste sample should not be small, not less than 91 kg in order to avoid the high variance of the waste composition. therefore, the whole loads of three different trucks, one from each source were sorted. the minimum weight for loads sorted from the municipality was 215 kg in june 2013 and the maximum weight was 998.5 kg in august 2013. the minimum weight for loads sorted from the military was 312 kg in june 2013 and the maximum weight was 779 kg in april 2014. the minimum weight for loads sorted from private companies was 213 kg in february 2014 and the maximum weight was 1028 kg in july 2013. each load was spread flat on a plastic sheet on the ground and was sorted manually by 10 laborers into 10 different components: paper/paperboards, plastics, food, textiles, leather/ rubber, metals, glass, wood, yard trimming and other (includes electrical/ electronic apparatus, nappies/sanitary products, paint waste, used batteries, ceramics, dead animals, used tires and other inert materials). standard personal safety procedures such as gloves, masks, aprons and safety boots were used during the segregation process. each component was weighed using a balance with a 1000 kg scale and the weights were recorded. the percentage composition of each component was calculated. all percentages were arcsin transformed before analysis and normal distribution assumption was verified. the whiskers on bar graphs represent standard error (se). after considering various models of anova, the analysis of variance (anova) completely randomized design was selected as the best to fit the experimental design used in this study. if there were significant differences among sources and components, the tukey test was used as a post-hoc comparison to detect the location of significant differences. comparisons of solid waste composition with those of previous studies, where possible, were performed using one sample t-tests with a non-zero µ. all analyses were performed using excel and past running on a windows platform. 4. results and discussion all solid waste collected in al jabal al akhdar, except for the construction and demolition waste, is sent to the municipal dumpsite; the latter is used as landfill for natural depressions and is not included in this study. the solid wastes received by the dumpsite were analyzed under three separate waste streams; municipal, military and from private companies. the composition of the waste in each stream needs to be known to determine possible improvements that can be recommended specifically to the stakeholder who is responsible for that waste stream (e.g. the military). while some studies use categories such as recyclables, organics etc., to classify waste [13, 14], ten basic, descriptive categories were used here. this simple classification is easily understood by all stakeholders from uneducated lay people to those with advanced technical knowledge. assessing the percentage of recyclables or organic material for example, could be easily determined from these categories. from municipality records and personal observation of the loads of waste being delivered to the dumpsite, it is estimated that about 2560 tons are being generated annually in al jabal al akhdar. the estimated quantity of waste generated was calculated for each source from the number of trucks entering the dumpsite and the weight of the sampled loads. the estimated annual contribution of waste collected by the municipality was around 76.8% and the remaining waste was from the military (7.4%) and private companies (15.8%). table 1 shows the composition of solid waste from the three sources in al jabal al akhdar for the period june 2013 – may 2014; the total weights of the 12 samples taken within each category are given. the three main categories of waste received from the municipality were plastic (26.7%), food (14.4%) and paper (17.9%) which represent 60% of the total waste. the anova showed that there were significant differences (figure 2a) among the mean percentages of the 10 categories (f0.05, 9,110 = 1.97; p<0.05). post-hoc comparisons using the tukey test showed that food and paper were not significantly different from each other (p>0.05), while plastic was significantly higher than all other categories (p<0.05). these three main categories were significantly different from the other seven categories (p<0.05). the seven minor categories (5-7% of the composition) were not significantly different from each other (p>0.05). composition of solid waste 5 table 1. total sample weights by category from the three sources for the period from june 2013 to may 2014. the values in the parentheses are percentages. total weight of all samples (kg) municipality military private companies paper 320 (17.87) 257 (14.97) 217 (14.09) food 258 (14.41) 627 (36.48) 701 (45.45) plastic 478 (26.69) 229 (30.35) 236 (15.31) metal 104 (5.81) 139 (8.06) 110 (7.71) glass 117 (6.53) 75 (4.38) 106 (6.87) textiles 116 (6.48) 47 (2.72) 27 (1.66) wood 94 (5.25) 103 (5.99) 62 (4.04) yard trimming 87 (4.86) 124 (7.26) 0 (0) rubber & leather 90 (5.03) 62 (3.59) 40 (2.59) others 127 (7.09) 55 (3.20) 44 (2.83) total 1,791 (100) 1,718 (100) 1,543.5 (100) all the categories of municipal solid waste were generated primarily by households, as is similar to municipal waste generated elsewhere [15,16]. the mean percentage of food waste (14.4%) was significantly higher (p<0.04) compared to the urban samples taken by the operator of al multaqa landfill, muscat in 2012 and 2013 (9.8%) [17]. the actual food waste in al jabal al akhdar is likely to be higher than the 14.4% reported in this study. this may be due to the fact that local residents feed their food wastes to domestic animals and discard only the surplus. in addition, cats, dogs and feral donkeys scavenge for food from the collection bins and only the remaining food waste is taken to the dumpsite. figure 2a. percentages of different categories of municipal waste generated. the bars labeled with the same letters are not significantly different from each other (tukey test, p > 0.05). a recent study in muscat, oman showed that food represented 28.2% of the municipal waste [18]. for a city generating 750 tons of municipal waste per day, this seems to be an overestimate. the sample size used by these investigators was very small (5 kg of a random sample of 20 kg) in relation to the total amount of waste dumped. abdalqader and hamed [19] stated that in order to study the composition, the minimum weight of the solid waste samples should not be less than 91 kg. small sample sizes are likely to provide inaccurate results. other researchers indicated that the samples of solid waste should range between 50-136 kg [20]. according to another study conducted in different districts of muscat governorate, oman in 1998 [21], the food wastes accounted for 38.8% based on a total of 10 samples of 800 – 850 kg taken from five dumpsites. this estimate also may not be very accurate as there were relatively low numbers of samples. the mean percentage of plastic waste (26.7%) was higher than that (8.5% and 17.2%) reported by el zawahry et al. [21] and palanivel and sulaiman [18] respectively in muscat. however, it is not significantly different from the percentage (24.3%) reported by the operator of al multaqa landfill (p>0.05). the percentages reported for plastic by unep’s international environmental technology centre [22] for accra, ibadan, dakar, abidjan, and lusaka were less than 10%. this may be due to the prevalent reuse of plastic bottles and containers in africa or to the restricted use of plastic bags [23]. the environmental protection agency (epa) of the united states showed that plastics comprised 12.8% of the total msw generation in 2013 [15]. the high plastic component in al jabal al akhdar may be attributed a a b c c c c c c c 0 5 10 15 20 25 30 35 40 45 paper food plastic metal glass textiles wood yard rubber & leather others m e a n p e rc e n ta g e s abdullah i. al-mahrouqi and reginald victor 6 to the activity of both local people and international tourists who tend to leave behind plastic packaging, especially plastic food containers, and plastic water and soft drink bottles in the area. there is no restriction on the use of plastic and plastic products in oman, leading to the high quantities of plastic in solid waste. figure 2b. percentages of different categories of waste generated by military. the bars labeled with the same letters are not significantly different from each other (tukey test, p > 0.05). figure 2c. percentages of different categories of waste generated by private companies. the bars labeled with the same letters are not significantly different from each other (tukey test, p > 0.05). paper and cardboard waste contribute 17.9% of the total waste collected by the municipality in al jabal al akhdar. this was lower than that (28.8%) reported by palanivel and sulaiman [18] and close to the 16.3 % recorded by el zawahry et al. [21]. the 21.4% reported by the operator of al multaqa landfill was not significantly different from that reported for al jabal al akhdar (p>0.05). the data from usepa showed that paper and cardboard accounted for 27.0% in 2013 [15]. the results of anova showed that there were no significant differences (p>0.05) among the percentage compositions of all categories of waste between the military and the private companies (figure 3). for both these sources, the three main categories, plastic, food and paper represent 65 74% of the total waste. the major component is the food waste, comprising 37% of the military and 45% of the private companies’ waste. food waste is significantly higher in the military and the private companies when compared to the municipal waste (p<0.05). military and private companies cater to a large number of personnel and waste large quantities of food. in these organizations, food is a b a c c c c c c c 0 10 20 30 40 50 60 paper food plastic metal glass textiles wood yard rubber & leather others m e a n p e rc e n ta g e s a b a c c c c c c c 0 10 20 30 40 50 60 70 paper food plastic metal glass textiles wood yard rubber & leather others m e a n p e rc e n ta g e s composition of solid waste 7 purchased in bulk and any food that is not used by the expiry date is disposed of. the quantity of food cooked is more than they actually consume, resulting in large quantities of waste food. figure 3. comparison between each category coming from 3 different sources, with similar letters showing no significant differences (p >0.05) and different letters indicating significant differences (p< 0.05). the percentage composition of plastic and paper was significantly lower (p<0.05) for the military and private companies when compared to the municipality. both military and companies use less diversity of materials as opposed to individual households. in households, consumer spending patterns and the phenomenon of “use and throw” result in the generation of more plastic and paper which are the main constituents of packaging materials. paper and cardboard wastes are mostly generated by the commercial establishments in the area and are collected by the municipality. in contrast, the generation of paper and cardboard wastes discarded by the military and the private companies are relatively less. there were two other categories of waste where the municipality was significantly different (p<0.05) from the military and private companies. textile wastes were higher in the municipality. both military and commercial activities generally do not dispose of clothing and bedding materials whereas in households, the opposite is the norm. the military and private companies use these materials for a long period, and when discarded, they are usually taken by people with low income and eventually end up in the municipality waste. the category designated as ‘others’ was higher in the municipality waste, and it contained sanitary napkins and animal carcasses. this is also a reflection of the diversity of consumables used by families as opposed to personnel living in camps. other items in this category are used tires and oil filters. even the military and private companies change their old tires and oil at workshops outside their own camps; these also end up in the municipality waste. al jabal al akhdar is a rural area in the sultanate of oman where solid waste is still managed by traditional systems of collection and disposal. it is useful therefore to make a comparison between this study and other studies from both developing and developed countries. studies in san quintin and vicente guerrero, northern mexico [24], darjeeling, india [4] and muar, malaysia [25], representing rural regions and developing countries, showed similarities to al jabal al akhdar in that food is one of the major categories in the household and municipal waste along with paper and plastic. in developed countries however, paper and paper board are the dominant waste, followed by food. for example, usepa [15] estimated that paper and paperboard represent 28.0% followed by food waste at 14.5%. the united states (u.s) produces and uses a third of the world's paper, and an average u.s citizen uses more than 300 kg of paper per year. in the united states, the use of paper is not controlled by legislation as it is considered to be biodegradable. a a a a a a a a a a b b b a b b a a b b b b b a ab b a b b 0 10 20 30 40 50 60 70 paper food plastic metal glass textiles wood yard trimming rubber & leather others m e a n p e rc e n ta g e s categoties municipality military private companies abdullah i. al-mahrouqi and reginald victor 8 5. conclusion the ultimate aim of this study was to produce an integrated waste management plan for the entire al jabal al akhdar area taking into account the anticipated urban expansion, tourism and development. data on waste composition and characteristics are essential in order to properly plan and design waste management systems. this study indicates that the municipality should implement a system for the collection and recycling of plastic waste. most mountain areas with high impact tourism have put a ban on the use of plastic bags in all commercial establishments and this strategy should be considered seriously for al jabal al akhdar. the military and private companies should reduce the quantities of food waste by improved planning and management of the catering services. organic waste should be composted for use in agriculture. the data presented in this study provide a benchmark for future studies in al jabal al akhdar. 6. acknowledgements this work was supported by a scholarship awarded by sultan qaboos university to one of us (a.i. almahrouqi) for the doctoral research. we thank al jabal al akhdar municipality for their support during waste segregation and for giving us permission to work at their dumpsite. the authors also thank mr. peter sinclair reid for his help in reviewing 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university of glasgow, scotland, uk. *email: hqzahoor@gmail.com. abstract: the influences of hall currents and heat transfer on peristaltic transport of a nanofluid in a vertical porous tapered channel through a porous medium are investigated theoretically and graphically under the assumptions of low reynolds number and long wavelength and the flow investigated is in a wavy frame of reference. analytical solutions are obtained for temperature, axial velocity, stream function and pressure gradient. graphical results are sketched for various embedded parameters. keywords: peristaltic flow; heat transfer; nanofluid; tapered channel; hall currents and porous medium. ي وسط مساميف هقناة رأسية مستطيل عبرالتاثير المشترك لكل من االنتقال الحراري وتيارات الهول على النقل التمعجي لمائع نيوتوني الحقيد زهورس و عبد اللطيف إبراهيم حمدأ قي وسط هقناة رأسية مستطيل عبرتم دراسة التاثير المشترك لكل من االنتقال الحراري وتيارات الهول كرنت على النقل التمعجي لمائع نيوتوني :ستخلصم اد اطار االسن عبروكبر الطول الموجي . تمت دراسة السريان عدد رينولد بناًء على فرضية صغر الدراسة نظريا واستنتجت الرسومات مسامي. تمت نتائج المستخلصة الموجي . وتم حساب دالة التوزيع الحراري والسرعة المحورية ودالة السريان وكذلك تدرج الضغط خالل السريان .وتم مناقشة واظهار ال المختلفة. من خالل الرسومات .مساميسط و وتيارات هول ،قناة متباعدة ،مائع نانوي ،انتقال حراري ،نقل تمعجي : كلمات مفتاحية 1. introduction ass transfer and heat transfer from different geometries embedded in a porous medium have many geophysical and engineering applications such as thermal insulations, drying of porous solids, cooling of nuclear reactors, underground energy transport, and crude oil extraction. the study of fluid flow through a porous medium and heat transfer constitute a fundamental study of nature and have great practical importance in several physical problems; these include porous heat exchangers, sewage of water in river beds, filtration and purification processes, for example. their industrial importance has led to many experimental and analytical studies of flow and heat transfer in a porous medium in the presence of a magnetic field. mcwhirter et al. [1], and geindreau and auriault [2] have discussed magnetohydrodynamic (mhd) flow through a porous medium in great details. the tapered channel is specially designed to assist in the management of subglottic, tracheal, and glottic stenosis. the superior end conforms to the contours of the glottis, while the larger inferior portion simultaneously acts as a stent for the trachea. the design of the tapered end is such that it projects up beyond the true vocal cords to the level of the laryngeal ventricle. peristaltic flow is a phenomenon found in several industrial and physiological processes. within the body peristaltic flows occur widely in fluid processes such as in urine transport from kidney to bladder through the ureter, transport of lymph in the lymphatic vessels, swallowed food through the esophagus, spermatozoa transport in the human reproductive tract, vaso motion of small blood vessels, etc. in addition to that, peristaltic pumping occurs in many practical applications involving biomechanical systems. the mechanism of peristaltic flow can be best explained by comparing the experimental clinical data and mathematical results. a perfect mathematical study can be served to many peristaltic flows occuring in the human body. many research attempts had been made to understand peristaltic action in different situations. the first attempt was made by latham [3] and some of the interesting investigations in the same direction are given in references [4–7]. moreover, the flow through a porous medium has also attracted the attention of many m ahmed i. abdellateef and syed. z. ul haque 108 researchers in the past few decades because of its important practical applications, as it occurs in sandstone, limestone, filtration of fluids and seepage of water in river beds, wood, and in human lungs, the bile duct, the gall bladder with stones, and in small blood vessels etc. shehawey et al. [8] formulated a mathematical model for the peristaltic transport of a viscous incompressible fluid through a porous medium bounded by two porous plates and el shehawey et al. [9] studied the peristaltic transport in an asymmetric channel through a porous medium. vajravelu et al. [10] examined peristaltic flow through vertical porous tube. srinvas and kothandapani [11] investigated the influence of heat and mass transfer on mhd peristaltic flow through a porous space with compliant walls. srinvas and gayathri [12] continued this work and discussed the peristaltic transport of newtonian fluid in an asymmetric channel of a porous medium with heat transfer. the hall effect is important when the hall parameter which is the ratio between the electron-cyclotron frequency and the electron-atom-collision frequency is high. this can occur if the collision frequency is low or when the magnetic field is high. this is a current trend in mhd because of the important influence of the electromagnetic force. there has been considerable study of hall effects and heat transfer effects on flow to determine the efficiency of certain devices such as heat exchangers and power generators. attia [13] examined unsteady hartmann flow with heat transfer of a viscoelastic fluid taking the hall effect into consideration. asghar et al. [14] studied the effects of hall current and heat transfer on flow due to the pull of an eccentric rotating disk. hayat et al. [15] studied the hall effects on peristaltic flow of a maxwell fluid in a porous medium. abo-eldahab et al. [16, 17] investigated the effects of hall and ion-slip currents on mhd peristaltic transport and couple stress fluid. for further information the references [18–25] provide additional source. the aim of this paper is to investigate the effects of hall current and heat transfer on peristaltic transport of a newtonian nanofluid in a tapered channel through a porous medium. nomenclature a1, b1 wave amplitudes er reynolds number d1+d2 two-dimensional channel width  dimensionless wave number λ wavelength of the peristaltic wave 1 m hall current parameter 1 c wave speed m magnetic field parameter ϕ phase difference k̂ thermal conductivity f  density of the fluid tn thermophoresis parameter p  density of the particle bn brownian motion parameter q velocity vector rg thermal grashof number s t fluid temperature in static condition rb local nanoparticle grashof number d/dt material derivative p pressure rise p pressure f friction force c nanoparticle volume fraction k porosity parameter b d brownian diffusion coefficient θ temperature distribution t d thermophoretic diffusion coefficient  dimensionless nanoparticle volume fraction d amplitude ratio 2. formulation of the problem consider the peristaltic transport of a nanofluid in a two-dimensional channel of width 1 2( )d d . the flow is induced by propagating a sinusoidal wave with constant speed ‘c’ along the channel walls (as shown in fig. 1). we denote the channel walls by 1 h and 2 .h 1 1 1 1 1 right wall 2 ( , ) = cos[ ( )] h x t d k x a x c t      (1) 2 2 2 1 1 eft wall 2 ( , ) = cos[ ( ) ] lh x t d k x b x c t         (2) where 1 a and 2 a are the wave’s amplitudes,  is the wave length, 1 c is the wave speed, and  )(0   is the phase difference. it should be noted that 0= corresponds to a symmetric channel with waves out of phase and that combined effects of hall current and heat transfer 109 for  = the waves are in phase. further, 1121 ,,, badd and  satisfy the following inequality 2 2111 2 1 2 1 )(cos2 ddbaba   . the walls 1 = hy and 2 = hy , are maintained at temperatures 1 t and 2 t respectively. the governing equations for the flow and heat transfer of an incompressible nanofluid in the absence of body force are: 0,=q (3) ,= 2 fqp dt qd f   (4) 2 0 ( ) = ( ) [ ( ) ( ) ( ) ( )], ( ) t f p b ddt c k t c d c t t t dt t           (5) , )( = 2 0 2 t t d cd dt cd t b  (6) where f is the density of the fluid, p is the density of the particle, q is the velocity vector, f is the body force, s t is the fluid temperature in static condition, d dt represents the material derivative, p is the pressure , c is the nanoparticle volume fraction, b d is the brownian diffusion coefficient and t d is the thermophoretic diffusion coefficient. we now introduce a wavy frame ),( yx moving with velocity 1 c away from the fixed frame ),( yx by the transformation ),,(=)(,=,=,=,= 11 txpxpvvcuuyytcxx  (7) figure 1. the simplified model geometry of the problem. where ),( vu are the velocity components in the wavy frame ),( yx , p and p are pressures in wavy and fixed frame respectively. the pressure p remains constant across any axial station of the channel under the assumption that the wavelength is large and the curvature effects are negligible. after using these transformations, the governing equations in steady case become: 0,= y v x u      (8) ahmed i. abdellateef and syed. z. ul haque 110 )( )(1 )(=][ 12 1 2 1 2 2 2 2 vum m b v ky v x v y p y v v x v u o                    (9) 2 2 2 2 [ ] ( ) u u p u u u v x y x x y                  2 * 0 0 12 1 1 ( ) ( ) ( ) (1 ) o b g t t g c c u m v u mk             (10) 2 2 2 2 2 2 0 [ ] = ( ) [ {( ) ( )} {( ) ( ) }] ( ) r b t t t t t c t c t u v d x y y y x xx y d t t t y x                            (11) )( )( )(=][ 2 2 2 2 0 2 2 2 2 y t x t t d y c x c d y c v x c u t b                 (12) where f p r c c )( )( =    is the ratio between the effective heat capacity of the nanoparticle material and heat capacity of the fluid. the corresponding no-slip boundary conditions are: 1 1 1 1 1 2 2 2 = , = , = at = , = , = , = at = . u c c c t t y h u c c c t t y h   (13) consider the following non-dimensional variables and parameters: 2 1 1 1 2 1 2 1 1 1 1 1 1 12 2 1 1 1 1 1 1 1 00 0 = , = , = , = , = , = , = , = , = , ( ) ( ) = , = , = , = , = , = , = , ( ) ˆ( )( ) = , = , = , ( ) ( ) p t ss r e t s f p b b f f d d p h hu v x y ct u v x y p t h h c c d c d d c d t tt td a a c d d b a p r n d d d t t c c d cc c k n g c cc                      2 1 1 ( ) = ,s r g d t t c    * 2 2 2 11 0 0 1 1 2 1 22 1 1 = , = , = , = , = r g d c b d k kk b k m k k c a d d     (14) where st the fluid temperature in static condition, d the amplitude ratio, er the reynolds number,  the dimensionless wave number, 1 m the hall current parameter, m the magnetic field parameter, k̂ -the thermal conductivity, and bn , tn , rb and rg are the brownian motion parameter, thermophoresis parameter, local nanoparticle grashof number, and local thermal grashof number respectively. with the help of eq. (2.14) in eqs.( 2.8)–(2.13) under the assumptions of long wavelength and low reynold number approximation takes the form 0,= y v x u      (15) 0= y p   (16) u m m k bg y u x p rr ) )(1 1 (= 2 11 2 2        (17) 2 2 2 )()(=0 y n yy n y tb            (18) combined effects of hall current and heat transfer 111 2 2 2 2 =0 yn n y b t       (19) the corresponding boundary conditions become: ,=0,=,=1,= ,=0,=1,=1,= 20 1 hymu hyu     (20) where ))/((= 120 ss ttttm  , the wall temperature ratio. the solution of eqs. (2.18,2.19), valid in 12 hyh  satisfying the corresponding boundary conditions (20) is given by  bnhsybns eea 1 1 11 1=   (21) )()(1= 11 hys n n b t  (22) by substituting eqs. (2.21)-(2.22) in eq. (2.17) and solving it analytically as a second order ordinary differential equation, we get a solution in the form, y b nsyaya ecececyccxu 1 6 2 5 2 432 =)(   (23) 3. rate of volume flow the instantaneous volume flow rate in the fixed frame is given by ,),,(= 1 2 ydtyxuq h h (3.1) where 1 h and 2 h are functions of tx , . the rate of volume flow in the wave frame is given by ,),(= 1 2 ydyxuq h h (3.2) where 1 h and 2 h are the functions of x alone. if we substitute equation (1.7) into (2.1) and make use of (2.2), it is found that the related rates of volume flow is: .= 2111 hchcqq  (3.3) the time-mean flow over a period t at a fixed position x is defined as: , 1 = 0 * qdt t q t  (3.4) substituting (2.3) into (2.4), and integrating, we get: .= 2111 * dcdcqq  (3.5) on defining the dimensionless time-mean flows q and q in the fixed and wavy frame respectively as: ,=and= 1111 * dc q q dc q q (3.6) one finds that (2.5) may be written as: .1= dqq  (3.7) from eq. (2.23), with the help of eqs. (3.1)-(3.7), we get the pressure gradient. the pressure rise p and the friction force f (at the walls) for a channel of length l , in their non-dimensional forms, are given by ,= 1 0 dx x p p     (3.8) .)(= 2 1 1 0 1 dx x p hf h    (3.9) .)(= 2 2 1 0 2 dx x p hf h    (3.10) the integrals in equations (3.9)-(3.10) are not integrable in closed form, they are evaluated numerically using a ready package of nintegrate library from mathematica 7. ahmed i. abdellateef and syed. z. ul haque 112 nintegrate uses an algorithm called ‘integration strategies’ that attempts to compute an integral which satisfy user specified precision or accuracy goals. the corresponding stream functions ( y u   = , x v     = ) are evaluated with boundary condition 0= at 1 2 1 2 = ( )z h h . 4. graphical results and discussion here we discuss the quantitative effects of sundry parameters used in analysis with the help of graphs and results. first, let us discuss the variations observed for the pressure rise distributions versus the time average flux ( q ), for different values of the local nanoparticle grashof number ( r b ), local thermal grashof number ( rg ), porosity parameter ( k ), thermophoresis parameter ( tn ), non-uniform parameters ( 1k ) and ( 2k ), hall parameter ( m ). it is noticed in figure 2(a) that with an increase in the local nanoparticle grashof number ( r b ), pressure rise reduces but figure 2(b) shows the opposite behavior and pressure rise increases with the increase in the thermal grashof number ( rg ). at the same time figure 2(c) shows the pressure rise plunges with the increase in porosity parameter ( k ), showing anticlockwise rotation in the graph. figure 2(d) shows that with an increase in the thermophoresis number ( tn ) pressure rise reduces. figures 2(e) and 2(f) give the effect of the non-uniform parameters ( 1k ) and ( 2k ) on the pressure rise in the flow, and show that it plunges with the increase of the non-uniform parameters ( 1k ) and ( 2k ) showing anticlockwise rotation in the graph. in the retrograde pumping region the pressure rise decreases with an increase in non-uniform parameters ( 1k ) and ( 2k ). finally, in figure 2(g) the hall parameter ( m ) gives the opposite effect to the porosity parameter ( k ), where the pressure rise increases in the retrograde quadrant with an increase in hall parameter ( m ) and goes in clockwise rotation. figure 2. variation of pressure rise over the length versus .q a b c d combined effects of hall current and heat transfer 113 figure 2. contd. a fluid particle that moves with a velocity that is different from its neighbours will be subjected to a frictional force, such forces also exist between a particle and a rigid boundary. the friction forces 1 f  and 2 f  on the right and left walls respectively can be obtained by integral evaluations of the analytic results gained for the pressure gradient dx dp . the average of the right friction force (on the right flexible wall) as well as the average of the left friction force (on the left flexible wall) are plotted in figure 3. figure 3. variation of frictional forces. e f g a b ahmed i. abdellateef and syed. z. ul haque 114 figure 3. contd. we notice from these figures that the right and left wall friction forces have the opposite behavior as compared to the pressure rise. the right friction force behaves similarly to the left friction force for the same values of the parameters; however, the absolute value of the right friction force is greater than that of the left friction force at the same values of the parameters. trapping is the development and transport of an internally circulating bolus of fluid. in this bolus a fluid travels along the wave as it propagates. the effect of the hall parameter ( m ) on the trapping can be observed through figure 4 where the size of the bolus reduces with an increase in hall parameter ( m ). the influences of phase c d e f g h combined effects of hall current and heat transfer 115 difference ( ), porosity parameter ( k ), wall temperature ratio 0m , non-uniform parameters ( 1k ) and ( 2k ), hall parameter ( m ) and thermophoresis parameter ( tn ) are analyzed through figures (4) and (5). we notice that the size of the trapped bolus increases with an increase in porosity parameter ( k ) and wall temperature ratio 0m but it reduces with an increase in thermophoresis parameter ( tn ) and the hall parameter ( m ). we can also observe that streamlines get shifted due to the change in the values of phase difference ( ) and wall temperature ratio 0m , and non-uniform parameter ( 1k ) and ( 2k ). figure 4. streamlines for different values of , k, m0 when 0.2 ,tn  0.4,bn  0.4,q  0.4,rb  0.6,rg  0,m  1 0,k  2 0.k  a b  = c d  =0 k = 0.6 m0 = -1 ahmed i. abdellateef and syed. z. ul haque 116 figure 6 depicts the variations of temperature profile ( ) and nanoparticle volume fraction ( ) for different values of the thermophoresis parameter ( tn ), wall temperature ratio 0m and non-uniform parameters ( 1k ) and ( 2k ). it is seen in figures 6(c), 6(e) and 6(g) that the heat distribution ( ) increases with an increase in non-uniform parameter ( 2k ), thermophoresis parameter ( tn ) and temperature ratio 0m . on the other hand, figures 6(b), 6(d), 6(f), and 6(h) show two different behaviour of the nanoparticles volume fraction ( ) profiles. it decreases with the increase of the thermophoresis parameter when 0tn  , wall temperature ratio 0m and non-uniform parameters ( 1k ) and ( 2k ). an opposite trend is observed when 0tn  . 1 0.6k  2 0.6k  7m  nt = 0.9 figure 5. streamlines for the different values of 1 ,k 2 ,k m, tn when 0.4 ,bn  0.4,q  0.4,rb  0.6,rg  0.2,k  0 2.m  e f h g combined effects of hall current and heat transfer 117 figure 6. concentration profile  and heat distribution . a b c d e f ahmed i. abdellateef and syed. z. ul haque 118 figure 6. contd. 6. conclusion the pressure rise 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channel. numer. meth. partial diff. equa. journal, 2010, 26, 747–770. 23. gharsseldien, z.m., mekheimer, k.s. and awad, a.s. the influence of slippage on trapping and reflux limits with peristalsis through an asymmetric channel. app. bionics biomec., 2010, 7, 95–108. 24. srinivas, s. and muthuraj, r. effects of chemical reaction and space porosity on mhd mixed convective flow in a vertical asymmetric channel with peristalsis. math. comp. model., 2011, 54, 1213–1227. 25. kothandapani, m. and prakash, j. effect of radiation and magnetic field on peristaltic transport of nanofluid through a porous space in a tapered asymmetric channel. j. magnet. magnet. mater. 2015, 378, 152–163. appendix   0 1 2 2 1 1 1 2 1 1 1 = , = 1s n h s n hb b m m a a k me e      ,     21 0 1 1 = hhn mn s b t   1 1 1 1 72 1 3 2 2 s = , = s n h b r t r r b b n a be c c g a c a n a                                          2 1 122 12 11 2 11 84 1= a pg n nba ga nsa e a e cc r b tr r b b nhs b nhs                              2 21111 122 12 21 2 11 9 1 a phsbhsbg n nba ga nsa e a e c rrr b tr r b b nhs b nhs ,                                2 1 122 12 11 2 11 12 5 1= a pg n nba ga nsa e a e ec r b tr r b b nhs b nhs ha                                   2 1 122 72 11 2 11 22 7 1 a pg n nba ga nsa e a e ec r b tr r b b nhs b nhs ha                                  2 21111 122 12 21 2 11 12 1 a phsbhsbg n nba ga nsa e a e e rrr b tr r b b nhs b nhs ha ,           b tr r b n anb ag asn c 1 1 2 2 1 26 1 = , 2 11 7 = a hsbgp c rr  , ( 2 ) 3 2 1 2 1 2 7 78 9 = , = h h a h a c e c c e c  received 7 february 2016 accepted 4 september 2016 squ journal for science, 2022, 27(2),119-124 doi:10.53539/squjs.vol27iss2pp119-124 sultan qaboos university 119 optical properties of photonic crystal fibers with fluid cores mohammed salim jasim al-taie gifted guardianship committee, directorate of education, misan, iraq *email: mohammed.altaie@iraqiggc.edu.iq. abstract: the objective of this research is to compare pulses travelling through different photonic crystal fiber cores (dpcfc) using both finite element method (fem) /split step fourier method (ssfm). a unique dcpcf design with exceptionally high non-linearity has been introduced to achieve ultra-high pulse amplitude. via a generalized nonlinear equation, we evaluate the refractive index ratio and dispersion, for each type which is used, as well as output amplitude for different cores in different photonic crystal fiber core by utilizing the solution for the nonlinear schrodinger equation (nlse). lastly, the findings are compared to different photonic crystal fiber design parameters. this paper provides a photonic crystal fiber design consisting of multiple liquid cores and theoretically solved nonlinear equations. it was discovered in this design that the refractive index of propylene glycol (c3h8o2) is greater than ethylene glycol’s (c2h6o2), and that both are far greater than silica's refractive index (sio2). propylene (c3h8o 2 ) has a lower dispersion than ethylene glycol (c2h6o2) and silica (sio2). the output amplitudes of (c3h8o2) and (c2h6o2) were then shown to be substantially bigger than the output amplitudes of (sio2) with respect to distance and time. this emphasizes the need for using certain liquids as cores in holey fibers, dependent upon their use. keywords: photonic crystal fiber; split-step fourier; finite element method; non-linear schrodinger equation; solution pulse. بلورة الفوتونية ذات النوى السائلة متأللياف اللالخصائص البصرية محمد سالم جاسم الطائي فورييه ذات ستخدام طريقة العناصر المحدودة وطريقة إوى ألياف بلورة فوتونية مختلفة بعبر ن المتنقلةالهدف من البحث هو مقارنة النبضات :صلخمال لة ال خطية معممة ، تقديم تصميم جديد من هذا النوع بوجود ال خطية عالية بشكل استثنائي لتحقيق سعة نبضة فائقة. من خالل معادلمنقسمة , تم الخطوط ا ختلفة. اعتمادا على معادلة شرودنكر الالخطية. أخيًرا ، تمت مقارنة النتائج بمعايير التصميم الم نسبة معامل اإلنكسار و التشتت لنوى مختلفه ، تم حساب تم اكتشاف في هذا قدم هذا البحث تصميًما من الياف بلورة فوتونية والمتكونة من نوى سوائل متعددة معتمدة على معادالت ال خطية تم حلها نظريًا. حيث ليكا, كما يظهر أن البروبيلين جاليكول التصميم أن معامل انكسار البروبيلين جليكول أكبر من اإليثيلين جليكول، وكالهما أكبر بكثير من معامل انكسار السي لسوائل قيد الدراسة ومقارنتها مع السليكا حيث ظهر ان األتساع اكما تم عرض نسبة اتساع الخرج للنبضة في ،له تشتت أقل من اإليثيلين جاليكول والسليكا لزمن . وهذه النتائج تؤكد الحاجة إلى استخدام سائل معين في قلب ليف البلورة للبروبيلين جاليكول و اإليثيلين جاليكول اكبر بكثير من السليكا مع المسافة وا التطبيقات المختلفة. في الستخدامها الفوتونية لزيادة كفاءتها واداؤها خطية ، نبضة سوليتون.الال فورييه المنفصل ، طريقة العناصر المحدودة ، معادلة شرودنجر طريقة، بلورة الفوتونيةلياف الأ :مفتاحيةالكلمات ال mohammed salim jasim al-taie 120 1. introduction luidfilled core photonic crystal fibers (fcpcfs) have received a great deal of interest in recent years because of the wide range of uses they might have in a variety of industries [1-15]. filling the core section of the pcf with fluids results in unique optical features such as wideband single-mode guiding, ultraflattened dispersion, large birefringence, huge or ultratiny effective areas , should it be tailored mode area, significant nonlinearity, and so on [16]. using various fluids to fill in the core of pcfs, should it be a multiple assessment refractive index may be obtained. by filling the core with different fluids, several characteristics of pcfs, including effective area, dispersion, and nonlinearity, may be adjusted [17-20]. the variation in refractive index between its core and the cladding in a fcpcf is significantly greater than in a silica core pcf[21-22]. the effective area of the modes of the fcpcf is inversely related to the fiber's nonlinearity [23-24]. it is generally understood that the size of the air hole, and therefore its effective area, is the control parameter in a pcf for adjusting nonlinearity and dispersion. many academics are interested in the soliton pulse in pcfs with various structures, which is one of their applications [25-27]. pcfs have a higher dispersion than silica fibers, according to research. as a result, the dynamics of solution may be investigated on centimeter-length scales. the purpose of this study is to develop the proposed pcf design for ultra-high pulse amplitude. we use the finite element technique to compute the dispersion and nonlinear coefficients in this work. the technique of computation of the pulse amplitude in a pcf is investigated using the finite element technique, which solves the wave equations, and the split-step method, which solves the nlse with an exponentially decreasing dispersion profile for constant design parameters for various core fluids. 2. high nonlinear photonic crystal fiber design we computed the transmission constant of two distinct fluid photonic crystal fibers (pcfs ) with propylene (c3h8o2) and ethylene glycol ( c2h6o2) in the core region. the finite element method (fem) is a commonly utilized mathematical technique for evaluating the field of electromagnetic radiation of pcf travel modes. pcf's effective refractive index was investigated using fem. the pcf was determined by the diameter of the air hole (figure 1, d), the distance between the air holes (figure 1, λ), and number of air holes (figure 1, n). the investigated pcf had a lot of nonlinearity, and the parameters were λ= 3𝜇𝑚, d = 1.68 𝜇𝑚, n = 6. following up on these results, a new pcf was created by filling the core region with fluid. figure 1. (a) longitudinal section of the photonic crystal fiber, (b) cross-section of the photonic crystal fiber. by using finite element method (fem), the effective refractive index of the fluid filled pcf is greater than that of the pcf with a solid core structure because the refractive index of propylene glycol and ethylene glycol is higher than that of silica, as shown in figure 2. f (b) (a) optical properties of photonic crystal fibers with fluid cores 121 figure 2. the relationship between the refractive indices of sio2, c3h8o2 and c2h6o2. the group velocity dispersion (gvd) of propylene glycol and ethylene glycol was determined using the transfer function. figure 3 illustrates the variance in gvd as a function of λ, for different fluids with d = 1.68m and λ = 3m. figure 3. the dispersion of cores consisting of sio2, c3h8o2, and c2h6o2. the computed wavelength dependency of the nonlinearity for various core regions in pcfs is shown in figures 2 and 3, where the nonlinearity is calculated on a logarithmic scale due to the higher fluctuation in fcpcfs than that found in silica core pcfs. the greatest effective area a pcf can support is determined by the fluid in the core. the effects of the intensity dependent nonlinearity is shown to be minimized when the effective area is raised. the nonlinearity of the fcpcf is a few hundred times greater than that of the silica core pcf, as seen in figure 3. 2. pulse amplitude in photonic crystal fibers consider the following nlse of the form in order to understand the mechanics of pulse amplitude in pcf[2832]. (𝜕𝐴 𝜕𝑧⁄ ) − ∑ ( 𝑖 𝑛+1 𝑛! ⁄𝑛≥2 ) 𝛽𝑛 ( 𝜕𝑛 𝐴 𝜕𝑇𝑛⁄ ) = 𝑖𝛾⃓𝐴 2⃓𝐴 (1) and mohammed salim jasim al-taie 122 𝐴(0, 𝑇) = √𝑃° sech ( 𝑇 𝑇° ⁄ ) exp (𝑖𝛼 𝑇 2 2⁄ ) (2) where a is the wave's slowly varying envelope intensity, z is the fiber's lengthwise position in meters, and t is the reference frame's duration in seconds. the parameter (𝛾) is used to indicate the kerr nonlinear factor. figure 4 illustrates the pulse amplitude of propylene glycol and ethylene glycol as a function of time at a wavelength of 835 nm, and figure 5 depicts the impact of core fluids on pulse amplitude as a function of length in pcf, after solving equation (1) theoretically using ssfm. figure 4 shows a sequence of intensity pulses for each core material. it is obvious from this graph that the amplitude of the pulses for propylene glycol and ethylene glycol are larger than that of silica, which is lower, and that it is higher for pcf with a fluid core than for pcf with a silica core. because fcpcf can reach extremely high nonlinearity, very high pulse amplitude may be easily achieved by filling the core area with fluid, as illustrated in figures 4 and 5. as a result, it is worth noting that our newly developed pcfs are very well suited for constructing nonlinear devices, in addition to increasing the amplitude of the pulses. conclusion in conclusion, the pulse amplitude in fcpcf with c3h8o2, c2h6o2 and sio2 fluid cores was investigated using a fem and an ssfm. in comparison with the amplitude ratio of silica-core pcf, we have successfully proven that the novel fluid core photonic crystal fiber we have developed can reach ultra-high pulse amplitude. in addition, the refractive index and dispersion for different liquid cores were studied. the objective of this research was to compare output pulse propagation through different cores of holey fiber (dchf) using both finite element (fem) and split step fourier methods (ssfms) to solve the nonlinear schrodinger equation. in conclusion, it turns out that the pulse amplitude in different cores of holey fiber, which consist of c3h8o2 and c2h6o2, is much larger than the amplitude ratio of silica-core photonic crystal fiber. this gives great importance to using certain types of liquids as cores in holey fiber, depending upon the various uses and applications they will be put to, and according to the designers' needs. conflict of interest the author declares no conflict of interest. acknowledgment many thanks to professor h.a. sultan. who read my numerous revisions and helped make some sense of the confusion. also thanks to my family members, who offered support. thanks to the university of basrah college of pure science for providing me with the scientific resources to complete this project. figure 4. the difference in amplitude of different core materials with respect to time. figure 5. the difference in amplitude of different core materials with respect to length. optical properties of photonic crystal fibers with fluid cores 123 references 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light irradiation faisal al-marzouqi 1,2 and rengaraj selvaraj* 1 1 department of chemistry, sultan qaboos university, p.o. box 36, p.c. 123, al-khoudh, muscat, sultanate of oman; 2 department of process engineering, international maritime college oman, p.o. box 532, pc 322, falaj al qabail, suhar, oman.,*e-mail: rengaraj@squ.edu.om. abstract: a graphite-like carbon nitride (g-c3n4) nanosheet sample was synthesized from a melamine precursor by a method of simple direct heating in a semi-closed system followed by thermal oxidation etching at 550 °c for 12 h. the sample was labelled as (g-c3n412h) and was systematically characterized. moreover, the results were then compared with a pristine g-c3n4 sample for the degradation of bisphenol a (bpa) present in water. bisphenol a (bpa) is an endocrine disruptor. it is known that the bpa is one of the most harmful organic materials and that it does not degrade easily in the environment. it was therefore selected as a target to test the photocatalytic activity of prepared carbon nitride nanosheets under direct solar irradiation. the results showed the structure of the g-c3n4 nanosheets when the sample had been treated for a longer time compared to the regular treatment time. the optical band gap results remained the same, indicating the existence of a g-c3n4 backbone structure. however, the xps and ftir spectra showed some modification on g-c3n4 after longer etching treatment time such as the c-h, co and n pyridinic structure. the photocatalytic degradation of bisphenol a by the g-c3n4 nanosheets under solar irradiation was much better (around 60%) than that with the g-c3n43h bulk sample (around 30%). this enhanced photocatalytic activity can be attributed to multiple factors such as the smaller particle size, rich carbon surface and high surface area exhibited by the g-c3n4 nanosheets. this further indicates that g-c3n4 can be used with solar irradiation to treat wastewater containing endocrine disruptor chemicals. keywords: bisphenol a; carbon nitride; graphite; nanosheet; photocatalyst. إشعاع ضوء تحت g-c3n4( باستخدام شرائح نانومترية من الكربون المنترد bpa)ئي للبيسينفول أ الضوالتحفيزي التكسير الشمس المباشر فيصل المرزوقي ورنجراج سلفراج شبه بوتقة الميالمين في لمركبمباشرة ال الحرارية معالجةال باستخدام الشبيهة بالجرافين g-c3n4شرائح الكربون المنترد من تحضير عينات :صلخمال العينات تم دراسة لتحويل المادة الى شرائح نانومتريه صغيرة. ساعة 21مئوية لمدة 555األكسدة الحرارية عند درجة بمتبوًعا ه. كان التحضيرمغلق bisphenol a بيسفينول أيم مركب غير معالجة باألكسدة الحرارية من حيث قوتها لتحط g-c3n4 تمت مقارنة النتائج مع عينةحيث بشكل منهجي. (bpa) .من المعروف أن مادةو بيسفينول أ هو مادة معطلة لعمل الغدد الصماءالالموجود في الماء bpa تحللهي من أكثر المواد العضوية ضرًرا وال ت ان العينات مباشر. أظهرت النتائج الشمسي اإلشعاع مساعدةنومترية بالنا هذة الشرائحتم اختياره كهدف الختبار النشاط التحفيزي ل لذلك،بسهولة في البيئة. حيث اكتسب العينة القدرة على فصل نواقل الشحنات لمدة .اكتسبت خصائص تحفيزية أكثر فعالية عندما عولجت لفترة أطول مقارنة بوقت العالج المعتاد -c وجود لكل منبعد وقت معالجة أطول مثل g-c3n4تركيب ال التعديل علىبعض ftir و xps أظهر أطياف كما،أطول مقارنة بالعينة الغير معالجة h و co و n بيريدين. كان التحلل الضوئي لـ bisphenol a بواسطة الصفائح g-c3n4 ( من ذلك 05تحت اإلشعاع الشمسي أفضل بكثير )حوالي٪ يُعزى هذا التحسين على نشاط التحفيز الضوئي إلى عوامل متعددة مثل حجم ٪(. يمكن أن 05)حوالي لغير معالجة باألكسدة الحرارية مع العينة ا -g م شير إلى أنه يمكن استخداالشرائح النانومترية. ان هذه الدراسة تالكربون ومساحة السطح العالية التي تظهرها بالجسيمات األصغر وسطح الغني c3n4 اإلشعاع الشمسيبمساعدة هذه المحفزات الضوئية وؤدي إلى اختالل الغدد الصماء لمعالجة مياه الصرف التي تحتوي على مواد كيميائية ت. .المحفزات الضوئية ، الكربون المنترد، الجرافيت، شرائح نانومترية ،البيسفينول أ :مفتاحيةالكلمات ال photocatalytic degradation of bisphenol a (bpa) 87 graphical abstract 1. introduction owadays, a significant awareness has been established with regard to the impact on human health of the organic and inorganic contaminants in the water and environment. these toxic wastes are growing yearly in our environment due to both increased development and energy demand. recently there have been more and more studies highlighting the presence of these chemical pollutants in water. there are many ways in which these contaminants can reach water bodies, as emphasized in much research 1-4 . many organic pollutants have been found in the environment in levels of µg/l to ng/l. amongst all the organic contamination, the pharmaceuticals and personal products and the endocrine disrupting chemicals have attracted more attention due to their potential risk to human health . 5 furthermore, the polycarbonate resins and antioxidant materials used to stabilize plastics mainly depend on the use of bisphenol a (bpa). bpa has been identified as an endocrine disrupting pollutant that changes the function of the endocrine system and consequently causes adverse effects in the health of an organism. 6 thus developing efficient techniques to remove emerging contaminants from water and wastewater is a very urgent need. the degradation of such pollutants using active photocatalysts is a promising technique to treat wastewater. 7 several photocatalysts, such as metal oxides and metal sulphides have been applied for this purpose 8 . there is a growing awareness of visible active photocatalysts. 9,10 unfortunately, most metal based material shows a weak light absorption, low stability and is of high price. 11-14 recently, carbon based photocatalysts have emerged as promising conducting materials due to their high charge mobility. carbon nitride (g-c3n4) is an interesting photocatalytic material. wang et al and his co-worker have published regarding the use of bulk carbon nitride as an active photocatalyst for hydrogen development under irradiation with visible light. 15 a great deal of attention has focussed on the use of g-c3n4 for pollutant degradation and chemical synthesis. most of these studies used bulk carbon nitride material. the carbon nitride (g-c3n4) constructed of nano sheets has a 2d polymer semiconductor structure that is very similar to that of graphene (figure 1a). the band gap of this graphite like carbon nitride (g-c3n4) photocatalyst was measured to be around 2.7 ev 16-17 . the g-c3n4 has shown interesting properties including a suitable redox potential, a band structure located in the visible light region unlike the band structure of tio2 which is located in uv region (figure 1b), thermal and chemical stability, and an ease of preparation that would allow for large-scale production from low-cost precursors. 18,19 n faisal al marzouqi and rengaraj selvaraj 88 figure 1. (a) the chemical structure of graphite-like carbon nitride (g-c3n4) sheet and (b) the band gap structure comparison of graphite-like carbon nitride (g-c3n4) with titanium dioxide. the carbon nitride (g-c3n4) semiconductor can be prepared via a thermal polycondensation process either in a low vacuum system or under high pressure. 20-22 moreover, several research groups have successfully prepared carbon nitride (g-c3n4) under ambient pressure in a semi-closed system, which would be more convenient from an industrial point of view 23,24 . unfortunately, the resulting product was a bulk carbon nitride material and its activity was considered insignificant. the transformation of g-c3n4 bulk material to nanosize can be achieved by different methods such as acidification and sonication 25 . the thermal oxidation process has been less investigated and therefore, enhancement of g-c3n4 photocatalytic performance is targeted to transfer the g-c3n4 bulk material to nanosize materials via this process. to enhance the degradation of bisphenol a via g-c3n4 nanosheets obtained from g-c3n4 bulk materials via thermal oxidation process. the report here, pointed out an enhancement of the degradation of bisphenol a with help of g-c3n4 nanosheets obtained from g-c3n4 bulk materials via thermal oxidation process under solar light irradiation. 2. experimental section 2.1 materials and preparation the nitrogen rich precursor (melamine) was supplied by sigma-aldrich and was used in the synthesis of g-c3n4 without further purification. the preparation took place in a muffle furnace, where melamine powder was subjected to direct heating in a semi-closed system. a small amount of melamine powder (1g) was placed in a crucible with a cover. the direct heating increased the temperature from room temperature to 550 °c at a heating rate of 20 °c/min. the thermal etching process was conducted at 550 °c for 12 h, and the g-c3n4 nanosheets were obtained. (for comparison, 1 g of melamine powder was heated at 550 °c for 3 h to prepare the g-c3n4 bulk material.) the product was collected for further analysis. 2.2 characterization crystal property was investigated by x-ray diffraction (xrd) analysis, using a benchtop x-ray diffractometer (miniflex600). the morphology was examined and elemental surface analysis (edx) performed with a transmitted electron microscope (tem) of model (jem-1400-jeol, japan). x-ray photoelectron spectroscopy (xps) measurements were conducted using multi-probe x-ray photoelectron spectroscopy (xps) (omicron nanotechnology, germany). the results were analysed using the casa xps software (casa software ltd). uv-vis diffuse reflection spectroscopy (uv-vis drs) was performed on a uv-vis spectrometer lambda 650s (perkin elmer), and the infrared spectra were obtained using cary 600 ftir (agilent technologies). optical properties were investigated via photoluminance (pl) with the help of a perkinelmer ls55 spectrometer. the particle sizes were measured using a microtrac particle sizer. the surface analysis obtained by brunauer emmett teller (bet) surface area analysis using asap2010 under liquid n2 with 50 p/po points, micromeritics, usa. 2.3 photocatalystic activity test bisphenol a (bpa) is an endocrine disruptor which was selected to be used for testing the photocatalytic activity of prepared nanosheet and pristine carbon nitride samples. all photoreaction experiments were carried out in a photocatalytic reactor batch system consisting of a cylindrical borosilicate glass reactor vessel with an effective volume of 500 ml. the activity studies were conducted in an open atmosphere with an air diffuser fixed at the reactor to photocatalytic degradation of bisphenol a (bpa) 89 uniformly disperse the air into the solution. the reaction suspensions were prepared by adding 0.1 g of as -prepared gc3n4 into 250 ml of aqueous bisphenol a (bpa) solution with an initial concentration of 10 mg/l. prior to illumination, the reaction suspensions were magnetically stirred for 30 min in darkness to ensure adsorption-desorption equilibrium between the photocatalyst and the bisphenol a (bpa). during illumination (under solar light of average 1400 w/m 2 ), about 6 ml of the suspension solution were taken from the reactor at scheduled interval. the samples were centrifuged at 8000 revolutions per minute for 5 min and were then filtered to remove the catalyst. the filtrate was analysed using a shimadzu1800 uv-vis spectrophotometer. 3. results and discussion 3.1 characterization of g-c3n4 nanosheets the edx analysis (fig. 2a) revealed the presence of carbon (c) and nitrogen (n) as the main elements. a weak signal was detected from the platinum coating. this result indicates the high purity of the samples. the morphology of the samples showed a sheet structure, which is a characteristic shape of g-c3n4. tem analysis (fig2b and 2c) showed the clear transformation of the multilayer bulk structure (dark colour) to nanosheet structure (transparent colour). figure 2. (a) edx spectrum of g-c3n4 nanosheet and sem image (b) and (c) tem images of g-c3n4 bulk and nanosheet respectively. the xrd results for the g-c3n4 samples are shown in fig. 3. carbon nitride materials exhibit two diffraction peaks at 27.90 o corresponding to the (002) plane typical for the interlayer stacking of the c-n conjugated aromatic systems and a peak at 13.05 o for the (100) plane and representing the interplanar separation of tri-s-triazine units. 28 the position of the diffraction peaks was retained during the treatment process, showing the existence of the main structure of g-c3n4. however, the overall diffraction intensity was reduced by increasing the etching treatment from three to up to 12 hours. the (001) plane peak disappeared after 12 h of treatment, and this can be considered to be a consequence of the reduced structural correlation length prompted by a decrease in the number of layers. this result reflects the formation process of the g-c3n4 nanosheets. faisal al marzouqi and rengaraj selvaraj 90 10 15 20 25 30 35 40 (100) g-c 3 n 4 12hrs in te n s it y ( a .u ) 2 g-c 3 n 4 3h (002) figure 3. xrd patterns of g-c3n4 samples obtained after 3 and 12 h of heating. figure 4 presents the fourier transform infrared (ftir) spectrum of the as-prepared samples to identify the specific interaction of the functional groups. the result indicates the presence of the graphite-like structure of carbon nitride. the n-h stretching modes and the o-h from water absorbed on the surface are present in the broad peak observed in the range of 3000-3500 cm -1 (area 1). the bands around 1200-1600 cm -1 are characteristic of a typical stretching mode of cn heterocycles (area2). in addition, the s-triazine ring mode was observed at 801 cm -1 (area3). however, there was some broadening in the peak at 3000-3500 cm -1 , which is indexed to co vibration. 4000 3500 3000 2500 2000 1500 1000 791 898 11181630 3074 3175 3247 32 g-c 3 n 4 12hrs t ra n s m it ta n c e wavenumber (cm -1 ) g-c 3 n 4 3h 1 figure 4. ftir spectrum of g-c3n4 samples obtained after 3 and 12 h of heating. 3.2 optical properties of nanosheets the uv-vis diffuse reflectance spectroscopy (uv-vis drs) was conducted to assess the optical properties of the g-c3n4 samples. fig. 5a illustrates the main absorption results for g-c3n4 heated for 3 and 12 h. the optical absorption edge of g-c3n4 heated for 3 occurs at 390 nm and then red shifts to a longer wavelength for g-c3n4 heated for 12 h, to 410 nm. the effect of a longer thermal oxidation treatment is consistent with the reported results. 29,30 moreover, the gc3n412h sample was more efficient than the g-c3n43h sample in absorbing near uv and visible range up to 470nm. the spectra exhibit a long absorption tail for the samples treated for 12 h, and this can be attributed to structural defects photocatalytic degradation of bisphenol a (bpa) 91 formed in the sample treated for a longer time. the tauc plot was used to calculate the optical band gap. 31 the tauc plots (the curve of (αhυ) 2 versus e where e is the energy in ev and a is the absorption) are shown in fig. 5b and 5c. the band gap value of g-c3n4 was calculated to be 2.7 ev for g-c3n4 heated for 3 and 12 h. the analysis of the band gap values shows that the main structure of g-c3n4 was present and dominant in all samples. figure 5. (a) the uv-vis absorption spectra for g-c3n4 samples. (b) and (c) represent the tauc graph with estimated band gap value for g-c3n4 samples. figure 6a showsthe chemical composition of the constituent elements of the g-c3n4 , obtained by xps analysis. the xps spectra reveal that the main elements present were carbon, nitrogen and some oxygen. the high resolution spectra of carbon and nitrogen peaks are shown in fig. 6b. the binding energies at 286.7, 288.4 and 289.2 ev are indexed to carbon from c-nh2, c-n and c=n respectively, while the binding energies at 397.1, 397.1 and 400.3 ev are attributed to nitrogen from c=nc, n-(c)3 and c-n-h respectively. moreover, some changes occurred for the carbon and nitrogen peaks after treating the sample up to 12 hours. low intensity core level peaks were detected indicating the surface modification of the sample. two peaks appear at binding energies 284.27 and 290.2 ev which could be attributed to c-c or c-h carbons while the other peak at 290.2 ev can be assigned to co resulting from the etching process, and adsorbed on the sample surface 32-33 . this result is compatible with broadening observed in the ftir result. for the nitrogen, the peak at binding energy 393.6 ev can be assigned to edge type n pyridinic which was reported previously for the sample prepared at higher energy 34-36 . the amounts of each element and the carbon to nitrogen ratio (c/n) (wt%) are shown in table 1. there was a slight increase in the c/n ratio. this enhancement may indicate a carbon-rich surface which may enhance the photocatalytic activity by promoting charge carrier separation 37 . faisal al marzouqi and rengaraj selvaraj 92 figure 6. (a) the xps survey of g-c3n4 and (b) comparison of high resolution spectra of c1s and n1s for the g-c3n4 3h and g-c3n4 12h . table 1. the amount of c, n, and o in different g-c3n4 samples. xps surface elemental analysis content (%) c n o c/n g-c3n4 3h 42.23 56.92 0.65 0.74 g-c3n4 12h 43.68 55.54 0.78 0.78 photocatalytic degradation of bisphenol a (bpa) 93 the photoluminescence emission (pl) spectra of as-obtained g-c3n4 samples are shown in fig. 7. the pl measurement was performed at room temperature for the g-c3n4 3h and g-c3n4 12 h samples at excitation wavelengths of 360 nm. the main emission peak is located at about 450 nm for both samples. the emission peak resulted from the photo-generated electron-hole pairs process in the g-c3n4. moreover, the emission intensity indicates the rate of photo generated electron-hole pairs. the spectra show that the g-c3n4 heated for 12 h had a higher intensity compared to that for the g-c3n4 heated for 3 h. the decrease in the intensity can be explained by the electron trapping process that occurs within the bulk material due to a crystal mismatch, which prevents electron-hole mobility. moreover, the formation of nanosheets promoted the charge mobility in the g-c3n4 heated for 12 h. 38 400 450 500 550 600 650 0 50 100 150 200 250 300 350  em =450 nm in te n s it y ( a .u ) wavelenghth (nm) g-c 3 n 4 3hrs g-c 3 n 4 12hrs  ex =370 nm figure 7. the comparison of photoluminescence (pl) spectra of g-c3n4 prepared at different thermal oxidation times. 3.3 particles size and bet analysis the reduction of g-c3n4 multilayered structure (bulk) to few-layered g-c3n4 nanosheets was followed by size particles analysis with the help of a particle sizer. the measurements were performed for both the sample heated for 3 hours and the sample heated for 12 hours. the particle size distributions are shown in fig. 8a and 8b, the average particle sizes being 4967 and 1783 nm for g-c3n4 3h and g-c3n4 12h respectively. this decline in the particle size is attributed to the thermal oxidation etching process. moreover, the bet surface area and porosity of the samples was analysed, with the result showing a type 3 shape of isotherms according to the iupac classification (fig. 8c). this result indicates the occurrence of slightly mesoporous-like structure due to the aggregation of sheets to form the bulk gc3n4, leaving pores in between. 39 the bet surface area was found to be 94.2435 and 94.2435 m 2 /g, where the bjh adsorption surface area of pores was found to be around 123.0573 and 37.8759 m 2 /g for g-c3n4 3h and g-c3n4 12h respectively. this decrease indicates the transformation of the multilayers of g-c3n4 3h (bulk) to a few layers of gc3n4 nanosheets after 12h, where a significantly low amount of surface area was available for nitrogen adsorption due to the overlap of the single nanosheets 40 . faisal al marzouqi and rengaraj selvaraj 94 figure 8. histogram of corresponding particle size distribution (a) g-c3n4 3h, (b) g-c3n4 12h (c) bet surface area plot of g-c3n4 samples 3.4 evaluation of the photocatalytic activity bisphenol a was chosen as a pollutant to determine the photocatalytic activity of the as-obtained catalysts on endocrine disrupting chemicals. bisphenol a is often used as a model for hard degraded endocrine disrupting chemical pollutants. the performance of the g-c3n4 nanosheets was studied with the help of uv-vis absorption spectra changes where the maximum absorptive energy is at 278 nm. fig. 9a shows that the band intensity at 278 nm gradually declines with an increase in the irradiation time. these results indicate that bisphenol a underwent degradation under the catalysis of g-c3n4. fig. 9b shows a comparison of the photocatalytic degradation between g-c3n4 bulk and g-c3n4 nanosheets. bisphenol a degraded faster using g-c3n4 heated for 12 h (around 60%) than with g-c3n4 bulk material (around 30%). 4. conclusion in this work, photocatalytic enhancement has been achieved for degradation of bisphenol a (bpa) through gc3n4 nanosheet photocatalysis, the nanosheet samples being obtained by direct heating of melamine followed by thermal oxidation etching for 12 h. the g-c3n43h bulk material was obtained to conduct a comparison by performing the etching process for only three hours. moreover, the g-c3n412h nanosheet samples show very good photocatalytic activity under solar irradiation when compared to the bulk samples. this enhancement of the photocatalytic activity can be attributed to multiple factors such as the smaller particle size, carbon-rich surface and high surface area exhibited by the g-c3n4 nanosheets. such g-c3n4 nanosheets have good potential for use in advanced water and wastewater treatment to eliminate endocrine disrupting chemicals under solar light irradiation or reduce them to a very low level. photocatalytic degradation of bisphenol a (bpa) 95 figure 9. (a) time-dependent uv-vis absorption spectra of bisphenol a (10mg/l) degradation with g-c3n4 12 h nanosheets under solar light irradiation [catalyst dosage 100 mg, solution volume 250 ml, source of light solar] (b) photocatalytic degradation of bisphenol a with g-c3n4 prepared at different thermal oxidation time under solar light irradiation. conflict of interest the authors declare no conflict of interest. acknowledgment faisal al marzouqi acknowledges the international maritime college oman, sultanate of oman. rengaraj selvaraj acknowledges dr. myo tay zar myint from surface science lab, department of physics, college of science, sultan qaboos university and the central analytical and applied research unit (caaru) college of science, sultan qaboos university, oman. references 1. ribeiroa, a.r., nunesb, o.c., pereiraa, m.f.r. and silvaa, a.m.t. an overview on the advanced oxidation processes applied for the treatment of water pollutants defined in the recently launched directive 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of oman, muscat, *email: elhadi@squ.edu.om, ** directorate general of information technology, ministry of health, muscat, oman, ***hospital information system department, sultan qaboos university hospital, alkhod, oman. یة في عمانصحنظم المعلومات ال ، عبدالرحمن الطوقي، ناصر الشملي و علي عبدهللا الحمداني ، أحمد الحوسني، خالد داي،محمد الھادي الھاشمي ود و یحوى ھذا البحث دراسة للمنظومات الطبیھ فى عمان و مقوماتھ التقنیھ.كما یتولى البحث بالدراسھ و التقییم لحد :خالصة (التشغیل) للمنظومات المستخدمھ فى المؤساسات الحكومیھ و االھلیھ. تعمل ھذه الدراسھ وظائف وعملیات حمایة االعمال على دعم عمل وتحقیق اھداف المنظومات الطبیھ بشكل عام وخصوصا فیما یتعلق بتحسین النوعیھ الشاملھ و الزیاده فى ندرس فى ھذه الورقھ و التى یمكن اعتبارھا خطوه فى الطریق .المستھلكین لھا التنسیق بین المقدمین للخدمات الطبیھ و للوصول الى نظام صحى وطنى شامل,ندرس النظم المتاحھ و المستخدمھ فى عمان من حیث الوظائف و التراكیب. abstract: this paper is a review of oman's major health information systems (hiss) and their enabling technologies. the work assesses the scope, functionality, security, and interoperability of the used systems. the review aids in achieving the objectives of his systems of improving the global quality of health care, attaining increased coordination between health care providers and consumers, promoting the use of guidelines and policies, and improving the speed of simultaneous access and distribution of medical records and other resources. this paper, which can be considered as a building block towards the development of a nation-wide health care system, studies existing systems and identifies their functions and structures. keywords: health information systems; oman; heath care; information technology. 1. introduction atient-centered and information-rich health care systems, in which medical information follows the patient, and information tools guide medical decisions are aspired for by every health care provider and consumer. health information technology (hit) is an enabling technology that encompasses various hardware and software systems used for storing, processing and exchanging medical information. such systems promise to p mohammed elhadi, et al 102 have the potential of transforming traditional health care delivery by bringing information when it is needed and where it is needed; thereby, improving the quality of health care and reducing the cost of delivery (ortiz and clancy, 2003) (usa hhs, 2004) (cht and idx systems corporation, 2005). numerous health care related software systems are in use these days under various names such as computer patient record (cpr), patient medical record (pmr), computerized medical record (cmr), electronic patient record (epr), electronic medical record (emr), digital medical record (dmr), patient medical record information (pmri), personal health record (phr), electronic health record (ehr), picture archiving and communication (pacs), medical diagnostic imaging support (mdis) and many more (who, 2004). all of these are just different ways of referring to similar if not the same entity representing the core of information about patients. we will be using the ehr as our reference in this paper. this article looks at the current status of health information systems (his), their enabling technologies and similar products and services that exist in oman. the work will assess the scope, functionality, security, and interoperability of the considered systems. work done in this direction will aid in achieving the objectives of his systems of improving global quality of the health care through the computerized support of various functions. this work will also help in improving all of the basic functions of his such as scheduling, patient information capturing and retrieval, diagnosis decision support, protocol consultation, care plan management, drug management, scheduling for surgery processing, patient education, quality assurance, and financial transactions. this work will also help in attaining increased coordination between different health care providers and consumers, promote the use of guidelines and policies, and improve the speed of simultaneous access and free distribution of medical records and resources. currently, all the major public health institutions in oman are computerized; that includes all the national referral hospitals, regional referral hospitals, polyclinics and extended health centers, and all the health centers built after 1995. therefore, it is important to integrate these individual information systems into a connected nation-wide system that provides secure coordinated-access and efficient processing of health information. this article is a step towards developing such a system. we will look at existing systems and identify their functions and structures. special attention will be devoted to assessing the level to which the reviewed software systems serve the general requirements of his including: scope of content, information capture, report generation, information representation, decision support, security and confidentiality, performance, interoperability and adherence to software engineering principles. the rest of the paper is organized as follows: section 2 is a general overview of hiss in oman including geo-political and medical aspects; section 3 contains a review of common his functionalities and standards; section 4 provides a description of two exemplary and most commonly used systems in oman; and section 5 is the conclusion. 2. health information systems in oman the sultanate of oman has a wide geographical area with a sparse and small population scattered all over the country. this poses a great challenge to health care delivery. there is also movement of inhabitants between the country side and major cities. some of its nomadic inhabitants (chatty, 1983) also move around periodically with the change of seasons, adding more difficulties to the healthcare management. oman, a developing country, has a lot to gain from information technology in the field of health care. the topology of the country and the demography of its population lend themselves well to the use of enabling technologies in health care. his can expedite the delivery of the much needed health services and improve the utilization of existing services provided by the ministry of health and its affiliated institutions including in particular the sultan qaboos university hospital (squh). existing systems can benefit from some improvements in a number of areas mainly coverage and integration. 2.1 oman geo-political and medical perspectives review of health information systems in oman 103 although oman is an upper middle income country, offering healthcare to its small population is hampered physically and financially by its relatively large size and difficult terrain. oman’s population is scattered over large areas of sparsely populated settlements, many with fewer than 500 inhabitants. expenditure on healthcare has, however, made quantum leaps. as of 2004, the results are impressive: 56 government hospitals, 166 government health centers, clinics and dispensaries, 13.9 doctors and 35.2 nurses and midwives per 10,000 inhabitants. life expectancy today stands at an average of almost 74 years compared to 49 in 1970, and infant mortality per 1,000 is down from 118 to 16.2 by 2004 (escwa, 2005) (emro, 2006). oman’s healthcare system today is a public model, with health services predominantly financed and provided by the government which accounts for 95% of all hospitals, 80% of doctors, 94% of nurses and 83% of other paramedic professionals. although there are 631 private clinics, just 20% of these provide limited specialty care (wilkie, 2005). the present responsibilities of the ministry of health (moh) as stated in the sultanate of oman national health policy statement (ministry of health , 1992) include: • establishing the health policies in the general frames of the country’s strategy. • planning the health care human resources in the framework of the country’s strategy and this includes establishing health institutes in different specialities. • providing information and health statistics and conducting studies in the different health areas. • providing health services (preventive and curative) for the citizens and residents of oman. • conducting training and skill development programmes for the medical staff. • co-operating with medical colleges in training of medical students in the moh institutions. • educating people about health issues and encouraging them to take care of the hygiene and of their health. • working on improving the coordination with gulf cooperation council (gcc), arab countries and international community in health matters. oman is divided into 11 health regions. each health region is autonomously operated and headed by a director general of health services reporting to the undersecretary of health affairs. the health policies and guidelines are formulated by the directorate general of health affairs. the health service in oman is divided into primary, secondary and tertiary care services. the primary healthcare is mainly ambulatory service except in some regional health centers where they have delivery facilities. there are also some wilayat (states) hospitals or local hospitals which deliver only primary healthcare services. the secondary healthcare comprises polyclinic or extended health centers, which are ambulatory and referral regional hospitals with inpatients facilities. there are four main tertiary healthcare hospitals, all located in muscat and each of which is dedicated to certain specialties. those hospitals are the royal hospital, khoula hospital, nahdha hospital and ibn sina hospital. all hospitals report to the undersecretary of health affairs except for the royal hospital which reports directly to the minister of health. the referral hospitals and the tertiary hospitals in muscat are autonomous in their operations and managed by an executive director, with the exception of the royal hospital which is managed by a director general. the ministry of health is looking at further streamlining of its operations. the ministry has been running a pilot study experiment in muscat governate for the last three years with the intention of extending the autonomy scheme to the wilayats. 2.2 health plans and e-government initiative the omani government has made it a strategic goal to use information technology as a tool in supporting its operation and delivery of services with the e-government initiative. the national it authority was created to streamline and coordinate all the it activities by creating nationaland sector-wide group of interest. several projects such as the government network, a high bandwidth multi-protocol label switching (mpls) network, and the educational portal have already been initiated. as part of the e-government initiative, the ministry of health would have to propose a nation-wide e-health portal plan that would link together all the healthcare mohammed elhadi, et al 104 providers in order to exchange the necessary health information and also to build up the national unique patient repository. this is in-line with international aspirations and with the world health organization (who) resolution (who, 2004), passed by the 58th world health assembly, calling all the member states to have a national ehealth strategic plan that would link together all the institutions providing healthcare services. 2.3 oman health service providers a number of health care providers exist in oman ranging from moh to some private providers. the majority of the services, however, are provided by moh which provides about 90% of the health care in oman. other important players include sultan qaboos university hospital (squh), armed forces hospitals, royal oman police hospitals and petroleum development of oman (pdo) hospitals. 2.3.1 ministry of health the initiative of using information technology to support healthcare activities has started since the commissioning of the royal hospital in 1986 to buy a system running only on wang computers. the system turned out to be expensive to acquire and maintain and did not fulfill the requirements of the hospital and the ministry of health. this failure has hampered the utilization of it in healthcare in the whole ministry of health for a very long time. in the early 90’s, the ministry of health decided to look seriously at the wide utilization of it in the healthcare system and all the other support to the healthcare activities in the ministry. a specialized dedicated unit to look at it activities in the whole ministry of health was created. a team comprising, clinicians, other medical staff, administrators and it staff was commissioned by the minster of health to advice him on the utilization of information technology tools in the healthcare institutions. the main recommendation of the team was to acquire internal expertise for developing in-house all the software requirements to manage the healthcare activities. in 1997, the first pilot project at a health center, wadi al jawahir in the suwaiq wilayat was successfully completed. in 1998, nizwa hospital was equipped with a full fledged his. since then a massive deployment program has been initiated. there are over 140 fully computerized health institutions to an almost paperless status and 3 hospitals are film-less. the strategy adopted by the ministry is to make computerization an integral part of new institutions. every year some selected old institutions are included in the computerization program based on the size and the workload. all major institutions are already computerized including the national referral hospitals, the regional referral hospitals, the polyclinics, extended health centers, and the health centers built after 1995. 2.3.2 sultan qaboos university hospital sultan qaboos university hospital (squh) has started its operations with a health information system package called gerber ally, which was selected from a tendering process. realizing the need for a better system, squh floated a tender for a new his package. after lengthy evaluation, trakcare his package was selected and it is currently in use. 2.3.3 other health providers a number of other providers do exist in oman but are mostly independent institutions. they include: • the army medical services (ams). they purchased an his package from a local supplier. the acquired package did not cover all the processes in the hospital. processes such as the laboratory, pharmacy, and clinical documentation were still manually performed. at the beginning of 2006, the ams acquired a new health information system which provides the necessary functionalities of the hospital. • the royal police hospital started with a pilot project that provided an archiving system (document scanning). however, the implementation was not very successful, and at the beginning of 2000, a new hospital information system was acquired. review of health information systems in oman 105 • pdo has also acquired an his package, which is running for several years now. the maintenance and support of the package are still a concern for pdo. for the private health institutions, automation of health care still needs to be put as a high priority. patients’ billing is the main concern at this time. it is the only fully computerized process. 3. his requirements, functionalities and standards importance of hiss requires their professional development and conformance with high standards. any his has to adhere to standards and provide for some common and basic set of accepted requirements and functionalities. many standards have been emerging but there still is no fully developed and accepted international single standard. as such, we have decided to approach the issue from two perspectives. on one hand we looked at commonly desired features and attributes and on the other we surveyed available standards. commonly desired features are in a way, a bottom up approach that would list essential and desirable features current systems have or should have. we are adopting a list of functionalities surveyed in literature and expressed by some of the constituents we have been talking to in the course of the survey. in particular we have heavily followed and used the functional categorizations provided by beale (2001) which divides the features and functionalities of his systems in the following manner (each of which is further elaborated on in section 3.2): • minimal functionalities: minimum set of services to be provided by any his. • full functionalities: a set of functionalities that are optionally provided by hiss. • enterprise functionalities: a much wider and more complex set of functionalities that can be provided by systems to support enterprise-wide use. • local requirements: a set of functionalities derived from local and regional geo-political, legal and medical nature of the country and the region. this set relates to data ownership, legal procedures for security and confidentiality and similar issues of concern in oman. 3.1 the electronic health record an important and focal component of any health systems is the health record and of particular interest in any his is the concept of electronic health record (ehr). 3.1.1 definition there is no single agreed upon definition for the electronic health record or ehr. it has been called differently at different times and places including: computer-based patient record (cpr), electronic patient record (epr), electronic health care record (ehcr) and national health record (nhr). many definitions are cited in the literature (nhr task force, 2002) (handler et al, 2003). ehr is a repository of patient-centered records containing contributions by health care providers in the course of a lifelong care process. centered on patient's information, the ehr automates and streamlines the clinical workflow taking care of communication loops that result in delays or gaps in care. ehr supports data collection and storage for different types of users ranging from clinical to administrative including billing, quality assurance, reporting, planning, monitoring and reporting. 3.1.2 ehr content, usage and ownership a number of issues are the subject of debate in the literature on what makes up ehr, their usage and ownership. many models were proposed that describe the content of an ehr (sowa, 2000, bird et al., 2003). the basic data content of ehr includes but not limited to: mohammed elhadi, et al 106 • persistent information: this is typically static data that remains valid for the life of the record. it includes patient identification, medical, family and social history, medications, therapies, precautions (such as allergies), drug intolerances, immunizations and vaccinations. • test results: records of data and results of tests undertaken by a patient. • healthcare professionals' input and contribution such as histories, examinations, diagnoses, orders, care plans and summaries. another type of data advocated by many researchers (beale, 2001) to be included in ehr is “context” information. each item of knowledge in the ehr relates to certain time, place, clinician and patient particularities during care. numerous other data items that should be included in ehr record have been cited and discussed in the literature. (beale, 2001) contain discussions of items such as orders and pathology, vital signs data such as “diagnostic sequences”, imaging, and multimedia items, demographic information, and clinical guidelines. it should be noted, however, that not every aspect which concerns the subject of care is of interest to every ehr user. clinical data and knowledge content of the ehr is provided and used by different constituents. sources of such knowledge include: • clinicians who provide their observations, summaries and care plans. • associated health workers such as social workers and nurses, who enter their observations and measurement. • laboratory staff that provide raw data such as test results. • patients: who provide symptoms, complaints, etc. healthcare professionals need to be able to use the data in the ehr to support views and high level concepts such as: • trends • timeline views and problem threads. • automatic processing, decision support and statistical and epidemiological systems. the issue of ownership of ehr is unclear and is subject to the level of maturity of the society. it is influenced by: • ownership of the technical infrastructure on which the records reside. • responsibility for data management. • legal ownership of the content. • access rights for public, research, and business sectors. consensus appears to exist on the right of the consumer to the ownership of health record. 3.1.3 architecture and implementations as this paper does not concern itself with architectural and implementations issues of the ehr, we would just like to mention the following in this respect: • architecture undoubtedly matters as far as quality of his systems is concerned. • many proposed architectures and implementations are provided (beale, 2002, bird et al., 2003, hl7, 2004, katrhakis and tsiknakis, 2006). 3.2 his important functionalities as have been mentioned in the previous sections, and with lack of an agreed upon standard, we adopted and closely followed the classifications used by beale (2001). 3.2.1 minimal functional ehr environment in reality ehr is complicated, non-standardized and fragmented across many providers. clinical care and administration routines can start with minimal functionalities. the following are some exemplary but limited services that an ehr should provide: review of health information systems in oman 107 identification service a minimal identification service containing sufficient demographic information on patients, health professionals, and institutions is needed. light directory access protocol (ldap) service or patient identification service (pids) are normally used to provide this functionality. terminology controlled vocabularies and terms from multiple vocabularies are typically made available by a single service in the his environment. such services are used by decision support and by clinical models. an example of this is the terminology query service (tqs), or lexicon query service (lqs), of the object management group (omg). this enables heterogeneous systems to publish their medical terminologies in a form that can be queried for equivalences and definitions independent of the underlying implementations. digital imaging and communications in medicine (dicom) is a standard for handling, storing, printing, and transmitting information in medical imaging. it includes a file format definition and a network communications protocol. the national electrical manufacturers association (nema) holds the copyright to this standard. international classification of diseases (icd) is used to standardize classification of diagnoses, procedures and pathological classification. reference data good level of reference data for drug descriptions is essential. clinical models health information systems based on formal domain models are known as “archetypes”. these are models used to define rules for specific clinical concepts used in the health records. they enable significant improvements in both the clinical quality of systems, as well as their economics. the good european health record and synex systems both include archetype repositories. query and update service primary interface to the ehr to be used by applications and users is an integral part of ehr. 3.2.2 full functional environment a more capable and complete his would include some or all of the following: workflow management care delivered by multiple parties is represented as a network of actions by professionals or providers. rather than being managed on ad-hoc basis by medical staff, it would be more efficient and complete if it can be managed as a process using automated workflow systems. event management events and orders make up a big part of the actions that take place in a health system. a record of the major actions, such as prescriptions, requests for pathology and surgery are included in the her but many of the many intermediate steps (e.g. the more complex pathology tests, surgery) are not of interest in the her. such events are essential for order management. many orders take place in the context of well-known workflows. multimedia and genetics imaging test results such as x-ray, ultrasound, magnetic resonance imaging (mri), nuclear scans, electrophysiology such as electrocardiography (ecg) and electroencephalogram (eeg), and genetics data make up the most detailed and bulky data. such data are logically integrated with the ehr, but usually served from mohammed elhadi, et al 108 specialized computer systems with special storage devices designed to satisfy the storage and retrieval patterns associated with large data. specific items, usually of diagnostic significance, may be added to the ehr. demographics and party identification most providers record more demographic information than needed by the simple id service in a basic environment. such information is usually for practice management, billing and administration, but may also be clinically relevant. most health bodies have a “minimum data set” which includes a large number of demographic details for patients and health professionals. pids is possibly the most appropriate service for demographic information and identification in health environments today. guidelines, protocols and care pathways guidelines and protocols are considered as the decision-making and planning tools of the clinician. their use allows other users to understand the reasons for decisions, so that investigations can be effective. work in the guidelines area includes the arden syntax (pryor et al, 1993) (arden syntax), the glif language (glif), asbru (asbru), and proforma (proforma). decision support decision-support systems require disciplined patient data organization in order to function properly. they rely heavily on coded terms, and formal clinical models in order to navigate data intelligently. in secondary care contexts of the future, decision support may be the primary reader of ehr data. clinical modeling clinical models are representations of physiological and pathological phenomena that are used for predicting patient evolution. they may be locally developed in more advanced provider institutions, typically those attached to universities or medical colleges. such organizations are likely to be a source for clinical models for other providers to use. mobile computing hand-held computing devices are becoming more common in hospitals and health care institutions. the ehr needs to be available for viewing and potentially updating via relatively low-bandwidth interfaces, which may also need to support asynchronous transfers. 3.2.3 provider enterprise functionalities enterprise-wide care is the ultimate objective of health care. it requires that his have the following capabilities: administration and billing managing beds, operating rooms and other resources along with the ability to communicate relevant financial documents between patients, other providers and health insurers or the government is an important consideration. resource location this is an enterprise-level service that responds to distributed queries in the open environment. it enables requestors to know what information is available inside the provider environment. portal an enterprise-level access provided to satisfy the various needs of not just clinical users, but also of population queries, government, insurance organizations, and patients themselves. review of health information systems in oman 109 a number of prototypes have been built indicating likely directions where patients would be able to control access to their records, via an “econsent” mechanism. they would be able to enter their own data and to perform basic queries and obtain summaries of their health records. data sources investigations raw data comes to the ehr from numerous sources including provider institutions and home such as wearable devices. data used is likely to be formatted using a messaging standard such as hl7 or edifact to guarantee some level of uniformity for the information receiver. outside the provider enterprise parties outside the provider enterprise such as patients, government agencies, insurance organizations, researchers and educators interface with the services provided inside the enterprise via a secure gateway, typically implemented as a web portal interface. a patient’s health record information may reside in more than one provider environment, and is logically assembled via distributed web clients which make use of the resource location facility to determine where data exists for a given patient. online resources numerous online resources which are used and operated by ehr environment providers are beginning to appear including terminologies, clinical guidelines, drug and interaction data, public demographics, and libraries of domain models. making use of such resources would be an important cost-effective measure. 3.2.4 other functionalities and requirements another set of requirements that we consider important are listed in this section. some of these requirements are local to oman and are based on local geopolitical, legal and medical issues (such as data ownership, legal procedures for security and confidentiality). confidentiality legislation oman like everywhere else needs to develop proper legislation to regulate patient data confidentiality and access. patient information should be held under legal and ethical obligations of confidentiality. information provided in confidence should not be used or disclosed in a form that might identify a patient without his or her consent except in circumstances where it is reasonable to expect that the information will be held in confidence. patients trust the providers or allow them to gather sensitive information relating to their health and other matters as part of their seeking treatment. they do so in confidence and they have the legitimate expectation that staff will respect this trust. ownership regulations data contained within the medical record belongs to the patient, whereas the physical form which the data takes belongs to the entity responsible for maintaining the record. in many countries the patient has the right to ensure that the information contained in their record is accurate. patients can request their health care provider to remedy factually incorrect information in their records. unique identification mohammed elhadi, et al 110 the use of a unique national medical record number (mrn) is a critical issue for any his. it provides accurate and efficient access to the patient medical information whenever and wherever it is needed. in oman, this issue is currently being addressed and investigated and work is in progress to come up with a solution. common repository data storage is another important factor in his. more than one approach exists. a choice has to be made whether to use a national common repository for all health information systems or to have data distributed among providers in oman. integration with existing systems due to the existence of different systems in the country under public, private and other domains, systems will need to be integrable and interoperable. support for educational and research work need arises in many hospitals and medical institutions for data and systems to be available for educational, training and research purposes. his will need to be able to support such needs technically and at the same time address the confidentiality and security of the information being used. beside the educational module, the system can support also the researchers by allowing the developer to write reports to extract data required for the researchers. for example the system should allow searching for a specific disease using different criterion such as time span, gender and similar restrictions. the system should have online facility to provide some statistics enquiry for specific information that can help the researches in analyzing and finding the right information from the system. 3.3 ehr standards the main purpose for developing and adopting national and international ehr standards is to facilitate the achievement and improvement of the ehr functionalities and requirements. interoperability is one of the key ehr requirements. it is the most lacking for information management and will greatly benefit from ehr standardizations (hl7, 2004, katrhakis and tsiknakis, 2006). the three main organizations currently active in ehr standardization are iso (international standard organization), cen (committee european normalization – the european standard organization), hl7 (health level seven) (hl7, 2004, katrhakis and tsiknakis, 2006, bott, 2004, schloeffel, 2004). the openehr foundation (openehr) and integrating the healthcare enterprise (ihe) are not health standard bodies but they have made an important impact on the ehr standardization. the following subsections provide an overview of the five organizations and their roles in ehr standards. 3.3.1 iso / tc 215 the (iso) health informatics committee (iso/tc 215) is the main international organization for health information standards. it currently has 25 participating countries and 16 observering countries. some of ios/tc 215 ehr standards are completely developed by tc 215 working groups, while others are developed using existing ehr standards from other national and international organizations such as ieee, cen, and hl7 (ocean informatics, 2007, schloeffel, 2004). tc 215 is currently composed of 9 working groups each focusing on important issues such as data structure and interchange, security devices, … etc (iso/tc 215). 3.3.2 cen/tc 251 review of health information systems in oman 111 the committee european de normalization (cen) is the main organization for standards for those countries that are members in the european union. cen/tc 251 is the health informatics technical committee of cen. it is composed of the following four working groups (cen/tc 251): • wg1: information models – developing ehr models and general message descriptions. • wg2: terminology and knowledge bases semantically organizing health information so it can be used in the domains of healthcare informatics. • wg3: security, safety and quality – developing techniques for protecting confidentiality, integrity, availability, accountability, and security. • wg4: technology for interoperability working on middleware, medical imaging, multimedia, and medical device communication in integrated healthcare. cen/tc 251 has two ehr standards which are developed by performing major revisions for its previously published pre-standards (hl7, 2004, schloeffel, 2004). the first standard is cen 13606 “electronic health record communication”. it consists of 5 parts: (1) reference model, (2) archetype interchange specification, (3) reference archetypes and term lists, (4) security features, and (5) exchange model. the second standard is cen 12967 “health informatics service architecture” (hisa) which is a high-level service-based architecture. hisa standard is composed of three parts: (1) enterprise view, (2) information view, and (3) computational view. it provides a reference model for health care information technology services, thus facilitating building and purchasing of interoperable ehr systems. 3.3.3 hl7 health level seven (hl7) is us-based, not-for-profit, ansi-accredited health information standard organization (ocean informatics, 2007, shaver, 2006) (hl7). it has more than 2,400 members including 90% of the largest healthcare information systems venders. hl7 is traditionally used to develop specifications for application-level messaging between health information systems (i.e., interoperability standards). in 2000, its mission was revised to support the electronic health record (ehr). hl7 “version 2.x” messages standards are widely used in the united states and other countries. these standards are typically used between health information systems inside the same hospital, and/or between hospitals and external laboratories. in 1997, hl7 version 3 (or v3) was developed with a new set of standards. its aim was to define application messages based on formal models. a restricted process is used to construct message content schemas including the reference information model (rim), domain information models (dim), restricted message information models (rmim), common message element types (cmet), and hierarchical message definition (hmd). hl7 version 3 uses extensible mark-up language (xml) to generate message schemas. the clinical document architecture (cda) is the first ehr-related hl7 standard (hl7, 2004). cda is an xml specification for clinical documents. it forms an important sub-component of the ehr (not full ehr specifications) and is compatible with the equivalent components in cen 13606 and openehr standards. 3.3.4 open ehr the openehr foundation is an independent, not-for-profit organization that brings together an international community to facilitate creating and sharing of electronic health records via open-source, standards-based implementations (beale and heard, 2006). it was jointly founded in 1999 by the university college of london and ocean informatics. openehr uses a two-level modeling approach to define a common specification for sharing electronic health records (ehrs) within an open architecture (garde et al, 2007). the two-level modeling is used to separate knowledge from information. the first level is the reference information model which can safely store and exchange any clinical information. the second level is used to model the knowledge using openehr archetypes. openehr formalizes the electronic health records in terms of reference model (rm), archetype model (am), service model (sm), and terminology and other ontologies (openehr). openehr uses an xhl-based data mohammed elhadi, et al 112 format to support the sharing of ehr data. it uses a consistent approach for transmission and storage of ehr. it is compatible with other ehr standards such as hl7 version2.x messages and hl7 clinical document architecture (cda). 3.3.5 integrating the healthcare enterprise (ihe) integrating the healthcare enterprise (ihe) is not-for-profit multinational healthcare initiative aimed to accelerate the adoption of information standards needed to support ehrs. ihe was jointly founded in 1998 by the healthcare information and management systems society (himss) and the radiological society of north america (rsna). ihe does not develop new ehr standards but it rather drives the adoption of ehr standards to address specific clinical needs (eichelberg et al, 2005) (ihe). ihe integration profiles are used to select and recommend appropriate ehr standards for a specific healthcare need, develop restrictions, eliminate ambiguities, reduce configuration and interface costs, and ensure high levels of interoperability. ihe has developed a unique process for ehr standards adoption (ihe). the process involves repeating the following major steps in a yearly cycle: • identifying interoperability problem by clinicians and it experts. • integrating profile specification. health care it professionals identify relevant ehr standards and specify how to apply them to address the specified problems. • testing systems at the ihe connectathon. vendors implement ihe integration profiles for their products, and test their products for interoperability at the annual ihe connectathon. • publishing integration statements. two steps are performed to simplify the systems acquisition process: (a) venders publish ihe integration statements for their products, and, (b) users can refer to the ihe integration profiles in requests for proposal. 3.3.6 harmonization the harmonization of ehr standards is extremely important to facilitate the interoperability between different health information systems that use different ehr standards. ios/tc 215 has performed a very important role in ehr harmonization at the international level (hl7, 2004). the three main standard development organizations (iso/tc 215, cen/tc 251 and hl7) have signed agreements and mous (memorandum of understanding) to further coordination and collaboration among them with particular emphasis in ehr harmonization (hl7, 2004, schloeffel, 2004, ribick, 2006). they have developed shared plans to strengthen the delivery of standards-based health solutions for all customers, and improve the safety, accessibility, quality, and effectiveness of health service delivery. 4. main his systems in oman the ministry of health (moh) is the main provider of health care in oman. moh has a comprehensive his system called al-shifa (arabic for recovery). it is an automation of most processes of healthcare delivery in moh hospitals and health centers. the second most important his system in the country is the sultan qaboos university his system called trakcare. given the importance of these two systems and their coverage of an estimated 95% of his usage in the country, we present in this section a detailed description of these two systems. there are over 140 computerized health institutions in oman. all major institutions are already computerized. in addition, the strategy states that the usage of it in all processes of the heath cares delivery system in order to streamline them and make them cost effective. it also calls for making of all it applications tailored to all requirements of the local health institutions, and also providing necessary information for planning and other research purposes. 4.1 the moh al-shifa system review of health information systems in oman 113 the computerization in moh started in 1987, at the royal hospital, a national referral hospital. in 1990, a specialized and dedicated unit for it was created in the ministry. in 1997, the first computerized health center was implemented using an in-house developed system. in 2004, the information technology unit of the moh was upgraded to the level of directorate general with 4 departments and 15 sections, to become the directorate general of information technology (dgit). the e-health strategy of the ministry of health is built around al shifa. each healthcare institution has al shifa customized to fit its specific requirements. as a second phase, an e-referral engine has been built to allow the exchange of necessary medical information. it covers the request for appointment for further specialized treatment, investigation referrals, request for second opinion and referrals feedback. the system has also a management module, which provides the status and the necessary management information for referrals. the system is under implementation. moh expects to complete the implementation of all healthcare institutions linked to the ministry head-quarters by the end of 2007. other institutions outside moh would have to use it for transferring patients to the ministry of health institutions after 2007. the e-referral engine has been built on the guidelines for referral established by the directorate general of health affairs the third phase would be an establishment of unique identification and building a national e-health record repository. for the unique identification, under the e-government initiative, the existing national identification number for omani and the residency number for expatriate have been selected. the ministry of health is exploring the feasibility of establishing the national e-health record repository with the necessary securely mechanisms. 4.2 system overview al-shifa hospital information management system is a client-server system. it is a fully integrated graphical user interface application system for hospital management that is built around oracle 9i database and developed using oracle developer 6i that runs under the platform of windows 2000/linux. the system uses a single menu that represents the fundamental components of the electronic medical record. it allows on-line access to admission, discharge, transfer, radiology and laboratory test results, etc. as per user access privileges. 4.2.1 main features the system was built to fit the local environment and it complies with user requirements supporting easy electronic exchange of medical information among health institutions. adherence to international standards and interoperability were considered during the design and implementation phases. the whole system (including the source code) is owned by the moh. therefore, any modification or customization is done in a cost effective manner. the system maintains an audit trail that records the previous information prior to making the changes, the changes made, the user’s name that made the changes and the date and time of the changes. the system has been built in compliance with e-health's internationally recognized standards, namely the hl-7, the cen/tc-251, the iso-215, snomed-ct, etc. short messeging (sms) and email services have been integrated in the system and are used to inform and remind patients about thier appointments in the various health care institutions. the system provides comprehensive data inquiry reports based on the user-defined search criteria. 4.2.2 system description and functionality al-shifa hospital information management system is made of the following components: patient and clinical information management the clinical system is a sub-system of the his that brings a patient’s comprehensive medical record to a single screen. it provides the physician instant access to almost any desired level of underlying clinical details. the system also protects information from inappropriate access and provides control over who is exactly permitted to read, write and delete patient information. mohammed elhadi, et al 114 the clinical system is represented by sub-modules and processes which allows doctors to perform tasks such as visit creation and admission, patient’s laboratory and radiology orders, examination and medication, diagnosis and progress, vital information and history, nursing notes and other information relating to a patient’s care. the clinical workbench enables users to take notes, place new orders for the patient, review existing orders, pre-operation orders, inpatient discharge orders, etc. doctors can access the notes and records entered by the nurses such as vital signs and nursing notes, intravenous (iv) fluids, nursing procedures, medication executions and other related nursing care. medication and pharmacy management the medication module automates the process of writing and tracking prescribed medications. all medications are recorded regardless of the patient’s visit status whether the patient is outpatient department (opd), accident and emergency (a&e), inpatient or daycare. the medication module is interfaced with the pharmacy module so that prescribed medications are automatically sent online for quick dispensing. a facility to view the non-availability of the drug in the pharmacy is provided to inform the doctor of the availability of particular medicine. the medication module is also interfaced with the medication dispensing in the nursing module so that prescribed medications for inpatients are carried out according to the dosage and course prescribed by the doctor. prescribed medicine deletion is allowed only if the medicine has not been dispensed to the patient. if it is decided to discontinue the ongoing medication, the system records the date and time and the name of the doctor stopping the medicine. the medication history module maintains the details of each medicine being prescribed. it includes the order date, the dosage details, the doctor’s name, stop date and the reason for discontinuing. it also maintains a record of dispensing details such as dispensing quantity, dispensed location and the name of the staff that administered the medicine. medication literature and overview are available and could be seen by the doctor prior to medicine prescription. information included in the literature relates to dosing information, pharmacokinetics, cautions and clinical applications. radiology and clinical laboratory management requesting laboratory tests is a quick and easy process, which uses a single screen to enter the test information. a wide variety of ordering parameters allows the doctor to designate test orders and set priorities. the system has also the ability to alert the doctor if a repeated order is made as well as the cost of each investigation. the visit history function provides a complete record of the previous laboratory investigation details arranged according to the type of visits. within each visit, the date, time and the details of the results of each investigation are recorded. the blood request function is interfaced with the laboratory system that enables the doctor to order online blood bags required for a patient's surgery procedures or in any given situation wherein a blood transfusion is required. blood requirement details such as blood type, blood group, bag and required volume, required date and the reason must be filled in. the ultrasound module runs as a part of the clinical system allowing the doctor to enter the examination results of the fetus and the female genital tract. the laboratory system has the facility to maintain an audit trail that records the previous investigation results prior to recall. 4.2.3 system's protection and security the system has been designed with compliance of the main elements of e-security: confidentiality, integrity, and availability. the system is isolated physically from the internet. it does not allow the use of removable storage such as usb memory and cds within the health net. review of health information systems in oman 115 within the system, access to the different functions and processes are controlled through strong users’ profiles and by user identification and password to restrict unauthorized users from gaining access to other modules from which they are prevented from entering or updating. the critical components are implemented in redundant fashion to insure high availability to the patient record. the e-security team in dgit is working on implementing an e-security policy, which includes many instructions to the system users and administrators. the system provides full data security that can limit specific functions and process by username and password. in addition, the system provides control over access to menus, icons that represent a particular process and functions for each user or groups of users. the system can identify the user of a particular function or process so that an audit trail of changes made to the patient record is maintained. the system records the previous data, the changes made, the user who made the changes and the date and time. 4.2.4 future plans the following are moh planned future extensions to al-shifa system: • a national repository of e-health record • e-referral engine, which automates the following functions: • request for appointment • consultation feedback • request for second opinion • investigation referral • creating e-health legislation • links among all health institutions • use of national id number • tele-education project • integration of financial, hr, administration and clinical systems • disaster recovery system 4.2.5 challenges the following are difficulties to related to the adoption of the moh al-shifa system: • lack of it experienced technical staff • lack of training programs for medical staff. • no standard requirements (each hospital has its own requirements) • cost of e-links (expensive) 4.2.6 levels of functionality and compliance with standards al-shifa system provides for the most basic functionalities any his system is expected to do, taking relevant standards into account. however, it lacks formal commitments to standards. it is expected that once the systems is fully functional and all planned enhancements are done, it will comply with major international standards. 4.3 the squ trakcare system the sultan qaboos university hospital uses an his system called trakcare. it is an integrated hospital management system that provides computerized support for a number of clinical, administrative and financial operations at the hospital. the squ hospital started using this new trakcare system in july 2006, replacing an older his system which was in use since 1992. trakcare is a ready made package system developed in australia. this section describes to some level of detail the trakcare system. mohammed elhadi, et al 116 4.3.1 system overview trakcare is an integrated hospital management system composed of a set of components serving the different needs of the various hospital departments as discussed in the next section. the system uses a proprietary relational database management system called cache. at the heart of the system is the patient administration and clinical system (cis, pacs, dicom, file systems) along with the integrated human resource and finance management system (hrfms) application. remote access to the system can be provided using the internet. 4.3.2 main features one of the main features of trakcare is the ability to define patient and data flows. the system can be configured to route information relating to patients to specific locations or departments in the hospital based on the defined hospital policies. in addition, the system allows users to define clinical pathways and use them to route patients. trakcare is a web-based system which allows remote access using internet connections. the system also provides mobile support allowing users to record information at the point of care. it is possible to link to any other system or devices conforming to the hl7 protocol. the system provides access to live data for the medical students to work on without affecting the original data which is a good feature for the university hospital. 4.3.3 system description and functionality trakcare is composed of different modules serving the needs of the various hospital departments. the following are brief descriptions of the main system modules: patient administration system (pas) the patient administration system is the entry point of patients to the medical facility. it provides functions to manage patients from the point of admission until discharge. it involves patient registration, admission, inpatient and outpatient management, billing and medical records. clinical information system (cis) the clinical information system provides the necessary tools and functions to manage patient clinical data. the clinical information system is further divided into sub-modules which allow the management of clinical records, patient orders, medical and nursing notes: • electronic patient record: alerts, allergies, patient medical history, family-history and interactive icons. • operation notes: pre-anaesthesia, post anaesthesia and ot notes. • student electronic patient record (sepr) pharmacy management system (pms) the pharmacy management system supports the workflow of inpatient and outpatient pharmacies. pms provides formulary, dispensing, and manufacturing functions. it supports the pharmacy's day to day work cycle from ordering till dispensing. also this module links with inpatient medicine dispensing and substitutions medicine. radiology management system (rms) currently squh is using rms from siemens which is going to be interfaced with trakcare for the necessary data, reports, orders and images to flow between the two systems. the rms module provides functions to run and manage the radiology department. it provides scheduling, inventory, reporting, and film tracking. results entry can be done using text or voice recording. review of health information systems in oman 117 laboratory management system (lms) the lms module provides support for the various laboratory departments. the system supports both uni and bydirectional integration to most of the lab instruments. lms provides the necessary functions to manage specimen receipts, results entry, and results authorization. non-medical services trakcare includes a number of non-medical support services for handling patient accounting, inventory management, and central supplies management. patient accounting: trakcare includes a patient-accounting sub-system supporting the following: • accounting for individual patients. • accounting for corporate patients with and without shared costs. • insurance schemes with and without shared costs. • multiple payers per patient episode. • multiple insurance schemes. the user can define the patient billing rules using a table-driven interface. patient accounting reports can be generated regularly or on-demand. the patient accounting module supports financial management of multiple sites with autonomous or centralized control. in terms of insurance management, the accounting module supports the handling of multiple insurance plans with user-defined parameters for each insurance plan. a contract management feature supports the billing and collection of vendor billing accounts. activities affecting a patient's account are recorded and transaction histories can be viewed on-line. inventory management: this module allows computerized handling of purchasing and stock management. purchase orders entry, approvals, and status tracking are supported. the purchase orders can be triggered by the inventory levels. individual stock items can be assigned batch controls, shelf life restrictions, and stock locations, replenish source, minimum/maximum quantity, re-order level and quantity. this stock system of trackcare is interfaced with the human resources and financial system to transfer data from main stores to various locations. supplies: this module allows management of sterile supplies, linen and disposable supplies. supported functions include items categorization, sub-stores identification, and item-location association. additional features: trackcare includes a number of additional features supported for mobile as well as webbased access to medical information. the following features are supported by the system: (1) mobile information system: palm devices can be used for uploading, accessing and updating offline medical information during ward rounds and during home nursing visits. (2) web interface: webtrack supports web-based access using standard web browsers. the main supported web-based operations are patient registration, online appointments, access to patient records, and online orders. (3) sms: the short messaging system (sms) for patient's appointment. 4.3.4 areas of improvement the trakcare system supports many of the important health care functions as described above. some areas that are missing or require improvement are listed below: medical audit medical audit is the evaluation of medical care in retrospect through analysis of medical records. it relates to examination and verification of dealings of medical care. medical audit is vital for the measurement of the quality of care given to the practice population. medical audit requires standard setting, data collection, comparison with standards, review of data and standards, review of current practice, change in that practice and further data collection and comparison with the original data. mohammed elhadi, et al 118 medical referrals in order to obtain appropriate medical care, patients can be referred or transported from one hospital to another based on the capacity, capability and quality of medical care provided by hospitals. therefore, enabling patient care records to be shared among hospitals is essential not only in delivering the quality of medical care services but also in saving medical expenses. there is a need for a unified referral information system in which patient care records can be shared among hospitals over the internet. mobile computing the ubiquitous access to information anytime, anywhere in the medical field is very important. one of the promising ubiquitous computing models is the mobile clinical information system using hand-held computing devices. the system should enable doctors to access patient clinical test results from any location, make clinical orders instantly, and send the consultation requests to the specialists using a portable device (fischer et al., 2003, ebell et al., 1997, greiver, 2001). 4.3.5 integration with other systems with recent movements toward shared clinical data, integration between different medical information systems is becoming more and more important. data integration, particularly in a medical environment, is an important issue that must be considered seriously. the integration of data from a variety of sources will improve the clinical decision-making process (stead et al., 2000). medical data representation and communication standards should be deployed for interoperability among various systems. 4.3.6 challenges being an international system and the system is to be customized; the involvement of users was required in defining all aspects of the system. the package lacked certain functionalities which are being built. the functionalities missing were iv processing, discharge summary and pharmacy processing for total parentental nutrition (tpn), diet processing, etc. alternate manual procedures had to be found for these. many of the users had very little experience in using computers for day to day work and hence took time to get used to the new system. 4.3.7 levels of functionality and compliance with standards the trakcare system is compliant with the following standards: • international classification of diseases (icd) • digital imaging and communications in medicine (dicom) • systematized nomenclature of human medicine (snomed) • health level 7 protocol (hl7) 5. conclusion the health sector in oman has a lot to offer and certainly to gain through the adoption and use of information technology. enabling technologies in health care can provide efficient access to the much-needed health services. currently the country’s needs in health care are mostly catered for by the ministry of health and its affiliated institutions including in particular the sultan qaboos university hospital. most health care providers in the country are under direct supervision of moh. this makes it easier in some ways to automate and generalize the health services. although it may not be fully utilized, al-shifa system is in prominent use in all health centers in oman. it still needs and has the potential to be improved in a number of aspects. coverage and integration being the most needed aspects of improvement. further developments are needed in areas of legal aspects, confidentiality and ownership. since the technology is growing very fast in the health sector, and as there are many systems in oman, we believe that it is the right time to take the necessary steps toward review of health information systems in oman 119 integrating these systems. this will improve patient care delivery by reducing health care cost, providing fast and simultaneous access to the same patient record from any hospital in oman, and enabling the creation and use of a national healthcare database in oman. 6. references arden syntax. url: http://cslxinfmtcs.csmc.edu/hl7/arden/ asbru. the asgaard project. url: http://www.asgaard.tuwien.ac.at beale, t. 2001. health information standards manifesto. v2.5, december 2001. url: http://www.deepthought.com.au/health/his_manifesto/his_manifesto.pdf. beale, t. 2002. unified ehr standards – is convergence possible? stud health technol inform.87: 78–97. beale, t. and heard, s. 2006. openehr architecture: architecture overview, openehr release 1, the openehr foundation, september, 2006. bird l., goodchild, l. and tun, z. 2003. experiences with a two-level modeling approach to electronic health records, the journal of research and practice in information technology, 35(2): 121-137. bott, o.j. 2004. the electronic health record: standardization and implementation. 2nd openecg workshop, 2004, berlin, germany. cen/tc 251. european committee for standardization technical committee on health informatics. url: http://www.centc251.org/ chatty, d. 1983. the bedouin of central oman. journal of oman studies, 6: 149-162. cht, idx systems corporation, 2005. accelerating transformation through health information technology. washington, dc: summary of findings from the cht connectivity conference, october 18, 2005. url: http://www.healthtransformation.net/ ebell, m.h., gaspar, d.l. and khurana, s. 1997. family physicians’ preference for computerized decisionsupport hardware and software. the journal of family practice, 45(2): 127–128. eichelberg, m., aden, t., riesmeir, j., dogac, a. and laleci, g.b., 2005. a survey and analysis of electronic healthcare record standards. acm computing surveys, 37(4): 277-315. emro, 2006. regional health systems observatory, who. url: http://gis.emro.who.int/healthsystemobservatory/pdf/oman/full%20profile.pdf. escwa. 2005. national profile for the information society in oman, 2005 url: http://www.escwa.org.lb/wsis/reports/docs/oman_2005-e.pdf. fischer, s., steward, t.e., mehta, s., wax, r., and lapinsky, s.e. 2003. handheld computing in medicine. j. of the american medical informatics association, 10: 139-49. garde, s., knaup, p., hovenga, e. and heard, s. 2007. towards semantic interoperability for electronic health records: domain knowledge governance for openehr archetypes. methods inf med; 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however, it has no effect on the fraction of the prey outside refuge, in the long run. it is shown that the intensity of fear harms predator population size. numerical simulations show that the application of zcontrol will force the system to reach any desired state within a limited time, whether the desired state is a constant state or a periodic state. our results show that when the refuge size is taken to be a non-constant function of the prey outside refuge, the systems change their dynamics. namely, when it is a linear function or an exponential function, the system always reaches the predator-free equilibrium. however, when it is taken as a logistic equation, the system reaches the co-existence equilibrium after long term oscillations. keywords: predator-prey; refuge; fear; z-control and adaptive control. z نموذج المفترس والفريسة مع ملجأ وخوف وتحكم خان ليل أحمدجال،كوكب العامري و قمر ىإبراهيم مجتب المفترس يكون مستقًرا بشكل يتضمن الخوف والملجأ. تظهر نتائجنا أن التوازن الخالي من الذي في هذه الورقة ، نعتبر نموذج المفترس والفريسة :صلخمال نظهر أيًضا أن مقارب عالميًا إذا كانت النسبة بين معدل وفاة المفترس ومعدل تحويل الفريسة إلى مفترس أكبر من قيمة الفريسة في الملجأ عند التوازن. القدرة االستيعابية. تظهر المحاكاة العددية أنه عندما نقطة توازن التعايش مستقرة محليًا بشكل مقارب إذا كانت قيمة الفريسة خارج الملجأ أكبر من نصف تبين أن شدة الخوف لها يليزداد جزء الفريسة داخل الملجأ ، ولكن ليس لها أي تأثير على جزء الفريسة خارج الملجأ ، على المدى الطو ،تزداد شدة الخوف سيجبر النظام على الوصول إلى أي حالة مرغوبة خالل فترة زمنية zتطبيق التحكم تأثير سلبي على عدد الحيوانات المفترسة. تظهر المحاكاة العددية أن خارج الملجأ ، فإن محدودة ، سواء كانت حالة الرغبة حالة ثابتة أو حالة دورية. تظهر نتائجنا أنه عندما يتم اعتبار حجم الملجأ وظيفة غير ثابتة للفريسة ون دالة خطية أو دالة أسية ، فإن النظام يصل دائًما إلى التوازن الخالي من الحيوانات المفترسة. ومع ذلك ، عندما يتم . أي عندما تكديناميكياتهااألنظمة تغير أخذها كمعادلة لوجستية ، يصل النظام إلى توازن التعايش بعد التذبذبات طويلة المدى. التحكم التكيفي. ،التحكم -z،يخاف أ،. لج،فريس ،المفترس:مفتاحيةالكلمات ال predator-prey model with refuge, fear and z-control 41 1. introduction redator-induced stress in prey animals has not been much studied by physiologists or population ecologists. canon [1] studied the concept of predator induced stress in a prey population. population ecologists have focused their studies on predator induced stress effects on the birth rate of free-living prey populations and found that it affects the demography process of prey animals seriously. by experiments in laboratories and field studies it has been demonstrated that mere exposure of prey animals to predators affects the birth rate of prey, and this phenomenon of behavioral change of demography is called the “ecology of fear”, “degree of fear” or “cost of fear” by ecologists. only a little work has been done on the subject of stress induced in a prey population due to predators. the concept of stress was limited to humans and it was thought that stress in a prey population is transitory and that it is not lifelong. ecologists in the 1990’s [2-4] verified experimentally that fear of predators is a more powerful cause of demographical change in a prey population than direct killing, shortage of food, or parasitic infection. fear of predators in prey persists even in the absence of predators and has long-lasting effects on their production of prey species. sapolsky [5] explained the concept of stress in zebras due to fear of lions. zanetteet al. [6] reported, after experimental verification, that the sparrow reduces offspring production by 40% just with intimidation by predators where direct killing is stopped by some means. zanetteet al.[6], eggers et al. [7], and travers et al. [8] verified that female sparrows lay fewer eggs and, due to incubation disruption, fail to hatch eggs. due to fear, they bring less food to their nests and, as a result, a greater proportion of their nestlings starve to death. creel et al. [9], creeland christianson [10], and creel et al. [11] reported that in the national parks, usa, due to intimidation by wolves, elk pregnancy rates decline. recently, moncluset al. [12] examined an association between predator risk and birth rate of prey. field studies have demonstrated that playback of predator sounds can affect the emotions of prey. remagehealey et al. [13] demonstrated that a playback sound of dolphins affects the emotions of gulf toad fish. mateo [14] found that playback of the call of predators’ alerts squirrels and that they communicate predator risk to each other. the playback sound of predators increases the glucocorticoid level in prey and hence increases the fear or stress in the prey population. wanget al. [15] studied how fear of a predator reduces the reproduction of prey animals and found that it could destabilize the system. a refuge is an area, such as island, where wild animals obtain protection from predation. in this protected territory the chances of being hunted by predator are reduced and these areas reduce the chances of extinction of prey species due to predatory killing. it is a natural phenomenon of prey species in an ecosystem to seek protection from predation (cowlishaw [16], sih [17]). refuge habitats are of different types, such as burrows, trees, cliff faces, or dense vegetation (clarke et al. [18], dill and houtman [19], berger [20], cassine[21]). coral reefs provide refuge for prey fish (friedlander and martine [22], sandinet al. [23]). various control systems are used to prevent a species from drastic oscillations and avoid extinctions in an ecological system. the literature records various techniques for control in the multi-species lotka-volterra system. these controls are called adaptive control, back idea of control, impulsive control and applications of control theory to lyapunov functions. one can refer to [24,25,26], where z-control obtains the desired steady state quickly and prevents high amplitude oscillations. the z-type control method is an error-based dynamic method, and in this method, it is certain that error function converges to zero. the error between desired outputs and actual outputs go to zero exponentially. there are two ways to apply z-control in a predator-prey system. the first method is called direct control, where both prey and predator are controlled simultaneously to bring the population to a desired level. the second method is called indirect control, where either prey species or predator species is controlled through immigration, emigration or culling. the second species automatically comes to the desired level exponentially. our model is similar to t h a t o f wang et al. [27], and we examine this model by introducing predator fear. prey only come out of refuge when they feel t h e r e i s less predation; otherwise, they go back to the protected area. we use two control measures to bring the model population of prey and predator to a desired level, and thus we can save it from becoming extinct. 2. model formulation we studied a model where a prey species lives in two different habitats. one is called t h e refuge habitat where the prey species is saved from predation. it is assumed that all resources required for the growth of the prey species are available inside the refuge habitat and that their population grows logistically. it is also assumed that t h e prey species is fully protected from predation inside t h e refuge habitat. when pressure of predation fear i s released, then t he prey species moves to a second habitat outside the refuge and in this habitat t h e prey species can be killed by predators under the law of mass action. as predation fear increases in the prey species due to the presence of predators, the prey species migrates to the refuge habitat. in the absence of a prey species, predators die exponentially, because predators can only consume prey outside the refuge habitat. this predatorprey interaction is modelled by the following diagram and system of differential equations: p ibrahim m. elmojtaba et al. 42 figure 1. compartmental representation of the model. 𝑑𝑥1 𝑑𝑡 = 𝑎𝑥1 (1 − 𝑥1 𝑘 ) − 𝛼𝑥1 1+ 𝑒𝑦 + 𝛽𝑥2 𝑑𝑥2 𝑑𝑡 = 𝛼𝑥1 1+ 𝑒𝑦 − 𝛽𝑥2 − 𝑏𝑥2𝑦 𝑑𝑦 𝑑𝑡 = 𝑐𝑥2𝑦−𝑑𝑦 (1) all variables and parameters in model (1) are positive and defined below: 𝑥1 prey density in the refuge habitat. 𝑥2 prey density outside the refuge habitat. 𝑦 abundance of predator species. 𝑑 death rate of the predator. 𝑘 carrying capacity of the prey in the refuge habitat. 𝑏 feeding rate of the predator on the prey outside the refuge habitat. 𝑐 conversion rate of prey to predator. 𝛼 migration rate from the refuge habitat. 𝛽 immigration rate into the refuge habitat. 𝑎 birth rate of prey species inside refuge. 𝑒 the fear parameter. 3. mathematical analysis of the model 3.1 positivity of solutions model (1) describes the dynamics of animal populations and therefore it is very important to prove that all quantities will remain positive for all time. we want to prove that all solutions of the model with positive initial data will remain positive for all time t>0. we can easily verify that 𝑑𝑥1 𝑑𝑡 | 𝑥1=0 = 𝛽𝑥2 ≥ 0 predator-prey model with refuge, fear and z-control 43 𝑑𝑥2 𝑑𝑡 | 𝑥2=0 = 𝛼𝑥1 1 + 𝑒𝑦 ≥ 0 𝑑𝑦 𝑑𝑡 | 𝑦=0 = 0 ≥ 0 . (2) hence, all solutions will remain positive for all time. 3.2 boundedness proposition 1the trajectories of system (1), are bounded. proof. let 𝑤 = 𝑥1 +𝑥2 +𝑦. take the time derivative along the solution of model (1) 𝑑𝑤 𝑑𝑡 = 𝑑𝑥1 𝑑𝑡 + 𝑑𝑥2 𝑑𝑡 + 𝑑𝑦 𝑑𝑡 = 𝑎𝑥1 (1− 𝑥1 𝑘 )− 𝑏𝑥2𝑦 + 𝑐𝑥2𝑦 − 𝑑𝑦 for any positive constant 𝑞we have: 𝑑𝑤 𝑑𝑡 +𝑞𝑤 ≤ 𝑎𝑥1 − (𝑏 − 𝑐)𝑥2𝑦 + 𝑞𝑥1 + 𝑞𝑥2 +𝑞𝑦 where 𝑥1 ≤ 𝑘and 𝑥2 ≤ 𝑘. so 𝑑𝑤 𝑑𝑡 + 𝑞𝑤 ≤ (𝑎 + 2𝑞)𝑘 − [(𝑏 −𝑐) 𝑑 𝑐 − 𝑞]𝑦 because𝑥2 > 𝑑 𝑐 . now iff 𝑏𝑑 𝑐 > 𝑞 +𝑑, then 𝑑𝑤 𝑑𝑡 + 𝑞𝑤 ≤ (𝑎 +2𝑞)𝑘 let (𝑎 +2𝑞)𝑘 = 𝐿.therefore, we have 𝑤 ≤ 𝐿 𝑞 + 𝐴𝑒−𝑞𝑡 from which we can deduce that lim 𝑡→∞ sup𝑤 ≤ 𝐿 𝑞 independently of the initial conditions. this completes the proof. corollary 1: if 𝑏𝑑 𝑐 > 𝑞 +𝑑 > 0, then the region ∅ = {0 ≤ 𝑥1,𝑥2 ≤ 𝑘,0 ≤ 𝑦,𝑥1 +𝑥2 +𝑦 ≤ 𝐿 𝑞 } is an invariant region for model 1. proof. this is a direct conclusion of proposition 1 3.3 equilibrium analysis let𝑥1 ̅̅̅̅ ,𝑥2̅̅̅and �̅� be the equilibrium values of 𝑥1,𝑥2and𝑦.we find three biologically meaningful equilibrium points (i)𝐸0̅̅ ̅ = (0,0,0). the extinction of all populations, this equilibrium always exists. ibrahim m. elmojtaba et al. 44 (ii) 𝐸1̅̅ ̅ = (𝑘, 𝛼𝑘 𝛽 ,0).the prey species survive inside and outside the refuge habitat and the predator goes to extinction. (iii) 𝐸2̅̅ ̅ = (𝑥1̅̅̅ ,𝑥2̅̅̅ , �̅�). all populations survive. note that at this equilibrium, and using the third equation of system (1), we get: 𝑥2̅̅̅ = 𝑑 𝑐 (3) from the second equation of system (1) at equilibrium we have 𝑥1̅̅̅ = 𝑥2̅̅̅ (1+ 𝑒�̅�)(𝛽 + 𝑏�̅�) 𝛼 . (4) using the first equation of system (1) at equilibrium and substituting (4) we get 𝑓(�̅�) = 𝑎𝑥2̅̅̅ 𝑘𝛼 𝑒2𝑏2�̅�4 + 2𝑎𝑥2̅̅̅ 𝑒𝑏 𝑘𝛼 (𝑏 + 𝑒𝛽)�̅�3 + [ 𝑎𝑥2̅̅̅𝑏 2 𝑘𝛼 + 𝑎𝑥2̅̅̅𝑒 2𝛽2 𝑘𝛼 + 𝑎𝑒( 4𝑥2̅̅̅𝛽 2 𝑘𝛼 − 1)]�̅�2 +[𝑎𝑏( 2𝑥2̅̅̅𝛽 𝑘𝛼 − 1) + 𝑎𝑒𝛽( 2𝑥2̅̅̅𝛽 𝑘𝛼 − 1) +2𝑏]𝑦 ̅+𝑎𝛽( 𝑥2̅̅̅𝛽 𝑘𝛼 − 1) = 0 (5) if 1 2 < 𝑥2̅̅̅̅ 𝛽 𝑘𝛼 < 1 , then there will be only one positive root of �̅� of (5), because 𝑓(0) = 𝑎𝛽( 𝑥2̅̅̅̅ 𝛽 𝑘𝛼 − 1) < 0 , and lim�̅�→∞ 𝑓(�̅�) = ∞ , and then by the continuity of 𝑓(�̅�) and zero-point theorem,𝑓(�̅�) = 0 has one positive solution, so there will be a unique positive coexistence equilibrium. 3.4 stability analysis in this subsection, we examine the stability of the system about the equilibrium points found in the previous subsection. (a) stability analysis of the equilibrium (i): consider a small perturbation about the equilibrium𝑥1 = 𝑥1̅̅̅+𝑢, 𝑥2 = 𝑥2̅̅̅+𝑣 and 𝑦 = �̅� +𝑤.substitutingthese into the system (1), and neglecting products of small quantities, we obtain the stability matrix: ( 𝑎 − 𝛼 𝛽 0 𝛼 −𝛽 0 0 0 −𝑑 ) the corresponding characteristic equation is: −(𝜆 + 𝑑)(𝜆2 +𝜆(2+𝛽 −𝑎)−𝑎𝛽) = 0 (6) one of the values of 𝜆 is positive, so (0,0,0) is unstable and hence the both populations will never be extinct. (b) stability analysis of the equilibrium (ii): theorem 1. the predator free equilibrium𝐸1̅̅̅̅ = (𝑘, 𝛼𝑘 𝛽 ,0)of system (1) is locallyasymptotically stable if 𝑐𝛼𝑘 𝛽 < 𝑑, and unstable if 𝑐𝛼𝑘 𝛽 > 𝑑 .in fact, we can prove that 𝐸1̅̅̅̅ is globally asymptotically stable if 𝑐𝛼𝑘 𝛽 < 𝑑. predator-prey model with refuge, fear and z-control 45 proof. using the above mentioned, we obtain the stability matrix ( −𝑎 − 𝛼 𝛽 𝛼𝑏𝑘 𝛼 −𝛽 −𝛼𝑏𝑘 𝛽 −𝛼𝑏𝑘 0 0 𝑐𝛼𝑘 𝛽 − 𝑑 ) and the corresponding characteristic equation is ( 𝑐𝛼𝑘 𝛽 − 𝑑 − 𝜆)[𝜆2 +(𝑎 + 𝛼 +𝛽)𝜆+𝑎𝛽] (7) all roots will be negative if 𝑐𝛼𝑘 𝛽 < 𝑑, and hence this equilibrium will be stable. if 𝑔(𝑡) is a continuous and bounded function, then we define: 𝑔∞ ≜ lim 𝑡→∞ 𝑆𝑢𝑝 𝑔(𝑡), 𝑔∞ ≜ lim 𝑡→∞ 𝐼𝑛𝑓 𝑔(𝑡) for a system (1) with initial conditions 𝑥1 = 𝑥1(𝑡),𝑥2 = 𝑥2(𝑡)and = 𝑦(𝑡) , we have 0 ≤ 𝑥1∞ ≤ 𝑥1 ∞ ≤ ∞, 0 ≤ 𝑥2∞ ≤ 𝑥2 ∞ ≤ ∞, 0 ≤ 𝑦∞ ≤ 𝑦 ∞ ≤ ∞ . using fluctuation lemma [28], we can say that there is a sequence {𝑡𝑛}, and when 𝑡𝑛 → ∞ we have 𝑥1(𝑡𝑛) → 𝑥1 ∞and 𝑑𝑥1(𝑡𝑛) 𝑡𝑛 → 0 as 𝑛 → ∞. on substituting 𝑡𝑛 into the third equation of system (1), we have 𝑑𝑦(𝑡𝑛) 𝑡𝑛 = (𝑐𝑥2(𝑡𝑛)−𝑑)𝑦(𝑡𝑛) taking the limit on both sides lim 𝑛→∞ 𝑑𝑦(𝑡𝑛) 𝑡𝑛 = (𝑐 lim 𝑛→∞ 𝑥2(𝑡𝑛)−𝑑) lim 𝑛→∞ 𝑦(𝑡𝑛) which gives 0 = (𝑐𝑥2 ∞ − 𝑑)𝑦∞ therefore 𝑦∞ = 0or 𝑥2 ∞ = 𝑑 𝑐 . adding the first and second equations of system (1), we obtain 𝑑𝑥1(𝑡𝑛) 𝑡𝑛 + 𝑑𝑥2(𝑡𝑛) 𝑡𝑛 ≤ 𝑎𝑥1(𝑡𝑛)(1− 𝑥1(𝑡𝑛) 𝑘 ) taking the limit on both sides lim 𝑛→∞ 𝑑𝑥1(𝑡𝑛) 𝑡𝑛 + 𝑑𝑥2(𝑡𝑛) 𝑡𝑛 ≤ lim 𝑛→∞ 𝑎𝑥1(𝑡𝑛)(1− 𝑥1(𝑡𝑛) 𝑘 ) ibrahim m. elmojtaba et al. 46 0 ≤ 𝑎𝑥1 ∞ (1− 𝑥1 ∞ 𝑘 ) therefore either 𝑥1 ∞ = 0or 0 < 𝑥1 ∞ ≤ 𝑘. according to the limit theorem [29],we get lim𝑡→∞ 𝑥1(𝑡) = 𝑘. the second equation of system (1) yields 𝑑𝑥2(𝑡𝑛) 𝑡𝑛 ≤ 𝛼𝑥1(𝑡𝑛)−𝛽𝑥2(𝑡𝑛) taking the limit on both sides lim 𝑛→∞ 𝑑𝑥2(𝑡𝑛) 𝑡𝑛 ≤ 𝛼 lim 𝑛→∞ 𝑥1(𝑡𝑛) −𝛽 lim 𝑛→∞ 𝑥2(𝑡𝑛) which gives 𝑥2 ∞ ≤ 𝛼𝑘 𝛽 therefore, and using the limit theorem we have lim 𝑡→∞ 𝑥2 = 𝛼𝑘 𝛽 again, using the second equation of system (1), we have 𝑑𝑥2(𝑡𝑛) 𝑡𝑛 ≤ 𝛼𝑥1(𝑡𝑛)−𝛽𝑥2(𝑡𝑛) similarly, 0 < 𝛼𝑥1 ∞ −𝛽𝑥2 ∞; i.e. 𝛼𝑥1 ∞ > 𝛽𝑥2 ∞. if 𝑥1 ∞ = 0, then 𝑥2 ∞ < 0, which is not possible. therefore, we take,𝑥1 ∞ = 𝑘. if we consider,𝑥2 ∞ = 𝑑 𝑐 , then 𝑑𝑥2(𝑡𝑛) 𝑡𝑛 ≤ 𝛼𝑥1(𝑡𝑛)−𝛽𝑥2(𝑡𝑛) taking the limit on both sides 0 ≤ 𝛼𝑘−𝑘 𝑑 𝑐 hence 𝑑 ≤ 𝑐𝛼𝑘 𝛽 this inequality is not true also because for stability of 𝐸1̅̅ ̅, we need 𝑑 > 𝑐𝛼𝑘 𝛽 . therefore, the predator free equilibrium is globally asymptomatically stable if 𝑘 > 𝛽𝑑 𝑐𝛼 ; i.e. maximum prey population inside the refuge is greater than 𝛽𝑑 𝑐𝛼 . (a) stability analysis of the equilibrium(iii): theorem 2. the equilibrium point 𝐸2̅̅ ̅is locally asymptotically stable if𝑥1̅̅̅ > 𝑘 2 . proof. the stability matrix of the system (1) around the equilibrium point 𝐸2̅̅ ̅ is ( 𝑝1 𝑝2 𝑝3 𝑞1 𝑞2 𝑞3 0 𝑐�̅� 0 ) predator-prey model with refuge, fear and z-control 47 the corresponding characteristic equation is 𝜆3 + (−𝑝1 − 𝑞2)𝜆 2 +(𝑝1𝑞2 −𝑝2𝑞1 −𝑐�̅�𝑞3)𝜆+(𝑐�̅�𝑞3𝑝1 −𝑐�̅�𝑝3𝑞1) = 0 (8) where 𝑝1 = − 𝛼𝑥1̅̅̅ 𝑘 − 𝛽𝑥2̅̅̅ 𝑥1̅̅̅ < 0 𝑝2 = 𝛽 > 0 𝑝3 = 𝛼𝑒𝑥1̅̅̅ (1 + 𝑒�̅�)2 > 0 𝑞1 = 𝛼 1 + 𝑒�̅� > 0 (9) 𝑞2 = −𝛽 − 𝑏�̅� < 0 𝑞3 = − 𝛼𝑒𝑥1̅̅̅ (1 +𝑒�̅�)2 − 𝑏𝑥2̅̅̅ < 0 the equation (8) can be written as 𝜆3 + 𝑎1𝜆 2 +𝑎2𝜆+𝑎3 = 0 (10) where 𝑎1 = (−𝑝1 −𝑞2),𝑎2 = (𝑝1𝑞2 −𝑝2𝑞1 −𝑐�̅�𝑞3)and 𝑎3 = 𝑐𝑦( 𝑞3𝑝1 −𝑝3𝑞1).the routh-hurwitz criteria for the third order system is given by: 𝑎1 > 0, 𝑎3 > 0and 𝑎1 𝑎2 > 𝑎3. here 𝑎1 = (−𝑝1 −𝑞2) > 0 𝑎3 = 𝑐𝑦( 𝑞3𝑝1 −𝑝3𝑞1) = (−𝑎+ 2𝑎𝑥1̅̅̅ 𝑘 )( 𝛼𝑒𝑥1̅̅̅ (1 + 𝑒𝑦)2 + 𝑏𝑥2̅̅̅)+ 𝑏𝛼𝑥2̅̅̅ 1+ 𝑒𝑦 > 0 if 𝑥1̅̅̅ > 𝑘 2 . now to show that 𝑎1 𝑎2 > 𝑎3; i.e. −(𝑝1 +𝑞2)(𝑝1𝑞2 −𝑝2𝑞1 −𝑐�̅�𝑞3) > 𝑐𝑦( 𝑞3𝑝1 −𝑝3𝑞1) which, after simplification, gives (𝑝1𝑞2 −𝑝2𝑞1)(−𝑝1 −𝑞2) > 𝑐𝑦(𝑞2𝑞3 +𝑝3𝑞1) > 0 now 𝑝1𝑞2 −𝑝2𝑞1 = ( 𝛼𝑥1̅̅̅ 𝑘 + 𝛽𝑥2̅̅̅ 𝑥1̅̅̅ )(𝛽 +𝑏𝑦)− 𝛽𝛼 1 +𝑒𝑦 = 𝛼𝑥1̅̅̅ 𝑘 (𝛽 + 𝑏�̅�) ibrahim m. elmojtaba et al. 48 so, clearly,𝑝1𝑞2 −𝑝2𝑞1 > 0. note that −𝑝1 −𝑞2 > 0; therefore, 𝑎1 𝑎2 > 𝑎3. hence the co-existing equilibrium𝐸2̅̅ ̅ = (𝑥1,̅̅̅̅ 𝑥2̅̅̅, �̅�) will be asymptotically stable if 𝑥1̅̅̅ > 𝑘 2 . hence the co-existing equilibrium will be stable if therefuge prey population at equilibrium is higher than the carrying capacity of the prey in the refuge habitat. 4. z-control to achieve predator population and prey population inside and outside the refuge to a desire level, direct zcontrol strategy is used. the direct z-control are functions that a r e incorporated in each equation of the system (1). this system is then described as follows 𝑑𝑥1 𝑑𝑡 = 𝑎𝑥1 (1 − 𝑥1 𝑘 )− 𝛼𝑥1 1+ 𝑒𝑦 + 𝛽𝑥2 − 𝑢1(𝑡)𝑥1 𝑑𝑥2 𝑑𝑡 = 𝛼𝑥1 1+𝑒𝑦 −𝛽𝑥2 −𝑏𝑥2𝑦 − 𝑢2(𝑡)𝑥2 (11) 𝑑𝑦 𝑑𝑡 = 𝑐𝑥2𝑦 − 𝑑𝑦 − 𝑢3(𝑡)𝑦 then we define the error functions as 𝑥1 − 𝑥1𝑑 = 𝑒1 = 𝑢1, 𝑥2 −𝑥2𝑑 = 𝑒2 = 𝑢2, 𝑦 − 𝑦𝑑 = 𝑒3 = 𝑢3, where 𝑥1𝑑,𝑥2𝑑 and 𝑦𝑑 are desiredstates of prey inside the refuge, prey outside the refuge and the predator population respectively. these functions decay exponentially with time, i.e. 𝑒1,𝑒2 and 𝑒3 tends to zero. for achieving our purpose we adopt �̇�1 = −𝜆1𝑒1, �̇�2 = −𝜆2𝑒2and �̇�3 = −𝜆3𝑒3, with𝜆1,𝜆2,𝜆3 > 0.now we have �̇�1 − �̇�1𝑑 = −𝜆1(𝑥1 −𝑥1𝑑) �̇�2 − �̇�2𝑑 = −𝜆2(𝑥2 − 𝑥2𝑑) (12) �̇� − 𝑦�̇� = −𝜆3(𝑦 −𝑦𝑑) finally, with (11) and (12) we get the following three control functions 𝑢1 = 1 𝑥1 [𝑎𝑥1 (1− 𝑥1 𝑘 )− 𝛼𝑥1 1 + 𝑒𝑦 +𝛽𝑥2 −�̇�1𝑑 +𝜆1(𝑥1 − 𝑥1𝑑)] 𝑢2 = 1 𝑥2 [ 𝛼𝑥1 1 +𝑒𝑦 − 𝛽𝑥2 − 𝑏𝑥2𝑦 − �̇�2𝑑 +𝜆2(𝑥2 − 𝑥2𝑑)] (13) 𝑢2 = 1 𝑦 [𝑐𝑥2𝑦 − 𝑑𝑦 −𝑦�̇� +𝜆3(𝑦 −𝑦𝑑)] 5. adaptive non-linear control we start by first non-dimensionalizing the system (1) by using the following transformations: 𝑥1 𝑘 = 𝑋1, 𝑥2 𝑘 = 𝑋2,𝑒𝑦 = 𝑌, 𝛼 𝑎 = 𝛼1, 𝛽 𝑎 = 𝛽1, 𝑏 𝑎 = 𝑏1,𝑎𝑡 = 𝜏, 𝑐𝑘 𝑎𝑒 = 𝑐1, 𝑑 𝑎 = 𝑑1.now the system (1) takes the non-dimensional form 𝑑𝑋1 𝑑𝜏 = 𝑋1(1 − 𝑋1)− 𝛼1𝑋1 1 + 𝑌 + 𝛽1𝑋2 𝑑𝑋2 𝑑𝜏 = 𝛼1𝑋1 1+𝑌 − 𝛽1𝑋2 −𝑏1𝑋2𝑌 (14) predator-prey model with refuge, fear and z-control 49 𝑑𝑌 𝑑𝜏 = 𝑐1𝑋2𝑌 −𝑑1𝑌 we use non-linear feedback control for the system (14). this system can be represented as 𝑑𝑋1 𝑑𝜏 = 𝑋1(1 − 𝑋1)− 𝛼1𝑋1 1 +𝑌 + 𝛽1𝑋2 + 𝑢1 𝑑𝑋2 𝑑𝜏 = 𝛼1𝑋1 1+𝑌 − 𝛽1𝑋2 −𝑏1𝑋2𝑌 + 𝑢2 (15) 𝑑𝑌 𝑑𝜏 = 𝑐1𝑋2𝑌 −𝑑1𝑌 + 𝑢3 where 𝑢1,𝑢2 and 𝑢3are adaptive nonlinear feedback control functions which will be the functions of 𝑥1,𝑥2 and y. if these feedback functions stabilize the system, then in a n infinitely long time state the variables converge to zero. let 𝑒𝛼1 = 𝛼1 − �̂�1,𝑒𝛽1 = 𝛽1 − �̂�1,𝑒𝑏1 = 𝑏1 − �̂�1,𝑒𝑐1 = 𝑐1 − �̂�1,𝑒𝑑1 = 𝑑1 − �̂�1be unknown estimators, which give �̇�𝛼1 = −�̂�1̇, �̇�𝛽1 = −�̂�1 ̇ , �̇�𝑏1 = −�̂�1 ̇ , �̇�𝑐1 = −�̂�1̇, �̇�𝑑1 = −�̂�1 ̇ . to prove the global stability, we choose lyapunov function as 𝑉(𝑋1,𝑋2,𝑌) = 1 2 𝑋1 2 + 1 2 𝑋2 2 + 1 2 𝑌2 + 1 2 𝑒𝛼1 2 + 1 2 𝑒𝛽1 2 + 1 2 𝑒𝑏1 2 + 1 2 𝑒𝑐1 2 + 1 2 𝑒𝑑1 2 which has the derivative �̇� = 𝑋1 [𝑋1 −𝑋1 2 − 𝛼𝑋1 1+ 𝑌 + 𝛽𝑋2 + 𝑢1]+ 𝑋2 [ 𝛼𝑋1 1 +𝑌 − 𝛽𝑋2 − 𝑏1𝑋2𝑌 + 𝑢2]+ 𝑌[𝑐1𝑋2𝑌 −𝑑1𝑌 + 𝑢3]+ 𝑒𝛼1�̇�𝛼1 + 𝑒𝛽1�̇�𝛽1 + 𝑒𝑏1�̇�𝑏1 + 𝑒𝑐1�̇�𝑐1 +𝑒𝑑1�̇�𝑑1 choosing adaptive non-linear controls 𝑢1 = −2𝑋1 + 𝑋1 2 + �̂�1𝑋1 1 +𝑌 − �̂�1𝑋2 𝑢2 = − �̂�1𝑋1 1+𝑌 +�̂�1𝑋2 + �̂�1 ̇ 𝑋2𝑌 − 𝑋2 (16) 𝑢3 = −�̂�1𝑋2𝑌 + �̂�1𝑌 − 𝑌 using (16) in �̇�, we have �̇� = (−𝑋1 2 − 𝑋2 2 −𝑌2)+ 𝑒𝛼1 𝑋1𝑋2 1 + 𝑌 −𝑒𝛽1𝑋2 2 −𝑒𝑏1𝑋2𝑌 + 𝑒𝑐1𝑋2𝑌 − 𝑒𝑑1𝑌 2 −𝑒𝛼1�̂�1̇ −𝑒𝛽1�̂�1 ̇ − 𝑒𝑏1�̂�1 ̇ − 𝑒𝑐1�̂�1̇ − 𝑒𝑑1�̂�1 ̇ (17) = (−𝑋1 2 − 𝑋2 2 − 𝑌2)+ 𝑒𝛼1 (− 𝑋1 2 1 +𝑌 + 𝑋1𝑋2 1 +𝑌 − �̂�1̇) +𝑒𝛽1 (𝑋1𝑋2 − 𝑋2 2 − �̂�1 ̇ ) +𝑒𝑏1 (−𝑋2 2𝑌 − �̂�1 ̇ )+ 𝑒𝑐1(𝑋2𝑌 2 − �̂�1̇)+ 𝑒𝑑1 (−𝑌 2 − �̂�1 ̇ ) considering parameter estimators �̂�1̇ = − 𝑋1 2 1 + 𝑌 + 𝑋1𝑋2 1 + 𝑌 +𝑒𝛼1 �̂�1 ̇ = 𝑋1𝑋2 − 𝑋2 2 + 𝑒𝛽1 (18) �̂�1 ̇ = −𝑋2 2𝑌 + 𝑒𝑏1 �̂�1̇ = 𝑋2𝑌 2 +𝑒𝑐1 ibrahim m. elmojtaba et al. 50 �̂�1 ̇ = −𝑌2 + 𝑒𝑑1 using dynamics of unknown estimators (18) in (17) we will find �̇� = (−𝑋1 2 − 𝑋2 2 − 𝑌2)− 𝑒𝛼1 2 −𝑒𝛽1 2 − 𝑒𝑏1 2 − 𝑒𝑐1 2 − 𝑒𝑑1 2 clearly the system will be globally stable, because �̇� < 0. 6. numerical simulation in this section, we performed several numerical simulations for the system (1) to confirm our theoretical results and to acquire more knowledge about its dynamics and general behavior. the parameter values used are listed in the following table, some of them might be changed in order to study their effect: table 1. parameter values used for simulations. 6.1 effect of adaptive control to study the effect of adaptive control on the system, we look at the stable co-existence equilibrium point. (figure 2) shows that without the adaptive control the system took a long time to converge to this stable equilibrium point. however, with the use of adaptive control it is clear that the time to reach the equilibrium point is very short, and the system almost instantly started to reach this stable equilibrium point, as seen from (figure 3). 6.2 effect of the intensity of fear parameter value 𝑎 0.07 𝛼 0.035 𝛽 0.0119 𝑘 0.8 𝑏 0.0112 𝑐 0.04 𝑑 0.07 𝑒 50 figure 3.the effect of adaptive control on the convergence of the co-existence equilibrium point. the parameters are 𝑎 = 0.1,𝛼 = 0.035,𝛽 = 0.00119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.45,𝑑 = 0.07 and 𝑒 = 20. figure 2. the convergence of the co-existence equilibrium point. the parameters are 𝑎 = 0.1,𝛼 = 0.035,𝛽 = 0.00119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.45,𝑑 = 0.07 and 𝑒 = 20. predator-prey model with refuge, fear and z-control 51 to study the effect of the intensity of fear, we simulate our model with parameter values taken from table1, and the intensity of fear taken between 0.1 to 100. it is clear that when the intensity of fear increases, the fraction of the prey in the refuge increases. however, it has no impact on the fraction of prey outside the refuge, as shown from figures 4-5. on the other hand, when the intensity of fear increases, the fraction of predators decreases as shown in ( figure6), which dictates that fear is not in the favor of the predator. 6.3 application of z-type control with constant desired state figures 7 9 show that with the help of z-type control all three populations, t h e prey in the refuge, the prey out of the refuge and the predators reaches the desired states as indicated. clearly the time needed to reach the desired states is very short, and this is due to the power of z-type control, which takes the output to the desired state rapidly. figures 1 0 1 2 show the control profile of all three populations, where ( figure13) shows the error profiles of all three control profiles. figure 4.the effect of the fear intensity on the prey in the refuge. the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04 and 𝑑 = 0.07. figure 5.the effect of fear intensity on the prey out the refuge. the parameters are𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04 and 𝑑 = 0.07. figure 6. the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04 and 𝑑 = 0.07. ibrahim m. elmojtaba et al. 52 figure 12. . the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119, 𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07and 𝑒 = 5. figure 8. 𝑥2𝑑 = 1. the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07 and 𝑒 = 50. figure 9.the convergence of the predator to its constant desired states 𝑦𝑑 = 0.5. the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07 and 𝑒 = 50. figure 10. the parameters are 𝑎 = 0.07,𝛼 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07 and 𝑒 = 50. figure 11. the parameters are 𝑎 = 0.07,𝛼 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07 and 𝑒 = 50. figure 7.the convergence of the prey in the refuge to its constant desired states 𝑥1𝑑 = 1.5. the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07 and 𝑒 = 50. predator-prey model with refuge, fear and z-control 53 6.4 application of z-type control with periodic desired state figures 14-16 show that z-type control could be used to achieve a periodic desired state. from a biological point of view, it is very important to be able to reach a stable limit cycle instead of a constant equilibrium point, as periodic solutions (i.e. limit cycles) are of great interest for ecosystems and more generally for conservation biology. for the purpose of simulation, we consider the desired state to be of the form 𝑥1𝑑 = 𝑟1 + 𝜔1 cos 𝜋𝑡 100 𝑥2𝑑 = 𝑟2 + 𝜔2 cos 𝜋𝑡 200 𝑦𝑑 = 𝑟3 + 𝜔3 cos 𝜋𝑡 100 figure 13. . the parameters are 𝑎 = 0.07,𝛼 = 0.035, 𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07and 𝑒 = 50. figure 14.the convergence of the prey in the refuge to its periodic desired states. the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07,𝑒 = 50,𝑟1 = 1, 𝑟2 = 0.8, 𝑟3 = 0.8 ,𝜔1 = 0.5,𝜔2 = 0.25,𝜔3 = 0.8. figure 15.the convergence of the prey out the refuge to its periodic desired states.the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07,𝑒 = 50,𝑟1 = 1, 𝑟2 = 0.8, 𝑟3 = 0.8 ,𝜔1 = 0.5,𝜔2 = 0.25,𝜔3 = 0.8. ibrahim m. elmojtaba et al. 54 figure 17. . the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07,𝑒 = 50,𝑟1 = 1, 𝑟2 = 0.8, 𝑟3 = 0.8 ,𝜔1 = 0.5,𝜔2 = 0.25,𝜔3 = 0.8. figure 16. . the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07,𝑒 = 50,𝑟1 = 1, 𝑟2 = 0.8,𝑟3 = 0.8 ,𝜔1 = 0.5,𝜔2 = 0.25,𝜔3 = 0.8. figure 18. . the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07,𝑒 = 50,𝑟1 = 1, 𝑟2 = 0.8, 𝑟3 = 0.8 ,𝜔1 = 0.5,𝜔2 = 0.25,𝜔3 = 0.8. figure 19. . the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07,𝑒 = 50,𝑟1 = 1,𝑟2 = 0.8,𝑟3 = 0.8 ,𝜔1 = 0.5,𝜔2 = 0.25,𝜔3 = 0.8. figure 20. . the parameters are 𝑎 = 0.07,𝛼 = 0.035,𝛽 = 0.0119,𝑘 = 0.8,𝑏 = 0.0112,𝑐 = 0.04,𝑑 = 0.07,𝑒 = 5,𝑟1 = 1, 𝑟2 = 0.8, 𝑟3 = 0.8 ,𝜔1 = 0.5,𝜔2 = 0.25,𝜔3 = 0.8. predator-prey model with refuge, fear and z-control 55 6.5 effect of different forms of 𝜷 it is more realistic than not to assume the refuge size (i.e. 𝛽) is not constant. figures 21-23 show the fractions of prey in the refuge, the prey outside the refuge and the predator, where we took different forms of 𝛽. it is clear that when 𝛽 is taken as a linear function (i.e. 𝛽(𝑡) = (𝑎 +𝛽0)𝑥2) or as an exponential function of the prey outside the refuge (i.e. 𝛽(𝑡) = 𝑎𝑥2 exp(𝛽0) ), then both the prey outside the refuge and in the refuge reach their stable equilibrium and the predator goes to extinction. however, when 𝛽 is taken as a logistic function of the prey outside the refuge (i.e. 𝛽(𝑡) = 𝑎𝛽0𝑥2 (1 − 𝑥2 𝑘 )), then all three populations co-exist together after initial small oscillations. note that 𝛽0 is a positive constant and represents the base-line value for 𝛽. 7. conclusion all animals are threatened by predators and face the risk of predation. prey populations change their behavior due to their fear of predators. in this paper we have studied the dynamics of predator-prey interaction where prey reside in two habitats, namely refuge and out of refuge. in refuge, the prey is safe from predatory killing and has sufficient resources to survive, and the population in the refuge grows logistically. out of refuge, predators interact with the prey and may kill them. prey live under the fear of predation, but when predator fear is diluted, prey come out of their refuge. on increasing predation fear, prey take shelter in the refuge. we obtain three biologically feasible equilibria and discuss their stability. the equilibrium free from prey and predator population will always exist and it is unstable i.e. prey, and predator populations will never be extinct. the equilibrium having zero predator population and non-zero prey population will always exist, and it will be globally stable if the maximum prey population inside the refuge is greater figure 23. ibrahim m. elmojtaba et al. 56 than 𝛽𝑑 𝑐𝛼 . otherwise it will be unstable. the co-existing equilibrium will be asymptotically stable if 𝑥1̅̅̅ is bigger than half of the carrying capacity, and otherwise will be unstable. to bring the population to the desired level and to protect it from extinction, we use z-control, where the population reaches the desired level in a short time. we performed a simulation where the desired state was limit cycles instead of an equilibrium point. numerically it is shown that as the intensity of fear increases, the population of the prey in refuge increases, while the population of the predator decreases i.e. fear is not in the favor of predator populations. to make our study more ecologically realistic, we took different forms of refuge size (𝛽) i.e. linear, exponential, and logistic instead of constant. we observed that when refuge size 𝛽 is linear or exponential, the prey out of the refuge and in the refuge tend to attend their stable equilibrium and predators go to extinction. if we consider refuge size as a logistic function of the prey out of refuge, then after a little oscillation all three populations co-exist. the adaptive control inputs for asymptotic stability are obtained as non-linear feedback. we examined the stability of the system with and without control and noted that the system with control approaches stability faster than the system without control. conflict of interest the authors declare no conflict of interest. acknowledgement the authors would like to acknowledge anonymous reviewers, whose comments helped to increase the clarity and readability of the paper. references 1. canon, w.b., bodily changes in pain, hunger, fear and rage. d. appleton and company, new york, 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infections: methods for the study of asymptotic behavior, communication on pure and applied mathematics, 1985, 38, 733-753. 29. castillo-chavez, c., thieme, h.r., asymptotically autonomous epidemic models, applied mathematical science, 1994. received 8 december 2020 accepted 28 february 2021 https://doi.org/10.1007/s12591-018-0430-x squ journal for science, 2015, 20(1), 62-69 © 2015 sultan qaboos university 62 investigation of the direction of spontaneous magnetisation at 0 k in hoco2 and tmfe2 carlo carboni* and eman al-abri department of physics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: carlo@squ.edu.om. abstract: the direction of spontaneous magnetisation at 0 k across a phase orientation boundary in rare-earth laves phase compounds is computed as a function of the ratio of magnetic to electrostatic interactions. the phase boundary and range of parameters used for the computation correspond to the portion of the orientational phase diagram where experimental data can be obtained. in the series of pseudo-binary compounds (gdx ho1-x )co2 and (yx ho1-x )co2 the range of parameters covers the continuous transition from the <100> to the <110> orientations. the nmr measurements on this series show that the direction of spontaneous magnetisation is at intermediate orientation between the <100> and <110> directions. the material tmfe2, which is in the vicinity of a discontinuous orientational boundary, is also discussed. keywords: lanthanides; crystal field; laves phase; phase transition. tmfe2و hoco2( لمركبي okعنذ الصفر المطلق )دراسة االتجاه للتمغنط التلقائي ايمان العبريو كارلو كاربوني )انصفش انمطهق( عبش حذ تُجًٕ انطُس انمغىاطٕسٓ فٓ مشكباث انعىاصش األسضٕت k 0تم حساب اتجاي انتمغىظ انتهقائٓ عىذ دسجت انحشاسة ملخص: باعتباسي دانت فٓ وسبت انتفاعالث انكٍشبٕت إنّ انتفاعالث انمغىاطٕسٕت. حذ انطُس انمغىاطٕسٓ َمذِ –( laves phasesانىادسة َانتٓ نٍا أطُاس الفز ) رنك انجزء مه بٕاوٓ انطُس انتُجٍٕٓ انزْ ٔمكه استخالص وتائج تجشٔبٕت مىً. أما بانىسبت نسهسهت انمعامالث انتٓ تم استخذامٍا فٓ انحساب تخص انّ اال 〈 〉 فإن مذِ انمعامالث ٔغطٓ اإلوتقال انمتصم مه اإلتجاي . ( ) ( مثم pseudo – binaryانمشكباث انتٓ ٔطهق عهٍٕا) َُْ انمغىاطٕسٓ نٍزي انسهسهت مه انمشكباث تُضح أن اتجاي انتمغىظ انتهقائٓ ٔكُن متُسطا بٕه االتجإٌه ان قٕاساث انشوٕه انى 〈 〉 تجاي 〈 〉 َ 〈 〉 َانتٓ تقع عهّ مقشبت مه حذ تُجًٕ انطُس انمغىاطٕسٓ انمىقطع. تىاقش ٌزة انُسقً أٔضا انمادة ، انحقم انبهُسْ ، الثٕىٕذاث. اوتقال طُسْ ، طُس الفز: كلمات مفتاحية 1. introduction ne of the characteristics of rare-earth ions is that the spin-orbit coupling in the 4-f shell is much larger than the interactions experienced by the ion when embedded in a crystal. as a result j, the total angular momentum of the 4f shell, remains, in a first approximation, a good quantum number in the solid [1]. the states of the ion subjected to the crystal-field and the magnetic interactions experienced in the solid are well described to first order by the simple effective electronic hamiltonian [2]. (1) where hz stands for the magnetic interaction of the 4f shell with the host crystal and hcf is the crystal-field interaction which is the electrostatic interaction of the 4f shell with the electric field gradients due to the surrounding ions. in the zeeman representation, the eigenstates of the electronic hamiltonian are expressed as linear combinations of j m states. since at room temperatures and below only the ground j-manifold is populated the index j is dropped and the electronic states are written | ⟩ ∑ | ⟩ o investigation of the direction of spontaneous magnetisation 63 each electronic state | ⟩ has a magnetic moment associated to the expectation value ⟨ | | ⟩ of the zcomponent of the angular momentum j tied to the corresponding aspherical distribution of the 4f electrons. the 4f shell and therefore the magnetic moment have a preferred orientation with respect to the electric field gradients at the ion’s site in the crystal. different states have different preferred orientations. this feature is responsible for the wealth of magnetic structures and magnetic transitions displayed by rare-earth compounds. in particular, when a low-lying excited state has a strongly preferred orientation conflicting with that of the ground state, a change in the orientation of spontaneous magnetization can occur as the temperature is increased and the excited state becomes populated [3]. we note in passing that the gadolinium ion gd 3+ being in an s state, the crystal-field interaction is zero in first order and therefore, in first order, gd 3+ has no preferred orientations. at zero-temperature, the direction of spontaneous magnetization in magnetic rare-earth compounds is determined solely by the ground state of the 4f shell. the nature of the ground state depends of course on the parameters in the hamiltonian in equation 1; as the parameters are varied, the direction of spontaneous magnetisation may change. for ions at a site of cubic symmetry the hamiltonian can be expressed in the dimensionless form given in equation 7 below which it depends on two parameters only. al-abry et al. [4, 5] have done a systematic investigation of the direction of spontaneous magnetization at zero temperature in the two-parameter space for all the values of j found in the ground state of lanthanide ions. in the present paper we discuss the direction of spontaneous magnetization in two compounds, hoco2 and tmfe2. in these compounds the rare-earth ion is at a site of cubic symmetry and the parameters for these compounds place them near a boundary between two regions in the parameter space with different orientations of spontaneous magnetization for the ground state. the crystal-field hamiltonian is expressed as a linear combination of the steven’s operators [6]. ∑ ∑ the are the crystal-field parameters. at a site of cubic symmetry there are only four non-vanishing terms in the expansion: and are the non-zero parameters. furthermore there is a relation between the two fourth order and between the two sixth order terms; therefore only two parameters are required to describe the crystal field [7]. the crystal-field hamiltonian is written (2) with and following lea, leask and wolf [6] the hamiltonian is recast in the form { ( ) } (3) where w is an energy scale factor and the unitless parameter x gives the ratio of the fourth to sixth order crystal-field terms. ( | |) f4 and f6 are numerical factors depending on the particular value of j [7]; the magnetic interaction is (4) where br is a vector that represents the sum of all the effective magnetic fields acting on the rare-earth ion; these can arise because of exchange, the dipolar field or an externally applied field. gj is the landé g-factor and b is the bohr magneton. following mcmorrow et al. [8] we introduce the vector   )5( carlo carboni and iman al-abri 64 and write the electronic hamiltonian { ( ) } )6( this hamiltonian involves three parameters, w, x and the vector  for the purpose of the present work which is concerned with the direction of spontaneous magnetization, it is more convenient to recast the hamiltonian in a twoparameter dimensionless form by dividing by the energy factor w. the hamiltonian becomes { ( ) } )7( the magnitude of the vector parameter represents the relative strength of the magnetic to the electrostatic interactions; the balance between the relative strengths of |r| and x determines the direction of spontaneous magnetization [4, 5]. given the values of x and |r| and the orientation (of r, the direction of spontaneous magnetization which is the direction of the angular momentum j can be in principle computed by diagonalising the hamiltonian 7. however, for arbitrary values of (the computed direction of j will not in general be parallel to the input direction of r. to be the direction of spontaneous magnetization, the value of () must satisfy the two conditions that the computed direction of j is parallel to r, and that the energy of the state is at a minimum with respect to () [4, 5]. 2. results and discussion in this work the evolution of the direction of spontaneous magnetization in the parameter space was computed as in reference [4] by varying systematically the parameters x and |r| and finding for each value of (x, |r|) which values of the polar angles () give the lowest energy for the ground state and the computed orientation of j parallel to the input  table 1 gives a summary of the values of w, x and r for hoco2 and tmfe2 derived from data published by various authors. the different experimental techniques used by the authors lead to a scatter in the values of the parameters. in most cases such an uncertainty in the parameters is not a problem. however, in the cases of ho 3+ in hoco2 and tm 3+ in tmfe2, because these compounds are close to a boundary between regions of different directions of spontaneous magnetization in the {r, x} parameter space, a small variation in the values of the parameters can lead to an erroneous direction of spontaneous magnetization. table 1. the parameters for hoco2 and tmfe2 derived from published data. a: gignou et al.[9], b: aubert et al. [10], c: castets and gignoux [11], d: germano and butera [12], e: martin et al.[13] derived values of b4 and b6 from the data of atzimony et al.[14], f: yanovsky et al. [15], g and h derived by bleaney [18] from rhyne and koon [16] and koon and rhyne [17], i: bleaney [18]. ion j compound w (k) x |r| ref ho 3+ 8 hoco2 0.60 -0.4687 46.6 a 0.60 -0.4665 45.8 b 0.30 -0.4839 60.2 c tm 3+ 6 tmfe2 0.59 0.555 99 d 0.58 0.649 89 e 0.54 0.721 86 f 0.59 0.353 78 g 0.61 0.627 76 h 0.44 0.64 105 i  the relevant portions of the orientational phase diagram for the two ions ho 3+ (j = 8) and tm 3+ (j = 6) are given in figures 1-a and 1-b. the published parameters for the two compounds given in table 1 are also shown in the figures. in the notation of al-abry et al (4, 5), the boundary in the case of j = 6 is of the type da where the transition is discontinuous across the boundary. at a critical value of the parameters the two orientations (110) and (111) have the same energy but all the orientations in the plane containing these two directions have a higher energy. there is a sudden change of direction of spontaneous magnetization at the critical value. for j = 8 the boundary is of the type c where there are two critical values for the parameters; between these two values the direction of spontaneous magnetization is at an intermediate orientation between the (100) and the (110) axis. there is a continuous rotation of the direction of spontaneous magnetization. figures 1-c and 1-d show the computed directions of spontaneous magnetization across the boundary for the two cases. investigation of the direction of spontaneous magnetisation 65 figure 2. the variation of <jz> across the boundary. a: for j = 8 and b for j = 6. the computed values of 〈 〉 corresponding to figures 1-c and 1-d are shown in figure 2-a and 2-b. as one might expect, in figure 2-a for the case of ho 3+ , the value of 〈 〉 varies continuously across the boundary and the first derivative is continuous. for tm 3+ , 〈 〉 is continuous through the boundary but there is a discontinuity with a change of sign in the first derivative. we note that for j = 8 the change in the value of 〈 〉 across the boundary is about 3%,whereas in the case of j = 6 the variations of 〈 〉 in the vicinity of the boundary are of the order of 0.02%. figure 1. a and b: the relevant areas of the orientational phase diagrams for j = 6 and j = 8; the letters in brackets refer to the references in table 1. c and d are the computed direction of spontaneous magnetisation across the phase boundary. c d a 40 50 60 70 80 7.7 7.6 7.5 7.4 │r│ < j z > j = 8 x = -0.466 <110> <100> b j = 6 │r│= 80 5.926 5.922 5.920 5.918 5.916 5.914 5.912 5.924 0.6 0.62 0.64 0.66 0.68 <111> <110> < j z > x carlo carboni and iman al-abri 66 we consider first the case of hoco2. the direction of spontaneous magnetization was investigated experimentally by 165 ho:ho 3+ nmr. the holmium nucleus has spin 7/2, the nmr spectrum presents seven quadrupole-split lines. the frequency at of the central line of the spectrum is directly related to the expectation value 〈 〉 which can be computed from the hamiltonian in equation 7 [1, 2] 〈 〉 (8) where a0 is the free-ion dipolar hyperfine coupling constant (a0 = 6497 mhz for holmium); a” is the contribution arising from the direct interaction of the nucleus with the surroundings in the crystal and a” is a small contribution that can be treated as a free parameter. because of the large value of a0, any small change in the value of 〈 〉 results in a large shift in the nmr frequencies. in materials where the value of 〈 〉 depends strongly on the orientation of the ion with respect to the crystal axis, the nmr spectrum is a powerful tool to determine the direction of magnetization [19]. in practice it is difficult to control experimentally the parameters |r| and x. however, in the case of hoco2, the value of |r| can be decreased by doping the compound with non-magnetic yttrium or increased by doping with gadolinium which has a larger spin than holmium and, as mentioned in the introduction, does not contribute to the anisotropy because gd 3+ is in an s state. a series of compounds (ho1-ygdy)co2 (y = 0.0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.97) was prepared by arc-melting. assuming for the sake of computation that the value of |r| is 46.6 for pure hoco2 (table 1) the concentrations of gadolinium chosen correspond to |r| = 46.6, 48.1, 49.8, 54.0, 58.1, 62.0, 85.4 respectively. to obtain lower values of |r| a compound doped with 5% of yttrium corresponding to the value of |r| = 44.3 was prepared. the value of the molecular field experienced by the ho 3+ ion in the pseudo-binary compounds was estimated following mcmorrow et al [8]. it is expected that these values of |r| take the compound across the orientational phase boundary. the nmr spectra were taken on the 2-8 ghz spectrometer at the university of manchester (uk) [20] at liquid helium temperatures. a preliminary outcome of some of the still unpublished measurements on some of the (ho,gd)co2 compounds was presented at the xiii congress ampere [21]. in the concentrated hoco2 compound and in the (ho,gd)co2 compounds with low gadolinium concentration two overlapping spectra are observed. for concentrations of gadolinium above 50% a single spectrum is observed which is consistent with the <100> orientation of spontaneous magnetisation. the nmr spectrum of 165 ho:hoco2 is shown in figure 3. the presence of two spectra indicates that there are two inequivalent sites with slightly different strengths of the exchange interaction. in the transition region this results in a significant shift of the nmr spectrum. the explanation for the two sites has not yet been unequivocally established. the two obvious possible causes, an impurity in the starting materials for the sample preparation or closure domains or domain walls were discarded by repeating the measurements with specimens of hoco2 prepared at other institutions including a single crystal on loan from laboratiore louis neel, grenoble. an 8 t field was applied to the single crystal specimen. in all experimental conditions two spectra are observed in hoco2. we will not attempt here to give any plausible explanations for the presence of the two sites. figure 3. the observed spectrum for hoco2 is the superposition of two 7-lines spectra. for each compound we have derived the values of at of each of the two overlapping spectra. in figure 4 we have plotted all the measured values of at as a function of concentration. the conclusion than can be drawn from the figure 5 is that two spectra are observed only for compounds with a value of │r│ that places them in the transition region. therefore, the pure compound hoco2 is inside the transition region. hoco2 polycrystal t = 4.2 k ba = 0 6000 6200 6400 6600 6800 7000 frequency (mhz) e c h o a m p li tu d e ( a r b . u n it s) investigation of the direction of spontaneous magnetisation 67 figure 4. summary of the frequency of the central line of all the spectra observed. the dashed line is a guide to the eye; the vertical line corresponds to the hoco2 compound. in order to obtain a comparison between computation and experiment we have derived the values of <jz> using equation 8. we have considered a” as a free parameter for each compound and allowed a” to vary linearly with concentration from 392 mhz in the concentrated compound to 356 mhz in the compound with 40% gadolinium. we have also assumed that the low frequency spectrum corresponds to the values of │r│ estimated for the specimen preparation and that the high frequency spectrum corresponds to a site with a value of │r│ increased by 9. the values of <jz> thus obtained are compared to the values computed using the parameters of aubert et al (10). the figure shows a very good agreement between the measurements and the computation. figure 5. the values of <jz> derived from the measurements are compared to the computed values (solid line). turning now to tmfe2 we note that some of the parameters given in table 1 give the <111> as direction of spontaneous magnetisation for the ground state, while others give the <110>. the parameters of germano and butera (12) give a reorientation of the spontaneous magnetisation as a function of temperature from the <110> at low temperatures to <111> above 55 k. as noted in figure 3, there is only a small (0.02%) change in <jz> across the phase boundary. therefore, nmr cannot be used to ascertain the direction of spontaneous magnetisation at low temperatures. the direction of magnetisation can be obtained from the 57 fe mössbauer spectrum since the iron sites are not magnetically equivalent [14]. a detailed study of the 57 fe mössbauer spectrum by al-sariri (22) confirmed that the direction of magnetisation in tmfe2 is <110> at all temperatures. the specimen used for the mössbauer measurements by al-sariri was a crushed single crystal obtained from university of birmingham (uk). 20 40 60 80 10 f r e q u e n c y ( m h z ) 6700 6600 6500 6400 6300 % of gd % of y 40 50 60 70 80 7.7 7.6 7.5 7.4 < j z > │r│ carlo carboni and iman al-abri 68 3. conclusion this work has shown that a boundary in the orientational phase diagram can place constraints in the range of the values for the parameters of the hamiltonian. these constraints make it possible to refine the values of the parameters. the nmr data shows that hoco2 is just inside the intermediate region on the <110> side of the boundary. therefore, the parameters that describe best the ho 3+ ion in this compound are those of abert et al [4]. for tmfe2 most of the experimental data available would indicate that the <110> is the orientation of spontaneous magnetization at all temperatures; therefore the parameters given by yanovsky et al. [15] are probably incorrect. however, the analysis given by sariri, based on unpublished high field 169 tm:tmfe2 nmr [23] and in some pseudo-binary alloys would indicate that magnetostriction is not negligible. an extra term needs to be included in the crystal-field hamiltonian in order to take the magnetostriction distortion into account. 4. acknowledgements the experimental part of this work was done during the time the author c c was at the university of manchester (uk) supported by grants from the uk engineering and physical science research council (epsrc). the authors are also grateful to prof mah mccausland and dr d stp bunbury for comments, discussions and support. references 1. mccausland, m.a.h. and makenzie, i.s. nuclear magnetic resonance in rare earth metals, taylor and francis ltd., london, 1980. 2. bunbury, d.st.p., carboni, c., mccausland, m.a.h., cone, r. and mroczkowsky, s. and ross, j.w. the hyperfine splitting of the ground state and first excited state of holmium in yttrium hydroxide. j. phys. condens. matter. 1995,7, 6125-6136. 3. koehlera, m.r., garleab, v.o., mcguirec, m.a., jiaa, l., keppensa, v. spin reorientation and magnetoelastic coupling in tb6fe1−xcoxbi2 (x = 0, 0.125, 0.25, and 0.375) alloy system. j. alloys and compounds, 2014, 615, 514– 520. 4. al abry, e. 2003 m.sc. thesis, the orientation of the direction of spontaneous magnetization of rare-earth ions at a site of cubic symmetry. department of physics, college of science, sultan qaboos university, sultanate of oman. 5. carboni, c., al-abry, e. and arafin, s. the direction of spontaneous magnetisation of lanthanide ions at a site of cubic symmetry. squ j. science, 2007, 12(1), 53. 6. stevens, k.w.h. matrix elements and operator equivalents connected with the magnetic properties of rare earth ions, proc. physi. soci., a, 1952, 65, 209. 7. lea, k.r., leask, m.j.m. and wolf, w.p. the raising of angular momentum degeneracy of f-electron terms by cubic crystal fields. j. phys. chem. solids, 1962, 23, 1381-1405. 8. mcmorrow, d.f., mccausland, m.a.h., han, z.p. exchange and crystal field interaction of ho 3+ in a gdal2 single crystal: an nmr study. j. phys condens. matter, 1989, 1, 10439-10458. 9. gignoux, d., givord, f., and lemaire, r. magnetic properties of single crystals of gdco2, honi2 and hoco2 phys. rev b, 1975, 12, 3878-3884. 10. aubert, g., gignoux, d., givord, f., lemaire, r. and michelutti, b. magnetization reorientation in hoco2, solid state commun, 1978, 25, 2, 85–87. 11. a castets, d gignoux and b hennion, new aspects of the magnetic excitations in hoco2. phys. rev. b, 1982, 25, 337-348. 12. germano, d.j. and butera, r.a. heat capacity of, and crystal field effect in, the rfe2 intermetallic compounds, phys. rev. b, 1981, 24(7), 3912-3927. 13. martin, k.n., de groot, p.a.j., rainford, b.d., wang, k., bowden, g.j., zimmermann, j.p. and fanghor, h. magnetic anisotropy in the cubic laves refe2 intermetallic compounds. j. phys. condens. matter, 2006, 18, 459 478. 14. atzmony, u., dariel, m.p., bauminger, e.r., lebenbaum, d., nowik, i. and ofer, s. spin-orientation diagrams and magnetic anisotropy of rare-earth-iron ternary cubic laves compounds. phys. rev., 1973, b 7, 4220-4232. 15. yanovsky, r., bauminger, e.r., levron, d., nowik, i. and ofer, s. crystalline fields, exchange interactions and spin reorientations in tmxho1−x fe2 systems, studied by a 170 yb mössbauer probe. solid state commun. 1975, 17, 1511-1514. 16. rhyne, j. and koon, n.c. magnetic excitations in hofe2. j. appl. phys., 1978, 49, 2133-2135. 17. koon, n.c. and rhyne, j. excited state spin waves in erfe2. solid state commun., 1978, 26, 537-540. 18. bleaney, b., bowden, g.j., cadogan, j.m., day, r.k. and dunlop, j.b. a mossbauer study of the cubic laves phase intermetallic compound tmfe2. j. phys. f, met. phys., 1982, 12, 795-811. 19. waind, p.r., mackenzie, i.s. and mccausland, m.a.h. anisotropy and asymmetry of the hyperfine spectrum of holmium in magnetically ordered ral2 alloys. j. phys f, 1983, 13, 1041-1056. 20. carboni, c., mackenzie, i.s. and mccausland, m.a.h. nuclear magnetic resonnance at microwave frequencies, hyperfine interactions, 1989, 51, 1139-1144. investigation of the direction of spontaneous magnetisation 69 21. bunbury, d.stp., carboni, c., mccausland, m.a.h. and prakash, o. nmr studies of spin reorientation in (ho,gd)co2. unpublished proc. xxiii congress ampere (istituto superiore di sanita roma), 1986. 22. al sariri, m. m.sc. thesis, crystal field and magenic anisotropy in tmfe2. department of physics, college of science, sultan qaboos university, sultanate of oman, 2010. 23. carboni, c. anisotropy in rfe2 intermetallics: an nmr study. squ j. science, 2009, 14(1), 71-83. received 14 october 2014 accepted 2 january 2015 squ journal for science, 2022, 90-99 doi: 10.53539/squjs.vol27iss2pp90-99 sultan qaboos university 90 solving unconstrained optimization problems by a new conjugate gradient method with sufficient descent property farzad rahpeymaii 1* , majid rostami 2 1 department of mathematics‎, technical and vocational university (tvu), tehran, ira‏n, 2 department of mathematics‎, technical and vocational university (tvu), tehran, ira‏n, *email: rahpeyma_83@yahoo.com. abstract: ‎there have been some conjugate gradient methods with strong convergence but numerical instability and conversely‎. improving these methods is an interesting idea to produce new methods with both strong convergence and‎ ‎‏‏ ‎numerical stability‎. ‎in this paper‎, ‎a new hybrid conjugate gradient method is introduced based on the fletcher‎ ‎formula (cd) with strong convergence and the liu and storey formula (ls) with good numerical results‎.‎ ‎new directions satisfy the sufficient descent property‎, ‎independent of line search‎.‎‎under some mild assumptions‎, ‎the global convergence of new hybrid method is proved‎.‎‎numerical results on unconstrained cutest test problems show that the new algorithm is‎‎very robust and efficient‎. keywords: conjugate gradient methods; unconstrained optimization; global convergence; sufficient descent property;‎‎numerical results. يهلکافخاصية اإلنحدارا مترافقةال ميولمن خالل طریقة ال ةغيرالمقيّد لمسائ تحسينحل و پيمایی، مجيد رستمی هفرزاد را إلنتاج‏‏‏فكرة‏مثیرة‏.‏تحسین‏هذه‏الطرقكسیا،‏لکن‏غیر‏مستقّرة‏وغیرثابتة‏عددیا‏و‏عةقوب‏توافقتهناك‏بعض‏من‏طرق‏اإلنحدار‏المزدوج،‏التی‏‏:لخصمال (‏cdة‏فلجر‏)طرق‏جدیدة‏بالتقارب‏العددی‏القوی‏و‏الثابت.‏فی‏هذه‏المقالة،‏قد‏عّرفت‏و‏قدّمت‏طریقة‏اإلنحدار‏المزدوج‏المرّکب‏الجدید‏علی‏أساس‏صیغ ‏المستقلة‏عن‏البحث‏بنتائج‏رقمیة‏جیدة.‏تحت‏الشروط‏القیاسیة‏(‏lsاستوری‏)بالتقارب‏القوی‏و‏صیغة‏لیو‏و ‏الجهات‏الجدیدة وبالنتائج‏العددیة‏الجیدة. تدّل‏علی‏أّن‏الخوارزمیة‏‏ cutestاختبار‏القضایا‏والمسائل‏غیر‏المقیدة‏على‏النتائج‏‏العددیة‏‏.الخطي،‏تم‏اثبات‏التقارب‏الجماعي‏للطریقة‏المركبة‏الجدیدة ‏الجدیدة،‏قویّة‏جدّا.‏ ‏ النتائج‏العددیة.‏-التقارب‏الجماعی،‏شرط‏التقلیل‏الکافی‏-التحسین‏غیر‏المقیّد‏-اإلنحدار‏المزدوجطرق‏‏:الكلمات المفتاحية 1. introduction ‎onsider the unconstrained optimization problem‎ 𝑓(𝑥), 𝑥∈ℝ𝑛 𝑚𝑖𝑛 )1) ‎where 𝑓: ℝ𝑛 → ℝ is a smooth nonlinear function whose‎‎gradient at 𝑥 is available 𝑔 ≔ 𝑔(𝑥) = ∇𝑓(𝑥). ‎there are many iterative methods to solve‎‎‎unconstrained optimization problem including the newton methods‎, ‎the quasi-newton‎ ‎methods, trust-region methods [21]. 1.1 conjugate gradient method ‎the conjugate gradient (cg) methods are famous iterative methods for solving large-scale unconstrained‎ ‎optimization problems whose iterative scheme is‎ c solving unconstrained optimization problems 91 𝑥𝑘+1 ≔ 𝑥𝑘 + 𝛼𝑘 𝑑𝑘 , 𝑥0 ∈ ℝ 𝑛 . (2) here 𝑥0 ∈ ℝ 𝑛 is an initial point‎, ‎𝛼 > 0 is a step size‎, ‎which is obtained by an exact or inexact line search methods‎‎and 𝑑𝑘 is a search direction computed by‎ 𝑑𝑘 = { −𝑔𝑘 , 𝑘 = 0, −𝑔𝑘 + 𝛽𝑘 𝑔𝑘−1, 𝑘 ≥ 1, (3) ‎in which 𝛽𝑘 is a scalar‎, ‎called the cg parameter and 𝑔𝑘 ≔ 𝑔(𝑥𝑘 )‎.‎ ‎different choices for cg parameter are available‎, ‎some of which are as follows‎ 𝛽𝑘 𝐹𝑅 ≔ ‖𝑔𝑘‖ 2 ‖𝑔𝑘−1‖ 2 , fletcher & reeves (fr) [8] (4) 𝛽𝑘 𝐻𝑆 ≔ 𝑔𝑘 𝑇𝑦𝑘−1 𝑑𝑘−1 𝑇 𝑦𝑘−1 , hestenes & stiefel (hs) [15] (5) 𝛽𝑘 𝐶𝐷 ≔ − ‖𝑔𝑘‖ 2 𝑔𝑘−1 𝑇 𝑑𝑘−1 , fletcher (cd) [7] (6) 𝛽𝑘 𝑃𝑅𝑃 ≔ 𝑔𝑘 𝑇𝑦𝑘−1 ‖𝑔𝑘−1‖ 2 , polak & ribire − polyak (prp) [23,24] (7) 𝛽𝑘 𝐷𝑌 ≔ ‖𝑔𝑘‖ 2 𝑑𝑘−1 𝑇 𝑦𝑘−1 , dai & yuan (dy) [4] (8) 𝛽𝑘 𝐿𝑆 ≔ − 𝑔𝑘 𝑇𝑦𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 , liu & storey (ls) [20] (9) 𝛽𝑘 𝐻𝑍 ≔ (𝑦𝑘−1 − 2𝑑𝑘−1 ‖𝑦𝑘−1‖ 2 𝑑𝑘−1 𝑇 𝑦𝑘−1 ) 𝑇 𝑔𝑘 𝑑𝑘−1 𝑇 𝑦𝑘−1 , hager & zhang (hz) [13] (10) ‎in which ‖ . ‖ is the euclidean norm and 𝑦𝑘−1 ≔ 𝑔𝑘 − 𝑔𝑘−1‎. ‎these methods require‎ ‎low memory. ‎in order to guarantee the global convergence of cg methods‎, ‎the search direction 𝑑𝑘 must satisfy‎‎‎the sufficient descent condition [1] 𝑔𝑘 𝑇 𝑑𝑘 ≤ −𝑐‖𝑔𝑘 ‖ 2, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑘 ≥ 0, (11) ‎in which 𝑐 is a positive constant‎. ‎in cg methods to solve (1) ‎, ‎after determining the descent‎‎‎search direction satisfying 𝑔𝑘 𝑇 𝑑𝑘 ≤ 0 for all 𝑘 ≥ 0‎, the step size 𝛼𝑘 needs to be found‎, ‎which‎‎‎can be computed by inexact line search‎‎‎such as armijo‎, ‎goldstein and wolfe conditions‎. ‎for a given constant 𝜌 ∈ (0,1)‎, the armijo line search is‎ 𝑓(𝑥𝑘 + 𝛼𝑘 𝑑𝑘 ) − 𝑓(𝑥𝑘 ) ≤ 𝜌𝛼𝑘 𝑔𝑘 𝑇 𝑑𝑘 . (12) ‎the armijo condition (12) along with 𝑔𝑘+1 𝑇 𝑑𝑘 ≥ 𝜎𝑔𝑘 𝑇 𝑑𝑘 , 0 < 𝜌 < 𝜎 < 1, (13) ‎is called the wolfe line search [21].‎‎in addition‎, ‎in a strong wolfe line search‎, ‎(13) is changed as‎ |𝑔𝑘+1 𝑇 𝑑𝑘 | ≤ −𝜎𝑔𝑘 𝑇 𝑑𝑘 . (14) 1.2 applications of cg method conjugate gradient methods play an important rol‏e in solving large-scale unconstrained optimization problems‎ ‎which‎ arise in economics, engineering, sciences and so on. currently, the ‎u‎nconstrained‎ ‎optimization problem‏s in impulse noise removal and image restoration have been solved by cg method‏s [2,17]. 1.3 contribution ‎although ls has a good performance in practice‎, ‎it is generally not a strong convergence‎.‎‎on the other hand‎, ‎in cd with strong convergence the numerical results are not efficient.‎‎the purpose of this paper is to overcome these drawbacks‎. ‎we improve and combine ls and cd‎‎‎to obtain a new method with a good performance in practice and strong convergence properties‎.‎ ‎the new method always produces a sufficient descent direction which the global‎‎ ‎convergence of it is established under some suitable assumptions‎.‎ ‎also‎, ‎we give some preliminary numerical experiments to illustrate the efficiency of new method‎. ‎in section 2‎, ‎we describe our proposed‎‎‎method and give its algorithm‎. ‎the sufficient descent condition of new direction and‎‎‎the global convergence of the new algorithm are established in section 3‎.‎‎in section 4‎, ‎we report some numerical results to show the efficiency of new method‎.‎‎finally‎, ‎we give our conclusion in section 5‎. rahpeymaii f. rostami m. 92 2. motivation and proposed algorithm ‎in this section‎, ‎we describe the new method to solve unconstrained optimization problem (1).‎‎the ls proposed by liu and story [02] ‎. ‎the global convergence of‎‎‎ls with grippo & lucidi line search is established in [11] ‎. ‎this method has good numerical‎‎ ‎results but its global convergence properties are not strong‎. ‎many researchers have proposed several modifications‎‎‎of ls‎, ‎see ‎[19,26,27]. fletcher in [7] proposed cd‎‎for a general objective function with strong convergence properties‎, ‎but in numerical performance is weak‎. ‎we improve and combine cd‎‎‎and ls to obtain a new method with both the strong convergence and the good numerical results‎.‎‎based on ls and cd parameters‎, ‎we obtain‎ 𝛽𝑘 1 ≔ − 𝑔𝑘 𝑇𝑦𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 𝑎𝑛𝑑 𝛽𝑘 2 ≔ − ‖𝑦𝑘−1‖ 2 𝑔𝑘−1 𝑇 𝑑𝑘−1 . (15) ‎here‎, 𝛽𝑘 1: = 𝛽𝑘 𝐿𝑆 and in the numerator of 𝛽𝑘 2 term ‖𝑦𝑘−1‖ 2 has replaced ‖𝑔𝑘 ‖ 2 in parameter ‎𝛽𝑘 𝐶𝐷 . therefore‎, ‎the new conjugate gradient parameter is obtained by‎ 𝛽𝑘 𝑛𝑒𝑤 : = 𝑡𝑘 𝛽𝑘 2 − 𝛽𝑘 1, (16) with 𝑡𝑘 ≔ 2 𝑔𝑘 𝑇𝑑𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 . (17) the ‎parameters ‎𝛽𝑘 1, 𝛽𝑘 2‎ and 𝑡𝑘 guarantee‏ the sufficient descent property ‎and‎ the global convergence. furthermore, these parameters improve numerical results of new method in compared to cd and ls methods‏. now, ‎by substituting (15) and (17) in (11) ‎, ‎we get‎ 𝛽𝑘 𝑛𝑒𝑤 : = −2 𝑔𝑘 𝑇𝑑𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 ‖𝑦𝑘−1‖ 2 𝑔𝑘−1 𝑇 𝑑𝑘−1 + 𝑔𝑘 𝑇𝑦𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 . (18) ‎finally‎, ‎the new search direction 𝑑𝑘 is computed by‎ 𝑑𝑘 = { −𝑔𝑘 , 𝑘 = 0, −𝑔𝑘 + 𝛽𝑘 𝑛𝑒𝑤 𝑑𝑘−1, 𝑘 ≥ 1. (19) ‎algorithm 1 solves the smooth unconstrained optimization problem (1).‎‎it takes the initial point 𝑥0 ∈ ℝ 𝑛 as input and uses the following parameters‎:‎𝜀 > 0 (minimum threshold for the stopping test)‎, 𝜅 ∈ (0,1) and 0 < 𝜌 < 𝜎 < 1 (line search parameters), 𝑘𝑚𝑎𝑥 (maximum number of iterations), and‎ 0 < 𝛼𝑚𝑖𝑛 < 𝛼𝑚𝑎𝑥 < ∞ (minimum and maximum values for 𝛼𝑘). ‎it returns 𝑥 ∗ ≔ 𝑥𝑘 and 𝑓 ∗ ≔ 𝑓𝑘 as an optimum and its function value‎. note that 𝛼𝑚𝑖𝑛 and 𝛼𝑚𝑎𝑥 prevent the production of too small and large step size, respectively. algorithm 1 a new conjugate gradient method (s0) compute the initial function value 𝑓0 ≔ 𝑓(𝑥0), the initial gradient vector 𝑔0 ≔ 𝑔(𝑥0) and set 𝑑0 ≔ −𝑔0. (s1) if ‖𝑔𝑘 ‖ ≤ 𝜀 or 𝑘 > 𝑘𝑚𝑎𝑥 , stop. (s2) find 𝛼𝑘 satisfying (12) and (14) and restrict 𝛼𝑘 = 𝑚𝑎𝑥{𝛼𝑚𝑖𝑛 , 𝑚𝑖𝑛{𝛼𝑘 , 𝛼𝑚𝑎𝑥 }}. then, compute 𝑥𝑘+1 ≔ 𝑥𝑘 + 𝛼𝑘 𝑑𝑘 , 𝑓𝑘+1 ≔ 𝑓(𝑥𝑘+1) and 𝑔𝑘+1 ≔ 𝑔(𝑥𝑘+1). (s3) calculate 𝛽𝑘+1 1 and 𝛽𝑘+1 2 by (15), obtain the parameter 𝑡𝑘+1 by (17), determine the parameter 𝛽𝑘+1 𝑛𝑒𝑤 by (16) and 𝑑𝑘+1 ≔ −𝑔𝑘+1 + 𝛽𝑘+1 𝑛𝑒𝑤 𝑑𝑘. (s4) replace 𝑘 by 𝑘 + 1 and go to (s1). 3. convergence analysis in this section, the sufficient descent property and the global convergence of the algorithm 1 are established. to do so, we make some assumptions on the objective function. (h1)‎‎the level set 𝐿(𝑥0) = {𝑥 ∈ ℝ 𝑛 | 𝑓(𝑥) ≤ 𝑓(𝑥0)} is bounded‎, ‎i.e.‎,‎‎there exists a constant 𝐵 > 0 such that‎ ‖𝑥‖ ≤ 𝐵, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑥 ∈ 𝐿(𝑥0). (20) (h2)‎ ‎‎in some neighborhood ω ⊆ 𝐿(𝑥0),‏‎the gradient of the objective function 𝑓 ‎is lipschitz continuous‎, ‎i.e.‎, ‎there exists a constant 𝐿 > 0 such that‎ ‖𝑔(𝑥) − 𝑔(𝑦)‖ ≤ 𝐿‖𝑥 − 𝑦‖, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑥 ∈ ω. (21) ‎from (h1) and (h2)‎, ‎there exists a positive constant 𝛾 such that‎ ‖𝑔(𝑥)‖ ≤ 𝛾, (22) ‎see [21]‎. ‎we now show that the generated directions by algorithm 1 satisfy the sufficient descent‎‎‎condition (11) with 𝑐 = 7 8 ‎ independent of line search type‎. lemma 1 ‎suppose that the direction 𝑑𝑘 is generated by algorithm 1‎. ‎then‎, ‎we have‎ 𝑔𝑘 𝑇 𝑑𝑘 ≤ − 7 8 ‖𝑔𝑘 ‖ 2. (23) proof ‌‌by multiplying (19) in 𝑔𝑘 𝑇 and using (18), ‎we obtain‎ solving unconstrained optimization problems 93 𝑔𝑘 𝑇 𝑑𝑘 = −‖𝑔𝑘 ‖ 2 + 𝛽𝑘 𝑛𝑒𝑤 𝑔𝑘 𝑇 𝑑𝑘−1 = −‖𝑔𝑘 ‖ 2 + ( 𝑔𝑘 𝑇 𝑦𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 − 2 𝑔𝑘 𝑇 𝑑𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 ‖𝑦𝑘−1‖ 2 𝑔𝑘−1 𝑇 𝑑𝑘−1 ) 𝑔𝑘 𝑇 𝑑𝑘−1 = −‖𝑔𝑘 ‖ 2(𝑔𝑘−1 𝑇 𝑑𝑘−1) 𝟐 + (𝑔𝑘−1 𝑇 𝑑𝑘−1)(𝑔𝑘 𝑇 𝑦𝑘−1)(𝑔𝑘 𝑇 𝑑𝑘−1) − 2‖𝑦𝑘−1‖ 2(𝑔𝑘 𝑇 𝑑𝑘−1) 𝟐 (𝑔𝑘−1 𝑇 𝑑𝑘−1) 𝟐 . ‎take‎ 𝜐𝑘 ≔ 2(𝑔𝑘 𝑇 𝑑𝑘−1)𝑦𝑘−1 �̃�𝑘 ≔ 1 2 (𝑔𝑘−1 𝑇 𝑑𝑘−1)𝑔𝑘 . ‎using 𝜐𝑘 𝑇 �̃�𝑘 ≤ 1 2 (‖𝜐𝑘 ‖ 2 + ‖ �̃�𝑘 ‖ 2), we get 𝑔𝑘 𝑇 𝑑𝑘 ≤ 1 θ1 2 (−‖𝑔𝑘 ‖ 2θ1 2 + 2θ2 2‖𝑦𝑘−1‖ 2 + 1 8 θ1 2‖𝑔𝑘 ‖ 2 − 2‖𝑦𝑘−1‖ 2θ2 2) = − 7 8 ‖𝑔𝑘 ‖ 2, where θ1 ≔ 𝑔𝑘−1 𝑇 𝑑𝑘−1 𝑎𝑛𝑑 θ2 ≔ 𝑔𝑘 𝑇 𝑑𝑘−1. ‎ therefore‎, ‎the search direction 𝑑𝑘 always satisfies the sufficient descent condition‎.  lemma 2 ‎suppose that (h2) holds and the tuning parameter 𝛼𝑚𝑎𝑥‎ is given. ‎then‎, ‎there exists a constant ω1 > 0 such that‎ |𝛽𝑘 1| ≤ 𝜔1 ‖𝑑𝑘−1‖ ‖𝑔𝑘−1‖ 2 . (24) proof ‎from lemma 1‎, ‎we have‎ 𝑔𝑘−1 𝑇 𝑑𝑘−1 ≤ − 7 8 ‖𝑔𝑘−1‖ 2, so that 1 |𝑔𝑘−1 𝑇 𝑑𝑘−1| ≤ 8 7‖𝑔𝑘−1‖ 2 . (25) ‎by the definition of 𝛽𝑘 1‎, we obtain‎ |𝛽𝑘 1| = |− 𝑔𝑘 𝑇 𝑦𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 | = | 𝑔𝑘 𝑇 𝑦𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 |. ‎then‎, ‎from the cauchy-schwarz inequality‎, ‎(h2), (22) and (25), ‎we get‎ |𝛽𝑘 1| ≤ ‖𝑔𝑘 ‖‖𝑦𝑘−1‖ |𝑔𝑘−1 𝑇 𝑑𝑘−1| ≤ 8𝛾𝐿𝛼𝑘−1‖𝑑𝑘−1‖ 7‖𝑔𝑘−1‖ 2 = 𝜔1 ‖𝑑𝑘−1‖ ‖𝑔𝑘−1‖ 2 , with 𝜔1: = 8𝛾𝐿𝛼𝑚𝑎𝑥 7 .  lemma 3 suppose that (h2) holds and the tuning parameter 𝛼𝑚𝑎𝑥‎ is given‎. ‎then‎, ‎there exists a constant ω2 > 0 such that‎ |𝛽𝑘 2| ≤ 𝜔2 ‖𝑑𝑘−1‖ 2 ‖𝑔𝑘−1‖ 2 . (26) proof (h2)‎, ‎(15) and (25) result in‎ |𝛽𝑘 2| = |− ‖𝑦𝑘−1‖ 2 𝑔𝑘−1 𝑇 𝑑𝑘−1 | = ‖𝑦𝑘−1‖ 2 |𝑔𝑘−1 𝑇 𝑑𝑘−1| ≤ 8𝐿2𝛼𝑘−1 2 ‖𝑑𝑘−1‖ 2 7‖𝑔𝑘−1‖ 2 = 𝜔2 ‖𝑑𝑘−1‖ 2 ‖𝑔𝑘−1‖ 2 , where 𝜔2 ≔ 8𝐿2𝛼𝑚𝑎𝑥 2 7 .  lemma 4 ‎if (h2) holds‎, ‎then there exists constant 𝜔3 > 0 such that‎ |𝑡𝑘 | ≤ 𝜔3 ‖𝑑𝑘−1‖ ‖𝑔𝑘−1‖ 2 . (27) rahpeymaii f. rostami m. 94 proof ‎the cauchy-schwarz inequality‎, ‎(17)‎, ‎(22) and (25) imply‎ |𝑡𝑘 | = |2 𝑔𝑘 𝑇 𝑑𝑘−1 𝑔𝑘−1 𝑇 𝑑𝑘−1 | ≤ 2 ‖𝑔𝑘 ‖‖𝑑𝑘−1‖ |𝑔𝑘−1 𝑇 𝑑𝑘−1| ≤ 16𝛾‖𝑑𝑘−1‖ 7‖𝑔𝑘−1‖ 2 = 𝜔3 ‖𝑑𝑘−1‖ ‖𝑔𝑘−1‖ 2 , in which 𝜔3 ≔ 16𝛾 7 .  lemma 5 suppose that (h1) and (h2) hold. ‎if the sequence {𝑑𝑘 } be generated by algorithm 1,‎‎then there exists a constant 𝑀 > 0 such that‎ ‖𝑑𝑘 ‖ ≤ 𝑀, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑘 ≥ 0. (28) proof ‎we use induction to prove this lemma. first(22)‏ implies that ‖𝑑0‖ = ‖𝑔0‖ ≤ 𝛾. from the assumption of induction ‖𝑑𝑘−1‖ is bounded. hence, the exists constant 𝑀 ∗ > 0 such that‎ ‖𝑑𝑘−1‖ ≤ 𝑀 ∗. (29) now, the definitions of 𝑑𝑘 and 𝛽𝑘 𝑛𝑒𝑤‎, give‎ ‖𝑑𝑘 ‖ = ‖−𝑔𝑘 + 𝛽𝑘 𝑛𝑒𝑤 𝑑𝑘−1‖ ≤ ‖𝑔𝑘‖ + |𝛽𝑘 𝑛𝑒𝑤|‖𝑑𝑘−1‖ ≤ ‖𝑔 𝑘 ‖ + (|𝛽 𝑘 1| + |𝑡𝑘||𝛽𝑘 2|)‖𝑑𝑘−1‖. ‎we get from (22)‎, (29) and lemmas 2-4 that‎ ‖𝑑𝑘 ‖ ≤ 𝛾 + (𝜔1 ‖𝑑𝑘−1‖ ‖𝑔 𝑘−1 ‖ 2 + 𝜔2 𝜔3 ‖𝑑𝑘−1‖ 3 ‖𝑔 𝑘−1 ‖ 4 ) ‖𝑑𝑘−1‖ ≤ 𝛾 + ( 𝜔1 𝜀2 ‖𝑑𝑘−1‖ + 𝜔2𝜔3 𝜀4 ‖𝑑𝑘−1‖ 3) ‖𝑑𝑘−1‖. ≤ 𝛾 + ( 𝜔1 𝜀2 𝑀∗ + 𝜔2 𝜔3 𝜀4 (𝑀∗)3) 𝑀∗ ≔ 𝑀. ‎ the following result is a theorem in [29]. lemma 6 let 𝑑𝑘 be a sufficient descent direction and assume the step size 𝛼𝑘 satisfies the strong wolfe line search (12) and (14). then, based on (h1) and (h2), we have ∑ (𝑔𝑘 𝑇𝑑𝑘) 2 ‖𝑑𝑘‖ 2 < +∞. ∞𝑘=0 (30) theorem 1 let 𝑑𝑘 be a sufficient descent direction and {𝑥𝑘 } be the generated sequence by algorithm 1. also, (h1) and (h2) hold. then lim𝑛→∞ inf ‖𝑔𝑘 ‖ = 0. (31) proof from lemma 5, we obtain ∑ 1 ‖𝑑𝑘‖ 2 ≥ ∑ 1 𝑀2 = +∞∞𝑘=0 . ∞ 𝑘=0 (32) we use contradiction to prove this theorem. hence, there exists a constant 𝜖 > 0 such that ‖𝑔𝑘 ‖ ≥ 𝜖. (33) let ξ𝑘 = 𝑔𝑘 𝑇𝑑𝑘 ‖𝑔𝑘‖‖𝑑𝑘‖ . (34) using lemma 1, we obtain ξ𝑘 = 𝑔𝑘 𝑇𝑑𝑘 ‖𝑔𝑘‖‖𝑑𝑘‖ ≤ − 7 8 ‖𝑔𝑘‖ 2 ‖𝑔𝑘‖‖𝑑𝑘‖ = − 7 8 ‖𝑔𝑘‖ ‖𝑑𝑘‖ , (35) so that ξ𝑘 2 ≥ 49 64 ‖𝑔𝑘‖ 2 ‖𝑑𝑘‖ 2 . (36) from (33), (34) and (36), we can obtain 49 64 𝜖2 ‖𝑑𝑘‖ 2 ≤ 49 64 ‖𝑔𝑘‖ 2 ‖𝑑𝑘‖ 2 ≤ ξ𝑘 2 = (𝑔𝑘 𝑇𝑑𝑘) 2 ‖𝑔𝑘‖ 2‖𝑑𝑘‖ 2 ≤ (𝑔𝑘 𝑇𝑑𝑘) 2 𝜖2‖𝑑𝑘‖ 2 . (37) solving unconstrained optimization problems 95 by taking sums from both sides (37) and using lemma 6, we have ∑ 1 ‖𝑑𝑘 ‖ 2 ≥ ∑ (𝑔𝑘 𝑇 𝑑𝑘 ) 2 ‖𝑑𝑘 ‖ 2 < +∞ ∞ 𝑘=0 , ∞ 𝑘=0 which contradicts with (32). hence, the proof of the desired result is completed.  4. numerical experiments ‎this section gives numerical results of some algorithms on a set of the nonlinear unconstrained optimization‎‎ ‎ ‎test problems from cutest collection [11], ‎given in table 1‎. ‎the dimensions of test problems are from 2 to‎‎12005 while the initial points are standard ones proposed in cutest‎.‎ ‎we apply the following algorithms to solve these test problems‎:  m1: conjugate gradient method with 𝑑𝑘 ≔ −𝑔𝑘 + 𝛽𝑘 1𝑑𝑘−1.  m2: conjugate gradient method with 𝑑𝑘 ≔ −𝑔𝑘 + 𝛽𝑘 2𝑑𝑘−1.  m3: conjugate gradient method with 𝑑𝑘 ≔ −𝑔𝑘 + 𝛽𝑘 𝑛𝑒𝑤 𝑑𝑘−1.  m4: conjugate gradient method with 𝑑𝑘 ≔ −𝑔𝑘 + 𝛽𝑘 𝑛𝑒𝑤+𝑑𝑘−1 and 𝛽𝑘 𝑛𝑒𝑤+ ≔ 𝑚𝑎𝑥{0, 𝛽𝑘 𝑛𝑒𝑤 }.  dy: conjugate gradient method with 𝑑𝑘 ≔ −𝑔𝑘 + 𝛽𝑘 𝐷𝑌 𝑑𝑘−1.  hz: conjugate gradient method with 𝑑𝑘 ≔ −𝑔𝑘 + 𝛽𝑘 𝐻𝑍 𝑑𝑘−1. all algorithms are implemented in matlab 2011 programming environment on a 2.3hz intel core i3 processor‎ laptop and 4gb of ram with the double precision data type in linux operations system‎. all algorithms are terminated whenever the inequality‎‎‖𝑔𝑘 ‖ < 10 −6‎ holds or the maximum number of iterations exceeds 10000‎. ‎the tuning strong wolfe line search parameters are taken as‎ 𝜌 = 0.0001, 𝜎 = 0.9, 𝛼𝑚𝑖𝑛 = 10 −8 and 𝛼𝑚𝑎𝑥 = 10 8. ‎here‎, ‎we use the performance profiles of dolan & more [5] to compare m1‎, m2‎,‎ m3, m4, dy ‎and hz‎‎ algorithms on the test problems‎.‎‎we consider 𝑃 as designates the percentage of problems which are solved‎‎‎within a factor 𝜏 of the best solver‎. ‎the horizontal axis of the figure gives the percentage of the test problems‎‎‎for which an algorithm is the fastest (efficiency)‎, ‎while the vertical axis gives the percentage of the test problems‎‎ ‎that were successfully solved by each algorithm (robustness)‎. ‎figures 1-3 show that m4 is the best in terms of the total number of iterations‎,‎ ‎the total number of function evaluations and time in seconds‎‏ ‎in comparison with others‎. table 1. test functions taken from cutest collection. no. test function dim no. test function dim no. test function dim 1 3pk 3 49 dqdrtic 10000 97 nondia 1000 2 aircrftb 8 50 dqrtic 5000 98 nondquar 3000 3 allinit 4 51 edensch 100 99 oscipane 5000 4 allinitu 4 52 eg2 1000 100 oscipath 2 5 arglina 500 53 eg3 10000 101 oslbqp 8 6 arglinb 200 54 eigena 2550 102 palmer1c 8 7 arwhead 5000 55 engval1 100 103 palmer1d 7 8 bard 3 56 engval2 3 104 palmer2c 8 9 bdqrtic 100 57 errinros 50 105 palmer3c 8 10 beale 2 58 expfit 2 106 palmer4c 8 11 biggs6 6 59 extrosnb 1000 107 palmer5c 6 12 biggsb1 100 60 fletcbv2 10000 108 palmer6c 8 13 box2 3 61 fletchcr 500 109 palmer7c 8 14 box3 3 62 fminsrf2 5625 110 palmer8a 6 15 brkmcc 2 63 fminsurf 5625 111 palmer8c 8 16 brownden 4 64 freuroth 2 112 penalty1 100 17 broydn3d 5000 65 genhumps 500 113 penalty2 50 18 broydn7d 500 66 genrose 500 114 powellbc 1000 19 broydnbd 5000 67 growthls 3 115 powellsg 5000 20 brybnd 500 68 gulf 3 116 qr3dls 610 21 chainwoo 1000 69 hairy 2 117 quartc 25 22 chnrosnb 50 70 hatfldd 3 118 rosenbr 2 23 cliff 2 71 hatfldf 3 119 s308 2 rahpeymaii f. rostami m. 96 24 cosine 1000 72 hatfldfl 3 120 schmvett 100 25 cragglvy 1000 73 heart6ls 6 121 sensors 2 26 cube 2 74 heart8ls 8 122 sineval 2 27 cubene 2 75 helix 3 123 sinvalne 2 28 dallasm 196 76 hilberta 10 124 sisser 2 29 dallass 46 77 hilbertb 10 125 snail 2 30 deconvu 63 78 himmelba 2 126 sparsine 1000 31 denschna 2 79 himmelbc 2 127 sparsqur 10000 32 denschnb 2 80 himmelbf 4 128 spmsrtls 4999 33 denschnc 2 81 himmelbg 2 129 srosenbr 1000 34 denschnf 2 82 himmelbh 2 130 tame 2 35 dixmaana 9000 83 humps 2 131 testquad 100 36 dixmaanb 3000 84 jensmp 2 132 tointgor 50 37 dixmaanc 3000 85 kowosb 4 133 tointgss 10000 38 dixmaand 3000 86 liarwhd 5000 134 tointpsp 50 39 dixmaane 3000 87 loghairy 2 135 tointqor 50 40 dixmaanf 3000 88 mancino 100 136 tquartic 10 41 dixmaang 3000 89 matrix2 6 137 tridia 5000 42 dixmaanh 3000 90 methanol 12005 138 vareigvl 500 43 dixmaani 3000 91 modbeale 2 139 vibrbeam 8 44 dixmaanj 3000 92 morebv 5000 140 watson 12 45 dixmaank 3000 93 msqrtals 1024 141 weeds 3 46 dixmaanl 3000 94 msqrtbls 1024 142 woods 100 47 dixon3dq 1000 95 mine5d 10733 143 yfitu 3 48 djtl 2 96 noncvxu2 1000 144 zangwil2 2 figure 1. dolan-more performance profiles for the total number of iterations. solving unconstrained optimization problems 97 figure 2. dolan-more performance profiles for the total number of function evaluations. figure 3. dolan-more performance profiles for the time in seconds. rahpeymaii f. rostami m. 98 5. conclusion in this paper‎, ‎we proposed a new conjugate gradient method for solving the unconstrained optimization problems with improving and combining ls and cd parameters‎. ‎the new search directions of our algorithm satisfy‎‎ ‎the sufficient descent condition‎. ‎it inherits the strong global convergence properties of cd‎‎‎and the numerical efficiency of ls‎. ‎the global convergence under some mild assumptions is stablished‎.‎‎our numerical experiments show that m4 is better than other algorithms in terms of‎‎‎the total number of iterations‎, ‎the number of function evaluations and time in seconds‎. conflict of interest the authors declare no conflict of interest. acknowledgment the authors would like to thank the editor and reviewers for their valuable comments which helped to improve the manuscript. references 1. al-baali, m. descent property and global convergence of the fletcher-reeves method with inexact line search, ima journal of numerical analysis, 1985, 5, 121-124. 2. alhawarat, a., salleh, z. and masmali, i.a. a convex combination between two di_erent search directions of conjugate gradient method and application in image restoration, mathematical problems in engineering, 2021. 3. conn, a. r., gould, n.i.m. and toint, 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unconstrained optimization, siam journal on optimization, 2001, 12(1), 209-237. 11. gould, n.i.m., orban, d. and toint, p.l. cutest: a constrained and unconstrained testing environment with safe threads, technical report, ral-tr-2013-005. 12. griewank, a. the global convergence of broyden-like methods with a suitable line search, journal of the australian mathematical society ser. b, 1986, 28, 75-92. 13. hager, w.w. and zhang, h. a new conjugate gradient method with guaranteed descent and an efficient line search, siam journal on optimization, 2005, 16(1), 170-192. 14. hager, w.w. and zhang, h. the limited memory conjugate gradient method, siam journal on optimization, 2013, 23(4), 2150-2168. 15. hestenes, m.r. and stiefel, e.l. methods of conjugate gradients for solving linear systems, journal of research of the national bureau of standards, 1952, 49, 409-436. 16. kimiaei, m. and ghaderi, s. a new restarting adaptive trust-region method for unconstrained optimization, journal of the 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ribiere, g. note sur la convergence de directions conjugees, rev. francaise informat recherche opertionelle, 3e annee, 1969, 16, 35-43. 24. polyak, b.t. the conjugate gradient method in extreme problems, ussr computational mathematics and mathematical physics, 1969, 9, 94-112. 25. rahpeymaii, f., kimiaei, m. and bagheri, a. a limited memory quasi-newton trust-region method for box constrained optimization, journal of computational and applied mathematics, 2016, 303, 105-118. 26. yang, x., luo, z. and dai, x. a global convergence of ls-cd hybrid conjugate gradient method, advances in numerical analysis, https://doi.org/10.1155/2013/517452. 27. zhang, l. a new liu-storey type nonlinear conjugate gradient method for unconstrained optimization problems, journal of computational and applied mathematics, 2009, 225, 146-157. 28. zhou, q., zhou, f. and cao, f. a nonmonotone trust region method based on simple conic models for unconstrained optimization, applied mathematics and computation, 2013, 225, 295-305. 29. zoutendijk, g. nonlinear programming, computational methods. in: abadie j. (ed) integer and nonlinear programming. amsterdam, north-holland, 1970, 37-86. received 13 july 2021 accepted 16 june 2022 https://www.sciencedirect.com/science/journal/03770427 https://doi.org/10.1155/2013/517452 ferrocenylethynyl a versatile platform for new molecules to novel materials squ journal for science, 2014, 19(1), 15-42 © 2014 sultan qaboos university 15 ferrocenylethynyl a versatile platform for new molecules to novel materials hakikulla h. shah, rayya a. al-belushi and muhammad s. khan* department of chemistry, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *e-mail: msk@squ.edu.om. abstract: ferrocenylethynyl is a key starting material for the synthesis of fascinating new molecules and novel functional materials. it combines the robust and redox-active ferrocene moiety with the rigid-rod ethynyl unit. the ferrocene center provides chemically and electrochemically switchable material properties whereas the ethynyl backbone facilitates electron delocalization along the molecule, yielding materials with the potential for a wide range of applications from sensors to bio-organometallics and pharmaceuticals, from catalysts to nonlinear optical materials, and from fuel additives to chelating agents. however, lifetime performances and costs still need to be optimized to make ferrocenylethynyl-based materials commercially competitive. efficient synthetic methods are already in place which could play a key role in the progress of these materials. this review discusses the main approaches adopted in the synthesis of ferrocenylethynylbased molecules and materials. representative examples of each method are reported, highlighting its significant achievements together with the open issues and challenges to be faced by future researchers in this area. keywords: ferrocene; ethynyls; electrochemistry; synthesis; organometallic. مبتكرةمواد في تحضير منصة متعددة لجزيئات جديدة -يثينيل إفيروسينايل خان محمد صالح الدينريا البلوشية ووشاه حقيق هللا ٚثُٛبٚم انًبدة األسبسٛت فٙ تذعٛش جضٚئبث جذٚذة يًٓت ٔيٕاد ٔظٛفٛت. ْزِ انًبدة تجًع بٍٛ انفٛشٔسٍٛ انز٘ ٚتًٛض إفٛشٔسُٛبٚم ٚعتبش :ملخص ٔاإلٚثُٛبٚم انًسطخ. انفٛشٔسٍٛ ٕٚفش خصبئص انًٕاد انتشغٛهٛت انكًٛٛبئٛت بقٕتّ ٔصالبتّ ٔقذستّ انُشطت عهٗ انتأكسذ ٔاألختضال ٔانكٓشٔكًٛٛبئٛت بًُٛب ٔجٕد اإلٚثبٍٚ كخهفٛت نهًبدة ٚعًٍ عذو تًشكض فعبل نإلنكتشَٔبث عهٗ غٕل انجض٘ء ٔانز٘ ٕٚنذ يٕاد راث ادتًبنٛت هضٚت اإلدٛبئٛت ٔاألدٔٚت ٔيٍ انعٕايم انذفبصة إنٗ انًٕاد انعٕئٛت غٛش نإلستخذاو فٙ يذٖ ٔاسع يٍ انتطبٛقبث يٍ انًجسبث إنٗ انععٕٚت انف ٔانتكبنٛف بذبجت نهتذسٍٛ نجعم ُٙانعًش انضي كفبءة آخشِ. ٔنكٍ ٔببنشغى يٍ رنك، فإٌ انخطٛت ٔيٍ يعبفبث انٕقٕد إنٗ انعٕايم اإلستببغٛت إنٗ عشضْزا انُٕع يٍ انًٕاد. ْزا ان فٙ يُٓبجٛت انتذعٛش انفّعبل دٔسا ْبيب فٙ تفعٛم . ٔتهعب انتطٕٚشاثيُبفست تجبسٚب ُٛبٚم إٚثفٛشٔسُٛبٚم اند يٕا ٚثُٛبٚم، ٔٚتى خالل عشض يُٓجٛبث انتذعٛش فٛشٔسُٛبٚم اانُٚبقش أْى يب تى انتٕصم إنّٛ فٙ تذعٛش انجضٚئبث ٔانًٕاد انًكَٕت أسبسب يٍ هٗ انُتبئج انًًٓت انتٙ تى انتٕصم إنٛٓب ٔانتذذٚبث انتٙ ٚجب يٕاجٓتٓب فٙ األبذبث األيثهت انتٕظٛذٛت يع إنقبء انعٕء ع غشح بعطانًختهفت انًستقبهٛت فٙ ْزا انًجبل. ععٕٚت يعذَٛت.ٔتذعٛش ،كٓشٔكًٛٛبئٛت ،إٚثُٛبٚم ،: فٛشٔسٍٛمفتاح الكلمات ferrocenylethynyl a versatile platform 16 contents 1. introduction 1.1 synthetic flexibility: tuning the properties of ferrocenyl materials 2. synthetic protocol for ferrocenylethynyl connected to conjugated organic spacers 2.1 type i ferrocene materials 2.2 type ii ferrocene materials 2.3 type iii ferrocene materials 2.3.1 electrical conductivity 2.3.2 electronic properties 2.4 type iv ferrocene materials 2.4.1 effect of spacer group 2.4.2 effect of chain length 2.4.3 effect of electrolyte 3. ferrocenylethynyls connected through a metal bridge 3.1 ferrocene termini linked to metal bridge by covalent bond 3.2 tuning the properties by metal bridging 3.2.1 electro-luminescence property 3.2.2 electronic communication 3.2.3 redox control 3.3 ferrocene termini linked to metal bridge by coordination bond 4. present outlook and future directions 5. acknowledgements 6. references 1. introduction ven six decades after its discovery, ferrocene still remains a hot topic for new materials researchers. ferrocene and ferrocene-based materials are versatile and have been successfully used in a variety of domains such as electrochemistry [1-4], sensors [5], nonlinear optics and luminescent systems [6,7], pharmaceuticals [8,9], automobiles [10,11], fine organic synthesis [12], materials chemistry [13-17], liquid crystals [18-20], paramagnetic and ferromagnetic systems [21,22] and bio-organometallic chemistry [23], etc. during its long journey ferrocene chemistry has witnessed the emergence of many structural motifs built around the ferrocene platform, suitably grafting ene, phenylene(ethylene) and ethynyl spacers between two ferrocenes or between a ferrocene and an organic/inorganic group. compounds having an ene-terminus in the arm(s) are building blocks for metathesis and polymerization reactions leading to organometallic oligo/polymers or metallophanes. on the other hand, examples of motifs having conjugated all π-arms are relatively rare and are viewed as promising candidates in building nanoarchitectures. it is now generally accepted that an unsaturated adjunct acts as a messenger to facilitate communication between the arm and the redox centre. this leads to synergistic perturbation of the electronic, opto-electronic and electrochemical properties of the molecule. not surprisingly, compounds belonging to such motifs find end applications in diverse areas ranging from metallo-mesogens through nlo-active organometallics to redox-switch receptors. the significant potential of this special class of ferrocenes is expected to witness further exploration on many fronts. togni et al. [24,25] and others have shown that chiral and achiral ferrocenyl phosphines can be used as ligands in organic synthesis and asymmetric catalysis for carbon–carbon, carbon–heteroatom coupling, carbonylation, hydroformylation, hydrogenation, olefin polymerization and cycloaddition [26,27]. gallei et al. have shown that the oxidation state of the ferrocene can affect the wettability of surfaces modified with poly(vinylferrocene) or poly(2-(methacryloyloxy)ethyl ferrocenecarboxylate) [28]. kadkin has reviewed monoand di-substituted ferrocenes containing liquid crystals and shown that liquid crystalline ferrocene exhibits unique physical properties [29]. undoubtedly, the design motif in ferrocene-based architectures plays the most important role in delivering the targeted property. linearly substituted ferrocenes having substitution at one or both cyclopentadienyl (cp) rings constitute a very large sub-group of ferrocene architectures. very e hakikulla h. shah et al 17 broadly, these are of three types olefinic, ethynyl and cumulenic as shown in chart 1. in the past two decades different research groups have developed a range of these architectures with the sole aim of tuning their chemical, electrochemical, spectroscopic and opto-electronic properties. as a result, they have gained prominence as new generation molecular materials, -conjugated multi-metallic systems and as redoxswitchable receptors. in this review, we have concentrated on ferrocenyl alkyne type molecules and materials and focused on this special class of ferrocenyl materials, with a view to developing a comparative assessment of recent advances in their synthesis and properties. we have also attempted to look closely into these systems under sub-categories representing types of spacers in the backbone chain and to highlight selected examples. 1.1 synthetic flexibility: tuning the properties of ferrocenyl materials ferrocene derivatives with linear, unsaturated side-arms show unique properties compared to their saturated analogues. some of these properties include electrical conductivity, thermal stability, magnetic, electronic, redox, and non-linear optical behaviour. this can be attributed to the electronic interaction of both metaland ligand-based orbitals of ferrocene platform with the orbitals of the -conjugated substituents in the side chain. not surprisingly, some of the properties are dramatically dependent on the nature and conjugation length of the substituents. in this section, we closely look into these properties with special emphasis on the electronic, redox and optical effects of ferrocenes with an ethynyl conjugation. in the ferrocenyl alkynes, the linear alkyne arm(s) may bear all carbon or hetero elements, heterocyclic rings, conjugated and non conjugated spacers and may have an extended -conjugation with another ferrocene nucleus. four structural types represent the majority of ferrocenes with a linear open-arm motif depending on whether the ferrocene nucleus is monoor di-substituted or whether the ferrocene acts as a pillar to form “molecular clefts” (see chart 2). within the linear open-end motifs, those in which the ferrocene unit is connected to an unsaturated alkyne side-arm, -conjugated to the cp ring are of significant interest. herein we review recent advances in their synthesis and properties and attempt to look closely into these systems under sub-categories representing types of attachments in the side chain and to draw attention to selected examples in detail. fe fe fe c=c=c n ferrocenyl alkene ferrocenyl alkyne ferrocenyl cumulene chart 1. linear structures of ferrocene. fe fe fe fe spacer i ii iii iv fe chart 2. types of ferrocenes with an unsaturated backbone. ferrocenylethynyl a versatile platform 18 2. synthetic protocol for ferrocenylethynyl connected to conjugated organic spacers several methods for syntheses of ferrocenyls with an ethynyl backbone using the cross-coupling reactions, such as sonogashira coupling, negishi coupling, stille coupling and stephens-castro coupling, have been reported in the literature (see scheme 1). in this section, we examine the synthetic routes in detail. successive sonogashira coupling of iodoferrocene with ethynyl substrates has been achieved in the presence of catalytic amounts of pdcl2((pph3)2)/cu(oac)2 in i pr2nh at 90 °c to give ferrocenylethynyl complex (a) in high yield [30]. iodoferrocene has also been the starting material for the synthesis of many ferrocenylethynyl derivatives through various coupling pathways [31-33]. stille coupling using 4pyridyl(trimethylstannyl)ethyne and iodoferrocene has also been used to synthesize ferrocenylethynyl compound (b). negishi coupling of the organozinc component with iodoferrocene has also been used for generation of extended ferrocenylethynyl (c) [34]. the stephens-castro coupling has been utilized by reacting iodoferrocene with the corresponding copper arylacetylide to synthesize arylferrocenylethyne (a) in 26–50% yield in refluxing dmf rather than the usual pyridine as solvent. it is noteworthy that refluxing equimolar amounts of iodoferrocene and cuprous phenylethynyl in pyridine for 8 h under n2 provides the same ferrocenylphenylethyne (a) in 84% yield. in an analogous manner, coupling of iodoferrocene and cuprous ferrocenylethynyl produces the bis-(ferrocenylethynyl) (fc-c≡c-fc) in 85% yield. 2.1 type i ferrocene materials among the methods described, sonogashira coupling has been the most extensively used due to its good yield and better quality of end product [35]. furthermore, most of the terminal ethynyl compounds are not stable in air and at ambient temperature. ethynylferrocene is stable at room temperature, easy to handle and gives higher yield compared to the iodoferrocene starting material. hence, it is a good choice as the key starting material for coupling reactions with the dihalo-aromatic and hetero-aromatic spacers to obtain the desired cross-coupled products. often this reaction is accompanied by a minor by-product arising from the homocoupling of the ethynyl units, which can be avoided by maintaining a rigorous inert atmosphere. the (1:1) sonogashira coupling of ethynylferrocene with mono-halo aromatics such as benzene, naphthalene, anthracene, etc., or mono-halo hetero-aromatics such as thiophene, pyridine, bipyridine, etc., or with monohalo mixed hetero-aromatic ligands has given rise to novel compounds which have direct applications or which act as precursors for further new materials developments. fe i fe n fe fe fe pd (pp h 3 ) 4 pd (pp h 3 ) 4 , 2 4 h stille coupling stephens-castro coupling sonogashira coupling negishi coupling 45 -50 °c, 24 h dm f/py reflux cu ph ph zncl2 pyr snm e 3 ph pdcl 2 (pph 3 )2 , cu(oac) 2 ipr 2 nh, 90°c (a) (b) (c) (a) scheme 1. synthetic protocol for ferrocenylethynyl connected to conjugated organic spacers. general representation of ethynylferrocenes capped with aryl and various substituted aryls (r) placed in conjugation with the ethynyl unit is shown in chart 3 [36]. the use of a wide range of „r‟ shows that the reaction tolerates both electron-withdrawing as well as electron-donating spacers providing functional molecules and new materials [37]. for example, the compound prepared by the coupling of ethynylferrocene with 4-bromopyridine serves as a ligand with terminal pyridine as the coordinating site (5,6) [38]. a similar coordination site is also provided by dangling ligands like 4-brc6h4c≡n. the reaction leads to compound 7 in 84% yield [39]. this compound with an additional c≡n ligating site serves as the basis for the preparation hakikulla h. shah et al 19 of oligonuclear ferrocene-based transition metal complexes [34,40]. by coupling ethynylferrocene with the appropriate mono-bromooligothiophene, substituted thiophene and fused thiophene unit, a new series of type i ferrocenyl derivatives has been synthesized (8-12) [41]. compound 13 is a much more extended phenylethynyl congener linked to a metallic end-cap via a fluoren-9-one spacer [42]. extended one-dimensional conjugated compounds (14-16) have also been synthesized by incorporating oligothiophene spacers on the ethynyl skeleton (chart 4). fe r r = cl no2 n n c n s s o o s oo ss n = 1, 2, 3 1 2 7 3 65 4 8-10 1211 chart 3. general chemical structures of some mono-(ferrocenylethynyl) derivatives. fe pt pet3 pet3 ph fe pt pet3 pet3 ph s n = 1, 2, 3 o 13 14-16 chart 4. general chemical structures of one-dimensional mono-(ferrocenylethynyl)compounds with extended conjugation. fe n fe n w(l)(co)4 (pd(pph3)2) 2+ 2(otf)2 l = co, pph3, pme3, p(ome)3 fe fe+(co)3 h h 17 18-21 22 chart 5. general chemical structures of mono-(ferrocenylethynyl) compounds. interestingly, placing a benzonitrile and pyridine group on the ethynyl skeleton has provided an added opportunity for further coordination to a metal complex precursor such as a pd(pph3)2 unit (17), giving rise to the trimetallic species and subsequent metal coordination to tungsten providing mixed-valence bimetallic fragments (18-21), that are potential candidates for molecular wires (chart 5). indeed, an insight into the ferrocenylethynyl a versatile platform 20 delocalization along the conjugated backbone can be obtained from the analysis of their strong ligand to metal charge-transfer bands [34,40]. ferrocenylethynyls capped with electron-accepting groups result in nonlinear optical properties. compound 22 is an example having a tricarbonyl(cyclohexadienyl) iron(1+) unit acting as the electron accepting cap [43]. the interesting aspect of the molecule is that, it not only shows a high hyperpolarisability () value of 100 x 10 −30 esu (in comparison to  = 16.9 x 10 −30 esu for 4-nitroaniline), but also has a chiral electron accepting organometallic end-group. thus, type i ferrocenylethynyls capped with aromatic, hetero-aromatic and metallic substituents are synthesized with the aim of exploiting optical, optoelectronic and other material properties. 2.2 type ii ferrocene materials the second type of motif consists of two cis-disubstituted ferrocene units interlinked by extended ethynyl bonds. examples of this type of ferrocenes are rare. in the late 60s, hedberg and co-workers reported the synthesis of biferrocenylene (without the ethynyl bridge) [44], they were followed by rosenblum and coworkers who reported the first member of this class of ferrocenes having bridging ethynyl groups [2.2]ferrocenophane-1,13-diyne (see chart 6 ) [45]. chart 6. chemical structure of bi(ferrocenylethynyl) compound. this was achieved by coupling of the cuprous salt of 1-ethynyl-1′-iodoferrocene. later, livanda and coworkers investigated this compound for its electrochemical properties and presented a comparison with the biferrocenylene [46]. the monocation of [2.2]ferrocenophane-1,13-diyne had a near-infrared band (λ 1760 nm, ε 2100) at lower energy and higher intensity than the corresponding biferrocenylene monocation [47]. the electrochemical and spectral results suggest that [2.2]ferrocenophane-1,13-diyne is a delocalized analogue of the biferrocenylene cation. 2.3 type iii ferrocene materials the third type of motif consists of two trans-disubstituted ferrocene units linked by extended ethynyl units to form oligomers and polymers. ingham et al. were the first to synthesize monomeric, dimeric and polymeric ferrocenylethynyls incorporating the phenylene spacer by reacting 1,1′-diiodoferrocene with mono and bis-alkynyltrimethylstannanes [48]. they also reported a crystal structure of the bis(phenylethynylferrocene) which showed a cis conformation. yamamoto and co-workers [7] were one of the earlier research groups to report the synthesis of a series of ferrocenylethynyl polymers (24-28) incorporating carbocyclic and heterocyclic spacers using sonogashira synthesis. they also reported a model compound (29) for comparison which showed cisconformation similar to earlier reports (see chart 7). fe r n r = n s c6h13 c12h25 c12h2524 n c12h25 c12h25 fe fe 29 (cis-model compound) 2625 27 28 fe 3 4 5 9 10 6 7 8 1' 2' 3' 4'5' 9' 10' 6' 7'8' 1 2 chart 7. general chemical structures of ferrocenylethynyl polymers. fe fe 23 hakikulla h. shah et al 21 electrochemical investigation of these materials showed broadening in the cylic voltammetry peaks. they compared the cv peak broadening of the poly(ferrocenylethynyl)s with that of a diphenylethynylferrocene model compound and further compared both of these with the cv peak of parent ferrocene. they found that the parent ferrocene peak compares well with that of the diphenylethynylferrocene model compound, which eliminated the involvement of the diethynyl bridging unit in the broadening of the cv peaks. plenio et al. conducted a more systematic study by synthesizing a series of ferrocenylethynyl oligomers and performing a systematic evaluation of the cyclic voltammograms and also complementing the results by differential pulse voltammograms [49]. both groups proposed that the broadening in the cv could be due to the presence of closely spaced redox processes of the adjacent ferrocene units in the polymer. 2.3.1 electrical conductivity designing and preparing molecular wires with good charge transport capacity is of crucial importance to the development of molecular electronics. when ferrocene is incorporated in the organic chain it enhances the charge mobility along the chain. a recent report demonstrates how the conductivity of an oligo(pphenylene ethynylene) chain (30-36) increases (figure 1) by incorporating ferrocene into molecular backbones (37-40). lu et al. [50] have successfully enhanced the molecular conductance of oligo(pphenylene ethynylene)s (30-36) in both tunnelling and hopping conduction regimes. specifically, they found that the increased degree of molecular conductance in the hopping regime is much more than that in the tunnelling regime [50]. in figure 1 a plot of ln r (r = resistance) vs. molecular length shows that molecules of the same length containing ferrocene i.e. (37, 38, 39 and 40) in the backbone have lower resistance which implies they have higher conductance compared to the purely organic oligo(p-phenylene ethynylene)s (30, 32, 34 and 36) respectively. 2.3.2 electronic properties the electronic structure of ferrocene includes three highest filled levels resulting from dxy, dx2−y2 (e2g) and dz 2 (a1g) orbitals, which are essentially metal-based, while the next highest orbitals (e1u) are principally ligand-based. the molecular orbitals resulting from the dxz and dyz bonding interactions (e1g) are occupied, while the antibonding counterpart (e∗1g) remains vacant. the molecular orbital energy level diagram of ferrocene and those with maximum d-character (highlighted in the box) are shown in figure 2 [51]. generally, two prominent bands are observed for ferrocenyl compounds in the visible region. in agreement with previous experimental work and theoretical treatment, the higher energy band (300–390 nm) is assigned to a –* intra-ligand transition, and the lower energy band (400–500 nm) is assigned to a metal to ligand charge-transfer band (mlct). in addition, another very weak band at higher wavelength (about 500 nm), assigned as d–d transition, is sometimes discernible as a shoulder on the mlct band [52]. attaching a conjugated system to ferrocene causes significant perturbation of the ligand-based (e1u) orbitals. with increasing conjugation length, the energy of the * orbital is lowered resulting in a red shift of the –* transition [53]. an increase in wavelength with degree of conjugation is also observed for the ferrocenylethynyl derivatives having fluorenone spacers. it is also clear that the increase in the number of ethynyl units from n = 1 to 2 leads to further red shift in the absorption maxima, consistent with the more extended -conjugation. for example, there is a linear relationship reported between the λmax for d-d transition and 1/n (n = number of ferrocenylethynyl units) for monomers and oligo-ynes with a limiting value of 472 nm for 1/n = 1/∞ (figure 3). these effects have been found to be linear in ferrocenylethynyl poly-ynes and oligo-ynes. in addition, the extinction coefficient is reported to increase with „n‟. it is thus evident that the ferrocene d-d transition is coupled to the conjugated main chain [49]. the spectra and extinction coefficients of the ferrocenylethynyl oligo-ynes in ch3cn and ch2cl2 show only a weak solvatochromic effect between the two solvents. since solvatochromic behaviour reflects the polarizability of a chromophore, studying the electronic spectra provides an important means to measure the magnitude of nonlinear properties in a donor-acceptor bridged molecule [49]. ferrocenylethynyl a versatile platform 22 figure 1. chemical structures of oligo(p-phenylene ethynylene) chains (30-36) without and with ferrocene (37-40) and plot of ln r vs. molecular length (bottom). adapted with permission from ref [50]. copyright (2012) american chemical society. nh2h2n 30 h2n 31 nh2 h2n nh2 h2n nh2 h2n nh2 o o o o h2n nh2 o o o o h2n nh2 o o o o o o o o 32 33 34 35 36 fe nh2 o o h2n o o o o o o fe nh2 h2n o o o o fe nh2 h2n fe h2n nh2 38 37 39 40 hakikulla h. shah et al 23 fe e*1g a*2u e*2g a*1g a2u e*1g (xz, yz) a'1g(z 2) e2g x2-y2, xy e1u e1g a2u a1g a1g, a1u e1g, e1u d (a1g, e1g, e2g) p (a2u, e1u) s (a1g) metallocene homo and lumo (orbitals with d-character) figure 2. molecular orbital energy levels in ferrocene. adapted with permission from ref [51]. figure 3. plot of variation of λmax with 1/n (λmax d-d transition, n = number of ferrocene). adapted with permission from ref [49]. copyright (2000) wiley-vch verlag gmbh, weinheim. chart 8. selected bis(ferrocenylethynyl) compounds. fe r n s ** n = 1, 2, 3 s o o s oo ss n n z z = co, ch2, c(c6h13), fe h h , nn fe s o ln o f3c r = ln = la, nd, eu, yb 54,55 61-64 56-60 5352 49-51 4847 4645 n = 1, 2 fe fefe fe ferrocenylethynyl a versatile platform 24 2.4 type iv ferrocene materials the fourth type of motif consists of two ferrocene units linked by ethynyl fragments and organic/inorganic spacers. by tuning the size and shape of the spacers, elegant molecular architectures with possible electronic communication between the metal centres along the conjugated backbone have been achieved. the sonogashira coupling has also been extended to the bis(ferrocenylethynyls) by reacting ethynylferrocene with dihaloaryl precursors in the presence of pdcl2(pph3)2 and cui catalysts in refluxing i pr2nh. similar to the mono(ferrocenylethynyl) compounds, a variety of bis(ferrocenylethynyl) compounds have been prepared by incorporating aromatic, hetero-aromatic, mixed hetero-aromatic and metal bridging ligands. a few representative examples are shown in chart 10. a few examples of ferrocenyl end-capped ethynyl complexes incorporating a wide range of aromatic and hetero-aromatic spacers (r) are presented in chart 8 [44,41,53,54]. the electron donating or electron withdrawing properties of the conjugated spacer groups have been used to tune the redox properties of the ferrocenylethynyl dyads (45-51) [35,54]. zhu et al. demonstrated that the potential difference (δe) between the two redox waves of the bis(ferrocenylethynyl) can be varied from 0.38 to 1.12 v, depending on the length and substitution of the oligothiophene group (49-53) [41]. along this line, wong et al.[53] designed a series of ferrocenyl end-capped derivatives (54-55) by varying the number of ethynyl units and the nature of the fluorene spacer in order to study the combined effect of the nature of spacer and the number of ethynyl units [53]. electrochemical studies reveal that the half-wave potential of the terminal ferrocene becomes more anodic upon increasing the number of ethynyl units. secondly, on changing the 9-substituent of the central fluorene ring from electron-rich alkyl (57) or ferrocenyl group (59-60) to an electron-deficient oxo group (56), the half-wave potential of the terminal ferrocene can be made more anodic. yuan et al. have designed a series of bis(ferrocenylethynyl) complexes incorporating 1,10-phenanthroline spacer [55]. these bidentate ligands were used to synthesise a series of rare-earth β-diketonate complexes 61-64. the presence of ferrocene in these complexes has been reported to shift the ligand absorption band to longer wavelengths, which in turn facilitates the excitation of these complexes by ultraviolet radiation and also by visible light. 2.4.1 effect of spacer groups shah et al. recently reported a new series of bis(ferrocenylethynyl) complexes incorporating novel heterocyclic spacers [1]. they also synthesized one mono(ferrocenylethynyl) compound for comparison with the bis(ferrocenylethynyl)s (see chart 9). the objective was to create donor-acceptor type structural motifs to enhance the communication between the two ferrocene termini. broadened cv peak potentials for complexes 66-70 were observed without significant splitting of the mid-point potential. this was attributed to considerably longer fe-fe distance of around ~14 å in complexes 66-70, as established by x-ray crystallographic studies. plenio and others have attributed similar broadening of the cv peak to the presence of closely spaced redox processes in those ferrocenylethynyl poly-ynes and oligo-ynes reported previously [49,56-58]. the cv features were reproduced by digital simulation which confirmed that the broadening in the cv peaks can be reconciled with the presence of two individual, closely spaced, one-electron processes (see figure 4). the δe1/2 values suggest that they belong to class ii according to the robin and day classification scheme, with modest coupling [59]. r = n s n nn phph s 65* n none s nn ff * 65 was synthesized by oxidative homocoupling of ethynyl ferrocene in the presence of o2 ** 71 is a mono(ferrocenylethynyl) complex s s s s s s br fe 71** fe r fe 6766 70 68 69 chart 9. chemical structures of bis(ferrocenylethynyl) complexes (65-70) and a mono(ferrocenylethynyl) complex (71). hakikulla h. shah et al 25 figure 4. selected simulation curves (red circles) matched with cyclic voltammograms (black line) for bis(ferrocenylethynyl) complexes 65(a), 66(b), 68(c) & 70(d). reprinted with permission from ref [1]. copyright (2013) american chemical society. recent reports suggest that electron withdrawing spacers play a positive role in improving the communication between the terminal ferrocene units [60-62]. solntsev and co-workers demonstrated significant electronic communication in bis(ferrocenyl) complexes separated by electron withdrawing spacers having fe-fe distance <8å [60]. similar trends were seen in complex 67. despite a fe-fe distance of 13.494 å, it showed δe1/2 110 mv, which was not too dissimilar compared to values for para-diferrocenylbenzene [63]. the electron withdrawing nature of the spacer influences the net conjugation effect over-riding the fe-fe distance separation in this particular comparison. another example demonstrating the effect of the spacer group is the bimetallic complexes reported by mercs et al., where the bis(nhc) spacer exhibited weaker interactions (δe1/2 = 42−80 mv) despite having direct metal-nhc connections and fe-fe distances of less than 11 å [56]. complexes 66-70 with fe-fe distance of ~14 å and δe1/2 values of 50 to 110 mv represent long-range intra-molecular electronic communication [64,65]. the formation of the monocationic species was investigated by spectro-electrochemical methods (figure 5). the changes in the spectrum in response to the applied potential confirmed the formation of an ivct band as a result of mono-oxidation. the spectro-electrochemical experiments showed that upon oxidation of reported complex 65 to 65 + , the intensity of the low energy mlct bands decreases, while the intensity of the higher energy, predominantly π π* band, increases. the nir band was assigned as an ivct transition as this band disappears on further oxidation by increasing the potential [64]. similar observations were found for complexes 66-70. the ivct nature was further confirmed by comparing the bis(ferrocenylethynyl) complexes with the mono(ferrocenylethynyl) complex, both containing the dithienothiophene spacer. the mono(ferrocenylethynyl) complex 71 showed no band in the nir region; instead it showed a band at 760 nm which was assigned as a lmct band and has been previously reported for mono(ferrocenylethynyls). complexes 65 and 67 were studied computationally to get a better insight into the intra-molecular interaction processes (see figure 6). for 65 the homo shows extensive delocalization across the whole molecule, with contributions of 26 (fe), 11 (c5h4) and 23% (cc-cc) from the contributing fragments. similarly, the homo for 67, though less symmetrical than for 65, has contributions of 33, 20 (fe, fe), 11, 8 (c5h4, c5h4), 7, 7 (cc, cc) and 14% (c6nsn). 2.4.2 effect of chain length electrochemistry has been extensively used to study the property sequence that occurs on changing the length and nature of the conjugated substituents attached to the ferrocene platform. chain lengthening of the -conjugated system results in a non-linear decrease of the redox potentials due to charge delocalization and stabilization of the ferrocenium formed. good dependence of chain lengthening and redox potential is observed in the ferrocene dimers with ethynyl bridges. due to the two redox centres, these complexes are expected to show two redox potentials. the peak separation denoted by δe1/2 indicates the extent of ferrocenylethynyl a versatile platform 26 internuclear electron transfer. dependence of electron transfer with chain length is clearly established in the bis(ferrocenylethynyls) such as fc2(c≡c)n (n = 0, 1, 2, 3,) [46,65,66]. another notable feature is the dependence of the fc/fc + redox potential on the chemical nature of the conjugated spacer group in the ferrocenyl derivatives. electron withdrawing fragments attached to the terminus of the conjugated spacer stabilize the neutral fc over the cationic fc + , and result in an anodic shift of the redox-wave compared to that of the free ferrocene. figure 5. uv-vis spectra of complexes 65(a), 66(b), 70(c) & 71(d). (i) data for the neutral spectra, (ii) the mono-cation, and difference spectra (iii-v) are shown. adapted with permission from ref [1]. copyright (2013) american chemical society. some good examples are given by maragani et al. who have synthesized a series of monofunctionalized ferrocenyl ethynyls and investigated the donor-acceptor interaction between the ferrocene and the ligands [67]. in the bis(ferrocenylethynyls), the nature of the spacer group has been very well utilized to tune the redox properties and the intra-molecular electronic communication of the complexes [35,53]. wong et al. have incorporated electron-rich and electron-deficient groups in the bis(ferrocenylethynyl) complexes and presented a systematic study of the redox behaviour of the ferrocenes. the study reveals that the redox potential can be made anodic with the use of electron-deficient spacers in the bis(ferrocenylethnyls) and vice versa. in the same report, they also varied the (c≡c)n unit from 1 to 2 and found that the increase in the ethynyl unit also increased the redox potential in the complexes [53]. figure 6. homo of complexes 65 (left) and 67 (right). reprinted with permission from ref [1]. copyright (2013) american chemical society. 2.4.3 effect of electrolyte there are few examples of higher number of ferrocenes connected through a bridging organic spacer. compound 72 reported by fink et al. having three ferrocene termini connected by the triethynylbenzene core is noteworthy as it may be viewed as a potential precursor for the production of metal-aromatic poly-yne hakikulla h. shah et al 27 networks [69]. diallo et al. have reported examples of six ferrocenes connected to a hexaethynylbenzene core [69]. they demonstrated that redox chemistry of such molecules is highly sensitive to an ion-paring dependant electrostatic effect. they used substituted and un-substituted ferrocene and presented a fine work of electrochemistry demonstrating the effect of a supporting electrolyte on the redox process of these complexes (see chart 10). figure 7 shows the cv of the tri-ferrocenylethynyl benzene and hexa-ferrocenylethynyl benzene. the top figures show the cv from the traditional electrolyte i.e. tetrabutyl ammonium hexafluorophosphate, while the bottom cvs resulted on changing the electrolyte to tetrabutyl ammonium tetra aryl borate. this change in the electrolyte resulted in separation of the ferricenium signals as shown in the bottom figures. similarly, when one of the hydrogens on the cp in the hexa-ferrocenylethynyl benzene was substituted with methyl groups, all the six cv signals could be separated. figure 7. cvs of complexes 72(a), 73(b) and 75(c) under [n-bu4n]pf6 (top) and [n-bu4n]bar4 (bottom) electrolyte. reprinted with permission from ref [69]. fe r rr fe r rr fe r r rfe r r r fe r r r fe r r r r'r r'r r r'r' r r' r r r' r = r' = h r = r' = ch3 r = h, r' = ch3 73 fe fe fe 72 74 75 chart 10. chemical structures of tri(72) and hexa-ferrocenylethynyl complexes (73-75) investigated by diallo et al. [69]. ferrocenylethynyl a versatile platform 28 3. ferrocenylethynyls connected through a metal bridge 3.1 ferrocene termini linked to metal bridge by covalent bond since the last decade intense efforts have been made to generate ferrocenylethynyls containing different metal bridging groups [70-73], or metal-containing fragments [74], in the study of electronic communication between the redox-active termini through organic [63,75] or metal-containing fragments [74]. fefe l = co, c5h5n, p(ome)3 76-78 ru pbu3 bu3p co l chart 11. general chemical structure of ferrocenylethynyls connected through ruthenium metal units. the compounds shown in chart 11 are a few good examples of ferrocenylethynyls containing different metal bridging groups [74]. these are synthesized by a multi-step process and the ancillary ligand „l‟ on the central metal is varied to tune the interaction between the ferrocene termini. interestingly, it was found that the fe-fe interaction is enhanced when an electron donating ligand is used, and reduced when the ligand is electron withdrawing. the dependence of the electronic communication between the two ferrocene units on the ancillary ligand at the central ruthenium metal lying in conjugation to the extended ethynyl chain demonstrates the potential of the metal bridging units. 3.2 tuning the properties by metal bridging besides the study of electronic communication between the redox active termini through organic spacers [63,75], efforts have also been made to generate ferrocenylethynyls containing different metal bridging groups during the last decade. in these studies, ferrocenyl pendant groups are commonly used as redox centres, and ethynylferrocene commonly serves as the key starting material. placing equivalent redox-active groups as end-caps in molecular arrays is often used to evaluate whether intra-molecular electronic communication occurs through metal-containing fragments and clusters. they have been attached to mono [70,72,76,77] or dinuclear [78,79], organometallic and coordination compounds. however, examples of metal clusters capped by equivalent ferrocenyl groups are rare. 3.2.1 electro-luminescence property the example below from albinati et al. [80] shows a bis(ferrocenylethynyl) complex (79) where the fc units are connected via a pt6(μ-ptbu2)4(co)4 metal cluster (figure 8, top). no significant electronic communication was observed between the two terminal fc units as shown by the unsplit redox wave at 0.3 v (figure 8, bottom). when investigated by spectro-electrochemistry, this compound, upon oxidation, gave an emission in the visible region. the emission band was carefully examined and found to be resulting from the metal cluster unit. this implies that the redox property of the ferrocenes in the molecule could be controlled by external application of visible light. it was suggested that the emission energy generated by the central metal cluster component could be utilized in three different ways as typified in figure 9. type-d means that the metal cluster could be utilized as electron donor to the adjacent acceptor units, type-a represents the metal cluster as acceptor component which accepts electron from the adjacent units and a:d type means that the metal cluster is utilized in a way that can help the electron flow from the donor unit to the acceptor unit. hakikulla h. shah et al 29 figure 8. crystal structure of pt6(μ-ptbu2)4(co)4(c≡c-fc)2 (79) (see structure: purple pt, red fe, green p, blue o; fc = [(η-c5h5)fe(η-c5h4)]) (c2fc2) (left) and cv and dpv (right). reprinted with permission from ref [80]. copyright (2005), wiley-vch. figure 9. schematics of charge flow in pt6(μ-ptbu2)4(co)4(c≡c-fc)2 complex. reprinted with permission from ref [80]. copyright (2005), wiley-vch. 3.2.2 electronic communication another example of metal cluster assisted efficiency enhancement is given by xu et al. (see figure 10) [81]. they reported that insertion of a ru2(dmba) bridging unit into the 1,4-bis-(ferrocenyl)butadiyne [(c2fc)2] (80) dramatically enhances the electronic coupling between two fc units in the ru2(dmba)4(c2fc)2 complex (81). figure 10. crystal structure of c4fc2 (80) left and ru2(dmba)4(c2fc)2 complex (81) right. reprinted with permission from ref [81]. copyright (2004) american chemical society. although the distance between the two termini in ru2(dmba)4(c2fc)2 is significantly larger (11.60 å) than in the bis(ferrocenyl)-1,4-butadiyne (6.63 å), the strong electronic coupling results from the metal cluster which can act as the bridge assisting the electron flow in one direction (type-a:d as explained above). the work was further extended to explore if the metal bridge can assist the coupling when the distance between the ferrocene termini is further increased by adding ethynyl units (figure 11). figure 11. crystal structure of c8fc2 (82) and trans-(fcc4)ru2(y-dmba)4(c4fc) complex (83); here y-dmba is n,n‟dimethylbenzamidinate. reprinted with permission from ref [82]. copyright (2005), american chemical society. ferrocenylethynyl a versatile platform 30 figure 12. cv and dpv of ru2(dmba)4(c2fc)2 complex. reprinted with permission from ref [83]. copyright (2004), american chemical society. it was observed that the metal bridge allowed efficient coupling even on increasing the distance between the ferrocene units. the cv and dpv of ru2(dmba)4(c2fc)2 (figure 12) consists of one one-electron reduction at −1.22 v (a) attributed to the ru2 core, and three one-electron oxidations (b−d) between 0.4 and 1.0 v. one of the three oxidations is ru2-based because all ru2(dmba)4(c2r)2 compounds undergo oneelectron oxidation in this region [83]. the dpv peaks were assigned after confirmation from the spectroelectrochemistry results which showed the clear increase and decrease in the peaks c and d upon sequential oxidation of the terminal ferrocenes. they also examined the spectral absorption band on oxidation which further supports that peaks c and d belong to the oxidation of ferrocenyl units. 3.2.3 redox control ferrocene can work as an electron reservoir, and its metal-assisted assembly is highly intriguing in terms of molecular quantum devices, as demonstrated by long et al. in a cobalt complex containing four ferrocenes shown in figure 13 [70,84]. figure 13. crystal structure of (η 5 -c5h5)2fe)4(η 4 -c4)co(η 5 -c5h5) complex (84). reprinted with permission from ref [70]. copyright (2005), american chemical society. figure 14. cv and dpv of (η 5 -c5h5)2fe)4(η 4 -c4)co(η 5 -c5h5) complex (84). reprinted with permission from ref [70]. copyright (2005) american chemical society. hakikulla h. shah et al 31 complexes containing two ferrocenes communicating with each other are considered as building blocks of quantum cellular automata, where the ferrocenes can be sequentially oxidized and reduced to conduct the signals in single molecular electronic devices. similarly, complexes with a higher number of ferrocenes are of special interest for logic gates like applications. long et al. isolated the different oxidized forms of the complex shown below. in a 1:1 mixture of ch3cn and ch2cl2 the cyclic and square wave voltammetry gave good resolution with unambiguous evidence of three redox couples as can be seen in the voltammograms (see figure 14). in addition, the unresolved structure in the peak at the most positive potential in the square wave voltammetry suggests the presence of a fourth couple. the e1/2 potentials for the 1 0 /1 1+ , 1 1+ /1 2+ , 1 2+ /1 3+ , and 1 3+ /1 4+ couples are −0.085, 0.075, 0.225, and 0.283 v, respectively (δep = 0.08 ± 0.02 v), relative to the potential for the ferrocene/ferrocenium couple [70]. 3.3 ferrocene termini linked to a metal bridge by a coordination bond the ferrocenylethynyls containing different metal bridging groups were produced by multi-step covalent synthesis methods. these types of syntheses are labour intensive and frequently suffer from low yield of the final product. also the final products are quite often not stable under aerobic conditions. coordination-driven synthesis emerged as a breakthrough to overcome many of these problems associated with purely covalent synthesis methods. rationally designed self-assembled supramolecular structures that create self-organized, functional materials are of fundamental interest for application in catalysis [85], gas storage or gas/molecule separations [86], in nanotechnology [87,88], and in electronic materials [89,90]. organic molecules can self-assemble into well-ordered structures, but often with limited conductance. conductivity can be influenced and improved by using coordination complexes in which metal centers are incorporated into a molecular backbone. such structures self-assembled on insulating surfaces have been reported for highly conducting nano-ribbons [89]. solution based rational self-assembly is a promising approach for the formation of microstructures with desired shapes [91-93]. scientists have coupled ferrocene to coordinating ligands like pyridine, benzonitrile, etc. and utilized these ferrocenyl derivatives to construct a wide range of metal complexes. the beneficial redox property of the ferrocene is successfully exploited in designing coordination complexes with supramolecular assemblies which would be impossible by conventional covalent synthesis. the use of ferrocene containing ligands imparts redox switching, mixed-valence and offers a host of other interesting properties to the coordination complexes. in addition, incorporation of ferrocenyl or ferricenyl building blocks offer further material tuning opportunities and access to novel mixed-valence materials [94,95]. ferrocenyl functionalized coordination complexes are of particular interest due to the robust and switchable chemical nature of the ferrocene. ferrocene also exhibits attractive electrochemical features: fast electron-transfer rate, low oxidation potential, and two easily accessible stable redox states (neutral ferrocene and oxidized ferricenium). ferrocene-modified surfaces have been demonstrated to efficiently communicate via a lateral electron hopping process[96,97] and were recently highlighted for applications in charge storage components and in semiconductor-based memory devices with the bound ferrocene center as the memory element [98]. figure 15. crystal structure of tetra(ferrocenylpyrimidinyl)ni(scn)2 complex (85). reprinted with permission from ref [98]. copyright (2003), american chemical society. ferrocenylethynyl a versatile platform 32 a good example of beneficial mono functionalization of ferrocene with a coordinating ligand and its use to obtain novel coordination complexes was given by horikoshi et al. [99]. a simple ferrocenyl pyridine ligand when combined with transition metal salts, produce mixed-metal polynuclear complexes with structural diversity. reaction of 5-ferrocenylpyrimidine with m(scn)2 (m = ni, co) produces the pinwheellike 4:1 complexes (ni complex (85) shown in figure 15). the complexes are regarded as electro-active ferrocene clusters. some other strategies have also been proposed to obtain coordination complexes of varied size, shape and chemical combinations. the coordination of bifunctionalised ferrocene with a pyridinyl group to the metal “nodes” was utilized by wei et al. [100]. the primary structure formed by coordination bonds in cooperation with weak non-covalent interactions, such as h-bonding and  stacking, organizes these primary structures into supramolecular architectures [101]. the self-assembly of small “building blocks” with transition metal ions generates cages, capsules, macrocycles, helices, networks, and other supramolecular architectures (figure 16) for research in supramolecular chemistry, materials chemistry, and crystal engineering [102-104]. careful design and synthesis of these novel architectures are essential for the creation of new functional materials with solvent inclusion or gas-adsorption characteristics or with special optical, electronic, magnetic, and catalytic properties [105,106]. figure 16. chemical structure of bifunctionalised ferrocene with pyridinyl group (left) and their possible structure with metal (right). reprinted with permission from ref [99]. copyright (2010), american chemical society. copper(i) is well recognized for its ability to form multi-nuclear (cluster) species of various shapes and sizes, on reaction with a range of bridging and terminal ligands. in these clusters weak bonding interactions between the closed-shell metal centers are generally present [107-111]. a range of different architectures broadly categorized as a to d generating network and chain structures shown in e to h have been reported (see figure 17). these clusters such as rhomboid (cux)2 dimers [111,113-115], cubane(cux)4 tetramers [114-116], infinite (cux)∞ zigzag [117-120] or stair-step polymers [117,118] (x= halide) have been investigated by many research groups for their rich photo-physical properties. structures with pyridine ligands in particular have been extensively studied for their extraordinary photoluminescence properties [121-130]. several strategies for rational syntheses of complexes with four redox sites have been reported. these often require considerable synthetic effort to prepare, and can be plagued by low yields and largely amorphous final structures. when issues such as structural precision, synthetic ease and building-block versatility come into question, coordination-driven self-assembly provides a powerful alternative to the purely covalent synthesis of multifunctional molecules [125]. at the molecular level a symmetric mixed-valence complex is the building-block for the quantum-dot cellular automata [70]. arrays with four redox sites are also considered more versatile for efficient cell designs in logic applications [85,126]. functionalization of the py-x to ferrocenylethynylpyridine in the (cux)4(py-x)4 series has allowed ready access to a series of tetraferrocenylethynylpyridinyl copper complexes (86-88) and, in the presence of triphenylphosphine coligand, gave di(ferrocenylethynylpyridinyl triphenylphosphine)copper square complexes (89-91) via coordination-driven self-assembly (see scheme 2). hakikulla h. shah et al 33 figure 17. different architectures obtained from cu-halide in the presence of coordinating ligands. reprinted with permission from ref [110]. copyright (2012), the royal society of chemistry. the tetra(ferrocenylethynylpyridinyl) copper complexes undergo partial or full oxidation under mild electrochemical conditions and the electro-crystallized products show distinct morphologies such as dendritic for complex 86 while lettuce or flower like for complexes 87 and 88 (see figure 18). for the electrocrystallized di(ferrocenylethynylpyridinyltriphenylphosphine) copper complexes (89-91), the sem analysis confirmed the spontaneous formation of electro-crystallized full oxidation products with distinct morphology such as leaf-like for complexes 89 and 90, and cabbage-like morphology for complex 91 (see figure 18). fe fe n cu x cu x fe n fenph3p pph3 i cu cu cu i i i cu n fe n n fe n cui, pph3 dcm, 24 hrs cui dcm, 24 hrs l 89-91(x=cl, br, i) cu x cu x fe n fen 87-88 (x=cl, br) fen fe n 0.5 cui dcm, 24 hrs 86 fe scheme 2. synthesis of tetra(ferrocenylethynylpyridinyl) copper halide complexes (86-88) and di(ferrocenylethynylpyridinyl triphenylphosphine) copper halide complexes (89-91). copper compounds are widely used as catalysts and electro-deposited cu-based microstructures are of interest for applications in catalysis [129-132]. furthermore, the shapes of the electro-deposited ferrocenylethynyl a versatile platform 34 microstructures have been shown to enhance the catalytic activity and selectivity of metallic catalysts [132]. thus, the three types of distinct morphologies observed for the electro-crystallized products by changing the chemical composition (x = cl , br , i ) indicate the potential of the system for controlling the shape of the electro-deposited microstructures. recently, noorduin et al. have demonstrated the potential of systematic change in the chemical composition during layer by layer growth of their crystal. they grew the crystals layer by layer to obtain novel microstructures as shown in figure 19. using this strategy they were able to generate a beautiful library of microstructures [133]. the electro-crystallized di(ferrocenylethynylpyridinyl triphenylphosphine)copper complexes were found to be dimeric dicationic products of the parent neutral complexes. these electro-crystallized ferrocenylethynyl materials could be a new entry to the family of ferroelectric materials [134-136]. the different shapes obtained by changing the chemical composition and stoichiometry present an approach to controlling the morphologies of the electro-deposited cu-based microstructure, and are of high recent interest for fundamental studies and for potential applications in catalysis and other fields [129-132]. the ferrocenylethynyls have thus shown that they have enormous potential for further functionalization and hold promise for generating novel materials for scientific and technological development. figure 18. sem images of electro-crystallized products from oxidation of complexes 86-91 (a-f). 86-88 reprinted with permission from ref [127] and 89-91 from ref [128]. figure 19. layer by layer growth of crystal by changing the chemical composition. reprinted with permission from ref [134]. 4. present outlook and future directions ferrocenylethynyl has been used widely as a platform for developing new materials, which have been investigated extensively over the past decade. this has allowed a thorough understanding of the structureactivity-function relationships of materials of this type, giving the inspiration to develop more advanced 1 st lay er 2 nd layer 1 layer 3 nd layer hakikulla h. shah et al 35 materials for practical applications in the near future. while ferrocenyls are recognized redox-active molecules, examples presented in this review highlight the rich diversity of ferrocenylethynyl-based molecules and materials for numerous emerging applications. connecting ferrocenylethynyl units to organic and inorganic structures provides a versatile approach for constructing new materials with novel properties. the four types of connection of ferrocenylethynyl with diverse organic structures presented in this review have led to new catalyst systems, materials for sensors, pharmaceuticals, anti-cancer reagents, and precursor molecules for further coordination to metals and redox active complexes. a host of other molecules using the four types of connection could be synthesized which would be of interest to the new materials industries. specifically, incorporation of photoand thermally-active spacers such as azobenzenes in the bis(ferrocenylethynyl) complexes should prove very interesting as the azobenzene has the inherent property of switching between cisand trans-conformation under the influence of an external applied field, leading to dual control over the new materials. another novel approach presented here is the connection of ferrocenylethynyls to metal frames covalently and via coordination. the ferrocenyl units covalently connected to metal frames have shown improved conductivity and enhanced intra-molecular communication. examples by lu et al. have demonstrated an improvement in conductivity of the oligo-ynes on incorporation of ferrocene units. the coordination of functionalized ferrocenylethynyls have been shown to give electro-active clusters as demonstrated by horikoshi et al. shah et al. have recently shown that the new diand tetraferrocenylethynylpyridinyl copper(i) halide complexes are conveniently accessible by coordination-driven self-assembly, and fascinating new materials have been produced by charge-driven electro-crystallization. these polynuclear complexes oxidize under mild conditions to form partiallyor fully-oxidized electrocrystallized products. the inherent structural features based on the aromatic ring system and ethyne as well as metal cluster components potentially provide high electron-mobility, and therefore these crystalline materials with partially and fully occupied ferrocene electronic band structure will be of interest in future electronic materials and in optical components. the incorporation of pf6 into the structure can be considered as a “structurally well-defined” doping with implications for photo-excitation and electronic conductivity [137,138]. furthermore, a combination of mobile electrons and structural rearrangements, which are possible in these novel materials, provides an entry into a new class of multi-ferroelectronics [134,139]. 5. acknowledgements the literature survey leading to this review paper was conducted with funding from the research council of oman under the open research grant program: org/squ/ei/13/015. msk acknowledges sultan qaboos university for a research grant: ig/sci/chem/13/01 and for a research leave while hhs and raal-b acknowledge sultan qaboos university, oman for phd scholarships. references 1. shah, h.h., al-balushi, r.a., al-suti, m.k., khan, m.s., woodall, c.h., molloy, k.c., raithby, p.r., robinson, t.p., dale, s.e.c. and 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box: 36, pc 123, al-khoud, muscat, sultanate of oman. *email: arshadali@squ.edu.om. abstract: al wusta is a desert area in the sultanate of oman which is famous due to the discovery of a number of martian and lunar meteorites since the start of the present millennium. according to the meteoritical bulletin database, 137 approved martian meteorites have been found worldwide, including 17 from oman (4 from zufar, 13 from al wusta region). interestingly 11 finds in the last 15 years have been of sayh al uhaymir (sau) 005 and its pairings. these finds (estimated mass = 11.2 kg) are linked to 10 search expeditions carried out between november 26, 1999 and march 2, 2014 by the swiss group from the university of bern and several anonymous meteorite hunters. the bulk of these meteorites (~97%) is in the possession of anonymous collectors, negatively affecting oman’s natural heritage and denying further research opportunities, given their associated scientific value. sau 005 and its pairings belong to the shergottite group of the shergotty-nakhla-chassigny (snc) meteorites, originating from various depths within the martian mantle. we discuss the recently published oxygen isotope data of bulk and mineral fractions of sau 008 recovered during the very first expedition in 1999 in the context of other shergottites found in oman. the bulk oxygen isotope data of sau 008 and dhofar 019, another martian meteorite from oman, show a narrow range in δ18o values. their δ17o values are remarkably close to identical and fall linearly on a martian fractionation line above the terrestrial fractionation line (tfl) by + 0.32‰, suggesting that mars’ mantle is homogeneous in oxygen isotopes. petrographic and mineralogical data of sau 005 and other pairings published in the meteoritical bulletin are compiled, and it is noted that all the meteorites are identical and are likely paired. the story behind these rare extra-terrestrial specimens demands a local meteorite museum and preliminary testing laboratory at sultan qaboos university (squ) to protect this treasure trove of omani heritage. keywords: mars; oxygen isotopes; snc meteorites; oman. المريخية وقريناتها، المنطقة الوسطى، سلطنة عمان 005 مراجعة لنيازك سيح األحيمر أحمد الرواس و عفت جابيين ،صبحي نصير، أرشاد علي في سلطنة عمان باكتشاف عدد من النيازك المريخية والقمرية منذ مطلع القرن بالمنطقة الوسطى الصحراوية تشتهر منطقة سيح األحيمر :ملخصال منطقة المن 13من ظفار، 4نيزك من عمان ) 17نيزك مريخي في العالم تتضمن 137الحالي. وطبقا الى بيانات نشرة النيازك فقد نم العثور على رحالت 10. عثر على هذه الموجودات خالل األحيمر خالل الخمس عشر سنة الماضيةور عليها في سيح نيزكا تم العث 11الوسطى(. ومن المثير ان . من المحتمل ان 2014مارس 2الى 1999نوفمبر 26استكشافية من قبل مجموعة جامعة بيرن السويسيرية وكذلك صيادو النيازك خالل الفترة من ( في أيادي %97تقع معظم نيازك سيح األحيمر المريخية )لذي وقع في الصحراء. زك األصلي اكلغم( الى نفس الني 11.2تعود جميع هذه النيازك ) ورديفاتها الى مجموعة الشيروجيت ضمن نيازك 005تتبع نيازك سيح األحيمر مجهولين، وهذا يؤثر على التراث العماني الطبيعي وقيمته العلمية. ة. نناقش في هذا البحث بيانات نظائر االوكسيجين المنشورة لمعادن وتركيب نيزك شاسجني ذات األصل المريخي من اعماق مختلف -نخالالشيروجيت مقارنة مع النيازك المريخية االخرى من عمان. تظهر بيانات نظائر 1999وهو من اول النيازك التي عثر عليها خالل عام 008سيح االحيمر وتقع على خط 17. هذه البيانات متشابهة في قيم االكسيجين 18يم االكسيجين نطاق ضيق من ق 008وسيح االحيمر 019لنيزك ظفار 18االكسيجين تم تجميع ومناقشة البيانات % مما يدل على تجانس نظائر االكسيجين في المريخ. 0،32تمايز المريخ وفوق خط تمايز الصخور القارية بقيمة + تواجد نيازك سيح االحيمر وتوزعها عمل متحف خاص . يتطلب ورديفاتها 005يمرالمعدنية والمجهرية المنشورة حول النيازك المريخية من سيح األح .بالنيازك ومختبر متخصص لها في الجامعة لحماية التراث العماني ش ن ش(. ) شاسجنيت-نخليت -شيروجيتالمريخ، نظائر األكسجين ، نيازك :مفتاحيةالكلمات ال arshad ali et al 30 1. introduction eteorites are extra-terrestrial objects that land on earth after extensive travel in space. our earth is constantly showered by chunks of meteorites from the asteroid belt and neighboring planets. these alien rocks heat up when they enter the earth’s atmosphere due to friction and give them a dark and shiny surface called a fusion crust. this unique visual characteristic helps in tracking down meteorites particularly in flat, light-colored deserts due to the color contrast [1]. the sultanate of oman has been the hub of meteorite search since the start of this millennium. in the early years, private collectors took advantage of the free trafficking of meteorites across oman’s borders, leaving the country deprived of its national treasure [1]. fortunately, oman has recently regulated the export of meteorites for the protection of future meteorite finds; however, damage has already been done to some precious samples including sayh al uhaymir (sau) 005 and most of its pairings. al wusta is the desert area in oman where several martian and lunar meteorites have most commonly been spotted by the commercial meteorite dealers and international scientific teams. until recently (april 2016), meteoritical bulletin has reported 137 approved martian meteorites including 17 from the sultanate of oman (table 1). table 1. martian meteorite finds from the sultanate of oman. approved name classification find location year mass (g) dhofar 019 shergottite-basaltic (ol phyric) zufar 2000 1056 dhofar 378 shergottite-basaltic zufar 2000 15 dhofar 1668 shergottite zufar 2011 6.1 dhofar 1674 shergottite zufar 2010 49.2 jiddat al harasis 479 shergottite al wusta 2008 553 jiddat al harasis 910 shergottite al wusta 2011 27 sau 005 shergottite-basaltic (ol phyric) al wusta 1999 1344 sau 008 shergottite-basaltic (ol phyric) al wusta 1999 8579 sau 051 shergottite-basaltic (ol phyric) al wusta 2000 436 sau 060 shergottite-basaltic (ol phyric) al wusta 2001 42.3 sau 090 shergottite-basaltic (ol phyric) al wusta 2002 94.8 sau 094 shergottite-basaltic (ol phyric) al wusta 2001 223 sau 120 shergottite-basaltic (ol phyric) al wusta 2002 75 sau 125 shergottite-basaltic (ol phyric) al wusta 2003 31.7 sau 130 shergottite-basaltic (ol phyric) al wusta 2004 279 sau 150 shergottite-basaltic (ol phyric) al wusta 2002 107.7 sau 587 shergottite (ol phyric) al wusta 2014 4.7 since the year 2000, the rate of meteorite finds has been rapid, triggering a delay in the reporting and classification of an exponentially increasing number of new samples [1]. for classification of a new meteorite, a submission is made to the meteoritical bulletin in the form of a template filled with some basic details such as find/fall location, date of recovery, latitude and longitude and mass, along with some visual observations of the sample at the time of recovery. quite often, further petrographic, mineralogical, geochemical and isotopic data is also included for classification of the meteorite. these unique samples may represent tiny pieces from the core or mantle of other planets; providing us with the opportunity to learn more about the earth’s interior, given that the earth is inaccessible at such depths. in order to learn about the origin of extraterrestrial materials in space, multiple stable isotope ratios of oxygen are commonly utilized. oxygen is the most abundant element in the earth’s crust and mantle and the third most abundant, after hydrogen and helium, in the solar system [2]. it has three isotopes; 16o, 17o and 18o, differing in their masses and abundances in nature. the lightest isotope (16o) comprises > 99% of the oxygen abundance in nature. oxygen isotope ratios are conventionally expressed using the delta (δ) notation as: δ18o = (18rsample – 18rvsmow)/ 18rvsmow where 18r =18o/16o and δ17o = (17rsample – 17rvsmow)/ 17rvsmow where 17r =17o/16o delta values are commonly expressed as permil (i.e., ‰). when oxygen isotope compositions of terrestrial silicate rocks and minerals are plotted on a three-isotope diagram of 18o and 17o values, the resultant straight line of slope1/2 [3, 4] is commonly referred to as the terrestrial fractionation line (tfl). the tfl serves as a reference line to evaluate the provenance of meteorites. offsets in oxygen isotope ratios relative to the tfl are used to characterize meteorite groups (figure 1). a meteorite sample is mostly made up of silicate minerals and in order to liberate all the oxygen from it, the laser-fluorination technique is used. this method has been used globally at various laboratories for precise 17o and 18o measurements of terrestrial rocks [5-13] and meteorites [14-19] since the 1990s. the m review of the sayh al uhaymir (sau) 005 31 significance of triple oxygen isotopes is unprecedented in the realm of geochemistry and cosmochemistry, and the study of their relationship has found widespread and diverse applications in various fields including meteoritics. this system provides key information about the origin of rocks and the processes they underwent in the past. oxygen isotope data of samples formed from any terrestrial chemical or physical process (e.g., melting-crystallization or evaporation-condensation) fit on the tfl having a slope of ~0.52 [4]. conventionally, the offsets (i.e., 17o; negative or positive) from the tfl are calculated (17o = δ17o – 0.52 δ18o; [20]) to study the unique oxygen isotope signatures of meteorites. however, miller [21] proposed the use of prime notation (′17o, ′18o), which takes into account the linear function relationship between 17o and 18o for a sample measured with respect to a reference, instead of the conventional approximation of a power law function. construction of the tfl, based on various types of terrestrial materials, is a pre-requisite to conduct geochemical and cosmochemical studies in a stable isotope laboratory. over half a century ago, [22] started reporting oxygen isotope data of various types of meteorites using the conventional method of oxygen extraction by fluorination (e.g., f2, hf, brf5, clf3) of samples at 500-700 oc in nitubes. more recent studies have employed affordable and reliable laser systems (e.g., co2 & nd:yag lasers) for heating the samples in a fluorinating atmosphere [5, 19, 23-25]. compared to conventional fluorination methods, the laser fluorination technique is advantageous owing to its significant sample size reduction (1000-1500%) and improved reaction efficiency (e.g., 300%) without compromising the precision and accuracy of the data. it also has the considerable benefit of operating at high temperatures in order to react refractory mineral phases such as olivine and some oxides. in addition, oxygen produced by conventional methods typically involves conversion to co2 gas by reacting with hot graphite rods prior to analysis on a mass spectrometer. this requires further c-isotope corrections than if using oxygen gas as an analyte. as a result, the laser-fluorination technique is a preferred method to extract oxygen and measure triple oxygen isotopes online or offline. we include the sayh al uhaymir (sau) 005 meteorite and its pairings in this review to assess their oxygen isotope data of bulk materials and separated fractions, along with published data of other martian meteorites from oman. in addition, an account of the collection history and petrographical/mineralogical details of sau 005, plus pairings, are compiled and discussed. 2. analytical description a comprehensive study has recently been carried out to analyze various samples from the shergotty-nakhlachassignite (snc) group, including meteorites found in oman (e.g., sau 008 and dhofar 019), for precise triple oxygen isotope measurements using the laser fluorination technique coupled with the mass spectrometer [19]. for bulk analysis, this study utilized a minimum of 50-100 mg of sample aliquot of both sau 008 and dhofar 019 meteorites to make powder. a small portion of the powdered material was pre-treated with 6m hcl at 70 °c for 2-3 minutes in order to remove the potential terrestrial weathering products, and so to obtain the actual isotope data of each meteorite. acid-treated and untreated bulk materials (1-2 mg) were loaded on the sample holder and placed in the sample chamber. after complete evacuation of the vacuum line, a reaction was performed by heating the sample with a 25w co2 laser (10.6 µm wavelength; merchantek, bozeman, mt, usa; model mir10-25) in a brf5 atmosphere to extract oxygen gas. similarly, separated fractions such as pyroxene and olivine for sau 008 and maskelynite for dhofar 019 were also irradiated with the laser to produce oxygen gas from the mineral framework. later, oxygen gas was purified using cryogenic metal traps and a heated kcl salt trap, giving yields of better than 95%. the triple oxygen isotope measurements were performed using a delta v plus mass spectrometer in dual inlet mode integrated with isodat3.0 software for system controls and data acquisition. data were reported as delta notation (δ) referenced to the vienna standard mean ocean water (vsmow). a detailed analytical methodology is described in [19]. arshad ali et al 32 figure 1. pictorial illustration of the triple oxygen isotope diagram. slope-1/2 line is referred to as the terrestrial fractionation line (tfl); triple oxygen isotope data from planet earth, moon and enstatite chondrites fall on the tfl; however, data from other extra-terrestrial bodies either fall above or below the tfl. some meteorites (with their place and year of fall) are shown for comparison. right bottom of the illustration (methodology) displays an image of a laser and brf5 (br attached to 5 fluorine atoms) for extracting oxygen gas from the crystal framework (e.g., olivine) of a meteorite (image: pallasite) followed by isotopic measurements using a mass spectrometer. individual images are taken from the internet. this illustration is not to scale. 3. discussion sample preparation and pre-treatment after extensive space travel, meteorites encounter terrestrial conditions for long periods of time, of thousands of years and more. terrestrial weathering will result in shifts in 17o of a meteorite towards the tfl compared to its actual value, due to the formation of secondary carbonate and oxide minerals. for example, meteorite data below the tfl, will move upwards, as in the case of pallasites, and that above will move downwards, as with snc meteorites, due to terrestrial weathering, so there is a two directional shift around the tfl depending on what type of meteorite is under investigation. if weathering is non-terrestrial, e.g., having occurred on the surface of mars, the trend will be different as evidenced by [26] from the lafayette meteorite. they reported heavier δ18o and higher ∆17o values for low-t mineral (e.g., iddingsite) formed on the surface of mars. antarctica has a large population of meteorites which have remained preserved under the ice cover for extended periods of time. a recent study [18] has reported contrasting weathering trends in antarctic and non-antarctic meteorite finds. a reasonable interpretation of this paradigm is that whenever there is terrestrial weathering in a non-antarctic environment, the data will go up due to secondary carbonate and oxide minerals, whilst in an antarctic environment, the data of weathered meteorites will go down possibly due to antarctic snow which is extremely low in δ18o compositions [e.g., longhovde area has -30‰; 27], that could become incorporated into the weathering products. oxygen isotope data of snc meteorites from the sultanate of oman the published oxygen isotope compositions of snc meteorites from the sultanate of oman are compiled in table 2 and plotted in figure 2. the few data points showing a scatter in ∆17o values (figure 2) are likely to be review of the sayh al uhaymir (sau) 005 33 associated with either terrestrial weathering (assuming that samples were analyzed without acid-treatment given the absence of such details reported in the literature) or due to analytical artifacts in δ17o measurements (17o abundance = 0.04%; see figure 1). however, recently researchers [19] have analyzed snc meteorites and they have found no significant variation in ∆17o values between the untreated and acid-treated samples. their data did not support the idea of scatter in ∆17o due to a weathering phenomenon. however, it is noted that the data of acid-treated samples are skewed towards lower values. they argued that the discrepancy is caused by the elimination of carbon dioxide gas from the carbonates (i.e., originated on mars surface) after acid treatment. carbonates are typically heavy in oxygen isotopes [28-31]. a recent work [19] also commented on the most common interferences (m/z = 33) on δ17o values. traces of fluorination by-products such as nf3 and cf4 are caused by inefficient removal of these species when they are trapped with extracted oxygen gas on adsorbing media (i.e., molecular sieves 13x and 5å) at liquid-n2 temperature. these analytical artifacts directly affect 17o data. table 2. triple oxygen isotope compositions of bulk and separated fractions of snc meteorites from the sultanate of oman. sample type δ17ovsmow (‰) δ18ovsmow (‰) δ17o (‰) n reference dhofar 019 bulk 2.299±0.102 (se) 3.826±0.189 (se) 0.310±0.006 (se) 3 [19] dhofar 019 bulk 2.569 4.474 0.216 ̶ [32] dhofar 019 bulk* 2.890 4.937 0.325 2 [19] dhofar 019 bulk 2.99 5.4 0.18 ̶ [33] dhofar 019 mask 2.918 4.985 0.328 2 [19] dhofar 378 bulk@ 2.52 4.46 ̶ ̶ [34] jah 479 bulk§ 2.951 5.070 0.315 ̶ [35] sau 008 bulk* 2.696 4.544 0.335 2 [19] sau 008 bulk 2.212 3.677 0.300 2 [19] sau 008 px 2.673 4.533 0.318 2 [19] sau 008 ol 2.518 4.223 0.324 2 [19] sau 094 bulk§ 2.51 4.25 0.28 ̶ [36] sau 0150 bulk§§ 2.78 4.74 ̶ ̶ [37] ol = olivine. px = pyroxene. mask = maskelynite. jah = jiddat al harasis. sau = sayh al uhaymir. se = standard error. se calculated by dividing the sd (standard deviation) with the square root of n. n = number of individual runs. samples marked with asterisk (*) were analyzed without acid treatment. @oxygen isotope data were obtained by t. k. mayeda and r. n. clayton (university of chicago, usa). §oxygen isotope data were obtained by i. franchi (open university, uk). §§oxygen isotope data were obtained by r. n. clayton (university of chicago, usa). sayh al uhaymir (sau) 005 recovery site sayh al uhaymir (sau) 005 and pairing meteorite finds are associated with several years of searches in the desert of al wusta, oman. the latitude and longitude values, number of pieces, total mass recovered during each search and details of the finder are given in table 3. the greatest part of the total mass of sau 005 and pairings was recovered in the early years (1999-2000) and the tiniest mass of all (4.7 g) was found in the latest search carried out in 2014 (figure 3). the heaviest pieces of all the finds were scattered in the middle of the find locations spanning an area of 2 km wide and 4 km long (figure 4). it seems plausible that sau 005 suffered shattering twice: first in the earth’s atmosphere due to heat generated by friction, and then by break-down due to impact on the ground causing heavily cracked pieces to fall apart within the vicinity of the larger stones (e.g., sau 005 and sau 008). for example, a lone piece of sau 120 (75 g) has a well preserved fusion crust [37] which could have broken down from the original rock at a certain height in earth’s atmosphere. consequently, the stone would have had sufficient time to react with the ambient air due to frictional heat, and as a result, developed a thick fusion crust. however, sau 150 [37] shows relatively thinner fusion crust supporting the idea that this meteorite did not have sufficient interaction time to develop a thick fusion crust, as generally observed in other pieces (e.g., sau 150). moreover, sau 587 [38] is characterized by the presence of partial fusion crust, owing to its possible break down after impact with the ground. arshad ali et al 34 figure 2. comparison plot of δ17o vs. δ18o data published for bulk materials and separated fractions (i.e., px, ol, mask) of snc meteorites from the sultanate of oman. solid and dashed lines represent the martian fractionation line [mfl; 19] and standard error respectively. ut = untreated. at = acid-treated. px = pyroxene. ol = olivine. mask = maskelynite. tfl = terrestrial fractionation line. other data sources: [32-33, 35-36]. table 3. sayh al uhaymir (sau) martian meteorite finds in chronological order from the sultanate of oman. name location date latitude (n) longitude (e) pcs mass (g) finder/main mass sau 005 al wusta nov. 26, 1999 20°59.76´ 57°19.55´ 3 1344 anonymous/anonymous sau 008 al wusta nov. 26, 1999 20°58.83´ 57°19.14´ 2 8579 anonymous/anonymous sau 051 al wusta aug. 01, 2000 20°58.435´ 57°19.248´ 1 436 anonymous/anonymous sau 094 al wusta feb. 08, 2001 20°59.469´ 57°20.326´ 1 223.3 m. h. & l. m. (bern)/nmh sau 060 al wusta jun. 27, 2001 20°58.8´ 57°19.1´ 1 42.3 m. h. & l. m. (bern)/nmh sau 090 al wusta jan. 19, 2002 21°00.0´ 57°19.2´ 2 94.8 anonymous/anonymous sau 150 al wusta aug. 10, 2002 20°59.313´ 57°19.117´ 1 107.7 r. & s. b. (bart)/bart sau 120 al wusta nov. 17, 2002 21°00.2´ 57°19.3´ 1 75 anonymous/anonymous sau 125 al wusta nov. 19, 2003 21°00.4´ 57°19.3´ 1 31.7 not given sau 130 al wusta jan. 11, 2004 21°00.2´ 57°19.1´ 4 278.5 not given sau 587 al wusta mar. 02, 2014 21°00.764´ 57°19.238´ 1 4.7 anonymous/anonymous m. h. & l. m.= marc hauser & lorenz moser. bern = university of bern, switzerland. nmh = natural history museum bern, switzerland. r. & s. b. = rainer & sven bartoschewitz. bart = bartoschewitz meteorite laboratory, germany. pcs = pieces. 0.15 0.20 0.25 0.30 0.35 0.40 0.45 3.5 4.0 4.5 5.0 5.5 bulk-ut + fractions [19] bulk-at [19] other published data ∆ 1 7 o δ18ovsmow(‰) tfl sau 008 ol sau 008 px dhofar 019 mask dhofar 019 bulk sau 008 bulk review of the sayh al uhaymir (sau) 005 35 figure 3. pie chart showing recovered mass of the sayh al uhaymir (sau) 005 martian meteorite and its pairings found in various years from the sultanate of oman. sau 005+pairings find history and review of published data extremely fresh pieces of sau 005/008 were recovered by anonymous meteorite hunters on november 26, 1999 (table 3). however, a few cracks partially filled with calcite were seen owing to the terrestrial weathering processes. both meteorites show porphyritic texture with large olivine phenocrysts (table 4) in a fine-grained groundmass of pigeonite and maskelynite [39]. olivine shows mosaicism and planar deformation and clinopyroxene grains (pigeonite) that are also twinned and fractured, all of which are possibly associated with the strongly shocked (s5) nature of these finds. in the following year, anonymous finders tracked down a piece of sau 051 which is considered to be a pairing of sau 005/008, based on texture, mineralogy (table 4) and proximity in find locations. a shock stage s5 is assigned to this find and calcite veins [36] are also reported. the next year 2001, marc hauser and lorenz moser from the university of bern, switzerland, found sau 060 and sau 094, one stone apiece, during two separate expeditions. the main mass of the meteorites is curated at the natural history museum bern, switzerland. the mineralogical characteristics of these samples, e.g., large olivine phenocrysts (ave. max. size = 1.5mm) embedded in a fine-grained (ave. max. size = 0.3mm) groundmass of maskelynite and pigeonite [36], are comparable to those of sau 005/008/051 and they are considered as pairs [40]. moreover, both pieces display the same shock stage (s5) associated with shock twining, mosaicism and local oxidation in olivine [36]. it is also reported that sau 094 has abundant partially recrystallized veins and pockets containing glass vesicles due to shock melting [36]. compared to sau 094, sau 060 is slightly weathered with small rusty pockets of fe-hydroxide, a likely replacement of an unknown pre-existing phase [36]. the porosity of meteorites plays an important role in terrestrial weathering caused by water and moisture. x-ray tomographic analysis of sau 094 revealed pores of up to 3mm size and they constitute 0.4 vol% of the sample [36]. sm-nd data of ten fractions (e.g., wr, px) from sau 005/094 form a linear array between 147sm/144nd and 143nd/144nd ratios yielding a crystallization age of 445±18 ma [41]. later, it was discovered that sau 008 and sau 094 have ε142nd values of 0.647 and 0.569 [42] respectively which is significantly higher than the average chondritic (i.e., -0.18 ± 0.08) and terrestrial standard (i.e., 0 ± 0.03) values [43-44]. the ε142nd enrichment in these samples is interpreted as being derived from an incompatible-traceelement-depleted source formed during the first 500 ma of evolution of mars. 1999 2000 2001 2002 2003 2004 2014 arshad ali et al 36 figure 4. (a) a location map taken from [45]. (b) find locations of various sau 005 and pairing meteorites from al wusta, oman. the recovery area is 2 km x 4 km. approved names of all finds are shown with recovered masses (g) in brackets, along with number of pieces. reds are the main mass of these fin ds, recovered during the first expedition in 1999. purples were found as one piece having a mass of over 100g. four more pieces of sau 090/120/150 were recovered during three separate searches in 2002. two of the three searches were performed by anonymous hunters who recovered two pieces of sau 090 and one piece of sau 120, while in the third search rainer and sven bartoschewitz from bartoschewitz meteorite laboratory, germany were successful in finding a piece of sau 150 (table 3). no textural and petrographic details of sau 090 are provided in the meteoritical bulletin [34]. on the other hand, sau 120 is reported as a gray-greenish stone with well-preserved fusion crust. the textural characteristics of sau 120 are identical with other previously found pieces such as sau 005/008/051/060/090/094 [37]. the sau 150, a find by rainer and sven bartoschewitz, was studied in detail for its © 2016 cnes/spot image 2885 sau587 (4.7 g) 21 00.764,57 19.238 sau125 (31.7 g) sau120 (75 g) 4 x (278.5 g) sau130 sau090 (94.8 g) x 2 sau005 (1344 g) x 3 sau150 (107.7 g) sau094 (223.3 g) sau008 (8579 g) x 2 sau051 (436 g) sau060 (42.3 g) (a) (b) review of the sayh al uhaymir (sau) 005 37 geochemistry and oxygen isotopes [37]. it is an olive-brown colored stone of relatively angular shape with one small area of thin black-brown fusion crust. this piece was recovered on a miocene fresh-water limestone gravel plateau. it displays a porphyritic texture with 2mm sized olivine phenocrysts embedded in a matrix of feldspathic glass and pigeonite. minor ca-poor pyroxenes with a composition of en65-66fs34-35 are observed. recrystallization of shock-melt veins and pockets is also noticed. a single piece of the sau 125 was found by an unknown person in 2003 and it is considered as paired with sau 005/008/051/060/090/094/120 [46]. the very next year, four pieces of sau 130 were recovered by an anonymous finder and these samples were cited as paired with all the previously found meteorites including sau 005/008/051/060/090/094/120/125 [46]. a compilation of petrographic, geochemical and isotopic data of sau 005 and pairings found until 2004 is available at the martian meteorite compendium [47]. lastly, after a nineyear hiatus, a small piece (4.7 g) of the sau 587 was recovered from the close vicinity of the previous find locations by an anonymous collector in early 2014. according to the meteoritical bulletin [38], it is a small greenish-gray stone with some fusion crust. typical mm-sized olivine phenocrysts set within a fine-grained basaltic groundmass, dominantly of pigeonite and maskelynite, show a porphyritic texture. a high degree of shock metamorphism is associated with strong mosaicism of olivine, conversion of plagioclase to maskelynite and abundant melt veins and pockets [38]. furthermore, intense fracturing is observed. however, this sample is moderately weathered, with only a few of the larger cracks being partially filled with calcite. it is paired with the sau 005/008. owing to the discovery of 10 pairings of the sau 005 (table 3) from the al wusta desert and strewn field (figure 4b) with an area of 4 km by 2 km, it is suggested that a large piece of the rock may have broken down into several varyingly sized pieces before landing on the earth’s surface. the shattering of the rock may have been triggered by the frictional heat in the air, thus causing it to break twice, first in the air followed by the impact on the ground. table 4. petrological data of sayh al uhaymir (sau) 005 martian meteorite and pairings from the sultanate of oman. name major phases (write-up in meteoritical bulletin) minor phases shock stage ref. remarks sau 005 ol (fo64-71), pig (en61-70wo6-13), mask (an51-65or0.3-0.9) aug, pho, opa strongly shocked [39] sau 008 same as above same as above same as above [39] sau 051 ol (fo61-68), pig (en60-68wo7-12), mask (an59-67) not given s5 [36] paired with 005/008 sau 094 ol (fo65-69), pig (en60-68wo7-9), mask (an55-64or5-9) aug, chr, pyr s5 [36] sau 060 ol (fo63.1-70.8), pig (en60-69.6wo7.1-8.6), mask (an 61.4-68.3or0.5-1.6) aug (rare) s5 [34] aug = en47wo35 sau 090 not given not given not given [34] sau 150 ol (fo67-74), pig (en62-69wo7-11), mask (an 53-66or0.3-0.8) ca-poor px s5 [37] a patch of fusion crust sau 120 not given not given not given [37] paired with all finds sau 125 not given not given not given [46] paired with all finds sau 130 not given not given not given [46] paired with all finds sau 587 ol (fa34±0.5), pig (fs25.2±2wo9.2±1.6), mask (an 60.4-65.9or0.4-o.6) pho, sul, chr not given [38] shock metamorphism ol = olivine. pig = pigeonite. mask = maskelynite. aug = augite. pho = phosphate. opa = opaques. chr = chromite. pyr = pyrrhotite. px = pyroxene. sul = sulfide. 4. conclusion martian meteorites provide an unprecedented means of information about mars and are rarely found, compared to other types of meteorites. the sultanate of oman has contributed 17 approved martian meteorites to the 137 found globally. most of them were recovered from the al wusta desert in searches during the last15 years. the bulk of the main mass of sau 005 and its pairings (i.e., 10.9 kg out of total 11.2 kg) recovered from the sultanate is in possession of anonymous collectors, depriving oman of its heritage and denying further research opportunities, given its associated scientific value. sau 005 and its pairings are of the shergottite type of the shergotty-nakhla-chassigny (snc) meteorites which originate from the martian mantle. the published oxygen isotope data of bulk and mineral fractions of sau 008 and dhofar 019 display a narrow range in δ18o values. these data are indistinguishable in terms of δ17o, and fall linearly on a martian fractionation line above the tfl by +0.32‰, suggesting that mars’ mantle is homogeneous in oxygen isotopes. petrographic and mineralogical data of sau 005 plus pairings are identical, suggesting that all the pieces belong to the same meteorite. up until 2014, eleven pieces of sau 005 and its pairings have been recovered, and the strewn field has an area of 4 km by 2 km suggesting that the meteorite may have shattered twice, first in the air prior to landing on the earth due to frictional heating, and secondly by impact with the ground. 5. recommendations the history of sau 005 and its pairings demands a local meteorite museum and preliminary testing laboratory at sultan qaboos university (squ) to protect this treasure trove of omani heritage. 6. acknowledgements arshad ali et al 38 we thank beda a. hofmann, elias m.s. numan and an anonymous reviewer for providing constructive comments and suggestions that have helped improve this review paper. references 1. nasir, s., 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mathematics, faculty of science, cairo university, giza 12613, egypt. *email: afghaleb@gmail.com. abstract: a numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. one surface of the body is subjected to a given periodic displacement and robin thermal condition, while the other is kept fixed and at zero temperature. other conditions may be equally treated as well. the volume force and bulk heating simulate the effect of a beam of hot particles infiltrating the medium. the present study is a continuation of previous work by the same authors for the halfspace [1]. the presented figures display the process of propagation and reflection of the coupled nonlinear thermoelastic waves in the slab. they also show the effects of volume force and heat supply on the distributions of the mechanical displacements and temperature inside the medium. the propagation of beats provides evidence for sufficiently large time values. keywords: finite difference method; heat supply; nonlinear thermoelasticity; nonlinear wave propagation; volume force. الحل العذدي لمسألت غيز خطيت أحاديت البُعذ في المزونت الحزاريت بقوة حجميت وتغذيت حزاريت في شزيحت مسطحت فت وائل محمود وأحمذ فؤاد غالب وإنعام خليفت راوي وحسن أحمذ سكي حسن وعادل عطيت مشزَّ ًجٌد لٌة حجمْت مخغْزة ًحغذّت حزارّت معنمذَ حال عذدّا ٌمسأٌت شزًط حذّت أحادّت اٌبُعذ فِ اٌمزًنت اٌحزارّت اٌالخطْت فِ شزّحت النيائْت، ملخص: ىنان ذٌهو ًجٌد شزط رًبن اٌحزارُ، بْنما ُّثبَّج اٌسطح آخز ححج درجت حزارة صفزّت. معاٌشزّحت إساحت دًرّت ِ. ُّعطَ أحذ سطح فِ اٌشزّحت حُحاوِ اٌشزًط اٌمسخخذ مت حأثْز شعاع من اٌجسْماث اٌساخنت اٌخِ حسمظ عٍَ سطح اٌشزّحت ًحخخزليا ٌمسافت ما.ُّعخبز ًإمىانْت ٌفزض شزًط أخزٍ. ار اٌمٌجاث اٌمزنت اٌحزارّت ، ُدرسج فْو ىذه اٌمسأٌت فِ نصف اٌفزاغ. حُبْن األشىاي اٌمعزًضت انخش [1]اٌبحث اٌحاٌِ امخذادا ٌبحث سابك ٌنفس اٌمؤٌفْن اٌشزّحت. وما حبْن أّضا حأثْز اٌمٌة اٌحجمْت ًاٌخغذّت اٌحزارّت عٍَ حٌسّع وً من اإلساحت اٌمْىانْىْت ًاٌحزارة ِاٌالخطْت اٌمخشاًجت ًانعىاسيا من سطح .داخً اٌٌسظ. ُّبْن اٌحً اٌممذََّ ًجٌد ظاىزة اٌضزباث فِ األسمنت اٌىبْزة نسبْا اٌمزًنت اٌحزارّت اٌالخطْت، االنخشار اٌمٌجِ اٌالخطِ، اٌمٌة اٌحجمْت، اٌمنبع اٌحزارُ، طزّمت اٌفزًق اٌمنخيْت. :مفتاحيتكلماث 1. introduction he propagation of nonlinear waves in thermoelastic solids is one of the main topics of continuum mechanics. mathematical models describing this phenomenon have been treated by many authors [2, 3]. in classical thermodynamics, the basic equations of thermoelasticity yield systems of nonlinear partial differential equations of mixed type for which few exact solutions exist. of theoretical importance are investigations dedicated to the existence, uniqueness and stability of the solutions for such systems as in [4-17]. the formation, the development of discontinuities and blow-up of the solutions are treated in [8] and[18-22]. nonlinear thermoelasticity with finite velocities of propagation of thermal disturbances was considered in [23], and in relation to an electric field in [24]. problems including moving boundaries and multiphase systems with interfaces related to melting, solidification and evaporation processes were treated in [25-27]. the methods of solution of the various systems of equations of nonlinear thermoelasticity are numerous. they are mainly based on finite elements or finite differences [6, 12, 20, 2838]. in [30] the author uses an uncoupled numerical scheme to investigate wave propagation driven by initial conditions only. it relies on a finite element technique for the spatial variable, in combination with an uncoupled difference scheme for the time variable. the method of finite volumes is used in [27, 39]. an extended finite element method to treat crack propagation, stress concentration or flows with interfaces is used in [40]. in [32], the authors treat t numerical solution to a one-dimensional, nonlinear problem 61 a one-dimensional problem for a half-space with prescribed harmonic displacement at the boundary. a poincaré expansion in a small parameter was used to obtain the near-field solution, while the multiple-scale technique took care of the far-field solution. in both methods, the authors obtained a particular solution for the thermoelastic problem, a solution that does not satisfy any thermal boundary conditions at the bounding surface. other techniques for tackling nonlinear initial/boundary-value problems of continuum mechanics are also available in the literature. examples are the method of finite volumes, which relies on the possibility of writing the basic field equations in the form of conservation laws [39], and the differential quadrature method introduced by richard bellman and collaborators [4143], which is an efficient computational tool for finding solutions of nonlinear initial/boundary-value problems and was successfully applied for solving various engineering problems. this last method makes it possible to avoid difficulties that may arise from quasi-linearization. in the present work, we use a restriction to thermoelasticity of a fully nonlinear model introduced in [44] to solve a concrete problem of nonlinear wave propagation in a slab, under volume force and bulk heating. one face of the slab is under periodic displacement and robin thermal condition, while the other one is fixed and kept at zero temperature. this is a continuation of previous work by the same authors for the half-space [1]. the main differences here reside in the fact that the far boundary is now fixed, and the time values are allowed to become large enough so as to capture the reflected waves from both surfaces of the slab. other boundary conditions are also possible without any further complications. in this model, the governing field equations, constitutive relations and boundary conditions are derived in material form within the frame of rigorous thermodynamics. for details concerning the material form of the equations of continuum mechanics, we refer to [45]. an illustrative application of the present model on onedimensional wave propagation was treated in [46] using a multiple scale technique. another application was considered in [47] for a one-dimensional, nonlinear thermoelastic wave propagation in a half-space using a finite difference scheme. amirkhanov [39] investigated a similar problem for a slab using finite volumes, but with no bulk force and for a different boundary condition and for a different heat supply. a problem for a half-space was treated in [1]. it was shown that the proposed numerical method correctly represents the phenomenon of thermoelastic wave propagation. the case with three displacement components was investigated in [48]. the present model of thermoelasticity relies on the hypothesis that all material coefficients of the medium are functions of strain. this is equivalent to using a free energy function which can be expanded in taylor's series in its arguments: strain and temperature. such an approach provided a consistent way to derive the governing system of equations for thermoelasticity for such media, uniformly approximated up to the desired degree of accuracy in terms of the small parameter of strain. details may be found in [44]. the motivation for introducing body force and heat supply is as follows: let a beam of heated particles be directed towards the slab. a fraction of those particles penetrates the medium, as a result of which momentum and heat supply are transmitted to the particles of the medium. thus a field of volume force is created and a bulk heat source is established inside the medium. the authors are not aware of any available experimental evidence that can be used to infer a mathematical form of these fields. for the present purposes, this phenomenon has been modeled using sufficiently smooth functions that decrease exponentially with time and with depth for both the volume force and the heat supply. other forms could also be used for a concrete form of the heat supply function [39]. the left bounding surface of the slab is subject to a given displacement and to a heat radiation condition, while the right boundary is kept fixed and at zero temperature. these rest conditions allow the use of the same numerical technique as in [1]. the study of systems of nonlinear parabolic, or mixed parabolic-hyperbolic equations presents many technical difficulties and may be carried out using different numerical techniques, as is apparent from the given list of references. the merits and disadvantages of each method may be found in specialized textbooks or monographs. in view of the simplicity of the domain geometry, we have opted for a finite-difference scheme which has been tested for effectiveness and reported in previous publications [47, 49-52]. in each case, the numerical results have rendered correctly all the expected characteristics of the solution. the present system of equations was investigated in [1, 47]. in the second of these references, it was shown that one of the characteristic curves of this system clearly expresses parabolicity, meaning that a temperature field installs instantaneously in the half-space. the other characteristic corresponds to the propagation of a coupled thermoelastic wave. in dimensionless variables, the velocity of propagation of this latter wave is close to unity, being slightly affected by both strain and temperature. this is clear from the form of the equation of motion. thus there is only one time scale to be considered, as distinct to other studies where two time scales are necessary for the description of the model [53]. the model does not involve any phase transitions as in other publications that deal with the problems of melting, solidification and evaporation [26, 27] and the extension to include such effects requires more elaboration on the method used and the computational techniques. moreover, the calculations have avoided the regions where shock formation occurs because the method does not allow consideration of allow one to effectively consider this phenomenon, especially in the presence of reflected waves. attention has been mainly focused on the process of reflection of waves at the boundaries. beats are shown to develop due to the interaction of different wave components with slightly different frequencies. wael m. mohamed et al 62 2. formulation of the problem let l be the thickness of the slab. the basic field equations and boundary conditions for the in-depth mechanical displacement and temperature as given in [1,47] read: 2 1 2 (1 2 3 ) = ( ) ( , ), tt xx x x x x x u u u u u f x t         (1) 21 ( ) ((1 ) )) = ( , ), 0 < < , 2 x x t x x x au bu u g x t x l      (2) under the initial conditions ( , 0) = ( , 0) = 0, t u x u x (3) ( , 0) = ( , 0) = 0, t x x  (4) 0 x l  and the boundary conditions 0 (0, ) = (1 cos ), (1 (0, )) (0, ) = , 0, x x u t u t u t t h t     (5) and ( , ) = 0, ( , ) = 0.u l t l t (6) the symbols u and denote, respectively, the dimensionless elastic displacement and the dimensionless temperature, x and t are the spatial (depth) coordinate and the time. the suffixes suffices denote differentiation. the constants involved in these equations have obvious physical significance as expressing the dependence of the different material coefficients on strain [32]. they will be assumed to have the following orders of magnitude: 1 3 1 = (1), = (1 10 ), = (10 ),o o to o     3 1 1 2 = (10 ), = (10 ), = (10 ),o a o b o    = (1), = (1).o h o the above governing equations were derived in [32] on the basis of rigorous thermodynamics and in material configuration. therefore, the boundary conditions are set on a well-defined boundary and do not involve any approximations. the dimensionless heat flow vector component ,q specific entropy ,s and stress component are determined from the constitutive relations by the expressions: = (1 ) , x x q u   (7) 21 = , 2 x x s au bu   (8) 2 3 1 2 1 = ( ). 2 x x x x u u u u          (9) a finite difference method is used to find a numerical solution of the previous coupled equations under the prescribed initial and boundary conditions. the numerical method and the results are briefly discussed in the following sections. more details may be found in [1, 47]. 3. finite difference scheme a combined approach of quasilinearization and the finite difference iterative method is used to solve the problem. this method has been tested for accuracy and efficiency in previous work [49-52]. details of the method may be found in these references, and also in [1]. let ( )nu and ( )n  denote the numerical values of u and  at the n -th iteration and let (0)u and (0) be the initial guess. we consider the picard approximation [54] for equations (1) and (2) under which the functions in the sequence ( )n u and ( )n  satisfy the boundary conditions specified for u and . there is linear convergence of the sequence ( )nu and ( )n  to the solution of the original nonlinear problem. for the computational work, consider a finite interval on the x -axis. the domain in the x t plane is discretized by a grid with step length =x h and time step =t h . the exact values of u and  at the grid point ( , ) ( , )x t rh sk are denoted by ,r su and ,r s . one takes 2 , 1, 1 1, 1 1, 1 1, 1 1 | = [ ] ( ), 4 x r s r s r s r s r s u u u u u o h h             2 2 2 2 , 1, 1 1, 1 1, 1 1, 12 1 | = [( ) ( ) ] ( ), 8 x r s r s r s r s r s u u u u u o h h             , 1, 1 , 1 1, 1 1, 1 , 12 1 | = [ 2 2 2 xx r s r s r s r s r s r s u u u u u u h              2 1, 1 ] ( ), r s u o h    numerical solution to a one-dimensional, nonlinear problem 63 2 , , 1 , , 12 1 | = [ 2 ] ( ), tt r s r s r s r s u u u u o k k      2 2 , 1, 1 1, 1 1, 1 1, 1 1 | = [ ] ( ), 4 xt r s r s r s r s r s u u u u u o h k hk              , , 1 , 1 1 | = [ ], 2 r s r s r s       2 , 1, 1 1, 1 1, 1 1, 1 1 | = [ ] ( ), 4 x r s r s r s r s r s o h h                  2 , , 1 , 1 1 | = [ ] ( ), 2 t r s r s r s o k k        2 , 1, 1 , 1 1, 1 1, 1 , 1 1, 12 1 | = [ 2 2 ] ( ), 2 xx r s r s r s r s r s r s r s o h h                        substituting this into (1) and (2) and neglecting the truncation error, the resulting equations take the form 1 1 1 1 = 4 r r r r qu q u qu w d       2 2 1 3 1 4 5 5 2 4 9 3 4 2 [ ( ) ( ( ) 4 ) ( )] r r r q v d v d d q d q r d q q d         2 2 1 23 1 24 25 5 22 4 21 3 4 22 [ ( ) ( ( ) 4 ) ( )] r r r q y d y d d q d q z d q q d         2 2 1 3 1 4 25 5 2 4 21 4 2 [ ( ) ( ( ) 4 ) ( )] r r r q y d y d d q d q r d q d        2 2 2 1 23 1 24 5 5 22 4 9 4 22 [ ( ) ( ( ) 4 ) ( )] 2 , r r r r q v d v d d q d q z d q d k          (10) 2 2 1 1 1 8 4 2 3 2 4 28 3 28 = ( ) ( ) r r r p p p d p d p d p d p d             5 1 6 1 7 2 5 1 26 1 27 28 [ ] [ ] r r r r r r p r d r d r d p z d z d z d           5 1 6 1 7 2 [ ] r r r p z d z d z d      5 1 26 1 27 28 [ ] 2 , r r r r p r d r d r d k        (11) = 1, 2, , 1, = 0,1, 2, , = 0,1, 2, ,r n s n ( ) ( ) ( ) ( 1)1 , 1 , , 1 , 1 , , , , n n n ns s r s r r s r r s r r s r r s z              ( ) ( ) ( ) ( 1)1 , 1 , , 1 , 1 , , , , n n n ns s r s r r s r r s r r s r u v u w u y u u         2 22 2 2 1 2 1 2 3 4 5 ,2 3 2 4 3 = , = 2(1 ), = , = , = , = , , 22 8 8 r s r k kk k k q q q q q q q f hh h h h       1 2 3 4 5 ,2 2 3 = , = 2 1, = 2 1, = , = , = , , 28 2 r s r k b a k p p p p p p p p g hh h h      1 1 1 2 1 1 3 1 = 1 , = , = 2 , r r r r r r r d qv q v qv d v v d v v          4 1 5 1 1 6 1 = 2 , = 2 , = , r r r r r r r d v v d v v v d v v         7 1 8 1 2 1 9 1 1 = , = , = , r r r r r r r d v v d pr p r pr d r r          21 1 1 22 1 1 23 1 = , = , = 2 , r r r r r r d z z d y y d y y         24 1 25 1 1 26 1 = 2 , = 2 , = , r r r r r r r d y y d y y y d u u         27 1 28 1 1 = , = , r r r r d u u d u u      and the superscript n denotes the final number of iterations required to obtain an acceptable approximation to the values of ,r su and ,r s at the grid points on the line =t sk subject to ( 1) ( ) 8 , , | |< 10 , 1 < < 1max n n r s r s r u u r n     (12) and ( 1) ( ) 8 , , | |< 10 , 1 < < 1.max n n r s r s r r n      (13) wael m. mohamed et al 64 the local truncation error of schemes (10) and (11) is of the order 2 2 ( )o h k . 4. numerical method the difference scheme (10) and (11) as presented in [47] is a three-level iterative scheme. it may be written in the form 1 1 1 = , r r r qu q u qu f     (14) 1 1 1 = , r r r p p p g        (15) = 1, 2, , 1, = 0,1, 2, , = 0,1, 2, ,r n s n where 2 1 2 1 3 1 4 5 5 2 4 9 3 4 2 = 4 [ ( ) ( ( ) 4 ) ( )] r r r r f w d q v d v d d q d q r d q q d           2 2 1 23 1 24 25 5 22 4 21 3 4 22 [ ( ) ( ( ) 4 ) ( )] r r r q y d y d d q d q z d q q d         2 2 1 3 1 4 25 5 2 4 21 4 2 [ ( ) ( ( ) 4 ) ( )] r r r q y d y d d q d q r d q d        2 2 2 1 23 1 24 5 5 22 4 9 4 22 [ ( ) ( ( ) 4 ) ( )] 2 , r r r r q v d v d d q d q z d q d k          (16) 2 2 8 4 2 3 2 4 28 3 28 5 1 6 1 7 2 = ( ) ( ) [ ] r r r g d p d p d p d p d p r d r d r d           5 1 26 1 27 28 5 1 6 1 7 2 [ ] [ ] r r r r r r p z d z d z d p z d z d z d           5 1 26 1 27 28 [ ] 2 , r r r r p r d r d r d k        (17) and 1 2 3 4 5 1 2 3 , , , , , , , , ,q q q q q q p p p p and 4 p are defined above. for = 0,s one has 1,1 1 ,1 1,1 ,0 1, 1 1 , 1 1, 1= 4 ( )r r r r r r rqu q u qu u qu q u qu            2 1,1 1, 1 1,1 ,1 1, 1 , 1[( )( 2 2 )r r r r r rq u u u u u u           1,1 1, 1 ,1 1,1 , 1 1, 1( )(2 2 )]r r r r r ru u u u u u           1,1 ,1 1,1 , 1 1, 1[ 2 2 ]r r r r ru u u u u         2 2 5 1,1 1,1 1, 1 1, 1 [ (( ) ( ) ) r r r r q u u u u           4 ,1 , 1 1,1 1,1 1, 1 1, 14 ( )] [ ]r r r r r rq               3 4 1,1 1,1 1, 1 1, 1[ ( )]r r r rq q u u u u          2 ,0 2 , r k f (18) 1,1 1 ,1 1,1 1, 1 2 , 1 1, 1=r r r r r rp p p p p p                 4 1,1 1,1 1, 1 1, 1( )r r r rp u u u u         2 2 3 1,1 1,1 1, 1 1, 1 [( ) ( ) ] r r r r p u u u u           5 1,1 1, 1 1,1 1, 1 ,1 , 1[( )( )r r r r r rp u u u u            1,1 1, 1 ,1 , 1 1,1 1, 1( )( )r r r r r ru u u u            ,1 , 1 1,1 1, 1 1,1 1, 1( )( )]r r r r r ru u u u            ,02 .rkg (19) from initial conditions (3), (4) , 1 , 1 , 1 , 1 , , | = , | = , 2 2 r s r s r s r s t r s t r s u u u k k         then numerical solution to a one-dimensional, nonlinear problem 65 ,1 , 1 ,1 , 1 ,0 ,0 | = = 0, | = = 0. 2 2 r r r r t r t r u u u k k       hence ,1 , 1 ,1 , 1= , = .r r r ru u    therefore, (14) and (15) finally assume the form 1 1 1 1 = , r r r qu q u qu f     (20) 1 1 1 2 = , r r r p p p g        (21) = 1, 2, , 1, = 0,1, ,r n n where 2 2 1 2 1 23 1 24 25 5 22 4 21 3 4 22 = 2 2 ( ) 2 ( ( 4 ) ( 2 )) 2 , r r r r r f v q y d y d d q d q z d q q d k            1 5 1 26 1 27 28 = 2 ( ) 2 . r r r r g p z d z d z d k        schemes (14), (15) and (20), (21) form two tridiagonal linear systems of equations that are used, together with conditions (5) and (6), to find the values of ,r su and , ,r s = 0,1, 2, ,r n and = 1, 2,s . the numerical method for solving schemes (14), (15) and (20), (21) subject to the given initial and boundary conditions is as follows: (i) for the first time level 1. put ( ) ,0 ,1 , , , n r r r r r r v u w v y u   ( ) ,0 ,1 , , , n r r r r r r r s r z     for all r . 2. calculate ( 1) ,1 ( ) n r r u u   from scheme (20) by the backward sweep method using the given boundary conditions and the initial conditions. 3. calculate the values of ( 1) ,1 ( ) n r r     from (21) by the backward sweep method using the calculated values of r u (calculated from (2)), the boundary conditions and the initial conditions. 4. use the calculated values of r u (set ( 1) ( 1) ,1 ,1 , n n r r r r y u z      ) to calculate improved values of ( 1) ,1 n r u  from scheme (20). 5. from scheme (21), calculate improved values of r  using the improved values of r u calculated in the previous step. 6. repeat the iterative procedure (4) and (5) until conditions (12) and (13). (ii) repeat the same at further times, where the values obtained for r u , ( = 1, 2,..., )r n i and r  ( = 0,1...., )r n from step (i) and initial conditions (3), (4) are the initial conditions for schemes (14), (15), while their boundary conditions are given by (5). in order to solve (20), (21) one uses thomas' algorithm [55] to avoid round-off error growth in machine computation, as follows: 1. to solve (20), take the solution of (20) in the form 1 = , = 1, 2, ,1. r r r r u a u b r n n     (22) substitute the values of 1r u  from (22) into (20) and compare the coefficients of the resulting equations with (22). this gives the relations: 1 1 = , r r e q qa   = , r r q a e (23) 1 1 = , = 1, 2, , 1.r r r qb f b r n e    (24) taking = 0r in (22) and using the boundary condition 0 = (1 cos ),u u t we get 0 0 1 0 (1 cos ) = ,u t a u b  then 0 0 0 = (1 cos ), = 0,b u t a (25) where 0 u is given. the scalars r a and r b are computed from 23 in a forward sweep-manner subject to the initial values given by (25) and initial conditions (3), (4). using the stored values of r a and , r b the solution r u is obtained by a backward sweep subject to the known boundary condition n u . system (14) can be solved in a similar manner. wael m. mohamed et al 66 2. to solve (20), take the solution in the form 1 = , = 1, 2, ,1, r r r r c d r n n       (26) then substitute the values of 1r   from (26) into (21) and compare the coefficients of the resulting equations with (26). this gives the relations: 1 = 2 , r r k c   1 = , r r c k (27) 1 1 = , = 1, 2, , 1.r r r pd g d r n pk    (28) in this case, one uses the boundary condition (1 ) = . x x u h   one has 1 1 1= , = , 2 r r r r x x u u u h h        hence, 1 0 1 1 =0 =0 | = , | = . 2 x r x r u u u h h      therefore, 1 0 1 1 0 (1 ) = ( )( ) = , 2 x x h u u u h h h            so we may write 1  in the from 2 1 0 1 1 0 2 = . h h h u u         (29) equation. (21) at = 0r is 1 0 1 =0 2 = 1| . r p p p g       (30) substitute the value of 1  from (29) into (30) to get 2 =0 1 0 1 0 1 | (1 ) = , 2 r gh h h u u p       (31) which can be written in the form 1 0 1 =0 1 0 0 2 2 1 0 1 0 ( ) ( 1 | )( ) = . 2 ( ) r h u u g h u u h u u h h p h u u h h                      (32) taking = 0r in (26) and comparing with (32), we get 2 1 0 1 0 = , h u u h h kk h u u          0 1 = ,c kk (33) =0 0 1 | = , 2 r g d pkk  (34) where 1 u is obtained from (1), =0 1 | r g can be determined from (31), knowing the initial condition. similarly as in (1), cr and dr are computed from (27) in a forward sweep manner ( = 1,..., 1)r n  subject to the initial values given by (33). using the stored values of r c and , r d the solution r  is obtained by a backward sweep subject to the known boundary condition = 0. n  system (15) can be solved in a similar manner. 5. stability the study of stability of the difference scheme used for the system of equations introduced earlier relies on the investigation of the eigenvalues of the amplification matrix a defined by , 1 , = , r s r s a b     where ,r s denotes the vector of unknowns at level , .r s the non-homogeneous terms are obviously included in the matrix term ,b hence they do not affect the eigenvalues of .a thus, the stability is the same as for the associated numerical solution to a one-dimensional, nonlinear problem 67 homogeneous difference scheme [56]. this has been investigated in [47]. according to this reference, the homogeneous schemes associated with the nonhomogeneous difference schemes (10-11) are unconditionally stable and the local truncation error is of the second-order in both temporal and spatial dimensions. the numerical results show good stability up to sufficiently large values of time. however, the present scheme does not capture the formation of discontinuities which must occur at the (dimensionless) breaking distance 310l  [32, 47]. 6. numerical results and discussion the numerical calculations for the mechanical displacement and temperature distributions in the slab were carried out for the following values of the slab thickness l and the amplitude 0u of the prescribed harmonic displacement at the boundary: 0 = 600, = 0.008.l u the volume force and heat supply functions are both taken as smooth functions decreasing exponentially with x and t in the form: 2 ( , ) = ( , ) = (1 ) . t t x f x t g x t t e e e     (35) this is different from the expression for the heat supply function used in [39]. the figures show the effect of three factors: the boundary displacement, the volume force and the heat supply. each figure has four components, labeled from (a) to (d): label (a) corresponds to the case when the motion is caused only by the boundary displacement, i.e. when = = 0f g . labels (b) and (c) correspond respectively to the cases when 0, = 0f g and = 0, 0.f g  label (d) corresponds to the case when 0, 0.f g  relatively large values of time were needed to evidence the reflection of the waves from both boundaries. one notices the remarkable stability of the solution on these large time intervals. figures 1-2 show in perspective the distributions of the mechanical displacement and of the temperature as functions of the distance, for the different time values. the reflection of the wave is obvious and is accompanied for both the displacement and the temperature by a reverse of the amplitude. this is due to the nature of the imposed boundary conditions at the far boundary of the slab. for the chosen values of the different physical parameters, it is seen from figure 1 that the mechanical displacement produced only by the heat supply is always negative due to dilatation, and is much smaller than that driven only by the volume force, hence this force shadows the effect of a heat supply. thus the figures corresponding to labels (b) and (d) (the two bottom figures) are almost identical. one cannot draw the same conclusion about the distribution of temperature in the slab. in fact, figures 2-c and 2-d show marked differences near the left boundary where the heat supply is concentrated. a small thermal disturbance associated with the thermoelastic wave is seen on figure 2-c progressing in the positive direction and then reflecting from the far boundary. figures 2-c and 2-d clearly show the mixed parabolic-hyperbolic character of this heat wave. figures 3-4 represent the distributions of displacement and temperature as functions of time at the location = 400x in the slab. one clearly sees on these figures the instants of time when the waves reflected from the left and from the right boundaries reach the considered location in the slab. one can notice from figure 3 that the amplitude of the temperature decays with time, a fact that is compatible with the chosen function of heat supply. figures 5-6 show the distributions of displacement and temperature in the slab at two time levels = 2100t and = 2200.t here, the wave front is moving to the left after the second reflection on the right boundary and before reaching the left one. one can clearly see a phenomenon of beats ahead of the wave. the region occupied by the beats disappears gradually as the wave front moves further. figures 7-8 show the effect of variation of the thermoelastic coefficient ( 1  ) on wave propagation, as viewed by an observer fixed inside the slab at the location = 400.x as this coefficient gets larger, one clearly sees on figure 7-a the shift of the wave front conditioned by the small increase of the velocity of propagation of the thermoelastic wave. we have also treated the case with only one period of the driving mechanical displacement at the left boundary. the mechanical boundary condition in this case is: 0 (1 cos ), 0 < 2 ; (0, ) = 0, > 2 . u t t u t t       (36) the corresponding results are shown on figures 9-14. in particular, figure 10-c shows the thermoelastic wave propagating on the background of the heat supply, while figures 13-14 show the propagation of beats. wael m. mohamed et al 68 figure 1. displacement u. figure 2. temperature . numerical solution to a one-dimensional, nonlinear problem 69 figure 3. displacement u as a function of time at x = 400. figure 4. temperature as a function of time at x = 400. wael m. mohamed et al 70 figure 5. displacement u for large times. figure 6. temperature for large times. numerical solution to a one-dimensional, nonlinear problem 71 figure 7. displacement u as a function of time at x = 400 for two values of . figure 8. temperature as a function of time at x = 400 for two values of . wael m. mohamed et al 72 figure 9. displacement u for one pulse. figure 10. temperature for one pulse. numerical solution to a one-dimensional, nonlinear problem 73 figure 11. displacement u as a function of time at x = 400 for one pulse. figure 12. temperature as a function of time at x = 400 for one pulse. wael m. mohamed et al 74 figure 13. displacement u for one pulse for large times. figure 14. temperature for one pulse for large times. numerical solution to a one-dimensional, nonlinear problem 75 7. conclusions the following conclusions are due: 1. a finite difference iterative method has been used to solve a one-dimensional, nonlinear problem of thermoelasticity involving bulk force and heat supply in a slab. a periodic boundary displacement and robin thermal condition pertain at the left boundary of the slab, while complete rest prevails at the other boundary. in a previous work, the used numerical method was shown to exhibit unconditional stability. an iteration process at each time level and the use of thomas' algorithm to avoid round-off error growth and minimize the storage machine computation guarantees the efficiency of the method and good accuracy. the present calculations confirm these facts up to sufficiently large values of time to allow multiple reflections at both boundaries. the (dimensionless) time period, however, could not exceed the dimensionless breaking distance, so that the calculations did not capture the shock wave formation. 2. the method was successfully applied to other boundary displacements, not necessarily periodic. in particular, the case of a boundary displacement consisting of only one time period was also considered. plots are provided for this case (c.f. figures 9-14). other boundary conditions on the right face of the slab are also possible, without any further complications. 3. as concerns the used set of equations, the present work is closely related to [32, 39, 47] and is a continuation of [1]. 4. the wave nature of the solution is clearly represented, while the diffusive character of heat propagation can also be seen on the plots (c.f. figures 2-c and 10-c). thus the mixed parabolic-hyperbolic character of the solution is evidenced. therefore, one may conclude that the proposed numerical method has correctly reproduced the main characteristics of the solution. 5. the successive reflections at the boundaries as viewed by an observer located inside the medium are illustrated on figures 3,4 and 11,12. 6. the small increase in the velocity of propagation of the thermoelastic wave due to heat is illustrated on some plots by comparing the results for two values of the thermoelastic coefficient (c.f. figure 7). 7. the study of the wave propagation at sufficiently large time values has put in evidence a phenomenon of propagation of beats. this is a result of the interaction of different wave components with slightly different frequencies. 8. the solutions presented may be used to study the propagation of nonlinear coupled thermoelastic waves at sufficiently small times, before shock formation, so that the results of [1] for the half-space are fully retrieved. in addition, the results may be used to detect the existence of a force field or a heat supply distribution in the medium. references 1. mahmoud, w., ghaleb, a.f., rawy, e.k., hassan, h.a.z. and mosharafa, a. numerical solution to a nonlinear, one-dimensional problem of thermoelasticity with volume force and heat supply in a half-space. arch. appl. mech., 2014, 84, 9-11, 1501-1515. arch. appl. mech., doi 2014, 10.1007/s00419-014-0853-y. 2. maugin, g.a. physical and mathematical models of nonlinear waves in solids. in: jeffrey, a. and engelbrecht, j. 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(ii) wave generation in a perfect electric conductor, int. j. appl. electromagn. mat. mech., 1998, 9(4), 359 379. 47. rawy, e.k., iskandar, l. and ghaleb, a.f. numerical solution for a nonlinear, one-dimensional problem of thermoelasticity. journal of comp. appl. math., 1998, 100, 53-76. 48. mahmoud, w., ghaleb, a.f., rawy, e.k., hassan, h.a.z. and mosharafa, a. numerical solution to a nonlinear, one-dimensional problem of anisotropic thermoelasticity with volume force and heat supply in a half-space. interaction of displacements. arch. appl. mech., 2015, 85(4), 433-454. arch. appl. mech.doi 2014, 10.1007/s00419-0140921-3. 49. jain, p.c. and iskandar, l. numerical solutions of the regularized long-wave equation. comp. meth. appl. mech. eng., 1979, 20, 195-201. 50. jain, p.c., iskandar, l. and kadalbajoo, m.k. iterative techniques for non-linear boundary control problems. proc. int. conf. on optimization in statistics, academic press, new york. 1979, 289-300 51. iskandar, l. new numerical solution of the korteweg-devries equation. appl. numer. math., 1989, 5, 215221. 52. elzoheiry, h., iskandar, l. and mohamedein, m. sh.el-deen. iterative implicit schemes for the two-and threedimensional sine-gordon equation. j. comp. appl. math., 1991, 34, 161-170. 53. luongo, a., paolone, a. and di egidio, a. multiple timescales analysis for 1:2 and 1:3 resonant hopf bifurcations. nonlinear dynamics, 2003, 34(3), 269-291. 54. bellman, r.e. and kalaba, r.e. quasilinearization and nonlinear boundary-value problems. american elsevier, new-york. 1965. 55. mitchell, a.r. and griffiths, d.f. the finite difference method in partial differential equations, wiley, new york, 1990. 56. thomas, j.w. numerical partial differential equations: finite difference methods. texts in applied mathematics, springer, 1995. received 1 august 2014 accepted 9 november 2014 squ journal for science, 2016, 21(1), 48-63 © 2016 sultan qaboos university 48 effects of second-order slip and viscous dissipation on the analysis of the boundary layer flow and heat transfer characteristics of a casson fluid mohammad m. rahman 1* and ioan pop 2 1 department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. 2 department of mathematics, faculty of mathematics and computer science, babeş-bolyai university, 400084 clujnapoca, romania. *email: mansur@squ.edu.om. abstract: the aim of the present study is to analyze numerically the steady boundary layer flow and heat transfer characteristics of casson fluid with variable temperature and viscous dissipation past a permeable shrinking sheet with second order slip velocity. using appropriate similarity transformations, the basic nonlinear partial differential equations have been transformed into ordinary differential equations. these equations have been solved numerically for different values of the governing parameters namely: shrinking parameter , suction parameter ,s casson parameter , first order slip parameter ,a second order slip parameter ,b prandtl number pr, and the eckert number ec using the bvp4c function from matlab. a stability analysis has also been performed. numerical results have been obtained for the reduced skin-friction, heat transfer and the velocity and temperature profiles. the results indicate that dual solutions exist for the shrinking  0  surface for certain values of the parameter space. the stability analysis indicates that the lower solution branch is unstable, while the upper solution branch is stable and physically realizable. in addition, it is shown that for a viscous fluid     a very good agreement exists between the present numerical results and those reported in the open literature. the present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a casson fluid. therefore, this study has importance for researchers working in the area of non-newtonian fluids, in order for them to become familiar with the flow behavior and properties of such fluids. keywords: boundary layer; casson fluid; dual solutions; shrinking surface; second-order slip; stability analysis. تأثير اإلوزالق مه انذرجة انثاوية و انتبذد انهزج عهى تحهيم انتذفك عبر انطبقة انمتاخمة و خصائص اإلوتقال انحراري نسائم كاسون محمذ مىصور رحمه و آيون بوب ٌٙذف ٘زا اٌبحث إٌى دساست اٌتذفك اٌّطشد عبش اٌطبمت اٌّتاخّت ٚخصائض إٔتماي اٌحشاسي ٌسائً واسْٛ ِع ٚخٛد دسخاث حشاسة :انمهخص ٔزالق ِٓ اٌذسخت اٌثأٍت. ٚتعتّذ طشٌمت اٌحً عٍى استخذاَ تحٌٛالث اٌتشابٗ إِتغٍشة ٚتبذد ٌزج حٛي سطح رٚ ٔفارٌت ٚلابً ٌإلٔىّاش ٚفً ظً ٚخٛد ٚاٌتً ٌتُ ِٓ خالٌٙا تحًٌٛ اٌّعادالث األساسٍت فً إٌّٛرج اٌشٌاضً اٌّستخذَ ٚاٌتً ً٘ عباسة عٓ ِعادالث تفاضٍٍت خزئٍت غٍش خطٍت إٌّاسبت ٌداد حٍٛي عذدٌت ٌالحتىان اٌسطحً إ. ٚتُ "matlabإٌى ِعادالث تفاضٍٍت اعتٍادٌت ٚاٌتً ٌتُ حٍٙا بطشق اٌتحًٍٍ اٌعذدي باستخذاَ بشٔاِح "  ماي اٌحشاسي ٚسشعت تذفك ٚدسخاث حشاسة اٌسائً باستخذاَ لٍُ ِختٍفت ٌعذة عٛاًِ فٍزٌائٍت ًٚ٘ ِعاًِ االٔىّاشٚاالٔت ٚ ِعاًِ االِتصاص أٚ ، وّا تُ اٌمٍاَ بتحًٍٍ ثباث ecٚ إوٍشث prٚأعذاد باسٔذتً bٚاٌثأٍت aٚ ِعاِالث اإلٔزالق ِٓ اٌذسخت األٌٚى ِٚعاًِ واسْٛ sاٌشفظ ( ٚرٌه ٌمٍُ ِحذد ٌٍّعاِالث اٌفٍزٌائٍت، وّا 0اٌحٍٛي اٌعذدٌت أٌضا. ٚلذ أشاسث إٌتائح إٌى ٚخٛد حٍٛي ِزدٚخت فً حاي األسطح إٌّىّشت ) ت إٌى ٚخٛد أظٙشث ٔتائح تحًٍٍ االستمشاس إٌى عذَ استمشاس اٌدزء اٌسفًٍ ِٓ اٌحً بٍّٕا اٌدزء اٌعٍٛي ِٓ اٌحً ِستمش ٌّٚىٓ تحمٍمٗ فٍزٌائٍا، إضاف )تعٍك باٌسائً اٌٍزج تٛافك بٍٓ ٔتائح اٌذساست اٌحاٌٍت ٚاٌذساساث اٌسابمت فٍّا ٌ    . إْ إٌتائح اٌحاٌٍت تعذ لٍّت ٚخذٌذة فً دساست اٌتذفك ( ِداي اٌّطشد عبش اٌطبمت اٌّتاخّت ٚخصائض االٔتماي اٌحشاسي ٌسائً واسْٛ حٛي سطح لابً ٌالٔىّاش. ٚتعذ ٘زٖ اٌذساست راث أٍّ٘ت ٌٍباحثٍٓ فً ت سٍٛن ٚخٛاص ٘زٖ إٌٛعٍت ِٓ اٌسٛائً.اٌسٛائً غٍش ٍٔٛتٍٍٕت ٌّعشف سائً واسْٛ، اٌطبمت اٌّتاخّت، إٔىّاش األسطح، اإلٔزالق ِٓ اٌذسخت اٌثأٍت، حٍٛي ِزدٚخت، تحًٍٍ االستمشاس.: انكهمات انمفتاحية effects of second-order slip and viscous dissipation 49 1. introduction n the past several decades, there has been an increasing interest in the flows of newtonian and non-newtonian fluids over stretching/shrinking sheets because of their applications in processing industries such as paper production, hot rolling, wire drawing, glass-fiber production, aerodynamic extrusion of polymer fiber extruded continuously from a dye with a tacit assumption that the fiber is inextensible, etc. the cooling of a long metallic wire in a bath (an electrolyte) is another physical situation belonging to this category. glass blowing, continuous casting, and spinning of fibers also involve the flow due to a stretching surface. during its manufacturing process a stretched sheet interacts with the ambient fluid thermally and mechanically. the thermal interaction is governed by the surface heat flux. this surface heat flux can either be prescribed or be the output of a process in which the surface temperature distribution has been prescribed. however, in real life situations one encounters a boundary layer flow over a non-linear stretching surface. for example, in a melt-spinning process, the extrudate is stretched into a filament while it is drawn from the dye. finally, this surface solidifies while it passes through an effectively controlled cooling system in order for the final product to achieve top quality. other examples include drawing of copper wires, continuous stretching of plastic films and artificial fibers, hot rolling, glass-fiber, metal extrusion, metal spinning, etc. (see sparrow and abraham [1], and abraham and sparrow [2]). the pioneering work on the steady boundary layer flow due to a linear stretching sheet was done by crane [3]. thereafter, various aspects of this problem have been studied extensively in newtonian and non-newtonian fluids. however, the extension of the theory of newtonian fluids to the theory of non-newtonian fluids has been proved to be not so straightforward (see, for example, skelland [4], denn [5], rajagopal et al. [6], bird et al. [7] and slattery [8]). it is now generally recognized that, in real industrial applications, non-newtonian fluids are more appropriate than newtonian fluids. these fluids have wide-ranging industrial applications, such as in the design of thrust bearings and radial diffusers, drag reduction, transpiration cooling, thermal oil recovery, etc. in certain polymer processing applications, one deals with the flow of a second-order (viscoelastic) fluid over a stretching surface. such fluids are referred to as fluids of the differential type, that is, fluids whose stress is determined by the rivlin–ericksen tensors (see rivlin and ericksen [9]), or fluids of the rate type, such as the oldroyd-b fluid (see oldroyd [10]), 3 rd grade fluid (see hayat et al. [11]) etc. polymers mixed in newtonian solvents and polymer melts, such as high-viscosity silicone oils or molten plastics, are examples of such fluids. but in practice, many materials, like melts, muds, printing ink, condensed milk, glues, soaps, shampoos, sugar solution, paints, tomato paste, etc., show various characteristics which are not properly understandable using newtonian theory. hence, to analyse such fluids it is essential to utilise non-newtonian fluid mechanics. however, the main difficulty is to make a single constitutive equation which covers all the properties of such non-newtonian fluids. because of this, numerous non-newtonian fluid models have been proposed in the literature. in nature, some non-newtonian fluids behave like elastic solids, i.e. with small shear stress no flow occurs. casson fluid is one such fluid. so, for flow to occur, the shear stress magnitude of a casson fluid needs to exceed the yield shear stress, as otherwise the fluid behaves as a rigid body. this type of fluid can be categorised as a purely viscous fluid with high viscosity. several models have been suggested for non-newtonian fluids, with their constitutive equations varying greatly in complexity. some authors (fredrickson [12]) studied casson fluid for the flow between two rotating cylinders. eldabe and elmohands [13] investigated the steady-flow behavior of a viscoelastic flow through a channel bounded by two permeable parallel plates, and boyd et al. [14] discussed steady and oscillatory blood flow taking into account casson fluid. mernone et al. [15] described the peristaltic flow of a casson fluid in a twodimensional channel. mustafa et al. [16] studied the unsteady boundary layer flow and heat transfer of a casson fluid over a moving flat plate with a parallel free stream and solved this problem analytically using the homotopy analysis method. pramanik [17] studied casson fluid flow and heat transfer past an exponentially porous stretching surface in the presence of thermal radiation. the objective of the present study is to analyze the boundary layer development (both momentum and thermal energy) of a casson fluid past a permeable shrinking sheet with second-order slip velocity and viscous dissipation. applying similarity transformations, the basic nonlinear partial differential equations are transformed into ordinary ones which are then solved numerically for different values of the governing parameters. a stability analysis is carried out for the acceptance of the physically realizable solutions. numerical results are obtained for the reduced skin-friction coefficient, rate of heat transfer and the velocity and temperature distributations. i mohammad m. rahman and ioan pop 50 figure 1. the geometry of the problem of a shrinking surface. 2. basic equations consider the steady two-dimensional flow of a casson fluid past a permeable shrinking sheet with the velocity )(xu w , while the second-order wall velocity slip is )( slip xu . the sheet is situated at 0y , the flow being confined to 0y , where y is the coordinate measured in the normal direction to the surface and the coordinate x is measured along the surface of the sheet as shown in figure 1. it is assumed that the temperature of the surface of the sheet is ( ), w t x while the constant temperature of the ambient (inviscid) fluid is ,t  where   txt w )( (heated sheet). we assume also that the rheological equation of state for an isotropic and incompressible flow of a casson fluid can be written as, nnn /1/1 0 /1   (1) or, (see nakamura and sawada [18]) ji n n y bji e p 2 2 /1                    (2) where  is the dynamic viscosity, b  is plastic dynamic viscosity of the nonnewtonian fluid, y p is yield stress of fluid,  is the product of the component of deformation rate with itself, namely, ijij ee , and ij e is the th ji ),( component of the deformation rate, and that the constant n takes the value 1n in many practical applications. under these conditions, and along with the assumption that the viscous dissipation term in the energy equation is taken into consideration, the boundary layer equations which govern this problem are 0 u v x y       (3) 2 2 (1 1 / ) u u u u v x y y            (4) 2 2 2 (1 1 / ) p t t t u u v x y y c y                      (5) subject to the initial and boundary conditions 0 slip , ( ) ( ), ( ) at 0 0, as w w v v u u x u x t t x y u t t            (6) u w t w t y x  0 boundary layer v 0 u w effects of second-order slip and viscous dissipation 51 where u and v are the velocity components along x and y axes, t is the fluid temperature,  is the thermal diffusivity of the fluid,  is the kinematic viscosity, p c is the specific heat at constant pressure,  is the constant stretching ( 0 ) or shrinking ( 0 ) parameter, 2 / b c y p   is the non-newtonian (casson) parameter, and where we assume ( ) w u x cx and 2 0 ( ) w t x t t x    , )0(0 t to be the temperature characteristic of the sheet. further, following wu [19] (used also by fang et al. [20], mahmood et al. [21]), the wall second-order slip velocity )( slip xu , is given by 2 2 2 2 2 2 3 3 1 1 24 2 ( ) (1 ) = aslip 2 2 23 2 4 l l u u u u u x l l b k y ykn y yn                              (7) here )1,/1min( n kl  and  is the momentum accommodation coefficient with 10  . based on the definition of l , it is seen that for any given value of n k , we have 10  l . since the molecular mean free path  is always positive it results in b being a negative number. it is important to mention that wu’s [19] second order slip velocity model is valid for any arbitrary knudsen number and it matches better with the fukui–kaneko results which are based on the direct numerical simulation of the linearized boltzmann equation [22]. we look for a similarity solution of equations (4)-(7) of the form: ycttttfxc w  /),/()()(),(   (8) where  is the stream function, which is defined in the classical form as yu  / and xv  / . thus, we have )(),('  fcvfxcu  (9) where prime denotes differentiation with respect to  . substituting (7) into eqs. (4) and (5), we obtain the following ordinary (similarity) equations 2 (1 1 / ) ''' '' ' 0f f f f    (10) 21 '' ' 2 ' (1 1 / ) '' 0 pr f f ec f        (11) subject to the boundary conditions     as0)(,0)(' 1)0(),0(''')0('')0(',)0( f fbfafsf (12) where cvs / 0  is the constant parameter of suction ( 0s ) or injection ( 0s ), a is the first order velocity slip parameter with 0/  caa , b is the second order slip velocity with 0/  cbb ,  /pr  is the prandtl number and ( ) / ( ( ) )w p wec u x c t x t    is the constant eckert number. it is worth pointing out that for  , eq. (10) reduces to eq. (7) for a viscous (newtonian) fluid, as shown by fang et al. [20]. the physical quantities of interest are the skin friction coefficient f c and the local nusselt number xnu , which can be easily shown to be given by 1/ 2 1/ 2 re (1 1 / ) ''(0), re '(0) x f x x c f nu       (13) where re ( ) / x w u x x  is the local reynolds number. 3. stability analysis solving eqs. (10) and (11) with the boundary conditions (12), it has been shown that dual (upper and lower branch) solutions exist for the case of a shrinking sheet )0(  . thus, in order to see which solution is stable, and that it is physically realizable in practice, a stability analysis of these solutions is necessary. in this respect, we write eqs. (1)-(3) corresponding to the unsteady flow and heat transfer as 0 u v x y       (14) mohammad m. rahman and ioan pop 52 2 2 (1 1 / ) u u u u u v t x y y               (15) 2 2 2 (1 1 / ) p t t t t u u v t x y y c y                         (16) subject to the initial and boundary conditions 0 0 slip 0 : , 0, for any , 0 : , ( ) ( ), ( ) at 0 0, as w w t v v u t t x y t v v u u x u x t t x y u t t                  (17) where t denotes time. following weidman et al. [23], rosca and pop [24-25], and rahman et al. [26-28], a dimensionless time variable  has to be introduced. the use of  is associated with an initial value problem and this is consistent with the question of which solution will be obtained in practice (physically realizable). thus, the new variables for the unsteady problem are ( , ), ( , ) ( ) / ( ), / , w c x f t t t t c y c t                  (18) thus, eqs. (14)-(16) can be written as 2 3 2 2 3 2 (1 1 / ) 0 f f f f f                          (19) 2 2 2 2 2 1 2 (1 1 / ) 0 pr f f f ec                                 (20) subject to the boundary conditions     as0),(,0),(' 1),0(),,0('''),0(''),0(',),0( f fbfafsf (21) to test the stability of the steady flow solution )()( 0  ff  and )()( 0   satisfying the boundary-value problem (19)-(21), we write (see weidman et al. [23] or rahman et al. [26-28]) ),()(),(),,()(),( 00   gefeff   (22) where  is an unknown eigenvalue parameter, and ),( f and ),( g are small relative to )(0 f and )( 0  introducing (22) into equations. (19) and (20), we get the following linearized problem 3 2 2 0 0 03 2 (1 1 / ) ( 2 ') '' 0 f f f f f f f f                       (23) 2 0 0 02 2 0 2 1 ( 2 ') 2 pr 2 (1 1 / ) '' 0 g g f f f g f ec f                            (24) along with the boundary conditions 2 3 2 3 (0, ) 0, (0, ) (0, ) (0, ), (0, ) 0 ( , ) 0, ( , ) 0 as f f f f a b g f g                               (25) the solution )()( 0  ff  and )()( 0   of the steady equations (10) and (11) is obtained by setting 0 . hence )( 0 ff  and )( 0 gg  in (23) and (24) identify initial growth or decay of the solution (22). with respect to this, we have to solve the linear eigenvalue problem 0''')'2(''''')/11( 0000000  fffffff  (26) effects of second-order slip and viscous dissipation 53 0 0 0 0 0 0 0 0 0 1 '' ' ( 2 ') 2 ' 2 (1 1 / ) '' '' 0 pr g f g f g f ec f f         (27) along with the boundary conditions 0 0 0 0 0 0 0 (0) 0, '(0) ''(0) '''(0), (0) 0 '( ) 0, ( ) 0 as f f a f b f g f g           (28) it should be stated that for particular values of  ,  , a , b , ec , and pr the stability of the corresponding steady flow solution )( 0 f and )( 0  is determined by the smallest eigenvalue  . as has been suggested by harris et al. [29], the range of possible eigenvalues can be determined by relaxing a boundary condition on )( 0 f or )( 0 g . for the present problem, we relax the condition that 0 ( ) 0g   as  and for a fixed value of  we solve the system (26)-(27) along with the new boundary condition 0 (0) 1g  . 4. numerical technique following rahman et al. [26-28], the ordinary differential equations (10)-(11) subject to the boundary conditions (12) are solved numerically using the function bvp4c from the very robust computer algebra software, matlab. the function bvp4c requires writing equations (10)-(11) as first order differential equations by introducing new variables: one for each variable in the original problem plus one for each derivative up to the highest order derivative minus one. it then implements a collocation method for the solution of the following boundary value problem ( , )x w t x  , a t b  (29) subject to the two-point boundary conditions ( ( ), ( )) 0bc x a x b  . (30) the approximate solution ( )t is a continuous function that is a cubic polynomial on each subinterval 1 [ , ] n n t t  of the mesh 0 1 2 .......... n a t t t t b     . it satisfies the boundary conditions ( ( ), ( )) 0bc a b   (31) and it also satisfies the following differential equations (collocates) at both ends and mid-point of each subinterval ( ) ( , ( )) n n n t w t t   (32) 1 1 1 (( ) / 2) (( ) / 2, (( ) / 2)) n n n n n n t t w t t t t          (33) 1 1 1 ( ) ( , ( )) n n n t w t t       (34) these conditions result in a system of nonlinear algebraic equations for the coefficients defining ( )t , which are solved iteratively by linearization. here ( )t is a fourth order approximation to an isolated solution ( )x t , i.e. 4 || ( ) ( ) ||x t t k h  , where k is the maximum of the step sizes 1n n n h t t    and k is a constant. for such an approximation, the residual ( )r t is the ordinary differential equation and is defined by ( ) ( ) ( , ( ))r t t w t t   . (35) in this approach mesh selection and error control are based on the residual of the continuous solution. the relative error tolerance was set to 7 10  . the condition   needs to be replaced by a suitable finite value of  , say   . we started the computation at a small value, for example, 5 , then subsequently increased the value of  until the boundary conditions were verified. in using this method, we chose a suitable finite value of  , namely 20   for the upper branch (first) solution and   in the range 40-60 for the lower branch (second) solution. the present problem may have more than one solution. thus the bvp4c function requires an initial guess of the desired solution for the system (10)-(11). the guess should satisfy the boundary conditions and reveal the characteristics of the solution. the bvp4c method always converges to the first solution even for poor guesses of the initial conditions. thus, determining an initial guess for the first (upper branch) solution is not difficult. on the other hand, it is very difficult to come up with a sufficiently good guess for the second (lower branch) solution of the system (10)-(11). to overcome this difficulty, we need to start with a set of parameter values for which the problem is easy to solve. then, we use the obtained result as the initial guess for the solution of the problem with small variation of the parameters. this is repeated until we reach the right values of the parameters. this technique mohammad m. rahman and ioan pop 54 is called continuation. examples of solving boundary value problems by bvp4c can be found in the book by shampine et al. [30] or through an online tutorial by shampine et al. [31]. the numerical simulations are carried out for various values of the physical parameters such as casson parameter (  ), suction parameter ( s ), shrinking parameter (  ), first order slip parameter ( a ) and second order slip parameter ( b ), eckert number ( ec ) and prandtl number ( pr ). because of the almost complete lack of experimental data, the choice of the values of the parameters is dictated by the values chosen by previous investigators. the value of the prandtl number is set equal to 1 throughout the paper unless otherwise specified. the values of the other parameters are mentioned in the description of the respective figures. it is worth mentioning that for a viscous fluid (   ) and for 1  (stretching sheet), in the absence of fluid suction 0s  and second order slip parameter 0b  , equation (10) 2 0f ff f     subject to the boundary conditions (0) 0f  , (0) 1 (0)f af   , ( ) 0f    matches with that of wang [32-33], anderson [34], and sahoo and do [35]. wang [32-33] and anderson [34] obtained an exact solution of (9) subject to the above-mentioned boundary conditions. to test the accuracy of the current numerical solution, the values of (0)f  and ( )f  are compared with analytical values reported by wang [32-33] and sahoo and do [35] in table 1. this table shows that the numerical values produced by the current code and the exact analytical solutions reported by wang [32-33] and shahoo and do [35] are in very good agreement. this gives us confidence to use the present code. it can further be mentioned that for a viscous fluid (    ) eq. (10) 2 0f f f f     along with the boundary conditions (0)f s , (0) (0) (0)f af bf     , ( ) 0f   as   exactly matches with the corresponding eq. (10) and boundary conditions (12) of rosca and pop [24] when the buoyancy force in their model is neglected. we also mentioned that for 1   (shrinking sheet), the above-stated equation together with the corresponding boundary conditions also matches with eqs. (7)-(8) of fang et al. [20]. table 2 shows the comparison of the values of (0)f  for 1a  and several values of s and b when 1   with those reported by fang et al. [20], and rosca and pop [24]. in fact, the results show excellent agreement among the data, thus giving us confidence to use the present matlab code. 5. results and discussion the numerical simulation of eqs. (10) to (11) subject to the boundary conditions (12) are carried out for various values of the physical parameters , ,s , ,a ,b ec and pr for obtaining the condition under which the dual (upper and lower branch) solutions for the steady flow of a casson fluid over a shrinking surface may exist. miklavčič and wang [36] have studied the steady viscous (newtonian) fluid flows over a permeable linearly shrinking surface and have shown that suction at the wall will generate dual solutions only when the suction parameter s is greater than or equal to 2. table 1. comparison of results (0)f  and ( )f  with the first order slip parameter a when   , 0,s  and 1  . a (0)f  ( )f  current result sahoo and do [35] wang [32] current result sahoo and do [35] wang [32] wang [33] 0.0 0.2 0.3 0.5 1.0 2.0 3.0 5.0 10 20 1.000000 0.776377 0.701548 0.591195 0.430159 0.283979 0.214054 0.144840 0.081242 0.043788 1.001154 0.774933 0.699738 0.589195 0.428450 0.282893 0.213314 0.144430 0.081091 0.043748 1.0 0.701 0.430 0.284 0.145 0.0438 0.999973 0.919076 0.888544 0.839278 0.754859 0.657267 0.598141 0.524529 0.431842 0.349999 1.001483 0.919010 0.888004 0.838008 0.752226 0.652253 0.590892 0.513769 0.413655 0.322559 1.0 0.887 0.748 0.652 0.514 0.332 1.0 0.8393 0.7549 0.5982 0.4331 effects of second-order slip and viscous dissipation 55 table 2. comparison of (0)f  for 1a  , 2, 3s  and 1, 2b    when 1   . s a b present study rosca and pop [24] fang et al. [20] lower branch upper branch lower branch upper branch lower branch upper branch 2 2 3 3 1 1 1 1 -1 -2 -1 -2 0.25659275 0.22573384 0.20223817 0.18809181 0.29054789 0.18465688 0.23201653 0.1369054 0.2565 0.2257 0.2022 0.1868 0.2905 0.1846 0.2320 0.1369 0.2565 0.2257 0.2022 0.1868 0.2905 0.1847 0.2317 0.1371 figure 2. variations of (0)f  for different values of  at 2  when 1,a  1b   , 2.5,s  1,ec  and pr 1 . figure 3. variations of (0) for different values of  at 2  when 1a  , 1b   , 2.5s  , 1ec  , and pr 1 . in figures 2 to 7, we have investigated the variation of the reduced skin friction coefficient   1/ 2 / ( 1) re ''(0) x f c f    and the reduced local nusselt number (or heat transfer from the surface of the sheet) 1/ 2 re '(0) x x nu    of a casson fluid for different values of  , s and  respectively, keeping the values of the other parameters 1a  , 1b   , 1ec  , and pr 1 fixed. from these figures we see that the number of solutions depends on the shrinking parameter  , suction parameter s , and casson parameter  . in figures 2 and 3 we have identified two critical  ’s say s  and c  such that 0 c s    where s  is the critical value of  for the lower branch and c  is the critical value of  for the upper branch in which the solution exists. that is, for a casson fluid flow over a shrinking sheet, there exist dual solutions when 0 s    , one solution which is the upper branch when , c s     and no solution when c  . thus, for c  the full navier-stokes equations and energy equation need to be solved. figure 2 also shows that values of (0)f  for both the upper and lower branches decrease with the increase of  when other parameter values are fixed. for the upper branch solution these values are higher than the corresponding lower branch solution. now the question is which of these solutions is physically acceptable. from the stability analysis it is found that the upper branch solution is stable and physically acceptable whereas the lower solution branch is unstable and physically unacceptable. table 3 presents the smallest eigenvalues  for the upper branch solution at several values of ,a b and . this table shows that smallest eigenvalues for the upper branch solution are positive, hence the perturbed part f of the solution f will be diminished and converged to the steady state solution 0 f when   as can be seen from eq. (22). thus, the upper branch solution is stable and physically acceptable. on the other hand the smallest eigenvalues for the lower branch solution are negative which indicates that the perturbed part f of the -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 -0.2 0 0.2 0.4 0.6 0.8 1 1.2  f   ( 0 ) [ s , f  (0)] = [-1.5357, 0.440185] [ c , f  (0)] = [-3.0993, 1.028130] upper branch solution lower branch solution -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0 2 4 6 8 10 12 14 16 18 20    ( 0 ) [ s , f  (0)]= [-1.5357, 2774.813008] [ c , f  (0)]= [-3.0993, 0.511846] lower branch solution upper branch solution mohammad m. rahman and ioan pop 56 solution f will grow enormously with time when   as can be seen from eq. (22). therefore, the lower branch solution is unstable and not physically realizable. figure 3 shows that values of (0) for the upper branch solution increase with the increase of  whereas they decrease with the increase of  . as  approaches to s  , the values of (0) increase very rapidly. at s   , this value is (0) 2774.813  . in the figure we have truncated the lower branch solution as in this scale upper branch solution is not visible properly. table 3. smallest eigenvalues  for different values of a , b when 0    (casson fluid) and   (newtonian fluid) at 2.5s  , 0.5   , 0ec  , pr 1 . a b  smallest eigenvalues  upper branch, c  lower branch, s  0 1 1 1 1 1 -1 -1 0 -1 -1 -1 2 2 2 10 100  1.5528 1.5880 1.8004 1.6276 1.6342 1.9308 -0.1262 -0.1316 -0.1443 -0.1973 -0.2169 -0.2193 in figures 4 and 5, respectively, the effects of the suction parameter s on the reduced skin friction coefficient and nusselt number are displayed. these figures confirm that dual solutions can be found when 0 s s s  , one solution when 0 c s s s s   and no solution when c s s . the critical 2.1001 s s  belongs to the lower branch solution while 1.6993 c s  belongs to the upper branch solution when other parameters values 1,   1,a  1,b   2  , 1ec  , and pr 1 are fixed. the critical 1.6993 c s  is lower than the value 2 calculated by miklavčič and wang [36] for a steady viscous (newtonian) fluid flow over a permeable linearly shrinking surface. thus, for a casson fluid, flows over a shrinking surface a minimum fluid withdrawal from the boundary layer compared to the viscous fluid will produce dual solutions. the values of (0)f  for the upper branch solution first increase with the increase of s up to a certain value when 1cs s s  (say), then decrease with the further increase of 1 s s . on the other hand, the values of (0)f  for the lower branch solution first decrease up to a certain value with the increase of s when 2ss s s  (say), then they increase with the further increase of 2 s s . it is worth noting that 2 1 s s . the values of (0)f  for the upper branch solution are higher than those of the lower branch solution within the solution domain 4.23 s s s  . for 4.23s  an opposite trend is observed. on the other hand values of (0) (figure 5) for the upper branch solution increase with the increase of c s s while for the lower branch solution these values first decrease to a minimum value when 3s s s s  (say) then start to increase with the further increase of the suction parameter. it is to be mentioned that to display both the solutions branch in the same scale we have truncated the lower branch solution vertically while plotting. effects of second-order slip and viscous dissipation 57 figure 4. variations of (0)f  for different values of s at 1   when 1a  , 1b   , 2  , 1ec  , and pr 1 . figure 5. variations of (0) for different values of s at 1   when 1,a  1,b   , 2,  1ec  , and pr 1 . figure 6. variations of (0)f  for different values of  at 1   when 1a  , 1b   , 2.5,s  1,ec  and pr 1 . figure 7. variations of (0) for different values of  at 1   when 1a  , 1b   , 2.5s  , 1,ec  and pr 1 . in figures 6 and 7 we have displayed the reduced skin friction coefficient and reduced nusselt number for various values of the casson parameter  when 1,   1,a  1,b   2.5,s  1ec  , and pr 1 . for these studied parameter values two critical values of  , one for the lower branch 1.1818 s   and the other for the upper branch 0.5620, c   are identified for the existence of the solution. these figures show that dual solutions can be found when s   . the upper branch solution is always bigger than the lower branch solution. within the region 0.85 c    the upper solution increases quite rapidly to its maximum value 0.3333 then starts to decrease with the further increase of  . as mentioned earlier a large  i.e.   corresponds to the viscous (newtonian) fluids. figure 6 clearly indicates that as  becomes large the physically realizable values of (0)f  approach to their asymptotic value 0.2724. figure 7 indicates that the asymptotic value of the reduced 1.5 2 2.5 3 3.5 4 4.5 5 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 s f   ( 0 ) [s s , f  (0)] = [2.1001, 0.263762] [s c , f  (0)] = [1.6993, 0.322851] upper branch solution lower branch solution 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 4 5 6 7 8 9 10 s   ( 0 ) [s c , f  (0)] = [1.6993, 0.774767] [s s , f  (0)] = [2.1001, 1428.250813] upper branch solution lower branch solution 0 1 2 3 4 5 6 7 8 9 10 0.22 0.24 0.26 0.28 0.3 0.32 0.34  f   ( 0 ) upper branch solution lower branch solution [ c , f  (0)] = [0.562, 0.298691] [ s , f  (0)] = [1.1818, 0.240036] 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10    ( 0 ) upper branch solution lower branch solution [ s , -  (0)] = [1.1818, 1662.724374] [ c , -  (0)] = [0.562, 1.438864] mohammad m. rahman and ioan pop 58 nusselt number is 2.2421 when  becomes large. this figure clearly reveals that the rate of heat transfer in a casson fluid is lower compared to the rate of heat transfer in a viscous (newtonian) fluid. table 4. critical  and corresponding values of (0)f  for different a , b , and  when 2.5s  , 1ec  , and pr 1 . a b  upper branch solution lower branch solution c  (0)f  s  (0)f  0 -1 2 2.5 5  -2.0712 -2.4046 -3.4199 -5.3429 1.027056 1.176313 1.590792 2.271937 -1.0955 -1.2444 -1.6454 -2.3477 0.440174 0.528697 0.767231 1.155035 1 -1 2 2.5 5  -3.0993 -3.5834 -5.0176 -7.6291 1.028129 1.179225 1.599951 2.293422 -1.5357 -1.7732 -2.4330 -3.5028 0.440184 0.528737 0.772045 1.155058 1 0 2 2.5 5  -2.0002 -2.2196 -2.8136 -3.7550 1.002087 1.151879 1.577269 2.281026 -2.0001 -2.2195 -1.9169 -2.5438 0.996414 1.147576 0.771982 1.155041 table 5. critical  and corresponding values of (0) for different a , b , and  when 2.5s  , 1ec  , pr 1. a b  upper branch solution lower branch solution c  (0) s  (0) 0 -1 2 2.5 5  -2.0712 -2.4046 -3.4199 -5.3429 0.550963 0.426726 0.090219 -0.434987 -1.0955 -1.2444 -1.6454 -2.3478 2642.053988 3003.454371 4323.338580 6507.086524 1 -1 2 2.5 5  -3.0993 -3.5834 -5.0176 -7.6291 0.511845 0.359193 -0.024985 -0.610166 -1.5357 -1.7732 -2.4330 -3.5028 2774.813008 3652.195429 4201.941189 6579.395747 1 0 2 2.5 5  -2.0002 -2.2196 -2.8136 -3.7550 0.018269 -0.193895 -0.698576 -1.568783 -2.0001 -2.2195 -1.9169 -2.5438 -0.026184 -0.242078 3387.651463 5567.562933 in tables 4 and 5 we have investigated in details the effects of the first order slip parameter a , second order slip parameter b on the critical  , reduced skin friction coefficient and local nusselt number for different values of the casson parameter  when 2.5s  , 1ec  , and pr 1 are fixed. from table 4 we notice that the critical | | c  for the upper branch solution as well as | | s  for the lower branch solution increases with the increase of the casson parameter  , first order slip parameter a , and absolute value of the second order slip parameter | |b . we also notice that values of (0)f  increase with the increase of a as well as | |b for a fixed value of the casson parameter  . thus, the presence of first and second order slip parameters broadens the solution space before the boundary layer is going to separate. table 5 shows that the critical | | c  increases with the increase of the casson parameter  , first order slip parameter a , and second order slip parameter | |b . the effects of second-order slip and viscous dissipation 59 local nusselt number ( (0) ) decreases with the increase of  and a , while it increases with the increase of | |b . for large  , the local nusselt number becomes negative which indicates that heat transfer takes place from the fluid to the surface. figure 8. velocity profiles ( )f  for different values of  when 1   , 1a  , 1b   , 2.5s  , 1ec  , and pr 1 . figure 9. temperature profiles ( )  for different values of  when 1   , 1a  , 1b   , 2.5s  1,ec  and pr 1 . figure 10. velocity profiles ( )f  for different values of s when 1   , 1a  , 1b   , 2  , 1ec  , and pr 1 . figure 11. temperature profiles ( )  for different values of s when 1   , 1a  , 1b   , 2  , 1ec  , and pr 1 . the variations of the dual solutions in terms of dimensionless velocity '( )f  and temperature ( )  profiles of a casson fluid for different values of the casson parameter , suction parameter ,s second order slip parameter b , first order slip parameter ,a and eckert number ec are demonstrated in figures 8 to 16 for a shrinking surface ( 1   ) when for pr 1 . it is seen from figure 8 that the hydrodynamic boundary layer thickness for the upper branch solution is always thinner than that of the lower solution branch. this figure also 0 1 2 3 4 5 6 7 8 9 10 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0  f  (  )  = 1.2, 2, 10, 50 upper branch solution lower branch solution  = 1.2, 2, 10, 50 0 1 2 3 4 5 6 7 8 9 10 -0.5 0 0.5 1   (  )  = 2, 10, 50  = 2, 10, 50 lower branch solution upper branch solution 0 1 2 3 4 5 6 7 8 9 10 -1 -0.8 -0.6 -0.4 -0.2 0  f  (  ) upper branch solution lower branch solution s = 2.5, 3, 3.5 s = 2.5, 3, 3.5 0 1 2 3 4 5 6 7 8 9 10 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1   (  ) upper branch solution lower branch solution s = 2.5, 3, 3.5 mohammad m. rahman and ioan pop 60 reveals that the velocity profile ( )f  increases with the increasing values of the casson parameter  for the upper branch solution. for smaller values of  the rate of increase in velocity is quite rapid compared to the rate of increase for large values of  . for large values of   , the fluid behaves like a viscous (newtonian) fluid. on the other hand the temperature of the casson fluid and hence the thickness of the thermal boundary layer decreases for the upper branch solution with the increase of  (see figure 9). an opposite trend is observed for the lower branch solution. these figures clearly demonstrate that the thicknesses of the hydrodynamic and thermal boundary layers are thinner for a viscous (newtonian) fluid compared to the casson fluid. figure 10 reveals that the velocity profile ( )f  increases, and hence the hydrodynamic boundary layer thickness decreases, with the increasing values of the suction parameter s for the upper branch solution. a reverse effect of s on the velocity profiles is observed for the lower branch solution. figure 11 shows that the temperature profiles (𝜂) in the vicinity of the surface decrease with the increase of s either for an upper solution branch or for a lower solution branch. the thickness of the thermal boundary layer for the upper solution branch is lower than the corresponding thickness of the lower solution branch. figure 12. velocity profiles ( )f  for different values of b when 1   , 1a  , 2.5s  , 2  , 1ec  , and pr 1 . figure 13. temperature profiles ( )  for different values of b when 1   , 1a  , 2.5s  , 2  , 1ec  , and pr 1 . the dimensionless velocity '( )f  and temperature ( )  profiles of a casson fluid due to the second order slip parameter b and first order slip parameter a are displayed in figures 12-15, when 2  , 2.5s  , 1   , pr 1 . it is seen that the velocity distributions ( )f  (figures 12 and 14) of the casson fluids within the boundary layer increase with the increase of | |b as well as with the increase of a for the upper branch solution, whereas for the lower solution branch these distributions decrease except very close to the surface of the shrinking sheet where they increase with the increase of the parameter | |b and also with the increase of a . the thicknesses of the thermal boundary layer decreases with the increase of the parameter | |b and also with ,a as can be seen from figures 13 and 15. thus, the second and first order slip parameters reduce the thicknesses of the hydrodynamic and thermal boundary layers. we notice that the effect of a is more pronounced than the effect of b on the velocity and temperature fields. therefore, first and second order slips play an important role in modeling boundary layer flows with casson fluids over a shrinking surface. finally, the effect of the eckert number ec on the temperature distribution is depicted in figure 16 when 1   , 2  , 1a  , 1b   , 2.5s  , and pr 1 . for these studied parameter values we notice that temperature distribution within the boundary layer for the upper branch solution increases with the increase of ec . an increasing ec generates more frictional heating which in turn induces the flow rate to increase. an opposite effect of ec on the temperature distribution is observed for the lower branch solution. 0 1 2 3 4 5 6 7 8 9 10 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0  f  (  ) upper branch solution lower branch solution b = 0, -0.5, -1 b =0, -0.5, -1 0 1 2 3 4 5 6 7 8 9 10 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1   (  ) upper branch solution lower branch solution b = 0, -0.5, -1 b = 0, -0.5, -1 effects of second-order slip and viscous dissipation 61 figure 14. velocity profiles ( )f  for different values of a when 1   , 1b   , 2.5s  , 2,  1ec  , and pr 1 . figure 15. temperature profiles ( )  for different values of a when 1   , 1b   , 2.5s  , 2,  1ec  , and pr 1 . figure 16. temperature profiles ( )  for different values of ec when 1   , 1a  , 1b   , 2.5s  , 2  , and pr 1 . 6. conclusion in this paper we investigate the steady forced convective boundary layer flow and heat transfer characteristics of a casson fluid over a permeable shrinking surface with variable temperature in the presence of second-order slip at the interface. a numerical simulation is carried out to investigate the existence of the dual solutions. the critical shrinking, suction and casson parameters have been identified for the existence of the dual solutions. following our numerical computations it is concluded that dual solutions exist only when 0 s    , s s s and s   for fixed values of the other parameters where the subscript s stands for the solution corresponding to the lower branch. the upper branch solution is found to be stable and hence physically 0 1 2 3 4 5 6 7 8 9 10 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0  f  (  ) a = 0, 1, 5 upper branch solution lower branch solution a = 0, 1, 5 0 1 2 3 4 5 6 7 8 9 10 -2.5 -2 -1.5 -1 -0.5 0 0.5 1   (  ) lower branch solution upper branch solution a = 0, 1, 5 a = 0, 1, 5 0 1 2 3 4 5 6 7 8 9 10 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1   (  ) ec = 0.1, 1, 3 ec = 0.1, 1, 3 upper branch solution lower branch solution mohammad m. rahman and ioan pop 62 acceptable, while the lower branch is unstable and hence physically not realizable. the critical | | c  corresponding to the stable solution increases with the increase of the casson parameter , first order slip parameter ,a and magnitude of the second order slip parameter | | .b the rate of heat transfer in a casson fluid is lower than the rate of heat transfer in a viscous (newtonian) fluid. the thicknesses of the hydrodynamic and thermal boundary layers are thicker for a casson fluid than a viscous (newtonian) fluid. the presence of first and second order slip parameters broaden the solution space before the boundary layer is given a chance to separate. an extension of this work is underway exploring the heat transfer augmentation considering casson fluidbased nanofluid. 7. acknowledgement we would like to express our thanks to the very competent reviewers for their valuable comments and suggestions. m.m. rahman is grateful to the research council (trc) of oman for funding under the open research grant program: org/squ/cbs/14/007 and dr. n. al-salti, department of mathematics and statistics, sultan qaboos university for translating the english 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university 77 optimization of independent variables for the production of extracellular alpha amylase by bacillus subtilis imd34 using plackettburman design henshaw effiom* and josiah lennox antimicrobials and bioactive molecules research group, microbiology department, faculty of biological sciences, university of calabar, nigeria. email: henzefilo@yahoo.co.uk. abstract: bacillus species are widely used for thermostable α-amylase production for various applications such as in the detergent and food industries. this research aimed to study the production of α-amylase by b. subtilis imd34 in submerged fermentation conditions using plackett-burman (pb) design, along with the optimization of certain environmental factors for optimal growth of amylolytic bacteria. plackett-burman design was used to evaluate the effect of ten independent variables on α-amylase production. maximum enzyme activity was recorded in a medium containing (g/l); starch (6.0), peptone (12.0), k2hpo4 (1.0), na2hpo4 (2.0), nacl (0.6), na2so4 (0.1), mgso4.7h20 (1.0), fecl3.6h2o (0.02), cacl2.2h2o (0.02) and with an agitation speed (200 rpm). from the pareto chart it was observed that the most important independent variables for amylase production were starch, peptone, nacl, mg2so4, cacl2.2h2o and agitation. optimization of environmental parameters to assess their effect on the growth of bacteria showed that optimal ph, incubation time and temperature were recorded at 6, 48h and 37˚c. evaluating independent variables statistically using pb design revealed that some of the medium’s components had a positive impact on αamylase production by b. subtilis imd34. keywords: optimization; independent variables; alpha amylase; bacillus subtilis imd34; plackett-burman design. ستخدام تصميم إب bacillus subtilis imd34بواسطة تحسين المتغيرات المستقلة إلنتاج أميلز ألفا خارج الخلية burman-plackett هينشو إفيوم و جوسيا لينوكس المستقر حراريا α-usacuba ج إنزيم ألفاتستخدم على نطاق واسع في إنتا sullccab البكتيريا العصويةمن بين البكتيريا ، من المعروف أن :صلخمال لتخمير في حالة ا 43dmi عصويةبواسطة بكتريا إنزيم ألفالتطبيقات مختلفة مثل المنظفات والصناعات الغذائية. كان الهدف من هذا البحث دراسة إنتاج بكتيريا. تم استخدام تصميم بالكيت بورمان لتقييم تأثير عشرة لبورمان مع تحسين بعض العوامل البيئية للنمو األمثل ل-المغمور باستخدام تصميم بالكيت ophi. ( ، 6..0ببتون )( ، ال0.6تم تسجيل أقصى نشاط لإلنزيم في وسط يحتوي على )جم / لتر( ؛ النشا ) أنزيم ألفا.متغيرات مستقلة على إنتاج (0.6 ، )0u.ophi )..6( كلوريد الصوديوم ، )0( ، )6.0ui( . hi )6.0( ،3) hi. o.6 )0.6( ، a2cm.0o.h )6.6.( ، 2u2c...o.h )6.6.( سرعة التحريك ، ).الببتون كانت النشا اإلنزيمدورة في الدقيقة(. من مخطط باريتو لوحظ أن أهم المتغيرات المستقلة إلنتاج 66 ، . أظهر تحسين المعلمات البيئية لتقييم تأثيرها على نمو البكتيريا أنه تم تسجيل درجة التحريض hi ،2u2c...o.h .(3، كلوريد الصوديوم ، أن psدرجة مئوية. كشف تقييم المتغيرات المستقلة إحصائيًا باستخدام تصميم m 6ساعة و i4و 0الحموضة المثلى ووقت الحضانة ودرجة الحرارة عند .s. ba slclb 43dmiبواسطة أنزيم ألفالى إنتاج بعض مكونات الوسيط كان لها تأثير إيجابي ع .، تصميم بالكيت بورمان sullccab ba slclb 43dmi، لمتغيرات المستقلة ، ألفا أميليز، االتحسين :مفتاحيةالكلمات ال henshaw effiom and josiah lennox 78 1. introduction mylases are enzymes which hydrolyze starch molecules to give diverse products including dextrin and progressively smaller polymers composed of glucose units. they are a class of industrial enzymes having an approximately 25% share of the market for enzymes [1]. these enzymes are very useful in industrial processes such as making starch, paper and detergents, and in the brewing, textile and pharmaceutical industries. although there are large number of microorganisms capable of producing useful enzymes, bacterial amylase is generally preferred for starch liquefaction due to its high stability [2] and neutral to alkaline ph. in the food industry, amylases are used in the production of glucose syrups, crystalline glucose, high fructose corn syrups, maltose syrups, and for the reduction of viscosity of sugar syrup and the reduction of haze formation in juices, as well as for solubilization and saccharification of starch for alcohol fermentation in the brewing industry and retardation of staling in the baking industry [2]. in the detergent industry amylases are used as an additive to remove starch based dirt, as well as forin warp sizing of textile fibers in the textile industry. conventionally the production of alpha amylase has been carried out by submerged fermentation [3,4] of a number of bacterial species such as bacillus subtilis, b. stearothermophilus, b. amyloliquefaciens, b. licheniformis, b. acidocaldarius and b. marcesens [3,5,6]. designing an appropriate fermentation medium for highly efficient enzyme production is imperative and necessary as the medium’s constituents and incubation condition can significantly affect the yield of this product [7-9]. screening of independent variables in the medium used can be carried out by pb experimental design [10]. it is a partial factorial design where a large number of independent variables (n) are studied in small number of experiments (n+1) [11-12]. there are reports on the use of pb design for medium composition for enzyme production by bacteria [3,4,5,7,8,13-17]; however information on the use of pb design to study the influences of independent variables on the production of α-amylase by b. subtilis imd34 along with the optimization of environmental process parameters for the growth of this bacterial strain is not available. in this research, ten independent variables, namely starch, peptone, mgso4, k2hpo4, nahpo4, nacl, na2so4, fecl3.6ho, cacl2.2h2o, and agitation speed were screened for their influences on α-amylase production by b. subtilis imd34 under submerged fermentation using pb design. in addition, the optimization of certain environmental factors including ph, temperature and incubation time on the growth of this bacterial strain was studied. 2. materials and method 2.1. microorganism and cultivation bacillus subtilis imd34 was obtained from department of the microbiology, university of ibadan, ibadannigeria. all chemicals used in the experiment were of analytical grade. the organism was maintained on a nutrient agar (oxoid, difco, usa) slant and preserved at 4˚c. 2.2. plackett-burman experimental design the importance of each independent variable including starch, peptone, mgso4, k2hpo4, na2hpo4, nacl, na2so4, fecl3.6h2o, cacl2.2h2o, and agitation speed in the fermentation medium required for enzyme production in a shake flask culture using b. subtilis imd34 was screened for. the pb experimental design of twelve runs (table 2) for ten variables, nine nutritional factors and one environmental factor (table 1), were used to evaluate the influence of each on α-amylase production. in table 2, each row represents an experiment and each column represents an independent variable. for each variable two different concentrations, high and low, were tested (table 1). 2.3. submerged fermentation all experiments were carried out in triplicate using 250 ml erlenmeyer flasks containing 30 ml fermentation media as per experimental design, with ph adjusted to 7.0. flasks were autoclaved at 15psi and 121˚c for 15 minutes, after which they were inoculated with an 18h old culture with a cell concentration of 1.6x10 5 using aseptic procedures, and then incubated on an orbital incubator shaker (model 10x400.xx2.c, sanyo gallenkamp plc, uk) at 37˚c and 100 rpm for 24h [3,18]. 2.4. enzyme extraction assay the culture fluids were centrifuged using a refrigerated high-speed ultra-centrifuge at 10,000xg (4˚c) for 5 minutes, after which the filtrates (supernatants) were assayed for extracellular 2-amylase using the dnsa reagent method [19]. boiled culture served as a control. a standard curve was prepared with glucose, and the calibration curve so established was used to convert the spectrophotometer values to glucose equivalent, and activities were calculated [18, 20]. 2.5. optimization of environmental process parameters environmental process variables such as incubation time, temperature, and ph were varied to evaluate their effects on enzyme production and growth of b. subtilis imb34. the fermentation medium as defined by pb design above was employed for the optimization process. the effect of incubation time on growth and amylase production a optimizatioin of independent variables for the production of extracellular alpha amylase 79 was evaluated at 12h, 24h, 36h, 48h, 60h, 72h, and at each 12 hourly interval growth (optical density) was measured at 610 nm using a perkin-elmer lambda uv/vis spectrophotometer, and the enzyme activity was assayed as stated above. the incubation temperature was studied at (25˚c, 37˚c, 45˚c and 55˚c) and the ph of the fermentation medium was also varied (ph:4, ph:6, ph:7, ph:8 and ph:10). the procedure for measuring the growth (optical density) and enzyme assay as described above was adopted. the data were statistically evaluated adhering to the following formula a) the effect of each independent variable was evaluated with the equation below exi = 2(∑hxi-∑lxi)/n [13], where, exi is the concentration effect of the independent variable, hxi and lxi are the concentrations of amylase at high and low levels of the same variables, and n is the number of trials (12). when the sign is positive, the influence of the variable on enzyme production is greater at high concentrations, and when negative the influence is greater at low concentrations. b) the mean square of each variable was calculated as follows vxi = ( ∑hxi-∑lxi)/n [13] where vxi is the mean square of the variable. factors showing larger effects were identified using f-test [13]. percentage concentration was calculated from f-test. 3. results and discussion amylases are ubiquitous enzymes produced by plants, animals and microorganisms, in which they play a dominant role in carbohydrate metabolism. amongst the sources of amylase, microbes have been paid a great deal of attention because of their greater stability and safe use [21]. among bacteria bacillus species are known to be widely used for thermostable amylase production for various applications such as fermentation, detergents, food etc. [1, 22]. to enhance the production of amylase by b. subtilis imd34 using pb design, ten independent variables were screened to evaluate their effects on enzyme production, and in addition, the optimization of certain environmental factors for the growth of b. subtilis imd34 was investigated. the amylase activities from the twelve runs are presented in table 2, where the results indicate a variation in amylase production with a range from 0.134-0.547uml -1 by b. subtilis imd34. these results have shown the need to screen the medium’s components for efficient amylase yield [7, 14, 15, 23, 24, 25]. figure 1 shows that the most important independent variables for amylase production were starch, peptone, nacl, mg2so4, cacl2.2h2o and agitation.the highest amylase activity was recorded in trial number 9 containing (g/l); starch (6.0), peptone (12), k2hpo4 (1.0), nahpo4 (2.0), nacl (0.6), na2so4 (0.2), mgso4.7h2o (1.0), fecl3.6h2o (0.02), and cacl2.2h2o (0.02), with an agitation speed of 200rpm. the data in table 2 was statistically evaluated to ascertain the effect of each independent variable and its contribution to amylase production, as presented in table 3.a positive effect indicates a direct relationship and the contribution of independent variables to the considered response (amylase production), and a negative effect indicates an inverse relationship between the variable and the response (table 3). a positive sign for the effect means that by increasing the independent variable from low to high level leads to an increase in the response. an effect with a negative sign means that by changing the level of the independent variable from low to high, the response decreases. results from table 3 indicate that starch, peptone, nacl, mgso4.7h2o, cacl2.2h2o and increased agitation speed each showed a positive effect on amylase production while k2hpo4, na2hpo4, na2so4 and fecl3.6h2o had negative effects. in this study, the positive effect shown by starch and peptone, cacl2 and 2h2o is consistent with the research of bansode [8], who reported the positive effect of the media components, starch, tryptone and cacl2.2h2o, on amylase production using bacteria. a similar report by [7] revealed that peptone, agitation and mgso4.7h2o directly affected the rate of amylase production from the fungus aspergillus tubingensis 1. agitation intensity influences the mixing and oxygen transfer rate during submerged fermentation, and thus product formation [25]. starch has been found to be the best carbon source for the production of amylase by b. stearothermophilus [26]. the commercial production of amylase is carried out in stages, essentially because the environmental factors required for the optimum growth of bacteria being employed for production may differ from those required for the maximum production of enzymes. in this study three environmental factors including ph, temperature and incubation time were optimized to ascertain the optimal conditions for bacterial growth. optimum temperature, ph and incubation time were determined by varying incubation temperature (25˚c, 37˚c, 45˚c, 55˚c) (figure 3), adjusting the fermentation medium ph (4, 6, 7, 8, 10) (figure 4), and incubating the medium for various periods of time (12h, 24h, 36h, 48h, 60h, 72h) (figure 2). results obtained showed the optimum temperature for growth of b. subtilis imd34 to be 37˚c (od600nm; 2.12) (figure 3). optimal growth of amylolytic b. amyloliquefaciens at 36˚c has been reported [27] and b. subtilis at a range of 35-37˚c [18]. the optimum ph for optimal bacterial growth (od600nm; 1.89) was observed at ph 6. the ph of the growth medium plays an important role by inducing morphological change in the organism and in enzyme secretion. it has been suggested that the metabolic activity of bacteria is very sensitive to the ph level of their media [16]. the result obtained in this study is similar to the observation of [27] who reported ph 6.5 to be the most favourable for growth of b. marcescen. the ph dependent changes in the growth might have been due to ph control of metabolic gene expression [17]. the optimum incubation time for growth (od600nm; 2.64) was observed at 48h (figure 2). this result agrees with the earlier report by [18] who found that the optimum incubation time for optimal growth of bacillus sp. was in the range 36-48h. the effect of incubation time on optimal growth decreases as its duration increases because the growth of the cells may reach their peak, move through the stationary phase without numerical increase and enter the decline phase [29]. henshaw effiom and josiah lennox 80 table 1. plackett-burman design for studying the influences of ten variables on α-amylase production by b. subtilis imd 34. independent variables units low level(-) high level(+) z1: starch z2: peptone z3: k2hpo4 z4: na2hpo4 z5: nacl z6: na2so4 z7: mgso4.7h2o z8: fecl3.6h2o z9: cacl2.2h2o z10: agitation speed g/l g/l g/l g/l g/l g/l g/l g/l g/l rpm 3.0 6.0 1.0 2.0 0.6 0.1 0.5 0.02 0.01 100 6.0 12.0 2.0 4.0 1.2 0.2 1.0 0.04 0.02 200 table 2. plackett-burman experimental design in 12 runs for studying the influences of independent variables on αamylase production in shake culture and amylase activity. trials no z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 amylase activity(uml -1 ) 1 + + + 2 + + 3 + + + 4 + + 5 + 6 + 7 + 8 + + 9 + + + 10 + + + 11 + + + 12 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 0.513 0.352 0.284 0.243 0.501 0.314 0.223 0.134 0.547 0.172 0.412 0.182 table 3. effects of independent variables on α-amylase production by b. subtilis imd34 in shake culture. independent h variables l ms effect f-value % contribution starch 3.243 peptone 2.127 k2hpo4 1.587 na2hpo4 1.702 nacl 1.423 na2so4 1.413 mgso4.7h2o 1.782 fecl3.6h2o 1.524 cacl2.2h2o 1.674 agitation speed 1.824 1.124 0.212 1.520 0.141 1.810 0.012 1.791 0.131 1.645 0.045 1.522 0.061 1.325 0.064 1.487 0.071 1.534 0.052 1.642 0.021 0.216 989.12 0.084 201.41 -0.043 62.03 -0.024 44.01 0.052 32.41 -0.023 95.38 0.018 55.26 -0.017 22.41 0.041 8.49 0.032 5.92 65.23 13.28 4.09 2.90 2.14 6.29 3.64 1.48 0.56 0.39 optimizatioin of independent variables for the production of extracellular alpha amylase 81 figure 1. pareto chart of the influences of independent variables on the response variable by b. subtilis imd34 figure 2. growth pattern of b. subtilis imd34 for various incubation times. figure 3. growth pattern of b. subtilis imd34 at different incubation temperatures. cacl2.2h20 fecl3.6h2o nacl na2hpo4 mgso4.7h… k2hpo4 (na4)2so4 peptone starch 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 12 24 36 48 60 72 g ro w th (o d 6 0 0 n m ) 0 0.5 1 1.5 2 2.5 25 37 45 55 g ro w th (o d 6 0 0 n m ) (response is b. subtilis imd34 amylase, α = 0.1) incubation time temperature na2so4 henshaw effiom and josiah lennox 82 figure 4. growth pattern of b. subtilisimd34 at various ph. conclusion this study revealed, using pb design, that certain independent variables in the composition of the growth medium used had a positive impact on α-amylase 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kallur, r.i. and kalural, b.b. amylase production and application. european journal of experimental biology 2012, 4, 1044-1055. received 21 november 2021 accepted 24 july 2022 solving the flood propagation problem with newton algorithm on parallel systems squ journal for science, 17 (1) (2012) 147-156 © 2012 sultan qaboos university 147 solving the flood propagation problem with newton algorithm on parallel systems chefi triki department of mechanical and industrial engineering, sultan qaboos university, muscat, oman, email:chefi@squ.edu.om. abstract: in this paper we propose a parallel implementation for the flood propagation method flo2dh. the model is built on a finite element spatial approximation combined with a newton algorithm that uses a direct lu linear solver. the parallel implementation has been developed by using the standard mpi protocol and has been tested on a set of real world problems. keywords: newton equations, direct solver, mpi, load balancing. حل مشكلة انتشار الفيضانات باستخدام خوارزمية نيوتن على أجهزة الحواسيب المتوازية شافي التريكي على أجهزة الحواسيب flo2dh نامجرباستخدام بقترح هذه الورقة طريقة لحل مشكلة انتشار الفيضانات ت خص:مل luتحليل اللى تقريب العناصر المحدودة مع خوارزمية نيوتن التي تستخدم إالمتوازية. وقد تم بناء نموذج الحل باالستناد وجرى اختباره على مجموعة من mpi المباشر. كما تم وضع الحل على أجهزة الحواسيب المتوازية باستخدام بروتوكول المسائل التطبيقية. 1. introduction he solution of most of the mathematical models arising in several contexts of hydraulics and hydrology still remains a big challenge. the choice of the most appropriate method for the solution of the problem under examination is often subject to a trade-off between numerical stability and computational complexity. moreover, the time execution is often too long to be acceptable for the requirements of the decision makers. this paper has the intention of contributing in this direction for a particular problem: the flood propagation modeling. the aim is to provide a parallel implementation of the well known software flo2dh, a code built on a finite element spatial approximation combined with a newton algorithm to solve the linear systems. more specifically, we focus our attention on the solution of the linear system arising in every iteration of the newton method. we discuss the advantages of direct methods (vs. iterative methods) and we propose a parallel implementation based on an lu decomposition approach. t chefi triki 148 the parallel solution of direct methods has been the subject of intensive research activity to solve many problems arising in a wide range of contexts (scott, 2001; scott, 2002; amestroy et al., 1998; mallya et al., 1997). moreover, several existing approaches have been proposed for the parallel lu decomposition and for the parallelization of flood modeling systems (hluchy et al., 2002, 2006). however, to the best of our knowledge, this paper represents a first contribution for the parallel solution of the lu decomposition within the flo2dh code to solve the flood propagation problem. the only work dealing with this problem which we are aware of, has implemented an iterative method (a stabilized version of the conjugate gradient algorithm) that allows only an approximate solution to be obtained and not the exact one (abdeouahed et al., 2000). our parallel direct approach is, thus, useful, not only when a high numerical precision is required but also when it can serve as a benchmarker for the development of iterative methods within a flood propagation solver. the paper is organized as follows: in section 2 we define the application context of our contribution. in section 3 we present our parallel approach and discuss the different issues related to its implementation. in section 4 we report our experimental results, and in section 5 we give some concluding remarks. 2. computational fluid mechanics computational fluid mechanics is a tool that helps to solve a wide range of problems in fluid mechanics and heat transfer. we usually categorize common fluids as either gas or liquid. a fluid is any material medium that can not support shearing or stresses and remain at rest, from the macroscopic standpoint. the most important properties of fluids are density, viscosity, surface tension, cavitation and boiling. fluid flow plays an important role in practice. a detailed description of the flow is usually necessary for better understanding and ultimately solving a number of industrial and scientific problems. each kind of flow has its proper mathematical description. by mixing together different kinds of flows, the mathematical description becomes more complex. this description uses sets of partial differential equations which in most of the cases have no analytical solution. for this reason numerical methods are used to solve this kind of problems. in computational fluid mechanics, the flow region or calculation domain is usually divided into a large number of finite volumes or cells. the governing partial differential equations are discretized by using a finite difference, a finite volume or a finite element technique. an example of a small 2-dimensional (2d) finite element (fe) mesh is depicted in figure 1. such a discretization generates a set of algebraic equations (corresponding to the respective partial differential equations) which are solved by numerical procedures. the resulting solution thus represents the values of the dependent variables at discrete locations, and the intermediate values are obtained by interpolation. it is worthwhile noting that most of the problems arising in computational fluid mechanics are characterized by a large number of equations and, consequently, the solution process may take several hours. in order to decrease the execution time it is important to take advantage of parallel computing facilities to run, at least, the most time consuming parts of the simulation. in this paper we focus on the solution of the flood propagation problem by using the public domain flo2dh simulator for which we propose a parallel implementation. 3. parallel implementation before presenting our parallel implementation, we need to describe with some details the characteristics of the simulator flo2dh. 3.1 flo2dh simulator flo2dh is part of the united states federal highway administration's finite element surface-water modeling system (feswms). it is a computer program that simulates the movement of water and noncohesive sediment in rivers, estuaries, and coastal waters (froehlich, 2002). the sequential version of the flo2dh simulator uses the finite element method for the differential solving the flood propagation problem 149 equations computation (froehlich, 2002; dabaghi et al., 2004). the solution space (water surface) is divided into a number of elements depending on the expected precision (see figure 1). more elements in the computational model means higher resolution and precision, but also more computational load. figure 1. carre test problem a small 2d fe mesh (partitioned into 3 sets). the flo2dh simulator is written in fortran 77 and fortran 90 programming languages. the source code, around 2000 pages long, contains a lot of physical and mathematical computations that are not only very complex, but also characterized by a high degree of dependence. (indeed, our tentative of assigning the task of automatic parallelization of the whole code to a parallel compiler has given very poor results). therefore parallelizing the whole code seems to be laborious and not promising. for this reason we decided to focus our attention on the most time consuming parts of the code with the aim of decreasing the total execution time of the simulator. even though intuition led us to think that the solution of the linear set of equations at each step of the newton method is the most time consuming part of the code, we decided to carry out a time measurement experiment in order to confirm our intuition. the experiment also had the objective of discovering the percentage of the total time which this consumes and the theoretical speedups that may be expected. on the basis of our experiment, carried out on a set of 5 test problems with different sizes and by using one processor of the sgi origin 300 supercomputer, a subroutine called xfront turned out to be the most computationally extensive fraction of flo2dh. the results reported in table 1 show, indeed, that the code spends up to 80% of the total time in executing subroutine xfront, whereas no one of the other subroutines of flo2dh takes a significant amount of time. table 1. execution times (seconds) and percentages problem carre madora etape1 solstat etape2 number of nodes 97 437 6413 4223 13876 xfront total time xfront/total time 0.46 0.58 0.79 1.55 1.85 0.84 7.85 15.8 0.50 34.86 41.94 0.83 205.6 255.9 0.80 chefi triki 150 by analyzing the source code we observe that: • subroutine xfront is responsible of generating the system of linear equations for each element and then for calling subroutine xassemble; • xassemble is responsible for forming the matrix a from the values of each element and for solving the system of equations (froehlich, 2002): = ,ax b (1) where a is a large sparse matrix, b is a vector, and x is the variables vector. forming and solving the system of linear equations =ax b is, thus, computationally the most intensive part of flo2dh. parallelizing the subroutine xfront represents an opportunity to solve the flood propagation problem faster. according to amdahl's law and the time measurements reported in table 1 it is possible to estimate the maximum theoretical speedup expected from running subroutine xfront on an 8-processor machine (the case of test problem madora that has a fraction of 16% of non parallelizable code): 1 = 3.77 . 1 0.16 0.16 8 s   (2) however, besides calling xassemble, xfront calls also a set of subroutines which are responsible for hydrodynamics computations and that are not suitable to be parallelized because of the data dependence. this fact, together with the unavoidable communication overhead, should further worsen the above theoretical speedups of our parallel implementation. figure 2. sparse matrix in dbbd form with processes assignment. 3.2 parallel frontal solver in the sequential version of flo2dh, the frontal method is used to solve the set of equations = .ax b this method makes an lu decomposition of the matrix a followed by a forward and a backward substitution. an attractive feature of this method is that the workload could be separable into small tasks, and it is not necessary that each task has the whole matrix a available in order to make the lu decomposition. computations are just done over a small part of the whole matrix a. this part, called a front, is formed by the summation of the equations for each element. the variables which are fully summed are then decomposed and eliminated from the front (froehlich, 2002). an efficient implementation should ensure that the size of the front matrix must be very small compared with matrix a in order to save memory. the next step consists in choosing a parallelization approach for solving the =ax b system. there are two main approaches: direct and iterative algorithms. even though direct methods need a considerable number of floating point operations (high load), they are characterized by a high stability of the solution. for this reason we decided to implement a direct method, giving, in this way, particular attention to the solution’s precision at the cost of a possible slight loss in efficiency. solving the flood propagation problem 151 the parallel frontal method works in a similar way to the sequential frontal method. the whole load is divided into a number of tasks that are assigned to the parallel processes. each process has its own front and performs its computation over a proper part of the matrix a. the algorithm can be particularly suitable for parallelization whenever: first, the matrix a has the following doubly bordered block diagonal (dbbd) form: =                 1 1 2 2 n n 1 2 n a c a c a a c c c c e (3) where submatrices ia are i in n , ic are in k and ci are ik n , and second, ik n (i.e. the black part of the matrix in figure 2 is as small as possible). in our case it is possible to decompose matrix a into the above form by using the partitioning and resequencing algorithms that will be described in the sequel of this section. thus, the partial frontal decomposition is performed on each of the submatrices: =       i ii i i a c a c e . (4) parallel frontal algorithm: 1. factorization perform a partial lu decomposition of each i a (in parallel) form the interface problem by summing the schur complement matrices remaining after performing all the possible eliminations on the submatrices factorize the interface matrix 2. forward elimination perform a forward elimination on each submatrix (in parallel) send data to the interface problem perform a forward elimination on the interface matrix 3. back substitution perform a back substitution on the interface matrix send data to all the processors perform a back substitution on the submatrices (in parallel) figure 3. a 4-element problem (left) and its graphical representation (right). chefi triki 152 the master-slave paradigm has been chosen to implement the parallel frontal method and the library mpi has been used a message-passing protocol. besides assigning the tasks to be performed by each process, the master manages also the communication (signals and data) with the slaves. no inter-slave communication happens in our implementation. this parallel frontal method is particularly suitable for a coarse-grained parallelism. as the number of processes increases the communication becomes very time consuming and the algorithm's performance decreases. moreover, in any parallel implementation, it is necessary to take care of some important issues such as load balancing, resequencing, and code optimization. this will be the subject of the remaining part of this section. 3.3 load balancing in order to obtain an efficient load balance it is important, in our case, that matrix (3) has all the matrices , ,1 na a of equal size and, furthermore, has ,ik n a characteristic that strongly depends on the mesh topology. the load balancing problem can be transformed into a graph partitioning problem that is defined as follows: each vertex represents the computation to be performed over a data unit and each edge indicates the dependence between data units. in the case of the frontal method a data unit corresponds to an element and the dependence (edge) between elements corresponds to the eventual sharing of at least one node. the weight of an edge is defined as the number of nodes that are shared by two elements, as shown in figure 3, whereas all the vertices are assigned the weight 1. the graph partitioning problem consists in dividing the graph into disjunctive sets. each vertex can belong to only one set and the following conditions have to be satisfied: • the sums of vertex weights for all the sets are of (almost) equal value; • the sum of edges between the sets has to be as small as possible. the graph partitioning problem is known to be np-hard (wikipedia). thus, for its solution, it is necessary to use heuristic approaches since exact methods can not be satisfactory. in our implementation we have used the graph partitioning software chaco (hendrickson and lelan, 1994). this software package provides several graph partitioning heuristics and has the advantage of being extremely configurable. on the basis of an empirical consideration we have chosen to implement, in our parallel code, the spectral partitioning method combined with the kerningham-lin refinement approach (rotta, 2008). the solution quality of the graph partitioning heuristic can be seen, for example, in figure 1 for problem carre and in figure 4 for problem ourika (the colors refer to the elements to be assigned to the processes). 3.4 element resequencing in frontal methods the order in which the elements are processed is very important in order to keep the front as small as possible. as a result, once the graph partitioning has been done, it is necessary to resequence the elements to define the order in which the vertices should be processed. since the graph resequencing problem is np-hard (george and liu, 1981) we have implemented two different heuristics for its solution, the first based on the reverse ordering algorithm of cuthill and mckee (george and liu, 1981) and the second, a greedy approach. reverse cuthill-mckee ordering algorithm: the cuthill-mckee ordering algorithm divides the nodes into level sets. a level structure rooted at a node r is defined as the partitioning of v into levels 1 2( ), ( ), , ( )hl r l r l r such that 1. 1( ) = { }l r r and 2. for > 1, ( )ii l r is the set of all nodes that are adjacent to nodes in 1( )il r but are not in 1 2 1( ), ( ), , ( ).il r l r l r the cuthill-mckee algorithm orders, within each level set ( ),il r the first nodes that are neighbours of the first solving the flood propagation problem 153 node in 1( ),il r then those that are neighbours of the second node in 1( ),il r and so on. the reverse cuthillmckee algorithm reverses the order found by cuthill-mckee. figure 4. ourika test problem partitioned into 7 sets. in this work we have also implemented a heuristic based on a greedy approach. in this method the ordering is constructed by taking into account the specific features of the problem under examination so as to minimize some objective quantity at each step of the iterative process. in terms of graph resequencing, the basic ordering process used by our greedy algorithm can be summarized as follows: greedy ordering algorithm: 1. initialization: construct the undirected graph 0 g corresponding to the mesh; 2. generic iteration: for = 1, 2,k until =kg  : choose a vertex k v from k g with the minimal number of firstly occurred nodes. if there are several such vertices choose the one with the maximum number of lastly occurred nodes. eliminate k v from k g to form 1k g  . the resulting ordering is the sequence of vertices 1 2{ , , }.v v 3.5 performance optimization once a functional parallel code has been developed it is necessary to optimize its performance. for this purpose we have used two different techniques: mpe library: helps in finding the parts of the parallel program that are suitable for being optimized so that their execution time is reduced. the mpe software package performs this task by using a performance visualization approach. complier switch: this task is both architecture and compiler dependent. 3.6 mesh visualization our parallel code has been enriched by certain tools that help both the developer and the user in controlling the execution process and checking the solution quality. among the tools that are particularly useful for the solution of large scale problems we mention the visualization program plplot library (lebrun and furnish, 1994), which has been used to depict the meshes of our test problems in this paper. chefi triki 154 4. numerical results the validation of our parallel code has been done by using a set of test problems that refer to real world applications. the data concern a set of rivers located in morocco, algeria, and lebanon (dabaghi et al., 2004). the architecture platform used is the sgi origin 300 running the operating system irix 6.5 using the mipspro (fortran and c) compilers. the cpu time has been measured on the master program by using the dtime function. our experimental results have been collected in table 2. we report, for each test problem, the computational time (t) of both subroutine xfront and the whole flo2dh simulator when executed sequentially, on 4 processors (1 master and 3 slaves), and on 8 processors (1 master and 7 slaves). the corresponding speedups (s) are reported in table 2 and also depicted (for the case of 8 processors) in figure 5 (the test problems are identified by their number of nodes). the collected results show that (i) the best speedups are obtained for test problem etape2 which is characterized, according to table 1, by a low fraction of code that is not parallelizable, (ii) the worst speedup is obtained for test problem etape1 which is characterized by a high fraction of code that is not parallelizable and finaly (iii) the speedup values increase as the number of processes increases for most of the test problems with the exception of carre and madora. this is due to the fact that these two problems are very small, so that the parallelized load is not able to compensate the communication overhead. table 2. execution times (seconds) and speedups problem & sequential 4 processes 8 processes # of nodes t t s t s carre 97 xfront fes2dh 0.46 0.58 0.12 0.22 3.83 2.63 0.15 0.25 3.06 2.32 madora 437 xfront fes2dh 1.55 1.85 0.90 1.29 1.72 1.43 0.95 1.34 1.63 1.38 etape1 6413 xfront fes2dh 7.85 15.8 5.91 14.65 1.32 1.07 3.58 12.27 2.19 1.28 solstat 4223 xfront fes2dh 34.86 41.94 22.41 30.23 1.55 1.38 13.09 20.92 2.66 2.00 ourika 22292 xfront fes2dh 161.92 181.41 125.84 133.47 1.29 2.19 74.01 81.67 2.19 2.22 etape2 13876 xfront fes2dh 205.6 255.9 90.43 145.75 2.27 1.75 40.38 95.81 5.09 2.67 normal 13896 xfront fes2dh 190.16 276.86 91.4 146.8 2.08 1.89 39.7 95.2 4.79 2.91 moyen 55179 xfront fes2dh 1800 2930 886 1600 2.03 1.83 402 1113 4.48 2.63 these results deserve some comments. first, we note that the collected speedups for flo2dh are often within the theoretical bounds (expected speedups) calculated in section 3.1. as far as the parallelized subroutine xfront is concerned, the obtained speedups could be considered satisfactory especially for big problems, i.e. for a high number of nodes. the exception of test problem ourika is explained by the fact that the graph partitioning algorithm was not able, in this case, to ensure that ik n (see section 3.3). in the second comment, we want to stress the fact that even though the parallel version of flo2dh does not markedly improve the computational performance of the sequential version, it continues to have its practical and empirical importance. from the practical point of view, our implementation has permitted the direct method, and solving the flood propagation problem 155 also, but with a lesser order of importance, the simulator flo2dh, to be run faster. whenever additional fractions of the simulator are parallelized, flo2dh could further benefit in terms of efficiency. from an empirical point of view, our code could become a benchmarker for evaluating the solution quality of other codes using iterative solvers. these advantages could even become more significant whenever the solution of large scale problems is faced. we expect, indeed, from our parallel code, to be able to solve large problems (with a huge number of elements) that are unsolvable on conventional computers because of lack of memory. high performance facilities will allow, in this case, not only a temporal advantage (speedup) but also a spatial advantage (memory) by exploiting the distributed resources that could not be available otherwise. figure 5. speedups on 8 processors. 5. conclusions in this paper we dealt with the flood propagation problem and we proposed a parallel implementation of the simulator flo2dh for its solution. our parallelization effort has focused on the solution of the linear system arising in the newton method since it is the most time consuming part of the simulator. we proposed an appropriate matrix decomposition and we implemented graph-partitioning and element-resequencing strategies in order to balance the load among the processes. we tested the performance of the parallel code on a set of reallife problems and we obtained satisfactory speedups, especially for non trivial problems. our experimental experience has been restricted to the solution of a set of test problems that are characterized by a limited size. this was due to the difficulty of collecting the necessary data for real large-scale problems. we expect, however, from our parallel code, to be able to solve large scale problems that currently sequential computers, even though quite powerful, are not able to solve. finally, we notice that our parallel implementation can be improved in various ways. one of these is to perform the graph partitioning not at each iteration of the newton method, as in the current version, but only when necessary. in this case it is necessary to define a criterion that decides whether the current partitioning is still valid. this can be the subject of future research. chefi triki 156 6. references abdeouahed, m., karrakchou, s., nakhle, b. and talamali, s. 2000. elaboration et implementation hpcn de crucid. technical report, inria-rocqencourt. amestoy, p.r., duff, i.s. and l'excellent, j.-y. 1998. multifrontal parallel distributed symmetric and unsymmetric solvers. technical report ral-tr-1998-051, rutherford appleton laboratory, oxford, uk. hendrickson, b. and leland, r. 1994. chaco: software for partitioning graphs. sandia technical report sand94-2692. (http://www.cs.sandia.gov/~bahendr/chaco.html). dabaghi, f., guelmi, n., henine, h., nakhle, b., kacimi, a. and taik, a. 2004. flood forecasting and flood wave propagation modeling. t.r. d4.2 inria. froehlich, d.c. 2002. user's manual for feswms flo2dh. u.s. department of transportation. fhward-03-053. george, a. and liu, j.w. 1981. computer solution of large sparse positive definite matrices. prentice hall, qa 188.g46. hluchy, l., tran, v.d., astalos, j., dobrucky, m., nguyen, g.t. and froehlich, d. 2002. flood modeling system and its parallelization. in proc. international conference on parallel computing in electrical engineering, poland, pp. 277-281. hluchy, l., habala, o., maliska, m., simo, b., tran, v.d., astalos, j. and babik, m. 2006. grid based flood prediction virtual organization. in proc. second ieee international conference on escience and grid computing, the netherlands. mallya, j.u., zitney, s.e., choudhary, s. and stadtherr, m.a. 1997. a parallel frontal solver for large scale process simulation and optimization. aiche j., 43: 1032-1040. mpi the message passing interface standard (http://www-unix.mcs.anl.gov/mpi). mpe (library and tools) performance visualization for parallel programs (http://wwwunix.mcs.anl.gov/perfvis). lebrun, m.j. and furnish, m. 1994. the plplot plotting library (http://plplot.sourceforge.net/docbookmanual/plplot-5.9.9.pdf). rotta, r. 2008. multi-level graph clustering (http://studiy.tu-cottbus.de/~clustering/algorithms : refinement #kernighan-lin_refinement). scott, j.a. 2001. the design of a portable parallel frontal solver for chemical process engineering problems. computers in chemical engineering, 25: 1699-1709. scott, j.a. 2002. parallel frontal solvers for large sparse linear systems. technical report ral-tr-2002-033, rutherford appleton laboratory, oxford, uk. wikipedia. 2012. (http://en.wikipedia.org/wiki/graph-partitioning). received 9 may 2011 accepted 15 october 2011 http://studiy.tu-cottbus.de/~clustering/algorithms squ journal for science, 2023, 28(1), 1-9 doi:10.53539/squjs.vol28iss1pp1-9 sultan qaboos university 1 toxicological evaluation of the leaves of mangifera indica l. (mango) on albino rats (rattus norvegicus) tajudeen olanrewaju yahaya 1 *, titilola f. salisu 2 , esther o. oladele 3 , clement yaro 4 , nura iliyazu 1 , adam tukur 1 , abdulrazaq izuafa 1 and muhammad a. yari 1 . 1 department of biological sciences, federal university birnin kebbi, pmb 1157, kebbi state, nigeria; 2 department of zoology and environmental biology, olabisi onabanjo university, agoiwoye, ogun state; 3 biology unit, distance learning institute, university of lagos, nigeria; 4 department of animal and environmental biology, university of uyo, akwa ibom state, nigeria *email: yahaya.tajudeen@fubk.edu.ng. abstract: the increasing use of plant-based medicines necessitates safety evaluations of all medicinal plants. this study evaluated the effects of mango (mangifera indica) leaf extracts on albino rats (rattus norvegicus). the phytochemistry of the plant’s extract was evaluated, followed by a determination of its acute toxicity using 24 rats. thereafter, the chronic toxicity of the extract was determined using another set of 24 rats, separated into four groups of six rats each. rats in group 1 (the control) were administered distilled water, while groups 2, 3, and 4 received daily doses of 1000, 2000, and 3000 mg kg -1 body weight, respectively. the rats’ body weights and reactions were monitored for 90 days before blood, liver, and kidney samples were collected for hematological and histopathological examinations. the phytochemistry revealed phenols, alkaloids, tannins, flavonoids, steroids, glycosides, and saponins. the acute toxicity test recorded no mortality at doses up to 5000 mg kg -1 , and all the rats behaved normally, except for one that was sluggish. the chronic toxicity test revealed no significant (p>0.05) weight difference between the control and treated rats. the packed cell volume, hemoglobin, and red and white blood cells of the rats fed 2000 and 3000 mg were significantly altered (p<0.05), while lymphocytes exhibited no significant alterations in any of the groups. the treated rats’ livers revealed dose-dependent necrosis, whereas their kidneys showed atrophy and epithelial cell degeneration. the results obtained suggest that a single dose of the plant’s extract is not harmful, but repeated high-concentration dosing for a long time may result in toxicity. keywords: acute toxicity; livers; medicinal plants; necrosis; red blood cells. تقييم السموم في أوراق مانغيفيرا إنديكال مانجو )على جرذان ألبينو( راتوس نورفيغيكوس تاج الدين أوالنريواجو يحيى ، تيتيال فوزية ساليسو ،إستر أو. أوالدي، كليمنت يارو ، نورا إليازو، عبدالرزاق إيزوافا، محمد أ. ياري مانجيفيرا )المانجو أوراق مستخلصات آثار الدراسة هذه قيمت .الطبية النباتات جميع في لألمان تقييمات إجراء النباتية لألدوية المتزايد االستخدام يستلزم الملخص: تحديد تم ، ذلك وبعد را.فأ 24باستخدام حادة سمية ذلك وتلت النبات، الستخراج النباتية الكيمياء تقييم تم وقد .(نورفيجيكوس راتوس )البرص فئران على (إنديكا ) 1 المجموعة في الجرذان إعطاء تم .فئران ستة مع منها كل مجموعات، أربع إلى مقسمة فأرا، 24من أخرى مجموعة باستخدام للمستخلص المزمنة السمية مراقبة تم .التوالي على الجسم، وزن من كغم 1ملغم 3000و 2000و 1000من يومية جرعات 4و 3و 2المجموعات تلقت بينما المقطر، الماء (المكافحة عن النباتية الكيمياء كشفت .النسج أمراض وعلم الدم فحوصات إلجراء والكلى والكبد الدم من عينات جمع قبل يوما 90لمدة وتفاعالتها الجرذان جسم أوزان ملغم 5000إلى تصل بجرعات وفاة أي الحادة السمية إختبار يسجل ولم .والصابونات والجليكوزيدات والستيرويدات والفالفونويدات والتانينات والقلويات الفينوالت عنصر بين الوزن في (p>0.05)كبير فرق عن المزمنة السمية إختبار يكشف لم .بطيئة كانت واحدة باستثناء طبيعي، بشكل الجرذان جميع وتتصرف ،-1الكغم من الخاليا تظهر لم بينما ، (p<0.05)كبير بشكل للجرذان والبيضاء الحمراء الدم وخاليا والهيموغلوبين، المعبأة، الخاليا حجم تغيير تم فقد .المعالجة والجرذان التحكم الخاليا وتنكس ضمورا الكلى أظهرت حين في الجرعة، على يعتمد نخر عن المعالجة الجرذان أكباد كشفت .كبيرة تغييرات أي المجموعات جميع في اللمفاوية يؤدي قد طويلة لفترة التركيز عالية الجرعات تكرار ولكن ضارة، ليست النبات مستخلص من واحدة جرعة أن إلى عليها الحصول تم التي النتائج تشير .الظهارية .السمية إلى .الحمراء الدم خاليا النخر، الطبية، النباتات الكبد، الحادة، السمية :الكلمات المفتاحية mailto:yahaya.tajudeen@fubk.edu.ng. toxicological evaluation of the leaves of mangifera indica l. (mango) 2 1. introduction here has been a global renaissance in plant-based medicines since the middle of the 19 th century because they are affordable, potent, and simple to prepare. worldwide, approximately 21,000 medicinal plants have been documented for disease treatment [1]. the renaissance is partly because plants contain many bioactive compounds used to produce pharmaceutical drugs [2]. at the minimum, 30% of pharmaceutical drugs are derived directly or indirectly from medicinal plants [3]. plant-based medicines are used to treat ailments by at least 80% of the world’s population [4]. mango (mangifera indica l.), which belongs to the family anacardiaceae, is a cosmopolitan tree, whose parts are often used to make plant-based medicines [5]. extracts of m. indica are used to treat diabetes, bronchitis, diarrhea, asthma, kidney diseases, scabies, respiratory problems, syphilis, and urinary disorders [6-8]. the plant is antimicrobial, antioxidant, antidiabetic, and immunomodulatory, and it combats tumors [4]. m. indica contains abundant minerals, such as nitrogen and potassium, and also contains protein [9, 4]. the plant is also rich in phytochemicals, including mangiferin, phenolic acids, benzophenones, flavonoids, carotenoids, quercetin, isoquercetin, ascorbic acid, and tocopherols [10-12]. the oil from m. indica contains monoterpenes, sesquiterpenes, non-terpenoid hydrocarbons, oxygenated hydrocarbons, α-gurjunene, transcaryophyllene, α-humulene, α-selinene, α-glucosidase, and camphor [10, 13]. in recent times, however, there has been a growing concern about the safety of plant-based medicines. studies have shown that some plant-based medicines are toxic due to their constituents, while others induce toxicity due to interactions and contamination during production [2]. the toxic effects of plant-based medicines on humans depend on the chemical composition of the medicine and the extraction methods used, as well as on the state of the consumer’s cell membrane, cell surface, tissues, and extracellular matrix [10, 12]. thus, there is a need for toxicological studies of all plants used in making plant medicines [8]. although there are several studies on the health-promoting efficacy of m. indica, there is a dearth of studies on the toxicity of the plant [10, 13]. consequently, this study evaluated the toxicity of m. indica leaf extracts in albino rats (rattus norvegicus). 2. materials and methods 2.1 management of experimental animals twenty-four (24) male and female albino rats (rattus norvegicus) with a mean weight of 185±10 g and aged 50 days were used for this study. the rats were housed in well-ventilated metallic cages (six rats per cage) in a well-ventilated animal house at a room temperature of about 32 °c. before beginning the experiment, the rats were given 14 days to acclimate to their new environment. water and pellet feeds from premier feed mills in ibadan, nigeria, were freely available to the rats. 2.2 collection of plant materials and identification fresh leaves of m. indica were plucked within the kebbi metropolis in february 2021. the leaves were identified by a botanist in the department of biological sciences, federal university birnin kebbi, kebbi state, nigeria. a sample of the authenticated materials was deposited in the department’s herbarium with voucher number fubk/a/6. 2.3 preparation and extraction the plant’s leaves were gently washed with distilled water, dried in the shade, pulverized into powder, and sieved through a stainless-steel mesh with a diameter of 200 mm to ensure size consistency. to extract the bioactive components, 150 g of the powdered material was soaked in 900 ml of 98% methanol for 48 hours. the extract obtained was filtered using a muslin cloth, and the methanol was evaporated using a rotary evaporator at 45 °c until a constant dry weight of the extract was achieved. the dried extract was kept in a desiccator. 2.4 qualitative screening of the extracts the qualitative screening was conducted using conventional procedures as detailed by yahaya et al. [2]. test for flavonoids a small quantity of 10% ferric chloride solution was mixed with 0.5 g of the extract. the presence of flavonoids was indicated by the appearance of a green or blue color. test for tannins five milliliters (5 ml) of water were added to 0.5 g of the extract, followed by a few drops of 10% ferric chloride. the presence of tannins was indicated by a blue-black, green, or blue-green precipitate. test for alkaloids for 2 minutes, 0.2 g of the extract was boiled with 2% h2so4. a few drops of dragendorff’s reagent were added after the liquid was filtered. the presence of alkaloids was revealed by an orange-red precipitate. t tajudeen olanrewaju yahaya et al. 3 test for steroids one milliliter (1 ml) of the extract and 5 ml of anhydrous acetic acid were mixed thoroughly. four (4) drops of the above mixture were placed in a porcelain dish, and one drop of concentrated h2so4 was added. a change in color from rose, through red, violet, and blue, to green showed the extract contained steroids. test for glycosides one milliliter (1 ml) of the extract was mixed with 1 ml of glacial acetic acid containing one drop of ferric chloride solution. exactly 1 ml of concentrated h2so4 was added to the liquid, which resulted in the development of two layers. the presence of glycosides was shown by the development of a brown ring at the interface of the two layers. test for saponins in a graduated cylinder, 1 ml of the extract was diluted to 20 ml with distilled water, and wa s shaken for 15 seconds. the presence of saponins was shown by the formation of a foam layer after 15 minutes. test for phenols exactly 0.5 g of the extract was dissolved in 2 ml of distilled water, and a small quantity of ferric chloride was added. the presence of phenols was determined by the appearance of a red, purple, or green color. 2.5 acute toxicity test the acute toxicity of m. indica extracts was determined using the "classical ld50" approach as outlined by trevan [15]. twenty-four (24) rats (males and females) were randomly divided into four groups, each of six rats. group 1 was the control, while groups 2, 3, and 4 were orally administered 1000, 3000, and 5000 mg of m. indica leaf extract per kg of body weight of the rats, respectively. the rats were monitored for 72 hours to establish the general toxicity of the extracts based on observation of behavioral change. 2.6 chronic toxicity test a new batch of 24 rats was separated into four groups, each containing six rats. m. indica leaf extracts were administered to groups 2, 3, and 4 on a daily basis in doses of 1000, 2000, and 3000 mg kg -1 body weight of the rats, respectively. group 1 was designated as the control group, with rats receiving only standard feed and water. the rats’ weights were tracked and general observations recorded for 90 days before the animals were sacrificed via cervical dislocation. hematological tests were performed on blood samples, and histological examinations were performed on the liver and kidneys. 2.7 body weight measurement the rats’ body weights were measured at the start of the experiment using a digital weighing scale manufactured by kern, germany. throughout the rest of the experiment, the measurements were taken every other day in the morning. 2.8 hematological examination each rat was held firmly to a workbench using office pins. about 2.5 ml of blood was drawn from the rats’ tails into ethylenediamine tetra acetic acid (edta) bottles using a 5 ml syringe and a 20-gauge needle. the sysmex auto-analyzer was used to assess the amounts of blood parameters, including packed cell volume (pcv), hemoglobin (hb), white blood cells (wbc), red blood cells (rbc), and lymphocytes (lym). 2.9 histopathological analysis the rats’ liver and kidney tissues were processed for histological analysis, as described by yahaya et al. [16]. the rats’ chests were cut open in a dorsal-ventral orientation with a surgical blade. the livers and kidneys were collected, and about 5 mm of each tissue was stored in 10% neutral buffered formalin. the tissues were dehydrated in increasing volumes of alcohol before being embedded in paraffin wax (65, 80, and 100%). with a rotary microtome (model yr421), the embedded tissues were sectioned at 5 μm, placed on glass slides, and air-dried. hematoxylin and eosin dyes were used to stain the slides, which were then examined under a light microscope for histological abnormalities. 2.10 data analysis all of the analyses were performed using the statistical package for social sciences (spss) version 20 for windows. the analysis of variance (anova) was used to compare data between the test and control groups. the statistical significance level was set at p<0.05. toxicological evaluation of the leaves of mangifera indica l. (mango) 4 3. results 3.1 phytochemicals in the extract table 1 below shows the phytochemicals detected in the crude extracts of m. indica leaves. phenols and flavonoids were abundant, while glycosides, alkaloids, tannins, saponins, and steroids were present in moderate amounts. table 1. phytochemicals detected in the crude extracts of m. indica leaves. ++ indicates abundantly available ; + indicates moderately available 3.2 acute toxicity of the extracts table 2 shows the reactions of the rats treated with different doses of m. indica leaf extracts. no deaths were recorded, and all the rats behaved normally, except for one in the group fed 5000 mg kg -1 , which was sluggish. table 2. reactions of the treated rats (n = 6 per group) to different doses of m. indica leaf extracts. group dosage (mg kg -1 body weight) observation period (hour) behavioral change mortality 1 distilled water 72 none 0 2 1000 72 none 0 3 3000 72 none 0 4 5000 72 sluggishness (n=1) 0 3.3 effects of the extracts on body weight the body weights of the rats treated with m. indica leaf extracts are shown in table 3. compared with the control, no significant differences (p>0.05) were observed. table 3. change in body weights of the treated rats (n = 6 per group) to different doses of m. indica leaf extracts. dosage (mg kg -1 body weight) initial body weight (g) final body weight (g) control (distilled water) 197.33±5.32 a 210.34±6.31 a 1000 ml 200.01±2.31 a 205.39±6.09 a 2000 ml 198.35±1.31 a 212.00±3.22 a 3000 ml 201.33±3.34 a 206.15±3.54 a values were expressed as mean ± sd (n = 6); values with the same subscript "a" are not significantly different from control at p> 0.05 (anova). 3.4 effects of the extracts on hematological parameters table 4 compares the hematological parameters of rats fed m. indica leaf extracts to those of the control rats. the packed cell volume (pcv), hemoglobin (hb), and red blood cells (rbc) of the treated rats were reduced, and this reduction was significant (p<0.05) in the rats fed 2000 and 3000 mg of the extracts. the white blood cells (wbc) of the treated rats were increased, but significantly only in the group fed 3000 mg. there was no noticeable change in the lymphocytes (lym) of the treated rats. alkaloids inference tannins + saponins + phenols ++ steroids + flavonoids ++ glycoside + tajudeen olanrewaju yahaya et al. 5 table 4. hematological parameters of rats treated with m. indica leaf extracts. parameters control 1000 mg 2000 mg 3000 mg pcv (l l-1) 28.18±2.83 a 26.63±3.49 a 25.90±2.50 b 22.67±2.7 b hb (g dl-1) 11.63±1.83 a 11.00±0.89 a 0.9.37±0.58 b 6.82±0.22 b wbc (mc mm-3) 1.28±0.87 a 1.31±0.55 a 1.59±0.40 a 2.99±1.6 b rbc (mc mm-3) 5.06±0.78 a 4.94±0.60 a 3.91±0.18 b 3.64±0.67 b lym (c µl-1) 82.83±6.49 a 82.17±1.73 a 82.27±0.99 a 82.63±0.95 a values were expressed as mean ± sd (n = 6); mean values with different subscripts "a" and "b" along the same row are statistically different from control at p< 0.05 (anova). pvc = packed cell volume; hb = hemoglobin; wbc = white blood cells; lym = lymphocytes. 3.5 histopathological effects of the extracts figures 1a–d show the liver tissues of the control and treated rats. normal hepatocytes were observed in the liver of the control rats, while dose-dependent necrosis was observed in the treated rats. the kidney tissues of the control and treated rats are shown in figures 2a–2d. normal hepatocytes were observed in the control group, while the rats fed 1000, 2000, and 3000 mg kg -1 of the extracts revealed mild atrophic glomerulus, tubular atrophy, and epithelial cell degeneration. a b c d figure 1. photomicrography of the liver tissues of the control and treated rats. a = control rats showing normal hepatocytes. b = rats treated with 1000 mg kg -1 m. indica extract showing mild necrosis. c = rats treated with 2000 mg kg -1 m. indica extract showing moderate necrosis d = rats treated with 3000 mg kg -1 m. indica extract showing moderate necrosis. toxicological evaluation of the leaves of mangifera indica l. (mango) 6 a b c d figure 2. photomicrography of the kidney tissues of the control and treated rats. a = control rats showing normal glomerulus b = rats treated with 1000 mg kg -1 m. indica extract showing mild atrophic glomerulus c = rats treated with 2000 mg kg -1 m. indica extract showing tubular atrophy d = rats treated with 3000 mg kg -1 m. indica extract showing epithelia cell degeneration (outer layer) 4. discussion the toxicity of mangifera indica leaves was evaluated in this study. the study was conceived to determine the safe doses of the plant extract to prevent or minimize its health hazards among users worldwide, particularly in nigeria. table 1 shows that the plant contains bioactive substances, including phenolic acids, alkaloids, tannins, flavonoids, steroids, glycosides, and saponins. these substances are well known for their health-boosting activities, but some of them could induce toxicity at certain doses. in the current study, the acute toxicity test of the plant’s extract revealed no mortality nor any abnormality at doses up to 5000 mg kg -1 (table 2), which is the upper limit at which a single dose of an extract is considered non-toxic [2, 17]. table 3 further demonstrates the plant’s non-toxicity, as there was no significant difference in body weight between the treated and control rats. these results are consistent with those of zhang et al. [18], ahomadegbe et al. [19], easl [20], and reddeman et al. [21], all of whom reported the non-toxicity of the plant. table 4, however, shows that long-term dosing (90 days) at 2000 and 3000 mg kg -1 body weight significantly altered the hematological parameters of the treated rats. the packed cell volume (pcv), hemoglobin (hb), and red blood cells (rbc) were reduced, while the white blood cells (wbc) were increased. this result contradicts that of ogbe et al. [22] and abidakun et al. [23], who observed an increase in pcv, hb, and rbc in experimental animals treated with mango extract. the inconsistency of the current study with the previous ones might be due to the longer duration and higher concentrations used in this study. in contrast to the current study’s 90-day treatment with 1000, 2000, and 3000 mg kg -1 body weight, ogbe et al. [22] and abidakun et al. [23] gave experimental animals 20 mg for 14 days and 1 mg for 40 days, respectively. the plant contains alkaloids and saponins, which, at high concentrations and duration, can accumulate to toxic levels and tajudeen olanrewaju yahaya et al. 7 destroy blood cells [24, 25]. the plant also contains tannins, which have been implicated in iron deficiency, resulting in anemia [26]. figures 1a-d and 2a-d further show that m. indica extracts can be toxic at high concentrations and over long periods of time. the treated rats’ livers developed dose-dependent necrosis, while their kidneys developed atrophic glomerulus, tubular atrophy, and epithelial cell degeneration. atiba et al. [27] reported abnormal liver morphology, such as an enlarged central vein and reduced sinusoids, in rats treated with m. indica leaf extracts for a long time. zhang et al. [18] also reported enlargement of liver and kidney tissues in rats dosed with m. indica for 90 days. amien et al. [28] and nadella and kumar [29], on the other hand, found that m. indica has chemo-protective effects on the kidneys and livers. however, the studies that reported chemoprotective effects used lower concentrations and shorter durations. for instance, amien et al. [28] dosed experimental animals with 300 mg kg -1 for 14 days, while nadella and kumar [29] dosed them with 150 mg kg -1 for 10 days. the reported histopathological effects could be due to potentially toxic phytochemicals in the extracts, primarily alkaloids, saponins, and tannins. high doses and prolonged use of an alkaloid-containing substance can result in hepatocyte necrosis and renal failure [30, 31]. tannins have also been linked to liver necrosis and kidney problems [32]. additionally, liver and kidney damage due to necrosis of liver cells and renal tubules has been reported among mice treated with high concentrations of saponins [33, 34]. toxicants primarily target the kidneys and liver because these organs process all foreign substances in the body [2, 35]. 5. conclusion the results showed that m. indica leaves contain pharmacologically important phytochemicals such as mangiferin, phenolic acids, flavonoids, carotenoids, alkaloids, tannins, quercetin, isoquercetin, ascorbic acid, and tocopherols. however, some of these compounds, especially tannins, saponins, and alkaloids, could be toxic at certain doses. a single dose of the plant’s extract is not expected to be toxic, as it is non-toxic at doses up to 5000 mg kg 1 , which is the maximum dose at which an extract can be considered non-toxic. however, repeated high-concentration and long-duration dosing may induce toxicity, as evidenced by the alteration of the hematological parameters and tissues of the treated rats. conflict of interest the authors declare no conflict of interest. acknowledgment not applicable ethical statement this study was conducted in accordance with the ethical standards of the european and german animal welfare legislation, declaration principles set out by helsinki and the national institutes of health guidelines for care and use of animals in research. all protocols were approved by the local ethics committee of the federal university birnin kebbi, nigeria (regulation cee 86/609). references 1. gururaja, g.m., mundkinajeddu, d., kumar, a.s., dethe, s.m., allan, j.j., agarwal, a. evaluation of cholesterol-lowering activity of standardized extract of mangifera indica in albino wistar rats. pharmacognosy research, 2017, 9(1), 21-26. https://doi.org/10.4103/0974-8490.199770. 2. yahaya, o.t., oladele, e.o., bunza, m.d.a., yusuf, a.b., izuafa, a., danjuma, j.b. hematotoxicity and nephrotoxicity of long-term administration of guiera senegalensis (j.f. gme), cassia occidentalis (linn), and ziziphus mauritiana (lam) leaves obtained in birnin kebbi, nigeria. journal of herbmed pharmacology, 2022, 11(3), 367-374. https://doi.org/10.34172/jhp.2022.42. 3. ramírez-atehortúa, a.m., morales-agudelo, l., osorio, e., lara-guzmán, o.j. the traditional medicinal plants cuphea calophylla, tibouchina kingii, and pseudelephantopu spiralis attenuate inflammatory and oxidative mediators. evidencebased complementary and alternative medicine, 2018. https://doi.org/10.1155/2018/1953726. 4. pan, j., yi, x., wang, y., chen, g., he, x. benzophenones from mango leaves exhibit alpha glucosidase and no inhibitory activities. journal of agricultural and food chemistry, 2016, 64(40), 74757480. https://doi.org/10.1021/acs.jafc.6b02404. 5. guo, l., gong, s., wang, y., sun, q., duo, k., fei, p. antibacterial activity of olive oil polyphenol extract against salmonella typhimurium and staphylococcus aureus: possible mechanisms. foodborne pathogens and diseases, 2020, 17, 396-403. https://doi.org/10.1089/fpd.2019.2713. 6. kulkarni, v.m., rathod, v.k. extraction of mangiferin from mangifera indica leaves using three phase partitioning coupled with ultrasound. industrial crop and product, 2014, 52, 292-297. https://doi.org/10.1016/j.indcrop.2013.10.032. 7. kumar, y., kumar, v., sangeeta, c. comparative antioxidant capacity of plant leaves and herbs with their anti-oxidative https://doi.org/10.4103/0974-8490.199770 https://doi.org/10.34172/jhp.2022.42 https://doi.org/10.1155/2018/1953726 https://doi.org/10.1021/acs.jafc.6b02404 https://doi.org/10.1089/fpd.2019.2713 http://dx.doi.org/10.1016/j.indcrop.2013.10.032 toxicological evaluation of the leaves of mangifera indica l. 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mnemonics; thermodynamics; maxwell equations. جهاز متطور لتقوية الذاكرة في العالقات الديناميكية الحرارية يونجهن كيم و رينجراج سلفراج اقتراحه بشكل دائرة ديناميكية حرارية. تم جهاز متطور لتقوية الذاكرة في العالقات الديناميكية الحرارية ما بين متغيرات الحالة والمستطاعات :ستخلصم ومعادالت maxwellومعادالت legendre(، عالقات g,a,u&h( ومربع خارجي )t,p,v&sإلى مربع داخلي ) bornبناًء على فصل مربع الـ الدائرة الديناميكية الحرارية تحتوي على سهم ة.حساب المتغيرات ومعادالت التفاضلية في متغيرات الديناميكية الحرارية أصبح باألمكان استذكارها بسهول في وسطها الذي يستخدم الستخالص عالمة العالقات الديناميكية الحرارية بسهولة ومن دون مجهود. .ماكسويلالهندسة الكيميائية، مقويات الذاكرة، الديناميكية الحرارية، معادالت : كلمات مفتاحية 1. introduction arious relations, such as legendre transforms, maxwell equations, equations to compute variables, and differential equations for variables, are found in thermodynamics [1-3]. despite their best efforts in studying the actual logic that underlies the thermodynamic relations, many students have trouble remembering these relations between the four state variables (temperature, t; pressure, p; volume, v; entropy, s) and the four thermodynamic potentials (internal energy, u; helmholtz energy, a; enthalpy, h; gibbs energy, g). therefore, several mnemonic schemes to help recall the thermodynamic relations based on the famous max born square [1-5] have been developed. using the max born square, a three-dimensional extension was proposed by phillips [3] and a similar thermodynamic cube was suggested by pate [2]. a simpler mnemonic diagram for thermodynamic relationships was also proposed by rodriguez and bralnard [5] and was modified as several mnemonic patterns [4]. as an improved mnemonic tool, a circle type named ‘thermodynamic circles’ was also proposed by natarajan [1]. other diagrams such as an energy pie have been suggested to provide differential expressions of the potentials as well as maxwell relations [6]. however, these schemes still require complicated rules to remember the positive or negative signs in front of the terms in the thermodynamic relations [4,5]. three-dimensional cube [2] or octahedral mnemonic devices [3] are complicated and also difficult to remember. to overcome this drawback, separating the max born square into two sections was suggested, and this makes recalling the equations much more straightforward [7]. the zhao model is a very powerful tool compared to the others, but decision as to sign (+ or –) still remains challenging. therefore, the mnemonic circle found in the thermodynamic field is suggested here based on separating the max born square into an inner square (t, p, v, and s) and an outer circle (g, a, u, and h). the thermodynamic circle has a cross-arrow at its center and this constitutes a key component for determining the sign of each of the relations. this cross-arrow constitutes an improvement upon the mnemonic device proposed by zhao [7] and enables one to determine the signs of thermodynamic variables intuitively . v an improved mnemonic device for thermodynamic relations 103 2. suggested mnemonic as shown in figure 1(a), the thermodynamic circle is composed of three components; an inner square (four state variables), an outer circle (four thermodynamic potentials), and a cross-arrow (sign determination). the direction of the cross-arrow determines the signs of all relations, and thus it acts as a vector which is fully described by both a magnitude and a direction. for example, when the path of some relation follows the reverse direction to the ts arrow, it has a negative sign in the target relation. the product of ts and pv has same dimension unit as thermodynamic potentials with outer circle (g, a, h, and u). figure 1. scheme to recall the legendre transforms for four thermodynamic potentials. 3. use of the mnemonic tool 3.1 relations between neighboring potentials (u, a, h, and g) legendre transforms of the four thermodynamic potentials are determined in the following way. as shown in figure 1a, internal energy (u) is separately formed by two different neighboring potentials,. by drawing a curved arrow from one corner of the potential to target potential, passing by the nearer center-arrow (ts or vp) diagonally, the target potential has two relations. for example, the curved arrow from h, passing by the nearby vp arrow (opposite direction, therefore negative sign), forms u equal to h – pv. in addition, the curved arrow from a, passing by the nearby ts arrow (same direction, therefore positive sign) forms u equal to a + ts. other potentials (h, g, and a) are formulated in the same way, as in with figures 1b-1d. with intuitive decision of the sign from the directions of ts and vp, legendre transforms of the four potentials can be recalled easily as u = h – pv = a + ts, h = u + pv = g + ts, g = h – ts = a + pv, and a = u – ts = g – pv. 3.2 differential forms of the potentials the differential expressions (du, da, dh, and dg) for the four thermodynamic potentials are easily determined by drawing two curved arrows. as shown in figure 2a, two curved arrows depart from p and t toward the derivative of the target potential (du) crossing at the intersection of the two arrows (nearby center-arrow), following which the direction of the curves tds and pdv mirror each other. thus, (+tds – pdv) gives du. in the same fashion, figures 2b -2d provide dh = tds + vdp, dg = –sdt + vdp, and da = –sdt – pdv. again, all signs (+ or –) of derivatives are determined by the direction of the ts and vp arrows. rengaraj selvaraj and younghun kim 104 figure 2. scheme to recall the differential form of four thermodynamic potentials. 3.3 relations for compute variables (t, p, v, and s) one can also remember the relations for thermodynamic state variables from the partial derivatives of the thermodynamic potentials. this is schematically shown in figure 3, and the sign of the partial differential of a potential with respect to the conjugate variable is again determined by the ts and vp arrows. for example, as shown in figure 3a, two curved arrows depart from t and pass through s, then reaching the nearby potentials (h and u) and finally terminating in the reverse direction (p and v). thus the two curved arrows give t = (∂h/∂s)p = (∂u/∂s)v. since the two curved arrows follow the same direction as the ts arrow, the partial differential has a positive sign. similarly, other variables can be recalled, based on figures 3b-3d, as v = (∂h/∂p)s = (∂g/∂p)t, s = –(∂g/∂t)p = –(∂a/∂t)v and p = –(∂a/∂v)t = –(∂u/∂v)s. figure 3. scheme to recall the compute variables from partial differentials of four thermodynamic potentials with respect to the conjugate variables. an improved mnemonic device for thermodynamic relations 105 3.4 maxwell relations the maxwell relations have the form of partial derivatives of the four thermodynamic state variables (t, p, v, and s), and, with the same diagrams, one can also easily remember the maxwell equations using simple schemes (figure 4). in a similar way to that above, two curved arrows separately depart from t and p, pass through v and s to reach s and v respectively (figure 4a). since the direction of the psv curve is opposite to the vp arrow, the partial derivative has a negative sign. namely, this yields the partial derivative of t (or p) with respect to v (or s) at constant s (or v), and so one can obtain (∂t/∂v)s = –(∂p/∂s)v. other maxwell equations can be obtained as shown in figures 4b -4d: (∂v/∂s)p = (∂t/∂p)s; (∂v/∂t)p = –(∂s/∂p)t; –(∂p/∂t)v = –(∂s/∂v)t. figure 4. scheme to recall the maxwell relations involving the four thermodynamic state variables. 4. impact on student learning to confirm the real effectiveness and efficiency of this tool for the recall of thermodynamic relations, a serial test was carried out on junior students (98) in college. firstly, after teaching the actual logic of thermodynamic relations (legendre transforms, maxwell equations, equations to compute variables, and differential equations for thermodynamic variables), a test of their memorization of the 4 relations was conducted. most of the students only recalled legendre transforms. as the next step, the zhao model was used to recall the thermodynamic relations. about 29.6% of students succeeded in recalling the 4 relations within 10 mins, but the signs in front of the terms were still confused. finally, the mnemonic tool proposed herein was taught to students, and ca. 77.5% of the students were found to have memorized all the relations perfectly. the students were surprised at themselves for recalling the thermodynamic relations so accurately and readily. 5. conclusion the thermodynamic circle is a mnemonic device that allows for easier recall of the thermodynamic relations between thermodynamic state variables and potentials. separating the max born square into two components was first suggested by zhao, and the circle-type mnemonic device suggested here is an improved form. the thermodynamic circle has a cross-arrow at its center which is helpful to intuitively determine the sign of various terms (sign of ts/vp, partial derivatives, and maxwell equations). the author would like to add a whimsical tip for recalling the energy conservation law. most of us use the qwerty keyboard daily, and we can find the following conservation law equation at our fingertips: q + w = e = rt. rengaraj selvaraj and younghun kim 106 references 1. natarajan, k., graphical summaries for maxwell relations of closed and open thermodynamic systems. inter. j. mech. eng. edu., 2014, 42, 1-17. 2. pate, s.f., the thermodynamic cube: a mnemonic and learning device for students of classical thermodynamics. am. j. phys., 1999, 67, 1111-1113. 3. phillips, j.m., mnemonic diagrams for thermodynamic systems. j. chem. edu., 1987, 64, 674-675. 4. pogliani, l. and la mesa, c., the mnemonic diagram for thermodynamic relationships. j. chem. edu., 1992, 69, 808-809. 5. rodriguez, j. and bralnard, a.j., an improved mnemonic diagram for thermodynamic relationships. j. chem. edu., 1989, 66, 495-496. 6. fieberg, j.e. and girard, c.a., mnemonic device for relating the eight thermodynamic state variables: the energy pie. j. chem. edu., 2011, 88,1544-1546. 7. zhao, j.c., a mnemonic system for thermodynamics. mrs bull., 2009, 34, 92-94. received 1st august 2016 accepted 4 september 2016 squ journal for science, 2015, 20(1), 29-38 © 2015 sultan qaboos university 29 an efficient parallel gauss-seidel algorithm on a 3d torus network-on-chip khaled day 1 * and mohammad h. al-towaiq 2 1 *department of computer science, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. 2 jordan university of sciences and technology, jordan.*email: kday@squ.edu.om. abstract: network-on-chip (noc) multi-core architectures with a large number of processing elements are becoming a reality with the recent developments in technology. in these modern systems the processing elements are interconnected with regular noc topologies such as meshes and tori. in this paper we propose a parallel gaussseidel (gs) iterative algorithm for solving large systems of linear equations on a 3-dimensional torus noc architecture. the proposed parallel algorithm is o(nn 2 /k 3 ) time complexity for solving a system with a matrix of order n on a k×k×k 3d torus noc architecture with n iterations assuming n and n are large compared to k. we show that under these conditions the proposed parallel gs algorithm has near optimal speedup. keywords: network-on-chip; 3d torus; parallel algorithm; linear system of equations; gauss-seidel method. خوارزمية غاوس سيذال متوازية فعالة باستخذام شبكة تورس على رقاقة ثالثية األبعاد و محمذ طويق دايخالذ أصبحج األَظًت انًخعذدة انُٕاة راث انشبكت عهى سقاقت ٔاحذة ٔانخً ححخٕي عهى عذد كبٍش يٍ ٔحذاث انًعانجت حقٍقت ٔاقعٍت بفضم :ملخص ابك انخطٕساث انحذٌثت فً يجال انخكُٕنٕجٍا. فً ْزِ األَظًت انًخطٕسة ٌخى سبظ ٔحذاث انًعانجت بشبكاث راث أشكال ُْذسٍت يُخظًت كشكم انخش نحم أَظًت يعادالث خطٍت راث أحجاو كبٍشة فً صيٍ يعانجت ال يخٕاصٌت حكشاسٌت خٕاسصيٍت غأس سٍذال . َقخشح فً ْزِ انٕسقت ٔشكم حٕسس o(nnحذٔد صٌخجأ 2 /k 3 ٔعذد k×k×kباسخخذاو شبكت حٕسس ثالثٍت األبعاد بحجى nٔرنك نحم َظاو يعادالث خطٍت ٌكٌٕ فٍٓا عذد انًعادالث ( انًخٕاصٌت انًقخشحت راث حسشٌع خٕاسصيٍت. َبشٍْ أَّ فً ْزِ انحانت حكٌٕ انkكبٍشة يقاسَت بقًٍت n ٔnيع فشضٍت أٌ قٍى nحكشاس فً انخٕاسصيٍت ٌكاد ٌكٌٕ األيثم. .غأس سٍذالطشٌقت ٔ يخٕاصٌت، َظاو يعادالث خطٍت خٕاسصيٍتشبكت عهى سقاقت ٔاحذة، شكم حٕسس ثالثً األبعاد، : كلمات مفتاحية 1. introduction n this paper we propose a parallel gauss-seidel algorithm based on message passing for solving a system of linear equations: ax = b where a is an n by n dense matrix, b is a known n-vector and x is an n-vector to be determined. systems of linear equations are of immense importance in mathematics, and to its applications to areas in the physical sciences, economics, engineering, social sciences and biological sciences, among many others. even complicated situations are frequently approximated by a linear model as a first step. the solution of a system of nonlinear equations is achieved by an iterative procedure involving the solution of a series of linear equations. similarly, the solution of ordinary differential equations, partial differential equations and integral equations using the finite difference method leads to a system of linear or nonlinear equations. linear equations also arise frequently in numerical analysis. there are two classes of methods for solving linear systems of equations: direct and iterative methods. a direct method is a fixed number of operations carried out once, at the end of which the solution is produced. gauss elimination and related strategies on a linear system is an example of such methods. direct methods are often too expensive in terms of computation time, memory requirements, or both. as an alternative, linear systems are usually solved with iterative methods. a method is called iterative when it consists of a basic series of operations which are carried out over and over again until the answer is produced, some exception error occurs, or a limit on the number of iterations is exceeded [1]. for early parallel computers such as the cm-2 and the intel ipsc/860 [2], it was observed that the single iteration steps of most iterative methods offered too little opportunity for parallelism in comparison with, for instance, direct methods for dense matrices. in particular, the inner products required per iteration for many iterative methods were i khaled day and mohammad h. al-towaiq 30 identified as obstacles because of communication. this has led to attempts to combine iteration steps, or to combine the message passing for different inner products. the gauss-seidel is one of the most efficient iterative methods for solving linear systems that arise in solving partial differential equations. many parallel implementations have been proposed including those reported in [3-8]. some implementations have been developed for regular problems such as the laplace equation [9, 10], circuit simulation problems [11], power load-flow problems [12], and for many applications of inter-dependent constraints, or as a relaxation step in multi-grid methods [3]. in [13] several parallelization strategies for the dense gauss-seidel method are presented. these strategies are compared and evaluated through performance measurements on a large range of hardware architectures. the authors found that these new architectures do not offer the same trade-off in terms of computation power versus communication and synchronization overheads as do traditional high-performance platforms. in 1999, wang and xu [14] presented a specific technique for solving convection-dominated problems. their algorithm uses crosswind thin blocks in a block gauss-seidel method. their method is based on a special partitioning technique for a block iterative method for solving the linear system derived from a monotone discretization scheme for convection diffusion problems. they conclude that crosswind grouping is essential for the rapid convergence of the method. in 2005, grabel et al. [15] presented two simple techniques for improving the performance of the parallel gauss-seidel method for the 3d poisson equation by optimizing cache usage as well as reducing the number of communication steps. in 2006, nobuhiko et al. [16] presented a novel parallel algorithm for the block gauss-seidel method. the algorithm is devised by focusing on reitzinger's coarsening scheme for those linear systems derived from the finite element discretization with first order tetrahedral elements. the time consumed on communication between processors limits the parallel computation speed. with advances in technology, chips with a large number of cores (processing elements) are becoming a reality. communication between processing elements in such multi-core systems was initially based on buses. when the number of cores increased, the bus became a performance bottleneck. in recent years, networks-on-chip (nocs) have been used instead of buses for interconnecting the on-chip processing elements, which has resulted in faster inter-processor communication. the topology of the network-on-chip has a major impact on the communication performance of the multi-core system [17]. several topologies have been proposed and studied for nocs including mesh-based and tree-based topologies [17]. the emerging three-dimensional (3d) integration and process technologies allow the design of multi-level integrated circuits (ics). this creates new design opportunities in noc design. for example, a considerable reduction can be achieved in the number and length of global interconnections using three-dimensional integration. motivated by these new developments in technology and by the resulting improved performance of interprocessor communication on modern 3d network-on-chip systems, we propose, and analyze the complexity of, a new parallel implementation of the gauss-seidel algorithm on 3d torus noc architectures. the proposed algorithm uses message passing for inter-processor communication. it is an extension of our previous similar algorithm on 2d torus noc [18]. a shorter version of this paper has been presented in [19]. the rest of the paper is structured as follows: in section 2 an introduction is presented including a description of the sequential gauss-seidel algorithm to be parallelized, as well as an introduction to the 3d torus noc architecture. we describe the proposed parallel algorithm in section 3, and we evaluate its performance in section 4. the paper is concluded in section 5. 2. preliminaries a. the gauss-seidel sequential agorithm the gauss-seidel (gs) algorithm is an improvement of the jacobi algorithm. gs corrects the i th component )( m i x of the vector x (m) in the order i = 0, 1, …., n-1. the approximation solution is updated immediately after the new component is determined. the newly computed component )1( m i x can be changed within a working vector which is redefined at each relaxation step, and this results in the following iterative formula [10]: ii n ij m jij i j m jiji m i axaxabx /)( 1 1 )( 1 0 )1()1(        (1) in matrix notation, equation (2) becomes: 0,)( )()1(   mbuxxld mm . (2) in (2) l, d, and u are the lower, diagonal, and upper triangular parts of matrix a respectively. figure 1 outlines the sequential gs algorithm. an efficient parallel gauss-seidel algorithm 31 figure 1. the sequential gauss-seidel algorithm. it is well known that the gs algorithm will always converge if the matrix a is strictly or irreducibly diagonally dominant. the sequential gs algorithm has time complexity o(nn 2 ) for n iterations and therefore requires large execution time for large problem sizes (n), hence the need for faster parallel implementations. b. the 3d torus network-on-chip architecture an n-dimensional torus network, also called a wrap-around mesh or toroidal network, is a cartesian product of n cycle networks. two-dimensional mesh-based topologies (such as 2d mesh and 2d torus) have been the most popular among the known noc topologies. their popularity is due to their modularity (they are easily expandable by adding new nodes and links without modifying the existing structure), their ability to be partitioned into smaller meshes, their simple xy routing strategy, and their facilitated implementation. they also have a regular structure and short inter switch wires. they have been used in several chip multiprocessors such as the raw processor [20], the trips processor [21], the intel 80-core terascale processor [22], the 100-core tile-gx100 processor from tilera [23] and the single-chip cloud computer (scc) of intel [24]. the emerging three-dimensional (3d) integration and process technologies allow the design of multi-level integrated circuits (ics) [25]. this creates new opportunities in noc design [26, 27]. for example, a considerable reduction can be achieved in the number and length of global interconnections using three-dimensional integration. 3d nocs are more advantageous than 2d nocs in providing better performance for large multi-core systems [28]. long horizontal wires in 2d nocs can be replaced by very short vertical links in 3d nocs. despite being available for quite a while, the 3d torus architecture now has the potential to be one of the most attractive interconnection topologies for future large noc systems. this is because nowadays severe challenges are faced due to the rising number of cores (nodes). petascale and exascale installations require, and will require, hundreds or thousands of cores to efficiently work together. the 3d torus topology offers the ability to add nodes without affecting performance and reliability. it is also important for future large multi-core systems to consume less energy. connecting nodes using a 3d torus topology means that each node is connected to the adjacent ones via short cabling (except for the wrap-around links) in 6 different “directions”: x+, x-, y+, y-, z+, z-. the pair-wise connectivity between nearest neighbor nodes of a 3d torus helps to reduce energy consumption and communication latency. a 3 dimesional torus interconnection topology is illustrated in figure 2. sequential gs algorithm { input a, b, x, tolerance, n for m = 0, 1, …, n { for i = 0,…, n-1 { sum = 0 for j = 0, 1, …., i-1 sum = sum + for j = i+1,…, n-1 sum = sum + } if ( ) { output the solution exit } = } } khaled day and mohammad h. al-towaiq 32 figure 2. the 3d torus noc topology. 3. the proposed parallel gs algorithm in our proposed parallel gs algorithm, we partition the n×n matrix a into blocks of n/k 3 columns each, and scatter them to the k 3 processors of a k×k×k 3d torus. the k 3 processors are identified by (x, y, z) coordinates, 0 ≤ x, y, z ≤ k-1, as illustrated in figure 2. processor (x, y, z) is connected to the six neighboring processors (x-1, y, z), (x+1, y, z), (x, y-1, z), (x, y+1, z), (x, y, z-1) and (x, y, z+1). the +1 and -1 operations in these expressions are modulo k in order to include the wrap-around links. we also assign sequential processor numbers (ids) to the k 3 processors as follows: the processor whose coordinates are (x, y, z) is assigned the sequential id: id(x, y, z) = x + ky + k 2 z. in this way, the k 3 processors are also identified with sequential ids in the range 0 ... k 3 -1 as illustrated in figure 3. figure 3. sequential ids of the processors in plane z = 0. figure 4 outlines the steps of the proposed parallel gs algorithm. given the problem inputs a, b, x and tolerance, processor 0 (the master processor) partitions matrix a into blocks of n/k 3 columns each, and scatters them to the processors. processor r receives the r th block of the matrix containing the aij elements for i and j in the ranges: 0 ≤ i < n and r(n/k 3 ) ≤ j ≤ (r+1)(n/k 3 )-1, respectively. then processor 0 scatters the elements of the vector x to the processors. processor pr receives the r th segment of n/k 3 elements of the vector x, i.e. the xj elements for j in the range r(n/k 3 ) ≤ j ≤ (r+1)(n/k 3 )-1. after scattering a and x, processor 0 broadcasts the value of tolerance to all processors. the rest of the algorithm is similar to the sequential algorithm, in except that the loop for calculating and summing the aijxj’s is done in parallel by the k 3 processors. processor number r calculates the partial sum of the aijxj’s, j = r(n/k 3 ), …,(r+1)(n/k 3 )-1, corresponding to the r th block of matrix a and the r th segment of vector x received by this processor. the partial sums are then collected and summed (reduce-sum) at processor 0, which completes the calculation of the new xi element. processor 0 then sends the new xi to the processor in charge of xi, that is pi/(n/k 3 ). x y z 0 1 2 k-1 k k+1 k+2 2k-1 2k 2k+1 2k+2 3k-1 (k-1)k+1 k 2 -1 (k-1)k (k-1)k+2 an efficient parallel gauss-seidel algorithm 33 figure 4. the proposed parallel gauss-seidel algorithm. notice that this parallel gs algorithm is based on parallelizing the calculation of sum inside the inner loop of the sequential algorithm (figure 1). each processor is in charge of a distinct block of columns of matrix a and of a distinct segment of vector x elements, allowing it to contribute to summing the aijxj’s in a distinct range of j. more precisely, processor pr (i.e. with sequential id r) is in charge of the j range: r (n/k 3 ) ≤ j ≤ (r+1)(n/k 3 )-1. the partial sums calculated in parallel by the different processors are gathered by the master, forcing all processors to synchronize at this point before proceeding to the next i iteration. this yields a correct parallelization of the calculation of sum of the sequential algorithm. 4. analysis of the parallel gs algorithm table 1 outlines timing expressions for the various steps of the parallel gs algorithm of figure 4. we assume it takes an amount of time tcopy to copy the value of a real number from one memory location to another, tmultiply to multiply two real numbers, tadd to add two real numbers, and tsqrt to calculate the square root of a real number. expressions for tbroadcast, tscatter, and treduce-sum which correspond to the time required for group communication operations (broadcast, scatter, reduce-sum) in the k×k×k torus will be derived later in this section. parallel_gs algorithm { //let r be the sequential id of local processor (0 ≤ r < k 3 ) if (r = 0) //master processor { input a, b, x, tolerance partition a into k 3 blocks of n/k 3 columns each scatter the blocks of columns of a to the k 3 processors partition x into k 3 segments of n/k 3 elements each scatter the segments of elements of x to the processors } else { receive the r th block of n/k 3 columns of a receive the r th segment of n/k 3 elements of x } for m = 0, 1, …, n { if (r = 0) oldx = x for i= 0,…, n-1 { sr = 0 for j = r(n/k 3 ), …, (r+1)(n/k 3 )-1 sr = sr + if (r = 0) { gather and sum the partial sums: send xi to processor pi/(n/k 3 ) } else { send partial sum sr to processor 0 (contribute to gather) if (r = i/(n/k 3 ) ) receive xi } } if (r = 0) and (||x-oldx|| < tolerance) terminate computation } } khaled day and mohammad h. al-towaiq 34 table 1. complexity of the parallel gs algorithm. algorithm step time complexity 1. scatter the blocks of columns of a t1 = tscatter(n 2 ) = o(n 2 k) 2. scatter the segments of vector x t2 = tscatter(n) = o(nk) 3. broadcast tolerance t3 = tbroadcast(1) = o(k) 4. save old x t4 = ntcopy = o(n) 5. calculate the sr partial sums t5 = (n/k 3 )(tmultiply + tadd) = o(n/k 3 ) 6. reduce-sum the sr partial sums t6 = treduce-sum = o(k) 7. calculate xi t7 = 2(tmultiply + tadd) = o(1) 8. send xi to processor i/(n/k 3 ) t8 = tsend(1) = o(k) 9. termination test t9 = n(2 tadd + tmultiply) + tsqrt = o(n) it can be seen from figure 4 that the total time required by the parallel gs algorithm is given by: ttotal = t1+t2+t3+n[t4+n(t5+t6+t7+t8)+t9] (3) it remains to derive expressions for tbroadcast, tscatter, and treduce-sum which correspond to the timing on the 3d torus of the group communication operations broadcast, scatter, and reduce-sum respectively. a. the cost of broadcasting on the 3d torus the broadcasting of a message of size s from a source node to all other nodes in the k×k×k torus can be done in time:   combroadcast tskst ..2/3)(  , where tcom is the time needed to send a single number from one processor to a neighboring processor in the k×k×k torus. this expression is justified as follows: broadcasting in the k×k×k torus can be done in three phases as illustrated in figure 5. in the first phase, the message is propagated on the x dimension in both directions (x+ and x-), starting at the source node and making use of the wrap-around links on the x dimension if needed. this x broadcasting phase requires  2/k communication steps. figure 5. broadcasting on the 3d torus in 3 phases. in the second phase of the broadcasting, all the nodes which received the message during the first phase (the nodes located on the source row) initiate parallel propagations of the message across the y dimension in both directions (y+ and y-), making use of the wrap-around links on the y dimension if needed. this phase also requires  2/k singlehop communication steps. in the third phase of the broadcasting, all the nodes which received the message during the first and second phases (i.e. all the nodes located on the source plane) initiate parallel propagations of the message across the z dimension in both directions (z+ and z-), making use of the wrap-around links on the z dimension if needed. this third phase also requires  2/k single-hop communication steps. the total time required by this broadcasting algorithm is therefore:   )(2/3)( skstkst combroadcast  . figure 6 shows an implementation of this broadcasting algorithm on the k×k×k torus. 1 1 1 1 3 3 3 3 2 2 2 3 2 2 2 2 2 2 an efficient parallel gauss-seidel algorithm 35 broadcast(m, source = (xs, ys, zs)) { //let local = (clocal, ylocal, zlocal) if (local = source) { send m to (xlocal + 1, ylocal, zlocal) send m to (xlocal 1, ylocal, zlocal) send m to (xlocal, ylocal + 1, zlocal) send m to (xlocal, ylocal 1, zlocal) send m to (xlocal, ylocal, zlocal + 1) send m to (xlocal, ylocal, zlocal 1) } else { receive m //let sender = (xsender, ysender, zsender) if(ylocal = ysource) and (zlocal = zsource) // phase 1 { if(xsender = xlocal – 1) send m to (xlocal + 1, ylocal, zlocal) else send m to (xlocal 1, ylocal, zlocal) send m to (xlocal, ylocal + 1, zlocal) send m to (xlocal, ylocal 1, zlocal) send m to (xlocal, ylocal, zlocal + 1) send m to (xlocal, ylocal, zlocal 1) } else if (zlocal = zsource) // phase 2 if(ysender = ylocal – 1) send m to (xlocal, ylocal + 1, zlocal) else send m to (xlocal, ylocal 1, zlocal) send m to (xlocal, ylocal, zlocal + 1) send m to (xlocal, ylocal, zlocal 1) else // phase 3 if(zsender = zlocal – 1) send m to (xlocal, ylocal, zlocal + 1) else send m to (xlocal, ylocal, zlocal 1) } } figure 6. implementation of the 3d torus broadcasting algorithm. b. the cost of scattering on the 3d torus similarly to broadcasting, scattering a message of size m in the k×k×k 3d torus (each processor will receive one chunk of the message of size m/k 3 ) can also be done in three phases, except that not the whole message propagates in the three phases. during the first phase, when a node receives a message, it extracts its part of size m/k (to be scattered across the y dimension during the second phase) and divides the remaining part into two equal parts and sends one of them to the x+ neighbor and the other to the xneighbor. the sizes of the messages propagated in this way on the x dimension are therefore successively: (m-m/k)/2 = m(k-1)/2k, m(k-3)/2k, m(k-5)/2k, …, and m(k-(k-2))/2k = m/k, assuming without loss of generality that k is odd. the time for the first phase of the scatter operation is therefore: 8/)2...)3()1(()2/( comcom mktkktkm  . during the second phase of the scatter operation, the same steps can be followed across the y dimension starting at the processors of the source row, each with an initial message of size m’ = m/k. using the same analysis as of the first phase yields the timing expression m’ktcom/8 = mtcom/8 for the second phase. a similar calculation gives the timing expression mtcom/8k for the third phase. the total time for the scatter operation is therefore tscatter(m) = m(k+1+1/k)tcom/8 = o(mk). c. the cost of reduce-sum on the 3d torus the reduce-sum group communication operation is the operation of gathering while summing a set of numbers initially scattered at all processors (one number per processor). the final sum is collected at one sink processor. this khaled day and mohammad h. al-towaiq 36 operation is needed in the parallel gs algorithm to collect and sum up the sr partial sums. it can be done by reversing the three phases of the broadcasting operation. during the first phase, partial sums across dimension z are calculated in parallel by a sequence of summing and sending on the z+ or zdirection (whichever is closer) to the sink plane. this yields a set of partial sums stored at the processors of the sink plane. during the second phase, the processors on the sink plane calculate partial sums across dimension y in parallel by a sequence of summing and sending on the y+ or ydirection (whichever is closer) to the sink row. this yields a set of partial sums stored at the processors of the sink row. the processors on the sink row then calculate the final sum by a sequence of summing and sending on the x+ or xdirection (whichever is closer) to the sink processor. the final sum will be stored at the sink processor. each of the three phases requires  2/k steps of summing and sending. the resulting total time of the reduce-sum operation is therefore:   )()(2/3_ kttkt addcomsumreduce  . d. overall cost of the parallel gs algorithm notice that t1, t2, t3, t6, and t8 in expression (3) of the total execution time of the parallel gs algorithm correspond to communication steps, while t4, t5, t7 and t9 correspond to computation steps. using the obtained timing expressions of the broadcasting, scattering and reduce-sum operations, the total communication time tcomm is given by the following: tcomm = t1 + t2 + t3 + nn[t6 + t8] = o((kn 2 + nnk)tcom) notice that tcomm is proportional to tcom (the single hop communication cost) which is much faster on noc networks than on cluster or multiprocessor networks. therefore the proposed parallel gs algorithm runs faster on a noc than on a loosely coupled cluster or a tightly coupled multiprocessor. the total computation time tcomp is given by: tcomp = n[t4+n(t5 + t7)+t9] = o(nn 2 /k 3 ) the complexity of the total execution time ttotal of the parallel gs algorithm is therefore: ttotal = tcomm + tcomp = o(kn 2 + nnk + nn 2 /k 3 ) (4) when the size of the linear system n and the number of iterations n are large compared to the number of processors k 3 (in the order of k 4 or larger), the total execution time ttotal of the parallel gs algorithm in expression (4) is dominated by the term nn 2 /k 3 which is k 3 times smaller than the time of the sequential algorithm. we can therefore conclude that, when the problem size n and the number of iterations n are large compared to k, the proposed parallel gs algorithm has a near optimal speedup (nearly equal to the number of processors k 3 ) and hence a near optimal efficiency. remember that the speedup of a parallel algorithm is defined as the time of the sequential algorithm divided by the time of the parallel algorithm, while the efficiency is defined as the speedup divided by the number of processors. figures 7 and 8 illustrate how the speedup and efficiency increase as n and n increase. figure 7. speedup and efficiency of the parallel gs algorithm as a function of n. an efficient parallel gauss-seidel algorithm 37 figure 8. speedup and efficiency of the parallel gs algorithm as a function of n. 5. conclusion we have proposed a parallel gauss-seidel iterative algorithm for solving large systems of linear equations on a 3d torus network-on-chip architecture. the proposed algorithm makes use of the x, y, z interconnects with wraparound links of the 3d torus for efficient group communication operations between the processors including broadcasting, scattering and reduce-sum operations. these efficient group communication operations are at the heart of the proposed algorithm. we have shown that the proposed parallel algorithm has near optimal speedup when solving large linear systems that require a large number of iterations. this work can be extended by an experimental or simulation-based performance evaluation of the proposed parallel algorithm. references 1. adams, l. and xie, d. new parallel sor method by domain partitioning, siam j. sci. comp., 1999, 20(22), 2261-2281. 2. krystynak, j. and nitzberg, b. performance characteristics of the ipsc/860 and cm-2 i/o systems, proceedings of the seventh international parallel processing symposium, newport, ca, 13-16 april 1993, pp. 837-841. 3. adams, m.f. a distributed memory unstructured gauss-seidel algorithm for multigrid smoothers, proc. of 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1999, 21(2), 620-645. 15. grabel, j., land, b. and uebertholz, p. performance optimization for the parallel gauss-seidel smoother, pamm, 2005, 5(1), 831-832. khaled day and mohammad h. al-towaiq 38 16. nobuhiko, o., takeshi, m. takeshi, i. and masaaki, s. a parallel block gauss-seidel smoother for algebraic multigrid method in edge-element analysis, papers of technical meeting on static apparatus, iee japan, 2006, vol. 6, no. 58-61, 63-75, pp. 55-60. 17. benini, l. and micheli, g.d. networks on chips: technology and tools, morgan kaufmann, 2006. 18. al-towaiq, m. and day, k. parallel gauss-seidel on a torus network-on-chip architecture, j. interconnection networks, 2012, 13(1, 2), 1-14. 19. day, k. and al-towaiq, m. a parallel gauss-seidel algorithm on a 3d torus network-on-chip architecture, 10th hipeac conference on high performance and embedded architecture and compilers, january 19-21, 2015, amsterdam, netherlands. 20. taylor, m.b., lee, w., amarasinghe, s. and agarwal, a. scalar operand networks: on-chip interconnect for ilp in partitioned architectures, int’l symposium on high-performance computer architecture (hpca), 2003, pp. 341-353, anaheim, california. 21. gratz, p., kim, c., sankaralingam, k., hanson, h., shivakumar, p. and burger, s.k. on-chip interconnection networks of the trips chip, ieee micro, 2007, 27(5), 41-50. 22. hoskote, y., vangal, s.r., singh, a., borkar, n. and borkar, s. a 5-ghz mesh interconnect for a teraflops processor, ieee micro, 2007, 27(5), 51-61. 23. ramey, c. tile-gx100 manycoreprocessor: acceleration interfaces and architecture, hot chips 23, stanford, ca, august 17, 2011. 24. howard , j. et. al, a 48-core ia-32 processor in 45 nm cmos using on-die message-passing and dvfs for performance and power scaling, ieee journal of solid-state circuits, january 2011, 46(1), 173-183. 25. feero, b.s. and pande, p.p. networks-on-chip in a three-dimensional environment: a performance evaluation, ieee trans. on computers, january 2009, 58(1), 32-45. 26. pavlidis, v.f and friedman, e.g. 3-d topologies for networks-on-chip, ieee tvlsi, 2007, 15(10), 1081-1090. 27. marcon, c. et. al., tiny noc: a 3d mesh topology with router channel optimization for area and latency minimization, proc. 27th international conference on vlsi design, 5-9 jan 2014, mumbai, india, 2014, pp. 228-233. 28. kourdy, r. and nouri, m.r. performance comparison of 2d and 3d torus network-on-chip architectures, journal of computing, 2012, 4(2), 119-122. received 26 october 2014 accepted 15 february 2015 squ journal for science, 2016, 21(1), 26-40 © 2016 sultan qaboos university 26 kinematics of post-obduction deformation of the tertiary ridge at al-khod village (muscat, oman) andreas scharf*, frank mattern and sawsan s. al-sadi department of earth sciences, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: scharfa@squ.edu.om abstract: structural investigations in post-obductional paleocene to eocene limestones of the tertiary ridge reveal a ~1 km long wnw-ese striking strike-slip fault system within the ridge, consisting of two main sub-parallel, strike-slip faults. considering the geometry of the harding strain ellipse, the orientation of structures between the two strike-slip faults (e.g., riedel shears, folds, reverse faults) point to left-lateral motion. the abundance of large-scale folds (up to 100 m in wave length and amplitude) between the two strike-slip faults led us to the interpretation of transpressive conditions in a first approximation. moreover, the tertiary ridge of the study area consists of three distinct structural domains. the faults of domain a and c are oriented wnw-ese, but the trend of the faults in the central domain b differs by ~10°. the left-lateral strike-slip fault system exists only in domain b. we propose that the direction of greatest stress during miocene plate convergence (sigma 1) was oriented 032°/212°. considering the trend of the strike-slip zone and the orientation of sigma 1, the left-lateral motion must have been transpressive. sigma 1 is perpendicularly oriented to the domains a and c. prior to the miocene d2 compressional event the study area was affected by a d1 extensional event, related to the opening of the red sea and the gulf of aden or to gravity-driven normal faulting. the d2 compressional/transpressional structures of the miocene are reactivating the d1 structures of the oligocene. keywords: tertiary ridge; oman; collision; strike-slip faulting; transpression; sigma 1. بمسقط، الحركاث األرضيت الخي حدثج بعد عمليت اعخالء صخور األفيواليج في صخور حقبت الحياة الحديثت في قريت الخوض، سلطىت عمان أودرياس شارف, فراوك ماحر, سوسه السعدي غزب تإذجاي كيهُمرز مه ألكصز يمرذ جاوثي صذع َجُد ػه انخُض تقزيح انجيزيح انصانس انؼٍذ نصخُر انثىيُيح انذراساخ كشفد :الملخص كانطياخ انجيُنُجيح انرزاكية فإن نهجٍذ؛ ٌارديىج نشكم َفقا مرُاسييه. جاوثييه صذػيه مه انصذع يرأنف شزق. جىُب شزق-غزب شمال انطياخ َجُد كصزج يفسز قذ انصذػيه. طُل ػهّ يساريح جاوثيح حزكح حذَز إنّ ذشيز انجاوثييه انصذػيه تيه انُاقؼح انمرىُػح َانصذع تحيذ انمُجُدج انجيُنُجيح انرزاكية إلخرالف وظزا جاوثيح. إوظغاطيح تظزَف يمراس انجاوثي انصذع أن ػهّ انمرُاسييه انصذػيه تيه نحيذ.ا مه األَسظ انىطاق في انجاوثي انصذع يرُاجذ مخرهفح. وطاقاخ شالشح إنّ انحيذ ذقسيم يمكه فإوً انخُض تقزيح انصانس انؼٍذ صخُر انقُج َاذجاي انجاوثي انصذع اذجاي ػهّ تىاءا غزب. جىُب-شزق شمال كان انميُسيه ػصز أشىاء انؼظمّ انقُج اذجاي تأن انذراسح ذقرزح انمىطقح نٍا ذؼزضد انري اإلوظغاطيح انرشٌُاخ قثيم جاوثيح. اوضغاطيح ظزَف خالل ذشكهد نهصذع انيساريح انجاوثيح انحزكح فإن انؼظمّ في َذسثثد ػذن، خهيج َ األحمز انثحز وشُء مغ ذُافقد االَنيجُسيه ػصز خالل ذمذديح ذشٌُاخ انمىطقح شٍذخ انميُسيه، ػصز خالل انميُسيه، ػصز خالل الحقا جاوثيح اوضغاطيح/اوضغاطيح ذشٌُاخ إنّ انؼاديح انصذَع ٌذي ذؼزضد انذراسح. تمىطقح ػاديح صذَع ذشكم تانمىطقح. حانيا مالحع ٌُ كما جاوثيح صذَع إنّ ػاديح عصذَ مه ذحُنٍا إنّ أدِ مما .(1انقُج انؼظمّ )سيجما ،وضغاط جاوثيا ،صذع جاوثي ،وضغاطا ،ُػمان ،صخُر انؼٍذ انصانس انجيزيح :الكلماث المفخاحيت 1. introduction he tertiary ridge is a geomorphological ridge that extends over a distance of 30 km from al-khod village (west of muscat) to the east (figures 1 & 2). our studies concern the western part of the ridge, where it is narrow, easy to access and favourably exposed. the ridge consists of three paleocene to eocene formations that dip to the nne. whereas the oldest and youngest formations (jafnayn and seeb fms.) are represented by competent limestone beds, the intervening rusayl fm. consists of various lithologies, t deformation of the tertiary ridge 27 including large quantities of marl, making this formation significantly less competent than the underlying and overlying formations (e.g., [1-3]). figure 1. outcrops of maastrichtian to eocene post-obductional sediments of northern oman. modified from [1]. dotted box shows the outline of figure 2. figure 2. simplified geological map of the greater study area. the study area is shown in the dotted box (figure 5). squ – sultan qaboos university campus. simplified from [4]. whereas the sedimentary rocks of the tertiary ridge are well described and understood (e.g., [1-3]), its deformation has remained a largely untackled issue, despite the high visibility of the superbly and invitingly well-exposed folds within the rusayl and jafnayn fms. as in the road outcrop, which cuts across the ridge along the road leading from the north into the village of al-khod (figure 3a, b), or as in natural outcrops ~1 km farther ese in the western part of the ridge (figure 3c). andreas scharf et al. 28 figure 3. folds of the tertiary ridge (a-c). a. folded and faulted rusayl fm. eastern side of the al-khod road cut, north of al-khod village. the guard rails are 2 m high. b. small scale fold in the rusayl fm. eastern side of the al-khod road cut, north of al-khod village. c. large scale fold in the jafnayn fm. (dashed line). natural outcrop in the tertiary ridge. note the ridge character. houses in the foreground belong to al-khod village. paleocene to eocene deformation is largely extensional [5]. however, this extension is followed by some compressional deformation, still during the eocene. extension is attributed to paleogene gravity collapse of the oman mountains [5, 6], possibly dating as post-middle eocene [6]. a different cause was identified by [7]. they suggested that paleogene/neogene to quaternary extensional faulting along wnwstriking faults was due to the flexural bulging of the under-riding arabian plate within the arabia-eurasia collision zone. some workers have distinguished a late cretaceous to early eocene phase of extension, oriented ene-wsw as well as two oligocene intervals of extension, oriented nne-ssw and nnw-sse [8]. whereas many studies have concentrated on the regional extensional deformation (e.g., [7, 9, 10 and sources therein]), very little has been published on post-cretaceous compressional structures, the work by [8] being a notable exception. they determined a late oligocene/early miocene to pliocene compressional phase with two episodes of different stress directions: e-w to ne-sw (early miocene) and n-s to nne-ssw (pliocene). it must also be mentioned that compressional deformation may be concentrated along pre-existing deformation of the tertiary ridge 29 faults [5]. compressional deformation was initiated in northern oman coevally with the onset of the arabiaeurasia collision zone in the zagros mountains [8]. with regard to regional strike-slip tectonics, [8] noticed that conjugate strike-slip faults are associated with the compressional stage, and that sigma 1 was oriented e-w to ne-sw. they observed three sites with conjugate sets of strike-slip faults in the jafnayn fm. in the muscat area with right-lateral faults striking nesw and left-lateral faults, striking e-w. near al-khod village they found strike-slip and reverse faults, revealing a ne-sw orientation of sigma 1. it is also worth noting that the wnw-striking hatta zone, at the western end of the batinah coast, has a left-lateral paleogene to neogene history [10]. paleogene to neogene sinistral shearing was also determined for the nw-striking maradi fault [7]. in both cases, the sinistral shear sense can be explained by the orientation of (rotating) sigma 1, as detected by [8]. our study is the first detailed structural analysis of a ~2 km wide segment of the tertiary ridge near al-khod village. we determine the origin of conspicuous folds within parts of the tertiary ridge, the orientation of sigma 1 during convergence, and decipher the structural evolution of the tertiary ridge. moreover, we compare our results with information on other structures, and we deduce the mechanical relationship of the ridge‟s structures to plate-scale tectonic processes after a brief description of the tectonic framework and the lithological units, we present a tectonic map of the tertiary ridge, revealing the orientation and kinematics of the observed structural features (strike-slip, reverse and normal faults, riedel shears, slicken lines and folds), and corresponding cross sections. following this descriptive section, we offer a genetic interpretation of the observed structures in terms of stress orientation, time of deformation and related plate tectonic processes. finally, we compare our results with published data. we believe our results will contribute to the understanding of the geodynamic evolution of the oman mountains after the ophiolite obduction during late cretaceous times. 2. geological background 2.1 regional tectonic framework northern oman was the site of large scale tectonic ophiolite emplacement during the upper cretaceous [11]. the ophiolite is derived from a part of the tethys ocean, which was located to the northeast of oman. all margins of the arabian plate are characterized by tectonic activities (figure 4). in the north, the plate is taking part in the arabia-eurasia collision, forming the zagros and makran fold and thrust belts. the onset of the deformation of the zagros mountain belt dates with 22 ma and the convergence since that time amounts to 440 km [12]. to the southwest and south, the arabian plate terminates at the active spreading axes of the red sea and the gulf of aden, respectively. the age of the southern red sea is 30 to 24 ma and the amount of extension measures about 300 km [13, 14 their figure 3]. although the age of the gulf of aden is younger (20 ma) the amount of extension is 100 km larger [8, 15]. towards the east and the west, the arabian plate is limited by the dextral owen transform fault and the sinistral dead sea transform zone, respectively. the owen transform fault has an age of 8 ma and a rate of dextral lateral motion of 2 mm/a [16]. the dead sea transform fault has an age of 14 ma [17, 18] with 100-105 km of displacement motion [19]. 2.2 age and type of post-obduction deformation the oman mountains show clear sings of uplift. uplift may have begun during late stages of ophiolite obduction onto the arabian plate during the late cretaceous, and may have been localized and facilitated by pre-existing basement structures [7, 24]. uplift of the domes of the oman mountains ensued along basement ramps [25]. following the late cretaceous ophiolite obduction, the arabian plate was also affected by continental rifting started during the early oligocene to early miocene in the southwest and south with a rapid stage during the early miocene [13] (figure 4). rifting proceeded into the nearly synchronous opening of the nnw-sse-striking southern part of the red sea and the ene-wsw-striking gulf of aden [13]. this may have resulted in the formation of se-nw-directed extensional structures in the arabian plate, including the oman mountains. on the other hand, the extensional structures may be related to flexural bulging [7] and gravitational collapse structures [9]. the latter could possibly explain a tectonic transport of the postobductional sedimentary cover toward the ne, towards the gulf of oman. andreas scharf et al. 30 figure 4: tectonic setting of the arabian plate. red and blue coloured symbols indicate divergence and convergence with overall amount and age, respectively. green arrows show present-day gps values with respect to fixed europa from iran [20] and white arrow from oman [21]. a – [22]; b – [19]; c – [17]; d – [18]; e – [13]; f – [14]; g – [8]; h – [15]; i – [16]. map modified from [23]. immediately after, or in part overlapping with, the extensional tectonics, the arabian plate underwent ~ne-sw directed compression in the course of plate convergence with eurasia forming the zagros fold-andthrust belt. this started during the early miocene (23-16 ma [22, 26-32]) and is an ongoing process as shown, for example, by present-day convergence rates, determined by gps measurements, between arabia and eurasia with 36.5 mm/a near the strait of hormuz [20] (figure 4), contributing to the cenozoic and recent uplift of the oman mountains. 2.3 lithology the post-obductional sediments of the study area can be divided into the 800 m thick late campanian to early maastrichtian al-khod fm. and three younger formations which collectively comprise the tertiary ridge [1] (figure 5). these three formations are the jafnayn, rusayl and seeb fms. the thicknesses of these formations are 126 m, 144 m and 600 m, and their ages are of late paleocene to eocene, early eocene, and middle to late eocene, respectively [1-3]. the contacts between the three formations within the tertiary ridge are conformable, whereas the contact between the al-khod fm. with the overlaying jafnayn fm. is marked by a fault at the southern margin of the ridge [1]. the al-khod fm. consists mainly of interbedded conglomerate, lithic sandstone and shale [1]. the jafnayn and seeb fms. chiefly consist of nodular or nonnodular limestone and marly wackestone, whereas the rusayl fm. consists of shale and marl in which a central limestone unit is embedded [1]. 3. methods the structures observed in the field were mapped and measured with modern fabric compasses after [33]. because of the conspicuous folds and the obvious straight character of the tertiary ridge, we considered as possible genetic causes conventional compression and/or transpression and used the harding strain ellipse as a tool for the tectonic interpretation [34]. in addition, we used shear sense criteria for the kinematic analysis of slickensides (see appendix [36, his fig. 4.17]). satellite imagery helped to identify deformation of the tertiary ridge 31 segments of different strike of the tertiary ridge. we will refer to the extensional structures as “d1” and to younger compressional structures as “d2”. the measurements of the individual structures and their locations are shown in the appendix. 4. structural results 4.1 left-lateral strike-slip deformation the tertiary ridge near al-khod village consists of three structural domains (domains a, b and c; figure 5). domain a is located west of the road cut, whereas domain b represents the main part of the study area. domain b starts east of the road extending for ~1 km. east of domain b starts domain c. the two mapped and proposed main faults of domains a and c have the same orientation (strike: ~122° to 302°), whereas the two mapped main strike-slip faults in domain b are slightly oblique (~10°) to the main faults in the two domains (strike: ~112° to 292°). domain c is inaccessible for field work. figure 5. tectonic map of the tertiary ridge at the al-khod village. based on the analysed structures, sigma 1 is oriented perpendicular to the strike of the tertiary ridge of domains a and c. note that the d1 extensional structures are reactivated as d2 compressional structures. inset at the lower part shows leftlateral harding strain ellipse [34] for a theoretical pattern of structures between two strike-slip faults. a nw striking strike-slip fault could only be observed in domain b. its shear sense is sinistral (figures 5 & 6) as indicated by the geometric relationships between the fault and associated structures, including riedel shears, folds, reverse and normal faults. we observed numerous horizontal and gently dipping slickenlines, indicating that strike-slip was significant in the tertiary ridge. however, our slickenside analyses sensu [35] also revealed a strike-slip that was opposite to the sinistral motion. there are also slickensides, showing dip-slip or oblique slip, sometimes in one and the same outcrop. the strike-slip motion probably occurred not only along a single fault but rather within a shear zone, composed of two sub-parallel faults (figures 5 & 6). the first of these is largely located at the boundary between the al-khod and the jafnayn fms (domain a). within domain b this fault shifts into the jafnayn fm. (figure 5). the second fault is assumed to be located to the north within the rusayl fm. (figure 5). andreas scharf et al. 32 figure 6. cross section perpendicular to the strike of the tertiary ridge. see figure 5 for a trace of the cross sections. a-aˈ is located in domain a and b-bˈ is located in domain b. note that the d1 extensional structures are reactivated as d2 compressional structures. in domain a the southern fault is found at the contact between the al-khod and the jafnayn fms. towards the east, in domain b, the fault is shifting into the jafnayn fm. we point out that the incompetent, marly rusayl fm. is highly deformed over its entire thickness. deformation in the rusayl fm. is stronger than in the jafnayn fm. and much stronger than in the seeb fm. evidently, strain is most concentrated in the rusayl fm. at and near the road cut in domain b five clear evidence for a left-lateral strike-slip fault within the rusayl fm. exists: (1) deformation within the rusayl fm. is most intense near the contact to the seeb fm. (figures 3 & 5); (2) several fault planes with riedel shears and slickenlines are found within the rusayl fm. and at the lowermost part of the seeb fm. (stops 28 – 31, appendix). although the mineral steps along the fault plains do not show a conclusive indication for the sense of shear, the overall orientation of the riedel shears with respect to the mapped main strike-slip fault points to sinistral motion; (3) there is a text-book example of a coarse tectonic breccia along a vertical riedel shear plane or “riedel fault” within the rusayl fm. (figure 7a, stop 29, appendix); (4) this breccia is found on a large (≤ 100 m long) asymmetric limestone boudin within the central part of the rusayl fm. the displacement of 50 m between two asymmetric boudins is sinistral (figure 7b, stops 31 & 32, appendix); (5) there is steepening of the bedding plane of the rusayl fm. and the lowermost part of the seeb fm. in proximity of the contact between the two formations (figure 7c). this steepening indicates the presence of an overall subvertical fault within the rusayl fm. because of its steep character this sub vertical fault is considered as a strike-slip fault. this makes it very likely that a major strike-slip fault is located within this formation. the majority of the structures of domain b are concentrated within the jafnayn and the rusayl fms. only a few structures are found in the lowermost part of the seeb fm. the overall compression is assumed to be perpendicularly oriented to the tertiary ridge in domains a and c and, hence, nne-ssw directed (032° to 212° ±2°; figure 5). deformation of the tertiary ridge 33 figure 7. tectonic structures along the tertiary ridge in domain b. a. coarse tectonic breccia on a vertical riedel shear (stop 29, appendix). b. asymmetric limestone boudins in the central part of the rusayl fm. note the vertical fault plane on the boudin with the tectonic breccia of figure 7a is investigated by the first author. the dashed lines mark the contact of the shale with the two limestone boudins (left limestone stop 29; right limestone stop 31). c. steepening of the bedding plane of the dark rusayl and the lowermost part of the lighter seeb fms. note a reverse fault with a top to the nne displacement within the shale of the rusayl fm. and a subvertical fault at the contact between rusayl fm. and seeb fm. (stop 33, appendix). 4.2 structural elements the measurements of the individual structures and their locations are shown in the appendix. the size of the ne to sw striking riedel shear faults measures several square meters. the orientation of these ene to wsw striking sub-vertical faults is oblique (~30-40°) to the main strike-slip fault (figure 5). their obliquity indicates that they are riedel shears of the strike-slip fault. no sense of shear indicators (e.g., mineral steps) along the riedel faults could be found. normal faults are observed along the road cut at the transition between domains a and b. some of these normal faults have an oblique displacement (e.g., stop 16). these andreas scharf et al. 34 faults range from several square centimeters to some square meters in size with a dip-slip displacement of several centimeters to a maximum of two meters. folds at the scale of several meters to 100 meters were measured. the larger folds are visible along the folded lower and upper contacts of the rusayl fm. (figure 5). the orientation of all these folds is similar, displaying steep to subvertical fold axial planes, striking ~nnw to sse and dipping steeply to the wsw, and fold axes plunging gently to moderately towards the nw. exceptions are one fold with a fold axis, plunging to the south (stop 17, figure 3b) and another fold with a fold axis plane, striking to the nne (stop 8, figure 3c). the shape of the folds is mostly tight. one syncline, however, is open (stop 14, appendix and figure a1). according to figure 5, the general direction of dip in the three formations is nne. at the easternmost part of the study area (transition between domains b & c, stops 8 & 9) the al-khod fm. dips more steeply than the overlying jafnayn fm., which indicates a low-angle discontinuity between both formations. many faults are steeply-dipping and strike nw; those found west of the road cut especially are possibly d1 normal or d2 reverse faults, since they display sub-vertical slickenlines. one of the faults shows a completely different orientation (strike to the ne) with dip-slip slickenlines. the measurements of the individual structures and their locations are shown in the appendix. 5. synthesis of faulting and geodynamic interpretation on the basis of field observations along the study area, two main phases of deformation have been recognized. we describe them in order of age, from older to younger. 5.1 ne-sw directed extensional phase a set of se-nw striking normal faults, belonging to d1 within both the jafnayn and rusayl fms. indicates ne directed extension (stops 9 & 10). similar striking extensional structures were identified along the northern and southern margins of the gulf of aden in oman [36, 37], in yemen [38], socotra island [39] and in the oman mountains, including the tertiary ridge [9]. these extensional structures are associated with oligocene rifting of the gulf of aden [8] or are gravity-driven, facilitating tectonic transport away from the oman mountains and towards the gulf of oman [9]. since the tertiary ridge strikes ~122°-302°, at a high angle but not perpendicular to the proposed ne direction of extension, extension with a horizontal component (oblique extension,) along the d1 normal faults cannot be excluded. if a strike-slip component was involved during the d1 extensional phase, this horizontal component must have been dextral. 5.2 ne-sw directed compressional phase figure 8. provides a schematic model for the d2 compressional phase, which is marked by a left-lateral strike-slip fault, traced within the jafnayn fm. and a proposed second left-lateral strike-slip fault within the rusayl fm. (figure 5). the d2 shear sense within domain b is interpreted as sinistral, based on analysis of the geometric relationships between the small-scale structures (riedel shears, folds and reverse faults) with that of the main fault(s), and a comparison of these relationships with those shown on the harding strain ellipse [34]; figure 5). field observations and measurements reveal that the compressional structures (folds & reverse faults) are oriented around 45° with respect to the main strike-slip fault. riedel shears are oriented at relatively low to moderate angle to the main strike-slip fault. these observations match with the sinistral harding strain ellipse (figure 5). the fact that compressional structures are more prevalent than extensional ones leads us to interpret transpressional conditions for domain b. the model of figure 8 shows the mechanisms of d2 transpressional left-lateral strike-slip faulting which was controlled by the orientation of the tectonic structures relative to the direction of d2 compressional stress (sigma 1). the direction of sigma 1 is slightly oblique (~10°) to the main strike-slip faults in domain b which induces oblique, left-lateral motion (figure 5), while to the east and west of domain b, the tectonic units are perpendicularly oriented to sigma 1, resulting in reactivation of the extensional structures as reverse faults without horizontal movement (figure 5). this model suggests that the pre-existing d1 normal faults formed during the ne oriented extensional phase were reactivated as d2 reverse faults during this ne compressional phase (domains a & c; figure 5). deformation of the tertiary ridge 35 figure 8. schematic model for the post-obductional stress development and type of faulting along the tertiary ridge at the al-khod village. ne-sw directed red arrows indicate the d1 extensional direction during the oligocene. blue arrows indicate the d2 direction of greatest stress during miocene compression (this study). the direction of d2 is perpendicular to the tertiary ridge in the domains a and c. dotted box indicates the study area (figure 5). figure 9. juxtaposition of late cretaceous to pliocene stress direction in the post-obductional sediments in the vicinity of muscat obtained from [8] and from this study (see exact locations in figure 6 of [8]). andreas scharf et al. 36 figure 9 provides a comparison of the late cretaceous to pliocene stress directions in the post-obductional sediments in the vicinity of muscat obtained from [8] and from this study (see exact locations in figure 6 of [8]). the estimated ne-sw direction of d1 extension (sigma 3) in our study coincides with the „probable oligocene extension stage a‟ of [8]. the different directions of extension in figure 9 point to both orogenic collapse plus regional extension due to rifting as mentioned in section 5.1. the final development of the leftlateral transpressive belt in domain b in our study area is most likely a result of compression during the early miocene. a pliocene age can be excluded because the stress direction (sigma 1) during that time was more n-s directed, which is slightly oblique to our measurements of 032° to 212° (figures 8 & 9). 6. conclusion the present work integrates field mapping and satellite image analysis to reveal the mechanisms, fault kinematics, and relative age of faulting within the tertiary ridge in the vicinity of al-khod village. the tertiary ridge was affected by the d1 extensional event, which may be related to the opening of the red sea and the gulf of aden in oligocene times. d1 normal faults where reactivated during the d2 compressional event during the miocene. a strike-slip fault system occurs in two sub-parallel wnw-ese striking branches of a left-lateral strike-slip fault zone that have accommodated transpressional stress in between them (figure 5). this system formed owing to ~nne-ssw d2 compressional forces, perpendicular to the overall trend of the tertiary ridge in the study area. a new model explains the mechanisms of d2 strike-slip faulting (figure 7). the driving forces for the post-oligocene compressional deformation of the post-obduction succession in the vicinity of al-khod village are related to the contemporaneous collision between the arabian and the eurasian plates, resulting in the formation of the zagros fold-and-thrust belt. because domain b of the tertiary ridge is slightly oblique (~10°) to the direction of d2 collision/compression, transpressional deformation ensued. if the direction of sigma 1 was the same along the entire tertiary ridge as in the vicinity of al-khod village, then similar structures must exist in the remaining part of the ridge. compressional structures should be found in parts of the tertiary ridge that are oriented wnw-ese, similarly to in domains a and c. in differently oriented parts, transpressional structures should be present. these structures should either be of sinistral or dextral shear origin, depending on the polarity of their obliquity with respect to the orientation to sigma 1. 7. acknowledgment this article is the overall result of a final year project of sawsan s. al-sadi, submitted in may 2015 to the college of science at sultan qaboos university (squ). we are indebted to mohammed al wardi (squ) for helpful discussions, the translation of the abstract and the title into arabic, and as a reviewer. finally, we thank two anonymous reviewers and dr. iftikhar ahmed (squ) for critical and constructive comments. references 1. nolan, s.c., skelton, p.w., clissold, b.p. and smewing, j.d. maastrichtian to early tertiary stratigraphy and paleogeography of the central and northern oman mountains. in the geology and tectonics of the oman region, (eds. robertson, a.h.f., ries, m.p. and ries, a.c.), geological society, london, special publications, 1990, 49, 495-519. 2. dill, h.g., wehner, h., kus, j., botz, r., berner, z., stüben, d. and al-sayigh, a. the eocene rusayl formation, oman, carbonaceous 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a.h.f. mesozoic-tertiary tectonicsedimentary evolution of a south tethyan oceanic basin and its margins in southern turkey. in tectonics and magmatism in turkey and the surrounding area, (eds. bozkurt, j. a. winchester, e. and piper, j. d. a.), geological society special publication, 2000, 173, 97-138. 31. sherkati, s., letouzey, j. and frizon de lamotte, d. central zagros fold-thrust belt (iran): new insights from seismic data, field observation, and sandbox modeling. tectonics, 2006, 25, tc4007, doi: 10.1029/2004tc001766. 32. vergés, j., saura, e., casciello, e., fernàndez, m., villaseñor, a., jiménez-munt, i. and garcíacastellanos. crustal-scale cross-sections across the nw zagros belt: implications for the arabian margin reconstruction. geological magazine, 2011, 148, 739-761, doi: 10.1017/s0016756811000331. 33. clar, e. ein zweikreisiger geologenund bergmannskompaß zur messung von flächen und linearen (mit bemerkungen zu den feldgeologischen messungsarten). verhandlungen der geologischen bundesanstalt wien, 1954, 201-215. 34. harding, t. p. petroleum traps associated with wrench faults. american association of petroleum geologists bulletin, 1974, 58, 7, 1290-1304. 35. angelier, j. fault slip analysis and paleostress reconstruction. in continental deformation, (ed. hancock, p.l.), pergamon press, oxford, 53-100. 36. lepvrier, c., fournier, m., bérard, t. and roger, j. cenozoic extension in coastal dhofar (southern oman): implications on the oblique rifting of the gulf of aden. tectonophysics, 2002, 357, 279-293. 37. fournier, m., bellahsen, n., fabbri, o. and gunnell, y. oblique rifting and segmentation of the ne gulf of aden passive margin. geochemistry geophysics geosystems, 2004, 5, q11005, doi: 10.1029/2004gc000731. 38. huchon, p. and khanbari, k. rotation of the syn-rift stress field of the northern gulf of aden margin, yemen. tectonophysics, 2003, 364, 147-166. 39. fournier, m.p., huchon, k., khanbari, k. and leroym, s. asymmetry and segmentation of passive margin in socotra, eastern gulf of aden, controlled by detachment faults. geochemistry, geophysics, geosystems, 2007, 8, q03007, doi: 10.1029/2006gc001526. appendix: the stops of the study area (figure 5) are shown in figure a1 and listed in tables a1-a4. figure a1. location map of the study area. deformation of the tertiary ridge 39 table a1. bedding-plane measurements after [1] stop# n e elevation [m] measurements 1 23°34'13.1'' 58°07'40.9'' 89 065 / 58 8 23°33'52.3'' 58°08'14.2'' 111 010 / 41 9 23°33'54.3'' 58°08'14.0'' 129 009 / 16 15 23°34'19.5'' 58°07'41.3'' 109 247 / 75 19 23°34'18.4'' 58°07'34.9'' 85 028 / 55 22 23°34'31.1'' 58°07'26.0'' 99 040 / 84 23 23°34'38.4'' 58°07'21.5'' 89 030 / 78 27 23°33'57.7'' 58°07'24.6'' 109 130 / 60 table a2. fold measurements after [1] stop# n e elevation [m] fold axis fold axial plane 7 23°34'02.4'' 58°08'07.2'' 138 006 / 60 nne-ssw/subvertical 13 23°34'04.1'' 58°08'12.0'' 152 336 / 48 se-nw/subvertical 14 23°34'05.8'' 58°08'08.4'' 135 330 / 25 se-nw/subvertical 17 23°34'24.4'' 58°07'43.1'' 127 208 / 29 nne / ssw table a3. riedel-shear measurements after [1] stop# n e elevation [m] measurements 6 23°34'03.6'' 58°08'03.8'' 119 060 / 90 070 / 90 062 / 90 10 23°24'00.0'' 58°08'20.3'' 150 062 / 90 086 / 90 070 / 90 060 / 90 072 / 90 12 23°34'00.4'' 58°08'13.7'' 173 235 / 43 28 23°34'14.5'' 58°07'57.2'' 196 359 / 86, with 272 / 16 slicken lines 29 23°34'14.5'' 58°07'55.7'' 172 015 / 87 30 23°34'15.0'' 58°07'56.4'' 172 016 / 67, with 302 / 40 slicken lines andreas scharf et al. 40 table a4. fault measurements after [1] stop# n e elevation [m] type of fault fault plane slicken lines 2 23°34'12.5'' 58°07'44.2'' 104 strike-slip fault 200 / 60 200 / 60 3 23°34'09.0'' 58°07'46.00'' 100 faults (undifferentiated) 070 / 55 078 / 35 011 / 77 032 / 47 140 / 31 102 / 26 334/ 69 032 / 47 4 23°34'08.5'' 58°07'49.7'' 106 strike-slip fault 096 / 80 160 / 10 5 23°34'04.3'' 58°08'01.4'' 108 strike-slip fault 028 / 84 6 23°34'03.6'' 58°08'03.8'' 119 strike-slip fault 120 / 90 10 23°34'00.0'' 58°08'20.3'' 150 strike-slip fault 096 / 90 098 / 90 102 / 90 16 23°34'20.6'' 58°07'42.1'' 118 normal fault 189 / 70 268 / 33 18 23°34'22.7'' 58°07'41.8'' 128 normal fault 296 / 69 349 / 67 20 23°34'22.1'' 58°07'30.1'' 87 normal fault 192 / 78 21 23°34'27.4'' 58°07'29.2'' 138 normal fault 208 / 81 28 23°34'14.5'' 58°07'57.2'' 196 strike-slip fault 213 / 86 123 / 09 31 23°34'17.9'' 58°07'51.1'' 126 strike-slip fault 213 / 60 310 / 07 32 23°34'22.4'' 58°07'42.2'' 173 strike-slip fault 018 / 83 33 23°34'21.7'' 58°07'41.8'' 139 reverse fault 238 / 51 243 / 45 references clar, e. ein zweikreisiger geologenund bergmannskompaß zur messung von flächen und linearen (mit bemerkungen zu den feldgeologischen messungsarten). verhandlungen der geologischen bundesanstalt wien, 1954, 201-215). received 4 october 2015 accepted 3 january 2016 squ journal for science, 2015, 20(1), 83-92 © 2015 sultan qaboos university 83 determinants of contraceptive practice in oman by using multilevel modeling moza s. al-balushi*, mohammed s. ahmed and m. mazharul islam department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: p890778@student.squ.edu.om. abstract: in this paper, multilevel logistic regression models are developed for examining the hierarchical effects of contraceptive use and its selected determinants in oman using the 2008 oman national reproductive health survey (onrhs). comparison between single level and multilevel logistic regression models has been made to examine the plausibility of multilevel effects of contraceptive use. from the multilevel logistic regression model analysis, it was found that there is real multilevel variation among contraceptive users in oman. the results indicate that a multilevel logistic regression model is the best fit over ordinary multiple logistic regression models. generally, this study revealed that women’s age, education, number of living children and region of residence are important factors that affect contraceptive use in oman. the effect of regional variation for age of women, education of women and number of living children further implies that there exists considerable differences in modern contraceptive use among regions, and a model with a random coefficient or slope is more appropriate to explain the regional variation than a model with fixed coefficients or without random effects. the study suggests that researchers should use multilevel models rather than traditional regression methods when their data structure is hierarchal. keywords: multilevel modelling; hierarchical; logistic regression; contraceptive. محذدات تطبيق وسائل منع الحمل في عمان باستخذام نمورج متعذد المستويات مسهرول اسالمم. موزه البلوشية، محمذ أحمذ، انعىايم عًاٌ وحسذَذ انسًم فٍالَسذاس انهىخسخٍ نذساست آثاس انهشيُت نالسخخذاو وسائم يُع ث نيخعذدة انًسخىَا حى حطىَش ًَىرج فٍ هزِ انىسلت :ملخص دة انًسخىَاث (. ولذ حى يماسَت بٍُ يسخىي وازذ ويخعذonrhsانعًاَُت انىطُُت نهصست اإلَدابُت ) 8002باسخخذاو يسر انخٍ حؤثش عهً هزا انًخغُش و الَسذاس انهىخسخٍ حبٍُ أٌ ث نيخعذدة انًسخىَا حسهُم ًَىرجوسائم يُع انسًم. يٍ السخخذاو انخعذد فٍ انًسخىيًُارج االَسذاس انهىخسخٍ نفسص آثاس ن الَسذاس انهىخسخٍ هى ث نانًسخىَا يخعذدة اٌ ًَىرجانًسخىَاث بٍُ انًسخخذيٍُ وسائم يُع انسًم فٍ سهطُت عًاٌ. وحشُش انُخائح إنً نخعذدهُان حباٍَ انبالٍُُ عهً لُذ عذد األطفال انخسصُم انعهًٍ نهًشأة، وأٌ عًش انًشأة، وهزِ انذساست كشفج فمذ . عًىيا، انخمهُذٌ َسذاس انهىخسخٍاال ًَىرجاألَسب عهً انخسصُم ونعًش انًشأة، بٍُ انًُاطك انخباٍَ. حأثُش سهطُت عًاٌ وسائم يُع انسًم فٍٍ سخخذيانالحٍ َانُساء عهًيهسىظ حؤثش بشكمويُطمت اإللايت انسُاة زُث اٌ فٍ اسخخذاو وسائم يُع انسًم انسذَثت بٍُ انًُاطك اخخالف يهسىظَعٍُ أٌ هُان وخىد انبالٍُُ عهً لُذ انسُاةعذد األطفال و انعهًٍ نهُساء ثابخت أو يٍ انًعايالث ان هًعانزٌ َسخىٌ ًُىرج انيٍ بٍُ انًُاطك يالءيت نخفسُش انخباٍَعشىائٍ أو انًُسذس هى أكثش انًعايم انًُىرج انزٌ َسخىٌ عهً ان بُُت انبُاَاث حكىٌ يٍ انطشق انخمهُذَت االَسذاس عُذيا هى األَسب إنً أٌ اسخخذاو ًَارج يخعذدة انًسخىَاث نهبازثٍُ انذساستحمخشذ دوٌ آثاس عشىائُت. و .هشيُت يىاَع انسًم. و انهىخسخٍ االَسذاسًَىرج حعذد انًسخىَاث ، انهشيُت ، : كلمات مفتاحية 1. introduction tratified multistage cluster sampling designs are the norms for most national level socioeconomic, demographic and health surveys because of cost, time and efficiency considerations. as these survey designs are hierarchical in nature, data collected in these surveys often introduce multilevel dependency or correlation among the observations that can have implications for model-based statistical inference, although these samples provide efficient estimates of the descriptive population quantities [1-4]. the individual observations in hierarchical data structures are not completely independent, and the results of the analysis can be affected by this clustered structure of the underlying data. for example, households from the same community or geographical area are more homogenous than households in different communities. standard statistical techniques such as regression models have problems dealing with the hierarchical data structure because they assume independent and normally distributed errors with a constant variance (homoscedasticity) s moza s. al-balushi et al 84 [1, 5-8]. analyzing variables from different levels without taking into account the hierarchical data structure leads to misleading estimation results and interpretation because one faces the problem of heteroscedasticity. to overcome these problems, a methodology of multilevel modeling has been developed recently, taking the hierarchical data structure into account and satisfying the assumption of independence and heteroscedasticity, which obviously leads to correct analysis and proper interpretation of the data. multilevel models are useful in determining the direct effects of the individual and the group explanatory variables. there is an increasing use of multilevel models for the analysis of clustered data. these models are also referred to as mixed effects models, random effects models, or hierarchical models in the literature [1-4,9,10]. many popular statistical packages, such as hlm, mlwin, r, sas, stata, and spss have the capacity to fit multilevel models. methodological work on analyzing multilevel models has been done by many [e.g., 5-7,11], who gives an illustrative introduction to multilevel models. the primary objective of this paper is to develop an analytical framework of multilevel analysis for studying contraceptive use in oman utilizing the 2008 oman national reproductive health survey (onrhs) data, which is hierarchical in nature as it followed a multistage cluster sampling design. although the hierarchical effect of contraceptive use in oman is still unknown, information regarding this would be very important for policy purposes. 2. data and methods 2.1 data the data used in this study come from the 2008 oman national reproductive health survey (onrhs). the 2008 onrhs was tagged on to the world health survey in oman (owhs) in 2008. the 2008 owhs was designed by the world health organization (who) as part of comprehensive standardized data collection on population health in different countries. both the onrhs and owhs were implemented by the ministry of health of oman. the details of the owhs may be seen in [12]. the onrhs used a sub-sample of 3,703 omani households out of 5,464 households selected for the 2008 whso. the onrhs considered ever-married omani women of reproductive age of 15 to 49 years. ultimately 4,560 women were successfully interviewed, who constitute our study sample. the sample was calculated to provide national estimates, as well as separate estimates for both rural and urban areas. the sample of the 2008 onrhs was selected following a multistage stratified cluster sampling design. stratification was made on two factors: level of urbanization (urban/rural) and geographical distribution. administratively, oman was divided into 10 regions at the time of survey (currently 11 regions). the survey covered all the 10 regions of oman, dividing into 10 urban and 10 rural strata. equal samples were selected from all strata, with increased samples from urban muscat. from each stratum, 10 clusters were selected randomly. the 2003 population census ‘enumeration areas’ (eas) were considered as clusters. the 2003 census has defined the ea as the area assigned for one enumerator. there are a total of 3167 eas in the country. each ea contains on average 110 households (both omani and non-omani) arranged in two or more enumeration blocks (ebs). twenty four households were selected systematically from the selected eas. eas were used as the primary sampling units (psus). as the 2008 onrhs data is of hierarchical structure, the hierarchy for our study follows individuals as level-1 and regions as level-2. the survey considered non-pregnant currently married women as the respondents for current contraceptive use. after excluding currently pregnant and widowed or divorced women, we were left with 3056 women as our study population. 2.2 study variables the study considered current use of contraceptive methods by currently married non-pregnant women of reproductive age as the dependent variable. the current use covers both modern and traditional methods of contraceptive. the variable is categorical which we dichotomous as follows: those women currently using any of the methods as 1 and those not currently using any method coded as 0. the explanatory variables considered for this analysis include age of the women, region of residence, number of living children, level of education, place of residence, type of family and economic status or wealth quintiles. a shortcoming of the dataset used is that it contains no information on household income or wages, household expenditure patterns and community characteristics. however, the dataset contains information about house fixed and durable assets such as tv, refrigerator, car, house etc. these variables were used to construct a proxy index of household economic status or wealth index using the principal components analysis. it is a composite measure of the cumulative living standard of a household, which places individual households on a continuous scale of relative wealth. the wealth index is divided into four categories, with the lowest one representing the poorest 25 percent and the highest one representing the wealthiest 25 percent of households see [13]. this wealth index has the advantage of providing a reasonably reliable measure of the household’s economic status, and it is not affected by the endogeneity and transitory nature of labour income. determinants of contraceptive practice 85 2.3 analytical methods 2.3.1 multilevel logistic regression model as mentioned earlier, as our basic data structure is of two-levels, with individual women as level-1 and region of residence as level-2, we concentrate on a two-level logistic regression model. our outcome variable ijy is a binary response for individual i (i=1, 2,…, nj) and group j (j = 1,2,…, k) and we have one explanatory variable at individual level ijx . then pr ( 1)ij ijp y  can be defined as the probability of the response equal to one and ijp can be modeled using a logit link function where ijy has a bernoulli distribution. then we can write the two level model as . 1 log 10 jij ij ij ux p p            (combined model) (1) this is a formal model, where j refers to the level 2 unit (region) and i to the level 1 unit (women), such that ju is the random effect of level 2 and a standard logistic regression model will be without j u . conditional on j u and ij y s being assumed to be independent, model (1) can be written as follows, splitting up into two models: one for level 1 and the other for level 2. , 1 log 10 ijjj ij ij x p p            (level-1 model) (2) and jj u 00  (level-2 model) (3) and, ju is normally distributed with 0)( jue and .)var( 2 uj u  model (1) is the simplest possible multilevel model for binary data. 3. results 3.1 differentials of contraceptive use: bivariate analysis table 1 presents the percentage distribution of currently married and non-pregnant women using any of the family planning methods by selected socio-economic and demographic factors. the survey data indicate that 29% of the eligible women were using any family planning methods. women’s age shows significant (p < 0.01) association with contraceptive use. the association is curvilinear, as the rate of contraceptive increases with the age of women until 35 years and then decreases. contraceptive use rate is higher among women living in urban areas than their rural counterparts (30% vs. 26%) but the difference is not statistically significant. however, the contraceptive use rate varies significantly among the 10 geographical regions considered in this study. musandam (45%) followed by muscat (38%) show higher prevalences of contraceptive use and al-dhakhlia (18%) the lowest. women’s education and number of living children show significant association with contraceptive use in oman. 3.2 single level logistic regression analysis the single level standard logistic regression analysis results are reported in table 2. the results indicate women’s age, educational level, number of living children, and region of residence as significant predictors of contraceptive use in oman. after controlling for other factors, the age of women shows significant negative association with contraceptive use. young women of age 15-29 are 2 times more likely to use some family planning method than their older counterparts. married women who had secondary education were 2.8 times more likely to use contraception than uneducated woman. similarly, woman who had college, university and higher education were 3.1 times more likely to use contraception than uneducated woman. the likelihood of contraceptive use by married women who had (5-7) children was 3.7 times greater than by married women who had (0-2) children. similarly, married women who had more than seven children were 3.4 times more likely to use contraception than married women who had (0-2) children. 3.3 multilevel logistic regression analysis of contraceptive use in this study we consider multilevel models allowing between-region variance of modern contraceptive use. the data have a two-level hierarchical structure with women at level 1, nested within 10 regions at level 2. the multilevel logistic regression analysis was used for comparisons and analysis of the effects of socio-economic and demographic variables on modern contraceptive use among women, and to estimate any residual correlations across regions in predicting modern contraceptive use in oman. the multilevel modeling process was performed stepwise. the first step moza s. al-balushi et al 86 examined the null model (or empty model) of overall probability of modern contraceptive use without adjustment for predictors. the second step included both the analysis of single and multilevel models for random intercept and fixed slope multilevel analysis. the third step considered a model for two level random intercept and random slope (random coefficient) multilevel logistic regression analysis. table 1. percentage distribution of women currently using contraceptive by background characteristics 15-49 (n =3056 ). background characteristics categories using contraceptive yes no total 28.9 71.1 age of women* 15-24 22.5 77.5 25-29 28.1 71.9 30-34 35.1 64.9 35-39 31.6 68.4 40-44 32.2 67.8 45-49 18.9 81.1 place of residence urban 30.1 69.9 rural 25.6 74.4 region* muscat 37.5 62.5 dhofar 26.4 73.6 al-dakhlyah 17.8 82.2 north sharqiah 19.2 80.8 south sharqiah 23.1 76.9 north batinah 32.7 67.3 south batinah 28.8 71.2 al-dhahirah 31.5 68.5 musandam 44.7 55.3 al-wasta 31.3 68.8 women education* illiterate 19.2 80.8 primary+ literate 28.3 71.7 preparatory completed 35.1 64.9 secondary completed 30.1 69.9 college/university 35.1 64.9 number of living children* (0-2) children 21.8 78.2 (3-4) children 33.0 67.0 (5-7) children 38.2 61.8 more than seven children(ref) 26.3 73.8 economic status poor 31.2 68.8 lower middle 26.7 73.3 upper middle 27.1 72.9 rich 30.5 69.5 living arrangement nuclear family 31.8 68.2 extended family/composite 26.3 73.7 3.3.1 multilevel logistic regression model comparison we compare the three possible multilevel logistic regression models (empty model, random intercept model and random slope model) using a deviance-based chi-square value and the akaike information criterion (aic). the deviances of the empty model with random intercept (deviance = 3634) and the random intercept and fixed slope model (deviance = 3403) indicate that the random intercept and fixed slope model is better than the empty model with regard to random intercept. in addition to this, the aic value of the empty model with random intercept (aic = 3638) is larger than that for the random intercept and fixed coefficient model (aic = 3419), which implies that random intercept and fixed slope is better than the empty model with random intercept in predicting contraceptive use across regions. the deviances of a fixed slope and random intercept (deviance = 3403) and random slope model (deviance = 3386) show that the random slope model is better than the random intercept and fixed slope model. the aic value of the random coefficient model (aic = 3406) is smaller than that of the random intercept and fixed coefficient model (aic = 3419), implying that the random coefficient model is better compared to the random intercept and fixed slope model in describing contraceptive use status (see table 3). 3.3.2 empty random intercept logistic regression analysis the simplest non-trivial specification of the hierarchical linear model is one in which only the intercept varies between level two units and no predictors (explanatory) variables are entered in the model. a random intercept or variance components model allows the overall probability of contraceptive use to vary across regions. an interceptonly multilevel model has been estimated to predict the probability of women who use contraception; this is described in equation (8), where j refers to the level 2 unit (region) and i to the level 1 unit (women) and which is still a single level model. determinants of contraceptive practice 87 table 2. maximum likelihood estimate for binary logistic regression of predicting contraceptive use. covariate   s.e. p-value or 95% c.i. or lower upper age of women 0.003 15-24 0.80 0.251 0.001 2.226 1.360 3.641 25-29 0.73 0.215 0.001 2.076 1.361 3.166 30-34 0.63 0.202 0.002 1.876 1.263 2.785 35-39 0.33 0.184 0.077 1.385 0.966 1.986 40-44 0.57 0.181 0.001 1.777 1.247 2.533 45-49 (ref) 1.000 place of residence urban -.068 0.111 0.538 0.934 0.752 1.160 rural 1.000 region 0.000 muscat 0.83 0.217 0.000 2.285 1.494 3.496 dhofar 0.45 0.225 0.044 1.573 1.012 2.444 al-dakhila -0.23 0.237 0.339 0.797 0.501 1.268 south sharqiah 0.19 0.239 0.421 1.212 0.192 0.239 north batina 0.74 0.207 0.000 2.106 0.745 0.207 south batina 0.45 0.215 0.035 1.572 0.452 0.215 al-dhahirah/ 0.57 0.240 0.018 1.765 0.568 0.240 musandam 1.33 0.400 0.001 3.776 1.329 0.400 al-wasta/ 0.87 0.427 0.042 2.387 0.870 0.427 north sharqiah (ref) 1.000 women education 0.000 illiterate (ref) 1.00 primary/ literate 0.51 0.148 0.001 1.664 1.246 2.222 preparatory completed 1.03 0.191 0.000 2.814 1.936 4.089 secondary completed 1.02 0.183 0.000 2.787 1.945 3.992 college/university 1.14 0.203 0.000 3.127 2.102 4.651 number of children 0.000 (0-2) children (ref) 1.000 (3-4) children 0.73 0.136 0.000 2.065 1.582 2.695 (5-7) children 1.31 0.161 0.000 3.694 2.696 5.061 >7 children 1.24 0.196 0.000 3.446 2.345 5.064 economic status 0.151 poor 0.28 0.128 0.027 1.327 1.032 1.705 lower middle 0.11 0.132 0.402 1.117 0.863 1.446 upper middle 0.08 0.124 0.542 1.079 0.845 1.376 rich(ref) family type nuclear family 0.27 0.089 0.002 1.221 1.017 1.465 extended/composite(ref) constant -3.59 .319 126.641 1 0.000 ref = reference category table 3. summary of three possible multilevel logistic regression model selection criteria 3. model selection criteria multilevel empty model multilevel random intercept model multilevel random slope model deviance 3634 3403 3386 aic 3638 3419 3406 the results of the multilevel empty model are presented in table 4. the ratio of women who use contraception to women who do not by using ml estimate from the standard logit model is exp (-0.900) = 0.407 that is the same sample ratio of 884 women who used contraception to 2173 women who did not . this is the odds-ratio when no predictors have been considered in the model. this ratio is estimated to be exp(-0.917) = 0.400, exp(-0.938) = 0.391, exp(-0.928) = 0.395, and exp(-0.931) = 0.394 from multilevel model by mql-1, mql-2, pql-1 and pql-2 multilevel estimation methods respectively. by comparing the odds-ratio, it can be said that under all multilevel methods, the standard logistic model odds-ratio has overestimated. from table 4, it can be noticed that that there is a significant difference between the results of the standard logistic model and the multilevel logistic model. failing to take into account the clustering within clusters (level 2), the standard logit model has overestimated the odds-ratio by about 1.85% (-0.900 ( -0.917)*100/0.917), 4.05%, 3.02% and 3.33% and compared to the multilevel model by using the corresponding methods mql-1, mql-2, pql-1 and pql-2. the fixed intercepts for all the multilevel estimated methods are similar methods and the random quantity including its standard error at cluster level for pql-1 and pql-2 are high compared to all other methods. moza s. al-balushi et al 88 table 4. estimation of parameters and standard errors of an intercept-only, fixed effect, and random effect logit model for predicting the probability of contraceptive use. model logit mql-1 mql-2 pql-1 pql-2 fixed effect intercept -0.900 (0.062) -0.917 (0.096) -0.938 (0.101) -0.928 (0.099) -0.931 (0.102) random effect intercept 0.094 (0.036) 0.095 (0.037) 0.106 (0.042) 0.107 (0.042) n 3056 3056 3056 3056 3056 significant ( p < 0.05) the likelihood ratio statistic for testing the null hypothesis that 2 0u  = 0 can be calculated by comparing the two-level model with the single-level model without the level 2 random effects. the difference in -2*log likelihood between an empty model with random effect from table 4 and an empty model without random effect from (single level logistic regression analysis) is (3979 -3634)=345, which constitutes strong evidence that the between-regions variance is non-zero. this implies that the empty model with random effect is better than the empty model without random effects. the decrease in deviance is 345, showing that the multilevel model fits the data dramatically better than the standard logistic regression. conversely, the variance of the random effect of the random intercepts ( 2 0u  =0.107, p-value =0.0116) reveals that there is significant difference in contraceptive use across the regions. the empty model with random effect also helps to calculate the between-region variations, by the help of the intra-class correlation coefficient (icc). icc is estimated by 2 2 2 / ( ) u u e      , where 2 2 / 3 e   is the variance of the standard logistic distribution. then icc = 0.0315, which implies that 3.15% of the variation in the contraceptive use is attributable to unobserved regional characteristics. 3.3.3 multilevel random intercept and fixed coefficient model analysis the random intercept and fixed coefficient logistic regression is the same as the empty random intercept logistic regression model, but with additional explanatory variables to allow for the effects of women’s age, educational level, region, number of living children, living arrangements and economic status. in the random intercept and fixed coefficient multilevel logistic regression model, we allowed the probability of contraceptive use to vary across regions, but we assumed that the effects of the explanatory variables are the same for each region. that is, the random intercept varies across region, but women’s level explanatory variables are fixed across regions. the results are presented in table 5. for the single level model, place of residence and women’s education were found to be significant determinants of variation in contraceptive use in all regions with respect to reference categories, and while it is not with the multilevel model (see table 5). the estimated coefficients and odds-ratio have a similar interpretation, as in an/the ordinary logistic regression discussed above. the p-value differs for the same explanatory variables, such as place of residence and economic status (poor), between single level and multilevel ;these were not significant for the single model but are significant under the multilevel model. this is because analyzing variables from different levels without taking into account the hierarchical data structure leads to misleading estimation results, as one faces the problem of heteroscedasticity. the individual observations in a hierarchical data structure are not completely independent and the results if analysis can be effected by this cluster structure of the underlying data. women in the same region are more homogenous than women in different regions. the results in table 5 indicate that women’s age, educational level, number of children, and living arrangements were found to be significant determinants of variation in contraceptive use in all regions, with the respecting reference categories and place of residence was not significant under both modeling. on the other hand, the ‘poor’ category for economic status was found to be a significant determinant of variation in contraceptive use in all regions with the respecting reference categories under the multi-level, while it was not significant under the single-level model. the random part of the random intercept and fixed slope model showed that the intercept variance of the random effect was 0.123, whereas the variance of the intercept for the empty model was 0.107. the variance of the intercept for the empty multilevel model decreased compared to that under random effect of the intercept and fixed slope model. the reduction of the random effects of the intercept variance was due to the inclusion of fixed explanatory variables. that is, taking into account the fixed independent variables can provide extra predictive value on contraceptive use in each region. the significance of random effect intercept variance indicates that there is significant regional random effect variation on contraceptive use among women (see table 5). this implies that there is still unexplained variation in contraceptive use across regions. it is observed that there exist significant differences between the   coefficients of these two models for each of the explanatory variables. also the   coefficients of the standard model have been either under or overestimated for   coefficients in comparison with those of the multilevel model. the difference in   coefficients estimated from a multilevel and from a standard level model arises because of the addition of the random effects, and implies that a single level model for this outcome is not appropriate. determinants of contraceptive practice 89 table 5. results of random intercept and fixed coefficient logistic regression analysis. covariates single level multilevel )(  s.e. p-value or )(  s.e. p-value or age 15-24 0.672 0.246 0.006 1.958 0.725 0.259 0.005 2.064 25-29 0.598 0.210 0.004 1.819 0.690 0.221 0.002 1.995 30-34 0.563 0.197 0.004 1.756 0.604 0.207 0.004 1.829 35-39 0.297 0.181 0.101 1.346 0.275 0.188 0.145 1.316 40-44 0.567 0.179 0.002 1.763 0.571 0.184 0.002 1.771 45-49 (ref) place of residence urban -0.024 0.102 0.816 1.024 -0.025 0.116 0.829 0.975 rural education illiterate (ref) primary/ literate 0.524 0.144 0.000 1.690 0.603 0.153 0.000 1.828 preparatory c 1.056 0.186 0.000 2.875 1.145 0.197 0.000 3.141 secondary c 1.060 0.176 0.000 2.885 1.145 0.192 0.000 3.142 college/univ 1.226 0.195 0.000 3.409 1.279 0.279 0.000 3.595 no. of living children (0-2) ch (ref) (3-4) ch 0.715 0.134 0.000 2.044 0.741 0.140 0.000 2.099 (5-7) ch 1.245 0.159 0.000 3.475 1.354 0.165 0.000 3.874 8+ 1.120 0.193 0.000 3.066 1.318 0.201 0.000 3.734 wealth quintile poor 0.151 0.118 0.199 1.163 0.369 0.132 0.005 1.446 lower middle -0.036 0.122 0.768 .965 0.165 0.136 0.223 1.180 upper middle 0.003 0.119 0.978 1.003 0.111 0.127 0.383 1.118 rich (ref) family type nuclear family 0.169 0.091 0.064 1.185 0.167 0.095 0.081 1.181 extended family (ref) constant -2.976 0.261 0.000 0.051 -3.399 0.304 0.000 0.35 random intercept variance c. s.e. )var( 2 0 ju u 0.123 0.054 0.022 ref = reference category 3.3.4 multilevel random slope model analysis so far we have allowed the probability of contraceptive use to vary across regions, assuming that the effects of the explanatory variables are the same for each region. we will now modify this assumption by allowing the difference between urban and rural families within region to vary across regions. to allow for this effect, we will need to introduce a random coefficient for place of residence. the model will be fitting has the same form as the random slopes model considered in the previous section, but since the variable ‘place of residence’ has only two categories, we use the more general term ‘coefficient’ rather than ‘slope’ to describe its effect. the results are presented in table 6. the results indicate that the women’s age, educational leveland number of children are significant determinates of variation in contraceptive use in all regions with respect to the corresponding reference categories under multilevel modeling (see table 6). table 6 also shows that the values of )var( 0 2 0 ju u and )var( 1 2 1 ju u are the estimated variance of intercept and slope of place of residence. the wald test has been used to test the significant of the parameters 2 0u  , 2 1u  and 10u  . the test statistics of the first parameter is 4.883, which we compare to a chi-squared distribution on 1 d.f. we conclude that there is a significant difference between the regions. the test statistics of the second and third parameters is 3.574, which is approximately chi-squared distributed on 2 d.f. (p =0.167). at 10% we conclude that both parameters are non –zero, which implies that the effect of urban and rural middle does indeed vary across the region. on average (after adjusting for the effects of age and the other explanatory variables), the log-odds of using contraception are 0.035 higher for urban areas than for rural areas. depending on the value of 2 1u  , the difference in a given region will be larger or smaller than 0.035. the last column of table 6 shows that the   coefficient under single level analysis corresponding to place of residence covariates has been under estimated about 42% compared with the multilevel estimate. similarly, the   coefficients for the women’s age group (25-29) of the single level model have been under estimated by almost 31%. the   coefficient under single level analysis corresponding to the women’s age covariate for its all categories has been under moza s. al-balushi et al 90 estimated with different percentage compared with multilevel estimate. on the other hand the   coefficients for the women’s education group (college/university) of the single level model have been over estimated by almost 13%. thus it is evident that if the multilevel effect is not taken into account in multivariate modeling, the estimates will be either underestimated or overestimated considerably. these results imply that a single-level multivariate model for this outcome variable is not appropriate. table 6. results of random slope logistic regression model analysis of contraceptive use. covariate single level model multilevel model over/under estimation   s.e. p value or   s.e. p-value or age 15-24 0.672 0.246 0.006 1.958 0.856 0.345 0.019 2.354 -0.27 25-29 0.598 0.210 0.004 1.819 0.782 0.086 0.000 2.186 -0.31 30-34 0.563 0.197 0.004 1.756 0.664 0.214 0.002 1.943 -0.18 35-39 0.297 0.181 0.101 1.346 0.367 0.178 0.072 1.443 -0.24 40-44 0.567 0.179 0.002 1.763 0.612 0.187 0.001 1.844 -0.08 45-49 (ref) place of residence urban 0.024 0.109 0.816 1.024 0.034 0.218 0.559 1.035 -0.42 rural (ref) education illiterate (ref) primary/ literate 0.524 0.144 0.000 1.690 0.472 0.120 0.000 1.603 0.10 preparatory completed 1.056 0.186 0.000 2.875 0.978 0.249 0.000 2.955 0.07 secondary completed 1.060 0.176 0.000 2.885 0.950 0.187 0.000 2.586 0.10 college/university 1.226 0.195 0.000 3.409 1.067 0.286 0.000 2.907 0.13 children ever born (0-2) child (ref) (3-4) child 0.715 0.134 0.000 2.044 0.736 0.118 0.000 2.088 -0.03 (5-7) child 1.245 0.159 0.000 3.475 1.311 0.392 0.000 3.710 -0.05 >7 1.120 0.193 0.000 3.066 1.217 0.347 0.000 3.377 -0.09 hh economy poor 0.151 0.118 0.199 1.163 0.302 0.241 0.129 1.353 -1.00 lower middle -0.04 0.122 0.768 0.965 0.132 0.170 0.279 1.141 4.67 upper middle 0.003 0.119 0.978 1.003 0.099 0.220 0.568 1.104 -32.00 rich (ref) family type nuclear family 0.169 0.091 0.064 1.185 0.217 0.137 0.166 1.242 -0.28 extended family (ref) constant -2.98 0.261 0.000 0.051 -3.250 0.637 0.000 0.039 -0.09 random intercept variance component s.e. )var( 0 2 0 ju u 0.133 0.058 )var( 1 2 1 ju u 0.243 0.126 ),cov( 1001 jju uu -0.115 0.072 ref = reference category 4. discussion and conclusion this study analyzed determinants of contraceptive use in oman using the multilevel modeling technique with application to the hierarchical data from the 2008 oman national reproductive health survey. different models are fitted to the data to identify potential determinants of use of modern contraception among women in the reproductive age group. first, bivariate analysis with the chi-square test and the ordinary logistic regression model was fitted to the data and significant variables were considered for further investigation in multilevel models. secondly, the multilevel models were fitted. the multilevel model was step wise; on the first step the intercept only or the empty model was fitted to check whether multilevel effects or heterogeneity exists among the hierarchies. in the next step the random intercept and fixed slope model, usually called the random intercept model, was fitted, and finally the random intercept and random slope (random slope model) was fitted. determinants of contraceptive practice 91 our study found that multilevel effects are all significant and have to be taken into consideration in logistic regression modelling. the results for ordinary logistic regression reveals that region of residence, women’s age (in categories), educational level, number of living children, and type of family are the most important explanatory variables for use of contraception in oman. women use of modern contraception was significantly associated with regions of residence. this might be because of the fact that regions are highly correlated, and therefore the assumption of independence of higher level (regions) in classical regression analysis might seriously bias the standard errors of regression coefficients [3, 17]. the odds of using modern contraception in rural and urban areas were not significantly different. this might be due to the fact that the access to contraceptive commodities and women’s knowledge, attitudes and practice are uniform in both rural and urban areas. it is also observed that the odds of contraceptive use do not vary significantly among the different economic groups in oman, which contradicts the findings in other studies elsewhere. multilevel models fitted to the data also indicate that contraceptive use was significantly associated with region of residence; women’s educational attainment, age group, number of living children and type of family. the fixed parts of the effects of explanatory variables or factors included in the multilevel models have similar interpretations as those of the multiple logistic regressions analysis but the random parts of the intercept and the coefficients provide additional information. the random intercept in the random intercept and fixed slope model is significantly different from zero (p <0.05) indicating that use of contraception differs from region to region. the deviance based chi-square test for random effects in the random intercept model is also high. this indicates that the random intercept model with the fixed slope is found to give a better fit than the empty model for predicting the use of modern contraceptives across regions of oman. the variance component of random intercept is also large which further supports the fact that there is a high variability in modern contraceptive use in oman across regions. within region variation further implies that use of contraceptives within regions is less likely (or heterogeneous) than between regions. thus multilevel analysis has demonstrated that different regions have significantly different mean effects. this is in line with the findings of other studies [e.g.,14-16]. the random coefficient estimates for intercepts and the slopes vary significantly at 5% significance level, which implies that there is a significant variation in the effects of religion women’s age, educational level and number of living children; these variables differ significantly across the regions. the variance component for the random intercept is large compared to its standard error. thus there remains some regional-level variance unexplained in the final model. hence using ordinary logistic regressions is not advisable for predicting modern contraceptive use in such a data set without accounting for the effect of regions. on the other hand, it was found that the random intercept and explanatory variables provide additional information. first, the variances of the random components related to the random term were found to be statistically significant, implying the presence of differences in the use of modern contraceptives across the regions. secondly, from those explanatory variables considered here, the effects of the religious beliefs of a woman, her place of residence and her exposure to family planning messages on the radio differs from region to region. third, the interaction between random parts of religious beliefs and place of residence create significant differences in the use of modern contraception across regions. this result supports the findings of other studies [e.g.,15-17]. we observed considerable differences in β coefficients when the multilevel effects were not taken into consideration. ordinary multiple logistic regressions underestimate or overestimate the coefficients compared to the multilevel regression. hence, ignoring the multilevel effects will result in a serious bias of the estimates of the coefficients of the parameters. generally, a slight reduction of standard errors in single level analysis might imply that ignoring the effect of regional variations will decrease the precision of the estimates [18]. 5. acknowledgement the authors would like to thank the ministry of health of oman, especially the director of planning and research, for providing the raw data file of the 2008 national reproductive health survey of oman. the views expressed herein are solely those of the authors and do not necessarily reflect the views of any institution. references 1. snijders, t.a.b. and bosker, r.j. multilevel analysis: an introduction to basic and advanced multilevel modeling. sage publications, london, 1999. 2. raudenbush, s.w. and bryk, a.s. hierarchical linear models: applications and data analysis methods. thousand oaks, ca: sage publications, london, 2002. 3. goldstein, h. multilevel statistical models. edward arnold: london, halsted press, new york, 1995. 4. austin, p.c., goel, v., van walraven c. an introduction to multilevel regression models. can j. public health, 2001, 92, 150-4. 5. goldstein, h. multilevel models in educational and social research. griffin: london, oxford university press: london, 1987. 6. goldstein, h. performance indicators in education. statistics in society, d. dorling and s. simpson. part vi, pp. 281-286, arnold, london, 1999. moza s. al-balushi et al 92 7. hox, j.j. multilevel analysis: techniques and applications. lawrence erlbaum associates, inc., mahwah, nj, 2002. 8. harttgen, k. and misselhorn, m. a multilevel approach to explain child mortality and undernutrition in south asia and sub-saharan africa. discussion paper, ibero-america institute for economic research, no. 152, 2006. 9. kreft, i. and de leeuw, j. introducing multilevel modeling. sage publications, london, 1998. 10. goldstein, h. nonlinear multilevel models, with an application to discrete response data. biometrika, 1991, 78(1), 45-51. 11. bryk, a.s. and raudenbush, s.w. hierarchical linear models. newbury park, ca: sage publication, london, 1992. 12. al-riyami, a., abdel el aty, m.a., jaju, s., morsi m., al-kharusi, h. and al-shekaili, w. oman national reproductive health survey. muscat: ministry of health, sultanate of oman, 2008. 13. filmer, d., pritchett and l.h. estimating wealth effects without expenditure data or tears: an application to educational enrolments in states of india. demography, 2001, 38(1), 115-132. 14. khan, h.t.a. a hierarchical model of contraceptive use in urban and rural bangladesh. contraception, 1997, 55: 91-96. 15. khan, h.r. and shaw, j.e.h. multilevel logistic regression analysis applied to binary contraceptive prevalence data. j. data science, 2011, 9, 93-110. 16. kalam, e.m.n. and khan, h.t.a. modeling contraceptive prevalence in bangladesh: a hierarchical approach. asian meta centre, research paper series, no. 21, 2002 17. ferede, t. multilevel modeling model of modern contraceptive use among rural and urban population of ethiopia. am. j. math. stat., 2013, 3(1), 1-16. 18. goldstein, h. multilevel statistical models. edward arnold, london, 2003. received 30 november 2014 accepted 31 march 2015 squ journal for science, 2021, 26(1), 8-21 doi:10.24200/squjs.vol26iss1pp8-21 sultan qaboos university 8 a surface network based on polytyramine/ gold nanoparticles: characterization, kinetics, thermodynamics and selective determination of norepinephrine emad a. khudaish* and arwa al-maskari department of chemistry, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman. *e-mail: ejoudi@squ.edu.om. abstract: a solid-state sensor was fabricated by a spontaneous electrochemical deposition of polytyramine (ptyr) film onto a glassy carbon electrode (gce) which was further peripherally supported by gold nanoparticles (aunps). the surface materials of the developed sensor (aunps.ptyr-gce) were characterized by x-ray photoelectron spectroscopy (xps), electrochemical impedance spectroscopy (eis), cyclic voltammetry (cv) and differential pulse voltammetry (dpv). the rate constant of charge transfers (kct) of the as-prepared sensor (8.77 × 10 -4 cm/s) was evaluated by fitting the charge transfer resistance (rct) data in the presence of ferric-ferrous hexacyanide redox couple solution, [fe(cn)6] 3-/4. the voltammetric behavior of norepinephrine (nor) was confirmed to follow an irreversible reaction mechanism at which the estimated diffusion coefficient value was 7.39 × 10 -5 cm 2 /s. the sensor showed a large enhancement on nor oxidation and comparatively lowered its detection limit (dl3) to 0.130 m (22 ppb). it was also applied for selective determination of nor in the presence of high concentrations of ascorbic acid (aa) and uric acid (ua). the interference study highlighted the great stability of the proposed sensor by generating a similar sensitivity as in the pure nor solution. the analytical performance of the proposed system was validated successfully for pharmaceutical and biological samples with tolerable recovery percentages. keywords: polytyramine; gold nanoparticles; norepinephrine; ascorbic acid and uric acid. ،والحرارية الديناميكيا الحركية ،ذرات النانو لعنصر الذهب : دراسة تشخيص البناء سطح شبكي من بوليمر التيرامين و بناء نتاايية يي تحيي النورابنرريناال روى المسكريأعماد خديش و ر التيرامين على سطح قطب الكاربون الزجاجي وتدعيمه بطبقة بناء مستشعر صلب الحالة بواسطة التراكم االلكتروكهربائي لطبقة رقيقة من بوليم :صيخمال حساب ثابت من ذرات النانو لعنصر الذهب . تم دراسة و تشخيص المادة المترسبة على السطح بواسطة الطرق الضوئية والكهروكيميائية المختلفة و كذلك عكسي لمادة النورابنفرين و تقييم معامل روليتي . تم اثبات السلوك الغيرتمؤكسد( الك-سرعة انتقال االلكترونات للمستشعر باستخدام مسبار )مختزل جزء من المليون . تم دراسة االنتقائية التحليلية 0.000ظهر المستشعر قابلية عالية على اكسدة النورابنفرين الى حدود دنيا تصل الى أاالنتشارية )النفاذية( . االسكوربيك و حامض اليوريك كمواد بيولوجية متداخلة قادرة على تشويش االشارة الكهربائية . كذلك تم تقييم للنورابنفرين بوجود تراكيز عالية من حامض .القدرة التحليلية للمستشعر المطور على تقدير النورابنفرين في عينات حقيقية صيدالنية و بيولوجية .حامض اليوريك حامض االسكوربيك، ،لعنصر الذهب ذرات النانو ليمر التيرامين، نورابنفرين،بو :مرتاحيةالكيمات ال a surface network based on polytyramine/gold nanoparticles 9 1. introduction onstruction of chemically modified electrodes based on the incorporation of, or a coating of, specific conducting materials is one of the central research activities of the past decades [1,2]. the selection and characterization of modified surface materials are playing important roles in testing the stability, the reproducibility and the analytical performance of certain electro-active substances. the deposition of polymeric nanocomposite materials onto electrode surfaces by electrochemical means is an interesting topic in terms of producing a uniform coating with layers of specific thickness [3,4]. tyramine (tyr) has received considerable attention as an ideal monomer for electrochemical deposition due to the presence of a free amino functional group that simplifies doping of organic or inorganic materials [5,6]. moreover, the phenolic functionality can be easily oxidized for initiation of a polymeric reaction and formation by propagation steps for a final generation of the polymer [7,8]. polytyramine (ptyr) film deposited on different substrates under various experimental conditions has been studied to understand its structure, composition, thermal and mechanical properties, along with its conductivity for sensing applications [9-11]. there has been great interest in nano-sized elements such as gold nanoparticles (aunps) for the fabrication of electrochemical sensors due to their outstanding physical and chemical properties, comprising their small size, high catalytic activity, large surface area, and their having compatible environment [12,13]. moreover, electrode modification by doping of aunps onto a polymeric moiety such as ptyr can be functionalized for improving the electronic conductivity of surface materials which enhances the kinetics of the electron transfer process. the presence of a free amino group makes ptyr an attractive structure for further modification by attachment of an active electron mediator such as aunps. the resulting aunps. ptyr-gce modified electrode is expected to have a characteristic active surface area, a larger adsorption domain, and hence a greater catalytic capacity. catecholamines are vital neurotransmitters that control the physiological processes in human bodies by regulating communication within the neural network [14]. they are released from noradrenergic neurons in the central nervous system (cns) and sympathetic nervous system (sns) for many neurophysiological processes such as monitoring heart rate, fatty acid placement, stress sensing, body temperature, learning, and memory [15,16]. damage in secretion or uptake of neurotransmitters is known to cause neurodegenerative diseases and psychiatric disorders [17]. nor is one significant transmitter which has a strong influence on attention and response activities within the brain, is a blood pressure controller, and regulates emotional excitement and mood disorders [18]. it has an important role in the treatment of hypertension, bronchial asthma, organic heart disease and myocardial infarction, and in cardiac surgery [19]. abnormal levels of nor in plasma and urine are utilized as a biomarker for several diseases such as hypertension, diabetes mellitus ketoacidosis, neuroblastoma and parkinson’s disease [20,21]. therefore, a large number of methods have been developed for the sensitive and selective quantification of trace amount of nor in biological samples or pharmaceutical formulations [22,23]. a nonconventional method for rapid detection with great precision and reproducibility has been an urgent demand for neurotransmitter analysis that includes the application of electrochemical sensors with highly reactive surface materials [24,25]. electrochemical approaches applying various systems of interest have been proposed for selective and sensitive analysis, based on active surface modifications including the attachment of metal nanoparticles to conducting polymers [26], surfactant assisted metal oxide nanoparticles [27], self-assembled l-cysteine/aunps/mwcnt [28], and a graphene modified electrode [29], among many others. in the present work, the attachment of aunps has been achieved by direct surface casting a drop of aunps over the pre-fabricated (ptyr-gce) surface. the rich π-bonding electrons of the polymer backbone attract strongly to electrons of gold atoms in the outer orbitals. the resulting modified electrochemical system (aunps.ptyr-gce) was studied to explore its composition, stability and electrochemical performance for the selective determination of norepinephrine (nor) in the presence and absence of electrochemically active interference biological species such as ascorbic acid (aa) and uric acid (ua). furthermore, the analytical performance of the proposed sensor was tested for real samples (pharmaceutical ampoule solution and plasma blood). 2. experimental section 2.1 apparatus and chemicals a bas 50w potentiostat was used to control all electrochemical measurements that were conducted in a threeelectrode cell. a bare gce (before modification) was used as the working electrode (we), a platinum coil as the counter electrode (ce) and ag/agcl/kcl(sat.) as the reference electrode (re). the potentiostat and electrodes were purchased from bas (bioanalytical system, west lafayette, in, usa). the we was regularly polished prior to each experiment to a mirror surface using a polishing cloth and alumina slurry (5.0 and 1.0m), rinsed with acetone and washed fully with distilled water, then ultra-sonicated in water for 5 min using jac ultra sonic (labkorea inc, korea), and finally rinsed thoroughly with distilled water. the tyramine (tyr) monomer, norepinephrine (nor), ascorbic acid (aa), uric acid (ua), potassium ferrohexacyanate, k4(fe(cn)6, potassium ferrihexacyanate, k3(fe(cn)6, and sulfuric acid (h2so4), all were of analytical grades purchased from sigma-aldrich chemie, germany. potassium orthophosphate (kh2po4) and c emad a. khudaish and arwa al-maskari 10 dipotassium phosphate (k2hpo4) were obtained from bdh, uk. gold nanoparticles (aunps) of 30 nm size come with a citrate ligand (nanopartz inc., usa). a moderately alkaline background electrolyte (ph = 7.4) made of 0.1 m phosphate buffer solution (pbs) was used for selective determination of nor in the electrochemical cell (size = 20 ml) which was degassed for 10 min prior to measurement with oxygen-free nitrogen gas, and which was blanketed throughout the experiment. 2.2 fabrication of the surface network the proposed aunps.ptyr-gce surface network was fabricated by deposition of ptyr onto the clean gce via reversible voltammetric cycling followed by a drop casting of 20 l aunps. the electrochemical deposition of the ptyr was achieved by continuous scanning of the we potential between 0 mv and 1400 mv vs. ag/ agcl at 50 mv/s for 30 scans (15 cycles) in 0.1 m of h2so4 containing 20 mm tyr monomer. the deposition time limit for controlling the thickness of the ptyr film is a crucial factor to build up a sensitive surface material possessing a good conductivity. therefore, lowering the number of repetitive cycles to 15 was sufficient to fabricate a thin and stable platform for doping electroactive materials such as aunps and presenting an active surface for electron shuttling with the electrode substrate. the electrode sensitivity decreases dramatically with a larger deposition time limit of ptyr (above 20 cycles), in agreement with previous experimental data describing the surface resistivity, passivation and limitation of active area due to increasing film thickness [30]. 2.3 characterization of the surface network the surface materials of the modified electrode were essentially identified (structure, composition and reactivity) using various analytical tools. an x-ray photoelectron spectroscopy (xps) machine (omicron nanotechnology xps system, germany) was employed to determine the composition of materials deposited onto the gce. the obtained xps spectra of individual components were de-convoluted using a gaussian lorentzian function after background subtraction with a shirley function in casa xps software (casa software ltd, uk). the binding energies were calibrated with respect to a adventitious c 1s feature at 284.6 ev. electrochemical impedance spectroscopy (eis) experiments using a bi-potentiostat pc-14 (gamry, usa) were conducted to identify the resistivity of the deposited materials on the electron transfer processes. the eis data were recorded in a three-electrode cell containing 5 mm of [fe(cn)6] 3-/4 solution within a frequency range of between 100 khz to 1 hz at an amplitude of 5 mv. randle’s equivalent circuit was used to demonstrate the electrochemical properties at the solid/electrolyte interface at open circuit potential. cyclic voltammetry (cv) and differential pulse voltammetry (dpv) techniques (bas software, usa) were used for electrochemical deposition of the modified electrode, reactivity and selectivity tests, and analytical performance for sensitivity of determination of nor in artificial and real samples. 2.4 preparation of real samples a noradrenaline ampoule (1 mg/ml) and plasma blood samples were obtained from squ hospital, muscat, oman. the drug solution was diluted 10 times with pbs (0.1 m of ph = 7.4) to prepare a 0.591 mm stock solution which was applied directly for dpv measurements of nor. on the other hand, the plasma blood was diluted 3 times with pbs and the standard addition method for as-prepared 0.5 mm of nor was applied. the recovery percentage of nor in both real samples was computed to evaluate the sensitivity and reliability of the proposed sensor. 3. results and discussion 3.1 fabrication of the surface network materials electrochemical deposition of ptyr film on the gce surface was obtained by repetitive voltammetric scanning of 30 segments (15 cycles) using the cyclic voltammetry (cv) method. the electrode potential was reversibly stepped between 0 and 1400 mv vs ag/agcl at a rate of 50 mv/s in an electrochemical cell containing 20 mm of tyr monomer dissolved in 0.1 m h2so4. figure 1 shows an irreversible anodic peak for tyr oxidation at 1175 mv (for the first cycle) which decreases significantly at the preliminary four successive cycles. moreover, the anodic peak potential is shifted negatively to 1125 mv in the fourth cycle. the above trend suggests a surface passivation due to the generation of low conductivity short oligomers. the growth of the polymeric film in the subsequent cycles from cycle 5 (dotted black) to cycle 15 (solid black) as shown in the inset is associated with reduction of the surface resistivity, apparent by a spontaneous increase of the anodic peak current at 1135 mv. the propagation of the polymer (pt yr) is predominantly carried out by the formation of cationic radical intermediates due to an oxidation reaction of the phenolic group present in the tyr monomer [31]. the phenoxy cationic radical produced in the initiation step undergoes a dimerization reaction by attacking a new tyr molecule (linkage via the ortho position in the aromatic ring). with subsequent cycling, the oligomerization process is continued to form an insoluble propagated polymer that is deposited onto the electrode surface in a mechanism consistent with those demonstrated for ptyr deposition at sputtered [32] and graphite [33] electrodes. in the present experimental conditions, the 15 repetitive cycles were appraised to build a thin polymeric film on the electrode surface. it was observed that the anodic peak current adopted nearly a constant value above 15 cycles, indicating the growth of a thicker film. the thickness and the amount of ptyr deposited on the https://www.sciencedirect.com/science/article/pii/s0013468614010135#bib0130 https://www.sciencedirect.com/science/article/pii/s0013468614010135#bib0135 a surface network based on polytyramine/gold nanoparticles 11 electrode surface are directly affected by the nature of the electrode substrate, the concentration of tyr monomer and electrolyte composition (mostly the ph), the number of potential cycles and scan rates. it should be noted that the oxidation of tyr in an acidic medium results in the formation of ptyr with a rich number of free cationic amino groups (one per a chain). accordingly, the experimental conditions and data presented in figure 1 were selected to generate a thin ptyr platform film for doping active surface materials such as gold nanoparticles (aunps). the above pattern of fabrication increases the electrode surface area and enhances the electron transfer kinetics with the targeted electroactive species. for this task, a drop of 20 l aunps was mechanically added onto the moiety of the fabricated ptyr modified surface. the proposed sensor (aunps.ptyr-gce) was characterized using various analytical tools and finally applied for the selective determination of nor in artificial and real samples. figure 1. reversible potentiodynamic waves (15 cycles) using gce in 20 mm of acidified tyr monomer. the electrode potential scanned between 0 and 1400 mv at a rate of 50 mv/s. 3.2 characterization of surface materials 3.2.1 xps studies the xps core level spectra of c 1s peaks obtained from different samples are shown in figure 2. the xps spectra of a bare gce surface shown in figure 2 (a) produces approximately an equal percentage of (c-c)/ (c-h) sp 2 hybridization obtained at (284.5 ev) and sp 3 hybridization at (285.0 ev), respectively. the structure and percentage of (c-c)/(c-h) function are changed upon deposition of the polymer and came as a single peak at its preference position of 284.6 ev with 93.6% as shown in figure 2 (b). two extra convoluted peaks were obtained at 285.7 ev (21.3%) and 287.1 ev (12.6%) characterized for functional groups of (c-n)/(c-o) and (c=o), respectively. upon casting of the aunps, the c 1s spectra for the fabricated (aunps.ptyr-gce) shows some distinctive features on the nature of surface functionalities in terms of binding energies and percent concentrations. figure 2 (c) depicts three convoluted peaks obtained at 284.8 ev (79%), 285.9 ev (38.3%) and 289 ev (32.1%) assigned to (c-c)/(c-h), (c-n)/(c-o), and (c=o), respectively. emad a. khudaish and arwa al-maskari 12 figure 2. xps spectra for surface samples; (a) c 1s of pristine gce, (b) c 1s of ptyr-gce, (c) c 1s of aunps.ptyrgce, and (d) au 4f of aunps onto ptyr moiety. the above characteristic topographies presented in figure 2 (b) and (c) are evidence for successful deposition of ptyr and the construction of the proposed (aunps.ptyr-gce) sensor. the presence of aunps on the surface materials is confirmed by the high resolution xps spectra for the au 4f pattern shown in figure 2 (d). two deconvoluted peaks at electronic states of 82.7 ev (au 4f7/2) and 86.3 ev (au 4f5/2) [34] were obtained with a spinorbit separation of 3.7 ev confirming the attachment of au species onto the surface moiety [35]. the experimental data and all features presented in figure 2 are evidence for successful surface modification and the final preparation of the proposed sensor. 3.2.2 eis and electrochemical studies the structure of the solid/liquid interface is subject to some limiting factors that affect the reactivity of the fabricated sensors. restriction factors are centralized by the internal resistance generated by surface modification and can be represented by the impedance of the electrodes under investigation. the internal resistance is composed of three components: charge transfer resistance (rct) which arises by surface activation, the omhic component which is described by the solution resistance (rs) due to solution resistivity and the nature of surface materials, and finally the concentration or mass transport resistance (generally considered as a pure diffusion). these important features can be studied efficiently using the electrochemical impedance spectroscopy (eis) under experimental conditions of a narrow potential window and a wide frequency range. the nyquist plot presented in figure 3(a) demonstrates the applied potential at the open circuit value of a redox probe (5 mm of [fe(cn)6] 3-/4) which is characterized by both faradaic and non-faradaic processes. the faradaic process is initiated by the surface activation process and defined by the electrode kinetics (fast or slow). therefore, it is a direct measurement of (rct) and describes the extent of impedance (inhibition) of the electron transfer process at the modified surfaces. mathematically, it is inversely proportional to the rate constant of the electron transfer process (kct) induced by surface materials and simply given by (rct * kct = k) [36], where k is a constant equal to 0.749 cm.ohm/s for the present experimental conditions, which involve the transfer of a single electron (n = 1) at ambient temperature (t = 298 k). the non-faradaic process arises due to charging of the double layer capacitance (cdl) via electrostatic attraction of ions at the interface satisfied by the value of potential across it. in addition, a typical semicircular curve with resistance zone combines both (rct) and the uncompensated solution resistance (rs) imposed by the working electrolyte, both obtained at high frequency. the mass transport process (diffusion) is depicted as a straight line obtained at low frequencies. a surface network based on polytyramine/gold nanoparticles 13 figure 3. (a) eis spectra represented by nyquist plot for bare gce (black open circle), ptyr -gce (red cross) and aunps.ptyr-gce (blue closed circle) in the presence of 5 mm [fe(cn)6] 3/4 . (b) cvs for bare gce (black), ptyrgce (red) and aunps.ptyr-gce (blue dotted) in the presence of 5 mm [fe(cn)6] 3/4 . the eis fitting data for all electrodes depicted in figure 3(a) have different values of rct owing to the nature of the surface materials. for instance, the bare gce (black open circle) produces a value of 470 ω which increased extremely to 2360 ω prior to deposition of ptyr onto gce (red cross). the value of rct obtained for aunps.ptyr-gce (blue closed circle) is lowered dramatically to 855 ω. apparently, introducing of aunps as a new member of the surface materials improves the kinetics (decreases the surface resistivity) of the fabricated sensor. consequently, the computed (kct) value for the proposed (aunps.ptyr-gce) sensor was 8.77 × 10 -4 cm/s, higher by 2.8 times over that (3.18 × 10 -4 cm/s) of the (ptyr-gce) modified electrode. it is obvious that the presence of exterior aunps increases both the electrode conductivity and the active surface area. figure 3(b) depicts the electrochemical behavior of bare gce (solid black) and as-prepared modified electrodes ptyr-gce (solid red) and aunps.ptyr-gce (dotted blue), respectively, in the presence of a redox probe (5 mm of [fe(cn)6] 3-/4) using the cv method. both bare gce and aunps.ptyr-gce produce very well-defined and comparable reversible redox waves with peak potential separation (ep = ep,a  ep,c) of 106 mv and 188 mv, respectively. in the case of ptyr-gce, the calculated (ep = 282 mv) value becomes much larger due to the evident potential shift (far positive and negative) of both anodic and cathodic peaks, suggesting slow electrode kinetics. the presence of aunps emad a. khudaish and arwa al-maskari 14 onto the ptyr moiety improves the electron transfer process by lowering the electrode over-potential by approximately 100 mv. moreover, the response currents (anodic and cathodic) of the aunps.ptyr modified surface are much greater than that recorded for the virgin ptyr surface, consisting with the experimental data of eis presented in figure 3(a). the above characteristic mapping confirms a successful construction of modified electrodes and the importance of aunps as a reactive dopant. a further investigation on the behavior of nor oxidation at various electrodes was conducted to characterize the significance of aunp doped surface materials. figure 4 depicts the electrochemical oxidation of 50 m nor at various electrodes in 0.1 m of pbs (ph = 7.4) and (v = 50 mv/s) using the dpv technique. the electrochemical measurements were expressed by the change in the current response of nor oxidation (i) after eliminating the current response of the background electrolyte generated by each electrode. obviously, the current response at the bare gce is the lowest compared to the as-prepared modified electrodes which can be attributed to weak adsorption of nor. in the intermediate (ptyr-gce) surface, the current response is little higher than the bare substrate due to the presence of more active surface sites to attract nor. the proposed sensor (aunps.ptyr-gce) shows a prominent current response approaching 1.75 times greater than that of the (ptyr-gce) modified electrode. the presence of aunps has an evident synergism action for accelerating the electron transfer process with nor and also offers a wide adsorption assembled surface for stronger bonding. it should be noted that the peak potential of nor oxidation is shifted in a more negative direction by 25 mv compared to the modified ptyr-gce. it is good evidence for a rapid electrochemical reaction that is explicitly pertinent to the surface materials of the proposed sensor. figure 4. dpv current responses at 50 mv/s for the oxidation of 50 m nor in 0.1 m pbs (ph = 7.4) recorded at bare gce (black), ptyr-gce (red) and aunps.ptyr-gce (blue). 3.2.3 the behavior of nor oxidation at aunps.ptyr-gce the electrochemical behavior of nor at the developed aunps.ptyr-gce was monitored using the cyclic voltammetry (cv) technique as shown in figure 5 (a). apparently, the reaction mechanism of nor is following an irreversible mode concluded by the growth of an anodic peak at 240 mv in the forward scan corresponding to nor oxidation, which increases linearly with increasing [nor]. in the reverse cathodic scan, only a peak shoulder of constant current response is collected at 130 mv for the entire [nor] range. this trend can be attributed to the reaction mechanism of nor oxidation which involves a cyclization step [37]. it is important to note that some literature reports that nor experiences a reversible reaction by varying the recorded anodic and cathodic peaks with electrode scan rates without considering the size (ratio) of both obtained peaks. figure 5 (b) depicts the linear relationship of the anodic peak current (ip) as a function of [nor] collected from the basic experimental data of figure 5 (a). the resulting slope of (0.0577 a/m) is important to calculate the diffusion coefficient of nor applying the randles-sevcik equation for irreversible processes [36]. the calculated value is 7.39 × 10 -5 cm 2 /s assuming a transfer of two electrons (n = 2) by nor oxidation. the obtained value for the present system is approximately two times greater than (3.30 × 10 -5 cm 2 /s) evaluated at a zno/cnts modified electrode [38]. a surface network based on polytyramine/gold nanoparticles 15 figure 5. (a) cv waves for the behavior of nor at aunps.ptyr-gce (v = 50 mv/s) in pbs (ph = 7.4) recorded for a range of [nor]; (a) 0, (b) 5, (c) 10, (d) 15, (e) 20, (f) 25, (g) 30, (h) 35, (i) 40, and (j) 50 m. (b) the linear relationship of ip vs [nor] of the original dpv data presented in fig. 5 (a). the minimum and maximum boundaries of nor diffusion coefficient values were not identified since this thermodynamic parameter is affected by the electrolyte composition, the nature of surface materials, the ionic or molecular size, and the temperature. the reactivity of the proposed sensor (aunps.ptyr-gce) was tested under experimental conditions given in figure 5 (a) for 10 cycles (20 segments) in the presence of 50 m of nor. the anodic peak current decreased spontaneously with subsequent cycles to fall to 86.0% (in the last three cycles) of its ideal initial value as shown in figure 6. this marks a change in the nature of the surface due to the accumulation of inactive oxidation byproducts. moreover, it describes the robustness and stability of the developed sensor against surface poisoning. it is worth noting that the oxidative pathway of nor is initiated by the transfer of two-electrons and two-protons, forming an unstable oquinone derivative that rapidly cyclized via intermolecular attraction to produce a leucochrome derivative. the reaction is propagated to the formation of an electrochemically inactive melanin polymeric species [37, 39]. figure 6. the reactivity test of aunps.ptyr-gce (current response as a function of repetitive cv cycles) for the oxidation of 50 m nor in 0.1 m pbs (ph = 7.4). emad a. khudaish and arwa al-maskari 16 ho ho nh2 oh norepinephrine o o nh2 oh o-quinone ho ho oh nh leucochrome inactive melanine polymer scheme 1. the oxidative pathway of nor describing the cyclization step and end propagation mechanism for the formation of inactive melamine polymer. 3.2.4 selective determination of nor at aunps.ptyr-gce the practical application of aunps.ptyr-gce for nor quantification is presented in figure 7 employing dpv in 0.1 m of pbs (ph = 7.4) at (v = 50 mv/s). a well-defined anodic peak current was obtained at 192 mv vs ag/agcl corresponding to nor oxidation, which directly correlated to successive increments of [nor]. the stability and reactivity of the sensor is diagnosed by bringing the anodic peak to a constant potential value for the entire applied [nor] range. the linear plot of (ip) as a function of [nor] shown in the inset of figure 7 produces a slope of (0.1189 a/m), by which the calculated detection limit (dl3) was 0.130 m (22 ppb). figure 7. (a) dpv current responses for nor oxidation at aunps.ptyr-gce (v = 50 mv/s) in pbs (ph = 7.4) recorded as a function of [nor]; (a) 0.5, (b) 1, (c) 2, (d) 3, (e) 4, (f) 5, (g) 6, (h) 7, (i) 8, (j) 9, (k) 11, (l) 13, (m) 15, (n) 18, and (o) 22 m. (b) the linear relationship of ip vs [nor] of the original data presented in figure 7(a). a surface network based on polytyramine/gold nanoparticles 17 table 1 lists the analytical performance of various modified electrodes [40-46] for nor quantification in terms of detection limit, sensitivity and applied electrochemical method. the present electrochemical system is highly competent and exhibits superior performance to some relevant polymeric constituent surfaces. inspection of the competency of the proposed sensor was performed by selective determination of nor in the presence of aa (250 m) and ua (50 m) as electroactive interference species. figure 8(a) shows the dpv anodic peak for nor oxidation obtained at 192 mv which increases gradually with subsequent addition of nor for a concentration range between 0.5 m and 25 m. the inset of figure 8(a) shows that the dpv anodic peaks for aa and ua oxidation (in the absence of nor) occurred at 2 mv and 266 mv, respectively. table 1. the analytical performance of various modified electrodes in terms of detection limit, sensitivity and method employed for nor quantification. ________________________________________________________________________ modified dl sensitivity method ref. electrode (m) (a/m) ________________________________________________________________________ pdan/gce 1.82 0.012 dpv [41] ppy/b-cd-me 0.80 0.050 swv [42] bha and tio2 nps 0.50 0.199 dpv [43] poly(glutamic acid) mcpe 0.43 0.094 dpv [44] cace/gce 0.28 0.044 dpv [45] mwnts-zno/ch-spe 0.20 0.059 swv [46] poly(cresol red)/gce 0.20 0.156 dpv [47] aunps.ptyr/gce 0.13 0.119 dpv present ________________________________________________________________________ a potential distance of 190 mv from aa and 74 mv from ua is adequate to overcome any possible overlap of anodic peaks of the three species. moreover, the adsorption capacity of the electrode surface materials is capable of assembling all molecules and their byproducts indicating a robust and reactive sensor. a close scrutiny of the linear plot, (ip) vs [nor], given in figure 8(b), demonstrates that the slope of (0.1015 a/m) is consistent with that in the absence of aa and ua (shown above in the insert of figure 7) which is evidence of good reproducibility and the stability of the present sensor. moreover, the calculated detection limit (dl3) was 0.142 m (24 ppb). the reliability and sensitivity of the present electrochemical system were tested for the determination of nor in drug and blood plasma samples using a dpv method as described above in section 2.4. the average recovery percentage (n = 3) of nor listed in table 2 was obtained by conversion the dpv peak current into [nor] using the regression data illustrated in figure 8(b). the minimum (95%) and maximum (101%) of reported percentages under the present experimental conditions describe the extent of reactivity and analytical performance of the sensor developed for sensitive nor determination. emad a. khudaish and arwa al-maskari 18 figure 8. (a) dpv current responses for selective determination of nor in the presence of 250 m [aa] and 50 m [ua] at aunps.ptyr-gce (v = 50 mv/s) in pbs (ph = 7.4) recorded for a range of [nor]; (a) 0.5, (b) 1, (c) 1.5, (d) 2, (e) 3, (f) 4, (g) 5, (h) 6, (i) 8, (j) 10, (k) 13, (l) 16, (m) 19, (n) 22, and (o) 25 m. insert is the dpv response in the absence of nor. (b) the linear relationship of ip vs [nor] of the original dpv data presented in figure 8 (a). table 2. the recovery percentage of nor in pharmaceutical ampoule and plasma blood samples. ______________________________________________________________________________ [actual] [found]  rsd (a) recovery samples (m) (m) (%) ______________________________________________________________________________ ampoule (1) 0.591 0.565  0.021 95.6 (2) 1.182 1.150  0.027 97.3 (3) 2.364 2.327  0.035 98.4 (4) 4.728 4.783  0.028 101.2 (5) 9.456 9.464  0.019 100.1 plasma (1) 0.00 n.d. ----- (2) 0.50 0.475  0.017 95.0 (3) 1.00 0.956  0.026 95.6 (4) 3.00 2.980  0.029 99.3 (5) 6.00 6.092  0.034 101.5 (6) 9.00 9.068  0.034 100.8 ______________________________________________________________________________ (a) relative standard deviation (n = 3). the electrochemical stability of the developed sensor in the last injection of nor (25 m) nor in the presence of (250m aa) and (50 m ua) was verified by dpv repetitive scanning for 12 runs with 5 min intervals. the anodic peak potential of nor oxidation was consistently obtained at 192 mv and decreased negligibly with subsequent runs to approach 2.6% of its maxima in the last run, suggesting a reliable and stable sensor for selective nor quantification in real samples. 4. conclusion this paper describes an approach for the fabrication of a solid-state sensor based on electrochemical polymerization of tyramine (ptyr) film onto the surface of a glassy carbon electrode (gce) followed by a drop casting of gold nanoparticles (aunps). the as-prepared surface materials (aunps, ptyr-gce) were characterized using surface image spectroscopy and electrochemical methods. these comprehensive investigative methods explore properties of the built up surface materials such as composition and structure, resistivity and reactivity, and analytical a surface network based on polytyramine/gold nanoparticles 19 performance. the proposed sensor was tested 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l., min, q., xiang, j., wang, q., xie, j., yue, y., wu, s., li, x., ding, h., a di sposable electrochemical sensor for simultaneous determination of norepinephrine and serotonin in rat cerebrospinal fluid based on mwnts-zno/chitosan composites modified screen-printed electrode, biosensors and bioelectronics 2015, 65, 3138. 47. chen, w., lin, x., luo, h., huang, l., electrocatalytic oxidation and determination of norepinephrine at poly(cresol red) modified glassy carbon electrode, electroanalysis 2005, 17, 941-944. received 7 september 2020 accepted 20 january 2021 squ journal for science, 2017, 22(1), 10-15 doi: http://dx.doi.org/10.24200/squjs.vol22iss1pp10-15 2017 sultan qaboos university 10 morphometry of organs in sheep fed a diet containing tannins and polyphenols osman mahgoub1*, ibrahim inwa2, isam t. kadim1, mohamed h. tageldin1 and kaadhia al-kharousi 1department of animal and veterinary sciences, college of agricultural and marine sciences, p.o. box 34, pc 123, al-khoud, muscat, sultanate of oman; 2department of anatomy, college of medicine & health sciences, sultan qaboos university, p.o. box 35, pc 123, alkhoud, muscat, sultanate of oman. *e-mail: osmahgob@squ.edu.om. abstract: the aim of this study was to use morphometry to investigate the essential organs of sheep fed with nonconventional diets. twelve male omani sheep were fed with one of two types of roughages supplemented with a commercial concentrate for 63 days and then slaughtered. the volumes of their kidneys, testes, and livers were measured. random samples from the organs were fixed in formalin and embedded in paraffin. random five micrometer sections from each block were stained with hematoxylin and eosin. images from four random fields were taken from each slide using a digital camera attached to the microscope and then loaded onto a stereology software installed on a personal computer. morphometric measurements of body organs were taken. animals fed diets containing tannins had lower final total body weight and lower weights and volumes of their livers, testes and kidneys. there was high variability in the results of intestinal parts measurements, but there was a general trend of the treated animals having higher duodenal and ilial height, villus height, crypt depth and epithelial thickness. the only significant diet effect was higher liver l and lower vfrac cytoplasm in the control animals than in those treated. the only significant treatment effect on the kidney measurements was a higher tube length/density in treated animals. there were no treatment effects on the testes measurements. the current study indicates that sheep may safely utilize diets containing the levels of polyphenols and tannins used here with no drastic effects on the digestive system and vital organs. keywords: oman; sheep; tannins; morphometry. التراكيب الدقيقة ألعضاء جسم الضأن التي تمت تغذيتها على أعالف تحتوي على التانين والبوليفونوالتم تقنية قياس ااستخد عثمان محجوب وإبراهيم إنوا وعصام كاظم ومحمد حسن تاج الدين وكاذية الخروصي كان الهدف من هذه الدراسة هو استخدام تقنية قياس التراكيب الدقيقة لبعض أعضاء الجسم المهمة في الضأن التي تمت تغذيتها على علف غير :ملخصال م يوماً ثم ذبحت بعد ذلك. ت 63تقليدي. تمت تغذية اثني عشر من ذكور الضأن العماني على أحد نوعي علف خشن باإلضافة إلى علف تجاري مركز لمدة في البارافين. تم صبغة شرائح ميكرومترية طمرهاقياس حجم كل من الكلية والكبد والخصية ومن ثم تم أخذ عينات من كل عضو وحفظها في الفورمالين ثم ام كاميرا رقمية اختيرت عشوائياً من كل مكعب بصبغة الهيماتوكسلين واإليوزين. تم أخذ صور من أربع مجاالت عشوائياً من كل شريحة مجهرية باستخد ات موصلة بمجهر ومن ثم تحميلها على برنامج تجسيم حاسوبي على جهاز كمبيوتر شخصي ثم تم أخذ قياسات تراكيب األعضاء. كان وزن جسم الحيوان نه في الحيوانات التي تغذت على التي تغذت على العلف المحتوي على التانين عند نهاية التجربة ووزن وحجم الكبد والكلية والخصية في نهاية التجربة أقل ع كبر في الجزء األول الغذاء العادي. كان هناك تباين كبير في قياسات مناطق األمعاء المختلفة ولكن كانت هناك اتجاه عام بأن الحيوانات المعالجة لها عرض أ وكانت هناك فروقات معنوية بسيطة في قياسين في الكبد وقياس في والثاني من األمعاء والزغابات المعوية وعمق السراديب المعوية وسمك الخاليا الطالئية. ين والبوليفينوالت الكلية بينما لم تكن هناك تأثيرات معنوية في الخصية. بينت الدراسة بأن الضأن يمكن تغذيته بصورة مأمونة على أعالف محتوية على التان ثيرات ضارة على الجهاز الهضمي وبعض األعضاء المهمة في الجسم.على المستويات التي تم استخدامها في هذه الدراسة بدون تأ .عمان ، الضأن ، التانين ، قياس األشكال :مفتاحيةالكلمات ال 1. introduction ow quality non-conventional feeds (ncf) usually contain high fibre and low protein, minerals and vitamin levels. the ncf feeds usually contain polyphenols and condensed tannins that may cause antinutritional effects [1]. the tannins have been proved to form combinations with proteins in the rumen rendering them unavailable for digestion [2,3]. tannins interfere with nutrient digestion and promote excretion of endogenous nitrogen in monogastric animals by forming tannin-enzyme complexes [4]. tannins might also cause physical damage to the digestive system and other vital organs such as the kidney and liver [5,6]. research has indicated different responses to tannin consumption in various animal species. for instance, oral administration of tannic acid produced coagulative and hemorrhagic necrosis l mailto:osmahgob@squ.edu.om morphometry of organs in sheep fed diet 11 in the liver of mice but produced no similar effects in sheep [7]. the current study aimed to investigate the effects of feeding feeds containing phenols and tannins on the morphometry of a number of organs in sheep. 2. materials and methods twelve 1-year old male omani sheep (body weight 31.8 ± 1.2 kg) were fed one of two types of roughage: rhodesgrass hay (rgh) or urea-treated palm frond (utpf) for 63 days. both groups also received 400 g of a commercial concentrate daily. at the end of the feeding period, the animals were slaughtered. the use of experimental animals and the methodology for the trial was approved by the college of agricultural and marine science research committee under project number: sr/agr/plnt/01/01. levels of phenols and condensed tannins were analysed following standard methods [8]. the reference volumes of the kidneys, testes, and liver were estimated using water immersion volumetry [9,10]. organs including the abomasum, duodenum, jejunum, and ileum were fixed in 10% buffered formalin. systematic random samples of tissue were embedded in paraffin. random five micrometer sections were obtained from each block and stained with h&e and then observed with a leica microscope (microscope specs). images from four random fields were taken from each slide using an olympus digital camera (dp12) attached to the microscope. the images were then loaded onto histometrix, a stereology software (histometrix mil6, kinetic imaging ltd uk) installed on an ibm compatible personal computer. the volume density (vf) of the nucleus in hepatocytes was estimated by point counting by generating an array of random points grid on the image and counting the total number of points,  p, falling within the nucleus and dividing it by the number of points falling within the whole cell [11]. cell nuc nucf p p v    )( (1) the absolute volume of the hepatocyte nucleus (v(nuc)) was determined by the point-sampled intercept method [12]. the four random sections showing whole cells from each animal, an unbiased counting frame with superimposed random test points was applied on each selected section. if a test point fell on a nucleus profile, a line, l0 , in an isotropic uniform direction (iur) was drawn through the point to the nuclear boundary. the volume of the nucleus, nucv , was then estimated from the following equation:  3 0 3 lv nuc  (2) estimates of absolute hepatocyte cell volume (v) were obtained by using the volume density of the nucleus, and volume-weighted mean nuclear volume: )( nucv nuc cell v v v  (3) the surface density measurements (sv) of intestinal villi and the filtration barrier of the kidney were estimated by applying line probes on to an image of the villi/glomerulus and counting the intersections between the line probe and villus/glomerular surface  i. the classical relationship which describes sv, the surface density, in terms of the intersection count  i and the total length of line probe, l, is l i s v   2 (4) where sv is the surface density  i is the number of intersections l is the total length of line probe falling within the object. for the length density measurements (lv,), the probability that a given structure is hit by a randomly positioned and randomly oriented section is proportional to its linear dimension or length. the number of times a linear structure is cut by or intersects a section will depend on the total length of the structure and the area of the section surface. the length density of renal tubules and seminiferous tubules was estimated by counting the number of tubule profiles, q, in an area of the section. the relationship which describes lv, the length density, in terms of the intersection count q and the area of the section is a q l v   2 (5) where lv is the length density  q is the number of intersections a is the total area of section. osman mahgoub et al 12 the volume of renal glomeruli was determined by the point-sampled intercept method [12]. on each of four random sections showing whole glomeruli at a magnification of ×40, an unbiased counting frame with superimposed random test points was applied. if a test point fell on a glomerulus profile, a line, l0, in an isotropic uniform direction (iur) was drawn through the point to the glomerular boundary. the volume of the glomerulus, glomv , was then estimated from the following equation:  3 0 3 lv glom  (6) to study the effects of diet, data were subjected to the analysis of variance using the general linear models procedure in the sas windows version [13,14]. significant differences between treatment means were assessed using the least significant difference procedure at the p<0.05 level. 3. results feed analyses indicated that animals fed the urea-treated palm fronds (utpf) were subjected to a lower nutritional regime compared to those fed the rhodesgrass hay (rgh) as their diet had a higher fibre content and higher levels of phenols and condensed tannins (table 1). table 1. chemical composition of ingredients of experimental feeds. feed ingredient experimental diets commercial concentrate utpf rgh dm (g/kg) 862 892 916 crude protein (g/kgdm) 180 85 10 ether extract (g/kgdm) 21.5 11 15 neutral detergent fiber (g/kgdm) 182 740 614 acid detergent fiber (g/kgdm) 56 580 370 hemicellulose (g/kgdm) 126 160 243 ash (g/kgdm) 73 120 95 ca++ (g/kgdm) 12 7.4 5 po4(g/kgdm) 8 1.1 0.20 ge (kj/g) 183 192 173 total extractable phenols a 16.6 112.6 32.1 extractable condensed tannins b 0 12.8 0 total extractable phenols expressed as gram equivalent tannic acid/kgdm. b extractable condensed tannins expressed as gram equivalent leucocyanidins/kgdm. animals fed utpf had lower final weight, lower weight of liver, testes and kidney as well as lower volumes for the same organs either in absolute terms or as per kg/bw (table 2). table 2. body organ weight and volume in omani sheep fed either urea-treated palm frond (treated) or rhodesgrass hay (control) plus a commercial concentrate for nine weeks. parameter experimental group pse effect of diet treated control final body weight (kg) 31.70 35.92 0.837 ** liver weight (g) 311.7 388.6 3.33 *** liver weight/bw 9.7 10.4 0.27 ns testes weight (g) 110.6 128.3 6.52 * testes weight/bw 3.4 3.4 0.21 ns kidney weight (g) 39.0 40.1 1.02 ns kidney weight/bw 1.21 1.10 0.019 ** liver volume (ml) 272.7 352.8 10.03 *** testes volume (ml) 90.0 106.8 8.01 * kidney volume (ml) 23.3 26.1 2.55 ns pse : pooled standard error ns : not significant p<0.05; ** p<0.01; *** p<0.001 morphometry of organs in sheep fed diet 13 there was high variability in the various measurements of organ morphometry including those of intestinal parts. however, there was a general trend of the utpf fed animals having higher values for duodenal and ilial height, villus height, crypt depth and epithelial thickness (table 3). measurements on the jejunum, however, showed an opposite trend with values from utpf fed animals being significantly lower than those of the control group, and only significant in the villus height. table 3. morphometry of the small intestine of omani sheep fed urea-treated palm frond (treated) or rhodesgrass hay (control) plus a commercial concentrate for nine weeks. parameter type of diet pse effect of diet treated control duodenum: duodenum height (um) 979.0 790.2 63.78 0.09 duodenum villus height 603.5 505.7 54.96 ns duodenum crypt depth 368.0 285.5 24.15 0.06 duodenum epithelial thickness 45.0 37.3 4.28 ns jejunum jejunum total height 844.5 1066.5 106.52 ns jejunum villus height 427.8 652.5 59.49 * jejunum crypt depth 419.5 416.0 50.0 ns jejunum epithelial thickness 22.3 26.7 1.84 ns ilium ilium total height 996.3 969.2 79.83 ns ilium villus height 507.5 543.2 47.46 ns ilium crypt depth 489.5 428.7 56.17 ns ilium epithelial thickness 23.3 26.5 1.47 ns pse : pooled standard error ns : not significant p<0.05; ** p<0.01; *** p<0.001 there were no significant effects of diet on the morphometry of the liver except for the liver length density which was higher and the volume of fraction cytoplasm which was lower in control animals (table 4). the only significant treatment effect on the kidney measurements was a higher value of tube length/density in treated vs. control animals. there were no treatment effects on the testes measurements, either for tube volume, length, length/density or number of nephrons per area (table 4). table 4. morphometry of the liver, kidney and testes of omani sheep fed urea-treated palm frond (treated) or rhodesgrass hay (control) plus a commercial concentrate for nine weeks. parameter treatment pse effect of diet treated control liver: volume density (vf) 2.73 3.53 1.021 ** volume fraction cytoplasm 0.75 0.65 0.035 * anon 8.16 10.37 1.14 ns volume fraction sinus 0.174 0.105 0.064 ns nuclear size 4.57 4.28 0.789 ns absolute volume of hepatocyte nucleus 0.14 0.16 0.020 ns kidney: tube volume 2.23 2.62 2.537 ns tube total length (µ) 2.80×1011 2.15×1011 3.36×1010 ns length density 0.013 0.008 0.001 * glomeruli number per area 0.00005 0.00004 0.00002 ns glomeruli size 19140 25133 3873 ns surface density 0.089 0.090 0.012 ns surface area 2.17×10-12 2.3×10-12 4.17×10-12 ns testes: osman mahgoub et al 14 tube volume 9.68 1.07 6.92 ns tube length 5.41×109 6.19×109 0.901×109 ns tube length/density 0.0006 0.0006 0.00009023 ns number/area 0.0003 0.0003 0.00004 ns pse : pooled standard error ns : not significant p<0.05; ** p<0.01; *** p<0.001 table 4. contd. 4. discussion the utpf with its higher fibre content and lower digestibility coefficients resulted in larger volumes of faeces and lower viscosity of gut contents in the sheep, a characteristic of highly fibrous diets [3]. the utpf also contained higher levels of phenols and condensed tannins, which have been known to have antinutritional effects [2,15]. animals fed the utpf consumed approximately 550 g/d of utpf and therefore, must have ingested considerable amounts of condensed tannins. it has been reported that similar levels of condensed tannins in sheep have reduced protein degradation in the rumen and increased protein flow to the intestine [16,17]. there was an indication of these classical effects of tannin-containing feeds in ruminants from a digestibility trial using utpf with sheep [3]. higher levels of nitrogen in the faeces indicate lower nitrogen retention, which is a characteristic of dietary tannins, which bind to proteins in the rumen and consequently reduce digestion and absorption in the gut [2,4,5]. there are also reports that tannins may form complexes with carbohydrates and minerals and consequently inhibit microbial and digestive processes in ruminant animals, resulting in depressed rumen digestive function [2,15]. the low body and organ weights and volumes of the animals fed diets containing tannins was expected as the highly fibrous feeds with anti-nutritional factors would restrict feed intake and consequently negatively influence the body weight of experimental animals. the size of testis is indicative of reproductive efficiency in male farm animals. the weight of the testis of the sheep in the current study was equivalent to 0.35% of body weight. this is in line with observations indicating that testis mass as a proportion of body weight decreases with increasing size of mammals [18]. it has been reported that the gonadosomatic index (testes mass/body mass) in cats was as low as 0.08% [19]. therefore, it appears that tannin consumption did not directly affect testis size and consequently would not affect reproductive efficiency in male sheep at the levels used in the present study. on the other hand, tannins in monogastric animals produce a significant effect on the weight of some body organs. some reports have indicated that tannins significantly increase pancreas weight but not liver weight in chickens [20]. in the latter study, the weight of the pancreas from birds which had received the highest amount of tannins was more than double that of the control birds. significant enlargement was detectable only at tannin concentrations above 13.5 g/kg. as the tannin content increased from 13.5 to 25 g/kg and from 25 to 50 g/kg the pancreas increased in weight by 33 and 10 % respectively. the high variability in the measurements of the organ morphometry in the present study was in line with the conclusion of a prior study that biological variation between individuals is likely to be the major factor influencing the overall precision and efficiency of nested sampling schemes for morphometric analysis of thin sections [21]. therefore, it was recommended that it is important to examine more animals to reduce the variance of the group mean [21]. similar to the findings of the current study, there have been reports that duodenal villus height and height to crypt depth ratio were significantly lower in animals fed similar non-conventional feeds [6]. also there have been findings indicating a trend of decreasing villus height and villus surface area in the proximal duodenum [5]. conflicting reports on the effects of tannins on the morphometry of the intestine have been attributed to differences in species and to the site of sampling due to the wide variations in intestinal structure along the digestive tract [6]. villus height and crypt depth decreases from the proximal to the distal regions of the small intestine [22]. the effects on liver morphometry were minimal and may have no biological explanation. therefore, they were in line with those indicating that oral administration of tannic acid to sheep produced no effects on their livers, unlike inter-peritoneal administration of tannins [7]. the significant treatment effect of the higher values for kidney tube length/density in treated animals may have no serious impact on sheep health with normal glomeruli number and size, as seen in this experiment. the lack of treatment effects on the testes measurements substantiates the observations on testis size and volume discussed earlier on. 5. conclusion in general, the findings of the current experiment indicate that feeding non-conventional diets containing high levels of polyphenols and tannins does not produce significant effects on the morphometry of sheep intestines and vital organs. morphometry of organs in sheep fed diet 15 6. acknowledgements we acknowledge sultan qaboos university for funding the research through a strategic grant: sr/agr/pint/01/01. references 1. kumar r. anti-nutritional factors, the potential risks of toxicity and methods to alleviate them. fao 102, animal production and health paper: 2000, 145-160. 2. robins c. and brooker j.d. the effects of acacia aneura feeding on abomasal and intestinal structure and function in sheep. animal feed science and technology, 2005, 121, 205-215. 3. mahgoub, o., kadim, i.t., tageldin, m.h., al-marzooqi, w.s., khalaf, s.q. and ambu ali, a. clinical profiles of sheep fed non-conventional feeds containing phenols and condensed tannins. small ruminant research, 2008a, 78, 115-122. 4. longstaff, m. and mcnab, j.m. the inhibitory effects of hull polysaccharides and tannins of field beans (vicia faba l.) on the digestion of amino acids, starch and lipids and on digestive enzyme activities in young chicks. british journal of nutrition, 1991, 65, 199-216. 5. walton j.p., waghorn g.c., plaizier j.c., birtles m. and mcbridge b.w. influence of condensed tannins on gut morphology in sheep fed lotus pedunculatus. canadian journal of animal science, 2001, 81, 605-607. 6. mahgoub o., kadim i.t., tageldin m.h., al-marzooqi w., khalaf s.q., al-amri i. and ambu ali a. 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(ed.), kluwer academic publishers. 2003, 102 pp. 9. scherle w. a simple method for volumetry of organs in quantitative stereology. mikroskopie, 1970, 26, 57. 10. weibel e.r. stereological methods. volume 1: practical methods for biological morphometry. academic press. london 1979. 11. howard c.v., reed m.g. unbiased stereology. three-dimensional measurement in microscopy. oxford: bios scientific publishers, uk. 1998. 12. gundersen h.j.g. and jensen e.b. stereological estimation of the volume-weighted mean volume of arbitrary particles observed on random sections. journal of microscopy, 1985, 138, 27-142. 13. ott, r.l., 1993. analysis of variance in some standard experimental designs. in: introduction to statistical methods and data analysis. duxbury press, belmont, ca. pp 842-928. 14. sas institute inc. sas user's guide: statistics. version 5, sas institute inc., cary, nc. 2000. 15. perez-maldonado r.a. and norton b.w. the effects of condensed tannins from desmodium intortum and calliandra calothyrsus on protein and carbohydrate digestion in sheep and goats. british journal of nutrition, 1996, 76, 515-533. 16. waghorn g.c., jones w.t. and shelton i.d. the nutritive value of lotus corniculatus l. containing low and medium concentrations of condensed tannins for sheep. proceedings of the new zealand society of animal production, 1987, 47, 75-80. 17. waghorn g.c. effect of condensed tannin on protein digestion and nutritive value of fresh herbage. proceedings of the australian society of animal production, 1990, 18, 412-415. 18. kenagy g.j. and trombulak s.c. size and function of mammalian testes in relation to body size. journal of mammalogy, 1986, 67, 1-22. 19. franca l.r. and godinho c.l. testis morphometry, seminiferous epithelium cycle length, and daily sperm production in domestic cats (felis catus). biology of reproduction, 2003, 68, 1554-1561. 20. ahmed a.e., smithard r. and ellis m. activities of enzymes of the pancreas, and the lumen and mucosa of the small intestine in growing broiler cockerels fed on tannin-containing diets. british journal of nutrition, 1991, 65,189-197. 21. gupta m., mayhew t.m., bedi k.s., sharma a.k. and white f.h. inter-animal variation and its influence on the overall precision of morphometric estimates based on nested sampling designs. journal of microscopy, 1983, 131, 147-154. 22. van leeuwen p, jansman j.m. and wiebenga j. dietary effects of faba-bean (vicia faba l.) tannins on the morphology and function of the small-intestinal mucosa of weaned pigs. british journal of nutrition, 1995, 73, 3139. received 29 august 2016 accepted 14 february 2017 squ journal for science, 2016, 21(2), 139-149 © 2016 sultan qaboos university 139 symmetry of the pyritohedron and lattices nazife o. koca*, aida y. al-mukhaini, mehmet koca, and amal j. al-qanobi department of physics, college of science, sultan qaboos university, p.o. box 36, pc 123 al-khoud, muscat, sultanate of oman. *email: nazife@squ.edu.om. abstract: the pyritohedron consisting of twelve identical but non regular pentagonal faces and its dual pseudoicosahedron that possess the pyritohedral (th) symmetry play an essential role in understanding the crystallographic structures with the pyritohedral symmetry. the pyritohedral symmetry takes a simpler form in terms of quaternionic representation. we discuss the 3d crystals with the pyritohedral symmetry which can be derived from the coxeter-dynkin diagram of d3. keywords: pseudoicosahedron; pyritohedron; lattice; coxeter groups and quaternions. كات الفراغيةيوالشب البايرايتذو التركيب المشابه لمعدن تماثل متعدد األوجه القنوبيجمعه المخيني، محمد كوجا وأمليوسف عايدة نظيفة كوجا، المحتوي على اثني عشر وجها متماثال كل منها هو مضلع خماسي غير منتظم إن متعدد األوجه ذو التركيب المشابه لمعدن البايرايت :صمستخل ورات ذات ونظيره شبيه ذي العشرين وجها المنتظم والذي يتميز بتناظر األوجه الموجود في معدن البايرايت يلعبان دورا أساسيا في فهم تراكيب البل يرايت صورة بسيطة باستخدام التمثيل المعتمد على العدد التخيلي الرباعي. تناقش هذه الورقة التماثل الموجود في معدن البايرايت. يأخذ تماثل معدن البا .𝐷3دنكن -البلورات ثالثية األبعاد والتي لها تماثل شبيه بمعدن البايرايت والتي يمكن اشتقاقها من مخطط كوكستر لتركيب المشابه لمعدن البايرايت، الشبيكة الفراغية، مجموعات كوكستر، شبيه ذي العشرين وجها المنتظم، متعدد األوجه ذو ا: مفتاحيةكلمات الرباعيات. 1. introduction ymmetry describes the periodic repetition of structural features. any system exhibits symmetry if the action of the symmetry operations leaves the system apparently unchanged. crystals possess a regular, repetitive internal structure, therefore they have symmetry. coxeter groups are the symmetry groups generated by reflections [1]. they describe the symmetry of regular and semi-regular polytopes in arbitrary dimensions [1]. the coxeterweyl groups acting as discrete groups in 3d euclidean space generate orbits representing vertices of certain polyhedra [2-3]. rank-3 coxeter-weyl groups 𝑊(𝐷3)and 𝑊(𝐵3 ) ≈ 𝐴𝑢𝑡(𝐷3) define the point tetrahedral and octahedral symmetries of the cubic lattices [4]. in this work we use coxeter-dynkin diagram 𝐷3 and construct the pyritohedral group and the related polyhedra in terms of quaternions by finding the vertices of the pseudoicosahedron with pyritohedral symmetry. we organize the paper as follows. in section 2 we introduce quaternions and their relevance to o (3) and o (4) transformations. the sets of quaternions defining the binary tetrahedral and binary octahedral groups are given. section 3 explains coxeter-dynkin diagram of 𝐷3 in which the simple roots (lattice generating vectors) and the group generators are expressed in terms of imaginary quaternionic units and the reflection planes of the diagram 𝐷3 are identified as certain planes of the unit cube. section 4 deals with the construction of the icosahedron, dodecahedron, pseudoicosahedron and pyritohedron from the pyritohedral group derived from the 𝐷3 diagram as its automorphism group. it is noted that the truncated octahedron, the wigner-seitz cell of the bcc lattice, splits into two pseudoicosahedra which are mirror images of each other. in section 5 we discuss the pseudoicosahedron and its dual pyritohedron to give a description of those crystals possessing pyritohedral symmetry. s mailto:nazife@squ.edu.om nazife o. koca et al 140 2. quaternions and their relevance to the isometries of the o (3) and o (4) transformations quaternions are vectors in four dimensions provided with a rule for multiplication that is associative but not commutative, distributive through addition, contains an identity, and for each nonzero vector in four dimensions has a unique inverse [5] the quaternionic imaginary units 𝑒𝑖 , (𝑖, 𝑗, 𝑘) = (1, 2, 3) satisfy the relation: 𝑒𝑖 𝑒𝑗 = −𝛿𝑖𝑗 + 𝑖𝑗𝑘 𝑒𝑘 (1) where ijk  is the levi-civita symbol that is completely antisymmetric in the indices. a real quaternion q can be written in general as 𝑞 = 𝑞0 + 𝑞1 𝑒1 + 𝑞2𝑒2 + 𝑞3𝑒3 (2) with 𝑞0, 𝑞1, 𝑞2, 𝑞3 ∈ ℝ, ℝ being the set of real numbers; 𝑞0 is called the scalar part and (𝑞1 𝑒1 + 𝑞2𝑒2 + 𝑞3𝑒3) is the vector part of a quaternion. the conjugate of a quaternion is defined as �̅� = 𝑞0 − 𝑞1𝑒1 − 𝑞2𝑒2 − 𝑞3𝑒3. (3) the norm of unit quaternion q is |𝑞| = √𝑞�̅� =1 and 𝑞−1 = �̅�. the scalar product of two arbitrary quaternions 𝑝 and 𝑞 is defined as (𝑝, 𝑞) = 1 2 (�̅�𝑞 + �̅�𝑝) = 1 2 (𝑝�̅� + 𝑞�̅�) . (4) the transformations of an arbitrary quaternion 𝑡 → 𝑝𝑡𝑞 and 𝑡 → 𝑝𝑡̅𝑞 define orthogonal transformation of the group 𝑂(4). it is clear that the above transformations preserve the norm 𝑡𝑡̅ = 𝑡0 2 + 𝑡1 2 + 𝑡2 2 + 𝑡3 2 . we define the above transformations as abstract group operations by the notations 𝑡 → 𝑝𝑡𝑞 ∶= [𝑝, 𝑞]𝑡, 𝑡 → 𝑝𝑡̅𝑞 ∶= [𝑝, 𝑞]∗𝑡. (5) dropping also t, the pair of quaternions define a set closed under multiplication. the inverse elements take the forms [6]: 1 1 [ , ] [ ,q], ([ , ] ) [ , ] .p q p p q q p       (6) with the choice of q p , the orthogonal transformations define a three parameter subgroup (3)o . the transformation [ , ] and [ , ]p p p p  leaves the 𝑆𝑐(𝑡) = 𝑡0 invariant. therefore in 3d euclidean space one can assume that the quaternions consist of only vector components, namely 1 1 2 2 3 3 t t e t e t e   , satisfying 𝑡̅ = −𝑡. with this restriction to the 3d space the element [ , ]p p  takes a simpler form [ , ] [ , ].p p p p    therefore the transformations of the group (3)o can be written as [ , ]p p where the sandwiching operator [ , ]p p represents the rotations around the vector 𝑉𝑒𝑐(𝑝) = (𝑝1, 𝑝2, 𝑝3) and [ , ]p p is a rotary inversion [1]. reflection of a vector λ represented as a quaternion with respect to a plane orthogonal to the unit pure quaternion 𝑞 can be written as λ → −𝑞λ̅𝑞. (7) if we apply another reflection to the vector λ it will lead to a rotation. the product of two reflections is a rotation. we will display some of the finite subgroups of quaternions related to the tetrahedral and octahedral groups. the set 𝑇 is given by the group elements 𝑇 = {±1, ±𝑒1, ±𝑒2, ±𝑒3, 1 2 (±1 ± 𝑒1 ± 𝑒2 ± 𝑒3)} (8) and is called the binary tetrahedral group of order 24. another set of 24 quaternions is defined by 𝑇 ′ = { 1 √2 (±1 ± 𝑒1), 1 √2 (±1 ± 𝑒2), 1 √2 (±1 ± 𝑒3), 1 √2 (±𝑒1 ± 𝑒2), 1 √2 (±𝑒2 ± 𝑒3), 1 √2 (±𝑒3 ± 𝑒1) } . (9) symmetry of pyritohedron and lattices 141 the set 𝑂 = 𝑇 ∪ 𝑇′ forms binary octahedral group of order 48. these sets play an important role in the definition of the pyritohedral subgroup. 3. finite coxeter groups, cartan matrix and root systems in 1934 coxeter classified all finite euclidean reflection groups [7-8]. a coxeter group is a group 𝑊(𝐺) which has a presentation with a very special form 𝑊(𝐺) = ⟨𝑟1, 𝑟2, … , 𝑟𝑛 |(𝑟𝑖 𝑟𝑗 ) 𝑚𝑖𝑗 = 1⟩ (10) where 𝑟1, 𝑟2, … , 𝑟𝑛 are the reflection generators of the group. all information of a root system can be encoded by coxeter-dynkin diagrams and the cartan matrix c. the simple roots 𝛼1, 𝛼2, … , 𝛼𝑛 of the coxeter-dynkin diagram are the vectors orthogonal to certain hyperplanes with respect to which the simple reflection acts as an arbitrary vector 𝜆 as [1]: 𝑟𝑖 𝜆 = 𝜆 − 2(𝜆,𝛼𝑖) (𝛼𝑖,𝛼𝑖) 𝛼𝑖 . (11) the cartan matrix is a square integer matrix that links the simple roots of a given group through the following relation: 𝐶𝑖𝑗 = 2(𝛼𝑖,𝛼𝑗) (𝛼𝑗,𝛼𝑗) . (12) the inverse of the cartan matrix is related to the metric of the dual (reciprocal) space as: 𝐺𝑖𝑗 = (𝐶 −1)𝑖𝑗 (𝛼𝑗,𝛼𝑗) 2 (13) the basis vectors in the dual space are called the weight vectors, denoted by 𝜔𝑖 , satisfying the scalar product: 𝐺𝑖𝑗 = (𝜔𝑖 , 𝜔𝑗 ). the simple roots and weight vectors are related to each other by (𝜔𝑖 , 2𝛼𝑗 (𝛼𝑗,𝛼𝑗) ) = 𝛿𝑖𝑗 and 𝛼𝑖 = 𝐶𝑖𝑗 𝜔𝑗 . 3.1 coxeter-dynkin diagram of 𝑾(𝑫𝟑) the coxeter-dynkin diagram of 𝐷3 with the quaternionic simple roots is shown in figure 1. the angle between two connected roots is 120°, otherwise they are orthogonal. figure 1. the coxeter-dynkin diagram 𝑫𝟑 with quaternionic simple roots. an arbitrary quaternion 𝜆 when reflected by the operator 𝑟𝑖 with respect to the hyperplane orthogonal to the quaternion 𝛼𝑖 , is given in terms of quaternion multiplication [6] as 𝑟𝑖 𝜆 = − 𝛼𝑖 √2 𝜆̅ �̅�𝑖 √2 : = [ 𝛼𝑖 √2 , − 𝛼𝑖 √2 ] ∗ 𝜆 :=[ 𝛼𝑖 √2 , 𝛼𝑖 √2 ] , 𝑖 = 1, 2, 3. (14) the generators of the coxeter group 𝑊(𝐷3) are then given in the notation of (14) by 1 1 2 1 2 1 2 1 2 1 1 1 1 [ ( ), ( )] [ ( ), ( )] 2 2 2 2 r e e e e e e e e         , 2 2 3 2 3 2 3 2 3 1 1 1 1 [ ( ), ( )] [ ( ), ( )] 2 2 2 2 r e e e e e e e e         , (15) 3 2 3 2 3 2 3 2 3 1 1 1 1 [ ( ), ( )] [ ( ), ( )] 2 2 2 2 r e e e e e e e e         . 𝛼2 = 𝑒2 − 𝑒3 𝛼1 = 𝑒1 − 𝑒2 𝛼3 = 𝑒2 + 𝑒3 nazife o. koca et al 142 they generate the coxeter-weyl group 𝑊(𝐷3) of order 24, isomorphic to the tetrahedral group, the elements of which can be written compactly by the notation 𝑊(𝐷3) = {[𝑇, �̅�] ∪ [𝑇 ′, −�̅� ′]}. (16) here 𝑇 and 𝑇′ are the sets of quaternions given in (8-9). when the simple roots are chosen as in figure 1, then the weight vectors are determined as 𝜔1 ≡ (100) = 𝑒1, 𝜔2 ≡ (010) = 1 2 (𝑒1 + 𝑒2 − 𝑒3), (17) 𝜔3 ≡ (001) = 1 2 (𝑒1 + 𝑒2 + 𝑒3). using the orbit definition 𝑊(𝐷3)(𝑎1𝑎2𝑎3) ≔ (𝑎1𝑎2𝑎3)𝐷3 all the orbits can be determined. 3.2 coxeter-dynkin diagram 𝑾(𝑫𝟑) with dynkin diagram symmetry the symmetry of the union of the orbits (010)𝐷3 ∪ (001)𝐷3 requires the dynkindiagram symmetry : 𝛼1 → 𝛼1, 𝛼2 ↔ 𝛼3 as shown in figure 2. it leads to the transformation on the imaginary quaternions 𝛾: 𝑒1 → 𝑒1, 𝑒2 → 𝑒2 , 𝑒3 → −𝑒3. the dynkin-diagram symmetry operator reads 𝛾 = [𝑒3, −𝑒3] ∗ = [𝑒3, 𝑒3] which extends the coxeter group 𝑊(𝐷3) to the octahedral group 𝐴𝑢𝑡(𝐷3) ≈ 𝑊(𝐷3) ∶ 𝐶2 of order 48, the automorphism group of the root system of 𝐷3 . 𝑂ℎ ≈ 𝐴𝑢𝑡(𝐷3) = {[𝑇, ±�̅�] ∪ [𝑇 ′, ±�̅�′]}. (18) figure 2. the dynkin-diagram symmetry . the maximal subgroups of the octahedral group 𝐴𝑢𝑡(𝐷3) ≈ 𝑂ℎ, each of order 24, are shown in figure 3. in the next section we work on pyritohedral group. figure 3. the maximal subgroups of the octahedral group. the maximal subgroups chiral octahedral group tetrahedral group pyritohedral group octahedral group α 1 α 2 α 3 symmetry of pyritohedron and lattices 143 4. pyritohedral group and related polyhedra pyritohedral symmetry is well known in crystallography as the symmetry of the pyritohedron. the group of this symmetry is an important discrete point group of crystallography. the polyhedra with this symmetry can be derived from the coxeter-dynkin diagram of 𝐷3. the pyritohedral group ]},[],{[ ttttth   consists of rotation generators in addition to the dynkin diagram symmetry  of d3. the group can be represented as 𝑇ℎ = 𝐴4: 𝐶2 =< 𝑟1𝑟2, 𝑟1𝑟3, 𝛾 > where (: ) denotes the semi direct product. this is the rotational symmetry of a cube with stripes on its faces as shown in figure 4. the rotation generators 𝑟1𝑟2 𝑎𝑛𝑑 𝑟1𝑟3 of d3 generate the subgroup ],[ )( tt c dw a  2 3 4 of order 12, where a4 is an even permutation of 4 vertices of a tetrahedron. the chiral tetrahedral group 4att ],[ consists of 8 rotations by 1200 around the 4 diagonals of the cube, 3 rotations by 1800around the x, y and z axes, and the unit element [9]. pyrite crystals often occur in the forms of cubes with striated faces as in figure 4, octahedra and pyritohedra (a solid similar to dodecahedron but with non-regular pentagonal faces) or some combinations of these forms. figure 4. the cube with stripes on its faces possesses the pyritohedral symmetry. 4.1 construction of the vertices of the pseudoicosahedron we denote a general vector of d3 by 1 1 2 2 3 3a a a      where the weight vectors are defined in (17). we note that the orbit of the pyritohedral group generated by the vector  with different values of 𝑎𝑖 forms different polyhedra. for instance: 𝑎1 = 1, 𝑎2 = 𝑎3 = 0 corresponds to an octahedron. 𝑎1 = 𝑎3 = 0, 𝑎2 = 1 or 𝑎1 = 𝑎2 = 0, 𝑎3 = 1 corresponds to a cube. 𝑎1 = 0, 𝑎2 = 𝑎3 = 1 corresponds to a cuboctahedron. 𝑎1 ≠ 0, 𝑎2 = 𝑎3 ≠ 0 gives ))(( 21 1 2 11 ee a a ea  , and the orbit corresponds to a pseudoicosahedron as discussed below. applying some of the rotation elements of the pyritohedral symmetry on a general vector of 1 1 2 2 3 3 a a a      , one can generate five triangles sharing the vertex  as shown in figure 5(a), which consist of two equilateral and three isosceles triangles. the vertices 2 1 2 1 2 , and ( )r r r r   form an equilateral triangle with an edge length squared: 2 2 1 1 2 2 a a a a  . similarly, the vertices 2 1 3 1 3 , and ( )r r r r   form the second equilateral triangle with the edge length squared: 2 2 1 1 3 3 a a a a  . the line between the vertices  and 2 3 r r  has a length squared: 2 2 2 3 a a . if we impose all the edge lengths to be equal, we would have five equilateral triangles around one vertex and obtain the relation nazife o. koca et al 144 2 2 2 2 2 2 1 1 2 2 1 1 3 3 2 3 a a a a a a a a a a       . (19) suppose the dynkin-diagram symmetry as shown diagrammatically in figure 2 leaves the general vector  invariant   . this symmetry exchanges 𝜔2 and 𝜔3, so that 332211233211  aaaaaa  . (20) from (19) one gets ,32 aa  and a general vector can be written in terms of quaternions as 1 1 2 3 1 1 2 ( ( )) ((1 ) )a x a x e xe         (21) where 32 1 1 aa x a a   is a parameter which could be computed from (19). if we take a general value for x in the vector given in (21), the action of the pyritohedral group on  will generate the set of 12 vectors (apart from the scale factor a1): 𝑇ℎ  = ±(1 + 𝑥)𝑒1 ± 𝑥𝑒2, ±(1 + 𝑥)𝑒2 ± 𝑥𝑒3, ±(1 + 𝑥)𝑒3 ± 𝑥𝑒1. (22) factoring (19) by a1 one obtains the equation 2 1 0x x   . the solutions of this equation are 1 5 1 5 and 2 2       . these values of x will lead to five equilateral triangles sharing the vertex  . substituting and   respectively for x in (22) we obtain two sets of 12 vertices as: 1 2 2 3 3 1 { , , }e e e e e e         , (23a) 1 2 2 3 3 1 { , , }e e e e e e         . (23b) these sets of vertices represent two mirror images of an icosahedron with a scale factor difference. multiplying the vertices in (23b) by 3  one obtains the following set of quaternions: 1 2 2 3 3 1 { , , }e e e e e e         . (24) the vectors here have the same norm as in (23a). the icosahedron represented by (23a) is shown in figure 6(a). table 1 summarizes the action of the pyritohedral group on  for various values of x: (a) (b) figure 5. (a) five triangles meeting at one vertex, (b) the normal vectors of the triangles surrounding . symmetry of pyritohedron and lattices 145 table 1. the action of the pyritohedral group for various values of x. 211 xeex  )( ht polyhedra generated x or x )( 21 ee   or )( 21 ee   1 2 2 3 3 1 { , , }e e e e e e         or 1 2 2 3 3 1 { , , }e e e e e e         icosahedron 0x or 1x 1e or 2e 321 eee  ,, octahedron 2 1 x )( 21 2 1 ee  133221 eeeeee  ,, cuboctahedron other x 211 xeex  )( 1 2 2 3 3 1(1 ) , (1 ) , (1 )x e xe x e xe x e xe         pseudoicosahedron the vertices of the dual of the icosahedron, say the set of vectors of (23a), can be determined as [9]: 1 2 2 3 3 1 1 { , , } 2 e e e e e e           , (25a) 1 2 3 1 ( ) 2 e e e   . (25b) the 20 vertices in (25a and 25b) represent a dodecahedron as shown in figure 6 (b). its mirror image can be obtained by replacing   . (a) (b) figure 6. (a) icosahedron, (b) dodecahedron (dual of the icosahedron). the vectors in (25b) represent the vertices of a cube which is invariant under the pyritohedral symmetry. similarly, the other 12 vertices of (25a) form another orbit under the pyritohedral symmetry. they are obtained for x in (22) leading to a pseudoicosahedron. nazife o. koca et al 146 4.2 construction of the vertices of the pyritohedron from the pseudoicosahedron we can compute the dual of the pseudoicosahedron in equation (22) for an arbitrary value of x. this can be achieved by determining the vectors normal to the faces of the pseudoicosahedron in (22). the normal vectors of the five triangles in figure 5 (b) can be determined as follows: the normal vector of the triangle with the vertices 2 1 2 1 2 , , ( )r r r r   can be taken as 3 because 1 2r r is a rotation around 3  for 1 2 3 3 r r   . similarly, the normal vector of the triangle with the vertices  2 3131 ( and ), rrrr can be taken as 2 that is 2231  rr . the vertices generated by the pyritohedral group from either 2 or 3 would lead to the vertices of a cube given in (25b). the vectors normal to the isosceles triangles shown in figure 5 (b) can be computed as follows: 1 1 2 4 1 3 5 1 3 (1 ) , (1 ) , (1 ) . b e x e b x e e b x e e          the vectors 2 and 3 are in the same orbit under the pyritohedral group. moreover, )( 23   is orthogonal to 211 xeex  )( which means the scalar product of )( 23   and  is zero: 023  )),((  . on the other hand, one can prove that 541 and bbb , are also in one orbit under the pyritohedral group. they form a plane orthogonal to the vector 211 xeex  )( . as these five vertices should determine the same plane then one can show that 0 21  )),((  b is the necessary condition to determine the scale factor  . from this relation we obtain 𝜌 = 1+2𝑥 2(1+𝑥)2 where the scale factor implies that 𝑥 ≠ 1 and 𝑥 ≠ − 1 2 . then the vectors 1 4 5 2 3 , , , and b b b     determine a pentagon, non-regular in general (four edges of the same length and one edge different), as shown in figure 7. applying the pyritohedral group on these 5 vertices we obtain 20 vectors where ℎ = 𝑥 (𝑥 + 1)⁄ . the following 20 vertices of the pyritohedron split into two orbits: 12 vertices form a pseudoicosahedron and 8 vertices (±𝑒1 ± 𝑒2 ± 𝑒3) form a cube . {±(1 − ℎ2)𝑒1 ± (1 + ℎ)𝑒2, ±(1 − ℎ 2)𝑒2 ± (1 + ℎ)𝑒3, ±(1 − ℎ 2)𝑒3 ± (1 + ℎ)𝑒1}, (±𝑒1 ± 𝑒2 ± 𝑒3) (27) the pyritohedron has a geometric degree of freedom with two limiting cases as shown in figure 8. (26) 𝜌𝑏4 𝜌𝑏5 𝜌𝑏1 𝜔2 𝜔3 figure 7. the plane determined by the vectors normal to the faces of the pseudoicosahedron in equation (22). https://en.wikipedia.org/wiki/limiting_case_(mathematics) symmetry of pyritohedron and lattices 147 when h = 0, the 12+8 vertices in (27) represent the centers of edges and the vertices of a cube as in figure 8 (a). when h =1, the vertices in (27) represent a rhombic dodecahedron as shown in figure 8 (b). the regular dodecahedron represents a special intermediate case (𝑥 = −𝜎 or 𝑥 = −𝜏) where all edges and angles are equal. 5. vertices of the pseudoicosahedron and the pyritohedron in a lattice the simple cubic lattice consists of the vector 𝑚1𝑒1 + 𝑚2𝑒2 + 𝑚3𝑒3 where 𝑚𝑖 ∈ 𝒁, 𝑖 = 1,2,3. now, we can discuss the pseudoicosahedron and its dual pyritohedron relevant to crystallography. many candidates of pseudoicosahedra and its dual pyritohedra can be obtained as a structure in the simple cubic lattice. the vertices of pseudoicosahedron and its dual pyritohedron for various x (and corresponding h) values are given in table 2 and are plotted in figure 9. as mentioned in section 4.2, when 𝑥 → 0 (ℎ → 0 ) the pseudoicosahedron is converted to an octahedron and the pyritohedron becomes a cube. the set of vertices of the pseudoicosahedron and the pyritohedron belong to the simple cubic lattice. the unit cubic cell can be stacked in the pseudoicosahedron or in the pyritohedron as long as the vertices are chosen from the simple cubic lattice. table 2. pseudoicosahedron and its dual (pyritohedron) for arbitrary x values. x h vertices of pseudoicosahedron vertices of pyritohedron (up to a scale factor) 5 3 5 8 ±8𝑒1 ± 5𝑒2, ±8𝑒2 ± 5𝑒3, ±8𝑒3 ± 5𝑒1) for 𝑎1 = 3 with faces isosceles triangles with edge ratios 1,1,√50 49⁄ . {±39𝑒1 ± 104𝑒2, ±39𝑒2 ± 104𝑒3, ±39𝑒3 ± 104𝑒1}, 64(±𝑒1 ± 𝑒2 ± 𝑒3) 1 1 2 (±2𝑒1 ± 𝑒2, ±2𝑒2 ± 𝑒3, ±2𝑒3 ± 𝑒1) with faces isosceles triangles of edge ratios 1,1, √ 2 3 . {±3𝑒1 ± 6𝑒2, ±3𝑒2 ± 6𝑒3, 3𝑒3 ± 6𝑒1}, 4(±𝑒1 ± 𝑒2 ± 𝑒3). 1 10 1 11 (±11𝑒1 ± 𝑒2, ±11𝑒2 ± 𝑒3, ±11𝑒3 ± 𝑒1) for 𝑎1 = 4, faces of with isosceles triangles of edges 1,1,√2 111.⁄ {±110𝑒1 ± 132𝑒2, ±110𝑒2 ± 132𝑒3, ±110𝑒3 ± 132𝑒1}, 111(±𝑒1 ± 𝑒2 ± 𝑒3). figure 8. special cases of pyritohedron for (a) h =0, (b) h =1. nazife o. koca et al 148 pseudoicosahedron pyritohedron (dual of pseudoicosahedron) 𝑥 = 5 3 ℎ = 5 8 𝑥 = 1 ℎ = 1 2 𝑥 = 1 10 ℎ = 1 11 figure 9. the pseudoicosahedron and its dual (pyritohedron) for various x values. for a general x, the union of two pseudoicosahedra 1 2 2 3 3 1 (1 ) , (1 ) , (1 )x e xe x e xe x e xe         , 1 2 2 3 3 1 (1 ) , (1 ) , (1 )xe x e xe x e xe x e         (28) represents the vertices of a non-regular truncated octahedron which can be derived as the orbit of the coxeter group 𝑊(𝐵3) denoted by 𝑎1(1, 𝑥, 0)𝐵3 . this belongs to the simple cubic lattice if 𝑎1 and 𝑎1𝑥 = 𝑎2 are integers, which implies that x should be a rational number. in other words, as long as 𝑎1 and 𝑎2 are integers the pseudoicosahedron with the vertices can be embedded in a simple cubic lattice. ±(𝑎1 + 𝑎2)𝑒1 ± 𝑎2𝑒2, ±(𝑎1 + 𝑎2)𝑒2 ± 𝑎2𝑒3, ±(𝑎1 + 𝑎2)𝑒3 ± 𝑎2𝑒1 (29) 6. conclusion the polyhedra possessing the pyritohedral symmetry have been constructed in terms of quaternions. crystals with pyritohedral symmetry exist in the form of a stratified cube, an octahedron and a pyritohedron. it is expected that crystal structures in the form of a pseudoicosahedron as well as a pseudoicosidodecahedron may exist. the relevance of the pseudoicosahedron to pyritohedral crystals could stimulate research in application to material science. representation of the pyritohedral symmetry and crystal vectors in term of quaternions is more demanding, but may lead to a new understanding of crystal structures and their symmetries. we are anticipating that this finding will form a link between quaternions and crystallography. symmetry of pyritohedron and lattices 149 references 1. coxeter, h.s.m. regular polytopes (3rd ed.) new york: dover publications, 1973. 2. koca, m., al-ajmi, m. and koc, r. polyhedra obtained from coxeter groups and quaternions, j. math. phys, 2007, 48, 113514-113527. 3. koca, m., koca, n.o. and koc, r. catalan solids derived from three dimensional root systems and quaternions, j. math. phys, 2010, 51(4), 043501-043513. 4. conway, j.h. and smith d.a. on quaternions and octonions: their geometry, aritmetic and symmetry, a.k. peters, ltd. natick, m.a., 2003. 5. hamilton, s.w.r. lectures on quaternions, london: whittaker, 1853. 6. koca, m., koc, r. and al-barwani, m. non-crystallographic coxeter group h4 in e8. j. phys. a: math. gen. a, 2001, 34,11201-11213. 7. coxeter, h.s.m. discrete groups generated by reflections. annals of mathematics, 1946, 35, 588-621. 8. steinberg, r. finite reflection grouups. trans. am. math. soc., 1959, 493-504. 9. koca, m., koca, n.o. and al-shu’eili, m. chiral polyhedra derived from coxeter diagrams and quaternions, squ j. sci., 2011, 1, 16, 63; arxiv: 1006.3149. received 7 june 2016 accepted 4 september 2016 squ journal for science, 2021, 26(2), 98-106 doi:10.53539/squjs.vol26iss2pp98-106 sultan qaboos university 98 green preparation of aluminum-based metalorganic framework (al-mof) from waste plastic bottles and waste aluminum scraps saleh n. al-busafi* and yahya a. al-shafouri department of chemistry, college of science, sultan qaboos university, p.o.box 36, alkhodh 123, oman, * e-mail: saleh1@squ.edu.om. abstract: the vast use of polyethylene terephthalate (pet) drinking water bottles has increased dramatically worldwide in recent decades, inflicting severe consequences on the environment. according to the latest survey, a million plastic bottles are bought around the globe every minute. the non-biodegradable nature of pet materials has led to a huge accumulation of plastic in waste landfills. among the current recycling methods used to solve this environmental problem is chemical recycling. in this method, pet bottles are converted back cleanly into their starting materials: terephthalic acid and ethylene glycol. this paper unveils the exploitation of recycling products from pet bottles and aluminium scraps in order to prepare a metal-organic framework (mof) material. the characterization of the prepared mof substance was carried out using different techniques such as ir, xrd, sem and elemental analysis. keywords: polyethylene terephthalate (pet); aluminium scarp; metal-organic framework (mof). الصناعية من مخلفات األلومنيوم (al-mof)تصنيع مركب كيميائي من معدن األلومنيوم مرتبط بمادة عضوية ومخلفات العلب البالستيكية صالح البوصافي و يحيى الشافوري أدت الى تراكم هذه العلب في البيئه البولي إيثيلين تيريفثاالتالزياده المتطرده في استخدام علب المشروبات البالستيكية المصنعة من مادة إن :صلخمال ه نسبيا. أفضل الحلول بشكل ملحوظ. أن خطورة هذه المواد ناتجه في المقام األول من مقاومتها للتحلل البيولوجي في البيئه وبالتالي بقائها لفتره زمنيه طويل إلعادتها الى موادها األوليه وهي:حمض التيريفثاليك وإيثيلين جاليكول. في المطروحه للتخلص من النفايات البالستيكية هي إعادة تدوير هذه المواد كيميائيا حويلها الى مادة كلوريد هذه الورقه العلمية قمنا بتدويرعلب الماء البالستيكيه كيميائيا وإنتاج مادة حمض التيريفثاليك وأيضا قمنا بتدوير خردة األلمنيوم وت ين المادتين )حمض التيريفثاليك و كلوريد األلمنيوم( النتاج مادة مبلمرة تحتوي على فلز األلمنيوم مرتبط بوحده األلمنيوم. وفي النهاية قمنا بتفاعل هات وسائل الكم الطيفي لتحديد صفات المركب الجديد. . تم اسخدام al-mof)عضوية ) .عضويه-فلزيهمركبات ، خردة األلمنيوم ،بولي اثيلين تيري فثاالت :مفتاحيةالكلمات ال mailto:saleh1@squ.edu.om green preparation of aluminum-based metal-organic framework (al-mof) 99 1. introduction sed plastic drinking bottles, among other plastic waste, present a serious environmental problem in our society. although plastic materials have been playing a significant role in our modern life for their use in such as food packaging, water and beverage packaging, and mobile phone manufacturing, among other useful daily life applications [1], their non-degradable nature leads to rapid accumulation in the surroundings causing appalling environmental effects [2]. in particular, polyethylene terephthalate (pet) plastic, which is produced by the condensation reaction of terephthalic acid (benzene dicarboxylic acid, bdc) and ethylene glycol (eg) has received the greatest attention because of its widespread use in manufacturing most water and soft-drinks bottles [3]. the vast growth of the use of pet plastics globally is reflected in the increased worldwide production of these materials, which reached over 26 million tonnes (around 68 billion bottles) in 2019, of which bottled beverages was the largest end-use market accounting for 30% of global pet packaging consumption [4]. in oman, almost 50% of the plastic wastes, or 190,000 metric tonnes, dumped in landfills in 2019 were of pet [5]. currently, the common practice for disposing of used pet bottles is by landfilling, which has led to serious environmental problems due to the poor biodegradability of pet bottles [6]. another reported method is for recycling pet bottles by converting them back to their chemical constituents, bdc and eg [7]. this chemical method of recycling pet drinking bottles is considered a green and economical source of terephthalic acid and can contribute an acceptable way to eliminate pet waste landfilling, and thus lead to a cleaner environment. another issue is that global aluminium production reached 63.7 million metric tonnes in 2019 with 5.8 million metric tonnes being from gulf cooperation countries (gcc) countries [8]. due to its marvellous industrial properties such as light weight, conductivity, and corrosion resistance, aluminium finds its way into the manufacturing of a wide range of metallic applications such as automobiles, aeroplanes, kitchen tools, cabinets, foils, beverage cans, cables, and window and door frames [9-10]. to meet the increasing global consumption of aluminium, huge amounts of bauxite must be excavated, which in turn produces a significant amount of wastes. one way to minimize the production of bauxite, and hence reduce the burden on the environment, is by recycling used aluminium. statistics show that for every 1 kg of recycled aluminium, 8 kg of bauxite can be saved [11]. in this context, waste aluminium foils and cans have been recycled to prepare alumina (al2o3) and aluminium nitrate al(no3)3 [12-14]. in addition, aluminium scraps resulting from machining and trimming operations can be recycled to make beneficial chemicals. during the past two decades, metal-organic frameworks (mofs) have become the focus of much investigation due to their versatile properties such as high surface area, high porosity, and tuneable pores [15-17]. mofs are coordination polymers prepared from metal ions (clusters) and organic linkers, giving rise to extended 3-d open framework structures, with incorporated solvent molecules [18]. mofs have rapidly found their way in many applications such as separations, gas storage, heterogenous catalyses, molecular recognition, and drug delivery [19-23]. different metals such as al, ni, co, cu, zn, cr, ga, fe, v, and zr have been used to construct mofs [24-26]. among the known mofs, mil-53 (al) has attracted attention due to its double structural transitions (breathing) upon some gas adsorption [27, 28]. in addition, mil-53 (al) has been used as a catalyst for friedel-crafts alkylation of benzene with ethanol [29]. the source of aluminium in all reported syntheses of mil-53 (al) is either al(no3)3.9(h2o) or alcl3.6(h2o) [30, 31]. terephthalate (benzene dicarboxylate, bdc) is used extensively as an economical and viable source of a dicarboxylate linker to construct many nanoporous mofs such as mil-101(cr), mil-47(v), and mil-53(al, ga, cr) [32]. in this paper, we report the synthesis of mil-53 (al) from terephthalic acid produced from recycled drinking water bottles and aluminium chloride hexahydrate produced from recycled aluminium scrap as shown in scheme 1. 2. materials and methods 2.1 general all reagents are commercially available and were used as received without further purification. waste drinking pet bottles were washed well and cut into small pieces and used to prepare terephthalic acid. aluminium scraps were collected from maabella industrial state and used to prepare alcl3.6(h2o). melting points were determined using stuart smp20 digital melting point apparatus (sls scientific laboratory supplies, uk). infrared spectra (ir) were measured on agilent technologies cary 630 ft-ir (agilent technologies, usa). 1 h nmr and 13 c nmr spectra were carried out in a jeol 400 mhz spectrometer (japan) with cdcl3 as the nmr solvent. elemental analysis measurements were performed using the euro vector chn elemental analyser ea3000 model. aluminium content in mif-53 was performed on an icp-oes instrument using the nitric acid extraction method. esi-ms spectra were recorded with agilent, 6460 triple quad lc/ms, 1200 infinity series (germany) equipped with an electrospray ionization (esi) interface and operated by mass hunter software. powder xrd diffraction (pxrd) measurements were performed on a malvern panalytical x’pert pr instrument using cu k1.5405 å. the microstructure and sample surface morphology of alcl3.6(h2o) and mil-54(al) were examined with scanning electron micrographs (sem) model jsm-7600fjeol. u saleh n. al-busafi and yahya a. al-shafouri 100 scheme 1. graphic illustration of the synthesis of mil-53 (al) from recycled pet bottles and aluminium scraps. 2.2 conversion of pet bottles into terephthalic acid clean pet chips (10 g) and koh (10 g) were mixed with water (10 ml) and ethanol (200 ml) in a roundbottomed flask (500 ml) and the mixture was heated under reflux for one day. after cooling to room temperature, the white solid was filtered by suction and allowed to dry. the resulting white solid was dissolved in water and the solution was acidified by adding aqueous h2so4 (1m) until the white solid reappeared. the solid was filtered by suction filtration, and dried first under vacuum and then in the oven to yield 8.42g (84.2% w/w) of a white solid. mp 298.2 ºc, elemental analysis: %c = 58.091, %h = 3.234, %o = 38.676 (empirical formula = c8h6o4); ir (neat): 2515-3311(broad band), 1672, 1574, 1509, 1422, 1279, 927, 878, 782, 726 cm -1 . 1 h-nmr (400 mhz, cdcl3): ppm = 8.04 (4h, s); 13 c-nmr (100.6 mhz, cdcl3): 𝛿ppm = 129.64 (4c), 134.60 (2c), 166.89 (2c). esi m/z: calcd for c8h6o4 166; found 166. 2.3 conversion of aluminium scraps into alcl3.6h2o aluminium scraps (10 g) were transferred to a conical flask containing 375 ml hcl (6 m) and the mixture was stirred at room temperature. the exothermic reaction started after 1 minute and lasted for 30 minutes. then the cold mixture was filtered to remove the unreacted al pieces by suction and the clear filtrate was left in the fume ho od for one week until yellow crystals of aluminum chloride hexahydrate formed. the mixture was filtered by suction and the yellow crystals were dried under vacuum to yield 27.60 g (30.8%). the yellow crystals decomposed after 300 0 c, ir (neat): 2600-3200 (broad band), 2405, 1950, 1622, 1139, 817, 758, 608 cm -1 . 2.4 synthesis of mil-53 (al) from terephthalic acid and alcl3.6h2o a mixture of terephthalic acid (1.0 g, 6.1 mmol), alcl3.6h2o (1.5 g, 6.1 mmol), dmf (150 ml) and acetic acid (1.5 ml) was heated under reflex for 3 days. the white solid was filtered by suction, then washed with dmf to remove unreacted terephthalic acid, and next washed with water several times to remove dmf. the product was dried first under vacuum and then in the oven to yield mil-53 as a white solid 1.75g. the white solid decomposed after 300 ºc. elemental analysis: %c = 39.078, %h = 2.636, %o = 44.450, %al = 13.820%, (empirical formula = c6h5alo5); ir (kbr): 1695, 1594, 1509, 1413, 1274, 988, 833, 751 cm -1 . 3. results and discussion 3.1 preparation of terephthalic acid from pet drinking bottles scheme 2. conversion of pet drinking bottles into terephthalic acid. green preparation of aluminum-based metal-organic framework (al-mof) 101 hydrolysis of pet can be achieved either under acidic or basic conditions. the process under an acidic condition was reported to be slow compared to that under a basic one [33]. moreover, hydrolysing pet under a basic condition enabled us to separate the unreacted pet flakes before the acidifying step. after mixing pet pieces with potassium hydroxide in a mixture of ethanol and water (20:1), a white potassium terephthalate salt rapidly started to appear. after 24 hours of heating under reflux, the white solid, along with unreacted pet flakes, was separated and dissolved in water. another filtration was done to separate the unreacted pet, followed by acidification with aqueous h2so4 to recover terephthalic acid as a white solid. 3.1.1 ir analysis the ir spectrum of the prepared terephthalic acid revealed the characteristic broad stretching o-h band of carboxylic acid in the range 2515-3311 cm -1 and a strong c=o stretching band at 1672 cm -1 (figure 1). the lower wavenumber of c=o is due to conjugation with a benzene ring. other distinctive bands appeared at 1574 (c=c stretching), 1279 (c-o stretching), and 782 (c-h bending). the ir spectrum showed good matching when compared with a previously reported spectrum [34]. figure 1. (a) ir spectrum of the prepared terephthalic acid and (b) the reported spectrum 3.1.2 nmr analysis the 1 h-nmr spectrum of the prepared terephthalic acid exhibited a characteristic signal at 8 ppm for the four hydrogens in the benzene ring (figure 2). the other signal at 2.5 belongs to the dmso-d6 solvent used in the nmr analysis. in addition, the 13 cnmr spectrum showed two signals for the benzene ring carbons, one signal at 129.6 ppm for the four ch carbons and one at 134.6 ppm for the two quaternary carbons. the signal at 166.9 ppm is for the carboxyl group. the nmr spectrum of the prepared terephthalic acid exactly matched the reported one [35]. 3.2 preparation of alcl3.6h2o from aluminium scraps scheme 3. conversion of al scraps into hydrated aluminium chloride. saleh n. al-busafi and yahya a. al-shafouri 102 one minute after mixing aluminium scraps with hcl (6 m) an exothermic reaction started, indicating a reaction between al and hcl. the heat subsided after 30 minutes to give a milky mixture which was filtered to remove unreacted al scraps. the mixture was then left out in the fume hood to evaporate slowly, and following this, left in the sun until yellow crystals formed. figure 2. (a and a′) 1 hand 13 c-nmr spectra of the prepared terephthalic acid and (b and b′) of the reported sample 3.2.1 ir analysis the main characteristic ir band of aluminium chloride is the al-cl bond stretching located at 610 cm -1 as depicted in figure 3 [36]. the other bands belong to water molecules, which are the o-h stretching broad band at 3500 cm -1 and the o-h bending (scissoring) which appears at 1622 cm -1 . furthermore, a smaller band is located at 2404 cm 1 , which is the result of coupling of the scissors-bending and another broad liberation band at 812 cm -1 [37]. figure 3. (a) ir spectra of the prepared alcl3.6h2o and (b) of the reported one. green preparation of aluminum-based metal-organic framework (al-mof) 103 3.2.2 xrd and sem analysis the xrd pattern of the prepared aluminium chloride hexahydrate is in accordance with the reported pattern [38]. the pattern showed coinciding 2θ values at 8.4º, 9.2º, 10.1º and 28.1º (figure 4). the sem image of the prepared alcl3.6h2o shows granular particles with a size of about 233 μm. figure 4. (a) xrd pattern and (b) sem image of the prepared alcl3.6h2o. 3.3 preparation of aluminium-terephthalate framework, mil-53 (al) scheme 4. synthesis of mil-53 (al) from hydrated aluminium chloride and terephthalic acid. the reaction of terephthalic acid with alcl3.6h2o was carried out in a refluxed dmf for 3 days. a white mil-53 (al) solid formed in the reaction flask after 5 hours. tlc study showed total consumption of terephthalic acid. the prepared white solid polymer showed good thermal stability and resisted melting even after heating to above 300 ºc. elemental analysis of aluminium in the resulting solid was performed in icp-oes and it was found to contain 13.82% of al. other elemental analyses for carbon, hydrogen and oxygen were carried out in a euroea elemental analyser and they were found to constitute 39.08%, 2.64%, and 44.45%, respectively. 3.3.1 ir analysis the ir spectrum of the prepared mil-53 (al) revealed the expected characteristic absorption bands, such as c=o stretching bands at 1695 cm -1 , a c = c stretching band at 1594 cm -1 , a c-o stretching band at 1400 cm -1 , and an aromatic c-h bending band at 751 cm -1 (figure 5). in addition, the stretching band of the al-o single bond appears at 600 cm -1 , which is in agreement with the reported absorption [39]. figure 5. ir spectrum of mil-53 (al). saleh n. al-busafi and yahya a. al-shafouri 104 3.3.2 xrd and sem analysis figure 6 illustrates the xrd pattern and sem image of mil-53 (al). the main 2θ values found in the xrd graph are: 9.5 o , 15.3 o , 17.9 o and 20.6 o which are comparable to the values in the literature [40]. sem images of mil53 (al) reveal an irregular brick-like morphology of the crystallites, with a size distribution of 100 to 500 nm (figure 6(b)). figure 6. (a) xrd pattern and (b) sem image of the prepared mil-53 (al). 4. conclusion in this study, an aluminium mof (mil-53 (al)) material was prepared from recycled pet drinking water bottles and aluminium scraps. the characterization of the prepared substance was carried out using elemental analysis, ir, nmr, xrd, and sem techniques. investigation of the use of this material as a gas and pollutant absorbent is in progress. conflict of interest the authors declare no conflict of interest. acknowledgment we acknowledge, with thanks, the financial support from the sultan qaboos university (grant ig/sci/chem/18/05). the authors would like to thank caaru for providing xrd patterns and sem photos. references 1. wang, s.b., wang, c.s., wang, h.p., chen, x.l., wang, s.b. sodium titanium tris(glycolate) as a catalyst for the chemical recycling of poly(ethylene terephthalate) via glycolysis and re-polycondensation. polymer degradation and stability. 2015, 114, 105-14. 2. gleick, p.h. bottled and 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https://doi.org/10.1007/s13738-011-0064-1. 40. yi luan, yue qi, hongyi gao, radoelizo s. andriamitantsoa, nannan zheng and ge wang. a general postsynthetic modification approach of amino-tagged metal-organic frameworks to access efficient catalysts for the knoevenagel condensation reaction. journal of materials chemistry a. 2015, 3, 17320-17331. https://www.researchgate.net/publication/281700560. received 14 february 2021 accepted 25 july 2021 http://dx.doi.org/10.1590/0104-1428.2201 http://dx.doi.org/10.1590/0104-1428.2201 http://www.tandfonline.com/loi/ycmq20 squ journal for science, 2021, 26(2), 141-151 doi:10.53539/squjs.vol26iss2pp141-151 sultan qaboos university 141 ϯ some preliminary numerical results were presented at 5 th international conference on numerical analysis and optimization (nao-v), january 2020, muscat, oman improved fletcher–reeves methods based on new scaling techniques ϯ amal al-saidi 1,* and mehiddin al-baali 2 1 department of mathematics, sultan qaboos university, muscat, sultanate of oman. 2 department of mathematics, sultan qaboos university, muscat, sultanate of oman; and gerad-hec, montréal, canada. *email: amal2.alsaeedi@moe.om. abstract: this paper introduces a scaling parameter to the fletcher-reeves (fr) nonlinear conjugate gradient method. the main aim is to improve its theoretical and numerical properties when applied with inexact line searches to unconstrained optimization problems. we show that the sufficient descent and global convergence properties of albaali for the fr method with a fairly accurate line search are maintained. we also consider the possibility of extending this result to less accurate line search for appropriate values of the scaling parameter. the reported numerical results show that several values for the proposed scaling parameter improve the performance of the fr method significantly. keywords: unconstrained optimization; large-scale optimization; line search framework; nonlinear conjugate gradient methods; fletcher-reeves method. جديدةموازنة تقنيات إستنادا إلى ريفز المحسنة -فليتشر طرق أمل السعيدي و محي الدين البعلي ة عدديالنظرية وال الصفات. الهدف الرئيسي هو تحسين ةغيرالخطي ةطرق التدرج المترافقفي ريفز -رفليتش لطريقة موازنةيقدم هذا البحث معامل الملخص: نحدارالكافي والتقارب اإلفي البعليصفات الحفاظ على بين إمكانيةغيرالمقيدة. ن على مسائل األمثليات ةتقريبي بحثمستقيمات عند تطبيقها مع لتلك الطريقة قيم مناسبة ستخدام إتقريبي ببحث مستقيمهذه النتيجة إلى عميمعتبارأيًضا إمكانية تاإل. نأخذ في ة معقولةدقتقريبي ببحث مستقيممع frلطريقة لامشال .بشكل ملحوظ frن أداء طريقةيتحسل موازنةالعديد من قيم معامل الوجود . تظهرالنتائج العددية موازنةلمعامل ال ريفز. -فليتشر، طريقة ةغيرالخطي ة، طرق التدرج المترافقالبحث مستقيم، مسائل ذات أبعاد عالية، غيرالمقيدة األمثليات الكلمات المفتاحية: 1. introduction this paper is concerned with the line-search fletcher-reeves (fr) conjugate gradient (cg) method for solving the unconstrained optimization problem min 𝑥∈𝑅𝑛  𝑓(𝑥), (1) where f: rn → r is a smooth function and its gradient 𝑔(𝑥) = ∇f (x) is available for any value of x. for a given starting point x1, the method defines a sequence of points {𝑥𝑘} iteratively as follows. on each iteration, once the function value 𝑓𝑘 = 𝑓(𝑥𝑘) and the gradient value 𝑔𝑘 = 𝑔(𝑥𝑘) are calculated, a search direction 𝑑𝑘 is defined such that the descent property 𝑑𝑘 𝑇𝑔𝑘 < 0 holds, assuming 𝑔𝑘 ≠ 0 since 𝑔𝑘 = 0 holds at a solution of problem (1). then it is possible to find a positive steplength αk and hence a new point mailto:amal2.alsaeedi@moe.om amal al-saidi and mehiddin al-baali 142 𝑥𝑘+1 = 𝑥𝑘 + 𝛼𝑘𝑑𝑘 (2) such that the function reduction 𝑓𝑘 − 𝑓𝑘+1 is sufficiently positive (see for example fletcher [1]). in the class of cg methods, the search direction 𝑑𝑘 is defined initially by the steepest descent choice 𝑑1= −𝑔1 that satisfies the above descent property for k = 1 . the other directions are defined by 𝑑𝑘+1 = −𝑔𝑘+1 + 𝛽𝑘𝑑𝑘, (3) where βk is the cg parameter. in particular, fletcher and reeves [2] propose the positive value of 𝛽𝑘 = ∥∥𝑔𝑘+1∥∥ 2 ∥∥𝑔𝑘∥∥ 2 (4) (referred to as 𝛽𝑘 𝐹𝑅), where || ∙ || denotes the euclidean norm. if the exact line search equation 𝑑𝑘 𝑇𝑔𝑘+1 = 0 (5) is satisfied, which is guaranteed if the steplength αk = α ∗ is obtained by solving the minimization subproblem α∗ = arg min𝛼 𝑓(𝑥𝑘 + 𝛼𝑑𝑘) exactly, then the above descent property with 𝑘 replaced by 𝑘 + 1 is also satisfied. since solving this subproblem exactly (referred to as exact line search) is impractical, inexact line search is usually used so that the descent property may not hold. in this case, choice (4) is replaced by 𝛽𝑘 = 0 (i.e., direction (3) is reset to that of the steepest descent) so that the descent property holds for all k (for further detail, see for example fletcher [1], nocedal and wright [3] and pytlak [4]). because this resetting may destroy the useful features of the cg method, in certain cases, many choices for replacing the cg parameter fr formula have been proposed (see for example hager and zhang [5] and the references therein). if exact line search is employed and f (x) is quadratic, all the directions generated via (3) are mutually conjugate. hence, the gradients of 𝑓(𝑥) at the different iterates are mutually orthogonal, i.e., we have 𝑔𝑘+1 𝑇 𝑔𝑘 = 0, (6) and these formulae are reduced to the fr one (see e.g. [1, 3, 4]). our aim in this paper is to maintain the global convergence property of the fr method and improve its behavior by scaling formula (4) by 𝜉𝑘 before using it in (3) (as in al-baali [6]). therefore, the resulting scaled direction 𝑑𝑘+1 = −𝑔𝑘+1 + 𝜉𝑘𝛽𝑘𝑑𝑘 (7) would be close to the steepest descent one if 𝜉𝑘 is chosen sufficiently close to zero. hence, by continuity, the corresponding class of scaled cg methods (referred to as scfr when 𝛽𝑘 = 𝛽𝑘 𝐹𝑅) would satisfy the descent and convergence properties that the steepest descent method has. it is important to mention that powell [7] and essentially zoutendijk [8] show that the fr method with exact line searches converges globally, in the sense that lim𝑘→∞ inf ‖𝑔𝑘‖ = 0. this result has been extended by al-baali [9] to inexact line searches with a fairly accurate values of αk, known as the first practical global convergence result for the fr method (see for example nocedal [10]). al-baali has obtained this result based on showing that the sufficient descent condition 𝑑𝑘 𝑇𝑔𝑘 ≤ −𝑐∥∥𝑔𝑘∥∥ 2 (8) holds for some positive constant c, assuming the steplength αk satisfies the strong wolfe conditions 𝑓𝑘+1 ≤ 𝑓𝑘 + 𝜌𝛼𝑘𝑔𝑘 𝑇𝑑𝑘, | 𝑔𝑘+1 𝑇 𝑑𝑘 | ≤ −𝜎𝑔𝑘 𝑇𝑑𝑘, (9) for 0 < ρ < σ < 1 2 . it is worth noting that a value of 𝛼𝑘 > 0 which satisfies these conditions, for 0 < ρ < 1 2 and ρ < σ < 1, can be found in a finite number of operations whenever the above descent property holds (see for example al-baali and fletcher [11] and fletcher [1]). in section 2, we show that the scfr class of methods with 𝜉𝑘 ∈ (0, 1] maintains the sufficient descent property that the fr method has for the strong wolfe conditions (9) with σ < 1 2 . we will also enforce this property for any line search technique with sufficiently small values of the scaling parameter ξk. in addition, that section defines some choices for 𝜉𝑘. in section 3, we introduce the quasi-newton feature to 𝜉𝑘 for the fr method as considered by al-saidi et al. [12] for the scaled cg methods. section 4 shows that the proposed class of scfr methods maintains the global convergence property that the fr method has when the strong wolfe conditions are employed with σ < 1 2 . in section 5, we study the behavior of the proposed scfr methods by applying them to a set of standard test problems. it is shown that the proposed scaling technique improves the performance of the fr method significantly in many cases. finally, section 6 concludes the paper. 2. the scfr class of methods we now define the scaled fr (scfr) class of methods as suggested by al-baali [6] for the cg class of methods. the author replaces the search direction (3) by (7), for k > 1, where 0 < 𝜉𝑘 ≤ 1 is the scaling parameter, and maintains 𝑑1 = −𝑔1. since the value of 𝜉𝑘 = 0 reduces this direction to that of the steepest descent, it follows by improved fletcher–reeves methods 143 continuity that the scfr class of methods, with values of 𝜉𝑘 sufficiently close to zero, has the sufficient descent and global convergence properties that the steepest descent method has. we first define some values of 𝜉𝑘 that enforce the sufficient descent condition (8) as follows (al-baali [6]). we note that this condition holds for k = 1 and c = 1. we now prove this condition for k ≥ 1 as follows. on substituting (7) into (8) with k replaced by k + 1, we have 𝑔𝑘+1 𝑇 𝑑𝑘+1 = −∥∥𝑔𝑘+1∥∥ 2 + 𝜉𝑘𝛽𝑘𝑑𝑘 𝑇𝑔𝑘+1 ≤ −𝑐∥∥𝑔𝑘+1∥∥ 2 . (10) hence, 𝜉𝑘𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1) ≤ (1 − 𝑐)∥∥𝑔𝑘+1∥∥ 2 (11) or equivalently by the fr formula (4), 𝜉𝑘(𝑑𝑘 𝑇𝑔𝑘+1) ≤ (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 , (12) where 0 < c ≤ 1. this upper bound on c is included because condition (11) cannot hold for c > 1 and 𝑑𝑘 𝑇𝑔𝑘+1= 0 (the exact line search option). we note that (11) holds if its left hand side is nonpositive or either 𝜉𝑘, 𝑑𝑘 𝑇𝑔𝑘+1 or βk is sufficiently close to zero. this paper assumes that the cg parameter βk is given by the fr formula (4), unless otherwise stated, and defines 𝜉𝑘 such that (11) holds whether dk satisfies the sufficient descent condition (8) or not. for convenience, we start with the following result of al-saidi et al. [12] assuming βk satisfies (8). theorem 1. consider the scfr class of methods, defined by (2), (4) and (7) and assume that the search direction (7) with 𝜉𝑘= 1 satisfies the sufficient descent condition (8). then, this condition remains satisfied for 0 ≤ 𝜉𝑘 ≤ 1. proof. when k = 1, 𝑑𝑘= −𝑔𝑘 and hence condition (8) holds with c = 1. for k ≥ 1, it follows from (7) that 𝑔𝑘+1 𝑇 𝑑𝑘+1 = −∥∥𝑔𝑘+1∥∥ 2 + 𝜉𝑘𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1). (13) if 𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1) < 0, it follows that 𝑔𝑘+1 𝑇 𝑑𝑘+1 ≤ −∥∥𝑔𝑘+1∥∥ 2 , which is (8) with c = 1 and k replaced by k + 1, since 𝜉𝑘 ≥ 0. otherwise, if 𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1) ≥ 0, then (13) implies 𝑔𝑘+1 𝑇 𝑑𝑘+1 ≤ −∥∥𝑔𝑘+1∥∥ 2 + 𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1), since 𝜉𝑘 ≤ 1. hence, by the theorem assumption we obtain (8) with k replaced by k + 1. □ we note that this result remains valid for any value of c > 0 if the choice 𝜉𝑘 = 1 is used when 𝛽𝑘(dk t 𝑔𝑘+1) ≤ 0 as we consider below for some choices of 𝜉𝑘. it is important to note that if the strong wolfe conditions (9) are employed with σ < 1/2, then the sufficient descent condition (8) holds for c = 𝑐σ ≡ 1−2σ 1−σ (see al-baali [9], for detail). thus, for any choice of c ≤ cσ, 𝜉𝑘 = 1 and the scfr method is reduced to the standard fr method. however, using values of c > 𝑐σ require defining 𝜉𝑘 < 1, for which we suggest the following way. if condition (11) holds with 𝜉𝑘 = 1, then we use this value so that the cg search direction is unchanged. otherwise, we choose 𝜉𝑘 such that condition (11) holds with equality. thus, we choose 𝜉𝑘 = { (1 − 𝑐)∥∥𝑔𝑘+1∥∥ 2 𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1)      if 𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1) > (1 − 𝑐)∥∥𝑔𝑘+1∥∥ 2 , 1     otherwise, (14) or equivalently for the scfr method, 𝜉𝑘 1 = { (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 𝑑𝑘 𝑇𝑔𝑘+1      if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 , 1     otherwise. (15) in this case, it follows that 𝜉𝑘 1𝛽𝑘 = { (1 − 𝑐)∥∥𝑔𝑘+1∥∥ 2 𝑑𝑘 𝑇𝑔𝑘+1      if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 , 𝛽𝑘 𝐹𝑅     otherwise (16) which shows that scaling is employed only when αk is sufficiently remote away from the right hand side of a minimizer α∗. to be precise, 𝜉𝑘 = 1 is used when 𝛽𝑘(𝑑𝑘 𝑇𝑔𝑘+1) ≤ 0, although in this case (11) holds for any value of 𝜉𝑘 > 0. to obtain the least change in the cg parameter, c should be chosen close to zero (in practice, the value of c = 0.001 seems reasonable as observed by al-saidi [13]). we also note that 𝜉𝑘 1= 1 usually is used for a fairly accurate line search (σ ≤ 0.1). thus, we consider the outline of the scaled fr (scfr) method as in algorithm 1 that is reduced to the standard fr method if 𝜉𝑘=1 for all k. if in step 2 exact line searches (or nearly so) are employed for all k, then algorithm 1 is reduced to the standard fr method. in practice, we observed that the above scaling technique improves the performance of the fr method significantly in several cases (see section 5, for details). amal al-saidi and mehiddin al-baali 144 algorithm 1 (scfr) step 0: given ε > 0, 0 < c ≤ 1 and x1, let 𝑑1= −𝑔1 and set k = 1 step 1: stop if ||𝑔1||≤ ε step 2: compute a positive steplength αk which satisfies certain standard conditions step 3: compute a new point by (2); 𝑥𝑘+1 = 𝑥𝑘 + 𝛼𝑘𝑑𝑘 step 4: define the fr parameter βk by (4) step 5: define 𝜉𝑘 (e.g., by (14)) step 6: compute a new search direction by (7); 𝑑𝑘+1 = −𝑔𝑘+1 + 𝜉𝑘𝛽𝑘𝑑𝑘 step 7: set k := k + 1 and go to step 1. it is important to realize that the choice of 𝜉𝑘 1 in (15) is independent of the line search technique. however, if the strong wolfe conditions (9) are employed, the first case of (15) could be replaced by a smaller value to obtain 𝜉𝑘 2 = { (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 𝜎|𝑑𝑘 𝑇𝑔𝑘|      if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 , 1     otherwise. (17) this choice satisfies the sufficient descent condition (11) with 𝜉𝑘 = 𝜉𝑘 2, because 𝜉𝑘 2 ≤ ξk 1 and we have 𝑑𝑘 𝑇𝑔𝑘+1 > 0 and ξk 2(𝑑𝑘 𝑇𝑔𝑘+1) ≤ ξ1(𝑑𝑘 𝑇𝑔𝑘+1) = (1 − c) ∥∥𝑔𝑘∥∥ 2 . indeed, replacing 𝜉𝑘 2 by a smaller value, which we consider below, maintains the sufficient descent condition (12). in practice, for c = 0.001, we observed that choice (17) works better than (15). we now consider the rearrangement of al-baali [6] for the fr parameter as 𝛽𝑘 = 𝜂𝑘 𝑇𝑔𝑘+1, 𝜂𝑘 = 𝑔𝑘+1 ∥∥𝑔𝑘∥∥ 2 , (18) which is possible for most cg methods (e.g., see hager and zhang [5] and narushima and yabe [14] and the references therein). using this form and observing that 𝑑𝑘 𝑇𝑔𝑘+1 ≤ ∥∥𝑑𝑘∥∥∥∥𝑔𝑘+1∥∥, (19) the first case of (15) can be reduced to obtain 𝜉𝑘 3 = { (1−𝑐)∥∥𝑔𝑘∥∥ 2 ∥∥𝑑𝑘∥∥∥∥𝑔𝑘+1∥∥ if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 1 otherwise. , (20) to increase the interval for the scaling parameter, we use (19) again in the condition of (20) so that we obtain the following choice of al-baali [6]: 𝜉𝑘 4 = { (1−𝑐)∥∥𝑔𝑘∥∥ 2 ∥∥𝑑𝑘∥∥∥∥𝑔𝑘+1∥∥ if ∥∥𝑑𝑘∥∥∥∥𝑔𝑘+1∥∥ > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 1 otherwise . , (21) we note that the interval for using 𝜉𝑘 < 1 in (21) is larger than or equal to that used by (20) so that sufficiently large values of c might be used. indeed, in practice, we observed that choice (17) is preferable to (21). thus, we will not provide further details about (21). 3. a quasi-newton feature one feature for choices (20) and (21) is given by al-baali [6] who shows that the values of 𝜉𝑘 ≤ (1−𝑐) ∥∥η𝑘∥∥∥∥d𝑘∥∥ , where η for the fr formula is given in (18), enforce some positive eigenvalues of the sccg matrix 𝐻𝑘+1 = 𝐼 − 𝜉𝑘𝑑𝑘𝜂𝑘 𝑇, (22) noting that direction (7) (similar to that of perry [15]) can be rearranged as follows 𝑑𝑘+1 = −𝐻𝑘+1𝑔𝑘+1. (23) thus, we introduce another feature to the scfr method like that of al-saidi et al. [12] for the cg methods by modifying the scaling parameter 𝜉𝑘 such that ideally the quasi-newton condition 𝐻𝑘+1𝛾𝑘 = 𝛿𝑘 , (24) where 𝛿𝑘 = 𝑥𝑘+1 − 𝑥𝑘, 𝛾𝑘 = 𝑔𝑘+1 − 𝑔𝑘, (25) holds, assuming 𝐻𝑘+1 approximates the inverse of hessian of 𝑓(𝑥) at 𝑥𝑘. because, in general, we cannot fulfill condition (24), we let improved fletcher–reeves methods 145 𝜉𝑘 = arg min 𝜉 ∥∥𝐻𝑘+1𝛾𝑘 − 𝛿𝑘∥∥ = arg min 𝜉  ∥∥𝛾𝑘 − 𝛿𝑘 − 𝜉(𝜂𝑘 𝑇𝛾𝑘)𝑑𝑘∥∥. (26) solving this minimization problem (see for example al-saidi et al. [12]), it follows that 𝜉𝑘 𝑞 = (𝛾𝑘−𝛿𝑘) 𝑇𝑑𝑘 𝜂𝑘 𝑇𝛾𝑘∥∥𝑑𝑘∥∥ 2 . (27) on substituting 𝜂𝑘 for the fr formula (18), (27) is reduced to 𝜉𝑘 𝑞 = (𝛾𝑘−𝛿𝑘) 𝑇𝑑𝑘∥∥𝑔𝑘∥∥ 2 𝛾𝑘 𝑇𝑔𝑘+1∥∥𝑑𝑘∥∥ 2 . (28) to maintain the search direction differs from that of the steepest descent, the values of 𝜉𝑘 should be bounded away from zero. since, in addition, the first case of (15) enforces the sufficient descent condition (12) with equality, and that replacing 𝜉𝑘 by a smaller value keeps inequality (12) holds, we may enforce 𝜉𝑘 ∈ [ĉ, 1], where ĉ is a small positive number. thus, we modify (15), which defines 𝜉𝑘 1, to 𝜉𝑘 𝑞1 = { (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 𝑑𝑘 𝑇𝑔𝑘+1      if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 and 𝜉𝑘 𝑞 ∉ [�̂�,1], min{ (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 𝑑𝑘 𝑇𝑔𝑘+1 ,𝜉𝑘 𝑞 }     if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 and 𝜉𝑘 𝑞 ∈ [�̂�,1], 1     otherwise. (29) and modify (17), which defines 𝜉𝑘 2, to 𝜉𝑘 𝑞2 = { (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 𝜎|𝑑𝑘 𝑇𝑔𝑘|      if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 and 𝜉𝑘 𝑞 ∉ [�̂�,1], min{ (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 𝜎|𝑑𝑘 𝑇𝑔𝑘| ,𝜉𝑘 𝑞 }     if 𝑑𝑘 𝑇𝑔𝑘+1 > (1 − 𝑐)∥∥𝑔𝑘∥∥ 2 and 𝜉𝑘 𝑞 ∈ [�̂�,1], 1     otherwise. (30) since choices (29) and (30) can be rewritten as 𝜉𝑘 𝑞𝑖 = min(max( 𝜉𝑘 𝑞 , ĉ) ,𝜉𝑘 𝑖), for 𝑖 = 1,2 respectively, we observe that 𝜉𝑘 𝑞𝑖 ≤ 𝜉𝑘 𝑖 . similarly, we modify any 𝜉𝑘 𝑖 , for i = 1, 2, 3, 4, to 𝜉𝑘 𝑞𝑖 = min(max(𝜉𝑘 𝑞 , ĉ), 𝜉𝑘 𝑖 ). in practice, we observed that these modified choices with 𝜎 = 0.1 and ĉ = 0.001 improves the performance of 𝜉𝑘 2 (further possible choices and details can be seen in al-saidi [13]). therefore, the above choices for 𝜉𝑘 are chosen to enforce the sufficient descent condition as shown in the following result which is an extension to theorem 1. theorem 2. consider the scfr class of methods, defined by (2), (4) and (7), and let 𝜉𝑘 = 𝜉𝑘 𝑖 or 𝜉𝑘 = 𝜉𝑘 𝑞𝑖 , for 𝑖 = 1,2,3,4. then, the sufficient descent condition (8) holds for all k ≥ 1. proof. it is obvious for k = 1. for k ≥ 1, 𝜉𝑘 = 𝜉𝑘 𝑖 , 1 ≤ i ≤ 4, are chosen such that inequality (12) holds which is equivalent to the sufficient descent condition (10). since 𝜉𝑘 𝑞𝑖 ≤ 𝜉𝑘 𝑖 , 1 ≤ i ≤ 4, inequalities (11) and (12) remain satisfied so that condition (10) holds. hence, condition (10) implies (8). □ introducing other features to the scaling parameter 𝜉𝑘 are also possible. in particular, we could introduce the useful conjugacy condition γ𝑘 𝑇 𝑑𝑘+1= 0. this equation with (7) holds if 𝜉𝑘 = 𝜉𝑘 𝑐 ≡ γ𝑘 𝑇 𝑔𝑘+1 β𝑘γ𝑘 𝑇 𝑑𝑘 which exists if the wolfe condition holds. similarly if we consider the modified conjugacy condition of dai and liao [16], γ𝑘 𝑇 𝑑𝑘+1= td𝑘 𝑇 𝑔𝑘+1 where t ≥ 0 is a scalar, we obtain 𝜉𝑘 = (𝛾𝑘−𝑡𝑑𝑘) 𝑇𝑔𝑘+1 𝛽𝑘𝛾𝑘 𝑇𝑑𝑘 which reduces direction (7), for any βk to the class of dai and liao. it is worth noting that al-baali [6] defines a bound on 𝜉𝑘 to ensure that matrix (22) is positive definite, but we do not consider it here because it may increase the value of 𝜉𝑘 so that the sufficient descent condition (11) may not hold. 4. global convergence property we now study the possibility of imposing the global convergence property lim 𝑘→∞  inf ∥∥𝑔𝑘∥∥ = 0 (31) to the scfr methods which we proposed in the previous sections such that the sufficient descent condition (8) holds for all k ≥ 1. therefore, we first state the following standard assumptions on the objective function. assumption 1. 1. the level set ℒ = {x: f (x) ≤ f (x0)} is bounded, 2. t he objective function f is continuously differentiable in some neighborhood 𝒩 of ℒ, 3. the gradient 𝑔(𝑥) 𝑖𝑠 lipschitz continuous, that is there exists a positive constant l such that ∥ 𝑔(𝑥) − 𝑔(�̃�) ∥≤ 𝐿 ∥ 𝑥 − �̃� ∥ for all 𝑥, �̃� ∈ 𝒩. (32) amal al-saidi and mehiddin al-baali 146 supposing assumption 1 holds, powell [7] and zoutendijk [8] prove the ideal result that the fr method, defined by (2), (3) and (4), satisfies the global convergence property (31) if exact line searches are used. this means that impractical choice of 𝜎 = 0 in (9) is considered. al-baali [9], however, considers the practical strong wolfe conditions with 𝜎 < 1 2 to show that the sufficient descent condition (8) holds and extends the above global convergence result to the practical fr method. this result has been extended by touati-ahmed and storey [17] to the interval 0 ≤ βk ≤ 𝛽𝑘 𝐹𝑅, while gilbert and nocedal [18] have extended it to −𝛽𝑘 𝐹𝑅 ≤ 𝛽𝑘 ≤ 𝛽𝑘 𝐹𝑅. (33) thus, we obtain the following convergence result for the scfr methods. theorem 3. suppose assumption 1 holds and let the scfr class of methods be defined by (2), (4), (7), and |𝜉𝑘| ≤ 1. if the strong wolfe conditions (9) are employed with 𝜎 < 1 2 , then the scfr methods converge globally in the sense that limit (31) holds. proof. the scfr methods are defined in the previous sections like the fr method, except that the fr formula 𝛽𝑘 𝐹𝑅 > 0, defined by (4), is replaced by 𝛽𝑘 𝑆𝑐𝐹𝑅 = 𝜉𝑘𝛽𝑘 𝐹𝑅. because |𝜉𝑘| ≤ 1, conditions (33) hold and hence the result follows from that of gilbert and nocedal [18]. □ 5. numerical results to show the efficiency of the proposed scaling technique for the fletcher-reeves method, we describe some numerical results. the results are obtained by applying the fr method with several scaled choices to a set of 46 different type of unconstrained optimization problems; their function names are given in table 1. they belong to the cute [19] and moré, garbow and hillstrom [20] collections of test problems. we also include the simple quadratic function of al-baali (see for example al-saidi [13]). for each type of problem, we let the dimension n varies as 2, 10, 100, 1000, 10000 so that the total number of test problems is 230. all th e scfr methods that we consider are defined by algorithm 1 and differ only in step 5 for defining the scaling parameter 𝜉𝑘 unless otherwise stated. for the purposes of an accurate comparison, we use in step 2 for all methods the matlab line search program routine of albaali (which essentially written in fortran by fletcher) which computes a value of the steplength αk that satisfies the strong wolfe conditions (9) as described in al-baali and fletcher [11] and fletcher [1]. the run was stopped as in step 1 when either ||𝑔𝑘|| ≤ 10 −6 or the number of iterations reaches 10 5 . we consider the following algorithms:  fr; the standard fr method, defined by algorithm 1 with ρ = 10 −4 and σ = 0.1 in step 2 and 𝜉𝑘 = 1 in step 5. table 1. the test functions. number function’s name number function’s name 1 a simple quadratic function 24 trecanni 2 extended white and holst 25 zettl 3 extended rosenbrock 26 shallow 4 extended freudenstein and roth 27 generalized quartic 5 extended beale 28 axis parallel hyper-ellipsoid 6 extended wood 29 leon 7 raydan 1 30 generalized tridiagonal 1 8 generalized tridiagonal 1 31 generalized tridiagonal 2 9 diagonal 4 32 power 10 extended himmelblau 33 quadratic qf1 11 extended hiebert 34 extended quadratic penalty qp2 12 fletchcr 35 dixon and price 13 extended powell 36 quartic 14 nonscomp 37 diagonal4 15 extended denschnb 38 colville 16 extended quadratic penalty qp1 39 schumer steilitz 17 extended penalty i 40 sphere 18 de jong’s 41 sum squares 19 hager 42 powell singular 20 extended maratos 43 qing 21 cube 44 generalized psc1 22 three hump function 45 perturbed quadratic 23 booth 46 diagonal 2 improved fletcher–reeves methods 147  scfri; same as fr except that in step 5, 𝜉𝑘 = 𝜉𝑘 𝑖 , for i = 1, 2, 3, 4, defined by (15), (17), (20), and (21), respectively.  scfrqi, i ≤ 4; same as scfri except that in step 5, 𝜉𝑘 = 𝜉𝑘 𝑞𝑖 = min(max( 𝜉𝑘 𝑞 , ĉ) ,𝜉𝑘 𝑖) with ĉ = 0.001, where 𝜉𝑘 𝑞 is given by (28). we observed that scfr1, scfr4 and scfrqi, for i = 1, 3, 4, are less efficient than the others. therefore, we will not give further details about them. although it is possible to study the behaviour of other methods that we considered here, we do not consider them in our comparisons because they were less efficient than the above algorithms. for a useful comparison, we used the performance profiles tool of dolan and moré [21], which compares some solvers on the above set of problems in terms of the number of line searches, the number of function evaluations, the number of gradient evaluations and cpu time, required to solve the problems. in general the performance profile 𝑃𝑀(𝜏), 𝜏 ≥ 0, is defined by the formula 𝑃𝑀(𝜏) = number of problems where log2(𝜏𝑃,𝑀) ≤ 𝜏 total number of problems , (34) where 𝜏𝑃,𝑀 is the performance ratio of the number of line searches (similarly for the other measures) required to solve problem p by a method m to the lowest number of line searches required to solve problem p. the ratio 𝜏𝑃,𝑀 is set to ∞ (or some large number) if the method m fails to solve problem p. the value of pm(τ) at τ = 0 gives the percentage of test problems for which the m method is the best. the value for τ large enough is the percentage of test problems that m method can solve. the relative efficiency and reliability of each method can be directly seen from the performance profiles: the higher the particular curve, the better is the corresponding method. the performance profiles for the fr, scfr2, scfr3 and scfrq2 algorithms are given in figures 1. we observe that all scaling techniques improve the performance of the fr method substantially. we also observe that scfr2 is slightly better than scfrq2 and both of them perform better than scfr1. thus, scfr2 seems to be the best o f the scfr algorithms. figure 1. comparison among fr, scfr2, scfr3 and scfrq2 for σ = 0.1. (a) # line searches (b) # function evaluation (c) # gradient evaluation (d) cpu time amal al-saidi and mehiddin al-baali 148 (c) # gradient evaluation (d) cpu time figure 2. comparison among fr, scfr2, scfr3 and scfrq2 for σ = 0.9. (a) # line searches (b) # function evaluation to give further idea about the behaviour of these methods for a large value of σ, we repeated the run for the previous four methods but with 𝜎 = 0.9 instead of 𝜎 = 0.1 in step 2. the comparisons are given in figures 2. although these figures show that the fr method failed to solve about 40% of the test problems which is expected, the three scfr methods solved almost all problems successfully. thus, the scfr methods are superior to the fr method. to choose the best choice for σ, we repeated the run for the best scfr2 method, using the values of σ = 0.1, 0.4, 0.7, 0.9 and 0.9999 (for the first value, the method is referred to as scfr2). the comparisons are given in figures 3. we observe that the performance of the scfr method as improves as σ decreases in terms of the number of line searches, function evaluations and gradient evaluations. however, the choice σ = 0.1 is significantly better than the others in terms of cpu time. thus, σ = 0.1 is the best value for all the measurements. another useful observation is that the scaled methods solved all problems for not only 𝜎 < 1/2 but also for 𝜎 ≥ 1/2. thus, the scaled technique improves not only the good behaviour of the fr method when σ is sufficiently small but also solved problems that cannot be solved by the fr method. we now compare the scfr2 method with some useful cg methods such as the polak-ribière-polyak [22, 23], dai-yuan [24] and hager-zhang [25] methods. these methods (referred to as prp, dy and hz) are defined by algorithm 1 with 𝜉𝑘 = 1 in step 5 and βk in step 4 is given respectively by the following formulae: 𝛽𝑘 𝑃𝑅𝑃 = 𝛾𝑘 𝑇𝑔𝑘+1 ∥∥𝑔𝑘∥∥ 2 , (34) 𝛽𝑘 𝐷𝑌 = ∥∥𝑔𝑘+1∥∥ 2 𝑑𝑘 𝑇𝛾𝑘 (35) and improved fletcher–reeves methods 149 (d) cpu time (c) # gradient evaluation 𝛽𝑘 𝐻𝑍 = (𝛾𝑘 − 2 ∥∥𝛾𝑘∥∥ 2 𝛾𝑘 𝑇𝑑𝑘 𝑑𝑘) 𝑇 𝑔𝑘+1. 𝛾𝑘 𝑇𝑑𝑘 . (36) using 𝜎 = 0.1, the comparisons of the methods are given in figures 4. we see that scfr2 performs a little better than dy and a little worse than prp and hz. thus, the scfr2 method is efficient and there is a room for improving it. the above numerical results show indeed that all the scfr methods perform well and the scfr2 method is the best of them. 6. conclusion we show that introducing a simple scaling technique to the well-known fletcher-reeves method maintains its global convergence property, improves its performance significantly and solved problems that cannot be solved by the fr method. since the scfr methods work well when the strong wolfe conditions are used with σ ≥ 1/2, it is expected to extend their global convergence to σ < 1. it is also worth testing further possible choices for the fr scaled parameter (e.g., similar to that applied to the dy method by esmaeili et al. [26]). conflict of interest the authors declare no conflict of interest. acknowledgment the authors would like to thank the editor and two anonymous referees for their critical and constructive comments figure 3. scfr2 comparison among the values of σ = 0.1, 0.4, 0.7, 0.9 and 0.9999. (a) # line searches (b) # function evaluation amal al-saidi and mehiddin al-baali 150 which improve the quality of the paper. we would also like to thank lucio grandinetti, calabria university, italy, and ekkehard sachs, trier university, germany, for the useful discussions on the preparation of the paper. the first author would like to thank the oman ministry of education for the award of a scholarship. figure 4. comparison among scfr2, prp, dy and hz for σ = 0.1. references 1. fletcher, r. practical methods of optimization, 2nd edition, 2013, wiley, chichester, england. 2. fletcher, r., and reeves, c. function minimization by conjugate gradients, computational journal, 1964, 7, 149-154. 3. nocedal, j., and wright, s. j. numerical optimization, 2nd edition, 2006, springer, london. 4. pytlak, r. conjugate gradient algorithms in nonconvex optimization, 2009, springer, berlin. 5. hager w., and zhang, h. a survey of nonlinear conjugate gradient methods, pacific journal of optimization, 2006, 2, 35-58. 6. al-baali, m. a general class of conjugate gradient methods, 22 nd international symposium on mathematical programming (ismp), pittsburg, usa, 2015. 7. powell, m.j.d. nonconvex minimization calculations and the conjugate gradient method. in numerical analysis, lecture notes in mathematics (ed. griffiths d.f.), springer, 1984, 1066, 122-141. 8. zoutendijk, g. nonlinear programming, computational methods, in integer and nonlinear programming (ed. j. abadie), north-holland, amsterdam, 1970, 37-86. 9. al-baali, m. descent property and global convergence of the fletcher-reeves method with inexact line search, ima journal of numerical analysis, 1985, 5, 121-124. 10. nocedal, j. theory of algorithms for unconstrained optimization, acta numerica, 1992, 1, 199-242. 11. al-baali, m., and fletcher, r. an efficient line search for nonlinear least squares, journal of optimization theory and applications, 1986, 48, 359-378. 12. al-saidi, a., al-baali, m., fasano, g., and roma, m. new scaled and shifted conjugate gradient methods for (a) # line searches (b) # function evaluation (c) # gradient evaluation (d) cpu time improved fletcher–reeves methods 151 large-scale unconstrained optimization, technical report dm215, department of mathematics, sultan qaboos university, muscat, oman, 2021. 13. al-saidi, a. improved conjugate gradient methods for large-scale unconstrained optimization, phd thesis, sultan qaboos university, muscat, oman, 2021. 14. narushima, y., and yabe, h. a survey of sufficient descent conjugate gradient methods for unconstrained optimization, sut journal of mathematics, 2014, 50, 167-203. 15. perry, j. m. a class of conjugate gradient algorithms with a two-step variable-metric memory, discussion paper 269, center for mathematical studies in economics and management sciences, northwestern university, evanston, illinois, usa, 1977. 16. dai, y. h., and liao, l. z. new conjugacy conditions and related nonlinear conjugate gradient methods, applied mathematics and optimization, 2001, 43, 87-101. 17. touati-ahmed, d., and storey, c. globally convergent hybrid conjugate gradient methods, journal of optimization theory and applications, 1990, 64, 379-397. 18. gilbert, j. c., and nocedal, j. global convergence properties of conjugate gradient methods for optimization, siam journal on optimization, 1992, 2, 21-42. 19. bongartz, i., conn a. r., gould, n., and toint, ph. l. cute: constrained and unconstrained testing environment, acm transactions on mathematical software, 1995, 21, 123-160. 20. moré, j. j., garbow, b. s., hillstrom, k. e. testing unconstrained optimization software, acm transactions on mathematical software, 1981, 7, 17-41. 21. dolan, e. d., moré, j. j. benchmarking optimization software with performance profiles, mathematical programming, 2002, 91, 201-213. 22. polak, e., and ribière, g. note sur la convergence de directions conjugées, rev. francaise informat recherche opertionelle, 1969, 3e annee 16, 35-43. 23. polyak, b. the conjugate gradient method in extreme problems, ussr computational mathematics and mathematical physics, 1969, 9, 94-112. 24. dai, y. h., and yuan, y. x. a nonlinear conjugate gradient method with a strong global convergence property, siam journal on optimization, 1999, 10, 177-182. 25. hager, w., and zhang, h. a new conjugate gradient method with guaranteed descent and an efficient line search. siam journal on optimization, 2005, 16, 170-192. 26. esmaeili. h., rostami, m., and kimiaei. m. extended dai-yuan conjugate gradient strategy for large-scale unconstrained optimization with applications to compressive sensing, filomat, 2018, 32 (6), 2173-2191. received 30 june 2021 accepted 6 september 2021 squ journal for science, 2015, 20(1), 70-76 © 2015 sultan qaboos university 70 crystal field parameters and optical parameters of nd 3+ in sodium bismuth silicate glass vinoy thomas 1 , ramakrishna p.g.p.s. sofin 2 *, mathew allen 3 and hysen thomas 1 1 department of physics, christian college chengannur-689122, university of kerala, india. 2 department of physics, college of science, sultan qaboos university, p.o. box 36, pc 123, al khod, sultanate of oman. 3 udsmm, université du littoral côte d'opale, 59140 dunkerque, france. *email: sofins@squ.edu.om. abstract: neodymium doped sodium bismuth silicate glasses were prepared by the melt quench technique. optical absorption spectra of the nd 3+ ion in the present glassy systems were recorded in the uv-vis-nir region. taylor series expansion method was adopted for theoretical evaluation of various crystal field parameters such as the slater-condon (f2,f4,f6), spin orbit  f4 and racah parameters (e1,e2,e3). oscillator strength and electric dipole line strength of the observed transitions were evaluated with the help of judd-ofelt (jo) theory. radiative transition probability (a), total radiative transition probability (at), radiative life time (rad), branching ratios () and integrated absorption (a) cross section for stimulated emission between the meta stable state 4 f3/2 and 4 ij ( j= 15/2,13/2,11/2 and 9/2) levels were calculated using jo parameters. optical basicity of the glass was found to increase with the addition of bismuth. keywords: silicate glasses; optical absorption spectroscopy; racah parameters. انصوديوو انزجاجى انمشوبة بايونات اننوديوو موثعوامم مجال انبهور و انعوامم انضوئية نسيهيكات بز تومس يسنانن و ه اثيوم ،سوفيناو كاريشنا بيالي جوباال ر ،تومس ينويف nd ذحضيز سيهكاخ صىديىو انثشيىز انشجاجيح انًشىتح تايىَاخ انُىديىو ذى :مهخص 3+ . كًا ذى قياص يطياف خًاديإلاتىاسطح ذقُيح انشوتاٌ ndانضىئً اليىَاخ يرصاص اإل 3+ نحساب عىايم انًجال يرذاديح اإل( taylorكًا ذى اسرخذ يد سهسهح ذيهز ) uv-vis-nir فً هذا انُظاو فً حيش spin orbitو slater-condon(f2,f4,f6)َظزيا يثم: انثهىري انًخرهفح كذنك ذى حساب شذج racah parameters (e1,e2,e3)و حرًانيح إ وشعاعً إلاَرقال حرًانيح اإلإنحساب كم يٍ judd-ofelt (jo)تُظزيح سرعاَح تاإلانًالحظح َرقاالخ نإلانرذتذب وشذج خط ثُائً انقطة انكهزتً تيٍ ييرا انحانح انًسرقزج َثعاز اإلانًركايهح انًىحاج يٍ يرصاصيح اإلو انُسثح انفزعيح ويساحح انًقطع شعاعً اإلانًركايهح وعًز انحياج شعاعيح َرقانيح اإلاإل نهحانح. نىحظ سيادج انقاعذج انضىئيح نهشجاجخزي األو انًسرىياخ .انضىئً و يعايالخ راخاإليرصاص يطيافانشجاج ، سيهيكاخ : كهمات مفتاحية 1. introduction ver since the discovery of the solid state laser in 1961, a great deal of effort has been made to study the optical properties of rare earths and rare earth doped systems due to their unique uses in optical amplifiers, fiber lasers, telecommunications and display devices [1-3]. attractive optical absorption and emission in the uv-vis-nir region of the rare earths make them ideal candidates for optical applications in this region. a large variety of laser glasses doped with the nd 3+ ion have been investigated with the purpose of generating efficient emission around 1050 nm [4] . heavy-metal silicate glasses possess lower phonon energies compared to other oxide glasses and display strong visible and near infra-red fluorescence of rare earth ions within the system [5]. though there have been a large number of reports on various rare earth doped glassy systems, the synthesis and optical analysis of neodymium doped bismuth silicate glasses has rarely been studied. at comparatively low bi2o3 content (≤10 mol%), bi2o3 incorporates into the interstices of glass as a network changer which does not cause a large-scale structural rearrangement of the local glassy network. at higher concentrations of bi2o3 (>10 mol%), bi2o3 enters into glasses as a network former and a large-scale structural rearrangement of the local glass network takes place, which leads to significant variation of its optical properties [6-7]. in this context, an optical analysis of neodymium doped bismuth (10 mol%) sodium silicate glass is deserving of special attention and importance. the purpose of the present study is to derive various spectroscopic parameters such as slater condon, racah, spin-orbit and judd ofelt parameters and to evaluate the   f4  e crystal field parameters and optical parameters 71 radiative parameters, such as radiative transition probability, radiative life time and absorption cross section for stimulated emission for the possible transitions. 2. experimental a neodymium (1.5 mol %) doped sodium bismuth silicate glassy system with composition (in mol%) 15 na2o10bi2o3-75 sio2 was prepared by the well-known melt quenching method. appropriate amounts of bi2o3 (99.99% purity, sigma aldrich), na2co3 and sio2 (99.99% purity, sigma aldrich) were mixed and ground continuously using an agate mortar. the powder mixture was placed in a porcelain crucible and melted in a box furnace at a temperature of 1200 0 c for 3 hours. the melt mixture was poured into a stainless steel mold heated to 100 0 c. then the sample was annealed at a temperature of 200 0 c for 1hour. the density of the sample was measured by archimedes’ principle using xylene as the immersion liquid. the u-v visible-nir absorption spectrum of the sample was measured on a uv-visible-nir spectrophotometer varian cary 5000 in the wavelength span of 450 nm to 950 nm. 3. results and discussion figure 1 shows the optical absorption spectra of 1.5 mol % nd2o3 doped sodium bismuth silicate glass. the transitions of the nd 3+ ion occurs due to the transition from the ground state 4 i9/2 to various excited states [8-9]. the location intensity and breadth of the absorption bands are determined by the interaction of nd 3+ ions with the local crystalline field. each absorption band usually consists of a multiplicity of stark levels; unlike the regular local crystal field experienced by nd 3+ in crystalline hosts, the crystal field’s sites in glass are randomly distributed. this distribution results in the inhomogeneous broadening of the absorption spectra of the nd 3+ ion. figure 1. absorption spectra of nd 3+ in sodium bismuth silicate glass. 3.1 bonding properties and nephleuxetic ratio indirect but convincing information regarding the re-ligand bond strength can be obtained from the nephelauxatic ratio(β). the nephelauxatic ratio is given by   ⁄ (1) where νm and νa are the wavenumbers (cm -1 ) of the particular transitions in the host matrix and aqua, respectively. the larger value of the nephelauxatic ratio indicates a reduction in the strength of the covalent bond between the re ion and ligand. the nephelauxatic parameter is directly related to the bonding parameter (δ) as ̅ ̅ ⁄ (2) and ̅ is the average value of the β for observed transitions. the positive or negative sign of δ indicates covalent or ionic bonding of the rare earth-ligand bond. the small positive value of δ (0.0166) in the sodium bismuth silicate glass indicates the decrease in strength of covalency of the re-o bond in the prepared sodium bismuth silicate glass compared to other silicate glass systems [10]. 3.2 crystal field parameters (slater-condon, racah and spin-orbit parameters) the slater-condon parameters (f) generally represent the radial integral part of the electrostatic interaction matrix elements of a trivalent rare earth ion and can be represented as [11] ramakrishna pillai gopala pillai sumesh sofin et al 72 jijik k k k drdrrrrr r r d e f )()( 22 1 2      (3) where k = 2, 4, and 6: r< and r> represent the distances from the nucleus to the nearer and farther electrons respectively. r(ri) and r(rj) represent the normalized wave functions of the i th and j th electron, dk are constants. similarly the spin orbit interaction parameter 4f represents the radial integral part of the spin orbit interaction matrix element and is given by    0 4 222 4 )()( drrrrr ff   (4) where r rv rcm f    )( 2 224   and v(r) is a potential function for the interaction. for a free ion these interaction parameters are constants. but, when the ion is under the influence of another interacting field (ligand field or crystal field), these parameters change due to the overlapping of the 4f wave functions of the rare earth ion with that of the surrounding ligand ion. as a result of this overlapping effect, the distance between the nucleus and the electron of the rare earth ion changes slightly, which in turn affects the energy levels and spectroscopic parameters. the observed energy levels of the neodymium ion can be calculated using the taylor series method. in this method the energy of any level in the rare earth spectra is taken as a function of various types of interactions, such as electrostatic interaction spin-orbit interaction etc. [12]. according to this method, the energy of a rare earth ion can be represented as   f4,ki ffe  (5) where fk is the slater radial integral and  f4 the spin-orbit interaction parameter. relation (5) can be expanded in a taylor series as [13] ... e f f e ee f4 f4 j 6,4,2i i i j ojj          (6) the values of the partial derivatives were taken from the literature [8]. knowing the values of the partial derivatives and zero order energy values, 642 ,, fff  and   f4  can be determined. once these  values are determined the slater condon parameters can be determined as 0 2 2 2 f f δf  0 4 4 f f f  4 6 0 66 fff  fff 4 0 44   (7) where 0 0 0 2 4 6 4 , , and o f f f f  represent the zero order parameters. the racah parameters ( e i ) are related to slater-condon parameters as 1 2 4 6 1 9 70 231 2002e f f f        2 2 4 6 1 9 3 7e f f f     3 2 4 6 1 3 5 6 91e f f f   (8) the calculated values of all the spectroscopic parameters are given in table 1. all the spectroscopic parameters, viz. the slater-condon (f2,f4,f6), spin-orbit (4f) and racah parameters (e 1 ,e 2 ,e 3 ), and the hydrogenic ratios (e 1 /e 3 , e 2 /e 3 , f 4 /f 2 , f 6 /f 2 ) are found to be constants irrespective of the matrix composition. therefore these parameters can be considered to be fundamental constants for trivalent neodymium in a given matrix. crystal field parameters and optical parameters 73 table 1. calculated values of slater-condon( f), racah (e  ) and spin-orbit (4f) parameters in sodium bismuth silicate glass and similar glasses. energy parameters sodium bismuth silicate [present glass] sodium borate [9] sodium phosphate [8] f2( cm -1 ) 284.36 330.05 314 f4( cm -1 ) 46.54 50.8 47 f6( cm -1 ) 2.642 5.14 4.8 4f( cm -1 ) 865.61 870.47 926 e 1 ( cm -1 ) 3993.3 5001.5 4792 e 2 ( cm -1 ) 18.13 23.89 22.6 e 3 ( cm -1 ) 486.87 494.81 471 3.3 judd ofelt parameters the electronic transitions of the trivalent lanthanides can be regarded as a sum of the electric dipole (fed) and magnetic dipole (fmd) contributions, i.e. f = fed+fmd (9) for rare earth ions, line strengths of magnetic dipole (md) transitions are much less than the line strengths of electric dipole (ed) transitions (s md jj’<<s ed jj’) and are usually neglected in the calculation of oscillator strengths. the experimentally measured oscillator strengths of various absorption transitions of the nd 3+ ion in the present glassy systems are found to be in good agreement with those of other oxide systems (see table 2). oscillator strength (f) can be expressed in terms of the molar extinction coefficient (), and the energy of the transition in wave number () by the relation (10) [14]. fexp= 4.32 x 10 -9 ()d (10) according to jo [15-16] theory, oscillator strengths of 4f4f transitions of a rare earth ion can be described as a simple linear combination of three phenomenological parameters (=2,4,6) as 2 6,4,2 222 '' 9 )2( 3 8 )12(                 juj n n h mc j f ed (11) table 2. energy oscillator strength and electric dipole line strength of all observed transitions in sodium bismuth silicate glass. transition from 4 i9/2 to energy ( cm -1 ) fmeasured (10 -6 ) sed (10 -20 ) 4 g9/2 19504 1.07 0.504 4 g7/2 18527 0.669 0.3324 4 g5/2 17390 1.239 0.665 2 g7/2 16946 1.543 0.837 2 h11/2 16621 0.268 0.148 4 f9/2 14602 0.138 0.086 4 s3/2 13467 1.562 1.066 4 f7/2 13260 0.269 0.186 4 f5/2 12500 0.459 0.3376 2 h9/2 12317 1.053 0.786 4 f3/2 11211 0.645 0.529 where (2j+1) is the degeneracy of the ground state, m the mass of the electron, and  the mean energy of the 'j'j  transition,  u is a unit tensor operator of rank  and  u ’s are parameters known as j-o intensity parameters. the calculated values of jo parameters (-0.41 x 10 -20 cm 2 , 3.14 x 10 -20 cm 2 , 2.61 x 10 -20 cm 2 ) and the quality factor (4/6 = 1.2) for the sodium bismuth silicate glass are found to be in good agreement with those of other similar glasses [17]. ramakrishna pillai gopala pillai sumesh sofin et al 74 3.4 radiative transition parameters once the jo parameters  have been determined, they can subsequently be utilized to calculate the properties of transitions that have not been experimentally measured, including the radiative lifetime. the values of the radiative transition probability (a), total radiative transition probability (at), radiative lifetime () fluorescence branching ratio (r) and the integrated absorption crossection for stimulated emission are evaluated using the expressions     ed 22322 jj ed s 9 2nn 1j2h3 e64 a             (12) rad 1 jj ed a   (13)   'j 'jj rad a 1 (14) the relative amplitudes of the fluorescence transitions or fluorescence branching ratio is given by   'j 'jj 'jj 'ajj a (15) the branching ratio is the ratio of the radiative transition probability to the total radiative relaxation rate. it measures the percentage of emission for a given transition from a state with respect to all other transitions from this state. for the nd 3+ ion, the only excited manifold that is not relaxed predominantly by the multiphonon process is the 4 f3/2 manifold. this level fluoresces in four bands centered at approximately 880, 1060, 1350 and 1800 nm corresponding to the 4 i9/2, 4 i11/2, 4 i13/2, 4 i15/2 excited states respectively. since the matrix elements  jiuf 422/34 are zero for the nd 3+ ion, the 2 parameter will not have any effect on the stimulated emission parameters of nd 3+ ions. the calculated values of the radiative transition probability (a), total radiative transition probability (at), radiative life time (rad) and fluorescence branching ration are given in table 3. figure 2. possible radiative channels of nd 3+ from 4 f3/2 level. the integrated absorption crossection or effective crossection (a) for a stimulated emission of the active ion are directly evaluated using the expression 22 8 1 cn a a    (16) from table 3 it is clear that the 4 f3/2 4 i11/2 transition has a promising stimulated absorption crossection and branching ratio and hence this transition in sodium bismuth silicate glass can be utilized for optical applications. crystal field parameters and optical parameters 75 table 3. radiative transition rate, radiative life time, branching ratio and absorption crossection for stimulated emission for all the relevant transitions. level from 4 f3/2 energy cm -1 sed x10 22 cm 2 a (s-1) a t (s-1)  radiative life time rad(s) absorption cross section for stimulated emission (a) 10 18 cm 2 4 i15/2 5450 7.308 9 1760 0.005 568 0.12 4 i13/2 7520 55.33 144 0.08 1.38 4 i11/2 9520 150.8 794 0.451 4.69 4 i9/2 11530 86.83 813 0.461 3.34 3.4 optical basicity and ionic polarisability of the glass optical basicity represents the basicity of glasses in terms of electron density carried by oxygen. the theoretical optical basicity of a glass system is calculated using the relation [18-19]. th= x(na2o) (na2o)+ x(sio2) (sio2)+ x(bi2o3) (bi2o3) (17) where x(na2o) ,x(sio2) and x(bi2o3) are the equivalent fractions of different oxides and  (na2o), (sio2) and  (bi2o3) are the optical basicity values assigned to the constituent oxides [5, 20]. the oxide ion polarisability can be calculated from the theoretical optical basicity as th ( ) (18) it was observed that ionic polarisability increases when optical basicity increases. the bismuth free glass has an optical basicity of 0.787 which increased to 1.185 on addition of 10 mol % of bi2o3. the glass hence possesses high optical basicity and ionic polarisability compared to other similar glasses [21]. 4. conclusion uv-vis-nir absorption spectroscopy of neodymium doped sodium bismuth silicate glasses, prepared by the melt quench technique, was carried out. from the detailed analysis of the spectra, various crystal field parameters such as slater-condon, spin-orbit and racah parameters were calculated. oscillator strength, electric dipole line strength and different radiative properties of the observed transitions were evaluated with the help of judd-ofelt theory. optical basicity of sodium silicate glass was found to increase with the addition of bismuth. references 1. lingling, p., tao h., hui, c. and tiejun, z. spectroscopic properties of gd2o3:dy 3+ nanocrystals. j. rare earths, 2013, 31, 235-240. 2. bensalem, c., mortier, m., vivien,d., gredin, p., patriarche, g. and diaf, m. thermal and 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approach. j. solid state chem., 2005, 178 , 831-846. 8. kumar, g.a., unnikrishnan, n.v., venugopal, c. and biju, p.r. spectroscopic parameters of nd 3+ ion in phosphate glasses. j. noncryst. solids., 1997, 221, 47-58. 9. kumar, g.a., biju, p.r. and unnikrishnan, n.v. evaluation of spectral parameters of nd3+ ion in borate glasses. part i slater–condon, spin orbit and racah parameters. phys. chem. glasses., 1998, 39, 188-191. http://www.sciencedirect.com/science/article/pii/s1002072112602646 http://www.hindawi.com/17645925/ http://www.hindawi.com/89260352/ http://www.hindawi.com/13598256/ http://www.hindawi.com/64628171/ http://www.hindawi.com/59163070/ http://www.hindawi.com/39261317/ http://www.hindawi.com/70609491/ http://www.ncbi.nlm.nih.gov/pubmed/22772261 ramakrishna pillai gopala pillai sumesh sofin et al 76 10. sharma, y.k., surana, s.s.l. and singh r.k. optical absorption and fluorescence spectra of pr(iii) doped boro silicate glasses and their judd-ofelt analysis to study 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phys.,1962, 37, 511-520. 17. takebe, h., nageno, y. and morinaga, k. compositional dependence of judd-ofelt parameters in silicate, borate, and phosphate glasses. j. am. cer. soc., 1995,78,1161-1168. 18. dimitrov, v. and komatsu, t. average single bond strength and optical basicity of na2o-geo2 glasses. j. cer. soc. jap., 2009, 17, 1105-1111. 19. dimitrov, v. and komatsu, t. electronic polarisability, optical basicity and single bond strength of oxide glasses. j. chem. tech. metallurgy, 2013, 48, 549-554. 20. duffy, j.a. optical basicity: a practical acid–base theory for oxides and oxyanions. j. chem. edu.,1996,73,1138-1142. 21. upender, g., vardhani, c.p., suresh, s., awasthi a.m. and chandra, v. structure, physical and thermal properties of wo3-geo2-teo2 glasses. mat. chem. phys., 2010, 121, 335-341. received 15 october 2014 accepted 2 april 2015 http://link.springer.com/search?facet-author=%22hans-herbert+schmidtke%22 http://www.sciencedirect.com/science/article/pii/s0254058405004748 http://www.sciencedirect.com/science/article/pii/s0254058405004748 http://onlinelibrary.wiley.com/doi/10.1111/jace.1995.78.issue-5/issuetoc squ journal for science, 2022, 27(2),100-106 doi:10.53539/squjs.vol27iss2pp100-106 sultan qaboos university 100 topo-groups and atychonoff type theorem mohammad shahryari department of mathematics, college of science, sultan qaboos university, p.o. box 36, alkhod, pc 123, muscat, sultanate of oman, email: m.ghalehlar@squ.edu.om. abstract: we define a topo-system on a group as a set of subgroups satisfying certain topology-like conditions. we study some fundamental properties of groups equipped with a topo-system (topo-groups) and using a suitable formalization of a subgroup filter, we prove a tychonoff type theorem for the direct product of topo-compact topogroups. keywords: topo-groups; topo-systems; filters of subgroups; subgroup ultra-filter ونظرية من صنف تيخونوف ةفضائي -زمر محمد شهرياري سوف نقوم بدراسة بعض محددة.فضائية على الزمرة بأنه مجموعة من الزمر الجزئية التي تحقق شروط شبه فضائي يتم تعريف نظام :صلخمال الزمر الجزئية، سوف نبرهن نظرية من صنف فالتر( و باستعمال تشكيالت مناسبة من فضائية -)زمر فضائيالتي تملك نظام للزمر ساسيةالخصائص األ فضائياً. المتراصة الفضائيةباالستنساخ الضربي للزمر تيخونوف والتي تتعلق .فضائية، فالتر الزمر الجزئية، فالتر فائقة للزمر الجزئية نظم ،زمرفضائية :مفتاحيةالكلمات ال 1. introduction in this article, we introduce an interesting topology-like concept concerning groups (which, by almost the same method, can be defined for other algebraic systems, see [1]). given an arbitrary group g, we define a topo-system on g, as a set of subgroups satisfying certain conditions like a topology on a set. we will call such a group a topo-group. these topo-groups are not rare and as we will see, there are many examples of topo-groups. we investigate fundamental notions concerning topo-groups and we see that many basic concepts of topology can be introduced in the frame of topo-groups. a filter of subgroups of a group g will be defined in such a way that we will be able to formulate a tychonoff type theorem for the direct product of topo-compact topo-groups. throughout this article, sub(g) and sub∗(g) will be used for the set of subgroups and the set of non-identity subgroups of g, respectively. also, for a set of subgroups s={ai}i∈i, the notation <ai : i ∈ i> represents the subgroup generated by s. for basic concepts of group theory, the reader can see [2]. definition 1.1. let g be a group and t ⊆ sub(g) be a set satisfying: a) 1 and g ∈ t, b) if {ai}i∈i is a family of elements of t, then < ai : i ∈ i > ∈ t, and c) if a and b are elements of t, then a ∩ b ∈ t. then we call t a topo-system on g and the pair (g,t) a topo-group. elements of t will be called t-open subgroups. example 1.2. it is quite easy to find many examples of topo-groups. here, we give a list of such examples: 1the set t = sub(g) is a topo-system and we call it the discrete topo-system on g. 2the set t = {1, g} is a topo-system and we call it the trivial topo-system. topo-groups and a tychonoff type theorem 101 3let b ⊆ g and tb = {a ≤ g : b ⊆ a} ∪ {1}. this is the principal topo-system associated with b. 4let tcf = {a ≤ g : [g : a] < ∞} ∪ {1}, where [g : a] is the index of a inside g. this is the cofinite toposystem on g. 5let tn = {a ≤ g : a is normal in g}. this is the normal topo-system on g. 6let tchar = {a ≤ g : a is characteristic in g}. this is the characteristic topo-system on g. recall that a is a characteristic subgroup of g if it is invariant under every automorphism of g. 7let g be a topological group and t be the set of all open subgroups of g together with the identity subgroup. then t is a topo-system on g. 8let v be a variety of groups and tv = {a ∈ g : g/a ∈ v} ∪ {1}. then tv is a topo-system on g and, in fact, we have tv = th ∩ tn, where h = o v (g) is the v-residual of g (i.e., the smallest normal subgroup of g, such that g/h belongs to v). definition 1.3. a subgroup a ≤ g is t-closed if for all x ∈ g \ a, there exists b ∈ t such that x ∈ b and a ∩ b = 1. it is easy to verify that 1 and g are t-closed, and the intersection of any family of t-closed subgroups is t-closed. let x ≤ g and x ∈ x. suppose there is a t-open a with x ∈ a ≤ x. then we say that x is an interior element of x. the set of all interior elements of x is denoted by x ◦ and it is called the interior of x. clearly, the interior of x is a t-open subgroup. as an example, in the case of the normal topo-system (see the above example), we have x ◦ = xg, the core of x (i.e., the maximal normal subgroup of g included in x). in the case of the co-finite topo-system, it can be verified that x ◦ = 1 or x. for any subgroup x, the boundary is ∂x = x \ x ◦ . a point x ∈ g is a limit point of x, if for all t-open a containing x, we have |a ∩ x| ≥ 2. the t-closure of x is the subgroup generated by x and its limit points. clearly, it is t-closed. unlike the ordinary topology, there is no symmetry between the concepts of t-open and t-closed subgroups. for example, if any subgroup of a topo-group g is t-open, we cannot say that any subgroup is t-closed as well. for example, consider the group 𝐺 = 𝑍 × 𝑍4 with the discrete topo-system. then the subgroup a = <(0,2)> is not tclosed. in general, we have the following proposition. proposition 1.4. let all cyclic subgroups of g be t-closed. then all non-identity elements of g have prime orders. proof. let x ∈ g be a non-identity element. then a = <x 2 > is t-closed. if x does not belong to a, then there is a b ∈ t containing x such that a ∩ b = 1. so, <x> ∩ a = 1 and hence x 2 = 1. if x ∈ a, then x has finite order n. suppose n = ab. then <x a > is t-closed and hence x ∈ <x a > or <x a > ∩ <x> = 1. (1) in the first case we have x b = 1 and in the second case, we have x a = 1. so, n is a prime. definition 1.5. a subgroup x ≤ g is a topo-compact subgroup if any t-open covering of x has a finite sub-covering, i.e., if x ⊆ ∪ i∈iai, with ai ∈ t, then there is a finite subset j ⊆ i, such that x ⊆ ∪ i∈jai. in the special case x = g, we say that g is topo-compact. for example, a group is topo-compact with respect to the discrete topo-system if it is a finite union of cyclic subgroups. in fact, such a group is finite or infinite cyclic as the next proposition shows. proposition 1.6. let (g,t) be topo-compact and suppose that t is the discrete topo-system. then g is finite or infinite cyclic. proof. we have g = ∪ x∈g<x> and all <x> are t-open. so, by topo-compactness, 𝐺 =< 𝑥1 >∪< 𝑥2 >∪ ⋯ ∪< 𝑥𝑛 > , (2) for some finite set of elements. now by a theorem of neumann (see [2], page 120), we may assume that any <xi> has a finite index. suppose g is infinite. then all <xi> are infinite as they have finite index, and hence g is torsion free. assume h ≤ g to be a non-identity subgroup and h ∈ h to be a non-identity element. then, there is an index i such that h ∈ <xi> and therefore [<xi> : <h>] is finite. so, already [g : <h>] is finite and hence h has finite index. a theorem of fedorov (see [3], page 446) says that if any non-trivial subgroup of an infinite group has finite index, then the group is isomorphic to the infinite cyclic group z. this completes the proof. the concept of topo-compact groups may have many interesting interpretations if we consider different toposystems. it can be verified that a t-closed subgroup of a topo-compact group is a topo-compact subgroup. if (g,t) is a topo-group and h ≤ g, then the set s = {a∩h : a ∈ t} generates a topo-system on h, which is an induced topo-system on h. we denote this topo-system by tind. we give a recursive construction of the elements of tind. let t0 = s and for any ordinal α (see [4]) also for limit ordinals we set mohammad shahryari 102 𝑇α = ⋃ 𝑇β β<α then it can be shown that tind = ∪ αtα. now, if (h,tind) is a topo-compact topo-group, then it can be proved that h is a topo-compact subgroup of g. the converse situation is very complicated because the t-open subgroups of (h,tind) have very complex structures. also if h∈ g, then one checks that the set is a topo-system on the quotient group g/h. so, we call it the quotient topo-system. if {(gi,ti)i∈i} is a family of topogroups and 𝐺 = ∏ 𝐺𝑖𝑖 , then the set {∏ 𝐴𝑖 𝑖 :  𝐴𝑖 ≤ 𝐺𝑖 , 𝑎𝑛𝑑 𝑎𝑙𝑚𝑜𝑠𝑡 𝑎𝑙𝑙 𝐴𝑖 = 𝐺𝑖 } is a topo-system on g. note that, the situation here is much better than the case of ordinary product topology because of the following two trivial equalities: 1. (∏ 𝑨𝒊𝒊 ) ∩ (∏ 𝑩𝒊𝒊 ) = ∏ (𝑨𝒊 ∩ 𝑩𝒊)𝒊 2. < ∏ 𝑨𝒊𝒋𝒊 :  𝒋 ∈ 𝑱 >= ∏ < 𝑨𝒊𝒋:  𝒋 ∈ 𝑱𝒊 > definition 1.7. let (g,t) and (h,s) be two topo-groups. a continuous map (or a topomorphism) is any homomorphism f : g → h with the property f −1 (b) ∈ t, for all b ∈ s. an invertible topomorphism with a continuous inverse is a topeomorphism. clearly, the projections πj: ∏ 𝐺𝑖𝑖 → gj are topomorphisms and also the natural map q : g → g/h is also a topomorphism. if h is a subgroup of a topo-group (g,t), then the inclusion map j : (h,tind) → (g,t) is a topomorphism, too. remark 1.8. let (g,t) be a topo-group. we can define a topology on g with the basis t. let us denote this topology by t∗. a subset x ⊆ g is open if x is a union of elements of t. this topology is never hausdorff but g is compact if and only if g is topo-compact. for a subgroup h ≤ g with the induced topo-system tind, we have (t ∗)ind ⊆ (tind)∗. we close this section with two more examples of interesting topo-systems on arbitrary groups. example 1.9. let g be a group and h ≤ k ≤ g. we define t h,k = {a ≤ g : [a,k] ⊆ h} ∪ {g}, (3) where [a,k] is the commutator subgroup generated by all commutators [a,b] = aba −1 b −1 , with a ∈ a and b ∈ k. clearly, 1 and g belong to t h,k . this set is closed under intersection, so let {ai}i∈i be a family of elements of t h,k . suppose a1,...,an are elements from the union of ai’s and x ∈ k. we have . (4) now, for any u ∈ k, we have aiua − i 1 u −1 ∈ h, so for some hn ∈ h, . continuing this way, for some hn−1 ∈ h, we have . (5) finally, we get [a1a2 ...an,x] = h1h2 ...hn, (6) for some h1,...,hn ∈ h. this shows that ∏ 𝐴𝑖𝑖 ∈ t h,k . example 1.10. let g be group and h ≤ g be a fixed subgroup. define 𝑇𝑐𝑜𝑛𝑗 (h) = {a ≤ g : h ⊆ n(a)}, where n(a) is the normalizer of a in g. it can be verified that tconj(h) is a topo-system on g. hausdorff topo-groups suppose (g,t) is a topo-group and for any x,y ∈ g with <x> ∩ <y> = 1, there exist a,b ∈ t with the properties x ∈ a, y ∈ b, and a ∩ b = 1. then we say that (g,t) is a hausdorff topo-system. a subgroup a ≤ g is weak t-closed, if for all x with <x> ∩ a = 1, there exists b ∈ t such that a ∩ b = 1. recall that, in each ordinary hausdorff topological space, every compact subset is closed. by a similar argument as in the ordinary topological spaces, one can see that the following proposition holds. topo-groups and a tychonoff type theorem 103 proposition 2.1. let (g,t) be a hausdorff topo-group and a be a topo-compact subgroup. then a is weak t-closed. clearly, any discrete topo-group is hausdorff. if g is infinite and (g,tcf) is hausdorff, then for all non-identity x,y ∈ g, we have < 𝑥 >∩< 𝑦 >≠ 1 (7) so the intersection of any two non-trivial subgroups of g is non-trivial. clearly, such a group is torsion free or a pgroup for some prime. the groups z, q and zp∞ are examples of such groups. torsion free non-abelian groups with this property are constructed by adian and olshanskii, [5]. an elementary argument shows that g can be embedded in q if g is an r-group (i.e., a group satisfying x m = y m ⇒ x = y for any non-zero m). the next proposition shows that the p-group case can be investigated by a very elementary argument, and so the hardest part of the problem is the case of torsion free groups which are not r-groups. proposition 2.2. let g be an infinite p-group which is hausdorff with respect to the topo-system tcf . then g has a unique subgroup of order p. the converse is also true. proof. let g be a p-group and the intersection of any two non-trivial subgroups of g be non-trivial. suppose x is a non-identity element of g. then <x> has a subgroup a of order p. for any non-identity subgroup b ≤ g, the intersection a∩b is non-trivial, so a ⊆ b, and hence a is a unique subgroup of g of order p. conversely, suppose g has a unique subgroup of order p, say a. then clearly, for any non-trivial subgroup b, we have a ⊆ b, and hence every two non-trivial subgroups of g have a non-trivial intersection. note that the subgroup a in the proof of the above proposition is minimum in the set of non-trivial normal subgroups of g. therefore, by a well-known theorem of birkhoff (see [1]), such a group g is sub-directly irreducible. corollary 2.3. any infinite p-group which is hausdorff with respect to the topo-system tcf is sub-directly irreducible. for any group g, the normal topo-group (g,tn) is hausdorff if and only if g satisfies <x> ∩ <y> = 1 ⇒ <x g > ∩ <y g > = 1, (8) where <x g > and <y g > denote the normal closure of <x> and <y>, respectively. in the next theorem, we give some properties of this kind of groups. note that a q-group is a group in which every element x has a unique m-th root x 1/m , for every non-zero integer m. theorem 2.4. let g be a torsion free group which is hausdorff with respect to the topo-system tn. then for any x,u ∈ g, there are non-zero integers m and k such that ux k u −1 = x m . further, if g is also a q-group, then there exists a family of normal subgroups ai, such that 1𝐺 = ⋃ 𝐴𝑖𝑖 , 2𝐴𝑖 ≅ 𝑄, 3𝐴𝑖 ∩ 𝐴𝑗 = 1. as a result, g is abelian. proof. let a = g \ 1 and define a binary relation on a by x ≡ y ⇔ <x> ∩ <y> ≠ 1. this is an equivalence relation on a. let e(x) be the equivalence class of x and {ei = e(xi) : i ∈ i} the set of all such classes. then we have 𝐺 = ⋃ ⋃ < 𝑦 𝑦∈𝐸𝑖𝑖 > now, since <x> ∩ <y> = 1 ⇒ <x g > ∩ <y> = 1, (9) so, < 𝑥 𝐺 >⊆ ⋃ < 𝑦 𝑦∈𝐸(𝑥) >. let u ∈ g be arbitrary. then there is y ∈ e(x) such that uxu −1 ∈ <y>. hence, for some i, m and k we have uxu −1 = y i , x m = y k . therefore, for any x,u ∈ g, there are non-zero integers m and k such that ux k u −1 = x m . now, suppose g is a q-group. then, we have ei = {y ∈ g : ∃m,k (non-zero) x m = y k } ⊆ {𝑥𝑖 α : α ∈ q} ⊆ g. mohammad shahryari 104 suppose ai = {𝑥𝑖 α : α ∈ q}. then, any ai is a subgroup of g and clearly, we have 1-2-3. note that, since for any u ∈ g we have uxiu −1 = 𝑥𝑖 α, for some α ∈ q, so ai is a normal subgroup. now, [ai, aj] ⊆ ai ∩ aj, so, by 3, we have [ai, aj] = 1. this shows that g is abelian. we can use the malcev completion of torsion free locally nilpotent groups (see [6] and [7]) to prove the next result on hausdorff groups with respect to tn. theorem 2.5. let g be a torsion free locally nilpotent group which is hausdorff with respect to tn. then g is abelian. proof. the same argument as above shows that for any x,u ∈ g, there are non-zero integers m and k such that ux k u −1 = x m . now, suppose g∗ is the malcev completion of g. we know that g∗ is a q-group. by the notations of the above proof, let ai = {𝑥𝑖 α : α ∈ q}, which is a subgroup of g∗. a similar argument shows that 1 − 𝐺 = ⋃ 𝐴𝑖𝑖 , 2 − 𝐴𝑖 ≅ 𝑄, 3 − 𝐴𝑖 ∩ 𝐴𝑗 = 1. since xjxix − j 1 = 𝑥𝑖 α , for some α ∈ q, so [xi, xj] ∈ ai and similarly it also belongs to aj. this shows that xi and xj are commuting. therefore, we have [x p i ,x q j] = 1 for all p,q∈ q . so, [ai ,aj] = 1, which shows that g is abelian. filters of subgroups for standard notions of filter theory, the reader could use [8]. a filter of subgroups (or a subgroup filter) is any subset f ⊆ sub∗(g), with the following properties: a) g ∈ f. b) if a ≤ b ≤ g and a ∈ f, then b ∈ f. c) if a and b ∈ f, then a ∩ b ∈ f. example 3.1. for any group g, the sets {g} and sub∗(g) are trivial examples of subgroup filters. for each x ∈ g, there exists the principal filter of subgroups fx = {a ∈ sub∗(g) : x ∈ a}. if g is an infinite group, then the set fcf = {a ≤ g : [g : a] < ∞} is the co-finite filter of subgroups. like ordinary filters, any filter of subgroups has finite intersection property (”fip” for short): 𝐴1, … , 𝐴𝑛 ∈ 𝐹 ⇒ ⋂ 𝐴𝑖 𝑛 𝑖=1 ≠ 1. on the other hand, a subset s ⊆ sub∗(g) with fip is contained in a unique minimal filter of subgroups (which is the subgroup filter generated by s); if we define , then the subgroup filter generated by s is equal to fs = {b ≤ g : a ⊆ b for some a ∈ s∗}. let p(g) be the power set of g and f1 ⊆ p(g) be an ordinary filter. then clearly the set f = f1 ∩sub∗(g) is a filter of subgroups. the converse is also true: proposition 3.2. let f ⊆ sub∗(g) be a subgroup filter. then there is an ordinary filter f1 ⊆ p(g) such that f = f1 ∩ sub∗(g). proof. let f1 = {x ⊆ g : a ⊆ x for some a ∈ f}. it can be easily verified that f1 is an ordinary filter and f = f1 ∩ sub∗(g). definition 3.3. an ultra-filter of subgroups is a subgroup filter f ⊆ sub∗(g) such that for any finite set of subgroups a1,...,an, the condition ∪ iai ∈ f implies ai ∈ f, for some i. proposition 3.4. let f1 ⊆ p(g) be an ordinary ultra-filter. then f = f1 ∩ sub∗(g) is an ultra-filter of subgroups. proof. suppose a1 ∪ a2 ∪ ···∪ an ∈ f, where a1, a2, ..., an are subgroups. suppose by contrary that none of ais belong to f. then, clearly, none of ais belong to f1, and as f1 is an ordinary ultra-filter, we have g \ a1, g \ a2, ..., g \ an ∈ f1. this means that topo-groups and a tychonoff type theorem 105 ⋂(𝐺 ∖ 𝐴𝑖) 𝑛 𝑖=1 ∈ 𝐹1 and hence, ∅ = (⋂ (𝐺 ∖ 𝐴𝑖 ) 𝑛 𝑖=1 ) ∩ (⋃ 𝐴𝑖 𝑛 𝑖=1 ) ∈ 𝐹1 (10) which is a contradiction. proposition 3.5. let f be a subgroup filter on g. then there exists an ultra-filter of subgroups containing f. proof. we have f = f1 ∩ sub∗(g) for some ordinary filter f1, but there exists an ordinary ultra-filter f2 such that f1 ⊆ f2. now, f* = f2 ∩sub∗(g) is a subgroup ultra-filter containing f. definition 3.6. let g and h be two groups and f ⊆ sub∗(g) be a filter of subgroups. let f : g → h be a group homomorphism and define f∗(f) = {a ≤ h : f −1 (a) ∈ f}. (11) one can see that this is a subgroup filter on h and further, it is a subgroup ultra-filter, if f is so. the following definition connects two notions of topo-groups and ultrafilters of subgroups. definition 3.7. let (g,t) be a topo-group and f ⊆ sub∗(g) be a subgroup ultra-filter. let y ∈ g. we say that f converges to y, if for all a ∈ t with y ∈ a, we have a ∈ f. in this situation we write f → y. note that if (g,t) and (h,s) are topo-groups, and if f : g → h is a topomorphism, then for an ultra-filter of subgroup f, the condition f → x implies f∗(f) → f(x), for all x ∈ g. we are now ready to prove the main theorem of this section: theorem 3.8. let (g,t) be a topo-group. then g is topo-compact if and only if any ultra-filter of subgroups converges to some point in g. proof. let g be topo-compact and f be an ultra-filter of subgroups on g. suppose by contrary that f does not converge to any element of g. so, for all y ∈ g, there exists a t-open subgroup ay ≤ g such that y ∈ ay and ay does not belong to f. we have g = ∪ yay, so g can be covered by a finite number of ay’s, say 𝐴𝑦1 , … , 𝐴𝑦𝑛 . hence 𝐴𝑦1 ∪ ⋯ ∪ 𝐴𝑦𝑛 = 𝐺 ∈ 𝐹 and therefore 𝐴𝑦𝑖 ∈ 𝐹, for some i, since f is an ultra-filter. this is a contradiction, so f has at least one convergence point in g. now, suppose that g is not topo-compact. hence, there is a covering g = ∪𝑖∈𝑗 𝐴𝑖 , where each ai is t-open and 𝐺 ≠∪𝑖∈𝑗 𝐴𝑖 for any finite subset j ⊆ i. this means that the set s = {g \ ai : i ∈ i} (12) has ‘set-fip’ (i.e., the intersection of any finite number of its elements is non-empty) and so there exists an ordinary ultra-filter f1 containing s. let f = f1 ∩ sub∗(g). then f is a subgroup ultra-filter. for any y ∈ g, we have y ∈ ai for some i. but as f1 is an ultra-filter, ai does not belong to f1 and already it does not belong to f. this shows that f does not converge to y. we say that two elements x and y in a group g are cyclically distinct if <x> ∩ <y> = 1. so, the above theorem says that a topo-system is topo-compact if and only if every ultra-filter of subgroups has at least one point of convergence up to the cyclic distinction. a similar assertion holds for hausdorff topo-groups. theorem 3.9. a topo-group (g,t) is hausdorff if and only if any ultra-filter of subgroups in g converges to at most one point (up to cyclic distinction). mohammad shahryari 106 proof. let f be an ultra-filter of subgroups in g and (g,t) be hausdorff. let x and y be cyclically distinct but f → x and in the same time f → y. we know that there are a, b ∈ t containing x and y, respectively and a ∩ b = 1. but then we have also a, b ∈ f and so 1 = a ∩ b ∈ f, which is impossible. conversely, let (g,t) be not hausdorff. then there are cyclically distinct x and y, such that for all t-open subgroups a and b with x ∈ a and y ∈ b, we have 𝐴 ∩ 𝐵 ≠ 1. suppose s = fx ∪ fy. then clearly s has fip and hence there exists an ultra-filter of subgroups, say f, such that s ⊆ f. now suppose a ∈ t and x ∈ a. then 𝐴 ∈ 𝑆 ⊆ 𝐹 and therefore f → x. similarly, we have f → y. a tychonoff type theorem it seems that many known theorems of topology have versions in topo-groups. once we prove such a theorem, it is possible to translate it into the language of groups and find an interesting theorem of group theory. in this section, we prove an analogue of the compactness theorem of tychonoff (see [8]) for topo-groups. theorem 4.1. let {(gi,ti)}i∈i be a family of topo-compact topo-groups. then g = ∏ 𝐺𝑖𝑖 is also topo-compact. proof. let f ⊆ sub∗(g) be a subgroup ultra-filter. we prove that it converges to at least one point in g. note that (πi)∗(f) is an ultra-filter of subgroups in gi and since gi is topo-compact, so it converges to some point xi ∈ gi. suppose x = (xi) ∈ g. we prove that f → x. let a ≤ g be t-open and x ∈ a. we may assume that 𝐴 = ∏ 𝐴𝑖𝑖 , with ai ∈ ti and such that almost all ai = gi. since xi ∈ ai, so ai ∈ (πi)∗(f), i.e. πi −1 (ai) ∈ f. now, clearly 𝐴 = ⋂ π𝑖 −1(𝐴𝑖 ) 𝑖 , and the intersection consists of finitely many non-trivial elements of f, so it belongs to f and this shows that f → x, therefore g is topo-compact. conflict of interest the author declares no conflict of interest. acknowledgment the author would like to thank m.h. jafari for the useful discussion and i. al-ayyub for arabic translation of the abstract. references 1. burris, s. and sankappanavar, h.p. a course in universal algebra, the millennium edition, 2012 update. 2. scott, w.r. group theory, dover, 1987, springer-verlag, new york, heidelberg, berlin, new jersey. 3. passman, d.s. the algebraic structure of group rings, wiley, new york, london, sydney, 1977. 4. thomas, j. set theory, springer, 2006, 73-90, berlin, heidelberg. 5. olshanskii, a.y. geometry of defining relations in groups, kluwer academic publishers, 1991, 296-307. 6. majewicz, s. on classes of exponential a-groups, comm. alg., 2010, 38(4), 1363-1384. 7. temple, h.f. remarks on the malcev completion of torsion free locally nilpotent groups, cahiers de topologie et géométrie, 1994, 350(1), 75-84. 8. wilansky, a. topology for analysis, dover publication, new jersey, 2008, 121-134. received 22 september 2021 accepted 26 april 2022 squ journal for science, 2023, 28(1), 17-24 doi:10.53539/squjs.vol28iss1pp17-24 sultan qaboos university 17 comparative study on the phytochemical, antistaphylococcal and antioxidant properties of the stem bark of jatrophacurcas l and jatrophagossypifolia l oyetayo, v.o.* and temenu, o.e. department of microbiology, federal university of technology, akure, nigeria. *email: ovonew67@gmail.com. abstract: this study was conducted to assess the phytochemical, antistaphylococcal and antioxidant properties of the leaf and stem bark of jatrophacurcas and jatrophagossypifolia. ethanolic extracts of the leaf and stem bark of j. curcas and j. gossypifolia were obtained using standard methods. qualitative and quantitative phytochemical properties of the jatropha plant was assessed using standard methods. antistaphylococcal and minimum inhibitory concentrations of the extracts were assessed against staphylococcal aureus obtained from different sources using agar diffusion method. the ferrous ion and hydroxyl radical scavenging activity of the extracts were also determined using standard methods. quantitative phytochemical screening revealed that the distribution of phytochemicals in the two jatropha species do not follow a regular trend. however, saponin was highest in j. curcas stem bark (35.64 mg/g) while j. gossypifoliastem bark and leaf have the highest flavonoid (31.35 mg/g) and alkaloids (23.20 mg/g) respectively. the antistaphylococcal effect of the combined extract was higher and significantly different (p≤0.05) than when used singly. the highest antistaphylococcal effect (19.83mm) was recorded for the combination of j. curcas and j gossypifolia leaf (jcl and jgl) against staphylococcus aureus obtained from blood. antioxidant assay of extracts revealed a concentration-dependent effect. the antioxidant activities of the extracts vary from one extract to the other. the results obtained from this study indicates that bioactive compounds present in j. curcas and j gossypifolia can be exploited as source of effective antistaphylococcal and antioxidant compounds. keywords:comparative; antioxidant; antistaphylococcal; leaf; stem bark; extract; jatrophacurcas; jatrophagossypifolia. دراسة مقارنة حول الخصائص الكيميائية النباتية والمضادة للمكورات العنقودية ومضادات األكسدة للحاء الجزعي لنباتي من صنف الجاتروفاكوركاس وجاتروفا جوسييفوليا و يناتيم يز.و ف.و أويتيو الدراسة لتقييم الخصائص الكيميائية النباتية والمضادة للمكورات العنقودية والمضادة لألكسدة من أوراق وسيقان الجاتروفا كوركاس و أجريت هذه :صلخمال تم باستخدام الطرق القياسية. جوسيبيفولياتم الحصول على المستخلص الكحولي من أوراق وسيقان الجاتروفا كوركاس و جاتروفا .جوسيبيفولياجاتروفا لمكورات العنقودية الذهبية تقييم الخصائص النوعية والكمية الكيميائية النباتية لنبات الجاتروفا باستخدام الطرق القياسية. تم تقييم النشاط المضاد الميكروبي ل الشوارد الحرة للمستخلصات أيًضا التي تم الحصول عليها من مصادر مختلفة باستخدام طريقة انتشار األجار. تم تحديد األنزيمات المضادة لألكسدةو رخر. ومع لل كان باستخدام الطرق القياسية. كشف الفحص الكيميائي النباتي الكمي أن توزيع المواد الكيميائية النباتية في نوعي جاتروفا تختلف من نوع أل اتروفا جوسيفوليا وأوراقه أعلى نسبة من الفالفونويد جم( بينما كان لحاء ساق الجمجم/ 46.53جذع جاتروفا كركاس ) السابونين أعلى في لحاء /جم( على التوالي. كان التأثير المضاد للمكورات العنقودية لكال المستخلصين معا أعلى ومختلفًا ارختالفًا مجم 34.32مجم/جم( والقلويدات ) 43.46) مم( لمزيج من الجاتروفا كركاس وأوراق الجاتروفا 38.94ت العنقودية )( عند استخدامه منفردًا. تم تسجيل أعلى تأثير مضاد للمكوراp≤2.26معنويًا ) زات. تختلف جوسيفولياضد المكورات العنقودية الذهبية المأرخولة من الدم. وتبين من نتائج مضادات األكسدة للمستخلصات انها تتناسب طرديا مع التركي . تشير النتائج التي تم الحصول عليها من هذه الدراسة إلى أن المركبات النشطة بيولوجيًا األنشطة المضادة لألكسدة في المستخلصات من مستخلص إلى آرخر و يمكن استغاللها كمصدر فعال لمضادات المكورات العنقودية ومضادات جوسيبيفوليا المستخلصة من أوراق وسيقان الجاتروفا كوركاس و جاتروفا األكسدة. األكسدة مضادات المكورات العنقودية ؛ اللحاء الجذعي ؛ جاتروفا كركاس جاتروفا جوسيبيفوليا.مقارنة؛ مضادات :مفتاحيةالكلمات ال mailto:ovonew67@gmail.com oyetayo, v.o. and temenu, o.e. 18 1. introduction iseases of man caused by microorganisms have become a major threat to human health and existence. staphylococcus species are very important pathogen responsible for bacterial infections in hospitals and communities worldwide. they are very diverse and are implicated in various infection processes especially in immunecompromised individuals and those with implant devices such as shunts and catheters [1]. staphylococcus aureus has been recognized as a versatile microorganism worldwide [2]. it is a human pathogen and a part of the normal flora of human skin [3]. it can colonize and infect both patients and healthy people with life threatening effects [4]. staphylococcusspecies generally exhibit multiple antibiotic resistances [5, 6]. resistance of microorganisms to commonly used antimicrobial agents is a major challenge in the treatment of diseases of microbial origin. hence, the search for antimicrobial agents that are safe and most importantly effective against diseases of microbial origins has doubled/tripled in the last three decades. this is as a result of resistance developed by microorganisms against commonly used antimicrobial agents, the safety of these antimicrobial agents and the side effects associated with the use of antibiotics in the treatment of gastroenteritis and other infections [7]. plant-based bioactive compounds have recently become of great interest in the search for suitable, safe and friendly alternatives to those existing antimicrobials which are becoming less effective. researchers have made tremendous efforts to discover new antimicrobial compounds from natural products especially of plant origin. ncube et al. [8] submitted that medicinal plants are the richest bio-resource of drugs of the traditional system of medicines, pharmaceutical intermediates and chemical entities for synthetic drugs. moreover, many people all over the world have resorted to the use of herbal medicine for the treatment of various health challenges [9]. jatropha species are among these medicinal plants that have attracted interest as potential sources of antimicrobial agent. they belong to the family euphorbiaceae. they contain secondary metabolites such as alkaloids, tannins, flavonoids, steroid, saponins and phenolics which are known to possess medicinal properties [10, 11]. the stem bark, root, leaf, sap, seed and the oil from the seed of jatropha species had been used for treating various ailments ranging from skin diseases, parasitic diseases, urinary tract infections, bleeding of gum and toothaches, treatment of wound and sores, fever and many others [12-18]. jatropha curcas and jatropha gossypifolia are commonly found in nigeria. these two plants had found wide use in ethno-medicine especially in rural parts of nigeria. the present study is therefore aimed at comparative study of the phytochemical properties, antioxidant and antistaphyloccal activities of leaf and stem bark extracts of j. curcas and j. gossypifoliasingly and in combination. 2. materials and methods 2.1 collection and preparation of jatropha species extracts fresh leaves and stem bark of jatropha curcas l and jatropha gossypifolia l were collected from a local farm at oke-aro in akure, ondo state, nigeria. the plants were identified and authenticated by a plant scientist in the department of crop science and pest management, federal university of technology, akure. the stem bark and leaf were rinsed with clean water and sun-dried for three weeks under shade and then pulverized using a mechanical grinder. the pulverized plant material was kept in an air-tight cellophane bag until required. powdered jatropha species (200 g) of the leaf and stem bark were each placed in 1000 ml of 99.7% ethanol (analytical grade) and kept in conical flasks, each was shaken in a rotary shaker at 121rpm for 24 hrs. after 24 hours, the suspension was filtered with a double-layer muslin cloth and whatman no. 1 filter paper. the resulting filtrates were concentrated under reduced pressure in a rotary evaporator (re 52a; union laboratory, england) at 40 o c. 2.2 test organism,staphylococcus species all staphylococcus species were grown on mannitol salt agar plates at 37 o c for 24 hours. the isolates were maintained on agar slant and stored in the refrigerator at 5 o c until used. 2.3 quantitative phytochemical analysis of jatropha species quantitative phytochemical screening of the crude extracts of the stem bark and leaf of jatropha species was performed using standard procedures as described by harborne [19]; trease and evans [20]. the quantity of the following phytochemicals viz; saponin, tannin, flavonoid, cardiac glycosides and alkaloids were assessed in the extracts obtained from the two jatropha species. 2.4 determination of total phenolic content the total phenol content of leaf and stem bark was determined (gallic acid equivalent) as described by singleton et al. [21] with slight modifications. briefly, 200µl of the extract dissolved in 10% dmso (240 µgml -1 ) was incubated with 1.0 ml of folin-ciocalteu reagent (diluted 10 times) and 800 µl of 0.7 mol l -1 na2co3 for 30 minutes at room temperature. then, the absorbance was measured at 765 nm on a shimadzu uv mini 1240 spectrophotometer (shimadzu, japan). all measurements were done in triplicates. results are expressed as mg gae / 100 g dry ethanol extracts. d comparative study on the phytochemical, antistaphylococcal and antioxidant properties 19 2.5 determination of antistaphylococcalproperties of jatropha species antistaphylococcal activity of stem bark and leafextracts of jatropha species was determined by agar well diffusion method as described by abubakaret al. [22]. staphylococcus species obtained from different sources were cultivated on nutrient broth at 32 °c for 18 hours. the inoculum size was adjusted by serial dilution to obtain 0.5 mcfarland turbidity standards. the extract was reconstituted in 20% v/v of dimethyl sulfoxide (dmso). an aliquot of 0.1 ml containing organism was aseptically transferred and evenly spread onto the dried surface of the sterile mueller hinton agar plate. a well of 8 mm was bored in the agar plate with a sterile cork borer. each extract was sterilized through a membrane filter (0.22 μm) and 0.1 ml was aseptically introduced into the well in the petri dishes already inoculated with staphylococcus species with the aid of a micropipette. a volume of 0.1 ml of ciprofloxacin was used as positive control while 20% of dmso served as a negative control. the plates were incubated at 37 °c for 24 hours. the diameter of the inhibition zones was measured in millimeters. 2.6 antioxidant assay the following antioxidant assays were performed on the stem bark and leaf extracts obtained from jatropha species. 2.7 hydroxyl radical scavenging ability of stem bark and leaf extracts of jatropha species the determination of the scavenging effect on hydroxyl radicals was carried out as described by oyetayo et al. [23]. the reaction mixtures in a final volume of 1.0 ml, containing 0.4 ml of 20 mmol/ml sodium phosphate buffer (ph 7.4), 0.1 ml of 0.125-2 mg/ml extracts, 0.1 ml of 60 nmol/l deoxyribose, 0.1 ml of 10 mmol/l hydrogen peroxide, 0.1 ml of 1 mmol/l ferric chloride, 0.1 ml of 1.04 mmol/l edta and 0.1 ml of 2 mmol/l ascorbic acid was incubated at 37 ̊c for 1 hour. solutions of fecl2 and ascorbic acid were made up immediately before use in de-ionized water. the reaction was stopped by adding 1 ml of 17 mmol/l thiobarbituricacid (tba) and 1 ml of 17 mmol/l trichloroa cetic acid (tca). the mixture was boiled for 15 min, cooled in ice and then the absorbance was measured at 532 nm using a unico 2100 spectrophotometer (as). 2.8 ferrous ion chelating ability assay the fe 2+ chelating ability of leaf and stem bark ethanol extracts was determined by employing a modified method of puntel et al. [24]. freshly prepared 500 µmol l -1 feso4 was added to a solution containing 168µl of 0.1 moll 1 tris-hcl (ph 7.4), together with 218 µl of saline and an ethanol extract (1-5 mg /ml). the solution was incubated for 5 minutes, followed by the addition of 13 µl of 0.25%, 1,10 phenantroline (w/v). absorbance was read at 510 nm. fe 2+ chelating ability was expressed as percentage inhibition. 2.9 statistical analysis experiments were carried out in replicates and data obtained were analyzed by one way analysis of variance (anova) and means were separated by duncan multiple range test (spss 17.0 version). differences were considered significant at p ≤ 0.05. 3. results the distribution of the phytochemicals in the two jatropha species does not follow a regular trend as revealed by quantitative phytochemical screening (table 1). saponin was highest and significantly different (p≤0.05) in j. curcas stem bark (35.64 mg/100 g) when compared to other extracts, while j. gossypifolia stem bark and leaf has the highest flavonoid (31.35 mg/100 g) and alkaloid (23.20 mg/100g) respectively. the phenolic contents of the different parts of the jatropha species vary and are significantly different (p≤0.05). the leaf extract of j. curcas has the highest total phenol (2.2 mggae/g) while the least was recorded in the leaf extract of j. gossypifolia (0.8 mggae/g) (figure 1). table 1. quantitative phytochemical contents of leaf and stem bark extracts of two jatropha species. phytochemicals jcl jcs jgl jgs saponin 4.30±0.29 a 35.64±1.56 c 14.03±1.21 b 13.67±0.41 b tannin 0.93±0.03 a 0.98±0.12 a 7.20±0.93 b 9.02±0.23 c flavonoid 1.11±0.05 a 10.15±0.28 b 22.81±0.37 c 31.35±2.38 d cardiac glycosides 7.73±0.32 d 1.95±0.06 a 5.15±0.14 b 6.85±0.23 c alkaloid 3.87±0.11 a 5.05±0.06 a 23.20±2.42 b 2.90±0.11 a key jcl: j. curcas leaf extract, jcs: j. curcas stem bark extract. jgl: j.gossypifolia leaf extract, jgs: j. gossypifolia stem bark extract. oyetayo, v.o. and temenu, o.e. 20 figure1. total phenolics of extracts obtained from jatropha species. bar with different superscript are significantly different (p≤0.05) key jcl: j. curcas leaf extract jcs: j. curcas stem bark extract jgl: j.gossypifolia leaf extract jgs: j. gossypifolia stem bark extract there were significant differences between and within groups in the antistaphylococcal activity of the extracts against staphylococci used in this study except for j. curcas leaf extract (jcl) and j. gossypifolia stem bark extract (jgs) where there were no significant differences (p≥0.05) within the two groups (table 2). the antistaphylococcal activity of the combined extracts was higher and significantly different (p≤0.05) than when used singly. the highest antistaphylococcal effect (19.83 mm) was obtained for the combination of the leaf extracts of the two jatropha species (jcl and jgl) against s. aureus isolated from blood. j.curcas stem bark extract (jcs) displayed the least antistaphylococcal effect of 7.00mm against s.aureus isolated from urine. table 2. antistaphylococcal property of the stem bark and leaf extract of jatropha species. source of staph. jgl jcl jgs jcs jcl&jgl jcs&jgs cpx pow skin swab urine blood nose atcc 25923 10.50±1.73 11.00±1.93 12.00±1.43 12.50±0.55 10.93±1.81 14.33±0.58 15.25±0.96 13.13±3.36 11.80±4.66 13.67±1.03 14.62±2.45 12.67±0.58 16.25±2.22 14.00±3.42 11.60±4.72 15.00±2.19 14.65±3.16 12.33±1.53 9.50±4.04 11.50±4.31 7.00±1.00 12.17±2.64 12.46±3.16 7.33±1.53 15.75±2.63 17.75±4.03 15.00±1.22 19.83±2.99 15.04±1.93 17.00±1.00 18.25±0.50 14.00±1.07 14.20±1.10 16.33±1.37 14.92±2.17 13.83±0.76 21.25±2.22 24.25±1.67 32.60±1.14 22.83±1.17 24.23±1.75 27.33±1.16 key pow: post operative wound jcl: j. curcas leaf extract jcs: j. curcas stem bark extract jgl: j.gossypifolia leaf extract jgs: j. gossypifolia stem bark extract cpx: ciprofloxacin the antioxidant capacity of the extracts is revealed in figures 2 and 3. ferric ion chelating activity of the two jatropha species was observed to be concentration dependent. the higher ferric ion chelating effect (72%) was displayed by extract obtained from the stem bark of j. curcas (jcs) while the least (56%) was recorded for extract obtained from j. gossypifolia stem bark extract (jgs) at a concentration of 5 mg/ml. hydroxyl ion scavenging activities of the jatropha species were also concentration dependent. the highest hydroxyl ion scavenging ability (88%) was obtained for j. curcas lea extract (jcl) while the least (55%) was obtained for j. gossypifolia leaf extract (jgl). 0 0.5 1 1.5 2 2.5 jcl jcs jgl jgs t o ta l p h e n o l (m g g a e /g ) ethanolic extracts of jatropha species d c b c comparative study on the phytochemical, antistaphylococcal and antioxidant properties 21 figure 2. ferric ion chelating ability of of the stem bark and leaf extracts of two jatropha species. key jcl: j. curcas leaf extract jcs: j. curcas stem bark extract jgl: j.gossypifolia leaf extract jgs: j. gossypifolia stem bark extract figure 3. hydroxyl ion scavenging of leaf and stem bark extracts of two jatropha species. key jcl: j.curcas leaf extract jcs: j.curcas stem bark extract jgl: j.gossypifolia leaf extract jgs:j.gossypifoliastem bark extract 4. discussion the medicinal properties of plants have been identified since time immemorial and they are now recognized as a source of bioactive compounds which can be exploited for the development of novel biopharmaceutical agents. plants synthesize secondary metabolites, many of which are important in promoting good health in animals and humans [25]. these secondary metabolites such as alkaloids, tannins, anthraquinones, saponin, glycosides and so on are important for the survival of plants in their ecosystem. jatropha species are important medicinal plants that have folkloric applications. in the present report, quantitative phytochemical screening of ethanolic extracts obtained from the leaf and stem bark of two jatropha species, j. curcas and j. gossypifolia, was not similar to the report of atamgba et al. [26] which revealed that the phytochemicals are more present in leaf than in the stem bark. however, in the present report, saponin and flavonoid were higher in j. curcas stem bark (35.64 mg/100 g) and j. gossypifolia stem bark extract (31.35 0 10 20 30 40 50 60 70 80 1 2 3 4 5 f e c h e la ti n g ( % ) concentration of extract (mg/ml) jcl jcs jgl 0 20 40 60 80 100 1 2 3 4 5 h y ro x y l io n s ca v e n g in g ( % ) concentration of extract (mg/ml) jcl jcs jgl jgs oyetayo, v.o. and temenu, o.e. 22 mg/100g) while cardiac glycosides and alkaloids were highest in the leaves of j. curcas (7.73 mg/100 g) and j. gossypifolia (23.20 mg/100 g ) respectively. there was no relative increase in the phytochemical content as one moved from the stem bark to the leaf. secondary metabolites such as alkaloids, tannins, anthraquinones, saponin, and glycosides produced by plants have potent antimicrobial effects [27]. these secondary metabolites are known to exert considerable antimicrobial activity through different mechanisms [28]. specifically, saponins are stored in plant cells as inactive precursors but are readily converted into biologically active antibiotics by enzymes in response to pathogen attacks [29, 30] the total phenol content obtained in the leaf and stem bark of the two jatropha species varies from 0.8 mggae/g to 2.2 mggae/g. othman et al. [31] had earlier reported the total phenol content in leaves and stem of j. curcas plant collected from malaysia as 1.33 mg gae/g and 0.11 mg gae/g respectively. akhtar et al. [32] also reported higher level of total phenol in the leaf of j. curcas than the stem bark as observed in this study. the total phenol content in the leaf (2.2 mggae/g) and stem bark (1.5 mggae/g) of j. curcas were however higher and significantly different from what was obtained in j. gossypifolia leaf and stem bark. j. curcas had been reported to have high content of phenolic compounds [33, 34]. recently, vega-ruizet al. [35] also reported that j. cinerea and j. cordata two species of jatropha collected in mexico are important source of phenolic acids and flavonoids. the ethanolic extracts of the two jatropha species show good antistaphylococcal effects. there was no significant difference in the antistaphylococcal activities exhibited by the leaf and stem extracts of the plant. however, combination of the leaf extracts and stem bark extracts of the two jatropha species exhibited higher and significantly higher antistaphylococcal effect. rampadarath et al. [36] reported inhibition of the growth of s. aureus, s. epidermidis, pseudomonas aeruginosa, escherichia coli, bacillus cereus, b. subtilis and proteus vulgaris by methanolic extract of the leaves of j. curcas. moreover, igbinosa [37] had earlier observed the antibacterial effect of the crude root extracts of j. carcus. in another report, the essential oil obtained from j. gossypifolia was found to exhibit strong antibacterial activity against escherichia coli, enterococcus faecium, and s. aureus [38]. the antibacterial effect observed in this study may lay credence to the ethnomedicinal uses of jatropha species in the treatment of wounds and sore. felger and moser in 1973 [35] reported the use of j. cinerea roots by the seri ethnic group in the state of sonora (mexico) to cure dysentery and the sap to treat mouth ulcers. another species of jatropha, j. cordata root is also used by ethnic groups in the state of sonora, mexico to combat toothache and the stem and leaves are used to cure gum disease [39]. extracts obtained from the leaf and stem bark of j. curcas and j. gossypifolia exhibited concentration-dependent antioxidant activity. sunday et al. [40] had earlier observed that extracts of j.curcas(leaves and stem bark extract) and j. gossypifolia (leaves and stem bark extract) exhibited effective antiradicals’ potencies against the different oxidants, indicating they are good electron donors. in another recent report, extracts of leaves and stems from j. cinerea and j. cordata collected in mexico were found to possess good antioxidant activity [35]. the antioxidant activities of plants had been attributed to the total phenol and other antioxidant compounds such as volatile oils, amino acids, vitamins and others [41]. the total phenol obtained in this study was high enough to elicit appreciable antioxidant activity. it has been reported that a significant correlation between antioxidant activity and total phenolic contents is prove that phenolic compounds is a major contributor to the antioxidant activity of different parts of jatrophas pecies [32]. 5. conclusion the results obtained from this study conclusively indicate that 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https://doi.org/10.1186/1472-6882-10-4 squ journal for science, 2016, 21(1), 64-68 © 2016 sultan qaboos university 64 reduction of linear functional systems using fuhrmann's equivalence mohamed s. boudellioua department of mathematics and statistics, college of science, sultan qaboos university, p.o. box: 36, pc 123, al-khod, muscat, sultanate of oman. *email: boudell@squ.edu.om abstract: functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. the problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by serre. finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help in solving the linear functional system. in this paper, fuhrmann's equivalence is used to present a constructive result on the reduction of under-determined linear functional systems to a single equation involving a single unknown. this equivalence transformation has been studied by a number of authors and has been shown to play an important role in the theory of linear functional systems. keywords: linear functional systems; reduction; fuhrmann's equivalence; quillen-suslin theorem; lin-bose conjecture. (fuhrmann) اختصار األنظمة الذالية الخطية باستخذام تكافؤ فورمان محمذ الصالح بودليوة ة األبعاد. حسخخذو األَظًت انذانٍت فً دساست أَظًت انًعادالث انخفاضهٍت انجضئٍت ٔاألَظًت انخفاضهٍت راث اإلعالاث انضيٍُت ٔكزنك األَظًت يخعذد :الملخص نشٌاضً انفشَسً ٔلذ حًج دساست اخخصاس األَظًت انذانٍت انخطٍت إنى أَظًت ححخٕي عهى عذد ألم يٍ انًعادالث ٔانًجاٍْم ألٔل يشة يٍ طشف انعانى ا . ٔانٓذف األساسً يٍ عًهٍت االخخصاس ْزِ ْٕ حسٍٓم دساست ْزِ األَظًت يٍ حٍث حهٓا أٔ حطبٍك طشق عذدٌت عهٍٓا َسخخذو فً ْزا انبحث (serre)ساس نخمذٌى َخٍجت بُاءة الخخصاس بعض األَظًت انذانٍت انخطٍت َالصت انخعٍٍٍ حٍث أٌ انُظاو انًخخصش ٌحخٕي عهى يعادة ٔاحذة (fuhrmann)حكافؤ فٕسياٌ ًت انذانٍت انخطٍت.راث دانت يجٕٓنت ٔاحذة. ْزا انخكافؤ حى دساسخّ يٍ طشف عذد يٍ انباحثٍٍ ٔحبٍٍ يٍ رنك أٌ ْزا انخكافؤ ٌهعب دٔسا يًٓا فً َظشٌت األَظ بٕص.-َظشٌت نٍٍٔ سٕسهٍ-حكافؤ فٕسياٌ، َظشٌت كٌٕهٍ ،خخصاسانخطٍت انذانٍت، اال تاألَظً: الكلمات المفتاحية 1. introduction olynomial matrices play an important role in the theory of linear systems described by ordinary differential equations (see for example rosembrock [1] and kailath [2]). in this case, the polynomial matrices involve a single indeterminate with coefficients in the field of real or complex numbers. the study of linear systems of ordinary differential equations is thus reduced to the study of matrices over the ring [ ]s or [ ]s . these rings have the euclidean division property which makes it possible to establish canonical forms such as the smith normal form. in fact, the polynomial theory of such systems can be regarded as more or less complete. in the case of linear functional systems, arising for example from partial differential equations or delay-differential equations, the resulting system matrices involve polynomials in more than one indeterminate. since multivariate polynomial rings do not have the euclidean division property, it is no longer possible to extend most of the results obtained for the single indeterminate case. throughout this paper unless specified otherwise, [ ] denotes the polynomial ring in the indeterminates with coefficients in an arbitrary but fixed field k. first we present a few definitions that will be needed later in the paper. p reduction of linear functional systems 65 definition 1.1 given a matrix q p t d   , the i th order invariant polynomial i  of t is defined by : 1 ; 1 = 0; min( , ) i ii i r r i p q            (1) where r is the normal rank of t , 0 = 1 and i  is the greatest common divisor of all the i i minors of .t as in the single variable case, the zero structure of a multivariate polynomial matrix is a crucial indicator of its properties. however, unlike the single variable case, the zero structure of a multivariate polynomial matrix is not completely captured by the invariant polynomials but by the invariant zeros as defined by the following. definition 1.2 [3, 4, 5] let 1 = [ , , ] n d x x , q p r d   , ( > )p q be a full row rank matrix and i the ideal generated by the i i minors of r and ( ) i v the algebraic variety defined by: ( ) = { | ( ) = 0, }. n i v p p    the i th order invariant zeros of r are the elements of the variety ( ) i v . definition 1.3 let 1 = [ , , ] n d k x x . the general linear group ( )pgl d is defined by:  ( ) = | : = =p p p pp pgl d m d n d mn nm i      an element ( ) p m gl d is called a unimodular matrix. it follows that m is unimodular if and only if the determinant of m is invertible in d , i.e., is a non-zero element of .k definition 1.4 two polynomial matrices 1 t and 1 s of appropriate dimensions, are said to be zero-left-coprime ( zlc ) if the matrix  1 1t s admits a right-inverse in d . similarly, 2t and 2s , of appropriate dimensions, are said to be zero-right-coprime ( zrc ) if the matrix  2 2 t t t t s has left-inverse in d . one of standard tasks carried out in systems theory is to transform a given system representation into a simpler form. an equivalence transformation used in the context of multidimensional systems is fuhrmann's equivalence [6] and is defined by the following. definition 1.5 (fuhrmann's equivalence) let ( , )t m n denote the class of ( ) ( )r m r n   matrices with elements in d where ,m n are fixed positive integers and > min( , )r m n . 1 t and 2 t are said to be fuhrmann-equivalent (f-e) if there exist matrices 1 s , 2 s of appropriate dimensions with elements in d such that 2 1 2 1 =s t t s (2) where 1 1 ,t s are zlc and 2 2 ,t s are zrc. in the case when 1 t and 2 t have the same size and 1 s and 2 s are square, the transformation in (2) reduces to the classical unimodular equivalence. f-e has been studied by a number of authors. for instance, pugh et al. [7, 8] have shown that it exhibits fundamental algebraic properties amongst its invariants. in particular, they have shown that it preserves the invariant polynomials as well as the the invariant ideals. lemma 1.1 [7] suppose that two matrices 1 t and 2 ( , )t m n are related by f-e and let [ ] [ ] [ ] 1 1 1 1 2 , , , t t t h    where [ ] [ ] 1 1= min( , ), t t h r m r n  denote the invariant polynomials of 1 t and [ ] [ ] [ ] 2 2 2 1 2 , , , , t t t k    where [ ] [ ] 2 2= min( , ), t t k r m r n  denote the invariant polynomials of 2 t , then [ ] [ ] 1 2= for = 0,1, , max( 1, 1) t t h i i k i c i k h       (3) where [ ] [ ] 1 2= 1, = 1 for any < 1, \ {0}. t t j j i j c   lemma 1.2 [8] suppose that two matrices 1 t and 2 t ( , )m n are related by f-e and let [ ] 1 t j for [ ] [ ] 1 1= 1, , = min( , ) t t j h r m r n  denote the ideal generated by the j j minors of 1 t and [ ] 2 t i , for [ ] [ ] 2 2= 1, , = min( , ) t t i k r m r n  denote the ideal generated by the i i minors of 2 t . then [ ] [ ] 1 2= , = 0, , t t h i k i i h   (4) mohamed s. boudellioua 66 where = min( 1, 1)h h k  and for any >i h , [ ] [ ] 1 2= 1 or = 1 in case < or < . t t h i k i i h i k       the problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by serre [9]. such a process is based on the application of the well known quillen-suslin theorem. theorem 1.1 [10, 11] let k be a principal ideal domain and  1= , , nd k x x and let q p r d   be a matrix which admits a right-inverse p q r d   , i.e., = qrr i . then there exists a unimodular matrix ( )pn gl d such that  = 0 .qrn i (5) 2. reduction using fuhrmann's equivalence the reduction of a multivariate polynomial matrix in the context of multidimensional systems theory was first studied by frost and boudellioua [12]. they obtained necessary and sufficient conditions under which a square multivariate polynomial matrix is unimodular equivalent to a simpler form. this corresponds to the reduction of a determined linear functional system into a single equation in one unknown function. boudellioua and quadrat [13] generalized this result to underdetermined systems using a module theoretic approach. their result gives necessary and sufficient conditions for the reduction of a linear system to a system containing a single equation with several unknown functions. boudellioua [14] generalized the earlier result to under-determined systems thereby giving necessary and sufficient conditions for the unimodular equivalence of an under-determined linear system to one containing a single equation involving only one unknown function. the results mentioned so far are based mainly on unimodular equivalence. this transformation has the disadvantage of establishing a connection between matrices and hence systems which have the same size. boudellioua [15] used fuhrmann's equivalence to reduce a class of determined linear functional systems to a system containing a single equation in one unknown. in this paper, we extend this latter result to the under-determined case. before presenting the main result of this paper, we first state the following result which is a statement of the positive answer of the lin-bose conjecture [16]. this theorem which will be used later is given by fabianska and quadrat [17]. theorem 2.1 [section 5 of [17] ] let =d 1 [ , , ] n k x x be a commutative polynomial ring over a field k and q p r d   a full row rank matrix. then the following two assertions are equivalent: 1. the ideal ( ) q i r generated by the q q minors of r is principal, i.e. can be generated by the greatest common divisor  of these minors. 2. there exist , ' q p '' q q r d r d     , and ( )pn gl d such that:  = , det( ) = , = 0 .'' ' '' ' qr r r r r n i (6) theorem 2.2 let 1 = [ , , ] n d k z z and q p t d   , >p q with full row rank, then t is fuhrmannequivalent to the row vector 1 ( 1)p q t d     :  = 0 .t  (7) where d is the gcd of the q q minors of t , if and only if there exist a vector qu d which admits a left inverse in d such that the matrix  t u has a right inverse over d and the ideal generated by the q q minors of t is principal. proof. let q p t d   and suppose that there exist a vector q u d satisfying the given condition. then by the quillen-suslin theorem there will exist a square ( 1) ( 1)p p   matrix 1( )pk gl d such that    1 1 = 0 q k m n t u i x t       (8) where 1 ( 1) 1 p q t d     . it follows from (8) that: 1 1 =tn ut (9) reduction of linear functional systems 67 where ,t u are, by assumption, zlc and 1 1 ,t n are zrc (since 1( )pk gl d ). by virtue of lemma 1.1 and lemma 1.2, fuhrmann's equivalence preserves the determinantal ideals and the invariant polynomials of the matrices. hence the ideal generated by the elements of 1 t is also principal and generated by the single polynomial  . hence by virtue of the lin-bose theorem 2.1, there exists a matrix 2 1 ( ) p q n gl d    such that  1 2 = 0 .t n t   (10) from which 1 2 =tn n ut (11) where again ,t u are by assumption zlc and 1 2,t n n are zrc, since 11 2 2 1 = . nn n n tt           (12) now suppose that q p t d   is f-e with 1 ( 1)p q t d     , then there exist matrices 1 p n d   and ( 1)p q p q d     such that =nt tq , where ,n t are zlc and ,t q are zrc. by the quillen-suslin theorem, there exist zrc matrices q u d and ( 1) 1p q y d     such that 1 ( ) p t u gl d q y         (13) where the matrices t and u must be zlc. it is worth mentioning at this stage that finding a vector ,u d when it exists, such that the condition in theorem 2.2 is satisfied is not a straight forward task. on simple examples over a commutative polynomial ring 1 = [ , , ] n d k x x with coefficients in a computable field k (e.g., =k ), one may take a generic vector q u d with a fixed total degree in the i x 's and compute the d -module  1 1 ( 1)/ ( )q p td d t u   by means of a gröbner basis computation and check whether or not this d -module vanishes on certain branches of the corresponding tree of integrability conditions (see pommaret and quadrat [18]) or on certain obstructions to genericity ( see levandoskyy and zerz [19]). 3. conclusion we have presented a constructive result for the simplification of a class of linear functional systems. more specifically, we have given necessary and sufficient conditions under which a rectangular multivariate polynomial matrix can be reduced by fuhrmann's equivalence to a form that corresponds to the reduction of a linear functional system to a single equation with only one unknown function. the result can be easily implemented on a computer algebra system such as maple using the oremodules package (see chyzak et al. [20]). 4. acknowledgment the author wishes to express his thanks to sultan qaboos university (oman) for supporting this research (grant no. ig/sci/doms/15/01). references 1. rosenbrock, h.h. state space and multivariable theory, 1970, nelson-wiley, london, new york. 2. kailath, t. linear systems, 1980, prentice-hall. 3. youla, d.c. and gnavi, g. notes on n -dimensional system theory. ieee trans. circuits and systems, 1979, 26(2), 105–111. 4. youla, d.c. and pickel, p.f. the quillen-suslin theorem and the structure of n-dimensional elementary polynomial matrices. ieee trans. circuits and systems, 1984, 31, 513–517. 5. zerz, e. topics in multidimensional linear systems theory, 2000, springer, london. 6. fuhrmann, p.a. on strict system equivalence and similarity. int. j. control, 1977, 25(1), 5-10. 7. pugh, a.c., mcinerney, s.j., hou, m. and hayton, g.e. 1996. a transformation for 2-d systems and its invariants. in proceedings of the 35th ieee conference on decision and control, pages 2157–2158, kobe (japan). 8. pugh, a.c., mcinerney, s.j. and el-nabrawy, e.m.o. zero structures of n -d systems. int. j. control, 2005,78(4), 277–285. 9. serre, j.p. sur les modules projectifs. séminaire dubreil-pisot, 1960/61, 2, 23-34, in jean-pierre serre, oeuvres, mohamed s. boudellioua 68 collected papers, 1960-1971, 2, 23-34. 10. quillen, d. projective modules over polynomial rings. invent. math., 1976, 36, 167-171. 11. suslin, a.a. projective modules over polynomial rings are free. soviet math dokl., 1976, 17(4), 1160–1164. 12. frost, m.g. and boudellioua, m.s. some further results concerning matrices with elements in a polynomial ring. int. j. control, 1986, 43(5), 1543-1555. 13. boudellioua, m.s. and quadrat, a. serre's reduction of linear functional systems. mathematics in computer science, 2010, 4(2), 289–312. 14. boudellioua, m.s., further results on the equivalence to smith form of multivariate polynomial matrices. control and cybernetics, 2013, 42(2), 543–551. 15. boudellioua, m.s., on the simplification of systems of linear multidimensional equations. in the sage days 24 workshop on symbolic computation in differential algebra and special functions, 2010, hagenberg (austria). 16. lin, z. and bose, n.k., a generalization of serre's conjecture and related issues. linear algebra and its applications, 2001, 338, 125–138. 17. fabianska, a. and quadrat, a. applications of the quillen-suslin theorem in multidimensional systems theory. in h. park and g. regensburger, editors, gröbner bases in control theory and signal processing, radon series on computation and applied mathematics 3, 2007, pages 23–106. de gruyter publisher. 18. pommaret, j.f. and quadrat, a. formal elimination for multidimensional systems and applications to control theory. mathematics of control, signal and systems, 2000, 13, 193–215. 19. levandovskyy, v. and zerz, e. obstructions to genericity in the study of parametric problems in control theory. in h. park and g. regensburger, editors, gröbner bases in control theory and signal processing, radon series on computation and applied mathematics 3, 2007, pages 127–149. de gruyter publisher. 20. chyzak, f., quadrat, a. and robertz, d. oremodules: a symbolic package for the study of multidimensional linear systems. in j. chiasson and j.j. loiseau, editors, applications of time-delay systems, lncis 352, 2007, pages 233–264. springer, http://wwwb.math.rwth-aachen.de/oremodules/. received 7 april 2015 accepted 13 september 2015 squ journal for science, 2015, 20(2), 78-87 ©2015 sultan qaboos university 78 rolling optimization method for humanoid robots riadh zaier department of mechanical and industrial engineering, college of engineering, sultan qaboos university, p.o. box: 33, al khod, pc 123, muscat, oman. email: zaier@squ.edu.om. abstract: in this paper, a method of optimizing the rolling amplitude needed for a stable and smooth walking movement of a humanoid robot is considered. the optimization algorithm was based on minimizing a cost function defined by the rolling overshoot. the amplitude of the rolling during locomotion was calculated using the lateral zero moment point (zmp) position. the initial value of the rolling was the static rolling that corresponds to the position of the zmp at the center of the support polygon. the algorithm consisted of performing a zmp calculation at two points that correspond to single support phases. simplifying the robot as an inverted pendulum, the gyro feedback controller parameters were tuned to have a passive-like walking motion and a faster response of the robot state to the equilibrium point at single support phase. experimental results, using hoap-3 of fujitsu, showed that the algorithm was successfully implemented along with the locomotion controller. with the optimal rolling technique, the humanoid robot could exhibit a stable and smooth walking movement. keywords: humanoid robot; locomotion control; rhythmic motion; rolling optimization; zero moment point (zmp). نسان اآللي لإلمثلى التفاف طريقة رياض الزاير نٍ، انزوبىث. وتستُذ ِا نإلَساٌَطىر فٍ هذِ انىرقت دور طزَقت يثهً عٍ طزَق ضبظ انقًُت انالسيت نهحصىل عهً حزكت يشٍ يستقزة وسهست ملخص: ٌ لالل انحزكت ًُالهذا انَجاد انقًُت انصغزي نذانت انكهفت انتٍ َحذدها انتجاوس فٍ يُالٌ انجسى انفىقٍ نهزوبىث. َتى احتساب قًُت إهذِ انطزَقت عهً ض. تعتًذ هذِ انطزَقت عهً عًهُت زفٍ يزكش انًضهع انًفت zmpانجاَبٍ، حُث أٌ انقًُت األونُت نهًُالٌ ثابتت وتتىافق يع يىقع zmpباستخذاو يىقع ضبظ انًعطُاث انتٍ تتحكى فٍ فٍ َقطتٍُ تتىافق يع يزاحم دعى واحذة. كًا تى تبسُظ انزوبىث بانبُذول انًقهىب وانذٌ َساعذ بذورِ عهً zmpحساب َساٌ وعهً استجابت أسزع فٍ تحىَم حزكت انزوبىث إنً َقطت انتىاسٌ عهً رجم واحذة.إلحزكت انذوراٌ انجاَبٍ وانحصىل عهً حزكت شبُهت بحزكت ا تقُُت نذا فإٌاح يع وحذة تحكى انحزكت. َشاء انخىارسيُت قذ تى بُجإنشزكت فىجُتسى، أٌ hoap-3نٍ َِساٌ اإلأظهزث انُتائج انتجزَبُت، باستخذاو ا ًكٍ اإلَساٌ اِنٍ يٍ انًشٍ بحزكت يستقزة وسهست شبُهت بحزكت اإلَساٌ.تانذور األيثم (zmp). انحزكت اإلَقاعُت، اإلَساٌ اِنٍ، انًُالٌ األيثم، انتحكى فٍ انحزكت، َقطت انصفز نعشو انذوراٌ :كلمات مفتاحية 1. introduction n recent years, a humanoid robot, particularly the biped robot has been drawing attention of many researchers. the majority of researches regarding the biped robot simplifies it as an inverted pendulum [1] and uses zero moment point (zmp) [2-6], and controls the zmp to keep it inside the supporting polygon. in this approach, a humanoid robot and the surrounding environment of the robot are accurately modeled and differential equations are solved. however, the modeling becomes difficult if there is an unknown element such as gear backlash, belt tension changes etc. moreover, since solving differential equations consumes time, it is difficult to perform real-time control. more recently, biologically inspired control strategies have been proposed to generate autonomously adaptable rhythmic movement. these are based on a neural network, termed as central pattern generator (cpg) [7-16] that is capable of generating a rhythmic pattern of motor activity in the absence of sensory input signals. taga [8, 9] has demonstrated that bipedal locomotion can be realized as a global limit cycle generated through entrainment between the neural network consisting of a neural oscillator, and the physical system. these approaches aim to efficiently control the robot so as to allow the humanoid robot to perform various motions with stability, while eliminating the need for modeling a humanoid robot or the surrounding environment. however, these control approaches suffer a lack of stability robustness since no sensory feedback has been used other than that used for the cpg entrainment. in other words, any small disturbance acting on the humanoid robot during locomotion may risk its falling. to face these problems, the i rolling optimization method for humanoid robots 79 robot walking control includes feedback control based on the rotation angle or gyro sensor placed on the upper side of the robot. to find the proper parameters of the gyro feedback loop, details of the robot model should be provided as mentioned in [1, 2]. some trial in dealing with the locomotion controller using piecewise linear oscillator has been proposed [17-19]. however, the rolling has been not optimized and therefore a rolling overshoot during locomotion can be observed. in this paper, therefore, the proposed approach consists of reducing the control input by tuning the amplitude of the rolling during locomotion. indeed, by reducing the fluctuation or overshooting of the zmp attributed to the feedback control, it becomes possible to improve the walking performance of a robot. the impact of reducing the feedback control to its minimum can be seen in the improvement of robot walking performance. moreover, if the feedback control frequently causes fluctuation or overshooting of the zmp, the motors used in the walking control get exhausted. thus, reducing the feedback control as much as possible is also a key to the reduction of motor fatigue. the rest of this paper is organized as follows. section 2 describes the locomotion controller, section 3 presents the method of adjusting the rolling amplitude, section 4 describes the optimization algorithm, section 5 presents the experimental results, and section 6 is the conclusion. 2. locomotion controller the structure of the humanoid robot considered in this paper is made by fujitsu laboratories ltd. [20,21], there being 6 actuated joints at each leg, and one at the torso, as is shown in figure 1. the gyro sensor is placed at the upper side of the robot and 4 force sensors are placed under the sole plate of each leg. figure 2 shows the implementation of the gyro sensor in a feedback loop that controls the hip and ankle joints. . figure 1. humanoid robot structure. figure 2. sensor implementation and control. right yaw hip right roll hip right pitch hip right pitch knee right pitch ankle right roll ankle right leg left leg force sensor force sensor sole plate body gyro sensor pitch waist joint left yaw hip joint left roll hip joint left pitch hip joint left pitch knee joint left pitch ankle joint left roll ankle joint y 1 1 mass gyro/x k b b k )(t l fb  )(t r fb  riadh zaier 80 the controller is of a proportional derivative (pd) type, which may be classed as a damper spring system. on the other hand, to ensure a smooth landing of each leg with a flat foot on a flat ground, the swing leg should touch the ground softly. to satisfy this condition instead of using an impact model, we simply use two pds controllers that work as spring and damper, and get inputs from the force sensors located under each leg. the outputs of these pds are fed to the hip, knee, and ankle joints of the landing leg. for this, consider the mass spring damper model that can be expressed by the following: yss fyk dt dy b dt yd m  2 2 (1) where bs is the coefficient of friction, ks is the coefficient of spring, y is the displacement of the mass m along the vertical axis, and fy is the external force acting on the supporting leg. to satisfy the constraint of parallel landing of the sole plate on the flat ground, and under the assumption that the thigh and shank of the robot have the same length, and with respect to the angles definition in [20], this condition can be satisfied as follows:           )()()( )(2)( )()()( ttt tt ttt sl p hm lkm sl p am    , (2) where p am , km , and p hm  are the pitching motor commands to the ankle, the knee and the hip, respectively. the overall control structure is depicted in figure 3. figure 3. overall control system of the robot locomotion. the optimization algorithm is implemented in the central control unit, which takes input from the gyro sensor and force sensor control unit as well as commands from upper level control via the communication interface unit. a detailed diagram of the central control unit, in which there is a motion generating unit and rolling amplitude adjustment unit, is illustrated in figure 4. the latter unit calculates the optimized rolling value and adapts the motion generator accordingly. central control unit gyro sensor gyro sensor control unit joint control unit joint joint control unit joint force sensor control unit force sensor force sensor control unit force sensor communication interface memory rolling optimization method for humanoid robots 81 figure 4. central control unit structure. lifting landing rolling double support phase m single support phases c1 c2 c3 switching switching switching mass m g figure 5. state flow of stepping motion with compliance controller ci and gyro feedback g. figure 5 shows the state flow of the stepping motion, which consists of three sequential phases; rolling, lifting, and landing. the locomotion pattern is designed based on the rolling motion pattern: the robot starts rolling toward one of its legs, then lifts the other leg and moves it forward to make the stride. once the swing leg lands on the ground the robot rolls towards the other leg and repeats the same sequence. it is assumed that the landing of each leg is accomplished with a flat foot on flat ground. at the end of the single support, the swing leg should touch the ground softly. to satisfy this condition, instead of using an impact model, two oscillators that work as dampers and get inputs from the force sensors located under each leg are used. the outputs of these oscillators are fed to the hip, knee, and ankle joints of the landing leg. the compliance controllers ci and the gyro feedback g stabilizing the movement are designed for each phase of the walking. both feedback controllers and motion phases are switched simultaneously, such that the overall stability of the robot is maintained. 3. method of adjusting the rolling amplitude figure 6 explains how the rolling amplitudes are adjusted. at the time of shifting from the lifting motion to the landing motion; the rolling to left and right becomes the maximum, that is, the rolling amplitudes are al and a2. the rolling amplitude adjusting (raa) unit tunes the rolling amplitudes a1 and a2 so that the gyro feedback control at those points of time when the rolling to left and right reaches its maximum is reduced as much as possible. rolling amplitude adjusting unit central control unit force sensor data compliance control unit correcting unit feedback control unit gyro sensor data central control unit riadh zaier 82 figure 6. method of adjusting rolling amplitude by a gyro sensor feedback. figure 7 illustrates a relationship between a sideways moving amount xzmp and a sideways moving velocity vzmp of the zmp. figure 7-a represents a case when the rolling amplitudes are not adjusted and figure 7-b represents a case when the rolling amplitudes are adjusted to optimum values. when the rolling amplitudes are not adjusted, fluctuation or overshoot occurs in xzmp due to the gyro feedback control performed at the point of time of xzmp = a1 or xzmp = a2. in comparison, as illustrated in fig.7-b; because of the optimum adjustment of the rolling amplitudes, the need to perform gyro feedback control at the point of time of xzmp = a1 or xzmp = a2 is eliminated. (a) (b) figure 7. phase portrait of the zmp; (a) with rolling overshoot, (b) without rolling overshoot. more particularly, the raa unit calculates the value of a cost function j that represents the amount of gyro feedback control for the rolling motion of each single cycle and then adjusts the rolling amplitudes so that the value of the cost function j becomes the minimum. the cost function j is defined as follows: 1 2 zmp av (x x ) , t t j dt  (3) where xav represents the average value of xzmp, tl represents the point of time at which the maximum rolling occurs, and t2 represents the point of time at which the rolling starts to decrease. moreover, t1 and t2 can be determined according to the cycle of the rolling motion. figure 8 is a graph for explaining the fluctuation of the rolling during locomotion and figure 9 illustrates the cost function j and explains its minimization procedure, where α represents an adjustment amount calculated for each cycle by the raa unit. the adjustment amount α is defined as below. max max ( ) , v roll v   (4) rolling optimization method for humanoid robots 83 figure 8. fluctuation of the rolling motion during locomotion. figure 9. cost function versus rolling amplitude. where vmax represents the maximum value of the sideways moving velocity of the zmp, v(rollmax) represents the sideways moving velocity of the zmp at that point of time at which the maximum rolling occurs (roll max), and β represents an experimentally obtained constant number having the default value of 1. in this way, the raa unit calculates the cost function j and the adjustment amount α for the rolling motion of each single cycle, and then adjusts the rolling amplitudes so that the value of the cost function j is minimized. this enables achieving a reduction in the gyro feedback control at the points of time when the rolling to left and right is at its maximum. the correcting unit in figure 4 is a processing unit that corrects, by using the output of the compliance control unit and the feedback control unit, the start time of the rolling angle. 4. optimization algorithm figure 10 represents a flowchart for explaining a sequence of operations of the rolling amplitude adjustment process performed by the raa unit. this adjusting unit calculates the sideways moving amount xzmp using the force sensor data (step s1) and calculates the value of the cost function j (step s2). then, the raa unit calculates the sideways moving velocity vzmp (step s3) and calculates the adjustment amount at step s4. subsequently, the raa unit determines whether the calculated value of the cost function j is smaller than a value jo of the cost function that was calculated for the cycle of the previous rolling motion (step s5). if the value of the cost function j is not smaller than the value jo, then the raa unit inverts the sign of α (step s6). meanwhile, the initial value of jo is the value of the cost function j calculated for the first cycle. then, the raa unit corrects the rolling amplitudes a1 and a2 by subtracting from it the adjustment amount α (step s7) and notifies the corrected rolling amplitudes a1 and a2 to the motion generating unit (step s8). upon receiving the corrected rolling amplitudes a1 and a2, the motion generating unit reflects the corrected rolling amplitudes a1 and a2 in the control information generated for the subsequent cycle. subsequently, the raa unit determines whether the robot has come to a halt (step s9). if the robot has not come to a halt, then the raa unit sets the value of the cost function j calculated for the current cycle as the value jo (step s10) and returns to step s1 to perform the rolling amplitude adjustment for the subsequent cycle. on the other hand, if the robot has come to a halt, then the process is terminated. in this way, since the raa unit performs the rolling amplitude adjustment for each cycle of rolling motion, it becomes possible to reduce the gyro feedback control. as described riadh zaier 84 above, in the present embodiment, the motion generating unit generates the control information with respect to a walking motion having no movement in the front-back direction; the compliance control unit performs the compliance figure 10. algorithm of adjusting rolling amplitude. front zmp f1 f2 f3 f4 x y l x2 x1 y1 y2 d l figure 11. sole reaction forces on the foot and zmp. control based on the force sensor data; and the feedback control unit performs the zmp feedback control based on the force sensor data and performs the gyro feedback control, based on the gyro sensor data, at the points of time when the rolling to left and right becomes the maximum. then, the raa unit calculates the value of the cost function j and the adjustment amount α for each cycle of rolling motion, and adjusts the rolling amplitudes so that the value of the cost function j becomes smaller. the motion generating unit reflects the changes of the rolling amplitudes in the control information for the subsequent motion cycle. such a configuration enables achieving reduction in the gyro feedback control and achieving improvement in the robot’s walking while reducing the motor exhaustion. according to an embodiment, motors are switched less often in a gyro feedback control. 5. experiment instead of writing equilibrium equations of forces and moments acting on the robot body, the analysis simply utilizes the sole reaction forces measured by sole sensors as shown in figure. 11. the idea is based on the evaluation of the shift in the zmp position, using foot force sensor data. let d(xm,ym) be the zmp. at any arbitrary point m(xi,yi) inside the supporting polygon, the reaction torque t(tx ty) for one foot can be written as follows. ))(())(( 212431 ffyyffyyt iix  , (5) rolling optimization method for humanoid robots 85 1 4 2 2 1 3 ( )( ) ( )( ), y i i t x x f f x x f f      (6) application program interface user application motion pattern generator usb thread sm 2 high speed fifos slow speed fifo linux sm 1 kernel windows /linux socket figure 12. structure of the motion control system. where all forces are defined in figure. 11. if we consider the supporting polygon for the two feet, then we have      4 1 3142242311 )(/)()( i l i r i llrrllrr m ffffffxffffxx (7)      4 1 2121243431 )(/)()( i l i r i llrrllrr m ffffffyffffyy (8) where r if represents the sole reaction force applied on the right foot and l if represents the sole reaction force applied on the left foot, and i varies from 1 to 4. therefore, the zmp is calculated during normal condition (no large perturbation is present). the data has to be recorded at each single support phase. a perturbation is considered large when the deviation in the angular velocity exceeds a threshold that is defined experimentally, using gyro sensor data. on the other hand, four postures are defined (learned in advance) to which the robot will shift its pose, when it stops walking. these postures consist of moving the leg to front, back, right, or left, according to the zmp position. then, a feedback controller will be activated at the final posture controlling the waist joint and the legs of the robot. the experiment is conducted using the humanoid robot hoap-3 of fujitsu [20], which has 28 degrees of freedom and is 60 cm tall and weighs 8.8kg. the real-time control algorithms are implemented in real-time threads running in the rtlinux kernel space, as shown in figure 12. kernel mode shared memory (sm) is constructed for the communication between real-time threads. the control period is 1 ms, and the interface between the motion pattern generator and the robot uses a real-time usb driver thread. xm ym z m p p o si ti o n ( c m ) 10 8 2 6 4 0 4 .0 5.0 6.0 time (s) figure 13. plot of the zmp during normal walking. figure 13 shows the zmp location during walking of hoap-3 in the absence of disturbance, which is calculated using (7) and (8). figure 14 plots the hip rolling joint output and sole reaction force acting on the left leg. it shows how the robot starts lifting using the virtual spring energy. moreover, here it can be seen that, when the robot is lifting, the rolling angle is almost zero. it is also zero at the landing time. the robot, when landing, relies on gravity only. riadh zaier 86 0 1 2 3 4 50 0 -50 100 0 20 40 standing phase time (s) 60 hip rolling motion lifting landing l e ft l e g v e rt ic a l so le r e a c ti o n f o rc e ( n ) a n g u la r p o si ti o n ( d e g ) figure 14. plot of the zmp during normal walking. a n g u la r v e lo c it y ( d e g /s ) time (s) (a) a n g u la r v el o ci ty ( d eg / s) time (s) (b) figure 15. gyro sensor outputs: (a) without rolling tuning, (b) when using the optimization algorithm. there are no constraints on the zmp to be satisfied. figure 15 shows the gyro sensor output, which represents the oscillation speed of the upper body of the humanoid robot. the upper graph (a) shows the case before using the proposed optimization algorithm, while the lower graph (b) shows the case when using the algorithm. in contrast to the result proposed in [17-19], where the locomotion controller was designed using a piecewise linear oscillator, the attenuation of the oscillation of the upper body was not discussed and therefore a rolling overshoot during locomotion has been observed. 6. conclusion the rolling amplitude needed for a stable locomotion of a humanoid robot was obtained by minimizing its rolling overshoot. the amplitude of the rolling during locomotion was calculated using the lateral zmp position. the optimization algorithm consisted of performing a zmp calculation at two points that correspond to single support phases, and when the rolling is at its maximum value. as a result, the robot could roll and walk with the minimum gyro rolling optimization method for humanoid robots 87 feedback control. experimental results, using hoap-3 of fujitsu, showed that the algorithm was successfully implemented along with the locomotion controller. the robot had a passive-like walking motion. 7. acknowledgements the experimental work was conducted at fujitsu laboratories limited, japan. references 1. kajita, s., kanehiro, f., kaneko, k., yokoi, k. and hirukawa, h. the 3d linear inverted pendulum mode: a simple modeling for a biped walking pattern generation. proc. of the ieee/rsj international conference on intelligent robots and systems, october 29 november 3, 2001 maui, usa. 2. huang, q., yokoi, k., kajita, s., kaneko, k., arai, h., koyachi, n. and tanie, k. planning walking patterns for a biped robot, ieee trans. on robotics and automation, 2001, 17(3), 280-289. 3. vukobratović, m. and borovac, b. zero moment point thirty five years of its life, j. humanoid robotics, 2004, 1(1), 161-162. 4. kajita, s., matsumoto, o. and saigo, m. real-time 3d walking pattern generation for a biped robot with telescopic legs, proc. of the 2001 ieee international conference on robotics and automation, may 21-26, 2001, seoul, korea. 5. kajita, s., kanehiro, f., kaneko, k., fujiwara, k., yokoi, k. and hirukawa, h. a real-time pattern generator for biped walking, proc. of the 2002 ieee international conference on robotics and automation, may 11-15, 2002, washington, dc, usa. 6. kagami, s., nishiwaki, k., kitagawa, t., sugihiara, t., inaba, m. and inoue, h. a fast generation method of a dynamically stable humanoid robot trajectory with enhanced zmp constraint, proc. of ieee international conference on humanoid robotics, september 7-8, 2000, cambridge, usa. 7. grillner, s. neurobiological bases of rhythmic motor acts in vertebrates, j. science, 1985, 228, 143-149. 8. taga, g. a model of the neuro-musculo-skeletal system for human locomotion, i. emergence of basic gait, j. boil. cybern, 1995, 73, 97-111. 9. taga, g., yamaguchi, y. and shimizu, h. self-organized control of bipedal locomotion by neural oscillators in unpredictable environment, j. biological cybernetics, 1991, 65, 147-159. 10. ijspeert, a.j. central pattern generators for locomotion control in animals and robots: a review neurobiology of cpgs, j. neural networks, 2008, 21, 642-653. 11. li, c., lowe, r., duran, b. and ziemke, t. humanoids that crawl: comparing gait performance of icub and nao using cpg architecture, proc. of the 2011 ieee international conference on computer science and automation engineering, 10-12 jun, 2011, shanghai, china. 12. li, c., lowe, r., duran, b. and ziemke, t. modelling walking behaviors based on cpgs: a simplified bioinspired architecture from animals to animates, lecture notes in computer science, 2012, 7426, 156-166. 13. li, c., lowe, r., duran, b. and ziemke, t. humanoids learning to walk: a natural cpg-actor-critic architecture, j. frontiers in neurorobotics, 2013, published online. 14. matsuo, t., sonoda, t. and ishii, k. a design method of cpg network using energy efficiency to control a snake like robot, proc. of the fifth ieee international conference on emerging trends in engineering and technology, november 5-7, 2012, himeji, japan. 15. nakamura, y., mori, t., sato, m. and ishii, s. reinforcement learning for a biped robot based on a cpg-actorcritic method, j. neural networks, 2007, 20(6), 723–35. 16. tomoyuki, t., azuma, y. and shibata, t. acquisition of energy-efficient bipedal walking using cpg-based reinforcement learning, proc. of the ieee/rsj international conference on intelligent robots and systems, october 11-15, 2009, st. louis, mo, usa. 17. zaier, r. and nagashima, f. motion pattern generator and reflex system for humanoid robots, proc. of ieee/rsj international conference on intelligent robots and systems, october 9-15, 2006, beijing, china. 18. zaier, r. and kanda, s. piecewise-linear pattern generator and reflex system for humanoid robots, proc. of the 2007 ieee international conference on robotics and automation. april 10-14, 2007, rome, italy. 19. zaier, r. and kanda, s. new approach of neural network for controlling locomotion and reflex of humanoid robot, in humanoid robots, intech international publishers, book edited by ben choi, isbn 978-953-761944-2, 2009, 365-388. 20. murase, y., yasukawa, y., sakai, k. and ueki, m. design of compact humanoid robot as a platform, proc. of the 19th annual conference of the robotics society of japan. september 18-20, 2001, tokyo, japan. 21. hoap-3, fujitsu automation ltd, http://home.comcast.net/~jtechsc/hoap-3_spec_sheet.pdf. received 1 july 2014 accepted 15 september 2014 squ journal for science, 2022, 27(2),84-89 doi:10.53539/squjs.vol27iss2pp84-89 sultan qaboos university 84 prevalence of gastrointestinal helminthes in pigs reared in research farms of michael okpara university of agriculture, umudike, south eastern nigeria ebube charles amaechi 1 *, miracle innocent dike 2 , onyinye mkpola ukpai, blessing uzoamaka ejike 3 . 1 department of zoology, university of ilorin, ilorin, nigeria; 2 department of zoology and environmental biology, michael okpara university of agriculture, umudike, nigeria; 3 department of biology/microbiology, abia state polytechnic, aba, abia state; *email: ebubeamechi@yahoo.com. abstract: gastrointestinal parasitism in swine production is a world-wide problem especially in tropical resourcepoor countries. these infections in animals result in significant economic losses. this study aimed to assess the prevalence and spectrum of gastrointestinal parasites of pigs reared in two research farms in michael okpara university of agriculture, umudike, south eastern nigeria. from april, 2016 to july, 2016, 220 samples of pig faeces from two research farms (casap research farm and mouau commercial pig farm) were analyzed using floatation and direct smear methods to identify varied parasitic stages present in the faeces. data generated showed an overall prevalence of 64.6% (142/220) in the two farms. five parasite species made up of four nematode and one cestode were observed namely ascaris suum (26.4%), trichuris suis (26.4%), strongyloides spp (21.9%), oesophagostomum dentatum (20.0%) and pseudanoplocephala spp. (5.6%). mixed infections were also observed. those within the ages of 0-8months had the highest prevalence (74.12%). further, 67.42% male pigs and 62.60% of female pigs were found to be infected with one or the other endoparasite revealing a high prevalence of parasitic problems within umudike. it is recommended that pigs should be treated regularly to prevent or reduce infection to the barest minimal level. keywords: abia state; cestode; faecal samples; gastrointestinal parasites; nematode pig farming; umudike. ، جنوب شرق أوموديكي ،عة لجامعة مايكل أوكبارا للزراعةالديدان المعوية في الخنازير التي تربى في المزارع البحثية التابانتشار نيجيريا أونيني مكبوال أوكاي و بلسينج أوزواماكا ايجيكيوبي تشارلز أمايه، ميراكل انوسنت دايك ، بأ العدوى في الحيوانات تؤدي إلى يعتبر التطفل المعدي المعوي في إنتاج الخنازير مشكلة عالمية خاصة في البلدان الفقيرة بالموارد االستوائية. هذه :صلخمال في جامعة مايكل للخنازير التي تمت تربيتها في مزرعتين بحثيتين المعدية المعويةخسائر اقتصادية كبيرة. هدفت هذه الدراسة إلى تقييم انتشار الطفيليات عينة من براز الخنازير من مزرعتين بحثيتين 661، تم تحليل 6102إلى يوليو 6102أبريل ، جنوب شرق نيجيريا، منموديك، أوأوكبارا للزراعة البراز. التجارية للخنازير( باستخدام طرق التحليل المختلفة لتحديد المراحل الطفيلية المتنوعة الموجودة في mouauومزرعة casap)مزرعة أبحاث الطفيليات مكونة من أربعة نيماتودا و ( في المزرعتين. لوحظ وجود خمسة أنواع من0.6/661٪ )2..2أظهرت البيانات الناتجة انتشاًرا إجماليًا بنسبة فَُر الِخْنزيِرّي )سيستود واحد وهي ٪( 61.1٪( ، العقدية )60.2، األسطوانيات البرازية ) ٪(..62٪( ، الدودة السوطية الخنزيرية )..62الصَّ ٪(. عالوة على 06..2أشهر ) 8-1نسبة انتشار بين األطفال الذين تتراوح أعمارهم بين ٪(. كما لوحظت عدوى مختلطة كانت أعلى6.2وسيدانوبلوسفاال. ) ٪ إناث الخنازير مصابة بواحد أو الطفيل الداخلي اآلخر مما يكشف عن انتشار كبير لمشكلة الطفيليات26.21الخنازير و ٪ ذكور6..22جد أن ذلك، و . وتوصي نتائج هذه الدراسة بعالج الخنازير بانتظام لمنع أو تقليل العدوى إلى أدنى حد ممكن.umudikeداخل .أبيا؛ الديدان، عينات البراز، طفيليات الجهاز الهضمي، تربية الخنازير النيماتودا، أوموديكوالية :مفتاحيةالكلمات ال mailto:ebubeamechi@yahoo.com prevalence of gastrointestinal helminthes in pigs 85 1. introduction ig farming has become a significant source of economic growth for many countries that are dependent on agriculture such as nigeria [1]. increasing development has led to rapid and rising demand for animal protein. the benefits of pig farming include promoting the socio-economic status of the populace since the pig has the advantage of being highly prolific when compared to other livestock [2]. pigs can convert more energy and nutrients into protein and as a result they grow faster. they survive and produce more by consuming small amounts of low-quality food, and hence do not need much involvement in terms of labour and feeding costs [3]. despite the advantages of pig production outlined, quite a number of factors militate against growth in the industry, factors such as poor veterinary services, lack of credit facilities, non-usage of modern technological advancement and great loss due to endemic disease, especially helminthic diseases. helminthiosis constitutes a major impediment to efficient and profitable pig production worldwide [4,5]. gastrointestinal parasites occur in pigs in all production systems and parasites have been identified in both intensively and extensively managed pigs, as well as in pigs kept on research farms. thus, pigs will likely play a role as a reservoir of parasites of humans [3,6,7]. due to the fact that parasites rarely cause clinical disease in pigs, little attention has been paid to the animal. commonly encountered important intestinal parasites of pigs include ascaris suum, oesophagostomum spp., hyostrongylus rubidus, ascarops strongylina, physocephalus sexalatus, strongyloides ransomi and trichuris suis [8]. the objective of this study was to estimate the prevalence and spectrum of gastrointestinal parasites of pigs reared in two research farms in umudike, abia state, nigeria. this will improve the understanding of their epidemiology and transmission in order to guide effective control. 2. methodology 2.1 study area the study was carried out in michael okpara university of agriculture (mouau) umudike in ikwuano local government area of abia state. mouau is located at latitude 5 0 40 1 and 6 0 4 1 north, and longitude 7 0 10 1 and 7 0 34 1 east of ikwuano local government area. the climate is purely tropical with wet and dry seasons. the rainy season goes from march to october while the dry season is from november to february. the mean daily rainfall and relative humidity are 146.5 mm and 80% respectively. the mean daily temperature ranges from 21.9 0 c to 31.5 0 c. michael okpara university of agriculture commercial pig farm and its research pig farm are supervised by the college of animal science and animal production (casap). the swine unit consists of breeding, farrowing, finishing and experimental pens. the pens are stocked with different breeds of pigs comprising pure duroc, strains of large white, hamphire and local breeds. the total number of pigs in the swine unit at the time of sampling which took place between april-july 2016 was 172 pigs in mouau commercial pig farm and 70 pigs in casap research pig farm. the parent stock was sourced from reputable commercial pig farms operating intensive production systems. fenbendazole and ivermectin were the two anthelminthic treatments administered three months earlier, prior to the study. 2.2 collection and examination of fecal samples fecal samples were collected from 220 pigs for parasitological examination. the faecal samples were collected directly from the rectum of the pigs with a pair of forceps, a disposable hand glove, or just as they were being dropped on the ground while watching. about 5 g of each captured faecal sample was put in a separate screw cap bottle containing 10% of formalin and was properly labeled indicating the age and sex of the pigs. these were then transported immediately to the department of zoology and environmental biology laboratory of michael okpara university of agriculture umudike for examination and identification. 2.3 floatation technique this method was demonstrated by [9]. about 3 g of faecal sample was emulsified in 30 ml of distilled water in a beaker and thereafter filtered using sieves of various mesh sizes (30, 60 and 90 mm). the strained material was immediately transferred into centrifuge tubes and centrifuged at 1,500 revolutions per minute (rpm) for 5 minutes. the clear supernatant in each tube was discarded and sugar solution of specific gravity (specific gravity of 1.2) was added to the sediment in each centrifuge tube until a convex meniscus was formed. each tube was then covered with a glass cover slip and allowed to stand for 10 minutes. each cover slip was then gently lifted from each tube and placed on a clean grease-free slide and examined under the ×10 and ×40 objectives of the microscope for the presence of eggs of helminth parasites. 2.4 direct smear method this method was also demonstrated by [9]. a small quantity of the faecal sample was placed on the clean grease free glass slide with a glass rod and a smear was made. a drop of 1% normal saline was added and thoroughly mixed with the sample. the slide was covered with a cover slip and examined under a microscope for the presence of eggs of helminth parasites. the eggs of helminths were identified using keys adopted by [10]. p ebube charles amaechi et al. 86 2.5 data analysis differences in the prevalence of parasite infections between age groups and sex were analyzed using chi-square tests at a level of p = 0.05. 3. results two hundred and twenty pigs were examined for the presence of intestinal parasites from two farms namely casap research farm and mouau commercial pig farm. a total of one hundred and forty two pigs (142) were infected giving an overall prevalence of 64.55% (table 1), in the two farms. fifty eight (58) pigs were examined from casap research farm while one hundred and sixty two (162) were examined from mouau commercial farm. there was no significant difference in the prevalence from either farm (p > 0.05). overall, sex related prevalence was higher in the males than in the females (table 2). there was no significant difference in the sex prevalence (p>0.05) those animals aged 0-8months had the highest prevalence (74.12%) in both the different farms (table 3). the prevalence amongst the different ages was significant (p < 0.05) five parasite species made up of four nematodes and one cestode were observed namely ascaris suum (26.4%), trichuris suis (26.4%) ,strongyloides spp (21.9%), stephanurus dentatus (20.0%) and cestode/pseudanoplocephala spp (5.6%),(table 4). mixed infections were also observed. the combinations of trichuris suis and strongyloides spp (29.41%) and of ascaris suum, trichuris suis and strongyloides spp (29.41%) occurred most frequently (table 5). table 1. prevalence of infection by farms. farm no. examined no. infected percentage of infection mouau commercial farm 162 102 62.92 casap research farm 58 40 68.97 total 220 142 64.55 df =1, x 2 =3.5, p >0.05 table 2. sex related prevalence among the pigs. sex no. examined no. infected percentage of infection (%) male 89 60 67.42 female 131 82 62.60 total 220 142 df =1, x 2 =2.8, p>0.05 table 3. age related infection rate among the pigs. age (months) no. examined no. infected percentage of infection (%) 0-8 85 63 74.12 9-16 99 60 60.61 >16 36 19 52.77 df =3, x 2 =6.5, p < 0.05 prevalence of gastrointestinal helminthes in pigs 87 table 4. prevalence of single parasite infection. parasites no. infected percentage of infection ascaris suum (n) 33 26.4 trichuris suis (n) 33 26.4 strongyloides spp (n) 27 21.6 oesophagostomum dentatum 25 20.0 pseudanoplocephala spp. 7 5.6 total 125(56.82) df =4, x 2 = 7.8, p > 0.05 table 5. prevalence of mixed parasite infection. parasites no. infected percentage of infection (%) ts+ss 5 29.41 ss+od 2 11.76 as+ps 1 5.88 as+ts 3 17.65 as+ts+ps 5 29.41 as+ts+od 1 5.88 total 17 (12.0%) key: ts= trichuris suis ss= strongyloides spp as=ascaris suum od= oesophagostomum dentatum ps=. pseudanoplocephala spp 4. discussion pig farming has become a significant source of economic growth for most tropical countries. helminthic diseases have been reported to be a major impediment to efficient and profitable pig production worldwide [1]. the present study aimed at determining the spectrum and prevalence of gastrointestinal parasites of pigs managed in two research farms at michael okpara university of agriculture, umudike, abia state, south eastern nigeria. the results of this work revealed a high prevalence of infection of 64.6% among the pigs investigated. this result agrees with the findings of [11] who reported a prevalence of 64.6% in pigs in shimoga region of karnataka. higher rates of 68.7%, 79.2%,80%, 92.7% and 100% gastrointestinal parasitic infection have, however, been reported in pigs reared in several countries such as west indies, south africa, burkinafaso, nigeria and gabon [12,13,14,6]. it would seem that the infection was low compared to these other findings. this seemingly low prevalence compared to these other studies could be as a result of the management practices in the farms that were visited, such as daily cleaning and disinfecting of the pens, giving high quality commercial feed in addition to self-prepared feed containing ingredients such as maize grain, cassava and plantain peels, and to the application of anthelminthic drugs to the pigs. anthelminthic drugs such as fenbendazole and ivermectin were being administered on a three months’ basis in the farms studied to help minimize the survival and transmission of parasites within the host system. the results obtained in this study could, however, also be influenced by the period of the investigation (april to july) which happens to be the rainy season period. the rainy season is favorable for the survival, development and transmission of parasitic infections. high stocking density on the farms is also a factor that would have affected the prevalence rate of the parasites in the farms. high stocking density increases the contamination of the environment with these parasitic eggs or larvae and thus makes the infective stages more accessible to susceptible animals. lower parasitic prevalences of 37.77%, 38.8% and 42.7% in pigs of india and nigeria have been reported [15,16,17] five intestinal parasites of veterinary importance were observed in the study: four nematodes (ascaris suum, trichuris suis, strongyloides spp, oesophagostomum dentatum) and one cestode (pseudanoplocephala spp). however, a previous study in nigeria by [17] identified eight parasites, ascaris suum, trichuris suis and strongyloides spp included [13]. in south africa four parasites including ascaris suum and trichuris suis. a. suum and t. suis have been observed to affect growing animals, as compared to o. dentatum that affects adult animals. this is in accordance with the present study, in which both these parasites were found to be most prevalent when compared to others. the transmission of all these parasites is faecal-oral and direct, via eggs containing an infective third stage larva (l3) as in the case of a. suum and t. suis, and free living l3 as seen in o. dentatum. the relatively low spectrum of parasites observed could be linked to the intensive husbandry system used in raising the pigs. the overall prevalence (26.4%) of a. suum in this study was similar to a study from india [18], who recorded a 27.5% prevalence rate. it was, however, lower than the prevalence recorded for other studies, namely 40% by [14] in bukinafaso, and 44.5% by [13] in south africa. lower prevalence rates of 11.1% and 14.7% were recorded in nigeria ebube charles amaechi et al. 88 [16,17] in the present study, trichuris suis occurred in similar proportions of 26.4%. this is higher than the report of [16,17] who recorded 12.2% and 0.7% rates respectively. higher prevalence of 50.6% of t. suis was reported in south africa [13]. the higher prevalence of a. suum and t. suis in this study might be connected to the fact that eggs of whipworms are hard and so can withstand adverse environmental conditions for a long period of time [19]. the prevalence of strongyloides spp observed in the present study (21.9%) is similar to the findings of [14] in bukinafaso, who reported a 21% rate. it is, however, higher than the report of [17] in nigeria who recorded a 2.0% prevalence rate. the level of infection observed in this study might be due to the atmospheric conditions (rainy season) which favoured the proliferation of the parasite. the larvae require the right environmental temperature and moisture content for development and survival of the eggs. the prevalence of oesophagostomum dentatum observed in the present study (20.0%) is higher than the findings of [16] 1.1% prevalence rate. most workers in other parts of the world did not report this parasite. the parasite might be location specific. the prevalence of pseudanoplocephala spp. was observed in the present study (5.6%). it was however the least prevalent. this was lower than the findings of [20] in nigeria who reported a 17% prevalence rate. transmission of pseudanoplocephala spp from pigs to humans has been established; therefore it could be zoonotic and hence a public health concern. in terms of infections, single infections were more prevalent (56.8%) than mixed infections (12.0%). this also agrees with the findings of [16]. mixed infections were also observed, namely the combinations of trichuris suis and strongyloides spp and that of ascaris suum, trichuris suis and strongyloides spp. [7] reported similar findings in nigeria. polyparasitism in pigs is a common phenomenon which shows the rate of transmission to man. the piglets of 0-8months were more infected in the two farms combined (74.12%) than the other pigs in the different age groups. piglets are more susceptible to parasitic infection as their immune systems are still in the development process and they may not be able to resist infection like the older pigs. similar observations have been made by others [16, 21]. in the present study, more males (67.42%) were infected than the females (62.60%). this is in consonance with the report of other authors in nigeria and botswana [16,22] but contrasts with the reports of [14,23]. previous workers, however, attributed a higher prevalence rate in females due to a decreased resistance in females especially in relation to pregnancy and lactation. our present result may possibly not show this effect because the female pigs may have had a stronger host genetic resistance compared to the males. the results of this work provide a baseline data about the parasite fauna in intensively managed pig farms in michael okpara university of agriculture, umudike. this would go a long way to help plan and improve on the present management practices already in place to reduce parasitic infection of pigs. 5. conclusion this work has revealed the prevalence of infection with intestinal parasites among the pigs studied (64.55%). the piglets of 0-8months were more frequently infected than the pigs in other age groups. it is also evident that pig faeces could be a source of re-infection to the pigs if they are not cleaned out on time. eating infected or improperly cooked pork meat could infect the consumer (zoonosis). in view of this, it is recommended that pig pens should be cleaned on a regular basis and should be treated regularly to prevent or reduce infection to the barest minimum level. conflict of interest the authors declare no conflict of interest. acknowledgements the head, department of zoology and environmental biology is highly appreciated for granting us access to the laboratory facility. all the laboratory staff that assisted in the work are also appreciated. ethical statement the protocol was approved by the ethical committee of michael okpara university of agriculture, umudike. references 1. ohaeri, c.c.,and okoro, c.t. gastrointestinal parasites of pigs in a commercial farm in isiala-ngwa north, abia state, nigeria. nigerian journal of parasitology, 2012, 33(1), 63-66. 2. tufare, a., awol, n., tadese, f., tsegaye, y.,and hadush, b. parasites of pigs in two farms with poor husbandry practices in bishoftu, ethiopia. onderstepoort journal of veterinary research, 2015, 82, 1-5. 3. kristina, r., ian, d., maximilian, b., michel, d., delia, g., and peter-henning, c. prevalence and risk factors for gastrointestinal parasites in smallscale pig enterprises in central and eastern uganda. parasitology research, 2017, 116, 335-345. prevalence of gastrointestinal helminthes in pigs 89 4. nissen, s., poulsen, i.h., nejsum, p., olsen, a., 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research international, 2018, 15(2), 3013-3019. 18. kaur, m., singh, b.b., sharma, r. and gill, j.p.s. prevalence of gastrointestinal parasites in pigs in punjab, india. journal of parasitic disease, 2017, 41(2), 483-48. 19. urquhart, g.m., armour, j., duncan, j.l., dunn, a.m.and jennings, f.w. veterinary parasitology,2 nd edition.wiley-blackwell, science ltd, new york, 1996. 20. olaniyi, a.j. public health implications of gastrointestinal parasites of pigs in kwara state, nigeria. journal of animal and veterinary advances, 2014, 13, 783-785. 21. okoroafor, u.p.,unigwe, c.r.,okorofor, j.c., isegbe, e.i., ogbu, u.m.,and atoyebi, t.j. a survey of gastrointestinal parasites of pigs that arrived for slaughter at bodija abattoir, ibadan, oyo state, nigeria. international journal of pure and applied science and technology, 2014, 20(2), 53-57. 22. nsoso, s.j., mosala, k.p., ndebele, r.t.,and ramabu, s.s.the prevalence of internal and external parasites in pigs at different ages and sexes in southeast district, botswana. onderstepoort journal of veterinary research, 2000, 67, 217-22. 23. atawalna, j., attoh-kotoku, v., folitse, r.d.and amenakpor, c. prevalence of gastrointestinal parasites among pigs in the ejisu municipality of ghana. scholarly journal of agriculture and veterinary science, 2016, 3(1), 3336. received 17 january 2022 accepted 16 june 2022 squ journal for science, 2023, 28(1), 10-16 doi:10.53539/squjs.vol28iss1pp10-16 sultan qaboos university 10 haematological and biochemical changes in albino rats in response to bisphenol a (bpa) exposure enwongo effiong nduonofit and obemeata emmanuel oriakpono* department of animal and environmental biology, faculty of science, university of port harcourt p.m.b. 5323, port harcourt, rivers state, nigeria. *email: obemeata.oriakpono@uniport.edu.ng. abstract: the aim of this study was to investigate the haematological and biochemical alterations in albino rats induced by bisphenol a (bpa). fifteen adult male albino rats were procured and separated into 3 different groups viz: group 1 (control), group 2 (50 mg/kg), group 3 (250 mg/kg); and were orally administered bpa at doses of 50 and 250 mg/kg/week. after 6 weeks of exposure, blood samples were collected for haematological and biochemical assay. the parameters analyzed included: red blood cell count, haemoglobin concentration, packed cell volume, white blood cell count, differential white blood cell count, kidney and liver function tests. the results obtained revealed that there was a sequence of significant decrease (p<0.05) from the control group to group 3 (250 mg//kg) of the bpa-treated groups in the following parameters; total rbc count 7.33-4.40, hb concentration 16.63-11.13 and pcv count 43.67-34.67. a significant increase (p<0.05) was observed in all leucogram values of bpa-treated groups when compared to the control. the serum levels of ast (44.67-71.00), alt (13.33-46.67), alp (64.00-86.67), na + , k + , urea and creatinine significantly increased (p<0.05) in the groups that received bpa-treatment. there was also a non-significant reduction (p>0.05) in total protein (72.67-61.00) and albumin (49.00-25.00) in bpa-treated groups when compared to the control. these findings demonstrate that exposure of albino rats to bpa resulted in haematological defects and alteration in several biochemical parameters that indicate renal and hepatic toxicity. keywords: biochemical assay; bisphenol a; haematogical assay. spb( a lo b psib)التغيرات الدموية والكيميائية الحيوية في الجرذان البيضاء استجابةً لتعرض نوانجو إفينيوج و أوبيميتا أوريكبونو أ تم شراء خمسة عشر ذكوًرا من .(bpa)كان الهدف من هذه الدراسة هو التحقيق في التغيرات الدموية والكيميائية الحيوية التي يسببها بيسفينول أ :صلخمال /مجم 250) 3، المجموعة (كجم /مجم 50) 2، المجموعة (مجموعة التحكم) 1المجموعة :مجموعات مختلفة 3الجرذان البيضاء البالغة وتم فصلها إلى أسابيع من التعرض ، تم جمع عينات الدم لفحص الدم والكيمياء 6بعد .أسبوع /كغم /ملغم 250و 50بجرعات bpa؛ وكانت تدار عن طريق الفم (كجم الدم البيضاء ، تعداد خاليا الدم البيضاء تشمل المعلمات التي تم تحليلها ؛ خاليا الدم الحمراء ، تركيز الهيموجلوبين ، حجم الخاليا المكدسة ، خاليا .الحيوية من مجموعة التحكم إلى (p <0.05)أظهرت النتائج التي تم الحصول عليها أن هناك تسلسل انخفاض معنوي .التفاضلية ، فحص وظائف الكلى والكبد ، تركيز 4.40-7.33دد كرات الدم الحمراء في المعلمات التالية ؛ إجمالي ع bpaمن المجموعات المعالجة بـ (كجم /مجم 250) 3المجموعة للمجموعات leucogramفي جميع قيم (p <0.05)لوحظت زيادة معنوية .34.67-43.67وعدد خاليا الدم الحمراء 11.13-16.63الهيموغلوبين ast (44.67-71.00) ،alt (13.33-46.67) ،alp (64.00-86.67)زادت مستويات مصل .بالمقارنة مع المجموعة الضابطة bpaالمعالجة بـ ،na + ،k + اليوريا والكرياتينين بشكل ملحوظ ،(p <0.05) في المجموعات التي تلقت عالجbpa. كان هناك أيًضا انخفاض غير معنوي(p> توضح هذه النتائج .مقارنةً بمجموعة التحكم bpaفي المجموعات المعالجة بـ (25.00-49.00)واأللبومين (61.00-72.67)في البروتين الكلي (0.05 .أدى إلى عيوب دموية وتغيير في العديد من المعلمات البيوكيميائية التي تشير إلى سمية كلوية وكبدية bpaأن التعرض لـ .ثنائي الفينول أ؛ فحص الدم .فحص الكيمياء الحيوية :مفتاحيةالكلمات ال haematological and biochemical changes in albino rats 11 1. introduction isphenol a (bpa) is a synthetic organic compound that is widely used throughout the world. it is primarily known as an important ingredient in the production of polycarbonate (pc) plastics and epoxy resins. it serves as an intermediary to the manufacture of various products. bpa is widely used because it is lightweight and for its rigidity, lucidity and resistance to temperature. polycarbonates are used in plastic containers especially in the food industry and for domestic products such as for plastic bottles, and for lenses, sports safety equipment and components of medical devices. epoxy resins are used as protective coatings in metal cans in order to protect the integrity and safety of our food supply by preventing corrosion and contamination of canned foods and beverages with metals and bacteria, hence extending their shelf life. thus besides many other applications, both pc and epoxy resins are widely used as food contact materials (fcms) which means that they are used for the manufacture of items that have direct contact with food [1]. these items include: infant feeding bottles, tableware, food containers, water bottles, ovenware, water pipes and so on [2]. food contact materials, however, comprise only about 3% of produced pc plastics and 10% of epoxy resins [3]. the general human population can be exposed to bpa through the oral, inhalatory and dermal routes [4, 8], but the most significant mode of exposure of humans to bpa is through food, being present in canned food and drinking water as a result of the leaching of this chemical from the plastic lining of cans of drinks and food. the leaching of bpa from plastic is increased when it is cleaned with a strong detergent, when it contains acidic liquids or when it is exposed to high temperatures. it is also known to leak into food from the protective inner epoxy resin coating of canned food, and this usually occurs when the cans are being heated during sterilization or food preparation [9]. moreover, the high production volume of bpa is ubiquitous and this leads to contamination of the environment, especially the soil and groundwater [10]. bpa is absorbed from the gastrointestinal tract into the blood and redistributed to other tissues [11]. it is highly conjugated in the liver to form bisphenol a glucuronide, a major metabolite, which is excreted in urine [12] and this has been detected in the urine and serum samples of individuals in the usa [13]. these studies have shown that humans are being exposed to bpa. bpa has been demonstrated in both in vivo and in vitro experiments to act as an endocrine disrupting chemical [14]. this has raised great concern with regards to human health. the harmful effects of bpa are mainly linked to its estrogenic activity [15]. the exposure of different laboratory animals to bpa elucidates the multiple effects on the male and female reproductive systems. different doses of bpa caused inhibition in spermatogenesis and seminiferous tubules in male chicks [16]. bpa is also known to cause a decrease in sperm count and motility and also to affect sperm morphology of adult male rats [17,18]. bpa has been associated with declined semen quality and increased sperm dna damage; this also supports the toxicity of bpa on germ cells [19]. this study therefore investigated the effect of oral administration of bpa in adult male rats by examining alterations in their haematological and biochemical parameters. 2. materials and methods 2.1 test material bisphenol a [2, 2-bis (4-hydroxyphenyl propane)] (purity 99.9%, cas no. 80-05-7) was procured from geochem ventures limited, choba, rivers state. bpa solution was prepared by dissolving this chemical in olive oil on a weekly basis according to the dose to be orally administered to each of the groups. 2.2 test animals a total of fifteen (15) adult male albino rats, weighing 180-230 grams were used to carry out these studies. the rats were bred in the animal house with a 12-hour light and 12-hour dark photoperiod, in the department of animal and environmental biology, university of port harcourt. before the administration of this chemical, the test animals were allowed to acclimatize to the laboratory environment for a period of fourteen days. they were kept in a wooden cage and given a standard feed and water throughout the study. 2.3 experimental design the rats were divided into three groups with each group containing five animals which were approximately equal to their average body weight. the doses were selected according to jayashree et al. [20]. the oral ld50 of bpa in rats was 3250 mg/kg body weight as described by msds [21]. the experimental groups were designated as follows: group i: control (vehicle-treated, n = 5); group ii (received 50 mg/kg body-weight/week bpa, n = 5); group iii (received 250mg/kg body-weight/week bpa, n = 5). bpa was administered weekly via the oral route for 6 weeks. all experimental procedures and animal use were approved by the university of port harcourt local committee on research ethics. at the end of the experiment, the test animals were sedated by placing them in a sealed jar containing cotton wool soaked with chloroform anaesthesia. blood samples were obtained by cardiac prick and 1 ml of blood was placed in an ethylenediaminetetraacetic acid (edta) anticoagulant tube for measurements of haematological parameters. the blood was centrifuged at 6000 rpm for ten minutes to separate the serum which was used for the measurement of biochemical parameters. b enwongo e. nduonofit and obemeata emmanuel oriakpono 12 2.4 haematological assays red blood cell (rbc) and leucocyte counts were ascertained using an improved neubauer haemocytometer. packed cell volume (pcv) was estimated by the micro haematocrit technique. haemoglobin (hb) concentration was assessed with drabkin’s method [22]. the differential leucocyte count was performed on giemsa stained blood smears [23]. 2.5 biochemical analysis of serum 2.5.1 kidney function the levels of urea and serum creatinine were ascertained using the principles of tabacco, and fabiny and eringhausen respectively [24, 25]. the method for electrolyte [calcium ion (ca 2+ ), chloride ion (cl ), potassium ion (k + ), and sodium ion (na + )] analysis was performed by direct measurement [26]. the activity of the specific ion in the sample at the electrode was joined with an electrical potential which was measured by a voltmeter. voltage is theoretically proportional to ionic activity. the voltage was finally converted to an electrical signal and displayed as a value on the screen. the bicarbonate (hco3 ) analysis was carried out using standard laboratory procedures [27]. 2.5.2 liver function serum samples were assayed for aspartate transaminase (ast), alanine transaminase (alt) and alkaline phosphatase (alp) using standard diagnostic kits with a clinical spectrophotometer. serum total protein (tp) was ascertained using the method of weichselbaun, while albumin (alb) was ascertained using the method of dumas and biggs [28, 29]. 2.6 statistical analysis the results were presented as mean ± standard deviation and subjected to analysis by using one-way analysis of variance (anova). a post hoc test was used to determine the significant difference among means of different groups. the spss (statistical package for social sciences) software (version 20) was used for the analysis of data and the level of significance was set at p≤0.05. 3. results 3.1 effects of bpa on haematological parameters of albino rats table 1 shows the effect of bpa on some haematological parameters. there was a significant decrease (p<0.05) in rbc count, hb concentration and pcv in rats after oral administration of both doses (50 and 250 mg/kg) of bpa when compared to the control. the results also revealed that there was a significant increase (p<0.05) in white blood cell (wbc) count and in the percentage of neutrophils, lymphocytes, monocytes and eosinophil in the groups that received bpa-treatment when compared to the control. table 1. effect of oral administration of bpa on some haematological parameters of albino rats. parameters control 50 mg/kg 250 mg/kg rbc (x10 9 /l) 7.33±0.41 a 6.23±0.25 b 4.40±0.46 c hb (g/dl) 16.63±0.31 a 13.33±0.35 b 11.13±0.83 c pcv (%) 43.67±1.53 a 40.00±1.00 b 34.67±1.53 c wbc (x10 9 /l) 8.07±0.31 a 9.50±0.20 b 10.03±0.15 b neutrophils (%) 23.00±2.00 a 28.67±1.53 a 36.00±3.46 b lymphocyte (%) 45.33±4.51 a 53.33±1.53 b 59.00±1.73 b monocyte (%) 5.00±0.00 a 7.00±0.00 b 7.67±0.58 c eosinophil (%) 2.67±0.58 a 4.00±0.00 b 5.33±0.58 c data are presented as mean ± sd; values with different superscript characters ( a-c ) indicate a significant difference (p≤0.05); rbc red blood cell; hb haemoglobin concentration; pcv packed cell volume; wbc white blood cell; (n = 5) haematological and biochemical changes in albino rats 13 3.2 effect of bpa on renal function of albino rats figure 1 shows a summary of the effect of bpa on kidney parameters. the mean values of serum urea, creatinine, na + , k + and ca 2+ increased significantly (p≤0.05) in the groups that received bpa-treatment when compared to the control. the table also reveals that there was no significant difference (p>0.05) in the level of serum hco . figure 1. effect of oral administration of bpa on renal function of albino rats. data are presented as mean ± sd. values with different superscript characters ( a-c ) indicate a significant difference (p≤0.05). na + = sodium ion; k + = potassium ion; ca 2+ = calcium ion; hco3 = bicarbonate ion; (n = 5) 3.3 effect of bpa on liver function of albino rats figure 2 shows the effects of bpa on liver parameters. the mean values of ast, alt and alp increased significantly (p<0.05) in rats after oral administration of both doses (50 and 250 mg/kg of bpa) when compared to the control. the mean values for total protein and albumin showed no significant difference (p>0.05) in the group that received bpa treatment when compared to the control. figure 2. effect of oral administration of bpa on liver function of albino rats. ast = aspartate transaminase; alt = alanine transaminase; alp = alkaline phosphatase; tp = total protein; alb = albumin; (n = 5). 0 20 40 60 80 100 120 140 160 180 urea (mmol/l) creatinine (µmol/l) na+ (mmol/l) k+ (mmol/l) ca2+ (mmol/l) hco(mmol/l) m e a n c o n c e n tr a ti o n parameter control 50mg/kg 250mg/kg 0 10 20 30 40 50 60 70 80 90 100 ast (u/l) alt (u/l) alp (u/l) tp (g/dl) alb (g/dl) m e a n c o n ce n tr a ti o n parameters control 50mg/kg 250mg/kg enwongo e. nduonofit and obemeata emmanuel oriakpono 14 4. discussion the current research revealed that the oral exposure of adult male rats to bpa resulted in a significant decrease in the rbcs count, hb concentration and pcv compared to the values for the control. the data obtained were close to the results of ulutas, and of yamasaki and okuda [30, 31]. they both determined the impact of bpa on rats at a dose of 125 mg/kg and 100 mg/kg respectively and later discovered that this chemical had instigated a significant decrease in total erythrocyte count, hb concentration and pcv. the decrease in rbcs may signify a disruption in erythropoiesis or may be due to damaged erythrocytes [32]. these defects may also lead to a reduction in the lifespan of rbcs. the decrease in haemoglobin content of blood may be due to the decrease in rbc count, destruction of synthesized rbc or destruction of rbc membranes [32]. erythrocyte deformation might cause low oxygen levels and dysfunction of cellular respiration or radical-induced stress which might cause haemolysis; therefore altering the total erythrocyte count [33]-[34]. the decrease in the concentration of haemoglobin may result in stress which can cause deleterious effects in the experimental animals [35]. pcv is a major haematological parameter that changes with environmental stress [36]. the reduction in pcv value is result of a decrease in the total rbc count. there was also a significant increase in leucogram values of bpa-treated groups in comparison with the control. this may signify that this compound has the capacity to induce some non-specific immune response in the test animal [36]. this would help in resisting potential pathogens in the test animal. the elevated leucogram values of bpa-treated groups might initiate a defense mechanism against this chemical. the elevated values of wbc may be to enhance wound healing and inflammatory disease [37]. the results also revealed that there was a significant increase in serum urea, creatinine and some electrolytes (na + , k + ) in bpa-treated groups in comparison with the control group. these alterations in renal function are close to the results obtained from previous research [38,39]. sangai and verma stated that the nephrotoxic effect of bpa is as a result of kidney damage which leads to the accumulation of toxic metabolites in the body [40]. there was an insignificant increase in serum ca 2+ whereas a non-significant reduction was also noticed in the level of hco3 in bpa-treated groups in comparison with the control groups. the above results confirmed that electrolyte imbalance is characterized as renal problems [41]. the increases in urea, creatinine, na + and k + indicate renal impairment which resulted in the accumulation of unwanted materials. the current research revealed that rats exposed to bpa displayed a significant increase in ast, alt and alp levels in comparison with the control group. serum ast, alt and alp have been proven to be released into the blood when the liver is damaged [42]-[44]. adedapo and aiyelotan had previously reported similar higher levels of serum hepatic enzymes [37]. according to korkmaz et al., exposure to bpa might result in a rise in oxidative stress in the liver which explains the higher levels of ast, alt and alp [14]. there was an insignificant reduction in the serum levels of total protein and albumin in the groups that received bpatreatment. the reduced level of total protein in bpa-treated groups may suggest impairment of liver function which might result in a disease condition called hypoproteinemia. 5. conclusion it can be concluded that oral administration of bpa for 6 weeks in adult male rats resulted in haematological defects and alteration of several biochemical parameters that indicate renal and hepatic toxicity. conflict of interest the authors declare no conflict of interest. acknowledgment the authors acknowledge the contribution and support of staff 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(eds.) enzymes lubbok, texas, 2005, 352-390. 44. walaa, m.s., walaa a.m. and nabil, t.m. bisphenol a toxicity in adult male rats: hematological, biochemical and histopathological approach. global veterinaria, 2015, 14(2), 228-238. received 2 august 2021 accepted 15 december 2022 squ journal for science, 2017, 22(1), 40-47 doi: http://dx.doi.org/10.24200/squjs.vol22iss1pp40-47 2017 sultan qaboos university 40 incidence matrices of directed graphs of groups and their up-down pregroups wadhah s. jassim department of mathematics, faculty of science, soran university, soran, erbil, iraq. email: wadhahjasim@maths.soran.edu.krd. abstract: the aim of this work is to give a definition of the incidence matrices of the directed graph of groups, construct an up-down pregroup of the incidence matrices of the directed graph of groups and then give an algorithm for the up-down pregroup of the directed graph of groups. keywords: incidence matrix of x-labeled graph; up-down pregroup; directed graph of groups and incidence matrix of a directed graph of groups. سفل ما قبل زمرهاأ -على ألبيانات الزمر الموجه و مصفوفات الوقوع وضاح س. جاسم سفل ما قبل زمره أعلى أبناء ،سفل ما قبل زمرها أ –على ت الوقوع لبيانات الزمرالموجه وأهو اعطاء تعريف لمصفوفا هدف بحثنا هذا :ملخصال الزمر الموجه.سفل ما قبل زمره لبيانات أ –على أمن ثم اعطاء خوارزمية لبناء ت الوقوع لبيانات الزمر الموجه ولمصفوفا مصفوفة الوقوع لبيان بيانات الزمر الموجه و ،سفل ما قبل زمره أ -على أ ،x –مصفوفة الوقوع للبيان المحمول بعناصر ا لمجموعه : مفتاحيةالكلمات ال الزمر الموجه. 1. introduction n [1] we gave the definition of the incidence matrices of xlabeled graphs. in [2], [3] we gave the definition of the directed graph of groups, constructed graph of groups for pregroups directly from the ordered tree of pregroups, and from that directed graph of groups we constructed the up-down pregroups, and then we showed those two pregroups are isomorphic. in [4] rimlinger gave an example of a pregroup p of finite height; he said “but jim shearer and i spent a very long evening with the computer and verified the pregroup axioms”. i bear this point in mind. in [2], [3] we have a direct method to obtain examples of pregroups in the form of up-down pregroups from any directed graph of groups, but sometimes those graphs of groups are large, and then will take a long time to find those up-down pregroups. in [1] we defined the incidence matrices of x-labeled graphs. the main aim of this work is to represent the directed graph of finite groups in terms of the incidence matrices of x-labeled graphs, so that by adding certain conditions to allow the incidence matrices of the x-labeled graph to be more confident with the definition of the directed graph of groups; we can then write a computer program to record all elements of the up-down pregroup of that directed graph of groups, as an application of the incidence matrices of x-labeled graph. therefore, this paper is divided into s i x sections. in section 2, we give the basic concepts of graphs, pregroups and incidence matrices of x-labeled graphs. in section 3, we give the definition of incidence matrices of directed graphs of groups. in section 4, we construct the up-down pregroup of the incidence matrices of the directed graph of groups. in section 5, we define an algorithm on the incidence matrices of the directed graph of groups, so we can then write a computer program for this algorithm. 2. basic concepts 2.1 pregroups the idea of pregroups goes back to baer [5] and the definition of pregroup was given independently by stallings [6] in 1971. the theory of pregroups has been developed by [4], stallings [6], hoare [7] and hoare – jassim [3] and others. we now return to the original definition of pregroups [6]. i incidence matrices of directed graphs 41 let p be a set with an element 1  p and a mapping of a subset d of p  p into p, denoted by ( x, y)  xy. we shall say that xy is defined instead of ( x, y)  d. suppose that there is an involution on p denoted by x  x 1 , such that the following axioms hold: p1: x1 = 1x for all x  p, p2: xx 1  1  x 1 x for all x  p , p3: if xy is defined, then y 1 x 1 is defined and ( xy) 1  y 1 x 1 . p4: if xy and yz are defined then (xy)z is defined if and only if x(yz) is defined, in which case the two are equal and we will say xyz is defined. p5: for any w, x, y and z in p, if wx, xy and yz are defined, then either wxy or xyz is defined . hoare [7] showed that we could prove axiom p3 above by using the following proposition, and axioms p1, p2 and p4. definition 2.2. [7]: for any x  p, put l(x)  {a  p: ax is defined}. we write x  y if l( y)  l( x), x  y if l( y)  l( x) and l( x)  l( y) , and x ~ y if l( x)  l( y) . it is clear that ~ is an equivalence relation compatible with . the following results are taken from stallings [6] and rimlinger [4]. (see [7] for shorter proofs). proposition 2.3. (i) if x  y or y  x , then x 1 y and y 1 x are defined. (ii) if xa and a 1 y are defined, then ( xa)(a 1 y) is defined if and only if xy is defined, in which case they are equal.  by using axiom p5 above (which will be denoted by p5(i)) rimlinger [4] proved conditions p5(ii) and p5(iii) of lemma 2.4 below. lemma 2.4 [7]. the following conditions on elements of p are equivalent: p5(i). if wx,xy and yz are defined , then either wxy or xyz is defined . p5(ii). if x 1 a and a 1 y are defined but x 1 y is not , then a < x and a < y. p5(iii). if x 1 y is defined, then x  y or y  x .  therefore, we will say p is a pregroup if it satisfies axioms p1, p2, p4, and the conditions of lemma 2.4, above. the universal group of a pregroup p [13] is denoted by u (p) and has the following presentation  p; x.y  xy whenever xy is defined, for x, y, p . now if p is a pregroup, then (p, ) is tree like partial ordering; that is p/~ has a minimum element and, for any x,y and z in p , x  z and y  z we have x  y or y  x . moreover rimlinger in [4] defined that for any element x in p, we say that x has finite height n  0, if there exists a maximal totally ordered subset {x0 , x1 ,, xn } of p such that 1  x0  x1    xn  x . he also showed that the elements of p form an order tree (denoted by o ) whose vertices , [x], are the equivalence classes of the elements of p under ~, and whose edges e, are formed by joining each vertex [x] of height n > 0 to the unique vertex [y] of height n – 1 satisfying ][][ xy  , and all edges e of o are directed away the base vertex [ 0 x ] of height 0. in [8] stallings constructed an up – down pregroup for a free group f generated by },{ bax  of infinite height, and he showed that u(p) the universal group of a pregroup p is isomorphic to f. in [2,3] we gave the definition of a directed graph of groups which consists of a directed graph y, with a base vertex  v and a spanning tree t, whose edges are directed away from the base vertex  v , together with a group v g for each vertex v and for each directed edge ye  , a subgroup e g of )( ei g which is embedded in )( e g  by e  which is defined by eee ayya 1 )(   , where e ga  and e y is the labeled of the edge e. it is denoted by ),,,,,( * eev vtygg  . we also constructed a directed graph of groups of p directly from the order tree o of p and then showed that the fundamental group of a graph of groups ),,,,,( * 1 eev vtygg  is isomorphic to u(p) , we constructed an up – down pregroup q directly from the directed graph of groups ),,,,,( * eev vtygg  of a pregroup p and we showed that u(q) is isomorphic to ),,,,,( * 1 eev vtygg  and then that )()( puqu  . wadhah s. jassim 42 2.5 incidence matrices of x – labeled graphs in [1] we gave the definition of the incidence matrices of x – labeled graphs (where an x-labeled graph is a directed graph with each edge labeled by an element x of the subset x of the group f and x generating the group f), and some definitions and results related to it. recall that from graph theory the directed graphs  are without loops, because we cannot define the incidence matrices of directed graphs . the incidence matrices of directed graphs  are with n vertices and m edges (i.e. it is mn  matrices ][ ij x , where mjni  1,1 ) such that: since all edges e in x – labeled graphs are labeled 1  xxx and the incidence matrices of the directed graphs do not deal with the labeling of edges, we will put more conditions on the incidence matrices of directed graphs as below to obtain the definition of the incidence matrices of the xlabeled graphs. definition 2.6: let  be any x – labeled graph without loops (where },{ bax  ), then the incidence matrix of the x – labeled graph  is an mn  incidence matrix ][ ij x , where mjni  1,1 ) with ij x entries such that xxlabelse ewithincident xxlabelse ande notisv andei v if v if if x x x j j j j i j i i ij            )( )( 0 1  n.b. incidence matrices of x – labeled graphs  will be denoted by )( x m . for example: the cayley graph ),( xf of the group f generated by fx  , the cayley coset graph )(h of the subgroup h of f, the core graph of the cayley coset graph )(h   of the subgroup h of f and the product of core graphs )( ~ )( kh   are xlabeled graphs. now if },{ bax  and the x – labeled graph  has loops with labeling a or b, then choose a mid point on all edges labeled a or b to make all of them two edges labeled aa or bb respectively . therefore in the rest of this work we will assume that all x – labeled graphs are without loops. definition 2.7: let )( x m be an incidence matrix of x –labeled graph . if )( x m doesn't contain any row i r with non zero entries ij x and ik x in 1  xx such that ikij xx  , then )( x m is called a folded incidence matrix of x – labeled graph . now we give the basic definitions and some results on the incidence matrix of x – labeled graph )( x m , as given in [1]. let )( x m be an mn  incidence matrix ][ ij x of x – labeled graphs , and let i r and j c be a row and a column in )( x m respectively. if ij x is a non – zero entry in the row i r , then i r is called an incidence row with the column j c at the non – zero entry ij x 1  xx , and if the non – zero entry xx ij  , then the row i r is called the starting row (denoted by ))( j cs of the column j c , and the row i r is called the ending row ( denoted by )( j ce ) of the column j c if 1  xx ij . if the rows i r and k r are incident with column j c at the non – zero entries ij x and kj x respectively, then we say that the rows i r and k r are adjacent. if j c and h c are two distinct columns in )( x m such that the row i r is incidence with the columns j c and h c at the non – zero entries ij x and ih x respectively (where 1 ,   xxxx hij ), then we say that j c and h c are adjacent columns. for each column c there is an inverse column denoted by c such that )()(),()( cscececs  and cc  . the degree of a row i r of         )(1 0 )(1 ji ji ji ij evif ewithincedencenotisvif eivif x  incidence matrices of directed graphs 43 )( x m is the number of the columns incident to i r and is denoted by deg( ). i r if the row i r is incident with at least three distinct columns j c , h c and k c at the non – zero entries , then the row i r is called a branch row. if the row i r is incident with only one column j c at the nonzero entry ij x 1  xx and all other entries of i r are zero, then the row i r is called an isolated row. a scale in )( x m is a finite sequence of form kkk rcrcrcrs k ,,,,,,, 121 112211      , where ,1k , jj rcs j   )( , and 1 1 ( ) ( ),1 .j j j j e c r s c j k        .the starting row of a scale kkk rcrcrcrs k ,,,,,,, 121 112211      is the starting row 1 r of the column 1 c and the ending row of the scale s is the ending row k r of the column 1k c and we say that s is a scale from 1 r to k r and s is a scale of length k for 21  kj . if )()( sess  , then the scale is called a closed scale. if the scale s is reduced and closed, then s is called a circuit or a cycle. if )( x m has no cycle, then )( x m is called a forest incidence matrix of x – labeled graph γ. two rows i r and k r in )( x m are called connected if there is a scale s in )( x m containing i r and k r . moreover )( x m is called connected if any two rows i r and k r in )( x m are connected by a scale s. if )( x m is a connected and forest , then )( x m is called a tree incidence matrix of x – labeled graph γ. let  be a subgraph of γ, then )( x m is called a subincidence matrix of )( x m , if the set of rows and columns of )( x m are subsets of )( x m and if c is a column in )( x m , then )(),( cecs and c have the same meaning in )( x m as they do in ( ). x m  if )()(  xx mm , then )( x m is called a proper subincidence matrix of )( x m . a component of )( x m is a maximal connected subincidence matrix of )( x m . if )( x m is a subincidence matrix of )( x m , and every two rows i r and k r in )( x m are joined by at least one scale s in )( x m , then )( x m is called spanning incidence matrix of )( x m and )( x m is called spanning tree of )( x m if )( x m is a spanning and tree incidence matrix . the inverse of )( x m is an incidence matrix of 1 x labeled graph γ. now by direct calculations and the definitions above, we can prove the following results. lemma 2.8: if )( x m is a tree incidence matrix of x – labeled graph γ with n rows, then )( x m has n –1 columns. 3. incidence matrices of directed graphs of finite groups. definition 3.1: an incidence matrix of a directed graph of finite groups consists of an incidence matrix of x labeled graph )( x m with a spanning tree matrix of xlabeled graph )(tm x , and a base row 1 rr   , together with a finite group r g for each row r, and a finite group c g for each column c , such that: 1) the columns of )( x m are directed away from 1 rr   ; 2) each column group c g is a subgroup of )( ci g ; 3) each column group c g is embedded in )( ct g by a fixed monomorphism c  , defined by ccc ayya 1 )(   , c ga  , and c y = )( j cs is the nonzero entrance of j c of )(/)( tmm xx  . it is denoted by ),),(),(,,( cxxcr rtmymgg   . n.b.: any incidence matrix of a graph of groups may be made into an incidence matrix of a directed graph of groups, that by choosing )(tm x , a base row 1 rr   , an orientation on columns and then identifying c g with the image of )( ci g under the )( x m relevant monomorphism. wadhah s. jassim 44 for each directed column ),( tjijj xxc  in )( x m , let  c be c, and let ),( 1 ijtj xxc   be the inverse column with starting row )()( 1 jj cecs   , and )()( 1 jj csce   , where, jjij ycsx  )( , 1 )(   jjtj ycex and j y are the entries of the column j c , such that 1 j y , if ),( tjijj xxc  is in )(tm x . n.b. we will denote j c y by j y , (where, j c y are nonzero entries of ),( tjij ccj yyc  , xy ijc  , 1  xy tjc ), such that j c y is equal to 1 or -1, if )(tmc xj  . example: in this example, we will give a directed graph of groups and then, construct the incidence matrix of this directed graph of groups ),),(),(,,( cxxcr rtmymgg   . let the directed graph of groups ),,,,,( * eev vtygg  be as follows: 1 1 1 1 1 figure 1. the directed graph of groups constructed in [3] p72 of the pregroup given in [4] p41. the incidence matrix of the above directed graph of groups ),),(),(,,( cxxcr rtmymgg   is as below: 1 2 3 4 5 6 7 8 1 2 3 1 1 1 4 1 5 6 7 {1} {1, } {1, } {1} {1} {1} {1, } {1, } {1} 1 0 0 0 1 1 0 0 {1, } 1 1 0 0 0 0 0 {1, , , , } 0 1 0 0 0 0 0 0 {1, , , } 0 0 0 0 1 0 {1} 0 0 0 1 0 0 0 {1, } 0 0 0 0 0 1 1 1 {1, , , } 0 0 0 0 0 0 0 1 b b a a e e e e e e e e r b r x b b r a x bx ax bx r x r a r a a r                 figure 2. the incidence matrix of the directed graph of groups given in figure 1 above. }1{ 1   vv }1{1e },1{ 2 bv },1{ 2 be },,,1{ 3 bbv  x },1{ 3 be },,,1{ 11 4 bxaxbxxav  4 }1{ e  7 },1{ ea 6 },1{ va 6 }1{ e 7 },,,1{ vaa  8 },1{ ea 5 v }1{ 5 e incidence matrices of directed graphs 45 4. the up-down pregroup of an incidence matrix of a directed graph of finite groups. in this section we construct the updown pregroup of the incidence matrix of a directed graph of groups as below; let )( x m be the incidence matrix of a directed graph of groups ),),(),(,,( cxxcr rtmymgg   . the fundamental group of ))(( 11  x m has the following presentation:   )(/)(1),(1,),(;, 1 tmymcytmcygaaayyyg xxcxccccccr  . now for each directed column )(ymc x  , let c be also denoted by 1 c and let 1 c denote the inverse column with )()( 1 cecs   and )()( 1 csce   ; also let i c y be of form nn gyygygw n ..... 21 2110    , where 1 i and 1 i and 121 121 ,,,     n n ccc  is a circuit at  r , with rows     rrrrr n 121 ,,,  say, and where each i g is in ir g . a word of this form and any subword of it is reduced if it contains no subword cc yay .. 1 or 1 ).(.  ccc yay  , where c ga  . if it does contain such a subword, we can , using the relations, substitute )(a c  or a respectively to obtain a shorter word of the given form representing the same element. thus each element of the fundamental group is represented by a reduced word w of this form. its inverse is representable by the word 1 w defined in the usual way. moreover, by [13], the reduced word representing any element is unique modulo a succession of interleaving, i.e. substituting  hayga cc )(.. 1   for  ... hyg c or vice – versa for any c ga  . let )( x m be the incidence matrix of the directed graph of groups ),),(),(,,( cxxcr rtmymgg   and let n cccq ,,, 21  be an upward scale in )( x m which is a finite sequence of columns directed away of the base row r . let the rows of the scale q be n rrrr ,,, 21  . a word of type q is a word 12211 ..,....   nnn gygygygw  , where i ri gg  , 11  ni , and every word w must be reduced and i y is the nonzero entry of the starting row )( i cs of the column i c . now let k cccq ,,, 21  and h cccq  ,,, 21  be upward scales in )( x m both starting at  r . let 132211 .......   kkk gyggygygw  and 132211 .......   hh yggygygw  be words of type q and q respectively, where hk  . the word w is called an initial subword of the word w , written ww  , if jj cc  , and hence jj cc yy  , for kj 1 , and if jjjjjj gygyggygyg        ........... 111 1 1 1 1 1 1 1 1 1  is an element of , jr g for each j. lemma 4.1: the relation " is an initial subword of " is both transitive and tree incidence matrix like, that is ww  and ww  , then ww  , and if ww  , ww  , then either ww  or ww  . proof: the result follows directly from the definition. now let k cccq ,,, 21  and h cccq  ,,, 21  be upward scales in )( x m both of them starting at  r and ending at the same row r, and let k ggygygw ..... 32211  and h ggygygw  ...... 32211  be words of type q and q respectively, such that the elements h g and 1 k g are in r g , and then such a word 1ww is called an up – down word. for example, the word 1.1.1..1...1 xb is an up-down word, from figure 2 derived from the upward scales q, with rows  r and 5 r , and q , with rows  r , 542 &, rrr . let ))((  x mq be the set of all up-down words of the incidence matrix of a directed graph of groups )( x m . reducing an up-down word in )( x m gives another up-down. therefore, we assume that such a word is reduced. we use 1ww to denote an up-down word. lemma 4.2: let 1ww and 1zz be reduced up-down words, then )()( 111   zzww is in ))((  x mq if and only if w is an initial segment of z or z is an initial segment of w . proof: since the words 1ww and 1zz are both reduced, so reduction can only take place in the word )()( 111   zzww between the last c y of 1w and the first one of z . wadhah s. jassim 46 moreover )()( 111   zzww reduces to an up-down word if and only if either all c y in w or all c y in z are eliminated when putting )()( 111   zzww in reduced form. this happens if and only if w is an initial segment of z or z is an initial segment of w respectively. now we show that ))((  x mq is a pregroup. since ))((  x mq is a subset of ))(( 11  x m , so ))((  x mq satisfies conditions , 1 p 2 p and 4 p . it remains to be shown that ))((  x mq satisfies condition 5 p . define ))}((.;{)( 1111   x mqwwuuuuwwl , for ))(( 1   x mqww , as before. lemma 4.3: let 1ww and 1zz be reduced up-down words, then zw  , implies that 11   zzww . proof: suppose that zw  . to show 11   zzww , we must show that )( 1zzl is a subset of 1 ( ).l w w  if )()( 111   zzuu is in ))((  x mq , for some ))(( 1   x mquu , then , by lemma 4.2, z is an initial segment of u or u is an initial segment of z ( i.e. uz  or )zu  respectively. since zw  , in either case, by lemma 4.1, we have uw  or )wu  and then by lemma 4.2 again, )()( 111   wwuu is defined in ))((  x mq . therefore )( 1zzl is a subset of 1 ( ).l w w  hence 11   zzww . theorem 4.4: ))((  x mq is a pregroup. proof: to show ))((  x mq is a pregroup, we will show that ))((  x mq satisfies condition )( 5 iiip of lemma 2.4. therefore let 1ww and 1zz be reduced up-down words in ))((  x mq , and suppose that )()( 111   zzww is defined in ))((  x mq . hence by lemma 4.2, we have wz  or .w z  thus by lemma 4.3, 11   zzww or 1 1 .z z w w    therefore condition )( 5 iiip of lemma 2.4 holds in ))((  x mq . definition 4.5: the set of all up – down words of the incidence matrix of a directed graph of groups ))((  x mq is called the updown pregroup of ),),(),(,,( cxxcr rtmymgg   the incidence matrix of a directed graph of groups, where q is the updown pregroup of the directed graph of groups, as shown in [2] and [1]. theorem 4.6: the universal group of ))((  x mq (it is denoted by ))(((  x mqu ) is isomorphic to the fundamental group ))(( 11  x m . proof: since every element in ))((  x mq is an element in ))(( 11  x m , and since the tree incidence matrix )(tm x spans )(ym x and is directed away from r , every element of ))(( 11  x m can be written as a product of elements of ))((  x mq . moreover the partial multiplication in ))((  x mq implies the relations of ))(( 11  x m . 5. an algorithm for the up-down pregroup of incidence matrices of directed graphs of groups. let ),),(),(,,()( cxxcrx rtmymggm    be the incidence matrix of a directed graph of groups, then we use the representation of the directed graph of groups of an up-down pregroup, to write down all the elements of the up-down pregroup of that graph of groups by applying the following algorithm. the steps are given below: i) find all up words 1211 ......   nnn ijiiji gyggygw  of type upward scales 132211 ,,,,,,),(    nnn iiiiiiii rcrrcrcrrq  , where ik ri gg  , nk 1 and kj y is the nonzero entrance of the row k i r which is the starting of the column k j c , as defined above and then proceed step ii; ii) 1) if two up words 1211 .....   nnn ijiiji gyggygw  and 1211 ......   mmm ijiiii gyggygw  , ending at the same row i r , (i.e. row i r contains non-zero entrances of forms 1 ij x and 1 ik x ), then makes one of them an up word, say 1211 ......   mmm ijiiii gyggygw  and makes the other up word 1 ..... 211   nnniji gyggygw  , down word by changing the direction of all i g , columns and its entrance j y to be 111111 111 .....    ijiji gygygw nnn  , and by, identifying them we get an up-down word  1 .ww 111 32211 111 .............    ijjiimm gyyggyggygyg nnm  , (where, 1111 1 .    ninnn riii gggg ). then proceed to step iii; incidence matrices of directed graphs 47 2) if the up words 1211 .....   nnn ijiiji gyggygw  end at an isolated row, then change the direction of all columns and its label to be 111111 111 .....    ijiji gygygw nnn  , and by identifying them with the row i r that both of them end with i r , then we get an up-down word  1 .ww 1211 ..... nnn ijiiji gyggyg  . 11111 111 .....   ijiji gygyg nnn  = 1211 .....   nnn ijiiji gyggyg  . 1111 11 .....  ijij gygy nn  , ( where, 1111 1 .    ninnn riii gggg ). then proceed to step iii; iii) if there is no other up-down word, then stop. proposition 5.1: all up words 1211 ......   nnn ijiiji gyggygw  of type upward scales in ),),(),(,,()( cxxcrx rtmymggm    are same as all up words 1211 ......   nnn ijiiji gyggygw  of type upward paths in ),,,,,( ecr vtygg   . proof: since all vertices v and edges e in ),,,,,( ecr vtygg   are represented by rows r and columns c in ))( x m , and associated vertex groups v g and edge groups e g are represented by row groups r g and columns groups c g respectively, with entrances ij x of the labeled e y of the edges of ),,,,,( ecr vtygg   such that 1 e y if te  and 1 e y if tye  . therefore the direction and the labeling of columns of )( x m , are same as in ( , , , , , ). r c e g g y t v   hence all up words 1211 ......   nnn ijiiji gyggygw  of type upward scales in )( x m are same as all up words 1211 ......   nnn ijiiji gyggygw  of type upward paths in ),,,,,( ecr vtygg   . proposition 5.2: the algorithm must stop. proof: since the size of )( x m is mn  and all vertex groups and edge groups are finite, so )(xm is finite incidence matrix. by step i, we get all reduced upwords, by step ii we get all updown reduced words, and then by step iii, we will get all updown reduced words. since the origin xlabeled graph does not contain loops, so the set of all reduced up-down words is finite and then the algorithm must be stop after a finite time. 6. conclusion we have given a new application for the incidence matrices of x-labeled graphs. this application is the incidence matrices of directed graph of finite groups. therefore, we have added certain conditions to allow the incidence of x labeled graphs to be more confident with the definition of the directed graph of finite groups. by this way we can write a computer program to record all elements of the updown pregroups of that the directed graphs of finite groups. references 1. jassim, w.s. incidence matrices of x-labeled graphs and an application, sultan qaboos university journal for science, 2009, 14, 61-69. 2. hoare, a.h.m. and jassim, w.s. directed graphs of groups and their up-down pregroups, faculty of science bulletin, sana'a university, 2004, 17, 137-154. 3. jassim, w.s. pregroups and graphs of groups, ph.d. thesis, birmingham university, 1992. 4. rimlinger, f. pregroups and bass – serre theory. american mathematical society memoirs, 1987. 5. baer, r. free sums of groups and their generalizations iii. american journal of mathematics, 1950, 647-670. 6. stallings, j.p. group theory and three dim. manifolds. yale monographs, 1971. 7. hoare, a.h.m. pregroups and length functions. proceedings of the cambridge philosophical society. 1988, 2130. 8. stallings, j.p. adyan groups and pregroups, essays in group theory, msri publications 8ed. by s.m. gersten, 1987. 9. abdu, k.a. representing core graphs and nickolas's algorithm. m.sc. thesis, baghdad university, 1999. 10. chiswell, i.m. abstract length functions in groups. proceedings of the cambridge philosophical society. 1976, 417-429. 11. jassim, w.s. directed core graphs and their up-down pregroups, al-mustansiriya journal of science, 2006, 17(4): 68-81. 12. lyndon, r.c. length functions in groups. mathematica scandinavica, 1963, 209-234. 13. serre, j.p. 1968. groupes discrets. college de france. translation, trees. springer verlag, 1980. received 10 september 2015 accepted 7 december 2016 squ journal for science, 2022, 27(1), 19-34 doi:10.53539/squjs.vol27iss1pp19-34 sultan qaboos university 19 development and validation of an rp-hplcfld method for the determination of biogenic amines after pre-column derivatization with a new pyrazoline based reagent, 3naphthyl-1-(4-trifluoromethyl)-5(4-carboxy phenyl)-2-pyrazoline amal al sabahi, saleh al busafi, beena varghese, salma mohamed al-kindy* fakhreldin osman suliman department of chemistry, college of science, sultan qaboos university, box 36, al-khodh 123, oman, *e-mail: alkindy@squ.edu.om. abstract: application of 3-naphthyl-1-(4-trifluoromethyl)-5-(4-carboxy phenyl)-2-pyrazoline (nfcp) as a novel fluorigenic label for the derivatization of biogenic amines (bas) and separation by liquid chromatography (lc) was investigated. optimum conditions for the pre-column derivatization and chromatographic separation were investigated. the resulting derivatives are fluorescent at λex/λem: 380/460 nm. for the sake of evaluating the efficacy of the proposed analysis of bas of different nature, the formation of nine nfcp-bas derivatives was tested individually. simultaneous derivatization and separation of four bas (histamine, tyramine, tryptamine, and phenylethylamine) were achieved under the isocratic elution mode. furthermore, the derivatives were identified by the characteristic product ion obtained during lc-ms/ms analysis. the viability of the method was established by measuring levels of histamine in fresh and spoiled fish samples. histamine concentrations were found to be 0.4 µgg -1 and 4.1 µgg -1 in fresh and spoiled tuna fish samples respectively. as a simple, reliable, and sensitive pre-column derivatization method, this work provides for future research to develop a novel hplc method for the analysis of bas from food samples such as fish and various other matrices by utilizing the new pyrazoline compound. keywords: pyrazoline, biogenic amines, hplc, lc-ms/ms, sample analysis باستخدام ها قبل العمودلتحديد األمينات الحيوية التي يتم اشتقاق rp-hplc-fld فاعلية التحليل بطريقة من طوير والتحققت بيرازولين -2-كربوكسي فينايل(-4-5-ثالثي فلوروميثايل(-4)-1-نفثايل-3كاشف جديد قائم على البيرازولين، و فخرالدين عثمان سليمان سلمى الكندي ،بينا فرجيز أمل الصبحي، صالح البوصافي، البتتتتتايرازولين كمركتتتتتى فلوروستتتتتينى جديتتتتتد شتتتتتتقا -2-فينيتتتتتل الكاربوكستتتتتيل(-4)-5-ثالثتتتتتى فلتتتتتورو ميثيتتتتتل(-4)-1-نافثيتتتتتل-3استتتتتتخدم :صلخ مال (. تتتتتتم دراستتتتتة الىتتتتترو المثلتتتتتى شتتتتتتقا متتتتتا قبتتتتتل الفتتتتتتل (lc)األمينتتتتتات الحيويتتتتتة ومتتتتتن ثتتتتتم فتتتتتتلها عتتتتتن ريتتتتتق الكروماتوجرافيتتتتتا الستتتتتائلة نتتتانومتر. متتتن يجتتتل تقيتتتيم فاعليتتتة ريقتتتة التحليتتتل المقتر تتتة لتتت مينات λex / em: 380/460الكرومتتتاتوجرافي. الماتتتتقات الناتةتتتة ماتتتعة عنتتتد . تتتتم التحقتتتق متتتن ا شتتتتقا والفتتتتل المتتتت امن الحيويتتتة ات الطبيعتتتة المختلفتتتة ، تتتتم اتتبتتتار تكتتتوين تستتتعة ماتتتتقات باتتتكل فتتترد متتت المركتتتى الةديتتتد ألربعتتتتة مركبتتتتات ) يستتتتتامين ، وتيتتتترامين ، وتريبتتتتتامين ، وفينيتتتتل كيثيتتتتل يمتتتتين(. عتتتتالو علتتتتى لتتتت ، تتتتتم تحديتتتتد الماتتتتتقات بواستتتتطة ييتتتتو المنتتتتت ات الهيستتتتامين فتتتي عينتتتات . تتتتم كثبتتتات جتتتدو الطريقتتتة متتتن تتتتالة قيتتتا مستتتتويlc-ms / msاألساستتتى التتتا تتتتم الحتتتتوة عليتتت بواستتتطة تحليتتتل ميكروجرام/جتتتترام( فتتتتي عينتتتتات 4.1ميكروجرام/جتتتترام( و ) 4.4األستتتتماط الطازجتتتتة والفاستتتتد كتتتتل علتتتتى تتتتدي. وجتتتتد ي تركيتتتت الهيستتتتتامين كتتتتا ) بلي ا لتطتتتوير يستتتماط التونتتتة الطازجتتتة والفاستتتد علتتتى التتتتوالي. كطريقتتتة اشتتتتقا بستتتيطة وموثوقتتتة و ساستتتة قبتتتل الفتتتتل ، يتتتوفر تتتاا العمتتتل بحث تتتا مستتتتق جديتتتد لتحليتتتل درجتتتات األمينتتتات الحيويتتتتة فتتتى عينتتتات الطعتتتام مثتتتل األستتتماط ومتتتتواد يتتتتر متنوعتتتة متتتن تتتتالة استتتتخدام مركبتتتتات hplc ريقتتتة البيرازولين الةديد . salma al-kindy et al. 20 يف الكتلة/ يف الكتلة-، الكروماتوغرافيا السائلة hplcبيرازولين، األمينات الحيوية، الكروماتوغرافيا السائلة مرتفعة األداء :مفتاحيةالكلمات ال -ms/ms lc .تحليل العينات ، 1. introduction n area of research that is very active in separation science is the development of new fluorescent probes for tagging and labeling organic functional groups, before trace analysis using sensitive analytical instruments. among the more promising compounds that offer versatility, the heterocycles have generated an increasing interest for application in many areas. however, their application in fluorescent labeling is still limited. sufficient flexibility in synthetic strategies, derivatization procedures, and efficiency in modulating the charge transfer process throughout the system are the key aspects to consider while designing a labeling reagent. in this regard, one group of electron-rich nitrogen heterocycles, pyrazolines, has received our attention as a useful candidate for tagging the analytes of interest. there is a huge amount of research on the exploitation of the blue light emission efficiency of this organic skeleton in multi-disciplinary areas such as dye-sensitized solar cells, organic light-emitting diodes (oleds), organic field effect transistors (ofets), sensors, nonlinear optical (nlo) devices, the textile industry and electrophotography [1-9]. in the area of biomedical applications, these compounds are widely used as anti-microbial, anti-amoebic, anti-nociceptive, anti-cancer, anti-depressant, anti-inflammatory, anticonvulsant, anti-fungal, anti-hyperglycemic, anti-epileptic, anti-malarial, antipyretic, and so on [10-17]. it is known that the optical behaviors of pyrazoline derivatives are medium sensitive and they are being adapted to method development in bioanalytical applications. for this to be widely adopted, in this work we have evaluated the reactivity of a recently introduced pyrazoline dye, 3naphthyl-1-(4trifluoromethyl)-5-(4-carboxy phenyl)-2-pyrazoline (nfcp) for tagging biogenic amines (bas) under optimized derivatization conditions. biogenic amines are basic nitrogenous compounds with a small mass. they are present in large quantities in food and beverages. the main bas occurring in foods are histamine, tyramine, tryptamine, phenylethylamine, putrescine, cadaverine, spermine, and spermidine. they are formed as a result of enzymatic action on poor-quality raw materials, contamination, or are generated under unhygienic conditions during aging and storage, because of microbial decarboxylation of food amino acids [18-21]. when present in food samples in low concentration, bas do not pose a serious risk to humans. however, high levels of bas are notoriously worrisome in terms of the detrimental effects they can have on our health. for instance, cadaverine, histamine, and putrescine may cause hypotension. in severe cases, the presence of tyramine may bring about death while mild cases result in hypertension, headache, dizziness, cardiac palpitation, nausea, intracerebral hemorrhage, and anaphylactic shock syndrome [22-24]. the presence of bas in food samples indicates food spoilage; hence, the determination of bas is important for the quality control of food commodities. to this end, chromatographic techniques have found wide applications due to their high sensitivity and adaptability for simultaneous quantification of most bas [24]. since bas are either weakly chromophoric or nonfluorogenic; the tagging of these molecules to the chromophores or fluorophores is essential to improve the detection of derivatized bas using uv and fluorescence techniques [25]. it can be noted that pre / post-column derivatization technique with uv-vis /fluorigenic labels in conjunction with high-performance liquid chromatography (hplc), has successfully overcome the challenges in detection due to lack of volatility and chromophores. in addition, pre-column derivatizations of polar bas are often needed, to reduce their polarity and to improve the resolution in reversed-phase hplc columns [25]. various fluorescent reagents such as o-phthaldialdehyde (opa), 5-dimethylaminonaphthalene-1-sulfonyl chloride (dns-cl), benzoyl chloride, 9fluorenyl methyl chloroformate (fmoc-cl), 4-fluoro-3dinitrofluoro-methylbenzene (fnbt), 2-chloro-1,3-dinitro-5-(trifluoromethyl)benzene, 4-chloro-3,5-dinitrobenzotrifluoride (cnbf), 4-dimethylaminoazobenzene-4ˊ-sulfonyl chloride (dbs-cl), fluorescamine, mercaptopropionic acid (3-mpa), 2-mercaptoethanol, 6-aminoquinolyl-n-hydroxysuccinimidyl carbamate (aqc), para-nitrobenzyloxycarbonyl chloride (pnz-cl), and 3,5-dinitro benzoyl chloride (dnbz-cl) have proved their efficiency in bas labeling [26-38]. fish and fish products constitute an important source of proteins, minerals, and vitamins. fish foods that are widely consumed all over the world. they form an integral part of the regular diets of many due to their high nutritional content, low caloric value, ease of digestibility, and moderate cost. however, if not properly preserved, fish is easily perishable and is susceptible to the formation of bas, which leads to the loss of quality, and it can undergo deterioration and spoilage. the presence of bas in fish is an indicator of the quality of the freshness or spoilage of food and gives information about the edibility of fish [18]. hence, to this end, several studies on the determination of bas in fish have been reported in the literature [25, 27, 39-43]. these methods include liquid chromatography-tandem mass spectrometry [39, 40], ion chromatography [41], the hplc method with fluorescence detection [25, 27, 42], and the colorimetric and fluorescence method [43], to mention a few. to the best of our knowledge, the methods reported in the literature for the determination of bas are devoid of any compounds based on the pyrazoline scaffold. to a development and validation of an rp-hplc-fld method 21 address this omission, this work has focused on (i) testing the suitability of nfcp for the pre-column derivatization of bas, (ii) optimizing the derivatization as well as chromatographic parameters to maximize the yield and fluorescence response, (iii) confirming the structure of nfcp-bas using lc/ms/ms, (iv) demonstrating the practical application of the validated method on fish matrix. 2. experimental 2.1 reagents and chemicals analytical grade reagents purchased from sigma-aldrich, usa, and ultrapure water from a milli-q water purification system (millipore, billerica, ma, usa) were used in this study. the fish samples (goatfish, white tuna fish, and cobia fish) were collected from the local market. synthesis of nfcp has been published elsewhere [44]. the biogenic amines used in this study are 2phenylethylamine (pea), tyramine (tyr), dopamine (da), octopamine (oct), synephrine (syn), ephedrine (eph), histamine (his), tryptamine (try), and serotonin (ser). a 3 mmol l -1 stock solution of nfcp was prepared in acetonitrile. a standard stock solution of each of the studied bas (10 mmol l -1 ) was individually prepared in a phosphate buffer of ph 8.5. working solutions were produced daily by dilution with the same buffer. the activation reagents n-(3-dimethyl aminopropyl)-n'-ethyl carbodiimide hydrochloride, edc.hcl (0.1 mol l -1 ) and dimethylamino pyridine, dmap (0.4 mol l -1 ) were also prepared in acetonitrile. all standards were stored in a refrigerator at 4 c. all solutions were filtered through a 0.45 µm nylon membrane filter (thomas scientific, usa). 2.2 apparatus derivatization was carried out after mixing the contents on a stuart vortex mixer sa8 (uk) at 1400 rpm and heating on a b490 butchi heating bath (switzerland). a cole parmer ultrasonic instrument (cole parmer, usa) was used for degassing of the solvents, while clinspin horizon 642e -woodley equipment (fischer scientific, usa), was used for all centrifugation activities. monitoring of ph was carried out on a thermo ph meter (russell rl060p, singapore). 2.3 high-performance liquid chromatography (hplc) the analysis of nfcp-bas derivatives was performed on a hplc agilent 1260 infinity capillary lc, usa unit equipped with a g1376a binary capillary pump, g1377a autosampler, and coupled to a g1315c uv diode array detector and a g13218 fluorescence detector. the column compartment (g1316a) was maintained at a constant temperature by a thermostat. open lab chemstation (version c.01.04) software was used to control the chromatographic system. nfcp derivatized bas were separated on a reversed-phase poroshell ec-c18 column (100 mm× 3.0 mm, particle size 2.7 µm) and were eluted under isocratic conditions using 80:20, v/v acetonitrile and water mobile phase at a flow rate of 0.2 ml min -1 . the column temperature was maintained at 40°c throughout the separation process. before the analysis, the column was pre-equilibrated with the mobile phase for 30 min. 1 μl samples volumes were injected onto the column. detection in the uv mode was carried out at λmax of 360 nm. on the other hand, fluorescence was monitored at 460 nm with the excitation wavelength set up at 380 nm. all the sample analysis was performed in triplicate and the mean result was reported. 2.4 liquid chromatography-mass spectrometry (lc-ms/ms) for the mass-spectrometric analysis, a triple quadrupole mass spectrometer (shimadzu 8040, japan) was used. ionization was carried out with an electrospray ionization source (esi). the operating conditions were set as follows: esi temperature 400 c, the desolvation line (dl) 250 c, 3 l min -1 flow rate of argon (nebulizing gas), and 15 l min -1 flow rate of drying gas. the lc-ms was fitted with a poroshell ec-c18 column (100 mm, 3.0 mm, 2.7 µm) and controlled by lab-solutions software. separation of nfcp-bas was achieved using a mobile phase composed of a (acetonitrile), b (0.1% formic acid and water) at 80-20 % (v/v). the pump was operated under a low-pressure gradient at a flow rate of 0.2 ml min -1 . the oven temperature was set at 40 c for all of the separation processes. the mass analyzers q1 and q3 were operated at a unit mass resolution. 2.5 derivatization procedure the derivatization reaction is shown in scheme 1. to an eppendorf vial (2 ml), 100 µl of nfcp, edc. hcl, and dmap were added consecutively and the contents were vortexed for half a minute. then 100 µl of bas mixture was added dropwise with vortex mixing for at least 30 seconds, after which the mixture was made up to 1 ml with acetonitrile. the reaction mixture was maintained at 65 c for 40 min and cooled to ambient temperature before injecting a 1-µl sample into the hplc column. salma al-kindy et al. 22 scheme 1. derivatization reaction of nfcp with a representative amine, tyramine. reaction conditions: (i) acetonitrile, (ii) [nfcp/ba] 0.3/0.025 mmol l -1 , (iii) [edc/dmap] 0.1 / 0.4 mmol l -1 , (iv) temperature 40 0 c and (v) time 60 minutes. 2.6 pre-treatment of the fish samples the three fish samples (goatfish, white tuna fish, and cobia fish) were first divided into two portions. the first part was immediately stored in the freezer at -10 c and the latter which was kept at room temperature for 48 hrs. all fish samples (5 g of each) were homogenized separately before extraction using a mortar and dissolved in 10 ml of 5% trichloroacetic acid (tca). after being sonicated, the mixture was centrifuged at 6000 rpm for 30 minutes three times, to ensure complete extraction of biogenic amines. when not in use, the collected supernatant was stored at 4 c after filtration through a 0.45 µm filter paper. working solutions were prepared as follows: into a 5 ml volumetric flask were added 1 ml of the biogenic amine extract followed by 0.4 ml of 1 m naoh. the contents were made up to the mark with a ph 8.5 phosphate buffer solution. 2.7 analytical performance of the method the proposed method was validated in terms of the analytical parameters for quality assurance by the ich guidelines (international conference on harmonization tripartite guideline: validation of analytical procedures) [45]. linearity was assessed by plotting calibration curves of four bas' standard concentrations in the range between 0.5 µmol l -1 to 100 µmol l -1 . each standard was injected three times. correlation coefficients (r 2 ) were calculated using least-squares regression; the limits of detection (ld) and the limits of quantification (lq) were evaluated using the equation 3/m and 10/m respectively where  is the standard deviation of the y-intercept of the regression analysis and m is the slope of the calibration curve. accuracy was established by injecting standard solutions of bas at three different concentrations (4, 10, and 40) µmol l -1 , with six replicates. the intra-day and inter-day analysis, which is taken to be the relative standard deviations (rsd) was determined from the peak areas of the four derivatives’ six replicates (n=6) for three different concentrations above on the same day and four consecutive days, respectively. recovery and matrix effect was estimated by fortification of fresh and spoiled tuna extract with bas standard ranging from 0 to 25 µmol l -1 . standard additions plots were constructed and the slopes were matched with standard solutions prepared in water. the matrix effect is given by the equation = (sm/ss) × 100%, where sm and ss represent the slope of the calibration curve of each analyte in matrix solutions and standard working solutions, respectively. the recovery of histamine in this method was estimated by the standard addition method; by adding four concentration levels of histamine (2.5-25µmol l -1 ) to two types of fish samples (fresh and spoiled white tuna). 3. results and discussion 3.1 hplc and lc-ms/ms analysis conventionally, the reaction map for the condensation of amines and carboxylic acids involves thionyl chloride (socl2) or the combination of various activation reagents with some base catalysts. based on introductory experiences, it seemed likely that the conversion of –cooh to –cocl and later replacement by an amino group would be viable for the synthesis of crude derivatives; but it leads to unknown interference in the chromatogram. acetonitrile is appropriate for derivatization as well as chromatographic separation involving pyrazoline-based probes since most of the reagents used are soluble in acetonitrile and are favorably compatible with the hplc system. much of the literature features examples of different activation agents for an efficient coupling reaction to trigger a favorable development and validation of an rp-hplc-fld method 23 derivatization reaction with the desired chromatographic separations, [46-47] the most prominent example is the combination of 2, 2'-dipyridyl disulfide, (dpds) with triphenylphosphine (tpp) [46]. the high moisture sensitivity, storage under inert conditions to avoid inactivation and the relatively weaker derivative peaks reduce our interest in these reagents. on the other hand, 4-ethyl dimethylamino propyl carbodiimide with 4-dimethylaminopyridine (edc/dmap) couple was found to be best for the derivatization of bas at very low concentrations. in addition, it features longer stability and faster reaction, and more importantly, there is no need for product extraction from the reaction system before sample analysis in the hplc. for the derivatization of aromatic bas with edc, it was reported that the coupling efficiency is six times greater than its counterpart dcc (dicyclohexyl carbodiimide) when an equal concentration of both coupling reagents was used and its . superiority to four other coupling reagents was emphasized [47]. the edc.hcl (0.1 mol l -1 )/dmap (0.4 mol l -1 ) coupling system was selected as undoubtedly being the optimum for the reaction of biogenic amines with nfcp. as shown in figure 1, as the concentration of the labeling reagent increases, the fluorescence intensity of the derivatives and hence yield was observed to increase. a rapid increase in the intensity was observed when the concentration of npcp rises from 0.2 to 0.3 mmol l -1 . no further increase in the intensity was observed beyond 0.3 mmol l -1 . these results indicate that the maximum yield of the derivatives was obtained using an nfcp concentration of 0.3 mmol l -1 , which is equal to tenfold the concentration of the biogenic amine mixture (his, tyr, try, and pea) in the reaction vial. to drive the equilibrium towards the formation of the derivative a high excess of the reagent is required. similar results were previously obtained for the derivatization reaction of alcohols and nfcp label whereby an optimum concentration of nfcp to alcohol was 5:1 [48]. figure 1. effect of nfcp concentration on the labeling reaction of four biogenic amines. chromatographic conditions: poroshell ecc18 column (100 mm, 3.0 mm, 2.7 µm), acn-water (80 %v/v), flow rate 200 µl min -1 ; ex/em: 380/460 nm, column temperature 40 c; reaction conditions: [bas] 0.025 mmol l -1 , [edc/dmap] 0.1/0.4 mmoll -1 , acetonitrile, 65 c, 40 min. time and temperature are considered to be significant factors influencing reaction kinetics. therefore, to optimize these factors, the derivatization reaction was carried out at 20, 40, 60, 80, and 100 mins. figure 2 shows that a reasonable yield of the nfcp-bas derivatives was achieved at a reaction time of 20 minutes; however, the highest peak areas were attained at 40 minutes. reaction yields of the derivatives obtained at different temperatures were compared and it was found that his and tyr produced maximum efficiency at 65 c, whereas the peak area of try and pea derivatives at 50 c was slightly higher than those at 65 and 80 c (figure 3). accordingly, 40 minutes and 65 c were selected to be the optimal values for time and temperature, respectively. salma al-kindy et al. 24 figure 2. effect of derivatization time on the labeling reaction of four biogenic amines. chromatographic conditions: poroshell ecc18 column (100 mm, 3.0 mm, 2.7 µm), acn-water (80 %v/v), flow rate 200 µl min -1 ; ex/em: 380/460 nm, column temperature 40 c; reaction conditions: [nfcp] 0.3 mmoll -1 , [bas] 0.025 mmol l -1 , [edc/dmap] 0.1/0.4 mmoll -1 , acetonitrile, 65 c. figure 3. effect of derivatization temperature on the labeling reaction of four biogenic amines. chromatographic conditions: poroshell ecc18 column (100 mm, 3.0 mm, 2.7 µm), acn-water (80 %v/v), flow rate 200 µl min -1 ; ex/em: 380/460 nm, column temperature 40 c; reaction conditions: [nfcp] 0.3 mmoll -1 , [bas] 0.025 mmol l -1 , [edc/dmap] 0.1/0.4 mmoll -1 , acetonitrile, 65 c. it could be expected that the derivatization reaction involving –cooh and -nh2 is catalyzed in a basic media and that the ph of the solution has to be above the pka of amines. to switch on a nucleophilic development and validation of an rp-hplc-fld method 25 acyl substitution reaction, the phosphate, acetate, and formate buffers of ph 8.5 were employed and it was found that nfcp – bas derivatives were not formed with acetate and formate buffers. then, the optimum ph value of the phosphate buffer was examined (figure 4). since the maximum response was revealed as between ph 8 and 9.5, ph 8.5 was chosen for subsequent work. the optimized derivatization method was applied to nine bas of different nature: pea and tyr (primary), syn and eph (secondary), his and ser (highly polar), pea (less polar), da and oct. the formation of all derivatives was tested individually and finally, four of the bas (his, tyr, tryp, pea) were selected to perform the quality control procedure to validate our newly developed method. a graphical representation of the overall study is shown in scheme 2. figure 4. the effect of ph on the labeling reaction of nfcp-bas. chromatographic conditions: poroshell ecc18 column (100 mm, 3.0 mm, 2.7 µm), acn-water (80 %v/v), flow rate 200 µl min-1; λex/λem: 380/460 nm, column temperature 40 o c; reaction conditions: [nfcp] 0.3 mmoll -1 , [bas] 0.025 mmol l -1, [edc/dmap] 0.1/0.4 mmoll -1 , acetonitrile, 65 o c, 40 min. scheme 2: a graphical illustration of the overall study. among the analytical columns of varying particle and dimensions, a poroshell c18 column (100 mm × 3.0 mm × 2.7 µm) was found to be most efficient to elute the derivatives in good resolution and shortened analysis time. the best mobile phase was tested with acetonitrile-water composition, along with salma al-kindy et al. 26 phosphate, formate, and acetate buffers at ph 8.5, and no noticeable changes were observed. however, later in the method development, we chose pure water to overcome the risk of the accumulation of salts in the column, which would affect its lifetime. the proportion of water was limited to 20% to avoid the quenching of peaks. the optimum excitation wavelength was selected after scanning the analytical signals for the derivatives at different excitation wavelengths. a wavelength of 380 nm was found to be the best for the detection of all of the derivatives studied. moreover, the optimum emission wavelength was obtained by conducting multi-emission wavelengths at 380 nm using the fluorescence detector in the instrument. as a result, 460 nm was taken to be the optimum fluorescence wavelength for all derivatives throughout the run. besides the evident success of derivatization and hplc separation, it was noted that a sole peak appeared along with the main derivative peak of bas used for hplc analysis, but that it was only 1/10 of the size of the main peak height (figure 5a and 5b). interestingly, the resolution of the peaks of interest is not affected by these peaks. a change of column and acetonitrile gradient to separate the daughter peak from the parent was unsuccessful. finally, the four biogenic amines mixture was separated. the resultant chromatogram is shown in figure 6. figure 5a and 5b. chromatograms of dopamine and synephrine derivatives. chromatographic conditions: chromatographic conditions: poroshell ecc18 column (100 mm, 3.0 mm, 2.7 µm), acn-water (80 %v/v), flow rate 200 µl min -1 , ex/em: 380/460 nm, column temperature 40 c; reaction conditions: [nfcp] 0.3 mmoll -1 , [bas] 0.025 mmol l -1 , [edc/dmap] 0.1/0.4 mmoll -1 , acetonitrile, 65 c, 40 min. (5a) (5b) development and validation of an rp-hplc-fld method 27 figure 6. chromatogram of four biogenic amines derivatives with nfcp. chromatographic conditions: poroshell ecc18 column (100 mm, 3.0 mm, 2.7 µm), acn-water (80 %v/v), flow rate 200 µl min -1 ; ex/em: 380/460 nm; reaction conditions: [nfcp] 0.3 mmol l -1 , [bas] 0.025 mmol l -1 , [edc/dmap] 0.1/0.4 mmoll -1 , acetonitrile, 65 c, 40 min. nfcp peak at 2.1 min, histamine at 4.2 min, tyramine at 5.6 min, tryptamine at 7.7 min, phenylethylamine at 9.4 min. the four derivatives were characterized by ms/ms and the fragmentation patterns identified. characterization was brought about by the direct infusion of the standard solution derivative of each analyte at their retention times when passed through the hplc column with the same mobile phase and flow rate. in this study, the molecular ions and diagnostic fragments of all the nfcp – bas derivatives (except of histamine. because of their low abundance), were generated by negative ionization mode, [mh] . running the q1 scan for the peaks that appeared at specified retention times revealed that the molecular mass of smaller peaks matched well with the abundant production. in response to this, it is suggested that nfcp-bas derivatives exhibit cis-trans isomerism and eluted as two closer peaks since they have close polarity. it can be presumed that the dominant peak belongs to the trans-form and the cis-isomer migrates slowly and is then eluted as a baby peak. this trend was observed in the product ion spectra of all derivatives in which the parent peaks are at the m/z 562.3, 578.3, and 601.3, corresponding to the [m-h] of the derivatives in trans-form (figure 7). on the other hand, the small intensity peaks registered at m/z 563.62, 579.3, and 602.3 reflect the cis-form. the loss of cf3 and c4h8o fragments were shown in the spectra of tyr-derivative at m/z 509.1 and 541.3, but seem to be negligible. the [m-h] spectrum of his derivative shows the parent peak at m/z 577.5. 3.2 analytical parameters and sample analysis under the optimized derivatization, separation, and detection conditions, calibration curves for the four derivatives studied were linear, with the calibration equation of 42.35±(0.48)x+59.00±(15.22), 72.40±(1.00)x-106.65±(25.46), 74.50±(0.97)x+536.41±0.74) , 85.47± (0.86)x+220.93±(27.31) with r 2 values of 0.997, 0.996, 0.998 and 0.996 for his, tyr, tryp and pea, respectively. since the volume of the injected sample was 1μl, the lowest detection limits (lod) for pea, his, tyr, and try are 0.9, 1.1, 1.1, and 1.2 µmol l -1 and quantification (loq) limits are 3.2, 3.6, 3.5 and 4.1 µmol l -1 , respectively. the comparison of initial response with the peak areas of the bas derivatives stored in the instrument at room temperature for one week showed only minor variations of 1.1 to 9.9 %, highlighting its considerable stability. for assessing the stability of derivatives in the fish matrix, fresh tuna solution was spiked with bas and the differences in peak areas were analyzed for three consecutive days. the rsd values within 2.87 seem to be satisfactory for the first two days but a decrease in the absolute peak area on the third day emphasizes the derivative degradation after two days at room temperature. salma al-kindy et al. 28 figure 7. the lc-ms/ms spectra of nfcp(a) pea (b) tyr (c) try and (d) his derivatives. development and validation of an rp-hplc-fld method 29 the values obtained for intra-day precision range from 0.18-1.54, 0.32-1.41, 0.221.06, and 0.181.37 for his, tyr, tryp, and pea, verifying the excellent repeatability and reproducibility of the entire analytical procedure (table 1). table 1. intraday precision, stability of derivatives in the matrix, and the matrix effect. the superscripts ‘a’ denote concentrations in µmol l-1, ‘b’ stability measured in fresh tuna matrix, nm=not measured. his=histamine, tyr=tyramine, try=tryptamine, pea=phenylethylamine. rsd=rrelative standard deviation, sd= standard deviation. sm= slope of calibration curve of the analyte in matrix solutions, ss= slope of calibration curve of the analyte in standard working solutions. to assess the reliability and selectivity of the hplc method, the matrix effect was tested by adding 0 to 25 µmol l -1 standards to the fish sample solution, his, tyr, and tryp (pea, not measured). the slopes of the linear calibration curves for the studied biogenic amines in the solvent were compared with the slopes of the same analyte in the fresh or spoiled fish matrix. the matrix effect values obtained were 76.9, 81.1, and 87.7 % of the fish solution, respectively, which inferred the strong effect of the matrix solution on the complete derivatization of the mentioned bas. the fish extract is expected to also contain various amounts of biogenic amines other than the ones studied in this work and this broad matrix contribution may consume some amounts of the derivatization reagents leading to variable chances of the studied analytes to be derivatized. the selectivity of the assay was evaluated by analyzing extracts from three types of fish samples, and no interference from the matrix was observed with the evaluated bas in any of the samples studied as shown in figure 8. however, the presence of additional peaks, other than the studied bas, was observed in the chromatogram (figure 8). figure 8. chromatograms of biogenic amines (his, tyr, tryp, pea) spiked in the fish matrix solution at concentration, (i) 0, (ii) 5, and (iii) 10 µmol l -1 , after derivatization with nfcp at optimum conditions. 3.3 method application contemplated as major indices of fish spoilage and poisoning, the maximum acceptable limit of histamine in fish was adopted by european union and the u.s. food and drug administration as 200 mg kg −1 and 50 mg kg −1 , respectively [49-50]. the proposed method was evaluated in the determination of histamine in two types of fish samples (fresh and spoiled white tuna). the result indicates 0.4 µg g −1 of histamine in fresh goatfish as well as tuna samples and as expected, higher content (4.1 µg g −1 ) in spoiled tuna. on the other hand, no traces of histamine were found in the fresh cobia sample (table 2). biogenic amine precision (%rsd) stability (%rsd) b matrix effect sd (sm/ss)100% 4 a 10 a 40 a 2.5 5 10 his 1.55 1.30 0.18 1.05 0 1.05 76.9  3.7 tyr 1.41 0.93 0.32 1.19 1.04 81.1  12.0 try 1.06 0.75 0.22 2.89 1.07 2.87 87.7  1.7 pea 1.37 1.20 0.18 0.50 0.50 1.25 nm salma al-kindy et al. 30 table 2. quantification of histamine in different fish samples. nd-not detected 3.4 comparison with other methods to reveal the uniqueness of nfcp over other frequently used reagents for amine labeling, a comparison was done with the performance parameters of some existing methods. it is inferred from table 3 that the method developed has an advantage over other existing methods for some substances. among the reported reagents from references [51-61], the amine derivatives were detected by fluorescence (fl) response, whereas cnbf, dnbz-cl derivatives were by their absorption at 254 and 260 nm, respectively, and deemm by photodiode array (pd) detector at 280 nm. regarding the detection wavelength, except in opa and dns-cl (523 nm), all other derivatives were reported in the wavelength range between 315 and 440 nm. the typical intra-molecular charge transfer (ict) characteristics of pyrazoline derivatives are reflected in the optimal emission wavelengths of nfcpbas at 460 nm. moreover, the derivatization reaction is simple, being a single step of adding and mixing the reagents in less than one minute, and has reasonable reaction completion at 20 minutes. it does not require a lengthy procedure in extracting the derivative from the reaction media or derivative cleanup before injection. this is outstanding when revisiting reagents (fmoc-cl, opa, opa/2-me, bc, dnbz-cl, and dns-cl) which involve complications in the formation of multiple derivatives and significant interference if the excess reagent is not extracted or carefully controlled before chromatographic separation. table 3. comparison of the derivatization conditions and detection limit of some common reagents reported for amines. reagent matrix derivatization conditions lod ref. time temp alkaline medium ph µmol l -1 fmoc-cl fish 30 rt borate buffer. 10 1.97×10 -7 3.12 × 10 -6 50 opa fish >5 rt potassium borate buf 12 13.49* 51 opa-2me milk, beer >1 rt borate buffer. 10 9×10 -5 -3.1×10 -4 52 dns-cl wine 25 nr naoh 11 0.02-0.31 53 dbs-cl wine 116 70 hcl–tdpa 8.2 0.08-0.69 54 bc wine 10 25 naoh nr 6.44-18.22* 55 bcec-cl shrimp catsup 3 rt borate buffer. 9 1.77×10 -12 1.44×10 -11 56 eac food sample 1 6 55 borate buffer. 9.7 2.2×10 -3 -3.3×10 3 57 aqua musts, wines nr rt borate buffer. 8.8 4.53×10 -3 -0.20 58 dnbz-cl food sample 2 3 rt naoh nr 0.95-6.29 59 deemm wine 150 80 borate buffer. 9 0.20-0.39 60 cnbf nfcp beer fish 30 40 60 65 borate buffer. phosphate buffer. 9.5 8.5 0.056-0.87 0.9 1.2 61 current work reagent: fmoc-cl-fluorenylmethyloxycarbonyl chloride, opao-phthaldialdehyde, opa-2meo phthaldialdehyde/ 2-mercaptoethanol, dns-cldansyl chloride, dbs-cldabsyl chloride, bc-benzoyl chloride, bcec-cl2-(11h-benzo[a]carbazol-11-yl) ethyl chloroformate, eac-ethyl-acridine-sulfonyl found sample µmol l -1 sd µg/ g sample fresh tuna 0.800.23 0.4 spoiled tuna 7.380.66 4.1 fresh goatfish 0.790.23 0.4 fresh cobia nd nd development and validation of an rp-hplc-fld method 31 chloride, cnbf2-chloro-1,3-dinitro-5-(trifluoromethyl)benzene (4-chloro-3,5-dinitrobenzotrifluoride), dnbz-cl-3,5-dinitrobenzene chloride, deemmdiethyl ethoxymethylenemalonate, aqc6aminoquinolyl-n-hydroxysuccinimidyl carbamate; food sample 1 beer, cheese, fish, sausage and shrimp, food sample 2 fermented cabbage juices, soy sauces, misos (soy pastes), fermented fish sauces, and anchovy paste. time-min, temperature-c, rt-room temperature, nr-not reported, the superscript ‘*’ denotes lod in samples. one key feature that stands out is the stability of nfcpbas derivatives on exposure to daylight when compared to opa and dns-cl derivatives [40, 61-62], which are light sensitive. the ability of nfcp to react with various types of bas, including primary and secondary, makes it superior as a derivatization reagent over awards its transcendent specialty over opa and its analogs, which react only with primary amino groups. while comparing the lods reported for nfcp (0.9-1.2 µmol l -1 ) with other reagents, the proposed method can provide a potential alternative in the determination of amines. above all, nfcp, itself is highly fluorescent, can be synthesized easily in two steps from available, less expensive starting materials, and possesses a long shelf life. however, despite all the positive outcomes of nfcp derivatization and hplc analysis, the non-separable co-eluted peaks in the chromatogram need to be addressed by rescheduling the method development with chiral columns and other chromatographic parameters. 4. conclusion this work presents a pyrazoline-based compound, nfcp as an appealing pre-column derivatization reagent, which facilitates the rapid assay of bas of different nature. in contrast to the more labourintensive procedure involving hazardous organic solvents, nfcp seems to be highly reactive towards the selected bas under mild reaction conditions. the method developed showed linearity for standard bas quantification in the range of 0.5 to 100 µmol l -1 and detection limits of 0.9 1.2 µmol l -1 . the nuisance of less intense isomeric peaks that appears in the chromatogram is compensated for by the short elution time, feasibility, sensitivity, and reproducibility of this method. the difference in the histamine level estimated in fresh (0.4 µg g −1 ) and spoiled white tuna (4.1 µg g −1 ), proved the feasibility of this method to assess histamine toxicity hazards of seafood. with minor modification, there is ample scope with this method to broaden the 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journal of chromatography b., 2009, 877, 507-512. 62. dias, e.c., pereira, r.g.f.a., borém, f.m., mendes, e., de lima, r.r., fernandes, j.o., casal, s., biogenic amine profile in unripe arabica coffee beans processed according to dry and wet methods, journal of agricultural and food chemistry, 2012, 60, 4120-4125. received 24 october 2021 accepted 9 january 2022 https://doi.org/10.1002/bmc.5134 full page photo 143-198 squ journal for science, 12 (2007) © 2007 sultan qaboos university kähler manifolds positive ricci curvature boudjemaa anchouche department of mathematics and statistics, college of science, sultan qaboos university,p.o.box 36, pc 123, al-khodh, muscat, sultanate of oman, email: anchouch@squ,edu.om. ات ریتشي الموجبة تشعبات كایلر لمنحنی بوجمعة عنشوش الھدف من ورقة العمل التالیة ھي إعطاء نبذة عن تشعبات كایلر لمنحنیات ریتشي الموجبة. :خالصة abstract: the aim of this paper is to give an overview of some results obtained in the field of kähler manifolds of positive ricci curvature. keywords: kähler manifolds, positive ricci curvature, kodaira dimension. 1. introduction ifferential geometry is a cornerstone of modern mathematics. besides the natural beauty of the subject, it has found many applications in various branches of mathematics such as number theory, analysis, topology, algebraic geometry and also in some areas of physics, ranging from general relativity to string theory. recently one of the most famous conjectures in topology, the poincaré conjecture1, was solved by perelman2, a russian mathematician, using differential geometry, a work for which he was awarded the fields medal at the international congress of mathematics in spain, august 2006. an excellent account of perelman’s work is given by morgan and tian in 2007. the aim of this paper is to give an overview of an active research area of differential geometry, namely kähler manifolds of positive ricci curvature. since most of the proofs are either omitted or sketched and since we have in mind a reader who is not necessarily an expert in the field, we made an effort to introduce most of the basic notions and definitions, and we included references whenever needed, so that he/she can fill the gaps and go through the details by himself/herself. the paper is organized as follows. in part 1 we collect some basic riemannian geometry results mostly needed 1 the poincaré conjecture states that every simply connected closed three dimensional manifold is homeomrphic to s3 , where s3 is the three dimensional sphere. 2 building on r. hamilton’s work on the ricci flow. d boudjemaa anchouche in the following sections (readers with a background in riemannian geometry can skip it). for the sake of completeness we included some results3 in riemannian geometry even though they are not needed in the following sections. the main reasons for doing that are; first we believe that they are fundamental results and therefore should be known, and secondly it makes a smooth transition to kähler manifolds introduced in 2, since it gives a characterization of kähler manifolds in terms of holonomy groups. part 2 deals with kähler manifolds. part 3 deals with compact kähler manifolds of positive ricci curvature. part 4 deals with einstein-kähler metrics on fano manifolds. part 5 deals with noncompact complete kähler manifolds of positive ricci curvature. 1.1 riemannian manifolds this part is a collection of some definitions and results from riemannian geometry which will be needed in the following parts. the reason for including a section on holonomy groups, even though we don’t need it in the following parts, is our belief that it is a fundamental concept in riemannian geometry and therefore worth mentioning. some of the material covered in this part can be found in most differential geometry textbooks, such as kobayashi and nomizu, 1969, aubin 2001 and gallot and hulin, 1990. for an account of the development of riemannian geometry during the second half of the twentieth century, and its main contributors we suggest a book, recently published, by marcel berger(2000). we expect the reader to have some knowledge of general topology (munkres, 1975) is an excellent reference). as we said in the introduction, readers with a background in riemannian geometry can skip this part. 1.2 differentiable manifolds definition 1. a locally euclidean space m of dimension n is a hausdorff topological space that is locally euclidean, i.e., each point of m has a neighborhood which is homeomorphic to an open subset of n . definition 2. a c ∞ (resp. real analytic) structure ψ on an n − dimensional locally euclidean space m is a collection ψ ( ) iuα α αϕ ∈= , of pairs ( )uα αϕ, such that 1. ( ) iuα α∈ are open sets of m satisfying i u mα α∈∪ = . 2. u vα α αϕ : → , are homeomorphisms, where vα is an open subset of nr . 3. 1oα βϕ ϕ − : ( ) ( )u uu uβ ββ α α αϕ ϕ→∩ ∩ is a ( )resp real analyticc ∞ − . diffeomorphism. 4. the collection ( ) iuα α αϕ ∈, is maximal with respect to 3., i.e., given any pair ( )u ϕ, , where u is an open subset of m and u vϕ : → is a homeomorphism, where v is some open subset of nr , such that ( ) ( ) 1o u u u uα ααα ϕ ϕϕ ϕ − : → ,∩ ∩ 5. is a c ∞ − (resp. real analytic) diffeomorphism for all iα ∈ , then ( )u ϕ, ∈ ψ . the collection ( )i i i iu ϕ ∈, satisfying 1. , 2. and 3. above is called a c ∞ -atlas. definition 3. a c ∞ (resp. real analytic) manifold of dimension n is a pair ( )m , ψ , where m is a locally euclidean space of dimension n and ψ is a c ∞ − (resp. real analytic) differentiable structure on m . the manifold ( )m , ψ will be denoted simply by m . the pair ( )i iu ϕ, ( or ( iu , 1 i i nx x, ..., ) where 3 holonomy groups. kähler manifolds positive ricci curvature 1 i i i nx xϕ       = , ..., ) is called a local chart and 1 i i nx x       , ..., is called a local coordinate system (defined in i u ) associated to i ϕ . a manifold m is said to be compact (resp. noncompact) if the underlying topological space is compact (resp. noncompact). example 4. 1. every vector space has the structure of a c ∞ , noncompact manifold. in particular n has the structure of a c ∞ , noncompact manifold. 2. the unit sphere ( ) 1 1 2 1 1 1 1 n n n in i s x r xx + + + =   = ∈ | = ,, ...,    ∑ is a compact real analytic manifold. 3. the projective space ( )n p defined by ( ) { }( )1 0n n +:= ,  ‚p ∼ù where ( ) ( ) ( ) ( )0 0 0 0such thatn nn nx y x yy yx xλ λ ∗⇐⇒ ∃ ∈ = ,, ..., , ...,, ..., , ...,∼ is a compact actually real analytic manifold. 4. an open subset of a c ∞ − manifold is a c ∞ − manifold. 5. the set of p× q matrices with real entries ( )p,qm  is a finite dimensional real vector space, hence a c ∞ − manifold. 6. if 1 m and 2 m are c ∞ − manifolds, then 1 2m m× is a c ∞ − manifold. notation 5. 1. let u be an open subset of a manifold m and let k be either  or  . in what follows we will denote by ( )c u∞ , k (resp. ( )c u∞ , k ) the set of infinitely differentiable (resp. r − times differentiable) functions on u with values in .| 2. sometimes we use the word "smooth" to mean of class c ∞ . definition 6. a lie group g is a c ∞ − manifold endowed with a group structure which is compatible with its differentiable structure, i.e. g is a group and the map ( ) ( ) 1 g g g g h g h gh ν ν − : × → , , = ,a is of class c ∞ . let g and h be two lie groups. a map, or a morphism g hϕ : → , is a differentiable map, which is a group homomorphism. boudjemaa anchouche example 7. the following are lie groups. 1. every finite dimensional real vector space with its underlying abelian group structure is a lie group. 2. the torus ( )nn n/ /≅  r is a lie group4. 3. the linear group ( )gl n ,  is the set of all n n× invertible matrices with real entries. 4. special linear group: ( ) ( ){ }nsl n , a m det a 1 .= ∈ =  5. orthogonal group: ( ) ( ){ }no n , a gl n , a a i .= ∈ =  t 6. special orthogonal group: ( ) ( ){ }so n , a o n , det a 1 .= ∈ =  7. unitary group: ( ) ( ){ }nu n a gl n , a*a i ,= ∈ = where a* a .= t 8. special unitary group: ( ) ( ){ }su n a u n det a 1 .= ∈ = 9. simplectic group: ( ) ( ){ }sp n , a gl 2n , a ja j ,= ∈ =  t where n n o i j -i o   =     (10) if g and h are two lie groups, then the direct product g×h has a structure of a lie group. (11) if g is a lie group and h is a closed normal subgroup of g , then g h∕ has the structure of a lie group. readers who want more examples and desire to know more about lie groups, can consult (warner,1983, knapp, 2001, brocker and diek or helgason, 1978). remark 8. in all that follows we will assume, without loss of generality, that manifolds are connected. submanifolds definition 9. let m be a manifold of dimension n . a subset n of m is a submanifold of dimension p if for every point x n∈ , there exists a local chart ( )u , ,ϕ with m u∈ such that (1) ( ) 1 2u v v ,ϕ ≅ × where 1v (resp. 2v ) is an open subset of p (resp. n-p ). (2) ( ) { }1u n v 0 .ϕ ∩ ≅ × . the definition above can be reformulated as follows: for each x n∈ , there exists a local chart ( )( )1u, x ,..., x ,n with x u∈ such that ( ) ( ){ }ju n x u x x 0 for j p 1,..., n .ϕ ∩ ≅ ∈ = = + 4 the torus / nr z is isomorphic to ( ) 1s n , where { }1s 1 .z z= ∈  = kähler manifolds positive ricci curvature .n+1 fold of-is a submani ( ){ }n 1n n 1 21 n+1 ii 1s x ,..., x x 1++ == ∈ | =∑r ) 1( .example 10 (2) the set ( ) ( ){ }kp, q p.qm a m rank a k= ∈  =  . ( ) ( ) i p,q i k p,qm u m< ‚ is a submanifold of (3) let g be a lie group and let h be an abstract subgroup of g . it is well known that h is a submanifold of g (and hence a lie group) h⇔ is closed in g . tangent bundle the aim of this section is to define the tangent bundle tm of a differentiable manifold m . let m m∈ , and let f (resp. g ) be a differentiable function defined in a neighborhood u (resp. v ) of m . we say that f and g are equivalent, and we write f g< , if there exists a neighborhood w u v, m w,⊂ ∩ ∈ such that f in wg≡ . it is easy to see that r is an equivalence relation. the equivalence class of a function f defined in a neighborhood of m , called a germ of f at m , will be denoted by f . the set of germs at m will be denoted by me it can be shown that me is an − algebra. definition 11. a tangent vector at m m∈ is linear map mx :e , satisfying ( ) ( ) ( )ˆ ˆ ˆˆ ˆ ˆx f . fx x f ,g g g= + . ., xi e is an − derivation of the − algebra me definition 12. (1) the set of tangent vectors to m at a point m m∈ is called the tangent space to m at m and is denoted by mt m . (2) the dual of mt m , denoted by * mt m , is called the cotangent space of m at m . (3) the disjoint union m m mt m∈c (resp. * m m mt m∈c ), denoted tm (resp. *t m ), is called the tangent (resp. cotangent) bundle of m . 2. vector bundles definition 13. let m be a c ∞ -differentiable manifold of dimension n . a vector bundle of rank r is a differentiable manifold e together with: (1) a surjective c ∞ -differentiable map : e mπ → , such that for every x m∈ , ( ) 1 xe xπ −= has a structure of a real rdimensional vector space, where r is independent of x . (2) an open covering ( ) iuα α ∈ of m and diffeomorphisms αφ (called trivializations) ( )1u: e u u , r αα α α ϕ π −= → ×  , such that for each x u ,α∈ the map boudjemaa anchouche { }e r rxϕαχ → × →  is a  -linear isomorphism. the vector bundle is denoted by ( )e, m,π or simply by e . let uα and u β are two open subsets of m such that ( ) ( ) ( ){ }1 i i 1 1 1 1u u m, ,..., m u , ,..., , i ,r i i i i riπ ζ ζ ζ ζ α β− ≅→ × = ∈ ∈ =  . for each couple ( ),α β , consider the functions ( ) ( ) ( )( ) ' 1 , i, k 1 i, j : u u g r x x r g x g g β α β α α β β β α α ϕ ϕ − ≤ ≤ = ∩ → = o a l where ( ), i, k u u .g c β α α β ∞∈ ∩ for m u uα β∈ ∩ , the points ( )1 1m , ,..., r α αζ ζ and ( )2 1m , , ..., r β βζ ζ represent the same point on ( ) ( )1 u u u u re α β α βπ − ≅ ∩ → ∩ ×  , if and only if ( )1 2 i j 1 m m m and m , i=1, ..., r. r k gβ β ααζ ζ = = = = ∑ example 14. (1) if m is a differentiable manifold, then m r×  is a vector bundle called the trivial bundle of rank r . (2) let m be a differentiable manifold and consider the projection given by ( ) m : tm m x x m x t mif π π → = ∈a then it can easily be seen that ( )tm , m,π is a vector bundle of rank dim mn = r . similarly for t * m . (3) a vector bundle of rank 1r = is called a line bundle. (4) since a vector bundle is a family of vector spaces of a given dimension parameterized by a c ∞ manifold m , we can perform on vector bundles the same operations performed on vector spaces, such as the direct sum, the tensor product, the dualization, and so on. definition 15. a lie algebra is vector space v endowed with a bilinear map [ ] ( ) [ ] , : v v v , , ,ζ η ζ η × → a called the lie bracket, such that: (1) [ ] [ ], , , vfor allζ η ζ η ζ η= − ∈ , (2) [ ] [ ], , , , 0 for all , vζ η γ γ ζ η ζ η   + = ∈    (jacobi identity). let g be a lie group. it can be shown that the tangent space et g to g=g at the identity e has the structure of a lie algebra and the tangent bundle tg of g is trivial, more precisely tg g g≅ × . kähler manifolds positive ricci curvature definition 16. (1) a section s of the c ∞ -vector bundle ( )e , m ,π over an (open) subset u of m is a c ∞ -map s: u e→ such that us idπ =o . the space of c ∞ -sections of e over u is denoted by ( )u , eγ . if u m= , then we denote ( )u , eγ simply by ( )eγ . (2) a section of the vector bundle tm (resp. t * m ) over an open set u of m is called a vector field (resp. a differential form) defined over u . the space c ∞ -vector fields over u will be denoted by ( )u, tmγ . let m be c ∞ differentiable manifold of dimension , m mn ∈ and let ( )1 nx ,..., x be a local coordinate system defined in an open set u , with m u∈ . a c ∞ -vector field x over u may be written ( ) ( ) n i i=1 i x x x x ζ ∂ = ∂ ∑ where ( )i u,cζ ∞∈  . definition 17. the differential mdf of a function ( ) 1f u,c∈  at m m∈ is a linear form on mt m defined as follows: for each n i m i=1 i x t m x m ζ ∂ = ∈ ∂ ∑ , ( ) ( ) ( ) ( )m i i=1 i f df x x f m m n x ζ ∂ = = ∂ ∑ . in particular, for if x= , we have ( ) ( )i imd x x ζ= . hence we can write n m i i=1 i f df dx x ∂ = ∂ ∑ if ( )1 nx ,..., x is a local coordinate system defined in an open subset u of m , with m u∈ , then 1 n ,..., x x  ∂ ∂   ∂ ∂  (resp. ( )1 ndx ,..., dx ) is a c ∞ -frame of tm (resp. t * m ) over u . the frame ( )1 ndx ,..., dx is the dual of the frame 1 n ,..., x x  ∂ ∂   ∂ ∂  , i.e. i i, j, j dx x δ  ∂ =  ∂  where i, j, δ is the kronecker symbol. definition 18. let x and y be two vector fields defined in an open subset u of m . the lie bracket of x and y is the vector field [ ]x , y defined by [ ]( ) ( )( ) ( )( )x, y f x y f y x f ,= − where ( ) 2f u, tmc∈ . if ( )1 nu, x ,..., x is a local chart with m u∈ and if boudjemaa anchouche n n i i=1 i=1i i x and u x xi y inζ η ∂ ∂ = = ∂ ∂ ∑ ∑ , then [ ] n n i i=1 i=1 x, y x x x i j j j j i ζη ζ η  ∂∂ ∂ −  ∂ ∂ ∂  ∑ ∑ embeddings definition 19. let m and n be two c ∞ -manifolds. a c ∞ -map f : m n→ is a continuous map such that ( ) ( )-1ofo : u v mapis a cϕ ϕ ∞ψ → ψ − , for all charts ( ),u ϕ of m and ( )v, ψ of n such that ( ) 1u vϕ −⊂ . definition 20. let m and n be two c ∞ -manifolds and ( )m m f m df : t m t n→ , c ∞ -map. the differential is defined by ( ) ( ) ( )m ˆdf x x ofg g= , where g is a function defined in a neighborhood of ( )f m representing ĝ . it can be proved that the definition is independent of the choice of a representative of ĝ . if we put n =  in definition 20, then we get the differential of a function which was already defined in definition 17. definition 21. let m and n be two c ∞ -manifolds and f : m n→ a c ∞ -map. (1) the map f is said to be an immersion if : ( )m m f mdf : t m t n→ is injective for all m m∈ . (2) the map f is said to be an embedding if : (a) f is an injective immersion, and (b) f is a homeomorphism between m and ( )f m , where ( )f m is endowed with the induced topology of n . isomorphism of vector bundles definition 22. let e and f be two vector bundles over a differentiable manifold m. a map between the vector bundles e and f is a c ∞ map : e f,ν → such that: (1) ( )x xe f , for all x mν ⊆ ∈ , and (2) xx x xe : e fν ν= → is linear for all x m∈ . the vector bundles e and f are said to be isomorphic if there exists a map : e fν → such that x x x: e fν → is an ismorphism for all x m∈ . we denote this by e f≅ . a vector bundle (resp. a complex vector bundle) e over m is said to be a trivial bundle if kähler manifolds positive ricci curvature pull-back of vector bundles definition 23. let be a c ∞ -map between two c ∞ manifolds m and n and e a vector bundle over n . the pull-back bundle f * e is a vector bundle over m defined by ( ) ( )f mmf * e e= for all m m∈ . the transition functions of f * e are given by the pull-back of the transition functions of e . hermitian metrics on vector bundles definition 24. a c ∞ -frame over an open subset u of m is an r -tuple ( )1 ,..., rσ σ , where such ( )u, eiσ ∈ γ , such that ( ) ( )( )1 x ,..., r xσ σ is a basis for xe for all x u∈ . let u be an open subset of m such that ( )1u: e u u rϕ π ϕ−= → ×% , and let ( )1 i rei ≤ ≤ be the canonical basis of r to the trivialization ϕ , we associate the c ∞ -frame ( )1 i rei ≤ ≤% of ue , where ei% is defined by ( ) ( )1e x : x, e x ui iϕ −= ∈% then any section ( )s u, e∈ γ can be written as ( ) ( ) ( ) 1 s x x e x r i i i a = = ∑ % with ( )a u,i c ∞∈ r . conversely, to c ∞ − frame ( )1 ,..., rσ σ , ( )u, eiσ ∈ γ we can associate a trivialization of e over u as follows ( )( ) u 1 : e u x, a ,...., a r r ϕ → ×  a where ( )1a ,..., a r are defined as follows: ( ) ( ) 1 x a x r i i i σ σ = = ∑ , the definition of a c ∞ − frame for a complex vector bundle is obvious and is left to the reader. definition 25. let e be c ∞ − complex vector bundle of rank r over a c ∞ manifold m of dimension n . a hermitian metric h on e is a family ( )x mh x ∈ , where h x , is a hermitian inner product on e x , such that if ( ) ( )1 i re ,i c u ∞ ≤ ≤ ∈% c is a c ∞ − frame for the complex vector bundle e defined in an open set u , then, the functions ( ) ( )( ) i, j x i j h : u x h e , e ,x x →  % %a are smooth, i.e., ( )i, jh : u, i, j 1,..., r.c for all ∞∈ =c boudjemaa anchouche 3. tensor and differential forms in this section we will assume some knowledge of the properties of tensor and exterior algebras. let m be a differentiable manifold of dimension n and consider the following vector bundles ( )( )p,q m m m p,qt m:= t m ,∈t ( ) ( )( )p *m m mm : t mpa ∈= ∧t , ( ) ( )p *m m mp=0m : t ma ∞ ∈  = ⊗ ∧    t , where ( ) q-timesp-times * * m m m m mp,q t m t m .. t m t m .. t m= ⊗ ⊗ ⊗ ⊗ ⊗ 64474486447448 and ( ) p-times p * * * m m mt m t m ... t m∧ = ∧ ∧ 6447448 . definition 26. (1) the vector bundle ( )p,qt m (resp., ( ) ( )m , m pa a ) is called the tensor bundle of type ( ),p q (resp., the exterior p-bundle, exterior algebra bundle) over m . (2) a c ∞ − section of the vector bundle ( )p,qt m (resp. ( ) ( )m , m pa a ) is called a smooth tensor field of type ( ),p q (resp. a smooth differential p − form, a smooth differential form) on m . the set of all smooth sections of ( )p,q mt (resp., ( ) ( )m , m pa a ) will be denoted by ( )p,q mt (resp., ( ) ( )m , mpε ε ). if ( )1 xx ,..., n is a local coordinate system defined in an open subset u of m , with m u∈ , n 1 xi i =  ∂   ∂  (resp. { }n 1dxi i = ) is a c ∞ − frame for tm (resp. * mt m ) over u . therefore we get c ∞ − frames for ( ) ( )p,tm , t*mp q ∧ and ( ) p p 0 t * m ∞ =⊗ ∧ over u . for example, a differential p − form ω in u will be written ( ) ( ) 1 1 1 i 1 i ... i n x ,..., i x dx ... x , p p p i ia dω ≤ < < ≤ = ∧ ∧∑ where 1i , ..., i pa are c ∞ − functions in u . definition 27. let (resp. β ) be a p − form (resp. q − form). the exterior product of α and β , denoted by α β∧ , is a ( )p q+ -form defined by ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) p+q 1 p+q 1 p p 1 p+q 1 ,..., : ,..., ,..., pq s σ σ σ σ σ α β ξ ξ ε σ α ξ ξ β ξ ξ+ ∈ ∧ = ∑ , where 1 p+q ,...,ξ ξ are p q+ vector fields, p+q s is the group of permutations of the set { }1,..., p q+ and ( )ε σ is the signature of the permutation σ . kähler manifolds positive ricci curvature the exterior product is associative and satisfies ( ) ( ) ( )pq p q1 for m and mα β β α α ε β ε∧ = − ∧ ∈ ∈ . theorem 28. there exists a unique operator ( ) ( )d : m m ,ε ε→ such that (1) ( ) ( ) p p+1m mdε ε⊂ . (2) ( ) ( ) ( ) ( ) p pd d 1 d , m , mα β α β α β α ε β ε∧ = ∧ + − ∧ ∈ ∈ . (3) d d 0=o (4) if f c ∞∈ , then df is the differential of f . if ( ) p mα ε∈ , then ( ) p 1d mα ε +∈ is defined by ( ) ( ) ( ) ( ) ( ) p 1 1 p+1 p+1 i 1 i+jp 1 1 p+1 1 j p 1 ˆ,..., -1 ,..., , ˆ ˆ1 , , ,..., ,..., ,..., i i i i j i j dα ξ ξ ξ α ξ ξ ξ α ξ ξ ξ ξ ξ ξ + = + ≤ ≤ +  = +    −   ∑ ∑ where 1 p+1 ˆ , ...,ξ ξ are vector fields and îξ means that the vector field iξ is omitted. 4. riemannian manifolds definition 29. a riemannian metric on a c ∞ differentiable manifold m is a tensor field g of type ( )0, 2 , i.e., ( )0,g 2 m∈ t , such that at each mm m, g∈ is a positive definite symmetric bilinear form, i. e., ( ) { }mgm x, x 0, x t m 0 ,for all> ∈ â ( ) ( ) mgm x,y gm y,x x,y t mfor all= ∈ definition 30. a riemannian manifold is a pair ( )m,g , where m is a c ∞ differentiable manifold and g is a riemannian metric. let x and y be two elements of mt m , and let ( )1 nx ,...,x be a local coordinate system defined in an open subset u of m , with m u∈ , and suppose that n i=1 x x mi ξ ∂ = ∂ ∑ and n i=1 y x mi i ξ ∂ = ∂ ∑ then ( ) ( ) n ij i,j=1 gm x,y g m ,i jξ ζ= ∑ where ( )i,j mg m g ,x m x mi j  ∂ ∂ =   ∂ ∂  we write n i,j i,j=1 g g dx xi jd= ⊗∑ boudjemaa anchouche let ( )m, g be a riemannian manifold. using the metric g , it is possible to compute the length of any curve on m joining any two points x and y of m . definition 31. let ( )m, g and ( )n, h be two riemannian manifolds. a c ∞ − map f : m n→ , is said to be an isometry if f is a c ∞ -diffeomorphism and if for every m m∈ , and for every m, t mξ η ∈ , we have ( ) ( ) ( )( ) ( )m mf mh df , df gm ,ξ η ξ η= . we write g f * h= example 32. (1) since the tangent bundle of n is trivial, i. e., n n nt ≅ ×  , the euclidean metric on n denoted by ecg is defined by ( ) ( ) n 1 1 1 1m ,v , m ,v t∈  ( ) ( )( )ec 1 1 1 2 1 2g m ,v . m ,v v .v .= (2) consider the unit sphere ( ){ }n n+1 2 21 n+1 1 n 1s x ,..., x x ... x 1+= ∈ + + = . the euclidean metric on n+1 induces a metric on ns , i.e., if n n 1s i +→  is the obvious embedding of ns in n 1+ , then sn ecg i * g= is the "canonical" metric on ns , where ecg is the euclidean metric on n 1+ . (3) let ( ){ }2n n 2 21 n 1 nd x x ,..., x x x ... x 1 ,= = ∈ = + + < be the unit disc. since n n ntd d ,≅ ×  then a metric nd g on nd can be defined as follows ( ) ( )( ) ( ) d, x 22 g x, , x, : 1 x ξ η ξ η ⋅ = − (4) every compact connected lie group admits a bi-invariant metric, i.e., a metric for which left and right translations are isometries. for details see (gallot and hulin, 1990). partition of unity the aim of this section is to introduce a very powerful tool called" partition of unity" which allows one to construct global objects such as metrics, differential forms, vector fields,..., by gluing local ones. partition of unity plays also a fundamental role in the definition of integration on manifolds. definition 33. let m be a c ∞ -manifold and let ( )i iui ∈ be a covering of m . a c ∞ partition of unity subordinate to the covering ( )i iui ∈ is a collection of maps ( )i iiθ ∈ , where ( )m,i cθ ∞∈  satisfying: (1) supp ( ) ui iθ ⊆ for all i i∈ , where supp ( ) ( ){ }i xx m 0 .iϕ ϕ= ∈ ≠ (2) ( ) [ ]u 0,1 i ii i for allθ ⊆ ∈ kähler manifolds positive ricci curvature (3) for every x m∈ , there exists an open subset x xv , x v∈ such that xi v 0θ ≡ except for a finite set of iθ . (4) for every ( )i ix m , x 1iθ∈∈ =∑ ((3). implies that the sum is finite). definition 34. a hausdorff space m is said to be paracompact if every open covering { } iui i∈ of m there exists an open covering { }j j jv ∈ of m such that: (1) for every j j∈ , there exists j i i∈ such that ji v uj ⊂ (we say that { }j j jv ∈ is a refinement of { }i i iu ∈ ). (2) each point m m∈ has a neighborhood mw such that m j w v φ∩ ≠ only for finitely many values j of j (we say that { }j j jv ∈ is locally finite). paracompactness is a generalization of compactness (every hausdorff compact topological space is paracompact). theorem 35. let m be a paracompact c ∞ -manifold and let ( )i i iu ∈ be a covering of m . then there exists a c ∞ partition of unity subordinated to ( )i i iu ∈ . theorem 36. there exists at least one riemannian metric on any paracompact c ∞ -manifold. the construction goes as follows: let ( )i i,i iu ϕ ∈ be an atlas of m and let ( )i iiθ ∈ be a partition of unity subordinate to the covering ( )i i iu ∈ . fix a scalar product ( )q .,. on n where dim mn = . then it is easy to see that ( ) i i * i ig θ ϕ ∈  =  ∑ q is a metric on m . for more details, see (aubin, 2001). 5. the levi-civita connection definition 37. let m be a differentiable manifold. a linear connection ∇ on m is a map ( ): tm tm tm∇ ×  → ( ), y yξξ ∇a , satisfying the following conditions (1) if mt mξ ∈ and ( )y ∈γ τμ , then my t mξ∇ ∈ . (2) the restriction of ∇ to ( )m mτ ×  τμ is bilinear. (3) ( ) ( ) ( )mfy = f y f m yξ ξξ∇ ⋅ + ∇ for all ( )mt m, y tmξ ∈ ∈  and for all f differentiable function on m . (4) if ( )x tm∈ γ and ( )y tm∈γ are such that x is of class rc and y is of class 1rc + , then ( )x y tm∇ ∈ γ is of class rc . definition 38. (1) the torsion of a linear connection ∇ is a map t defined by ( ) ( ) ( )t : tm tm tmγ × γ → γ ( ) ( ) [ ]x yx,y t x,y yxx,y= ∇ ∇a boudjemaa anchouche where [ ]x,y is the lie bmcket of the vector fields x and y . (2) the curvature r of a linear connection ∇ is a two form with values in hom ( ) ( )( )tm , tmγ γ , defined by ( ) ( ) ( ) ( )( )r : tm tm hom tm tmγ × γ → γ , γ ( ) ( ) [ ]x y y x x,yx,y r x,y = ∇ ∇ − ∇ ∇ − ∇a for simplicity we write ( ) [ ] [ ]x yx y ,r x,y , ∇ ∇= ∇ ∇ − ∇ . remark 39. one can easily check that: (1) the curvature r is a (1, 3) tensor. (2) ( ) ( )r x,y r x,y= − . (3) if t 0= , then ( ) ( ) ( )r x , y r y, z x r z , x y 0z + + = (bianchi's identity). (4) the value of ( )r x , y z at a point m m∈ depends only on the values x , y and z at m . theorem 40. let ( )m , g be a riemannian manifold. then there exists a unique linear connection which is torsion free and compatible with the metric, i.e., a connection g∇ satisfying the following two conditions: (1) ( )t x , y 0= for all ( )x , y t m∈ γ . (2) ( ) ( ) ( )g gx xx g y, z g y, z g x, z⋅ = ∇ + ∇ for all ( )x,y,z tm∈ γ . where t is the torsion of the connection g∇ . the connection g∇ defined above is called the levi-civita a connection of the metric g and will simply be denoted by ∇ . for a proof, see (aubin, 2001). the vector field x y∇ is called the covariant derivative of the vector field y in the direction of the vector field x . the covariant differentiation can be extended to tensors of type ( )p,q , see (kobayashi and nomizu, 1969) . in a local coordinate system ( )1 nx ,..., x defined in an open subset u of m , we write i n k ij k=1j kx x x ∂ ∂ ∂ ∂ ∇ = γ ∂ ∂ ∑ . definition 41. the functions k ijγ defined in u are called the christoffel symbols of the levi-cevita connection ∇ . easy computations in a local coordinate system ( )1 nx ,..., x defined in an open subset u of m show that the christoffel symbols can be expressed in terms of the metric as follows nk k ij ijj i i j 1 g g g g 2 x x x=1      ∂ ∂ ∂ γ = + −   ∂ ∂ ∂  ∑ where ( )k 1 k, n g   ≤ ≤ is the inverse of the matrix ( )ij 1 i,j ng ≤ ≤ . kähler manifolds positive ricci curvature 6. sectional and ricci curvatures curvature is a fundamental and central concept in riemannian geometry. in this section we will introduce two types of curvatures, namely the sectional curvature and the ricci curvature. let ( )m , g be a riemannian manifold and r its curvature. using the metric g , we can view r as a ( )0, 4 tensor (denoted also by r ) as follows ( ) ( )( )r x,y,z,w : g r x,y z,w= . the properties of r can be summarized in the following proposition 42. the riemannian curvature r satisfies the following properties (1) ( ) ( ) ( ) ( )r x,y,z,w r y,x,z,w r x,y,z,w r y,x,w,z= − = = . (2) ( ) ( )r x,y,z,w r z,w,x,y= . let ( )m2,t mg be the grassmannian of 2-dimensional vector subspaces of mt m and let ( ) ( )m m m2,tm u 2,t m∈=g g be the corresponding grassman bundle. let mu be a two dimensional vector subspace of mt m with basis ( ),ξ η . then it can be shown that the real number ( ) ( )( ) ( ) ( ) ( ) m m 2 m m m g r , , g , g , g , ξ η ξ η ξ ξ η η ξ η = − t u is independent of the choice of the basis ( ),ξ η of mu . definition 43. let ( )m , g be a riemannian manifold. the sectional curvature of ( )m , g at m m∈ , denoted by ( )sect m , is the function ( ) ( ) ( ) ( ) ( ) m m m m sect m : 2, t m sect m → =  a g u u t u remark 44. if ,ξ η are two linearly independent vectors in mt m , then we put ( ) ( ) ( )msect m ,ξ η = t u . where mu is the plane spanned by the vectors ,ξ η . we will say that ( )sect resp. , , cc≥ ≤ > < if ( ) ( ) ( ) ( ) ( ) ( )( )m msect m , cg , resp.sect m , , , cg , ,ξ ξ ξ ξ ξ ξ ξ ξ≥ ≤ > < for all vectors, mt mξ ∈ and for all m m∈ . definition 45. let ( )m,g be a riemannian manifold. for each m m∈ , the ricci curvature tensor of ( )m,g at m , denoted by ( )gri mc is defined by ( ) ( ) ( ) g m mri m : t m t m , ric , c ξ η ξ η × →  a boudjemaa anchouche where ( ) ( )( ) ( )ni=1 ric , trace ric , ric , , e ,i ie ξ η ζ ξ ζ η ξ η = = ∑ a and ( )1i i ne ≤ ≤ is a mg -orthonormal basis of mt m . as defined, g ric is a bilinear form which will sometimes simply be denoted by ric if the metric is clear from the context, and ( )gri mc will simply be denoted by mric . as in the case of sectional curvature, we will say that ( )ri . , , cc c resp≥ ≤ > < if ( ) ( ) ( ) ( )( )m m m mric , cg , resp. ric , , , cg , ,ξ ξ ξ ξ ξ ξ ξ ξ≥ ≤ > < for all vectors mt mξ ∈ and for all m m∈ . 7. a volume comparison theorem the positivity of the ricci curvature imposes strong topological and geometric constraints on riemannian manifolds as shown in theorem 46, theorem 57 and theorem 58 below. theorem 46. ( myers, 1941) let ( )m,g be a complete riemannian manifold and suppose that gric ,c≥ where c is a positive constant. then m is compact and its fundamental group is .finite. remark 47. negative ricci curvature has no topological implications on riemannian manifolds of dimension 3≥ as is shown by the following result. theorem 48. (lohkamp, 1994) any manifold of dimension 3≥ admits a metric with negative ricci curvature. definition 49. let ( )m,g be a riemannian manifold and let ( ): a,b mγ → , be a differentiable map (called a smooth curve). the length of the curve denoted by ( )ι γ is given by ( ) ( ) ( ) ( )( )tg t , t dt , b a γ ι γ γ γ= ∫ & & where ( ) ( ) ( ) t d d t t d , t a,b , dt dt γ γ γ    = = ∈      & , dγ is the differential of the map γ and d dt is the unit vector on  . the length of a piecewise smooth curve is the sum of the lengths of its smooth pieces. definition 50. (1) the distance between two points x and y , denoted by ( )gd x , y , is the infimum of the lengths (with respect to the metric g ) of all piecewise 1c -curves from x to y . kähler manifolds positive ricci curvature (2) the metric g induces a distance function g d on m , giving a metric space ( )gm , d . we say that the metric g is complete if ( )gm , d is a complete metric space. remark 51. it can be proved that the topology of m induced by the metric gd is the same as the original topology of m . definition 52. the geodesic ball ( )gb m , r centered at m and with radius r is defined by ( ) ( ){ }g gb m , r x m d m , x r= ∈ < , where g d is the distance function induced by the riemannian metric. integration of differential forms on manifolds let m be an c ∞ -manifold of dimension n and let ϖ be a smooth n -form defined on m . the aim of this section is to give a meaning to the following expression m ρϖ∫ , where ρ is a compactly supported function on m , i.e., supp ( ) kρ ⊆ , where k is a compact subset of m . let us start first with the following definition 53. let m and n be two c ∞ -manifolds and f : m n→ a c ∞ -map. if φ is a smooth n -form on n , then f * φ is the smooth n -form defined on m by ( ) ( ) ( ) ( ) ( )( )1 n m 1 m nf mmf * ,..., : df , ..., df ,ξ ξ ξ ξφ = φ , for all m m∈ and for all 1 n m,..., t mξ ξ ∈ let m, ρ and ϖ w be as above. suppose first that supp ( ) iuρ ⊆ , where ( )i iu ,ϕ is a local chart and ( )1 nx ,...,x are the corresponding local coordinates. then ( ) ( )1i 1 n 1 n* x ,..., x dx ... dx ,iϕ ϖ ϑ− = ∧ ∧ where iϑ is a smooth function defined in ( )i iuϕ with real values. we put (1) ( ) ( )i i 1 im u * ϕ ρϖ ϕ ϖ−=∫ ∫ (2) ( ) ( ) ( ) ( )i i 1 i 1 n 1 n 1 nu o x ,..., x x ,..., x dx ... dxiϕ ρ ϕ ϑ − ∧ ∧∫ we have to prove that the definition is independent of the choice of the local chart containing the support of ρ . for this, suppose that ( )j ju ,ϕ is a local chart and ( )1 ny ,..., y are the corresponding local coordinates with supp ( ) juρ ⊆ , and put (3) ( )( )j j 1 jm uϕ ρϖ ϕ ϖ−=∫ ∫ (4) ( )( ) ( ) ( )j 1 j 1 n j 1 n 1 nu o y ,....,y y ,...,y dy ... dy ϕ ρ ϕ ϑ− ∧ ∧∫ where j ϑ is defined by ( ) ( )1j j 1 n 1 n* y ,...,y dy ... dyϕ ϖ ϑ− = ∧ ∧ boudjemaa anchouche in general the right hand side of the expressions (1) and (3) are not necessarily equal, but if we restrict ourselves to "orientable manifolds" then we can choose an atlas of local charts such that (1) and (3) are equal. to be more precise, let us introduce the following definition 54. (1) a c ∞ -manifold m is said to be orientable if there exists a c ∞ -atlas ( )i i i iu ,ϕ ∈ such that the jacobian jac ( ) 1 i joϕ ϕ − of the c ∞ -diffeomorphism ( ) ( ) ( )1i j j i j i i jo : u u u uϕ ϕ ϕ ϕ− ∩ → ∩ is positive for all i , j i∈ , i.e., ( ) ( )( ) 1 1 1 n 1 i j j n n 1 n y y x x jac o x : det 0 , y y x x ϕ ϕ ϕ− ∂ ∂  ⋅ ⋅ ⋅ ∂ ∂   ⋅ ⋅ ⋅ ⋅ ⋅   = >⋅ ⋅ ⋅ ⋅ ⋅   ⋅ ⋅ ⋅ ⋅ ⋅   ∂ ∂ ⋅ ⋅ ⋅ ∂ ∂  for all i , j i∈ and for all i jx u u∈ ∩ , where ( ) ( )( )1 n 1 nx ,..., x . y ,..., yresp is the system of local coordinates corresponding to the chart ( ) ( )( )j j i iu , . u ,respϕ ϕ . (2) the manifold m is said to be oriented if such an atlas has been chosen. (3) a chart ( )u,ϕ is said to be compatible with the orientation if ( )1ijac o 0, ifor allϕ ϕ − > . it can be shown that theorem 55. a c ∞ -man(fold m of dimension n is orientable if and only (f there exists a differential n -form ω such that m 0ω ≠ for all m m∈ . if m is oriented and the atlas ( )i iu ,i iϕ ∈ is compatible with the orientation, then ( ) ( ) ( )( )i i j j 1 1 i ju u * * , ϕ ϕ ϕ ϖ ϕ ϖ− −=∫ ∫ i.e., the integral m ρϖ∫ is independent of the choice of the local chart. suppose now that ρ is a smooth function defined on m with compact support. then we define m ρϖ∫ as follows im m i i xρϖ ρϖ ∈ = ∑∫ ∫ (5) where ( )i i ix ∈ is a partition of unity subordinate to an atlas ( )i iu ,i iϕ ∈ which is compatible with the orientation. the right hand side of (5) is a finite sum and it can be proved that it is independent of the choice of the partition of unity. kähler manifolds positive ricci curvature integration over riemannian manifolds. let ( )m, g be a riemannian manifold of dimension n , let ( ) ( )( )i 1 i nu, u, xϕ ≤ ≤= be a local chart, and suppose that f is a measurable function on m with compact support included in u . then the integral gm fdv∫ is defined as follows ( )( ) ( ) ( )( )( )1 1g ij 1 nm mfdv f x det g x dx ...dxϕ ϕ ϕ − −=∫ ∫ if f is a measurable function with compact support in m , then we define gm fdv∫ as follows i g i gm m fdv x fdv ∈ = ∑∫ ∫ where ( ) i i ix ∈ is a partition of unity subordinate to an atlas ( ) i i u ,i iϕ ∈ .it can be proved that the sum is well defined, i.e., only a finite number of terms in the sum are nonzero, the sum is independent of the choice of the atlas and of the partition of unity subordinated to it. suppose now that m is oriented and let ( ) i i u ,i iϕ ∈ =a be an atlas which is compatible with the orientation. let ( )u,ϕ be a local chart belonging to a and let ( )1 nx ..., x be the local coordinate system associated to ϕ and consider the following n -form: ( )( )x ij x1 ndet g x d ... dx ,ϖ = ∧ ∧ where det ( )ijg is the determinant of the metric n ij i ji=1 g g dx dx= ⊗∑ . consider another local chart ( ),v υ ∈/ a and let ( )1 ny ,..., y the corresponding local coordinates, and put ( )( )y ij 1 ndet g y dy ... dyϖ = ∧ ∧ an easy computation shows that x y in u vϖ ϖ= ∩ . therefore ϖ is a global n -form, called the volume form associated to the riemannian metric g and it will be denoted by g dv . definition 56. the volume of the geodesic ball ( )gb m , r denoted by ( )( )g gvol b m , r is given by ( )( ) ( )g g g b m,r vol b m , r : dvg= ∫ the following two results are very important and will be needed in part 4. theorem 57. (bishop and crittenden, 1964) let ( )m , g be a complete noncompact riemannian manifold of positive ricci curvature, dim m n=r . then ( )( ) ng gvol b m , r cr r 0 ,for all≤ > where c is a positive constant independent of r . there is a generalization of bishop's theorem by gromov, but for our purposes, bishop's theorem is enough. the proof of bishop's (resp. gromov's) theorem (theorem 57) uses special local coordinates coming from the exponential map and some properties of jacobi fields, for more details, see (gallot and hulin, 1990). boudjemaa anchouche theorem 58. (calabi, yau, see [14]) let ( )m,g be a complete noncompact riemannian manifold of nonnegative ricci curvature. then ( )( )g gvol b m,r cr r 0for all≥ > , large enough. de rham isomorphism definition 59. (1) a p form w is called closed, or d closed, if d 0ω = . (2) a p -form ω is called exact if dω β= for some ( )p 1− -form β . since 2d 0= , every exact form is closed. hence we see that the vector space of exact p -forms is a subspace of the space of closed p-forms. definition 60. the thp de rham cohomology group of m , denoted by ( ) p drh m , is given by ( ) { } { }pdrh m p / pclosed forms exact forms= − − de rham's theorem says that ( ) p drh m is isomorphic to the thp singular cohomology5 of m . more precisely consider the following map ( ) ( ) [ ] [ ] [ ]( ) *p dr p z x : h m h m , zω ω ω → = ∫  a where ( )ph m ,  is the singular thp homology group with real coefficients, ( ) * ph m,  its dual, w is a representative of its de rham cohomology class [ ]ω , and z is a thp cycle representing its real differentiable singular homology class [ ]z . the fact that the map x is well defined is an easy consequence of stokes theorem. for more details, see (warner, 1983). theorem 61. (de rham) the map x is an isomorphism. if m is a compact oriented manifold, then poincare duality implies that ( ) ( )* pph m , h m ,≅  combining de rham isomorphism and poincare isomorphism, we obtain ( ) ( )* pp drh m, h m≅ definition 62. let m be a compact manifold. the nonnegative integer ( )ib m defined by ( ) ( )ii drb m dim h m ,=  is called the i th− betti number of the manifold m . holonomy groups the aim of this section is to introduce the "holonomy group" of a riemannian manifold and to state two of the fundamental results in riemannian geometry, namely de rham's and berger's theorems. the material of this section will not be used elsewhere in this paper, so it may be skipped if the reader whishes to do so. to any riemannian manifold ( )m,g of dimension n n, we can associate a closed subgroup of ( )so n , called the holonomy group of the metric; lots of information about a riemannian metric is encoded in its holonomy group. let us first define the holonomy group. 5 for more details on singular (co)-homology, the readers can consult [20]. kähler manifolds positive ricci curvature let ( ): a,b mγ → be a smooth curve. the tangent vector d dt γ to the curve γ is defined by ( ) 00 0 tt d d , t a,b dtdt d γ γ    = ∈      , where dγ is the differential of the map γ and d dt is the unit vector on  . for a function f defined in a neighborhood of' ( )0tγ , we get ( ) ( ) ( ) 0t 0 d fd f t dt dt γγ   =     o let ( )m , g be a riemannian manifold of dimension n and let ∇ be the levi-cevita on m . definition 63. (1) a vector field x along a curve ( ): a,b tmγ → is a map ( )x : a , b tm→ such that ( ) ( ) ( )tx t t m t a,bfor allγ∈ ∈ . (2) a vector field x is said to be parallel along a differentiable curve γ if d dt x 0.γ∇ = let ( ) n i 1 n i=1 i x x ,..., , x and γ γ γ ∂ = = ∂ ∑ be the expression of the vector field x and the curve γ in a local chart ( )( )1 nu, x ,..., x . then ( ) ( )( ) ( ) ( ) j in n j k d ik j 1 i , k 1 jdt dx t d t x 0 t x t 0 dt dt xγ γ γ = =   ∂ ∇ = ⇔ +  =  ∂   ∑ ∑ . (6) let 1m and 2m be two points of m and let [ ]: a , b mγ → be a continuous curve which is smooth in ( )a , b , and joining 1m and 2m , i.e., ( ) 1a mγ = and ( ) 2b mγ = and let 1x be a vector in m1t m . since the equation (6) is linear, by cauchy's theorem, it has a unique solution ( )x t for all [ ]t a , b∈ satisfying ( ) 1x a x= . definition 64. the vector ( )2x x b= is called the parallel transport of 1x from 1m to 2m along the curve γ . the parallel transport along a piecewise smooth curve γ is defined in an obvious way. then to each piecewise curve γ is associated an isometry (with respect to the scalar product on m1t m and m2t m induced by g ) 1 2m m : t m t mγ →t this map is both linear and invertible and so defines an element of ( )mgl t m . let m m∈ and consider ( ) [ ] ( ) ( ){ }piecewise and smooth,o m : a,b ml a b mγγ γ γ= → = = . boudjemaa anchouche it can be shown that ( )o ml is a group under composition of paths. to a composition 1 2γ γo , we associate the linear transformation 1 2 1 2 m m o : t m t ml l lγ γ γ γ= →o definition 65. the holonomy of ( ) g or g∇ based at m is defined as ( ) ( ) ( ){ }gm mh o l l gl t m o mlγ γ∇ = ∈ ∈ the holonomy ( ) g mh o l ∇ is a subgroup of the orthogonal group ( )o n , moreover, it is a lie group. if ( ) 1 g mh o l ∇ and ( )2 g mh o l ∇ are the holonomy groups of the connection g∇ at the points 1 2m , m , then there exists an element ( )a o n∈ such that ( ) ( ) 2 1 g g 1 m mh o l ah o l a −∇ = ∇ this allows us to speak of "the" holorromy group of a riemannian manifold ( )m , g and denote it simply by ( )gh o l ∇ . if we consider in the definition of the holonomy group only contractible closed curves, then we obtain what is called the restricted holonomy group, and it can be proved that the two coincide in case the manifold m is simply connected. remark 66. the following set ( ) ( ) ( ){ }0 gm mh o l l gl t m l o m , is a contractible curveγ γ∇ = ∈ ∈ is a connected normal subgroup of ( ) g mh o l ∇ , and is called the restricted holonomy group. definition 67. (1) the representations of ( ) g mh o l ∇ in mt m are isomorphic and therefore called the holonomy representation. (2) a riemannian manifold ( )m , g is irreducible if its holonomy representation is irreducible. theorem 68. (de rham 1952) let ( )m , g be a connected, simply connected complete riemannian manifold. then: (1) there exists a canonical decomposition ( ) ( ) ( ) ( ) isometric 0 0 1 1 k km , g m , g m , g ... m , g≅ × × × where ( )0 0m , g is a euclidean space (possibly reduced to a point) and ( )i im , g , i 1,...,k= are irreducible simply connected complete riemannian manifolds. (2) for ( )1 km m ,...,m m= ∈ , let ( ) ( )i g m m ih o l o t mi ∇ ⊂ be the holonomy group of im at im and let ( )gmh o l ∇ be then the holonomy of ( )m , g at m . then ( ) ( ) ( ) ( )0 1 k 2 0 1 k g g gg m m m mh o l h o l h o l ... h o l ,∇ ≅ ∇ × ∇ × × ∇ where the action of ( ) ( ) ( ) 0 1 k 0 1 k g g g m m mh o l h o l ... h o l∇ × ∇ × × ∇ on 0 1 km m 0 m 1 m k t m t m t m ... t m ,≅ × × × is through the product representation. such a decomposition is unique up to an order. kähler manifolds positive ricci curvature the symmetric spaces were classified by e . cartan around 1920 and their holonomy groups are well understood. for example, a compact symmetric space is a homogeneous space g/h , where g is a compact lie group and h is the identity component of the fixed locus of an involution of g and the holonomy g/h is h 6. so we can exclude symmetric spaces from our study of the holonomy of riemannian manifolds. theorem 69. (berger, 1953) let ( )m , g be an irreducible simply connected riemannian manifold which is not isomorphic to a symmetric space. then the holonomy ( ) gh o l ∇ of ( )m , g is one of the following groups ( )gh o l ∇ dim m type of the metric so (n) n generic riemannian u (r) 2r kähler su (r) , r 3≥ 2r calabi-yau sp (r) 4r hyper kähler sp (r) sp (1) 4r quaternion kähler 2g 7 ricci flat spin(7) 8 ricci flat remark 70. (1) initially it was thought that there is no manifold with holonomy 2g or spin (7), but recently, d. joyce was able to construct a compact 7-dimensional manifold with holonomy 2g (see [28] ) , and a compact 8dimensional manifold with holonomy spin (7), (see joyce, 1996). (2) since ( ) ( ) ( ) ( )sp m su 2m u 2m so 4m⊂ ⊂ ⊂ we deduce that every hyperkahler manifold is a calabiyau manifold, every calabiyau manifold is a kähler manifold, and every kähler manifold is orientable. kähler manifolds will be introduced in part 2, but we will not study the other types of manifolds in this paper. (3) it is very well known that the groups appearing in berger's list (theorem 69) are connected to the three division algebras  (real numbers), c (complex numbers), h (quaternions). the connection is stated as follows ( )so n is a group of automorphism of n . ( )u n and ( )su n are groups of automorphisms of nc . ( )sp n and ( ) ( )sp sp 1n are groups of automorphisms of nh , where h is the space of quaternions. 2g and spin (7) can also be realized as automorphism groups of some other structures. kähler manifolds will be the subject of part 2. as for the other classes of manifolds, excellent accounts can be found in (salamon, 1989, joyce, 2000, beauville, 2006, bryant, ). part 2. kähler manifolds we have seen in the previous part that if the holomony ( ) ghol ∇ of a simply connected irreducible complete riemannian manifold ( )m,g of dimension 2n is icluded in ( )u n , then the manifold is "kähler". 6 for more details on symmetric spaces, see [23]. boudjemaa anchouche the aim in this part is to give a short introduction to" kähler manifolds". since we mentioned the hodge decomposition theorem without proof, skipped some other fundamental results in klihler geometry, and since most of the proofs are either sketchy or missing, we suggest the following references (kobayashi and nomizu, 1969, griffiths and harris, 1978 and demailly, ) for more detail. 9. holomorphic functions definition 71. let ω be a nonempty connected open subset of nc . a complex valued function f on ω is called holomorphic if for each ( ) 0 0 0 1 n, ...,z z z= ∈ ω , there exists a neighborhood u and a power series ( ) ( )1 n 1 n 1 n 0 0 0 ,..., 1 1 n n ,..., c z z ... z z α α α α α α ≥∈ − −∑  that converges to ( )f z for z u∈ , where 1 n,...,cα α are complex numbers and 0≥ is the set of nonnegative integers. we denote by ( )h ω the set of holomorphic functions on ω . let ( )1 nz z ,..., z= be the coordinate system of n . write 2 j-1 2 jz x 1xj = + − and identify n with 2 n via the correspondence ( ) ( )1 n 1 2 2nz ,..., z x ,x ,...,xa , and consider the following notation 2 1 2 2 1 2 1 1 : 1 , : 1 z 2 x x 2 x xz jj j j j j− −    ∂ ∂ ∂ ∂ ∂ ∂ = − − = + −      ∂ ∂ ∂ ∂ ∂∂    . (7) the following characterization of holomorphic functions is very useful theorem 72. ( ) ( )2oc j f f l 0 j 1, 2,..., n , z lh for  ∂ ω = ∈ ω  = =  ∂  where ( ) 2 ocll ω is the set of locally square integrable functions on ω and the derivative is taken in the sense of distributions. for a proof of theorem 72 see (ohsawa, 2002). definition 73. let ω (resp. ′ω ) be a nonempty connected open subset of n (resp. m ). (1) a map ( ) m1 k,..., :ϕ ϕ ϕ= ω →  is called holomorphic if each j :ϕ ω →  is holomorphic, 1 j m≤ ≤ . if ( )ϕ ′ω ⊆ ω , then we write ( )1 k,..., :ϕ ϕ ϕ ′= ω → ω suppose that m n= . a holomorphic map : ′ψ ω → ω is called a biholomorphism if there is a holomorphic map :φ ′ω → ω kähler manifolds positive ricci curvature such that o id o id ,and φ′ω ωψ ψ = ψ = where idω (resp. id ′ω ) is the identity map of ω (resp. ′ω ). in case ′ω = ω , a bihlomorphism :ψ ω → ω is called an automorphism of ω . the set of automorphisms of ω denoted by aut ( )ω is a group under composition of mappings. a beautiful theorem of h. carlan says that if ω is a bounded domain in nc , then aut ( )ω is a lie group. bedford & dadok and saerens and zame proved independently that any compact lie group can be realized as the automorphism group of a pseudoconvex domain in some nc 7 . 10. complex manifolds if in definition 2 we consider open subsets of n instead of open subsets of n , and biholomorphisms instead of c ∞ -diffeomorphism, then we get what we call" a complex structure" on m . definition 74. a complex manifold of dimension n is a pair ( )m,ψ , where m is a locally euclidean space of dimension n and ψ is a complex structure on m. the manifold ( )m, ψ will be denoted simply by m. the pair ( ) ( )( )i i i 1 nu , or u , z ,..., zϕ , is called a local complex chart and ( )1 nz ,..., z is called a local complex coordinate system defined in iu . we have already defined in the category of c ∞ manifolds what. we mean by a submanifold, an embedding, an immersion, a c ∞ -map between manifolds, isomorphism of vector bundles, pull back of vector bundles,...etc. with obvious modifications, we get the notions of complex submanifolds, holomorphic embeddings,...etc. for more details, the interested reader can consult (kobayashi and nomizu (1969) or other textbooks dealing with complex manifolds. if ( )i iu ,ϕ , is called a local complex chart and ( )1 nz ,..., z is a local complex coordinate system defined in iu , then ( ) n 2 ni iu .ϕ ⊆ ≅  put j 2 j-1 2jz x 1x i i= + − , j 1,..., ,n= and consider the following maps ( ) ( )( ) 2 n i 1 2 n : u m x m ,..., x m , i i i →  a ñ the maps ( ) ( )1 : u u u u ,α β β α β α α β− ∩ → ∩oñ ñ ñ ñ are c ∞ diffeomorphisms. the collection ( ) i i u ,i i ∈ ñ is a c ∞ -atlas on m. this c ∞ -structure on m is called the underlying c ∞ -structure of the complex manifold m. an example of a complex manifold, which will play a fundamental role in what follows, is given by: example 75. the projective space np the projective space deserves a special attention. since it plays a very important role in what follows, we will try to describe it in some detail. as a set, the projective space is defined by boudjemaa anchouche { }( )n n+1 \ 0 / ,=  p where the equivalence  is defined by ( ) ( ) *0 n 0 nz ,..., z w ,..., w ⇔ ∃ ∈ ch such that ( ) ( )0 n 0 nz ,..., z w ,...,w= h . denote by π the projection { } ( ) [ ] n+1 n 0 n 0 n : \ 0 z ,..., z z ,...,z , π → a p where [ ]0 nz ,...,z is the equivalence class of ( )0 nz ,..., z . the projective space np can be equipped with a complex atlas ( )i 0 i nu ,i ϕ ≤ ≤ as follows: let ( ){ }n+10 nu z ,...,z z 0 , i 0,..., n,i i= ∈  ≠ =% c and consider the following map ( ) n 0 i-1 i+1 n 0 n i i : u z z z z z ,...,z ,..., , ,..., , z z z z i i i i ψ →       %  a the maps iψ are continuous and it is clear that ( ) ( ) [ ] [ ]0 n 0 n 0 n 0 nz ,..., z y ,...,y z ,..., z y ,...,yi iψ = ψ ⇔ = let ( )u ui iπ= % .then the map [ ] n 0 i-1 i+1 n 0 n i i : u z z z z z ,..., z ,..., , ,..., z z z z i i i i ϕ →        a is a well defined bijective map. the maps iϕ are open, for, if v is an open subset of ui , then ( ) ( )( )1v vi iϕ π −= ψ is open. therefore the map iϕ realizes a homeomorphic between ui and n , moreover, the maps ( ) ( ) ( ) 1 j j 0 i-1 i+1 n-1 0 n-1 j j o : u u u u z z z z1 z ,...,z ,..., , , ,..., , z z z z z j i i i j i j j j ϕ ϕ ϕ ϕ− ∩ → ∩        a are biholomorphic. thus ( )i 1 i nu ,i ϕ ≤ ≤ as defined above is a complex atlas, which gives np the structure of a complex manifold. the projective space np is a compact complex manifold, since ( )n 2n+1s ,π=p where ( ){ }2 22n 1 n+10 n 0 ns z ,...,z z ... z 1+ = ∈  + + = . example 76. the following are complex manifolds: kähler manifolds positive ricci curvature (1) n . (2) any open subset of n . (3) let ( )r, ng be the set of all r -dimensional vector subspaces of n , called the grassmannian manifold of r linear subspaces of n . it can be proved that ( )r, ng is a compact complex manifold of dimension ( )r n r . 1f r 1= , then we get the projective space np . (4) if 1m and 2m are complex manifolds, then 1 2m m× is a complex manifold. more examples of complex manifolds will be given below. definition 77. a complex lie group is a complex manifold g endowed with a group structure such that the map ( ) ( ) 1 g g g g, h g, h gh , ν ν − × → =a is holomorphic. example 78. the following are complex lie groups: (1) the linear group ( )gl n, : is the set of all n n× invertible matrices with complex entries. (2) special linear group: ( ) ( ){ }sl n, a gl n, det a 1= ∈  =  . (3) the special orthogonal group ( ) ( ){ }nso n, a sl n, a a i= ∈  =  t (4) the complex symplectic group: ( ) ( ){ }sp n, a gl 2n, a ja j ,= ∈  =  t where n n 0 i j , i 0 −  =     and ni is the identity matrix of ( )gl n, . for more details, the interested reader can consult (warner,1983, knapp,2001 or helgason,1970). quotient manifolds a very important procedure to construct new complex manifolds from known ones is given as follows. let g be a subgroup of the group of automorphisms of a complex manifold m. it is easy to see that the relation  defined in m by x y if there exists an element g g∈ such that ( )y g x= is an equivalence relation. the set of equivalence classes is denoted by m / g .in general, the quotient space m / g of a complex manifold m is not necessarily a complex manifold. but by imposing some constraints on g, the complex structure on m will induce a complex structure on the quotient m / g . definition79. (1) a subgroup g of the automorphism group of a complex manifold m is said to be properly discontinuous if for every compact sets 1k and 2k of m, ( ){ }1 2g g g k k ,φ∈  ∩ ≠ < + ∞# i.e., the number of elements g g∈ such that ( )1 2g k k φ∩ ≠ is finite. boudjemaa anchouche (2) the subgroup g is said to be fixed point free if no element of { }mg \ id has a .fixed point, where mid is the identity automorphism of m. theorem 80. let g be a subgroup of the group of automorphisms of a complex manifold m. if g is fixed point free and properly discontinuous, then the quotient space m / g has a canonical structure of a complex manifold induced from that of m. example 81. torus. consider the vector space n (which has the structure of a complex lie group) and take 2n vectors ( )1 ,..., , j 1,..., 2nj j j nυ υ υ= = which are  -linearly independent. the vectors { }j 1 j 2n υ ≤ ≤ generate a discrete subgroup 2 n j j j j 1 g r r ,υ =   =  ∈    ∑  of n . then it can be shown that n n / g= t is a compact complex manifold (actually a compact complex commutative lie group) called a torus. the vectors { } 1 j 2nj υ ≤ ≤ are called the periods of nt and the matrix 1 n 1 1 1 1 2n 2 n ... . ... . . ... . . ... . ... υ υ υ υ        λ =         is called the period matrix. example 82. hopf manifold. let 1 n,...,ϕ ϕ an be n complex numbers such that j 1α > for j 1,..., ,n= and let g g= be the cyclic group generated by the automorphism ( ){ } ( ){ } ( ) ( ) n n 1 n 1 1 n n g : \ 0,..., 0 \ 0, ..., 0 z ,...,z z ,..., z .α α →  a the group g is fixed point free and properly discontinuous. therefore the quotient space ( ){ }( )1 n n,...,m \ 0,..., 0 / gα α =  , called the hopf manifold, is a compact complex manifold. it can be proved that 1 n,..., mα α is diffeomorphic to 2n-1 1s s× , where js is the j -dimensional sphere. example 83. iwasawa manifold. let m be the subgroup of ( )3gl  defined by ( ) 1 3 3 2 1 2 3 1 z z m 0 1 z z ,z ,z . 0 0 1      =  ∈          kähler manifolds positive ricci curvature denote by g the discrete group of matrices with entries in the ring of gaussian integers [ ] { }i a bi a,b= +  ∈  , i.e., ( ) [ ]( ) 1 3 3 2 1 2 3 1 z z g 0 1 z z ,z ,z i , 0 0 1      =  ∈          it can be shown g acts by biholomorphisms on m such that the quotient m / g , known as the iwasawa manifold, is a compact complex manifold, with ( )dim m / g 3= . blow-up of manifolds a second procedure to construct new complex manifolds from given ones is the blow-up. in this section we will explain what is meant by blowing up a complex manifold at a point. let us first start with a special case: nm = ∆ where n∆ is the unit polydisc, i.e., ( ){ }n 1 n 1 nz ,...,z 1,..., 1 ,z z∆ =  < < and consider the following set  ( ) [ ]( ){ }n n n-10 1 n 1 n i j j i: z ,...,z , w ,...,w z w z w 0∆ = ∈ ∆ ×  =p it can be shown that n 0∆ is a complex manifold and that { }  ( ) biholomorphic n n 1 0\ 0 \ 0 ,π −∆ ≅ ∆ and ( )1 n-10 ,π − ≅ p where π is the projection n n 0:π ∆ → ∆ ( ) [ ]( ) ( )1 n 1 n 1 nz ,...,z , w ,..., w z ,...,za the complex manifold n 0∆ is called the blow-up of n∆ and ( ) 1 0e π −= is called the exceptional divisor. consider now the general case, i.e., let m be a complex manifold, dim m n= and let m be a point of m. the "blow up" of m at m is defined as follows: let ( )u,ϕ be a local chart, with ( )m u, m 0ϕ∈ = and ( ) nu ,ϕ = ∆ the unit polydisc in nc . then definition 84. the blow up of m , denoted by  mm is defined as follows  { }( ) nm 0m : m \ m ,π= ∪ ∆ where { }( ) n0m \ m π∪ ∆ means that u is replaced with n 0∆ . it can be shown that the definition of  mm is independent of the choice of the local coordinates. from the definition, we see that  mm is a complex manifold which comes equipped with a projection  m: m m ,π → such that ( ) { } biholomorphism 1 mm \ m m \ m ,π − ≅ boudjemaa anchouche and ( ) 1 n-1mπ − ≅ p is called the exceptional divisor. 11. holomorphic vector bundles definition 85. let m be a complex manifold of dimension n . a holomorphic vector bundle of rank rover m is a complex manifold e together with (1) a surjective holomorphic map meπ →: , such that ( ) 1 x xe π −= has a structure of a complex r dimensional vector space, where r is independent of x . (2) an open covering ( )uα α ∈ of m and biholomorphisms α' called trivializations ( )1u: u u re α α α αϕ π −  = → ×  such that for each x uα∈ , the map { } r rx x ,e ϕ α→ × →  is a  -linear isomorphism. example 86. (1) if m is a complex manifold, then m r×  is a vector bundle of rank r , called the trivial bundle. (2) the tangent bundle 1,0 mt of a complex manifold m (see 9 below for a definition). (3) let m be a compact complex manifold and denote by m its universal cover, ( )1 mπ its fundamental group acting on m on the right, and let ( ) ( )1: m gl vρ π → be a complex linear representation of ( )1 mπ . then v m vρ ρ= × is a holomorphic vector bundle over m , where  m v m v/ ,ρ× = ×  and ( ) ( ) ( ) ( ) 1 1 2 2 1 1 2 1 2 1 m ,v m ,v g m m m .g v v such that and π ρ − ⇔ ∃ ∈ = =  g almost complex manifolds definition 87. an almost complex structure j on a c ∞ -differentiable manifold m is a section of ( )d mne t , such that at each m 2 m mm m , j id∈ = − t , where m m idt is the identity transformation of m mt . an almost complex manifold is a pair ( )m, j where m is a c ∞ -differentiable manifold and j is an almost complex structure. remark 88. (1) it can be shown that every almost complex manifold is orientable and of even dimension. (2) not every orientable manifold of even dimension can carry an almost complex structure, for example borel and serre (1951) proved that the spheres ns do not admit an almost complex structures if 2, 6n ≠ . proposition 89. every complex manifold cames an almost complex structure. let ( ) n 1 nz ,...,z ∈  , and put j 2 j-1 2 j z x 1x= + − with respect to the coordinate system ( )1 n n+1 2nx ,...,x ,x ,...,x , we define an almost complex structure as follows 2 j-1 2 j 2 j 2 j-1 j j , j 1, 2, ..., n. x x x x and    ∂ ∂ ∂ ∂ = = − =      ∂ ∂ ∂ ∂    (8) kähler manifolds positive ricci curvature therefore, every complex manifold is an almost complex manifold. the converse is not true in general, i.e., an almost complex manifold need not be a complex manifold. but if we impose some restrictions on the almost complex structure then the converse becomes true. define the torsion jn of an almost complex structure j by ( ) [ ] [ ] [ ] [ ]j x, y jx, jy x, y j x, jy j jx, y ,n = − − − where x and y are vector fields. the torsion jn is a tensor, called the nijenhuis tensor. definition 90. an almost complex structure is said to be integrable if has no torsion, i. e., if ( )j x, y 0n = for all vector fields x and y . theorem 91. (newlander and nirenberg, 1957) an almost complex structure is a complex structure if and only if it has no torsion. let m be a complex manifold and ( )j mnd∈ e t be the almost complex structure induced from the complex structure of m see birkenhake and lange (1992), where mt tangent bundle of the underlying c ∞ -manifold m . the endomorphism j extends to the complex vector bundle mt , where mt is the complexification of the real tangent space of the underlying c ∞ -manifold m , i.e., m m= ⊗  t t . from 2 mid= − tj , we deduce that 1,0 1,0m m m ,= ⊕  t t t { } { }1,0 1,0m x m jx 1x and m x m jx 1x= ∈  = − = ∈  = − − t t t t (9) then 1,0 mt is a holomorphic vector bundle of rank n and 1,0 mt is the conjugate of 1,0 mt , i.e., 1,0 1,0m m≅t t . we can identify mt with 1,0 mt via the correspondence ( ) 1,01m x x 1 jx m2 − −∋ ∈at t (10) consider a local complex chart ( )( )1 nu, ,...,z z where 2 1 2x 1xj j jz −= + − . then 1 2 n ,..., x x  ∂ ∂   ∂ ∂  constitutes a basis for mt over  . (also a basis for mt over c ), i.e., 1 2n 1 2n m span ,..., , m span ,..., , x x x x    ∂ ∂ ∂ ∂ = =    ∂ ∂ ∂ ∂       t t and 1 2n ,..., z z  ∂ ∂   ∂ ∂  (resp. 1 2n ,..., z z  ∂ ∂   ∂ ∂  ) a basis for 1,0 mt (resp. 1,0 mt ), where 1z ∂ ∂ and 1z ∂ ∂ are as in 7, in other words, 1 n 1 n m span ,..., , ,..., , z z z z  ∂ ∂ ∂ ∂ =   ∂ ∂ ∂ ∂    t and 1,0 1,0 1 n 1 n m span ,..., , m span , ..., z z z z    ∂ ∂ ∂ ∂ = =    ∂ ∂ ∂ ∂      t t the dual of the holomorphic vector bundle 1,0 mt will be denoted by 1 mω . let m and n be two complex manifolds. recall that a c ∞ -map f : m n→ between the underlying c ∞ manifolds is said to be holomorphic if boudjemaa anchouche ( ) ( )1o f o : u vϕ ϕ−ψ → ψ is a holomorphic map, for all local complex charts ( )u,ϕ of m and ( )v,ψ of n such that ( ) 1u vϕ −⊂ . at each point m m∈ , the differential ( )m f mdf : m n ,→t t is an  -linear map. by complexification, we get a linear map (denoted also by df ) ( ) ( ) ( )m f mdf : m n→ t t in general ( )( ) ( ) ( )1,0 1,0m f mdf : m n⊄t t it can be shown that theorem 92. let m and n be two complex manifolds and f : m n→ a c ∞ -map between the underlying c ∞ manifolds. then f is holomorphic if and only if ( )( ) ( ) ( )1,0 1,0m m f mdf m n m mfor all⊆ ∈t t 12. differential forms on complex manifolds let m be a complex manifold of dimension ,n ω a differential p -form, ( )u,ϕ a local chart and let ( )1 nz ,...,z be the system of complex coordinates associated to ϕ . put j 2 j-1 2 j z x 1x= + − . then ( )1 n n+1 2nx ,...,x ,x ,...,x are the local coordinates of the underlying c ∞ -manifold in u. in ( )( )1 n n+1 2nu, x ,...,x ,x ,...,x we write ( ) ( ) 1i i i 1 i<...<i 2n x a ,..., i x dx ... dx , p p pω ≤ ≤ = ∧ ∧∑ (11) where i a ,..., i p are complex valued functions on u. from j j 2j-1 2j j 2 j-1 2 jz z x 1x , z x 1x ,= = + − = − − we deduce that ( ) ( )2 j-1 j j 2 j 1 1 x z +z , x z z 2 2 1 j j= = − . hence , ( ) ( )2 j-1 j j 2 j j j 1 1 dx dz d and dx dz d . 2 2 1 z z= + = − − (12) by substituting 12 in 11, we get ( ) 11 j1 j k kj,...,j , k ,..., k r s p b dz ... dz dz ... dz . r sp s zω + = = ∧ ∧ ∧ ∧ ∧∑ definition 93. a differential form ( ) 1 1 1j1,...,j ,k ,...,k j j k k b z dz ... dz dz ... dz r s r s θ = ∧ ∧ ∧ ∧ ∧∑ (13) is called a differential form of type ( )r, s . then a p -form θ can be expressed in a unique way as kähler manifolds positive ricci curvature r,s r s p θ θ + = = ∑ , where r,sθ is a form of type ( )r, s , it can be shown that the type of a form is independent of the choice of the local complex coordinates. for a function ( ) 1f u,c∈  , we have n n i i i=1 i=1 f f df dz dz . z zi i ∂ ∂ = + ∂ ∂ ∑ ∑ we put n n i 1 i 1 f f f dz and f dz z zi ii i= = ∂ ∂ ∂ = ∂ = ∂ ∂ ∑ ∑ in the same way, for an ( )r, s form θ as in (13) with coefficients in ( ) 1 u, ,c  we put ( )( ) 11 1 j1 j k kj ,..., j ,k ,...,kb z dz ... dz dz ... dz ,r sr sθ∂ = ∂ ∧ ∧ ∧ ∧ ∧ ∧∑ and ( )( ) 11 1 1j ,..., j , k ,...,kb z dz ... dz dz ... dz .r sr s j j k kθ∂ = ∂ ∧ ∧ ∧ ∧ ∧ ∧∑ theorem 72 is equivalent to ( ) ( ){ }2locf f 0 .h lω = ∈ ω  ∂ = definition 94. a holomoryhic p -form is a ( )p, 0 form ω satisfying 0ω∂ = . remark 95. it is possible to define integration of smooth differential forms on any complex manifold, since it can be shown that every complex manifold is orientable. for a proof, see kobayashi and nomizu (1969). 13. kähler manifolds definition 96. a hermitian metric on an almost complex manifold ( )m, j is a riemannian metric g which is invariant under the almost complex structure, i.e., ( ) ( )g jx, jy g x, y= for all vector fields x and y . theorem 97. every paracompact almost complex manifold ( )m, j admits a hermitian metric. the proof goes as follows: let h be a riemannian metric on the underlying c ∞ -manifold m whose existence is guaranteed by theorem 36. then the metric g defined by ( ) ( ) ( )g x, y h x, y h jx, jy .= + for all vector fields x,y is a hermitian metric. the fundamental (1,1) -form associated to the hermitian metric g is given by ( ) ( )g x, y g x, jy .ω = a very important class of hermitian manifolds is given by what we call "kähler manifolds" . definition 98. a kähler manifold is a pair ( )m, g , where m is a complex manifold and g is a hermitian metric whose associated (1, 1) form g ω is closed, i.e., g d 0.ω = boudjemaa anchouche let ( )m, g be a hermitian manifold. then the hermitian inner product g in m mt can be extended to a unique complex symmetric bilinear form in the complex tangent space m t of m . if x and y are two holomorphic vector fields written in the local chart ( )( )1 nu, z ,...,z of m as n n i i i=1 i=1i i x and y , z z ξ ζ ∂ ∂ = = ∂ ∂ ∑ ∑ then ( ) n i, i jj i,j 1 g x,y g ,ξ ζ = = ∑ where ( )i, m m mj ji g m g , . z z   ∂ ∂ =   ∂ ∂  then the metric is usually written as ( ) ( ) n i, i jj i,j 1 g z 1 g z dz dz = = − ⊗∑ the matrix ( )( )i, 1 i nj 1 j n g z ≤ ≤ ≤ ≤ is a positive definite hermitian symmetric matrix. the associated (1, 1) form g ω is given by ( ) n g i, i jj i,j 1 1 g z dz dz .ω = = − ∧∑ the length of a tangent vector n i m i,j 1 i x m z ξ = ∂ = ∈ ∂ ∑ t , is given by ( ) n i, j i,j 1 x g z i jξ ξ = = ∑ theorem 99. a hermitian manifold ( )m, g is kähler if and only if one of the following conditions is satisfied. (1) i, k,g g z z j j i ∂ ∂ = ∂ ∂ ; (2) , ,g g z z i j i k k i ∂ ∂ = ∂ ∂ ; (3) for every m m∈ , there exists an open neighborhood u of m and a differentiable real junction f defined in u such that 2 i, jg u i j f 1 f . ., g z z i eω  ∂ = − ∂∂ = ∂ ∂ there are other equivalent characterization of kähler manifolds which will not be given here. example 100. (1) every hermitian manifold of dimension one is necessarily kähler. (2) the complex euclidean space nc equipped with the "euclidean" metric kähler manifolds positive ricci curvature ( ) n n ec 1 i,j 1 g z 1 dz dz . 1 dz dz eci i g i i i resp ω = =   = − ⊗ = − ∧    ∑ ∑ . is a complete kähler manifold with zero curvature. (3) the unit ball ( ) n 2n n 1 n i=1 b z z ,..., z z z 1 ,i    = = ∈  = <     ∑ is a complex manifold which can be endowed with a complete kähler metric, called the bergman metric, with negative curvature. (4) the complex torus n / λ , is a kähler manifold, since it can be shown that the euclidean metric on n induces a kähler metric on n / λ . (5) every complex sub manifold of a kähler manifold is kähler, it is enough to take the induced metric. example 101. the fubini-study metric on np . the projective space np carries a canonical metric called the fubini-study metric and defined as follows (the notations are those of example 75): [ ] n n 0 i-1 i+1 n 0 n i i : u z z z z z ,...,z ,..., , ,..., . z z z z i i i i ϕ ⊂ →        a p on ui , consider the closed (1,1) form defined by n k 0 z1 1n . 2 z k i i ω π =  − = ∂∂      ∑ then on u ,ui j , we have n k 0 2 n k 0 n k 0 z1 2 z z z1 1n 2 z z z1 1n 2 z k j j i k j i k i i ω π π π ω = = =  −  = ∂∂      −  = ∂∂      − = ∂∂      = ∑ ∑ ∑ the last equality is a consequence of the fact that z z i j is a nonvanishing holomorphic function on u ui j∩ , hence in 2 z z i j is pluriharmonic, i.e., 2 z 1 1n 0 z i j − ∂∂ = boudjemaa anchouche therefore we have a global (1,1) form, denoted by fsω , defined by fs ui iinω ω= for [ ]0 nz ,...,z ui∈ , put z w z j j i = . an easy computation gives ( ) ( ) ( ) ( ) ( ) 2n n n n 1 1 1 1 fs 22n j 1 1 w dw dw w dw w dw1 u , 2 1 w j j j j j j jj j j j i j inω π = = = = = + ∧ −− = + ∑ ∑ ∑ ∑ ∑ since the unitary group ( )u n 1+ acts transitively on np , and since fsω is invariant under ( )u n 1+ , it is enough to check the positive definiteness of fsω at the point [ ]1, 0,..., 0 . but at the point [ ]1, 0,..., 0 , we have [ ]( ) n fs j 1 1 1, 0,..., 0 dw dw , 2 j j ω π = − = ∧∑ which is positive definite. therefore ( ) n fs, gp is a kähler manifold, where fsg , called the fubini-study metric, is the kähler metric whose associated (1,1) form is fsω . the fubini-study metric can also be described as the kähler metric fsg on np whose associated (1,1) form fsω satisfies ( ) n * fs j 0 1 1n z , 2 j π ω π =  − = ∂∂     ∑ where { } ( ) [ ] n+1 n 0 n 0 n : \ 0 z ,...,z z ,...,z π → a p some basic properties of kähler manifolds can be summarized in the following theorem 102. let m be a compact kähler manifold. then (1) ( )2 kb m 1≥ , where ( )2kb m is the 2k th betti number of m . (2) every holomoryhic p form on m is closed. for a proof, see (griffiths and harris, 1978). hodge decomposition the following decomposition theorem, called the hodge decomposition theorem plays a fundamental role in the understanding of the structure of compact kähler manifolds. the existence of such decomposition implies restrictions on the topology of compact kähler manifolds. some of its corollaries will be used to construct compact complex manifolds without kähler structure. theorem 103. let m be a compact kähler manifold. then ( ) ( ) ( ) ( ) k i,j i j k i,j j,i h m, h m h m h m + = ≅ ⊕  =  (14) kähler manifolds positive ricci curvature where ( ) ( )i,j j imh m h m,≅ ω for the definitions of the spaces ( ) i,jh m and a proof of theorem 103, we suggest [21]. as a consequence of theorem 103, we have the following corollary 104. let m be a compact kähler manifold. then the odd betti numbers 0. (m are even, i.e., ( )2k 1b m+ are even. the proof of the corollary is straightforward. from (14), we deduce that ( ) ( ) ( ) ( ) i,j r i j r i,j j,i b m b m b m b m , + =  =  = ∑ where ( ) ( ) i,j i,jb m dim h m= . by putting r 2k 1,= + we get ( ) ( ) k s,2k 1-s 2k+1 s 0 b m 2 b m .+ =   =     ∑ remark 105. it is very important to mention that not every hermitian manifold is kähler, as is shown in the following examples. example 106. (1) let m / g be the iwasawa manifold defined in example 83. for a m∈ , we have 1 3 1 2-1 2 0 dz dz z dz a da 0 0 dz . 0 0 0    =       the one-forms 1 2dz , dz and 3 1 2dz z dz− on m are left invariants under g and therefore induce holomorphic one forms on the quotient manifold m / g . since 3 1 2dz z dz− is not closed, by theorem 102 the iwasawa manifold m / g carries no kähler structure. (2) let 1 n,..., mα α be the hopf manifold defined in example 82 and suppose that 2n ≥ . it can be shown that 1 n,..., mα α is diffeomorphic to 2n -1 1s s× . hence ( )1 n1 ,...,b m 1,α α = where ( )1 n1 ,...,b m 1,α α = is the first betti number of 1 n,..., mα α . then, by corollary 104, the manifold 1 n,..., mα α carries no kähler structure. 14. projective manifolds definition 107. a projective manifold (or a smooth projective variety) is a closed submanifold of np for some positive integer n . we collect some of the properties of projective manifolds in the following theorem 108. (1) if 1m and 2m are projective, then 1 2m m× is projective. (2) if m is projective, then mm % is projective, where mm % is the blow-up of m at m m∈ . boudjemaa anchouche (3) every compact riemann surface, i.e., compact complex manifold of dimension one, is projective. let n be an integer 2≥ . a torus n n / g= t is not necessarily projective (the notations are those of example 81). theorem 109. let n be an integer 2≥ . a torus n n / g= t is projective if and only if and only if the lattice a satisfies 1 1 1) 0 2) 1 j 0 − −  ∧ ∧ =  − ∧ ∧ > t t j for some alternating 2 2n n× integral matrix j , where the condition 2) above means that the matrix 11 −− ∧ ∧> j is positive definite. definition 110. a torus nt which is a projective variety is called an abelian variety. readers who want to know more on abelian varieties can consult (birkenhake and lang, 1992, griffiths and harris, 1978 or mumford,1974) . remark 111. every projective manifold m is necessarily kähler, since the restriction of the fubini-study metric of np to m is kähler. the converse is not true, i.e., not every kähler manifolds is projective. for example if we take any lattice λ not satisfying the conditions in theorem 109, then n n / g= t is kähler but not projective. therefore, we have {projective manifolds} ≠ ⊂ {compact kähler manifolds} definition 112. a quasi-projective variety is a an open subset (in the zariski topology) of a projective variety. the readers who want to know more about complex algebraic geometry, can consult the following references: demailly, , griffiths and harris, 1978 or shafarevich, 1977. part 3. compact kähler manifolds of positive ricci curvature (fano manifolds) compact kähler manifolds of positive ricci curvature playa very important role in the classification of complex algebraic varieties. the aim of this section is to give an overview of some of the main results in this area. in all what follows, we will assume some knowledge of sheaf theory, a very nice introduction can be found for example in kodaira, 1986 or griffiths and harris, 1978. 15. chern curvature of a hermitian line bundle let m be a compact complex manifold and consider the following exact sequence of sheaves * exp0 0 ,m m→ → → → o o (15) where  is the constant sheaf, mo the sheaf of holomorphic functions and * mo the sheaf of nonvanishing holomorphic functions. the exact sequence (15) induces an exact sequence of cohomology groups ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 * 1 1 1 * 2 0 h m, h m, h m, h m, h m, h m, h m, ... m m m m δ → → → → → → → →    o o o o (16) kähler manifolds positive ricci curvature the set of holomorphic line bundles on m constitute a group under the tensor product called the picard group and denoted by ( )pi mc .it can be proved that proposition 113. ( )pi mc is isomorphic to ( ) 1 *h m, mo . in what follows, we will identify ( )pi mc with ( )1 *h m, mo . definition 114. the image ( ) ( ) 2h m,lδ ∈  of a line bundle ( ) 1 *h m, ml ∈ o is called the first chern class of l and is denoted by ( )1c l . in what follows, we will identify ( )1c l to its image in ( ) 2 drh m using the following ( ) ( ) ( ) ( ) de rham isomorphism 2 2 2 1 drh m, h m, h mc l ∈ ⊂ ≅  definition 115. let m be a complex manifold of dimension n. the first chern class of m denoted by ( )1 mc is defined by ( ) ( )11 1 mm : kc c −= where 1 n 1,0 mk m , − = λ t is the anticanonicalline bundle of a complex manifold m . let ( ), hl be a hermitian line bundle over m , and let ( )iui ∈ be an open covering of m such that iu i uil → × ñ ׀ is an isomorphism. the point ( )m, uiζ ∈ ×  is identified with the point ( ) ( )( )1o m, m, g m uj i ji jζ ζ− = ∈ × ñ ñ . the functions g ji are nonvanishing holomorphic functions defined in u ui j∩ . it is very easy to check that the functions ( ) , g ji i j , satisfy the following relation g g 1 in u u g g g u u u ji ij i j ji ik jk i j kin = ∩  = ∩ ∩ (17) conversely, given a set of nonvanishing holomorphic functions g : u u ,ji i j∩ →  satisfying (17), we can define a line bundle with transition functions ( ) , g ji i j , as follows: we put ( )( )i iu /l = ×c   where c is the disjoint union, and ( ) ( )i ju z, z , uξ ξ′ ′× ∈ ×  ∋ if and only if z z′= and ( ),g z .i jξ ξ′ = for each m m∈ , and mv l∈ we define the norm h v with respect to the metric h as follows boudjemaa anchouche ( )2 m2 hv , je ϕζ −= where it j ϕ is c ∞ function defined in u ,j and ( ) ( )m, vjζ = ñ . the definition of i' implies that ,1n g in u u .i i i j i jϕ ϕ= + ∩ since ,i j g is a non vanishing holomorphic function, it follows that , 1n gi j is pluriharmonic, i.e., ,1 1n g 0.i j− ∂∂ = therefore 1 1 in u u ,i j i j− ∂∂ = − ∂∂ ∩' ' and hence defines a global (1,1) form on m . definition 116. the chern curvature of the hermitian line bundle ( ), hl , is the real closed (1,1) form given by h i1 ϕ= − ∂∂θ remark 117. let { }iui ∈ and { }, i,ji jg ∈ be as above, and assume that all the intersections u ui j∩ are simply connected (if nonempty). then { } ( )1 *,g h m,i j ml  = ∈  o . since the holomo1phic functions ,i jg are non vanishing on u ui j∩ , then choose a branch of log ,i j g , which is one valued holomo1phic function, and put ( )1 log log log 2ijk jk ik ij σ π − = − − +g g g then it can be shown that the chern class ( )1c l is given by ( ) { } ( )21 h m, .ijkc l σ = ∈   to state the next theorem we need the following definitions. definition 118. let m be a complex manifold. (1) a subset d of m is called a hypersurface if for every m m∈ , there exists a neighborhood u of m and a nonzero holomo1phic function f on u such that ( ){ }d u x u | f x 0 .∩ = ∈ = (2) a divisor d is a formal linear combination of a finite number of irreducible analytic hypersurfaces di with integer coefficients i.e., d d , .i i i ν ν ν= ∈∑  (a) the divisor d is said to be effective if 0iν ≥ , and it is called a reduced divisor if 1iν = for all i . (b) an effective divisor d diν= ∑ is called a simple normal crossing divisor if d is reduced, each component di is smooth, and for x d∈ , there exist ( )u,z , x u∈ , a local complex chart, such that { }1 ku d z u | z ...z 0∩ = ∈ = for some k n≤ . to each divisor d di iν ν= ∑ , we can associate a line bundle, denoted [ ]d as follows: let ( )ju ,z and j kx u u∈ ∩ , be two local coordinate systems and suppose that ( ){ }ii i i iu d z u | f z 0 ; i j,k,∩ = ∈ = = kähler manifolds positive ricci curvature where |fi is a holomorphic function in iu , i = j,k . then j i i f f k is a nonvanishing function in j k u u∩ put ( ) ( ) ( ) i j,k i i f z f z f z ij k ν   = π      (18) then it is easy to see that j,k f satisfies the condition (17), and hence are the transition functions of a line bundle. definition 119. the line bundle with transition functions { }j,kf defined in 18 is called the line bundle associated to the divisor d and denoted by [ ]d . remark 120. over projective algebraic manifolds, every line bundle l is of the form [ ]dl for some divisor d l , i.e., [ ]dll ≅ theorem 121. let ( ), hl be a hermitian line bundle over m and let hθ be its curvature. then ( ) ( )21 h dr 1 c h m 2 l π  − = θ ∈    , where h 1 2π  − θ    is the cohomology class of h 1 2π − θ in ( ) 2 drh m . moreover, h 1 2π  − θ    is independent of the choice of the metric h. for a proof, see griffiths and harris (1978). definition 122. let ml → be a line bundle over a compact complex manifold m, dim m n= and let ( ) ( )21 h m,c l ∈  be the first chern class of l . we say that ( )1c l is positive (resp. negative) and write ( )1 0c l > (resp. ( )1 0c l < ) if the cohomology class ( )1c l can be represented by a (1,1) closed real form n i j i,j 1 1 dz d , 2 i j z π = − ω = ∧∑ ' where the matrix ( )1 i n, 1 j n i jϕ ≤ ≤ ≤ ≤ is positive definite (resp. negative definite) at each point m m∈ . the line bundle l is said to be positive (resp. negative) if ( )1 0 ,c l > (resp. ( )1 0c l < ). remark 123. it can be shown that a line bundle ml → over a compact kähler manifold m is positive if and only if there exists a hermitian metric on l with positive curvature. the expression of the ricci curvature in the kähler case is very simple, more precisely we have proposition 124. let (m,g) be a compact kähler manifold, where ( ) ( ) n i, j i,j 1 g z 1 g z dz dzi j = = − ⊗∑ boudjemaa anchouche then ( )g i, jric 1 1 det g ,n  = − − ∂∂   and ( )g 1 1 ric c m , 2π   =   where g 1 ric 2π      is the de rham cohomology class of g 1 ri 2 c π 16. line bundles on projective spaces the aim of this section is to sketch a proof of the fact that the picard group of ( ) npic p is an infinite cyclic group and then construct a generator of ( ) npic p . proposition 125. ( )npic isomorph ≅ p proof. (sketch of a proof): we start from the following well known fact ( ) ( )n nr 0 if r odd b dim h , 1 if r even r = =    p p (19) from (103) and (19), we deduce that ( )np n 0 if p qdim h , 1 if p q q ≠ω =  =  p p in particular ( )n n np n 0dim h , 0 if p 1 (since ).= ≥ = ω p p pp o o (20) from the exact sequence (16), and (20), we deduce that ( ) ( ) ( )nn 1 n * 2 npic h , h , .≅ ≅ p p po the proposition follows from the well known fact that ( )2 nh , ≅ p a construction of a generator of ( ) npic p , called the tautological line bundle, goes as follows definition 126. the tautological line bundle over np , denoted by ( )n 1−po , is the line subbundle of the trivial bundle n n+1× p defined as follows: ( ) [ ]( ){ }n n n+11 , | .zz ξ ξ− = ∈ × ∈ p po the dual of the line bundle ( )n 1−po will be denoted by ( )n 1po , i.e., ( ) ( )n n *1 : 1− = p p o o for a positive integer k , we put kähler manifolds positive ricci curvature ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) n n n n n n n n k-times k-times k 1 1 ... 1 -k 1 1 ... 1 k k = ⊗ = ⊗ ⊗ = − ⊗ = − ⊗ ⊗ − 644474448 64444744448 p p p p p p p p o o o o o o o o a definition of ( )n 1−po ( )( )nresp. 1po in terms of its transition functions is left to the reader. it can be shown that proposition 127. the picard group of np is generated by the line bundle ( )n 1po , i.e., ( ) ( )nnpic 1= pp o for a proof proposition 127, see kodaira (1986). remark 128. (1) (2) if n k p is the canonical line bundle of np , then ( )n nk n 1≅ − −p po (3) if d is a smooth hypersurface of degree d in np , i.e., [ ] ( ){ }n0 n 0 nd z ,...,z | f z ,...,z 0 ,= ∈ =p where f is a homogeneous polynomial of degree d , then [ ] ( )nd d≅ po proposition 129. the fubini-study (1,1) form fsω on np represents the first chern class of the line bundle ( )n 1po , i.e., ( )( ) [ ]n1 fs1c ω=po therefore, ( )n 1op is positive. proof. (sketch of the proof) we will construct a hermitian metric on the line bundle ( )n 1po , and we will show that its curvature coincides with the fubini-study metric. since the fiber of the line bundle ( )n 1−po at a point [ ] nz ∈ p is given by [ ] ( )n , z 1 .z.− = po then, we define a hermitian metric h on ( )n 1−po as follows ( ) n 22 0 n h i i 0 z ,...,z z = = ∑ if { } ( ) ( ) n n+1 1 n 1 n : u \ 0 z ,...,z 1, z ,....,z s ⊃ →  a p is a local section, then ( ) n 22 0 n h i i 1 z ,....,z 1 zs = = + ∑ boudjemaa anchouche the curvature of the metric h is given by ( ) 2h 1 n h1 1n s z ,...,z= − − ∂∂θ hence the the curvature of the induced hermitian metric *h on the dual bundle ( )n 1op is given by ( ) ( ) * * 2 1 nh h 2 1 n h n 2 i i 1 1 1n s z ,...,z 1 1n s z ,...,z 1 1n 1 z = = − − ∂∂ = − ∂∂   = − ∂∂ +    ∑ ä it can be shown (see griffiths and harris, page 30) that hä ( therefore *h ä ) is independent of the local lifting (21) .by theorem 121, the (1,1) form *h 1 2π − ä represents the first chern class of the line bundle ( )n 1po . since the fubini-study metric fsω on np is equal to *h 1 2π − ä , we deduce that fsω represents the first chern class of the line bundle ( )n 1po . 17. kodaira embedding theorem as was said above, every projective manifolds is kähler, but the converse is not true. kodaira's embedding theorem gives a characterization of projective manifolds among compact kähler manifolds as those admitting positive line bundles, more precisely we have theorem 130. (kodaira, 1954) (kodaira embdding theorem) let ( )m, g be a compact kähler manifold and let ml → be a holomorphic line bundle. then l is positive if and only if there exists a holomorphic embedding n: mψ → p ( )m m ,ψa of m into some projective space such that ( )( )n* 1 l ν⊗ψ =po for some positive integer ν . proof. (sketch of a proof) suppose that such an embedding ψ exists. since fsω represents ( )( ) ( )n *1 fsc 1 , ωψpo represents ( )( )n1c 1  ψ  po and obviousely it is a positive (1,1) form. but ( )( ) ( )( )( ) ( ) ( ) n n * 1 1 1 1 c 1 c 1 , c c .l lν υ ν⊗  ψ = /  = = p p o o hence ( )* fs 1 ω ν ψ represents ( )1c l , i.e., l is positive. the converse is hard. for a proof, see (kodaira, 1954), or (griffths and harris, 1978). corollary 131. a compact kähler manifold ( )m, g with positive ricci curvature is projective. proof. by proposition 124, kähler manifolds positive ricci curvature ( )1 1 ric c m 2 gπ   =   hence -1 mk is positive. the corollary from the kodaira's embedding theorem by taking -1 mkl = . definition 132. a holomorphic line bundle ml → over a compact kähler manifold m is said to be ample (resp. very ample) if there exists an embedding nm υ/→ p for some positive integer n such that ( )( )n 1l ν ψ⊗ = po for some positive integer ( )( )( )n *. 1 .resp lν π= ψ p o theorem 133. a compact kähler manifold ( )m, g is projective if and only if there exists a kähler metric h (not necessarily equal to g ) such that the cohomology class [ ]hω is rational, i.e., [ ] ( ) 2 h h m, ,ω ∈  where hω is the (1,1) form associated to the kähler metric h . proof. (sketch of the proof) suppose that m is projective, i.e., i: embedding nm → p . then the restriction * fsi ω of the fubini-study metric on np to m is a kähler metric on m . since the fubini-study metric is the first chern class of the autological line bundle ( )n 1po on np , it has integral cohomology class, i.e., ( ) * 2 fsi h m,ω  ∈   . for the converse, see griffiths and harris (1978). as a consequence of hodge decomposition theorem, we have the following corollary 134. let ( )m, g be a compact kähler manifold satisfying ( )2 mh m, 0.=o (22) then m is projective. proof. (sketch of the proof) the assumption (22) is equivalent to ( ) ( )2,0 0, 2m, m, 0.h h= =  then hodge decompostion theorem implies that ( ) ( )2 1,1h m, h m, .≅  then there exists d -closed (1,1) -forms 1 ,..., kθ θ on m such that their cohomology classes [ ] [ ] ( )21 ,..., m,k hθ θ ∈  and [ ] [ ]{ }1 ,..., kθ θ constitute a basis for ( ) 2h m, .hence, there exists k real numbers 1 ,..., kα α suh that [ ] 1 k g i i i ω α θ = = ∑ . choose k rational numbers 1 ,..., kβ β suh that iβ is very close to iα and consider the following (1,1) form [ ] 1 . k i i i ϖ β θ = = ∑ then ϖ is d -closed, positive, and satisfies [ ] ( ) 2h m,ϖ ∈  .theorem 133 implies that m is projective. boudjemaa anchouche 18. fano manifolds definition 135. a projective manifold is said to be fano if 1 mk − is ample, where 1 mk − is the anticanonical line bundle. example 136. (1) there is only one fano manifold of dimension one, it is 1p . (2) fano manifolds of dimension two are called del-pezzo surfaces and are completely classified. they are 1 1 2× ×p p p , and ( ) 2 1p ,..., p , 1 k 8 ,k ≤ ≤p where ( ) 2 1p ,..., pkp is obtained by blowing up 2p at 1p ,..., pk in general position. (3) the projective space np is a fano manifold. (4) let m be a smooth complete intersection of ν hypersurfaces of degree 1d ,...,dν in np . then n 1 m i=1 k n 1 d .i ν −  = +    ∑op in particular, m is fano if and only if ii=1 d 1.n ν < +∑ (5) let g be a complex reductive group and p a parabolic subgroup of g . then the homogeneous space m g / p= is a fano manifold. from the algebro-geometric point of view, a fano manifold m is a smooth projective variety with ample anticanonical bundle 1 mk − , and from the differential geometric point of view, a fano manifold m is a compact complex manifold admitting a kähler metric with positive ricci curvature. the two definitions are equivalent by yau's solution of the calabi conjecture theorem 137. (yau, 1977) a smooth projective variety m is fano if and only if m admits a kähler metric with positive ricci curvature. as was mentioned before, there is close interplay between curvature and topology of a manifold. in the case of a compact riemannian manifold, we have seen (theorem 46) that the fundamental group is finite. in the kähler case we can say more. theorem 138. (kobayashi, 1961) a compact kähler manifold m with positive ricci curvature is simply connected, i.e., ( )1 m 0.π = the proof uses the riemann-roch-hirzubruch theorem, myer's theorem, and the following result of bochner proposition 139. a compact kähler manifold of positive ricci curvature admits no non-zero holomorphic p forms, for p 1≥ .. for a proof see kobayashi (1987). part 4. einstein-kähler metrics on fano manifolds definition 140. (1) a kähler metric h on a compact complex manifold m is said to be einstein-kähler if h hric c ,ω= where c is a constant, hω is the closed (1,1) form associated to the kähler metric h and hric is the ricci (1,1) form associated to the kähler metric h . (2) a compact kähler manifold m is said to be einstein-kähler if it admits an einstein-kähler metric. one of the main problems related to fano manifolds and not solved yet is to decide when a compact kähler manifolds of positive ricci curvature has an einsteinkähler metric. obstructions to the existence of einsteinkähler manifolds positive ricci curvature kähler metrics on compact kähler manifolds of positive ricci curvature were discovered by several mathematicians. below, we will introduce two obstructions discovered by matsushima and futaki and an invariant constructed by tian. 19. matsushima's obstruction let m be a complex manifold. an automorphism (biholomorphism) f : m m→ of m is a holomorphic map from m to m such that there exists a holomorphic map g : m m→ with mg o f f o g id= = , where mid is the identity map of m . the set of automorphisms of m , denoted by ( )aut m , has a structure of a group under the composition of maps. in case the complex manifold m is compact, we can say more, theorem 141. let m be a compact complex manifold. then ( )aut m is a complex lie group and its lie algebra ( ) ( )( )m ie aut m= ly consists of holomorphic vector fields of m . for a proof, see (kobayashi and nomizu, 1969). definition 142. a complex lie group g is called reductive if the lie algebra g of g is isomorphic to the complexification of the lie algebra k of a compact lie group k , i.e., ≅ ⊗  g k the lie algebra k is called a real. form of the lie algebm g . example 143. (1) if ( )g g n,= l , then g k=  , where ( )k u n= . moreover ( ) ( )nl n, m ,≅ g g= and ( ) ( ){ }*n a l n, a a 0 .u= = ∈  + =k g (2) if ( )g so n,=  , then g k=  , where ( )so nk = . moreover ( ) ( ){ }*o n, a l n, a a 0 ,= = ∈  + = g s g and ( ){ }a l n, a a 0 .∈  + =k = g t . (3) if ( )g sp n,=  , then g k=  , where ( )k sp n= . moreover ( ){ }a l 2n, a j ja 0 ,∈  + =g = g t and ( ){ }a l 2n, a j ja 0 .∈  =k = g t + more details about lie groups (resp. algebraic groups) can be found in (knapp, 2001) or (brocker, et al., 1985) (resp. (borel, 1991) or (humphreys, 1975). theorem 144. (matsushima, 1957) the automorphism group ( )aut m of a compact einstein-kähler manifold of positive ricci curvature is reductive. at the level of lie algebras, matsushima's theorem says that if m be a compact einstein-kähler manifold with non zero ricci curvature then the lie algebra ( )mi of infinitesimal isometries (or killing vector fields) is a real form of the lie algebra ( )h m of holomorphic vector fields, i.e., ( ) ( ) ( )h m m 1 m .i i= ⊕ − boudjemaa anchouche remark 145. if ( )1 m 0 ,c < then ( )aut m is finite, and consequently ( )h m 0.= . therefore matsushima's theorem is not obvious only when ( )1 m 0.c > . example 146. (futaki, 1988 ) let ( )2 1 2p ,p%p be the projective plane 2p blown up at two points 1 2p , p . it can be shown that ( )2 1 2p ,pp is a compact kähler manifold with positive ricci curvature whose automorphism group is not reductive, therefore it cannot carry an einstein-kähler metric. in dimension two, the reductivity of ( )h m is the only obstruction to the existence of einstein-kiihler metrics as shown by the following result theorem 147. (tian, 1990) any compact complex surface m with positive ricci curvature admits an einsteinkähler metric if ( )h m is reductive. in higher dimension, there are other obstructions to the existence of einstein-kähler metrics besides matsushima's obstruction. 20. futaki's invariant for the construction of futaki's invariant, we need the following lemma 148. let θ be a real ( )p,p form on a compact kähler manifold which is cohomologous to zero, i.e., dθ β= . then there exists a ( )p -1,p -1 form η such that 1 .θ η= − ∂∂ the proof uses the hodge theorem for the ∂ operator (see [33], proposition 7.24, for the details). let g ω be a (1,1) form associated to a kähler metric g and suppose that ( )1 mg cω ∈ .then g 1 ri 2 c π represents also ( )1 mc , and by lemma 148, we have g 1 ri 1 f , 2 gg c ωωπ − = − ∂∂ where f gω is a global function on m which is defined up to a constant. in (joyce, 2000), futaki introduced the following linear functional ( ) ( ) ( ) f n f gm h m: 1 x x x f . 2 gω ω π → − = ∫a cl l theorem 149. (futaki, 1983) the functional fl is independent of the choice of the kähler form ( )1 mcω ∈ . in particular f l is invariant under the automorphism group ( )aut m of m and fl is a lie algebra homomorphism. moreover, if m admits an einstein-kähler metric, then fl vanishes identically. kähler manifolds positive ricci curvature the following example exhibits an example of a compact kähler manifold m with positive ricci curvature such that ( )mh is reductive, but f l is not identically zero. example 150. (futaki, [18]) let r and s be two positive integers, 1 : r s rπ × →p p p the projection to the first factor, and 2 : r s sπ × →p p p the projection to the second factor. let ( ) ( )* *r,s 1 21 1 ,r s r sπ π= ⊕ → ×o op p p pe and let , m r s be the total space of the projective bundle ( ),r sep . it can be shown that (1) ( )1 r,sm 0 ,c > , (2) ( )r, sh m is reductive, (3) if r 1= and s 2 ,= , then f 0.≠l , therefore 1,2 m is a fano manifold which cannot carry an einstein-kähler metric with positive ricci curvature. there are other generalizations of futaki's invariant which we will not consider in this paper. 21. tian's invariant the vanishing of the futaki invariant is a necessary condition for the existence of a einstein-kähler metric but not a sufficient one. in tian (1997), tian constructed a compact kähler manifold which does not admit any einstein-kähler metric even though f 0=l . let us introduce tian's invariant: let ( )m, g be a compact kähler manifold of dimension n , and let ( ) ( )2 g m 1 p m,g c m, 0, sup 0 , 2 ω ω π  −  = ∈  = + ∂∂ =      φφ φ φ> where ( ) n g i, i jj i,j 1 1 g z dz dz ,ω = = − ∧∑ is the associated (1,1) form expressed in local holomorphic coordinates, and where " 0"ω >φ means that ω' is a positive definite (1,1) form. proposition 151. let ( )m, g be as above. then there exists two positive constants c and a such that c and α such that ( )z n gm e c ,α ω− ≤∫ ' for all ( )p m, g∈φ . consider the following invariant defined by tian (1997) : ( ) ( ) ( ){ }z ngmt m, g sup 0 c > 0, e c for all p m, g .αα ω−= >  ∃ ≤ ∈∫ φ φ boudjemaa anchouche theorem 152. (tian, 1997) let ( )m, g be a fano manifold of dimension n , where gω represents the first chern class of m , i.e., ( )g 1 mcω  =  . if ( ) nt m, g , n 1 > + then m admits an einstein-kähler metric. estimates of ( )t m, g were used by several authors to prove the existence of einstein-kähler metrics on certain fano manifolds. 22. uniqueness of einstenin-kähler metrics with positive ricci curvature let m be a fano manifold, and let ( )mek be the set of all einstein-kähler metrics on m . the automorphism ( )aut m acts on ( )mek via pull-back. let ( )0aut m be the identity component of ( )aut m . theorem 153. (bando and mabuchi, 1985) suppose that ( )mek φ≠ and let go be an einstein-kähler metric. then ( ) ( )0 0m aut m . ,ek g= , i.e., any einstein-kähler metric g is of the form * 0gψ for some ( )0aut m .ψ ∈ remark 154. if ( )h m 0= , then the einstein-kähler metric is unique if it exists. part 5. complete noncompact kähler manifolds of positive ricci curvature the structure of noncompact manifolds is richer and at the same time harder to explore than the structure of compact manifolds. complete noncompact kähler manifolds of positive ricci curvature are less studied, and therefore less understood compared to fano manifolds. nonetheless, lots of partial results have bee proved although a general theory is still missing. in this part, we will survey some of these results, close to the author's interests, obtained on this topic. 23. construction of complete kähler metrics of positive ricci curvature the problem of existence of complete kähler metrics of positive ricci curvature on smooth quasi-projective varieties was considered by several authors, among them s. t. yau, g. tian, r. kobayashi, s. k. yeung, and others. by solving certain complex monge-ampere equations, where the ideas are close to the ones introduced by yau in his solution of the calabi conjecture, g. tian and s. t. yau, proved the following theorem 155. (tian, yau 1990) suppose that m is a smooth complex projective variety and that d m⊂ is a smooth ample divisor. let ω be any smooth closed (1,1) form in the cohomology class [ ]( )( )1mk d −⊗ . then m \ d admits a complete kähler metric whose ricci curvature form is equal to the restriction of ω to m \ d . as a consequence, we get kähler manifolds positive ricci curvature corollary 156. let m and d m⊂ be as above. if [ ]( ) 1mk d − ⊗ is ample, then m \ d admits a complete kähler metric with positive ricci curvature. to state the next theorem, we need the following definition 157. a complete noncompact kähler manifold ( )m, g of dimension 2n ≥ with positive ricci curvature is said to be of standard type if it satisfies the following three conditions (1) n gm ric ,< +∞∫ (2) there exists a constant 1c such that for all r 0 ,> ( )( )g 0vol b x , rg (3) there exists a constant 2c such that for all m m ,∈ ( ) ( )( ) 2 2 c | sect m | , 1 r m ≤ + where ( )( )g 0vol b x , rg is the volume of the geodesic ball ( )g 0b x , r with respect to the metric g , ricg is the ricci (1, 1) form associated to the kähler metric g , and ( )sect m is the sectional curvature of g at the point m . simultaneously with tian and yau, using the continuity method for the monge-ampere equation, yeung obtained the following theorem 158. (yeung 1990) if m is a smooth projective variety with dim m 2≥ , and d is a smooth hypersurface such that the associated line bundles [ ]d and [ ]( ) 1 m k d − ⊗ are positive, then the affine variety m \ d admits a complete kähler metric of positive ricci curvature and of standard type. example 159. let nm , 2n= ≥p and let d be a smooth hypersurface in np of degree, where 1 d n≤ ≤ . since [ ] ( )nd d= po and [ ]( ) ( )n 1 mk d n 1 d − ⊗ = + − p o are positive, yeung's theorem, (theorem 158) implies that nm \ d= p admits a complete kähler metric of positive ricci curvature and of standard type. an extension of kobayashi's result (theorem 138) to the noncompact case was obtained by tsuji theorem 160. (tsuji, 1988) let m be a smooth projective variety and let d be a simple normal crossing divisor. if [ ]( ) 1mk d − ⊗ is ample then m \ d is simply connected, i.e., ( )1 m \ d 0π = 24. compactification of complete kähler manifolds of positive ricci curvature one way to approach noncompact complete kähler manifolds of positive ricci curvature is to try first to compactify them (if it is possible to do that), i.e., realize them as open subsets, in the zariski topology, of some projective manifolds, via some "noncompact" version of kodaira embedding. this was achieved by mok (1990) for complete kähler manifolds of positive ricci curvature and of standard type. more precisely, mok's result says that boudjemaa anchouche theorem 161. (mok, 1990) let ( )m, g be a complete noncompact kähler manifold of dimension 2n ≥ with positive ricci curvature and of standard type. then m is biholomoryhic to a quasi-projective variety m \ d , where m is a smooth projective variety and 1 jj 0 d d = = ∑ is a normal crossing divisor. more precisely, there exists a finite set of sections { } ( )n 0 qj mjs h m, k −⊂ of class 2l for some positive integer q , where -1 mk is the anticanonical line bundle, such that ( ) ( ) n q 0 n : m m p m s m ,..., s m , ψ → ⊂   a (23) is an embedding, and q : m m \ dυ =/ . mok's embedding theorem says more or less that -1 mk is "ample" and can therefore be seen as a noncompact analogue of kodaira's embedding theorem. remark 162. it can be proved, under the assumption of theorem 161, (see borel and serre, 1951) that ( ) ( )1 1m m \ d ,π π= < +∞# # and therefore 0 1h m, 0 m   ω =    remark 163. (1) the completeness of the metric in the noncompact case is crucial. all metrics are complete on compact manifolds. (2) the constmint on the volume growth is natural, since by combining the calabi -yau's theorem (theorem 58) and bishop's theorem (theorem 57), on a complete riemannian manifold with positive ricci curvature we have ( )( ) 2n1 g g 0 2c r vol b x , r c r≤ ≤ (3) an extension of mok's embedding theorem to the case of a volume growth slower than euclidean was obtained by to (1991). 25. logarithmic kodaira dimension of complete kähler manifolds of positive ricci curvature to introduce the logarithmic kodaira dimension of ( )m, d , we need some definitions. definition 164. a closed subset v of a complex manifold m, dim m ,n =  is called an analytic subvariety if for every m m∈ , there exists a neighborhood u of m and a finite number of holomorphic functions ( ) m m 1 mf ,...,fν on u , called defining functions, such that ( ) ( ) ( ){ }m m1 mv u x u | f x ... f x 0 .ν∩ = ∈ = = = a point m v∈ is called a smooth point, if there exists an open subset u′ of m and defining functions m m 1 kf ,...,f in u′ such that kähler manifolds positive ricci curvature ( ) ( ) m m 1 1 1 n m m 1 k 1 n m m k k 1 n f f . . . z z . . . . . f ,...,f rank rank k .. . . . . z ,...,z . . . . . f f . . . z z  ∂ ∂   ∂ ∂    ∂   = =  ∂      ∂ ∂   ∂ ∂  the integer k is called the codimension of v at m . the set of smooth points is denoted by smv . it can be proved that if smv is connected, then it is a complex submanifold of m of dimension kn , in which case we write odim v kc = . remark 165. the defining functions of an analytic subvariety in a neighborhood o.t a point are not unique. definition 166. let m and n be two projective algebraic manifolds. (1) a rational map ψ from m to n , denoted by : m ---nψ > , is given by a holomorphic map : m \ v n ,ψ → where v is a subvariety of m , such that odim v 2c ≥ . (2) we say that a rational map : m ---nψ > is birational, if there exists a rational map : n ---mφ > such that φψ o is the identity as a rational map. if such a birational map : m ---nψ > exists, then we say that the algebraic manifolds m and n are birational. let n: m ----φ > p be a rational map defined by a holomorphic map n: m \ v ----φ > p , where v is a subvariety of m , such that odim v 2c ≥ , and let ( )( ){ }nψ m, m m \ v .φ = ∈ × p denote by ψγ the closure (in the zariski topology) of ψ γ in nm × p and by n ψ2 ,π :γ → p the projection to the second factor. the image ( )mφ of m is given by ( ) ( )ψ2m .φ π= γ let m be a smooth projective manifold, d be a normal crossing divisor on m and let [ ]( )( ) [ ]( )( ){ }0m mm, k d : | h m, k d 0 .νν⊗ = ∈ ⊗ ≠ns let us assume that [ ]( )( )mm, k d 0⊗ ≠s , and for [ ]( )( )mm, k dν ∈ ⊗s , consider the rational map ( ) ( ) ( ) n 0 n : m --m m m ,..., m , ν ν ν ν ν ν φ φ >  =  a p φ φ where boudjemaa anchouche [ ]( )( )0 mn dim h m, k d 1,νν = ⊗ − and { }0 n,..., νν νφ φ is a basis for [ ]( )( )0 mh m, k d ν⊗ definition 167. the logarithmic kodaira dimension of m m \ d= , denoted by ( )k m , is given by ( ) ( ) [ ]( )( ) [ ]( )( ) ( ) [ ]( )( ) m max m m m, k d k m k m \ d dim m m, k d . m, k d if ifν φ φ φ ν −∞ ⊗ =  = = ⊗ ≠  ∈ ⊗   s s s remark 168. the logarithmic kodaira dimension has the following properties: (1) it is independent of the compactification, i.e., if biholomorphic biholomorphic 1 1 2 2m m \ d m \ d ,≅ ≅ where ( )1 2m . mresp is a smooth projective variety and ( )1 2d . dresp is a normal crossing divisor on ( )1 2m . mresp and if the isomorphism biholomorphic 1 21 2m \ d m \ d≅ extends to a birational map birational 1 2m ---m> then ( ) ( )1 21 2k m \ d k m \ d= (24) for a proof of (24) , see litaka (1977). (2) it is not a biholomorphism invariant. for a proof, see hartshorne (1970). theorem 169. (anchouche, 1998) let ( )m, g be a complete noncompact kähler manifold ( )m, g of dimension 2n ≥ with positive ricci curvature and of standard type and let ( )m, d be the compactification obtained in theorem 161. then ( )k m = −∞ proof. (sketch of the proof) in all what follows, we identify m with m \ d . remark first that [ ]( )( ) ( )0 , dm mh m, k d m, k ,ν ν⊗ ≅ ϒ where ( ),d mm, kνϒ is the set of meromorphic sections of mk which are holomorphic in m and admitting poles along the divisor d of order at most ν . step1: we establish the following inequality kähler manifolds positive ricci curvature ( ) ( ) ( )g g n 1 2 n 3 4 n 3 n n g g2g n b x,r b x,r 1 d 1 s c 1n , s ii i ν ω ω + + + =      ≤    π    ∫ ∫ where [ ]( )( )0 mh m, k ds ν∈ ⊗ is the section of the line bundle [ ]di defining the divisor di , i.e., ( )1ds 0 , si ii d id − = is the norm of the section sd, defined by a fixed hermitian metric hi on the line bundle [di], and 115111 is the norm of the section s with respect to the metric on mk induced from the metric g . step 2: let n 1 2n i 0 1 d 1 1n c qu 1n s s i i i i = =    ψ = − + +     π ∑ n 2 i 0 c qu 1n si =    ψ = +      ∑ where u is a solution of the equation ( )g u ricgr∆ = t (see mok, 1984) , g∆ is the laplacian associated to the kähler metric g,c is chosen in such a way that 1ψ and 2ψ are subharmonic functions, and si are the sections of q mk − appearing in mok's embedding theorem 161. therefore, we get the riesz representation ( ) ( ) ( )( ) ( ) ( ) ( )0 0 x n 0 0 g g b x ,r x x 1im g x , y y y , g j j jρ ρ ω → +∞ ψ = ψ + ∆ ψ∫ where ( ) 0xg .,.ρ is the green kernel of the geodesic ball ( )0b x , rg for the operator g∆ . step 3: there exist a constant c such that i n 2 dm mi 1 c 1 s c , i ω ω = − ≤ − ∂∂ ≤∏ where m ω is the fubini-study metric on m . step 4: using the previous steps, we get ( ) ( ) ( )( ) ( ) n 2n gg b x,r y y cr 1n r x 2 for 1, 2. g j iω∇ψ ≤ + =∫ the estimate above is the hardest pat of the proof. step 5: using the inequality obtained in step 4 and following a similar scheme developed by john-nirenberg, we get ( ) ( ) ( )( ) ( ) n 2n 2 2 ,r gg b x,r y y cr 1n r x r 2 for 1, 2. g j j iω +ψ − ≤ + + =∫ θ where ,ri θ is the solution of the following dirichlet's problem ( ) ( )0 in b x,rg , r g | b x,r, r g j j j  ∆ =  ∂ = ψ θ θ boudjemaa anchouche step 6: using the previous steps, we get ( ) ( ) ( )( )( ) n 1 2n 2 2 n 34 x 3 2n r c 1n r r x 2 s x c r n ν + + + +  + + + ≤ where the constants c and xc are independent of r . since n 2≥ , the theorem is obtained by letting r → + ∞ . for more details, see anchouche (1998). the vanishing theorem above puts a lot of restriction on the structure of the manifold m , for example if we assume that dim m 2=c then, as a consequence of theorem 169 and miyanishi's classification of open algebraic surfaces [40], we obtain the following theorem 170. (anchouche, 1998) let m be a complete kähler surface of positive ricci curvature and of standard type, and let ( )m, d be the compactification obtained in theorem 161. then (1) m is a rational surface. (2) each component j d of d is a smooth rational curve, i.e., jd is isomoryhic to 1p . (3) d is a tree. (4) none of the components j d is exceptional. the theorem above is a consequence of theorem 169 and miyanishi's classification of quasi projective surfaces of logarithmic kodaira dimension − ∞ . the fact that the kähler manifold m is of infinite volume implies part (4) of the theorem 170. in [2], it has been shown that the 2l sections of the line bundle q xk − , and the volume form of the metric g have no essential singularities near the divisor at infinity d . as a consequence we obtain a comparison between the form forms of the complete kähler metric g and the fubini-study metric of the compactification. in the case of dim x 2=c , we establish a relation between the number of components of the divisor d and the dimension of the logarithmic groups ( )i 1 h x, log d x .ω     26. acknowledgement the author is grateful to the referees for their suggested corrections and improvements. one of them has kindly sent us a very detailed report. we take this opportunity to express our deep gratitude and appreciation to him. last, but not least, i want to thank profs. m. s. narasimhan, s. veldsman and dr. m. benrhouma for reading the paper and for their comments. 27. references anchouche, b. 1998. sur la dimension logarithmique de kodaira des varietes kählcriennes completes de courbure de ricci positive. math zeit. 227: 403-421. anchouche, b. on the asymptotic behavior of complete kähler metrics of positive ricci curvature and of standard type. in preparation, 2007. aubin, t. a course in differential geometry. graduate studies in mathematics, 27. ams, providence, rhode island 2001. kähler manifolds positive ricci curvature bando, s. and mabuchi, t. 1985. uniqueness of einstein-kähler metrics modulo connected group actions, algebraic, geometry, sendai, adv. studies in pure math. 10 (1987). beauville, a. 2006. riemannian holonomy and algebraic geometry, http://math.unice.fr/~ beauvill/pubs/rha.pdf. berger, m. 2000. riemannian geometry during the second half of the twentieth century. university lecture series. 17. ams. berger, m. 1953. sur les groupes d'holonomie des varieties connections et des varieties riemanninnes. bul. soc. math. franc 83: 279-330. birkenhak, c. and lang, h. 1992. complex abelian varieties. grundlehren der mathematischen wissenschaften 302. springer verlag. bishop, r.l. and crittenden, r. 1964. geometry of manifolds, new york, academic press. borel, a. 1991. linear algebraic groups. second edition. graduate texts in mathematics, 126. springerverlag, new york. borel, a. and serre, j.p. 1951. determination des puissance reduites de steenrod dans la cohomoloie des groups classiques, applications, c.r. acad. sci. paris 233: 680-682. brocker, t. and tom dieck, t. 1985. representations of compact lie groups. graduate texts in mathematics 98, springer verlag. bryant, r. manifolds with g2holonomy. http://euclid.ucc.ie/pages/rtaff /mckay /talks/ g2. pdf # search= %22 bryant %20 holonomy %20 group %22. chavel, i. 1995. riemannian geometry, a modern introduction. cambridge university press, lo8. demailly, j.p. complex analytic and algebraic geometry. http://www-fourier.ujf-grenoble.fr /~ demailly /books.html. de rham, g. 1952. sur la reducibilite d'un espace de riemann, commm. math. helv. 26: 328-344. futaki, a. 1983. an obstruction to the existence of einstein klthler metrics. invent. math.73: 437-443. futaki, a. 1988. klthler-einstein metrics and integral invariants. 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breeds; dhofari goats; haematology; jabal akhdar; oman. الدم في سالالت الماعز العمانية الناميةتأثيرات العمر والساللة والجنس على مكونات جونسون .ھالبوسعيدي ويوجين .عثمان، راشد منور الهدى عصام الدين من مواليد ماعز ثالثة سالالت عمانية بصحة جيدة، ولدت وتربت في محطة التجارب الزراعية لجامعة السلطان قابوس، 67تم استخدام عدد :ستخلصم بعد الميالد 25والساللة والجنس في قياسات مكونات الدم. تم تجميع عينات من الدم عدة مرات من االسبوع األول حتى االسبوع لدراسة تأثيرات العمر (، تركيز pcv(، قياس نسبة الهيماتوكريت )wbc(، عدد كريات الدم البيضاء )rbcقياسات المكونات اآلتية : عدد كريات الدم الحمراء ) لدراسة (، ومتوسط هيموجلوبين mchc(، متوسط تركيز الهيموجلوبين في كرية الدم الحمراء )mcv(، متوسط حجم كرية الدم الحمراء )hb) الهيموجلوبين ( أعلى بداللة إحصائية في مواليد ماعز ساللة الباطنة عن ساللتي الجبل mch) ( وmcv(. في األسبوع األول كان قياس )mchكريات الدم الحمراء ) ي فارية، ولكن لم يكن هناك فرق بينهم في قياسات بقية المكونات. كانت هناك فروقات ذات دالالت احصائية بين السالالت في أعمار مختلفة فاألخضر والظ ( في كل pcv( و )hb(، مع فروقات ساللة ذات داللة احصائية عالية جداً في قياسات )mcv( و )wbc(، و )rbc( ،)mchكل من قياسات ) (، rbc( ،)mchcياسات كل المكونات تغيرت مع العمر بأساليب مختلفة في كل السالالت. لم يكن هناك تأثير للجنس على قياسات )األعمار. ق (pcv( ،)hb) ( أوwbc( ولكن قياسات كل من ،)mch( و )mcv في اإلناث كانت اعلى من الذكور بدرجة إحصائية عالية في األسبوع )هذه .12 ى أن قياسات مكونات الدم في سالالت الماعز العمانية النامية قد تتأثر بالعمر والساللة والجنس.الدراسة اشارت إل .الباطنة ، السالالت ، ظفاري ، ماعز ، مكونات الدم ، الجيل األخضر ، عمان: كلمات مفتاحية 1. introduction here are over two million heads of livestock in oman including 1.56 m goats [1], with three major breeds of goats, jabal akhdar (ja), batina (bat) and dhofari (dof). the ja breed is the largest in size among all goat breeds and mostly located in the interior of oman especially al jabal al-akhdar mountains (green mountains). they have back twisted-horns, long pendulous ears, long hair and are predominantly golden to brown in colour [2]. batina breed goats have long hair, pendulous ears and a larger mature body size than the dof goat, which resembles the short haired, prick-eared east african goat. the adult bat goat, found mostly in the batina coastal plain of north oman, batina may weigh 10–15 kg more than the dof goat. the home of dof goats is in the mountains of south oman, dhofar [3]. local breeds have shown good potential for production when subjected to improved management [2]. goats are mainly kept for meat in oman. their meat is preferred by omanis to that of imported breeds. local goats are sold for very high prices, and slaughtered at different social occasions. haematological values are important parameters for the health status assessment of individual animals. normal values can be altered by an animal’s exposure to abnormal conditions including environmental hazards, e.g. crude oil pollution [4], season [5], bacterial t mailto:hudaisam@gmail.com effects of age, breed and sex on haematological parameters 83 infections such as mastitis [6], mycoplasma [7] or parasitic infestation [8]. they can also vary due to physiological status, breed and sex, or with age [9-11]. to our knowledge there is no detailed published record on the normal haematological values in omani goat breeds. this is necessary for health assessment of goats by veterinarians in oman. therefore, the current study was conducted to provide reference values for haematology in healthy growing omani goats, as well as to study the effects of age, breed and sex on these values. 2. materials and methods in this study, a total of sixty seven apparently healthy kids were used, 19 of ja, 19 of bat and 29 of dof goat breeds, which had been raised in sultan qaboos university agricultural experiment station (aes). the animals were kept in clean partially shaded open yards equipped with feed and water troughs. kids were weaned at age 12–14 weeks and were provided with either a general ruminant concentrate, prepared in the aes feed mill, or a commercial concentrate (dairy 18; oman flour mill co., oman) at a rate of 250-300 g/head/day. they were fed regularly at 9:00 am. rhodes grass hay, either produced at aes or purchased through a local dealer, was offered ad libitum. the protein and some of the mineral concentrations in the various feeds are presented in table 1. the animals were allowed free access to salt licks (writex copper block, frank wright feeds international ltd, ashbourne, uk, table 1) and water. all animals were routinely subjected to anthelmintics and they were internal and external parasite free. table 1. protein and mineral contents of feeds and salt licks offered to growing kids of jabal akhdar, batina and dhofari omani goat breeds. feed trace elements (mg/kg dm) protein (%) copper zinc iron general ruminant concentrate 19.7 67.2 422 13.05 dairy 18 27.0 79.3 524 16.96 purchased hay 5.7 7.5 48 4.94 farm hay 4.5 9.5 58 9.62 salt lick (mg/kg) 400 2500 120 blood samples were collected at 8:00 am from the jugular vein in vacutainer tubes containing the anticoagulant edta for haematology determination. blood samples were collected at 1, 3, 8, 12, 16, 19 and 25 weeks. haematological parameters were obtained in fresh samples using a cell-dyn 3700 automated blood analyzer (abbott laboratory, diagnostic division, abbott park, il 60064, usa). the following parameters were analyzed: red blood cells (rbc), white blood cells (wbc), packed cell volume (pcv), haemoglobin concentration (hb), mean cell volume (mcv), mean cell haemoglobin concentration (mchc) and mean cell haemoglobin (mch). 2.1 statistical analysis general linear model statistical analysis was used to study the effects of age, breed and sex. the type iii method for sum of squares was used with the unbalanced model factorial design. the duncan multiple range test was used to compare the means. all analyses were carried out using spss 19 for windows personal computer package [13]. 3. results the means and ranges of haematological parameters in growing kids of the three omani goat breeds are shown in table 2. all haematological parameters changed during the experimental period. however, the trends in these changes were not similar across all the parameters. while wbc, rbc and mchc gradually increased, mcv and mch levels decreased from the first to the twelfth week (weaning age), then stabilised. however, haemoglobin was low at the first week, then increased at age 8 weeks. on the other hand, pcv dropped slightly from birth values in the second sampling at age 3 weeks, then returned to previous values and stabilised until the end of the experimental period. table 2. mean (± se) and range of haematological values in kids of three omani goat breeds at various ages. age (weeks) rbc (1012/l) hb (g%) pcv (%) mcv (fl) mch (pg) mchc (gm%) wbc (103/µl) birth 8.2 ± 0.33 (7.6-8.9) 9.0 ± 0.16 (8.7-9.3) 28.3 ± 0.66 (26.9-29.4) 37.2 ± 1.48 (34.3-39.9) 11.9 ± 0.46 (11.0-12.8) 32.2± 0.33 (31.5-32.8) 9.93 ± 0.39 (9.16-10.7) nur el huda et al 84 3 11.6 ± 0.36 (10.9-12.3) 8.9 ± 0.14 (8.6-9.1) 26.6 ± 0.41 (25.8-24.4) 24.7 ± 1.0 (22.7-26.7) 8.3 ± 0.35 (7.6-9.0) 33.4 ± 0.21 (33.0-33.8) 13.24 ± 0.44 (12.36-14.12) 8 19.6 ± 0.49 (18.7-20.6) 10.4 ± 0.13 (10.1-10.6) 28.4 ± 0.33 (27.7-29.0) 15.1 ± 0.65 (13.8-16.4) 5.6± 0.22 (5.1-6.0) 36.5 ± 0.18 (36.1-36.8) 19.06 ± 0.54 (17.97-12.14) 12 23.2 ± 0.47 (22.3-23.2) 10.1 ± 0.18 (9.7-10.4) 27.3 ± 0.31 (26.7-27.9) 12.1 ± 0.27 (11.5-12.6) 4.5 ± 0.11 (4.2-4.7) 36.9 ± 0.53 (36.0-38.0) 23.51 ± 0.56 (22.39-24.64) 16 25.2 ± 0.87 (23.5-26.9) 10.4 ± 0.13 (10.1-10.6) 27.4 ± 0.36 (26.7-28.1) 11.4 ± 0.37 (10.7-12.2) 4.3 ± 0.13 (4.0-4.6) 37.8 ± 0.19 (37.4-38.2) 22.95 ± 0.68 (21.58-24.32) 19 19.5 ± 0.96 (17.6-21.4) 10.4 ± 0.13 (10.1-10.7) 27.9 ± 0.34 (27.2-28.5) 15.7 ± 0.58 (14.5-16.9) 5.9 ± 0.20 (4.5-6.4) 37.5 ± 0.33 (36.8-38.1) 24.42 ± 0.73 (22.96-25.87) 25 20.0 ± 0.73 (18.5-21.4) 9.1 ± 0.12 (8.9-9.3) 25.2 ± 0.37 (24.5-25.9) 13.6 ± 0.57 (12.5-14.8) 4.9 ± 0.21 (4.5-5.3) 37.7 ± 0.33 (36.0-37.3) 24.56 ± 0.70 (23.16-25.94) table 2. contd. there were significant breed differences in rbc, mch, wbc, mcv, hb and pcv, but there was no breed effect on mchc (p>0.05). means of rbc values in different breeds are presented in table 3. significant breed differences were observed at week 3 (p<0.05) with the highest values for ja, and week 8 (p<0.05) and week 12 (p<0.001) with the highest values for bat. despite these differences all breeds followed similar trends of change during the study period. table 3. means (± se) of rbc (1012/l), hb (g%), and pcv (%) haematological blood parameter values in growing kids of jabal akhdar, batina and dhofari omani goat breads. (means followed by the same letters, or with no letter, are not significantly different (p>0.05)). breed jabal akhdar batina dhofari breed effect age mean se mean se mean se rbc (1012/l) birth 8.6 0.59 7.3 0.60 8.7 0.49 ns 3 13.0a 0.64 11.2b 0.70 10.5b 0.51 p<0.05 8 21.3b 0.90 19.6a 0.93 18.0b 0.72 p<0.05 12 22.4b 0.88 26.1a 0.88 21.2b 0.66 p<0.001 16 26.4 1.67 25.6 1.62 23.7 1.18 ns 19 18.3 1.86 21.1 1.75 19.1 1.34 ns 25 19.4 1.42 21.7 1.33 18.8 1.00 ns hb (g%) birth 9.1 0.3 9.2a 0.3 8.6 0.24 ns 3 9.4a 0.25 9.3a 0.27 7.9b 0.2 p<0.001 8 10.7a 0.23 10.6a 0.24 9.9b 0.19 p<0.05 12 10.9a 0.33 10.1a 0.34 9.2b 0.25 p<0.001 16 11.2a 0.18 10.7a 0.67 9.3b 0.23 p<0.001 19 11.2a 0.25 10.9a 0.25 9.3b 0.19 p<0.001 25 9.6a 0.22 9.3a 0.22 8.5b 0.17 p<0.001 pcv (%) birth 27.9 1.1 29.4 1.1 27.1 0.91 ns 3 27.8 a 0.73 27.9 a 0.8 24b 0.58 p<0.001 8 29a 0.6 29.1 a 0.6 27.1b 0.47 p<0.05 12 28.7a 0.56 28.7 a 0.6 24.6b 0.44 p<0.001 16 29.2a 0.66 28.4 a 0.7 24.6b 0.5 p<0.001 19 29.6a 0.63 28.8 a 0.6 25.2b 0.48 p<0.001 25 26.6a 0.68 26.2 a 0.7 22.8b 0.52 p<0.001 there were no significant (p>0.05) breed differences in either hb or pcv (table 3) at birth. thereafter, dof kids recorded consistently significant (p<0.001) but only at age 8 weeks, (p<0.05) lower values of hb and pcv throughout the experimental period than both ja and bat, which had similar values at all ages. there were significant breed differences for mcv (table 4) at birth (p<0.05) due to the highest mean value in bat, at week effects of age, breed and sex on haematological parameters 85 12 (p<0.05) where the ja mean value was higher than bat, and week 19 (p<0.05), where the ja mean value was higher than both bat and dof. table 4. means (± se) of mcv (fl) mch (pg) and wbc haematological blood parameter values (103/µl) in growing kids of jabal akhdar, batina and dhofari omani goat breads. (means followed by the same letters, or with no letter, are not significantly different (p>0.05)) breed jabal akhdar batina dhofari breed effect age mean se mean se mean se mcv (fl) birth 34.4a 2.5 43.1b 2.6 33.9a 2.1 p<0.05 3 22.6 1.79 27.6 1.95 23.9 1.42 ns 8 14.2 1.19 15.7 1.22 15.5 0.95 ns 12 13.0a 0.49 11.2b 0.49 11.9ab 0.37 p<0.05 16 11.7 0.71 11.6 0.69 11.0 0.5 ns 19 18.4a 1.13 14.3b 1.06 11.4b 0.81 p<0.05 25 14.8 1.1 12.7 1 13.5 0.78 ns mch (pg) birth 11.3b 0.84 13.6a 0.84 10.8b 0.68 p<0.05 3 7.7 0.61 9.3 0.68 7.8 0.49 ns 8 5.2 0.4 5.7 0.41 5.8 0.33 ns 12 5.0a 0.21 4.0b 0.21 4.4ab 0.16 ** 16 4.5 0.26 4.4 0.25 4.1 0.18 ns 19 7.0a 0.34 5.4b 0.36 5.2b 0.27 p<0.001 25 5.3 0.4 4.5 0.4 5.0 0.28 ns wbc (103/µl) birth 9476 712 10079 712 10229 576 ns 3.56 12905b 442 11131b 86b 15683a 629 p<0.001 8.27 18994b 542 17294b 1029b 20882a 801 p<0.05 12.44 24167 564 22505 1068 23870 804 ns 16.3 24046 684 21094 1305 23717 953 ns 20.3 24918b 729 21947 b 1359 26386 1041a p<0.05 25.15 25847 700 23669 1301 24167 950 ns at birth bat kids had significantly higher values for mch (p<0.05) than both ja and dof (table 4). after weaning, ja goats had the highest values but thereafter the only significant differences were at week 12, when ja mch values were higher than those for bat (p<0.01), and at week 19, when they were higher (p<0.001) than those for both bat and dof kids. dhofari kids had higher wbc count pre-weaning, than both ja and bat in week 3 (p<0.001) and week 8 (p<0.05) (table 4). post weaning, bat consistently recorded the lowest values but these were significantly lower than dof (0<0.05), which was the highest, only at week 20. there was no significant (p>0.05) effect of sex, or a clear tendency, on pcv, mchc or wbc during the experimental period, nor was there any significant (p>0.05) effect of sex on rbc at any time. however, there was a tendency (p=0.053) of higher values in females (8.9±0.49) compared with males (7.7±0.49) at birth. similarly, there was no significant (p>0.05) effect of sex on hb at any time. however, there was a tendency (p=0.084) of higher values in females (10.2±0.26) compared to males (9.6±0.28) at 12 week. male kids had a tendency (p=0.064) of higher mcv mean value at birth than females (38.5 ± 1.97 vs 35.9 ± 2.2, respectively). this tendency (p=0.062) in males continued in the next bleeding at age 3 weeks (26.3 ± 1.43 vs 22.7 ± 1.34, respectively). thereafter, female kids’ values exceeded those of males but this was significant (p<0.05) only at age 12 weeks (12.8 ± 0.36 vs 11.4 ± 0.37, respectively). a similar trend was in observed in mch, with a tendency (p=0.06) of higher values of mch in male kids (12.6 ± 0.64) than in females (10.8 ± 0.65) at birth, and at 3 weeks (p=0.075) (8.8 ± 0.5 and 7.7 ± 0.47, respectively). thereafter, female kids had higher values but the difference was significant (p<0.05) only at age 12 weeks (4.7 ± 0.16 and 4.2 ± 0.16, respectively). 4. discussion the haematological blood parameters, such as rbcs, hb, wbcs, can reflect physical changes occurring in an animal’s body. these changes could be due to diseases or normal physiological changes. haemoglobin is the substance responsible for transporting oxygen to body tissues and removing waste carbon dioxide. it also plays an important role in maintaining the ph of the blood. rbcs transport hb. reduction of hb or of rbcs results in low o2 in tissues, causing short breath, a symptom of anaemia. wbcs, or leukocytes, defend the body against invasions of foreign particles. their number can be used to detect the presence of pathogens in the blood of sick animals. nur el huda et al 86 the change of values with age of all the haematological parameters in the growing kids in this study is in line with other reports that either compared groups of young and adult goats [13-14], goats of many age groups [15-21] and sheep [10,11,15] or studied changes in growing animals as in calves [22,23] and swine [24]. the drop in hb and pcv values from birth to three weeks of age and the subsequent increase to previous values reported in this study is comparable to that in neonatal dwarf and landrace kids reported by mbassa and poulsen [17]. at early age the mean values of all parameters in omani kids were comparable to those reported by gutierrez, et al. [25] in 1 week old canary goat kids. at about three months of age, however, only pcv values were comparable to that of white german and coloured german noble breeds [26]. values of rbcs, hb, mch and mchc were higher while mcv and wbc were lower in omani kids than in german breeds. comparing omani kid’s values at the end of study period i.e. at age 25 weeks, with other goats, hb was comparable to that of barbari male goats at 9-12 months of age [28] lower than the mean value of adult west african dwarf goats [13] and within the goat range provided by the merck veterinary manual [29]. on the other hand rbcs, mchc and wbcs were higher while pcv, mcv and mch were lower in 25 weeks old omani kids than the values reported by sharma, et al., daramola et al., and the merck veterinary manual [13,27,28]. the differences between values obtained in the current study and other reports can be attributed to many factors including differences in climate [5], diet [29], management system [30-33] and breed. the latter cause is confirmed in the current study, as goats of all breeds were raised under the same conditions. breed difference in haematological values was also established in other goats in ethiopia [21], bangladesh [20], in northern nigeria [34] and mubi adamawa state of nigeria [35]. the dof breed had the lowest values for both hb and pcv and, mostly, the highest values of wbcs. that may indicate a lower health status of dof goat. that suggestion is supported also by the lower hb and pcv mean values in dof than those reported elsewhere [13,25-27] and below the range of the merck veterinary manual (2009)[25]. however, this difference could be due to difference in breed per se or to low acclimatization of dof to the different habitat of the study area (muscat) compared to dhofar, the original habitat of this breed. no record is available on the haematological values of this breed in its natural habitat. however, this supports the statement of daramola et al. [13] that it is difficult to establish a universal haematological profile. there was a significant sex difference only at age 12, the weaning age, where females had higher mcv and mch, although there were tendencies of higher values for females than male at early age on rbc, and on hb (at 12 week). there were higher mcvs in 0-3 m and 3-6 m old groups of female goats in borno state of nigeria [18]. in the latter report, sex also influenced rbc, hb and pcv. this was in contrast to the report of tibbo et al. [21] who found significantly higher pcv and rbc values in males than females in ethiopian native goats but no significant sex effect on mchc or wbc and reports of egbe-nwiyi et al. [18] with higher rbcs, pcv and mcv values in male goats between birth and 7 years. similarly, ramprabhu et al. 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197-198. 33. imasuen, j.a. effect of different management environment on hematological perfomance in west african dwarf (wad) goats. j. research in forestry, wildlife and environment, 2013, 4(2), 73-78. 34. njidda, a.a., hassan, i.t. and olatunji, e.a. haematological and biochemical parameters of goats of semi arid environment fed on natural grazing rangeland of northern nigeria. j agric. and vet. sci., 2013, 3, 01-08. 35. addass, p.a., midau, a. and babale, d.m. haemato-biochemical findings of indigenous goats in mubi adamawa state, nigeria. j agric. and soc. sci., 2010, 6, 14-16. 36. opara, m.n., udevi, n. and okoli, i.c. haematological parameters and blood chemistry of apparently healthy west african dwarf (wad) goats in owerri, south eastern nigeria. new york science journal, 2010, 3, 67-72. received 2 june 2015 accepted 8 march 2016 squ journal for science, 2017, 22(1), 53-55 doi: http://dx.doi.org/10.24200/squjs.vol22iss1pp53-55 2017 sultan qaboos university 53 finite dimensional chebyshev subspaces of  aref k. kamal department of mathematics and statistics, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman, email: akamal@squ.edu.om. abstract: if a is a subset of the normed linear space x, then a is said to be proximinal in x if for each xx there is a point y0a such that the distance between x and a; d(x, a) = inf{||xy||: ya}= ||xy0||. the element y0 is called a best approximation for x from a. if for each xx, the best approximation for x from a is unique then the subset a is called a chebyshev subset of x. in this paper the author studies the existence of finite dimensional chebyshev subspaces of   . keywords: best approximation; chebyshev subspaces; banach lattice.  في المدى محدودةالجزئية تشيبيشيف فضاءات عارف كمال بحيث ان المسافة aفي 0yتوجد نقطة xفي x, و كان لكل xمجموعة جْزئية من فضاء المتجهات المعياري aاذا كانت :ملخصال a) d(x, بين x وa | 0|تساويyx|| عندها نطلق على a " مجموعة تقريبية" في اسمx. 0النقطةy للنقطة تسمى "احسن تقريب " x منa اذا . .x" مجموعة تشيبيشيفية جزئية" من aوحيد عندها تسمى المجموعة aمن xفي xكان احسن تقريب لكل في هذه الورقة يدرس المؤلف امكانية وجود فضاءات جزئية تشيبيشيفية محدودة المدى في فضاء .متشابكات باناخ و فضاءات تشيبيشيف الجزئية، احسن تقريب: مفتاحيةالكلمات ال 1. introduction f a is a subset of the normed linear space x, then a is said to be proximinal in x if for each xx there is a point y0a such that the distance between x and a; d(x, a) = inf{||xy||: ya}= ||xy0||. in this case the element y0 is called a best approximation for x from a. if for each xx, the best approximation for x from a is unique, then the subset a is called a chebyshev subset of x. if q is a compact hausdorf topological space, then c(q) denotes the banach space of all continuous real valued functions defined on q equipped with the uniform norm, that is, || f || = max{| f(x) |: xq}. for 1  p ≤ , ℓp denotes the classical banach space of real sequences, and lp[0, 1] denotes the classical banach spaces of real measurable functions. finite dimensional chebyshev subspaces of banach spaces have been the center of attention of mathematicians for a long time (see for example: [1-5]. one of their important properties is that the single valued metric projection function is continuous. (see, for example, [6]). in 1956 mairhuber [7] proved a special version of what was subsequently called mairhuber's theorem. mairhuber's theorem asserts that for any compact hausdorff space q, and for any n ≥ 2, the banach space c(q) admits n dimensional chebyshev subspaces if and only if q is homeomorphic to a subset of a circle. ([8], theorem 2.3, page 218). it was shown also that if q is a compact hausdorff space, then the n dimensional subspace n of c(q) is a chebyshev subspace if and only if each g ≠ 0 in n has at most n1 zeros. ([8] theorem 2.2, page 215). in 1962, ahiezer [9] showed that l1[0, 1] has no finite dimensional chebyshev subspaces. it is easy to show that every finite dimensional subspace of a strictly convex space is a chebyshev subspace ([10] page 23). therefore for 1 < p < , every finite dimensional subspace of ℓp and every finite dimensional subspace of lp[0, 1] is a chebyshev subspace. in this paper the author studies the existence of the n dimensional chebyshev subspaces of   . this is an important space of sequences, but it is not clear if it has any finite dimensional chebyshev subspaces. in section 2 it is shown that for n>1, this banach space has no chebyshev subspace of dimension n. i mailto:mohammad@squ.edu.om aref kamal 54 before ending this section some terminologies and known results, that will be used later, will be mentioned. let ℓ denote the banach space all real bounded sequences x = (x1, x2, …) equipped with the norm ||x||∞ = sup{|xi|: i = 1, 2, ..}. the banach spaces x and y are said to be isometric to each other if there is a linear mapping  from x onto y such that ||(x)|| = ||x|| for each xx. it is clear that the isometry preserves the proximinality properties; that is, if  is an isometry from x onto y and a is a subset of x, then for any xx, d(x, a) = d((x), (a)). therefore x0 is a best approximation for x from a if and only if (x0) is a best approximation for (x) from (a). ( [11], page 143) shows that the space   is not separable. in theorem 1.1 there is another proof for this fact. theorem 1.1. : the space   is not separable. proof: for each 0<<1, let 0.123… be the binary representation of , where i = 1or 0 for all i = 1, 2, 3, … . define x   by x = (1, 2, 3…). the set a = {x; (0, 1)} is an uncountable subset of   , and if  ≠  then ||x  x||∞ = 1. now let b be any dense subset of   , and let  = 1 3 , then for any  (0, 1) one must have b(x, )  b = {xb; ||x  x||< 1 3 } ≠ . for each (0, 1) choose y to be any element in b(x, )  b. it will be shown that if  ≠  in (0, 1) then y ≠ y . if this is true, then since the interval (0, 1) is uncountable and {y; (0, 1)}  b, it follows that b is uncountable. assume that y = y for some  ≠  in (0, 1), then yb(x, )  b(x, ). but then ||x  x||∞ ≤ ||x  y||∞ + ||y  x||∞ < 1 3 + 1 3 < 1, which contradicts the fact that ||x  x||∞ = 1. theorem 1.2. : if q is a compact subset of the circle, then c(q) is separable. proof: it is clear that the set of all polynomial with rational number coefficients is a countable dense subset of c[0, 2]. so c[0, 2] is separable. now let s be the unit circle in rr. it will be shown that c(s) is separable. if this is true, then for any compact subset q of s, c(q) must be separable. for each point s there is a unique [0, 2) such that  = (cos , sin ). define : c(s)c[0, 2] by (f)() = f() if   2, and (f)(2) = (f)(0). it is clear that for each fc(s), the function (f) is continuous on [0, 2]. so  is well defined. it is also clear also that  is linear, and that ||(f)|| = ||f|| for each fc(s). so  is an isometry from c(s) into c[0, 2]. but c[0, 2] is separable, and therefore c(s) is also separable. for a proof of a more general case one can refer to ([12] proposition 7.6.2 page 126, and proposition 623 page 95). 2. main results let x be a linear space and let ≤ be a partially ordered relation defined on x. then (x, ≤) is said to be a lattice if for each x and y in x, the least upper bound xy and the greatest lower bound xy of x and y both exist in x. in this case if xx, then |x| is defined to be; |x| = xx. the banach space x is called a banach lattice if it is a lattice and for each x and y in x, if |x| ≤ |y| then ||x|| ≤ ||y||. the element e in the banach lattice is called a strong order unit if ||e|| = 1, and x ≤ e for all xx with ||x|| ≤ 1. the banach lattice is called an abstract m space if ||x+y|| = max {||x||, ||y||} for each x and y in x satisfying that xy = 0. for more information about banach lattices one can refer to [13]. the following theorem is theorem 4 page 59 of [14]. theorem 2.1. : let x be a real banach lattice. then x is isometric to c(q) for some compact hausdorff space q if and only if x is an abstract m space with a strong order unit. theorem 2.2. : the banach space   is an abstract m banach lattice with a strong order unit. proof: let ≤ be the relation defined on   such that for each (xi) and (yi) in   , (xi) ≤ (yi) if and only if xi ≤ yi for all i = 1, 2, … then  is a partially ordered relation on   . if (xi) and (yi) are two elements in   then the least upper bound, (xi)(yi), of (xi) and (yi) is (xi)(yi) = (max{xi, yi}), and the greatest lower bound is (xi)(yi) = ( min{xi, yi}). it is clear that if (xi) and (yi) are two elements in   then both (xi)(yi) and (xi)(yi) are also elements in   , and that if | xi | ≤ | yi | for all i =1, 2, … then ||(xi)||∞ ≤ ||(yi)||∞. therefore   with the relation ≤ is a banach lattice. if (xi) and (yi) are in   and (xi)(yi) = 0 then min{xi, yi} = 0 for all i =1, 2, … . therefore xi ≥ 0 and yi ≥ 0. for each i =1, 2, .. , if xi > 0 then yi = 0, and if yi > 0 then xi = 0. thus if min {xi, yi} = 0, then xi + yi = max{xi, yi}. so for any (xi) and (yi) in finite dimensional chebyshev subspaces of  55   , if (xi)(yi),= 0 then ||(xi) + (yi)||∞ = max{||(xi)||∞, ||(yi)||∞}. thus   is an abstract m space. finally the constant function e = (e1, e2, …) defined by ei =1 for each i = 1, 2, …, is a strong ordered unit for   . .is isometric to c(q)  there is a compact hausdorff space q such that: theorem 2.3. proof: by theorem 2.2,   is an abstract m banach lattice with a strong order unit, and by theorem 2.1, there is a compact hausdorff q such that x is isometric to c(q). the following theorem is an important theorem in approximation theory. theorem 2.4. (mairhuber's theorem): [15]: if n >1, and c(q) admits an n-dimensional chebyshev subspace, then q is homeomorphic to a subset of the circle. theorem 2.5. : if n >1, then   has no chebyshev subspace of dimension n. proof: by theorem 2.2,   is isometric to c(q) for some compact hausdorff space q. if this q is homeomorphic to a subset of the circle, then by theorem 1.2,   is separable. but by theorem 1.1,   is not separable. therefore, q is not homeomorphic to a subset of the circle. by theorem 2.4, if n >1, then   has no n-dimensional chebyshev subspace. 3. conclusion if x is the banach space   of all bounded sequences of real numbers then for n  2, x has no finite dimensional chebyshev subspaces of dimension n. references 1. borodin, p.a. chebyshev subspaces in the spaces l1 and c, mathematical notes, 91, issue 5(2012), 770-781. 2. deutsch, f., nürnberger, g., singer, i. weak chebyshev subspaces and alternation, pacific journal of mathematics, 1980, 89, 9-31. 3. garkavi, a.l. “on chebyshev and almost-chebyshev subspaces”, izvestiya rossiiskoi akademii nauk. seriya matematicheskaya, 1964, 28(4), 799-818. 4. rakhmetov, n.k. on finite-dimensional chebyshev subspaces of spaces with an integral matric, mathematics of the ussr-sbornik, 1993, 74(2), 361-382. 5. kamal, a. on copositive approximation over spaces of continuous functions ii. the uniqueness of best copositive approximation, analysis in theory and applications, 2016, 32(1), 20-26. 6. deutsch, f. and lambert, j. on continuity of metric projections, journal of approximation theory, 1980, 29, 116131. 7. mairhuber, j.c. on haar's theorem concerning chebyshev approximation problems having unique solution, proceeding of american mathematical society, 1956, 7, 609-615. 8. singer, i. “best approximation in normed linear spaces by elements of linear subspaces” springer-verlag, berlin, 1970. 9. ahiezer, n.i., krein, m.g. “some questions in the theory of moments”, translations of mathematical monographs, 2, american mathematical. society, providence, r.i ,1962. 10. cheney, e.w. “introduction to approximation theory”, mcgraw hill book company, new york, 1966. 11. kothe, g. “topological vector spaces i”, springer verlag 1969. 12. semadeni, z. “banach spaces of continuous functions i”, pwn, warsaw 1971. 13. schaefer, h. “banach lattices and positive operators”, springer-verlage, berlin heidelberg new york, 1974. 14. lacey, h.e. “the isometric theory of classical banach spaces”, springer verlag, 1970. 15. schoenberg i. and yang, c. on the unicity of solutions of problems of best approximation, annali di matematica pura ed applicata. 1961, 54, 1-12. received 17 may 2016 accepted 1 december 2016 http://www.sciencedirect.com/science/article/pii/0021904582900879 http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahukewib-sv-_frrahxj1hqkhtqlb_mqfggemae&url=http%3a%2f%2fwww.mathnet.ru%2fphp%2farchive.phtml%3fjrnid%3dim%26wshow%3dcontents%26option_lang%3deng&usg=afqjcnhfoeppuzjsktjzrs2wljwiwlbrow&sig2=jjaj3hdvln6eyy4pwb_2zw&bvm=bv.146094739,d.d24 http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahukewib-sv-_frrahxj1hqkhtqlb_mqfggemae&url=http%3a%2f%2fwww.mathnet.ru%2fphp%2farchive.phtml%3fjrnid%3dim%26wshow%3dcontents%26option_lang%3deng&usg=afqjcnhfoeppuzjsktjzrs2wljwiwlbrow&sig2=jjaj3hdvln6eyy4pwb_2zw&bvm=bv.146094739,d.d24 http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahukewid9z-pgpvrahxdoxqkhcwjcp8qfggzmaa&url=http%3a%2f%2fwww.global-sci.org%2fata%2f&usg=afqjcnhsk4udgfb7dx_pyg-marqemoi5ea&sig2=w0b3wbro-soympacuvsh8q&bvm=bv.146094739,d.d24 squ journal for science, 2017, 22(1), 16-28 doi: http://dx.doi.org/10.24200/squjs.vol22iss1pp16-28 2017 sultan qaboos university 16 study on the reactivity of amino acid chemosensor, npfnp, with ethanol: structural elucidation through single crystal xrd and dft calculations beena varghese, saleh n. al-busafi*, fakhr eldin o. suliman* and salma al-kindy department of chemistry, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman. *email:saleh1@squ.edu.om; fsuliman@squ.edu.om. abstract: a novel ethoxy derivative of an amino acid chemosensor, 3-naphthyl-1-phenyl-5-(2ʹ-fluoro-5ʹnitrophenyl)-2-pyrazoline (npfnp), has been synthesized and characterized by different spectroscopic methods. a single crystal of the ethoxy derivative, 3-naphthyl-1-phenyl-5-(2ʹ-ethoxy-5ʹ-nitrophenyl)-2-pyrazoline npenp, has been obtained and characterized. the structure holds interest as it carries biologically active pyrazoline as a central ring attaching to electron donating and withdrawing substituents. the major motivation for this work was to gain detailed insight into the structural parameters of this compound for investigating the influence of crystal packing and geometrical dimensions on optical properties. time-dependent dft calculations have been employed for comparing the xrd data with theoretical parameters. the results show that the dft method at b3lyp/6-31g level can well reproduce the structure of the title compound. keywords: pyrazoline; uv absorption; crystal structure; chemosensor; td-dft. مع اإليثانول: كشف التركيب الجزيئي عن طريق استخدام األشعة (npfnp) دراسة تفاعل كاشف األحماض األمينيه (dft)قياسات الكثافة اإللكترونيه للبلورات و (xrd)السينية سلمى الكنديو سليمان فخر الدين، صالح البوصافي، بينا فيرجاس باستخدام أجهزة (npfnp)لكاشف األحماض األمينيه (npenp)لقد تم تحضير ومعرفة التركيب الجزيئي لمشتقة اإلثوكسي :صخالمل تركيب السبكتروسكوبي المختلفه. وأيضا، تم تحضير بلورة نقيه لمشتقة اإلثوكسي ومن خالل استخدام األشعه السينيه تم الكشف، وألول مرة، عن ال ثالثي األبعاد لبلورات الكاشف . إن أهمية هذا العمل تنبع من محاولة تتبع العالقة بين التركيب ال(npfnp)الثالثي األبعاد لكاشف األحماض األمينيه لقد تم استخدام العمليات الحسابيه المتعلقه بنظرية الكثافة اإللكترونية لمقارنة القراءات الناتجة عن من جهة و خصائصه الضوئية من جهة أخرى. ت النظرية لمعرفة الركييب الثالثي األبعاد للكاشف.ااباستخدام األشعة السينيه مع القراءات النظرية. نتائج المقارنة تشير الى امكانية اإلعتماد إلى الحس .د ف ت -ت د ،كاشف كيميائي ،تركيب بلوري ،امتصاص فوق البنفسجي، بيرازولين: كلمات مفتاحيةال 1. introduction he rising prevalence of heterocyclic compounds in bio-analytical chemistry has attracted the increasing attention of researchers to pyrazoline derivatives. easily tunable properties suit these electron rich nitrogen heterocycles to be used extensively as useful synthons in organic synthesis [1-2] as well as for medicinal applications [3-4]. these significant key motifs in heterocyclic chemistry are known not only from their pharmaceutical applications but also as materials showing excellent optical properties. moreover, the synthesis of fluorophores with desirable properties based on a pyrazoline skeleton is of considerable interest in fluorescent materials research [5-8]. a lot of work has been focused on the synthesis, crystal structure, optical properties and quantum chemical calculations of novel pyrazoline derivatives [9-12]. the hydroxyl group is a functional element of many drugs and naturally occurring compounds; however, its detection is still a challenging analytical subject [13]. to date there have been relatively few compounds capable of tagging the hydroxyl groups directly. this inadequacy observed in the literature encouraged us to address this t mailto:saleh1@squ.edu.om study on the reactivity of amino acid chemosensor, npfnp, with ethanol 17 issue. very recently, 3-naphthyl-1-phenyl-5-(5ʹ-fluoro-2ʹ-nitrophenyl)-2-pyrazoline was synthesized and characterized by our group and this probe showed a good affinity towards amino acid groups [14]. as a continuation of the mentioned study, we inspected the preparation and usability of 3-naphthyl-1-phenyl-5-(2ʹfluoro-5ʹ-nitrophenyl)-2-pyrazoline npfnp, a constitutional isomer of the reported probe in which the fluorine atom is situated at carbon-2ʹ and the nitro group at carbon-5ʹ (see figure 1). n n f o2n 2' 5' 1 2 3 4 5 figure 1. structure of npfnp. in the present study we focus attention on the reactivity of npfnp with a –oh group by reacting the probe with ethanol and aim to understand the structural details of the ethoxy product, 3-naphthyl-1-phenyl-5-(2ʹ-ethoxy-5ʹnitrophenyl)-2-pyrazoline npenp in the solid state by means of x-ray crystallography (see figure 2). molecular geometries of npenp in both ground and excited states have been calculated using the density functional theory, and the trend of calculated homo-lumo gaps and geometrical parameters in excited state provides valuable information on the factors influencing the optical properties of npenp. n n o o2n ch2ch3 figure 2. structure of npenp. 2. experimental all reagents and solvents used in this study were obtained from sigma aldrich chemical company and were used without further purification. melting point was determined using gallenkamp mpa350 melting point apparatus. the purity of the synthesised compounds was checked by tlc and analyses were carried out on 0.25 mm thick pre coated silica plates (merck fertigplatten kieselgel 60f254). column chromatography was performed using merck silica gel 60 (40-63 µm). ir spectra were determined on a cary 630 ftir spectrometer (agilent technologies, usa). 1hnmr and 13cnmr spectra were recorded using a 400 mhz bruker spectrometer (bruker corp., uk). chemical shifts (δc) are quoted in parts per million (ppm) to the nearest 0.1 and 0.01 and are referenced to the solvent peak (cdcl3). mass spectra were obtained using a quattro ultima pt tandem quadrupole mass spectrometer (waters corp. ma, usa). a shimadzu beena varghese et al 18 (model multispec-1501) uv-vis spectrophotometer (shimadzu, japan) was used to collect absorption spectra. all measurements were done repeatedly, and reproducible results were obtained. the single crystal suitable for x-ray measurements was obtained by recrystallization from hot ethanol. the selected golden yellow crystal (0.350 x 0.300 x 0.250 mm3) of the compound was mounted on a bruker axs kappa apex-ii diffractometer at 293 (2) k with a graphite monochromatic mo-kα radiation (k = 0.71073 å). the corrections for lp factors and empirical absorption were applied to the data. the structures were solved by direct methods and refined by the full-matrix least-squares method 𝐹𝑜𝑏𝑠 2 using the shelxtl software package [15]. all non-h atoms were anisotropically refined. the anisotropic displacement factor exponent takes the form of 2π2 [h 2 a* 2 u 11 + ... + 2 h k a* b* u 12 ]. the hydrogen atom positions were fixed geometrically at calculated distances and allowed to ride on the parent c atoms. the final least-squares cycle gave r= 0.0975 and wr2 = 0.254 for 3547 independent reflections [r (int) = 0.0896]. atomic scattering factors and anomalous dispersion corrections were taken from international table for x-ray crystallography [16]. the quantum chemical calculations were carried out with gaussian 09w programs and gaussview 05 was used for visualization of structures. dft (density functional theory) calculations were performed by using a combination of becke’s three parameter hybrid exchange potential [17] with the correlation functional of lee et al. (b3lyp) [18]. the basis set used was 6-31g. 2.1 synthesis of compounds 3 and 5 2.1.1 synthesis of (e)-3-(2ʹ-fluoro-5ʹ-nitrophenyl)-1-(naphthalene-5-yl)prop-2-en-1-one (3) a mixture of 1-(naphthalene-4-yl)ethanone 1 (5.0 g, 29.4 mmol), 2-fluoro-5-nitro benzaldehyde 2 (5.0 g, 29.5 mmol) in 60 ml acetonitrile and aqueous potassium bicarbonate (5.2 g, 37.6 mmol) was refluxed for 2 hours. after stirring at room temperature for another 24 hours, the crude product was filtered and recrystallized from ethanol to give product 3 (3.6 g, 72.2 %) as an orange solid. mp: 127-128 oc; ir (kbr): υ 3083, 1664, 1603, 1214, 857, 554 cm-1; 1h nmr (400 mhz, cdcl3): δ (ppm) 7.64 (d, j= 8 hz, 1h), 7.92 (d, j=16.8 hz, 1h), 8.19 (dd, j1=14.8 hz, j2=21.2 hz); 13cnmr (100.6 mhz, cdcl3): δ (ppm) 129.05, 128.61, 126.59, 124.81. esi-ms [m + h] + calculated for c19h12fno3: 322.3, found: 322.1. 2.1.2 synthesis of 3-naphthyl-1-phenyl-5-(2ʹ-ethoxy-5ʹ-nitrophenyl)-2-pyrazoline (npenp) a solution of (e)-3-(2ʹ-fluoro-5ʹ-nitrophenyl)-1-naphthyl-prop-2-en-1-one 3 (2.5 g, 7.40 mmol) and phenyl hydrazine (1.2 g, 11.1 mmol) in ethanol (25 ml) was kept refluxing for 2 hours. after stirring at room temperature for another 24 hours, the crude product was filtered and re-crystallized from hot ethanol to give product 5 (2.5 g, 77.16%) as golden yellow crystals; mp:184-185 oc; ftir: υ 1025, 1254, 1325, 1496,1786 cm-1; 1h nmr (400 mhz, cdcl3): δ (ppm) 1.49 (t, j=6.9, 3h), 3.20 (dd, j=7.0, 16.9 hz, 1h), 4.05 (dd, j=12.4, 16.9 hz,1h), 4.21 (q, j=7.0 hz,2h), 5.52 (dd, j=7.0, 12.4 hz,1h), 7.47-9.54 (m, aromatic hydrogens); 13c nmr (100.6 mhz, cdcl3): δ (ppm) 15.1, 42.1, 58.0, 65.3, 113.7, 120.0-148.4, 161.0. esi-ms [m+h calculated for c27h23n3o3: 438.48, found: 438.2. 3. results and discussion 3.1 synthesis and 1h nmr characterization of npenp the synthesis of npenp commenced from an aldol reaction between 1-acetylnaphthalene 1 and 2ʹ-fluoro-5ʹnitro benzaldehyde 2 in acetonitrile using sodium carbonate as a base to give -unsaturated ketone 3 in 72 % yield. a cyclization reaction of compound 3 with phenylhydrazine in refluxing ethanol led to the formation of the pyrazoline derivative 4 which reacted in situ with ethanol to yield its ethoxy derivative 5 (scheme 1). the synthetic route adopted was straightforward, and npenp was obtained by following aromatic nucleophilic substitution, in which a no2 group stabilises the anion intermediate through resonance, and the fluorine atom para to -no2 can be easily replaced by the – oh group of the ethanol to yield the desired ethoxy derivative. the 1h nmr spectrum of the eight aliphatic hydrogens in npenp displayed in figure 3 exhibits three equally intense doublet of doublets, each accounting for one hydrogen atom on the pyrazoline ring; ha, hb and hc. among these, ha, a stationary proton near to the electronegative nitrogen atom, appears in the mid field region of 5.52 ppm. it is clear from the structure that the geminal protons hb and hc are not in the same space of the pyrazoline ring, so hb is shifted by the next benzene ring slightly to the left at a chemical shift of 4.03 ppm and hc is located at a chemical shift of 3.20 ppm. the –ch2hydrogens show a quartet signal at 4.21 ppm and the methyl group appears as a triplet at 1.49 ppm. study on the reactivity of amino acid chemosensor, npfnp, with ethanol 19 o + h o f no2 na2co3 ch3cn o f no2 h2n n h n n reflux ch3ch2oh reflux 1 2 3 5 reflux n n 4 f o2n o o2n ch2ch3 scheme 1. synthetic protocol of npenp 5. figure 3. the aliphatic 1h nmr spectrum (cdcl3) of npenp. 3.2 optical spectroscopy the npenp is a chromophoric π-system composed of three aryl substituents in the 1-, 3and 5positions of pyrazoline ring atoms. as shown in figure 4, this compound exhibits two prominent bands in all selected solvents, appearing at 298-312 nm and 373-391 nm, respectively, and the molar absorption coefficient values are in the same range of 6×104 m-1cm-1. the shorter wavelength is ascribed to a localized aromatic π-π* transition and the long wavelength is attributed to ict transitions [24]. however, in water there is a distinct bathochromic shift in the beena varghese et al 20 absorption maxima compared to those in non-aqueous solvents. the shift in magnitude of the peak position according to the polarity of the medium suggests that the ground state of the molecule is polar. figure 4. the absorption spectra of npenp in (i) water (ii) methanol (iii) acetonitrile (iv) dioxane (v) ethyl acetate and (vi) tetrahydrofuran. even though the molecule is designed in such a way that the aryl rings in this compound can communicate electronically through the pyrazoline π-system to produce an analytically useful signals, the question why the title compound is not fluorescent is crucial. in particular, the uv absorption spectra of npenp in solvents of differing polarity clearly indicate that there is an intramolecular charge transfer throughout the system in ground state. 3.3 x-ray crystallography to study the packing properties of npenp, good-quality single crystals suitable for x-ray analysis were grown in ethanol solvent by slow evaporation at ambient conditions and were found to have a monoclinic crystal lattice with the p21/c space group. the molecular view of fnpfe is shown in figure 5. a summary of crystallographic data collection parameters and refinement parameters are compiled in table 1. figure 5. ortep diagram and atom labelling of npenp. study on the reactivity of amino acid chemosensor, npfnp, with ethanol 21 table 1. crystal data and parameters of x-ray diffraction experiment for npenp. empirical formula c27h23n3o3 formula weight 437.48 temperature 293(2) k wavelength 0.71073 å crystal system monoclinic space group p21/c unit cell dimensions a = 15.8696(14) å ɑ= 90 b = 9.9425(9) å β= 111.652(4)° c = 15.5068(14) å  = 90° volume 2274.1(4) å3 z 4 density (calculated) 1.278 mg/m3 absorption coefficient 0.085 mm-1 f (000) 920 crystal size 0.350 × 0.300 × 0.250 mm3 theta range for data collection 2.470 to 24.095° index ranges -14<=h<=18, -11<=k<=11, -17<=l<=17 reflections collected 21823 independent reflections 3547 [r(int) = 0.0896] completeness to theta = 24.095° 98.1 % absorption correction semi-empirical from equivalents maximum and minimum transmission 0.9799 and 0.9702 refinement method full-matrix least-squares on f2 data / restraints / parameters 3547 / 76 / 298 goodness-of-fit on f2 1.020 final r indices [i>2 sigma(i)] r1 = 0.0975, wr2 = 0.2547 r indices (all data) r1 = 0.2052, wr2 = 0.3282 extinction coefficient n/a largest diff. peak and hole 0.629 and -0.244 e å-3 one phenyl moiety, a naphthalene ring and a substituted phenyl ring are bonded to the pyrazoline ring at the atoms of n2, c9 and c7, respectively. the n2—n3 (1.398 å) (6) and c9—n3 (1.283 å) (7) bonds have pure single and double-bond character, respectively. the torsion angle at (c9-c10-c15-c14) is -177.4 (5)o, which shows that the molecular structure adopts a trans configuration about the c9n3 bond. the dihedral angle between the pyrazoline and substituted phenyl ring (c4-c5-c7-c8) is found to be 74.5 (6)o. the conformation of the naphthalene (c8-c9-c10c11) and phenyl unit (c21-c20-n2-n3) with respect to the pyrazoline ring can be indicated by the torsion angles -1.3 (8)o and 23.1 (7)o, respectively. even though the n2 atom is not involved in conjugation with the pyrazoline double bond, it is sp2 hybridized with its lone-pair electrons delocalized through conjugation with the adjacent phenyl group, as shown by the n2‒c20 bond length (1.387 å) (7). this bond length is shorter than a c‒n single bond (1.47 å) and slightly longer than a cn bond (1.30 å). the sum of the three angles around n2 atom is 350o, which clearly indicates the pyramidal disposition of the bonds at the atom n2. the c‒c bond distances in its aromatic rings are in the normal range of 1.32-1.45 å, which is characteristic of delocalized aromatic rings [19]. the selected bond length, bond angles and torsion angles are presented in table 2. table 2. selected geometrical parameters by x-ray and theoretical calculations at b3lyp/6-31g level of theory in ground state and excited state for npenp. distance å bond x-ray ground state excited state c9‒n3 1.28 (7) 1.33 1.31 n2‒n3 1.39 (6) 1.35 1.40 c20‒n2 1.38 (7) 1.38 1.44 c5‒c7 1.49 (7) 1.51 1.50 c9‒c10 1.49 (9) 1.44 1.46 c4‒o3 1.33 (7) 1.42 1.49 bond angle (o) c8-c9-c10 121.8 (6) -106.3 -103.3 beena varghese et al 22 c9-n3-n2 109.6 (6) 110.1 111.2 c20-n3-n2 116.8 (5) 119.9 117.9 c5-c7-c8 113.0 (4) 114.7 112.3 o3-c4-c5 114.4 (5) 116.2 115.9 c11-c10-c9 117.0 (6) 125.4 118.6 n3-c9-c10 125.2 (6) 123.7 124.5 torsion angle angle (o) c9-c10-c15-c14 -177.4 178.5 178.6 c4-c5-c7-c8 74.4 127.6 129.0 c8-c9-c10-c11 -1.3 5.7 -11.6 c21-c20-n2-n3 23.0 -167.4 10.6 n3-c9-c10-c15 1.9 5.8 -11.5 table 2. contd. the 5-substituted phenyl ring on the asymmetric carbon of a pyrazoline moiety (c7) is oriented in such a manner that one of its hydrogen atoms (h27a) is located almost on top of the pyrazoline moiety at 2.6131 å distance from the center of the pyrazoline ring. the angles around the asymmetric carbon are 111.7o (4) (n2‒c7‒c5), 101.9o (4) (n2‒ c7‒c8), 113.0o (4) (c5‒c7‒c8), 110.0o (n2‒c7‒h7), 110.0o (c5‒c7‒h7), 110.0o (c8‒c7‒h7). the bond length of the c‒c single bond bridging the naphthalene, the 5-substituted phenyl group and the pyrazoline ring (c9–c10, c5‒ c7) is calculated to be 1.49å (9, 7). this bond is significantly shorter than a typical c–c single bond of 1.54å. this reflects an efficient charge delocalization over the pyrazoline π-system allowing electronic interaction between the attaching groups as they are electronically separated. analogously it is clear that the presence of an electron attracting nitro group and electron donating ethoxy substituent distorts the interatomic distances so that the bond length of c4‒ o3 reduces to 1.339 (7) å , in contrast to the normal c‒o bond of 1.43 å. the mean plane of the pyrazoline ring (n2/n3/c7/c9) makes dihedral angles of 16.3 (7), 1.3 (8) and 10.6 (7)0 with the phenyl ring (c20‒c25), naphthalene ring (c10‒c11), and substituted phenyl ring, respectively, and it exists in a flattened envelope conformation with one carbon atom (c8) deviating from the mean plane of the remaining four atoms. regarding the crystal packing, there are significant intramolecular c2‒h2o1 (2.34 å), c6‒h6n2 (2.455 å), c6‒h6o2 (2.408 å), c7‒h7o3 (2.478 å), c21‒h21n3 (2.426 å) hydrogen bonds-forming pseudo five membered ring [20]. the molecular conformation is further stabilized by ten intramolecular hydrogen bonds which involve all the fragments in npenp, serving as both acceptors and donors in a set of head to tail fashion. the c8‒ h8o3 (3.005 å, x, y, z), c16‒h16n3 (2.133 å, x, y, z), c25‒h25o2 (2.741 å, -x+1, +y+1/2, -z+1/2+1), c27‒ h27o2 (2.527 å, x, +y+1, +z), c19‒h19o1 (2.616 å, x-1, -y+1/2+1, +z-1/2) hydrogen bonding networks play an important role in bringing the molecules in close proximity to each other [21]. among these it is clear that three hydrogen bonds (o2h27, o2h25 and o2h6) are trifurcated since they share the same oxygen (o2) atom. the bond lengths between these atoms are 2.6131 å, 2.869 å and 2.424 å respectively. similarly another four hydrogen bonds (o3h8, o3h7 and n3h16, n3h21) are bifurcated and their bond lengths are 2.996, 2.477, 2.223, and 2.446 å, respectively, (table 3). table 3. parameters for the intraand inter molecular hydrogen bonding. d‒h d…..a h….a d‒h….a c2‒h2 (0.93) c2….o1 (2.66) h2….o1 (2.36) c2‒h2….o1 (2.34) c6‒h6 (0.93) c6…..n2 (2.83) h6….n2 (2.48) c6‒h6….n2 (2.45) c7‒h7 (0.98) c7….o3 (2.67) h7….o3 (2.47) c7‒h7….o3 (2.47) c8‒h8a (0.97) c8….o3 (3.08) h8a….o3 (2.99) c8‒h8a….o3 (3.00) c21‒h21 (0.93) c21….n3 (2.75) h21….n3 (2.44) c21‒h21….n3 (2.42) c16‒h16 (0.93) c16….n3 (2.89) h16….n3 (2.22) c16‒h16….n3 (2.13) c25‒h25 (0.93) c25….o2 (3.70) h25….o2 (2.86) c25‒h25….o2 (2.74) c27‒h27 (0.96) c27…..o2 (3.37) h27a….o2 (2.61) c27‒h27a….o2 (2.52) c19‒h19 (0.93) c19….o1 (3.49) h19….o1 (2.72) c19‒h19….o1 (2.61) donor‒hydrogen donor…acceptor hydrogen….acceptor donor‒hydrogen…acceptor study on the reactivity of amino acid chemosensor, npfnp, with ethanol 23 the establishment of ch‒π interactions consequently result in the stacking of the npenp molecules to be packed as a crystal along b axis like a chair as shown in figure 6. the molecular packing diagram shows two layers of molecules, which are independently arranged in the unit cell. in the extended structure of npenp it is clear that intermolecular ch‒π interactions within each unit and ππ contact between the individual chain of a single molecule in a zig-zag manner to produce chains running parallel to each other. figure 6. packing diagram of npenp viewed along b axis. 3.4 computational details the dft functional b3lyp coupled with the 6-31g basis set was used to perform geometry optimizations in vacuo, for comparing the xrd data with theoretical parameters. there are some differences between the experimental values and the calculated data as the geometry of the solid-state structure is subject to intermolecular forces, such as van der waals interactions, crystal packing forces and hydrogen-bond forces [22], but the calculated data corresponds to the isolated molecule in gas phase. as discussed previously for the crystal structure, the n2—n3 bond length (1.351 å) is slightly lower than the experimental value; surprisingly c9—n3 (1.335 å) shows deviation from the typical cn behavior of the pyrazoline ring (~1.28 å) in solid state. the bond length of sp2 hybridized n2 atom and the phenyl attaching carbon c20 is in good agreement with the experimental value, but the sum of the three angles around n2 atom is exactly 360o indicating that the bonds meeting at n2 are almost coplanar in gaseous phase and this high degree of coplanarity invokes electronic transitions in ground state (see figure 7). beena varghese et al 24 figure 7. the optimized molecular geometry of npenp in its ground state at b3lyp/6-31g level. the calculated torsion angle at c9-c10-c15-c14 is found to be 178.597o and the difference of about 180o from the experimental value corresponds to a rotation of 180o about the c9-c10 axis of the naphthalene ring, which does not affect the molecular stability. the bond length of the c9‒c10 single bond bridging the naphthalene ring (1.44 å) is found to be lower than that of the experimental value (1.49 å) and also lower than the c5‒c7 bond bridging the substituted phenyl group (1.51 å). it was noticed that the distance between the pyrazolinic nitrogen connecting to the attaching carbon of the phenyl ring is shorter (1.388 å) than a normal c‒n single bond (1.47 å). it implies that there is a chance for high degree electron density delocalization from the π-bridge towards the naphthalene and phenyl rings, which is crucial for the highly enhanced ict character in ground state. the computational analysis of the frontier molecular orbitals (see figure 8) provides more insightful information on the energies of occupied and virtual front orbitals and their influence on the excitation and emission properties of npenp. (i) (ii) figure 8. frontier orbitals of npenp calculated by the td-dft/ b3lyp/6-31g method on ground and excited state (i) npenphomo (g.s) (ii) npenphomo-1 (g.s) (iii) npenpelumo (g.s) (iv) npenplumo+1 (g.s) (v) npenpehomo (ex) (vi) npenphomo-1 (ex) (vii) npenplumo (ex) (viii) npenplumo+1 (ex). study on the reactivity of amino acid chemosensor, npfnp, with ethanol 25 (iii) (iv) (v) (vi) (vii) (viii) figure 8. contd. the energies of homo, lumo and their neighboring orbitals are all negative, which indicates the stability of npenp in ground state, whereas the molecule is instable in excited state. in ground state the homos are mainly localized on the naphthalene, pyrazoline and 1-phenyl rings and the lumo is fully populated on the 5-substituted phenyl ring. by contrast, the contribution of naphthalene and pyrazoline is increased in lumo+1 and the small energy gap (0.053 ev) underlines the highly delocalized nature of npenp in ground state. from the figure it is observable that beena varghese et al 26 the bent –ch2-ch3 group has no charge density distribution, neither on the homo nor on the lumo levels of npenp in both ground and excited state. on the other hand, there is a large distortion in the geometry of npenp in excited state accompanied by unfavorable changes in the basic dimensions, particularly in the bond length and bond angles involving the pyrazoline ring. there is perceptible lengthening of n2—n3 (1.407 å), n2—c20 (1.447 å) and c9-c10 (1.463 å) bond length in excited state geometry. the sum of the bond angles at n2 is found to be 347.28o and is considerably distant from the planarity. the dihedral angle c11-c10-c9-c8 (179.12o) is an indication of coplanar orientation of the pyrazoline and naphthalene rings in excited state while both the phenyl and substituted phenyl rings are folded slightly from their attached pyrazoline ring with torsion angles of 10.617o (c21-c20-n2-n3) and -50.496o (c4-c5-c7-c8), respectively (see figure 9). figure 9. the optimized molecular geometry of npenp in excited state at b3lyp/6-31g level. as shown, for npenp in excited state the electron densities of homo are mainly located on the naphthalene ring; there is an electron distribution from the substituted phenyl ring to the pyrazoline ring, except in case of the c8 carbon and a small node on the 1-phenyl ring. the increase in electron density on the left part including the pyrazoline and 1-phenyl rings was observed for homo-1 in excited state, and the lumo is equally delocalized on the naphthalene and 5-substituted phenyl rings with a small contribution on c-n=n. the lumo +1 looks like a flow of electrons from the 1-phenyl ring, including n2-c7, and as a separated cloud on the center of the 5-substituted phenyl ring. compared to the mos of the ground state (s0) the contribution of the 5-substituted phenyl ring is greater in excited (s1) state. this can increase the electron density on the conjugated back bone and its steric effects cause distortion of the conjugated back bone [23]. on the other hand, it is clear that the phenyl group at n2 also destroys the coplanar character of the conjugated backbone in excited state. this ensures that a steric effect arises due to the distorted geometry of npenp hampering the delocalization of a/ the lone pair of electrons of ‒n3 atom, and this may also disturb the conformational stability of cn‒n which in turn will cause a decrease in conjugation, and thereby decrease in charge transfer throughout the system and make the lumo-homo energy gap wider (0.134 ev). 4. conclusion combining computational studies with single crystal x-ray diffraction facilitates a deeper understanding of the geometry of npenp in solid and gaseous state. the analysis of the molecular geometry of npenp in ground state exhibits a very good agreement with the experimental data. considering the geometry of npenp in excited state, one can clearly find that non-planarity and proximity of atoms play an important role in hindering the delocalization of π electrons throughout the system. the high molar absorptivity of npenp underlines the importance of its mother dye npfnp in the determination of alcohols and phenolic derivatives. study on the reactivity of amino acid chemosensor, npfnp, with ethanol 27 5. acknowledgements beena varghese would like to thank squ for a phd scholarship. we also acknowledge saif (iit, madras, india) for providing crystallographic data. supporting information crystallographic data for the structure reported in this article have been deposited with the cambridge crystallographic data center with the deposition number 1056209. a copy of the data can be obtained free of charge from the director, ccdc, 12 union road, cambridge cb2 iez, uk; fax: +44(0)1222-336033; email: deposit@ccdc.cam.ac.uk. references 1. dai, y., guo, m., peng, j., shen, w., li, m., he, r., zhu, c. and lin, s.h. noncovalent interaction and its influence on excited-state behaviour: a theoretical study on the mixed coaggregates of dicyanonaphthalene and pyrazoline. chemical physics letters, 2013, 556, 230-236. 2. anam, f., abbas, a., lo, k.m., rehman, z.u., hameed, s. and naseer, m.m. homologous 1,3,5triarylpyrazolines: synthesis, ch….π interactions guided self-assembly and effect of alkyloxy chain length on dna binding properties. new journal of chemistry, 2014, 38, 5617-5625. 3. lone, i.h., khan, k.z. and fozdar, b.i. synthesis, physicochemical properties, antimicrobial and antioxidant studies of pyrazoline derivatives bearing a pyridyl moiety. medicinal chemistry research, 2014, 23, 363-369. 4. havrylyuk, d., zimenkovsky, b., karpenko, o., grellier, p. and lesyk, r. synthesis of pyrazolinethiazolidinone hybrids with trypanocidal activity. european journal of medicinal chemistry, 2014, 85, 245-254. 5. wang, h.y., shi, j.j., chen, g., xu, x.p. and ji, s.j. synthesis and characteristics of novel benzothiazoylpyrazoline derivatives containing carbazole. synthetic metals, 2012, 162, 241-246. 6. kumar, c.k., trivedi, r., kumar, k.r., giribabu, l. and sridhar, b. synthesis, characterization, electrochemistry and optical properties of new 1,3,5-trisubstituted ferrocenyl pyrazolines and pyrazoles containing sulfonamide moiety. journal of organometallic chemistry, 2012, 718, 64-73. 7. shi, h-p., dai, j.x., zhang, x.f., xu, l., wang, l., shi, l.w. and fang, l. experimental and theoretical study of two new pyrazoline derivatives based on dibenzofuran. spectrochimica acta part a: molecular and biomolecular spectroscopy, 2011, 83, 242-249. 8. singh, p., negi, j.s., singh, k., pant, g.j., rawat, m.s.m. and joshi, g.c. synthesis and structure dependent photophysical properties of novel 2-pyrazolines. synthetic metals, 2012, 162, 1977-1980. 9. wang, s.q., gao, y., wang, h.y., zheng, x.x., shen, s.l., zhang, y.r. and zhao b.x. synthesis, x-ray crystal structure and optical properties of novel 1,3,5-triarylpyrazoline derivatives and the fluorescent sensor for cu2+. spectrochimica acta part a: molecular and biomolecular spectroscopy., 2013, 106, 110-117. 10. zhao, p., zhou, s., guo, z. and zhu y. crystal structure, spectral properties and comparative studies on a 2pyrazoline derivative. spectrochimica acta part a: molecular and biomolecular spectroscopy, 2012, 94, 65-71. 11. zeng, y.m., chen, s.q. and liu, f.m. synthesis and crystal structure of new thiazolyl-pyrazoline derivatives bearing 1, 2, 4-triazole moiety. the journal of chemical crystallography, 2012, 42, 24-28. 12. chinnaraja, d., rajalakshmi, r., srinivasan, t., velmurugan, d. and jayabharathi, j. spectral studies of 2pyrazoline derivatives: structural elucidation through single crystal xrd and dft calculations. spectrochimica acta part a: molecular and biomolecular spectroscopy, 2014, 124, 30-33. 13. assaf, p., katzhendler, j. and haj-yehia, al. 2(4-carboxyphenyl) -6 -n, n-diethyl amino benzofuran; 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pyritohedron; lattice; coxeter groups and quaternions. تماثل متعدد األوجه ذو التركيب المشابه لمعدن البايريت في الفضاء االقليدي ذو األبعاد األربعة محمد كوجا نظيفة كوجا، أمل القنوبي و و الذي يمكن صياغته في االبعاد -( pyritohedralوصفنا امتدادا لتماثل تركيب متعددات األوجه من النوع المشابه لبلورة معدن البايرايت ) ستخلص:م باستخدام العدد المركب التخيلي ببلورة معدن البايرايت رباعية االبعادالمتصلة إلى الفضاء االقليدي ذو األبعاد األربعة ثم بنينا عناصر المجموعة -الثالثة ذات الرتبة الرابعة 4h( w (و w )4f (الرباعي )الكواتيرنيونات(، و اتضح أن هذه المجموعة من أكبر المجموعات الفرعية لكل من مجموعات الكوكستر ذوات العشرون 24اشتقاق احداثيات رؤوس تم مما يعني أنها مجموعة ذات صلة بالتركيبات البلورية فضال عن اشباه البلورية في األبعاد األربعة، كما ، و اتضح أن pseudo snub 24-cell يسمىمجسم رباعي األبعاد أهراما مثلثية و التي تمثل أسطح ل 96رباعي األسطح و 24وجها غير المنتظم و هي اتحاد ثالث مجموعات: اربعة و cell-pseudo snub 24رؤوس المزدوج لـ و أن 4d( w (الشبيكة الفراغية ذات الصلة هي جذر الشبيكة الفراغية لـ ، كذلك اشتققنا تمثيال جديدا لمجموعة تماثل جديد pseudo snub 24-cellو ( أخرىcell-24اربعة و عشرون خلية )( و 24cellعشرون خلية ) pseudo snub 24-cell المقابلة.األجسام رباعية األبعاد و رؤوس شبيه ذي العشرين وجها المنتظم، متعدد األوجه ذو التركيب المشابه لمعدن البايرايت، الشبيكة الفراغية، مجموعات كوكستر، : كلمات مفتاحية الرباعيات. 1. introduction attices in higher dimensions described by the affine coxeter groups, when projected into lower dimensions, may represent the quasicrystal structures [1-5]. it is known that the 4 a lattice projects into the aperiodic lattice with 5fold symmetry [1]. there is no doubt that the projections of the higher dimensional lattices may have some implications in physics. the exceptional coxeter-weyl group )( 4 fw describes the symmetry of the unique self-dual polytope, the 24-cell, which is the voronoi cell (wigner-seitz cell) of the 4 f lattice. the noncrystallographic coxeter group )( 4hw is the symmetry of the famous 600-cell and its dual 120-cell [6-7]. in this work we construct the 4d pyritohedral group from 4 d diagram. in technical terms the group  4 3 2 ( ) : w d s c of order 576 [8] can be expressed in terms of quaternions and we will determine its orbits as the pseudo snub 24-cell and l 4d pyritohedral symmetry 151 its dual polytope, which are related to the lattice )( 4 dw . all rank 4 coxeter-weyl groups can be represented, in compact forms, by quaternion pairs [9]. this paper is organized as follows. in section 2 we introduce the 4d pyritohedral symmetry derived from d4 diagram. in section 3 we construct the group  4 3 2 ( ) : w d s c and apply it to a vector to generate the vertices of a polytope which we call “pseudo snub 24-cell”. we find the facets of the pseudo snub 24-cell which consist of the pseudoicosahedra, tetrahedra and triangular pyramids. the vertices of the dual polytope of the pseudo snub 24-cell are constructed. finally, in section 4 we present a brief discussion on the physical implications of our technique. 2. 4d crystals with the pyritohedral symmetry derived from d4 diagram in the paper [10] we discussed the pyritohedral group * ],[],[ tttt  of order 24 which is derived from the coxeterdynkin diagram 3d by the rotation generators and the dynkin diagram symmetry. the straightforward generalization of this group to 4d is to start with the rotation generators of 4d and impose the dynkin diagram symmetry. we will see that the generated group from the diagram 4d is nothing other than the group * ],[],[ tttt  of order 576. it represents the symmetry of the snub 24-cell [6], [8]. the snub 24-cell is a convex uniform polytope in four dimensions consisting of 120 regular tetrahedral and 24 icosahedral cells. it has 96 vertices at each of which five tetrahedra and three icosahedra meet. snub 24-cell can be constructed from the 24-cell by dividing the edges in the golden ratio and truncating it in a certain way. this truncation transforms the 24 octahedral cells of the 24-cell to the 24 icosahedral cells of the snub 24-cell; the truncated vertices become 24 tetrahedral cells and the gaps in between are filled in by another 96 tetrahedra. 3. construction of the symmetry group of snub 24-cell 3 2 4 s c dw : )(       the coxeter-dynkin diagram 4d is shown in figure 1 with the quaternionic simple roots. the corresponding weights are determined as 1 2 1 3 1 2 3 4 1 2 3 1 1 1, 1 , (1 ), (1 ). 2 2 e e e e e e e              (1) note that 2 , 1, 2, 3, 4; ; , j=1,3,4. 2 2 i j t i t t        the set t is given by the group elements 𝑇 = {±1,±𝑒1,±𝑒2,±𝑒3, 1 2 (±1 ± 𝑒1 ± 𝑒2 ± 𝑒3)}, (2) and is called the binary tetrahedral group of order 24 . another set of 24 quaternions is defined by α 2 =e 1 -e 2 α 1 =1-e 1 α 3 =e 2 -e 3 α 4 =e 2 +e 3 figure 1. the coxeter-dynkin diagram 4d with the simple roots. https://en.wikipedia.org/wiki/uniform_4-polytope https://en.wikipedia.org/wiki/cell_(mathematics) nazife o. koca et al 152 𝑇′ = { 1 √2 (±1 ± 𝑒1), 1 √2 (±1 ± 𝑒2), 1 √2 (±1 ± 𝑒3), 1 √2 (±𝑒1 ± 𝑒2), 1 √2 (±𝑒2 ± 𝑒3), 1 √2 (±𝑒3 ± 𝑒1) }. (3) in terms of quaternionic simple roots, the group generators of )( 4dw can be written as 1 1 1 2 1 2 1 2 3 2 3 2 3 4 2 3 2 3 1 1 [ (1), (1)] , 2 2 1 1 [ ( ), ( )] , 2 2 1 1 [ ( ), ( )] , 2 2 1 1 [ ( ), ( )] . 2 2 r e e r e e e e r e e e e r e e e e               (4) they generate the coxeter-weyl group )( 4dw of order 192 [12]. the subsets of the quaternions  vvvt 0  and 321 vvvt  are defined as follows: these subsets are useful to denote the coxeter-weyl group )( 4dw in a compact form: }],[],[],[],[],[],{[)( *** 332211004 vvvvvvvvvvvvdw    . (6) note that the subset of the coxeter-weyl group 4 0 0 2 ( ) {[ , ] [ , ] [ , ]} w d v v v v v v c      (7) represents the proper subgroup and can be directly generated by the rotation generators 𝑟2𝑟1,𝑟2𝑟3,𝑟2𝑟4. let us impose the dynkin diagram symmetry which is the permutation group 𝑆3 of the simple roots 𝛼1,𝛼3 and 𝛼4 as shown in figure 2. },,,{ 3210 1 eeev  , )( 3211 2 1 eeev  , even number of (-) sign, )( 3211 2 1 eeev  , odd number of (-) sign, )}(),({ 3211 2 1 1 2 1 eeev  , )}(),({ 1322 2 1 1 2 1 eeev  , )}(),({ 2133 2 1 1 2 1 eeev  . (5) 4d pyritohedral symmetry 153 generator 1: ],[ qp generator 2: *],[ 33 ee  figure 2 . the action of permutation group 𝑺𝟑. the permutation group of order 6 can be generated, for example, by two generators [ , ]p q and * 3 3 [ , ]e e where 1 2 3 1 2 (1 )p e e e    and 1 2 3 1 2 (1 )q e e e    . they are the elements of 3 [ , ] [ , ] with [ , ] [1,1]p q v v p q     and 3 3 0 0 [ , ] [ , ]e e v v     . the group       2 4 c dw )( is invariant under conjugation by the group 𝑆3. we first note that the extension of the group of eq. (7) by the cyclic group of order 3 generated by the generator [𝑝,𝑞] is a group of order 288 which can be denoted by  4 3 2 ( ) : [ , ] w d c t t c  . (8) the extension of the group by full permutation group 3 s is given as the semi-direct product of two groups as:   *4 3 2 ( ) : {[ , ] [ , ] } w d s t t t t c  . (9) as we will see in the next section this is the symmetry group of the snub 24-cell as well as that of any pseudo snub 24cell. 3.1 construction of the vertices of the pseudo snub 24-cell the affine coxeter group 𝑊𝑎(𝐷4) =< 𝑟0,𝑟1,𝑟2,𝑟3,𝑟4 > can be generated by five generators by introducing 𝑟0 as shown in figure 3. 𝑟0 represents the reflection with respect to the hyperplane bisecting the line from the origin to the highest root 1 2 3 4 1 0 2 1 e             . the action of 𝑟0 on a general vector  is given as 0 2[( , ) 1] ( , ) r           [13]. figure 3. affine coxeter-dynkin diagram 𝑾𝒂(𝑫𝟒) with simple roots. α α 1 α α 4 α α 1 α 3 α 4 α 2 α 1 α 3 α 4 α 0 nazife o. koca et al 154 applying the group wa (d4) on a simple root we can generate the root lattice. we now derive the vertices of pseudo snub 24cell in terms of the root lattice vectors of d4. the lattice of d4 is self-dual so that we can express the dual lattice vectors in terms of the weight vectors [14]. table 1 shows the lattice vectors in terms of the root & weight vectors and quaternions. table 1. the construction of the lattice from wa (d4). wa(d4) generates lattice root lattice (real lattice) weight lattice (reciprocal lattice) vectors 44332211  bbbb  zb i  44332211  aaaa  za i  vectors in terms of quaternions 1 1 2 2 3 3 4 m e m e m e m     1 1 2 2 3 3 4 n e n e n e n     determine the lattice integereven 2 4 3 0   bm i i 3 0 even integer i i n   we impose the dynkin-diagram symmetry 𝑆3 on the vector  , that is, 3s    as shown in figure 2. the group 𝑆3 permutes the weight vectors 𝜔1 ,𝜔3 𝑎𝑛𝑑 𝜔4 but leaves 𝜔2 invariant. similarly, the generators 𝑟1 ,𝑟3 𝑎𝑛𝑑 𝑟4 are permuted and the generator 𝑟2 is left invariant under the group conjugation of 𝑆3.this implies that the vector  takes the form 2 2 1 1 3 4 ( ), , 1, 2. i a a a i         z (10) factorizing by 𝑎2 and defining the rational number 𝑥 = 𝑎1 𝑎2 the vector  reads in terms of quaternions ])()[( 212 121 xeexxa  . (11) note that the sum of the coefficients of the quaternionic units is an even integer as we mentioned earlier. for 0 and 2 1 1  ,x the vector  belongs to the set of quaternions, t  which is known to be the 24-cell. for these particular values of x, the group   *4 3 2 ( ) : {[ , ] [ , ] } w d s t t t t c  generates 24 vertices of 𝑇′. the 24-cell has 24 vertices and 24 octahedral cells where 6 octahedra meet at one vertex. the polytope 24-cell constitutes the unit cell of the 𝐷4 lattice. in terms of the quaternionic sets when t represents the unit cell of the root lattice, then the set 𝑇′ √2 represents its voronoi cell. applying the group elements represented by eq. (9) on the vector in (11) we obtain 96 vertices of pseudo snub 24-cell as the orbit of the group  4 3 2 ( ) : w d s c as expected for 576 6 96 . we list 96 vertices of the pseudo snub 24-cell omitting the overall factor 𝑎2 as follows: }.)()(,)()(,)()( ,)()(,)()(,)()( ,)()(,)()(,)()( ,)()(,)()(,)()({ 321321321 313131 323232 212121 211 211 121 211 211 121 211 121 121 211 121 121 )( xeexexexexxeexxeex xeexxexexxexxex exxexexexxxeexx exxexexexxxeexxxs     (12) dual dual 4d pyritohedral symmetry 155 the mirror image of the pseudo snub 24-cell can be obtained by applying any reflection generator of 𝐷4. for example, applying 𝑟2 on 𝑆(𝑥) in (12) interchanges 1 2e e and leaves the other quaternionic units unchanged. then under the action of the mirror operator 𝑟2 one can obtain the mirror image of the pseudo snub 24-cell in (12). both the pseudo snub 24-cell and its mirror image lie in the 𝐷4 lattice. it is clear that for 0 and 2 1 1  ,x the vertices of (12) reduces to the set 𝑇′. excluding these values of x, the set of vertices represent a pseudo snub 24-cell. only in the limit 2 51 x ( ,x ) the vertices given in (13) represent the snub 24-cell [8]. since in this case x is not a rational number, the vertices do not belong to the lattice 𝐷4. 𝑆 = { 1 2 (±𝜏 ± 𝑒1 ± 𝜎𝑒3), 1 2 (±𝜏 ± 𝑒2 ± 𝜎𝑒1), 1 2 (±𝜏 ± 𝑒3 ± 𝜎𝑒2), 1 2 (±𝜎 ± 𝑒1 ± 𝜏𝑒3), 1 2 (±𝜎 ± 𝑒2 ± 𝜏𝑒1), 1 2 (±𝜎 ± 𝑒3 ± 𝜏𝑒2), 1 2 (±1 ± 𝜏𝑒1 ± 𝜎𝑒2), 1 2 (±1 ± 𝜏𝑒2 ± 𝜎𝑒3), 1 2 (±1 ± 𝜏𝑒3 ± 𝜎𝑒1), 1 2 (±𝜎𝑒1 ± 𝜏𝑒2 ± 𝑒3), 1 2 (±𝜎𝑒2 ± 𝜏𝑒3 ± 𝑒1), 1 2 (±𝜎𝑒3 ± 𝜏𝑒1 ± 𝑒2).} . (13) table 2 summarizes the action of the group 3 2 4 s c dw : )(       on  given in (11) for certain x values. table 2. action of the group  4 3 2 ( ) : w d s c on  . x vertices polytope generated #vertices #cells type of cell 0 and 2 1 1  ,x 𝑇′ in (3) 24-cell 24 24 24 octahedra 𝑥 = 𝜎 s in (13) snub 24-cell 96 144 24 icosahedra, 24 tetrahedra, 96 tetrahedra 𝑥 = 𝜏 mirror image of s snub 24-cell 96 144 24 icosahedra, 24 tetrahedra, 96 tetrahedra any other 𝑥 s (x) in (12) pseudo snub 24-cell 96 144 24 pseudoicosahedra, 24 tetrahedra, 96 triangular pyramid 3.2 determination of facets of pseudo 24-cell it is known that every vertex of the snub 24-cell is surrounded by three icosahedra and five tetrahedra. we shall prove that the facets of the pseudo snub 24-cell consist of pseudo icosahedra, tetrahedra and triangular pyramids. in the pseudo snub 24-cell three pseudoicosahedra, one tetrahedron and four triangular pyramids meet at the same vertex. now we discuss the details of this structure. it is evident from the 𝐷4 diagram that each of the following sets of rotation generators (𝑟1𝑟2,𝑟2𝑟3),(𝑟3𝑟2,𝑟2𝑟4) and (𝑟4𝑟2,𝑟2𝑟1) generate a proper subgroup of the tetrahedral group of order 12 as shown in figure 4. nazife o. koca et al 156 1 2 3 figure 4. three proper subgroups of the tetrahedral group from the 𝑫𝟒 diagram. let us discuss how one of these groups acts on the vertex  . let us take the group ],[, 443221  ttrrrr  (case 1 in figure 4) which implies that the group consists of 12 elements leaving the weight vector t 4  invariant. the group generators transform quaternionic units as follows: 1 2 1 2 3 3 2 3 1 2 3 1 :1 1, :1 1, . r r e e e e r r e e e e         (14) the 12 vertices generated from 1 2 [(1 2 ) (1 ) ]x x e xe      (here we dropped the overall scale factor) the group  3221 rrrr , are determined as: 1 2 1 2 1 2 2 3 2 3 2 3 1 3 1 3 1 3 1 2 3 (1 2 ) (1 ) , (1 2 ) (1 ) , (1 ) (1 2 ) , (1 2 ) (1 ) , (1 2 ) (1 ) , (1 ) (1 2 ) , (1 2 ) (1 ) , (1 ) (1 2 ) , (1 ) (1 2 ) , (1 2 ) (1 ) , x x e xe x x e x e x xe x e x x e xe x x e x e x xe x e x xe x e x x e x e x x e xe x e xe x e x                                         1 2 3 1 2 3 (1 ) (1 2 ) , (1 ) (1 2 ) .e x e x e x e x e xe        (15) since the vector 4  is left invariant by the generators in (14) the center of the polyhedron of (15) can be taken as 4  up to a scale factor. one may check that the set in (15) is also left invariant under the group element * ],[ 44  . therefore, the set (15) is invariant under the larger group * ],[],[ 4444  ttttt h  of order 24 isomorphic to the pyritohedral group. if we define a new set of unit quaternions 03302201140 peppeppepp  ,,, and express the vectors in (15) in terms of the new set of quaternions, then the set of vertices in (15) represent a pseudoicosahedron as shown in figure 5(a). when the set of generators  4223 rrrr , (case 2 in figure 4) and  1224 rrrr , (case 3 in figure 4) respectively are applied to the vector  , one generates two more pseudo icosahedra with the centers represented by 1  and 3  respectively. the groups generating the vertices of the second and the third pseudo icosahedra can be written respectively as ttttt  11111  ,],[],[ * and ttttt  33333  ,],[],[ * .these groups are isomorphic to the pyritohedral group ]},[],{[ ttttth   . this is obtained if 1 1  is substituted above in the basis vectors 1 2 3 , and e e e in 3d. note that [1,−1] ∈ [𝑇,𝑇] is also an element of the group [𝑇,𝑇] which commutes with all elements and sends a quaternion to its negative 𝑞 → −𝑞. with the generator [1,−1] one obtains a larger group ttttttttttcth  2 ,],[],[ * of order 48 leaving the vector ±𝑡 invariant so that the group can be embedded in the group 3 2 4 s c dw : )(       12 different ways. the group [𝑇,𝑇] ∪ [𝑇,𝑇]∗ also leaves the set of quaternions 𝑇′ invariant. the largest subgroup which leaves t t   invariant can be written as ttttttttttct d  2 ,],[],[ * . now we continue to discuss the polyhedral facets having  as a vertex. let us consider the following five sets of rotational generators obtained from the generators of the coxeter-weyl group 𝑊(𝐷4): 4d pyritohedral symmetry 157 1 3 3 4 4 1 ( , , )r r r r r r , 2 1 2 3 2 4 ( , , )r r r r r r , 1 2 1 3 1 4( , , )r r r r r r , 3 1 3 2 3 4( , , )r r r r r r , 4 1 4 2 4 3( , , )r r r r r r . (16) the first two sets of generators are invariant under the conjugation of the permutation group 𝑆3 but the next three sets of generators are permuted among each other. let us determine the vertices of the polyhedra under the action of five sets. 1. the set of vertices 1 2 1 3 1 3 3 4 1 2 4 1 1 3 (1 2 ) (1 ) , (1 ) (1 2 ) , (1 2 ) (1 ) , (1 ) (1 2 ) , x x e xe r r x x e xe r r x x e xe r r x x e xe                         (17) represents a tetrahedron of edge length 2x as shown in figure 5(b). its center can be represented by 𝑝(1) = 𝜔2 = 1 + 𝑒1up to some scale factor. since the dynkin diagram symmetry 𝑆3 also leaves 𝜔2 = 1 + 𝑒1 invariant, the group 𝐶2×𝐶2 generated by the generators (𝑟1𝑟3,𝑟3𝑟4,𝑟4𝑟1) can be extended by the 𝑆3 symmetry to a group * ],[],[ 2222  tttt  of order 24 isomorphic to the tetrahedral group [10]. since 3s , the group tttttt d  22222  ,],[],[ * leaves the vertices of the tetrahedron in (17) invariant (figure 5b). note that this not a pyritohedral symmetry. this tells us that the number of tetrahedra generated by the conjugate tetrahedral groups is also 24. extension of the group by the generator [1,−1] leads to the group ttttt  22222  ,],[],[ * that is isomorphic to the octahedral group [10]. 2. the set of vertices .)()( ,)()( ,)()( ,)()( 3242 3232 2112 21 121 121 211 121 exexxrr exexxrr exxexrr xeexx     (18) determines a triangular pyramid with a base of equilateral triangle with sides 2x and the other edges of length √2(𝑥2 + 𝑥 + 1). the triangular pyramid is depicted in figure 5 (c). the hyperplane determined by these four vertices in (18) is orthogonal to the vector 21 122 exexp )()()(  . the group generated by these generators extended by the group 𝑆3 is the full group of symmetry 3 2 4 s c dw : )(       . 3. the set of vertices .)()( ,)()( ,)()( ,)()( 3141 3131 2121 21 211 211 1 21 121 exexxrr exexxrr exexxrr xeexx     (19) defines another triangular pyramid with the same edge lengths as above. the vector orthogonal to the hyperplane determined by the vertices in (19) is 21 213 eexxp  )()()( . 4. the set of vertices .)()( ,)()( ,)()( ,)()( 2143 3123 3113 21 121 121 211 121 exexxrr exxexrr xeexxrr xeexx     (20) also determines a triangular pyramid as above. the vector which is orthogonal to the hyperplane determined by the vectors of (20) can be computed as 31 124 eexxp  )()()( . 5. the set of vertices nazife o. koca et al 158 .)()( ,)()( ,)()( ,)()( 2134 3124 3114 21 121 121 211 121 exexxrr exxexrr xeexxrr xeexx     (21) defines another triangular pyramid with the same edge lengths as above. the vector orthogonal to the hyperplane of the vectors in (21) is 31 125 eexxp  )()()( . (a) (b) (c ) figure 5. facets of pseudo snub 24-cell: (a) pseudoicosahedron for 𝒙 = 𝝉, (b) tetrahedron with edges for 1x  , (c) triangular pyramid. since the group is the full symmetry group, all vectors 𝑝(𝑖), 𝑖 = 2,3,4,5 lie in the same orbit of the group 3 2 4 s c dw : )(       . below we list these five vectors up to a some scale factors representing the centers of the above polyhedra expressed in terms of the weight vectors 4 3 2 1 ,,,, i i  : .)()( )()( ,)()( ,))(()( ,)( 2431 2431 2431 2431 2 15 14 13 12 1      xp xp xp xxp p      (22) now their symmetries are more transparent under the permutation group: 𝑆3 permutes 𝜔1,𝜔3 𝑎𝑛𝑑 𝜔4 but leaves 𝜔2invariant; )(1p and )(2p are invariant under the group 𝑆3 but the others are permuted to each other. pseudo snub 24-cell consists of 𝑁0 = 96 vertices, 𝑁3 = 24 + 24 + 96 = 144 cells consisting of pseudo icosahedra, tetrahedra and triangular pyramids respectively. it has 𝑁1 = 432 edges and 𝑁2 = 480 faces. these numbers satisfy the euler characteristic formula 𝑁0 − 𝑁1+𝑁2 − 𝑁3 = 0. table 3 summarizes the facets of pseudo snub 24-cell. table 3. facets of pseudo snub 24-cell. group generators group which generates the vertices vertices center of polyhedron polyhedron (facet) generated < 𝑟1𝑟2,𝑟2𝑟3 > *],[],[ 4444  tttt  in (15) 𝜔4 pseudoicosahedron < 𝑟3𝑟2,𝑟2𝑟4 > * ],[],[ 1111  tttt  𝜔1 pseudoicosahedron < 𝑟4𝑟2,𝑟2𝑟1 > * ],[],[ 3333  tttt  𝜔3 pseudoicosahedron 1 3 3 4 4 1 ( , , )r r r r r r *],[],[ 2222  tttt   in (17) 𝑃(1) = 𝜔2 tetrahedron 4d pyritohedral symmetry 159 2 1 2 3 2 4 ( , , )r r r r r r 3 2 4 s c dw : )(       in (18) 𝑃(2) = (1 + 𝑥)(𝜔1 + 𝜔3 + 𝜔4) − 𝑥𝜔2 triangular pyramid 1 2 1 3 1 4 ( , , )r r r r r r in (19) 𝑃(3) = −𝜔1 + 𝜔3 + 𝜔4 + (1 + 𝑥)𝜔2 3 1 3 2 3 4 ( , , )r r r r r r , in (20) 𝑃(4) = 𝜔1 − 𝜔3 + 𝜔4 + (1 + 𝑥)𝜔2 4 1 4 2 4 3 ( , , )r r r r r r in (21) 𝑃(5) = 𝜔1 + 𝜔3 − 𝜔4 + (1 + 𝑥)𝜔2 table 3. contd. 3.3 construction of the vertices of the dual polytope of the pseudo snub-24 cell to construct the dual of the pseudo snub 24-cell we need to determine the centers (orthogonal vectors to the hyperplane) of the pseudoicosahedra, the tetrahedron and the four pyramids up to some scale factors. the centers of the first three pseudo icosahedra can be taken as the weight vectors 𝜔1,𝜔3 𝑎𝑛𝑑 𝜔4 as shown in table 3. the other vectors in (22) can be taken as the center (orthogonal vector to the hyperplane) of the tetrahedron and the centers of the four pyramids up to some scale vectors. let us denote by 𝑐(𝑖), 𝑖 = 1,2,…,5, the centers of the respective tetrahedron and the pyramids and define (23) so we have eight vertices including 𝜔1,𝜔3 𝑎𝑛𝑑 𝜔4 . to determine the actual centers of these polyhedra the hyperplane defined by the eight vectors must be orthogonal to the vector  .this will determine the scale factors and the centers of the cells which can be written as: 1 3 1 2 3 4 1 2 3 1 2 1 1 1, (1 ), (1 ), 2 2 1 2 (1) (1 ), 2 3 1 2 ( ) ( ), 2, 3, 4, 5. 3 7 3 e e e e e e x c e x x c i p i i x x                     (24) these eight vectors now determine the vertices of one facet of the dual polytope of the pseudo snub 24-cell. the center of this facet is the vector  . this is a convex solid with 8 vertices 15 edges and 9 faces possessing 𝑆3 symmetry. one can generate the vertices of the dual polytope by applying the group  4 3 2 ( ) : w d s c on the vertices (24) representing one of the facets of the dual polytope. one can display them as the union of three sets 2 1 2 1 2 ( ) 2 ( ) ( ) 2 3 3 7 3 x x t t r x x x x       (25) where tt  and are given in (2-3) and 𝑅(𝑥) can be written as follows 1 2 1 2 1 2 2 3 2 3 2 3 3 1 3 1 3 1 1 2 3 1 ( ) { (2 ) (1 ) , (1 ) (2 ) , 1 (1 ) (2 ) , (2 ) (1 ) , (1 ) (2 ) , 1 (1 ) (2 ) , (2 ) (1 ) , (1 ) (2 ) , 1 (1 ) (2 ) , (2 ) (1 ) , (1 ) r x x e x e x x e e x e x e x e x e x x e e x e x e x e x e x x e e x e x e x e e x e e x                                                       2 3 1 2 3 (2 ) , (1 ) (2 ) }.e x e x e x e e       (26) (1) (1), ( ) ( ), 2, 3, 4, 5c p c i p i i    nazife o. koca et al 160 as we substitute 𝑥 = − 1 2 in (25) what we obtain is set t, as expected because it is the dual of the set t  . if 𝑥 = − 2 3 , the dual polytope does not exist. the roots of the quadratic equation 2 3 7 3x x  =0 are irrational numbers which are already excluded since the vertices of the pseudo snub 24-cell and its dual must remain in the 𝐷4 lattice for x to be rational number. one wonders whether the vertices in (26) represent any familiar polytope. if we replace x by 𝑥 = − 1 𝑦+1 , the set 𝑅(𝑥 → − 1 𝑦+1 ), in (26) takes exactly the same form of 𝑆(𝑦) in (13) apart from a scale factor. this implies that 𝑅(𝑥) represents another pseudo snub 24-cell. this proves that every dual of a pseudo snub 24-cell includes another pseudo snub 24-cell in addition to the two sets of 24-cells t and t  . the pseudo snub 24-cell 𝑆(𝑥) turns out to be snub 24-cell whose cells are regular icosahedra and tetrahedra when or x x   . however, ( ) and ( )r r  represent two pseudo snub 24-cells, the mirror images of each other. in brief, when ( )s x represents a snub 24-cell in its dual, there exists an orbit with 96 vertices representing another pseudo snub 24-cell, albeit the coefficients of the unit quaternions are irrational numbers [8]. table 4 summarizes the way to obtain the dual of the snub 24-cell in terms of its vertices. table 4. dual polytope of the pseudo snub 24-cell. one facet (polyhedron) of pseudo snub 24-cell vertices of one facet of the dual of the pseudo snub 24-cell = centers of polyhedron apply  4 3 2 ( ) : w d s c on the vertices the dual of the pseudo snub 24-cell pseudoicosahedron (1) 𝝎𝟒 elements belong to t 24-cells (24 vertices) pseudoicosahedron (2) 𝝎𝟏 pseudoicosahedron (3) 𝝎𝟑 tetrahedron (1) (1)c p elements belong to ( 𝟏 + 𝟐𝒙 𝟐 + 𝟑𝒙 )√𝟐𝑻′ 24-cells (24 vertices) triangular pyramid (1) (2) (2)c p elements belong to ( )r x pseudo snub 24-cell (96 vertices) triangular pyramid (2) (3) (3)c p triangular pyramid (3) (4) (4)c p triangular pyramid (4) (5) (5)c p 4. conclusion we have studied the extension of the pyritohedral group  3 2 2 ( ) : w d c c  in 3d to the group  4 3 2 ( ) : w d s c acting in 4d euclidean space. we have constructed the 4d polytope with 96 vertices (pseudo snub 24-cell) with the facets as 24 pseudo icosahedron, 24 tetrahedron and 96 triangular pyramids. we also derived its dual polytope with 144 vertices forming three orbits under the group. the explicit construction of the group in terms of quaternions has been worked out. the relevance of the group and the polytopes to the root lattice of the affine coxeter group 𝑊𝑎(𝐷4) has been pointed out. we have pointed out that the dual of the pseudo snub 24-cell is the union of the sets 𝑇 𝑎𝑛𝑑 𝑇′ representing two 24-cells dual to each other and the set 𝑆(𝑥) with 96 vertices. for rational values of x the vertices belong to the lattice 𝐷4. the snub 24-cell is no more in the lattice 𝐷4but belongs to the quasi-lattice of the coxeter group 𝑊(𝐻4) which can be obtained by projection of the lattice 𝐸8 into 4d. references 1. baake, m., joseph, d., kramer, p., and schlottmann, m. root lattices and quasicrystals. j. physics a: mathematical and general, 1990, 23(19), l1037. 2. baake, m., kramer, p., schlottmann, m. and zeidler, d. planar patterns with fivefold symmetry as sections of periodic structures in 4-space. international j. modern physics,1990, b4, 2217-2268. 3. elser, v. indexing problems in quasicrystal diffraction. physical review b,1985, 32(8), 4892. 4. koca, m., koca, n.o. and koc, r. affine a4, quaternions and decagonal quasicrystals, int. j. geom. methods mod. phys. (ijgmmp), 2014, 11,1450031. 5. koca, n.o., koca, m.and koc, r. grouup theoretical analysis of aperiodic tilings from projections of higher dimensional lattices bn. acta cryst., 2015, a71, 175-185. 4d pyritohedral symmetry 161 6. coxeter, h.s.m. regular polytopes (3rd ed.) new york: dover publications, 1973. 7. koca, m., al-ajmi, m. and koc, r. group theoretical analysis of 600-cell and 120-cell 4d polytopes with quaternions. j. physics a: mathematical and theoretical, 2007, 40(26), 7633. 8. koca, m., koca, n.o. and al-barwani, m. snub 24-cell derived from the coxeter-weyl group w(d4). int. j. geom. methods mod. phys. (ijgmmp), 2012, 9, no. 8, 1250068. 9. koca, m., koca, n.o. and koc, r. catalan solids derived from three-dimensional root systems and quaternions. j. mathematical physics, 2010, 51(4), 043501. 10. koca, n.o., al-mukhaini, a., koca, m. and al-qanobi, a. quaternionic representations of the pyritohedral group, related polyhedra and lattices, arxiv: 1506.04600v1., 2015; symmetry of pyritohedron and lattices, squ j. science, 2016, 21(2), 139-149. 11. amstrong, m.a. groups and symmetry, springer-verlag, new york inc., 1988. 12. koca, m., koc, r. and al-barwani, m. non-crystallographic coxeter group h4 in e8. j. physics a: mathematical and general, 2001, 34(5), 11201-11213. 13. humphreys, j.e. reflection groups and coxeter groups, cambridge university press, 1990. 14. conway, j.h. and sloene, n.j.a. sphere packings, lattices and groups. springer science and business media, 2013, 290. received 6 june 2016 accepted 22 september 2016 http://arxiv.org/abs/1204.4567v1 squ journal for science, 2016, 21(2), 120-138 © 2016 sultan qaboos university 120 global dynamics and sensitivity analysis of a vector-host-reservoir model ibrahim m. elmojtaba1*, santanu biswas2 and joydev chattopadhyay2 1*department of mathematics and statistics, college of science, sultan qaboos university p.o. box 36, pc 123, al-khoud, muscat, sultanate of oman; 2agricultural and ecological research unit, indian statistical institute, 203 b.t. road, kolkata 700108, india. *email: elmojtaba@squ.edu.om. abstract: the role of animal reservoir in the disease dynamics is not yet properly studied. in the present investigation a mathematical model of a vector-host-reservoir is proposed and analyzed to observe the global dynamics of the disease. we observe that the disease free equilibrium is globally asymptotically stable if the basic reproduction number ( 0 r ) is less than unity whereas unique positive equilibrium is globally asymptotically stable if 0 > 1r and transcritical bifurcation occurs at 0 = 1r . our numerical result suggests that the biting rate plays an important role for the propagation of the disease and the recovery rate has not such important contrib ution towards eradication of the disease. we also perform sensitivity analysis of the model parameters and the results suggest that the death rate of reservoir may be used as a control parameter to eradicate the disease. keywords: vector-host-reservoir model; basic reproduction number; lyapunov function; bifurcation analysis; numerical simulation; sensitivity analysis. المستودع والناقل-ذج العائلنمووتحليل الحساسية ل شاملةة الكيالدينامي جويديف شاتوباديو ، سانتانو بيسواس*إبراهيم محمد المجتبى ية يكيعرف المستودع للمرض بأنه نوع حيواني يعتبر وجوده ضرورياً النتشار المرض. لم تتم دراسة دور المستودع الحيواني في دينام :مستخلص مجتمعات ، العائل ، ة مرض ينتشر بين ثالثة كياألمراض بعد بصورة جيدة ، و لدراسة هذا الدور فقد قمنا باقتراح نموذج رياضي يصف دينامي إلعادة اإلنتاج المستودع والناقل. لوحظ من خالل التحليل الرياضي للنموذج أن نقطة اإلتزان الخالية من الوباء مستقرة عالمياً إذا كان العدد األساسي (r0( أقل من وحدة واحدة بينما هنالك نقطة إتزان موجبة وهي مستقرة عالمياً إذا كان )r0 > 1 ويحدث ، )( تشعب أمامي عندr0 = 1). نتائج لقضاء على المحاكاة العددية أوضحت أن معدل العض يلعب دوراً أساسياً في إنتشار المرض بينما أن معدل التماثل للشفاء ليس له مساهمة ملموسة في ا دة اإلنتاج يتأثر بشدة بمعدل وفيات المستودع ، مما المرض. قمنا أيضاً بإجراء تحليل للحساسية لمعلمات النموذج ، والذي أظهر أن العدد األساسي إلعا يعني أنه يمكن إستخدامه كمعلمة تحكم للقضاء على المرض. .، المحاكاة العددية وتحليل الحساسية، العدد األساسي إلعادة اإلنتاج، دالة ليبونوف، تحليل التشعبالمستودع والناقل-نموذج العائل كلمات مفتاحية: 1. introduction enerally, a disease reservoir is defined as a species that is essential for the persistence and transmission of the disease [1]. there are several types of reservoirs depending on their role in the life cycle of the pathogen, some of which are not necessarily for the maintenance of the disease but they can get infected by the pathogen and transmit it [2]. several studies showed that lyme disease has many reservoir hosts; salkeld et al. [3] observed an apparent statewide association between squirrel infection prevalence and lyme disease incidence, which suggests that squirrels are an important reservoir host responsible for maintaining this zoonotic disease regionally through u.s.a., also craine et al. [4] showed that gray squirrels are major reservoirs for lyme disease in u.k., and richter et al. [5] proved that american robins act as reservoir hosts for lyme disease spirochetes across u.s.a. diniz et al. [6] showed that there are several potential reservoir hosts for leishmaniasis such as domestic dog and hamsters; dantas-torres [7] also proved that dogs act as a reservoir for leishmainasis, and faiman et al. [8] found that voles and rodents also act as major reservoirs for leishmaniasis in israel; quinnell et al. [9] discovered that wide range of wild and domestic animals play the role of reservoir for leishmaniasis such as the crab-eating fox, cerdocyon thous, opossums, didelphis spp., domestic cats, felis cattus, and black rat, rattus rattus. g global dynamics and sensitivity analysis of a vector-host-reservoir model 121 melaun et al. [10] showed that pets are suspected to be potential reservoirs for many viruses like bwamba virus, kaeng khoi virus, rift valley fever virus, toscana virus, western equine encephalitis, sindbis virus, chikungunya virus, ross river virus, the eastern equine encephalitis virus, the venezuelan equine encephalitis virus, yellow fever, japanese encephalitis, west nile fever, dengue fever, st. louis encephalitis, zika virus and tacaribe virus. besides viruses, some parasites are known, which occur in bats and humans, and can be transmitted through hemorrhagic insects. the first one is the chagas disease and the coccidian genus plasmodium, which is the pathogenic agent of malaria. quite a good number of studies have been carried out to observe the disease dynamics with different settings and assumptions (for example, see [11, 12, 13]). as far our knowledge goes, no research has been done to describe the dynamics of a general vector-host-reservoir model. keeping this factor in mind, we propose and analyze a non-fatal vector borne disease with reservoir. the basic aim of the present investigation is to observe the disease dynamics and to suggest some control strategies for eradication of the disease. in any epidemic model, the basic reproduction number plays an important role; we like to suggest the control strategies by sensitivity analysis of the model parameters related to basic reproduction number. the article is organized as follows: an introduction is given in section 1, the model is formulated in section 2, the model is fully mathematically analyzed in section 3, sensitivity analysis for the parameters of the model is carried out in section 4, some numerical simulation is givn in section 5 and the paper ends with a conclusion. 2. model formulation and equations to formulate this model, we will follow a model built by elmojtaba et al. [14] to describe the dynamics of visceral leishmaniasis, see also [14, 15, 16]. consider the transmission of a non fatal disease between our three different populations, human host population, ( ) h n t , reservoir host population, ( ) r n t , and vector population, ( ) v n t . human host population will be divided into three categories, susceptible individuals ( ) h s t , infected individuals ( ), h i t and those who are recovered and have permanent immunity, ( ) h r t . this implies that ( ) = ( ) ( ) ( ) h h h h n t s t i t r t  . similarly, the reservoir host population will be divided into two categories, susceptible reservoirs, ( ) r s t , and infected reservoirs, ( ) r i t , such that ( ) = ( ) ( ) r r r n t s t i t and the vector population have two categories, susceptible vectors ( ) v s t , and infected vectors ( ) v i t , such that ( ) = ( ) ( ) v v v n t s t i t it is assumed that susceptible individuals are recruited into the population at a constant rate h  and acquire infection with following contacts with infected vectors at a per capita rate v h i ab n , where a is the per capita biting rate of vectors on humans (or reservoirs), and b is the transmission probability per bite per human (as the case for malaria, [17, 18]). infected humans recover and acquire permanent immunity at an average rate  . there is a per capita natural mortality rate h  in all human sub-population. susceptible reservoirs are recruited into the population at a constant rate r  , and acquire infection following contacts with infected vectors at a rate v h i ab n where a and b as described above. a per capita natural mortality rate r  occurs in the reservoir population. susceptible vectors are recruited at a constant rate v  , and acquire infection following contacts with infected humans or infected reservoirs at an average rate equal to h r h r i i ac ac n n  , where a is the per capita biting rate, and c is the transmission probability for vector infection. vectors suffer natural mortality at a per capita rate v  regardless of their infection status. from the description of the terms, we get the following system of differential equations: = ' h h h h v h h h s s n abi s n    = ( ) ' h h v h h h s i abi i n    = ' h h h h r i r  (1) ibrahim m. elmojtaba et al 122 = ' r r r r v r r r s s n abi s n    = ' r r v r r r s i abi i n  = ' h r v v v v v v v h r i i s n acs acs s n n     = ' h r v v v v v v h r i i i acs acs s i n n   invariant region all parameters of the model are assumed to be non-negative, furthermore since model (1) monitors living populations, it is assumed that all the state variables are non-negative at time 0t  . this shows that the biologically-feasible region: 7 = {( , , , , , , ) : , , , , , , 0} h h h r r v v h h h r r v v s i r s i s i r s i r s i s i     is positively-invariant domain, and thus, the model is epidemiologically and mathematically well posed, and it is sufficient to consider the dynamics of the flow generated by (1) in this positively-invariant domain  . 3. analysis of the model in this section, we analyze system (1) to obtain the steady states of the system and their stability. we consider the equations for the proportions by first scaling the sub-populations for h n , r n and v n using the following set of new variables = , = , = , = , = , = ,vh h h r r h h h r r v h h h r r v ss i r s i s i r s i s n n n n n n and = v v v i i n ; and let = v h n m n be the vector-human ratio defined as the number of vector per human host (see similar definition in malaria models, in [19, 20]). note that the ratio m is taken as a constant because it is well known (see [21] pages 218220) that a vector takes a fixed number of blood meals per unit time independent of the population density of the host. similarly, we let = v r n n n be the vector-reservoir ratio defined as the number of vector per reservoir host. differentiating with respect to time t we get: =' vh h h h hs abmi s s   = ( ) ' vh h h h i abmi s i   =' h h h h r i r  (2) = ' r r v r r rs abni s s   = ' r v r r ri abni s i = ( ) ' v v r v v vh s ac i i s s    = ( ) ' v r v v vh i ac i i s i  with the feasible region (i.e. where the model makes biological sense) 7 = {( , , , , , , ) : h h h r r v v s i r s i s i r    0 , , ; 1; 0 , ; 1; 0 , ; 1} h h h h h h r r r r v v v v s i r s i r s i s i s i s i          . it can be shown that the above region is positively invariant with respect to the system (2), where 7 r  denotes the non-negative cone of 7 r including its lower dimensional faces. 3.1 basic reproduction number of the model to calculate the basic reproduction number we will use the next generation approach [22, 23], define f as the column-vector of rates of the appearance of new infections in each compartment; =v v v    , where v  is the column-vector of rates of transfer of individuals into the particular compartment; and v  is the column-vector of rates of transfer of individuals out of the particular compartment. hence, from our model we have global dynamics and sensitivity analysis of a vector-host-reservoir model 123 = ( ) v h v r h r v abmi s f abni s ac i i s          and ( ) = . h h r r v v i v i i               then the matrices f and v from the partial derivatives of f and v with respect to the infected classes computed at the dfe are given by 0 0 ( ) 0 0 0 0 0 0 = , = 0 0 0 h r v abm abn f and v ac ac                             then the basic reproduction number, 0 r defined as the spectral radius of matrix 1 fv  ; 2 2 1 0 ( ) = ( ) = ( ) h r r v h a bcn a bcm fv             r 3.2 local stability analysis of the disease-free equilibrium 0 e the disease-free equilibrium (dfe) of the system (2) is given by 0 0 0 0 0 0 0 0 = ( , , , , , , ) = (1, 0, 0, 0,1, 0,1, 0) h h h r r v v e s i r s i s i . using theorem 2 of van den driessche and watmough [23], we have the following lemma: lemma 3.1. the disease-free equilibrium is locally asymptotically stable if 0 < 1r and unstable if 0 > 1r . 3.3 global stability analysis of the disease-free equilibrium 0 e the following theorem shows that the dfe is globally asymptotically stable if 0 < 1r . theorem 3.1. the disease-free equilibrium point is globally asymptotically stable if 0 < 1r proof: consider the following lyapunov function = ( ) ( )r r r vh h hl ac i ac i i         with derivative = [ (1 ) ( ) ] ' r h h v h h l ac abm i r i i      ( )[ (1 ) ]h r v r rac abn i i i      ( )[ ( )(1 ) ]r h h r v v vac i i i i        2 2 2 2 1 [ ( ) ( )] ( (1 ) ) r h r v h v r h h v a bcm a bcn i a bcm i i                      2 2 1 1 2 ( (1 ) ) ( )( ) r h h v r h h h a bcm p i ac i                      2 1 2 1 2 ( )( ) ( )( ) r h h h h h r v ac p a bcn i i                      1 2 1 2 ( )( ) ( )( ) r h h r r h h h ac i ac i                       1 2 1 2 ( )( ) ( )( ) r h h h r h h r ac p ac i                       1 2 1 2 ( )( ) ( )( ) r h h h v r h h h v ac i i ac p i                       1 2 ( )( ) r h h r v ac i i           2 1 2 0 = ( )( )( 1) r v h h v i           r 2 2 2 1 2 1 ( (1 ) ) ( (1 ) ) r h h v r h h v a bcm i i a bcm p i                     ibrahim m. elmojtaba et al 124 2 1 2 1 2 ( )( ) ( )( ) h h r v r h h h v a bcn i i ac i i                      1 2 1 2 ( )( ) ( )( ) r h h h v r h h r v ac p i ac i i                       2 1 2 0 ( )( )( 1) r v h h v i            r and hence 0 ' l  if 0 < 1r . we observe that our system has the maximum invariant set for = 0 ' l if and only if 0 1r holds and = = = = = 0 h h h v r i p r i i . by lyapunov-lasallés theorem [20], all the trajectories starting in the feasible region where the solutions have biological meaning approach the positively invariant subset of the set where = 0 ' l , so that as t  , ( ) 1 h s t  , ( ) 1 r s t  , and ( ) 1. v s t  this shows that all solutions in the set where = = = = = 0 h h h v r i p r i i , go to the disease-free equilibrium 0 e . thus, 0 < 1r is the necessary and sufficient condition for the disease to be eliminated from the community. 3.4 existence of the endemic equilibrium 1 e in order to prove the existence of 1 e we equate the right hand sides of system (2) to zeros, and substitute = 1 h h h s i r  , = 1 r r s i and = 1 v v s i , to obtain (1 ) = ( ) v h h h h abmi i r i    (3) = h h h i r  (4) (1 ) = v r r r abni i i (5) ( )(1 ) = h r v v v aci aci i i  (6) from equations (4) and (5) we have: = h h h r i     (7) = vr v r abni i abni      (8) now substituting equations (7) and (8) in equations (3) and (6), respectively, then solving equations (3) and (6) we have either = 0 v i  , which gives the dfe, or v i  satisfies the following equation: 2( ) = 0 v v a i bi c     (9) where 3 2 2 = ( )h h a a b cmn      2 0 = ( )( 1) ( )[ ( ) ] v r h v h r h r h ab b a m n                  r 2 0 = ( )( 1) v r h c     r we note that < 0a , and > 0c when 0 > 1r , hence we have one and only one positive solution for equation (9) when 0 > 1r , and then we have the following lemma: lemma 3.2. the system (2) has precisely one positive endemic equilibrium 1 e given by 1 = ( , , , , , , ) h h h r r v v e s i r s i s i        and v i  satisfying equation (9), when 0 > 1r . 3.5 local stability analysis of the endemic equilibrium 1 e to investigate the local stability of the endemic equilibrium, we use the center manifold theorem, particularly, theorem 5 in castillo-chavez and song [25]. the jacobian of the system (2) at the disease-free equilibrium 0 e is given by: global dynamics and sensitivity analysis of a vector-host-reservoir model 125 0 0 0 0 0 0 0 ( ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( ) = 0 0 0 0 0 0 0 0 0 0 0 0 0 h h h r r v v m m n e n ac ac ac ac                                               j consider the case when 0 = 1r and suppose that = ab is chosen as a bifurcation parameter, then it can be shown that the jacobian of the system (2) has a right eigenvector given by 1 2 3 4 5 6 7 = ( , , , , , , ) t w w w w w w w w , where 1 7 = h m w w    2 7 = h m w w     3 7 = ( ) h h m w w       4 7 = r n w w    5 7 = r n w w   6 7 =w w and a left eigenvector given by 1 2 3 4 5 6 7 = ( , , , , , , )v v v v v v v v , where 1 3 4 6 = = = = 0v v v v 2 = h ac v   5 = r ac v  it can be shown that: 2 2 2 7 7 = [ ( 1)] ( ) h h h r r acm acm acn n a v w                   7 7 1 1 = [ ] h r b acm v w       it is clear that < 0a  and > 0b  , hence our system (2) undergoes a regular transcritical bifurcation at 0 = 1,r before the bifurcation the disease-free equilibrium is stable and there exists an unstable positive endemic equilibrium, and after the bifurcation the disease-free equilibrium became unstable the endemic equilibrium became stable. then we have the following result: lemma 3.3. the endemic equilibrium is locally asymptotically stable for 0 > 1r . 3.6 global stability of endemic equilibrium to prove the global stability of the endemic equilibrium we first start with some preliminaries. lemma 1. (lemma 2.1 in [26]) let ( )a t be a continuous, cooperative, irreducible, and  -periodic n n matrix function. let (.) ( ) a t be the fundamental matrix of the linear non-autonomous differential equation = ( )x a t x , where x is a 1n vector. let (.) 1 = ln ( ( )) a r    , where, (.) ( ( )) a r  is the spectral radius of the monodromy matrix (.) ( ) a  . then there exists a positive,  -periodic function ( )v t such that ( ) t e v t  is a solution of = ( )x a t x . ibrahim m. elmojtaba et al 126 definition 1 system (2) is uniformly persistent if  an > 0 (depending only on parameter values not on initial condition) such that for any initial value ( (0), (0), (0), (0), (0), (0), (0)) h h h r r v v s i r s i s i   r int(  r )  int(  r )   r  int(  r )   r  int(  r ) such that every solution ( ( ), ( ), ( ), ( ), ( ), ( ), ( )) h h h r r v s t i t r t s t i t s t i v t of the system (2) satisfies inf ( )limt hs t  … , inf ( )limt hi t  … , inf ( )limt hr t  … , inf ( )limt rs t  … , inf ( )limt ri t  … , inf ( )limt vs t  … , inf ( )limt vi t  … . definition 2 the system (2) is said to be permanent if there exists a compact region 0   int(  ) such that every solution of the system (2) with initial condition ( (0), (0), (0), (0), (0), (0), (0)) h h h r r v v s i r s i s i   r int(  r )  int(  r )   r  int(  r )   r  int(  r ) will eventually enter and remain in region 0  . clearly, for a dissipative dynamical system proving permanence is equivalent to proving uniform persistence. consider following sets: 7 =x  r , 0 =x  r int(  r )  int(  r )   r  int(  r )   r  int(  r ), 0 0 = \x x x . let, :f x x be a continuous map and we define following set 0 0 = { : ( ) , 0} n m x x f x x n    … . following lemma will be used to show uniform persistence of the system (2) lemma 2. ([27]) assume that 1. 0 0 ( )f x x and f has a global attractor a. 2. there exists a finite sequence 1 2 = { , ,...., } k m m mm of disjoint, compact, and isolated invariant sets in 0 x such that ( )m = =1( ) k x m i i x m      ; no subset of m forms a cycle in 0 x ; i m is isolated in x ; 0 ( ) = s i w m x  for each 1 i k„ „ then there exists > 0 such that 0 lim ( ( ), )inf n n d f x x   … for all 0x x . we claim the following result proposition 1 if 0 > 1r then the solutions of the system (2) is uniformly persistent. proof. consider the periodic semi-flow 7 7 :t   r r associated with the system (2) defined by: ( ) = ( , )t t x u t x , 7 x    r . let 1 p be the associated poincaré map defined as 1 := ( )p t  . we first show that 1 p is uniformly persistent with respect to 0 0 ( , )x x . it is clear that the set x and 0x are positively invariant for the system (2). now the bounded set  ( =  ) attracts every solution of the system (2) and also  is compact. thus the poincaré map 1p is point dissipative and compact on x . therefore, it follows from theorem 1.1.3 in [27] there is a global attractor a of 1p that attracts each bounded set in x . for the system (2) the set m  is defined as 0 1 0 = {( (0), (0), (0), (0), (0), (0), (0)) : ( (0), (0), (0), (0), (0), (0), (0)) , 0} n h h h r r v v h h h r r v v m s i r s i s i x p s i r s i s i x n     … . we claim that, = {( , 0, 0, , 0, , 0) : 0, 0, 0} h r v h r v m s s s s s s  … … … . it is clear that {( , 0, 0, , 0, , 0) : 0, 0, 0} h r v h r v s s s s s s m  … … … . now, let 0 ( (0), (0), (0), (0), (0), (0), (0)) \ {( , 0, 0, , 0, , 0) : 0, 0, 0} h h h r r v v h r v h r v s i r s i s i x s s s s s s … … … . if (0) = 0, (0) = 0, (0) = 0, > 0 h h r v i r i i , then we get (0) > 0, (0) > 0, (0) > 0, (0) > 0. h r v v s s s i from second equation of the system (2) we have, (0) > (0) (0) > 0 ' h v h i abmi s . (0) > (0) > 0 ' h h r i . (0) > (0) (0) > 0 ' r v r i abni s . global dynamics and sensitivity analysis of a vector-host-reservoir model 127 and (0) > (0)( (0) (0)) > 0 ' v v h r i acs i i . similarly, for other cases also. therefore, 0 ( (0), (0), (0), (0), (0), (0), (0)) h h h r r v v s i r s i s i x for all 0 < 1t = . this implies that = {( , 0, 0, , 0, , 0) : 0, 0, 0} h r v h r v m s s s s s s  … … … . now, 1 p has a unique fixed point 0 ( , 0, 0, , 0, , 0) h r v e s s s in m  . it is easy to show that 0 { }e is isolated in x and as 0 e is global attracting in m  therefore we have, 0 ( ) = ( ) { } x m m x e       , where, ( )x is the omega limit set of x . it is clear that no subset of 0 { }e can forms a cycle in 0 x . now, we shall show that, 0 0 ( ) = s w e x  , where, 0 ( ) s w e is the stable set of 0 e . let 0 0 0 = ( (0), (0), (0), (0), (0), (0), (0)) ( ) s h h h r r v v x s i r s i s i w e x  . since 0 0 x x , therefore by continuity of solution with respect to initial conditions we have, for any (0,1)  , there exists a > 0 such that 0 0 x x  satisfying 0 0 || ||<x e  , implies 0 0 || ( , ) ( , ) ||<u t x u t e  [0, ]t   . we claim that 0 1 0 sup || ( ) ||lim m m p x e   … 0 0 x x  . suppose if possible 0 0 x x  such that 0 1 0 sup || ( ) ||<lim m m p x e   . without loss of generality, we can assume that 0 1 0 || ( ) ||< m p x e  for all 0m … . therefore, we have 0 1 0 || ( , ( )) ( , ) ||< m u t p x u t e  , [0, ]t   and 0m … . for any, 0t … , let 1 =t m t  , where 1 [0, ]t  and = [ ] t m  is the greatest positive integer less than or equal to t  . then we have, 0 0 1 0 1 1 1 0 || ( , ( )) ( , ) ||=|| ( , ( )) ( , ) ||< m m u t p x u t e u t p x u t e   for all 0t … . let, 0 ( ( ), ( ), ( ), ( ), ( ), ( ), ( )) = ( , ) h h h r r v v s t i t r t s t i t s t i t u t x . it follows from previous argument that, 1 < ( ) < 1 , h s t   , 1 < ( ) < 1 r s t   , 1 < ( ) < 1 v s t   , 0 < ( ) < h i t  , 0 < ( ) < h r t  , 0 < ( ) < r i t  , 0 < ( ) < v i t  , 0t … . from the system (2) we have: (1 ) ( ) (1 ) (1 ) (1 ) h v h h r v r r v h r v v di abmi i dt di abni i dt di aci aci i dt                  … … … (10) let, 0 0 0 0 ( ) = , 0. abm bn m t ac ac                  hence we obtain, [ , , ] [ ( ) ( ) ( )][ , , ] . t t h r v h r v d i i i f t v t m t i i i dt   … now, choosing > 0 sufficiently small so that (.) (.) (.) ( ( )) > 1 f v m r       . thus by lemma 1 and standard comparison theorem [28]   -periodic function ( )f t such that 1( ) ( ) s t x t f t e… , where, ( ) = [ , , ] h r v x t i i i and 1 (.) (.) (.) 1 = ln ( ( )) > 0. f v m s r        this implies as t  , ( ) h i t   , ( ) r i t   and ( ) v i t   . this is a contradiction as 0 1 0 sup || ( ) ||< .lim m t p x e   therefore, we have, 0 1 0 sup || ( ) ||lim m t p x e   … 0 0 x x  . which is again impossible as 0 0 ( ) s x w e (as 0 ( ) s x w e implies 0 1 0 || ( ) ||= 0lim m t p x e  ). thus we have, 0 0( ) = s w e x  . therefore, by lemma 2 we have 1 p is uniformly persistent with respect to 0 0 ( , )x x . therefore, by theorem 3.1.1 in [27] the periodic semi-flow t is uniformly persistent in x . thus, if 0 > 1r then solution of the system (2) is uniformly persistent. next, we claim the following result proposition 2. if 0 > 1r then the endemic equilibrium 1 e is globally asymptotically stable. ibrahim m. elmojtaba et al 128 proof. let, 1 = ( ( ), ( ), ( ), ( ), ( ), ( ), ( )) h h h r r v v e s t i t r t s t i t s t i t . we shall first show that ( ( ), ( ), ( ), ( ), ( ), ( ), ( ), ( )) h h h h r r v v s t i t p t r t s t i t s t i t is globally asymptotically stable we construct following lyapunov function ( ) =| ( ) ( ) | | ( ) ( ) | | ( ) ( ) | | ( ) ( ) | | ( ) ( ) | | ( ) ( ) | | ( ) ( ) | . h h h h h h r r r r v v v v l t s t s t i t i t r t r t s t s t i t i t s t s t i t i t             we use following formula, | | = ( ) , ' ' x sgn x x to calculate the upper right-hand derivative (dini's derivative) of ( )l t . therefore, we have ( ) | | | | | | | | | | | | | | h h h h h h h h h r r r r r r v v v v v v d l t s s i i r r s s i i s s i i                       „ (11) let, = min{ , , } r v h k    . therefore, > 0k . now, ( ) (| | | | | | | | | | | | | |) h h h h h h r r r r v v v v d l t k s s i i r r s s i i s s i i               „ . which implies l is non-increasing on [0, ) . thus we have, ( ) = 0limt l t . therefore it follows that | |= 0limt h hs s  , | |= 0limt h hi i  , | |= 0limt h hr r  , | |= 0limt r rs s  , | |= 0lim t r ri i  , | |= 0limt v vs s  , | |= 0lim t v vi i  . thus, ( ( ), ( ), ( ), ( ), ( ), ( ), ( ), ( )) h h h h r r v v s t i t p t r t s t i t s t i t is globally asymptotically stable. 4. sensitivity analysis of 0 r 0 r is considered one of the most important quantities in epidemic theory [29], therefore studying the sensitivity of 0 r to the other parameters will give some more insight ideas about the best way of interventions to reduce 0 r below unity. there are many ways of conducting sensitivity analysis, all resulting in a slightly different sensitivity ranking [30]. following [31, 32, 33] we used the normalized forward sensitivity index also called elasticity as it is the backbone of nearly all other sensitivity analysis techniques [30] and are computationally efficient [31]. the normalized forward sensitivity index of the basic reproduction number, 0 r with respect to a parameter value, p is given by: 00 0 = p p s p    r r r (12) because our 0 r contains square root, then it is convenient to use this version of equation 12: 2 00 2 0 1 = 2 p p s p    r r r (13) using equation 13 together with parameter values given in the table 1, we have our sensitivity indices for 0 r with respect to the other model parameters, which is presented in table 2. table 1. parameter values for sensitivity analysis. parameter parameter description value source h  natural mortality rate of humans 0.00004 1day [34] r natural mortality rate of reservoirs 0.000274 1 day  [14] v  natural mortality rate of vectors 0.189 1day [35] a biting rate of vectors 0.285 [36] b progression rate of the disease in vectors 0.22 [36] c progression rate of the disease in human and reservoir 0.0714 [37]  recovery rate 0.1,0.5,0.9 assumed m vector-human ratio 5 assumed n vector-reservoir ratio 10 assumed global dynamics and sensitivity analysis of a vector-host-reservoir model 129 it can be seen from table 2 that the sensitivity index of a , b , c , n and v  are fixed for all values of  , which means that the effect of these parameters on 0 r is not affected by the recovery rate (i.e. different values of  ), where a , b , c and n has positive effect on 0 r , for example if the biting rate is increased by 10%, then 0 r will increase by 10%, and if c is decreased by 10% then 0 r will decrease by 5%, while v  has a negative impact on 0 r , therefor if for example v  is decreased (increased) by 10% then 0 r will increase (decrease) by 5%. table 2. sensitivity indices of 0 .r parameter sensitivity index = 0.1 = 0.5 = 0.9 a +1 +1 +1 b +0.5 +0.5 +0.5 c +0.5 +0.5 +0.5 n +0.499 +0.499 +0.499 m +0.0006 +0.0001 +0.00001  -0.0006 -0.0001 -0.00001 h  -2.7e-7 -1.1e-8 -3.4e-9 r  -4.99 -0.99 -0.55 v  -0.5 -0.5 -0.5 it is also clear that m ,  and h  have a very small effect on 0 r because their sensitivity indexes are very small (less than 0.001). however when the recovery rate,  , is small, then 0 r became very sensitive to r  , for example if r  is decreased (increased) by 10% then 0 r will increase (decrease) by 49.9%, this is also can be seen from figure 1, for example when = 0.1 , then 0 r ranges between 5.6 and 15.5 for different values of r  , and when = 0.5 0 r ranges between 1.1 and 3.9 for the same values of r  and when = 0.9 0 r ranges between 0.83 and 2.1 for the same values of r  , which shows the effect of r  on 0 r , and that effect is really clear for small values of  . different scenarios regarding disease control: • if the animal reservoir is kept out of the system (assuming that there is no transmission between reservoir and vector, or if the animal reservoir is kept away from humans so vectors can't transmit the disease from reservoir to human), then the threshold for the disease to invade the human population can be kept less than 1 easily, i.e. the disease can be eliminated. • if the human population is kept out of the system (assuming that all vectors stay near to the animal reservoir population to the their blood meal) then the threshold cannot be kept smaller than one which means that the disease will always persist in the reservoir and vector populations. • considering the full system, then the threshold can be kept less than one using one of the following control strategies:  applying human treatment at a very high rate, which is not cost-effective.  decrease the animal reservoir population throw culling and apply human treatment at a medium rate, which is not ethical and also not so cost-effective.  keep the vector biting rate in a low level either by using pesticides or changing the human behavior, and applying human treatment at a low rate. ibrahim m. elmojtaba et al 130 figure 1. values of 0 r for different values of r  with: (a) = 0.1 , (b) = 0.5 , (c) = 0.9. 5. numerical simulation of the model in this section we solve our model numerically with initial conditions: 0 0 0 0 0 0 0 = 0.9, = 0.1, = 0, = 0.9, = 0.1, = 0.8, = 0.2 h h h r r v v s i r s i s i . some of the parameter's values were obtained from literature, and some of them were assumed or made varying in order to study their role. the parameter values used are in table 3. table 3. parameter values for numerical simulation. parameter parameter description value source h  natural mortality rate of humans 0.00004 1day [34] r  natural mortality rate of reservoirs 0.000274 1day [14] v  natural mortality rate of vectors 0.189 1day [35] a biting rate of vectors variable variable b progression rate of the disease in vectors variable variable c progression rate of the disease in human and reservoir variable variable  recovery rate variable variable m vector-human ratio variable variable n vector-reservoir ratio variable variable varying the values of a, the biting rate of vectors simulation results show that when the biting rate of vectors is small that leads to some delay in the time needed for the epidemic curve to reach the peak in the infected human population; however, the peak itself remains the same for all values of the biting rate, therefore reducing the biting rate of vectors helps in reducing the prevalence of the disease in the human population; however, to reduce the epidemic's peak other intervention is needed. nonetheless, it seems to have less effect on other population as can be seen from figure 2. global dynamics and sensitivity analysis of a vector-host-reservoir model 131 figure 2. simulation results for different values of a. varying the values of b, the progression rate of the disease in vectors simulation results show that the epidemic curve remains the same for small and big values of b and it just shifted to the right, which means that when the time needed for the pathogen to progress within vectors is big, the disease will need more time to hit the population which gives a window for some interventions, as seen from figure 3. however, as we know this parameter is out of control. ibrahim m. elmojtaba et al 132 figure 3. simulation results for different values of b. varying the values of c, the progression rate of the disease in humans and reservoirs it can be seen from figure 4 that the effect of changing the values of c is almost the same as changing the values of b ; but the differences between the curves of the small value and big value of c is less than the differences between the curves of the small value and big value of b in infected human and infected reservoir populations, and the curves of different values of b and c are the same for the population of infected vectors, which means that the progression time of the pathogen within the vector has more effect than the progression time of the pathogen within the host or within reservoir. this is due to the fact that the vector population is much bigger than the other populations and the recruitment rate of the vector population is big compared to the recruitment rate of the other populations. global dynamics and sensitivity analysis of a vector-host-reservoir model 133 figure 4. simulation results for different values of c. varying the values of m, the vector-human ratio, and n, the vector-reservoir ratio results show that there is a positive relationship between m and the fraction of infected humans, and there is almost no relationship between m and the fraction of infected reservoir, which is something predictable, as seen from figure 5. also, there is a positive relationship between n and the fraction of infected reservoirs, and there is almost no relationship between n and the fraction of infected humans, as seen from figure 6. from figures 5 and 6 it can be shown that the effect of different values of m on the population of vectors is the same as the effect of different values of n on the population of vectors, and that is because it is assumed that vectors take a fixed amount of blood despite the available number of hosts or reservoirs, and also because it is assumed that vectors do not prefer humans over reservoirs. ibrahim m. elmojtaba et al 134 figure 5. simulation results for different values of m. global dynamics and sensitivity analysis of a vector-host-reservoir model 135 figure 6. simulation results for different values of n. varying the values of  (the recovery rate) simulation results show that recovery rate has a strong impact on the population of infected humans, and it has no effect on the reservoir population nor on the vector population; which shows that although the recovery rate is an important factor in the fight against the disease, it is not enough for eradication, and it should be accompanying other interventions on the other populations, as seen from figure 7. ibrahim m. elmojtaba et al 136 figure 7. simulation results for different values of . 6. conclusion we have developed a general model for the dynamics of a vector-host-reservoir model. our analysis of the model showed that the disease-free equilibrium is globally asymptotically stable when 0 r is less than unity; and unstable when 0 r is greater than unity, and our system posses only one endemic equilibrium which is globally asymptotically stable when 0 r is greater than unity. our sensitivity analysis shows that 0 r is sensitive to all of the parameters of the model either positively or negatively, and the most influential has been the natural death of the reservoir, r  which indicates that the best control strategy is culling the infected animals, and the second one is the biting rate, a which indicates that reducing the biting rate by using, for example, bed-nets is the second best control strategy against the disease. numerical simulations were used to examine the effect of all of the parameters of the model, and the results showed that reducing the biting rate of vectors helps in reducing the prevalence of the disease in the human population. however, to reduce the epidemic's peak other interventions are needed; nonetheless, it seems to have less effect on other populations. 7. 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oman; mass balance; profile; enrichment; economy. دراسة الحوازن الكحلي عمان:سلطنة وإعادة جوزيع العناصر في جربة الالجريث لصخور اوفيوليث سمائل، حركة اٌخشتاش ٚ خذ٠جح سّذٟ ع.صالح . شٍّد ٘زٖ فم١ح ٌٍرشتحرشتح اٌالذشا٠د ٌرّثً اٌطثماخ األٌ ػذج ِماطغدٛي ذشتح اٌالذش٠د د١ث ذُ جّغ ػذج ػ١ٕاخ ِٓ اٌذساسح اٌذا١ٌح ذرّذٛس :ملخص ذفاٚذا ت١ٓ ِخرٍف اٌطثماخ ٌىً ِمطغ اٌج١ٛو١ّائ١ح اٌّؼذ١ٔح ٚاٌخصائص ّىٛٔاخ ٔرائج دساسح اٌاٌشس١ً ٚ ط١ٛٞ. ت١ٕد ٚتشا إششق ٚ تشاإِٕاطك اٌذساسح تٕاء ػٍٝ ٔرائج دساب ٌٝ آخشٜ.إطمح ِٕٓ ِرج٠ٛح ذشو١ض ِخرٍف اٌؼٕاصش ِّا ٠ىْٛ ساجؼا اٌٝ اخرالفاخ فٟ ػٛاًِ اٌػادج ذٛص٠غ ٚإٙا ٚسّىفٟ خاصح اٌرشتح سفً أٌٝ أاٌسطخ ِٓ ٌٍؼٕاصشػثش ِمطغ اٌرشتح ذشاوُ أٚ ذششخِا إْ ٕ٘ان أذث١ٓ ساس١ح ٌٍرشتح اٌصخشج األذشو١ة ِماسٔح ِغ اٌرٛاصْ اٌىرٍٟ ٌىً طثمح حو١ض ػا١ٌاترش خذ١ّضد١ث تشا إششق ٚخاصح فٟ ِمطغ أْ ٔسثح اٌؼٕاصش ذضا٠ذخ فٟ وً ِٓ طثمح اٌساتشٚال٠د ٚ طثمح االوسا٠ذ ؼ١ٍّاخ اٌرج٠ٛح.ٌ ٔر١جح ٌٕا ل١ُ ضؼ١فح اذضخ اٌشس١ً(ٚ إتشا ٚ )ط١ٛٞٔسثح ػٕصش اٌسىأذ٠َٛ ػٍٝ اٌذذ٠ذ فٟ اٌرشتح ِٓ ِخرٍف ِٕاطك ٘زٖ اٌذساسحٚػٕذ دساسح ٌّؼظُ اٌؼٕاصش. ت١ٕد إٌسثح ت١ٓ ػٕصشٞ اٌثٛس٠َٛ ٚا١ٌٛسا١َٔٛ تأْ ػٛاًِ اٌرج٠ٛح تّٕطمح طٛٞ وّا .٠حٛاٌرجػ١ٍّاخ ٌرشاوُ ُِٙ ٌٍذذ٠ذ اثٕاء رٌه ٠ؼضٌٜٙزٖ إٌسثح ِّا .تشا ٚ اٌشس١ًإششق وأد ألً ِأوسذج ِّا ٘ٛ ػ١ٍٗ فٟ .ػّاْٚ دساب ذٛاصْ اٌىرٍٟ ،ذشاوُ ،ذشتح ،الذشا٠د: كلمات مفحاحية 1. introduction ateritic weathering is an important surficial erosional process which is active in the superficial zone of tropical regions. all laterites are marked by an enrichment of iron and a decrease of silica together with the highly soluble alkalis and alkaline earths as well as rare earth elements [1]. the composition and properties of laterites are controlled by the chemical and physical features of the parent rock. mobilization of trace elements during lateritization has been investigated in several studies [2-6]. this mobilization is dependent on the type of parent rock and the weathering conditions (t, eh, and solutions). lateritization of ultramafic rocks such as peridotite results in an enrichment of ni. most of the world's laterites are found in tropical areas such as indonesia, the philippines and new caledonia but some are also found in australia, brazil and west africa [7-11]. in this study, a mass balance was calculated in laterites in oman in order to determine the redistribution and mobilization of trace elements in the different lateritic zones developed on mafic and ultramafic rocks in this arid area during the cretaceous time. l salah al khirbash and khadija semhi 40 the current research is part of an ongoing research project by the first author, investigating lateritic soils from the northern oman mountains, where the samples were collected from each zone (from the surface downward to the parent rock) of the investigated laterite profiles [12]. the parent rocks consist either of layered gabbro or peridotite of about c.96.4 ma [13]. 2. geological background the development of lateritic paleosol profiles in oman is mainly related to the late cretaceous (coniacian to late campanian) tectonic evolution of the oman mountains, which are part of the alpine-himalayan fold belt [14,15]. a detailed description of these laterites is given in [12, 16, 17]. the laterites of the oman mountains belong to the qahlah formation that lies unconformably on the obducted semail ophiolite (96.4 ma.) [13,18] and grades into the late campanian–maastrichtian simsima formation. the qahlah formation represents the most basal, post-obduction terrigenous clastic facies in oman [14] and mainly contains conglomerate, sandstone, and siltstone [19]. this formation was assigned a maastrichtian age [14] based on the presence of loftusia. the late cretaceous laterites generally occur as patches having a lateral extension of more than 100 km, but are entirely absent at some locations [12]. the mineralogical and geochemical charcterization of nine laterite profiles from four separate areas (ibra, east ibra, al-russayl, and tiwi) located along a nw-se transect across the oman mountains (figure 1) have been previously reported [1,12,16,17], where they showed variations in their thickness as well as in their geochemical and mineralogical characteristics. for the purpose of this study, these nine profiles have been combined into seven profiles (figure 2), where the east ibra profiles # 1 and 2 were combined as one profile (designated as composite profile #1 and #2) and al-russayl profiles # 2 and 3 were combined as one profile (designated as composite profile #1 and #2). figure 1. geological and location map of the studied areas (adapted from [12,19]). the following lateritic zones were identified from the base upward: a) a protolith; b) a saprolite laterite; c) an oxide laterite (locally pisolitic and with multiple silcrete layers); and d) a clay laterite (figure 2) [16]. a. protolith corresponds either to serpentinized peridotite (east of ibra, al-russayl and tiwi profiles) or to layered gabbro (ibra profile) of the late cretaceous semail ophiolite. the serpentinized peridotite is > 20 m thick and occurs as a fine-grained, black to green rock. the layered gabbro protolith is > 20 m thick and consists of a coarse-grained dark green rock. mobilization and redistribution of elements in laterites of semail ophiolite 41 b. saprolite (3-60 m thick) is characterized by a pale reddish-brown to greenish color and abundant blocks ranging in size from a few cms to >6 m. the lower parts of the saprolite zone usually consist of greenish-white, friable material, while the upper parts consist of harder, reddish-brown material with abundant ferruginous pellets (pisoliths). c. oxide zone (1.5 to 84 m thick) is characterized by massive to nodular facies of yellowish, goethite-rich limonite, as well as massive hematite. it includes several 0.5 to 1 m thick, white to grey color, silcrete layers. d. clay laterite (1.5 to 15 m thick) is made up of hard, dark-brown material in the lower parts and light-brown, soft and friable fine-grained material in the upper parts. these paleosol lateritic profiles are capped unconformably either by clastics of the upper cretaceous qahlah formation, which is the case at east ibra, or by palaeogene carbonates of the jafnayn or abat formations at ibra, tiwi and al-russayl areas [16]. 3. materials and methods several samples were collected vertically throughout the different profiles to represent the various lateritic zones (figure 2). all samples were dried overnight at about 60 ºc. after drying, they were crushed and sieved to a fraction less than 2 mm and homogenized in an agate mill. two batches of each sample were prepared. one batch was used for identification of mineral composition while the other was used for chemical analyses. for chemical analysis, a 0.5 g sample was digested in aqua regia at 95 °c in a microprocessor controlled hot block for 2 hours. the solution was diluted and analyzed for trace elements by icp/ms using a perkin elmer sciex elan 9000 [12]. international certified reference materials usgs gxr-1, gxr-2, gxr-4 and gxr-6 were analyzed at the beginning and at the end of each batch of samples. internal control standards were analyzed every 10 samples and a duplicate was run for every 10 samples. the detection limit varied between 0.01 and 0.5 ppb. chemical composition was determined by (icp-aes) for major elements. analytical precisions ranged between 5 and 10%. all geochemical analyses were carried out at the activation laboratories ltd (canada). the qualitative mineralogical analysis was carried out in the department of earth sciences of sultan qaboos university (oman) using x'pert pro x-ray diffraction with a 45 ma, 40 kv generator settings. 4. results a. mineralogy of the laterite zones: mineralogy of laterites in the oman mountains is discussed in detail by alkhirbash et al. [16]. the following paragraphs summarize the most important lithological and mineralogical composition of the various zones of the investigated laterite sections. i. protolith: the protolith is composed of either black to green peridotite rock (the east ibra and tiwi profiles) or of dark green coarse-grained layered gabbro (ibra profile). xrd analyses showed the presence of lizardite, kaolinite, maghemaite, antigorite, and clinochrysotile, in addition to some other ni bearing minerals (figure 2). ii. saprolite laterite: the initial texture of the protolith is fully preserved in this zone and composed mainly of lizardite (after pyroxenes), some altered plagioclase, amorphous iron oxides, and quartz. the mineral composition obtained through xrd analyses is given in figure 2. iii. oxide laterite: hematite and goethite are the primary components of this zone giving a reddish colored appearance to the rock. the results of the xrd mineral analyses are given in figure 2. iv. clay laterite: this zone is characterized by fine-grained, compact iron-stained-looking material. kaolinite and iron oxides are the main components. calcite and quartz-filling fractures and blebs of amorphous silica are also observed. xrd mineral analyses are given in figure 2. v. silcrete layers: several silcrete layers are observed at different levels within the oxide zone, particularly in the profiles of east ibra and al-russayl (figure 2). these silcrete layers are hard, displaying massive vesicular and concretionary textures, and are composed of fine-grained amorphous silica or quartz. x-ray diffraction analysis confirmed the presence of quartz, hematite, and calcite in the silcrete layers. vi. ferricrete layers: the ferricrete layers have complex fabrics and are mainly composed of hematite and goethite (al-russayl profile #1) or of magnetite and hematite (ibra profile) (figure 2). salah al khirbash and khadija semhi 42 east ibra composite 1 & 2 profile main mineral assemblages hematite, goethite, clinochlore, montmorillonite, calcite, quartz lithology qahlah conglomerate oxide laterite quartz, goethite, clinochlore silcrete hematite, goethite, clinochlore, montmorillonite, calcite, quartz oxide laterite quartz, clinochlore, hematite, goethite silcrete quartz, goethite, nimite, hematite, clinochrysotile, nepouite, calcite, lizardite, forsterite, antigorite, quartz, clinochlore saprolite laterite: with boulders & pisolites clinochrysotile (serpentine) protolith (peridotite) ibra profile main mineral assemblages hematite, spinel, ferrian, goethite, clinochlore, kaolinite, nontronite (stilpnochloran), quartz, clinochlore, maghemaite lithology tertiary carbonate clay laterite hematite, kaolinite, clinochlore hematite, kaolinite, clinochlore, albite, quartz, , maghemaite, lizardite, calcite, quartz oxide laterite: nodular fabric-ferricrete saprolite laterite with pisolites and boulders clinochlore, calcite, kaolinite, lizardite, maghemaite, quartz, calcite, goethite protolith (layered gabbro) figure 2. lithostratigraphic description and xrd data of the studied laterite profiles. mobilization and redistribution of elements in laterites of semail ophiolite 43 main mineral assemblages lithology tertiary carbonate quartz, hematite halite silcrete/loose soil goethite, quartz, troilite, limonite quartz, goethite, gypsum, halite, illite oxide laterite (light) clay laterite (dark) clinochrysotile, enstatite, forsterite protolith (peridotite) figure 2. continued al russayl p rofile # 1 main mineral assemblages quartz, hematite, goethite, calcite, clinochlore, ankerite quartz, clinochlore hematite, quartz, clinochlore, goethite, ankerite, quartz, kaolinite, maghemite, montmorillonite, talc quartz, clinochlore quartz, antigorite, clinochlore, clinochrysotile, clinochlore, calcite clinochrysotile (serpentine), willemseite lithology qahlah conglomerate oxide laterite silcrete oxide laterite ( hematite ) with boulders & pisolites silcrete oxide laterite ( limonite ) protolith ( peridotite ) east ibra p rofile # 3 salah al khirbash and khadija semhi 44 main mineral assemblages lithology tertiary carbonate oxide laterite (light) clay laterite (dark) saprolite laterite: with boulders protolith (peridotite) main mineral assemblages lithology tertiary carbonate hematite, spinel, bohmite, kaolinite, dolomite,goethite, clinoclore, illite oxide laterite (hematite with limonite at base) dolomite, lizardite, calcite, talc hematite saprolite laterite: with boulders & pisolites lizardite, dolomite protolith (peridotite) alrussayl composite 2 & 3 profile quartz, calcite, lizardite, saponite, goethite, montmorillonite nontronite, allanite, illite goethite lizardite, quartz, montmorillonite (bentonite) nontronite, lizardite,ringwoodite, spinel, quartz, clinochlore, montmorillonite clinochrysotile, forsterite, enstatite,augite tiwi profile # 1 figure 2. continued mobilization and redistribution of elements in laterites of semail ophiolite 45 tiwi profile # 2 main mineral assemblages lithology tertiary carbonate hematite, goethite, clinochlore, willemseite oxide laterite clinochrysotile (serpentine), dolomite, lizardite, forsterite, actinolite, ankerite saprolite laterite: with boulders & pisolites lizardite, dolomite, augite protolith (peridotite) figure 2. continued b. geochemistry the geochemical characteristics of different sections in the same profile are given in detail in [12]. in this paper, geochemical composition of the laterite will be briefly described. average concentrations of elements at different zones are given in table 1. i. ibra profile: geochemical investigation of trace elements in ibra profile revealed that the content of ni is higher in the serpentinized peridotite than in the other zones (table 1). the ni average content increases from 2000 ppm in the protolith zone to 3000, 5000, 8000, 9000 and 18000 ppm in the saprolite, oxide, clay laterites, fe bed/ferricrete and serpentinized peridotite, respectively. the highest concentrations of cr were observed in the clay zone while the highest concentrations of zn were observed in the ferricrete zone (see table 1). the concentrations of most of the elements in the clay zone remain lower than in the other zones except for pb and ba. ii. east ibra profiles: in east ibra profile, concentrations of trace elements exhibit significant fluctuations from the surface to the zone at 50 m depth. the ni contents, for example, in the east ibra composite 1 and 2 profile range from 1000 to 9000 with important enrichment in the oxide zone (table 1). further, high concentrations of cr, v, zn, sr and ba were also observed in the oxide zone (table 1). in east ibra 3 profile, the highest concentrations of elements were observed in the oxide zone, except for sr, ba and possibly pb, which have leached to the lower zones (clay zone). the silcrete layer remains less enriched in most elements, when compared with the protolith zone. iii. al-russayl profile: the lateral distribution of trace elements through the al-russayl profile #1, shows that the concentrations of ni, v, cr and zn are higher in the oxide zone than in the other zones (see table 1) while ba, sr and pb have accumulated more in the ferricrete zone. in al-russayl composite profile 2 and 3, most of the elements, except ba and pb, are enriched in the clay zone when compared to the other investigated zones. salah al khirbash and khadija semhi 46 iv. tiwi profile: the lateral distribution of trace elements through the tiwi profile #1 showed that all elements (except ni) are more concentrated in the clay zone, compared to the saprolite and oxide zones. the distribution of elements in tiwi profile #2 shows that their concentrations in the oxide zone are higher than in the saprolite zone (see table 1). table 1. geochemical analyses (in ppm) of the studied laterites, oman mountains. profile zone/ element fe mn ti cr ni co v zn rb sr zr ba la pb sc ibra protolith 58496 859 120 2737 2000 100 2.3 25.0 0.4 23.4 0.1 14.8 1.2 0.2 7.7 serpentinite/ peridotite 72846 4101 300 2737 18000 1000 32.5 71.2 0.4 189.5 0.1 22.3 8.8 0.3 17.8 saprolite 250204 1505 4796 6158 3000 100 129.8 20.1 0.2 108.7 3.3 14.2 3.0 1.9 32.2 oxide 440897 729 1799 30105 5000 100 101.3 25.3 < 0.1 37.6 2.2 8.2 1.7 4.8 47.2 clay 325631 1232 1799 43789 8000 1000 79.3 21.0 2.3 68.1 0.8 17.0 7.0 12.2 42.8 ferricrete 396752 2528 1799 30105 9000 1000 126.5 115.9 < 0.1 152.0 1.9 12.5 13.9 7.1 60.3 east ibra composite 1 and 2 profile saprolite 70572 1085 120 3421 3000 0 10.5 33.5 0.3 43.9 0.2 10.5 0.0 0.2 9.2 oxide 239609 1869 600 16421 9000 1000 63.3 42.8 0.6 76.7 0.7 57.3 1.5 3.2 36.6 silcrete 56706 3235 150 6158 3000 100 7.5 15.0 0.4 30.0 0.3 58.0 0.6 0.5 8.9 clay bed 45603 171 3597 2053 1000 100 10.0 13.2 14.2 57.4 0.3 19.4 27.2 20.2 2.9 east ibra profile 3 protolith 59172 1264 600 2737 2000 100 30.0 28.8 0.1 22.2 <0.1 8.0 <0.5 0.1 16.6 oxide /clay 233455 1373 600 18473 7000 100 60.7 46.3 0.4 42.9 0.8 29.1 1.6 1.8 33.9 silcrete 33433 360 2398 1368 1000 100 12.0 26.9 8.3 20.0 0.5 37.6 16.9 0.9 2.7 clay 73265 1469 2998 2737 3000 100 24.5 44.5 6.6 80.5 0.9 170.0 14.7 9.8 8.7 alrussayl profile 1 oxide 270732 450 1199 51315 7000 100 59.3 130.6 0.6 124.0 1.7 5.6 7.0 4.1 42.5 silcrete 48540 82 3597 5474 100 100 9.0 13.8 0.8 46.7 1.2 8.6 1.4 2.7 1.9 ferricrete 508066 227 1199 26000 2000 100 49.0 47.7 0.4 459.0 1.8 22.6 1.2 5.1 10.2 alrussayl composite 2 & 3 profile protolith 57423 765 1269 2737 2000 100 6.0 18.6 0.1 43.9 <0.1 7.9 <0.5 0.2 6.0 clay 374335 6163 1199 26684 13000 1000 28.7 95.8 2.0 61.3 1.5 34.9 3.6 5.3 35.9 saprolite 42875 676 60 2053 2000 100 10.0 17.6 0.1 113.0 <0.1 13.4 <0.5 0.1 3.9 mixture/ (fe/clay) 101068 2010 600 13000 3000 100 27.5 31.6 1.4 89.1 0.8 68.1 2.8 7.0 9.9 tiwi profile 1 protolith 49729 673 60 2737 2000 100 9.0 12.2 14.4 < 0.1 8.0 0.1 6.2 saprolite 55482 754 60 2737 2000 100 11.3 17.2 0.2 36.0 0.2 10.4 < 0.5 0.1 6.1 clay bed 375594 1908 1799 19158 3000 1000 301.0 44.7 3.5 155.0 5.9 31.2 2.1 24.6 33.4 oxide 432418 584 1799 26684 4000 100 81.7 37.1 0.2 90.4 2.6 16.7 0.9 3.3 49.0 tiwi profile 2 saprolite 65816 853 90 2737 2000 100 9.8 18.1 0.3 34.2 0.1 6.9 <0.5 0.1 6.1 oxide/ ferricrete 249417 1043 600 13000 6000 100 56.8 57.0 0.5 54.8 1.5 13.8 2.7 0.9 37.5 c. mass balance to determine the relative enrichment or depletion of elements relative to the fresh parent rock within the weathering profile during lateritization, we calculated a mass balance. the mass balance model used, according to [15, 20-22] was as follows: % change = [(xa/ia)/(xp/ip)-1] *100 (1) where xa and xp are the concentrations of elements in the weathered samples and in the parent rock, respectively. ia and ip are the concentrations of the immobile element in the weathered samples and in the parent rock, respectively. in this calculation, the average density of rocks was taken in consideration. for parent rock, the measured average density is about 2.6 g per cubic cm, while for the laterite an average density of about 2.5 g per cubic cm was measured. elements such as th, zr and ti have been considered as immobile elements during weathering in previous studies [1, 21, 23-25]. in this study, the selection of immobile elements was established after a statistical investigation. in fact, statistical treatment of data revealed similar variations of concentrations of ti and th and zr. however, since mobilization and redistribution of elements in laterites of semail ophiolite 47 ti has been considered an immobile element during weathering of mafic rocks, for the mass balance calculation during this study the normalization of ni, co, v, zn, pb, sr, sc, and cr was established relative to ti. quantification of loss and gain of elements during lateritization was determined for each zone of each profile relative to the parent rock. the results are shown in table 2 as an average of the results for different depths from the same zone. the mass balance calculation for ibra revealed a depletion of most of the elements in all zones. only v and pb are enriched in the oxide and clay zones relative to the other elements (figure 3). the elements sc and cr are well correlated with fe (r = 0.7 and 0.6 respectively), while ni, zn, co and sr tend to be associated with mn rather than with fe. the mass balance calculation for east ibra composite profile 1 and 2 showed an enrichment of elements in the saprolite, oxide (upper and lower zones), and silcrete zones, except for zn which is depleted in the upper oxide zone while v and sc are depleted in the silcrete zone. element-element correlations indicate that cr, co, ni and zn are more strongly associated with fe oxide than with mn oxide. correlation coefficients with fe are about 0.96, 0.97, 0.9 and 0.8 for cr, co, ni and zn respectively. for east ibra profile 3, only upper and lower oxide zones are characterized by an enrichment in elements. the clay bed is depleted in ni, co, v, sr, zn, sc and cr and enriched in ba and pb, while the silcrete layer is depleted in all elements. in this profile, most elements are more concentreted with fe than with mn as the case of east ibra composite 1 and 2 profile. al and ni substitution in natural iron oxides (goethite, hematite and maghemite) from laterites has been previously studied [26, 27]. ni has been found more frequently with goethite but not with mn oxides. in contrast, [28] reported that ni might be associated with mn oxides more than with fe oxides in a philippine laterite. the lateral distribution of elements within every section of the al-russayl profile showed that all elements have been mobilized during lateritization, which has resulted in a zone of enrichment in the oxide in the al-russayl profile 1 and a depletion of elements in the silcrete zone and a depletion of ni, co and ba in parallel to an enrichment in the other elements in the ferricrete zone of the same profile relative to the fresh protolith. for al-russayl composite 2 and 3 profile, the weathering has induced an enrichment of elements in all investigated zones, except ba which is depleted in the clay zone. investigation of correlations between elements of al-russayl profiles indicates that ni is well correlated with mn, while cr and zn are more associated with fe than mn oxides, and co, sr and sc levels do not indicate any correlation with either fe or mn. table 2. mass balance data of the different laterite profiles. profile element/ zone ni co v zn sr ba pb sc cr ibra saprolite -100 -100 -3 -97 -86 -98 -98 -92 -100 oxide -81 -63 360 -95 -74 -93 183 -69 -18 clay -77 -48 182 -94 -70 -89 656 -72 14 e. ibra composite 1 & 2 profile saprolite 563 355 -3 381 767 402 395 110 386 lower oxide 769 392 29 270 1121 891 829 67 768 upper oxide 199 178 20 -25 49 292 1412 62 246 silicrite 269 254 -38 25 228 1632 772 -98 501 e. ibra profile #3 lower oxide 809 506 -39 266 549 382 163 55 424 upper oxide 174 163 28 -10 -3 153 754 55 397 clay bed -77 -56 -91 -82 -57 157 682 -92 -90 silcrete -88 -86 -94 -87 -88 -35 -11 -97 -94 al russayl profile #1 oxide 181 -20 692 463 126 1544 1544 468 1403 silcrete -100 -73 -60 -80 -72 -97 261 -92 -47 ferricrete -20 -20 555 106 738 -78 1945 36 662 alrussayl composite 2 & 3 profile saprolite 1502 1502 2570 1416 4024 121 701 941 1102 clay 421 702 284 313 12 -74 2025 380 682 mixture/(fe/clay) 140 60 634 172 225 3 5508 1719 661 tiwi profile #1 saprolite -24 -24 -5 7 89 52 -24 -25 -24 oxide laterite -96 -75 -15 -91 -73 -96 522 -86 -82 clay bed -95 -97 -77 -92 -84 -92 -17 -80 -75 tiwi profile #2 saprolite -49 -49 -45 -25 20 -58 -49 -50 -49 oxide/ferricrete -77 -92 -52 -65 -71 -97 -32 -54 -64 salah al khirbash and khadija semhi 48 for the tiwi area, a mass balance for the two profiles (1 and 2) was calculated. profile 1 is about 40 m thick from topsoil to bedrock, and represents the complete profile, while profile 2 is about 30 m thick. the mass balance calculation indicates that all investigated zones in tiwi profile 1 are characterized by a depletion of elements, with the exceptions of pb which is enriched in the oxide zone, and of sr and ba which were found enriched in the saprolite zone. in tiwi profile 2, all elements are depleted relative to the parent rock, except for sr which is slightly enriched in the saprolite zone. elements such as cr and zn are more concentrated with fe than with mn, while co and ni seem be carried by both fe and mn oxides [12]. the mass balance calculation using equation (1) in this study is coherent with values calculated using the model reported by braun [26] for calculation of the mass balance of elements in a lateritic terrain. in this previous study, the volume change in each zone of the soil, due to weathering, is considered in the calculation model. the calculation of the volume change in the present study indicated a decrease in the volume of the ibra profile due to collapse during weathering, while in the east ibra composite 1 and 2 profile, there was an expansion of the soil during weathering. such differences may reflect different paloclimatic conditions. 5. discussion the rate of accumulation of elements in soils depends on the susceptibility and resistance of rocks to weathering, the leaching process of elements, and their adsorption or fixation on clay and oxide phases. the mobility and accumulation of trace elements in the soil during weathering depends on their distribution between different mineral phases. the different zones of the investigated laterite profiles (ibra, east ibra, tiwi and al-russayl) vary in mineral composition and in the thickness of each zone. the zones of ibra profile are thicker than the zones in the other profiles, which may reflect an important weathering process and longer time of lateritization compared to the other profiles. moreover, ibra profile is characterized by a development of different zones during weathering, such as oxide, saprolite and clay zones, unlike other profiles where either the saprolite zone (as in the case of east ibra profile 3) or the clay zone (as in tiwi profile 2 and al-russayl profile 1) are missing. in terms of chemical composition, most of the elements investigated during this study do not exhibit the same fluctuations and behavior in the different zones of each profile. for example, in the east ibra sections, enrichment of elements occurred in the saprolite, silcrete and oxide zones while in al-russayl composite 2 and 3 profile, the enrichment which was calculated for elements occurred in the saprolite zone and exceeded that calculated for the same zone in the other profiles. a. mobilization of elements during laterization mass balance calculations relative to the fresh parent rock indicated that the mobilization of elements in each profile is dissimilar, and may indicate different weathering histories and different degrees of serpentinization. the laterite soil in the present study was developed on ophiolite rocks with slight differences between parent rocks in each section. the differences between sections in terms of geochemistry and mineral content may reflect differences in weathering conditions, including topography and drainage. the enrichment in heavy metals in soil zones is often inherited from the parent rock. their vertical distribution is controlled by their mobility during chemical weathering, adsorption by clay particles, the concentration of organic matter in the soil, and by their precipitation or their complexation with different ions. the variability in mobilization of elements during weathering can be expressed as a ratio between elements. the investigated ratios consist of ni/co, ni/cr and ni/zn. the ni/zn ratio increases in the following order: clay zone > oxide zone > saprolite for ibra profile, while the ni/co ratio is similar in oxide and clay zones. in the oxide and saprolite zones of this profile, the ni/zn and ni/co ratios are higher than in the parent rock, unlike the ni/cr ratio, which is lower. in the clay zone, both the ni/cr and ni/co ratios are lower than in the parent rock, while the ni/zn ratio is higher. investigation of these different ratios in different zones of ibra profile indicates the following order of mobility of elements: ni>co>zn. in east ibra composite 1 and 2 profile, the ni/zn ratio in each zone is higher than that of the parent rock, which reflects the higher mobility of ni and cr relative to zn and co. the ni/cr and ni/co ratios, on the other hand, are lower in the oxide and clay zones than in the parent rock. in east ibra profile 3, the ni/zn ratio in the oxide zone is higher than in the parent rock, while the clay zone has a similar ni/zn ratio to the parent rock. the ni/cr ratio in the oxide zone is lower than in the parent rock, but the opposite is the case in the clay zone while the ni/co ratios in both oxide and clay zones exceed that of the parent rock. comparison between the different zones indicates that the highest ni/zn and ni/co ratios characterize the oxide zone, and the highest ni/cr ratio characterizes the clay zone. for al-russayl profile 1, the ni/zn and ni/cr ratios in the oxide zone are lower than in the parent rock, unlike the ni/co ratio. for al-russayl composite 2 and 3 profile, the ni/zn ratio in the clay zone is higher than in the parent rock , opposite to the ni/co ratio for the same zone. in the saprolite zone, ni/zn, ni/cr and ni/co ratios remain similar to those of the parent rock. for tiwi section, the ni/zn ratio in the saprolite, clay and oxide zones is lower than in the parent rock. the ni/cr ratio in the clay and oxide zones is lower than in the parent rock, while the ni/co ratio in the oxide zone exceeds the ni/co ratio of the parent rock. mobilization and redistribution of elements in laterites of semail ophiolite 49 ni, zn, cr, and co are usually incorporated in the lattice of silicate or oxide minerals. higher ni/zn and ni/cr ratios in the clay zones of ibra, al-russayl composite 2 and 3 profile and east ibra 3 compared to the other zones, and additionally, a higher ni/co ratio in the feclay zone of al-russayl composite 2 and 3 profile, reflect the higher exchange capacity for ni in the clay zone. the association of ni with fe-mn oxides results in higher ni/zn, ni/co and ni/cr ratios in the oxide zone, as in east ibra profile 3. a saprolite zone (usually called the c zone or partially altered bedrock zone) is between the subjacent fresh or non-weathered parent rock zone and the superjacent clay/iron oxide zone (which is also called the b zone or zone of leaching). the saprolite zone then contains some metals that are produced from in situ weathering of minerals of the parent rock, and some that may have come from the overlying zones. therefore, the apparent increase of the ni/cr ratio in the saprolite zone of ibra, east ibra and al-russayl profiles compared to their parent rocks reflects the selective thermodynamic binding of the metals, or the stability constants of the metals with available ligands or chelates in the weathering zones. the selections are therefore influenced by (i) charge, (ii) ion size, (iii) ligand donor atoms, (iv) preferential coordination geometry or stereochemical control, (v) oxidation states, and for the transitional metals, (vi) spin-pairing stabilization [29-32]. in normal aqueous media, association of co to zn can be found in oxidation states of 2+. while ni, co, zn and cr can co-ordinate with water for hydrolysis reactions, they are also able to form bonds with s-donor ligands. smaller high charged ions are more strongly hydrated than larger low charged ions. replacement of coordinated water molecules around a smaller cation by organic ligands requires higher energy. therefore, a ni/zn increase in the saprolite zone may be explained in terms of the relatively higher mobility of ni influenced by the hydration effect, as well as by the ligand co-ordination effect. an increase in the ni/co ratio may be the result of a redox reaction effect, possibly in the upper organic-rich zone, besides the latter having a preference for o-donor ligands. b. redox conditions: ce occurrence in the soil as mobilization of ce during weathering is sensitive to redox conditions, an investigation of the correlation of ce with elements such as mn, ni, co, fe and cr indicated that ce exhibits three oxidation states, +ii, +iii and +iv. the first of these is not common. among these states, ce(iii) is soluble in a reduced environment, but the oxidized state of ce (ce iv) is insoluble [6]. in ibra profile only co and zn are well correlated with ce, unlike ni, fe, mn and co. in east ibra composite 1 and 2 profile, weak correlations were calculated between ce and cr, mn, fe, co and ni. in east ibra 3 profile the mobilization of co, cr and ni, which are well correlated with ce, seems to be affected by fluctuations of redox conditions in this profile. the increase of ce in this soil, due to the oxidation of ce(iii) to the less soluble ce (iv), correlates to a leaching of cr, fe and ni from the soil. in al-russayl profile 1 good correlations were calculated between ce and mn (r =0.93), co (r= 0.86), ni (r =0.9), zn (r = 0.98) but not with fe, while in al-russayl composite 2 and 3 profile, ce is well correlated with ni, mn and fe, but not with co and cr. in tiwi profile 1 and tiwi profile 2, cr, ni and zn seem to be affected by redox conditions of the soil since they exhibit good correlations with ce. c. sc-fe interaction in the soil although the soil chemistry for scandium (sc) is similar to that for fe and substitutes fe 3+ in primary minerals, sc is not affected by redox reactions. according to brown [33] in lateritic soils the fe-accumulation, lacking any redox influences, can be estimated from the sc/fe ratio. this fe accumulation is highlighted by the deviation of samples from the sc-fe linear relationship. the sc/fe ratio in different zones from different sections investigated during this study is about 0.09.10 -3 to 0.16.10 -3 . the oxide zones of tiwi 1 and ibra profiles and the clay zone of tiwi profile 1 and al-russayl composite 2 and 3 profile are characterized by lower sc/fe ratios because of significant accumulation of fe as compared to that of sc (figure 4). this enrichment of fe independently of redox conditions might reflect adsorption of fe on clay minerals, and/or a deposition of amorphous fe during the laterization processes. all zones of al-russayl composite 2 and 3 profile are characterized by similar ratios to that of the parent rock, which indicates a homogeneity in the distribution of these two elements during the laterization processes. in ibra profile, the sc/fe ratio in all zones is similar to that of the parent rock except in the serpentinized zone, where a high concentration of fe and low concentration of sc generate a lower sc/fe ratio than in the parent rock. in all zones of east ibra composite 1 and 2 profile, the sc/fe ratio is lower than in the parent rock because of the significant concentration of fe in the saprolite and the oxide zones, and because of an important depletion of sc in the silcrete and the clay zones. similar to the east ibra composite 1 and 2 profile, all zones of east ibra profile 3 are characterized by lower sc/fe compared to the parent rock. in tiwi profile 1, the clay zone is characterized by an important accumulation of fe which generates a sc/fe ratio lower than that of the parent rock. the other zones of tiwi profile 1 have a sc/fe ratio similar to that of the parent rock. the oxide zone of tiwi profile 2 is characterized by an important deposition of sc compared to the parent rock, which induces a sc/fe ratio higher than that of the parent rock. salah al khirbash and khadija semhi 50 d. rate of weathering and accumulation rate of ni an estimation of the duration of lateritization by lucas [34] indicated that about 17 to 34 million years (my) are needed to form a profile. the average thickness of the ibra profile of the present study is about 60 m (20 m for the layered gabbro zone, 20 m for the saprolite zone, 5 m for the oxide zone, 15 m for the clay zone). such a thickness corresponds to a rate of downward advance of the weathering front of 3 m per million years (my) if an average duration of 20 my is considered. such a rate might be overestimated or underestimated if all weathering conditions are taken into consideration. however, the leaching and distribution of elements may be accelerated for young profiles and under humid climate conditions [35]. based on a density of 2.5 g/cubic cm, we estimated that about 4000 g of ni may be extracted per 1my from 1 square meter of the layered gabbro zone developed in ibra profile and about 6000 g per 1my from 1 square meter of the saprolite zone and 2500 g per 1my from 1 square meter of the oxide zone and about 12000 g per 1 my from 1 square meter of the clay zone. similar estimations calculated for east ibra profiles showed that more ni can be extracted from the oxide zone of east ibra composite 1 and 2 profile than from the other zones of either the same profile or the east ibra profile 3. in contrast, the clay zone of east ibra profile 3 accumulated more ni than the clay zone in the east ibra composite 1 and 2 profile. e. dynamic of th and u thorium occurs in diverse rock types in association with u and rare earth elements. thorium is very insoluble during weathering compared to u. the u–th couple is useful in constraining paleo-redox conditions because 232 th, 235 u, and 238 u are long-lived radionuclides, which decay to different pb isotopes. th/u ratios may represent different stages of oxidation and leaching. th/u ratios may be used to estimate paleo-redox conditions at the time of deposition [36]. in oxidized environments, sediments may contain less u, and show high th/u ratios above the average upper continental crust ratio of 3.8 [37]. in sediments deposited in a reduced environment, the th/u ratio is low [38-40]. the th/u ratio is controlled by the weathering-erosion-diagenesis cycle [41]. due to large differences in th and u concentrations through different profiles, discussion of the th/u ratio will be based on data of individual profiles and not composed ones, as was done for mass balance calculations (table 3). in ibra profile, the th/u ratio ranges from 0.5 to 6.0 for the clay zone. for east ibra 1 profile, the average ratio is about 2.25. the other investigated zones are characterized by lower th and u concentrations, of less than the detection limit. for east ibra composite 2 and 3 profile, an average th/u ratio of about 4.4 was calculated for the upper oxide zone. table 3. u/th ratio of the different laterite profiles. ibra profile zone th (ppm) u (ppm) th/u clay laterite 0.6 0.1 6.0 1.4 0.8 1.8 0.5 0.9 0.6 oxide laterite 2.7 3.5 0.8 1.9 0.8 2.4 0.4 0.4 1.0 0.6 0.6 1.0 0.5 0.2 2.5 0.5 0.3 1.7 saprolite < 0.1 < 0.1 < 0.1 < 0.1 0.1 < 0.1 0.2 < 0.1 protolith < 0.1 0.2 < 0.1 < 0.1 < 0.1 < 0.1 0.2 < 0.1 0.1 < 0.1 mobilization and redistribution of elements in laterites of semail ophiolite 51 table 3 (cont.). u/th ratio of the different laterite profiles. the th/u ratio in al-russayl profile 1 is about 0.9 to 14. the highest values were calculated for the ferricrete zone. in al-russayl composite 2 and 3 profile, the th/u ratio is lower than that of al-russayl profile 1, and ranges from 0.5 to 5.4, with the highest value for the clay zone. for both tiwi profile 1 and tiwi profile 2, the th/u ratio is < 1. large fluctuations of the th/u ratio may be attributed to either the source or redox conditions in the profile. fluctuation of th concentrations may reflect different sources through the profile, while different concentrations of u reflect fluctuations in redox potential. the high th/u ratio (above that of continental crust) in the al-russayl profile e ibra profile 1 e ibra composite 2 and 3 profile zone th (ppm) u (ppm) th/u zone th (ppm) u (ppm) th/u clay bed 1.8 0.8 2.25 u oxide laterite 0.77 0.18 4.4 u oxide laterite 0.5 < 0.1 l oxide laterite <0.1 < 0.1 l oxide laterite 0.4 < 0.1 saprolite < 0.1 < 0.1 < 0.1 < 0.1 protolith < 0.1 < 0.1 saprolite 0.1 < 0.1 < 0.1 < 0.1 al-russayl profile 1 al-russayl composite 2 and 3 profile zone th (ppm) u (ppm) th/u zone th (ppm) u (ppm) th/u ferricrite 1.2 1.5 0.8 clay bed 1.4 0.5 2.8 oxide 1.3 0.5 2.6 oxide (limonite) 0.9 0.6 1.6 pockets green clay 2.2 2.5 0.9 clay laterite 1.6 0.3 5.4 0.6 0.7 0.9 saprolite 0.1 0.2 0.5 1.7 0.7 2.4 protolith < 0.1 < 0.1 ferricrite 1.4 0.1 14.0 tiwi profile 1 zone th (ppm) u (ppm) th/u clay bed 3.6 11.7 0.3 oxide 4.8 7.0 0.7 1.4 4.1 0.3 1.6 4.8 0.3 0.5 3.9 0.1 0.4 4.1 0.1 0.5 3.7 0.1 0.3 3.8 0.1 saprolite < 0.1 < 0.1 < 0.1 < 0.1 < 0.1 < 0.1 0.2 0.3 0.7 protolith < 0.1 < 0.1 < 0.1 < 0.1 tiwi profile 2 zone th (ppm) u (ppm) th/u ferricrite 0.4 2.8 0.1 oxide < 0.1 1.3 ferricrite < 0.1 < 0.1 saprolite < 0.1 < 0.1 < 0.1 < 0.1 0.1 < 0.1 < 0.1 < 0.1 salah al khirbash and khadija semhi 52 and all east ibra profiles may indicate an oxidizing environment, while the low th/u ratio (<1) in the tiwi profiles is indicative of a reducing environment. 6. conclusion investigation of laterite soils in oman which have developed on mafic/ultramafic rocks revealed differences in the thickness of the same zones (e.g. saprolite, oxide etc…) formed in different profiles. moreover these different profiles are characterized by a heterogeneous distribution of elements. such differences imply different conditions of weathering (differences in the local conditions of climate and topography). to estimate the gain and loss of elements through each profile, a mass balance was calculated, which showed that all elements have been mobilized and transferred downwards along the profile. the mass balance calculation for ibra profile relative to the parent rock revealed that most elements have been depleted in the saprolite, oxide, clay and ferricrete zones. in east ibra composite 1 and 2 profile, the mass balance calculation showed that all elements were enriched in the saprolite, oxide and silcrete layers and depleted in the clay zone, relative to the parent rock. in east ibra profile 3, only the oxide zone was enriched in all elements during weathering. for al-russayl profile 1, all elements were enriched in the oxide zone and depleted in the silcrete zone, while in al-russayl composite 2 and 3 profile, an enrichment in all elements was calculated in all investigated zones. for both tiwi profiles (1 and 2), all investigated zones are characterized by a depletion in elements. redox conditions during weathering were investigated using the correlation of elements with ce on the one hand, and th/u and sc/fe ratios on the other hand. investigation of sc/fe ratios in different zones indicated low values for tiwi 1 and ibra profiles and al-russayl composite 2 and 3 profile due to an important accumulation of fe independently of redox conditions. large fluctuations characterize the 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http://www.sciencedirect.com/science?_ob=publicationurl&_tockey=%23toc%235991%232008%23999499994%23681199%23fla%23&_cdi=5991&_pubtype=j&view=c&_auth=y&_acct=c000047883&_version=1&_urlversion=0&_userid=912155&md5=49cd60d087c415c5bac55fa8630c8c9a http://www.sciencedirect.com/science/article/pii/s0016703798001033 http://www.sciencedirect.com/science/article/pii/s0016703798001033 http://www.sciencedirect.com/science/journal/00167037 http://www.sciencedirect.com/science/journal/00167037 salah al khirbash and khadija semhi 54 37. taylor, s.r. and mclennan, s.m. the continental crust: its composition and evolution. blackwell scientific, oxford, 1985, p312. 38. mclennan, s.m. and taylor, s.r. th and u in sedimentary rocks: crustal evolution and sedimentary cycling. nature, 1980, 285, 621-624. 39. hemming, s.r. and mclennan, s.m. pb isotope compositions of modern deepsea turbidites. earth and planetary science letters 2001, 184, 489-503. 40. krogstad, e., m fedo, c., and eriksson, k.a. provenance ages and alteration histories of shales from the middle archean buhwa greenstone belt, zimbabwe: nd and pb isotopic evidence. geochimica et cosmochimica acta, 2004, 68, 319-332. 41. condie, k.c. chemical composition and evolution of the upper continental crust: contrasting results from surface samples and shales. chem. geol., 1993, 104, 1-37. received 25 december 2014 accepted 11 april 2015 squ journal for science, 2022, 27(2),107-118 doi:10.53539/squjs.vol27iss2pp107-118 sultan qaboos university 107 analysis of new type of second-order fractional linear multi-step method with improved stability h.m. nasir* and khadija al-hassani department of mathematics, sultan qaboos university, p.o. box: 36, al khod, muscat, sultanate of oman. *email: nasirh@squ.edu.om. abstract: we present and investigate a new type of implicit fractional linear multi-step method of order two for fractional initial value problems. the method is obtained from the second-order superconvergence of the grünwald-letnikov approximation of the fractional derivative at a non-integer shift point. the method coincides with the backward difference method of order two for the classical initial value problem when the order of the derivative is one. the weight coefficients of the proposed method are obtained from the grünwald weights and are hence computationally efficient compared with that of the fractional backward difference formula of order two. the stability properties are analyzed and it is shown that the stability region of the method is larger than that of the fractional adams-moulton method of order two and the fractional trapezoidal method. numerical results and illustrations are presented to justify the analytical theories. keywords: grünwald approximation; generating functions; fractional adams-moulton methods; backward difference method; super-convergence; stability regions. محّسنتحليل نوع جديد من الطريقة الكسرية الخطية متعددة الخطوات من الدرجة الثانية مع استقرار حنيفة محمد ناصر و خديجة الحسني متعددة الخطوات من الدرجة الثانية لمشاكل القيمة األولية الكسرية. يتم الخطية الكسرية نوع جديد من الطريقة الضمنية في هذا البحث نقدم :صلخمال وقد تبين ان هذه غير صحيحة. ذات قيمة إزاحة عند نقطة هالكسري هللمشتق جرنوالد الدرجة الثانية لتقريب ذوالفائق الحصول على الطريقة من التقارب واحدًا. يتم الحصول على هالقيمة األولية الكالسيكية عندما يكون ترتيب المشتق ئلهالعكسي من الرتبة الثانية لمستتطابق مع طريقة االختالف الطريقة ، وبالتالي فهي فعالة من الناحية الحسابية مقارنة بمعادلة الفرق الجزئي المتخلف من الدرجة الثانية. تم دجرنوال معامالت الوزن للطريقة المقترحة من أوزان الكسرية من الدرجة الثانية وطريقة شبه مولتن -أدمز طريقةمنطقة االستقرارلأكبر من المقترحة يل خصائص الثبات وتبين أن منطقة االستقرار للطريقةتحل . عرض النتائج العددية والرسوم التوضيحية لتبرير النظريات التحليلية وقد تمالمنحرف الجزئية. .االستقرار، منطقة التقارب الفائق ، الكسرية ، طريقة االختالف العكسيمولتن -ق أدمزطر، المولدة الدالة جرنوالد، تقريبات :مفتاحيةالكلمات ال h.m. nasir and khadija al-hassani 108 1. introduction consider the fractional initial value problem (fivp) 𝑡0 𝐶 𝐷𝑡 𝛽 𝑦(𝑡) = 𝑓(𝑡, 𝑦(𝑡)), 𝑡 ≥ 𝑡0, 0 < 𝛽 ≤ 1, (1) 𝑦(𝑡0) = 𝑦0, where 𝑡0 𝐶 𝐷𝑡 𝛽 is the left caputo fractional derivative operator of order 𝛽 defined in section 2, 𝑓(𝑡, 𝑦) is a bounded function satisfying the lipschitz condition in the second argument 𝑦 guaranteeing a unique solution to the problem [1]. there is no loss in considering the fractional order in the interval 𝛽 ∈ (0,1]. for, when 1 < 𝛽 ≤ 𝑛 = ⌈𝛽⌉, with appropriate initial conditions, the fivp (1) can be formulated as a system of fivp of order 0 < 𝛽/𝑛 ≤ 1, just as in the case of classical initial value problems (ivps) with higher integer order derivatives [2]. fractional calculus, despite its long history, has only recently gained a place in science, engineering, artificial intelligence, and many other fields [3-6]. in the recent past, many numerical methods have been developed for solving (1) approximately. we are interested in the numerical methods of the type commonly known as the fractional linear multi-step methods (flmms). the basic numerical method of flmm type of consistency order one for (1) is obtained from the grünwaldletnikov form for the fractional derivative [7,8]. the weight coefficients for this basic flmm are the grünwald weights obtained from the series of the generating function 𝜔1(𝑧) = (1 − 𝑧) 𝛽 . lubich [9] introduced a set of higher-order flmms as convolution quadrature methods for the volterra integral equation (vie) obtained by reformulating (1) (see also eg. [1]). the quadrature coefficients are obtained from the fractional-order power of a rational polynomial of the generating polynomials for the linear multi-step method (lmm) of classical initial value problems (ivps). as a particular subfamily of these flmms, the fractional backward difference formulas (fbdfs) were also proposed by lubich in [10]. another particular form of flmm type is the fractional trapezoid method of order 2. many researchers have utilized these formulations to construct variations of the flmms (see eg. [11] and the references therein). galeone and garrappa [12] studied some implicit flmms generalizing the adams-moulton methods for classical ivps. galeone and garrappa [13] and garrappa [14] have also investigated a set of explicit flmms generalizing the adams-bashforth methods. in this paper, we propose and analyze a new type of flmm of order 2. the method is computationally efficient and has improved stability. we also present algorithms to solve linear and non-linear fivps using the proposed flmm. we also compare the method with other known flmms of order 2 and show that the presented method outweighs the other methods in terms of stability and/or computational efficiency. we classify the previously known flmms into subclasses based on the form of their generating functions which indicate that our flmm presented here falls into a new subclass not encountered in the past literature. this paper is organized as follows. in section 2, the preliminaries and previous relevant works are summarized. in section 3, the new flmm of order 2 is introduced along with a computational algorithm. numerical examples for testing the method are given in section 4. in section 5, the stability of the method is analyzed. in section 6, the new method is compared with other flmms and section 7 draws some conclusions. 2. preliminaries for a sufficiently smooth function 𝑦(𝑡) defined for 𝑡 ≥ 𝑡0, the left riemann-liouville (rl) fractional derivative of order 0 < 𝛽 ≤ 1 is defined by (see eg. [20]) 𝑡0 𝑅𝐿 𝐷𝑡 𝛽 𝑦(𝑡) = 1 γ(1−𝛽) 𝑑 𝑑𝑡 ∫ 𝑡 𝑡0 𝑦(𝜏) (𝑡−𝜏)𝛽 𝑑𝜏, 0 < 𝛽 ≤ 1, (2) where γ(⋅) is the euler-gamma function. the left caputo fractional derivative of order 𝛽 > 0 is defined as 𝑡0 𝐶 𝐷𝑡 𝛽 𝑦(𝑡) = 1 γ(1−𝛽) ∫ 𝑡 𝑡0 𝑦′(𝜏) (𝑡−𝜏)𝛽 𝑑𝜏, 0 < 𝛽 ≤ 1. (3) in addition to the above two definitions, the grünwald-letnikov(gl) definition is useful for numerical approximations of fractional derivatives. 𝑡0 𝐺𝐿 𝐷𝑡 𝛽 𝑦(𝑡) = lim ℎ→0 1 ℎ𝛽 ∑ ∞𝑘=0 𝑔𝑘 (𝛽) 𝑦(𝑡 − 𝑘ℎ), (4) where 𝑔𝑘 (𝛽) = (−1)𝑘 γ(𝛽+1) γ(𝛽−𝑘+1)𝑘! are the grünwald weights and are the coefficients of the series expansion of the grünwald generating function analysis of a new type of second-order fractional linear multi-step method 109 𝜔1(𝑧) = (1 − 𝑧) 𝛽 = ∑ ∞𝑘=0 𝑔𝑘 (𝛽) 𝑧𝑘 . the coefficients 𝑔𝑘 (𝛽) can be successively computed by the recurrence relation 𝑔0 (𝛽) = 1, 𝑔𝑘 (𝛽) = (1 − 𝛽+1 𝑘 ) 𝑔𝑘−1 (𝛽) , 𝑘 = 1,2, . .. . (5) for theoretical purposes, the function 𝑦(𝑡) is zero-extended for 𝑡 < 𝑡0, hence the infinite summation in (4). practically, the upper limit of the sum is 𝑛 = ⌈(𝑡 − 𝑡0)/ℎ⌉. the three definitions are equivalent under homogeneous initial conditions [8]. 2.1 fractional linear multi-step methods among the several numerical methods to solve (1), we list the numerical methods that fall under the category of flmm. the fundamental and widely investigated numerical approximation scheme is the grünwald-letnikov method (also called the fractional backward euler method) obtained by replacing the fractional derivative operator in (1) with its ga operator 𝛿ℎ 𝛽 of order one [8]. 𝛿ℎ 𝛽 𝑦(𝑡): = 1 ℎ𝛽 ∑ ∞𝑘=0 𝑔𝑘 (𝛽) 𝑦(𝑡 − 𝑘ℎ) = 𝑓(𝑡, 𝑦) + 𝑂(ℎ). (6) by choosing the discretization step ℎ appropriately to align the discrete points 𝑡 − 𝑘ℎ with the endpoints of the problem domain [0, 𝑇] and assuming zero extension for the unknown function 𝑦(𝑡) for 𝑡 < 0, the infinite sum in (6) is reduced to a finite sum. dropping the first order error term, choosing ℎ = 𝑇/𝑁, 𝑁 ∈ ℕ, and denoting 𝑡𝑛 = 𝑛ℎ, 𝑦𝑛 ≈ 𝑦(𝑡𝑛) and 𝑓𝑛 = 𝑓(𝑡𝑛, 𝑦𝑛 ), (7) equation (6) gives the gl scheme ∑ 𝑛𝑘=0 𝑔𝑘 (𝛽) 𝑦𝑛−𝑘 = ℎ 𝛽 𝑓𝑛, 𝑛 = 1,2, . . . , 𝑁. a shifted gl approximation of (6) is given by replacing 𝑘 by 𝑘 − 𝑟 and a shifted gl scheme is then given by ∑ 𝑛𝑘=0 𝑔𝑘 (𝛽) 𝑦𝑛−𝑘+𝑟 = ℎ 𝛽 𝑓𝑛, 𝑛 = 1,2, . . . , 𝑁, (8) where 𝑟 is the shift. the shifted scheme is also of the first order when the shift 𝑟 is an integer. however, at 𝑟 = 𝛽/2, the scheme (8) gives super-convergence of order 2 [15]. 𝛿ℎ,𝛽/2 𝛽 𝑦(𝑡): = 1 ℎ𝛽 ∑ ∞𝑘=0 𝑔𝑘 (𝛽) 𝑦(𝑡 − (𝑘 − 𝛽/2)ℎ) = 𝑓(𝑡, 𝑦) + 𝑂(ℎ2). (9) however, this super-convergence scheme introduces an additional difficulty in dealing with values of the function 𝑦 at points not aligned with the grid points [15]. in section 3, we modify this super-convergence scheme to construct a new scheme of order 2. a general way to approximate the fivp (1) is to replace the fractional derivative by the form with general weights 𝑤𝑘 as ωℎ 𝛽 𝑦(𝑡): = 1 ℎ𝛽 ∑ ∞𝑘=0 𝑤𝑘 𝑦(𝑡 − 𝑘ℎ), (10) where the weights 𝑤𝑘 are to be determined for a desired order of consistency. thus, grunwald-type approximation schemes for the fivp have the form expressed in conformance with the classical backward difference form (bdf) as ∑ 𝑛𝑘=0 𝑤𝑘 𝑦𝑛−𝑘 = ℎ 𝛽 𝑓𝑛, 𝑛 = 1,2, . . ., (11) where 𝑤𝑘 are coefficients in the expansion of some appropriate generating function 𝑤(𝑧). in lubich [10], the weights 𝑤𝑘 in (11) are chosen as the coefficients of the series expansion of the generating function 𝑤(𝑧) = ( 𝜌(1/𝑧) 𝜎(1/𝑧) ) 𝛽 , (12) where 𝜌, 𝜎 are the generating polynomials of the lmm for classical ivp. it is enough to consider generating functions in the form 𝛿(𝜉) = ( 𝑎(𝜉) 𝑏(𝜉) ) 𝛽 𝑝(𝜉) 𝑞(𝜉) , (13) h.m. nasir and khadija al-hassani 110 where 𝑎, 𝑏, 𝑝, and 𝑞 are polynomials, and 𝜉 = 1/𝑧 [10]. the generating function of an flmm completely characterizes the approximation scheme, its stability, and the order of consistency through the following theorems. theorem 1 [16, 17, 18]. the order of an flmm with generating function 𝛿(𝜉) is 𝑝 if and only if 1 𝑥𝛽 𝛿(𝑒 −𝑥 ) = 1 + 𝑂(𝑥 𝑝). (14) moreover, the approximation corresponding to 𝛿(𝜉) satisfies, with 𝐷𝑡 𝛽 denoting the rl fractional derivative, 𝛿ℎ 𝛽 𝑦(𝑡) = 𝐷𝑡 𝛽 𝑦(𝑡) + ℎ𝑝 𝑎𝑝(𝛽)𝐷𝑡 𝛽+𝑝 𝑦(𝑡) + ℎ𝑝+1𝑎𝑝+1(𝛽)𝐷𝑡 𝛽+𝑝+1 𝑦(𝑡)+. . ., where 𝑦(𝑡) is assumed to be sufficiently smooth. theorem 2 [10] the stability region of an flmm with generating function 𝛿(𝜉) is given by 𝑆 = {𝛿(𝜉): |𝜉| > 1}. (15) 2.2. subclasses of flmms we classify the flmms in the literature into subclasses. this classification suggests that the proposed flmm in this paper belongs to a new subclass. 1. the fractional trapezoid subclass: the fractional trapezoidal method of order 2 (ft2) obtained from the trapezoidal rule for the ode has the generating function [10] 𝛿𝐹𝑇2(𝜉) = (2 1−𝜉 1+𝜉 ) 𝛽 . (16) it is the only method known so far in the form 𝛿(𝜉) = ( 𝑎(𝜉) 𝑏(𝜉) ) 𝛽 with deg𝑏(𝜉) ≥ 1. 2. the fbdf subclass: the fractional backward difference formula (fbdf) [13] obtained from the bdf for classical ode has generating function of the form 𝛿(𝜉) = (𝑎(𝜉))𝛽 . for orders 1 ≤ 𝑚 ≤ 6, a set of six fbdf methods have been obtained with polynomials corresponding to the generating polynomials of the bdf of order 𝑚 given by 𝑎(𝜉) = ∑ 𝑚𝑘=1 1 𝑘 (1 − 𝜉)𝑘 . the second order fbdf2, for example, is given by [10] 𝛿𝐹𝐵𝐷𝐹2(𝜉) = ( 3 2 − 2𝜉 + 1 2 𝜉2) 𝛽 . (17) 3. fractional adams subclass: the fractional adams methods have the generating functions of the form 𝛿(𝜉) = (1−𝜉)𝛽 𝑞(𝜉) , where the polynomial 𝑞(𝜉) is determined to have order 𝑝 of consistency for the method [11— 14]. when 𝑞(0) = 0, the method is explicit and is called fractional adams-bashforth methods [13,14] while 𝑞(0) ≠ 0 gives implicit methods which are called fractional adams-moulton methods (fams)[12]. the second order fam method is given by the generating function. 𝛿𝐹𝐴𝑀1(𝜉) = (1−𝜉)𝛽 (1− 𝛽 2 )+ 𝛽 2 𝜉 . (18) 4. rational polynomial subclass: in [19], a classical lmm type of approximation is proposed to obtain a class of flmms by approximating the generating function of the fbdf methods by rational polynomials in the form 𝛿(𝜉) = 𝑝(𝜉) 𝑞(𝜉) . this approach, however, reduces the order of the methods and requires higher degree polynomials 𝑝 and 𝑞, to achieve orders close to the order of fbdf considered. 3. a new fractional linear multi-step method we present the main result of constructing an flmm of order 2 which belongs to a new subclass. we need the following lemma from the taylor series expansion. analysis of a new type of second-order fractional linear multi-step method 111 lemma 1 let 𝑦(𝑡) ∈ 𝐶1[𝑎, 𝑏] and 𝑦′′(𝑡) exists. then, for 𝜇 ∈ (𝑎, 𝑏) and ℎ > 0, we have 𝑦(𝑡 + 𝜇ℎ) = (1 + 𝜇)𝑦(𝑡) − 𝜇𝑦(𝑡 − ℎ) + 𝑂(ℎ2). (19) the fractional derivative of the fivp (1) (assuming with no loss 𝑡0 = 0 and 𝑦(𝑡0) = 0) is replaced by the approximation with super convergence (9) of order 2. this gives, at 𝑡 = 𝑡𝑛, 𝛿ℎ,𝛽/2 𝛽 𝑦(𝑡𝑛) = 1 ℎ𝛽 ∑ ∞𝑘=0 𝑔𝑘 (𝛽) 𝑦(𝑡𝑛−𝑘+𝛽/2) = 𝑓(𝑡𝑛, 𝑦(𝑡𝑛)) + 𝑂(ℎ 2). (20) since 𝛽/2 is not an integer for 0 < 𝛽 ≤ 1, the point 𝑡𝑛−𝑘+𝛽/2 in (20) is not aligned with the discrete points in the computational domain {𝑡𝑚, 𝑚 = 0,1, . . . , 𝑁}. using lemma 1 with 𝑡 = 𝑡𝑛−𝑘 and 𝜇 = 𝛽/2, we replace 𝑦(𝑡𝑛−𝑘+𝛽/2) by (19). 1 ℎ𝛽 ∑ ∞𝑘=0 𝑔𝑘 (𝛽) [(1 + 𝛽 2 ) 𝑦(𝑡𝑛−𝑘 ) − 𝛽 2 𝑦(𝑡𝑛−𝑘−1)] = 𝑓(𝑡𝑛, 𝑦(𝑡𝑛)) + 𝑂(ℎ 2). (21) with the notations in (7), we obtain the new implicit flmm approximation scheme δℎ,𝛽/2 𝛽 𝑦𝑛 : = ∑ 𝑛 𝑘=0 𝑔𝑘 (𝛽) [(1 + 𝛽 2 ) 𝑦𝑛−𝑘 − 𝛽 2 𝑦𝑛−𝑘−1] = ℎ 𝛽 𝑓𝑛, 𝑛 = 1,2, ⋯, (22) where the function values 𝑦𝑛−𝑘 and 𝑦𝑛−𝑘+1 are properly aligned with the grid points in the computational domain. theorem 3 the generating function of the new implicit flmm is given by 𝛿(𝜉) = (1 − 𝜉)𝛽 𝑝(𝜉), (23) where 𝑝(𝜉) = (1 + 𝛽 2 ) − 𝛽 2 𝜉. moreover, the generating function satisfies 1 𝑥𝛽 𝛿(𝑒 −𝑥 ) = 1 + 𝑂(𝑥 2) confirming order 2 consistency. proof. the sum on the left side of (21) is manipulated, with 𝑝0 = 1 + 𝛽/2 and 𝑝1 = −𝛽/2, as follows: ∑ ∞𝑘=0 𝑔𝑘 (𝛽) (𝑝0𝑦𝑛−𝑘 + 𝑝1𝑦𝑛−𝑘−1) = 𝑝0 ∑ ∞ 𝑘=0 𝑔𝑘 (𝛽) 𝑦𝑛−𝑘 + 𝑝1 ∑ ∞ 𝑘=0 𝑔𝑘 (𝛽) 𝑦𝑛−𝑘−1 = 𝑝0 ∑ ∞ 𝑘=0 𝑔𝑘 (𝛽) 𝑦𝑛−𝑘 + 𝑝1 ∑ ∞ 𝑘=1 𝑔𝑘−1 (𝛽) 𝑦𝑛−𝑘 = ∑ ∞ 𝑘=0 (𝑝0𝑔𝑘 (𝛽) + 𝑝1𝑔𝑘−1 (𝛽) )𝑦𝑛−𝑘 , (24) where we have set 𝑔−1 (𝛽) = 0. the weights 𝑤𝑘 = 𝑝0𝑔𝑘 (𝛽) + 𝑝1𝑔𝑘−1 (𝛽) , 𝑘 = 0,1, . .. (25) are the coefficients of the generating function 𝛿(𝜉) = 𝑝0(1 − 𝜉) 𝛽 + 𝑝1𝜉(1 − 𝜉) 𝛽 = (1 − 𝜉)𝛽 (𝑝0 + 𝑝1 𝜉). moreover, we have 1 𝑥𝛽 𝛿(𝑒 −𝑥 ) = 1 − 𝛽(3𝛽+5) 24 𝑥 2 + 𝑂(𝑥 3) which, by theorem 1, confirms the order 2 consistency of the method. the generating function for the new flmm is of the form (23) and is different from those subclasses listed in subsection 2.2. therefore, it can be considered to belong to a new subclass in the family of flmms. the notion of super-convergence and nodal alignment have been applied for space fractional diffusion equations in [15] and [20]. the fractional adam-moulton method (fam1) [12] of order 2 derived from fractional newton-gregory functions and taylor series expansion methods, can also be derived from the super-convergence of the grünwald approximation in the form 1 ℎ𝛽 ∑ ∞𝑘=0 𝑔𝑘 (𝛽) 𝑦(𝑡𝑛−𝑘 ) = 𝑓𝑛−𝛽/2 + 𝑂(ℎ 2) by replacing the right-hand side with the respective second-order approximations 𝑓𝑛−𝛽/2 = (1 − 𝛽 2 ) 𝑓𝑛 + 𝛽 2 𝑓𝑛−1 + 𝑂(ℎ 2). (26) h.m. nasir and khadija al-hassani 112 the generating function for the fam1 is thus given by (18). dimitrov et al. [21] formulated an order 2 scheme with super-convergence from asymptotic expansions of the superconvergence. however, the non-aligned points of super-convergence have not been re-aligned in their work. to the knowledge of the authors, the application of super-convergence of grünwald approximation for time-fractional differential equations with re-alignments of the super-convergence point has not appeared before in the literature. the following theorem relates the proposed flmm scheme (22) with the fbdf of order 2 by lubich [10] and the fam1 of order 2 by galeone and garrappa [12]. theorem 4 when 𝛽 → 1, 1. the new flmm converges to the bdf2 method of order 2 for the classical ode by generating polynomial 𝛿(𝜉) = 3 2 − 2𝜉 + 1 2 𝜉2. 2. the fam1 converges to the fractional trapezoid method of order 2 with generating function 𝛿(𝜉) = 2 1−𝜉 1+𝜉 . proof. immediate by substituting 𝛽 = 1 in (18) and (16) respectively. 3.1. implementation here, we give two algorithms to compute the approximate solutions for the fivp for linear and non-linear cases respectively using the new flmm. for brevity, we use the following notations: for a sequence 𝑎 = {𝑎𝑘 }, the vector slice [𝑎𝑖 , 𝑎𝑖 + 1, … , 𝑎𝑗 ] is denoted by 𝑎𝑖:𝑗 . the convolution of two vectors 𝑎, 𝑏 of size 𝑛 + 1 is denoted by 𝑎 ∗ 𝑏 = ∑ 𝑛 𝑘=0 𝑎𝑘 𝑏𝑛−𝑘. we reformulate the new flmm scheme (22) with (24) and (25) as ∑ 𝑛𝑘=0 𝑤𝑘 𝑦𝑛−𝑘 = 𝑤0:𝑛 ∗ 𝑦0:𝑛 = 𝑤0𝑦𝑛 + 𝑤1:𝑛 ∗ 𝑦0:𝑛−1 = ℎ 𝛽 𝑓𝑛. (27) in the case of linear fivp, we have 𝑓(𝑡, 𝑦) = 𝜆𝑦(𝑡) + 𝑠(𝑡) for some constant 𝜆 and function 𝑠(𝑡). the scheme (27) for this case, with 𝑠𝑛 = 𝑠(𝑡𝑛), is then 𝑤0𝑦𝑛 + 𝑤1:𝑛 ∗ 𝑦0:𝑛−1 = ℎ 𝛽 (𝜆𝑦𝑛 + 𝑠𝑛 ) which gives 𝑦𝑛 = 1 𝑤0 − 𝜆ℎ 𝛽 [ℎ𝛽 𝑠𝑛 − 𝑤1:𝑛 ∗ 𝑦0:𝑛−1], 𝑛 = 1,2, . .. . algorithm 1 is given for the linear fivp. algorithm 1 (for linear fivp) 1. define 𝑠(𝑡) (for 𝑓(𝑡, 𝑦) = 𝜆𝑦 + 𝑠(𝑡)). 2. input 𝛽, 𝜆, ℎ, and 𝑁. 3. define 𝑔 with 𝑔0 = 1, 𝑔𝑛 = (1 − 𝛽+1 𝑛 ) 𝑔𝑛−1, 𝑛 = 1,2, … , 𝑁. 4. define 𝑝 = [1 + 𝛽/2, −𝛽/2]. 𝑤0:𝑁 == {𝑝 ∗ 𝑔𝑘−1:𝑘 , 𝑘 = 0,1, … , 𝑁}. 5. define array 𝒚 = {𝑦𝑘 , 𝑘 = 0,1, … , 𝑁} and set 𝑦0 = 0. 6. for 𝑛 = 1,2, … , 𝑁 𝑦𝑛 = 1 𝑤0 − 𝜆ℎ 𝛽 [ℎ𝛽 𝑠(𝑡𝑛) − 𝑤1:𝑛 ∗ 𝑦0:𝑛−1]. 7. return 𝒚. for non-linear fivp, the non-linear equation (27) in 𝑦𝑛 needs to be solved for the unknown 𝑦𝑛 . the newtonraphson method numerically solves this with an initial seed 𝑦𝑛,0 = 𝑦𝑛−1. algorithm 2 is given for the non-linear fivp. algorithm 2 (for non-linear fivp) 1. define 𝑓(𝑡, 𝑦), 𝑓𝑦 (𝑡, 𝑦). 2. input 𝛽, ℎ, and 𝑁. 3. define 𝑔 with 𝑔0 = 1, 𝑔𝑛 = (1 − 𝛽+1 𝑛 ) 𝑔𝑛−1, 𝑛 = 1,2, … , 𝑁. 4. define 𝑝 = [1 + 𝛽/2, −𝛽/2] . 𝑤0:𝑁 = {𝑝 ∗ 𝑔𝑘−1:𝑘 , 𝑘 = 0,1, … , 𝑁}. 5. define array 𝒚 = {𝑦𝑘 , 𝑘 = 0,1, … , 𝑁} and set 𝑦0 = 0. 6. 𝑇𝑜𝑙𝑒𝑟𝑒𝑛𝑐𝑒 = 10−15, 𝐸𝑟𝑟𝑜𝑟 = 108 . 7. for 𝑛 = 1,2, … , 𝑁 𝑥0 ← 𝑦𝑛−1. 𝑐𝑛 = 𝑤1:𝑛 ∗ 𝑦0:𝑛−1. 𝐸𝑟𝑟𝑜𝑟 > 𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 𝐹 = 𝑤0𝑥0 − ℎ 𝛽 𝑓(𝑡𝑛, 𝑥0) + 𝑐𝑛 . 𝐽𝐹 = 𝑤0 − ℎ 𝛽 𝑓𝑦(𝑡𝑛, 𝑥0). 𝑦𝑛 = 𝑥0 − 𝐹 𝐽𝐹 . 𝐸𝑟𝑟𝑜𝑟 = |𝑦𝑛 − 𝑥0|. 𝑥0 ← 𝑦𝑛 . 8. return 𝒚. analysis of a new type of second-order fractional linear multi-step method 113 table 1. computational order of the new flmm for example 1. 𝛽 = 0.4 𝛽 = 0.8 𝛽 = 1.0 𝑀 max. error order max error order max error order 8 6.533e-03 – 1.803e-02 – 2.538e-02 – 16 1.882e-03 1.79544 5.319e-03 1.76094 7.569e-03 1.74543 32 5.052e-04 1.89743 1.449e-03 1.87619 2.078e-03 1.86499 64 1.309e-04 1.94874 3.783e-04 1.93741 5.448e-04 1.93116 128 3.330e-05 1.97438 9.665e-05 1.96858 1.395e-04 1.96533 256 8.400e-06 1.98720 2.443e-05 1.98427 3.530e-05 1.98261 512 2.109e-06 1.99360 6.140e-06 1.99213 8.879e-06 1.99130 1024 5.285e-07 1.99680 1.539e-06 1.99606 2.227e-06 1.99564 2048 1.323e-07 1.99840 3.853e-07 1.99803 5.575e-07 1.99782 4096 3.309e-08 1.99920 9.640e-08 1.99902 1.395e-07 1.99891 table 2. computational order of the new flmm for example 2. 𝛽 = 0.4 𝛽 = 0.8 𝛽 = 1.0 𝑀 max. error order max error order max error order 8 1.698e-01 – 7.835e-02 – 6.985e-02 – 16 2.779e-02 2.61128 1.978e-02 1.98599 1.769e-02 1.98155 32 6.648e-03 2.06349 5.060e-03 1.96667 4.466e-03 1.98563 64 1.663e-03 1.99866 1.286e-03 1.97645 1.122e-03 1.99286 128 4.186e-04 1.99047 3.245e-04 1.98628 2.812e-04 1.99660 256 1.052e-04 1.99271 8.155e-05 1.99260 7.037e-05 1.99836 512 2.638e-05 1.99566 2.044e-05 1.99616 1.760e-05 1.99920 1024 6.605e-06 1.99764 5.117e-06 1.99804 4.402e-06 1.99960 2048 1.653e-06 1.99877 1.280e-06 1.99901 1.101e-06 1.99980 4096 4.133e-07 1.99938 3.202e-07 1.99950 2.752e-07 1.99990 4. numerical tests we used the new flmm to compute approximate solutions of the fivp (1) with a linear and a non-linear source function 𝑓(𝑡, 𝑦) in the time interval [0,1]. example 1: 𝐶 𝐷0 𝛽 𝑦(𝑡) = γ(𝑚 + 1) γ(𝑚 + 1 − 𝛾) 𝑡 𝑚−𝛾 − γ(𝑚) γ(𝑚 − 𝛾) 𝑡 𝑚−1−𝛾 + 𝜆𝑦(𝑡) + 𝑡 𝑚 − 𝑡 𝑚−1, 𝑦(0) = 0, where 𝜆 = −1 and we set 𝑚 = 5. the exact solution is given by 𝑦(𝑡) = 𝑡 𝑚 − 𝑡 𝑚−1. example 2: 𝐶 𝐷0 𝛽 𝑦(𝑡) = γ(2𝛽 + 5) γ(𝛽 + 5) 𝑡𝛽+4 − 240 γ(6 − 𝛽) 𝑡 (5−𝛽) + (𝑡 2𝛽+4 − 2𝑡 5)2 − 𝑦(𝑡)2, 𝑦(0) = 0, with exact solution 𝑦(𝑡) = 𝑡 2𝛽+4 − 2𝑡 5. the problems are solved for fractional order values 𝛽 = 0.4,0.8 and 1.0. the computational domain for both problems are {𝑡𝑛 = 𝑛/𝑀, 𝑛 = 0,1, ⋯ , 𝑀} and step size ℎ = 1/𝑀, where 𝑀 is the number of subintervals of the problem domain [0,1]. the problems were solved for 𝑀 = 2𝑗 , 𝑗 = 3,4, . . . ,12. the computational order of the new flmm method is computed by the formula 𝑝𝑗+1 = log(𝐸𝑗+1/𝐸𝑗 )/log(ℎ𝑗+1/ℎ𝑗 ) where 𝐸𝑗 , ℎ𝑗 are the merror and the step size for 𝑀 = 2 𝑗. h.m. nasir and khadija al-hassani 114 tables 1 and 2 list the maximum errors and computational orders for examples 1 and 2 respectively for various grid sizes 𝑀 = 8,16, . . . ,4096. the computational orders confirm the theoretical order 2 of the new flmm. 5. analysis of linear stability for the analysis of the stability of an flmm, we have the following preparations. the analytical solution to the test problem 𝐶 𝐷𝑡 𝛽 𝑦(𝑡) = 𝜆𝑦(𝑡), 𝑦(0) = 𝑦0 is given by 𝑦(𝑡) = 𝐸𝛽 (𝜆𝑡 𝛽 )𝑦0 , where 𝐸𝛽 (⋅) is the mittag-leffler function 𝐸𝛽 (𝑥) = ∑ ∞ 𝑘=0 𝑥 𝑘 γ(𝛽𝑘 + 1) . the analytical solution 𝑦(𝑡) of the test problem is stable in the sense that it vanishes in the 𝛽𝜋-angled region σ𝛽 = {𝜉 ∈ ℂ: |arg(𝜉)| > 𝛽𝜋 2 }, where the angle 𝛽𝜋/2 is measured from the positive real axis. the analytical unstable region is thus the infinite wedge {𝜉 ∈ ℂ: |arg(𝜉)| ≤ 𝛽𝜋 2 } = ℂ\σ𝛽 . for the numerical stability of flmm, we have the following criteria: definition 1 let 𝑆 be the numerical stability region of an flmm. for an angle, 𝛼, define the sector 𝑆(𝛼) = {𝜉: |𝜋 − arg(𝜉)| < 𝛼}, where the angle 𝛼 is measured from the negative real axis. the flmm is said to be 1. 𝐴(𝛼)-stable if 𝑆(𝛼) ⊆ 𝑆. 2. 𝐴-stable if it is 𝐴(𝜋 − 𝛽𝜋/2)-stable. that is, σ𝛽 ⊆ 𝑆. 3. unconditionally stable if it is 𝐴(0)-stable. that is if the negative real line (−∞, 0) ⊆ 𝑆. we analyze the stability of the new flmm through its stability region 𝑆 = {𝛿(𝜉) = (1 − 𝜉)𝛽 𝑝(𝜉): |𝜉| > 1} = ℂ\𝑆 𝑐 , where 𝑆 𝑐 = {𝛿(𝜉) = (1 − 𝜉)𝛽 𝑝(𝜉): |𝜉| ≤ 1} is the unstable region. theorem 5 the unstable region 𝑆 𝑐 is bounded and symmetric about the real axis. moreover, for 0 < 𝛽 ≤ 1, if the imaginary part of 𝜉, ℑ(𝜉) > 0, then the real part ℜ(𝛿(𝜉)) > 0 and ℑ(𝛿(𝜉)) < 0. proof. for the boundedness of 𝑆 𝑐, we see that for |𝜉| ≤ 1, |𝛿(𝜉)| ≤ (1 + |𝜉|)𝛽 [(1 + 𝛽 2 ) + 𝛽 2 |𝜉|] ≤ 2𝛽 (1 + 𝛽) < ∞. for the symmetry about the real axis, we immediately see that 𝛿(𝜉)̅ = 𝛿(𝜉). for 𝜉 = 𝑒 𝑖𝜃 , we have 1 − 𝜉 = (𝑒 − 𝑖𝜃 2 − 𝑒 𝑖𝜃 2 ) 𝑒 𝑖𝜃 2 = 2𝑖sin 𝜃 2 𝑒 𝑖𝜃 2 = 2sin 𝜃 2 𝑒 𝑖( 𝜃 2 − 𝜋 2 ) =: 𝑏𝑒 𝑖𝜙 , where 𝜙 ≡ 𝜙(𝜃) = 𝜃 2 − 𝜋 2 and 𝑏 ≡ 𝑏(𝜃) = 2sin 𝜃 2 = 2cos𝜙 > 0 for 0 < 𝜃 < 2𝜋. now, writing 𝛿(𝜉) = (1 − 𝜉)𝛽 + 𝛽/2(1 − 𝜉)𝛽+1, we have for the real part of 𝛿(𝜉), ℜ(𝛿(𝜉)) = 𝑏𝛽 [cos𝛽𝜙 + 𝛽cos𝜙cos(𝛽 + 1)𝜙] =: 𝑏𝛽 𝑔(𝜃) (28) where, with some trigonometric manipulations, 𝑔(𝜃) = (1 + 𝛽 2 ) cos𝛽𝜙 + 𝛽 2 cos(𝛽 + 2)𝜙. analysis of a new type of second-order fractional linear multi-step method 115 now, 𝑔′(𝜃) = −𝛽 (1 + 𝛽 2 ) [sin𝛽𝜙 + sin(𝛽 + 2)𝜙]𝜙′ = − 1 2 𝛽(2 + 𝛽)sin(𝛽 + 1)𝜙cos𝜙 > 0, because, for 0 < 𝜃 < 𝜋, 𝜙 ∈ (−𝜋/2,0) where cos𝜙 > 0 and (𝛽 + 1)𝜙 ∈ [− (𝛽+1)𝜋 2 , 0] in the quadrants iii and iv for 0 < 𝛽 ≤ 1 where sin(𝛽 + 1)𝜙 < 0. hence, 𝑔(𝜃) is increasing with 𝑔(0) = cos(𝛽𝜋/2) > 0. thus, 𝑔(𝜃) > 0 for 0 < 𝜃 < 𝜋. it then follows from the symmetry that ℜ(𝛿(𝜉)) = ℜ(𝛿(𝜉)̅) > 0 . for the imaginary part of 𝛿(𝜉), ℑ(𝛿(𝜉)) = 𝑏𝛽 [sin𝛽𝜙 + 𝛽cos𝜙sin(𝛽 + 1)𝜙] =: 𝑏𝛽 ℎ(𝜃) < 0, (29) because, when 0 < 𝜃 < 𝜋, we see that 𝜙 and 𝛽𝜙 are in the quadrant iv where cos𝜙 > 0 and sin𝛽𝜙 < 0, and (𝛽 + 1)𝜙 is in the quadrants iii and iv where sin(𝛽 + 1)𝜙 < 0. this gives ℑ(𝛿(𝜉(𝜃)) < 0 for 0 < 𝜃 < 𝜋. when 𝜋 < 𝜃 < 2𝜋, we again see that 𝜙 and 𝛽𝜙 are in quadrant i where cos𝜙 > 0 and sin𝛽𝜙 > 0, and (𝛽 + 1)𝜙 is in the quadrants i and ii where sin(𝛽 + 1)𝜙 > 0. this gives ℑ(𝛿(𝜉(𝜃)) > 0 for 𝜋 < 𝜃 < 2𝜋. and the proof is completed. theorem 5 tells us that the new flmm is 𝐴( 𝜋 2 )-stable for 0 < 𝛽 ≤ 1. we have a stronger result. theorem 6 the flmm in (22) is 𝐴-stable for 0 < 𝛽 ≤ 1. proof. from (28) and (29), the tangent at 𝜃 ∈ [0, 𝜋] on the stability region boundary {𝛿(𝜉): |𝜉| = 1} is ℎ(𝜃)/𝑔(𝜃) with its derivative given by 𝑑 𝑑𝜃 ℎ(𝜃) 𝑔(𝜃) = 𝛽(𝛽 + 1)(𝛽 + 2)cos2𝜙 2(𝑔(𝜃))2 > 0. thus, the tangent is monotonically increasing in [0, 𝜋] with minimum at 𝜃 = 0, (ℎ/𝑔)(0) = −tan(𝛽𝜋/2). therefore, from the symmetry, the unstable region is contained in the wedge {𝜉: |arg(𝜉)| ≤ 𝛽𝜋 2 } = ℂ\σ𝛽 meaning that the new flmm is 𝐴-stable. the 𝐴-stability confirms that, for 0 < 𝛽 ≤ 1, our new flmm is 𝐴(𝜋/2)-stable and hence unconditionally stable. figure 1. unstable regions and 𝐴-stable tangent boundaries for the new flmm in (23). in figure 1, the unstable regions and the a-stable tangent boundaries of the new flmm given by the generating function (23) for fractional order values 𝛽 = 0.25,0.5,0.75,1 are shown. note that the unstable region for a generating function 𝛿(𝜉) is given by the graph (see also (15) ) h.m. nasir and khadija al-hassani 116 𝑆 𝑐 = {𝛿(𝜉): |𝜉| ≤ 1}. 6. comparison of stability regions we compare the stability regions of previously established implicit flmms of order 2 with our new flmm which we now denote by nflmm2 for want of an abbreviation. for this, we consider the lubich’s fractional backward difference method fbdf2 [10], the fractional adamsmoulton method fam1 [6] and the fractional trapezoid rule [10, 22] given by their respective generating functions in (17), (18) and (16). (a) 𝛽 = 0.25 (b) 𝛽 = 0.50 (c) 𝛽 = 0.75 (d) 𝛽 = 0.90 figure 2. comparing the unstable regions of fam1, nflmm2 and fbdf2 for various 𝛽. in figure 2, the unstable regions for these flmms and our nflmm2 are shaded for various values of 𝛽. note that the straight lines in the figures depict the boundary of the stability region of the ft2 method in which the left sides of the lines are the stability region which also corresponds to the boundary of the analytical stability regions σ𝛽 . the unstable regions of ft2 are not shaded for clarity. the advantage of our nflmm2, in terms of the unstable regions (ur), is that the ur of the nflmm2 is smaller than that of the fam1 and is very much closer to the ur of the fbdf2. also, the ur of the ft2 is the largest among all the urs. we note this from the observation that the unstable regions (see also the figures in figure 2) satisfy the ordering 𝛿𝐹𝐵𝐷𝐹2(−1) < 𝛿𝑁𝐹𝐿𝑀𝑀2(−1) < 𝛿𝐹𝐴𝑀1(−1) < 𝛿𝐹𝑇2(−1) = +∞. the computational costs of all the flmms of order 2 in the general form (11) are the same. therefore, the efficiency of the methods is measured by the computational cost of the weights 𝑤𝑘 in (11). the weights 𝑤𝑘 of nflmm2 have the simplest computational effort as they involve only a linear combination of the grünwald weights 𝑔𝑘 (𝛽) given in (25) which can be recursively computed by (5) with only one previous weight. analysis of a new type of second-order fractional linear multi-step method 117 in contrast, the weights of fbdf2 require computations using miller’s formula (see eg. [12] ) with two previous weights. the weights of fam1 require more effort as its generating function involves a rational function. however, in this case, the right-hand side of the fam1 scheme has the form (26) with almost the same computational effort as nflmm2. nevertheless, the right-hand side of this scheme requires two coefficients and two values of the function 𝑓(𝑡, 𝑦) requiring an additional memory [6]. finally, computing the weights for ft2 needs more effort as it requires the first 𝑛 coefficients of its generating function and fft [12]. 7. conclusion we proposed and analyzed a new flmm of order two for fivps that falls under a new subclass of flmm. the new flmm is as 𝐴-stable as the other known order two methods. however, the proposed method has a larger stability region than that of the fam1 and ft2 methods. the computational cost of the nflmm2 is better than that of the fbdf2 method, whereas the fam1 requires an additional memory requirement in its iterations. hence, the proposed method can be considered competitive with the other methods of order 2 in terms of stability and/or computational cost. conflict of interest the authors declare no conflict of interest. acknowledgment the authors are grateful for the reviewers' constructive comments and suggestions to improve the presentation of the paper and to dr. kamel nafa for the proofreading and corrections. references 1. diethelm, k. the analysis of fractional differential equations: an application-oriented exposition using differential operators of caputo type. springer science and business media, 2010. 2. brandibur, o., garrappa, r., and kaslik, e. stability of systems of fractional-order differential equations caputoaputo derivatives. mathematics 2021, 9(8), 914-933. https://doi.org/10.3390/math9080914. 3. jia, j., huang, x., li, y., cao, j., and alsaedi, a. global stabilization of fractional-order memristor-based neural networks with time delay. ieee transactions on neural networks and learning 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quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives. numerical methods for partial differential equations, 2015, 31(5), 1345-1381. 21. dimitrov, y., miryanov, r., and todorov, v. asymptotic expansions and approximations for the caputo derivative. computational and applied mathematics, 2018, 37, 4, 5476-5499. 22. garrappa, r. trapezoidal methods for fractional differential equations: theoretical and computational aspects. mathematics and computers in simulation, 2015, 110, 96-112. received 29 april 2022 accepted 5 september 2022 squ journal for science, 2023, 28(1), 42-52 doi:10.53539/squjs.vol28iss1pp42-52 sultan qaboos university 42 adsorption of methylene blue onto hydrophobic activated carbon said m. al-mashaikhi, el-said i. el-shafey*, saleh al-busafi, fakhreldin o. suliman department of chemistry, college of science, sultan qaboos university, p.o. 36, al-khod 123, muscat, sultanate of oman. *email: elshafey@squ.edu.om. abstract: activated carbon (ac) was prepared from date palm leaflets using naoh activation. ac was oxidized using concentrated hno3 to produce oxidized activated carbon (on). alkylamines including methylamine (m), dimethylamine (dm), ethylamine (e), diethylamine (de), and diisopropylamine (dip) were covalently immobilized onto on to produce onm, ondm, one, onde, and ondip hydrophobic activated carbons, respectively. the surface area of ac (588 m 2 /g) decreased on oxidation with a further decrease on functionalization. these carbons were tested for methylene blue (mb) adsorption. an initial ph 7 was found to be optimum for the adsorption of mb. the hydrophobic activated carbons showed faster adsorption (except for onde), than ac with adsorption data following a pseudo-second-order kinetic model. the rate of adsorption increased with increasing temperature. the activation energy, ea, was less than 42 kj/mol indicating physical adsorption. equilibrium adsorption follows an l-type isotherm with the adsorption data following the langmuir model. the adsorption capacity of mb follows the order of ondip > one > ondm > ac > on > onm > onde. thermodynamic parameters indicate spontaneous and endothermic adsorption. carbon reuse for mb adsorption was more efficient for ondip, one, and ondm than ac. keywords: activated carbon; methylene blue; alkylamine; hydrophobic; adsorption. المثيليين األزرق على الكربون النشط الكاره للماء امتزاز ، صالح البوصافي، فخر الدين سليمان ييد الشافععسعيد المشايخي، الس حمض باستخدام تم أكسدة الكربون المنشطومن وريقات نخيل التمر باستخدام تنشيط هيدروكسيد الصوديوم. (ac) تم تحضير الكربون المنشط :صلخمال ، وثنائي ميثيل أمين (m) بما في ذلك ميثيل أمينإلنتاج الكربون الكاه للماء أمينات األلكيل تثبيت. تم (on) مؤكسدالكربون ال المركز إلنتاج النيتريك (dm) وإيثيل أمين ، (e) وثنائي إيثيل أمين ، (de) وثنائي أيزوبروبيل أمين ، (dip) نتاجإلتساهميًا onm و ، ondm و ، one و ، onde ، متر 855وتبين أن مساحة السطح للكربون النشط ). علي التوالي ل ondip و 2 تم /جرام( قد انخفضت باألكسدة وانخفضت أكثر مع تثبيت األلكيل أمين. و ق. تُظهر الكربونات المنشطة الميثيلين األزر زازاألمثل المتهو 7الرقم الهيدروجيني األولي .ووجد أن الميثيلين األزرق زالةال الناتج اختبار الكربون معدل . وقد زادحركي من الدرجة الثانيةالنموذج ال زازبيانات االمتاتباع مع ac من (onde) باستثناءللميثلين األزرق أسرع زازاالكارهة للماء امت l النوع تزانالفيزيائي. يتبع امتزاز اإل زازلى االمتكيلو جول / مول مما يشير إ 22طاقة التنشيط أقل من وتبين أناالمتزاز مع ارتفاع درجة الحرارة. <ondip> one> ondm> ac> on> onm ب :ترتيالتتبع الميثيلين األزرق امتزازسعة النجمير.ووجد أن نموذجلبيانات االمتزاز واتباع onde ا أسرع وأكثر لـتزازالكربون امت تدويردراسة ص للحرارة. أظهرت اوم تلقائي زازالديناميكية الحرارية إلى امت دراسةتشير .و ondip و one و ondm مقارنةً بالكربون المنشط. إمتزاز -الكيل أمين -الميثيلين االزرق -الكاره للمياه -الكربون النشط :مفتاحيةالكلمات ال adsorption of methylene blue onto hydrophobic activated carbon 43 1. introduction yes are toxic pollutants and can cause a threat to aquatic organisms and human health. recent data shows that there are more than 100,000 commercial dyes, with an annual production of over 70,000 tonnes/year [1,2]. the textile industry utilizes more than 10,000 tonnes of dyes every year from which 100 tonnes are discharged into the environment [2,3]. most of these dyes are toxic to the aquatic environment. their complex chemical structures make them resistant to degradation by light, heat, and oxidizing agents, increasing the danger of this type of chemicals [4-6]. the toxicity of azo dyes arises from the presence of amines, while the color of anthraquinone dyes remains in effluents for a long time as they are resistant to degradation. in addition, the high solubility of reactive dyes and their chemical stability in water causes serious problems for the aquatic environment [7]. in aquatic ecosystems, photosynthetic activity is affected by decreasing light penetration [2]. moreover, these harmful materials are carcinogenic to various fish species. dyes can cause damage to human health and reduce the effectiveness of the reproductive system, kidneys, brain, liver, and central nervous system [6, 8]. typical methods used for the removal of dyes from water include ozonation [9], photocatalytic degradation [10,11], advanced oxidation [12], microbial biodegradation [13], coagulation and flocculation [14], filtration and membrane-filtration processes [15]. such methods have the essential limitations of being complex and uneconomic [16]. adsorption has proven superior to other techniques in terms of flexibility, simplicity of design, and initial cost [17]. in previous studies activated carbon prepared from pepper stems showed an adsorption capacity of 174 mg/g with the best performance at ph 8.0 [18] and activated carbon prepared from date palm leaves using koh activation showed 270 mg/g, while after ethylamine functionalization the capacity increased to 393 mg/g with best performance at ph 7 [19]. dehydrated carbon at ph 7 had a capacity of 196 mg/g, and after functionalization using ethylamine showed 296 mg/g [20]. other adsorbents have also been used including clay [21], zeolite [22], bentonite [6], and biosorbents [23]. in this study, ac was prepared from date palm leaflets using naoh activation. ac was oxidized, using nitric acid, and was surface functionalized using alkylamines with different sizes of the alkyl groups via amide coupling to produce hydrophobic activated carbons. these carbons were tested for the removal of methylene blue (mb) from the aqueous solution in terms of kinetics and equilibrium. the effect of the different sizes of alkyl amines on the extent of functionalization and its performance towards methylene blue adsorption is a novel area of study and is discussed in this paper. 2. materials and methods 2.1 materials the chemicals used were of analytical grade. activated carbon (ac) was prepared from clean dried date palm leaves using naoh activation. ac was oxidized using concentrated nitric acid at 80 o c to produce oxidized activated carbon (on). on was covalently functionalized using methylamine (m), dimethylamine (dm), ethylamine (e), diethylamine (de), and diisopropylamine (dip) via amide coupling to produce the hydrophobic activated carbons: onm, ondm, one, onde, and ondip, respectively. the study of ac preparation, surface functionalization, and characterization was carried out in our laboratories, and published previously [24]. the stock solution of methylene blue (mb) (1000 mg/l) was prepared in deionized water. the standards and adsorption test solutions were prepared by suitable dilution in deionized water. 2.1 effect of ph on mb adsorption to investigate the effect of ph on mb adsorption, ~ 0.06 g of carbon was mixed with 25 ml of mb solution (100 mg/l) in clean glass vials at different initial ph values of 3.0-9.0. before the addition of the pre-weighed adsorbent, the ph was adjusted using a few drops of dilute naoh or hcl. at 20 o c, the samples were shaken regularly until equilibrium was reached. residual mb was analyzed using a varian/cary/50 conc uv-visible spectrophotometer at λmax 665 nm with deionized water as blank. for all carbons, initial ph 7 was found optimal for mb adsorption and, thus, was selected for the kinetic, equilibrium, and carbon recycle studies of mb adsorption. 2.2 kinetics of mb adsorption in the kinetic experiments, 0.12 g of carbon was mixed with 50 ml of mb solution (100 mg/l) at initial ph of 7. the adsorption vessels were shaken mechanically for 48 hours. at different time intervals, aliquots of supernatant were withdrawn and analyzed. the kinetic experiments were carried out at 20 and 40 o c. 2.3 equilibrium adsorption the equilibrium studies were carried out by mixing ~ 0.06 g of carbon with 25 ml of mb solution (50 – 1000 mg/l) at initial ph 7 at two temperatures of 20 and 40 o c. the adsorption vessels were kept under mechanical agitation until equilibrium was reached. residual mb was withdrawn and analyzed. d said al-mahaikhi et al. 44 2.4 adsorbent recycle for mb recovery, 0.12 g of carbon was added to 50 ml of mb solution (100 ppm) at initial ph 7 and was kept for 48 hours under agitation until equilibrium was reached. after equilibrium, samples were separated for analysis. the adsorbent was washed with a boiling solution of sodium hydroxide at ph 10 followed by deionized water. the samples were washed with dilute hcl to neutralize residual naoh, followed by deionized water until the adsorbent was acidfree. the carbon was partially dried and transferred carefully to a new adsorption vessel containing 50 ml of mb solution under the same conditions as the first adsorption cycle (100 ppm, ph 7). the adsorption mixture was left under agitation until equilibrium was reached and samples of mb were separated for analysis. residual mb concentration was determined using a varian/cary/50 conc uv-visible spectrophotometer at λmax of 665 nm with deionized water as blank. all the experiments and analysis were carried out at least twice. 3. results and discussion the study of ac preparation, surface oxidation, and functionalization using different alkylamines was carried out in our laboratories and published elsewhere, and included the carbons tested in this study [24]. a schematic representation of the seven carbons under investigation is presented in figure 1. fourier transform infrared (ftir), carbon, hydrogen, and nitrogen analysis (chn), and thermogravimetric analysis (tga) showed that surface functionalization was successful [24]. the surface areas for the carbons were 588, 259.3, 217.6, 150.3, 108.8, 93.2, and 72.0 for ac, on, onm, ondm, one, onde, and ondip, respectively. the extent of functionalization followed the order onm > ondm > one > onde > ondip [24] that corresponds to the size of the alkylamine immobilized. figure 1. schematic representation of (a) ac, (b) on, (c) onm, (d) ondm, (e) one, (f) onde, and (g) ondip [24]. oh oh oh n n n n o o o o o n oh (a) (b) (c) (d) (e) (f) (g) (f) adsorption of methylene blue onto hydrophobic activated carbon 45 as the size of alkylamine increases, the functionalization decreases due to steric effects [24]. these seven carbons were tested for mb adsorption in this study. 3.1 effect of ph on methylene blue adsorption the adsorption of mb depends on the ph of the aqueous solution. the amount of mb adsorbed was calculated from equation 1. qe = (co-ce)v/m eq. (1) where qe is mb adsorbed (mg/g) at equilibrium, co, and ce are initial and equilibrium mb concentration (mg/l), v is the volume in l, and m is the mass of adsorbent (g). as mb is a cationic dye regardless of the ph of the solution, the variation of mb adsorption with initial ph is mostly related to the surface properties at different ph values. as shown in figure 2a, mb adsorption remains almost constant for ac, onm, ondm, one, and ondip regardless of the initial ph values. however, for on and onde, a slight decrease at low ph was observed. the insignificant variation of mb adsorption onto onm, ondm, one, and ondip is related to the dominance of hydrophobic interaction forces between the hydrophobic surface and mb. however, mb adsorption onto ac is dominated by van der waals’ interaction forces, and  interactions [25]. mb adsorption onto on (phzpc 3.38 [24]) shows low adsorption at ph 3. at this ph, the surface is protonated and neutral. however at higher ph, adsorption increases and remains constant in the range of ph 7-9. in that range of ph, electrostatic interaction between the negatively charged on surface and mb cations dominate the adsorption process. thus, ph 7.0 was selected for further studies. one and ondip show higher mb adsorption than ac or on. onde shows less adsorption due to the limited extent of functionalization, selfadsorption, and entangling of immobilized diethylamine chains [24]. the final ph against the initial ph is presented in figure 2b. there is a slight increase in the final ph in the acidic range and this could be due to the protonation of unfunctionalized carboxylic groups. the final ph seems to be less than the initial ph in the alkaline initial ph range and this could be due to oh adsorption onto adsorbed mb molecules as a second layer. figure 2. (a) effect of ph on mb adsorption, (b) initial ph vs final ph for mb adsorption. 3.2 kinetics of mb adsorption the kinetics of mb adsorption is presented in figure 3. at 20 o c, approximate equilibrium was reached within 35 hours for ac and on, and ~ 24 hours for hydrophobic activated carbons. at 40 o c, the equilibrium time was reached faster for ondip, onde (12 hours), and ac and on (24 hours). mb adsorption was enhanced with the temperature rise. mb adsorption was found to vary almost linearly with the half power of time, in the initial stage of adsorption. this was observed by applying the pore diffusion model [26] (equation 2). qt = kd t 0.5 eq. (2) where qt is mb adsorbed at time t and kd is the pore diffusion constant (mg/g / h 0.5 ). as the temperature increases, kd values increase for all carbons investigated (table 1). kd (mg/g/hr 0.5 ) follows the order of ondip> one > ondm > on>onm> ac > onde at 20 o c. the same order is followed at 40 o c except for onm, which is slightly higher than on. said al-mahaikhi et al. 46 figure 3. kinetics of mb adsorption at (a) 20 o c and (b) 40 o c. mb adsorption kinetic data were investigated for pseudo-first-order and pseudo-second-order kinetic models (equations 3 & 4). log(qe-qt) = log qe – k1t/2.303 eq. (3) t/qt = 1/k2qe 2 + t/qe eq. (4) where k1 and k2 are pseudo-first-order rate constant (hr -1 ), and pseudo-second-order constant (g/mg/hr). the initial adsorption rate can be obtained from equation 5. h = k2qe 2 eq. (5) the plots of log (qe − qt) versus t show straight lines from which qe and k1 are determined. the linear plots of the pseudo-first-order model for mb adsorption show low correlation values (r 2 ) indicating poor fit to the model, table 1, and thus, the kinetic parameters of this model are not discussed. the linear plots of t/qt versus t for the pseudo-secondorder kinetic model show straight lines with high correlation values (r 2 ), table 1. such good fit suggests that the adsorption of mb complies very well with the pseudo-second-order kinetic reaction between mb and the carbons’ surfaces. this reflects that the rate of mb adsorption depends on both the adsorbent and adsorbate and the limiting step in the adsorption process involves sharing or exchange of electrons between the carbon surface and mb [27,28]. qe, h, and k2 values from the pseudo-second-order model are found to increase with temperature increase similarly to kd increase. the rise in temperature decreases the solvation layers around the adsorbent and adsorbate allowing faster diffusion and more access to active sites and consequently more mb uptake [29,30]. k2, h and qe follow the order of ondip> one > ondm > on  onm> ac > onde. ac shows fewer values of the rate constants because mb molecules diffuse through a network of porous structures within ac particles. ondip, one, ondm, and onm show faster adsorption than ac because the active sites here are externally immobilized chains. ondip and one show higher kinetic parameters of kd, k2, and h. onde shows the slowest mb adsorption due to the self-adsorption or entangling of immobilized chains [24]. on shows a faster kinetic process than ac and this is related to a different mechanism of electrostatic interaction involved between the negatively charged on and the positively charged mb. the activation energies, ea (kj/mol) for mb adsorption were calculated considering the rate constant (k2) due to the good fit to the pseudo-second-order model. the energy of activation, ea, was calculated from the arrhenius equation for two temperatures (equation 6). ' 2 2 1 2 1 1 ln( ) ( ) a ek k r t t   eq. (6) r is the gas constant (8.314 j mol -1 k -1 ), k2 is the rate constant at t1 (298 k) and k'2 is the rate constant at t2 (213 k). the lower values of ea indicate physical adsorption processes (ea <42 kj/mol), whereas higher values of ea (ea > 42 kj/mol) indicate chemically controlled processes [30]. the ea values for mb adsorption lie between 5.85 and 36.12 kj/mol (table 1) indicating physisorption domination. (b) (a) adsorption of methylene blue onto hydrophobic activated carbon 47 table 1. kinetic parameters of mb adsorption on ac, on, and on hydrophobic carbons at 20 and 40 o c. 3.3 equilibrium studies and temperature effect mb adsorption follows an l-type adsorption isotherm with better performance as the temperature rises (figure 4). mb uptake increases with the increase in dye concentration reaching a plateau at high mb concentrations. the concentration of the dye acts as a driving force to overcome mass transfer resistance for the transport of dye molecules from the aqueous solution to the carbon surface. when the surface is saturated with the dye molecules, available active sites decrease, obstructing further uptake of the dye molecules and reaching a plateau [31]. the increased mb adsorption is related to the desolvation of the carbon particles and dye molecules by temperature rise allowing more access to active sites and consequently, more mb uptake [29,30]. figure 4. adsorption of mb at (a) 20 o c and (b) at 40 o c (initial ph 7). the adsorption isotherms are used to characterize the adsorption systems. despite the availability of different isotherm equations, the most commonly used isotherms are the langmuir and freundlich isotherms (equations 7 and 8), respectively. ce/qe = 1/b.q + ce/q eq. (7) log qe = log k + (1/n) log ce eq. (8) where q is the monolayer capacity (mg/g), and b is the langmuir constant (l/mg). k (l 1/n mg 1-1/n /g) and 1/n are the freundlich constants, which are relative indicators of adsorption capacity and adsorption intensity, respectively. sorbent temp. pore diffusion constant, kd (mg/g / h 0.5 ) pseudo-first-order model pseudo-second-order model ea, (kj/mol) k1 (h -1 ) qe (mg/g) r 2 rate const. k2, (g/mg/h) initial adsorption rate, h, (mg/g/h) qe, (mg/g) r 2 ac 20 o c 5.34 0.081 4.29 0.9560 0.0029 4.99 41.32 0.9969 5.85 40 o c 9.53 0.169 6.12 0.8609 0.0034 8.10 43.78 0.9972 on 20 o c 9.28 0.149 4.96 0.9211 0.0061 8.25 36.90 0.9989 6.06 40 o c 12.17 0.158 5.15 0.9367 0.0711 13.21 43.10 0.9979 onm 20 o c 8.90 0.107 4.40 0.9520 0.0069 8.22 34.48 0.9944 16.43 40 o c 12.90 0.104 4.26 0.9645 0.0106 16.89 39.84 0.9989 ondm 20 o c 10.1 0.104 3.88 0.9153 0.0102 14.71 38.02 0.9988 26.47 40 o c 19.54 0.118 3.27 0.9512 0.0204 39.53 44.05 0.9998 one 20 o c 11.49 0.191 4.56 0.9611 0.0116 20.33 41.84 0.9994 28.81 40 o c 20.01 0.098 3.60 0.9325 0.0247 49.26 44.64 0.9999 onde 20 o c 0.95 0.094 2.93 0.8906 0.0039 0.662 13.09 0.9985 14.11 40 o c 2.51 0.137 3.75 0.9910 0.0056 2.37 20.58 0.9984 ondip 20 o c 13.63 0.139 3.85 0.9532 0.0137 25.19 42.92 0.9997 36.12 40 o c 27.45 0.126 2.78 0.8709 0.0353 73.53 45.66 0.9999 (a) (b) said al-mahaikhi et al. 48 the langmuir isotherm model assumes the formation of monolayer coverage of adsorbates at equilibrium as adsorption sites become occupied by the adsorbate, after which no adsorption can take place at the occupied sites [32]. in contrast, for surfaces having non-uniform energy distribution, the freundlich isotherm is extensively used [33]. adsorption data were found to fit the langmuir model well with high values of r 2 (table 2). on the other hand, the adsorption data do not show good fit to the freundlich model showing low correlation values of r 2 (table 2). mb adsorption favors monolayer formation at equilibrium following the langmuir adsorption model well. the adsorption capacity (q) of mb increased with the rise in temperature for all carbons tested. this could be due to the desolvation of dyes and the decrease in the thickness of boundary aqueous layers of carbons and mb molecules with temperature rise [29,30]. as a result, the mass transfer resistance of dye in the boundary layer decreases. q follows the order of ondip > one > ondm > ac > on > onm > onde. ondip, one, and ondm are hydrophobic activated carbons with incomplete surface functionalization due to the large size of the alkylamine immobilized. the unfunctionalized content of carboxylic groups acts as a barrier between the immobilized hydrophobic chains disallowing hydrophobic interaction between the immobilized chains or their entangling together [24]. this allows more interaction of mb molecules with the hydrophobic active sites and thus enhanced mb uptake. on the other hand for onm, surface functionalization extent is high and this provides small hydrophobic active sites (methyl group). thus, the large mb molecules can be adsorbed onto multiple active sites simultaneously. this restricts further access to the inner surface active sites and, thus, mb adsorption decreases. for onde, the long diethyl chains immobilized are probably self-adsorbed onto the carbon surface [24] or entangled with adjacent diethyl chains minimizing the uptake of mb dye. for ac, despite having a large surface area (588 m 2 /g), it shows less adsorption of mb compared with ondip, one, and ondm which possess lower surface area. it is expected that the immobilized hydrophobic chains onto ondip, one, and ondm can adsorb multiple molecules of mb. mb adsorption onto ac takes place mostly via van der waals forces and - interactions [19, 34, 35]. table 2. equilibrium parameters for mb adsorption at different temperatures. on shows less mb adsorption than ac and this is probably related to the incomplete saturation of the on surface by the mb molecule due to its larger size. another characteristic of the langmuir isotherm is the separation factor, rs, (equation 9). rs = 1/(1+bco) eq. (9) the effectiveness of the adsorption process can be predicted from the values of the separation factor. for rs = 0, the adsorption is irreversible, and when rs lies between 0 and 1, the adsorption is favorable [36]. if rs is larger than 1, the adsorption is unfavorable but if rs = 1, the adsorption is linear [36]. table 2 shows that rs is between 0 and 1 indicating that the adsorption of mb is favorable. as the values of rs approach zero, this indicates strong adsorption tending to irreversibility. the monolayer adsorption capacity of mb on adsorbents, in this study, can be compared with different adsorbents in other studies. for ac, prepared by phosphoric acid activation from coconut shell, mb capacity was 200 mg/g [37]. other adsorbents showed different capacities including ac prepared by potassium hydroxide activation (270 mg/g) [19], dehydrated carbon (196.1 mg/g) [20], ethylamine hydrophobic activated carbon (393 m 2 /g), lignin (34 mg/g) [38], d-fructose (83 mg/g) [39], and anaerobic activated sludge (91 mg/g) [40]. in another study, ac showed a sorbent sorption temp. o c langmuir constants separation factor, rs r 2 freundlich constants r 2 q (mg/g) b (l/mg) 1/n k ac 20 o c 88.5 0.040 0.04-0.33 0.9983 0.333 13.2 0.9719 40 o c 102.0 0.153 0.01-0.12 0.9999 0.288 24.2 0.8388 on 20 o c 81.3 0.052 0.03-0.28 0.9983 0.298 15.0 0.9681 40 o c 94.3 0.064 0.03-0.24 0.9985 0.367 40.7 0.9698 onm 20 o c 75.8 0.038 0.050.35 0.9970 0.303 12.9 0.9838 40 o c 86.2 0.075 0.02-0.21 0.9986 0.270 19.5 0.9678 ondm 20 o c 91.8 0.044 0.04-0.32 0.9968 0.318 14.9 0.9796 40 o c 112.4 0.129 0.01-0.14 0.9985 0.302 24.2 0.9328 one 20 o c 96.2 0.055 0.03-0.27 0.9981 0.314 16.73 0.9707 40 o c 122.0 0.117 0.02-0.15 0.9990 0.308 25.8 0.9371 onde 20 o c 19.04 0.032 0.06-0.38 0.9970 0.180 1.20 0.986 40 o c 30.86 0.058 0.03-0.26 0.9994 0.180 10.6 0.9277 ondip 20 o c 99.0 0.061 0.03-0.25 0.9981 0.308 18.14 0.9748 40 o c 131.6 0.158 0.01-0.11 0.9988 0.283 32.2 0.8543 adsorption of methylene blue onto hydrophobic activated carbon 49 capacity of 127.6 mg/g; however, on modification with sodium lauryl sulfate the capacity increased to 195.7 mg/g [2]. in this study, ac and ondip show adsorption capacities of 131.6 and 102 mg/g of mb, respectively. 3.5 thermodynamic parameters the thermodynamic parameters were calculated for the adsorption of mb onto the carbons under investigation. the parameters were calculated from the change in equilibrium constant, kc, at 20 and 40 o c. kc can be calculated using equation 10. kc = cae/ ce eq.(10) where cae is the amount of mb adsorbed (mg) per liter of solution, and ce is the equilibrium concentration of mb solution (mg/l). kc is estimated from the initial part of the adsorption isotherm where qe versus ce is linear. the gibbs free energy change of the adsorption (δg°), is related to kc as shown in equation 11 [41]. δg o = -rtlnkc eq. (11) where r is the gas constant (8.314 j mol -1 k -1 ) and t is the absolute temperature (k). the enthalpy (δhº) can be calculated from the van’t hoff equation (equation 12) [41]. 2 1 1 2 1 1 ln( ) ( ) o c c k h k r t t    eq. (12) where kc1 and kc2 are the equilibrium constants at t1 and t2, respectively. from δgº and h o , the entropy change, δsº, is calculated from equation 13. g o = h o ts o eq. (13) thermodynamic parameters for the adsorption of mb are shown in table 3. kc values increase with temperature indicating an endothermic nature of mb adsorption [41]. the negative values of δg o indicate spontaneous adsorption processes, which is usually the case for the adsorption of organic compounds from solution [42]. in addition, δg o values decrease further with the increase in temperature indicating that higher temperature enhances mb adsorption. onde shows a positive g o at 20 o c, indicating a nonspontaneous process at this temperature. table 3. thermodynamic parameters of mb adsorption on different carbons. carbon temp.(k) kc g o (kj/mol) h o (kj/mol) s o (j/mol) ac 293 9.07 -5.37 34.95 137.6 313 22.68 -8.12 on 293 10.39 -5.70 27.05 111.8 313 21.11 -7.94 onm 293 8.43 -5.19 36.90 143.3 313 22.20 -8.07 ondm 293 15.19 -6.63 34.78 146.3 313 37.83 -9.45 one 293 18.43 -7.10 35.75 143.8 313 47.09 -10.02 onde 293 0.96 0.09 38.46 131.0 313 2.64 -2.53 ondip 293 21.63 -7.49 31.55 133.3 313 49.49 -10.15 the positive values of δh o thermodynamically indicate an endothermic nature of mb adsorption. δh o values are less than 40 kj/mol, indicating the physical adsorption nature of the mb. δh o values higher than 40 kj/mol represent chemisorption processes [43]. the adsorption of methylene blue on ac showed an endothermic spontaneous process [43]. the positive value of δs o reveals an increase in the degree of randomness for all tested carbons at the solidsolution interface for mb adsorption. previous studies showed similar trends for mb adsorption [43-45]. said al-mahaikhi et al. 50 3.6 reuse of adsorbents for dye adsorption ac, ondm, one, and ondip were selected for this study (figure 5). ac shows less uptake in the second adsorption cycle showing 79 % uptake compared with the first adsorption cycle. it is known that ac has limited reuse because it is difficult to desorb the adsorbate molecules from deep locations inside the porous structure [41]. on the other hand, ondim, one, and ondip reached 98.6, 99.5, and 99.6 % of mb adsorption in the second adsorption cycle compared with the first adsorption cycle. figure 5. carbon reuse for mb adsorption. 4. conclusion ac, on, and on functionalized with different alkylamines (onm, ondm, one, onde, and ondip) were tested for mb adsorption. ph 7 was found to be optimum for mb adsorption. mb adsorption follows a pseudo-secondorder kinetic model with the rate of adsorption increasing with temperature rise. the activation energy, ea, was found to be less than 42 kj/mol indicating physical adsorption and diffusion-controlled processes. equilibrium adsorption follows l-type isotherms with the adsorption data fitting well with the langmuir model, and better than with the freundlich model. the adsorption capacity (q) was enhanced with temperature rise. the adsorption for mb follows the order of ondip > one > ondm > ac > on > onm > onde. the thermodynamic parameters show that the dye adsorption is endothermic 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gelatin/chitosan polymer blends. journal of textiles, coloration and polymer science, 2019, 16, 113-127. received 1 march 2023 accepted 12 april 2023 squ journal for science, 2021, 26(2), 126-140 doi:10.53539/squjs.vol26iss2pp126-140 sultan qaboos university 126 improved diagonal hessian approximations for large-scale unconstrained optimization ahmed al-siyabi* and mehiddin al-baali department of mathematics, college of science, sultan qaboos university, p.o. box 36, pc 123, al-khod, muscat, sultanate of oman. *email: aalsiyabi@squ.edu.om. abstract: we consider some diagonal quasi-newton methods for solving large-scale unconstrained optimization problems. a simple and effective approach for diagonal quasi-newton algorithms is presented by proposing new updates of diagonal entries of the hessian. moreover, we suggest employing an extra bfgs update of the diagonal updating matrix and use its diagonal again. numerical experiments on a collection of standard test problems show, in particular, that the proposed diagonal quasi-newton methods perform substantially better than certain available diagonal methods. keywords: unconstrained optimization; large-scale problems; quasi-newton methods; bfgs update. ذات أبعاد عالية مقيدةالغيرفي األمثليات قطريةتقريبات هس الحسين ت البعلي حي الدينم و السيابي حمدأ نفترض بعض الطرق المشابهة لطريقة نيوتن بمصفوفة قطرية لحل مسائل األمثليات غير المقيدة وبأبعاد عالية. يتم تقديم نهج بسيط وفعال :صلخمال بشكل bfgsلخوارزميات تلك الطرق من خالل اقتراح تعديالت جديدة إلى قطر مصفوفة هس التقريبية. إضافة إلى ذلك، نقترح تطبيق دستور التعديل كل افي على مصفوفة القطرالمعدلة واستخدام قطر المصفوفة الناتجة مرة أخرى. تُظهر التجارب العددية على مجموعة من المسائل النموذجية، بشإض خاص، أن طرق نيوتن المشابهة المقترحة لتعديل قطرالمصفوفة التقريبي تعمل بشكل أفضل بكثير من طرق قطرية معروفة. .bfgs تعديل، المشابهة ، طرق نيوتنذات أبعاد عالية لئاس، مةمقيدالغير األمثليات :مفتاحيةالكلمات ال improved diagonal hessian approximations 127 1. introduction this paper is concerned with quasi-newton methods for solving the large-scale unconstrained optimization problem min𝑥∈ℜ𝑛 𝑓(𝑥), (1.1) where 𝑓: ℜ𝑛 ⟶ ℜ is a twice continuously differentiable function. it is assumed that 𝑛 is large so that a matrix cannot be stored explicitly. the methods are defined like the newton method with line search framework, except that the hessian 𝐺(𝑥𝑘 ) = ∇ 2𝑓(𝑥𝑘 ) is replaced by a symmetric and positive definite matrix 𝐵𝑘 . this hessian approximation satisfies the so-called quasi-newton condition for 𝑘 > 1, assuming 𝐵1 is given (usually, 𝐵1 = 𝐼, the identity matrix). the quasi-newton methods are defined iteratively as follows. at the beginning of each iteration, 𝑥𝑘 is available (𝑥1 is given) so that the gradient 𝑔(𝑥𝑘 ) = ∆𝑓(𝑥𝑘 ) is computed. if this vector (denoted by 𝑔𝑘 ) is not sufficiently close to zero, a search direction 𝑠𝑘 is provided (𝑠1 = −𝐵1 −1𝑔1) such that the descent property 𝑠𝑘 𝑇 𝑔𝑘 < 0 holds. thus, a positive steplength 𝛼𝑘 which reduces 𝑓(𝑥𝑘 ) along 𝑠𝑘 exists. in practice, 𝛼𝑘 is usually chosen to satisfy the wolfe-powell conditions 𝑓𝑘+1 ⩽ 𝑓𝑘 + 𝜎0𝛼𝑘 𝑔𝑘 𝑇 𝑠𝑘 , 𝑔𝑘+1 𝑇 𝑠𝑘 ⩾ 𝜎1𝑔𝑘 𝑇 𝑠𝑘 , (1.2) where 𝑓𝑘 denotes 𝑓(𝑥𝑘 ), 0 < 𝜎0 < 0.5 and 𝜎0 < 𝜎1 < 1. then a new point is given by 𝑥𝑘+1 = 𝑥𝑘 + 𝛼𝑘 𝑠𝑘 . (1.3) for the next iteration, the hessian approximation 𝐵𝑘 is updated to 𝐵𝑘+1 in terms of the two vectors 𝛿𝑘 = 𝑥𝑘+1 − 𝑥𝑘 , 𝛾𝑘 = 𝑔𝑘+1 − 𝑔𝑘 , (1.4) such that the quasi-newton condition 𝐵𝑘+1𝛿𝑘 = 𝛾𝑘 (1.5) holds. hence, the next search direction 𝑠𝑘+1 is computed by solving the system of linear equations 𝐵𝑘+1𝑠𝑘+1 = −𝑔𝑘+1. (1.6) although there exist many quasi-newton updating formulae in the literature, we will focus on the popular bfgs update 𝐵𝑘+1 = 𝐵𝑘 − 𝐵𝑘𝛿𝑘𝛿𝑘 𝑇𝐵𝑘 𝛿𝑘 𝑇𝐵𝑘𝛿𝑘 + 𝛾𝑘 𝛾𝑘 𝑇 𝛿𝑘 𝑇𝛾𝑘 , (1.7) because this formula has the following useful features. it satisfies the quasi-newton condition (1.5) and maintains the hessian approximations positive definite if the curvature condition 𝛿𝑘 𝑇 𝛾𝑘 > 0 (1.8) holds, which is guaranteed if the wolfe-powell conditions (1.2) are satisfied. in addition, the corresponding bfgs method converges superlinearly for convex objective functions. (for more details, see, for example, fletcher [1]). since the updated matrix 𝐵𝑘+1 cannot be stored explicitly, for sufficiently large values of 𝑛 it is replaced by another matrix that can be stored implicitly, so that the search direction in (1.6) is simply computed for all 𝑘 (see for example, andrei [2], and nocedal and wright [3]). here, we consider several proposals for maintaining 𝐵𝑘 diagonal, although the quasi-newton feature (1.5) is not expected to be satisfied. thus, a number of diagonal updates have been proposed (see the next section), some of which satisfy the weak quasi-newton condition 𝛿𝑘 𝑇 𝐵𝑘+1𝛿𝑘 = 𝛿𝑘 𝑇 𝛾𝑘. (1.9) however, we will consider the possibility of improving the role of these matrices by trying to impose the quasi-newton feature through an extra bfgs updating strategy. ahmed al-siyabi and mehiddin al-baali 128 the rest of our work is organized as follows. in the next section, we discuss a selection strategy for diagonal entries of quasi-newton bfgs hessian and inverse hessian approximations. section 3 defines other diagonal updates (some satisfy the weak quasi-newton condition (1.9)). in section 4 we discuss the convergence property, while in section 5 some numerical results are presented. we will see that the proposed technique improves upon the performance of the diagonal matrix updates substantially. finally, we conclude in section 6. 2. diagonal quasi-newton bfgs updates although it is possible to define the inverse hessian approximation by employing a number of bfgs updates in terms of vector pairs {𝛿𝑖 , 𝛾𝑖 }, for some 𝑖 ≤ 𝑘, without storing a matrix explicitly (see, for example, buckley and lenir [4], fletcher [5], liu and nocedal [6], and shanno [7]). we do not consider them here because we focus on the simple diagonal hessian approximations and diagonal inverse hessian approximations. in this section, we describe the bfgs update for maintaining the hessian approximations 𝐵𝑘 or its inverse 𝐻𝑘 diagonal for all 𝑘. for convenience, we denote �̂� = diag [𝐵] ≡ diag [�̂�(1), … , �̂�(𝑛)] and note that for any two vectors 𝑢 and 𝑣 we have diag(𝑢𝑣𝑇 ) = diag[𝑢(1)𝑣 (1), … , 𝑢(𝑛)𝑣 (𝑛)] , diag(�̂�𝑢) = diag[�̂�(1)𝑢(1), … , �̂�(𝑛)𝑢(𝑛)] , diag(�̂�𝑢𝑣 𝑇 ) = diag[�̂�(1)𝑢(1)𝑣 (1), … , �̂�(𝑛)𝑢(𝑛)𝑣 (𝑛)] . thus, in particular, it follows from (1.7) that the diagonal bfgs update of a diagonal matrix �̂�𝑘 can be written as follows: �̂�𝑘+1 = �̂�𝑘 − diag(�̂�𝑘𝛿𝑘𝛿𝑘 𝑇�̂�𝑘) 𝛿𝑘 𝑇�̂�𝑘𝛿𝑘 + diag(𝛾𝑘𝛾𝑘 𝑇) 𝛿𝑘 𝑇𝛾𝑘 (2.1) or equivalently, �̂�𝑘+1 (𝑖) = �̂�𝑘 (𝑖) − (�̂�𝑘 (𝑖) 𝛿𝑘 (𝑖) ) 2 ∑  𝑛𝑗=1 �̂�𝑘 (𝑗) (𝛿 𝑘 (𝑗) ) 2 + (𝛾𝑘 (𝑖) ) 2 𝛿𝑘 𝑇𝛾𝑘 , (2.2) for 𝑖 = 1, … , 𝑛. we note that this formula requires the storage of only three vectors. we first consider the most efficient quasi-newton bfgs method that is defined by (1.3), (1.7) and (1.6). for convenience, we rewrite the bfgs update (1.7) as bfgs matrix function 𝐵𝑘+1 = bfgs(𝐵𝑘 , 𝛿𝑘 , 𝛾𝑘 ), (2.3) where bfgs (𝐵, 𝛿, 𝛾) = 𝐵 − 𝐵𝛿𝛿𝑇𝐵 𝛿𝑇𝐵𝛿 + 𝛾𝛾𝑇 𝛿𝑇𝛾 (2.4) is the bfgs formula for updating any symmetric matrix 𝐵 in terms of any two vectors 𝛿 and 𝛾. this formula has the useful features that it maintains the positive definiteness of 𝐵 if 𝛿 𝑇 𝛾 > 0 and satisfies the quasi-newton condition bfgs (𝐵, 𝛿, 𝛾)𝛿 = 𝛾. thus, the updated matrix (2.3) is maintained positive definitive if the curvature condition (1.8) holds. since the updated matrix (2.3) cannot be stored explicitly, gilbert and lemaréchal [8] suggest using the diagonal bfgs update �̂�𝑘+1 = diag[bfgs(�̂�𝑘 , 𝛿𝑘 , 𝛾𝑘 )], (2.5) which is equivalent to both (2.1) and (2.2), assuming �̂�1 is given diagonal. in this case, �̂�𝑘 remains diagonal and positive definite so that the search direction (1.6) is simply computed as 𝑠𝑘+1 = −�̂�𝑘+1 −1 𝑔𝑘+1, (2.6) without computing the inverse matrix �̂�𝑘+1 −1 (= �̂�𝑘+1, say) explicitly. in the next section, we will consider a modification of this method. improved diagonal hessian approximations 129 we now show that the inverse matrix of (2.3) which defines the bfgs inverse hessian approximation yields a choice for defining �̂�𝑘+1 explicitly as follows. let the bfgs inverse hessian approximation be defined by 𝐻𝑘+1 = bfgs −1(𝐻𝑘 , 𝛿𝑘 , 𝛾𝑘 ), (2.7) where for any symmetric matrix 𝐻 and two vectors 𝛿 and 𝛾, bfgs−1(𝐻, 𝛿, 𝛾) = 𝐻 + (1 + 𝛾𝑇𝐻𝛾 𝛿𝑇𝛾 ) 𝛿𝛿𝑇 𝛿𝑇𝛾 − 𝛿𝛾𝑇𝐻+𝐻𝛾𝛿𝑇 𝛿𝑇𝛾 . (2.8) thus, if 𝐻 is stored implicitly (particularly, when it is diagonal) such that the product 𝐻𝑢 is available for any vector 𝑢, then the product bfgs−1 (𝐻, 𝛿, 𝛾)𝑣, for any vector 𝑣, can be computed without storing the updated matrix bfgs−1 (𝐻, 𝛿, 𝛾) explicitly. hence, the search direction (1.6) for the next iteration can be computed directly by 𝑠𝑘+1 = −𝐻𝑘+1𝑔𝑘+1, (2.9) although 𝐻𝑘+1 is a dense nondiagonal matrix. this technique maintains the useful quasi-newton condition 𝐻𝑘+1𝛾𝑘 = 𝛿𝑘 and will be applied to some diagonal matrices to impose the quasi-newton condition again (see al-siyabi, [9]). as for the bfgs update, we now apply the diagonal technique to the inverse bfgs update (2.7) to obtain �̂�𝑘+1 = diag[bfgs −1(�̂�𝑘 , 𝛿𝑘 , 𝛾𝑘 )]. (2.10) although the inverse bfgs updated matrix bfgs (�̂�𝑘 , 𝛿𝑘 , 𝛾𝑘 ) −1 = bfgs−1 (�̂�𝑘 , 𝛿𝑘 , 𝛾𝑘 ), since �̂�𝑘 = �̂�𝑘 −1, we note that diag (bfgs(�̂�𝑘 , 𝛿𝑘 , 𝛾𝑘 )) −1 ≠ diag (bfgs−1(�̂�𝑘 , 𝛿𝑘 , 𝛾𝑘 )); i.e., the inverse of the diagonal updated matrix (2.5) differs from (2.10). therefore, for convenience, we rewrite the search direction (2.6) as follows: 𝑠𝑘+1 = −�̂�𝑘+1𝑔𝑘+1. (2.11) in practice, the diagonal choice (2.5)– (2.6) is preferred to (2.10)– (2.11). in fact, the diagonal inverse bfgs update of (2.10) has been suggested by gilbert and lemaréchal [8], as follows: �̂�𝑘+1 = �̂�𝑘 + (1 + 𝛾𝑘 𝑇�̂�𝑘𝛾𝑘 𝛿𝑘 𝑇𝛾𝑘 ) diag(𝛿𝑘𝛿𝑘 𝑇) 𝛿𝑘 𝑇𝛾𝑘 − 2 diag(�̂�𝑘𝛾𝑘 𝛿𝑘 𝑇) 𝛿𝑘 𝑇𝛾𝑘 , (2.12) or equivalently, �̂�𝑘+1 (𝑖) = �̂�𝑘 (𝑖) + (1 + ∑   𝑛 𝑗=1 �̂�𝑘 (𝑗) (𝛾 𝑘 (𝑗) ) 2 𝛿𝑘 𝑇𝛾𝑘 ) (𝛿 𝑘 (𝑖) ) 2 𝛿𝑘 𝑇𝛾𝑘 − 2 𝛿𝑘 (𝑖) 𝛾𝑘 (𝑖) �̂�𝑘 (𝑖) 𝛿𝑘 𝑇𝛾𝑘 , (2.13) with a certain positive definite diagonal matrix �̂�1 so that the updated diagonal matrices are maintained positive definite if the curvature condition 𝛿𝑘 𝑇 𝛾𝑘 > 0 is satisfied. now, the corresponding algorithm for the above diagonal quasi-newton updates can be outlined in the following way, where throughout the paper ∥⋅∥ denotes the euclidean vector norm. algorithm 2.1. step 0: given an initial point 𝑥1, a symmetric and positive definite diagonal matrix �̂�1 and 𝜖 > 0 (an acceptance tolerance on the gradient norm). set 𝑘 = 1 and compute the initial search direction 𝑠1 = −�̂�1 −1𝑔1. step 1: compute a steplength 𝛼𝑘 and a new point 𝑥𝑘+1 = 𝑥𝑘 + 𝛼𝑘 𝑠𝑘, such that the wolfe-powell conditions (1.2) hold. step 2: if ∥∥𝑔𝑘+1∥∥ ≤ 𝜖, then stop. step 3: compute the vectors 𝛿𝑘 = 𝑥𝑘+1 − 𝑥𝑘 and 𝛾𝑘 = 𝑔𝑘+1 − 𝑔𝑘 . step 4: define a new diagonal hessian approximation �̂�𝑘+1 by (2.1) using �̂�𝑘 , 𝛿𝑘 and 𝛾𝑘. step 5: compute the new search direction 𝑠𝑘+1 = −�̂�𝑘+1 −1 𝑔𝑘+1. step 6: set 𝑘 = 𝑘 + 1, and go to step 1. note that in steps 0 and 5, the search direction is computed without forming �̂�𝑘+1 −1 explicitly; i.e., it is calculated as 𝑠𝑘+1 (𝑖) = −𝑔𝑘+1 (𝑖) /�̂�𝑘+1 (𝑖) , for 𝑖 = 1,2, … , 𝑛. in step 4, we define �̂�𝑘+1 in particular by the diagonal bfgs hessian approximation (2.1) or equivalently (2.5), unless otherwise stated. however, if a diagonal inverse hessian ahmed al-siyabi and mehiddin al-baali 130 approximation is considered, using for example formula (2.10) for updating �̂�𝑘 to �̂�𝑘+1, then steps 0, 4 and 5 are used with �̂�𝑗 −1 replaced by �̂�𝑗 , for 𝑗 = 1, 𝑘 and 𝑘 + 1, respectively. 3. diagonal non quasi-newton updates in this section, we describe some diagonal hessian approximations �̂�𝑘 which satisfy certain useful properties. although it is possible to define diagonal inverse hessian approximations �̂�𝑘, we do not consider them here because they are inferior to the direct hessian approximations (al-siyabi [9]). nazareth [10] has proposed the following hessian approximation update: 𝐵𝑘+1 = 𝐵𝑘 + 𝛿𝑘 𝑇𝛾𝑘−𝛿𝑘 𝑇𝐵𝑘𝛿𝑘 (𝛿𝑘 𝑇𝐵𝑘𝛿𝑘) 2 𝐵𝑘 𝛿𝑘 𝛿𝑘 𝑇 𝐵𝑘 . (3.1) this satisfies the weak quasi-newton condition (1.9) and maintains the hessian approximations positive definite whenever the curvature condition (1.8) holds. the author suggests replacing 𝐵𝑘 by a diagonal matrix �̂�𝑘 to obtain the new diagonal hessian approximation �̂�𝑘+1 = �̂�𝑘 + 𝛿𝑘 𝑇𝛾𝑘−𝛿𝑘 𝑇�̂�𝑘𝛿𝑘 (𝛿𝑘 𝑇�̂�𝑘𝛿𝑘) 2 diag(�̂�𝑘 𝛿𝑘 𝛿𝑘 𝑇 �̂�𝑘 ), (3.2) or equivalently, �̂�𝑘+1 (𝑖) = �̂�𝑘 (𝑖) + 𝛿𝑘 𝑇𝛾𝑘−∑   𝑛 𝑗=1 �̂�𝑘 (𝑗) (𝛿 𝑘 (𝑗) ) 2 (∑  𝑛𝑗=1 �̂�𝑘 (𝑗) (𝛿 𝑘 (𝑗) ) 2 ) 2 (�̂�𝑘 (𝑖) ) 2 (𝛿𝑘 (𝑖) ) 2 , (3.3) for 𝑖 = 1, … , 𝑛. this also remains positive definite if the curvature condition (1.8) holds. although a formula for the inverse update of (3.1) can be used to define diagonal inverse hessian approximations �̂�𝑘, we do not consider it here, because the performance of the corresponding method is worse than that of the above one (for details, see al-siyabi [9]). moreover, zhu et al. [11] proposed the direct diagonal update �̂�𝑘+1 = �̂�𝑘 + 𝛿𝑘 𝑇𝛾𝑘 −𝛿𝑘 𝑇�̂�𝑘𝛿𝑘 tr(�̂�𝑘) 2 �̂�𝑘 , (3.4) where �̂�𝑘 = diag [(𝛿𝑘 (1) ) 2 , (𝛿𝑘 (2) ) 2 , … , (𝛿𝑘 (𝑛) ) 2 ], or equivalently, �̂�𝑘+1 (𝑖) = �̂�𝑘 (𝑖) + 𝛿𝑘 𝑇𝛾𝑘−∑   𝑛 𝑗=1 �̂�𝑘 (𝑗) (𝛿 𝑘 (𝑗) ) 2 ∑  𝑛𝑗=1 (𝛿𝑘 (𝑗) ) 4 (𝛿𝑘 (𝑖) ) 2 , (3.5) for 𝑖 = 1, … , 𝑛, which satisfies the weak quasi-newton condition (1.9). since the positive definiteness of this update is not guaranteed, the authors introduced the following safeguarding test. if the inequality �̂�𝑘+1 (𝑖) < 𝜖1 holds for any 𝑖 and some 𝜖1 > 0 (we used 𝜖1 = 10 −6), the authors suggest resetting the above updated matrix to the scaled identity matrix 𝜏𝑘 0𝐼, where 𝜏𝑘 0 = 𝛾𝑘 𝑇𝛾𝑘 𝛿𝑘 𝑇𝛾𝑘 (3.6) is suggested by oren and luenberger [12], which is positive if the curvature condition holds. thus, the authors propose the positive definite diagonal update as follows: �̂�𝑘+1 = { �̂�𝑘+1, if �̂�𝑘+1 (𝑖) ≥ 𝜖1, ∀𝑖, 𝜏𝑘 0𝐼, otherwise. (3.7) recently, sim et al. [13] proposed the following diagonal hessian approximation: improved diagonal hessian approximations 131 �̂�𝑘+1 = { �̂�𝑘+1, if �̂�𝑘 0 < 1 �̂�𝑘 0𝐼, otherwise, (3.8) where �̂�𝑘+1 (𝑖) = 1 1+𝜔𝑘(𝛿𝑘 (𝑖) ) 2 , 𝜔𝑘 = 𝛿𝑘 𝑇𝛿𝑘−𝛿𝑘 𝑇𝛾𝑘 ∑  𝑛𝑗=1 (𝛿𝑘 (𝑗) ) 4 , (3.9) and �̂�𝑘 0 = 𝛿𝑘 𝑇𝛾𝑘 𝛿𝑘 𝑇𝛿𝑘 . (3.10) since this self-scaling parameter of oren and luenberger [12] is positive if the curvature condition holds, the proposed diagonal matrix (3.8) is positive definite. the authors derived the above diagonal matrix �̂�𝑘+1 as follows. if �̂�𝑘 0 ≥ 1, then they use the other known scaled identity matrix �̂�𝑘+1 = �̂�𝑘 0𝐼. otherwise, they define positive definite �̂�𝑘+1 as an approximate solution of the constrained optimization problem min �̂�+  𝜓(�̂�+) = tr (�̂�+) − ln (det(�̂�+)) (3.11) s.t. 𝛿𝑘 𝑇 �̂�+𝛿𝑘 = 𝛿𝑘 𝑇 𝛾𝑘 , �̂� +diagonal, (3.12) assuming �̂�+ is positive definite and approximating the lagrange multiplier by a reasonable value of 𝜔𝑘 . since the 𝜓 function is useful for deriving the bfgs formula (byrd and nocedal [14]), it is expected that the first case in (3.8) would work well. in practice, this works a little better than (3.7) and slightly worse than the diagonal bfgs update (2.5) (see section 5 for details). andrei [15] considers the possibility of defining a diagonal quasi-newton hessian approximation (say, �̂�𝑘+1) without updating a matrix by enforcing the quasi-newton condition �̂�𝑘+1𝛿𝑘 = 𝛾𝑘 which he writes as follows: �̂�𝑘+1𝑆𝑘 = 𝑌𝑘 , (3.13) where 𝑆𝑘 = diag [𝛿𝑘 (1) , … , 𝛿𝑘 (𝑛) ] and 𝑌𝑘 = diag [𝛾𝑘 (1) , … , 𝛾𝑘 (𝑛) ]. because, in general, equation (3.13), subject to �̂�𝑘+1 positive definite, cannot be solved exactly, for 𝑖 = 1,2, … , 𝑛, the author suggests the choice �̂�𝑘+1 (𝑖) = { 𝛾𝑘 (𝑖) 𝛿 𝑘 (𝑖) , if 𝛾 𝑘 (𝑖) 𝛿 𝑘 (𝑖) ⩾ 𝜖2 1, otherwise, (3.14) where 𝜖2 > 0. he reports that the corresponding algorithm performs better than certain diagonal quasi-newton algorithms. we note that the second case in (3.14) has the drawback of losing the details of �̂�𝑘. therefore, we suggest the following modified diagonal choice �̂�𝑘+1 (𝑖) = { 𝛾 𝑘 (𝑖) 𝛿 𝑘 (𝑖) , if 𝜖2 ≤ 𝛾𝑘 (𝑖) 𝛿 𝑘 (𝑖) ⩽ 1 𝜖3 , �̂�𝑘 (𝑖) , otherwise, (3.15) where 𝜖3 > 0, which maintains the positive definite property. in practice, this choice works better than (3.14) (see section 5 for details). we let 𝜖3 = 10 −14 be small enough so that the second inequality in (3.15) was always satisfied in our experiment. although other useful choices for the second case in (3.15) are possible (see al-siyabi [9]), we do not consider them here because we can improve the choice (3.15) as follows. since the above choices for the hessian approximation �̂�𝑘+1 do not satisfy the quasi-newton condition (1.5), we suggest updating this matrix by any quasi-newton formula (in particular, the bfgs update). hence, replacing the updated matrix by its diagonal, as in (2.5), we obtain the positive definite improved diagonal bfgs update �̂�𝑘+1 = diag[bfgs(�̂�𝑘+1 ∗ , 𝛿𝑘 , 𝛾𝑘 )], (3.16) where �̂�𝑘+1 ∗ denotes any of the above �̂�𝑘+1. finally, the corresponding algorithm for the above diagonal quasi-newton updates can be outlined along the lines of algorithm 2.1, where the difference among the above updates occurs in step 4 for defining �̂�𝑘+1 (given in particular by (3.15)– (3.16), unless otherwise stated). we will show that this improves the performance of choice (3.15) in section 5. ahmed al-siyabi and mehiddin al-baali 132 4. convergence analysis in this section, we study the convergence property of our proposed diagonal hessian approximations. since they are maintained positive definite, the descent condition 𝑠𝑘 𝑇 𝑔𝑘 < 0 (4.1) is satisfied for all 𝑘. before presenting the convergence property, we first state the following standard assumption. assumption 4.1. a) consider the level set ω = {𝑥 ∈ ℜ𝑛 : 𝑓(𝑥) ≤ 𝑓(𝑥1)} and let ω̃ be an open set containing ω. b) the objective function 𝑓(𝑥) is bounded and continuously differentiable in ω̃. c) the gradient 𝑔(𝑥) is lipschitz continuous on ω̃, that is, there exist a constant l > 0 such that ∥ 𝑔(𝑥) − 𝑔(�̃�) ∥≤ 𝐿 ∥ 𝑥 − �̃� ∥, ∀𝑥, �̃� ∈ ω̃. (4.2) similar to the well-known result of zoutendijk [16], we state the following result. theorem 4.1. suppose assumption 4.1 holds. consider the iterations of the form (1.3), with 𝑥1 being any starting point, the search direction 𝑠𝑘 being defined such that the descent condition (4.1) holds and the steplength 𝛼𝑘 satisfies the wolfe-powell conditions (1.2). then, the so-called zoutendijk condition ∑  ∞𝑘=1 (𝑠𝑘 𝑇𝑔𝑘) 2 ∥∥𝑠𝑘∥∥ 2 < ∞ (4.3) is obtained. proof. similar to many analyses (see, for example, nocedal and wright [3]), we state the following proof (for complete illustration). rearranging the second wolfe-powell condition in (1.2) and using the lipschitz condition (4.2), it follows that 𝐿∥∥𝑠𝑘 ∥∥∥∥𝑥𝑘+1 − 𝑥𝑘 ∥∥ ≥ 𝑠𝑘 𝑇 (𝑔(𝑥𝑘+1) − 𝑔(𝑥𝑘 )) ≥ (𝜎1 − 1)𝑠𝑘 𝑇 𝑔𝑘 . substituting 𝑥𝑘+1 = 𝑥𝑘 + 𝛼𝑘 𝑠𝑘 and using (4.1), we obtain: 𝛼𝑘 ≥ 1 − 𝜎1 𝐿 |𝑠𝑘 𝑇 𝑔𝑘 | ∥∥𝑠𝑘 ∥∥ 2 . using this result, we rewrite the first wolfe-powell condition in (1.2) as follows: 𝑓𝑘 − 𝑓𝑘+1 ≥ 𝜎0(1 − 𝜎1) 𝐿 (𝑠𝑘 𝑇 𝑔𝑘 ) 2 ∥∥𝑠𝑘 ∥∥ 2 . by summing this expression over 𝑘 and using the assumed bound on the 𝑓𝑘, we obtain the zoutendijk condition (4.3). to obtain the global convergence result for algorithm 2.1, we assume the condition number of the positive definite diagonal hessian approximate �̂�𝑘 to be uniformly bounded, that is, there is a constant 𝑀 such that 𝜅(�̂�𝑘 ) = 𝜆1 𝜆𝑛 ≤ 𝑀, ∀𝑘, (4.4) where 𝜆1 and 𝜆𝑛 are the largest and smallest eigenvalues of �̂�𝑘 . theorem 4.2. suppose that 𝑓 satisfies assumption 4.1. let 𝑥1 be a starting point and �̂�1 be a positive definite diagonal matrix. consider algorithm 2.1 with 𝜖 = 0 in step 2, �̂�𝑘+1 in step 4 defined such that condition (4.4) holds and that step 1 defines the steplength 𝛼𝑘 such that the wolfe-powell conditions (1.2) hold. then, the algorithm converges globally, that is, lim 𝑘→∞  ∥∥𝑔𝑘 ∥∥ = 0. (4.5) proof. substituting 𝑠𝑘 = −�̂�𝑘 −1𝑔𝑘 into the zoutendijk condition (4.3), we obtain: 1 𝑀 ∑𝑘=1 ∞  ∥∥𝑔𝑘 ∥∥ 2 ≤ ∑𝑘=1 ∞   (𝑠𝑘 𝑇 �̂�𝑘 𝑠𝑘 )(𝑔𝑘 𝑇 �̂�𝑘 −1𝑔𝑘 ) ∥∥𝑠𝑘 ∥∥ 2 < ∞, where 𝑀 is given as in (4.4). hence, the limit (4.5) is obtained. 5. numerical results in this section, we study the performance of our proposed methods on a set of standard unconstrained optimization test problems. all the methods are implemented as in algorithm 2.1, differing only in step 4 for defining the hessian approximate �̂�𝑘+1 by the choices (2.5), (2.12), (3.2), (3.7) (with 𝜖1 = 10 −6), (3.8), (3.14) (with 𝜖2 = 10 −2 as in andrei [15]), and (3.15) (with 𝜖2 = 10 −2 and 𝜖3 = 10 −14). these choices (referred to as l1, l2, ..., and l7), improved diagonal hessian approximations 133 except for l7, have been proposed by gilbert and lemaréchal [8], nazareth [10], zhu et al. [11], sim et al. [13] and andrei [15], respectively. the choice l7 defines our proposed modification of l6. because the l2 update defines the inverse hessian approximate �̂�𝑘+1, steps 0, 4 and 5 are used with �̂�𝑗 −1 replaced by �̂�𝑗 , for 𝑗 = 1, 𝑘 and 𝑘 + 1, respectively. in all algorithms, we consider the followings. for step 0, we choose �̂�1 = 𝐼 and 𝜖 = 10 −7. for step 1, we calculate a value of the steplength 𝛼𝑘 such that the strong wolfe-powell conditions 𝑓𝑘+1 ≤ 𝑓𝑘 + 𝜎0𝛼𝑘 𝑠𝑘 𝑇 𝑔𝑘 , |𝑠𝑘 𝑇 𝑔𝑘+1| ≤ −𝜎1𝑠𝑘 𝑇 𝑔𝑘 (5.1) hold, using the usual values of 𝜎0 = 10 −4 and 𝜎1 = 0.9, which imply the wolfe-powell conditions (1.2). we used the matlab line search routine ‘lswpc’ of al-baali, which is essentially written with slight differences in fortran by fletcher. it is based on using quadratic and cubic interpolations for estimating a value of the steplength 𝛼𝑘. it also guarantees finding a positive value of 𝛼𝑘 in a finite number of operations (see al-baali and fletcher [17] and fletcher [1]). we stopped the run when either ∥∥𝑔𝑘 ∥∥ ≤ 10 −7 max{∥∥𝑔1∥∥, 1}, 𝑓𝑘 − 𝑓𝑘+1 ≤ 10 −14, or the number of line searches reached 105. all codes were written in matlab r2017b and the runs were made on a cpu processor with intel(r) core (tm) i7 (2.7 ghz) and 16.0 gb ram memory. the test problems were selected from the collection of andrei [18] (which belong to the cutest collection established by gould et al. [19], himmelblau [20] and moré et al. [21]). we picked 84 test problems (as given in table 1). for certain extended test problems (e.g., extended rosenbrock), increasing the number of variables does not increase the number of line searches, function and gradient evaluations required to solve the problems (see for example al-baali [22]). to avoid this occurrence, the author modifies the standard starting point �̅�1 to �̿�1, where �̿�1 (𝑖) = �̅�1 (𝑖) + 1 𝑖+1 , (5.2) for 𝑖 = 1, … , 𝑛. we used all 84 test functions with the standard starting points and their modifications (5.2) for n = 900, 9000 and 27000 to define three sets of test problems. each set (referred to as set1, set2 and set3, respectively) consists of 168 test problems. we also consider all the test problems as a single 504 test problem (referred to as set4). to study the behaviour of the above algorithms, we compared the numerical results required to solve the tests, using the performance profiles of dolan and moré [23] based on the numbers of line searches (#ls), function evaluations (#fun) and gradient evaluations (#gra) as well as the cpu time in seconds, required to solve the test problems. the dolanmoré performance profile can be briefly described as follows. it illustrates the relative solvers performance of the solvers on a set of test problems in terms of #ls (similarly for #fun, #gra and cpu time). in general, 𝑃𝑀 (𝜏), the fraction of problems with performance ratio 𝜏 ≥ 0, is defined by 𝑃𝑀 (𝜏) = number of problems where 𝑙𝑜𝑔2(𝜏𝑝,𝑀)≤𝜏 total number of problems . (5.3) here, 𝜏𝑝,𝑀 is the performance ratio of #ls required to solve problem 𝑝 by the m method to the lowest #ls required to solve problem 𝑝. the ratio 𝜏𝑝,𝑀 is set to ∞ (or some large number) if the m method fails to solve problem 𝑝. the values of 𝑃𝑀 (𝜏) at 𝜏 = 0 gives the percentage of test problems for which the method m performs to be best and the value for 𝜏 large enough is the percentage of test problems that the m method can solve. thus, a solver with high values of 𝑃𝑀 (𝜏) or one with corresponding figure located at the top right performs better than the ones located at lower levels. applying the above algorithms to the four sets, set1, set2, set3 and set4, of test problems, we obtained some numerical results. their comparisons are given in figures 1–4, respectively, with respect to #ls, #fun, #gra and cpu time for each figure. we observe that l7 appears to be the best, while showing to be a little better than l1, l2, l4 and l6, with l3 and l5 being a little worse than the other methods. to give another fair and useful comparison which shows the percentage improvement or worsening of the algorithms, we also considered the comparison rule of al-baali (see, e.g., al-baali [24] and essentially al-baali [25]). to compare two methods (say, m1 and m2) with respect to #ls (similarly for #fun, #gra and cpu time), the author proposes the average ratio measure of the form: 𝑟 = 1 𝑡 ∑  𝑡𝑖=1 𝑟𝑖 , (5.4) where 𝑡 is the number of test problems and ahmed al-siyabi and mehiddin al-baali 134 𝑟𝑖 = { 𝑝𝑖 𝑞𝑖 , if 𝑝𝑖 ≤ 𝑞𝑖 2 − 𝑞𝑖 𝑝𝑖 , if 𝑝𝑖 > 𝑞𝑖 (5.5) with 𝑝𝑖 and 𝑞𝑖 denoting #ls required to solve problem 𝑖 by the m1 and m2 methods, respectively. if only m1 or only m2 failed to solve the problem, we set 𝑟𝑖 = 2 and 𝑟𝑖 = 0, respectively. if both m1 and m2 methods either failed or converged to two different local solutions, for some test problem 𝑖 then we set 𝑟𝑖 = 1. the average ratio 𝑟 in (5.4) always falls in the interval [0,2]. a value of 𝑟 ≤ 1 indicates that m1 is better than m2 by 100(1 − 𝑟)%. otherwise, when 𝑟 > 1, m1 is worse than m2 (or m2 is better than m1) by 100(1 − 𝑟)% (for more details on this measurement ratio, see al-baali [24], for instance). using the same numerical results used to obtain the comparison figures 14 for set 𝑖, 𝑖 = 1, … ,4, we applied the above average ratio measure to compare l1, l2, ..., l6 versus l7 and obtained tables 2–5, using both the starting points for 𝑛 = 900, 9000, 27000 and all 3 values of 𝑛, respectively. since we have 𝑟 > 1 in all cases, it is clear that l7 gives the best performance, it being at least 10% better than l1, l2, l4 and l6, and more than 48% better than l3 in terms of #ls, #fun #gra and cpu time. thus, these observations agree with those in figures 1–4. we observe that the performance of l6 improves as n increases in comparison with l1, l2, and l4. we also observe that l1, l2 and l4 have nearly identical performances in terms of all measurements, whereas l3 is the worst among all the algorithms. since the l3, l4, l5, l6 and l7 methods do not consider imposing the quasi-newton condition (1.5), like that of l1 and l2, we suggest using (3.16) with �̂�𝑘+1 ∗ given by (3.2), (3.7), (3.8), (3.14) and (3.15), which define the former five methods, respectively. we compared the corresponding algorithms (referred to as l3a, l4a, l5a, l6a and l7a, respectively) and observed that each l𝑖a, for 𝑖 = 3, … ,7, performs better than l𝑖 and that the performance of l7a remains the best (see al-siyabi [9]). thus, we present only the comparison of l7a versus l7 as shown in figure 5 and table 6 for set4 of test problems. we notice that l7a outperforms l7 in terms of all measurements. moreover, l7a performs better than l7 by at least 6% in terms of #ls, #fun, #gra and cpu time, which provides further illustration of the comparison shown in figure 5. we also observe from the combination of figures 1–4 and figure 5 as well as tables 2–5 and table 6 that l7a performs substantially better than l6 with at least 15% improvement in terms of #ls, #fun and #gra and 20% in terms of cpu time. table 1. list of test functions. no. function’s name no. function’s name 1 extended freudenstein & roth 43 arglinb 2 extended trigonometric 44 arwhead 3 extended rosenbrock 45 nondia 4 generalized rosenbrock 46 nondquar 5 extended white & holst 47 bqdrtic 6 extended beale 48 eg2 7 extended penalty 49 dixmaana 8 perturbed quadratic function 50 dixmaanb 9 raydan 1 51 dixmaanc 10 raydan 2 52 dixmaand 11 diagonal 1 53 dixmaane 12 diagonal 2 54 dixmaanf 13 diagonal 3 55 dixmaang 14 hager 56 dixmaanh 15 generalized tridiagonal 1 57 dixmaani 16 extended tridiagonal 1 58 dixmaanj 17 extended tet (three exponential terms) 59 dixmaank 18 generalized tridiagonal 2 60 dixmaanl 19 diagonal 4 61 broyden tridiagonal 20 diagonal 5 62 almost perturbed quadratic 21 extended himmelblau 63 staircase 1 improved diagonal hessian approximations 135 table 1. continued 22 generalized white & holst 64 staircase 2 23 generalized psc1 65 liarwhd 24 extended psc1 66 engval1 25 extended powell 67 edensch 26 full hessian fh1 68 cube 27 full hessian fh2 69 nonscomp 28 extended bd1 (block diagonal) 70 quartc 29 extended maratos 71 diagonal 6 30 extended cliff 72 siquad 31 perturbed quadratic diagonal 73 extended denshnb 32 extended wood 74 extended denshnf 33 extended hiebert 75 cosine 34 quadratic qf1 76 generalized quartic 35 extended quadratic penalty qp1 77 diagonal 7 36 extended quadratic penalty qp2 78 diagonal 8 37 quadratic qf2 79 full hessian fh3 38 extended quadratic exponential ep1 80 sincos 39 extended tridiagonal 2 81 diagonal 9 40 fletchr 82 himmelbg 41 bdqrtic 83 himmelh 42 tridia 84 indef (a) number of line searches. (b) number of function evaluations. (c) number of gradient evaluations. (d) cpu times. figure 1. comparison among l1, l2, l3, l4, l5, l6 and l7, for set1; 𝑛 = 900. ahmed al-siyabi and mehiddin al-baali 136 table 2. average ratios 𝑟 for methods versus l7, for set1; 𝑛 = 900. method /measure #ls #fun #gra cpu l1 1.153 1.203 1.155 1.130 l2 1.074 1.158 1.0714 1.097 l3 1.598 1.622 1.596 1.597 l4 1.207 1.211 1.209 1.173 l5 1.214 1.232 1.211 1.224 l6 1.124 1.144 1.129 1.077 table 3. average ratios 𝑟 for methods versus l7, for set2; 𝑛 = 9000. method/ measure #ls #fun #gra cpu l1 1.190 1.259 1.205 1.281 l2 1.136 1.229 1.150 1.268 l3 1.479 1.542 1.506 1.566 l4 1.197 1.197 1.201 1.240 l5 1.237 1.249 1.250 1.290 l6 1.102 1.134 1.121 1.235 (a) number of line searches. (b) number of function evaluations. (c) number of gradient evaluations. (d) cpu times. figure 2. comparison among l1, l2, l3, l4, l5, l6 and l7, for set2; 𝑛 = 9000. improved diagonal hessian approximations 137 table 4. average ratios 𝑟 for methods versus l7, for set3; 𝑛 = 27000. method / measure #ls #fun #gra cpu l1 1.239 1.311 1.254 1.290 l2 1.137 1.232 1.152 1.166 l3 1.482 1.556 1.507 1.671 l4 1.228 1.222 1.225 1.223 l5 1.231 1.243 1.238 1.280 l6 1.079 1.114 1.095 1.096 (a) number of line searches. (b) number of function evaluations. (c) number of gradient evaluations. (d) cpu times. figure 3. comparison among l1, l2, l3, l4, l5, l6 and l7, for set3; 𝑛 = 27000. ahmed al-siyabi and mehiddin al-baali 138 table 5. average ratios 𝑟 for methods versus l7, for set4; 𝑛 ∈ [900, 9000, 27000]. method /measure #ls #fun #gra cpu l1 1.211 1.285 1.229 1.267 l2 1.126 1.222 1.141 1.191 l3 1.487 1.556 1.512 1.585 l4 1.203 1.200 1.204 1.217 l5 1.223 1.235 1.233 1.262 l6 1.087 1.118 1.101 1.145 (a) number of line searches. (b) number of function evaluations. (c) number of gradient evaluations. (d) cpu times. figure 4. comparison among l1, l2, l3, l4, l5, l6 and l7, for set4; 𝑛 ∈ [900, 9000, 27000]. improved diagonal hessian approximations 139 table 6. average ratios 𝑟 for l7a versus l7, for set4; 𝑛 ∈ [900, 9000, 27000]. method / measure #ls #fun #gra cpu l7a 0.942 0.933 0.934 0.943 6. conclusion we first studied some diagonal hessian approximation methods for large-scale unconstrained optimization, then presented new diagonal hessian approximations and established their global convergence. based on extensive numerical experiments, we observed that a number of our algorithms were more efficient and more robust than several similar available methods. two of the proposed methods require storing only a few vectors while sharing certain desirable features of the quasi-newton methods. conflict of interest the authors declare no conflict of interest. acknowledgment we thank the two anonymous referees for careful reading of the paper and for many constructive comments and suggestions. the first author would like to thank the oman ministry of education for the award of a scholarship. (a) number of line searches. (b) number of function evaluations. (c) number of gradient evaluations. (d) cpu times. figure 5. comparison among l7 and l7a, for set4; 𝑛 ∈ [900, 9000, 27000]. ahmed al-siyabi and mehiddin al-baali 140 references 1. fletcher, r. practical methods of optimization. john wiley & sons, 2013. 2. andrei, n. nonlinear conjugate gradient methods for unconstrained optimization. in springer optimization and its applications, 2020, volume 158. 3. nocedal, j., and wright, s. numerical optimization. springer science & business media, 2006. 4. buckley, a. and lenir, a. qn-like variable storage conjugate gradients. mathematical programming, 1989, 27(2), 155-175. 5. fletcher, r. low storage methods for unconstrained optimization. in computational solution of nonlinear systems of equations, e.l.allgower and k.georg (eds.), lectures in applied mathematics, vol.26, ams publications, providence, ri. mathematical programming, 1990, 91(2), 201-213. 6. liu, d.c. and nocedal, j. on the limited memory bfgs method for large scale optimization, 1989. mathematical programming, 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199-209 squ journal for science, 12 (2) (2007) © 2007 sultan qaboos university 199 an overview of some practical quasinewton methods for unconstrained optimization m. al-baali* and h. khalfan** department of mathematics and statistics, college of science, sultan qaboos university,p.o.box 36, pc 123, al-khodh, muscat, sultanate of oman, *email: albaali@squ,edu.om, **department of mathematics sciences, uae university, al-ain 17551, united arab emirates, email: humaidf@uaeu.ac.ae. دراسة حصریة لبعض الخوارزمیات التطبیقیة المشابھة لطریقة نیوتن للحلول المثلى غیر المقیدة محي الدین البعلي وحمید خلفان تعتبر الخوارزمیات المشابھة لطریقة نیوتن من الطرق التطبیقیة األكثر كفاءة لمسائل الحلول المثلى غیر المقیدة. :خالصة دراسة شاملة لبعض الخوارزمیات الحدیثة من ھذا النوع مع التركیز على الطرق المستخدمة في تقریب تتضمن ھذه المقالة مصفوفة المشتقة الثانیة ووسائل تطویرھا. abstract: quasi-newton methods are among the most practical and efficient iterative methods for solving unconstrained minimization problems. in this paper we give an overview of some of these methods with focus primarily on the hessian approximation updates and modifications aimed at improving their performance. keywords: unconstrained optimization, line search technique, quasi-newton methods. 1. introduction in this paper we give an overview of some line search quasi-newton methods for solving the unconstrained minimization problem ( )min nx r f x ∈ , (1) where f is a twice continuously differentiable function. emphasis will be on the hessian approximation formulas used in these methods, and techniques developed to improve their performance. the basic iteration of a quasi-newton method consists of the following. starting with an initial approximation 1 x to a solution x ∗ of (1), and an initial positive definite hessian approximation 1 b , calculate a new approximation at iteration k by m. al-baali and h. khalfan 200 1k k k kx x dα+ = + , (2) where k α is a steplength and k d is a search direction obtained by ( )1k k kd b f x−= − ∇ , (3) where k b is a positive definite n n× hessian approximation matrix chosen from the general broyden class of updates discussed in the next section. the steplength k α is calculated such that the wolfe conditions ( ) ( ) ( )1 1 (0 1 2) t k k k k k kkf x d f x f dxα ρ α ρ+ − ≤ ∇ , ∈ , / (4) and ( ) ( ) ( )2 2 1 1 t t k kk k k kf d f dx d xρ ρ ρα∇ ≥ ∇ , ∈ ,+ (5) are satisfied. the first condition ensures sufficient reduction in f , and the second one guarantees that the steplegnth is not too small relative to the initial rate of decrease in f . in practice, the strong wolfe conditions (4) and ( ) ( )2 t t k kk k k kf d f dx d xρα| ∇ |≤ − ∇+ are usually used. if beside the standard assumptions on f , f∇ is lipschitz continuous, the steplength kα satisfies the wolfe conditions, and the matrices k b are positive definite and have a bounded condition number, then iteration (2) is globally convergent. (see e.g. fletcher, 1987, dennis and schnabel, 1996, and nocedal and wright, 1999). in the next section we discuss some well-known members of the broyden class of hessian approximation updates. in section 3 we outline some approaches for improving the performance of some standard updates by modifications of the gradient difference ( ) ( )1k kf x f x+∇ − ∇ . in section 4 we discuss selfscaling quasi-newton methods aimed at handling ill-conditioned problems. some quasi-newton methods for large scale optimization are discussed in section 5. 2. quasi-newton updates setting 1kα = and 2 ( )k kb f x= ∇ in (2) and (3), respectively, we obtain the well-known newton method which converges quadratically to a solution x ∗ , if 1x is sufficiently close to x ∗ . for many practical problems, however, analytic second derivatives are unavailable, and the cost of approximating them by finite differences requires either an additional n gradient evaluations or 2( )o n function evaluations per iteration. quasi-newton updates for hessian approximation avoid these disadvantages by approximating 2 1( )kf x +∇ by a symmetric matrix 1k k k b b e+ = + , where k e is an n n× matrix, such that the secant equation 1k k kb s y+ = , (6) is satisfied, where 1k k k s x x+= − and ( ) ( )1k k ky f x f x+= ∇ − ∇ . an overview of some practical quasi-newton methods 201 the solution to equation (6), however, is not unique, and there is a variety of updating formulas obtained by imposing more conditions on 1k b + . if ke is assumed to be a symmetric rank-one matrix for instance, then (6) yields the unique symmetric rank-one update (sr1) ( ) ( ) 1 t k k k k k k k k t t k k k k k y b s y b s b b s y s b s+ − − = + . − (7) requiring k e to be a symmetric rank-two matrix, equation (6) yields a variety of possible updates such as the well-known (broyden fletcher goldfarb shanno) and (davidon fletcher powell) formulas. a more general formula satisfying the secant equation with k e symmetric and of rank two at most, known as the broyden class, is given by 1 ( ) t t tk k k k k k k k k kt t k k k k k b s s b y y b b w w s b s y s θ θ+ = − + + , where 1 2( )t k k kk k k k t t k k k k k y b s w s b s y s s b s /  = −    and θ is a parameter. this class includes as special case the bfgs update, when 0θ = ; the dfp update, when 1θ = ; and the sr1 update, when ( ) t t t k k k k k k ks y s y s b sθ = / − . (another family of updates was proposed by huang (1970), but is not discussed here since it was shown to be equivalent to the self-scaling broyden family discussed in section 5.) if k b is positive definite, and the curvature condition 0tk ks y > holds (which is guaranteed by the second wolfe condition (5)), then 1k b + is positive definite for any kθ θ> , where 1 , 1 t t k k k k k k k k kt t k k k k k k s b s y h y b h b h s y s y θ = = , = − , and 1 k kh b −= . since 0kθ < (by cauchy’s inequality), it clearly follows that any update with 0θ ≥ (such as the bfgs and dfp updates) preserves positive definiteness if the curvature condition holds. the sr1 update preserves positive definiteness only if either 1kb < or 1kh < , which may not hold even for quadratic functions. (see e.g. fletcher, 1987). powell (1976) showed that if f is a convex function and the wolfe conditions hold, then for any starting point 1 x and any positive definite initial matrix 1 b , the bfgs method converges globally; and if furthermore the true hessian 2 f x∗     ∇ is positive definite, then the rate of convergence is q -superlinear. this result was extended by byrd, nocedal and yuan (1987) to the interval 0 1θ≤ < , (updates belonging to [ ]0 1, are known as the convex class). although dixon (1972) showed that for a general nonlinear function f , all well-defined members of the broyden family with kθ θ≠ generate the same sequence of iterates when used with exact line searches, numerical experience showed that only some updates, which we discuss next, worked well in practice when inexact line searches are used; and that the performance deteriorates as θ increases above 0 (see e.g. byrd, liu and nocedal, 1992). m. al-baali and h. khalfan 202 the sr1 method enjoys some desirable features which are not shared by other standard updates. fiaco and mccormick (1968) showed that for a positive definite quadratic function, if the sr1 update is used with linearly independent steps, and all the updates are well-defined, then the solution is reached in at most 1n + iterations. furthermore, if 1n + iterations are required, then the final hessian approximation 1nb + is the actual hessian. this quadratic termination property is not generally true for other members of the broyden family, unless exact line searches are used. for general functions, conn, gould and toint (1991) proved that the sequence of sr1 hessian approximations converges to the true hessian at the solution provided that the steps are uniformly linearly independent; that the sr1 update denominator is always sufficiently different from zero, and that the iterates converge to a finite limit. hence under these conditions the rate of convergence is q -superlinear. if the assumption of uniform linear independence is dropped, then as shown in khalfan, byrd and schnabel (1993) the sr1 method converges ( 1)n + q -superlinearly provided that for all k, kb is positive definite and bounded. on the other hand, ge and powell (1983) showed that the sequence of matrices generated by the bfgs method converges to a matrix not necessarily equal to the true hessian. in order to obtain a well-conditioned update, davidon (1975) proposed the update 1 , 2 1 1 , . 1 k k k k k k k k h b h b h b h otherwise b θ − + ≤ − =    − (8) the first update in this formula is obtained by minimizing over θ the condition number 1( ( ) )k kb hκ θ+ , and the second one is the sr1 formula. practical experience, however, showed no significant improvement using this update (see e.g. al-baali, 1993 and lukšan and spedicato, 2000). since updates from the preconvex class work well in practice (see e.g. zhang and tewarson 1988 and byrd, liu and nocedal, 1992), al-baali (1993) reported improved numerical performance using the switching bfgs/sr1 update 0 1 1 otherwise 1 k k h b θ , ≥  =  , , − which preserves positive definiteness. lukšan and spedicato (2000) also reported competitive performance using this update. other updates of the switching type are given in al-baali, fuduli and musmanno (2004). an interval of globally convergent updates was tested by al-baali and khalfan (2005), defined by k k θ θ θ− +≤ ≤ , where 1 2 1 1 1 1k k k k kb h θ ν ν / ±  = ± , = − .    (9) their numerical experience indicated that several updates from this interval worked well in practice, especially the modified sr1 update an overview of some practical quasi-newton methods 203 1 1 max 1 1 1 min 1 1 k k k k k k k k b b b b b θ θ θ θ −    −           +          , =   = , , > −   , , <  − and the update defined by max( 1 )k kbθ θ −= , − which does not include the sr1 formula. the fast rate of convergence observed in the numerical experience with these updates suggests further study of their convergence properties. 3. modifying gradient-difference vector many approaches have been proposed to improve the quasi-newton hessian approximation updates. in this section we outline some recent suggested updates obtained by modifying the vector k y . zhang, deng, and chen (1999) suggested replacing k y in the bfgs formula by the vector 1 1 2 6( ) 3( )tk k k k k k k k k f f g g s y y s s ∗ + +− + += + || || (10) which has the property that ( )2 31 t k k k k k k s f x s y o s s ∗      +    ∇ − = || || || || and reduces to k y if f is quadratic. the resulting modified bfgs method retains global and q -superlinear convergence for convex functions, and performs slightly better than the standard bfgs method on some test problems. li and fukushima (2001) proposed using 2max 0 t k k k k k k k y s y y g s s ∗   − = + || || + ,   || ||   instead of k y in the bfgs update for ensuring that 0tk ky s ∗ > . they showed that for a general function, the resulting bfgs method with backtracking line search converges globally and superlinearly, under standard assumptions on the objective function. their numerical experience also indicated some improvement in performance. for other modifications of this type (yuan, 1991, xu and zhang, 2001, wei et al., 2004, and zhang, 2005). modifying k y was originally suggested by powell (1978) who proposed a bfgs method for constrained optimization with ( ) ( )1 ,k k k k ky y b s yϕ∗ = + − − m. al-baali and h. khalfan 204 where 0 1ϕ< ≤ . al-baali (2003b) used this modification for unconstrained problems and reported improved performance for the bfgs and many other methods. other approaches for improving hessian approximation involved employing multiple quasi-newton updates at each iteration, using information at the current and previous steps. some improvement was observed for certain type of test problems (khalfan, 1989, ford and tharmlikit, 2003, and al-baali, et al., 2004). 4. self-scaling quasi-newton methods the standard quasi-newton methods that we considered so far may have difficulties in solving some illconditioned problems. powell (1986) showed that, the bfgs and dfp methods behaved badly (the latter far worse) when applied to a simple ill-conditioned quadratic function. moreover, dai (2002) and mascarenhas (2004) gave examples of nonconvex functions, for which the bfgs method failed to converge to the solution of the problem. in this section we consider self-scaling hessian approximation updates for handling ill-conditioned problems. oren and luenberger (1974) proposed the two parameters class of self-scaling hessian approximation updates, ( )1 , , t t tk k k k k k k k kt t k k k k k b s s b y y b w w s b s y s θ θ+ κ   τ = τ β − + + τ    (11) where θ and τ are chosen such that the new update is optimally conditioned in some sense. for the parameters θ and τ the authors suggested the intervals 11, k k h b θ ≤ ≤ τ ≤ (12) to ensure that ( )( ) ( )1 11 ,k kb g b gκ θ τ κ− −+ ≤ when f is a quadratic function with a positive definite hessian g. using intervals (12), oren and spedicato (1976) proposed the class ( )1 k k k h b h τ θ τ − = − (13) which can be obtained by minimizing the condition number ( )( )1 , /k kb hκ θ τ τ+ over θ (see spedicato (1978)). notice that substituting 1τ = in class (13) gives the davidon optimally conditioned update, given in the first case of (8). moreover, as shown in al-baali (1995), class (13) can be also obtained by minimizing the same condition number over τ . in order to include members from the nonconvex class such as the sr1 update, and maintain positive definiteness, al-baali (1995) and hu and storey (1994) proposed the intervals , ,k k k kθ θ θ τ τ τ − + − +≤ ≤ ≤ ≤ (14) where ( )1 ,k k kh vτ ± = ± and where kθ ± and k v are defined by (9). the end points of intervals (14) define two self-scaling sr1 updates which are the same updates obtained by osborne and sun (1988) and wolkowicz (1996). the choice ( )1/ 1 0k kbθ τ += − ≤ with kτ τ += is preferable since methods from the preconvex class work well in practice. an overview of some practical quasi-newton methods 205 most of these self-scaling updates, however, do not generally improve the performance of the unscaled methods as reported by several authors. in fact, shanno and phua (1978) showed that the bfgs method worked better when scaling is used only for the initial hessian approximation 1 b . moreover, nocedal and yuan (1993) showed that, compared with the (unscaled) bfgs method, the best self-scaling bfgs algorithm of oren and luenberger (1974), 0θ = and 1/ kbτ = , performs badly, when used for solving a simple quadratic problem of two variables. they also showed that for the same problem, superliner convergence is not obtained unless certain steplegnth values are used which cannot be guaranteed in practice. al-baali (1998) however, extended the global and superliner convergence theory of byrd, liu and nocedal (1992) for convex functions to the self-scaling class, (11), on the intervals 1 2 3 1, ,kc c cτ θ τθ≤ < ≤ ≤ (15) where ( )1 2 3, , 0,1 ,c c c ∈ and reported that self-scaling methods from these intervals, outperformed corresponding unscaled methods. further numerical testing reported by al-baali and khalfan (2005) showed that these methods succeeded in solving more problems than the unscaled methods, especially when 1.θ ≥ using scaling only when 1,τ < also improves the performance of other self-scaling methods discussed above. for example, replacing the best self-scaling bfgs method of oren and luenberger (1974) mentioned above with 1 min ,1 , kb τ   =     the resulting method outperformed even the standard bfgs method. performance improvement was also reported, especially for the dfp method, by contreras and tapia (1993), and yabe, martines, and tapia (2004), when a similar self-scaling approach was used for a certain type of problems. 5. large-scale quasi-newton methods the storage and computational requirement of the methods we considered so far is ( )2nο for a problem of n variables. several modifications of quasi-newton updates have been proposed to improve their efficiency when this cost is excessive. in this section we consider two approaches that are used widely in practice: the limited-memory method which is suitable for problems in which the true hessian is not sparse, and the partitioned method which is the method of choice for problems with partially separable hessians. 5.1 limited-memory methods in these methods only a few vectors of length n are used for approximating the inverse of the hessian implicitly instead of storing a full n × n matrix. for example, if we write the bfgs update in the form 1 k, v , 1/ , t t t k k k k k k k k k k kh v h v i i y s s yρ ρ ρ+ = + = − = then using the m vector pairs { } 1, , , 1,..., 1,i i ks y i k k k m h += − − + can be expressed as m. al-baali and h. khalfan 206 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 2 1 1 2 2 2 1 1 2 . t t k k k m k m k m k t t t k m k k m k m k m k m k t t t k m k k m k m k m k m k t k k k h v v h v v v v s s v v v v s s v v s s ρ ρ ρ + − + − + − + − + − + − + − + − + − + − + − + − + − + = + + + + l l l l l l l in the limited-memory method of nocedal (1980), the matrix 1k m h − + is replaced at each iteration by a positive definite diagonal matrix ,kd and the search direction ( )1 1 1k k kd h f x+ + += − ∇ is obtained by 4mn multiplications involving the m pairs { },i is y and ( )1kf x +∇ as shown for example in nocedal and wright (1999). this method is referred to as the l-bfgs method and it converges only globally for convex functions as shown in liu and nocedal (1989). a compact representation of limited-memory methods for general quasinewton updates is given by byrd, nocedal and schnabel (1994). computational experience with ( )1/ ,k kd h i= a multiple of the identity matrix, indicates that for large scale problems in which ( )2 1kf x +∇ is not sparse, the l-bfgs method outperforms other methods such as the nonlinear conjugate gradient method; and that its performance improves substantially, in term of computing time, as n gets large. the method however may suffer from slow convergence, which costs more function evaluations, especially on very ill-conditioned problems (nocedal and wright, 1999). for large-scale leastsquare problems, al-baali (2003a) considered a modified l-bfgs method using a vector k y∗ , similar to the one discussed in section 3, instead of k y and reported substantial improvement in numerical performance. another limited-memory approach, is based on the fact that the standard bfgs method accumulates approximate curvature in a sequence of expanding subspaces, which allows using a smaller reduced matrix to approximate the hessian, that increases in dimension at each iteration. this feature is used to define limitedmemory reduced-hessian methods that require half the storage of conventional limited-memory methods. for more on these methods see gill, and leonard (2003 ) and lukšan and vlček (2006). 5.2 partitioned methods every function f with a sparse hessian can be written in the form 1 2( ) ( ) ( ) ( ),mf x f x f x f x= + + +l where each function if depends only on a few variables in , and 1 2 mn n n n= + +l (see griewank and toint (1982)). in a partitioned method the heassian of each element function i f is approximated using a quasinewton hessian approximation, i kb . these matrices are then assembled to define a sparse hessian approximation k b to ( )2 kf x∇ for finding the search direction by solving ( ).k k kb d f x= −∇ (16) if all the element functions ( )if x are convex, then the bfgs method converges globally, even if the system (16 ) is solved inexactly as shown in griewank (1991). the partitioned bfgs method performs well in practice provided that partial separability is fully exploited. practical implementation however, mostly use the an overview of some practical quasi-newton methods 207 sr1 method, 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research, 180: 48-56. received 13 february 2007 accepted 9 october 2007 squ journal for science, 2022, 27(1),52-62 doi:10.53539/squjs.vol27iss1pp52-62 sultan qaboos university 52 engineering properties of umm er radhuma limestone, southeast ataq, yemen ibrahim a. al-akhaly 1 * and abdelmonem m. habtoor 2 1 faculty of petroleum and natural resources, sana’a university; 2 faculty of oil and minerals, shabwah university, *email: ibnalakhly@hotmail.com. abstract: limestone in southeast ataq, shabwah governorate in yemen was studied to assess its engineering properties to ensure their compliance with the minimum construction requirements. this limestone is widely used as building stone in this area. six different sites were selected for sampling appropriate limestone rock for building stone. 42 representative samples were collected and tested for water content, water absorption, dry density, saturated density, specific gravity, porosity, void ratio, and uniaxial compressive strength to ensure their suitability for use in the production of dimension stone. tensile strength and elastic modulus were estimated. their low water absorption, density and porosity values make them suitable for constructing building foundations. their compressive strength, tensile strength and elastic modulus show their high resistance to crushing and bending effects. engineering properties data from southeast ataq limestone were compared with data from various parts of the world. the results showed that southeast ataq limestone is of good quality and satisfies the astm requirements as building stone. keywords: ataq; building stones; engineering properties; limestone; yemen. قَ،َاليمنت َعَ شرقَةَ،َجنوبَومَ ضَ مَالرَ يريَأ َحجرَجَ ةَلَ ندسي َاصَالهَ وَ الخَ ورَبت َاصَحَ رصَ وعبدالمنعمَمَ ليَإبراهيمَعبدالحميدَاألكحَ ة. حيث أقل المتطلبات الهندسي ام ب ان االلتز م ض ة، ل ندسي ه اله واص قييم خ ت ن، ل م بوة، الي تق، محافظة ش دراسة الحجر الجيري جنوب شرق ع م ت :صلخمال في البناء في تلك المنطقة. اُخت يرت ستة مواقع لجمع العينات المناسبة من صخور الحجر الجيري المستخدمة كحجر بناء. واسع يُستخدم هذا الصخر بشكل سبة الفراغ، والضغط متصاص الماء، الكثافة الجافة، الكثافة المشبعة، الوزن النوعي، المسامية، ن ختبار المحتوى المائي، ا عينة ممثلة، وتم ا 24حيث ُجمعت والمسامية ،الكثافة، االمتصاص المنخفض للماءف، لمعرفة مدى مالء متها لالستخدام كحجر بناء. وُمع امالت الُمرونة تقدير مقاومة الشدت ّم و ،حادي المحوراُ ا ظهرت أنها صخور ذات مقاومة عالية ، وُمعامالت الُمرونةومقاومة الشد ،مة الستخدامها كصخور لبناء األساسات. كما أن ق يم مقاومة الضغطكانت مالئ نت النتائج التي تم الحصول عليها مع نتائج اُخرى لصخور الحجر الجيري في أماكن مختلفة من العالم. وأظهرت النتائج أن لتأثيرات الكسر واالنح ناء. قُور المواد. ة الختبارات واصفات الجمعية األمريكيّ لمتطلبات مُ طابقةتق ذات نوعية جيدة كحجر بناء ومُ صخور الحجر الجيري المتواجدة في جنوب شرق ع ار الب ن اءق، ت ع :مفتاحيةالكلماتَال يري جر ح الة ، ندسي اص اله و ، الخ احج ن. م ، الي الج َ engineering properties of umm er radhuma limestone ataq 53 1. introduction imension stone is a natural stone that has been quarried, selected and processed to specific sizes or shapes, with or without one or more mechanically dressed or finished surfaces, for use as building facing, curbing, paving stone, monuments and memorials, and various industrial products [1]. it includes igneous rocks such as basalt and granite; metamorphic rocks such as gneiss and marble; and sedimentary rocks such as limestone, dolomite and sandstone. the dimension stone sector is developing strongly. china, india, turkey and iran lead the world in quarry production while china and italy lead in processed stone export [2]. the world quarry net product is expected to reach one hundred and twenty million tons in 2025 [3]. the main types of dimension (ornamental) rocks include granite, limestone, sandstone and marble [4]. since ancient times, limestone has been known as an inexpensive, reliable building material and used as a decorative and constructional material. it is frequently used as a building material in architectural applications mainly because of its availability; it makes up approximately 10% of the total volume of all sedimentary rocks. limestone rock can be granular or massive depending on the process of formation; generally, it is mainly composed of calcite and aragonite, which are different crystal forms of calcium carbonate. limestone can also originate from deposits of skeletal fragments of marine organisms such as coral. dolomite is formed when calcium carbonate (calcite) sediments are exposed to magnesium ions, which may be present in the groundwater. dolomitic limestone is composed of 50 to 90% calcite (caco3) and 10 to 50% of dolomite (camg(co3)2) [5,6]. knowledge of the engineering properties (physical and mechanical) of rock material is important to the construction industry. no safe design of a soundly engineered construction can be accomplished without the evaluation of the engineering properties of the materials used [7]. the physical properties of rocks are the fundamental properties, which influence strength and durability [8,9]. the amount of water absorbed by a stone can be indicated by porosity [8]. the durability of building stones depends chiefly on effective porosity, water absorption and strength, which indirectly influences the resistance of rock materials to crystallization pressure [10,11]. generally, their strength is used to categorize various rock types and determine their suitability for various end uses, especially for building stone. strength is the ability of a material to resist deformation induced by external forces, whereas the durability of building stone is the measure of its ability to endure and maintain its distinctive characteristics of strength and resistance under its working conditions of cyclic variations of temperature and moisture content, and in its chemical environment [12]. the consumption of natural resources has increased due to the increasing demand for their recent use in building decoration. at present, there are many operational dimension stone quarries of limestone in yemen, from which raw blocks are extracted and processed as building and ornamental stones. the reserves are virtually unlimited. therefore, it is very important to evaluate the rock quality and to determine the engineering properties of such limestone. this information could help present or future engineering projects using limestone in or around the quarry areas. limestone rocks dealt with in the present study belong to the paleocene [13]. despite their widespread occurrence in the southeastern part of yemen, there is a lack of studies on the engineering properties of these rocks as it applies to their commercial uses as building and ornamental stones. for local housing and construction, easily workable rock is required in preference to rock with attractive aesthetic qualities. the stone is shaped and worked to finished products (building blocks). the large scale economically viable use of rock for various building purposes requires that cheap and simple technology can be employed to reduce the cost. the limestone sector in yemen has a huge potential to play a key role in the economic development of the country. hence, testing such rocks for their engineering properties is imperative. this study aims to assess limestone of southeast ataq in shabwah governorate in yemen, based on some engineering properties, which are often considered fundamental for evaluating rock as building stone. study area the studied area is located about 8 km southeast of ataq city between latitude 14 o 27' 32" and 14 o 32' 46" n and longitude 46 o 51' 38" and 46 o 55' 52" e as shown in figure 1. it has a typical arid desert climate, being hot in summer and cold in winter. vegetation is scare but there are some desert plants scattered in the wadis and other flat areas. elevations in the area range from 1121 to 1594 m above sea level (figure 2). the studied limestone belongs to the paleocene umm er radhuma formation (figures 3 and 4). geology yemen has a great variety of rock units which can be considered as important sources of dimension stones and to be of economic importance. limestone is one of these rocks which is widely used in yemen as raw material in the cement industry and construction, and for ornamental stones. the study area has been studied geologically by many investigators. isakinet et al. [14] prepared a geological map of ataq quadrangle at scale 1:100,000 including the studied area. al-obaydee and al-dabbagh [15] have studied the geology of the area south of ataq. engineering geological studies have been carried out by al -dabbagh and alobaydee [16]. d ibrahim a. al-akhaly and abdelmonem m. habtoor 54 figure 1. satellite image showing the location of the studied area. figure 2. digital elevation model (dem) of the study area. engineering properties of umm er radhuma limestone ataq 55 figure 3. geological map of the study area and cross-section from a-b [14]. figure 4. photograph showing the umm er radhuma formation in the studied area. ibrahim a. al-akhaly and abdelmonem m. habtoor 56 figure 5. photograph showing concretions of chert in umm er radhuma formation in the studied area. the basement complex (proterozoic) is found in the southwestern part of the study area, and consists of biotite quartz feldspar schist ('ads formation), metabasalt, metarhyolite, biotite quartz feldspar and amphibolite schist with bands of marble (ray formation) and ataq magmatic complex (gabbro) [14]. the kohlan formation lies with nonconformity on the basement rocks. it consists of calcareous quartz and quartz sandstone with scattered quartz and granite pebbles. the shuqra formation (jurassic) lies with stratigraphic unconformity on the kohlan formation. it is represented by limestone with catinulina sandalina, ceratomya concentrica, fimbria quennelly cox, lopha costata and other fossils. the al mukalla formation (cretaceous) lies with unconformity on the shuqra formation. it is represented by fine grained to gravelly sandstone. the al mukalla formation is red, brown and brownish to reddish in the varieties containing hematite in cement and cross bedding with scattered quartz pebbles, and includes a partly violet colored interlayer of siltstones. the umm er radhuma formation (paleocene) lies with unconformity on the al mukalla formation (figure 3) [14]. it contains campanile briarti rutot et van den brocck, gisortia murchisoni arch, et haime, tiburnus aulacophorus cossm, and other fossils [14]. in the study area, limestone consists of nodular limestone. concretions of chert are common, and up to 3 to 10 cm across, of rounded and elliptical shape (figure 5). its thickness is about 60 m and joint spacing ranges from 2 to 3 m (extremely wide spacing and very large block sizes) and it is characterized by the presence of three orthogonal joint sets (ne-sw, nw-se and e-w). the continuity of joints in the rock mass is more than 20 m. the joint surfaces are generally planar and rough and have strong to very strong wall strength, and very narrow to wide aperture. the infilling materials are rock fragments and clay. the upper surface of the limestone is slightly weathered and the thickness of the weathered material ranges from 1 cm to about 2 cm. the limestone beds are inclined 5 o in ne direction. quaternary sediments consisting of loose or partly consolidated sediments of alluvial gravel deposits cover a great part of the study area. the thicknesses of these sediments may reach 5-10 m. 2. materials and methods limestones were extracted from umm er radhuma formation rocks in southeast ataq using hand tools, blasting and motorized machines. chemical analysis of 6 representative samples of limestone were carried out by xrf, unit model arl 9800 xp sim-seq in quality laboratory of amran cement plant, amran, yemen. 18 cube specimens of dimensions 5×5×5 cm were collected from the study area at 6 different sites (figure 3). the specimens were subjected to standard physical properties for rock, namely water absorption, dry density, saturated density, specific gravity, porosity, void ratio according to american society for testing and material, astm c97 [17]. 18 lump samples were collected to determine water content. 18 cube specimens of 10×10×10 cm dimensions were collected and prepared to determine uniaxial compressive strength (ucs) according to astm c170 [18]. each experiment was conducted on at least three specimens and the average of the obtained values was recorded. these experiments were carried out in the engineering geology department laboratories, faculty of oil and minerals, aden university. hardness testing involves the use of a schmidt impact hammer of type l for the hardness determination of in situ rock, with an impact energy of 0.74 nm applied following isrm [19]. the rebound value of the schmidt hammer is used as an index value for the intact strength of rock material, but it is also used to give an indication of the compressive strength of rock material [19]. the major advantage of the schmidt hammer is that it is portable enough to be easily transported to, and used in, the field. the measured test values were arranged in a descending order (20 engineering properties of umm er radhuma limestone ataq 57 reading points were taken and the mean value of the highest 10 points was considered). this average of rebound hardness of rock multiplied by the correction factor obtained by calibration test is recorded [19]. tensile strength was calculated according to al-derdi and al-harthi's equation [7]. tangent young's modulus was determined according to the chart of deere and miller [20], and then the dynamic modulus of elasticity was calculated according to al-derdi and al-harthi's equation [7]. 3. results and discussion 3.1 chemical characteristics the results of chemical analysis of the limestone samples are presented in table1. the cao content ranges from 42.32 to 54.89 % with an average value of 48.17 % (table 1). the mgo content ranges from 0.51 to 7.23 % with a mean value of 3.70 %. a value of mgo greater than 1% in limestone suggests that the mineral dolomite is present [21]. the caco3 content ranges between 75.33 and 97.70% and the mgco3 content ranges between 1.07 and 15.11 %. the sio2 content in the limestone samples ranges from 0.68 to 8.16 %. these values are comparable to those of similar limestone rocks elsewhere (table 1). the relatively higher content of sio2 can be attributed to chert nodules resulting from the influx of near shore materials into the basin of deposition. the concentration of al2o3 is very low, less than 0.25 %. the concentration of fe2o3 is also very low, at less than 0.06 %. concentrations of al2o3 and fe2o3 are low and may be indicative of the absence of phyllosilicates (clay) in the limestone. the concentration of the total alkalis (na2o+k2o) in the limestone rocks in the studied area is very low, less than 0.34 %. this value is similar to the alkali content of typical limestone bodies in pakistan [22] and nigeria [23] (table 1). loss on ignition (loi) ranges between 41.67 and 45.62 % (table 1). it reflects the content of volatiles (co 2, h2o) present in the limestone rocks. table 1. major element components of the limestone samples. site no. sio2 al2o3 fe2o3 cao mgo na2o k2o tio2 loi caco3 mgco3 1 5.87 0.25 0.06 47.07 4.54 0.04 0.01 42.00 83.78 9.49 2 0.68 0.06 0.03 54.89 0.51 0.01 43.76 97.70 1.07 3 2.46 0.22 0.04 52.00 1.82 0.02 0.01 43.10 92.56 3.80 4 8.16 0.23 0.04 42.32 7.23 0.16 0.03 0.01 41.67 75.33 15.11 5 5.29 0.09 0.03 47.98 3.93 0.34 0.02 42.01 85.40 8.21 6 5.05 0.11 0.03 44.74 4.15 0.13 0.02 45.62 79.64 8.67 min. 0.68 0.06 0.03 42.32 0.51 0.13 0.01 0.01 41.67 75.33 1.07 max. 8.16 0.25 0.06 54.89 7.23 0.34 0.04 0.01 45.62 97.70 15.11 ave. 4.59 0.16 0.04 48.17 3.70 0.21 0.02 0.01 43.03 85.74 7.73 pakistan [22] 3.72 1.16 0.41 49.68 2.79 0.15 0.07 42.05 88.43 5.83 nigeria [23] 3.71 1.10 1.78 50.20 0.85 0.01 0.05 0.07 41.70 89.36 1.78 3.2 engineering properties physical and mechanical characteristics of the limestone samples were determined, using procedures and specifications of astm, which are applicable in yemeni geotechnical tests. the tests carried out include the water content, water absorption, dry density, saturated density, specific gravity, porosity, void ratio and ucs. 3.2.1 physical properties a summary of the physical characteristics of the studied limestone compared to other limestone elsewhere is presented in table 2. 3.2.1.1 water content the water content of limestone is determined according to astm c97 [16]. from the laboratory results the water content by weight has a range of value of between 0.25 and 0.92 % with an average of 0.65 % (table 2). these values are within the range for limestone in portugal [24] (table 3). 3.2.1.2 water absorption the water absorption of limestone is determined according to astm c97 [16]. from the laboratory results the absorption by weight has a range of value between 0.73 and 4.12 % with an average of 2.38 % (table 2). these values ibrahim a. al-akhaly and abdelmonem m. habtoor 58 are within the range for limestone in jordan [25] and pakistan [26]. the values are however higher than those of limestone in turkey [27] (table 3). the astm standard [28] on the use of limestone for dimension stone recommends a maximum water absorption of 3% for high density limestone, 7.5 % for medium density limestone and 12% for low density limestone. limestone in southeast ataq area has high density according to astm specifications [28] (table 3). table 2. results of the physical properties of southeast ataq limestone. site no. water content (%) water absorption (%) dry density (gr/cm 3 ) saturated density (gr/cm 3 ) specific gravity porosity (%) 1 0.92 2.93 2.37 2.39 2.38 2.36 2 0.73 2.05 2.37 2.40 2.38 2.57 3 0.45 1.41 2.46 2.50 2.46 2.64 4 0.25 0.73 2.50 2.54 2.51 2.22 5 0.71 3.05 2.41 2.48 2.41 4.89 6 0.81 4.12 2.39 2.49 2.39 6.58 min. 0.25 0.73 2.37 2.39 2.38 2.22 max. 0.92 4.12 2.50 2.54 2.51 6.58 ave. 0.65 2.38 2.42 2.47 2.42 3.54 3.2.1.3 density rock density is a measure of mass of the rock contained in a given unit volume. the density of limestone is measured according to astm 97 [16]. dry density values range between 2.37 and 2.50 gr/cm 3 with an average of 2.42 gr/cm 3 , whereas saturated density values range between 2.39 and 2.54 gr/cm 3 with an average of 2.47 gr/cm 3 (table 2). these values are lower than those of limestone in pakistan [26], portugal [24], iran [29] and turkey [27]. the values are however higher than those of limestone in saudi arabia [7] (table 3). table 3. comparison of the engineering properties of southeast ataq limestone with other limestones. properties this study pakistan [26] jordan [25] portugal [24] iran [29] turkey [27] saudi arabia [7] astm specification requirements for limestone for dimension stone water content (%) (average) 0.25-0.92 (0.65) 0.39-0.95 < 3 [28] water absorption (%) (average) 0.73-4.12 (2.38) 0.50-6.54 2.62 0.02-0.10 hdl 3 mdl 7.5 ldl 12 dry density (gr/cm 3 ) (average) 2.37-2.50 (2.42) 2.56-2.89 2.60-2.64 2.31-2.70 2.63 2.16 hdl 2.56 mdl 2.16 ldl 1.76 specific gravity (average) 2.38-2.51 (2.42) 2.20-2.70 2.46-2.78 2.20 > 2.50 porosity (%) (average) 2.22-6.58 (3.54) 1.05-2.55 0.27-9.76 0.06-0.26 18.5 ucs (mpa) (average) 70-140 (99) 44-58 44-79 43-99 33-95 54-110 32-39 hdl 55 mdl 28 ldl 12 [28] tensile strength (mpa) (average) 4.36-11.10 (7.63) 5.30-13.80 2.38-3.30 hdl 6.9 mdl 3.4 ldl 2.9 tangent young's modulus (gpa) (average) 44.13-56.54 (48.73) 7.27-13.26 42-50 16.25-19.22 engineering properties of umm er radhuma limestone ataq 59 table 4. classification scheme for porosity of rocks [31]. classification porosity (%) compact <1 a few pores 1–2.5 slightly porous 2.5–5 significantly porous 5–10 many pores 10–20 a lot of pore space >20 the standard specification of astm [28] on the use of limestone for dimension stone is put at minimum of 2.56 gr/cm 3 for high density limestone, 2.16 gr/cm 3 for medium density limestone and 1.76 gr/cm 3 for low density limestone. limestone in southeast ataq area has medium density of oven dried and saturated conditions (table 2). generally, a higher density rock is probably harder, less porous and stronger. the density is important in calculating the weight of the rock in a wall constructional element. 3.2.1.4 specific gravity specific gravity values range between 2.38 and 2.51 with an average of 2.42 (table 2). these values are within the range for limestone in pakistan [26]. the values are, however. lower than those of limestone in jordan [25]. the values are higher than those of limestone in saudi arabia [7] (table 3). the specific gravity is important in calculating the weight of the rock in a wall constructional element. the standard specification of astm [28] on the use of limestone for dimension stone is put at minimum of 2.50 (table 3). 3.2.1.5 porosity porosity is one of the most important physical properties that determines the mechanical characteristics of rock, such as strength and deformability [30]. porosity is defined as being the ratio of the volume of void spaces within a rock to the total bulk volume of the rock. however, these spaces do allow for a little absorption of moisture and other liquids which can corrode or stain the limestone. water and acid rain can affect the appearance of limestone and its durability. limestone in the studied area has a porosity between 2.22 and 6.58 % with an average of 3.54 % (table 2). these values are within the range for limestone in portugal [24] and iran [29]. the values are however higher than those of limestone in turkey [27] (table 3). the values are lower than those of limestone in saudi arabia [7] (table 3). low porosity values make limestone suitable for various construction purposes. a low porosity of limestone gives it a low absorption value. a low absorption value in turn means that the rock has a high resistance to the disintegrating effect of frost. porosity has a direct and indirect effect on most of the physical properties of rocks, and is often considered an important rock parameter. an increasing porosity has an unfavorable influence on the weathering characteristics. moos and quervain [31] developed a classification scheme for porosity of rocks (table 4). according to this classification, the studied limestone rated as ‘few pores’ to ‘slightly porous’ (except that from site no. 6 which rated as ‘significantly porous’) and the effect of weathering will be of little implication. limestone in southeast ataq area has low porosity and medium density under oven dried and saturated conditions which indicate that it is a good quality strongly cemented and compacted rock unit. 3.2.2 mechanical properties compressive strength and tensile strength parameters are the widely used rock strength parameters for geotechnical analyses. 3.2.2.1 compressive strength strength is the ability of a material to resist deformation induced by external forces. the strength of a material is the amount of applied stress at failure [32]. the laboratory ucs is the standard strength parameter of intact rock material. rock strength is a very important criterion for classification of rocks in order to optimize construction usage and surface and/or subsurface structure designs [33]. the main purpose of this test is to ensure that the limestone is capable of withstanding external forces and shocks that may occur during installation and transportation astm c170 [17]. strength is crucial factor for the selection of rocks for building stones. the required value for limestone according to astm is 55 mpa for high density limestone. from the laboratory results the samples showed a range of ucs values between 70 and 140 mpa (table 6). these values are higher than those of limestone in pakistan [26], jordan [25], portugal [24], turkey [27], iran [29] and saudi arabia [7] (table 3) and meet the specification for use as construction stone and ornamental stone. the international society of rock mechanics (isrm) [34] classify rocks in the range of ‘extremely strong’ to ‘extremely weak’ depending on the compressive strength (table 4). limestone rocks in the studied area are strong to very strong according to isrm [34]. ibrahim a. al-akhaly and abdelmonem m. habtoor 60 3.2.2.2 tensile strength tensile strength describes the capacity of the rock to resist tensile stress. it is a key parameter for determining the load bearing capacity of rock, and is resistance to deformation or fracturing, during crushing, drilling, tunnel boring, and blasting, and is used to analyze the stability and serviceability of rock structures [35-37]. the tensile strength of rocks is much lower than the compression strength. there are direct and indirect methods for measurement of tensile strength. the indirect methods have been dominant in determining tensile strength of rocks due to their ease in sample preparation and testing procedure. modulus of rupture is a measure of the tensile strength induced by bending; it is highly affected by the stone’s surface condition on the face that is in tension. the modulus of rupture of rock generally increases as the water absorption decreases for rocks of equal grain size. the samples tested had a modulus of rupture within a range of values of between 4.36 and 11.10 mpa (table 6). these values are within the range for limestone in iran [29] and meet the specification for use as construction stone and ornamental stone. the values are, however, higher than those of limestone in saudi arabia [7] (table 3). the astm standard [28] on the use of limestone for dimension stone recommends a minimum of 6.9 mpa for high density limestone, 3.4 mpa for medium density limestone and 2.9 mpa for low density limestone. limestone in southeast ataq area has medium to high density compared to astm standard [28]. limestone with high tensile and compressive strengths indicates properties of absolute resilience and durability. on the basis of tensile strength all the samples of southeast ataq limestone are acceptable or good. 3.2.2.3 elastic modulus elastic modulus is an important parameter to describe the stress and strain relationship [38]. the type l schmidt hammer may be used to estimate the ucs and modulus of elasticity. deere and miller [19] developed a chart for estimating the tangent young's modulus (e) of the tested material. the e of the studied limestone ranged from 44.13±2 to 56.54±2 mpa with an average of 48.73±2 mpa (table 6). these values are within the range of limestones in turkey [27] and meet the specification for use as construction stone. the values are however higher than those of limestone in iran [29] and saudi arabia [7] (table 3). according to al-derbi and al-harthi's equation [7] the dynamic modulus of elasticity of the studied limestone ranged between 55.59±2 and 70.37±2 mpa with an average of 61.07±2 mpa (table 6). these values ar e higher than those of limestone in saudi arabia [7] (table 3). the modulus ratio (e/ucs) of the studied rocks was calculated and ranged between 404 and 802 with an average of 539 (table 6). the modulus ratio is around 300 for most rocks and more than 500 for strong rocks [39]. hence, the studied limestone is strong according to its modulus ratio [39]. table 5. engineering classification of intact rock on basis of strength [34]. classification ucs (mpa) extremely strong > 250 very strong 100 – 250 strong 50 – 100 medium strong 25 – 50 weak 5 – 25 very weak 1 – 5 extremely weak < 1 table 6. results of the mechanical properties of southeast ataq limestone. site no. ucs (mpa) average corrected rebound no. of schmidt hammer tensile strength (mpa) static young's modulus (tangent) (gpa) dynamic modulus of elasticity (gpa) modulus ratio classification of strength depend on isrm [34] 1 70 50 4.36 44.13±2 55.59±2 802 strong 2 85 51 6.74 46.89±2 58.88±2 552 strong 3 117 52 9.28 53.09±2 66.26±2 454 very strong 4 140 53 11.10 56.54±2 70.37±2 404 very strong 5 97 51 7.69 46.89±2 58.88±2 483 strong 6 83 51 6.58 44.82±2 56.41±2 540 strong min. ….... 70 50 4.36 44.13±2 55.59±2 404 max. 140 53 11.1 56.54±2 70.37±2 802 ave. 98.6 7 51.33 7.63 48.73±2 61.07±2 539 engineering properties of umm er radhuma limestone ataq 61 4. conclusion due to the wide occurrence, availability and low cost of limestones that pass the requirements stated by astm for building materials, they are widely used in the construction industry as building stone. the chemical, physical and mechanical characteristics of the southeast ataq limestone have been investigated to highlight its potential uses in construction. the chemical data of the limestone show that the limestone is comprised dominantly of calcite with some dolomite and it has a low level of impurities. the studied physical and mechanical properties show that southeast ataq limestone is of good quality compared with the astm requirements for building stone. an abundant quantity of the excellent quality limestone can be easily extracted. the net recovery may reach more than 90% of the actual quarry production. with the increase in demand for dimension stone in various building construction projects ranging from outdoor sculpture through interior and exterior cladding to floor covering, etc., the exploitation of limestone for dimension stone production will make a huge contribution to the development and growth of the yemeni economy, considering its good engineering properties as enumerated and discussed in this paper. conflict of interest the authors declare no conflict of interest. acknowledgment we would like to thank anonymous reviewers for their valuable comments which helped to improve the manuscript. references 1. astm c119. standard terminology relating to dimension stone. 2020. available: (www.astm.org). 2. careddu, n., capua, g., siotto, g., dimension stone industry should meet the fundamental values of geoethics. resources policy. 2019, 63, 101468. doi: 10.1016/j.resourpol.2019.101468. 3. montani, c., the world stone situation: a sector with great competitive resilience. in: directory confindustria marmomacchine/associazione italiana marmomacchine, milano, italy. 2019. 4. usgs, 2020, https://www.usgs.gov/ (accessed on 7 march 2021). 5. kuzvart, m., industrial minerals and rocks, 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(eds.), 2016, 295-300. 38. peng, s. and zhang, j., engineering geology for underground rocks. springer-verlag berlin heideelberg. 2007, 319p. 39. waltham, t., foundation of engineering geology. 3 nd ed. taylor & francis e-library. 2009, 98p. received 12 september 2021 accepted 30 october 2021 http://www.astm.org/ squ journal for science, 2021, 26(2), 76-85 doi:10.53539/squjs.vol26iss2pp76-85 sultan qaboos university 76 the deubiquitylase usp5 knockdown reduces semliki forest virus replication in hela cells amer nubgan department of biology, college of science, university of baghdad, baghdad, iraq *email: amer.nubgan@sc.uobaghdad.edu.iq. abstract: semliki forest virus (sfv), a member of the alphavirus genus in the togaviridae family, is a smallenveloped, positive-sense single-stranded rna (+ssrna) virus. the virus is spread by mosquitos and can infect humans, resulting in mild febrile disease with symptoms that include fever, myalgia, arthralgia, persistent headaches and asthenia. virulent strains of sfv in mice cause lethal encephalitis by infecting neurons in the central nervous system. in on-going experiments in the research group using a focused sirna screen we have investigated the role of deubiquitylases (dubs) during sfv infection (as a model alphavirus) and monitored the effect of dub depletion on cell viability after infection. we identified a group of dubs that have a pro-viral effect. the dub, usp5, from this screen was validated to determine its effect upon viral replication. here, we show that depleted usp5 in hela cells resulted in sfv rna and viral yield at 8 h post-infection being significantly reduced. in the multi-step viral growth curve assay, in the absence of usp5, similar yields of sfv were determined at 2 and 4 h post-infection. however, a significant reduction in the infectious viral particles release at 6, 8, 10 and 12 h post-infection was observed and this could be reversed by direct constraining viral replication. these results raise the potential for usp5 to play a distinct role in the replication of sfv, suggesting that usp5 may be a possible anti-viral therapy for alphavirus infection. keywords: alphavirus; rna virus; sfv; dub; usp5; sirna. يختزل قابلية فيروس غابة سمليكي على التكاثر في خاليا هيال usp5حذف انزيم الديبوكتيليز عامر نبَكان موجب جنس فيروسات الفا عائلة توكافيريدي، محتواه الجينومي من نوع الحمض النووي الريبي، خيط منفرد و ينتمي الى ،غابة سمليكي فيروس :صلخمال صغير. ينتقل عن طريق البعوض و يسبب إصابة لالنسان ينتج عنها مضاعفات مثل حمى خفيفة الشحنة وجزيئة هذا الفيروس محاطة بغالف و حجمها الخاليا مستمر و إعياء عام. سالالت هذا الفيروس الضارية تسبب التهاب الدماغ القاتل للفئران عن طريق إصابة وصداع المفاصلالعضالت و يرافقها ألم تحققنا من ،sirnaمن خالل التجارب المختبرية المستمرة في مختبرنا و باستخدام تقنية حذف الجين بواسطة الية العصبية في الجهاز العصبي المركزي. وذلك بحذف هذه االنزيمات من خاليا ( ألفا جنس لفيروسات كأنموذج)المضيف بفيروس غابة سمليكي اصابة خاليا اإلنسان اثناء انزيمات الديبوكتيليزدور يروس غابة توصلنا الى تشخيص مجموعة من هذه االنزيمات التي تلعب دور مباشر في احداث اصابة فا المضيف و مراقبة حيوية الخاليا بعد االصابة. واحد من هذه االنزيمات الذي ادى حذفه من خاليا هيال الى احداث اختزال معنوي في مستوى الحمض النووي الريبي usp5ال سمليكي. انزيم زمنية متعددة، خالل فترات المصابة الخاليا من المتحررة عدد جزيئات الفيروس عن التحري بينت نتائج ساعات من االصابة. 8غابة سمليكي بعد لفيروس 02و 01، 8، 6بشكل معنوي بعد المتحررة الفيروس جزيئات ساعات، بينما اختزلت إعداد 4و 2ال تتأثربعد المتحررة بأن عدد جزيئات الفيروس يلعب دور usp5ال انزيم مقارنة بالخاليا الطبيعية. أظهرت الدراسة الحالية بأن usp5االصابة في الخاليا المحذوف منها انزيم ال بدء وقت من ساعة فيروسات نوع الفا. االصابة في خاليا االنسان و بالتالي قد يكون استهداف و حذف هذا اإلنزيم من الخلية مضادا للحد من إصابات مميز في تكاثر واحداث . sirnaتقنية حذف الجين usp5، انزيم ،انزيمات الديبوكتيليز ،فيروس غابة سمليكي ،فيروس الحمض الريبي ،فايروس نوع الفا :مفتاحيةالكلمات ال the deubiquitylase usp5 knockdown 77 1. introduction he alphaviruses are a group of small-enveloped viruses with positive-sense single-stranded rna genomes; they belong to the alphavirus genus of the togaviridae family. alphaviruses are known to cause a variety of arthritic diseases and encephalitis in humans and animals. they have been classified as old world or new world viruses depending on their geographical distribution. those classified as old world viruses, include semliki forest virus (sfv), chikungunya virus (chikv), sindbis virus and ross river virus. these viruses typically cause fever, rash, and arthritic symptoms during infection. new world viruses include venezuelan equine encephalitis virus and eastern/ western equine encephalitis viruses [1]. most members of the alphavirus genus are arboviruses, which are transmitted to vertebrate hosts by arthropod vectors. the vectors include mosquitoes, ticks and lice, in which alphaviruses produce persistent, lifelong and asymptomatic infections [2]. sfv was identified in central, eastern and southern africa, and was first isolated in 1942 from ae. abnormalis mosquitoes in the semliki forest in uganda [3,4]. infection with sfv can result in a mild febrile illness with symptoms that include fever, myalgia, arthralgia, persistent headaches and asthenia during recovery. only one fatal case of sfv infection has been documented in humans, which was in a laboratory worker in germany, who was thought to be immunocompromised [5]. the basic life cycle of alphaviruses has been well studied [1,6]. the lifecycle starts with the attachment of the virus particle to the cellular receptor. e2 interacts with the cell surface receptor to initiate the endocytic internalization of the sfv virion, fusion of the viral envelope is triggered by low ph and the nucleocapsid is released into the cytoplasm. uncoating of the nucleocapsid frees the 12kb positive-sense ssrna genome, which is translated into four non-structural proteins (nsps 1-4). the nsps combine to generate a replicase complex, which generates dsrna that is then used to produce genomic and subgenomic vrnas. these replication proteins enable the replication of the input genomic rna and translation of the subgenomic mrna into structural proteins (e1, e2, e3 and k6). structural proteins are translocated across the endoplasmic reticulum, processed and transported through the golgi to the plasma membrane. cytoplasmic assembly of virus nucleocapsid, coat and genomic rna produces the nucleocapsid core, which associates with processed glycoproteins at the plasma membrane, resulting in budding [2,7]. ubiquitin is a 76-amino-acid polypeptide present in all eukaryotic cells [8]. all viruses rely extensively on host machinery to achieve successful infection. accordingly, viruses have evolved to enhance or inhibit ubiquitylation of specific substrates to either enhance viral replication or inhibition specific cellular processes [9]. ubiquitylation of protein is a reversible process, which facilitates the termination of ubiquitin-dependent signaling. the isopeptide that links ubiquitin and substrate and/or ubiquitin molecules in a polyubiquitin chain are cleaved by deubiquitylating enzymes (deubiquitylases or dubs) [10]. the human genome encodes about 100 dubs that are distinguished by their catalytic mechanisms and are grouped into six families according to their catalytic domains [11,12]. ubiquitin-specific protease 5 (usp5), also known as isopeptidase t (isot), disassembles an assortment of unanchored polyubiquitin chains (lys 6, 11, 27, 29, 33, 48 and 63) to recycle free mono -ubiquitin [11,13,14]. usp5 is believed to play a role in preventing the accumulation of poly-ubiquitin chains, which would otherwise overwhelm the proteasome by competing with ubiquitinated proteins targeted for degradation [10,15,16]. although dubs regulators of many specific cellular pathways that play a role during different virus infections, a functional role for individual dubs during alphavirus infection has not yet been established [17,18]. in on-going experiments in the research group, a screening of a dub sirna library identified a number of dubs that play functional roles during alphavirus infection. depletion of these hits in hela cells led to an increase in cell viability following sfv infection and subsequent experiments confirmed that depletion of these dubs lead to decreased virus replication (predicted to be pro-viral) and thus could potentially be candidate anti-viral targets. the dub, usp5, was further characterised and identified as being required for sfv replication. dubs have been closely studied as drug targets for cancer; and several dub-targeting drugs are under investigation [19,20]. the overall goal of this type of work is to identify dubs, such as usp5, that are required for efficient sfv replication, and so may lead to the identification of targets for anti-viral therapy to treat alphavirus infection. 2. material and methods cell lines and virus stocks. hela, baby hamster kidney-21 (bhk-21) and vero cells were cultured in dulbecco’s modified eagle’s medium (dmem) supplemented with 100 u/ml penicillin, 100 μg/ml streptomycin, 2 mm l-glutamine and 10% (v/v) heated-inactivated foetal bovine serum (fbs), termed growth media. maintenance medium dulbecco’s modified eagle’s medium was supplemented with 100 units/ml penicillin, 100 μg/ml streptomycin, 2 mm l-glutamine and 2.5% (v/v) fbs. all cell monolayers were grown under high humidity incubation at 37 °c and 5% co2, were mycoplasma-free and cultured for limited passages. sfv clone 4 was used throughout this study [21]. sfv was amplified and stocks titrated in vero cells. usp5 sirna knockdown. all individual usp5 sirnas were obtained from qiagen as follows: sirnas 1-4 were si00052416, si00052423, si00052430 and si03076717 respectively. the all-stars positive control (hs death; si04381048) and all-stars negative non-targeting control sirna (sicontrol or sic; si03650318) sirnas were purchased from qiagen. for deconvolution of the usp5 sirna pool, sirna knockdown was carried out in an opaquet amer nubgan 78 walled and clear-bottomed 96-well plate format. hela cells in a duplicate 96-well plate were reverse-transfected in triplicate with usp5 sirnas, corresponding to the original pool used in the preliminary screen (p), along with each individual sirna (sirnas 1-4) at a final concentration of 20 nm using lipofectamine rnaimax (invitrogen). at 72 h post-transfection (monitoring by microscope every 24 h), one plate was infected with sfv at a moi of 2 and the second plate was mock infected. at 16 h post-infection, cell viability was measured using the celltiter-glo assay (promega) in accordance with the manufacturer’s protocol. both a negative non-targeting control sirna control (sic) and positive control (hs death) were included. for usp5 knockdown in 6-well plate format, hela cells were reverse-transfected with individual sirnas at a final concentration of 20 nm. 72 h post-transfection (monitoring by microscope every 24 h) the cells were either infected with sfv at 2 moi or mock infected. the cells were incubated at 37 °c and 5% co2 for a further 8 h, before being used to monitor the efficiency of knockdown (usp5 mrna level) and viral infection (sfv rna level). supernatants were saved at 8 h post-infection to determine the levels of sfv virus. sfv yields were titrated by plaque assay. for sirna knockdown in 10-cm tissue culture format, cells were reverse-transfected with individual sirnas at a final concentration of 20 nm. cells were incubated at 37°c and 5% co2; the following day, 6 ml of fresh media was added to each dish. after 48 h, cells were harvested and reseeded at 1x10 6 cell/well into four wells of a 6-well plate. plates were incubated at 37 °c and 5% co2 for a further 24 h. 72 h post-transfection (monitoring by microscope every 24 h) the cells were either infected with sfv at 2 moi or mock infected. the cells were monitored for efficiency of knockdown (usp5 protein level) and supernatants were saved at different time points post-infection to determine the multi-step viral growth curves. rna extraction and qpcr. cell lysis and extraction of total rna was performed using rneasy plus mini kit (qiagen) in accordance with the manufacturer’s instructions. rna concentration and purity of each sample was assayed using a nanodrop nd-1000 spectrophotometer (thermo scientific, massachusetts, usa), and rna integrity was assessed by gel electrophoresis. using oligo-d(t) primer (promega) and revertaid h-minus m-mulv reverse transcriptase (thermo scientific), 1 μg of rna was reverse transcribed to cdna. quantitative pcr (qpcr) was performed (in triplicate) using the itaq™ universal sybr® green supermix (biorad 172-5121, usa), and a rotorgene q real-time pcr cycler (qiagen). the following pcr primers were used in this study: actb 5’caccttctacaatgagctgcgtgtg-3’(forward) and 5’-atagcacagcctggatagcaacgtac-3’ erse) [22]; usp5 5’-cgggaccaggccttgaa -3’ (forward) and 5’-tcgtcaatgtgactgaagatcca -3’ (reverse); sfv 5’-cgcatcaccttcttttgtg-3’ (forward) and 5’ccagaccacccgagatttt-3’ (reverse) [23]. a two-step qpcr cycling profile was performed for all primer pairs. an initial enzyme activation/denaturation step at 95 °c for 3 mins was followed by 40 cycles of 94 °c/15 s, 55 °c or 60 °c/30 s. melt curves were read at 0.5 °c intervals from 55 °c to 95 °c. qpcr data were analysed using rotor-gene software. cycle threshold (ct) values were determined for each sample and compared to beta-actin (actb), using the 2 -δδ ct method [24]. immunoblotting. protein lysates were generated from whole cell extracts by lysing cell pellets with laemmli buffer followed by incubation for 10 mins at 90 °c-100 °c, then centrifuged. the 1x laemmli buffer was prepared as follows: [50 mm tris-cl ph 6.8, 2% sodium dodecyl sulphate (sds) and 10% glycerol]. protein samples for loading were adjusted to a final loading volume using 1x laemmli buffer with 10% bromophenol blue (bpb) (w/v) and 1 m dithiothreitol (dtt); samples were heated at 90 °c-100 °c for 5 mins prior to analysis. equal amounts of each sample were loaded and run alongside the colourplus™ protein ladder (broad range, 11-245 kda). protein concentration was assessed using a bicinchoninic acid (bca) protein assay kit, (pierce, uk) in accordance with the manufacturer’s instructions. a final volume of 30 μg containing 25 μl of proteins was resolved on 10% sds-page gels, which were then transferred onto nitrocellulose membranes. membranes were then blocked on a rocker for 2 h in blotto [5% (w/v) skimmed milk powder in pbs plus 0.05% (v/v) tween 20] and prepped with appropriate primary antibodies. membranes were incubated overnight at 4°c. appropriate secondary antibodies labelled with hrp were used and signals detected by enhanced chemiluminescence (ecl) (pierce bio-technology) in accordance with the manufacturer's protocol. quantification of bands (densitometry) was performed using imagej. actin, actb, (abcam ab6276) and usp5 (proteintech 10473-1-ap) antibodies were used throughout this study. antirabbit and anti-mouse hrp-conjugated secondary antibodies were obtained from santa cruz biotechnology. multi-step viral growth curves. hela cells in 10 cm tissue culture dishes were transfected with either usp5 sirnas (1 and 4) or sic for 48 h before being seeded into three wells of a 6-well format. at 72 h post-transfection, cells at a confluence of 80%-90% were either infected with sfv at 2 moi or mock infected. after 1 h incubation at 37 ºc, viral inoculum was aspirated and cells were fed and kept with 1 ml pre-warmed maintenance medium for 2, 4, 6, 8, 10 and 12 h. at each time point, 200 µl of supernatant was collected and replaced with 200 µl of fresh, pre -warmed maintenance medium at set time points, then immediately frozen at -80 ºc. to assess the sfv titre, the frozen time point supernatants were defrosted and titrated by plaque assay in triplicate on bhk-21 cells twice, to give a total of six observations. the log10 values of the final sfv titres were confirmed and the means of two independent experiments were compared against sic values. plaque assays formation. sfv stocks were titrated using bhk-21 as follows: cells were cultured in a 6-well plate until around 80%-90% confluence. cells were then infected with 10-fold dilutions of sfv for 1 h. after 1 h adsorption at 37 ºc, viral inoculum was aspirated and 2x dmem (supplemented with 5% fcs) and 2% low melting point agarose the deubiquitylase usp5 knockdown 79 overlay were added. plaques were visualised at 72 h post-infection by staining with crystal violet. plaques were counted, and virus titres calculated as plaque forming units per ml (pfu/ml), taking into account the original dilutions made. 3. results deconvolution of usp5 sirna pool in previous results from our research group, a loss-of-function sirna screen was undertaken to identify dubs that may play a role during alphavirus replication (data are in the process of publication). a custom designed qiagen sirna library targeting 92 known or predicted dubs, in pools of 4 individual sirnas specific for each dub, was used to knockdown expression in hela cells in duplicate, prior to infecting one plate with virus and monitoring cell viability. we predicted that depletion of dubs could lead to either an increase or decrease in cytopathic effect (cpe) after sfv infection, as a result of decreased or increased replication respectively, reflecting proor anti-viral dub functions. to monitor this, the cell viability ratio for infected versus uninfected sirna depleted cells was determined, with the overall goal of identifying dubs reflecting pro-viral functions that may be potential therapeutic targets. the dub usp5 was further characterised and was identified as being (a pro-viral) required for sfv infection, acting at the role of viral replication in the original screen. using a deconvolution approach, dub was deemed to play a role in sfv infection if the pool of four sirnas and two or more of the individual sirnas resulted in an increase in cell viability (decrease in cpe), based on the assumption that it is unlikely that more than one sirna within a pool would have the same off-target effect. deconvolution of the usp5 sirna pool is shown in figure 1a. knockdown of usp5 in hela cells with the sirna pool again led to a 45% increase in cell viability after sfv infection. two individual usp5 sirnas, sirnas 1 and 4, also resulted in respective increases in cell viability of 53% and 47%. however, treatment of hela cells with usp5 sirnas 2 and 3 resulted in respective decreases in cell viability of 74% and 47% figure 1a. as usp5 was deconvoluted successfully, with pool and two individual sirnas giving positive results, it was decided that this dub would be followed up to investigate further its role during sfv infection. quality control of deconvolution for usp5 sirna pool poor transfection efficiency, poor knockdown efficiency of the target transcript and sirna-treatment toxicity, due to either depletion of the specific dub or off-target effects, are important variables that could potentially influence the data from these deconvolution experiments. to monitor transfection efficiency and toxicity, issues steps were included in this protocol. however, it was not possible to monitor the target knockdown efficiency in this protocol; this is addressed in the next section. transfection efficiency was monitored by using the all-stars hs death sirna, which induces a high degree of cell death by targeting and depleting essential human survival genes. hs death sirna induced cell death was monitored visually by light microscopy and cell viability was measured using celltiter-glo assay (cell viability luciferase assay). the celltiter-glo assay demonstrates an increase in cell viability based on atp levels. atp is an indicator of metabolically active cells, thus the number of viable cells can be assessed based on the amount of atp available. the atp cell viability luciferase assay offers a highly sensitive homogenous assay for quantifying atp in cell cultures. triplicate wells of the 96-well plate were treated with hs death sirna. cells were assessed at 72 h posttransfection; successful transfection of the hela cells should result in a high level of cell death. in all experiments, hs death transfected cells showed an estimated 85%-95% reduction in confluence, which was supported by monitoring the cell viability in the transfected, but uninfected plate which increased numbers of floating cells (died cells) were observed. monitoring of usp5 sirnas induced toxicity was carried out two ways. firstly, examination of cells by light microscopy was performed at 72 h post-transfection. the majority of the dub sirnas were associated with little visible direct toxicity. this was evidenced by an estimated confluency of cells of greater than 90%, with few floating cells in the media and healthy looking cells. these microscopy observations were supported by monitoring the cell viability in the transfected but uninfected plate. this was determined as part of the overall assay (to determine the ratio of cell viability of infected vs uninfected), but here it is analysed on its own, as a percentage relative to untransfected cells (h2o control wells were transfection without sirna to control the potential effect of transfection reagents on the cell) to assess sirna induced toxicity (after 88 h transfection). as predicted by the visual/cell viability evaluation at 72 h, transfection with hs death resulted in an 87% reduction in cell viability compared to untransfected cells in h2o control wells (figure 1b). a non-targeting control sirna (sic) had marginal effect on the cell viability ratio post-transfection, with changes of 4% observed. depletion of usp5 by either the pool of the four sirnas or individual sirnas (1 and 3) had no effect on cell viability respectively. however, individual sirnas (2 and 4) had a marginal reduction in cell viability of 1% and 6% respectively, (figure 1b). https://www.sigmaaldrich.com/catalog/product/mm/sct149 amer nubgan 80 figure 1. deconvolution and quality control for usp5 sirna pool. (a) hela cells were reverse-transfected in duplicate 96 well plate with usp5 sirnas corresponding to the original pool used in the preliminary screen (p) and each sirna individually (sirnas 1-4) along with the non-targeting control (sic). at 72 h post-transfection, one plate was infected with sfv at 2 moi, the second plate was mock infected. at 16 h post-infection cell viability was measured using the celltiter-glo assay. the percentage change in cell viability of infected vs. uninfected cells, relative to the sic treated control is shown. hs death was included as an additional control. the data shown are the mean of 3 independent experiments (+/sem). data were analysed against sic by one way anova with tukey-one-way test (*p≤0.05, **p≤0.01, ***p≤0.001). (b) data representing the cell viability of usp5 and control sirna treated cells 88 h post-transfection. the data shown are the mean of 3 independent experiments (+/sem). data were analysed against h2o control by one way anova with tukey-one-way test (*p≤0.05, **p≤0.01, ***p≤0.001). depletion of usp5 is reduced sfv replication usp5 was successfully validated by deconvolution, meeting the criteria that the original pool of four sirnas and at least two of the individual sirnas (1 and 4) repeated the effects observed in the original screen. thus, usp5 sirnas 1 and 4 were chosen to use for the follow up studies to investigate the role of usp5 during sfv infection. to verify the validity of the usp5 effect, several experiments were undertaken to determine if this was reflected at the level of virus rna. hela cells were reverse-transfected with usp5 sirnas (1 and 4) for 72 h before being infected with 2 moi of sfv and rna extracted at 8 h post-infection. sfv rna and usp5 mrna levels were then measured by qpcr. usp5 sirnas (1 and 4) led to usp5 transcripts being depleted by 88% and 85% respectively, which is statistically significant (p<0.05). for sfv rna levels, depletion of usp5 with sirnas 1 and 4 led to significant reductions in sfv rna of 76% and 69% respectively (figure 2a). the data were analysed and compared to sic using tukey-oneway anova. this showed that the differences were statistically significant (sirna 1 p≤0.001 and sirna 3 p≤0.001) (figure 2a). figure 2. usp5 depletion leads to a decrease in sfv genomic rna levels and sfv titre after infection. (a) hela cells were transfected with usp5 sirnas 1 or 4, or sic, incubated for 72 h before infecting with sfv at 2 moi. total rna was extracted at 8 h post-infection and analysed by qpcr for levels of sfv genomic rna and usp5 mrna. total rna was extracted 8 h post-infection, converted to cdna using oligo d(t) before being analysed by qpcr for levels of sfv genomic rna and usp5 mrna. data were normalised to actin and expressed as 2 -δδct relative to the sic control. (b) sfv present in the supernatants from these experiments were titrated on monolayers of the deubiquitylase usp5 knockdown 81 bhk-21 cells. the data show are the mean of 3 independent experiments (+/sem). data were analysed against sic by one way anova with tukey-one-way test (*p≤0.05, **p≤0.01, ***p≤0.001). it was also possible to determine the levels of sfv released from cells in these experiments. supernatants were saved at 8 h post-infection and titrated on bhk-21 cells. for the supernatant for cells treated with usp5 sirnas 1 and 4, the mean pfu/ml was 1.5 x 10 6 pfu /ml and 1.6 x 10 6 pfu /ml respectively. in comparison, supernatant from sic treated cells was 2.5 x 10 7 pfu /ml. data were analysed using tukey one-way anova as described previously. the results were statistically significant, with sirna 1 p p≤0.05 and sirna 3 p≤0.05 (figure 2b). immunoblot analysis also confirmed sirnas 1 and 4 led to a reduction in usp5 protein levels (figures 3a and b). figure 3. efficiency of sirna depletion of usp5 protein. hela cells were transfected with the qiagen usp5 sirnas 1 or 4 or sic. following 72 h incubation, the cells were lysed in laemmli buffer. 30 μg were then resolved by sds-page and immunoblotted for usp5 and actin. (a) proteins were visualised using ecl detection. (b) quantification of usp5 protein level was determined by quantitating relative to actin, and then compared to sic via image j analysis. data from one independent experiment. multi-step viral growth curves the preliminary screen and deconvolution assay reported the effect of usp5 depletion on virus infection by monitoring cell viability after 16 h post-infection. subsequent experiments confirmed the effects of depletion upon the production of viral rna and viral yield at 8 h post-infection. to test whether the absence of usp5 causes a defect in viral replication at different time points, hela cells were inoculated at a moi of 2, and comparisons were made between the depletion of usp5 by sirnas (1 and 4) treatment and sic treatment over the course of 12 h (figure 4a). no differences in sfv replication were observed between sic and the depletion of usp5 by sirnas (1 and 4) at 2 h and 4 h post-infection; sic produced less virus at 4 h post-infection compared to sirna 1 and 4 (figure 4a). in contrast, the sfv titre detected in sirnas 1 and 4 was significantly reduced after 6-12 h post-infection compared to sic (figure 4a). plaque sizes and phenotypic homogeneity following sfv infection were assessed. compared to sic, no differences in plaque size were detected with the depletion of usp5 by sirnas 1 or 4. immunoblot analyses of the efficiency of usp5 depletion mediated by sirnas 1 and 4 at 72 h post-transfection are shown in figures 4b and c. figure 4. depletion of usp5 leads to a decrease in sfv infectious particle release in multi-step growth curves. hela cells were transfected in a 10 cm dish with either usp5 sirnas 1 or 4, or sic. at 48 h cells were reseeded into duplicate 6 well plates. after a further 24 h, (a) one plate was infected with sfv at 2 moi. aliquots of the cultured supernatants were collected at the indicated time points (2, 4, 6, 8, 10 and 12 h) post-infection and sfv titres were quantified in triplicate on monolayers of bhk-21 cells. the data show are the mean of 3 independent experiments (+/ amer nubgan 82 sem). data were analysed against sic by one way anova with tukey-one-way test (*p≤0.05, **p≤0.01, ***p≤0.001). (b) representative immunoblot analysis of usp5 and actin in lysates from sirna treated cells. (c) quantification of usp5 protein level was determined by quantitating relative to actin and then compared to sic via image j analysis. data from one independent experiment. 4. discussion all viruses rely extensively on host machinery to achieve successful viral replication. accordingly, viruses have evolved to enhance or inhibit ubiquitylation of specific substrates to either enhance viral replication or inhibition specific cellular processes. the reverse reaction is undertaken by a large family of enzymes, termed deubiquitylases, or dubs. many of these are crucial, not only to virus replication, but also in the regulation of the immune system against infection and vesicle trafficking. however, the specific role of dubs in alphavirus infection had not been studied previously. several studies have been carried out using multiple genome-wide screens to illustrate the mechanisms of viral infection, including influenza virus, sindbis virus, west nile virus and hiv, and the host cell requirements to support or control infection [25–29]. in this study, sirna treatment of hela cells indicated a pro-viral role for usp5 during sfv infection. the longterm aim of the study was to identify potential targets for therapeutic intervention. several factors may explain the lack of overlap between the results of the preliminary screen and the deconvolution. it is possible that there may have been technical issues from generating the pools for use in this study, as the original screen pools purchased from q iagen were no longer available. furthermore, as revealed in a study by bushman and colleagues, data analysed from a screen performed in duplicate under identical experimental conditions, the yields of data sets only overlapped by an estimated 50% [30]. three important variables that could potentially influence the data from these deconvolution experiments are poor transfection efficiency, poor knockdown efficiency of the target transcript and toxicity due to sirna treatment, either due to depletion of the specific dub or off-target effects [31,32]. the approach used in these validation experiments was unable to monitor the target knockdown efficiency. this is addressed in the section investigating the effect of usp5 depletion on sfv replication by monitoring the levels of usp5 transcripts and protein. however, steps were included in the protocol to monitor both transfection efficiency and toxicity issues (figure 1b). transfection efficiency was monitored by using the allstars hs death sirna, which induces a high degree of cell death by targeting and depleting essential human survival genes [33]. in this study we propose that usp5 is essential for efficient sfv infection and replication. in its absence, induced by sirna depletion in hela cells, sfv replication and the release of infectious viral particles during infection were significantly reduced. qpcr and plaque assay were used to demonstrate the effect upon sfv rna levels and sfv titres at 8 h post-infection. in the multi steps viral growth curve assay, for the early hours of sfv infection, 2 and 4 h post-infection, similar sfv yields were determined among the sic and usp5 knockdown cells, suggesting that sirnas 1 and 4 against usp5 had no effect on sfv uptake. however, sfv showed a lower titre at 6, 8, 10 and 12 h postinfection, indicating that usp5 may play a role within the cell only and late in infection. taken together, these data implied that in hela cells, usp5 is required for efficient sfv replication. it has been reported that the depletion of usp5 in mammalian cells, and in yeast, leads to the accumulation of unanchored ubiquitin chains; depletion of usp5 may also inhibit the function of proteasomes [13,14]. many studies have shown that usp5 targets numerous cytosolic proteins and influences a broad range of cellular processes including dna repair, immune responses and tumour cell proliferation [35–37]. however, the mechanisms by which usp5 exerts this strong pro-viral effect are not obvious. previous studies indicate that dubs play a role as negative regulators of ifn and the production of proinflammatory cytokines such as mysm1, a20 and cyld [38–41]. panda and colleagues reported that the absence of mysm1 in murine macrophages led to the reduced replication of vesicular stomatitis virus as a consequence of increased type 1 ifn and pro-inflammatory cytokine production [41]. alphaviruses are very sensitive to ifns and pretreating cells with ifn inhibits viral replication [42]. findings by reynaud and colleagues suggest that ifnβ pretreatment could block alphavirus infection before rna begins to replicate, but that it did not affect the process of virus entry and virion disassembly [43]. ubiquitination and deubiquitination processes have been demonstrated to play regulatory roles, controlling various aspects of cellular pathways, including immunity [44–47]. normally, e3 ligases activate traf3/6 by adding k63-linked polyubiquitin chains, leading to the production of irf3/7 and nf-kβ. this subsequently causes the induction of pro-inflammatory cytokines and type 1 ifns [47,48]. thus, in the absence of usp5 there may be overproduction of cytokines such as ifnβ, which induces a strong anti-viral environment. this would make usp5 attractive to explore in basic experiments to characterise its role during alphavirus infection; in particular, it would be useful to identify those proteins with which usp5 may interact. 5. conclusion the overall goal of this type of work is to try to identify druggable proteins that may be possible to target during alphavirus infection. dubs are commonly studied as drug targets in cancer, and a number of drugs are under investigation. from the outcome of our investigation, it is possible to conclude that usp5 may be a target anti -viral therapy for alphavirus infection. there are a number of areas that could be followed up from this work, in addition to the deubiquitylase usp5 knockdown 83 the 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https://doi.org/10.1016/j.immuni.2011.11.010 https://www.ncbi.nlm.nih.gov/pubmed/?term=liu%20x%5bauthor%5d&cauthor=true&cauthor_uid=23953672 https://www.ncbi.nlm.nih.gov/pubmed/?term=wang%20q%5bauthor%5d&cauthor=true&cauthor_uid=23953672 https://www.ncbi.nlm.nih.gov/pubmed/?term=chen%20w%5bauthor%5d&cauthor=true&cauthor_uid=23953672 https://www.ncbi.nlm.nih.gov/pubmed/?term=wang%20c%5bauthor%5d&cauthor=true&cauthor_uid=23953672 https://www.ncbi.nlm.nih.gov/pubmed/23953672 squ journal for science, 2023, 28(1), 25-41 doi:10.53539/squjs.vol28iss1pp25-41 sultan qaboos university 25 role of nanotechnology in diagnosing, safeguarding, and treating covid-19 kenneth hulugalla a , panchali ranasinghe a , gareth r williams b , k.m. nalin de silva a,c and rohini m. de silva a * a centre for advanced materials and devices (camd), department of chemistry, university of colombo, colombo 00300, sri lanka, b ucl school of pharmacy, university college london, 29-39 brunswick square,london, wcin 1ax, uk, c department of chemistry, college of science, sultan qaboos university, muscat, sultanate of oman, *email: rohini@chem.cmb.ac.lk. abstract: coronavirus disease (covid-19) is arguably the worst health crisis the world has faced in the 21st century, and the world health organization declared this a “public health emergency of international concern” during the beginning of the pandemic and continued for a significant period of time. considering the public health risk and the delay in introducing a suitable medical intervention to eradicate this virus, many reserachers embarked on different technologies to develop a cure. nanotechnology has emerged as a promising weapon in the fight against covid-19 and other similar viral diseases. the unique qualities of nanomaterials make them excellent for a variety of applications, including the development of low-cost, real-time diagnostic systems, reusable personal protective equipment, and innovative carriers for biological cargo such as mrna in vaccines and crispr/cas9 in gene editing. in this review the current available pharmacological and non-pharmacological options that are being used around the world against covid-19 are compared with their nanotechnological counterparts. here, we also elaborate the advantages of currently available nanotechnology-based diagnostics, protective equipment, vaccines and therapeutics and discuss future directions and steps that should be taken to translate these technologies into a clinical setting to combat the covid-19 pandemic. keywords: covid19; sars-cov-2; nanotechnology; rna vaccine; lipid nanoparticles. covid-19دور تقنية النانو في تشخيص وحماية وعالج نالين دي سيلفا ، وروهيني م. دي سيلفا كينيث هولوغاال ، بانشالي راناسينغ ، غاريث ويليامز ، ك.م. ( هو أسوأ أزمة صحية واجهها العالم في القرن الحادي والعشرين ، وقد أعلنت منظمة covid-19يمكن القول إن مرض فيروس كورونا ) :صلخمال بالنظر إلى مخاطر الصحة العامة الصحة العالمية أن هذه "حالة طوارئ صحية عامة تثير قلقًا دوليًا" خالل بداية الجائحة واستمرت لفترة طويلة من الوقت. اء على هذا الفيروس ، شرع العديد من الباحثين في تقنيات مختلفة لتطوير عالج ، ظهرت تقنية النانو كسالح والتأخير في إدخال تدخل طبي مناسب للقض الصفات الفريدة للمواد النانوية تجعلها ممتازة لمجموعة متنوعة من التطبيقات ، وغيرها من األمراض الفيروسية المماثلة. covid-19واعد في مكافحة وات تشخيص منخفضة التكلفة في الوقت الحقيقي ، ومعدات حماية شخصية قابلة إلعادة االستخدام ، وناقالت مبتكرة للبضائع بما في ذلك تطوير أد في هذا البحث ، تتم مقارنة الخيارات الدوائية وغير الدوائية المتاحة حاليًا والتي في الجينات. crispr / cas9في اللقاحات و mrnaالبيولوجية مثل هنا، نوضح أيًضا مزايا التشخيصات القائمة على تقنية مع نظيراتها في مجال التكنولوجيا النانوية. covid-19ستخدامها في جميع أنحاء العالم ضد يتم ا ه التقنيات إلى بيئة النانو ومعدات الحماية واللقاحات والعالجات المتاحة حاليًا، ونناقش االتجاهات والخطوات المستقبلية التي يجب اتخاذها لترجمة هذ .covid-91سريرية لمكافحة وباء ، تقنية النانو ، لقاح الحمض النووي الريبي، الجسيمات الثانوية الدهنية. 2-، سارس كوف 91كوفيد :مفتاحيةالكلمات ال rohini m. de silva et al. 26 1. introduction he covid-19 pandemic caused by the sars-cov-2 virus is arguably the worst health crisis faced by humanity during the 21 st century, exerting a pervasive effect on all aspects of human life in almost every country worldwide. as of january 2023, more than 650 million cases have been recorded in a total of 222 countries, with over 6 million deaths [1]. the effects of sars-cov-2 stunned experts and the general public alike, primarily since it broke the patterns seen with all other recent coronaviruses such as sars -cov-1 in 2002 and mers-cov in 2012 [2,3]. these viruses are the closest comparisons to the covid 19, due to their chronological proximity and inclusion in the same family, but their impacts vary drastically. the sars -cov1 virus was responsible for 774 deaths from 8096 reported cases between 2002 and 2004, having a case fatality rate (cfr) of 10%. the mers virus showed a much higher cfr, with 850 deaths from 2400 reported cases for a cfr >35% [2]. the global cfr of sars-cov-2 pales in comparison, ranging between 2-4% currently, with some countries having cfr values as low as 1% (comparable to the typical influenza virus) and other developing countries having values as high as 25% (particularly due to the collapse of healthcare systems) [4]. however, this information is misleading with regards to the seriousness of sars -cov-2; albeit being less fatal than previous coronaviruses, it is much more contagious and widespread, leading to a truly global impact with social distancing steps, mask mandates and lockdowns being necessitated in many countries to control the virus [5]. dry cough, loss of taste and smell, fever, body aches, weariness, and potentially fatal acute respiratory distress syndrome (ards) are all symptoms of sars-cov-2 [6]. the virus mainly attacks the lungs, but it also has the ability to affect other organs such as the cardiovascular system, central nervous system, kidney and liver, [7] particularly in immunocompromised patients and individuals with comorbidities (e.g. diabetes, cancer, cardiovascular diseases, neurological diseases) [4]. vaccines against the virus hit the market in december 2020,[8] but it has constantly mutated to result in five major variants from different parts of the world including the uk (alpha), south africa (beta, omicron), brazil (gamma) and india (delta) [9,10]. the delta variant caused more severe disease than other variants in people who were not vaccinated. the procurement and availability of vaccines in developing countries has also been a major hurdle in combating the coronavirus and achieving herd immunity, with 69.5% of the world’s high income countries vaccinated with at least one dose as of january 2022, but with low income countries severely lagging with a meagre 10.9% vaccinated with at least one dose [11]. therefore, unless there is coordinated global action to improve vaccine equity, the probability of the emergence of a vacc ine-resistant variant is ever present. figure 1. schematic diagram of the sars-cov-2 virus showing the assembly of the genome (rna and nucleocapsid protein) and the envelope (spike glycoprotein (s), envelope protein (e) and membrane protein (m)). t role of nanotechnology in diagnosing safeguarding, and treating covid-19 27 due to the introduction of new strains and mutations, no effective treatment has been developed yet, with a range of antiviral and anti-inflammatory drugs being repurposed for relief of symptoms with varying degrees of success [9]. to overcome the limitations of traditional systems, a truly multidisciplinary approach is required, and sars-cov-2 has brought together scientists from every discipline. nanotechnology and nanomedicine offer a promising and proven alternative to conventional therapies, as exemplified by the effectiveness of nanoparticle based therapies for the treatment of other diseases, particularly cancer [12]. the chances of nanotechnology being a successful approach against covid-19 are also high due to several factors; sars-cov-2 is similar in size (60-140 nm) to most of the current food and drug administration (fda) approved nanodrugs, paving the way for “direct combat” therapy, [13] nanoparticles have been shown to enhance the stability of mrna vaccines [14], and the physicochemical properties of nanomaterials can be tuned to combat viruses [15]. these are a few potential uses of nanotechnology in combatting covid-19, but the opportuntities for the utilization of nanotechnology in the fight against the virus are in fact far greater, with applications in respiratory masks, gloves, personal protective equipment (ppe), air filtration systems, disinfectants, and detection kits for diagnosis [16]. this review focuses on the use of nanotechnology under the categories of treatment (e.g., nanoscale drug delivery systems), prevention (e.g., ppe, disinfectants and vaccines) and diagnostics (e.g., rapid detection assay kits). we critically discuss the advantages, shortcomings and future prospects for nanotechnology in the setting of covid-19. this review comprehensively considers the current knowledge of the subject and will help researchers and scientists to formulate innovative strategies to mitigate this ongoing pandemic. 2. the structure of sars-cov-2 and its effect on the human body 2.1 structure of sars-cov-2 the typical architecture of a virus comprises a virus-coded protein coat (envelope) that protects the viral genome, which could be made up of either rna or dna [17]. accordingly, as shown in figure 1, [18] the sars-cov-2 virus contains an envelope consisting of spike protein, envelope protein, and membrane proteins [19]. this envelope also shares the common feature of other coronaviruses, having a crown -like appearance [19] due to the presence of spike proteins made out of glycoproteins [20]. the genome contains a positivestranded rna molecule assembled with nucleocapsid protein [21]. the receptor-binding domain of the envelope shows an affinity towards the angiotensin-converting enzyme 2 (ace2) receptors in the lower respiratory tract [20]. 2.2 effect of sars-cov-2 on the human body the sars-cov-2 virus can spread covid-19 to the general public in a variety of ways. anyone can become infected if the minute liquid particles discharged from an infected person's mouth or nose contaminate their nose, mouth, or eyes [22]. according to case study reports, key symptoms can be classified as (1) otolaryngological (e.g. loss of sense of smell and taste, sore throat, cough, nasal congestion, earache, runny nose, tinnitus, hoarseness, etc); [23] (2) neurological (e.g. headache, dizziness, impaired consciousness, unstable walking, cerebral hemorrhage, cerebral infarction, etc); [24] (3) psychotic (e.g. delusions, orientation/attention disturbances, auditory and visual hallucinations, etc); [25] and, (4) dermatological (e.g. erythematous rash, urticaria and chicken pox-like lesions) [26]. when the viral genome is replicating, the monocytes in the host’s alveolar space secrete proinflammatory cytokines, chemokines and induce pneumocytes apoptosis. additionally, the chemokines and cytokines released by recruited macrophages promote capillary permeability and neutrophil recruitment. due to neutrophil degranulation, the alveolar-capillary barrier is broken, causing irreparable impairment to pneumocytes and endothelial cells. the generation of neutrophil e xtracellular traps (nets), in which the neutrophils release their intracellular content (mainly dna and proteins) into the extracellular compartment as a trap to apprehend pathogens, is also an important factor. irrespective of the mechanism, ultimately bl ood proteins transmigrate, causing interstitial and alveolar edema [27]. table 1 details a summary of the pathological conditions of several organs affected by covid-19. table 1. pathological conditions of the lungs, heart, placenta, kidney and gut caused by covid-19. organ pathological conditions reference(s) lungs  become deteriorated to the stage clinically known as acute respiratory distress syndrome (ards)  the histopathology leading to ards has been identified as diffuse alveolar damage (dad), in which the capillary endothelial cells and alveoli epithelial cells are permanently impaired with protein-rich fluid leakage into the interstitial and alveolar space  subsequent formation of hyaline membrane and intracapillary thrombosis causes surfactant stabilization, alveolar collapse, and 27 rohini m. de silva et al. 28 3. current management of covid-19 even after sars-cov-2 was declared a pandemic by the world health organisation (who) in march 2020, [31] there has been a dearth of drugs approved for the treatment of the virus, and not a single drug has been discovered solely for the purpose of combating covid-19. the us food and drug administration has already approved remdesivir (an antiviral drug originally developed to treat hepatitis c and ebola) [32]. several other immunomodulatory medicines, notably tocilizumab for the treatment of covid -19 patients with severe symptoms necessitating hospitalization, have also received emergency use authorisation [33]. non-pharmacological therapies have been the cornerstone in the care of covid-19 due to a lack of appropriate medicines. these include preventative measures such as social distancing, hand washing, using face masks, and reducing public gatherings, among others [34]. non-pharmacological treatments also include supportive therapies like oxygen therapy for those patients presenting with more severe symptoms and requiring hospitalization [27,35]. 3.1 pharmacological management there has been a definite increase in the understanding of how different drugs affect the virus as wel l as better understanding of the risk/reward ratio in the use of certain drugs. for example, there were studies in the initial days of the pandemic that advocated the use of medications like hydroxychloroquine, lopinavir/ritonavir, and ivermectin to treat covid-19 patients [36-38]. however, following the gathering of new information, the who issued strong recommendations against using these medications in patients with covid-19 of any severity [39]. the who now strongly recommends the use of il-6 receptor blockers (tocilizumab or sarilumab) and corticosteroids in patients with severe or critical covid -19 infection [39]. this is apart from the general antiviral treatments like vitamin c and d, zinc, and selenium which are used as immune boosters in covid-19 patients [40]. ultimately hypoxemia heart  myocarditis  inflammation in blood vessels  cardiac arrhythmias  acute coronary syndrome (acs)  covid-19 associated thrombophilia  release of proinflammatory cytokines (il-6)  exacerbation of earlier cases of severe coronary artery disease  stress cardiomyopathy  reduced coronary circulation  impaired oxygen supply causes the destabilization of coronary plaque microthrombogenesis 21 placenta  molecular pathological tests have detected sars-cov-2 antigens in the villous syncytiotrophoblasts on the villous chorion, chronic histiocytic intervillositis, and syncytiotrophoblast necrosis  the virus has not been detected within hoffbauer cells in the placenta 28 29 kidney  direct cytotoxic injury from the virus  imbalance in the renin-angiotensin-aldosterone system  cytokine-induced hyperinflammatory state  microvascular injury  hypercoagulable state  hypovolemia  kidney injury due to potential nephrotoxic agents and nosocomial sepsis 21 gut  shedding of the mucosal epithelium  erosion of the intestinal mucosa  focal inflammatory necrosis with haemorrhage  massive neutrophil infiltration and macrophage proliferation with minor lymphocyte infiltration  microbiological observations have identified fungal spores and gram-positive cocci  detection of rna of sars-cov-2 virus in intestinal macrophages supports the conclusion of possible gastrointestinal infection 30 role of nanotechnology in diagnosing safeguarding, and treating covid-19 29 remdesivir, an antiviral medication that works by blocking viral rdrp (rna -dependent rna polymerase), was shown to be selectively cytotoxic against sars -cov-2. it is one of the first drugs which have been used to treat covid-19 patients belonging to distinct categories such as pregnant women and immunocompromised individuals [41,42]. there is also an abundance of evidence in the form of case studies and clinical trials that have established the efficacy of this anti-viral drug [43]. it is currently being used as a covid-19 treatment option for both adults and paediatric patients above the age of 12 years after hospitalization [44]. another fda-approved therapy is casirivimab/imdevimab (regen-cov), a recombinant monoclonal medicine or antibody cocktail that specifically targets the rbd region of the sars cov-2 spike protein [45]. even though the clinical data pertaining to casirivimab is limited, it has so far shown lowering of viral load in patients at the initial stage of infection or a baseline viral load [46]. antiviral and antiparasitic agents are two classes of repurposed drugs that have been employed to tackle the covid -19 pandemic. most of these anti-viral drugs have been used in clinical practice during sars -cov-1 and mers outbreaks and have been identified as promising therapies against covid-19 [44]. lopinavir and ritonavir are used in combination for anti-hiv retroviral treatment, as well as being clinically tested as a sars-cov therapeutic intervention [47]. the active period of lopinavir or the exposure period in patient plasma is improved by ritonavir, which functions as an efficacious inhibitor of host proteases (particularly the p glycoprotein efflux mediator and cytochrome p450 3a4 enzyme) [44,47]. a study done during sars-cov-1 showed a curtailing of intubation levels and mortality rate upon use of this drug combination [48]. so far, lopinavir/ritonavir has shown mixed results as a therapy for covid-19. some studies indicate quick improvement and significant viral load clearance [38], whereas other clinical trials have concluded that it does not offer clinical improvement or diminished mortality rates compared to standard care [49]. as a result, further experimental and clinical trials should be conducted in order to gather in disputable proof. corticosteroids such as dexamethasone and methylprednisolone are currently used as supplementary drugs to alleviate the severe inflammatory responses which are often associated with accute respiratory disease syndrome (ards) and covid pneumonia [44,47]. multiple clinical studies have shown the benefits of corticosteroid therapy, such as the removal of ventilation and higher chances of extubation in patients. while more clinical trials are needed to determine the efficacy of corticosteroid s in covid-19 patients, their ability to combat ards symptoms has made them an effective therapy management strategy thus far [50,51,52]. tocilizumab (tcz) is a monoclonal antibody that inhibits the interleukin -6 receptor (il-6r) and is commonly used as a therapeutic immunosuppressant. as a result of its success in treating covid -19, it was approved by the fda as an emergency use therapy and by the who for the treatment of patients with severe covid-19, as stated previously. it is often used to treat covid-19 patients' hyperinflammation and other immunological reactions [44]. a range of clinical trials have thrown light on the efficacy of tocilizumab in patients, with strong reduction in inflammatory biomarkers, relief of cytokine storm in the respiratory system, scaling down of the requirement for intubation and cessation of clinical collapse [33,53-56]. among the other clinically studied and ongoing trials of supplementary treatments are studies on therapeutics that lessen the immune response or immunomodulators such as ifn-α2b, ifn-β1b, and ifn-β1a. ifn-α2b, in particular, has also been shown to cause a reduction in inflammatory cytokines such as il -6 and crp in the period of time over which virus can be detected in the upper airways of patients [57]. similarly, ifn-β1b has aided in the process of reducing mortality and improving discharge rate as well as giving positive progress in clinical wellbeing [58]. tissue plasminogen activator (tpa) is another type of supportive therapy which is usually administered to covid-19 patients with high thrombus formation risk. it has been proven that this therapeutic is capable of instantaneous dissolving of the thrombi , alongside ameliorating the respiratory condition of the patients [59]. as part of a comprehensive pharmacovigilance strategy, the efficacy and safety of existing covid-19 therapies should be closely monitored. efficacy and safety data for several repurposed and supporting medications have been mixed. multiple methodological flaws make it difficult to eva luate results from studies, the most prominent of which is the lack of a reliable covid-19 control therapy. antiviral therapy and a variety of supportive treatments, such as immunomodulation and antibody supplementation, will likely continue to play pivotal roles in covid-19 treatment. while new therapies are being developed, we can only hope that careful usage of the currently available medications will continue to help patients [44]. 3.2 non-pharmacological management the basic motive behind non-pharmaceutical interventions is to curb the transmission of sars -cov-2 infection. social distancing and lockdowns have been practiced with the main objective of reducing the rt value (time varying reproduction number) below 1. even though these drastic management decisions have created the desired effect, it has been achieved only with a pronounced socio -economic detriment [60]. supportive treatments are another category of non-pharmacological management used for covid-19 patients. the most common are oxygen therapy, the prone position, and nitric oxide inhalation [61]. rohini m. de silva et al. 30 under oxygen therapy, respiratory support is provided to hypoxemic patients where blood oxygen level is improved and maintained at least above 90% [62]. non-invasive ventilation is an assisted respiratory support technique which is used to avoid the difficulties faced during intubation [64]. it is usually approved for patients at early stages of covid-19 infection and also for individuals with milder immunosuppressive and cardiovascular complications but it only delays the invasive ventilation [65,61]. invasive ventilation involves positive pressure gradient ventilation directed via an endotracheal or tracheostomy tube. the most common techniques are synchronized intermittent mandatory ventilation (simv), pressure support (ps), positive end expiratory pressure (peep) and continuous positive airway pressure (cpap) [63]. extra corporeal membrane oxygenation (ecmo) is an advanced invasive ventilation technique typically recommended for individuals with limited organ failure and good premorbid functional status. since this is a final stage intervention, it is initiated only after the failure of other ventilation support , and after weighing the riskbenefit trade-off [65]. another advanced invasive ventilation strategy used to avoid intubation in patients with respiratory arrest and severe hypoxemia is the use of a high -flow nasal cannula. this allows sufficient tissue oxygenation of patients with acute respirato ry failure [66]. the prone position is a technique which improves ventilation perfusion by repositioning the heart in the chest to better recruit pulmonary alveoli. this has been proposed as an adjunct to other supportive therapies and several studies have shown that use of the prone position in covid-19 patients increases oxygenation [34,67,68]. from the results of current research, there is no specific non-pharmacological treatment that can be said to have great effectiveness against covid-19. studies have been conducted with small cohorts and the results are largely skewed, while the evidence is indirect. however, several approaches do show potential and there is a need for more rigorous clinical trials to be conducted to establish more reliable evidenc e with regard to nonpharmacological treatments. 4. nanotechnology in covid-19 nanotechnology has infiltrated practically every subspecialty of research, including chemistry, biology, medicine, agriculture, the food industry and cosmetics, since its inception. nanotechnology has shown promising results in treating viral infections such as hiv, herpes simplex and respiratory viruses [69]. during the covid-19 pandemic, nanotechnologists have played critical roles in multiple aspects, from diagnosis through treatment, prevention, and vaccine development [70]. nanotechnological strategies can be used either internally or externally to the human body to combat the disease. some novel products are already in use by healthcare professionals and the general public, while others are still in clinical trials. the notable characteristic of nanotechnology is that it can be engineered in such a way to avoid the drawbacks and enhance the preferable qualities of already available products [71]. the integrative approach of nanotechnology in the diagnosis of, and protection and treatment against covid-19, along with its uses in vaccine development, will be discussed in this section. 4.1 nanotechnology in diagnosis covid-19 diagnosis is critical in the fight against the virus and is required to prevent the virus from spreading further and increase the chances of saving lives through supportive care. chest computed tomography (ct) imaging, chest x-ray, nucleic acid-based methods (real-time polymerase chain reaction, rtpcr), and immunoassays or serology tests (enzyme-linked immunosorbent assays, elisa) are used in clinical practice to diagnose covid-19 [72,21]. despite its considerable drawbacks, rt-pcr is the predominantly used technique for diagnosis. the main drawbac ks include the inability to detect asymptomatic patients because it requires a comparatively high virus load (high lower detection limit) to declare as positive for covid-19, a lack of sufficient technical support (including laboratory facilities in rural or undeveloped areas of the world), and the unavailability of rt-pcr kits to fulfil the demand for tests. nanotechnology has helped to alleviate some of the existing challenges [73]. one-step reverse transcription loop-mediated isothermal amplification coupled with a nanoparticle-based biosensor assay (rt-lamp-nbs) and reverse transcription loop-mediated isothermal amplification combined with chemiluminescence (rt-lamp-cl) are two techniques that eliminate the need for costly pcr machines and the prolonged thermocycling times used in current pcr techniques [74]. rt-lamp-nbs has successfully combined nanotechnology and the rt-pcr technique. the temperature of the lamp primer sets, f1ab (opening reading frame 1a/b), and nucleoprotein genes of sars -cov-2 has been kept constant at 63 0 c for 40 minutes to isothermally amplify the nucleic acid molecules simultaneously. the nanoparticle -based biosensor has easily interpreted the results. according to the results, the sensitivity of the test has been 12 copies per reaction and there has been no cross-reactivity from other non-sars-cov-2 templates. from sample collection to result interpretation, this biosensor took approximately an hour, demonstrating the qualities which make it a potential novel biosensor [75]. similarly, using nanotechnology, rt-lamp can be paired with chemiluminescence to detect the presence of the virus by the emission of a chemiluminescence role of nanotechnology in diagnosing safeguarding, and treating covid-19 31 signal. here, the chemiluminescence signal is generated by a reaction between streptavidin modified a lkaline phosphate (alp) enzyme and biotin-labeled amplified products [74,73]. in clinical covid-19 diagnosis, a dual-functional plasmonic biosensor with the plasmonic photothermal (ppt) effect and localized surface plasmon resonance (lspr) sensing transd uction could be a viable alternative to the rt-pcr approach. in this innovation, the detection of sars-cov-2 is achieved by employing the nucleic acid hybridization theory. detection happens upon binding of chosen sequences from sars-cov-2 to two-dimensional gold nanoislands (aunis) which are functionalized with complementary dna receptors. thermoplasmonic heat is generated when the aunis chip is illuminated at the plasmonic resonance frequency, resulting in an effective diagnosis. even when the rna concent ration is as low as 0.22 pm, this biosensor has a strong affinity for pre-selected viral genome sequences, resulting in accurate detection in a multigene mixture [76]. a field-effect transistor (fet)-based biosensing device is another promising alternative to the rt-pcr technique. this device detects the presence of sars-cov-2 in swab specimens collected from the nose and throat via an antibody reaction mechanism. a distinct antibody against the sars-cov-2 spike protein was placed on a spin-coated graphene sheet to create the device. the results have shown that the lower detection limits of the device are 1 fg/ml when the sample is in phosphate-buffered saline, 100 fg/ml when in a clinical transport medium, 1.6 × 101 pfu/ml in culture media, and 2.42 × 10 2 copies/ml in clinical samples. since it does not require sample pre-treatment or labeling, this device is far superior to the traditional rt-pcr technique [77]. another nanotechnological intervention has resulted in a colorimetric biosensor using gold nanoparticles (aunps) to detect sars-cov-2 viral particles (rather than its genomic rna) in nasal and throat swabs. as shown in figure 2, 73,78 this sensor is based on a colloidal suspension of aunps functionalized with antibodies that target sars-cov-2 envelope proteins. when the suspension and the suspected sars -cov-2 viral sample are combined, a nanoparticle layer forms on the virion. the resonance peak in the extinction spectrum is shifted as a result of this interaction, resulting in a discernible color change verifying the presence of sars cov-2 [78]. currently, there are no mutation-specific probes that detect the specific sars-cov-2 mutation in a sample. nanotechnology could provide a solution for this. a simple aunp lateral flow assay was developed to detect isoniazid-resistant mutations in tubercolosis. the strip could potentially be modified in a short period to design a probe capable of detecting different mutations in sars-cov-2 samples [79]. 4.2 nanotechnology in safeguarding as previously stated, non-pharmacological management has been the key to controlling abrupt outbreaks and ensuring the protection of individuals who are actively involved in a patient's care, including those who handle live samples and those with co-morbidities. sophisticated and comfortable masks, ppe, and sanitizers thus have a major role to play in this battle. sars-cov-2 viral stability on inanimate surfaces varies depending on the substrate type and texture. it has been found that the residence times of sars-cov-2 vary from 4 hours to 7 days, including 4 hours on copper, 4 days on glass, 7 days on plastic, and 2 days on treated wood [80]. using ppe can prevent the direct contact of the body with sars-cov-2 infected matter. a ppe suit contains a face shield that seals the facial area and filters airborne particles,[81] preventing them from entering the respiratory tract. it is essential to have proper disposal mechanisms for used ppe because contaminated textiles can aggravate the spread of the disease. this dumping of biohazardous waste can be solved with self-cleaning/self-sterilizing and hydrophobic materials. the hydrophobic nature of a ppe material can act as a barrier against airborne droplets emitted during coughing or sneezing [70]. the fabrication of reusable ppe kits can be achieved by coating them with selfsterilizing materials. daylight-active, vitamin k-containing nanofibrous membranes composed of hydrophobic polyacrylonitrile and hydrophilic poly(vinyl alcohol-co-ethylene) have been used for the generation of reactive oxygen species which themselves have bactericidal and virucidal activity. this yields a product which can retain its microbicidal activity even after repeated exposure to bacteria and viruses, confirming it to have effective reusability while also being self-sterilizing. alternatively, tio2-crystal violet nanocomposites and cu2o nanoparticle-graphenebased nanocomposites have also shown virucidal activity, demonstrating self-cleaning and hydrophobic characteristics when present in textiles to be used as ppe material. 82 disinfectants and sanitizers are used to flush microbes from the animate and inanimate surfaces. shepros, a malaysian firm, has produced a sanitizer product that uses silver nanoparticles with a size of 25 nm and is now on the market. this product can be claimed to be effective against sars-cov-2 because it is microbicidal against a wide spectrum of species including viruses. the mechanism of action is known to be affecting the cellular metabolism and cell growth by suppressing the basal metabolism of the electron transport system. apart from being a potential antibacterial agent, a nonalcoholic aqueous-based colloidal silver solution has also demonstrated antiviral efficacy by inhibiting viral negative-strand rna production and viral budding. 83 in addition, nanofilms containing naclo2 crystals which can release disinfectant gas (clo2) after uv activation and exposure to moisture, silica/silver nanocomposites, poly(lactic-co-glycolic acid) (plga) nanoparticles containing essential oils, alkyl sulphate groups in a cyclodextrin carrier, and tungsten trioxide nanoparticles doped with rohini m. de silva et al. 32 palladium nanoparticles also have displayed sufficient virucidal activity for the effective use of those formulations in combating covid-19 [70]. figure 2. schematic diagram showing the mechanism by which the colorimetric biosensor detects sars-cov-2 using functionalized gold nanoparticles. when the antibodies on the surfaces of gold nanoparticles (colored in red, green and blue) combine with the envelope proteins of the virus, a nanoparticle layer is formed on the virus resulting a visible color change. one of the main personal preventive precautions during the covid-19 pandemic period has been to practice wearing a mask. this should ideally involve more than just putting on a mask; the mask should be compatible with the individual and capable of trapping and eradicating sars -cov-2 viral particles. 84 a recent study has shown that a sputter-coated silver nanocluster/silicate composite on a mask material has antiviral activity against sars-cov-2 .similarly, the copper 3d nanohack mask has been developed by printing apolylactic acid filament on the mask material. it is essential to assemble the mask by hand in the final stage into the three-dimensional form. especially, all the seams must be manually sealed for an airtight fit. 85 it is obvious that the selection of a fabric for the mask and heatand light-sensitive nano systems are crucial when developing an active mask to be effective against covid -19. a wide range of metal nanoparticles (silver, iron oxide and gold) have shown promising antiviral effects. antiviral activity of silver nanoparticles (agnps) mainly depends on the particle concentration, in addition to the size and shape of the nanoparticles [86]. there are different methods of synthesizing agnps that allow the synthesis of particles of varying sizes [87,88]. the virucidal effects of these agnps can be employed by incorporating them into ppe and masks. iron oxide nps have also demonstrat ed significant antiviral effects against the h1n1 influenza virus and could be tested for antiviral activity in safeguarding equipment against covid-19 [89,90]. one way in which antiviral nps could be implemented into masks or ppe is to combine them with polymers and form (nano)fibrous mats using techniques such as electrospinning [91,92]. there has been significant work performed investigating the potential of electrospun nanofibers as filters and for medical applications [93,94]. 4.3 nanotechnology in the treatment of covid-19 nanoparticles have on a number of occasions been examined as a viable alternative to standard antiviral drugs, since the latter have a number of disadvantages such as low bioavailability, hydrophobicity, and narrow spectrum [95]. nanoparticles small size, large surface area, long half-lives and ability to perform targeted delivery all make them excellent candidates for antiviral treatments. metal nanoparticles are able to deliver drugs to target viruses and have also been found to have innate antiviral activity [96,97,98]. polymeric nps have been investigated as therapies against h1n1 and h5n1 influenza, 99 polio, 100 herpes, hpv and dengue virus [101]. selenium nanoparticles (senps) have been shown to alter immunological function and diminish the formation of free radicals within host cells in several investigations [102]. various antiviral medicines, such as ribavirin (rbv) and zanamivir, have been delivered using senps as carriers. rbv has previously shown promise as a treatment for sars-cov, mers-cov, and most influenza viruses [103]. a recent study of se@rbv nps discovered that particles with sizes ranging from 65 to 100 nm inhibited apoptosis caused by h1n1 by blocking the caspase-3 pathway. the particles were found to provide a powerful antiviral effect, and , since covid-19 patients suffer from chronic inflammation and oxidative stress, this np therapy could be used to control inflammation and boost their immune response [104]. role of nanotechnology in diagnosing safeguarding, and treating covid-19 33 furthermore, gene editing via crispr/cas9 technology has also been investigated as a treatment method against covid-19. crispr has the potential to directly target and eliminate the viral rna and dna genome which can help in persistent infections [105]. there are concerns about using crispr/cas9 systems in vivo, due to their degradation by serum nucleases, unwanted stimulation of the innate im mune system and excretion via the kidneys [106]. nanoparticles have been formulated as carriers for numerous crispr/cas9 systems; cas9 mrna from streptococcus pyogenes was co-loaded into an lnp system with modified singleguide rna and evaluated in an animal model, yielding a stable and biodegradable nanosystem that could edit the transthyretin (ttr) gene in the mouse liver [107]. in another study, tt3 lipid-like nanomaterials were used to deliver crispr/cas9 to mice to lower hbv dna expression in the liver [108]. sars-cov-2 is a rapidly mutating virus that alters its genetic sequence and thereby its membrane proteins, resulting in reduced effectiveness of vaccines and antibodies, but crispr/cas9 technologies could be used to directly target the genomic rna and stop it from replicating [109]. since lipid-like nanomaterials have shown great potential in delivering gene editing crispr/cas9 systems to combat viruses in the liver, lungs and kidneys they could potentially be pursued as a treatment option for covid -19. nanocarriers, including organic-inorganic nanohybrids can also be used as encapsulation vehicles to transport drugs that require selective accumulation, or to reduce systemic side effects of certain antivirals, thereby improving patient compliance [110,111]. hydroxychloroquine is a drug used in covid patients to reduce viral load. however, it is responsible for many systemic side effects including retinopathy, myopathy and heart disease. these off-target issues might be mitigated by encapsulating the drug in nanocarriers. liposomes, polymeric nanoparticles and polymeric micelles (polymersomes) have all been investigated for this purpose [112]. combination therapy has also been proposed to increase the therapeutic efficacy of individual drugs while reducing the minimum required dose. a lopinavir/ritonavir loaded plga np formulation has been investigated in this regard and demonstrated potent antiviral activity while reducing the required dose. 113 therefore, nanomedicine has significant potential advantages in the treatment of covid -19, including reduced systemic side effects, and the capacity for targeted drug delivery. however, the adv erse effects of using nanomedicines should also be considered. since nanoparticles are manufactured from various different materials, they can cause toxicity at a molecular, cellular and tissue level due to their small size. tissue level inflammation, generation of reactive oxygen species and disruption of molecular compartments and loss of function are among some of the possible adverse effects [114]. since most of these studies have been conducted on animals, they are insufficient to determine clinical efficacy and further in vivo studies in humans are required, especially to evaluate the effect of nps on the human immune system. 4.4 nanotechnology in vaccines for covid-19 the pandemic's progressively catastrophic effects prompted a massive amount of effort from scientists all across the world, culminating in the world's fastest vaccine development process. clinical studies of vaccine candidates were conducted and concluded in months, whereas the same process would have taken years previously [115,116]. surprisingly, the first approved vaccines (pfizer/biontech and moderna) were the result of novel mrna-based technology with no previously approved clinical use, rather than traditional vaccine technologies based on inactivated virus particles. also, sign ificantly most of these vaccine candidates fall in the nanoscale size range, representing the first mass scale implementation of nanoscale vaccines in history [117]. the novel rna-based vaccines attempt to transfer the genetic code of specific viral prote ins to host cells, offering numerous benefits over traditional vaccines that elicit immune responses by injecting whole viruses. firstly, mrna is safer than injection of a whole virus since it is not infectious and cannot be incorporated into the host’s genome. in contrast to dna vaccines, which must reach the nucleus to be decoded, they do not require entry into the nucleus [118]. however, there are challenges in the implementation of this technology, mainly due to the ubiquitous presence of rna degrading enzymes (rnases) in the body and the negative charge of mrna, which makes crossing the cell membrane a challenge [119.120]. as a result, without a functional transport system that allows for the safe translocation of mrna across the plasma membrane and into the cytosol, it would be unlikely that enough mrna molecules would be available to deliver the high levels of expression required for immunogenic effectiveness. to solve this problem, researchers have designed lipid nanoparticle (lnp) based carriers that are positively charged and therefore form stable complexes with mrna. these are resistant to rn aases and can also facilitate the entry of the mrna into the cell, where it is translated to antigenic proteins. these are then expelled from the cell and stimulate the antibody production process [119]. the preliminary data from clinical trials of the pfizer/biontech bnt162b2 mrna vaccine and the moderna mrna 1273 vaccin e showed efficacies of 95% and 94.5% respectively [8,121]. the us fda and the european medicines agency (ema) approved these vaccinations for emergency use in late 2020, highlighting their unparalleled level of success with no major side effects [121,122]. it might seem strange that such an effective system could be built within the span of 12 months; however the fact is that lipid vesicles have been researched as drug delivery systems since the 1960s. liposomes were rohini m. de silva et al. 34 the precursors to lnps and during the past few decades, liposomes have proven to be an extremely versatile nanocarrier platform since they can transport both hydrophilic and hydrophobic compounds references. they have been enormously successful in the clinical setting with numerous liposome for mulations used in clinical trials for anticancer, antibiotic, and antifungal drug delivery. they were the first nanoscale drug delivery platform to be translated from the lab to the clinic [123]. despite their many benefits, liposomes suffer from a number of significant drawbacks, including a short circulation time, lack of selective targeting and in vivo instability [124]. couple this with the fact that the modern pharmaceutical industry is gradually moving away from chemical compounds to the delivery of small molecules and biologics which include complex, specialized therapies such as mrna, sirna and dna molecules that can combat disease at a genetic level, the need for a novel delivery system was sorely felt [125]. lnps include a cationic lipid that is able to complex with negatively charged genetic material like mrna and form a stable complex more resistant to enzyme degradation [126]. lnps have a structure that is similar to that of liposomes, but they differ in that they generate micellar structures within the core that can be modified according to formulation and manufacturing requirements [127]. lnps typically consist of a cationic ionizable lipid, cholesterol which acts a stabilizing agent, a pegylated lipid that increases circulation time by masking the lnps from reticulo-endothelial system (res) and a phospholipid that encapsulates the lipid structure [128]. the synthesis process of lnps also offers numerous advantages over conventional systems; use of microfluidics or t -junction mixing enables easy scale up for large scale manufacturing, the cost of raw materials is low, and manufacturing parameters like the components of the lipid matrix, surfactant and emulsifier concentrations, rate of stirring, and temperature can all be easily fine-tuned to obtain the perfect release profile [129,130]. there are certain logistical issues to be addressed such as the thermal instability of the mrna cargo which means they have to be stored and transported at ultra-low temperatures, resulting in their application in low-income countries being challenging [131]. it is also interesting to keep track of the more conventional vaccine formulations that have gained approval and monitor if the simpler logistical benefits will eventually result in these vaccines gaining prevalence, especially if a booster vaccination protocol is deemed necessary to maintain immunity [132,133,134]. however, the safety and effectiveness of the lnp mrna vaccines observed during the covid-19 pandemic will hopefully be translatable to other disease settings, for instance leading to preventive vaccines against influenza viruses, zika virus and rabies. 118 providing there are no long-term safety issues associated with the vaccines, caution and unease among patients should subside. this extent of nanotechnology vaccine use that has resulted from the covid-19 pandemic will undoubtedly have a positive impact on how regulatory bodies, industries, stakeholders and the general public view nanoscience and nanomedicine going into the future. 5. conclusion the covid-19 pandemic has created an unprecedented global health crisis that has affected both developed and developing countries equally. due to the rapid ly mutating nature of the virus, its pathogenicity, and the low availability of vaccines in low-income countries, it has been challenging to obtain herd immunity. therefore, in the absence of a proven and effective antiviral drug, scientists and physiaions have had to explore the repurposing of various treatments and the implementation of non -pharmacological measures. there have also been many attempts to apply novel technologies and therapies to combat the pandemic. nanotechnology has attracted particular interest to combat the sars-cov-2 virus and overcome the limitations of more conventional methods. nanomaterials have been used in many approaches to the fight against covid-19, the main ones being vaccines, treatment, diagnosis and protection. the mrna vaccines that were the first approved vaccines on the market helped save thousands of lives but would not have come to fruition so rapidly had there been no nanocarrier to carry the biological. this represents a significant milestone in the history of nanomedi cine. this success opens doors for nanocarriers to be used in engineering vaccines for other difficult -to-treat diseases. nanotechnology has also been used in protection against the virus in the form of disinfectant formulations, textiles and wearable ppe. furthermore, nanotechnology has also led to the development of new diagnostic biosensors that can detect the virus in real-time at an affordable cost. there is a significant burden on the healthcare sector due to the lack of an efficient tool that can dia gnose an infection in real-time, since the average time around the world for an rt-pcr report is 2-5 days. this burden could be reduced considerably by implementing these nanobiosensor diagnostics in a clinical setting. last but not the least, nanocarriers and other nanoparticle based therapies have been investigated as drug delivery systems to deliver repurposed antivirals and even gene editing platforms like crispi/cas9. these technologies have also shown early promise in the treatment of covid-19 but further research is required in this area. if there is any takeaway from this global pandemic, it is that humanity was not properly equipped to deal with it, and we must embrace and encourage new technologies and innovations to supplement and eventually repla ce the conventional treatments that have served us well so far. role of nanotechnology in diagnosing safeguarding, and treating covid-19 35 author contributions the review was written through the equal contributions of all authors. all authors have given approval to the final version of the manuscript. conflict of interest the authors declare no conflict of interest. acknowledgment we would like to thank national research council, sri lanka, national science foundation, sri lanka and sri lanka institute of nanotechnology for funding and other support. we would also like to thank mr. janaka sampath for editorial assistance. references 1. who coronavirus (covid-19) dashboard | who coronavirus (covid-19) dashboard with vaccination data, https://covid19.who.int/, (accessed 25 january 2022). 2. al-dorzi, h.m., van kerkhove, m.d., 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